Crocodile One Piece Emojis & Text

⣿⣿⣿⢿⡿⣿⣿⢿⣿⣿⢿⣟⣿⡿⢿⣏⡿⣯⡿⣯⡿⣿⣻⢿⣿⣻⡿⣝⣯⢿⣽⣿⣿⣽⣿⣹⣯⣻⡝⣯⣯⣽⣯⣻⡝⣯⢻⡝⣯⢻⡝⣯⡻⣝⣯⢻⣝⢯⣻⣝⡯⣟⣻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣾⡿⣿⣽⣾⣿⣳⣟⣯⢿⣯⡿⣟⡾⣽⣶⢿⣳⣿⡽⣯⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⠼⣯⢽⡞⣽⡝⡾⣝⡾⣫⢷⠾⣽⢾⣹⢮⢯⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣾⣝⡿⣽⣿⣞⣷⣯⢿⣻⣞⣿⣝⣯⡻⣞⢯⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡺⣽⢳⣻⡝⣯⢾⡝⣯⣻⢮⣟⡼⢯⠾⣭⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⣿⢿⣳⣯⡽⣻⣿⣞⡿⣽⡿⣽⣻⣞⣞⢮⣗⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣯⢳⡟⣽⡞⣽⣳⣭⠷⣾⣹⢯⡟⣵⡻⣜⢿⡦⠀⠀⠀⠀⠀ ⣿⣯⠷⣞⣽⡿⣾⣽⣻⣯⢿⣳⢯⣷⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠉⠛⠛⠛⠉⠉⠙⠂⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣷⢻⡵⣛⣧⠷⣞⢯⣳⡽⣞⣽⣣⢿⣹⢮⣽⢳⣄⠀⠀⠀ ⣿⣻⣏⣯⢷⣟⣿⣳⣿⣻⣿⢯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣭⣷⢫⣟⣭⢿⣱⠿⣼⢶⣫⢷⣫⢷⣚⡯⣞⡵⣄⠀ ⣿⣿⣽⣾⣏⣾⢷⣯⣟⢿⡹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⣚⣮⢷⣫⢟⣧⡟⣮⠷⣯⡞⣽⣺⢵⣛⡮⣗ ⣿⣿⣣⡿⣽⢯⣟⡾⣿⣫⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢂⠐⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠄⠙⢦⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢻⣯⢟⣿⣿⣟⣿⣮⡗⣯⡻⣖⣻⡭⣟⣧⢟⣧⢯⣳⢯⡽⣹ ⣿⣿⢷⣻⢯⡿⣽⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠞⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣹⠇⠀⠀⢈⢳⣦⣀⡀⠀⠀⠀⢻⣿⡼⣻⣿⣿⣷⢯⣳⢟⣭⠷⣝⣳⡞⣯⢾⣹⢮⡗⣯⣳ ⣿⣼⣿⣻⢿⣻⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⠃⠀⢸⣧⠇⠀⠀⠀⠀⣠⣤⣿⣿⣿⣟⡟⠀⠀⠀⠘⣧⣻⣿⣿⠿⠿⠿⠿⣿⣿⢧⣿⣿⣿⣟⣧⠿⣜⣿⢻⣇⡿⣇⡿⣇⡿⣼⢧⣇ ⣿⡽⣾⢭⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢉⣤⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣄⡀⠀⢻⡽⣽⣿⣿⣿⣞⡽⣏⣾⢳⣭⢷⣫⢷⣫⢷⣫⣗⢮ ⣟⡷⣯⣟⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⠶⠛⣉⣴⣾⡿⠛⣙⣿⣟⣿⡻⣿⣿⣿⡀⠀⠹⣿⣿⣵⣮⣵⣯⣍⣛⣦⣼⣿⢳⣿⣿⣿⢷⣛⣾⣱⡟⣮⢯⣳⢏⣷⢻⣼⣻⢮ ⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠚⠁⣠⣾⣟⣭⣴⣶⢾⣛⣛⣿⣿⣿⣼⡏⡷⠖⠂⠁⠙⣟⠿⣿⣷⣶⣿⣿⠏⠻⣯⡟⣾⣿⣿⣛⣮⢗⣧⠿⣭⡳⣏⡟⣮⡟⣼⢣⢯ ⣿⣯⢿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⠹⢿⣿⣿⣿⣿⣷⣿⡿⠛⠉⠉⢠⡞⠁⠀⠂⠀⠀⠘⢦⡀⠉⡌⠉⢁⠀⠀⢻⣽⡞⣿⣿⡵⣻⢞⣭⣟⡳⣏⡷⣹⢶⡹⣇⢻⢎ ⣿⣞⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣀⠀⣰⠖⠋⠁⠀⠀⠀⠀⠠⣀⣀⣹⠆⠀⠀⠘⠁⠢⣌⣷⣻⣽⣟⡾⣽⢫⡾⣼⢳⣽⡞⡽⣖⡷⣭⢻⡜ ⣿⣟⡶⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⣀⣧⠤⢻⠋⠘⠀⠀⠀⠀⠀⣠⣾⡿⢯⣽⣽⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣟⣞⡷⢯⣳⣏⡿⣜⣯⣳⡽⣞⡵⣻⣞ ⣿⡽⣾⣿⣿⣿⡟⣾⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⣿⡧⠐⠈⠀⠻⣄⠀⣄⣀⡼⢾⠉⠀⠘⠃⠀⠁⠀⠀⠀⠀⢷⣾⣿⣿⣗⣸⡿⠟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣎⡿⣝⣳⠾⣝⡷⣚⣷⡽⢮⣳⢏⣾ ⣿⣝⣿⣿⣿⢯⡽⣽⣿⣿⣿⣿⡿⣟⢳⣦⣿⠹⢿⣿⣿⣿⡅⢈⠐⣆⣦⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⣄⡀⠀⠀⠀⢸⣿⣿⣿⡞⣽⡭⢷⣻⣝⡾⣽⢲⣛⣖⢻⣎⢷ ⣿⡾⣽⣿⣻⢭⣻⣿⣿⣿⣿⣿⣷⡏⠛⣩⣽⣆⢸⠟⠿⣿⣷⣂⡴⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⡿⠿⠟⣟⣻⣿⠃⠀⣀⣀⣸⣿⣿⣿⣽⣧⣟⣯⣳⢾⣹⢳⢯⡟⡼⣆⢯⣳ ⣿⡽⣿⣯⣷⣯⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⠟⣿⣿⣀⡀⠻⢿⣿⡟⠫⣁⠂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⣫⣭⣿⣶⣿⣿⢻⣽⣿⣿⣟⣿⣿⣿⣿⣿⣛⣭⣾⢟⣫⢯⣽⣿⡿⣻⠻⡽⡳⣍⢾⣸ ⣟⣿⣿⡏⡀⠂⣿⣹⣿⣿⣿⣿⣿⣷⢦⡻⣬⣄⣙⣿⣷⣀⡈⣯⠁⠁⠆⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣯⣷⣿⣿⣿⣿⣥⣳⣷⣿⣿⣞⡶ ⡿⠉⠻⣿⡆⠐⣿⣿⣿⣿⣿⣿⣿⣿⣷⣙⠛⠓⠻⠷⡿⠋⣱⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣿⣿⣿⢿⣿⠿⡿⣛⠟⠛⣻⣿⠿⠿⠿⠿⣥⣯⣿⣣⣻⣿⣿⣟⣫⣿⣿⣷⣿⣿⣿⣟⡿⣼ ⣧⠋⠬⢿⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⣰⡟⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⠻⢿⢛⡟⡛⠛⠛⠛⠛⠙⠉⢁⣠⡄⠀⠀⣿⡿⣿⣟⡽⣫⡟⣽⡻⡽⢯⢿⣹⢟⡾⣹⣞⣳ ⡧⢃⠀⢂⠻⢿⣜⢿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡎⡵⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⢻⣟⣷⡾⠟⠀⠀⠀⣿⠿⣽⣟⠾⠷⣋⣵⡻⣽⣫⢿⣭⣻⢽⣳⣭⢷ ⣇⡀⠊⡄⢢⡀⡙⠻⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠴⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⠛⠛⠋⠀⠀⠀⠀⠀⡇⠀⡸⣿⠐⠘⡉⠉⡉⡙⠛⠾⢾⡭⡷⣯⠾⣽ ⡧⡹⠡⠄⢂⠰⠑⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢷⢩⠻⡿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠲⣿⡄⠐⠠⢡⠀⡰⠿⡷⢦⣭⡳⠽⠯⢓ ⣇⠑⡢⠌⢀⠒⠭⢢⣀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢎⣣⠓⣿⣜⡹⣛⠿⣶⢶⣤⣤⣀⣀⣀⡀⢀⠀⡀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣠⣄⣴⡟⠀⠐⣿⣿⠀⠢⡁⡐⢀⢀⠠⢀⢀⣀⣢⣼⣻ ⡇⠸⠀⡆⠀⠎⠱⣎⠸⢇⡆⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢆⡏⡰⢿⣇⢇⢷⡸⢹⢿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣏⡿⢿⡿⣿⡿⣿⣿⣿⡿⠇⠀⠀⠀⢿⣿⢀⠁⠀⠈⡀⢆⠀⠁⠈⢿⣱⣿⣸ ⣗⡀⢂⠀⡡⠘⢣⣈⢺⡘⡜⣄⠂⡐⠀⠈⠉⠉⣽⣶⣿⣿⣿⣧⠚⡴⣑⡚⠿⣮⡖⣙⢎⡵⡹⢿⣿⣾⣽⣻⡽⣞⢷⡞⣧⠿⣼⢽⣳⣞⣶⣿⢿⡿⡩⢦⡙⠦⡄⢡⣿⡿⢀⠊⠤⠁⡀⠆⡑⢂⠤⠀⠄⣈⠁ ⡧⢀⠡⠐⡠⠈⠱⣆⠀⢳⡘⡄⢣⠀⠡⢈⠉⠛⠛⠿⣿⣿⣿⣷⡏⡔⢧⡘⡝⢿⣟⡌⢞⡰⡝⣪⠜⣛⠿⣿⣻⡿⣯⢟⣷⡻⣝⣾⣿⡿⠋⠀⢸⣇⢳⢊⠵⣹⣾⣾⠛⡀⠆⣉⠰⠡⡐⠠⠁⠊⡔⡡⢌⡀⠃ ⡇⠠⢃⠐⡁⢂⠱⢎⢆⠀⠱⣌⠡⢂⠁⠂⠄⠂⠄⢀⠀⡨⣝⣛⡟⠓⡒⢓⢪⡑⣚⡟⢤⢓⠥⡓⢮⠱⢎⡵⢻⢿⣿⣯⠷⠿⠛⡿⠛⠀⠀⠀⢨⣿⣿⣾⣶⣧⣶⣨⡓⠴⣈⡐⠌⢂⠡⠡⠌⠠⠀⠑⢆⢠⠀ ⣧⢱⠎⠠⠌⡠⠈⣭⢊⣆⠀⡈⠣⢎⠀⠡⠂⠌⠐⠠⠐⠀⠉⣿⡿⣿⣯⣕⡢⢍⡙⡻⣮⣜⠢⡝⢢⢛⠬⠖⡭⣒⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣎⣄⠌⠡⠨⠑⡈⠄⡈⠠⠉ ⣏⢧⢫⡐⢁⠆⠐⢢⡁⢎⠳⣄⠁⠌⡚⠠⡁⠎⠠⠑⠂⡉⠂⠀⠙⢷⣿⣿⣿⣿⣿⣶⣭⣟⣺⡌⢣⢎⡹⢌⡱⢢⠍⣳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣈⠒⠄⡃⠄ ⣏⢮⠱⡄⡉⠶⢘⠤⠡⡌⠳⡌⠶⣀⠈⡑⠄⠢⢁⠌⠐⠠⠑⡈⢐⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢦⠑⡎⠴⡁⠎⡰⢈⠷⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡘⢄⢋ ⣏⠶⣩⠐⡡⢍⡜⣼⣣⠜⣡⠘⣄⠩⢗⡤⠈⡱⢂⠠⠃⡄⢡⠐⢌⠀⣦⣽⢿⣿⣿⣿⣿⣿⣿⣿⠇⣎⠱⡘⡰⢁⠆⡁⢎⠰⣿⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡌⢪⡐ ⣏⢮⡑⠬⠐⣬⢛⠶⣧⣈⠑⡛⠨⠃⢌⡐⠳⢔⡀⢂⠡⠒⡀⠌⠄⠂⢈⣿⣶⣻⣿⣿⣿⣿⣿⣿⢋⣦⡓⠄⢣⡉⠔⡀⠣⡜⢻⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣅⣶ ⣟⢾⡩⢖⣛⡶⣩⢻⣵⣉⠚⣅⠃⣬⡘⢄⠃⠤⡘⢁⠂⡁⠖⡈⠠⢁⠂⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠼⣷⡈⢢⠘⠤⡁⠒⠈⠞⠀⠀⠀⠀⠀⠀⢸⣿⣕⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠢⢌ ⣟⡎⣴⢋⡿⡼⣝⡣⢞⢂⠻⡌⠒⡔⣈⠡⠌⢆⠐⠉⢂⠡⠌⠠⢁⠂⠄⠁⠘⠿⣿⣿⣿⣿⣿⣿⡏⢒⣿⣧⠂⡘⢄⠂⡁⠀⠠⠀⠀⠀⠀⠀⠀⠸⢿⣿⣶⣫⢜⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡘⢤ ⣯⣼⢖⡫⣜⡹⢮⡱⢫⢬⡳⣍⠂⡑⣄⠃⠌⡸⢄⠂⡁⢂⠌⡐⠠⢈⠠⢁⠠⣐⠟⣿⣿⣿⣿⣿⣿⢐⠊⡻⢶⡀⠌⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣻⣿⣿⣯⣾⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡜⣸ ⡷⢮⣓⡳⣌⡳⢣⡝⣣⠞⡵⡘⡴⠐⡈⠰⣠⢙⡰⠂⠐⡀⠆⢠⠑⡀⠂⡄⠀⡘⢷⣯⣿⣿⣿⣿⣿⡂⠘⣄⣨⣵⣶⢶⡶⣶⣄⡀⣠⣤⡴⢾⡏⣟⢻⡛⡯⢏⡽⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹ ⣯⢳⡕⣫⠵⣩⣓⡼⡱⢏⡞⣱⢒⡡⠘⡠⢐⠣⡐⢡⠂⠡⠈⢤⠠⠁⠆⢠⠃⡀⠄⠹⣿⣿⣿⣿⣿⣷⢾⣻⣿⠹⣬⣓⢮⡝⣭⢻⢿⣶⣹⣧⢞⡬⢧⡛⡵⣋⡞⡵⢭⣿⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⣯⠷⣋⡷⣋⠷⣌⢳⡑⡎⣖⢣⠇⣀⢃⣦⠁⡆⢑⡀⢆⡡⡐⠈⡸⠄⡒⡀⠆⠡⠈⠔⠠⠻⣿⣿⣿⣯⣳⢣⡞⢿⣶⡭⣞⡹⢦⡻⡜⡽⢾⣽⣮⣝⣶⢭⢳⡍⣞⡹⣎⢾⡽⣍⢿⣿⣶⠙⡿⣿⣿⣿⣿⣿⣿ ⣯⣗⡻⣼⡱⣛⡌⢧⡱⠜⣤⠋⠰⡈⢦⠎⡵⢈⠆⡐⠂⠑⡌⡤⢓⠉⡔⢡⠊⢁⠸⠄⡡⡐⢻⣿⣿⣿⣿⣧⣛⠶⣱⢟⣧⡯⣇⠷⣹⡜⢯⢝⡿⣮⠞⣯⡶⣙⠮⡵⢎⢿⣿⡜⢮⣻⣿⣯⢔⢊⡝⠿⣿⣿⣿ ⣷⣎⢳⢣⠟⡴⡚⢆⢧⡋⡴⢈⡡⢘⢬⣋⡼⣆⠎⢐⢌⡠⢆⡘⠤⢃⢘⡄⡘⠄⡁⠚⡔⠐⡈⣿⣿⣿⣿⣿⣿⣯⣗⣯⡜⣻⢯⣞⡵⢺⠭⡞⣜⡻⣿⣚⣷⣭⢳⡹⣭⢚⣿⡜⣧⢳⣻⣿⣧⡧⣌⠣⣄⠉⠿ ⣿⡇⣯⢎⡽⢲⡹⢊⣎⠳⡅⢎⣠⠑⣦⢈⡵⢫⡌⣇⠊⢅⠂⠠⠐⡌⠌⠴⡰⢂⠌⠑⡀⢂⠠⠡⣽⣻⣿⣿⣿⣿⣿⣞⡷⣝⣎⠿⣷⣏⡳⠽⣬⠳⣝⣯⢞⣧⣳⠳⣎⢏⣾⣗⡎⢷⡩⣿⣿⣿⣿⣴⠡⣂⠄ ⣿⣷⢸⡞⣥⠛⡔⢫⡌⡗⢺⠐⡏⠓⢸⢲⠘⢣⡆⢱⠈⠂⠈⠁⠂⡄⠉⠂⠑⠈⡄⢡⠀⠂⠁⣦⠈⠙⢻⣿⣿⣿⣿⡝⣿⣽⣾⢪⡕⢻⣾⡝⢲⢻⡜⣽⡏⣾⣧⢻⡜⢺⣼⣿⡜⣧⢹⣿⣿⣿⣿⣿⣷⡕⡆ ⣿⡳⢯⣞⣭⠳⣍⠲⡍⡜⢦⣋⢼⡀⠱⡎⡝⢦⡙⠆⡌⡘⠠⠉⠠⠄⡁⢊⠠⠑⡀⠂⠌⠐⠄⠹⣿⣷⣦⣬⣽⡯⣿⣿⡝⣷⣟⣯⣙⢧⣛⢿⣗⢮⣱⢣⣿⣗⣻⡮⣝⠶⣍⣿⡱⢎⡳⢿⣿⣿⣿⣿⡿⣑⢫ ⣿⣹⣿⣿⢎⡟⣬⣓⡭⡜⡳⢌⢆⠰⣉⠒⡍⠦⣁⠖⠀⠄⢁⠌⠐⠄⡈⠐⢂⠱⡀⠅⢂⠡⠂⠀⠽⣿⣿⣿⣿⡝⡾⣿⣿⢭⣿⡿⣽⣞⡾⣮⡽⢷⣏⡞⡴⢿⡞⣷⢎⡻⢬⣻⣏⢯⣙⣾⣿⣿⣿⡟⠴⡡⢏ ⣿⣿⣿⣿⣮⢗⣲⢣⣷⡹⢇⡫⢔⡃⢦⡙⢬⠱⣈⠂⠌⣐⠎⠐⡈⡐⡈⠥⣈⢰⡈⠔⡈⠄⡈⠔⣀⠸⢿⣿⣿⡼⣙⢯⣿⡶⣭⢿⣿⣽⣻⢯⣿⣯⣿⡜⣧⣛⣿⣹⠮⣝⡧⣹⣿⣻⠼⣸⣿⣿⣿⢎⡱⡡⢏ ⣿⣿⣿⣿⣿⢾⡹⣼⡲⣝⣫⢖⡣⢜⠢⡜⢢⡑⠃⢄⠶⣩⠀⠜⢀⠅⡐⢢⠀⢆⠳⢈⠔⠂⡐⠀⠘⣧⡈⢿⣿⣶⣏⢾⣹⣿⣶⣫⢿⣯⣟⡿⣾⣽⣻⣏⢶⡹⣾⡟⡿⣌⣳⣱⡿⣿⡹⣾⣿⣿⣿⡘⢴⠱⣉ ⣿⣿⣿⣿⣿⡯⣝⣧⠻⡵⣫⢎⡼⢡⠓⣌⢣⠘⣠⠏⡲⠅⡈⠔⡨⠄⠱⢠⠉⠌⡞⡡⠌⠡⠌⡡⢀⢹⣷⡭⣿⣿⣿⣿⣾⣿⣷⢯⣯⢟⣿⣟⡷⣯⢷⣿⣧⣛⢶⣻⠷⣹⠦⣿⡗⣿⣱⣿⣿⣿⣿⣍⠦⣙⢴ ⣿⣿⣿⣿⣿⣽⢺⣜⢳⢳⢧⢚⡴⢣⡙⢤⢓⡡⢇⣎⠱⡁⢐⠨⡐⢌⠑⢂⠈⡸⣐⢣⢈⡑⢨⠐⢈⠸⢿⣿⣯⣿⣿⣿⣿⣿⣿⣟⣮⣟⢾⣿⡿⣽⣯⢿⣗⢮⢿⣹⡗⣣⣛⣿⣹⣿⣿⣿⣿⣿⣿⣿⣬⣿⠟ ⣿⣿⣿⣿⣿⣾⢧⠞⣭⣋⢾⡱⢎⠧⡙⢆⢣⡙⠦⣌⠇⡰⠈⢆⡐⡎⢜⠀⡆⠡⣏⠠⢡⠐⡆⠬⡄⢎⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣾⣛⣾⣿⡷⣯⣟⣿⣏⣯⢷⡏⣷⢾⡯⣼⣿⣿⣿⣿⣿⣿⣿⣯⡄⢏ ⣿⣿⣿⣿⣿⣟⣮⢻⡱⣏⢾⣙⢮⠱⣉⢎⠲⡙⢦⡉⠤⡐⡈⢂⡼⡑⢂⡼⢀⢃⠒⡈⢮⠐⠼⡁⠩⡘⡐⠤⠊⠻⣿⣿⣿⣿⣿⣿⣾⣳⣟⡾⣽⣿⣷⣻⢿⣟⣾⣻⢼⣫⣿⢵⣻⣿⣿⣿⣿⣿⣿⣿⣿⡴⠈ ⣿⣿⣿⣿⣿⣿⣎⣳⢹⢎⠳⡌⢎⡱⣉⢎⡱⢍⡒⣠⠛⡄⠰⡙⠴⡙⢠⢫⠀⠬⡐⢰⢈⠣⣐⠠⢁⠐⢄⠠⣹⣶⣶⣿⣿⣿⣿⣿⣿⣷⣯⣟⣷⣿⣿⣽⣻⣿⢾⡽⣯⣿⣟⠮⣵⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⢉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⠛⠻⢶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢫⢗⣴⡿⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢰⣜⣎⣎⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⢣⣫⠌⣽⢃⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢤⣀⣠⡟⣟⣘⠘⡆⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡴⠃⣰⡿⣴⡧⠷⠚⠉⠁⣀⣠⠤⢤⣒⣒⣂⣀⣠⣠⣄⣠⣤⣶⣿⡟⠙⠻⢼⣾⡞⡆⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣾⠟⠋⠙⣿⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣌⣙⠿⣕⡀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠴⠋⠀⣠⠔⣢⣼⣿⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢫⡙⠈⠳⣄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⠞⠁⢀⡤⣚⣵⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠲⣄⠈⣳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣴⣉⣀⣴⣫⣾⣿⣿⣿⣿⣿⡟⣿⣿⠋⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡈⢧⡈⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⣄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⢿⡜⣎⢦⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣻⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢀⣤⠶⢻⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣴⡿⡜⣾⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣿⣿⠟⠋⣽⣿⣿⣿⣿⣿⣧⠶⠚⢻⡏⠛⠲⢦⣀⠀⠀⣠⠀⠀⠀⢿⣿⠋⠀⠀⠸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡅⠙⠀⠘⣄⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⣼⡟⠁⠀⣠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⢇⠀⠀⠉⠈⠑⠀⠙⢦⠀⠀⢸⡏⠀⢀⣠⣶⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢸⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠁⠄⣰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠠⣄⣿⣶⣦⣄⡄⠀⠀⢄⣿⠆⠀⠘⠃⣰⣿⣷⡿⠿⠶⣦⡀⣿⣿⢻⣿⣿⣿⣿⡝⠻⣦⣠⠀⠇⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⢁⣴⡾⠿⢻⣿⣿⣿⣿⣿⣿⠀⣠⣾⠟⠉⠠⠶⠛⠇⠀⠀⣿⠁⠀⠀⠀⠈⠛⣙⣉⣉⣀⣠⡴⠛⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠙⠈⢡⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡖⣾⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⢿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠘⠂⠀⣀⣐⣀⣈⣁⡤⠤⠷⠶⣟⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠱⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⢯⡆⠐⡄⠀⠀⠀⣾⣿⡇⣿⣿⣿⣆⢹⣷⠞⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⢀⠀⢸⢀⣿⣿⣿⣿⠹⣇⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡃⠀⢳⢰⡀⣄⠈⣿⡀⣼⣛⢻⡏⣿⠃⠀⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣸⡤⢸⢸⡿⣿⢻⣿⡄⠉⠀⠀⠀⢸⠀⢠⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⣧⢷⡙⣮⢯⡧⣇⣯⣷⢹⣸⡆⠦⢽⣄⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠚⡟⠋⠹⢀⡟⡾⣾⣿⢸⠈⢻⣦⣄⣠⢄⡟⣀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⣤⠘⢿⡻⠈⠉⠁⠹⣜⢯⡓⢧⢳⡀⢸⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡼⣽⢗⣫⢏⡞⠀⠛⠿⡿⢃⡞⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣅⠀⠝⣆⠺⣔⢴⣬⣳⢭⣩⣦⢳⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣱⢗⣋⡽⢋⡀⠀⠀⡀⣠⠊⣰⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⢳⣌⡛⠋⠉⠁⠀⠈⠳⢼⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣴⡿⠉⠱⣶⠿⢟⡵⣺⠞⢁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⢀⠀⢦⡿⣔⠯⣷⠆⢻⣶⣬⣳⠲⠤⣄⣀⣀⣀⣤⠤⠤⢖⡻⣟⣭⣴⣿⠏⢳⣺⠴⢀⡀⢉⡜⡁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢥⣀⠉⠻⣋⠀⠀⠈⠓⢻⢎⠙⠒⠯⣄⡀⢀⣐⡶⠾⠛⠋⡽⣸⠃⠉⠀⠀⠀⢚⡩⠞⢡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠵⣶⡤⣄⡐⠦⠄⢸⢸⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣸⠁⡏⠄⣀⣀⣤⠮⣭⣤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⣿⣿⣿⣿⣿⣷⣦⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣷⣛⣉⣬⣤⣤⡈⠹⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠛⠒⢲⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢻⣿⣿⣿⣿⣿⣿⣧⠈⠙⠦⣄⡤⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⢉⣴⣾⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣤⣤⣴⣶⣭⡙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠱⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⢀⡴⠞⣡⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠥⠯⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠽⠦⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⢿⣦⡀⠀⠀ ⠀⣰⠏⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠙⠲⢤⠀⠀⠀⠀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠛⣆⠀ ⠼⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢆

⠀⠀⡶⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢶⡀⠀ ⢰⠛⠃⠀⢠⣏⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⣸⠇⠀⠈⠙⣧ ⠸⣦⣤⣄⠀⠙⢷⣤⣶⠟⠛⢉⣁⣤⣤⣤⣤⣀⣉⠙⠻⢷⣤⡾⠋⢀⣤⣤⣴⠏ ⠀⠀⠀⠈⠳⣤⡾⠋⣀⣴⣿⣿⠿⠿⠟⠛⠿⠿⣿⣿⣶⣄⠙⢿⣦⠟⠁⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⢀⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⣾⡏⢠⣿⣿⡯⠤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠤⠤⠽⣿⣿⡆⠹⣷⡀⠀⠀ ⠀⠀⢸⣟⣠⡿⠿⠟⠒⣒⣒⣉⣉⣉⣉⣉⣉⣉⣉⣉⣒⣒⡛⠻⠿⢤⣹⣇⠀⠀ ⠀⠀⣾⡭⢤⣤⣠⡞⠉⠁⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠈⢹⣦⣤⡤⠴⣿⠀⠀ ⠀⠀⣿⡇⢸⣿⣿⣇⠀⣼⣿⣿⣿⣷⠀⠀⣼⣿⣿⣿⣷⠀⢸⣿⣿⡇⠀⣿⠀⠀ ⠀⠀⢻⡇⠸⣿⣿⣿⡄⢿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⡿⢀⣿⣿⣿⡇⢸⣿⠀⠀ ⠀⠀⠸⣿⡀⢿⣿⣿⣿⣆⠉⠛⠋⠀⢴⣶⠀⠉⠛⠉⣠⣿⣿⣿⡿⠀⣾⠇⠀⠀ ⠀⠀⠀⢻⣷⡈⢻⣿⣿⣿⣿⣶⣤⣀⣈⣁⣀⡤⣴⣿⣿⣿⣿⡿⠁⣼⠏⠀⠀⠀ ⠀⠀⠀⢀⣽⣷⣄⠙⢿⣿⣿⡟⢲⠧⡦⠼⠤⢷⢺⣿⣿⡿⠋⣠⣾⢿⣄⠀⠀⠀ ⣰⠟⠛⠛⠁⣨⡿⢷⣤⣈⠙⢿⡙⠒⠓⠒⠒⠚⡹⠛⢁⣤⣾⠿⣧⡀⠙⠋⠙⣆ ⠹⣤⡀⠀⠐⡏⠀⠀⠉⠛⠿⣶⣿⣶⣤⣤⣤⣾⣷⠾⠟⠋⠀⠀⢸⡇⠀⢠⣤⠟ ⠀⠀⠳⢤⠾⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠷⠤⠾⠁⠀

⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠓⠒⢶⡲⣄⠉⢻⡿⣍⡛⣩⣽⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠏⠀⠀⣢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣶⠦⣄⣀⠀⠙⢾⡳⡀⠙⣾⣿⠟⣉⠴⠂⠐⠻⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣠⠞⠁⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠛⢓⣤⣬⣉⡳⣤⣭⣓⠮⣿⣵⠀⢹⣿⣴⢿⣍⡙⢲⣄⠀⠹⣟⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⠳⣤⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⠶⠾⠿⠛⢛⣒⠟⠛⠛⠛⠛⠿⢯⣻⣧⠘⣿⡷⠀⠜⠛⣄⠙⣷⣄⣘⣎⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣓⡭⣭⣭⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠀⠉⠀⠀⠀⠀⠈⣆⠹⣵⠬⣿⣦⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⣿⢫⣾⠵⠋⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢳⣧⡘⣷⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣷⡿⢁⡔⠀⠀⡇⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⣀⡠⠤⠀⠀⠀⠀⠀⢻⠈⣎⣧⣸⣶⡄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣾⣿⠟⣻⠀⠀⢠⡇⠀⢸⠤⠤⠼⠄⠠⠠⠔⠒⢒⣉⡭⣞⠿⠥⠄⢀⣀⡇⢻⠏⢿⣌⢻⡌⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠄⡏⠀⠀⢿⠂⢀⣼⣒⣒⣒⣶⣖⢶⡒⢒⣉⡥⠊⢁⡴⠒⠉⢩⠯⣇⠘⣴⣿⠉⢻⣿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⢻⣗⣦⣧⡄⠀⢁⣠⠾⣿⡀⠀⠈⠉⠉⠑⣟⣍⠁⢠⡞⠉⠀⣀⣴⡃⠀⢸⠀⣿⢿⢳⣄⣿⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣠⣿⡷⣾⢿⣳⡰⠋⢁⣠⣼⣿⣶⣄⣀⡀⠀⣸⣨⠿⠾⣅⣠⢾⣋⣉⣉⣙⣻⠀⣿⡌⢳⡼⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⣷⣿⣯⡟⢄⣑⣏⡶⢛⠷⠚⠒⢶⣶⣾⣿⣿⣷⣷⡶⣶⢿⡷⠯⢄⣀⡠⠿⢻⢸⣯⣧⣸⡇⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡘⣟⢯⣿⠟⠓⢲⣿⣛⣛⠒⣶⠒⢚⡭⠞⢹⠘⠛⠀⢧⢹⠸⡏⠓⠤⠤⠄⠀⢸⣾⢟⠈⢻⡇⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣷⡏⣸⣿⣆⡴⠋⠘⣿⠉⠛⢻⠚⠉⠀⢀⡜⠀⠀⠀⠘⠘⡄⠙⠦⣄⡀⠀⣀⣼⡏⠀⢗⢻⣷⣾⣽⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀ ⠀⠀⢘⡆⠀⠀⠀⠀⠀⣼⢹⠃⠀⣿⢷⣧⡿⡏⠀⠀⠀⠈⠓⠶⢼⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠉⠀⢸⡇⠀⠘⣿⡿⣼⢿⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⢹⣸⡀⠀⣿⢸⢳⡙⣿⡄⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢀⡤⢄⣠⡾⠃⠀⣀⣐⣲⡦⢬⣅⣱⠀⣸⢱⣧⣾⣆⠈⠳⠶⠤⣄⡀⠀⠀⠀⠀⢀⡸⠆⠀ ⠀⠀⢸⠀⠀⠀⣀⣤⠔⠋⣻⢧⠀⣿⡄⢻⣿⠸⣧⠀⢀⣴⢧⡾⠿⠧⠾⠿⠶⠶⠴⠺⡿⠛⢘⣛⣛⣋⡉⠤⠤⠴⣞⣿⠻⠀⣿⣿⣼⡻⡙⣄⣀⠤⠤⡄⠹⡄⠀⠀⠀⠿⠿⣯⡀ ⠀⠀⡾⠀⢠⣞⡁⠀⡴⠚⠁⠘⣧⣸⠙⣜⢿⣲⣿⢸⣸⣿⡿⢾⡿⠓⠾⠛⠛⠛⠛⠉⠉⠉⢉⣀⣀⣀⠀⠀⠀⠀⠋⣿⡇⠄⢸⢯⣏⢧⣧⠹⠿⣓⣦⣸⣰⠷⠒⠶⠶⣤⣄⠈⢧ ⠀⢸⡇⡴⠋⠈⠙⢺⣷⡖⠀⢠⣿⡏⢧⡈⢷⣝⢿⠀⢿⡹⣽⡄⠁⠀⢀⣤⣤⣴⣶⣶⣾⣿⡿⣿⣿⣿⣿⣿⣶⣤⣤⠇⢿⡄⣸⡏⠿⣮⣙⠷⣤⣈⣿⠛⢧⣄⡀⠀⠀⠀⠙⢷⣌ ⠀⢸⣻⣷⡃⠀⠀⣸⡿⠃⣴⡿⣩⠇⠀⣿⡌⣿⣿⣇⠘⠧⢇⠻⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⢿⣿⡟⠀⠘⡾⣻⡇⠀⠈⣿⠆⠀⣸⣿⠖⢶⣈⣿⡆⠀⠀⠀⠀⢻ ⠄⢹⡟⠁⠀⠀⠀⣿⠃⣬⢏⡴⠁⢀⠔⡹⣿⠘⣿⣿⣇⠀⠈⠀⠘⣿⡋⠁⠀⠀⣀⣀⣀⡠⠤⠤⠤⠶⠴⠦⣤⠟⣰⠃⢀⣷⣿⡇⢠⡞⠛⣶⡋⢿⣇⡴⡿⣿⢿⣗⠀⠀⠀⠀⢸ ⣶⡟⠀⠀⠀⠀⠀⣿⠀⣿⣸⠀⠀⢯⣏⠀⣿⣀⣿⢹⣿⠳⣄⠀⠹⣌⠻⢿⣛⣉⣀⣀⣀⣀⣀⣀⠤⠤⠖⠋⠁⣰⠃⠀⣸⣿⢸⣿⡄⠳⣄⠀⠉⠛⢿⣷⣿⡿⠀⣿⠄⠀⠀⠀⣼ ⣿⡆⠀⠀⠀⠀⠀⢹⢧⣌⣛⠲⣤⡈⠻⣶⠃⣿⣿⠀⢹⣷⡘⢷⡀⢈⠷⣤⣈⣉⢉⣉⣉⣉⣁⣀⣀⣤⣤⠖⢺⢷⡀⣰⣻⣿⢸⣿⣿⣷⡌⢧⠀⠀⢘⣿⣿⠃⠀⡿⠀⠀⠀⢠⣻ ⢿⣷⡀⠀⠀⠀⠀⠘⣾⡟⣍⠱⡈⣷⣄⣿⣿⢮⢿⡆⠈⢿⣷⡀⢿⡏⢰⡏⠉⢉⡟⡿⠉⢹⠉⣏⠀⢹⠸⡄⠸⡀⢳⣿⣿⡟⣼⣿⣿⡿⠁⣼⣀⡴⠟⢫⡏⢀⣼⠁⠀⠀⠀⣣⠋ ⢿⣹⣷⠀⠀⠀⠀⠀⠹⣿⡜⢧⣷⡏⠹⢿⣆⣿⣸⣿⡆⠀⣿⣷⠈⠃⢸⡇⠀⢸⠀⣷⠀⢸⠀⢹⡀⢸⡇⢻⠀⡇⠸⠿⣿⣳⣿⡿⣫⣴⣾⣿⠟⠀⣠⠏⠀⣾⠏⠀⠀⠀⡰⠃⠀ ⣦⣿⣿⣷⣄⠀⠀⠀⠀⠘⢿⣄⠀⠈⢦⡞⢹⢻⡿⢉⡇⠀⠘⡇⠀⠀⠘⢇⣀⢸⠀⢻⡀⢸⠀⠘⣧⣸⡇⠈⣧⠏⠀⢀⣿⣿⣿⣿⣗⣿⣿⡿⠃⡴⠃⠀⢴⠏⠀⠀⢀⡴⠁⢀⡼ ⣄⡈⠙⢛⣿⣿⣦⡀⠀⠀⠈⠻⣦⠀⠈⠳⡏⣿⢇⣬⣇⠀⢸⢀⡀⠀⠀⠈⠛⠛⠀⠘⠟⠚⠀⠀⠙⠉⠀⠀⠀⠀⢀⣟⡟⢿⣯⣹⡇⢸⣿⢫⠞⠀⢀⣴⠇⠀⠀⣠⠞⠀⣠⡾⣣ ⠉⠛⠒⢬⠍⢁⣨⣽⣶⢦⣀⣀⠈⠓⠄⠀⠹⣿⣘⣛⠃⠀⢸⣸⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡜⡾⢠⣼⡟⢹⣃⣸⣻⠋⠀⣴⡟⠁⠀⢠⡾⠋⣠⣾⡿⣡⡟ ⠀⣀⣠⠴⢲⠋⠁⢀⡏⠀⢻⡿⣿⣷⣶⣤⡀⠈⣿⣍⡕⢶⠈⢿⣿⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢤⢰⠘⡆⣄⡇⣧⣾⠋⠀⣼⣿⣿⠃⢀⣾⠋⠀⢀⣼⠟⢡⢾⣿⣿⠞⠋⠀ ⠋⠉⠀⠀⢸⣄⡴⠋⠀⠀⢸⣿⣿⣶⣭⣻⣿⠄⠘⢿⣏⠉⠀⠀⠸⣿⣰⡇⣀⠀⣿⢸⠸⢾⠀⢣⠀⡘⣏⣦⠹⣼⣾⣽⣇⡀⠀⣿⣿⠃⢠⡿⠃⢀⣴⡿⣿⠞⣣⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿⣯⣽⣿⣿⠄⢳⣄⡹⣷⡄⠀⠀⠈⠻⠷⣿⣧⣸⣾⡀⣿⣶⣸⣆⣳⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⠃⢠⡿⢁⣴⣿⣿⡟⠁⣰⡿⠋⠀⠀⠀⢀⣴ ⠀⠀⠀⣀⣀⣀⡤⠤⠾⢿⢿⣤⣿⣿⣿⣻⣿⠀⠀⠈⠙⣺⢿⣤⣀⠀⠀⠀⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⣀⣾⡏⣠⣿⣡⣾⣿⡟⠁⣠⡾⡋⠀⠀⢀⣤⣿⣿⣿

⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠁⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠀⠀⠀⠀⢀⡀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣶⡖⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⠀ ⣶⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀ ⣯⢿⣆⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠸⡟⣿⡇⠘⣿⣿⣿⣿⣿⣷⣄ ⣿⣿⣿⡯⢠⣿⣿⡿⣿⣿⢿⠏⠀⠂⠄⡀⠁⠹⡇⠀⢻⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⠾⣿⡇⣫⡾⡏⠎⢀⡤⠤⣄⠀⠀⠀⢁⠠⠄⢽⢻⣿⣿⠿⠀ ⢏⣿⣿⣿⣆⢻⣷⡣⣧⠅⢀⡈⠀⠀⠈⠀⠀⠀⡇⠤⠤⡀⢸⣿⣿⠀⠀ ⣿⣿⣿⣿⢻⣯⡸⠋⠺⡆⠘⡟⠒⠂⠤⠀⢀⣐⡁⠒⠐⢢⡿⠁⠈⠃⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⣷⣄⠹⢏⠁⠐⠒⠠⢤⣄⣝⣠⣋⣀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⣷⡤⡁⠂⠤⠤⠔⡋⠔⠁⠀⠀⠉⠀⠀⠀ ⣿⣿⣿⣿⣿⣻⣿⣦⡀⠸⣿⣿⡟⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢿⢿⣿⣯⠳⣄⣽⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠓⠒⠒⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠠⡀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢣⠀⠹⡀⢣⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢱⠀⡇⢠⠁⡀⢱⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⡞⠆⢠⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣶⣷⣾⣦⣧⣸⡟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠁⡀⠈⣦⣴⣾⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠉⢉⡍⠉⠉⠓⠒⠠⠤⠀⡤⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⢠⠀⢹⣀⣽⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠋⠀⠠⠩⠶⣄⣀⠀⢸⠁⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠘⡄⣰⣿⡿⠟⠋⠀⠰⠚⢁⣁⡶⠤⣤⣤⣶⣶⣾⣿⣿⣯⣤⣶⣦⣴⣴⣖⠢⠌⠁⢸⠀⠀⠀⠀⠀⡟⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⣸⠟⢉⡴⠞⠛⣰⣶⡾⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠙⠀⠀⣘⡄⠀⠀⠀⠀⢻⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⢧⡴⠊⠁⠀⢀⣤⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢤⡶⡈⢻⡄⠀⠀⢀⣸⢀⢸⣿⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⣀⣴⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣷⡜⡀⣟⠛⣖⠉⢹⠸⠟⣿⠀⠀⠀⠀ ⡴⢋⠔⡶⣻⣿⣿⣿⣿⣿⣿⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⡤⠿⣧⠻⣿⣿⣿⣿⣷⣄⢠⡅⢃⢸⠀⢿⡦⠸⡀⢠⠃⠀⠀⠀⠀ ⠔⢁⣤⣾⣿⠋⣿⣿⣿⣿⣿⠠⢽⢄⣀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⣀⡀⣹⡀⢻⣿⣿⣿⣯⠙⠻⢇⡎⢸⠀⣿⣿⣆⣷⡃⠀⠀⠀⠀⠀ ⠀⡼⡽⡵⠁⢸⣿⣿⣿⢻⡏⠀⠘⠀⠀⠉⠉⠀⠠⡄⠀⠀⠀⣴⡾⡛⢛⣽⠇⣀⣿⢹⣿⣳⣷⢀⣞⣠⠼⠒⠉⠁⠀⠈⠉⠲⢄⡀⠀⠀ ⡾⠉⣠⡅⢰⣿⣿⣿⣿⠈⡇⢠⡴⠖⠻⠶⡆⠀⠀⠁⠀⠀⠀⠈⠐⠻⢍⣩⣖⡽⡍⢸⣶⣧⢘⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠀ ⡇⠖⡧⡇⢸⡟⡸⠛⣿⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠙⠶⢀⣀⣠⠤⠒⠙⠁⠈⠀⡇⢸⣇⠜⡿⣿⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠙⡄⠇⠃⢎⠀⢻⠛⣿⡇⠀⣏⣹⠲⡶⠒⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⡠⢾⠇⢸⣡⣾⣧⠛⢀⣀⣠⠤⠒⠒⠉⠁⠀⠀⠀⠺⠀⠀ ⠁⠿⣀⠺⠶⡁⠘⡄⢾⣿⡀⢸⡙⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠒⠒⠒⠒⠾⠳⡟⢀⡟⠩⢻⠻⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄ ⣏⡒⠬⣙⠒⠚⣦⠘⠦⣙⢳⡀⢻⣦⣨⡦⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⡾⣇⣠⠂⢰⡇⡿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⠀⠉⠓⠒⠦⠤⠤⠤⠤⠬⢍⠳⣄⠙⢧⡁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠖⣡⣶⠟⠀⠀⠌⡈⠈⣷⣄⣁⣷⡠⠤⠤⠴⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣍⣓⠒⠶⠦⠴⠟⠒⣋⣉⣴⣾⡟⠁⢀⠀⠀⠰⠀⣼⣿⣇⢸⡟⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠁⠈⠉⠉⣛⣿⣿⣉⢿⡿⣻⡟⡀⠠⠋⠀⢀⠃⣼⣿⣿⣿⣷⢶⡧⣤⠤⠔⠛⠉⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⠠⠤⣀⠙⠛⠟⢻⣿⣳⣟⡎⢠⠃⣀⣤⠞⣾⣿⣿⣿⣿⣿⣼⡗⠸⠀⠀⠀⠀⠀⢀⡴⠁⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠻⣷⡄⠀⠈⠁⠒⠤⠄⠘⠿⠤⠗⠋⠁⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣖⢦⣤⣴⣾⣷⣦⣤⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠀⣸⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣷⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⢿⡇⠙⢭⣗⣤⣀⠈⢆⠀⠠⠔⠓⠒⠃⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠷⠒⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠀⠘⠿⠄⠀⠙⠂⠀⠀⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣠⣤⣤⣤⣴⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⡏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣀⣀⠀ ⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀ ⣿⣷⣦⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⣜⣻⣿⣷⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⣿⣿⣿⣿⣷⡠⣤⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠸⡇⢹⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆ ⣿⣿⣿⣿⣿⣧⠤⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠓⠤⣀⠀⠀⠈⠀⢿⣿⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⣼⣿⣿⡿⢹⠛⡝⣿⣿⡏⣼⠃⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠈⠛⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⡇⠈⣉⣻⠾⡿⠀⠃⠀⣤⡶⠾⠿⣶⣄⠀⠀⠀⠀⠀⢀⠄⠲⠞⠉⢹⡟⢹⣿⣿⣿⡟⠿⠧⠀ ⣿⣻⣿⣿⣿⣿⣿⡀⠺⣿⣿⡄⢧⣼⢀⡇⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⡏⠀⣀⣀⣀⠈⠀⢸⣿⣿⣿⡇⠀⠀⠀ ⣵⣿⣿⣿⣿⣿⡿⣿⣆⣿⠿⣿⣮⡙⢿⡃⠀⢠⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠉⠉⠹⠇⠀⣾⣿⠛⢿⣷⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡇⢻⣿⣆⢀⡿⠋⠙⢺⡇⠀⠀⣿⠉⠛⠓⠒⠤⠤⣀⣀⡀⠀⠊⠀⠉⠛⠓⠒⠒⣼⣿⠇⠀⠀⠈⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡉⠀⠀⠀⠈⣿⡄⠀⠹⣦⣼⠤⠤⠄⣀⣀⠀⠈⠉⠉⠙⠲⢶⠆⠀⣼⠗⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣻⣦⡀⠙⠣⣄⠀⠀⠀⠀⠉⠙⠒⢶⣼⣴⣯⣤⣼⣍⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣦⣀⠈⠓⠦⣄⣀⡀⠀⢀⣠⠿⠃⣠⠞⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠉⣉⣡⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣧⡀⠀⠈⢿⣿⣿⣿⡟⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡿⢿⣄⠀⠈⢻⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⢻⠛⣿⣿⣿⣿⡀⠻⣷⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠴⠶⠶⠶⠦⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⢀⣠⣺⣀⣐⣀⣁⣀⣀⣰⣤⣤⡀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⡠⠴⠿⠟⠛⠋⠉⠉⠉⠉⠀⠈⠉⠉⠙⠓⠾⠶⠦⣄⣙⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠙⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢡⢜⡯⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⣿⡟⠙⣿⣿⣿⣿⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡌⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⢞⡕⡣⣲⠄⠀⡶⢒⣤⣠⣴⣿⣿⣿⠟⠁⣿⠀⠀⠹⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣦⣒⠀⣀⢦⡀⠤⠀⠈⢧⢙⠻⡆⠙⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡴⠃⠃⢊⢞⠕⣠⡿⠛⣭⣾⣿⣿⣿⡿⠃⠀⠀⣿⠀⠀⠀⠙⣿⣿⣷⠀⠘⢿⣿⣿⣿⣿⣿⣷⣌⡢⡹⣴⡄⢾⢯⢯⠦⠙⠢⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢠⠎⣠⠟⠀⣾⣿⣿⣿⢻⡿⠁⠀⠀⠀⢻⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⢻⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⡋⠋⠁⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠐⠋⠘⠱⢁⣾⣿⣿⡿⢣⣟⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⠄⠒⠻⣿⠘⣿⣿⣿⣆⠘⢌⢻⣧⡠⡄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⢠⢏⣄⣤⣆⠀⢰⣇⠀⠀⣾⣿⣿⣿⠃⡼⠁⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⡆⢹⣿⣿⣿⣆⣌⡇⢻⣣⣸⣹⣶⠀⠀⠀⠀⠈⣷⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⢀⡿⣿⣼⣽⢹⡄⡏⡏⢹⡾⢿⣿⣿⠏⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⠀⠀⣿⣿⣿⣿⣿⡻⣏⢫⠇⢧⠋⢳⠀⠘⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⣼⡇⡿⢸⢱⢹⢻⢰⣶⢷⣥⠟⠀⠀⣿⣿⠀⠀⢀⣼⠟⠛⠛⢿⡆⠀⠀⠀⣿⡄⠀⠀⠀⠀⡟⠉⠁⠈⠻⣧⠀⢹⣼⣿⡎⠀⠀⠘⢷⣼⣸⡇⡇⠈⢲⢀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⢹⡇⣿⢸⢸⢸⢸⠸⣾⠋⠁⠀⠀⠀⢹⡟⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⡄⠀⠀⠀⠰⣤⣠⣄⣠⣤⣤⡀⠃⡟⠃⠀⠀⠀⠘⣿⣹⣧⣳⢰⣸⠸⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢹⢸⢸⢺⢟⡇⣾⠆⠀⠀⠀⠀⠀⣧⣠⣖⣦⠔⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣤⣈⣃⣀⠉⠙⠿⣠⡏⠀⠀⠀⠀⢠⣿⢃⣟⣟⣟⣟⢆⡀⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⠘⡄⣧⣿⠾⠞⢾⠀⠀⠀⠀⠀⠈⢹⡋⠉⣄⣠⢶⡖⠊⠉⠉⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠻⠓⣦⠀⣽⡒⡀⠀⠀⠀⣰⠇⢈⣟⡾⣾⣾⡟⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡐⡛⣜⣾⢏⡛⢻⡇⠀⠀⠀⠀⠀⠰⣧⠀⢹⡁⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣀⣀⢀⡟⠀⡟⡙⣃⢤⣶⠞⠷⣬⠏⠟⣴⣫⠏⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡻⡝⣾⢮⡙⢮⡇⠀⠀⠀⠀⢀⠀⢾⡆⠈⢧⣀⣠⣾⣿⣟⠿⠋⠀⠀⠉⠉⠁⠈⠙⠻⠿⣿⣿⣶⠟⠀⣸⣩⠾⠿⠋⠉⠱⣤⠈⠻⡮⠟⢁⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢷⡅⠙⠎⠁⠈⢷⣄⠀⠀⠀⢀⠀⣠⢽⡀⠀⠹⢿⡏⢁⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⢄⣀⢸⡿⢋⣀⣠⣿⠁⠀⠀⠀⠀⠀⡞⡇⢰⣷⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠰⢎⣻⣄⢄⠈⡀⢂⠈⢤⣹⡄⠀⠈⠙⠿⣍⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠽⠋⢡⡏⠉⢙⡿⠟⠀⠀⠀⠀⣰⣿⣷⠋⣿⠛⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⢀⡙⠷⣄⠲⠉⣣⣋⢱⣿⣶⣄⣀⡀⠈⠉⠙⠒⠒⠒⠒⠒⠉⠉⠁⠠⣶⣏⡀⠀⠈⠀⠀⠀⢀⡀⠀⢽⣹⣿⡀⠙⣦⠼⠶⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑⣒⣶⣨⠷⢮⣷⣶⣿⣿⡿⠿⢿⢿⣷⣶⣤⣤⣀⣀⣀⣠⣤⢶⣶⢻⣹⣯⣧⣀⣀⣀⡠⠞⠉⠙⠶⠦⡍⢁⣹⠆⣸⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠋⠁⠉⠀⠀⠀⠁⠀⠈⠹⠷⢤⣿⠀⠈⠻⣿⡿⠙⠩⢉⣿⣿⢹⡎⣆⣏⡿⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠑⢌⣀⠿⠿⣀⣤⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠷⠮⠵⠲⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠙⠶⢤⣽⣿⢻⢸⣵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠙⠶⠉⠻⢉⣡⡶⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⢙⡽⠚⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠗⠚⠉⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⢀⡄⣀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣤⣤⣀⢰⡌⡅⠙⡻⡆⣸⠏⠀⠀⠀⢀⣀⡤⢤⣾⣿⠋⠀⠀⠀⠀⣠⢞⣽⡿⠞⠡⢄⣠⠀⠀⠀⠀⠀⠖⣤⠐⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⢦⡀⢦⢠⣴⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣵⣙⡟⠁⠀⠀⢠⣿⡿⠀⠀⠀⠀⣠⣔⣳⣤⣾⣭⣿⣿⣴⣚⣋⣺⣭⣾⡛⢋⡡⣴⠾⣧⣞⣋⡏⠀⠀⠀ ⠀⠀⠀⠀⠸⣄⢦⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠋⠀⢠⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣵⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣁⢧⠀⣇⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⠿⠛⠛⠻⢿⣿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⢻⡟⠋⢹⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⡿⠟⠛⠛⠛⠿⢿⣿⣷⡀ ⠀⠀⢰⣿⣿⠟⠋⠁⠀⠀⠈⠳⡄⠀⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳ ⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠇⢸⠃⠀⠀⣀⣀⣠⣤⣤⣤⣶⣶⣦⣤⣿⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⣸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⢠⡏⠀⢀⣀⣀⣀⣤⣀⣀⠀⠀⠘⡇⣷⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣦⣠⣄⡀⠀⠀⠀⣀⣀⣀⣀ ⣸⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢻⣻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⣸⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣮⣭⣿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣶⣯⣝⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⠛⠋⠉⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣯⣿⣿⡿⠶⠿⠻⠯⠭⣉⠉⠉⠙⠻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⢠⣾⣧⣤⡖⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠉⠀⢄⣸⣿⣿⣿⣿⣿⣥⡤⢶⣿⣦⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣙⣛⣿⣿⣿⣿⡏⠀⠀⣀⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⣠⣶⣶⣶⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⢹⡏⠁⠀⠀ ⠀⠀⠀⢀⣿⡏⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⢀⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡘⣿⣿⣃⠀⠀⠀ ⣴⣷⣀⣸⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠹⣿⣯⣤⣾⠏⠉⠉⠉⠙⠢⠀ ⠈⠙⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠛⠉⢩⣷⣴⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣀⡠⠋⠈⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣦⠺⡉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⣙⠒⠈⠀⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣾⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠼⢒⣮⣵⠟⠚⣶⢽⡦⣌⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡾⠟⣷⣖⠚⠳⡦⣀⠀⠀⠀⠀⠀⠐⣻⠖⣠⢞⠁⠀⠀⠀⠀⠀⠀⠻⡸⡆⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⡏⣩⣿⠀⡇⠹⢵⡄⠀⠀⠀⠀⢻⠂⠊⡼⠀⠀⠀⠀⠀⠀⢠⣀⡳⡗⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⢿⣧⣧⠔⢃⡴⢁⡿⠦⣀⠀⢰⣿⡁⢐⠓⢛⣶⢤⡤⠘⠛⣯⣷⠔⢹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣹⣷⣖⣫⠤⡾⠃⢠⡿⠖⣾⢾⣧⣾⡀⠛⠛⠋⠀⢰⠀⠀⡆⠀⢸⢟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢰⣤⣈⣁⡀⠙⠻⣾⣳⣾⣿⢆⡜⠛⡦⠿⣿⣷⠀⠀⢀⣀⠤⠤⣤⣤⠤⣽⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡾⠋⠀⢀⣼⡟⠛⠛⠛⠛⢻⠿⢯⣾⣿⠋⢻⡖⠃⠀⠉⠛⣶⡚⠛⠂⠀⠀⠉⠉⣡⣿⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢏⠀⢀⣶⣿⢯⡀⠀⠀⠀⢠⠞⣀⡴⠛⢷⣤⣾⢿⣶⣄⠀⠀⡟⠻⣶⣤⣀⣁⣠⣼⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠙⠿⣟⠁⢀⣹⠄⠀⠀⠈⢿⣿⡿⠶⠋⠻⣿⣷⣽⢿⣷⣶⡇⠀⡆⠙⠻⠿⠋⠀⢇⠸⣯⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⣧⡀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⣠⠤⠶⠶⠶⠶⠾⠿⢻⡟⠁⣿⠀⠀⠸⣄⠀⠀⠀⠀⡞⠀⢿⣦⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⠁⠀⠀⠈⢿⣦⣄⣀⣴⣿⣿⠏⠀⡀⣀⠴⠋⠘⣆⠀⠀⠀⠀⠀⠀⣾⠇⠀⣿⡟⠓⠦⠽⣷⣄⠀⣠⠧⠤⠾⠿⡆⠀⣷⡈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠋⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⠿⠷⠚⠉⠛⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⢸⣿⠀⠀⣿⣷⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⡇⠀⢸⣷⡀⠀⠀⠙⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⢇⠀⠀⠀⠀⣿⣿⡄⠀⣿⣿⠀⠀⠀⠀⠈⡏⠀⠀⠀⢀⡴⡇⠀⢸⣿⣧⠀⠀⠀⢀⡴⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄⠀⢀⣙⢦⣄⠘⢦⡀⠀⠀⢸⠀⠀⠀⠀⡿⠁⡇⠀⣿⣿⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⠀⡇⠀⢸⢿⣿⡀⠀⢀⡜⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣧⡀⠀⢻⣷⣿⣿⣾⣿⣦⡀⠈⡇⠀⠀⠈⠀⢰⠀⠀⣿⣿⠀⠀⠀⠀⢀⣷⣤⠛⠀⠀⠀⢱⠀⠘⡆⢻⣇⠀⡼⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠻⡄⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⣧⠀⠀⡀⠀⢸⠀⠀⢻⣿⡤⠖⠒⠚⣽⡏⠉⠉⠉⠉⠑⢻⠀⠠⡇⠀⠹⣼⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⠿⠿⠿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠀⣴⠁⠀⢸⠀⠀⣿⡏⠀⠀⣠⠟⢠⡇⠀⠀⠀⠀⠀⢸⠀⢨⡇⠀⠀⠘⣧⠀⢀⣀⣀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠟⢷⠞⠧⡀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣠⣿⣿⣿⣾⠇⠀⠀⣸⠀⠀⢿⣧⣤⠾⠷⢶⣾⠷⠶⠶⣤⡤⣄⣸⡀⠀⡇⠀⠀⠀⣿⣶⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣼⣟⠓⡀⠹⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⣿⠘⡿⠀⠀⢸⣿⠀⠀⠀⡇⡇⢸⣿⠁⠐⡇⠀⠀⠀⣟⣥⣿⣿⣶⣆⣽⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⣿⠀⡇⠀⠀⢸⣿⠀⠀⠀⡇⡇⠘⣿⣄⠀⢿⡀⠀⢸⣿⣿⣿⣿⣿⣿⡛⣿⣷⣦⡹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⡀⠀⡽⢦⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⢸⠁⠀⢰⣿⠀⡇⠀⠀⢸⣿⠀⠀⠀⣇⡇⠀⣿⠹⡆⠀⢳⠀⢸⣿⠫⠽⠿⠿⠿⢿⣿⡿⢿⣿⣌⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢄⠀⠬⠳⡄⠀⠀⠀⢻⠁⠀⣿⠀⠀⠀⢸⡀⠀⠸⣿⣞⡇⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⣏⡿⠃⠀⣸⠃⠘⣿⡆⠀⠀⠀⠀⠈⢫⣿⣦⡙⣯⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡳⣄⠒⠙⢦⡠⢤⣼⣿⣿⣿⡄⠀⠀⠀⢣⡀⠀⠙⢿⣿⡄⠀⢸⣿⠢⢤⣤⣽⣇⣰⠟⠁⣠⠞⠁⠀⠀⣿⣿⡄⠀⠀⠀⢷⡌⢿⣿⣷⡘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⡍⣠⣿⠉⣷⣿⣿⣿⣿⢿⡆⠀⠈⠳⡄⠀⠈⠻⣿⣄⢸⣿⠀⠀⠈⣹⡟⠁⢀⡞⠁⣀⣤⣤⣤⣿⣿⡇⢸⠀⠀⠈⣿⡞⠉⠻⣇⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡈⣢⠏⣰⣿⣿⣿⣿⣿⣈⣛⣿⡆⠀⠙⣦⡀⠀⠙⣿⣿⣿⠶⢶⡾⠋⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⡿⠀⢸⠀⠀⠀⠘⡇⠀⠀⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⢴⡿⣾⣍⢧⣾⡿⠋⣛⢏⣷⣤⣀⠈⠳⣄⠀⠈⢻⡈⣦⠟⠀⠀⣰⣿⣿⣿⣿⠿⠿⠿⣿⣿⠁⠀⡼⠀⠀⠀⠀⠹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣄⡼⣟⠼⣿⠀⣿⠷⠏⣈⣛⣿⣿⣶⣬⣧⣀⣀⠳⣯⣤⣶⣾⣿⣿⣃⠬⠍⠙⢆⠀⠸⠺⢦⡀⡇⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠥⢈⣉⣙⠛⠚⠃⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀⠤⣠⡄⠀⠘⡄⠀⡇⠀⢹⡇⠀⠀⠀⣀⣀⡀⠘⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠦⣤⡈⠉⠉⠉⠓⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣩⠽⠒⠂⢉⠄⠻⠀⠀⠹⡄⠃⠀⢸⡇⠀⠠⣾⠟⠻⡿⠷⣼⠀

⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠋⠀⠀⠉⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠉⣿⣆⣀⠀⠀ ⢀⣶⣿⠿⠿⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠛⠻⢿⣷⡄ ⢸⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣷ ⠘⣿⣧⡀⠀⢀⣀⠀⠀⠀⠙⢿⣷⣄⠀⢀⣴⣾⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣷⣦⣀⠀⣰⣿⠟⠁⠀⠀⠀⣠⣀⠀⠀⣠⣿⠇ ⠀⠈⠻⠿⠿⠿⢿⣷⣄⠀⠀⠀⠙⣿⣿⣿⡿⠟⠋⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠉⠻⢿⣿⣿⣿⠋⠀⠀⠀⣠⣾⡿⠿⢿⣿⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣠⣾⣿⡿⠋⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⠿⣿⣷⣄⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠋⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣦⡀⠀⠘⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⣴⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⢠⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣁⣀⣀⣤⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣤⣤⣤⣌⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢠⣿⣿⣿⣿⡿⠛⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣆⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡏⠀⢠⣿⣿⣿⣿⡿⠷⠶⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠺⠿⠿⣿⣿⣿⣆⡀⠘⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡶⠾⠛⠋⠉⠁⠀⢀⣠⣤⣶⡶⠶⠾⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠷⠶⢶⣤⠀⠀⠀⠈⠉⠛⠻⠿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣥⣤⣤⣀⣀⣀⣀⣰⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣤⣤⣤⡤⠴⢶⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣿⣿⡿⠟⠁⠀⣀⣀⡀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⠉⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣤⡶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⡏⠉⢹⡟⠛⢻⡋⠉⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠈⠻⢿⣿⣿⣿⣿⣿⡇⠈⣿⠛⠓⣿⠷⠶⢾⡗⠛⢻⡏⠀⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⣴⣿⣿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣿⣶⣶⣿⠟⠁⠈⠻⣿⣿⣷⣄⠀⠀⠙⠻⢿⣿⣿⡷⢴⣯⣀⣀⣿⠀⠀⢸⣇⣀⣠⣷⡶⣿⣿⣿⠟⠋⠁⠀⣠⣴⣿⣿⡟⠁⠀⠈⠻⣿⣶⡿⢿⣶⣄⠀ ⢰⣿⠋⠁⠀⠈⠙⠁⠀⠀⢀⣴⣿⠟⢿⣿⣿⣶⣄⡀⠀⠈⠙⢿⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢰⡟⠉⠀⠀⣠⣴⣾⣿⡿⠟⠻⣿⣦⡀⠀⠀⠈⠁⠀⠀⠙⣿⡆ ⢸⣿⡀⠀⠀⠀⠀⠀⠀⢴⣿⠟⠁⠀⠀⠈⠛⢿⣿⣿⣷⣶⣤⣀⣻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣏⣠⣴⣶⣿⣿⡿⠟⠉⠀⠀⠀⠈⣻⣿⠆⠀⠀⠀⠀⠀⠀⣿⡇ ⠈⠿⣷⣦⣴⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣶⣶⣾⠿⠁ ⠀⠀⠀⠉⣿⣇⡀⠀⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⣠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠈⠉⠉⠉⠉⠉⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠞⡁⠀⠀⠀⠀⣀⣠⢠⣀⣀⣀⣤⣠⣀⡀⠀⠀⢠⣀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⣷⣶⡀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣶⣿⣿⣤⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⢠⡹⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢠⣽⡿⠟⠋⠠⠂⣀⣤⣶⣾⣿⣿⣿⣿⡿⢿⣶⣦⣄⢀⣄⡀⠀⣤⡍⠓⢦⡀⠀ ⠀⠀⠀⠀⢸⠀⡨⢞⣁⣴⣶⣶⣶⣿⣿⣿⡿⠃⡿⢻⣿⡿⠁⠈⢻⡍⢿⣿⣝⡻⢿⣅⠀⠀⠀⠙⡄ ⠀⠀⠀⠀⣨⠟⠁⢺⡿⢋⣾⣿⣿⣿⣿⡿⠁⢰⠃⢸⡿⠁⠀⠀⠸⡇⠀⢿⣿⣿⣦⣉⠀⠀⠀⠀⢸ ⠀⠀⣠⠞⠁⠀⠀⠀⣠⣿⣿⣿⡿⢹⣿⠁⠀⠈⢀⡞⢀⣀⡀⠀⠀⠁⠀⠘⣿⣿⣅⣤⣄⠀⠀⢀⡞ ⠀⢰⠃⠀⣠⣄⠀⢰⣿⣿⣿⣿⠃⢸⠷⣤⣀⣀⣈⣡⠟⢇⣁⣀⣤⣂⡀⠀⢻⣿⣿⣿⣿⠀⣠⠎⠀ ⢠⡇⠀⢰⣿⣟⠀⣾⣿⣿⣿⣿⠀⠺⠿⠿⠬⠛⠿⠋⠀⠞⠙⣿⣿⣿⡋⠀⣾⣿⣤⣿⡡⠞⠁⠀⠀ ⠈⡇⠀⢸⣿⣿⣳⢿⣿⣿⢿⡟⠀⠀⠀⠀⢀⡀⠰⠦⠀⢸⠿⠢⢍⡉⠁⢰⣳⡯⠛⠉⠀⠀⠀⠀⠀ ⠀⠱⡀⢼⣿⣿⣯⠼⢿⡹⢯⣿⠀⠀⠀⠔⠉⠀⢀⣀⣀⣀⡀⠀⠀⠱⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⣌⡛⠛⣧⣤⣼⣏⣙⣾⣇⠀⠀⢀⠴⠊⢁⡤⡤⣤⣈⠑⠲⢄⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠁⠉⠀⠀⠀⠀⠈⠳⣤⣄⡤⠊⠁⠘⠀⠇⠛⢉⣲⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣽⣿⣶⣾⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠈⠙⣿⣿⡼⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣧⠀⠀⠀⠀⠈⠉⠁⠈⢙⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢦⣤⡖⠛⠓⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠈⠉⠉⠐⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠒⠒⠋⠉⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣴⠶⠶⣦⣠⡾⣯⣽⣽⣦⠀⠀⣠⠟⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡻⡤⠴⣾⣿⣏⡵⣋⣁⣿⠀⠉⢁⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣛⡻⢯⣉⣉⡷⠋⠙⠛⠶⠚⢁⣠⣶⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠖⣺⣭⠿⠛⣋⡟⠀⠉⠁⠀⠀⣀⣠⣴⣾⣟⣷⣿⡟⣹⣿⣛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠿⣧⣤⡾⣻⠃⢰⣾⣯⣤⣤⣴⣶⣶⣿⡏⠙⠛⠀⠀⣰⣿⣿⣿⣿⡟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⢡⠇⢀⣿⠿⢻⣿⣿⣿⡖⠂⠀⢄⡄⣀⣴⡾⢻⣿⣿⣟⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⡆⢸⡟⢁⡴⢋⡄⣿⣿⣿⣮⡙⠻⠯⠭⠁⣰⠛⠛⣿⣟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⢻⡈⠇⠘⠀⣸⣿⣿⡿⣍⣻⠙⢷⣤⣴⠟⠁⠐⣰⠋⣿⠤⡟⠳⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡎⠁⠀⠀⠀⢿⣧⣾⠓⣿⡽⠀⠀⠈⡇⠀⢀⣼⡏⠀⡿⠲⡟⠀⠀⠀⠈⠉⠉⠛⠒⠶⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣇⢹⣭⠽⣷⡀⠀⠀⠁⠀⢚⣞⣀⡞⠳⡴⠯⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠛⡇⠀⠀⠀⣠⡿⠈⠳⣰⠊⣻⠷⣄⣴⣚⣽⣵⠛⡷⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⣼⠁⠀⡔⢀⡏⠀⠀⠀⠘⠲⠿⣄⣼⣀⡹⠤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢠⠏⠀⣰⠃⣸⠀⠀⠀⠀⠀⠀⢀⣠⣽⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢀⡞⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⡴⣿⡏⠉⠉⠙⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣄⠀⠀⠀⠀⠈⠋⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⢇⡞⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⣾⢠⠟⠙⠇⠚⠵⣷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⢷⡀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢯⡎⠀⠀⠀⠀⢠⡇⡉⠀⠀⠀⠀⢻⡏⠙⣦⢤⣤⢞⠙⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⣷⡀⠀⠀⣦⠀⠘⢽⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠋⠀⠀⠀⠀⠀⣾⠀⠒⠒⠒⠒⠛⠈⠛⢦⣿⣿⣿⣿⠜⠃⠀⠀⠐⠒⠦⠤⠤⠤⠴⠚⣼⠁⠀⠀⠀⠀⠹⣇⠀⠀⠈⣆⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⢀⡼⠃⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⢀⠤⠴⣛⣻⣛⠓⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠘⣦⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠀⣼⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢹⡇⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠘⣆⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⣧⠀⠀⠀⠀⠙⠶⢤⡾⠀⢸⡹⠤⠤⠄⠀⠀⠰⡄⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠈⢧⠀⠀⣿⡀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢸⡀⠀⠀⢸⠀⠀⠀⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣠⣴⣶⣻⡷⠻⣧⠀⠀ ⢻⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⠠⣇⠀⢻⠦⣀⡀⠀⠀⠀⠀⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⡵⠟⠋⠉⢳⠀⠸⣧⠀ ⠘⠷⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⠀⢀⡼⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣤⣤⣤⣤⡼⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣼⣴⡏⠀⢀⠀⡀⡷⢤⣤⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠒⠒⠛⠛⠛⢲⡄⢀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢉⣿⠀⠀⡞⣠⣷⣷⠀⠀⠀⠀⠀⠀⠘⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣠⣇⣀⢀⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣻⡤⢊⣼⣏⣋⡸⢦⣀⣀⣀⣀⡀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣹⣿⡿⣙⣹⡾⣋⣃⡸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣿⠃⠀⠀⠙⡉⢩⡟⠀⠀⠀⠀⠀

⣿⡻⣽⣦⡀⠀⠀⠀⠤⣄⣀⠸⣏⠹⡶⢟⣩⣖⣲⢻⣧⣴⡶⠚⠉⠁⣀⣀⣤⡤⠤⠤⣉⡛⢟⣒⡲⠶⢒⣡⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣮⣙⣿⣞⡁⠀⠀⠀⠉⠛⣿⡄⣿⠿⠻⠶⢗⡺⢷⣀⡤⠖⣛⡭⠟⢋⣠⠤⠀⣀⡴⣞⠽⠛⠛⠛⠯⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⣹⢿⣿⣿⣟⡳⣇⡙⠲⣄⣈⣷⠉⠒⠒⠒⠉⢀⡀⠹⣶⠊⢁⣴⡾⠋⡀⣠⠞⣡⠞⠁⢀⡆⢻⡄⠀⡈⠳⡄⠹⡷⣄⠀⠀⠀⠀⠀ ⣶⠋⠀⠀⠈⢙⣿⣿⣷⣿⣶⣶⡏⢙⣷⡀⠒⠒⢋⠁⠀⠀⣠⣿⠟⢋⡴⢋⡜⣁⡔⠁⠀⢠⡾⠁⢸⣿⡀⡇⠸⡜⣄⠹⣌⢷⡀⠀⢀⠾ ⣿⣿⣟⡲⣶⣿⡟⣷⣍⣻⣿⣫⠾⣓⣫⢿⣟⣉⠁⣀⣀⣴⡿⠁⡴⠋⢠⡿⠋⣁⠀⢀⣴⡟⠁⣠⠏⠈⡇⢹⡀⠹⡌⢦⢻⣦⣷⠖⠋⢢ ⡟⠛⠛⣿⣿⡟⢠⣿⣟⣷⡌⠒⠉⠉⢀⡠⣺⠿⣯⡽⣫⠋⢠⠞⢁⡴⣋⠤⣚⣥⡴⡻⢋⡴⠊⠁⠀⠀⢻⡘⡇⠀⢿⡘⡌⢿⠀⠀⠀⠀ ⣿⠀⠀⠿⠿⣧⢿⢿⡏⣟⠷⠤⠴⢒⡭⠚⢁⡴⣿⡝⠁⡰⠋⣰⠿⠚⠁⠾⠛⠵⠾⠟⠁⠀⠀⠀⠀⠀⠘⣇⢹⡀⠀⡇⡇⠸⡆⢠⠰⡀ ⡟⡇⠀⢀⡼⣡⠏⣼⢷⡈⠛⠒⠚⣃⣠⠴⢋⢞⡟⠀⡴⢃⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣧⡀⢹⢳⠀⣇⠀⠓⢬ ⣱⣧⣀⡞⡼⠃⢠⠏⣦⠿⢦⣉⣉⣡⠤⢴⣯⠏⠀⡼⢡⠿⠶⠾⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⡟⢠⢸⡦⡾⠟ ⠋⢠⠟⡼⠁⠀⢸⠀⡼⡄⠀⡴⠚⠙⢲⣿⠇⠀⣰⣳⠋⢀⣰⣯⡿⠓⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠸⡀⣷⣿⣶ ⢠⠏⣸⠃⠀⠀⢸⡄⢣⢳⡼⠀⡖⢓⣾⡟⠀⢠⢧⣧⣴⡿⣿⣾⣻⣿⣿⣦⡷⠿⠍⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠤⣤⡄⢿⠀⡇⢹⣿⠛ ⡞⢰⠃⠀⠀⣠⣿⣿⡈⢧⣳⢸⠀⡼⡼⠁⠀⡿⡞⠶⣶⠀⣿⡘⠿⢿⡿⠹⠇⠀⠀⠀⠀⠀⢠⣞⣯⣿⣽⣶⣖⢦⣀⠙⣸⡀⡇⠘⣏⣠ ⢁⡟⠀⠀⣼⣿⡿⠉⣧⡈⠻⡼⢀⢧⠃⠀⢰⢡⠇⠚⢹⠣⣌⣛⣛⣫⡤⠖⠀⠀⠀⠀⠀⠀⢸⡥⠾⣿⣛⣿⣿⣿⣧⣀⣿⡇⡇⠀⡿⠿ ⣼⠇⠀⣸⣻⣿⠃⢠⣯⢿⣆⠉⡿⣼⠀⠀⡞⣾⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡄⢿⣭⠽⠋⣼⠟⣾⣿⡇⡇⠀⡇⠀ ⣿⠀⢰⢧⣿⠇⢀⣿⡏⣾⣿⢷⢧⡇⠀⢀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠗⠉⠙⠒⠺⠏⢃⣾⡇⣿⠀⡇⠀⡇⠀ ⣿⡀⣿⣸⡟⠀⢸⣿⣷⡟⣡⢸⢰⠃⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠖⠋⠀⠀⠀⠀⠀⠀⢠⣞⡾⣷⡇⢸⠁⢸⠃⠀ ⣿⡇⣿⣿⡇⠀⢸⣿⣿⡵⠿⡿⣿⠀⠀⢸⣼⣄⠀⠀⠀⠀⠀⠀⢰⣶⣋⣉⣉⣉⣉⠓⢦⡄⠀⠀⠀⠀⠀⣠⣿⠏⠀⣿⠇⡼⠀⣿⠀⠀ ⣽⣧⣿⣿⡁⠀⢸⣿⣿⢻⣾⡇⣿⠀⠀⠘⣿⣟⢦⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⢀⣴⣻⣷⠀⢸⡟⣰⠇⣸⠃⠀⠀ ⣿⣿⣾⣿⡇⠀⢸⠿⣿⣆⢻⣷⣿⠀⠀⠀⣿⠈⢧⡝⢦⣀⠀⠀⠀⠀⠈⠙⠶⠤⠼⠛⠁⠀⠀⣀⠼⡟⣁⣇⡾⠀⡾⣱⠃⢠⠇⠀⠀⠀ ⣿⢻⡿⣿⣿⡄⢸⡌⣿⣿⣆⢿⣿⡷⡆⠀⢻⣦⠀⠳⣾⡌⣷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡛⠧⣭⠵⠋⢀⡾⡵⠃⡰⠋⠀⠀⠀⠀ ⡏⣼⣇⠘⣿⣷⣼⣿⣹⡿⣿⣿⣿⣧⢳⡀⠀⠹⣧⠀⠘⣗⣿⡘⡜⢹⢲⣤⣤⣤⣤⣶⡿⡏⢻⡍⠀⠀⠀⢠⢞⡞⠀⡴⠁⠀⠀⠀⠀⠀ ⠳⣿⣿⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⡙⠦⣄⠘⠻⣦⡈⠛⠷⡗⡏⡏⡟⡜⡽⢹⠛⣆⢳⡀⠹⣄⠀⡰⢣⡞⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢯⣹⣿⡿⠾⣿⣟⡿⠟⠛⣾⣟⠻⣦⣈⠓⣦⣌⠙⢦⡀⠙⢃⣧⢃⣇⣇⣿⣦⡈⢷⣿⠦⣌⡿⣵⡟⠀⢰⡇⠀⠀⠀⠀⢀⡠⠖ ⠀⠀⠀⠀⠻⢎⡻⣦⡀⠀⠀⠀⠀⠻⣿⣦⡈⠛⢿⣌⣿⡆⠀⣹⠀⠀⢸⣸⢹⢸⣿⣿⣿⣦⡈⠛⡿⣿⢿⠀⠀⠘⣿⡛⠒⠐⠋⠁⠀⣐ ⠀⠀⠀⠀⠀⠈⢳⣌⠛⢦⡀⠀⠀⠀⠈⢻⣷⡀⢀⣿⣿⠃⣰⠇⠀⠀⠀⠻⠸⢸⣿⣿⣿⣿⣷⣠⢷⣿⣾⣷⣄⡀⠈⠿⡆⠀⢀⣠⠼⢋ ⠀⠀⠀⠀⠀⠀⠀⢻⣇⠈⠻⣄⠀⠀⠀⠀⠙⢿⣾⣿⣿⠰⣏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⡇⣿⡙⡏⢻⣿⡆⠀⣿⠰⢧⣀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠹⣷⡄⠀⠀⠀⠈⣿⣿⣿⣷⣬⣳⣦⣀⠀⠀⠀⠀⢿⣌⠻⣿⢿⡇⣷⣿⣧⡇⣴⣿⢁⡴⣁⢦⡀⠀⠉⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⣆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠸⣿⣦⡘⢮⡻⣿⣿⣏⣼⣿⣿⠏⠀⠈⢷⣿⣧⣀⠣ ⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⣷⡀⠹⣦⣿⣿⣿⣿⣿⣦⣄⣀⡈⠻⣿⡻⣧ ⠇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠛⢿⣿⣿⠟⠛⠒⠀⠀⣠⣟⢿⣧⡀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣘⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠈⠉⣿⣷⠀⠻⣿⣏⠻⡿⣿⡿⠿⣦⣤⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠘⡟⢆⠘⢿⣦⠀⠀⠙⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⢀⣿⢸⠀⠀⠀⣷⠀⠀⠀⠻⣦⡀⠀⠀⠹⣿ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⢸⣧⡾⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠦⣤⣀⢻ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠻⢦⣄⣠⢟⡛⢧⣴⠃⢻⡄⠀⠀⠀⠀⠀⠀⢻⣿⣄⢀⣿⡿⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⢟⣷⣿⡿⣿⡛⢧⡀⠻⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣴⡋⠱⣿⣿⣿⣿⣿⡿⢂⡽⠆⢻⡄⠀⠀⠀⠀⠀⠀⠙⣿⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⣿⣦⣎⣤⣜⣿ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠙⠻⣦⡙⠿⣿⡿⢋⡴⠋⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⠖⢉⣨⣏⣵⡟⣿ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣦⣤⠊⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⠏⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠙⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⡿⠃⠀⠀⠀⣠⣶⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣦⡀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⡁⠀⠀⣠⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣄⠀⠀⣹⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡿⠁⢀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⢀⣿⣿⣿⡟⠛⠿⣿⣿⣿⣿⣿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⡄⠀ ⠀⣾⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⡀ ⢸⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣇ ⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿ ⠈⠛⠋⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠈⠛⠋ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⢠⣾⣿⣆⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣶⣦ ⢸⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⡇⠀⠀⢠⣿⣿⡿ ⠘⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⡄⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⠁⠀⠀⣾⣿⣿⡇ ⠀⢹⣿⣿⣷⡀⠀⢀⣿⣿⣿⣿⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⣴⣿⣿⣿⡏⠀⠀⣼⣿⣿⡿⠀ ⠀⠀⢻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣄⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⢀⣼⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠁⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⠟⢿⣿⣿⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⠟⠁⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠙⠿⣿⣿⣿⣷⣤⣀⣸⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣇⣀⣴⣿⣿⣿⡿⠟⠁⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⣿⣿⡇⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠋⣿⣷⣿⡦⠀⠀⠀⠀⢙⣿⡟⡿⢿⠿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣥⠀⠞⠿⠗⠋⠀⠀⠀⠀⠀⢸⣿⢿⣷⡎⢠⣗⡈⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣟⣸⣿⣧⣿⣿⣯⣉⣿⣟⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣤⣶⡿⠃⠀⠀⠛⢸⣿⣿⣿⣿⡏⠉⠉⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠖⢶⡞⠛⠋⠁⠀⠀⠀⣠⣿⠛⣿⢸⣿⡿⠁⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢀⣰⣾⣟⣿⣸⣿⡟⣿⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠖⠋⠀⠈⡇⠛⢿⣿⠷⠟⠀⠀⠀⣠⠤⠞⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣴⡯⠅⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣼⡵⣫⠴⠒⠛⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣠⢖⡽⡿⠊⠁⠀⠀⠀⠀⠀⠀⠘⠛⠓⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠴⠋⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠒⠢⠽⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠃⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⠏⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⣅⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⢠⡄⠀⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢻⡆⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⣁⠤⠴⠷⡦⠀⠀⠠⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢿⠀⠀⠀⠀⠀⢀⡴⢋⡴⠚⣡⠤⠶⠒⢾⠋⠉⠛⣟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣇⠀⠀⠀⢠⠟⣠⢞⡴⠚⠁⠀⠀⠀⠸⣧⣀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢳⠀⠘⣦⠀⠀⢼⡴⣡⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⠀⠈⢷⡀⠀⠀⠀ ⠀⠀⢀⣠⠴⢤⡀⠀⠀⠀⢰⣛⠲⠦⣸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣋⠀⠀⢠⡀⠳⣄⠈⢳⣄⠸⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠻⡀⠀⠀ ⠀⣾⠋⢡⣶⡌⢳⡄⠀⠀⣸⠋⠛⢦⣸⡈⣧⠀⣀⡀⠀⠠⡴⢜⣦⣿⡯⠀⠀⠈⠻⣄⠘⢧⣄⡹⢧⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀ ⢠⣼⢖⣯⣿⣧⣾⡇⠀⣸⠏⢀⣆⡿⣿⣿⡿⠖⠚⠙⠲⠕⢬⠺⡟⠋⠃⠀⠈⠢⡄⠈⠑⢮⣍⠛⠂⠀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄ ⠘⠷⠾⣿⣿⣿⣿⣿⣶⠃⠀⣸⣼⢻⣑⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢧⣀⠈⠙⠓⠚⠁⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⡟⣇⣇⢏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡄⣿⣾⣾⡟⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣤⢹⡼⡽⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢻⣼⣾⣜⠿⠏⠀⣸⠷⣄⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⡎⢳⢳⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣼⠋⠀⠉⠳⣄⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⠶⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⢠⣷⡀⢠⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⡘⠀⠀⢀⡞⢀⡎⠀⣧⠀⢳⠀⠐⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡵⠀⠀⠀⡜⠁⢰⠇⡤⠀⡾⠀⣼⠀⠀⠸⣇⠈⢧⠢⡘⣎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣾⠀⠀⡇⡼⠁⢀⣯⡼⡇⢸⠁⢸⣧⢤⡀⠀⢹⡀⠈⠳⡜⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⣸⠁⢀⣾⠞⠁⡇⡏⠀⣿⣇⣾⣃⣀⣀⣷⠀⠀⠘⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠇⢠⠞⠋⠀⠀⠃⣇⢸⡇⠉⣟⢳⣮⠵⣿⢀⠀⠀⠀⡙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⠀⢻⠀⠐⡄⠀⢰⡿⣾⡇⠀⠈⠉⠛⠋⢻⣿⢠⠆⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠉⠀⠈⡆⠀⣇⣰⠏⠀⠉⡷⠀⠀⠀⠀⠀⠀⣸⣟⡤⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣀⣆⠀⡽⣿⣿⣧⣤⣀⣉⣀⣠⡀⠀⠀⠀⠀⢈⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢾⣿⡁⠙⠃⠰⠋⢀⣄⣀⣀⠉⠳⠀⠀⣠⡟⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣦⣀⠀⠀⠀⢸⡇⠈⠀⠀⣠⣾⣷⣴⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠉⠳⣤⣤⣼⣷⣤⣴⠞⠁⢹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠈⣿⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠚⠉⡟⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠈⡇⠀⢿⡄⠀⠈⠉⠛⢶⠲⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠒⣻⠁⠀⠀⠀⣰⠇⢸⡀⢧⣄⡀⠀⠀⠀⣠⡶⠞⠋⠀⠀⣷⠀⠘⣷⣄⠀⠀⠀⠈⠦⠀⠀⠀⠀⠉⠉⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠘⠃⠀⠀⢀⣠⣿⢀⣾⣇⠀⠀⢹⠀⠀⠀⡟⠀⠀⠀⢀⣼⣿⣄⣼⠁⠉⠳⠶⣶⡶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠘⡿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢶⡟⠁⠀⣀⡤⠴⠚⠛⣻⠿⠚⠉⠀⢹⣾⠙⢿⣦⡀⢸⠀⠀⢀⡇⠀⢀⣴⣿⠟⠀⢻⠁⠀⠀⠀⠀⠈⢿⡀⠀⠀⠙⣷⣀⠀⠀⠀⠀⢻⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢃⡞⠀⣀⣼⠋⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⡿⠀⠈⠻⣷⣜⣧⠀⡾⣡⣶⡿⠛⠁⢀⣴⡏⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠘⣏⠛⠲⠦⢤⣍⣀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢸⡷⠚⣽⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢿⣿⣿⣿⠟⠉⠀⠀⣠⠎⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡀⠀⠀⠀⠙⣿⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡟⠁⢰⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⢀⠜⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠉⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠃⠀⢸⡇⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢈⣿⡟⠀⠀⠐⠁⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣀⣼⠇⠀⠀⠀⠀⣿⠀⠘⣇⠀⠀ ⠀⠀⠀⠀⢠⠏⣿⠀⠀⠘⡟⠛⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣠⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⢻⡆⠀ ⠀⠀⠀⣰⠟⢰⡏⠀⠀⢠⣧⡤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢻⠉⣷⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⠀ ⠀⠀⣠⡏⠀⣼⠇⠀⠀⣏⠈⠳⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣿⣿⡇⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠒⠲⡏⠀⠀⠀⠀⠀⠉⣷⠀⠀⠘⣇ ⠀⢠⡟⠀⢀⡏⠀⠀⠀⣻⣏⣍⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣷⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣇⠀⠀⠀⣀⣀⣀⢸⡀⠀⠀⢹ ⠀⣼⠀⠀⣼⡇⠀⠀⠀⣽⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢰⣿⣿⣿⣿⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣹⣿⣹⣻⢿⡈⣿⡇⡰⠇ ⣸⠇⠀⠀⣿⠀⠀⠀⢠⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠈⣿⡀⠀⠀⢉⢉⠉⠀⢻⡄⠀⠀

⠀⠀⡶⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢲⡀⠀ ⣰⠛⠃⠀⢠⣏⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⣸⡇⠀⠈⠙⣧ ⠸⣦⣤⣄⠀⠙⢷⣤⣶⠟⠛⢉⣁⣠⣤⣤⣤⣀⣉⠙⠻⢷⣤⡾⠋⢀⣠⣤⣴⠟ ⠀⠀⠀⠈⠳⣤⡾⠋⣀⣴⣿⣿⠿⠿⠟⠛⠿⠿⣿⣿⣶⣄⠙⢿⣦⠟⠁⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⢀⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⣾⡏⢠⣿⣿⡯⠤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠤⠤⠽⣿⣿⡆⠹⣷⡀⠀⠀ ⠀⠀⢸⣟⣠⡿⠿⠟⠒⣒⣒⣈⣉⣉⣉⣉⣉⣉⣉⣁⣒⣒⡛⠻⠿⢤⣹⣇⠀⠀ ⠀⠀⣾⡭⢤⣤⣠⡞⠉⠉⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠈⢹⣦⣤⡤⠴⣿⠀⠀ ⠀⠀⣿⡇⢸⣿⣿⣇⠀⣼⣿⣿⣿⣷⠀⠀⣼⣿⣿⣿⣷⠀⢸⣿⣿⡇⠀⣿⠀⠀ ⠀⠀⢻⡇⠸⣿⣿⣿⡄⢿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⡿⢀⣿⣿⣿⡇⢸⣿⠀⠀ ⠀⠀⠸⣿⡀⢿⣿⣿⣿⣆⠉⠛⠋⠁⢴⣶⠀⠉⠛⠉⣠⣿⣿⣿⡿⠀⣾⠇⠀⠀ ⠀⠀⠀⢻⣷⡈⢻⣿⣿⣿⣿⣶⣤⣀⣈⣁⣀⡤⣴⣿⣿⣿⣿⡿⠁⣼⠟⠀⠀⠀ ⠀⠀⠀⢀⣽⣷⣄⠙⢿⣿⣿⡟⢲⠧⡦⠼⠤⢷⢺⣿⣿⡿⠋⣠⣾⢿⣄⠀⠀⠀ ⢰⠟⠛⠟⠁⣨⡿⢷⣤⣈⠙⢿⡙⠒⠓⠒⠓⠚⣹⠛⢉⣠⣾⠿⣧⡀⠙⠋⠙⣆ ⠹⣄⡀⠀⠐⡏⠀⠀⠉⠛⠿⣶⣿⣦⣤⣤⣤⣶⣷⡾⠟⠋⠀⠀⢸⡇⠀⢠⣤⠟ ⠀⠀⠳⢤⠼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠷⢤⠾⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠿⠛⠛⠛⠛⠛⠛⠿⠷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀⠀⢀⣶⠶⣦⣀⣀⠀⠀⢠⠶⣦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⠀⣴⠖⠒⡄⠀⠀⢠⠖⠒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⠁⠀⢸⡇⠙⡇⠀⢸⡄⠘⣟⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⣀⠤⣄⠀⠀⠙⠲⠞⠁⠀⠀⠈⠛⠒⠛⠀⠀⣤⠖⠦⣄⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⡇⠀⠘⣿⠀⢹⢿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠁⠀⠀⠀⠸⣅⣠⠎⠀⢀⣀⡤⠶⠶⠶⠶⠶⠦⣄⣀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⣧⠀⠀⣿⠀⢸⡌⡟⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢀⣄⡀⠀⠀⢀⣠⠞⠋⠁⢀⣠⣤⠤⠤⠤⣤⣀⠉⠛⢦⡀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡀⠀⠀⣷⠀⢻⡀⢀⡿⠀⠀⡇⡇⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⣄⣾⠏⠀⠀⠀⢰⡋⢀⡇⠀⣰⠟⠁⢀⣴⡞⠉⠁⠀⠀⣠⠖⠲⣌⠛⢦⡀⠹⣆⠀⢰⠉⠉⡆⠀⠀⠘⣧⠀⠀⢸⡀⠘⣧⣼⠁⠀⢸⠀⡇⡇ ⠀⠀⠀⠀⠀⣠⣠⡀⢰⡟⣿⡀⠈⢻⡏⠀⠀⠀⠀⠈⠛⠉⠀⣰⠃⠀⣰⢋⡟⠑⠲⢤⣄⡼⠃⠀⣠⠞⠁⠀⠹⡄⠘⣆⠈⠓⠚⠁⠀⠀⠀⠻⣆⠀⠈⢷⡀⠸⡇⠀⢀⠃⢸⢡⡇ ⠀⠀⠀⠀⣸⠛⢻⣇⠸⣧⢸⣇⠀⠀⢿⡆⠀⠀⠀⢀⣀⡀⢀⡏⠀⢠⡗⠻⢤⣄⡀⠀⠀⠀⠀⣾⣅⡀⠀⠀⠀⣧⠀⢿⠀⠀⣀⣀⠀⠀⠀⠀⠻⣆⠀⠈⠳⡄⠀⠀⠀⢠⠃⣾⠁ ⠀⠀⠀⢰⣿⠀⠀⢿⡆⢿⡆⢻⡄⠀⠘⣧⠀⠀⠀⡟⠀⣿⠸⡇⠀⢸⠀⠀⠀⢀⡟⠁⠀⣤⣄⡀⠀⠉⢳⠦⠀⣸⠀⣸⠀⢸⡁⢈⡇⠀⠀⠀⠀⢹⣇⠀⠀⠁⠀⠀⠀⢀⡾⠋⠀ ⠀⠀⠀⢸⣿⣆⠀⠘⣿⠈⣷⡘⣧⠀⠀⢹⡇⠀⠀⠙⠛⠋⠀⢳⠀⠈⡇⠀⣰⠋⠀⢠⠞⣁⣠⣽⣶⣴⣋⣀⢀⡏⠀⡿⠀⠈⠙⠉⠀⠀⢀⣤⡴⠋⢹⡀⠀⠀⣀⣤⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⣿⡻⡄⠀⠸⣷⣻⡇⢹⠀⠀⢸⡇⠀⠀⠀⣀⡤⣄⠘⣦⠀⠹⣄⠀⣹⣷⠟⠋⠉⠀⠀⠀⠀⠀⠉⠙⠛⠺⠧⣄⡀⠀⠀⠀⠀⢘⣇⠀⠀⠈⢷⣴⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⡹⣄⠀⠉⠿⡇⢸⠀⠀⢸⡇⠀⠀⠀⠻⣄⢘⡇⠈⢦⡀⢨⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢰⡋⠉⠛⢦⣤⠼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣜⢧⡀⠀⠃⢸⠀⠀⠸⣧⠀⠀⠀⣤⠈⢉⠀⠀⢀⣽⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢻⡙⠛⠛⠛⢺⣧⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣟⣦⠉⠀⠀⠸⠀⠀⠀⠹⢷⣄⣠⡇⠀⣸⠁⣠⡟⠁⠀⠀⠀⠀⢀⣠⣶⠶⠟⠛⠋⠉⠛⠛⢶⣦⣄⣀⡀⠀⠀⣧⢀⠀⢿⡤⢤⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠶⡇⠀⣿⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⢏⣵⣿⣿⣿⠉⠙⣿⠸⡆⠈⣇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠳⢶⣤⣴⠏⣀⣴⡇⠀⢹⡀⠀⢀⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣇⠻⢿⣿⣿⠀⠀⢻⠀⢻⣼⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠞⠉⠀⣷⠀⢀⣷⠶⠛⣯⣿⣿⣿⣿⡇⠀⣴⠞⠉⣹⠀⠀⠈⠙⠚⠋⠁⠀⠀⢸⡇⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⠶⠶⣾⢹⣆⢸⣿⡆⠀⠙⠻⢿⠿⠟⠀⠀⠈⠙⢺⡋⠀⣀⡴⠒⠀⠀⠀⠀⣰⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣿⢿⣄⠀⠀⠀⠀⠀⠓⠦⠤⣶⢿⣛⣻⢟⠆⠀⠀⣀⣤⡾⠋⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⢿⠳⢦⣄⣀⠀⠀⠀⠰⠯⣛⣚⡫⠟⢀⣤⣾⢿⡥⢤⣀⠘⣇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢷⠀⠀⠉⠙⣻⡓⠶⣦⣤⣼⡷⠿⣏⢩⣿⣾⣇⠀⠈⣷⢻⡮⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⣠⣾⣻⠋⢹⠉⠁⢰⠃⠀⣿⡿⣄⠙⢮⡉⢿⡋⠈⢷⡙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣧⠞⣹⢁⡇⠀⢸⠀⠀⢸⠀⠀⡇⠙⢽⣦⠈⢣⠈⢳⡄⠈⢻⣮⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢾⣇⣴⠇⣼⠀⠀⢸⠀⠀⢸⠀⠀⢧⠀⠘⡟⢷⡀⢳⡀⠹⣆⠀⢿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣶⠞⣿⢹⣧⡏⢀⠏⠀⠀⢸⠀⠀⢸⠀⠀⢸⡆⠀⣿⠀⢳⠀⢷⠀⢸⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⢹⠀⠀⣸⢻⣼⢹⠃⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢧⠀⠸⡄⠀⣧⠈⣧⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⡤⠤⢾⢀⣰⠇⠀⠀⢿⣄⣸⣀⣀⠀⠸⡄⠀⠈⣇⢀⣀⣸⣄⣀⣷⢤⡾⠀⠈⠈⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣫⠵⠚⠉⠙⠓⠋⠉⠁⠀⠀⠀⠀⢷⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣇⡠⠚⠉⢿⢈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⣻⡵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⠳⣤⣀⢘⣮⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡴⣶⣚⣿⠿⠿⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡌⠉⠑⢲⡖⠶⢤⡀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣾⠽⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡖⣿⠁⠀⠀⠙⣆⣀⣀⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⢧⠀⠀⠀⠈⢹⡧⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣍⡁⠀⠈⢳⠀⠀⠀⢸⣀⣀⣠⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠋⠀⠀⠙⡄⣀⣨⠇⠀⢠⡎⠀⢸⠁⠀⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⠉⠉⠁⠀⠀⠀⠈⡙⠒⢛⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣦⣴⣾⡇⠀⣰⠋⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⣿⣿⣿⣷⣴⠃⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢻⣿⣿⣿⠏⠀⠀⣠⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠸ ⣾⣿⣿⡿⠀⠀⣴⣿⠁⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⠴⠾⠿⣟⠛⠲⠿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣀⣤⣿⣧⣀⣤⡇⠀⠀⠁⠀⠀ ⣿⣿⣿⡇⠀⠐⣾⡏⠀⢠⡟⣷⡀⠀⠀⠀⠀⢀⣴⣯⣁⠀⠀⠀⠀⠈⢣⡄⠀⠀⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠻⡄⠀⠉⠙⣿⣦⡀⠀⠀⠀ ⣿⣿⣿⠀⠀⢾⣿⠀⠀⠸⠿⠟⠁⠀⠀⠀⣠⠏⠀⠀⠘⠳⣄⠀⠀⠀⠀⠱⠀⠀⠈⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣤⡄⠀⠀⠀⠙⠆⠀⠀⠘⠀⠻⣆⠀⠀ ⣿⣿⡏⠀⠴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠘⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀ ⣿⣿⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣷⠀⠀⢀⣷⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⡇⠀⢸⡿⠀⠀⠀⠀⠀⠀⢠⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⠁⠀⣼⡟⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⠁⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡖⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⣷⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⠀⠀⠀⣿ ⣿⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠟⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠛⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⣸⣿ ⣿⡇⠀⢠⣿⣀⣠⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠴⠿⠿ ⣿⣇⣠⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠲⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⢲⡶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀ ⢰⠀⠀⠀⠀⠀⣼⣟⠁⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡏⢹⡗⠀⠀⢠⡶⡶⠖⠒⠒⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⢉⣽⠟⢻⣧ ⠘⠀⠀⠀⠀⢠⡿⠻⣷⣄⠀⠀⠀⠀⠀⠙⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠃⠀⠀⣸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣿ ⢂⡀⠀⠀⠀⢼⣷⠄⠀⠙⠳⣤⡄⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⢠⠏⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⢀⡴⠋⠀ ⠷⠃⠀⠀⠀⠘⢿⢷⣄⠀⠀⠀⠉⠛⢦⣤⡀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⠸⣦⣤⡴⠋⠀⠀⠀⠀⢀⣤⠖⠛⠁⠀⠀⣠⡴⠋⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠈⠛⠷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⠤⠤⣄⣀⣀⣀⣠⡇⠀⠀⢣⡀⠀⠀⠀⢀⣀⣠⡤⠴⠛⠉⠀⠀⢀⣠⡴⠟⠋⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⣀⠀⠀⠀⠀⠉⠙⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠁⠀⠀⠸⡟⠛⠛⠋⠉⠉⠁⠀⠀⣀⣀⣴⠶⠋⠉⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠈⠉⠓⠶⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⠀⠀⢀⣀⣠⣴⡶⠾⠛⠉⠁⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀ ⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠶⠿⢿⡆⠀⠀⣠⣿⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀⣤⠶⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣶⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⣾⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠤⠤⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⢀⣴⣻⣿⣯⠟⠋⠉⠙⠛⠻⢮⣙⢿⡿⣄⠈⠻⣽⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠿⠿⣒⣛⡯⠵⢚⣧⢖⣤⢆⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠏⠀⠀⠀⣠⠴⢋⡼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⢮⢷⡀⠈⠛⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼ ⣿⣿⣿⣿⣯⣭⣴⣶⣒⡩⢵⣞⡩⢞⡩⢶⡿⢟⣡⠀⠀⢀⣸⠀⡴⠃⠀⠀⠀⠰⠋⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⡤⢤⣀⡤⣀⠴⣫⢶⣿⢞ ⣿⣿⣿⠭⢽⣿⣿⣿⣷⣾⣿⣷⣾⣽⣞⣯⡖⢋⠠⠆⠀⣰⣫⣾⡁⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⣛⣯⢷⣛⣿⣫⣷⣫⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⠤⠘⠙⡱⠄⠂⠉⠀⠀⠀⠀⠉⠐⠰⠰⠲⢠⢤⣀⠀ ⠃⡜⡀⡀⡇⠁⠄⠄⠀⢊⠑⠐⡉⠄⠀⡂⠀⡀⡘⡀⡀⡇ ⠐⢄⣀⣘⣦⢾⠀⠌⣀⠎⠕⠪⣱⡀⠀⠘⣿⣬⣀⣠⠔⠀ ⠀⠀⠀⠈⢶⠖⠋⢁⠀⠤⠡⡤⠀⣀⣑⠸⢿⠅⠀⠀⠀⠀ ⠀⠀⠀⠰⢁⠄⢨⠔⡀⠁⠀⠈⠁⠂⢌⠢⡐⠄⠀⠀⠀⠀ ⠀⠀⠀⠰⡂⠌⠃⣴⣾⡄⣀⠀⣿⣶⣌⠀⣵⡸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⠭⢌⡉⠂⣹⠔⠈⣉⣴⡦⠘⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣯⡿⠻⡹⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣯⡧⠬⠮⠥⠤⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠪⠄⠘⣷⣖⣿⣛⣁⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣍⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠻⣿⣿⡄⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡟⠛⠋⠁⠀⠀⠀⠀ ⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠈⢿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣷⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⣻⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠻⣿⣿⡇⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⣿⣟⢿⣿⣿⣻⣿⣿⣿⡿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷ ⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡂ ⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⢔⣊⠤⢻⡟⠿⢄⣘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⡏ ⡻⣿⣿⣿⣿⣿⡇⢻⣿⡇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢻⠝⠉⠀⠀⢀⣥⣄⠀⠈⠹⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛ ⣿⣿⣿⣿⣿⣿⡇⠘⣿⡇⠀⠀⠀⠻⠗⠀⠀⠀⠀⠀⠐⠶⠋⠰⠁⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦ ⣿⣿⣿⣿⣿⣿⡇⠉⠙⣯⢉⠽⠗⠛⠻⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹⡅⠀⠀⢴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡁⠀⠁⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣧⡀⠈⠀⠀⠀⠈⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠐⠒⠒⢹⡤⠔⠃⠀⠀⠘⠁⣿⣿⡿⠛⣉⠥⣌⢻⠁⠀ ⣿⣿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡴⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⢶⠒⠉⠁⢙⣄⠀⠀⠀⠀⠀⣼⠏⢠⠊⠀⠀⢸⠀⠀⠀ ⠋⠀⠀⢿⠀⠹⣿⣿⣷⡀⠀⠉⠓⠒⠊⠁⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⢰⡏⢠⡯⠤⡀⠀⢣⣶⠀⠀ ⠀⠀⠀⠈⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠒⣀⣀⡀⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡈⠀⠀⡘⠀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢟⢆⣿⣧⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⢀⣀⣀⣀⣀⣀⣉⣒⣄⠀⠀⠀⠀⠀⠀⡰⠖⠊⠁⣀⠜⢁⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠪⡀⢿⣧⠀⠀⠀⠀⠀⢺⡤⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠝⠀⠀⠀⠀⣠⠜⠓⠒⠛⢉⡠⠔⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣿⢳⡀⠀⠀⠢⡀⠉⠒⠢⠤⠤⠄⠀⠀⠠⠤⠖⠊⠁⠀⠀⠀⣠⣾⣿⠓⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠶⣤⡄⠀⠀⠀⠀⠀⠒⠒⠒⠐⠒⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⡀⠀⠀⠀⠀⠀⣀⣤⡶⠿⢿⣻⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠳⢶⣞⡿⠋⠁⠁⠀⣿⡿⠋⡹⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠁⠀⠀⠀⠈⢹⠃⡴⠁⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⣶⢤⣄⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠠⡀⠀⠀⢠⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠹⠤⠔⢋⣰⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢒⣒⢲⡦⠀⢘⠀⡠⠊⠉⣩⠗⠈⠉⠉⢀⣀⡀⠀⠀⠀⡜⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠁⣸⡀⠀⠀⠘⠀⢇⠀⠀⢧⠀⠀⡠⢊⢠⣤⠞⠇⠀⠀⡆⣧⠀⠀⠀⠀⠀⢀⠀⠠⠀⠤⢖⠀⠀⠁⠀⠒⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢈⠓⡲⠊⠁⡄⠈⠉⠒⠚⠉⠉⢰⢁⣸⣀⣀⣀⠠⠖⠀⡱⠑⣀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⠀⢠⠔⠒⠂⢄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡆⠀⠀⢀⠌⠈⠉⠀⠀⢰⢇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡄⠀⠀⡰⠃⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣠⢤⣱⣇⣤⣔⣲⣸⣏⣄⣀⢈⡦⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠙⠠⣶⢁⡶⡄⠘⡄⠀⢸⠀⠉⠉⠈⠝⠀⠀⠀⢀⡀⠤⢪⠃⠀⣼⣿⣟⡳⣏⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⣠⠖⢲⠋⠀⠈⡇⠀⠀⠀⠀⠂⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡴⣋⣶⠥⠚⢉⡁⠄⠀⠀⠉⠉⠉⠛⠶⢦⣄⡗⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⢸⡰⢼⣻⠃⢀⠛⣄⠸⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣴⡿⢉⡀⠱⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⣁⣀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣏⣶⠟⠁⢠⠶⠷⠶⠶⠶⠶⠶⠶⢴⣤⣄⣀⠈⠛⢦⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⡰⠃⠀⡀⠑⠚⠁⠀⢸⠀⣠⠟⠉⢉⠩⣉⣙⣲⣦⣤⣀⡀⢧⠀⠀⢿⡼⣿⣾⠀⠛⠦⢏⠣⠎⠁⠐⠂⠒⠈⠲⡇⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⡵⠃⠀⡰⣁⣀⣄⣠⣀⣄⣠⣀⣄⣀⣀⣀⣉⡁⠀⠀⠱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠟⠒⠐⠒⠒⣺⠛⢀⣠⣾⠵⠒⠒⠒⠒⠒⠲⣦⣿⣿⡦⠤⠠⠝⢛⡩⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠈⡝⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⡰⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡄⠀⠀⠘⢆⠀⣠⠞⠁⠾⠋⣩⣤⠛⢶⡶⣶⠶⡶⣶⣾⣿⠿⢷⣀⠤⠔⠒⠁⠀⢀⡤⠊⢀⠇⠀⠀⠀⠀⠀⢠⠊⢀⡴⠒⠒⣄⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡇⠰⠶⠯⠾⠵⠛⠾⠙⠛⠛⠛⠟⠿⠭⠼⠑⠚⠐⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠢⡀⠀⠘⡴⠁⠀⠀⣠⣿⡿⠛⠆⠈⠃⢉⣙⣻⣉⣃⣀⣤⠘⢷⣤⣀⡀⠀⡴⣃⠄⠊⠁⠀⠀⠀⠀⠀⢀⠇⢠⡏⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡇⢀⡤⣠⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⢀⣴⠊⠉⠆⠀⣀⣀⠤⠤⠘⠒⠒⠛⠂⠉⣁⣤⢶⣿⡿⠋⢀⡠⠔⠊⠉⠉⠉⠉⠉⠙⠛⡇⠀⢸⣽⣷⠉⠉⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠓⠤⡀⠀⡟⠀⠀⠠⠚⠉⠀⠀⠀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢈⣀⣁⣀⣠⡠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠝⠈⠓⠒⠉⠀⠀⢸⠉⠀⠀⠀⠀⣀⣀⣠⢤⠴⣶⣯⣷⣾⠿⠋⣠⠖⠁⢀⣠⣴⣶⣿⣿⣷⣶⣦⣤⠃⠀⣸⡿⡟⢀⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⣠⠞⠀⠀⠀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡟⠁⠂⠁⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠙⠒⢲⡞⣍⣳⠬⢶⠻⡏⡟⣾⣷⢧⣤⣴⠃⢀⣴⣿⣿⣿⠿⣟⡿⣿⣿⣿⡟⠀⢀⡯⠊⠀⠘⢦⠰⠀⢀⠤⠀⠂⠤⣀⠀⠀⠀⢀⣨⠔⠊⠁⠀⠀⠀⠊⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡴⢦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⢰⣄⠀⠿⡀⠀⠀⠀⠀⢀⡏⠁⢀⠴⠚⠈⢷⣾⢿⣼⡄⠙⠧⣀⣾⣿⣿⣿⣭⢟⢫⡙⢭⣹⠟⠀⢀⡾⠒⠉⠉⠉⠀⣀⠆⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠋⠀⡠⠔⠀⠈⠀⠀⠀⠁⠢⡀⢀⣠⡀⠀⢀⠔⠈⣁⠱⠄⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡆⠀⠀⠀⠀⠰⣌⡣⣽⡀⢳⡀⢀⣴⡾⠟⠁⠀⠘⣗⣒⣊⠥⣀⠸⣿⣿⡦⣀⠈⠙⠻⠿⢯⣔⣊⣦⡽⠖⠋⠀⣠⣾⠁⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⣀⠠⠠⠤⠀⠠⠀⠀⠐⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠎⠀⠀⠀⣠⡴⢢⡀⠀⠀⢳⠎⡘⢀⡴⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⡿⡆⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠾⠿⠳⠶⠖⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢨⣋⠈⢷⡘⡏⠁⠙⡆⠀⠀⠀⢠⠚⠀⠀⠀⠈⠣⡘⠛⢯⠭⠵⠢⢄⣀⡀⠀⠀⢀⣀⣠⢴⣺⡝⠱⠀⠀⠀⢀⠌⠀⠀⢀⡴⠚⠉⠉⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⢠⠏⡆⢠⠇⠀⠀⣸⠀⠙⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⢧⠀⠀⠀⢳⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠛⠉⠉⣠⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠒⠊⠁⠙⢦⢹⠸⣌⠳⣘⠶⠃⠀⠀⣇⠀⣀⡎⠀⠀⢪⡏⠀⠀⣆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠁⣏⠀⠛⠋⣀⡤⠞⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⣿⠀⠀⠀⢺⠛⠛⠛⠛⠛⠛⠻⠟⠿⠿⠿⠿⠿⠭⠃⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⡜⠁⠀⠀⠀⠀⣀⠤⠐⠈⠉⠉⠁⠢⡤⡀⠀⠀⠀⠀⠀⡯⠷⣌⡷⠋⠀⠀⠀⠀⠘⢯⢼⠁⠀⠠⡏⢳⣄⠀⣿⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠘⢲⣒⠉⠁⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢀⡠⢚⣵⠋⠀⢻⣿⠀⠀⠀⢸⣦⣴⣦⣶⣶⣶⣶⣶⣦⣶⣤⣦⣤⣀⣀⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⠒⡈⢁⠀⠤⠠⠤⣤⠤⣀⠀⢁⠀⠱⡀⣀⠠⣤⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠾⡀⠀⠀⣷⢄⢿⡂⣹⡇⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⠎⠥⠜⠀⠀⠀⠀⣀⡤⠖⠋⣀⠠⠄⠒⠈⠁⠀⠘⠁⠀⠀⢸⣿⠀⠀⠀⡎⠀⢀⡀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⣧⠘⡀⠀⢣⡏⣸⠀⣀⣀⣀⡀⠀⠀⠀⣼⡟⠋⠀⠀⣷⡀⠀⠹⡌⠳⣷⣸⡏⢆⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣀⠮⠤⢄⡠⢤⠤⣶⡯⠗⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢸⣾⠀⠀⠀⡗⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠈⠓⠾⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢠⡄⢸⣺⡄⠁⠀⡸⢧⣻⠍⠟⠛⠛⢿⠷⠀⡀⠉⣠⣆⣤⡾⣿⣷⣄⠀⠈⢦⡈⢎⠳⣄⠱⡀⠀⠀⠀⠀⠀⠱⡆⠒⠒⠀⠁⠀⣠⠤⡤⠊⢀⣄⠀⡠⣤⡾⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡏⠀⠀⢸⠀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠄⣀⠀⠀⠀⠀⠀⠠⣄⡀⠘⢆⠣⠀⢧⠀⣿⠃⠀⠀⣽⢬⢯⡳⣷⢦⣤⠤⣿⠷⣷⡞⠉⢿⣿⡿⠃⣿⣏⢶⣄⠀⠙⠮⣀⠈⠳⡌⢢⡀⠀⠀⣀⡀⠈⠣⡀⠀⢠⠋⠀⠀⠀⢀⠎⢸⢉⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⢸⢻⡄⢰⡇⠀⠀⢸⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠋⠙⠛⠀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⡴⠀⠂⠠⡀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢄⡀⠉⢮⠂⡌⣆⠱⡘⠀⣿⠀⠀⠘⠀⠀⢳⡑⡞⣾⢋⣶⣀⠀⢹⣷⠀⠀⢀⡄⣠⡿⢿⡈⠙⢵⡢⢄⣈⣉⡒⠼⢦⠈⢦⣼⢫⣿⠞⠉⢉⡦⡇⠀⠀⠀⢠⢻⣆⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡳⣄⠀⠘⡧⣇⢸⡇⠀⠀⢸⠰⠴⣶⣶⣶⣶⣖⣶⣲⣖⣶⣶⡶⠦⢰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠒⠂⢄⡀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠑⠢⢙⠢⢸⡄⢷⠀⡏⠠⠀⠀⠀⠀⠘⣷⡄⠘⣿⣯⢿⣧⠀⢻⡆⠀⠺⡼⢋⣷⢬⣣⠀⡀⣀⢉⡒⢦⣌⣉⣉⡳⣼⢰⠏⣏⡀⣠⡿⠀⠀⠀⠀⢀⣼⢼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣼⣷⣤⣷⡹⡼⡇⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⠖⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠑⠢⡇⢼⢸⠁⠁⠀⠀⠀⠀⠀⡏⢣⠀⣿⣿⠏⠃⠀⢸⣷⣄⣤⣤⡽⠶⠚⠉⠛⡣⠄⠀⢀⠉⠈⠁⠀⠉⠉⠉⠉⠉⠉⢓⠃⠀⠀⠀⣠⣞⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣉⣧⠀⠀⢸⠀⠉⠿⠷⠶⠶⠾⠶⠿⠿⠻⠯⠉⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⣄⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢱⣸⡏⠈⠀⠀⣄⢀⣠⣾⣴⣦⡄⣻⠏⢠⣠⣿⣿⣝⣹⡞⣡⣴⠶⠛⣛⣩⣴⠎⢉⣉⣀⠀⠀⣀⣠⣴⣋⣠⣤⣴⠾⡀⠀⠀⠀⠽⣌⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⢤⡒⠒⠪⠳⣼⠀⠀⠈⡄⠲⠤⣤⢤⣤⢤⡤⢤⠤⡤⠶⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⢠⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢨⠞⠀⠀⠀⠀⡅⠉⠟⢻⠟⢻⠀⢹⣶⣿⡿⣿⠿⢡⣾⣿⠟⣡⣾⠟⠋⣁⣤⢤⣃⣤⡴⠞⡻⠍⠁⠀⠀⢠⡞⡍⠀⠙⠀⠀⠀⡴⡸⣏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢖⡫⣵⠶⠛⠉⠁⠀⠀⣱⠀⠀⠀⠀⢆⠀⠀⢣⠀⠀⠈⠉⠈⠁⠉⠈⠀⠁⠀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠈⠀⡇⠀⠀⣼⣤⠏⠀⢸⣷⠏⠀⠃⠀⠘⢿⣯⣴⣿⢇⣴⣿⡟⣡⣾⡏⠭⠘⠦⣄⠤⠤⠤⣤⠏⠀⣇⠀⠀⠀⠀⠀⢫⢉⣽⡾⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⢦⢿⢋⡧⠀⢀⣤⠦⣤⠀⠸⢤⠀⠀⠀⠀⠠⡀⠈⡇⠠⠿⠽⠯⠟⠹⠋⢋⡩⠚⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠐⠊⠁⠀⠉⠈⠁⠉⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠠⠃⢀⠇⠰⠾⠛⣉⣀⣀⢸⡿⢀⣠⣴⣶⣶⣿⡟⢻⣿⣿⠟⣹⣴⡿⢻⣧⡀⠀⠀⠀⠉⠓⠳⢿⡀⠀⡽⠄⠀⠀⠀⠀⠘⡟⢸⡇⣧⠀⠀⠀⠀⠀⢀⡴⣋⢶⠝⠁⠈⢻⢠⠄⠉⠀⠀⠈⠀⢠⢾⠀⠀⠀⠀⠀⠀⠁⠲⠤⠠⠄⠄⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣿⡍⣦⠀⠀⠀⠐⠀⢀⠞⣠⡄⠀⠰⣁⣠⡏⢨⣗⣾⠟⠋⢀⣀⠀⡇⣨⠿⣶⣶⣿⠛⠀⠀⠻⣿⣶⣦⢤⡒⠲⣊⣿⠃⠀⢷⠀⠀⠀⠀⠀⠀⠘⢤⣻⡌⣧⡀⠀⢀⣠⢏⡲⡱⠃⠀⠀⠀⠈⣏⣰⠄⠰⠚⠓⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠂⠒⠊⠁⠀⠀⢀⣠⢶⠿⣊⠟⠀⢀⣴⠿⠋⠀⣸⣷⠈⢠⣾⡿⠛⠛⠹⠟⠉⠀⠀⠉⠁⣀⣀⣾⣄⠣⡙⢷⡌⢦⣟⡿⠀⠀⡾⡆⠀⠀⠀⠀⠀⠀⠀⡱⢿⡰⣍⡛⢭⢢⡓⡼⠁⠀⠀⠀⠀⠀⢸⣁⣤⠠⣤⣌⠁⠀⠈⡇⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⢀⠤⢚⣹⣾⡿⠋⠁⠀⢀⣈⡠⢞⡍⢀⠏⣷⠀⠻⠋⠀⠀⢀⣀⣤⣤⠶⠒⢋⣩⣡⠴⠚⠙⢷⠘⡈⣹⠏⡞⢱⡏⡆⡷⠙⣄⠀⠀⠀⠀⠀⠀⠓⢬⢻⡴⡹⢌⡖⣭⠃⠀⠀⠀⠀⠀⠀⣜⡥⠄⠀⠀⠸⡆⠀⢈⣇⠠⠐⠈⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢀⠞⣡⣴⣿⡿⠉⠀⠀⠀⢸⠁⢀⡽⠎⢀⣎⣤⣿⣀⣤⢶⣶⠿⠿⠛⠉⣀⠤⠚⠛⠛⠒⠒⠒⠒⠊⢣⡿⠃⡼⠁⠸⡇⢹⣿⢠⠸⡄⠀⠀⠀⠀⠀⠀⠀⢯⣽⣎⠵⡸⡼⠀⠀⠀⠀⠀⠀⢰⡫⠴⠂⣶⣶⢦⡀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠈⠀⠀⢀⡴⢃⣨⠾⢻⠋⠀⠀⠀⠀⢠⠾⠚⠉⣠⣴⣿⠟⠋⣡⠔⠋⢉⣀⣤⠶⠾⠭⠖⠒⠒⠛⠛⠚⠓⠒⠋⣩⠏⠀⣸⠃⠀⠀⠀⠈⢿⡼⡀⠱⣄⠀⠀⠀⠀⠀⠀⠘⢄⣈⣷⡵⠃⠀⠀⠀⢀⡀⠴⣅⣀⠤⠚⠀⢨⠿⢁⣠⠇⠀⠀⠀⠀⠀⠀⢀⡴⠇⠒⠀⠁⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⣀⠧⠄⣢⠤⠟⠒⠛⠒⠢⢦⣽⠶⢦⣄⣀⠀⣠⡴⠚⣩⠴⢃⠴⢋⡠⠔⢊⡵⣎⡵⠴⡒⠒⣎⢉⣉⡭⠝⠋⣑⣲⡞⢡⠃⡰⠃⣴⠃⠀⠀⠀⠈⢆⢣⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠙⠙⠨⠭⠮⢭⡹⣄⣠⠒⠉⢢⣄⣰⠊⠀⡏⡩⠄⠒⠈⠐⡄⠀⠔⠋⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⣠⠤⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣍⢻⡯⠴⣉⣁⡖⠡⠂⠁⢠⡴⠿⠭⠴⠦⢤⠟⠛⣯⣁⣰⠤⢟⡋⡡⠊⠰⠁⡴⢡⢪⠎⠀⠀⠀⠀⠀⠈⢦⣣⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡾⠁⠀⣠⠔⠋⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡾⢀⠾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠓⢤⡀⠈⠹⠶⣖⠧⠤⠴⠶⢶⠶⢺⠛⠛⢹⣀⣤⠞⢋⠜⠀⡴⢁⡴⡑⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠑⠜⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣸⠗⡏⠀⠀⠀⢀⠤⠤⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠉⠲⣤⣀⠀⠈⠁⠀⠀⣀⣠⡬⣷⠺⡋⡏⠀⠔⠁⢀⢞⡠⢋⠖⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠈⠱⡄⠐⠂⠒⠐⠂⠤⠚⠀⠀⠀⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠐⠤⡀⠀⠀⠀⠀⠀⠀⢀⠆⣇⠀⠀⠀⠀⣾⠉⠀⢰⡏⣀⣠⣈⣿⢧⣌⡑⠤⡠⠤⣀⡀⠀⠀⠀⠀⠀⠈⢷⣦⡀⠙⢯⣙⠛⠶⣤⡀⣑⠊⠁⠀⠀⢱⣹⡀⠀⣴⠿⠋⣰⡫⠊⠀⠀⠀⢶⡒⠒⠒⠶⠶⣖⣦⡬⠭⠥⠤⠶⠖⠶⠆⠀⠙⠳⠖⠛⣦⣤⡤⠖⣲⠖⠊⠁⠀⠀⠀⠀⠀⠀⡠⠐⠁⢠⡴⢢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⠤⣤⡀⠈⡄⠀⠀⠀⠀⠀⣼⠏⠉⢀⠔⢦⠚⠹⠃⠀⣸⣾⠟⠛⠉⠛⠚⠶⣝⣒⢒⢶⣯⡇⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⠀⠉⠳⣄⠀⠉⠒⠬⣑⡚⢶⠦⠟⡇⠈⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠐⠂⠒⠒⠲⠤⢤⣤⣤⠴⠶⠶⠒⠛⢋⡩⠤⠶⠍⣀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜⢡⠀⣷⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠖⠉⢀⡽⣿⣬⢓⣦⡙⠶⢷⡀⠀⠀⠀⠀⣧⢦⠀⡯⣆⠘⠇⠘⣇⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⢿⣞⢆⠀⠀⠀⠀⠀⠀⠀⢱⠙⠷⣝⠢⢌⡑⠢⠄⣀⠀⠀⠈⠉⢹⢸⠀⠐⠋⠀⢀⣤⡶⠖⠂⠀⠀⠀⠀⠐⢄⠀⡀⠀⠤⠄⠒⣀⡀⠀⠀⢀⣠⣤⡴⠛⠓⠒⠒⠒⠤⣀⠉⠢⠀⠀⠀⠀⠀⢰⠀⠀⠄⢰⣣⠎⠀⣿⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣸⣠⢞⣭⠖⠓⠉⠉⠈⠉⠉⠒⠼⣒⠤⢄⡠⡇⠀⠀⡇⠳⣄⡀⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢯⡻⣦⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⡏⠒⠤⣒⠬⣉⠀⠂⠀⢏⣆⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣠⠴⠖⢚⣉⡥⠔⢒⡮⠙⠊⠀⠉⠉⠉⠐⠒⠤⡀⠈⢧⢣⠈⣦⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⣰⠃⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠉⣠⢲⣹⠟⠁⠀⣩⡽⢋⣴⠦⣀⠀⠀⠈⠙⢷⣝⢵⢢⡐⠁⢀⠈⠙⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⣽⡗⢄⠀⠀⠀⠀⠀⢳⠀⠀⠀⣾⠀⠀⡄⠀⠉⠙⠛⠶⠤⠸⠸⡆⠀⠉⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠁⠀⠊⠉⢉⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣸⢠⠀⣿⢣⠀⠀⠀⠣⡀⠀⠀⣠⠜⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣴⣵⠚⠀⠀⢀⣼⠟⣡⡾⠁⣠⣾⠟⢂⡀⠀⠀⠹⣿⣏⣿⣀⡘⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣇⢨⡂⠀⠀⠀⠀⠀⡇⠀⢸⡭⠀⣰⡇⠀⢀⡆⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠀⠙⠒⣒⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢸⠀⢿⢘⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⡟⠁⠀⠀⣰⡿⢃⣾⠏⢀⣶⠟⠁⢀⣴⡕⢤⠀⠀⠈⢿⣿⡗⠛⠛⠷⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⢢⢻⣆⠉⢆⠀⠀⠀⠀⢸⠀⣦⠇⣰⡟⠀⢀⠎⡇⠀⠀⠀⠀⠀⡇⠱⡤⠤⠄⠒⠐⠂⣉⣉⠠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠏⢸⣸⠸⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢱⠁⠀⢠⣾⠟⣰⡿⠁⣰⡿⠃⠀⣰⡿⠋⣠⣾⠵⡄⠀⠀⠡⣱⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣎⢲⡏⡸⠀⠈⢢⠀⠀⠀⢸⢰⡟⢠⡹⠀⢀⠎⠀⡇⠀⠀⣀⠠⠒⣁⠤⠴⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠡⢂⠎⠀⣇⡏⢸⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⠀⣴⡿⢃⣾⠏⣠⡾⠋⠀⣠⣾⠟⢀⣾⠟⢁⡴⡾⢆⠀⠀⠘⣇⡀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⢣⣹⣰⠏⠀⡇⠀⠰⡏⠀⠀⠀⢸⡞⠁⡵⠁⡠⢻⠀⠸⡁⣒⡡⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⠊⡰⠋⠀⣸⡟⠀⡎⠀⡐⠁⠀⠀⠀⠀⠀⠀⣀⡤⠤⣄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡸⠋⣰⡟⢁⣴⠟⠁⣠⣾⠟⢁⣼⠟⠁⣠⣾⠟⠁⣠⣷⠀⠀⠨⣷⠀⠀⠀⠀⠀⠘⣟⢧⡀⠀⠀⠀⠀⢠⣾⠵⠊⠁⠀⠀⡴⡷⠀⠀⡇⠀⠀⠀⢻⣀⡾⢁⠜⡱⢋⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠠⠀⢀⠀⠀⠀⠀⠀⠀⠠⠔⠊⢀⡨⢤⠞⠁⠀⢰⡟⠀⡜⠀⡘⠀⠀⠈⠀⠀⠀⠀⡰⠁⠀⡴⠸⡄⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠘⠃⣴⡿⠁⢀⣶⠟⢁⣴⡿⠉⢠⢞⡵⠃⢠⢞⡽⠃⣳⡃⠀⠈⢿⡀⠀⠀⠀⠀⠘⣞⡧⠀⠀⠀⣴⡿⠁⢀⣀⣀⡤⠔⣇⠀⠀⡴⠃⠀⢀⠔⣻⠏⠀⢡⠾⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢄⣀⡀⠀⠀⠈⢁⡠⠤⠐⠂⣠⠴⠋⡰⠋⠀⠀⢠⠟⠀⣰⠃⠀⡅⠀⡄⠀⠀⠀⠀⢰⡇⠀⠸⣇⣰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠾⠋⢀⣴⡟⢁⣴⡿⠋⢀⡴⡻⠋⢀⡴⣫⠋⢀⣴⡟⠙⣄⠆⠈⢳⡄⠀⠀⠀⠀⢿⠇⠀⠀⢠⡟⣩⠟⠁⠀⡞⠀⠀⠈⠳⠾⠔⠈⠀⣨⣿⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢤⡀⠀⠉⠉⠉⠀⢀⣠⠴⠋⠁⣠⠞⠀⠀⠀⣰⠋⠀⣰⠋⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⣄⠐⠿⠃⣠⡿⠋⠀⣤⣯⠞⠁⡴⣫⠞⠁⣠⣾⠋⢀⣼⡿⠳⢄⠀⠹⣦⡀⠀⠀⠀⢰⣤⡀⢸⢡⡟⠀⠀⢸⡇⠀⠀⠀⡴⠃⠀⡠⢮⡥⡮⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠙⠒⠒⠒⢋⡡⠔⠀⣠⠜⠁⠀⠀⣠⡾⠁⠀⡰⠃⠀⠀⠈⡀⠀⠣⠀⠀⠀⠀⠀⢣⠈⠑⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⡀⠚⠁⠀⣠⣾⠟⠁⣠⢞⡽⠁⢀⣾⠟⠁⣠⢯⠞⠀⠀⣸⡿⡀⠈⠓⢦⡀⠀⠀⢿⣷⣼⠀⠻⢤⠀⠀⠙⠶⠖⠀⠈⣍⣉⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠒⠒⠒⠈⠁⠀⣠⠞⠁⠀⣀⠤⣺⠋⠀⠀⡴⠁⠀⠀⠀⠀⢣⠀⠀⢀⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢄⠈⠛⠁⣠⢞⡵⠋⢀⡴⣻⠋⢀⡼⡵⠋⠀⢀⣾⠟⠀⠈⣵⠦⣀⠈⠛⢯⣏⡹⢻⡄⠀⠰⣄⡀⠀⠀⣦⣀⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⢀⡠⠞⠃⠠⢔⣈⡠⠖⠉⡇⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣽⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠐⠓⠋⠀⣠⢏⡼⠁⣠⢏⠞⠁⠀⣰⡿⠃⠀⣠⡾⠋⠀⣠⣷⢄⡀⠉⢷⡩⡏⠓⠒⠚⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⢁⠀⢀⠎⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠑⠋⢀⡴⣣⠋⠀⣀⣾⠏⠀⢀⣾⠏⠀⢀⣴⡟⠁⠀⣩⣦⠀⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⢃⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠉⠞⠁⠀⣴⡟⠁⢀⣴⡿⠁⠀⣤⣿⠋⠀⣠⣾⠟⠀⢑⣄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠛⠉⠀⣠⣾⠋⠀⢀⣾⡟⠁⢀⣴⡟⠁⠀⣴⠟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠁⠀⠀⣰⡿⠋⠀⣠⢾⠏⠀⣠⣾⠋⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠉⠁⢀⡴⡷⠋⢀⣴⠟⠁⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⢄⣀⢠⣎⣉⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡆⢀⠀⠀⠀⢤⢾⣱⣜⣾⣧⣶⣶⣶⣿⣷⣷⣶⣦⣤⣄⡀⣼⣞⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡿⡏⡇⡄⢀⣼⣷⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣢⡀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡇⠀⠀⣤⠻⡽⣼⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣌⢷⣿⣿⡿⠟⢋⡡⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣈⡙⠶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⢦⣸⠛⠛⢁⡀⣀⣈⢀⣴⣾⣿⣿⣿⠏⣿⢿⣿⣿⣿⡏⠈⢻⣿⠿⣿⣶⣔⢿⣦⣠⣮⣽⠛⠀⠀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⣠⠞⢩⣴⣿⡿⡿⣯⣷⣿⣿⣿⣿⣿⠏⢠⡿⢸⣿⣿⡟⠀⠀⠀⢻⡆⠘⣿⣿⣷⣝⠺⣿⣦⠀⠀⠀⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⣨⠟⠁⠐⢷⡹⠋⣰⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⠃⢸⣿⡟⠀⠀⠀⠀⠸⡇⠀⠘⣿⣿⣿⣷⣄⡁⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⢀⣼⣿⣿⣿⣿⠏⢸⣿⠇⠀⠠⠏⠀⢸⠏⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⣿⣿⣏⠉⡉⡀⠀⠀⠀⠀⣰⡇ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠀⢸⡟⠀⠀⠀⠀⠘⡏⣀⣿⡒⡿⠀⠀⠀⣀⠀⠀⠈⣿⣿⣿⣧⣿⣿⡆⠀⠀⣠⠏⠀ ⠀⣼⠃⠀⢀⣶⣖⡄⠀⣾⣿⣿⣿⣿⣿⠃⠀⢸⣛⣲⣦⣤⣤⣤⣴⡟⠙⣷⣤⣤⠴⠾⠥⣤⡀⠀⣿⣿⡿⠿⣿⣿⠃⢀⡴⠁⠀⠀ ⢸⡇⠀⠀⣼⣸⣻⢀⢰⣿⣿⣿⣿⣿⣿⠀⠸⢿⣶⣶⣦⠶⠋⡼⠟⠀⠀⡏⠉⣟⠻⣿⠿⣋⠁⠀⣿⣿⣮⣨⡾⣣⡼⠋⠀⠀⠀⠀ ⢸⡇⠀⠀⣿⣿⢸⡻⣸⣿⡟⣭⢿⣿⡽⠄⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⢻⣲⡦⣉⡋⠙⠏⠀⢸⠋⣞⣹⠗⠋⠁⠀⠀⠀⠀⠀⠀ ⠘⣇⠀⠀⢿⣾⣯⣝⠮⢹⣇⠇⣷⡹⣧⠀⠀⠀⠀⢀⡠⠚⠀⠀⠈⠁⠀⠘⠉⠀⠀⠙⢦⠀⠀⢸⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣆⠈⡪⠽⣿⣽⠶⠚⠻⣮⣙⠳⢿⡄⠀⠀⠀⠋⠀⠀⢀⣠⠤⠤⠤⠤⢄⣀⠀⠀⠈⠇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢶⣍⢻⠒⢺⠾⠩⠽⡇⣈⣙⣶⣷⡀⠀⠀⢀⡤⠚⠉⢀⣤⢴⢶⣤⣄⠉⠙⠲⢤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠈⠻⣦⣀⡉⢀⡠⠞⠉⢠⠏⠘⡄⠻⡍⠲⢦⣤⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡶⣤⣤⣄⣀⣤⣥⣤⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠛⠿⢿⣿⣿⡿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠇⠀⠀⠀⠉⢻⣿⣿⣣⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣿⣿⣯⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠋⠙⣿⣷⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠦⢶⠶⠒⡒⠒⢶⠲⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⣁⣤⣶⠼⠶⠶⠖⠒⠾⠿⢶⣤⣀⣉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⠓⠷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡞⠋⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣤⡶⠃⠀⠀⠀⠀⠀⣀⣤⣾⣿⢿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⢔⢿⢭⡀⢠⠤⣠⣠⣴⣿⣿⠟⣹⠃⠘⣿⣿⣿⠹⣿⣿⣿⣶⣄⡤⢀⢄⠀⡀⠐⣞⡟⡎⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠎⠰⠃⠑⠱⡗⣴⠟⣫⣾⣿⣿⡿⠁⠀⢸⠀⠀⠈⢿⣿⡇⠈⢿⣿⣿⣿⣿⣮⣵⣳⣦⣺⣿⠗⠈⠢⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡞⢔⠅⣼⣿⣿⢯⡟⠁⠀⠀⠘⠂⠀⠀⠀⠹⣿⡀⣀⣻⣷⢻⣿⣿⡟⢛⢿⣧⠁⠀⠀⠀⠀⠘⢧⠀⠀⠀ ⠀⠀⠀⠀⢠⢏⣖⣀⣠⠀⢠⡀⠀⣼⣿⣿⠏⡾⠉⠉⠙⠒⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠙⡌⣿⣿⣿⣄⣣⢻⣎⣖⣤⡀⠀⠀⠘⡇⠀⠀ ⠀⠀⠀⢠⡏⣼⣿⣾⣿⠷⣿⢿⡿⠿⣿⡟⠀⠀⢀⣤⣄⡀⠀⠀⢲⡀⠀⠀⠀⢀⣴⣶⣦⡀⢸⣿⣿⠿⡟⢯⠿⣿⡟⣳⢀⠂⠀⣷⠀⠀ ⠀⠀⠀⢾⣿⣽⣿⣿⣿⣿⡷⠋⠀⠀⣿⡇⠀⣴⠏⠉⠉⠛⠀⠀⢸⡷⠀⠀⠀⢛⠀⠀⠈⢓⡀⠿⣿⠂⠀⠈⢿⣯⣿⣿⣸⣧⠄⣿⠀⠀ ⠀⠀⠀⢸⡟⣿⣿⣿⣧⣹⠄⠀⠀⠀⢹⣀⣤⣅⠄⠀⠀⠀⢀⣀⣈⣉⣁⣀⣀⣈⣉⣻⠉⠛⠿⣆⡗⠀⠀⠀⢸⡿⣹⣿⣿⣯⣀⡏⠀⠀ ⠀⠀⠀⠘⡇⣧⣿⣿⠻⣻⠀⠀⠀⠀⠉⣟⠉⣥⠴⡖⠚⠉⠉⠁⣀⣀⣀⣀⣀⠀⠈⠉⠹⠳⡆⢹⡓⡀⠀⠀⡼⢁⣽⣿⣿⡿⡿⠁⠀⠀ ⠀⠀⠀⠀⣿⣯⣿⣿⢮⡹⡇⠀⠀⠀⠀⢻⡄⢻⡀⢀⣠⣴⣾⡿⠿⡿⠿⠿⠿⣿⣿⣶⣤⣸⠃⡾⢨⣵⠾⢏⠓⢮⡛⣾⠟⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡓⢯⡳⠘⣇⠀⠀⠀⠀⢈⣷⠀⠻⣿⡿⠛⢉⣀⣀⣀⣀⣀⣀⣈⠉⢿⠟⠁⢰⡟⠉⠁⠀⠀⣿⠀⣿⡡⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⢜⢧⡀⠘⠐⣈⢭⣷⡀⠈⠛⢯⣉⡁⠀⠀⠀⠀⣀⣨⠝⠋⡞⠉⣻⠿⠀⠀⠀⣰⣿⡔⢻⠓⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⣖⣙⢦⣋⣽⣛⣼⣿⣶⣤⣄⣀⠉⠉⠉⠉⠉⢁⣀⣴⣿⣦⠀⠀⠀⣠⠤⣄⡘⠾⠧⡈⢳⠛⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠛⠛⠉⠛⠛⠛⢿⣉⣿⠙⠿⣿⡟⠻⣾⣿⣿⣿⣿⣿⣯⡷⡖⠊⠁⠀⠈⠉⢧⡒⣵⡾⢀⡸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠾⠶⠶⠲⠤⠀⠀⠀⠀⠀⠀⠈⠙⢤⡀⠉⠳⠤⣿⣟⡿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠠⠖⠳⠏⠛⢋⣽⢶⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⣬⠟⠙⠁⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⠀⣔⡆⠦⣦⢠⡖⠋⠁⠀⠀⡀⣠⣶⠟⠋⠀⠀⣠⢤⣶⡖⡃⢂⠀⠀⠀⢀⢄⢠⡇⠀⠀ ⠀⠀⠀⢻⠰⣄⢦⢤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠋⠀⠀⣴⡿⠉⠀⠉⣡⣴⣤⣴⣿⣿⣭⣓⣲⣮⣷⣚⡣⡴⢶⣼⣻⡇⠀⠀ ⠀⠀⠀⠘⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣄⡀⣉⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⠁⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠉⠛⠛⠛⠿⠿⣿⣿⣿⣾⣷⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⡅⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡾⠿⠿⠿⠿⢿⣿⡄ ⠀⢠⡿⠿⠋⠁⠀⠀⠘⣆⢸⡇⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⢻⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡞⠀⠀⠀⠀⠀⠀⠈⢱ ⢠⠏⠀⠀⠀⢀⠀⠀⠀⠸⣦⣷⣣⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣈⣥⡀⡀⠀⠀⠀⠀⠀⠈ ⣸⣴⣾⣿⣿⣿⣿⣷⣦⡀⣿⣿⣿⣿⠛⠉⠉⠉⠉⠉⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣿⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣛⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⡿⠿⠿⢿⣛⠛⠛⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠲⠦⣤⡀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢠⠤⢤⠀⠀⢠⠖⢤⠀⠀⠀⠀⠀⠀⠉⠳⢴⡏⠈⢿⠙⡆⠀⣏⠹⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⠤⡄⠀⠈⠒⠊⠀⠀⠈⠓⠉⠀⢠⡒⠲⡄⠀⠀⠀⢸⡇⠀⢸⠀⡇⠀⢻⠀⢿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠑⠒⢁⣠⠴⠚⠉⢉⣉⡙⠓⠢⣄⠀⠉⠊⠀⠀⠀⠀⠈⡇⠀⢸⠀⣷⠀⢸⠀⢸⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣾⠃⠀⠀⡔⢙⠆⢀⡴⠋⢀⡤⠒⠉⠉⢀⠭⢝⠲⣄⠑⣄⠀⠴⠒⡆⠀⠀⣇⠀⠸⡆⠸⣄⡏⠀⡘⢻⡇ ⠀⠀⠀⢀⣤⡄⢰⡿⣇⠈⢻⡇⠀⠀⠀⠙⠉⢀⡞⠀⣴⡿⠓⠲⠤⡴⠃⢀⠜⠁⠈⢧⠈⡆⠘⠒⠁⠀⠀⠸⣆⠀⠹⡄⠻⠀⠀⠁⢇⡇ ⠀⠀⠀⣾⠉⢿⡘⣇⢻⡀⠀⢿⠀⠀⢀⡖⡆⢸⠀⢰⠃⠉⠒⣤⠀⠀⠀⠛⠢⢄⡀⠘⡄⢹⠀⡔⠢⡀⠀⠀⠙⣆⠀⠙⠄⠀⠀⢀⡼⠁ ⠀⠀⠀⣿⡀⠘⣷⢻⡌⣧⠀⠘⡇⠀⠘⠦⠆⠸⡄⠘⡆⢀⡔⠁⣠⠎⣉⣢⣤⡞⠁⢸⠁⡜⠀⠓⠚⠁⠀⣀⡤⠻⡄⠀⠀⣀⣴⠞⠁⠀ ⠀⠀⠀⣿⣧⠀⠹⣯⣧⢸⠀⠀⡇⠀⠀⢀⡤⢄⠳⡀⠱⣄⣩⡶⠛⠉⠉⠉⠉⠉⠉⠉⠒⠧⢄⡀⠀⠀⢀⣇⡀⠀⢳⣴⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣷⡄⠈⢻⢸⠀⠀⣇⠀⠀⠘⠦⠼⠀⠙⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⢯⣀⣙⣶⣞⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣌⠂⠀⠸⠀⠀⠹⣦⣀⣼⠀⡰⠀⡴⠋⠁⠀⠀⠀⣠⣤⠤⠶⠶⠦⢤⣄⣀⠀⠀⠈⡆⠈⢷⣀⣀⡼⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⡀⠀⠀⢀⡿⠶⡇⢸⠁⠀⠀⢀⣴⠛⠉⠀⠀⠀⠀⠀⡜⣽⣿⣿⡏⠙⡇⢢⢘⣇⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢶⣿⡤⠺⡇⠈⣇⣀⣴⣿⣿⣿⡆⠀⢀⣀⣀⠀⠹⢼⣻⡿⠃⠀⢡⢸⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣭⣤⣴⢷⠀⣿⡁⠘⢿⣿⣿⠇⠀⠙⢤⡞⠀⢀⡤⠀⠀⠀⢠⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣿⣷⡀⠀⠀⠀⠐⠦⢤⣾⣿⣿⡿⠀⠀⣠⡴⠋⢹⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠓⠦⠤⣄⣀⣘⠛⢻⣟⣡⡴⣿⣿⠒⢦⣸⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣠⣼⡷⢿⠛⢛⠋⢹⣶⡉⠻⡒⢶⠏⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣧⠞⡟⡜⠀⠀⠀⠈⠀⢸⠙⢷⡄⠱⡈⢧⡀⢳⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡧⡾⢡⠃⠀⡇⠀⠀⠀⠘⡄⠘⡝⢆⠙⡄⢳⠀⠻⠾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡏⠙⢹⣯⣿⠇⢸⠀⠀⠇⠀⢀⠀⠀⢧⠀⢇⠀⢇⢡⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⡤⣇⣠⠇⠀⢸⣄⣼⣀⡀⢸⡀⠈⣆⣀⣘⣄⣸⣦⡾⠀⠉⣱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠉⠉⠉⠀⠀⠀⠀⢻⡀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢠⢧⡖⠉⢹⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣤⣶⠮⠭⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠤⢤⣤⣀⡀⠀⠀⠀⢠⠋⠀⠉⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⠴⡏⠀⠈⢣⣀⣀⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠆⠹⡄⠀⠀⢹⠇⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠓⢤⠀⢘⡄⠀⣸⠒⡶⠚⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⠉⠉⠀⠀⠓⠴⠣⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠶⢤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢻⡄⠘⢦⠀⢀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢇⠀⠈⣧⠈⢧⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠘⡆⠈⡇⠀⡉⠁⠈⢳⣄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢠⣴⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣤⣤⣧⣤⣽⣀⣧⠘⡇⠘⡟⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢸⠈⠉⠸⡇⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠥⠤⢤⣙⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠋⠀⠀⠀⢀⠀⢳⠀⠀⣹⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠀⠀⡀⠀⢀⣠⠆⠀⠀⠈⠉⠉⠑⠒⠦⠄⡶⠊⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⣶⠀⠸⡇⢀⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⣾⡟⠁⠀⣬⣉⣙⣳⣄⠀⠀⠀⢰⠃⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⢻⠀⢀⣽⣿⣿⣿⠿⠋⠉⣀⠤⠶⠖⠢⡤⠴⠖⠀⣀⣀⣀⣠⣴⣶⣿⣿⠏⠈⠥⠤⠤⢶⣀⣀⡤⣌⡉⠳⠀⣿⠀⠀⠀⠀⠀⠀⢹⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠈⢣⣾⣿⠟⠉⣀⣤⡤⢀⣠⢀⣤⠔⠒⠚⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⠋⠲⣤⡉⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡀⠀⠀⣀⡞⠋⢀⡤⠟⠋⣀⣠⣵⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢤⣧⠀⠀⠀⠀⠀⠀⡇⠀⢈⣻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⡴⠛⠉⠀⠐⠈⣀⣴⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠰⣜⢳⡀⠙⣇⡀⠀⠀⠀⣀⡇⢠⠈⣷⢧⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣧⡝⡆⢸⡟⢿⡶⠋⠁⡇⢸⣣⠏⡏⠀⠀⠀⠀⠀ ⠀⡴⠋⣠⣤⡴⢺⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢙⣿⣧⠻⣿⣿⣿⣿⣿⣿⣦⡈⠉⠉⠟⢷⠈⡇⠀⣿⣦⠀⢧⠈⠀⣸⠇⠀⠀⠀⠀⠀ ⠞⣡⠞⠁⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠒⠉⠙⢿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣦⣿⠁⢸⠀⢹⢠⢻⢿⡇⠸⡆⣠⠏⠀⠀⠀⠀⠀⠀ ⠚⠁⣤⣾⡿⣻⠏⢰⣿⣿⣿⣿⣿⣿⠀⠒⣿⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⣠⣤⣄⣸⣧⠀⢻⣿⢻⣿⣿⠿⣄⠉⠟⢀⡟⠀⣸⠀⣌⣾⣼⠤⣿⣅⡀⠀⠀⠀⠀⠀⠀ ⠀⣰⢫⠟⡵⠃⠀⣿⣿⣿⣿⣿⢿⣿⠀⠀⠛⠀⠀⠀⠈⠉⠂⠀⢦⡀⠀⠀⠀⠀⣴⣾⢿⠛⠹⣭⠿⠆⣈⣿⠈⣿⢹⠹⣾⡆⢠⠟⣀⡴⠷⠚⠉⠁⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀ ⣰⠏⠛⣈⡇⢀⣴⣿⣿⣿⣿⣏⠈⣿⠀⢀⣤⣤⣶⣶⣦⡄⠀⠀⠀⢧⠀⠀⠀⠀⠘⠡⠼⣷⡋⠙⣦⠞⣻⡛⠀⣿⢨⣏⠉⢷⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀ ⡾⢠⢰⢻⡇⠸⣿⡿⢹⡿⣿⣿⠀⠉⠨⠟⠁⠀⠀⠀⠈⠁⠀⠀⠀⢧⡀⡀⠀⠀⠀⠀⢀⣠⢶⠟⠉⠿⢹⡇⠀⣿⠞⢸⢧⣿⣧⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀ ⣇⡸⢨⢻⡅⢰⠿⠀⣿⣀⡹⣿⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣠⡤⠴⠶⠋⠉⠀⠈⠀⠀⠀⢸⡇⠀⣿⠴⢋⣾⢹⣿⠀⡇⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⡿⠀⠀ ⠈⢧⠸⠀⠁⢯⣀⠀⢻⡏⢽⡼⣇⠀⢸⣄⡞⠛⣽⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣻⠃⢠⡏⣴⣿⣿⣎⠇⢀⣇⣤⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀ ⠁⠸⣅⡀⠾⢷⣈⡉⠘⡇⢰⣻⢻⡀⠈⣯⠳⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠶⠖⠒⠒⠒⢾⠷⣾⡟⠀⣸⠋⡩⢟⡟⢯⣳⣾⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀ ⡒⠤⣌⡙⠲⢤⡴⢖⣂⡘⢦⡙⠧⢷⡀⠘⣶⣄⠐⢆⣠⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⢁⣴⣷⠆⠀⡼⢀⣼⠋⡿⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠛⠦⢤⣉⣻⠀⠀⠈⠓⠂⠀⠙⠲⠬⣷⡀⠙⢾⡶⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⣾⠃⠘⠓⡿⢀⠄⣽⡀⠃⠧⢸⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⣿ ⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠲⠖⠛⠲⠎⢹⣄⡈⠻⢦⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣼⡽⠞⢉⣴⣾⡽⠃⠀⠀⢰⠁⡞⠀⣸⣿⡶⢤⣬⠷⠶⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣤⣬⡙⠛⠚⠷⠶⠒⠛⠛⠋⣉⣡⣤⡶⣿⡿⠁⠀⡤⡄⢀⠁⣸⠁⣰⣿⣿⣇⠸⣿⢹⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡌⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠉⠙⠓⢒⠖⣶⢿⡟⠛⡻⡿⡿⣽⡟⢁⠀⡴⠙⠀⠆⢠⠃⣰⣿⣿⣿⣿⣷⣭⣼⣃⣀⣀⣠⡤⠾⠛⠁⠀⠀⠀⠁⣡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⢲⣯⢟⣿⣎⡽⡟⣴⡿⡵⠉⡴⠁⠀⡈⢠⡏⣴⣿⣿⣿⣿⣿⣿⡇⠸⣆⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣧⣉⠙⠓⠦⣤⣀⠉⠀⠘⠹⠽⣽⣹⠃⡸⢁⣠⡴⠚⠏⡼⣿⣿⣿⣿⣿⣿⣿⣷⣼⣄⣀⠃⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋⠻⣿⣧⠀⠀⠀⠈⠉⠓⠶⠆⠈⡙⠳⠶⠟⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⣷⣶⣶⣿⣿⣿⣿⣶⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣾⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⠙⣟⠶⣄⡀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣞⣃⣸⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣛⣛⣛⣋⠉⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠙⣿⡄⠈⠙⢯⡬⠳⢤⡄⠈⣧⠀⠐⠛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠉⠛⠋⠛⠛⠛⠋⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡻⠄⠀⠋⠛⠳⠄⠀⠀⡉⠁⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣤⣀⡀⠀⢀⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⣿⣿⣿⣿⣷⣾⣷⡄⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡿⠋⠀⢻⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⡇⠈⣿⡙⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠀⠀⠀⣀⠀⠀⠹⣿⡇⢀⡘⣧⠸⣿⣿⣿⣿⣿⣿⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠶⠛⠋⣽⣿⣿⢹⠧⠴⠒⠋⠉⠀⠀⠀⠈⣿⡈⠉⠉⠉⢻⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠸⠀⢀⣤⣤⣄⠀⢸⡆⠀⠀⢽⣶⣤⣤⣈⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠻⣄⠀⠀⠀⢠⣴⣿⠿⢿⣿⡇⠀⠘⣿⠟⠛⠉⠁⣿⠁⠀⠀⢼⣭⣍⣑⣿⣄⢸⣿⣿⣿⡈⠙⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠶⠶⠾⢿⠁⣀⡬⠿⠖⠒⠒⠂⠀⠀⢸⣿⣇⣶⣶⠄⣀⣀⣠⠤⠤⠴⠤⠤⠤⣄⣈⣁⣐⡳⢞⣿⣿⡿⠷⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⡈⢻⠛⡋⠉⣀⣀⣀⣀⣤⣤⣀⣈⣀⣩⣽⠃⣸⣿⣿⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣷⠈⣿⣿⣿⣿⡿⠿⠟⠿⠻⠻⠿⢿⣿⠏⣰⣿⠟⠁⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡈⠛⢧⡘⢿⣯⠤⠤⠤⠤⠖⠒⠒⢲⡾⢃⡰⠋⠀⠀⠀⠀⠤⠤⢤⣖⡋⠀⣹⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⢠⡶⣾⡭⠥⠼⠇⠀⠀⠙⠲⣬⣛⠦⠤⠤⠤⠴⠚⣫⣴⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣶⣲⣶⣾⢻⢿⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣽⣧⣤⣄⠀⠀⠀⢠⣾⣿⣿⡇⠀⠙⢷⣿⣼⣿⣿⢏⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠒⠛⢿⣿⣶⣶⢲⡦⡴⣯⡆⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢀⣄⣀⣈⣿⣿⢸⣿⠁⣹⣷⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠑⢿⢻⣿⣿⣿⣿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⣣⠞⢋⣀⣀⠉⠙⣿⢭⣽⣻⣿⡿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⡇⠀⠈⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⢟⣵⠞⠉⠀⠈⠙⠳⣽⣿⡿⢠⡟⡇⣿⣿⣿⣿⡟⠈⠙⢢⡀⠀⠀⠰⠛⠁⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠞⢁⣤⠾⠛⢻⣷⣾⣿⡏⢀⣼⡇⣏⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⣟⠉⣁⣤⡴⠾⣿⡿⣿⣷⠟⢸⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⣠⣮⠀⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡇⠈⣽⠋⢹⠁⣠⣬⡟⠛⣧⣶⣸⡇⢷⣿⣿⣿⣿⡓⢦⣀⣰⠋⢿⡼⢻⠀⣠⡴⠋⢹⣿⣿⣿⣿⣇⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠈⠛⢠⣼⣾⣯⣭⣥⣤⣭⣬⣽⣧⣾⣿⣿⣿⣿⡇⠀⠈⠉⠀⠀⠀⠘⠋⠉⠀⠀⣸⣿⣿⣿⣿⣿⡄⡞⠈⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⣧⠤⠴⠿⢿⠀⢀⣴⢦⡸⣦⣄⣠⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀ ⠀⠀⣿⠀⠀⠀⠸⡄⢸⣿⣟⢿⡿⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣬⣟⣹⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠘⡇⠀⠀⠀⣧⣿⣿⣿⢷⣿⡟⣿⣿⣿⣿⣿⣿⣿⠹⣯⠿⠋⠀⣀⣩⡟⠛⠂⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⡇⠀⠀⠀⠘⣯⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⢸⣒⠂⠀⠀⠀⡙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⢠⠏⠀ ⠀⠀⠀⢡⠀⠀⠀⠀⠘⣿⣝⣿⡚⢀⣿⣿⣿⣿⣿⣿⣿⡻⠀⠀⢀⣶⣸⡷⢦⡀⡟⠯⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠈⢉⠀⠀⠁⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠚⠉⠉⠉⠉⠉⠉⠓⠲⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⢀⡾⢱⡇⣀⡀⠀⣆⠀⠀⠀⠀⠀⠻⡀⢀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣞⡷⢃⡜⢁⣾⢃⡟⣇⣿⡻⡄⠘⣆⠀⠀⠀⠀⠀⢻⠀⢦⠀⠀⠀⠈⣎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢏⡟⠀⡜⢀⡞⡇⣸⠀⢻⠸⣷⠹⡀⠹⡄⠀⠘⡄⠀⠈⣇⠘⣆⠀⢀⠀⡹⡀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣫⡞⠀⢸⠃⡼⠁⡇⡟⠀⠈⣧⣿⢳⡳⡀⢿⠀⣠⣷⠀⣿⢿⠀⡇⢰⢸⠀⢻⠁⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠶⠛⠋⣹⢁⡤⡞⢰⡇⠠⣇⡇⠀⠀⠈⣿⣷⠿⣿⣸⣇⢸⣿⠀⣿⣿⢠⠃⢸⢸⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣧⣿⣿⣇⢸⠁⠀⢸⣷⢀⣴⡞⣩⣻⣄⣻⣿⣿⣸⣿⠀⣿⣏⣼⠀⣼⣾⠀⣼⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡿⡿⣿⣼⣄⡀⠈⣿⡉⠺⣿⠻⣯⣹⣿⣿⣿⣿⢻⢰⣿⣿⡿⣷⣿⡏⠀⡏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣧⣳⣻⣿⣷⢿⣀⠈⢷⡀⢿⣈⡿⣿⣿⡟⡿⢙⣿⣿⣿⠁⠛⠙⣻⠃⢰⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⢯⣿⣿⡼⣾⡦⠈⠁⠀⠈⠉⠉⠉⠀⠁⢸⣻⠏⣏⠇⠀⣠⢿⡄⡾⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠈⢙⣿⣻⡇⠀⠀⠀⠀⠀⢀⣀⢀⣴⠾⠛⠓⠛⠶⠾⣯⣆⣷⣷⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⠉⢀⣀⠴⠶⠚⣉⣠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⢮⣦⣀⣙⣦⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠈⠳⣄⠀⠲⠚⠋⠉⣿⢀⡴⢋⡭⣕⣶⣀⣀⣶⠀⠈⣦⠻⡷⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣠⣿⠏⢠⠏⣠⠶⠛⢿⣁⠟⠀⠀⠘⣆⠳⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣀⣏⠀⣿⠀⠀⡼⠉⠀⠀⠀⢀⣿⣦⠙⣆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠉⣷⢻⡀⠉⠳⠚⠁⣠⣖⣙⢷⢾⠸⣿⠀⠈⢳⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣳⣄⠀⢀⣾⠟⠿⠿⠋⠘⣆⡏⡆⠀⠀⠙⠦⣀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠻⢷⣿⣁⠀⠀⠀⠀⠀⢿⣷⠃⠀⣀⠀⠀⠈⠓⠦⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⡼⢷⣿⠉⠙⠿⣶⢤⡀⠀⠈⣿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠉⢻⣿⠀⠀⠀⠈⢶⠉⢦⠀⠘⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣇⠰⠿⣽⢧⠀⣟⠀⣠⠇⢸⠆⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢻⠤⣶⣞⡼⢿⣏⣉⣉⣠⠾⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⡾⠀⣹⢻⡀⠈⢿⡉⠉⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠶⣏⡼⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣄⣀⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡿⠋⠛⣷⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⣎⠹⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠉⠑⠷⣀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢀⣠⠾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⠤⣿⣤⡀⠀⠀⠀⠀⠀⠀⢹⣀⣠⠞⠉⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠦⢄⣙⣦⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡤⣉⣙⣷⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡬⠽⠟⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣠⢴⣚⣩⣼⣿⣷⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣠⠶⢋⣣⠾⢿⣳⣸⣿⡟⣿⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠘⣇⣀⠴⣊⣿⣷⢻⢿⠿⢿⣧⣻⣽⣿⣿⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⣆⠀⠀⠀⠀⠀⠀⢻⣵⠾⢭⣘⣿⣿⣻⣄⣸⣿⣷⡽⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⣆⠀⠀⠀⠀⠀⠘⣿⡞⢳⡞⡟⢿⣯⠽⠟⠉⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣽⡄⠀⠀⠀⠀⠀⢸⡗⢺⣻⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⡿⢻⡀⠀⠀⠀⠀⠀⢻⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠋⠈⠉⠚⠛⠒⠒⠒⠒⠒⠚⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠁⠠⠄⠀⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠉⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿ ⣿⣿⠟⠁⠀⠊⠁⠀⠀⠀⠘⣶⣤⣤⣶⣶⣶⣶⣤⣴⠖⠀⠀⠀⠀⠀⡻⣿⣿⣿ ⣿⠃⢠⠀⠀⠀⠀⠀⣀⣴⣾⣿⡟⢹⣿⠻⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠐⠘⢿⣿ ⡏⠀⠂⠀⠀⠈⠉⣩⣿⣿⣿⠏⠀⠈⡏⠀⠈⢿⣿⡟⢿⣿⣿⣿⡛⠛⠀⠀⡈⣿ ⠁⠀⠀⠀⠀⢠⣾⣿⣿⠏⠏⠀⠀⠀⠹⠀⠀⠈⢿⡇⠈⣿⣿⣿⣿⣦⣄⠀⠁⢸ ⡀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠒⠂⠀⠀⠀⠀⠜⡇⠀⠘⠈⢿⣿⣿⡄⠀⠀⡀ ⡇⠀⠀⠀⠀⣸⢿⣿⠇⠠⠖⠒⠀⠀⠀⡄⠀⠀⠀⠒⠒⠄⠀⢸⣿⣿⣿⣆⠀⠀ ⣇⠀⠀⠀⠈⢀⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠸⠟⠻⣿⢦⠀⢸ ⣿⡄⠀⠀⠀⠀⢀⠈⠀⡖⠂⠀⣁⣀⣀⣀⣀⣀⣀⣈⠀⠈⠂⠀⠂⢀⠏⠀⠀⣾ ⣿⣿⣆⠀⡀⠀⠈⠊⠀⢰⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠁⠉⠀⠞⠀⢀⣼⣿ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⡙⣿⣿⡿⠿⠿⠿⠿⠿⢿⡿⠁⠀⠀⠀⠀⣠⣾⣿⣿ ⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠄⡠⠐⠀⠀⠀⣠⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡻⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠛⢹⣷⣿⣿⣷⡀⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠙⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡟⠀⠀⣀⣴⣾⣿⠿⠿⠿⠿⠿⠿⢿⣷⣦⣄⠀⠀⠻⣿⣄⠀⠀⠀ ⠀⠀⣴⣿⠋⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀⠘⣿⣧⠀⠀ ⠀⣼⣿⣿⣷⣾⡿⢋⣤⣶⣶⣦⣄⠀⠀⠀⠀⢀⣤⣶⣶⣤⡘⢿⣿⣿⣿⣿⣧⠀ ⢰⣿⠃⠀⣿⡿⢁⣾⣿⣿⣿⣿⣿⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⢻⣿⡇⠈⣿⣇ ⢿⡏⠀⢸⣿⠇⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠈⣿⣧⠀⠸⣿ ⠀⠀⠀⣾⣿⠀⠀⠘⠿⣿⣿⡿⠏⠀⢀⡀⠀⠙⢿⣿⣿⡿⠋⠀⠀⢹⣿⠀⠀⠀ ⠀⠀⠀⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⠀⠀⠀ ⢿⣧⠀⢸⣿⡟⠛⣿⡿⠿⠿⣿⠿⠿⢿⣿⠿⠿⣿⡿⠿⢿⣿⠟⠻⣿⡿⠀⣸⣿ ⠸⣿⣆⢀⣿⣷⡀⢸⡇⠀⠀⣿⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⣼⣿⡇⢠⣿⠇ ⠀⠹⣿⣿⡿⢿⣷⣿⡇⠀⠀⣿⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⣾⣿⠿⣿⣿⡟⠀ ⠀⠀⠹⣿⣦⠀⠙⢿⣿⣤⣠⣿⡆⠀⢸⣿⠀⠀⣿⣷⣠⣾⡿⠟⠁⣰⣿⠟⠀⠀ ⠀⠀⠀⠈⢿⣷⡀⠀⠉⠻⢿⣿⣷⣶⣾⣿⣶⣶⣿⡿⠟⠋⠀⠀⣼⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠉⠙⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠒⠤⢄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠁⠈⠻⣷⡄⠙⣷⣦⡾⢛⡿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠋⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢀⡠⠾⠯⣭⣒⢯⣕⣲⣬⣿⣆⠸⣿⣴⣗⡒⢤⡀⠹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⠣⢄⠞⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣶⣿⣉⣩⠝⠛⠛⠋⠛⠿⢿⠀⣿⠇⠸⠛⢆⢹⣦⢜⡞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⣸⣫⣵⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢻⡟⢿⡺⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡾⢋⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⡘⣿⣎⣧⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣿⠟⡏⠀⢰⠇⢀⡧⠤⠧⠀⠀⠒⢒⣨⢵⠶⠑⢀⣀⣇⢹⣟⣯⣻⡜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣘⡇⠀⠜⠀⣼⠟⠛⠻⠿⢿⣭⠁⠂⡡⠖⠉⢀⠞⢻⢸⣿⣇⠹⣧⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡆⠀⠀⠀⠀⠀⠀⠀⣼⠇⣰⣯⣽⣿⣄⠔⢋⣹⣷⣄⣀⠀⠀⣋⣷⢼⣁⣠⠞⠓⠒⢾⢸⣏⢻⣻⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⢱⠀⠀⠀⠀⠀⠀⢠⡟⢰⣿⣿⡟⢬⣏⣶⡻⠛⠛⢷⣿⣿⣿⣿⣶⢶⣿⡿⠭⠭⠽⢻⣼⣿⣄⡇⣇⣟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠈⡄⠀⠀⠀⠀⠀⣼⠃⣼⠏⣿⡋⢩⠿⣯⠭⣽⣉⠽⠚⢉⠁⠁⠸⠼⠸⣌⠑⠒⠀⢀⡿⢣⣸⣇⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⡼⡟⠀⣿⣴⣸⡟⠁⠀⠙⠦⣨⣇⣀⠤⠋⠀⠀⠀⠀⡆⠈⠑⠒⠒⢸⡇⠀⢿⣿⡿⡏⢇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⠀⠀⡇⠀⠀⠀⠀⣣⡇⠀⣧⡟⣟⢿⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⣠⢤⣤⣖⣀⣀⣰⡦⢼⣥⡆⢸⢻⣷⣷⠈⠲⠤⢤⡀⠀⠀⠀⣀⠇⠀ ⠀⢀⠃⠀⡠⠔⠊⡩⠿⡄⢿⡌⣿⣜⣇⣠⣾⣿⣿⣗⣛⣟⣛⣊⠿⠯⠤⠍⠉⠀⠒⠒⠻⣿⡅⢺⣿⣾⢹⢳⣴⡒⢢⢹⣀⣀⣀⠙⠻⣆ ⠀⢸⢀⠞⠓⠦⣯⠄⠀⣿⣿⡘⢮⡻⡇⢺⣿⣏⠛⠀⠁⣀⣀⣤⣤⣤⣶⣶⣶⣦⣤⣄⣀⡿⣇⢸⡿⣧⡻⣮⡉⢻⡾⣏⡁⠈⠉⠙⢦⡙ ⠀⣻⣿⠂⠀⢰⡿⢀⡴⢻⠇⢸⣎⢿⣿⡈⠇⡏⢷⣶⣿⠟⠋⠉⠉⠀⠀⠈⠉⠉⠻⢿⡿⡀⢹⣿⡇⠈⣹⠇⢈⣽⠗⢦⣹⡦⠀⠀⠀⢹ ⣀⡟⠁⠀⠀⢸⠃⡾⡔⠁⣰⠕⢿⠘⣿⣷⣄⠀⢀⠻⣍⣀⡠⠤⠤⠄⠒⠒⠀⢐⣰⠞⡱⠁⢸⣿⣇⠸⡋⠻⢅⣯⣴⣿⡟⢿⠀⠀⠀⢸ ⣿⠁⠀⠀⠀⢸⣆⠳⢧⣀⠹⣦⡞⣶⡇⢻⣏⠣⡀⠱⣌⡓⠒⠂⠐⠒⠒⠂⢉⣁⣠⣴⠁⢠⣿⣿⣿⣦⣝⢆⠀⠈⣿⣿⠃⢸⠃⠀⠀⣾ ⣿⣇⠀⠀⠀⠀⣿⡿⡙⣌⣷⣼⡷⣿⣷⠀⢿⣧⠹⡎⢸⠉⠙⡿⡏⠉⡟⡏⠙⡼⡄⢋⢳⣿⣿⣿⣿⣿⠟⣸⣀⠴⢛⡏⢀⡏⠀⠀⢀⠯ ⠻⣿⣆⠀⠀⠀⠘⣷⡙⠿⢏⢹⣧⣿⣿⣇⠈⢿⠇⠁⢸⠀⠀⠀⡇⠀⡇⢡⠀⡇⢱⢸⠀⠛⣿⣿⣿⣵⣾⣿⠋⢠⠎⢀⡟⠀⠀⢠⠊⢀ ⠛⠻⢿⣷⣤⡀⠀⠈⠻⣄⠈⢻⣰⣽⠃⣾⠀⢸⠀⠀⠈⠳⠶⠀⢷⣤⠇⠸⠷⠃⠈⠋⠀⣼⣿⣿⢻⡟⣿⡿⡔⠁⢀⡞⠀⠀⡰⠃⣠⢞ ⠛⠲⠬⠉⢉⣹⣦⣄⣀⠈⠂⠀⠹⣿⣾⡟⠀⢺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡽⢠⡿⢻⣃⣿⠞⢀⣴⠋⠀⣠⠞⢁⣾⣏⡾ ⣠⠤⠔⢺⠁⢀⠏⠈⢿⣻⡿⣶⣦⠈⣿⣴⣲⠈⠿⣇⢀⠀⠀⡄⠀⡀⠀⡀⠰⡴⡰⣤⣼⣷⡟⠀⣾⣿⠏⢠⡟⠁⣠⡾⣋⢾⣿⡿⠋⠀ ⠀⠀⠀⠘⠒⠁⠀⢀⣾⣿⣿⣿⣿⡃⣈⠻⣄⠀⠀⠻⣼⣴⣆⣃⡇⢹⣆⣆⢠⣿⣷⣽⡟⠛⠂⠀⣿⠏⢠⡟⢠⣾⣿⠟⣱⡿⠋⠀⠀⢀ ⠀⠀⢀⣀⣀⣠⣴⣿⣇⣽⣿⣿⣿⠁⠈⠓⣿⣧⣀⠀⠀⠸⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣰⡏⣰⣟⣴⣿⠟⢁⣴⠋⠀⢀⣠⣶⣿

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⢀⡄⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⢰⡟⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣻⠏⠀⠀⠀⠀⢶⢢⠀⢸⣷⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠑⢢⣄⠀⠀⠀⠀⢰⣶⣄⠀⣸⣿⣷⣧⣤⣒⡶⣦⣤⣼⡋⠀⠈⣿⣷⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢫⠱⣄⢀⣴⣦⣝⣻⣷⣾⣿⣫⠙⣿⣯⡿⢋⣿⣝⣿⣆⣠⣿⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⢷⣬⣽⣿⣿⡿⣿⣿⣯⣽⣿⣿⡿⠿⠷⠟⠁⢿⣹⣿⣬⣽⡟⠁⢸⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀ ⠓⠈⠉⠁⠒⠒⠒⠂⠀⠀⢱⠀⠀⠀⠀⠈⢿⣿⣵⣳⣷⠏⣟⣻⢿⢏⣿⣷⣦⣄⠀⠀⠈⠻⣿⣾⣥⣤⠀⠛⠉⠉⠉⢡⣾⣿⠛⢻⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠘⣿⢿⣿⡟⣰⣿⣿⡟⣼⠯⣿⡿⠁⠀⣾⣿⣏⣿⣿⠿⠇⠀⠀⠀⠀⠀⠘⣿⣿⣶⣾⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠸⣿⣏⣷⡟⣾⣿⡇⡏⠀⠀⢀⣀⠤⠛⢛⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠋⠁⠀ ⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡤⣿⡄⠀⠀⠀⠀⢱⣿⣿⡇⣿⣿⡀⣷⣄⠈⠻⡿⠇⣠⣾⣽⣿⠁⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣿⣿⣿⠟⠁⠀⡼⣾⣏⣷⡀⠀⠀⠀⠀⠻⣿⣷⣿⣿⣷⣵⣽⣿⣶⣴⣾⣏⣱⡿⠁⠀⣰⣿⣂⡔⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⠁⠀⢀⣸⣾⣏⣼⣾⣷⡀⠀⠀⠀⠀⠈⠻⣯⡉⢻⣿⣿⡃⠻⢿⣿⣿⣇⣳⣒⣻⣿⢿⢸⣾⣿⢳⠀⠀⠀⠀⠀⠒⠈⠁ ⣿⣿⣿⣿⣿⡇⠀⢀⣎⢿⣎⣿⣿⣿⢱⣷⡄⠀⠀⢡⠀⠀⢹⠱⡄⠹⣿⣷⣄⢸⣿⣿⣿⡷⢯⣻⣼⢿⣿⣿⠇⢸⠀⢀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡄⢰⡆⡬⣹⣿⣿⣿⣿⣿⢒⣷⡀⠀⢠⠆⠀⢸⠀⠘⢆⠈⢻⡟⠃⢿⡽⣿⣷⣎⣿⣯⠿⢏⣨⣀⣸⣴⣿⠟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⠐⣣⣿⣿⣿⣿⣛⣿⣭⣾⣾⣷⠀⠀⠀⠀⡎⠀⠀⠈⢆⠀⠹⣄⢰⡇⢩⠙⢌⣻⣿⣗⡶⣟⢃⡀⠙⡄⠀⠀⠀⠀⠈⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀⣀⣠⣴⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣶⣶⣶⣶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢰⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠖⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⣙⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⣿⣮⣻⣿⣿⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢿⣿⢸⣿⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⣿⣿⣗⣿⣿⣿⣷⠰⠾⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛ ⣿⣿⣿⣿⣿⣿⣿⣧⡤⠦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠁⠈⣿⣿⠀⠀⠀⠈⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⢿⣿⣿⣿⣿⠀⣰⣿⣿⣿⣿⠟⡽⢮⡻⣿⣿⣿⡟⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣼⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟⠀⠧⣤⣳⡘⣿⡿⠁⣿⠃⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⣿⣿⢣⣿⣿⣿⣿⣿⣇⠛⠀⣽⣿⣷⠀⢠⠤⢬⡏⣿⡇⠀⠁⠀⢠⢾⡿⠛⠉⠙⢿⣷⣤⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠁⠀⠀⣿⠏⠀⣿⣿⣿⣿⣿⠉⠛⠛⠀ ⣿⢏⣾⣿⣿⣿⣿⣿⣿⡄⠘⠻⣿⣿⣦⠸⣄⣾⡁⣿⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⡏⠀⢀⣀⣀⣀⡀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⢫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣷⡌⠻⣝⣿⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠚⠉⠉⠙⣿⡄⠀⣸⣿⣿⠿⣿⣿⡄⠀⠀⠀ ⣿⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⠉⠉⣿⣿⡿⣦⣀⣿⠀⠀⠀⢿⣿⢷⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠴⢄⣰⡄⢀⣈⡀⢰⣿⣿⠃⠀⠈⠻⣷⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣻⣿⡇⣸⣿⣿⣇⣠⠾⠋⠀⠀⠉⣿⡇⠀⠀⢸⡇⠀⢨⡀⠀⠉⠛⠓⠒⠤⠤⠤⣄⣈⣀⣀⠀⠀⠀⠉⠉⠉⢡⡿⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣣⣿⢻⣧⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢹⢿⡀⠀⠈⢿⣦⣼⡧⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠉⠉⠙⠓⣿⡆⠀⢀⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⡿⢻⣦⡀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣤⣰⣀⣴⣋⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣷⣿⣻⢿⣦⡀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠛⠛⣻⡟⠛⠛⠛⠛⠻⠿⠶⠄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣯⢿⣟⣟⣿⣦⣄⠀⠈⠙⠓⠶⢤⣤⣤⣤⡤⠞⠋⢁⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡆⠀⠀⠀⠀⢯⣞⢿⣎⣾⣾⡾⣮⣱⣶⣄⣀⠀⠀⠀⣀⣀⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣇⠿⣿⣿⣿⣿⣄⠀⠀⠀⢻⣿⢏⣾⣫⣿⡿⠛⠋⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡿⣤⣿⣿⣿⣿⣿⣧⡀⠀⠀⢻⣾⢏⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡧⡿⣿⣟⣿⣿⣇⠹⡿⣄⠀⠀⣩⢿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣻⡝⢸⡇⠃⣿⣿⣻⣿⣿⡄⠘⢻⣷⣾⣿⣼⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠙⠒⠲⣤⡀⠐⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢴⣻⣷⡦⠤⠀⠀⣈⣉⡲⣤⡀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢷⡀⠀⠀ ⠀⠀⢀⢾⣿⠯⣤⣀⡉⠉⠙⠻⠶⣤⣉⠳⢿⣦⣀⠀⠀⠀⠀⠀⠈⣧⠀⢣⠀⠀ ⠀⢠⡟⠛⣀⣀⣀⡈⠙⠛⠻⠶⠤⣄⡈⠓⠦⠙⢯⠁⠀⠀⠀⠀⠀⠻⠀⣼⡄⠀ ⣰⣿⡆⢠⡏⠀⠉⠉⠒⠦⢄⣀⢀⡈⠻⣄⡀⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⣿⡇⢥⠈⢧⡀⠑⢶⡆⠀⠀⠉⠓⢿⡶⣽⡙⢷⠸⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⢧⠘⣆⠈⢿⣄⣠⢷⡄⢀⣿⡅⠀⠈⠓⣇⠈⣀⣼⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣯⢧⠘⢧⠛⢿⣿⣟⣣⣿⢯⣤⡇⠀⠀⢠⣾⠟⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⡳⣌⠷⣄⣙⢿⣦⡇⠠⠞⠀⠀⢰⡷⠃⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠓⠮⣧⣍⠻⣧⣭⣿⣧⣄⣀⣀⣾⣦⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠓⠻⣿⣛⣽⣿⠿⢿⡏⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣻⡄⠀⠀⠈⣿⣛⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⠀⠀⠀⢸⡧⣽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣿⣻⣄⠀⢀⢏⣙⡾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣳⣿⡜⠿⣤⣟⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠙⣻⣿⣿⣿⣧⣿⣿⣿⣿⣇⣀⣼⣟⡡⠤⢽⣿⣿⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣶⡲⣄⣹⣿⡇ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣟⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣹⣬⣿⣿⡇ ⠀⠀⠀⣾⣿⣿⣿⣿⣇⣠⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⡇ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠿⠿⠋⠀ ⠀⠀⠀⠀⠈⠙⠛⠻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠉⢻⣿⣿⣿⣿⣿⣿⣿⠉⢙⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⠖⣱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣝⣤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠖⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠧⣔⣠⠶⢦⣤⣈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣴⠟⣶⣔⠲⡤⣀⠀⠀⠀⠀⢸⠇⣠⡎⠉⠀⠀⠈⠈⢎⣇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣼⠇⡄⢹⢳⡀⠀⠀⣸⡃⢰⣃⡀⠀⠀⣀⣰⡼⣻⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠙⢿⣋⠴⣋⡼⠉⣆⣤⣿⣆⣄⠰⠿⠟⠁⡀⠚⠋⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣄⣀⠉⠙⢿⣼⣧⣾⣥⡞⢯⢿⣿⡀⠀⢀⣀⠡⣤⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⡲⠃⢀⣰⡟⠛⠛⠛⠻⠟⢷⣿⠛⣷⡂⠀⠉⢷⣟⠛⠀⠀⠉⢁⣿⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠈⠣⣤⣿⠛⢠⠀⠀⠀⣯⣴⣏⣹⣶⣿⣿⣦⣀⡘⠙⠷⣦⣤⡴⢿⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢇⠀⠀⠀⠈⢱⣶⡾⠁⠀⠀⢈⣋⣉⣀⣈⢻⠿⡿⢻⡇⠀⢧⠀⠀⠀⢸⠀⣿⡌⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⠈⢷⣤⣀⣠⣿⡿⠁⣀⡠⠖⠙⡄⠀⠀⠀⠀⣰⠇⢸⣗⠒⠬⢷⣄⢀⡼⠤⠼⢧⠀⢿⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠊⠀⠀⠀⠀⠈⠙⢻⡿⠛⠋⠉⠉⠀⠀⠀⢹⠀⠀⠀⢀⣿⠀⢸⣿⡀⠀⠀⠻⡟⠀⠀⠀⢸⠀⢸⣧⠀⠀⠉⠐⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⣠⣾⡁⠀⠠⣄⠈⢦⡀⠀⠀⡆⠀⠀⢸⡿⡇⠘⣿⡇⠀⠀⠀⡃⠀⠀⡴⢻⠀⢸⣿⡆⠀⠀⡜⠀⠸⡀⠀⠀⠀⠀⠀ ⡴⠀⠀⠀⠀⣠⣾⣿⣿⣇⠀⠘⣾⣷⣦⣿⣦⠀⢱⠀⠀⠈⠀⠀⠀⣿⡇⠀⠀⢀⣇⡴⠋⠀⠘⡀⠸⡟⣷⠀⡸⠀⠀⠀⢃⠀⠀⠀⠀⠀ ⠳⡀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⠀⢀⠀⠀⠀⠀⣿⠧⠒⢒⣻⡏⠉⠉⠉⠘⡇⢀⡇⠘⢶⡇⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠈⠛⠛⢛⣿⡟⣿⠛⠛⠛⠛⠛⠛⠿⡟⠛⣿⣿⣠⡎⠀⢸⠀⠀⣿⠀⣠⠞⢰⡇⠀⠀⠀⠀⡇⠐⡇⠀⠈⣧⣀⣴⣦⡀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣥⡿⠇⠱⡄⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⠁⠀⢸⠀⠀⠟⣿⠉⠉⣿⠉⠉⣿⡏⣿⡇⠠⡇⠀⠀⣿⣻⣿⣯⢛⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⢆⠀⠈⢦⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⡞⠀⢠⠀⡆⠀⠀⣿⠀⠀⢻⡇⢻⣇⠀⣇⠀⢰⣿⣿⣿⣿⣟⣿⣿⣝⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠷⡄⠀⠀⠀⣿⡿⢿⠃⠀⠀⡇⠀⣼⣿⡇⠀⠀⣿⠀⠀⢸⡇⢸⣏⡇⠈⡆⢸⣿⠩⠟⠛⠻⣿⣿⠿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⡘⢉⢦⡀⠀⢸⣤⣼⡄⠀⠀⢇⠀⠹⣿⣇⠀⠀⣿⣀⠀⢸⡇⢸⠟⠁⡴⠃⠀⣿⡆⠀⠀⢠⡘⣿⣷⡽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⢦⡐⣹⡟⣿⣿⣿⣷⣦⡀⠈⢦⠀⠈⢻⣧⡀⣿⠈⠙⢻⡿⠃⣠⠊⢀⣀⣀⣿⣿⢰⠀⠀⢷⡼⠻⣧⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣙⡿⢣⣿⣿⣿⣿⣽⣿⣆⠀⠳⣄⠀⠹⣿⣿⠒⡶⠋⠀⣴⣷⣿⣿⣿⣿⣿⠇⢸⠀⠀⠈⢇⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠟⢻⣎⣾⡟⣩⣽⡿⣶⣤⡈⢢⡀⠘⢧⡖⠁⣀⣼⣿⠿⣿⣟⠛⢻⣏⠀⢸⠀⠀⠀⠘⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠗⠛⠿⠿⠡⠟⠉⠒⠚⠛⠛⠛⠓⠂⠈⠛⠛⠛⠛⠛⠊⡀⠈⣆⠀⡍⠓⡎⠀⠀⠀⠀⠈⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢄⡉⠑⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⢀⡨⠗⠚⡉⠳⠀⠘⡄⠂⠀⡇⠀⢠⡾⠻⣷⣼⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣠⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⣿⢋⣿⠋⠀⠀⠀⠀⠀⠘⢻⣹⠀⠀⢿⣿⡄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⢾⣿⣆⡀⢀⣰⣿⣿⣿⣧⢴⣒⣲⠶⣶⣶⣴⣾⡋⠀⠀⠘⣿⢿⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢫⡙⢦⡀⠀⢀⣤⣌⣹⠿⣷⣶⣾⣿⡛⣿⠛⣿⣿⣿⣵⠟⣹⣯⡿⣿⣦⠀⣠⣿⣾⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢳⣀⠙⢶⣿⣿⢿⡿⣷⣿⣿⡿⠿⣻⣧⣴⣿⣿⣿⣧⣾⠿⢻⣷⢻⣿⡛⠛⢿⣿⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀ ⡄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⢿⣇⣹⣿⣿⣿⣿⣿⡿⣿⡟⠉⠉⠉⠁⠀⠀⢻⣾⡿⣟⣿⡿⠋⠀⢀⣾⣀⣀⣀⣀⡀⢠⣾⣿⣿⣿⣿⣿⡄ ⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠈⢿⣟⣷⣮⣼⣿⡟⢸⣯⣽⣿⡿⣱⣿⣿⣿⣷⣦⠀⠀⢀⣀⣙⣿⣿⣿⣶⣶⡆⠀⠁⠀⠀⠀⠀⢀⣿⣿⣿⠉⢙⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⣷⡶⣿⣿⣿⢁⣾⣿⣿⣿⢃⡿⢯⣿⣿⡟⠁⠀⣼⣿⣿⣯⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠘⡾⢻⡏⡇⣾⢧⣿⣿⡟⢸⡇⠀⠉⠀⠀⠀⢀⡼⠻⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⠿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠸⣾⣹⣷⣿⢸⣿⣿⡇⢸⣇⠀⠀⢶⣶⣶⣦⠀⢀⣼⢿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣠⠤⠤⠤⡞⣻⣽⣆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣸⣿⣿⣇⢸⡿⣷⣄⡀⠙⠛⢃⣴⣾⢿⣿⣿⠃⠀⠀⣀⡀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⡴⣿⣿⣧⢿⣆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⣽⣟⡿⣟⣳⣾⣿⣿⣤⣾⣿⠁⠀⢀⣼⣿⣯⣴⠞⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⣰⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣸⡾⣿⢃⣷⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣍⠉⠻⣿⢻⣿⣻⠘⢿⣿⣿⣿⣿⡇⢻⡖⢚⣿⣿⠿⡁⣾⣾⣿⡿⣦⠀⠀⠀⠀⠤⠀⠦⠭⠭⠥ ⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⢿⣿⣽⣻⣿⣿⣿⡏⣽⣆⠀⠀⠀⠀⣆⠀⠀⠈⣯⠳⡄⠈⢿⣿⣧⡀⠀⢿⣿⣿⣿⣿⣷⣿⡻⣿⣸⣧⣷⣿⣿⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠀⢀⡀⠛⠦⣽⣽⣿⣿⣿⣿⣼⣟⢘⣆⠀⠀⠀⠸⡄⠀⠀⣸⠀⠹⣄⠈⠻⣿⣿⣷⠘⣿⣿⣿⣿⣯⣘⢿⣿⡿⣹⣿⡿⡿⠀⠀⡇⣀⣴⣿⡄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠀⣼⡇⢾⣇⣿⣿⣿⣿⣿⣿⣿⡏⣸⢻⣆⠀⠀⠸⠃⠀⠀⡿⠀⠀⠘⣆⠀⠙⢿⡍⠀⠛⣷⠻⣿⣿⠿⣾⣿⣶⣏⠛⠲⣿⡤⠴⢿⣿⠿⠛⠁⠀⠀⠀⠀⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⠈⢹⣾⣿⣿⣿⣿⣟⣫⣿⣥⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⢦⠀⠈⢻⣄⢀⣿⠀⡇⠈⠧⣌⣿⣿⣯⣽⢞⣋⢉⣀⠀⢙⣆⠀⠀⠀⠀⠀⠀⢀⡴

⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜ ⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜ ⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛ ⬛⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛ ⬜⬛⬛⬜⬛⬜⬜⬜⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜⬜⬜⬛⬜⬛⬛⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬛⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬜⬛⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬛⬜⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬛⬜⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜

🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜🟦🟦⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜🟦🟦🟦🟦⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜🟦🟦🟦⬜⬜⬜⬜⬜⬜⬛🟨⬛⬛🟦🟦🟦🟦🟦🟦🟦⬛🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦⬜⬜⬜⬛⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜🟦🟦🟦🟦⬜⬜⬜⬛🟦⬛⬛⬛⬛⬛⬛🟦🟦🟦🟦🟦🟦⬛🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜🟦⬜🟦🟦⬜⬜⬛🟦⬛🟫🟫🟫🟫🟫🟫⬛⬛🟦🟦🟦🟦🟦⬛🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟦⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🟦🟦🟦🟦⬛🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟦🟦⬛🟫🟫🟫🟫🟫🟫🟫⬛🟫🟫⬛🟦🟦🟦🟦⬛🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛⬛🟦🟦🟦🟦🟦⬛🟨 🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟦🟦🟦⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🟦🟦🟦🟦⬛🟨 🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟦🟦🟦🟦⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🟦🟦🟦⬛🟨🟨 🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛🟦🟦🟦🟦🟦⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🟦🟦🟦⬛🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦⬛⬛⬛⬛⬛⬛⬛⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛🟦🟦⬛🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜⬛⬛🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛🟫🟫🟫🟫🟫⬛🟦🟦⬛🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬛⬛🟦🟦🟦🟦🟦🟦🟦⬛⬛🏻🏻🏻🏻🏻⬛⬛⬛🏻🏻⬛🟫🟫🟫⬛🟦🟦⬛🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦🟦🟦⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻⬛🏻🏻🏻🏻🏻🏻🏻⬛🏻🏻⬛⬛⬛🟦⬛⬛🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦🟦⬛⬛🟦🟦🟦🟦🟦🟦🟦⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🏻⬛🟦🟦⬛🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦⬛⬛🟫🟫⬛⬛🟦🟦🟦⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦⬛🟫🟫🟫🟫🟫🟫⬛⬛⬛🏻🏻🏻⬛⬛⬛⬛⬛🏻🏻🏻⬛⬛⬛⬛⬛🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟦🟦⬛⬛🟫🟫🟫🟫🟫🟫🟫⬛🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜⬛🏻⬛⬜⬜⬜⬜⬜⬛🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨⬛⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🏻🏻🏻⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨⬛🟫🟫🟫🟫🟫⬛⬛🟫⬛🟫🟫🟫⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨⬛🟫🟫🟫🟫🟫⬛🏻🏻⬛🟫🟫🟫🟫⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨⬛🟫🟫🟫🟫⬛🏻🏻🏻⬛🟫🟫🟫🟫⬛🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜⬛🏻🏼🏼🏼🏼⬛⬜⬛🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨⬛🟫🟫🟫🟫⬛🏻🏻🏻🏻⬛⬛🟫🟫⬛🏻🏻🏻🏻🏻⬛⬛⬛⬛⬛🏻🏻🏼🏼🏼🏼⬛⬛🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨⬛🟫⬛🟫🟫⬛🏻🏻🏻🏻🏻⬛🟫🟫⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🏼🏼⬛🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨⬛🟫🟫🟫⬛🏻🏻🏻🏻🏻🏻⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🏻🏻🏻🏻⬛⬛🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨⬛🟫🟫🟫🟫⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨⬛🟫🟫🟫🟫⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬛⬛🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨⬛🟫🟫🟫🟫🟫⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨⬛🟫🟫⬛🟫🟫🟫⬛⬛🏻🏻🏻⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟫🟫⬛🟫🟫🟫🟫⬛⬛⬛🟫⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨⬛🟫🟫⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨⬛⬛🟨⬛🟫🟫🟫🟫🟫🟫🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟫🟫🟫🟫🟫⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟫🟫⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻🏻🏻🏻⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🏻🏻⬛⬛⬛🟥🟦🟦⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦⬛⬛⬛🟦🟦🟦⬛⬛⬛🏻🏻⬛🟥⬛🟦⬛🟥⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦⬛🟥🟥🟥⬛⬛🟦⬛🟥🟥⬛⬛🟥🟥🟥⬛🟦⬛🟥⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦⬛🟥🟥🟥🟥🟥⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛⬛🏻🏻⬛🟨🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦⬛🟥🟥🟥⬛🏻⬛🟥🟥🟥⬛⬛⬛⬛⬛🏻🏻🏻⬛🏻🏻⬛🟨🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦⬛🟥🟥⬛🏻🏻🏻⬛🟥⬛🏻🏻🏻⬛🏻🏻🏻🏻⬛🏻🏻🏻⬛🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦⬛🟥⬛🏻🏻🏻🏻⬛🏻🏻🏻⬛🏻🏻🏻🏻⬛🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨 🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟦🟦🟦🟦🟦⬛⬛⬛🏻🏻⬛🏻🏻🏻🏻⬛🏻🏻🏻⬛🏻🏻🏻🏻⬛🟨🟨🟨🟨🟨🟨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠙⢦⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⠑⡀⠀⢀⡞⡠⠖⠚⠢⡀⠉⠻⠿⠿⠿⠿⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣇⣇⣀⢸⣜⡀⠀⣀⠀⢸⠀⡄⠀⠀⠀⣀⠤⣀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡖⠋⠀⠀⠈⠙⠺⣉⣲⣍⣀⡼⢀⠜⠒⠒⠉⠉⢢⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠫⡄⠀⠀⠠⣸⡤⠤⠤⣰⣆⢀⡇⠀⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠤⠤⣤⠤⠤⣈⡉⠙⠚⠉⠙⠒⠢⠤⣤⠏⢀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⡔⡹⡇⢀⡜⡏⠀⠀⣠⡟⠑⠦⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡧⠔⠒⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢰⠃⡇⡎⢠⠃⢀⠔⢡⠃⠀⢠⡟⠢⡀⠀⠀⠀⠀⠀⠘⣿⠋⢀⡠⣴⠒⠂⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢇⠀⠛⠤⢿⣀⢸⣠⠊⠀⡞⠀⡰⢹⠃⠀⣵⡀⠀⠀⠀⠀⠀⢸⡴⠉⠀⠘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠈⠓⢤⣤⣤⣤⣍⡓⠤⣰⡵⠊⢀⠎⡠⠊⡏⢱⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⡌⠑⢤⠾⠊⢀⡜⢀⢾⢀⠀⠀⠀⠀⢸⠳⠤⠤⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠑⢤⣾⠚⣁⠞⢀⠇⠀⠀⢀⠇⠀⠀⠀⠀⢀⣀⡠⠐⠒⢄⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠀⢀⡜⠀⣀⠴⠃⠀⠀⠀⠀⣞⠕⠒⠧⢆⠀⢈⢦⠀⠀⠀⠀ ⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⡠⠞⠒⠂⣀⠴⠊⠁⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡇⢰⠠⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠣⣹⡀⠀⠀⠀⠀⣤⡀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣧⠀⢀⡀⣰⣿⣿⣏⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠧⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠛⠛⠀⠙⠃⠀⠈⠻⣿⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠒⠉⠀⠀⠙⠻⠿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣷⣦⣤⣤⣤⣾⣿⣿⣿⣿⡏⢦⡀⠀⠀⠀⠀⡔⠀⠀⣾⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⡠⠋⠀⠀⡴⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⢇⠘⠉⠁⠀⠀⡜⠀⠀⢰⠋⢧⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀ ⠀⠀⠀⠱⣰⡃⠀⠀⣸⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⡴⣅⣀⡤⠋⢀⣨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠑⠒⠚⠙⠒⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣀⡤⠒⠉⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⠤⠊⠀

🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻 🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🟩🟩🟩🟩🟩🟩🟩🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟥🟥🟥🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟩🟩🟩⬛⬛⬛🟩🟩🟩🟥🟥🟥⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟩🟩⬛⬛🟥🟩🟩🟥⬛🟩🟩⬛⬛🟩🟩🟩🟩🟩🟩⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥⬛⬛🟩⬛🟥🟥🟥🟩🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟩⬛🟥🟥🟥🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟩🟩🟩⬛🟥⬛⬛🟩🟥🟥🟥🟥🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬛🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻⬛⬛🟥🟥🟥🟥🟥🟩⬛⬛🟥🟥⬛🟩🟩⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥⬛⬛🟥🟥🟥⬛🟩🟥🟥🟥🟥⬛🟩⬛⬛⬛⬛⬛⬛⬛🏻🏻🏻🏻⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟩🟥🟥🟥🟥🟥🟥⬛🟥🟥🟥🟥⬛🟩🟩🟩🟩⬛🏻🏻🏻🏻🏻🟧🏻🏻⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻⬛⬛⬛🟥🟥🟥🟥🟩🟩⬛🟥🟥🟥⬛🟩🟩🟩🟩⬛🏻🏻🏻🏻🟧🟧🟧🏻⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛🟥🟥🏻🏻 🏻🏻🟩🟥🟥🟥🟥🟥🟩🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🏻🏻🏻🏻🟧🟧🟧🏻🏻⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥⬛🟩⬛🟥🏻🏻 🏻🏻🟩🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🏻🏻🏻🏻🏻🟧🏻🏻🏻⬛🟩🟩⬛🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🏻🏻 🏻⬛⬛⬛🟥🟥🟥🟥🟩🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🟩🟩⬛🟥🟥🟥🟥⬛🟩🟩🟩⬛🟥🏻🏻 🏻🏻🟩🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛🟩🟩⬛🟥🟥🟥⬛🟩🟩🟩⬛🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🏻🏻🏻🏻🏻⬛⬛🟩🟩🟩🟩⬛⬛⬛🟩🟩🟩⬛🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩⬛⬛⬛⬛⬛🟩🟩🟩🟩🟩🟩⬛🟩🟩🟩🟩⬛🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥⬛🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟩🟩🟩⬛🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥⬛🟩🟩⬛⬛⬛⬛⬛⬛⬛🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟩🟩🟩⬛🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛🟩⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥⬛⬛⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬛⬛⬜⬜⬛🟩🟩⬛⬛🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬜⬜⬛⬜⬜⬛⬛⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛⬛⬛🟩🟩🟩🟩🟩⬛⬛⬛⬛⬛⬛⬛🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛🟩🟩🟩⬛🟥🟥⬛⬛🟥⬛🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🟥⬛🏽🏽⬛⬛⬛🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🟥⬛🏽⬛⬛⬜⬜⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🟥⬛⬛⬜⬜⬛⬛🟩⬛🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛🟥⬛⬜⬛⬛🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩⬛⬜⬛🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩⬛🟩🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩⬛⬛⬛⬛⬛⬛⬛⬛🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥⬛🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟩🟩⬛🟥🟥🟥🟥🟥🟥🟥⬛🟩⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🏻🏻 🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻 🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣦⣤⣴⡄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣤⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⡿⠃⠀⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠉⠛⣻⣿⣿⣿⡿⠁⠀⠀⠀⢻⣿⡇⠘⡏⢿⣿⣿⣿⣿⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠠⠾⠛⣿⣿⢻⠧⠤⠒⠂⠀⠀⠹⣇⠐⠛⠺⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⣿⣿⠸⢀⣠⣤⣄⠀⡇⠀⠈⣶⣦⣤⡁⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣠⠞⠙⣤⣀⣀⡔⠛⠛⢿⣿⣀⡘⠛⠉⠀⠘⠃⠀⠀⠓⠷⠽⣷⣸⣿⣿⣇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⣦⡞⠉⠀⠀⠀⠀⠀⢸⣿⡙⣿⠶⠚⠉⠉⠉⣉⣉⠉⠋⣓⡿⢹⣿⡿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣧⠸⣾⣿⣿⠿⠿⠿⠿⠿⢿⡿⢁⣿⠟⠁⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡠⠤⡄⠙⠧⣙⢿⣖⠒⠒⠒⢀⣰⠞⡡⠊⠀⠀⠀⠐⠒⠲⢏⣀⠽⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⠏⠉⠁⠀⠀⠈⣳⣮⣭⣒⣋⣭⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣠⣏⣇⣀⡀⠀⠀⢠⣾⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠚⠻⢿⣶⡖⣷⡴⣿⠀⢠⣿⣿⡿⠁⠀⠀⠉⠉⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢁⡴⠒⠶⣿⣧⢿⣤⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠒⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢿⡥⠒⠒⠢⢤⣿⣿⢛⣿⣿⣿⣿⣿⠓⠦⡀⠀⠀⡠⠔⠚⢻⣿⣿⣿⡆⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢋⣠⠶⢲⣶⣶⣿⠁⣼⢸⣿⣿⣿⣿⠀⠀⠉⠀⡖⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠛⣏⣠⣴⠚⠿⣿⣿⠎⢸⢸⣿⣿⣿⣿⠀⠀⢀⣾⢀⡀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀ ⠸⠀⢸⠁⣿⡴⠿⠏⠹⠻⢾⣎⣿⣿⣿⡏⠙⠲⠏⠘⠋⢧⠴⠊⠀⣿⣿⣿⣿⡄⠰⠢⢄⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⣆⣀⣾⡏⠉⣩⣏⣿⣋⢋⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠃⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠙⢶⣄⠀ ⠀⣇⠀⠀⢻⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣤⠿⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠈⢧ ⠀⢸⠀⠀⠈⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⠛⠋⠁⢠⣶⠉⠁⠀⢼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢀⡞ ⠀⠈⡀⠀⠀⠘⣿⣿⣿⠇⣿⣿⣿⣿⣿⣷⠂⠀⢀⣨⣯⡀⢠⣤⣺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠁⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀

⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡖⢫⡽⠛⠿⠥⣶⣒⠛⠛⠭⢭⣶⣖⣦⢤⣄⣼⣽⢧⣌⠩⢭⡭⣩⣿⣿⣿⣟⣾⣆⣴⣿⣿⠟⣫⣿⡇⢸⡟⡆⠃⠀⣠⣶⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠁⠀⣤⣀⠀⠀⠀⠀⠈⠉⠲⢿⣝⠒⠦⣌⣩⠟⠉⠛⠛⠺⢭⣭⣙⣿⣿⢽⠋⠑⠻⢿⣟⢯⣷⣻⡇⢿⢧⠸⣿⣹⢼⣿⣿⣿⣿ ⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠀⠸⡄⠀⠀⣌⠉⠲⢦⣀⠀⠀⠀⠀⠉⠳⣌⢻⠋⠀⢀⣰⣶⣝⣲⣶⠞⠉⢠⡟⠉⠓⠒⠒⠿⠷⢛⣿⣧⡘⢿⣧⣌⣩⣾⠿⡏⠁⢸ ⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠃⠀⠀⠙⣄⢠⡈⠳⣄⠀⠈⠳⢦⣀⠀⠀⠀⠈⠻⣦⡀⠀⠙⢮⣙⠛⠋⠀⢠⣞⣶⢤⣤⣤⡲⢴⣚⠏⣹⣿⡿⣿⣿⣿⠋⠁⠀⣧⠖⠋ ⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣼⡇⠀⠀⠘⡇⣤⠀⠀⠈⢢⡳⣄⠈⠓⢦⡀⠀⠻⣷⣕⢦⡀⠀⠈⠻⣦⠀⠀⠀⠀⢀⣴⠯⠬⠭⠭⠝⠛⠋⠉⣠⠞⣱⡿⢿⡟⠹⢸⠀⣠⠞⠃⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⢀⣾⡾⠁⣰⠄⠀⣿⡘⣆⠀⠀⠀⠙⢮⡻⣦⣀⠉⠓⢤⣈⠛⢷⣝⢦⡀⠀⠈⢳⣤⣤⡴⠋⠁⠀⠀⠀⠀⠀⣀⡴⠚⢡⠞⡽⠃⣸⢹⠂⢸⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢀⣿⢫⠇⢀⢧⠀⢸⠉⢷⡈⢷⣄⠀⠀⠈⠙⢮⣻⣽⣶⣦⣌⣙⠲⠿⢾⡵⣄⠀⠀⠹⣷⣯⡉⠓⠒⠒⠒⠒⠋⣁⣠⠖⢁⠜⠁⢀⡿⢸⣾⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⣾⠃⡾⠀⢸⢸⠀⣿⠀⠀⠙⢦⡻⣟⠦⣄⠀⠀⠈⠙⠻⢦⣄⠈⠉⠙⠓⠿⣎⢧⠀⠀⠙⣎⠙⣶⠤⣀⣀⣀⣴⠟⠉⠻⣦⠀⢀⡼⡇⢸⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⣼⡇⢸⠇⠀⡇⣿⡀⡏⠀⠀⠀⠀⠙⠯⢷⣤⡙⠓⠶⠶⠒⠋⠁⠀⢀⣠⡤⠤⠈⢿⣳⡀⠀⠸⣦⣌⠙⠓⠚⢻⡇⢰⠟⣧⠘⣧⠞⣹⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣯⣴⣯⠤⡟⠀⢸⡇⡇⣷⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠈⢳⣵⡀⠀⠹⣮⡓⠦⣄⣸⡀⡾⠀⠘⡆⠸⡴⠃⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⠓⠀⡇⠀⢸⣷⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣴⣾⣯⠭⣽⣧⣼⣷⣻⡀⠀⢻⣯⣲⢤⣹⠀⡷⠦⠖⠃⠀⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⣿⠟⢁⣰⡇⠀⢸⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡽⢿⣿⣾⠿⠿⣿⡙⠛⢿⣿⣳⠀⠈⣷⠨⣷⣽⡆⣷⠞⢶⡄⢀⡇⣸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡷⡋⣤⣼⣿⡇⠀⠸⣇⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠻⠛⣿⡟⣿⢙⣿⣷⣸⣷⢀⡾⠛⢧⣧⠀⠘⡆⠈⢻⡇⠈⣳⠂⡇⣼⡸⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣫⢿⣋⣜⡿⡽⠁⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣿⠁⢻⣏⡻⠟⣰⢏⣼⡋⠁⠘⡎⡆⠀⢹⡀⠀⠳⠚⢁⣼⢡⠏⣱⡻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣀⡈⠑⠋⠚⠁⠀⡇⠀⢸⣵⠀⠀⠀⠀⠀⢀⣠⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣬⣽⣿⣿⠽⠛⠀⠀⠀⠀⢻⣱⠀⠈⣇⠀⠀⡶⢻⣵⣏⣴⡟⣡⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⣍⠉⠉⣩⣿⣿⣷⠀⠸⣿⣴⡶⢶⣾⣿⣿⣿⣶⣾⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣇⣧⠀⢸⡀⠀⣆⡼⣿⣯⣝⢿⣿⡾⣻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣶⣿⣿⠿⡿⡼⡆⠀⢧⣏⠘⣿⣷⡿⢯⣙⣷⡀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⡀⠀⡇⠀⣿⢸⠁⣾⠙⡆⢹⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡏⠁⢀⣹⡙⢧⠀⢸⣿⣸⣿⠟⣿⡾⠿⣿⡇⣼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⢸⣄⣿⠸⣸⢹⢸⡇⢸⠰⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣶⣿⡿⠛⢾⡄⠀⣿⡟⣻⢦⣙⡻⣿⡯⡞⠁⢸⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠀⠸⣿⣿⣆⠙⠾⣞⣃⡼⣰⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠛⠁⠀⠈⢧⠀⢻⣹⣧⠸⠋⡟⠙⠀⠀⠀⠀⠉⠓⠒⠁⠀⣠⡤⠖⠒⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⣽⣻⣷⡾⠿⡟⠀⡏⢸⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠘⡇⠈⣏⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⣀⣤⣶⣶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⡿⣹⣧⣤⡇⠀⣇⢸⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡀⠸⡜⣷⣽⣦⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣴⣾⣿⣿⣿⣫⠿⠿⢳⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⣷⣿⣼⣷⣿⣿⣇⠀⣿⡜⡄⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢷⠀⢷⡹⡍⢻⠷⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠁⣀⡤⠖⣻⠀⠀⠀⠀⢀⣴⣿⣿⡇⢀⣿⣼⣧⣿⡜⢿⣿⡄⣿⣷⣳⡀⢿⣧⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣀⣀⠄⠀⠀⠀⠈⣇⠈⢧⠹⣧⡜⠙⢧⡀⠀⠀⠀⠀⠀⠘⣿⣿⣡⠔⠋⠁⢀⡴⠃⠀⠀⠀⣠⣾⣿⣿⣿⡇⢸⡿⣿⢻⣽⢣⠈⣿⣷⣜⣿⣿⣷⣬⣿⣿⣷⣦⣤ ⠀⠀⠀⠀⠀⢀⡜⠋⠀⠀⠀⠀⠀⠸⡄⠸⣷⡹⣧⠀⢀⡟⢦⣀⠀⠀⠀⠀⠘⢿⣤⣤⡤⠖⠋⠀⠀⠀⣠⣾⣿⣿⡟⣿⣹⠀⣸⣾⣻⡿⠛⠋⠀⠘⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⢻ ⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠹⣄⠘⢷⣽⣏⢩⣠⣾⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣾⣿⡇⠀⣷⣹⣿⠑⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠋⢈⣿⢿ ⠀⠀⠀⠀⠀⣠⠇⠀⠀⢠⡾⠿⠛⢿⣿⠿⠿⡶⢸⣿⣿⣙⣻⠀⠀⠀⣯⠙⢷⣶⢤⣀⣠⣤⣾⣿⣿⠿⠿⠛⠻⢿⡿⡟⠀⢰⠇⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⣾⠋⢠ ⠀⠀⠀⠀⣴⠃⠀⠀⣰⡟⠀⠀⠀⢸⡇⠀⠀⣷⢸⠇⠀⢹⡟⠀⠀⣼⡟⠀⢸⣿⡄⢸⣅⣿⢣⣿⣿⡄⠀⠀⠀⠀⣿⠁⠀⠸⡆⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⢀⣾⠃⠀⣸ ⠀⠀⠀⠀⡸⠀⠀⣰⠏⠀⠀⢀⡄⠸⣧⠀⢀⡟⢸⡀⠀⣿⢗⢦⣰⣿⠃⠀⣸⣿⡇⢸⣿⣿⣿⣿⠟⣧⠀⠀⠀⠀⣿⠀⠀⠀⠹⣆⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⣼⠃⠀⣰⣿ ⠀⠀⠀⣠⠃⠀⣼⠏⠀⠀⢀⡾⣷⡀⠛⠛⢿⣷⢚⡛⡶⠿⢮⣳⡹⣟⠀⢠⣿⣿⡇⣾⣿⡇⣿⠃⠀⢻⠄⠀⠀⠀⠹⣷⡀⠀⣘⣾⣦⣴⣿⣿⠋⠀⠀⠀⠀⢀⡴⣿⠏⠀⠰⠟⠁ ⠀⡠⠔⠁⠀⣴⠏⠀⠀⠀⡾⠃⠘⣷⡄⠀⠀⠹⣷⣸⣿⠃⠀⢳⡹⡝⣦⣾⣟⣿⣾⠟⣡⡾⠁⠀⠀⡾⠀⠀⠀⠀⠀⠈⠻⣷⣽⣾⣿⣿⠟⠁⠀⠀⠀⠀⣰⠏⢰⡟⠀⠀⠀⠀⠀ ⠿⠤⠤⠄⣸⠋⠀⠀⠀⣼⠇⠤⠴⠾⢿⣄⠀⠀⠘⢷⣝⠶⠤⠴⠧⠷⠿⠿⠾⠿⠧⠾⠿⠤⠶⠶⠾⠧⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠧⠤⠤⠤⠤⠤⠾⠧⢤⣿⠀⠀⠀⢠⣿⡄ ⠀⠀⠀⠀⠙⠷⢦⣤⣼⣿⠀⠀⠀⠀⠀⢻⣶⡴⠿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠶⠿⠉⠿

⠀⠀⠀⠀⢠⡝⡼⢹⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠠⠀⠀⢸⡰⣙⢶⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⡆⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢨⠵⣩⢾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⡀⠀⠀⢣⣧⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠐⠀⠀⢘⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠄⣙⢮⡱⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣶⣒⠒⠒⠒⠒⠒⠈⠚⢿⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠈⠀⠀⠐⣮⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡏⢶⣱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠊⠉⢀⣠⢊⣼⣿⡝⠖⠒⠒⡾⣯⢲⢸⡆⠀⢷⠀⠀⠀⠀⠀⡀⠀⠀⢠⡗⠀⠀⡁⠄⠀⠀⠀⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡟⢦⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠤⠒⠊⠉⢉⣴⡿⠃⠀⠱⡴⡀⠔⠹⢿⡄⣂⣷⣀⣺⡄⣄⣀⠀⠀⡄⠀⠂⢸⡇⢠⠀⢡⠐⡀⠂⠀⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⢀⡟⢦⣹⡇⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⣀⡤⢶⡿⠋⠀⠀⠀⢀⣵⡿⠋⠀⠀⠀⢀⠹⡅⠀⠀⠈⣧⣸⠟⠉⠉⢛⠏⠛⠉⠳⢦⡀⡅⢸⡇⢸⠀⠂⢰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠷⡌⢯⣇⡠⠊⠀⠀⠀⠀⠀⢀⡤⠔⡫⣵⢞⡅⠀⠀⢀⣠⣾⡿⠃⠀⠀⡀⠀⠌⠆⢳⣶⠀⠀⢿⢿⠀⠀⡠⠊⠀⠀⢀⠀⠈⠳⡁⢸⡇⢸⠀⢂⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠉⠩⠋⠀⡠⠖⠋⢀⠤⠚⢁⡤⣪⠞⢚⣋⠀⠀⠩⣿⡿⠋⡀⠐⠈⠉⠉⠉⠻⣄⢸⢻⣔⡤⠼⠿⠤⣞⠀⠀⠀⡴⠋⠀⠀⠀⠙⣾⠀⡎⠐⠂⢸⠄⡁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⢧⡤⠊⢀⡤⠚⢁⣄⠖⠢⡘⠁⢰⡻⠃⠀⠀⠘⠋⠀⣾⠃⠀⠀⠀⠀⠀⢀⣈⡞⣝⡁⠀⠀⠀⠀⠈⢳⡀⣼⠁⠀⠀⢀⣶⣷⣻⡄⡃⠄⡁⢺⠁⡄⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⠀⠠⠀⠸⣤⠔⠁⣠⡴⠃⡌⠀⣤⡀⢠⣾⠃⠀⠀⡀⠀⡀⢰⠻⡀⠀⠀⠀⠀⠀⠘⠀⡇⢿⣇⠀⠀⠀⠀⠂⠸⣼⠇⠀⠀⠀⣼⣿⣿⡇⣣⠇⠸⠀⣽⠀⢆⠁⡂⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠄⠨⠀⠐⠀⠀⡏⢀⡾⠋⡠⠀⡇⢠⣿⣷⡀⢯⠀⠀⠈⢁⠀⠓⠌⢳⣱⡀⠀⠀⠀⠀⢀⣾⠀⠈⡾⡄⡀⢀⣀⠤⢾⣿⣰⣷⠄⢀⣿⣿⣿⡇⣛⡇⠈⡄⡞⠀⡌⠀⡇⠀⠀⠀⢀⠀⡀⠀⠂⠀⠄⠀ ⠀⠠⢁⠠⢀⠀⠈⡷⠋⠀⡰⠁⠀⡇⢸⣿⣿⣧⠈⡆⠀⠀⠀⢀⠤⢀⠀⠋⠹⠗⠶⠾⠚⠋⡁⠀⠀⠘⣟⡝⢻⠀⢰⣿⣿⣿⣿⡇⢠⣿⣿⣿⡇⣧⠇⠠⠀⣵⠀⠆⠁⡶⠀⠀⠈⠀⡀⠀⠀⠐⠀⠐⠀ ⠀⡡⠀⡧⠀⢀⠈⡧⠀⠀⠀⣰⠁⢣⠘⢸⣿⡟⠀⢸⠀⠀⢀⣇⣴⣲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢾⠀⢸⣿⣿⣿⣿⡇⠠⣿⣿⣿⠂⡟⢀⠁⠂⣓⠀⢡⠂⡏⠀⠀⠈⡀⠄⠀⠄⠐⠀⠈⠀ ⠀⡄⠡⡇⠐⡈⢀⢳⠀⠀⣰⠋⠀⠈⣆⠘⢿⣇⠀⢸⠀⠀⣸⡌⠀⢸⠉⠀⠙⡦⠤⣀⣀⠀⠀⠐⠒⠀⠁⠼⠋⠀⠀⣿⣿⣿⡿⠀⠀⣿⣿⣿⠀⣇⠂⠌⡄⣇⠘⠤⠀⡇⠀⢀⠆⠀⠄⠐⠂⠀⠀⢀⠀ ⠀⢆⢱⠁⢆⠀⢂⢸⠀⡼⠃⠂⠀⡰⠙⡄⠈⠛⢷⣼⠀⠆⠁⡇⠀⢸⠀⠀⠀⡇⠀⠀⡽⠉⠉⡃⠀⠀⠀⠀⢸⠀⠀⠈⠛⠟⠁⠀⠀⠙⠋⡏⢀⡿⢈⠎⡐⠼⠐⡊⠄⡗⠀⠀⠄⠂⠌⠀⡀⠀⠂⢀⠀ ⢀⢂⢞⠸⡀⢌⠂⣸⠀⠁⠀⢀⡜⠁⠀⠸⡄⠀⡼⢸⠀⠀⡀⣧⣤⣼⣤⣀⣀⣇⣀⣀⣃⢀⢀⡃⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠗⠌⡆⠡⣛⠠⣉⠐⡇⠀⠢⠌⠠⢈⠀⠄⠀⠌⡀⠀ ⠠⡍⡜⢠⠱⢨⠐⣯⠀⢀⣠⠏⠀⠀⠀⠀⢹⠀⢧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣧⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⡨⢄⠣⢜⠀⠰⠀⣳⠀⠐⣂⠁⢂⠀⠄⠡⠐⠠⠀ ⠡⢎⡹⢠⡓⠢⢌⡇⠀⡾⠋⠀⠀⠀⠀⠀⠈⡆⠘⠀⠀⠀⠀⢸⠟⢛⠻⠿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡟⠀⡏⢿⠀⢿⡆⠀⢀⣾⣿⡄⠀⠀⠀⣿⠇⢒⠡⡘⢨⠀⡑⠐⣸⠀⢁⡐⠈⠄⠂⠄⠁⡈⠐⡀ ⡡⢋⡼⢡⢎⡱⢬⣰⠎⠀⠀⠀⢀⣔⡄⠀⠀⡇⠀⠀⠀⠁⠀⢸⡆⢆⠢⠔⡠⢙⣶⡀⢊⢿⣿⣿⣿⡇⠰⡇⢻⡄⢺⣿⣄⣾⣿⣿⣿⠀⠀⢠⣿⡈⠆⡓⠤⣙⠠⠀⢅⠲⠀⠢⠄⢃⠌⡀⠂⡐⠀⠃⠄ ⣡⢣⢞⡡⢎⣐⡞⠁⠀⠀⠀⠀⠱⡋⠀⠀⠀⡇⠀⠀⡄⠀⡂⢸⠄⢂⡑⢌⡐⢂⠄⢻⡄⢒⢻⣿⣿⡇⢸⣏⠌⣧⠀⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⠀⢞⠀⡒⢨⠀⠄⢠⠢⡁⠰⢈⠂⠒⠀⠁⠄⠘⠄⠂ ⣉⠮⣜⠣⡜⣹⠃⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⢣⠀⠀⡇⠀⢣⢸⡆⢌⠑⡨⢑⠨⡐⣈⠳⣌⠘⢻⣿⡇⢸⡏⠰⢹⡄⠹⣿⣿⣿⣿⡿⠀⢀⡏⣿⠐⣨⠂⠱⣈⠂⠄⢊⢀⠃⡄⢊⡐⢂⠰⢀⠐⣀⠒⠠ ⡰⢋⡖⡱⢬⠇⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⢸⡇⢂⡑⠰⡈⢆⠑⡠⢂⠙⡏⠲⢻⡇⢸⣏⠸⣎⢻⡄⠙⢿⣿⡿⠁⢠⡟⠀⣿⠰⢀⠆⡱⠄⡐⠠⡉⠤⡁⠌⢢⢀⠣⡈⠄⠂⠄⡘⢀ ⠜⡣⢎⡑⠞⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢰⠀⠀⠇⠀⠈⠘⣿⣄⠸⠐⢨⠐⠌⡄⠃⠆⡄⢃⠄⢳⣼⣷⣅⣛⠃⠛⢦⣀⠀⠀⣠⡯⢀⢃⡏⣐⠣⡘⠠⣃⠄⠡⠘⡄⡁⠎⡄⠊⡄⢡⠈⡑⠌⠰⠀ ⢣⡝⢢⡙⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢸⠀⠀⢣⠀⠀⡇⡟⢯⣷⠍⠤⡉⠔⠨⡁⠎⠤⡁⢎⠠⢉⢿⡉⡙⠛⠞⠶⢛⢛⠛⣩⢁⠖⣸⡇⡐⢡⠜⣁⠂⠌⡐⢩⠐⡡⢃⠌⡑⢌⡐⠨⡐⠢⢑⠈ ⢣⠜⡡⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠓⠸⡈⢿⣮⡃⢄⠉⢆⡁⢎⠰⣈⠢⡁⠆⠄⢻⡄⡙⢢⠹⣐⠪⡑⢤⠋⡔⢸⡇⢰⠡⢎⡐⢍⠠⠑⣌⠢⡱⢘⠔⡡⢆⡌⡡⢂⡑⢌⠐ ⠦⡙⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⡄⠀⠀⠠⢇⠀⢻⣿⣮⣂⢂⠐⣂⢁⢂⠒⡌⡘⠤⠘⡗⢌⡡⢓⠌⡣⢍⠢⠇⡘⢼⠃⣌⠚⡤⢊⠜⠤⠙⡄⢣⢅⠫⡰⢁⠎⠤⡁⠆⡐⢨⠀ ⠳⠁⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡷⡀⠀⠀⢙⣆⠀⢘⣿⣿⣾⣷⣄⡈⠄⠃⠔⠨⡀⠥⣿⢂⠧⡫⢌⡑⡊⢜⡃⠜⣸⠁⡌⢒⠡⢃⠚⡀⢃⠌⡡⠎⢒⠡⠚⡜⠰⠑⠢⠑⠦⠈

⣶⣾⣿⢀⡞⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⣿⣿⣿⡾⠀⠀⣾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⠃⢀⣾⡇⢸⣇⠀⠀⠀⠀⠀⠘⣦⣀⣤⣾⣶⠦⢴⣧⣀⠀⠀⠀⠀⠀⠰⡴⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣀⣴⣇⣀⣴⠀⠐⠀⠀ ⣿⣿⡏⠀⣲⡿⠀⢸⣿⡆⠀⠀⠀⢠⠾⢭⡀⠀⠀⠈⢣⡀⠀⢿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⢏⠉⠉⢻⣦⡀⠀⠀ ⣿⣿⠇⢀⣿⠃⠀⠘⠛⠁⠀⠀⣰⠃⠀⠀⠙⢦⠀⠀⠀⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣆⠀⠀⠀⠃⠀⠈⠁⠙⣦⠀ ⣿⣿⠀⢸⡿⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⣇⠀⠀⣦⠀⣰⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧ ⣿⣿⠀⢸⡇⠀⠀⠀⠀⠠⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠛⠀⢸⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⣾⠃⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢰⠇⠀⠀⠀⠀⠈⣷⣠⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⣿ ⣿⡇⢀⣿⠀⡀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⠀⠀⠀⠀⠀⠈⠛⣁⣀⣀⣼⣿ ⣿⣇⡼⠟⠛⠁⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀ ⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠽⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⢀⣿⠃⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡟⣷⠄⠀⣠⣤⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⢛⡿⠿⣿ ⠘⠀⠀⠀⣼⠛⢷⣄⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟⠀⠀⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡾ ⣱⠄⠀⠀⢿⣇⠀⠈⠛⠦⣄⡀⠀⠀⠀⠉⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣧⠀⢸⡁⢀⡧⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡴⠋⢀ ⠁⠀⠀⠀⠈⠋⠻⣦⡀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣄⣀⡀⠀⠀⡟⠀⢹⡀⠈⠛⠉⠀⣀⣠⠴⠚⠉⠀⣀⣤⠞⠉⠀⣠⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⢻⠇⠀⠈⣿⠛⠛⠛⠉⠁⠀⣀⣠⡴⠞⠉⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠉⠛⠲⠶⢤⣤⣤⣀⣀⣸⡄⠀⠀⢸⣄⣠⣤⡶⠾⠛⠉⠁⠀⠀⣀⡴⠊⠁⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣦⠴⠛⠋⠉⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣒⣂⣤⣤⣆⣠⢄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢀⢴⣿⡿⠟⠋⠉⠉⠙⠻⢝⢿⣦⡈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣟⣓⣯⢽⣺⢽⡻⢞⣴⡴⠀⠀⠀⣦⢀⡞⠁⠀⢀⡞⡥⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠄⠀⠈⠀⢀⣀⠀⠀⣀⢄⣠⣮ ⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣮⣿⡭⠚⠡⠀⣸⣻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⣿⣿⣽⣯⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠛⠣⠤⠭⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣀⣠⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⡀⠀⣠⡤⣤⡀⠀⠈⡟⠉⠁⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣿⣅⣽⣿⣟⢟⣛⣷⠀⠊⣁⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣛⠯⣭⠽⠋⠙⠓⠚⣁⣴⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⠚⣩⡿⢋⣩⡟⠀⣀⣀⣠⡤⣶⠟⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⡹⡝⠁⣾⡿⣿⣿⣿⠋⠉⣁⠀⣀⡴⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣷⠀⡞⢁⠞⣡⣿⣿⣿⣏⠛⠛⢋⡴⠛⢻⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠧⠁⠈⢠⣿⢿⣻⣼⠉⠛⢶⠋⠀⣠⠇⢸⣚⡉⠓⠲⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢿⢻⣺⣿⡀⠀⠘⠀⢸⡏⣠⢯⣹⠤⠄⠀⠀⠀⠀⠀⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠔⠳⠀⠀⠀⡼⠈⠣⡜⢻⠦⣤⣖⡿⣟⣳⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⢀⠇⠀⡆⡼⠀⠀⠀⠈⠛⠲⣧⡼⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡜⠀⠘⢀⠇⠀⠀⠀⢀⣴⠞⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⡼⠀⠀⠀⣼⠀⠀⠀⠀⣏⡟⠑⠀⢲⣯⣣⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠉⢦⡀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠟⠀⠀⠀⢠⠇⢀⣀⣀⣀⢿⡉⣶⣶⣾⢸⠟⠀⠀⡀⠀⠀⠀⢀⣠⡇⠀⠀⠈⣧⠀⠀⢦⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⣠⠋⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⢀⣙⣿⣿⠿⠥⠄⢀⡀⠈⠉⠉⠉⢁⡞⠀⠀⠀⠀⠘⣧⠀⠈⢦⠀⠸⣷⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠀⢠⡇⢳⠀⠀⠀⠀⠁⠀⣏⠉⣇⠀⠀⠀⠀⠙⠂⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢣⠀⠙⣧⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⡜⠀⠈⡇⠀⠀⡀⠑⠲⡏⠀⡟⠒⠂⠀⠀⢰⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠃⢀⣸⣆⣀⠀⠀ ⢸⠀⠀⠀⠀⡜⠁⠀⠀⢸⠀⠀⣇⠀⢀⡇⠸⣇⠀⠀⠀⠀⢨⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⣚⡿⠿⢯⠉⣧⠀ ⠈⠧⢄⡤⠞⠀⠀⠀⠀⠈⡇⠀⢸⠀⡸⠛⠒⣇⠉⠁⠀⠀⠈⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣁⣀⣀⡼⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣼⡮⠀⢀⢀⣼⠂⠄⠀⠀⠀⡃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠉⢉⠉⠓⣄⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣇⣠⣧⠾⢿⡀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣷⡤⣤⣾⢶⣴⠏⢀⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠉⠉⠉⠀⠈⠉⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⢉⡿⠉⠉⠛⠛⡿⠃⠁⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠖⢶⠖⢦⡀⠀⢀⣠⠤⠒⠚⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⣠⢤⣄⢤⡄⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⡴⢻⠟⢹⡄⠈⣇⠈⣇⠀⣧⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠁⢰⠇⢰⠃⢠⡗⢲⡦⢄⡀⠀ ⣹⠀⡇⢸⡀⢸⡅⠀⢹⠀⢹⠄⢹⠀⠀⠀⠋⠀⠀⣀⠔⠲⣄⠀⢀⡤⠲⣄⠀⠀⠀⠀⢠⡏⠀⡏⠀⣾⠀⢸⡇⢸⠀⢸⠉⡇ ⢿⠀⢳⠀⣇⠈⣇⠀⣸⠀⠏⠀⣸⠀⠰⣄⠀⠀⠀⠧⣀⠀⠈⠙⠁⠀⣠⠼⠃⠂⠀⠀⠸⡇⠀⢧⠀⣇⠀⢸⠁⢸⠀⣸⠀⡇ ⠘⣇⠈⢧⠘⠆⠈⢻⠏⠀⢠⣴⠇⠀⠀⢠⣤⠀⠀⣀⡼⠧⠄⠘⠣⠽⠧⡄⠀⠐⠇⣀⠀⢿⣶⣄⣆⢹⠖⠃⢰⠃⢠⠇⣸⠃ ⠀⠘⢦⣌⣁⣀⣀⣠⣾⣷⡿⢻⠀⠀⠠⠀⠀⠀⣀⣻⣕⣩⣞⣉⣳⣄⣵⠋⠀⠀⠀⠀⠀⠀⢳⣝⡿⣷⣤⣄⣀⣰⣫⡴⠃⠀ ⠀⠀⠀⠉⠛⠛⠛⠿⣏⡉⠓⣊⣹⣆⠤⠖⠚⠉⠁⠀⠀⢠⡀⠀⠀⠀⠈⠉⠙⠒⠤⣀⠀⢴⣿⣿⣍⠽⠛⠛⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣯⠞⠋⢀⡀⠀⠀⢀⣀⠤⠤⠖⠷⢤⡤⣀⣀⣀⠀⠀⠀⠈⠙⢾⣋⡩⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠡⠀⠀⣀⠤⠒⠉⢁⣀⠠⠤⠀⠐⠛⠳⠤⢤⣈⠉⠑⠺⢵⡆⠀⠙⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⠴⠋⠀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠉⠳⣄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠀⡼⠃⠠⢀⡞⠁⠀⠀⢑⢦⡄⠀⠀⠀⠀⠀⠀⣤⢤⡆⠀⠈⠳⡀⠀⠘⣆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣼⠣⢨⡀⠘⡆⠀⢠⣾⣿⣭⣷⠀⠀⠀⠀⠀⠀⣿⣿⣯⣕⡆⠀⣹⡦⢀⣘⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠠⠁⣄⣹⡀⠘⣿⣿⣿⡽⠀⢴⣒⡶⠄⠀⢿⣿⣿⡯⠃⢠⠇⠁⠐⢢⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣳⡀⠀⠀⠀⠐⠦⣤⠿⣤⡼⠂⠀⠀⠀⢀⣴⠃⣈⣣⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣙⣶⡋⢀⣤⣠⣤⣶⡯⠼⠿⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣏⣿⣿⡟⢭⡧⢭⡷⣞⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢻⡿⣯⣿⣏⡿⠀⠹⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣉⣻⡄⢀⡀⠑⠊⠀⠁⣀⣀⠀⣳⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⡧⠼⢻⡋⠉⠉⠉⠉⠉⠉⠉⣉⣹⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡀⠀⠀⠀⠻⣽⣷⣶⣶⣶⣿⣿⡿⠋⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⠀⠀⣀⣈⣽⣿⡤⢨⣿⣭⣤⠤⢤⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠥⠷⠹⠀⠛⠒⠣⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡿⣯⣿⣦⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣿⡏⠻⣶⣶⠛⣉⣵⠶⣶⢿⣇⣤⣶⡶⠞⠋⠉⠁⠀⠀⣀⣀⣀⣤⣤⣉⠉⠻⠿⠓⠶⢶⣶⠶⠞⣡⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣄⠹⢿⣷⣤⡤⠆⠀⠀⠈⠙⠻⠶⣼⣧⠀⣷⠤⠭⢭⢝⣻⣅⣸⣿⡋⠛⢀⣀⡤⠴⢾⣿⠿⠟⢋⣁⡀⠀⠈⣉⡤⢶⣻⡿⠶⢦⣶⡛⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⣿⣿⣦⣿⣿⣷⣤⣀⣀⣀⣀⠀⠀⠈⢿⡇⢽⣟⠁⠈⠉⣩⡴⠋⠹⣷⡞⠋⢁⡴⠚⠉⣁⣴⠖⠋⠉⢁⣤⠞⣫⡷⠋⠁⢀⣤⠀⠈⠙⢷⣄⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡽⠿⢿⣿⣿⣯⣉⠿⣄⡈⠙⠷⣄⣸⣿⡄⠈⠙⠛⠋⠁⢀⣀⡄⠈⠻⢿⡋⢀⣴⣾⠟⠁⣀⢀⡴⠋⣡⡾⠁⠀⠀⣼⠀⢹⣷⠀⢠⡀⠙⢷⡀⠹⣿⢷⣄⠀⠀⠀⠀⠀⠀ ⣴⠿⠁⠀⠀⠀⠉⢛⣿⣿⣿⣾⣿⣶⣶⠾⡋⠛⣿⣆⠀⠶⠶⠚⠋⠁⠀⠀⠀⣨⣿⡿⠛⢁⣴⠟⣡⠏⢀⡴⠋⠀⠀⢀⣼⡏⠀⢸⣿⣆⢸⡇⠸⣦⢷⡀⢹⣦⠻⣆⠀⠀⠀⢠⣾ ⣿⣿⣶⡦⣤⣄⣴⣿⡿⣷⡙⠻⢿⣿⡿⢋⣵⣣⠾⣿⣿⡶⠶⠛⠁⠀⠀⢀⣴⣿⠏⠀⣠⠟⠁⣸⡷⠞⠋⠁⠀⠀⣴⣿⠟⠀⢠⡿⠘⣿⠀⢧⠀⠘⣆⠳⡄⢻⣧⠹⣧⣠⠶⠿⣄ ⣿⣿⣿⣷⣮⣿⣿⡿⠁⣽⣿⣶⡞⠻⢞⣋⣭⠶⠚⠋⠙⣳⣶⣦⣴⣶⣶⢻⡟⠁⢠⡾⠁⣠⡾⠋⢀⣴⠞⠁⣠⣾⡿⠃⣀⡴⠛⠁⠀⢻⡄⢸⡆⠀⢹⡆⢹⡄⣿⡿⠛⠁⠀⠀⠙ ⣟⠉⠉⠉⣿⣿⣿⠁⣰⣿⣿⣭⣿⡇⠀⠀⠀⠀⣀⡤⣞⡽⠟⢿⣾⣟⣹⠏⢀⡼⠋⢀⡶⢋⡤⠾⣋⣴⣶⠟⣫⣏⡤⠞⠋⠀⠀⠀⠀⠈⣿⡈⣇⠀⠀⢿⡈⣷⠘⣷⠀⠀⠀⠀⠀ ⣿⡇⠀⠸⠿⠿⢿⣶⣿⣿⣿⠀⡟⠷⣤⠤⠖⠛⣩⠖⠋⠀⣰⣿⣿⡟⠁⢀⡾⠁⣰⡿⠞⠋⠀⠶⠛⣩⣴⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⣆⠀⠸⡇⢻⠀⢿⡆⢠⡀⢷⡀ ⡿⣷⠀⠀⠀⣠⡾⢡⡞⢸⣿⡄⠙⠶⠦⠤⠾⠏⠁⣀⡤⠞⣹⣿⠟⠀⢠⡟⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢿⡀⠀⢳⢸⡄⠸⡇⠀⠻⢄⡓ ⣇⣿⠀⠀⣰⠏⣴⠏⠀⣾⢃⢻⣦⡀⠤⠤⠤⠖⠚⠋⢀⡾⣻⠋⠀⢠⡟⣠⠟⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣦⡾⢸⡇⠀⢻⡄⣄⣤⣽ ⣼⠻⠦⣼⠏⣾⠃⠀⢰⡟⡿⣾⠉⠛⠶⠶⢶⣶⠟⠛⡿⣿⠏⠀⢀⡟⣰⠟⠛⠛⢛⣿⣿⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣿⠀⣇⠘⣿⢿⣽⠁ ⠃⠀⣴⠏⡼⠃⠀⠀⢸⡇⣧⢿⡄⠀⣠⠞⠛⠉⠛⣾⣿⠇⠀⠀⣿⣳⠃⠀⣀⣟⣯⣽⠟⠓⢾⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢿⡀⢻⣼⣿⣶ ⠀⣼⠃⣼⠇⠀⠀⠀⢸⣇⢻⡌⢧⣰⠇⢀⡴⠶⣴⢿⠇⠀⠀⣾⣱⣇⣰⣿⣿⣿⣾⣿⣿⣿⣿⣤⣹⣷⣽⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⢹⡇⢸⡇⢸⣿⣿⠿ ⣸⠋⣰⠏⠀⠀⠀⢀⣾⣿⠀⢻⡌⣯⠀⣾⠀⢰⡟⡿⠀⠀⢸⢇⡟⣉⣛⠋⢱⣿⢻⣿⣿⣿⣿⢻⣿⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⡶⣿⠟⣛⣛⣟⡋⠉⠙⢷⠈⡇⢸⡇⠸⣿⠇⠀ ⡏⢠⡟⠀⠀⠀⣠⣿⣿⣿⣧⠀⢳⣾⡀⣿⢸⡟⣼⠁⠀⠀⣿⣼⠁⣉⣿⣆⠘⣿⣦⣉⣉⡿⠏⢘⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⢿⣻⣭⣯⣿⣿⣍⣷⡆⠀⢠⣷⠈⡇⠀⣿⣶⣾ ⢀⣾⠃⠀⠀⣴⣿⣿⡿⠁⢹⣦⡀⠙⣧⠻⣸⢷⡏⠀⠀⢸⣧⡿⠀⠉⢸⠋⠤⣬⣙⣛⣋⣤⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠛⣿⣯⣹⣿⣿⣿⣿⣧⣤⣾⣿⠀⡇⠀⣿⠿⠿ ⢸⣿⠀⠀⣰⢟⣿⣿⠃⢀⣾⣽⣷⣆⠈⢛⡟⣸⠀⠀⠀⡿⢸⠃⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢿⣏⣛⣿⠟⢡⣾⡿⣾⣿⣿⢀⡇⠀⣿⠀⠀ ⣿⡇⠀⢰⡏⣼⣿⠃⠀⣸⣿⠏⣸⣿⣧⣸⣇⡏⠀⠀⢰⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⠷⠤⣭⣭⣤⡴⢮⠁⣾⡏⣿⡏⢸⡇⠀⣿⠀⠀ ⣿⡇⠀⣿⢹⣿⡟⠀⢰⣿⣿⢠⣿⡿⠛⡿⢻⡇⠀⠀⣾⢳⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠈⠁⢀⡾⣿⣇⣿⠃⢸⡇⢀⣿⠀⠀ ⣿⣇⠀⡇⣼⣿⠀⠀⢸⣿⣿⣾⡏⣰⢂⡇⣾⠁⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣵⠟⣿⣿⠀⣿⠀⢸⡏⠀⠀ ⣿⣿⠀⣇⣿⣿⠀⠀⢸⣿⣿⣿⠰⠿⢸⠇⣿⠀⠀⠀⣿⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣞⣋⣉⣉⣉⡉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⢀⣿⡿⢠⡇⠀⣸⠁⠀⠀ ⣹⣿⠀⣿⣿⡟⠀⠀⢸⣿⣿⡟⢧⣤⣾⠀⣿⠀⠀⠀⢿⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⠇⠀⠀⠀⠀⠀⠀⣴⢿⣿⠀⠀⣸⣿⠃⣾⠀⢰⡟⠀⠀⠀ ⣿⣿⣧⣿⣿⣷⠀⠀⢸⣿⣿⣷⠘⣿⣿⠀⣿⠀⠀⠀⢸⣿⡟⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣛⠛⠛⠿⣿⡿⠋⠀⠀⠀⠀⢀⣴⡾⠿⡎⢹⡆⠀⣼⡇⣼⠃⢀⡞⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠀⠀⢸⡏⣿⣿⣧⠸⣿⣇⣿⠀⠀⠀⠘⣿⡇⠘⣷⡎⢻⣦⣄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠚⠋⠀⠀⠀⠀⣠⣴⠟⣿⣠⡼⢧⡟⠀⣠⠏⡼⠃⢀⡾⠁⠀⠀⠀⠀ ⣿⡟⣿⡿⣿⣿⣧⠀⢸⣇⣿⣿⣿⣆⢹⣿⣿⡷⣦⠀⠀⢻⣷⡀⠈⢻⣾⣠⠙⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⠻⠧⣭⡵⠖⠋⠀⣰⢏⡾⠃⢠⡾⠁⠀⠀⠀⠀⠀ ⡟⠀⣿⡇⠹⣿⣿⣦⢸⣿⡘⣿⣿⣿⣷⣿⣿⣇⠹⡄⠀⠈⠻⣷⡀⠀⠹⣿⢄⡇⢸⢉⠟⣦⣤⣀⠀⠀⠀⢀⣠⣤⣾⡟⢻⣿⠋⠀⠀⠀⠀⢀⡼⢫⠟⠁⢠⠟⠀⠀⠀⠀⠀⠀⠀ ⣧⣸⣿⣇⠀⢹⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣦⠻⣦⡀⠀⠙⢿⣄⠀⠙⢿⣇⣇⢸⢠⡇⣾⢹⠛⡿⣿⢿⣿⣟⠉⣇⠀⢻⣄⠀⠀⠀⢀⡞⣱⠟⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠻⣿⣿⣦⣤⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢈⣻⣷⡈⠛⢷⣄⠀⠙⢷⣤⡀⠘⠛⣿⣸⢠⡇⣿⣸⢁⡎⢸⡇⠙⢧⡸⣆⠀⠙⢧⣄⣤⢏⣼⡏⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⣯⡍⣿⣿⡿⠿⢿⣿⣟⣿⠿⠛⢻⣿⣯⠙⠿⣶⣄⡉⠳⣦⣄⠉⠻⣦⡀⠉⠛⢸⣧⡟⣿⢸⣇⣿⣿⣦⡈⢿⣿⡷⢤⣄⣽⢣⣿⡏⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣀⠴⠋ ⠀⠀⠀⠀⠈⠻⣮⡙⢷⣤⡀⠉⠉⠀⠀⠀⠘⢿⣿⣷⣄⠈⠻⣿⣦⡘⣿⣦⠀⠈⢻⡇⠀⠈⢹⣷⡏⣿⢸⣿⣿⣿⣿⣦⡉⠛⠒⣾⣿⣿⣿⠀⠀⠀⢿⣟⠲⠤⠄⠀⠒⠋⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠈⠿⣆⠙⢿⣦⡀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠈⢻⣿⣿⡿⠀⢠⡟⠁⠀⠀⠘⢻⡇⣿⢸⣿⣿⣿⣿⣿⣿⡀⡀⣇⢹⣍⣿⣄⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⣴⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠈⢻⣆⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⣼⣿⣿⠃⢀⡟⠁⠀⠀⠀⠀⠈⠃⠉⢸⣿⣿⣿⣿⣿⣿⣧⢿⡹⣿⣿⣿⣿⣷⣤⣄⠀⠙⢿⡀⢀⡤⠖⠋⠁⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠹⣷⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⠈⡇⣿⣧⢹⡎⠹⣿⣿⡆⠀⣸⡇⠛⠷⣤⡀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⣝⠷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣆⠙⣿⣿⣿⣿⠀⣷⢸⢹⣠⡇⢰⣿⡿⢁⣴⡛⢠⡀⠀⠀⠙⢃⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢸⣿⣷⡈⠹⣎⢿⣶⣿⣼⣸⠏⣰⣿⣿⣷⡟⠁⠙⢶⣽⣷⣦⠀⢸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⢿⣿⣷⡄⠈⢳⣽⡛⢻⣿⣼⣿⣿⣿⣏⠀⠀⠀⠀⢻⣿⣿⣷⣤⡙ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣆⠀⠻⣷⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠹⣿⣯⠻⣷ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠛⠒⠂⠀⠀⢀⣸⡟⢿⣿⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⢿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠉⠙⠚⣿⣿⡄⠀⢻⣿⣿⡽⣿⣿⣿⣿⣿⣿⣦⡀⠀⣹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠙⣿⣧⡈⠻⣿⣿⡃⠀⠙⠻⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⢸⡏⠳⠀⠉⢿⣷⡀⠀⠀⠀⠙⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⢀⣿⡇⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠈⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⢸⣿⣠⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠐⢶⣤⡀⠀⠀⢀⣴⣶⣤⠀⢠⡬⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⣼⣿⣿⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣜ ⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣶⠟⣡⣦⣙⣿⣿⡁⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⣸⣿⣿⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣹⣿⣿⣿⢿⣿⡛⢷⣄⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⣾⣿⣿⣿⣿⣾⣯⣿⡆⢙⣶⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠘⣿⣦⣤⠞⢁⣉⢻⣶ ⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠻⣿⣿⣿⣿⣿⠟⢁⣴⠟⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣀⡼⠛⢻⡿⠿⣻⣿⣽ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡈⠙⠛⠛⢃⣴⠟⠁⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⣾⡉⠀⣴⣾⣷⣾⣿⣬⣿ ⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣯⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠈⠻⢷⣈⢻⣿⣿⣿⣿⠋

⠀⠀⠀⠀⠀⠀⢀⠔⠚⣜⣁⣴⣿⣕⡛⠻⣴⡿⣗⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢊⡄⣆⡾⠽⠟⢛⣿⠓⠛⠛⠒⠻⠼⣿⡏⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡐⣄⠨⠋⢁⣀⠀⢰⣸⣿⣧⣄⡀⣀⡔⠀⠀⠙⠺⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡻⠁⠀⠐⢟⣵⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⠔⠀⠈⢢⠀⠀⠀⠀⠀⠀ ⠀⠀⡔⠀⠀⠀⣰⣿⣿⡿⠹⠘⣿⣿⠹⣿⢿⣿⣿⣿⣄⠀⠀⠀⠡⠀⠀⠀⠀⠀ ⠀⡌⠀⡠⡐⠚⣻⣿⡟⠀⠀⠀⠘⢿⠀⠘⡎⣻⣿⣿⣿⡿⠊⠀⠀⢡⠀⠀⠀⠀ ⠰⠀⠀⣕⣯⣾⣿⣿⠁⠀⠁⠂⠀⠀⠀⠈⠀⠀⠏⣿⣿⣖⣶⠆⠀⠀⡄⠀⠀⠀ ⢸⠀⠀⠉⣹⢿⣿⠏⢠⡞⠛⠄⠀⡀⠀⠘⠉⠑⠀⢹⣿⠻⣿⣿⠆⠀⡇⠀⠀⠀ ⢸⠀⢀⢀⠂⢸⣿⡀⠀⢀⠠⠄⠒⠒⠒⠂⠤⣴⡂⠸⡝⣷⣿⠯⠂⠰⠀⠀⠀⠀ ⠈⢆⢘⡻⣮⣷⡸⡇⠀⢡⡤⣶⡾⣿⡿⠓⣮⡞⠏⠀⢩⡚⢁⣁⡠⡃⠀⠀⠀⠀ ⠀⠀⠡⡹⡷⢽⣿⣷⡀⣴⣱⣕⠃⠈⢁⠲⠚⠹⢧⣡⠥⢫⣭⡦⠃⠈⠢⢀⠀⠀ ⠀⠀⠀⠀⠑⠌⡛⠟⠝⣾⢡⣥⣤⣤⣤⣤⡴⠖⢩⣁⣠⢾⡏⠀⠀⢀⠌⠀⠑⢄ ⠀⠀⠀⠀⠀⠀⠀⠈⡽⣶⣿⠉⠉⠛⢻⣻⢹⡟⣻⡤⠝⠁⠀⠰⠃⠐⠋⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⢄⣠⡗⡄⠃⠀⠀⠀⠈⠛⠘⡧⣺⡤⢼⠂⣲⢰⡿⡆⡜⢃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⡴⠶⠟⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣤⣤⣤⣴⣶⣶⡆ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡄⠀⠀⠀⢰⣾⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⣉⣿⣧ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣤⣤⣶⣶⣶⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⢸⣿⣤⣤⣤⣤⣶⡶⠶⠶⠾⠿⠿⠛⠛⠛⠛⢻⣿ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⠟⣿⣏⣉⣉⣀⣠⣤⣤⣤⣤⣶⣶⠶⠶⠶⠿⠿⢿⣿⣤⣴⣶⣾⣿⡉⠁⠀⠀⠀⢠⣤⡀⠀⠀⣀⣀⣀⣠⣤⣼⣿ ⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠁⠀⣿⣿⠋⠉⠉⠉⠉⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡏⠁⠀⠉⠻⣷⡶⠶⠶⠾⠿⠛⠛⠛⠛⠋⠉⠉⠉⣉⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣄⣠⣤⣤⣴⣿⣿⡷⠶⠶⠾⠿⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠈⢻⣦⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⡿⠟⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠈⣿⣏⠉⠉⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠙⣿⡏⠉⠉⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠛⠛⠛⠿⣿⡇⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣤⣄⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠈⠉⠉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⠀⠀⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⢰⣿⣀⠉⠛⠷⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠟⠋⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⠛⠉⠀⠀⠀⠀⠀⠀⠘⣧⡉⠛⠶⣤⣀⡀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠉⠙⠛⠳⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠶⠟⠛⣻⡿⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠛⠉⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⣷⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣤⡾⠛⠻⠷⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⣾⠋⠀⠀⠀⢿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⠉⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⢹⣏⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠸⣿⡄⠀⣠⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣴⣶⡌⢻⣇⠀⠀⠀⠀⠀⠸⣷⣼⣯⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣴⡟⠁⠀⠀⠘⣿⣀⣀⣀⣀⣤⣶⣿⣿⡟⣷⣼⣿⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠁⠀⣿⡿⠀⠘⠿⠟⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣤⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ 🟩🟩🟩⬜🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟩🟩🟩🟩⬜🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜🟩🟩🟩🟩🟩🟩⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟩🟩🟩🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜ ⬜⬜🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🏽🏽🟨🏽🏽🟨🟨⬜⬜⬜ ⬜⬜⬜⬜🟨🟨🏽🟨🟨🏽🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬜ ⬜⬜⬜⬜🟨🟨🏽🏽🟨🏽🏽🟨🏽🏽🟨🟨 ⬜⬜⬜⬜🟨🟨🏽🟨🟨🏽🟨🟨🏽🟨🟨🟨 ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 ⬜⬜⬜⬜⬜⬜🟨🟨🟨🏽🏽🟨🏽🏽🟨🟨 ⬜⬜⬜⬜⬜⬜⬜🟨🟨🏽🟨🟨🏽🟨🟨⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨⬜⬜⬜

⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜ ⬜⬛🟥🟥⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛🟥🟥⬛⬜ ⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜ ⬛⬛🟥🟥⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬛🟥🟥⬛⬛ ⬛🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛🟥🟥🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛🟥⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜ ⬜⬜⬛🟥🟥⬛🟥🟥🟥🟥⬛🟥⬛🟥🟥🟥🟥⬛🟥🟥⬛⬜⬜ ⬜⬜⬛🟥⬛⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬛🟥⬛⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥⬜⬜⬜⬜⬜⬜🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟧🟥🟥⬜⬜🟥🟥🟧🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟧🟧🟧🟥🟥🟥🟥🟧🟧🟧🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥⬜⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜⬜🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟥🟥🟥🟥🟧🟧🟧🟧🟧🟥🟥🟧🟧🟧🟧🟧🟥🟥🟥🟥🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥🟥🟧🟧🟨🟧🟧🟥🟥🟧🟧🟨🟧🟧🟥🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟧🟥🟥🟧🟨🟩🟨🟧🟥🟥🟧🟨🟩🟨🟧🟥🟥🟧🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟧🟧🟥🟨🟩🟩🟩🟨🟥🟥🟨🟩🟩🟩🟨🟥🟧🟧🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟧🟧🟧🟨🟨🟨🟨🟨🟨🟩🟨🟨🟨🟨🟨🟨🟩🟨🟨🟨🟨🟨🟨🟧🟧🟧🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟥🟥🟧🟧🟨🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟨🟧🟧🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟧🟨🟩🟩🟩🟨🟨🟪🟪🟪🟪🟪🟪🟦🟦🟨🟨🟩🟩🟩🟨🟧🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟨🟩🟩🟩🟨🟪🟪🟪🟪🟪🟪🟪🟪🟦🟦🟨🟩🟩🟩🟨🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜ ⬜⬜🟥🟥🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟦🟦🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟥🟥⬜⬜ ⬜🟥🟥🟧🟧🟧🟧🟧🟨🟩🟨🟨🟨🟪🟪🟪🟪🟪🟪🟪🟦🟦🟪🟪🟦🟦🟦🟨🟨🟨🟩🟨🟧🟧🟧🟧🟧🟥🟥⬜ 🟥🟥🟧🟧🟧🟧🟧🟨🟩🟩🟩🟨🟪🟪🟪🟪🟪🟪🟪🟪🟦🟦🟪🟪🟦🟦🟦🟦🟨🟩🟩🟩🟨🟧🟧🟧🟧🟧🟥🟥 ⬜🟥🟥🟧🟧🟧🟧🟧🟨🟩🟨🟨🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟦🟦🟦🟦🟨🟨🟩🟨🟧🟧🟧🟧🟧🟥🟥⬜ ⬜⬜🟥🟥🟧🟧🟧🟧🟧🟨🟨🟨🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟦🟦🟦🟦🟦🟨🟨🟨🟧🟧🟧🟧🟧🟥🟥⬜⬜ ⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟨🟨🟪🟪🟪🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜ ⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟨🟨🟪🟪🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜ ⬜⬜🟥🟥🟧🟧🟧🟧🟧🟨🟨🟨🟪🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟨🟧🟧🟧🟧🟧🟥🟥⬜⬜ ⬜🟥🟥🟧🟧🟧🟧🟧🟨🟩🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟩🟨🟧🟧🟧🟧🟧🟥🟥⬜ 🟥🟥🟧🟧🟧🟧🟧🟨🟩🟩🟩🟨🟪🟪🟪🟪🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟦🟨🟩🟩🟩🟨🟧🟧🟧🟧🟧🟥🟥 ⬜🟥🟥🟧🟧🟧🟧🟧🟨🟩🟨🟨🟨🟪🟪🟪🟦🟦🟦🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟩🟨🟧🟧🟧🟧🟧🟥🟥⬜ ⬜⬜🟥🟥🟧🟧🟧🟧🟧🟨🟨🟨🟨🟨🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟧🟧🟧🟧🟧🟥🟥⬜⬜ ⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟨🟩🟩🟩🟨🟪🟪🟦🟦🟦🟦🟦🟦🟦🟦🟨🟩🟩🟩🟨🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟧🟨🟩🟩🟩🟨🟨🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟩🟩🟩🟨🟧🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟥🟥🟧🟧🟨🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟨🟧🟧🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟧🟧🟧🟨🟨🟨🟨🟨🟨🟩🟨🟨🟨🟨🟨🟨🟩🟨🟨🟨🟨🟨🟨🟧🟧🟧🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟧🟧🟥🟨🟩🟩🟩🟨🟥🟥🟨🟩🟩🟩🟨🟥🟧🟧🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟧🟥🟥🟧🟨🟩🟨🟧🟥🟥🟧🟨🟩🟨🟧🟥🟥🟧🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥🟥🟧🟧🟨🟧🟧🟥🟥🟧🟧🟨🟧🟧🟥🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟧🟧🟧🟧🟥🟥🟥🟥🟧🟧🟧🟧🟧🟥🟥🟧🟧🟧🟧🟧🟥🟥🟥🟥🟧🟧🟧🟧🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥⬜⬜🟥🟥🟧🟧🟧🟧🟧🟥🟥🟧🟧🟧🟧🟧🟥🟥⬜⬜🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟧🟧🟧🟥🟥🟥🟥🟧🟧🟧🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟧🟥🟥⬜⬜🟥🟥🟧🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥⬜⬜⬜⬜⬜⬜🟥⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⣠⠞⢠⠖⠉⠉⠉⢭⣭⣀⡉⣍⠉⠉⠒⠭⣑⠤⡀⠀⠀⠀⠀ ⠀⠀⡞⠁⡰⠳⢦⣼⣿⡿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠈⠓⣌⢢⡀⠀⠀ ⠀⣸⠁⣰⣵⣾⣿⣿⡿⠹⣿⣿⢿⣟⣿⣿⣿⣿⣿⣦⡀⠈⢣⠱⡀⠀ ⠀⢯⢠⣿⠟⣿⣿⣿⡇⠀⣿⠛⣷⢙⣻⢌⣻⠟⣿⣿⣿⣆⠀⢧⢳⠀ ⠀⠘⡞⢡⣼⣿⣿⣯⣧⠀⠘⠆⢨⠋⢠⡤⢘⣆⢻⣿⣿⣿⠇⢸⠀⡇ ⠀⠀⢱⡼⢟⣿⣿⣿⠋⢑⣄⠀⠈⠢⠤⠔⣺⣏⠀⣿⣿⡏⠀⡼⠀⡇ ⠀⠀⠁⠘⢺⣿⣿⣿⣦⣈⣽⠀⠀⢀⡤⠊⢡⣾⠀⠸⣿⢃⡴⠁⡜⠁ ⠀⠀⠀⠀⠀⠻⠙⠟⣿⡀⢨⠭⠊⡡⠔⠀⢠⠃⡜⣿⡋⣁⡠⠊⠀⠀ ⠀⠀⠀⠀⡰⠉⢓⠀⠈⠳⢌⡳⢄⣀⠤⠒⢁⠞⡼⠙⡄⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⣣⣄⢸⠀⠀⠀⠀⠉⠑⠒⠤⢲⣥⠼⣤⣤⣱⡀⠀⠀⠀⠀ ⣠⠊⠁⠀⠀⠈⣞⣆⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠙⢿⣿⣧⡀⠀⠀ ⠄⠈⠉⠉⠙⢦⢻⠚⣄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠄⢌⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢀⠨⠐⢈⠊⢄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠁⠀⠃⠀⢀⣠⣤⣶⣶⣶⣶⣾⣾⡼⠃⢱⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠁⡄⢠⣰⣼⣿⠿⠿⠛⠉⠁⠀⠀⣀⣤⠊⢐⣠⣈⠁⠊⠈⠢⡀⠀⠀⠀⠀ ⠀⢸⠀⠐⣼⢟⡩⢄⣈⠥⠛⠳⣶⣾⣿⣿⣶⣿⡷⠪⠀⠁⡀⠀⠀⠏⢢⠀⠀⠀ ⠀⠘⡤⠊⠀⣡⣶⣿⡏⠀⠀⠀⠹⣿⢻⣿⣿⣿⣿⣦⡠⣊⠳⣀⢀⠀⡐⡇⠀⠀ ⡠⡪⣤⣶⣿⣿⡿⣿⠀⠀⠀⠀⠀⠹⠀⡹⡟⣿⣿⣿⡍⢛⠆⡏⣧⢀⠉⠇⠀⠀ ⠊⣴⡿⢹⣿⣿⡇⢺⠤⠄⡀⠀⠀⠐⢁⣤⣽⠸⡿⣿⣏⢛⠆⣇⠿⠮⠎⡀⠀⠀ ⡞⣳⢡⣿⣿⡏⡇⡤⠴⢤⠀⢱⠀⠀⠋⠶⣫⡴⠃⣯⣙⡞⠊⠀⠀⠀⠀⠈⠐⠀ ⠟⡿⠰⢡⣩⣇⢠⢄⣀⠀⠀⠨⠤⠔⠒⠉⠀⣀⠀⣗⣽⡇⠃⢀⠀⠤⠀⠀⢰⠀ ⡘⢄⡺⡄⢇⢿⡈⣗⢀⠀⣀⠠⠄⠐⠒⠒⠚⡾⣰⠋⠟⣶⣯⠀⠀⠀⠀⠀⠀⣢ ⠒⠭⠆⢈⣀⡑⣳⡘⢗⠋⠀⠀⠀⠀⢀⡀⢔⡵⠉⠒⠈⣎⣃⣄⡀⠠⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⢰⣿⣶⠭⠔⣒⣚⡫⣭⣶⠏⠠⠀⠙⣰⣿⡼⣁⠀⢀⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠄⡑⠯⠿⣿⡯⠐⢁⠠⣵⣿⣿⣿⡿⠋⠀⠀⢀⡠⠁ ⠀⠀⠀⠀⠀⠀⠀⢻⡟⠙⡇⠀⠈⠐⢨⠑⠋⠀⠀⡘⣿⣿⣿⣿⣿⣱⣾⣿⣷⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⢦⣀⠀⠸⠀⠀⢀⢼⠁⠹⣿⣿⣿⣿⣿⠿⠿⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠹⠆⠙⠇⠂⠁⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⢀⣠⣴⡿⠋⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢀⡴⢚⣽⢋⡤⢾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠇⣠⠏⢠⣿⠞⢉⡖⣃⣀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣼⠃⠀⠾⠣⠴⠿⠋⠉⠁⠀⠀⢠⣤⣤⣴⠿⠿⠿⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⢤⣀⣀⠀⠀⢸⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠶⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⣌⡉⠉⠑⠛⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠿⠛⠀⠀⠀⢰⢂⡞⠋⢷⠹⣦⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣮⢽⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⡄⠀⠀⢀⠆⢀⡇⡼⠁⠀⠈⢷⢿⢧⡀⢀⣹⡻⡄⠀⠀⠀⠀⠀⠀⠀⣦⣈⠳⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⡟⠃⠀⠀⣼⠀⣼⢷⠇⠀⠀⠀⠈⢿⣏⠳⡌⢧⣷⠙⣆⠈⢧⠀⠀⠀⠀⢨⡻⣏⠛⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⢻⠏⣠⡆⠀⠀⣿⢀⢿⡞⠀⠀⠀⠀⠀⠈⣿⡄⢻⡼⣯⣦⠘⡆⢸⡆⢠⠀⠀⠈⢳⣮⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⣴⣟⣾⠏⠀⠀⢸⣿⣸⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⢰⣿⡿⣜⣆⢹⡬⣷⠸⡇⠀⠀⠀⠹⣎⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⢀⠀⠀⢸⣿⣿⠸⣇⠀⠀⠀⠳⡄⠀⠀⢸⡏⠀⢿⣿⢿⣆⣧⣿⣼⡇⠀⠀⢿⣦⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣿⣥⠴⢾⠃⠀⢸⣹⣿⣴⠿⢲⡦⣤⣀⠻⡄⣰⡿⢳⣀⣨⣿⠾⢿⣿⣿⣿⡇⠀⠀⡘⣧⠈⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣠⡀⢸⣏⣿⠃⠀⢾⣷⡦⢹⠛⠻⠒⠛⢻⡏⠀⣼⣶⠀⢸⣿⣿⡇⠀⠀⢿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⡻⣦⡀⠈⣹⣁⡼⠀⢀⠀⠀⠘⢧⡀⠈⠁⢀⣼⠟⢸⣿⣒⣾⣦⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⢫⣿⣿⡀⠃⠉⠙⠛⠁⠀⠀⢸⠀⠀⠀⠸⢽⣿⣿⡿⠖⠀⣿⢿⠁⣼⠇⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠧⠖⠀⠀⠀⢀⡀⠀⠀⣸⡿⢿⣨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣙⣧⠀⠀⠰⠦⠤⠴⠶⠶⠒⠒⠒⠋⠉⠁⠀⣰⣏⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⣄⡀⠀⠀⠀⠲⠶⠒⠂⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⡾⣿⡗⠦⣄⡀⠀⠀⣀⡤⠖⢻⣯⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣤⣾⠃⢸⡟⢣⡇⡄⠀⠉⠛⠋⠁⠀⠀⢸⠉⠻⣇⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠉⡉⠀⠀⢻⠀⢸⠀⠜⠀⢿⠀⠀⠀⠀⠀⠀⣧⠘⣆⣀⣿⣤⣤⣧⣙⣓⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠯⠴⣿⠀⠀⡇⠀⠀⢸⠀⢸⡄⠀⠀⠈⢧⠀⢀⣠⠴⠖⠛⠉⢻⠀⠀⣀⡄⠀⠀⠀⠉⠛⠓⢺⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠙⠉⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⡀⠘⡷⠤⣄⣀⡬⠖⠻⣄⡀⠀⠀⠀⠈⣿⠘⡅⡇⠀⠀⠀⠀⠀⢰⢏⡴⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠈⡇⠀⢱⣀⡴⠋⠻⢦⡀⠈⢳⡄⠀⠀⠀⠹⡇⠷⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣷⢀⡼⠋⠀⠀⠀⠈⢟⠦⠀⠙⠆⢀⣠⣤⠤⠤⠤⠤⣤⣀⠀⠐⠋⠀⠀⠀⢀⡴⢊⣵⡟⢆⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠸⠃⠀⠀⢙⡞⠀⠀⠀⠀⠀⠀⠀⠑⣦⡴⠛⠉⠀⠀⠀⠀⠀⣀⠀⠀⠉⠓⢦⡀⠀⠒⠉⢀⠜⣫⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⢛⣿⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⣠⡜⠃⠀⠠⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠙⢷⣤⣠⡴⠋⠁⠀⠀⠀⢻⡀⠀ ⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣼⡟⠀⡟⠀⠀⠀⠀⠀⡿⠤⠞⠲⢤⣄⣀⠀⣴⠋⠀⠀⠀⠀⠙⢦⡀⠀⠀⡀⡃⠀⠀⠀⠀⢠⡼⠋⠹⣷⡀⠀⠀⠀⠀⠀⠀⢷⠀ ⠀⠀⠀⢀⣷⠀⠀⠀⢀⡴⠋⠰⣷⠇⠀⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⣹⢧⣀⢠⡶⣶⡄⠀⠀⠑⠀⠀⠏⠀⠀⠀⠀⠀⠀⢀⣀⠀⠹⡽⡄⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⣼⠟⠀⠀⠀⠚⠁⠀⠀⣿⠀⢰⠇⠀⠀⢺⠤⣀⠀⠀⠀⠀⣰⠏⠀⣨⢿⠿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⢿⢇⠀⠀⠀⠀⠀⢀⣧ ⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡏⠀⠀⠀⢸⠀⠙⠓⠒⠒⠂⣼⣄⣸⠁⠀⠀⡟⠀⠀⠀⠀⠀⣀⣀⡤⠴⠶⠒⠒⠒⠒⠒⠶⠤⣼⣾⡀⠠⠴⠖⠉⠉⡏ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣼⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢹⠀⢩⠇⠀⠠⠧⠤⠤⠖⠚⠋⠉⠀⠠⣄⠀⠀⢀⣀⣤⣤⣀⣀⣷⣼⡇⠀⠀⠀⠀⠀⡇ ⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠇⠀⠀⠀⠀⠈⡇⠀⣀⣀⣠⣤⠌⣧⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠛⠉⠀⠀⠀⠀⠀⣿⡽⠀⠀⠀⠀⠀⠀⡇ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣇⠘⠛⠛⠉⠀⢷⠒⠀⠛⠛⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣩⠄⢨⡉⠙⠓⠲⢤⣤⣀⡼⢻⠃⠀⠀⠀⠀⠀⢠⡇ ⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣻⡄⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠖⠚⠉⠁⢀⡀⠰⣇⣀⣀⣀⠀⣰⠈⢙⡏⠀⠬⢗⣲⣶⢤⡾⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠈⣧⡤⠶⠒⠋⠁⠻⣦⡀⠀⠀⠀⠴⠒⠒⠉⠉⠉⠀⠀⠿⢤⣉⣉⣩⣟⡽⠋⠀⠀⣀⡀⢀⢉⡿⠁⠀

⣿⡻⣦⡀⠀⠢⠄⣏⢛⡻⣶⣟⡶⢎⡉⣤⠴⢖⠒⢊⣩⡧⢂⡵⢎⡀⠀⠀⠀⠀ ⢉⡻⢿⣿⣲⣔⠠⣸⡞⠓⠒⢀⠘⢧⣊⡵⢊⣡⢔⠕⢁⠔⡆⠈⢢⠱⣦⠀⠀⠀ ⣯⡤⣤⣼⣟⢿⣿⣣⣽⣮⠍⠀⢀⡼⢋⠜⡱⠑⠁⣠⠞⣰⢻⢰⠐⡥⣱⣱⡤⢎ ⡟⢛⣿⣇⣿⢿⡌⢉⡠⡼⢻⣽⠟⡰⢡⡮⢐⡭⣾⡯⠊⠁⠀⡇⡆⢡⢋⢇⠀⠀ ⣷⠀⡨⡻⢹⡜⠪⢴⣊⢔⣿⠋⡜⡔⠁⠀⠀⠈⠁⠀⠀⠀⠀⠘⢶⡈⣿⢸⠐⠴ ⠞⡶⡝⠀⣟⡎⠒⡶⢖⣾⠃⣸⠜⢛⣿⣳⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠀⢿⣍ ⡰⡹⠀⢀⡟⠶⡎⡔⣺⠇⢰⡯⠶⣿⣿⣿⣿⠿⠁⠀⠀⣀⣠⣤⡤⠤⣸⢸⢸⡟ ⢳⠃⢠⣾⠿⡜⢇⣿⡏⠀⣾⠉⠣⣹⠾⣛⠬⠀⠀⠀⢰⡷⣿⣿⣿⣇⣸⢸⢸⣶ ⡟⢠⣿⡏⣸⣿⣆⣭⠃⢸⡍⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⡷⢝⣛⡕⢻⣿⢸⢸⠀ ⣇⢘⡿⠀⣿⡼⣩⣿⠀⠈⡇⠀⠀⠀⠀⢀⣀⣀⡀⠐⠉⠀⠀⠀⣰⡿⡾⡘⢸⠀ ⣿⣸⡇⠀⣿⣯⣽⢹⠀⢸⡧⡀⠀⠀⠈⢿⣶⣶⣬⡵⠀⠀⢀⣴⡏⢰⢇⠇⡆⠀ ⣿⣿⣧⠀⣿⣧⢻⣾⠀⢸⡏⢮⡦⣀⠀⠀⠙⠒⠛⠁⢀⣴⠯⣽⠇⣼⠎⡜⠀⠀ ⣇⡏⢿⣆⣟⣿⣿⣿⡶⡀⠳⡄⢻⣌⣷⣢⣄⣀⣠⣴⠻⡊⠉⢀⢬⢃⠌⠀⠀⠀ ⠙⢿⡼⣿⣿⣿⣿⣿⡵⣌⠢⣙⠢⡌⠻⢿⣤⠻⣎⠣⣧⡑⣤⣲⠃⡌⠀⠀⠀⠀ ⠀⠀⠙⢟⢦⡉⠀⠈⢻⣎⠙⢮⣷⢈⠇⠈⣿⣿⣿⣷⣌⢺⢿⣇⠀⢷⡂⠐⠈⣀ ⠀⠀⠀⠈⢳⡘⢆⠀⠀⠙⢧⣾⡇⡌⠀⠀⠈⠀⣿⣿⣿⣯⣿⢟⢷⡄⢱⠠⡊⢱ ⠀⠀⠀⠀⠘⡇⠈⢳⡄⠀⠘⢿⣿⣮⣷⣤⡀⠀⢷⡝⠿⣽⣿⢎⣾⡷⠫⣦⡀⢘ ⠀⠀⠀⠀⠀⡇⠀⠀⠹⡄⠀⠀⠙⣿⣿⣿⣿⠆⠘⣿⡎⢻⣿⣿⣿⣦⣀⡘⢿⣦ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠈⢻⣯⠉⠁⠐⠛⢿⡄⢻⡿⢿⣿⣿⣁⣸⣿ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠘⢆⠀⠀⠀⠹⣧⡀⠀⠀⢸⠟⠀⢹⠊⠻⡄⠈⠻⣿ ⠀⠀⠀⠀⡆⠀⠀⡀⠀⠀⡀⠈⢇⠀⠀⠀⠘⣷⡀⠀⣾⡇⠀⢸⠀⠀⠘⠢⣄⣸ ⠀⠀⠀⡸⠀⠀⠀⠙⡲⣮⣭⡿⡉⢇⠀⠀⠀⠈⢷⣼⡟⠀⠀⣸⠀⠀⠀⠀⠀⠙ ⠀⠀⢰⠃⠀⠀⢠⣎⢻⣿⣿⡿⡸⠊⢆⠀⠀⠀⠈⡿⠁⠀⢀⠇⠀⠀⣰⢶⣭⣷ ⠀⢠⠇⠀⠀⠀⠀⠈⠓⣍⡩⠊⠀⠀⠈⢆⠀⠀⢰⠃⠀⢀⡌⠀⠀⠸⢔⢾⣾⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⢔⡎⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡀⠀⠀⢸⡧⠁⠫⠞⠒⠉⠭⢵⡶⠤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠡⣒⠃⠁⣀⡤⡀⠀⡀⠀⠀⠈⢰⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⡪⠀⡀⣈⠃⠈⢿⡄⣗⠄⢄⠀⠀⢥⢯⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠼⣹⡔⠀⡇⡿⠀⠀⠘⣌⣾⣎⣜⣠⠀⠱⡷⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⡏⠤⠀⣿⡱⠄⡐⡄⣼⣘⡿⣾⣿⠀⣱⠳⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢷⣶⡿⣄⣛⡸⢉⠉⢅⣛⡸⢿⣤⣽⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢏⢷⡀⠀⠀⠸⣄⣈⡉⠁⡾⡱⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⣄⡉⠐⠒⠀⣠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠤⠤⢰⢡⢻⢀⠁⠈⢀⠏⢫⣲⠤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠴⠊⠛⠀⠁⠀⠘⣀⣘⠤⡐⠈⠙⡄⠀⠀⠈⠹⡓⢤⠀⠀⠀⠀ ⠀⠰⠁⠀⠀⠀⡄⠀⠀⡄⠗⠉⠱⠌⠂⢀⡉⠁⣀⠀⠊⠀⡠⣱⢄⠀⠀ ⠀⡆⠀⠀⢀⠴⠃⠀⢀⠎⠀⠀⢀⠜⠉⡀⠀⢀⠀⠈⠑⣌⡠⠃⠈⢂⠀ ⠀⢰⠀⢀⠜⢼⢀⠀⡘⠁⠈⢒⠦⣠⣄⠈⠂⠘⠀⠀⡈⠈⢳⠀⠀⠈⡄ ⢀⠃⠀⠀⠀⡆⠌⠀⠈⠓⠒⢸⢴⠉⡇⢀⡀⠄⠐⠚⠒⠒⢼⡆⠀⠂⡇ ⡌⠀⠀⠀⠀⢿⠀⠠⢰⠠⠤⠘⠆⠀⠀⠀⠀⠀⢱⠌⣉⡉⣹⠃⠀⠀⡇ ⠀⠀⠀⠀⢸⠀⡆⠀⠀⢂⡀⠤⢀⠀⠀⠀⠬⠄⠸⣀⢤⣯⠏⠈⠒⡖⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣒⣖⣀⣀⣆⡒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠀⠉⠁⠀⠀⠀⠀⡈⠉⠐⠓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣒⡅⠀⠀⠀⢀⣠⣤⣶⣶⣋⡀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⠚⡫⣠⢢⣤⣾⠟⢹⠈⢿⣿⠻⣿⣶⣄⡐⣄⢀⣶⢊⢢⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠠⠱⢡⣿⢿⠋⠀⠘⠀⠀⠻⣆⣘⣿⣿⣿⠻⣯⠉⠀⠀⠱⠀⠀ ⠀⠀⡰⣱⣴⣆⣤⣤⣿⡏⠊⠀⠈⠀⢀⠀⠀⠉⣀⣈⠸⣿⣦⢾⣿⡶⡀⠀⡇⠀ ⠀⠀⣷⣽⣿⢿⠓⠁⢸⠁⠴⠉⠙⠀⠰⣆⠀⠈⣁⢉⣀⢻⠂⠈⢾⢿⣇⡆⠃⠀ ⠀⠀⠇⣿⣿⢿⠀⠀⠈⡞⣃⠤⠐⠒⠂⣀⣀⠀⠒⠲⠌⢻⡀⠀⡘⣺⣿⣷⠃⠀ ⠀⠀⠸⣿⡿⡢⡆⠀⠀⢱⠰⣠⡴⠿⠋⠛⠋⠛⢿⣶⠃⡧⠖⠋⡝⠭⠫⠊⠀⠀ ⠀⠀⠀⠈⠦⡀⠵⡄⢂⣨⢧⡈⠳⠌⣉⣉⣉⠉⢖⡔⠰⠆⠀⢠⢧⢻⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡹⠦⠗⠶⠾⣟⡗⢶⡤⢤⣤⣶⣿⣇⡤⠔⠈⠂⠍⢢⡇⡡⠀⠀ ⠀⠀⠀⢀⠔⠓⠒⠂⠀⠀⠀⠀⠑⠄⡁⠺⡯⡻⠋⠀⠀⠀⠀⠀⠘⠉⠙⢢⠀⠀ ⠀⠀⡔⠁⠀⠀⠀⣀⣀⣀⡀⡀⢤⣠⠘⠈⠀⢠⡴⠋⢀⣠⡤⢀⠀⠀⠀⠀⡇⠀ ⠀⠀⢇⣮⣶⣾⣿⣿⣿⣿⣿⣿⣟⠁⠀⠛⢀⣠⣶⣷⣿⣷⣿⣷⣿⣦⣽⣾⠇⠀ ⠀⢀⣾⣿⣿⠛⠋⠉⠉⠉⠛⠛⠿⣿⠷⠿⢿⠟⠛⠛⠛⠛⠛⠛⠿⢻⣿⣿⣷⡀ ⠀⡼⠟⠋⠉⢂⢠⡄⠀⠀⠀⠀⡀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢡⠋⠀⠈⠉⢣ ⢘⣠⣤⣤⣄⠈⣾⣷⡶⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣄⣀⣠⣤ ⣿⣿⣿⣿⣿⣷⣽⡿⠁⠀⠀⢠⣿⣿⣿⣿⡟⠛⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿ ⣿⠿⠿⠟⢿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⣷⣿⣟⣿⣿⠿⠿⡛⠻⢿

⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⢰⠶⣤⡀⠀⠀⠀⠀⠀⠈⠉⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢀⡆⣾⠀⠹⣧⠘⣆⠀⢤⡄⠀⠀⢄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⠀⠀⠀⢀⡾⢸⢸⠀⠀⢻⣧⡋⢆⠈⢿⡖⡀⠈⢣⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡘⠀⠀⠀⠀⡞⢱⡟⠈⡆⠀⠀⣿⣿⡌⢆⠘⣷⠱⠀⠀⢣⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠁⠀⣼⠁⢸⠁⢸⡇⠀⢧⠀⠀⢸⡉⢷⡈⣆⢸⡆⢇⠀⠀⢃⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡞⠀⢐⡇⠀⡏⠀⢸⡇⠀⠈⡀⠀⠘⠇⠈⢷⠘⡄⢷⢸⠀⠀⢸⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⣼⡇⢰⠁⠀⢸⡇⠀⠀⠉⠀⠀⠀⠀⠀⢳⣸⡆⢸⡆⠀⠈⢷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⡿⡇⠸⠠⠒⠛⢟⠑⠲⠄⠀⠀⠀⠔⠋⠁⠀⠉⣽⣇⠀⠀⠸⡄⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⣧⢸⣷⣇⣀⢀⣤⣶⣾⣶⡄⠀⠀⠀⠀⢠⣴⣾⣿⣿⢿⣿⠀⢰⢰⡇⣇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⣸⡁⣿⡟⠘⢱⡛⣿⣷⠁⠀⢀⠀⠀⠀⠁⣿⣽⣿⡇⠉⠀⡎⢸⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣻⣷⢿⡀⠀⠘⢿⡿⠟⠀⠀⡸⠀⠀⠀⢀⡙⠻⢛⡁⢠⢠⢃⣿⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡇⠀⠙⠒⠒⠈⠀⠀⠳⠄⠀⠀⠀⠈⠉⠁⠀⣼⢃⣾⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡽⡿⡀⠀⡤⠄⠒⠒⠉⠉⠉⣉⣉⣉⣉⣉⣩⣿⠏⣾⠿⡇⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡳⠿⣷⡀⠱⣶⠒⠉⠉⠉⠉⠀⠀⠀⠀⢙⠏⡇⢸⠛⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠵⣄⠈⠓⠤⣀⣀⣀⣀⣀⡤⠖⠁⣠⡅⡟⢹⡇⠀⠀⠀⣀⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢯⠀⣿⠏⢲⣤⣀⣉⣛⣋⣀⣤⣴⡞⢹⣷⢸⡹⣿⠄⢠⠞⠁⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣴⡟⢀⡬⠀⣿⣿⣿⣿⡿⣿⠸⣿⡀⣿⠏⠙⠋⠀⠘⣄⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⢊⠉⠉⠉⠲⡈⠓⠛⠛⠛⡏⠉⠛⠿⠗⠋⡗⠋⠉⠁⠀⠀⠀⢀⣀⣧⣀⡀⠀⠀⡺⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⡇⠀⠈⠑⠤⡀⢣⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣠⣿⡏⠁⠀⠀⠈⠉⠙⠫⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠻⣄⠀⣀⡠⢴⡿⠛⠣⢤⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀ ⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣼⡇⠀⠀⠀⠈⠑⢦⠀⠀⠰⠚⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠑⠢⢄ ⠤⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡖⠦⠀⣠⡾⢿⣦⣀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⣠⣴⠾⢿⣷⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⢀⠔⢋⠇⠀⠸⣤⣾⣯⡄⠀⣈⣽⣿⣷⣶⣤⣤⣼⣤⣤⣴⣶⣾⣿⣿⣷⠄⠀⠙⢿⣾⡛⠙⠲⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠔⢁⠴⠃⠀⠀⣰⣿⣿⣿⡇⠐⣿⣿⣿⣿⡇⠀⣴⣾⣧⡀⠀⠸⣿⣿⣿⢟⣠⣤⣶⣄⠹⡗⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀

⠀⠀⠀⡠⠊⠀⠀⢀⠔⠉⠀⣀⠒⣆⢄⢀⠀⠈⠁⠢⡀⠀⠀⠀⠐⢄⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⡠⡁⠀⠀⡴⡉⡄⠸⣞⢂⢹⣢⠈⠄⠈⢆⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⠰⢡⠁⡄⠰⢸⡇⠃⠀⢛⢧⢂⢧⠃⠈⡄⠀⠆⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⡇⡎⢠⠇⡆⢸⡇⠸⠄⠘⠈⢎⢜⢰⠀⢰⠀⢰⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⢰⡆⡇⣨⡄⠠⠒⡗⠢⠀⠀⠔⢈⣉⣸⡄⠀⡆⢈⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠁⢇⢳⡟⣷⠰⡿⣿⡃⠀⠀⠘⢹⣿⡟⠃⡆⡇⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠺⣷⣡⠠⠝⠛⠄⢸⠀⠀⠨⠭⠁⡶⣸⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡃⣽⡄⢠⠐⣒⣀⡀⠀⠀⣀⡶⣑⢻⡹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⣄⠣⢀⡀⠀⢀⠠⢊⡇⢵⡋⠀⢀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣸⠉⠶⣤⣭⣴⣶⡇⣧⠟⠗⢐⠁⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⠤⢂⡀⠫⠑⠚⢒⠋⠛⠟⢓⠋⠈⢀⣀⠰⠅⣀⣀⠇⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⠣⠀⢈⣠⠧⠖⡂⠀⠀⠀⠈⡐⠖⢻⡇⠀⠀⠀⠉⠢⢀⠀⠀ ⠔⠈⠀⢀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠐⠀⠐⢁⠀⠀⠀⡇⠀⠀⠚⠀⠀⠀⠁⠂ ⠀⠀⠀⠀⢀⡤⢖⢄⡴⠷⣄⣀⠀⠀⠠⠀⠀⢀⣠⠴⢷⣄⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⡀⢔⡕⠀⢸⣾⣿⢠⣾⣿⡟⢛⣿⡛⠻⣿⣿⢇⣠⡙⠧⠀⠁⠂⢄⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⢒⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠌⠌⠎⠆⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⡠⢀⡿⡘⣸⡀⠘⡈⠺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠡⠋⠀⣥⡏⠻⠿⣧⡀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⣦⣖⣀⣃⡀⠀⢘⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣮⡈⠀⡆⠈⣠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠃⠀⠀⠀⠀⡟⠉⡆⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⠂⠜⠀⢠⢡⡐⢠⠀⠐⠈⢀⣆⡕⠄⣀⢃⡀⠈⠁⢢⡀⠀⠀ ⠀⠀⠀⢰⡜⣠⠒⠈⠝⠉⠀⡏⠳⣼⣀⣆⡴⠋⡸⠀⠀⠈⡆⠈⢓⠤⢄⣹⠀⠀ ⠀⠀⠀⢶⠋⠇⠀⡜⠀⠀⠀⡇⠀⢸⡿⠁⡠⢢⠃⠀⠀⠀⢇⠀⢸⠀⠀⠛⢄⠀ ⠀⠀⡠⡏⠀⡖⢲⠁⠀⠀⠀⡇⠀⢸⡇⠀⢀⠎⠀⠀⠀⠀⠈⣍⢉⠀⠀⡇⠘⡄ ⠀⠰⢁⠃⠰⡙⡜⠀⠀⠀⠀⢸⠀⣾⡇⢀⠎⠀⠀⠀⠀⠀⠀⡖⠚⠀⠀⠙⡄⢱ ⢀⠃⠸⠀⢸⠉⠇⠀⠀⠀⠀⠘⣴⣿⣧⠊⠀⠀⠀⠀⠀⠀⠀⠟⢻⠛⠻⠇⢗⠒

⣿⠀⠀⠀⠀⠀⢀⠠⠒⢙⠉⠑⠋⢽⠿⢒⠖⠿⠎⣻⡿⠟⠷⣾⣯⢻⡸⡍⣴⣿ ⠘⢄⠀⠀⠀⡐⢡⠀⠡⣈⠪⡑⠠⡀⠈⠪⡀⠺⠚⠋⣼⢤⣭⡭⠻⣾⣿⡞⢹⠜ ⠀⠈⡄⢀⣼⢡⢀⢖⡄⠐⢕⣬⣒⠝⣳⣦⠈⢢⡤⣊⣉⣈⠠⠂⡻⢹⣾⡗⠁⠀ ⠀⠀⡇⡞⡆⣼⠸⠈⠪⣷⡤⢈⣙⠯⠁⢚⢶⡀⢫⡲⢄⢤⢊⡲⣀⡇⡟⠀⠀⠀ ⠀⢰⡾⢲⠀⡟⡆⠀⠀⠀⠉⠀⠀⢠⣎⣤⣀⣻⡄⢻⣖⡀⣆⠀⠑⢰⠃⠀⠀⠀ ⢀⣼⣋⣼⠀⡿⠁⠀⠀⠀⠀⣀⡴⢯⢿⣯⣻⢹⢿⡀⠞⢺⢫⠁⣤⣿⠀⠀⠀⠀ ⣏⣃⣛⣸⠀⡇⠀⣀⣠⢄⠀⠀⠀⠙⠜⠻⠮⠃⠀⠧⠘⠈⠥⣖⣼⣽⡀⠀⠀⠀ ⠈⢶⠾⢿⡆⢿⣹⣿⣿⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠃⡟⣻⣋⡿⡁⠀⠀⠀ ⠀⠈⣶⠟⢲⢸⣿⡬⠿⠋⠠⢀⠄⢀⣀⣀⠀⠀⠀⠀⣇⢸⣷⣑⣯⠳⣿⠀⠀⠀ ⠀⠀⠃⠀⠀⠆⢾⣦⡀⠀⠀⠀⡊⣡⣴⣾⢧⠀⠀⠀⣹⢸⣿⣿⣆⢠⡈⡆⠀⠀ ⠀⠀⢀⡀⠀⠘⡘⣯⡓⢄⠀⠀⠘⣿⠩⠐⡸⠀⢀⣼⣿⢸⣿⣯⢻⣼⣷⣽⣦⣄ ⠀⠀⠐⠆⠀⣀⣱⡙⢷⣊⡕⠤⣀⠈⠂⠁⣀⣴⣿⣿⡏⡼⠟⠁⠀⢿⣿⡿⠋⡿ ⠀⠀⡎⢀⠎⠁⠉⠉⣿⠉⡇⢠⠇⣿⢹⣿⣿⡉⠀⢹⠀⢇⠀⠀⣴⠞⠉⠀⡜⢠ ⠀⡰⢠⠋⢀⠾⡘⠺⣿⣾⢺⣿⣠⣿⡼⡿⠃⡇⠀⠘⢄⣸⣦⡾⠁⠀⡠⡞⠀⠋ ⠓⠂⢇⣀⡞⠒⠛⣄⣨⠟⠒⠚⠛⠛⠚⠒⠒⠓⠒⠒⠒⠛⠛⠒⠒⠚⠲⠧⢤⠷

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⢠⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣅⣿⣷⣶⣶⣚⡛⠲⣀⠀⠀ ⢀⣴⡼⣽⣿⠣⡿⠈⡧⢻⣧⠘⠐⠄ ⠸⡍⢹⢻⢇⠼⠄⠄⢼⣜⣻⠂⠘⠃ ⠀⠈⠐⠉⢑⣻⣤⣠⡵⠋⠁⠀⠀⠀ ⠀⠀⠀⠈⡂⠘⣗⣐⡏⠁⠀⠀⠀⠀ ⠀⠀⠀⢠⢸⠝⠽⠺⡜⢤⡅⣶⡱⠀ ⠀⠀⠀⠞⣽⣶⣦⠅⠰⡿⡴⠀⡇⡄ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⡟⣿⣮⢢⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠒⣿⠛⠀⠛⢻⣦⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠪⡹⢄⢀⣠⣼⠟⠁⠀⠀⠀ ⠀⠀⠀⡠⠊⠉⣰⡎⢏⢰⡻⡿⠀⠀⠀⠀ ⠀⡠⠮⠴⣒⣩⣵⣶⣾⡿⢻⡇⣆⠀⠀⠀ ⣾⣤⣶⠿⢿⣽⣿⣿⣿⣉⡙⣿⡜⢦⠀⠀ ⠀⠉⠁⠀⡠⣼⡿⡏⠛⡫⣾⡓⢺⣞⣇⠀ ⠀⠀⠀⢜⡾⣽⣗⣇⠉⣯⡷⡷⢸⣼⢺⣆ ⠀⠀⡼⣊⣼⠟⡹⣿⢲⣻⣛⡿⣳⣫⣿⡜ ⡴⠮⣾⠋⠁⢉⣧⡽⢟⣏⡿⡋⣎⣿⢟⠌ ⠣⢀⠌⠱⡤⢾⠷⣾⣷⣷⣆⢳⣧⣕⣟⠀ ⠀⠀⠀⠀⠃⠀⠀⠁⠀⠁⠀⠉⠉⠉⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣲⣆⣲⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠛⣿⣿⣄⣑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣽⣿⣿⡿⠁⢰⣡⢿⣿⣆⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠃⠉⠁⡀⠰⡈⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣁⠹⣆⠠⠀⠀⠄⣠⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢌⡑⠠⠵⣬⡽⠒⠻⣿⣖⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⢀⣿⣿⠆⠟⣀⢼⣏⡻⣽⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠊⣁⣤⡴⠟⠛⣋⣽⣤⣼⣿⣿⣿⣿⣾⢦⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠋⠉⢉⣉⣤⣴⣾⣿⣿⣿⣿⣿⣿⣧⡕⣺⣿⣌⢷⡄⠀⠀⠀⠀⠀ ⢰⣷⣆⣴⣿⠿⣻⠿⣿⣷⣿⣿⣿⣿⣿⣋⣁⠀⠉⣿⣾⡌⢷⣄⠀⠀⠀⠀ ⠀⠙⠛⠛⠛⠉⠀⠀⠛⢋⣽⣿⣿⡿⣿⣿⡟⢏⢲⣿⣁⣿⣄⣽⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⢶⣿⢿⡟⣹⠀⠉⢉⡉⢻⣿⣏⠉⢹⡿⣯⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⢳⡿⢣⣿⡶⣿⠀⠉⠉⣟⣿⣿⣿⡤⢸⠇⣿⢞⣿⣆⠀ ⠀⠀⠀⠀⠀⡜⣱⠟⢡⣿⣿⢇⣿⣧⡀⢴⣿⣿⣧⢿⣄⡾⣼⡿⣸⡏⢿⡆ ⠀⠀⠀⠀⣼⠟⣁⣴⣿⠟⠉⣺⣿⣿⢛⣿⣻⣋⣛⣿⠟⣹⣯⣾⣿⣿⠌⡇ ⠀⢀⣴⣊⣡⣾⡿⠛⠁⠘⢛⢇⡟⣿⣿⣿⡟⢿⣿⡿⠋⡝⢿⣿⣿⠟⣠⠃ ⢰⠋⠙⠛⠿⣯⠀⠀⠀⢀⣾⡿⠟⢛⣳⣾⡶⡿⠏⣶⠂⣿⢾⡿⢡⡼⠁⠀ ⠈⠳⣀⢀⡴⠁⠳⣦⣠⣿⣷⣿⣿⣿⣿⣿⣿⣷⠀⢻⣶⣆⣀⡴⣿⠃⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⣻⣃⣚⣉⣅⣿⣛⠉⠙⠋⢙⠛⣿⣿⣿⣿⣿⣯⣳⣄⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡾⠀⠀⠀⢠⠄⠌⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⢔⡄⢿⡌⡄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠁⠀⠱⢄⢀⣬⣷⣤⣿⡻⣦⣯⢿⣿⣄⣸⣽⢰⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⡆⠀⠀⢲⣽⣏⣿⡿⣽⣿⣟⡛⠋⠳⣿⣾⠏⠸⠀⠀⢠⣶⢶⣦ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢿⣿⣏⣟⣿⡿⠿⠏⢰⣶⣿⠿⠏⠀⠀⠀⢻⣷⣾⠟ ⠀⠀⠀⠀⠀⠀⣀⢧⠀⠀⠀⣣⣿⣿⡏⣇⠀⣤⠆⣸⣿⠀⠀⠀⠀⣴⠟⠉⠁⠀ ⣠⣾⣿⡿⠋⢀⣾⣿⣧⠀⠀⠘⢿⣿⢿⣯⢿⣶⣿⡝⡇⣠⣿⣖⣾⠃⠀⠀⠀⠀ ⣿⣿⣿⠁⠀⣺⣮⣿⣯⢆⠀⠰⠀⠉⠢⠻⣧⡸⣿⣿⠾⣧⢷⣿⠁⠀⣀⠀⠀⠀ ⣿⣿⣿⡔⢣⣼⣿⣿⣟⣯⣧⠀⠀⡄⠀⢠⠘⣅⢹⠛⢟⣿⣏⣽⢈⢻⡉⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠒⠒⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡲⢋⠝⠋⣛⣳⡄⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠠⣴⠗⢀⠥⠂⢁⠤⠤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣛⠛⠉⠗⠒⠲⢤⣀⠀ ⠰⠃⠐⠀⠋⡠⠀⠮⠤⠤⠤⠤⡤⡄⠀⠀⠀⠀⠀⠀⢠⣽⠄⠀⠀⠀⠀⠀⢸⡆ ⠀⠜⠀⠀⠈⠀⢠⣤⣔⣒⡒⠒⠂⠁⠀⡀⢀⣀⣤⣶⣿⡟⠀⠀⠀⠀⠀⢀⡼⠀ ⠈⠀⠀⠀⠀⣰⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⢄⡴⠋⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⢀⣠⣴⡊⠁⠀⠀⠀⠀ ⠀⡠⠐⠉⢸⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣶⣿⣿⣿⡻⡄⠀⠀⠀⠀ ⠀⠁⠀⠀⣿⢹⣿⣿⣿⣶⣦⣶⣶⣶⣶⣶⣙⠋⠴⠛⣿⢛⡿⠬⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⠹⣿⣿⠛⠛⠛⢿⡇⠀⠉⠀⠘⠉⢰⣯⡊⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠘⠃⠀⠀⠀⠀⠠⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢲⣄⠀⠒⠂⠀⣀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⠀⢻⣿⣶⣴⣾⡟⢸⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⢀⣠⡤⠂⢠⠈⢿⣿⡿⣿⠃⠀⠙⣀⣀⣀⡀⠀⠙⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠉⠉⢇⠀⠈⡇⠘⣏⠀⡿⡰⠀⠀⢀⠛⠛⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠉⠉⠉⠗⠒⢿⡀⠸⡈⣠⠧⠞⠉⡏⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⢀⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⣀⠀⣀⣀⠀⢰⠐⢂⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣈⣾⠶⡿⢿⡩⢃⣡⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⣲⡝⣫⣃⣉⣠⡤⠖⢻⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⡔⡫⣻⣿⣄⠶⢖⠽⣿⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢛⠀⠀⡿⣳⡇⠑⠁⣰⢡⢽⠉⡐⠒⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢜⠀⠀⠇⠫⣳⢤⢴⢿⠇⠋⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡌⠐⡘⠀⠀⣠⠽⢯⡀⠀⠀⠀⠀⠀⠰⡀⠀⠸⢧⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⢀⠃⠀⠰⡼⣀⡹⣿⠀⠀⠀⠀⢀⠃⠘⡄⠀⡈⢷⡀⠀⠀⠀ ⢀⠎⠀⠀⣼⠈⠉⠁⠱⣿⡿⠥⠄⡁⠐⠂⡝⠀⠀⠘⡄⠰⡈⢷⡀⠀⠀ ⡄⠀⠀⢀⠃⢃⠀⠀⠤⡇⡧⠄⠀⢠⠀⡸⠀⠀⠀⠀⠈⢆⠐⠀⢣⠀⠀ ⢃⠀⣠⠂⠀⠘⠀⠀⠀⠇⡧⠄⠀⢸⠀⡇⠀⠀⠀⠀⠀⠈⡶⠝⠛⡈⡆ ⠀⠈⠀⠀⠀⠀⡇⢴⠊⡀⣔⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢠⠛⢛⠛⣄⠇ ⠀⠀⠀⠀⠀⠀⡇⠘⠎⠋⠙⠂⠀⠈⠀⡇⠀⠀⠀⠀⠛⡟⠛⠾⡽⠃⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⣿⣿⣿⣴⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡟⠹⣿⡿⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⣩⢿⣿⡏⣀⠀⠹⡇⢹⣹⣿⣿⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⣠⣾⡇⢀⣤⠄⡆⠈⣦⢤⢘⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⢪⡌⠒⠚⠀⢸⡗⢦⠤⠀⠑⡀⠩⢭⢟⣿⠓⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⠀⠀⢀⠻⡜⣿⣛⣋⠛⢛⢟⠜⠁⢀⣀⠜⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⢰⡿⠂⠁⠈⣱⣥⣖⣦⣵⣧⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠴⢶⣾⣗⣶⠀⣼⣿⠀⠙⠛⢿⣿⣿⡄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡮⣒⣐⢻⣻⣾⣾⣿⣇⡀⠀⠀⡈⢽⣿⣏⠒⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡫⠔⣶⣽⣃⡇⣿⣿⡇⠈⢠⠈⠀⢸⣿⣿⠀⠀⠀⠘⠆⡀⠀⠀⠀⠀⠀ ⠀⠇⡖⢉⡭⠛⠥⡏⣿⣿⠣⠤⠹⢢⠤⢺⣿⣿⡄⡤⣀⠀⠀⠈⠒⢄⡀⠀⠀ ⠀⢀⠐⠋⢹⣽⣯⣽⣿⣿⠀⠀⡀⡀⠀⢸⣿⣿⣷⠀⠀⠑⠠⣀⠀⠀⠙⠢⠀ ⠀⠸⠀⠘⣿⣿⡿⣿⣿⣿⠓⠋⢨⡇⠀⢼⣿⣿⣿⡆⠀⠀⠀⠀⠑⡄⠀⢠⠃ ⠀⠀⠀⠀⠙⠛⠁⠛⠛⠛⠃⠀⠚⠒⠈⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠀⠀⠁⠀

⠀⠀⠀⠀⠀⢀⠄⠒⠈⠉⠉⠉⠉⠐⠠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⢁⠀⣀⣤⣀⣠⣤⣄⣀⡀⣤⠑⡀⠀⠀⠀⠀ ⠀⠀⢀⠃⢀⢯⣦⣾⡿⠟⠛⠙⠋⠉⠙⠛⠓⠴⢄⡀⠀⠀ ⠀⠀⢸⠀⡴⢟⣉⣀⣤⣶⡞⣿⣿⠏⢷⢶⣄⢤⡴⠎⠐⠄ ⠀⠀⡨⠊⠸⢋⣿⣿⣿⡟⠸⢸⠏⠀⠈⠀⢻⣷⠭⠀⠀⠈ ⠀⠌⢀⡀⢠⣿⣿⠇⡿⣀⠀⣊⢶⡂⣀⡄⠈⣿⣶⡷⢀⠜ ⢸⠀⣶⣧⣾⣿⣿⠀⠛⠓⠋⣋⠘⣙⡿⠯⢀⡿⡾⠕⠁⠀ ⠘⠄⣟⣿⠼⣗⡾⡀⠀⠔⢁⠀⠀⢁⠈⠂⢸⠁⠀⠀⠀⠀ ⠀⠈⠚⠘⠓⠓⠚⠓⢄⣈⠀⠪⢹⠒⢨⠦⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠻⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⠀⠀⠙⠃⢙⣷⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡁⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⠤⠤⠄⠀⠀⠀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⠶⠖⠂⠈⡇⢹⠈⣧⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⠋⡹⢉⡇⢠⠤⡤⣀⠀ ⣏⢸⠀⡀⢠⠀⢑⢈⠇⢹⠀⠀⠈⠀⢀⠔⠲⢄⣀⠔⠲⡀⠀⠀⠀⣼⠀⡇⢸⠀⢸⠀⡇⢹⢹ ⢹⠘⡆⢣⠘⣄⡜⠈⠀⡜⠀⠑⠀⠀⠈⢲⡄⠀⠁⢠⡒⠁⠀⡀⠀⢿⣀⢃⢸⣀⠎⡸⠀⡇⣸ ⠀⢦⣈⠂⠁⢀⣵⣴⢿⠁⠀⡀⠉⠀⠐⣿⣈⣔⣢⣄⡻⠀⠀⠀⠁⠈⢿⣻⣦⣇⣀⢁⣜⡰⠁ ⠀⠀⠉⠛⠛⠻⢏⣉⣊⣱⡤⠔⠒⠉⠉⠀⢠⡀⠀⠀⠉⠁⠒⠤⣀⠰⣿⣿⡽⠛⠛⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡽⠋⠁⠐⢀⡠⠤⠒⠂⠀⢉⣖⠒⠂⠤⢄⣠⡀⠙⢷⡺⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⠀⣀⠔⢊⣁⠴⠒⠁⠀⠀⠀⠀⠈⠉⠒⢄⡈⠙⢦⡀⠑⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⢀⠞⠡⢠⠞⠁⠀⣒⣤⠀⠀⠀⠀⠀⣤⣤⡀⠉⢆⠀⠙⡄⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣏⠆⠄⠈⡆⠀⣿⣿⣿⡆⢀⣀⠀⠀⣿⣿⣿⡆⢨⠳⢠⢼⣠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⠄⣑⠚⡄⠙⠛⠋⢀⣘⣞⣡⠄⠙⠛⠋⣠⠊⣄⣀⠼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣹⣾⣁⣠⣤⣤⡮⠽⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣭⣿⣏⠳⡒⢿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣟⠀⠘⠋⠟⠓⠋⠀⢱⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠭⢿⠒⠋⠀⠀⠀⢉⣑⣾⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⡀⠀⠈⠻⣿⣶⠿⣿⡿⠟⠁⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⣶⣾⢻⠒⡟⣷⣿⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠎⠁⠀⢺⣤⡀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⠀⠐⣂⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⣿⣿⣿⣷⣦⣤⣴⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠳⣄⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⡝⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⡀⠀⠀⣠⠐⠀⠀⠀⠘⢦⢈⠳⡀⠀⢠⠞⠁ ⠀⠀⠀⢀⡴⠋⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⠁⠀⠀⠀⠙⢿⣿⣿⣿⡄⠻⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⠐⠎⢄⢢⠘⡤⡈⢢⡳⠳⡱⣤⠏⠀⠀ ⠀⠀⢠⠟⠁⠀⠁⠀⠀⢀⣤⣶⣿⣿⣿⣿⠃⠀⢸⡧⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⠀⠈⢿⣷⡄⠙⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢯⣣⠘⢎⢆⠱⡁⣿⠏⠀⠀⠀ ⠀⢠⠏⠀⣀⣀⣠⣤⣾⠿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⠀⠀⢙⣿⡄⠀⠙⢿⣿⣿⣿⡆⠹⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⢳⡳⡜⢮⡳⣘⡟⠀⠀⠀⠀ ⢀⡏⠀⠀⠀⠀⠈⠀⢠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡤⠞⠉⠈⠻⡄⠀⠈⠻⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠱⡕⡄⢳⣹⠃⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡇⠀⣠⣤⠤⠼⠤⣄⠀⠘⢿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⢵⠹⡄⣿⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⠀⢀⡴⠋⠀⢀⡵⠋⠁⠀⠀⠀⠀⠀⠙⠳⠴⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⣄⢹⡏⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⡞⠀⠸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⣿⣿⣿⣿⣿⣷⡰⡀⢼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠏⣸⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡀⢀⡴⠀⠀⠘⠀⢹⣿⣿⣿⣿⣿⡿⣧⠇⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠁⠀⣿⣿⣿⣿⣿⣿⣷⠒⠉⠁⣠⡤⠤⠤⣬⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣠⠕⠛⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⣉⡛⢮⡏⢸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠁⠀⢠⣿⣿⣿⣿⣿⡏⠻⡄⢠⠎⠁⢠⣶⡤⠀⠉⢸⠇⠀⠀⠀⠀⠀⠐⠢⠤⣤⡤⠔⠺⠟⣚⣩⣥⠥⣶⠦⣤⠀⠀⠀⠀⣾⡟⣠⠋⠀⢹⡌⡇⢸⠀⠀⠀⠀⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣿⣿⣷⡀⠀⠸⡀⠀⠈⠉⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⠉⠀⠀⠀⢀⣧⢀⡏⠀⠀⠀⠀⣿⢱⠷⠶⠀⢸⠃⣾⢺⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⣰⣿⠟⠁⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣰⠻⣦⡔⠒⠀⣀⡤⠔⠚⠁⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠧⡄⠀⠀⢰⠃⣾⠋⠉⢹⠀⢠⢿⣾⡄⠀⠀⠀⠀⠀ ⠀⢷⡀⠀⠀⠾⠋⠁⠀⢀⠀⢸⣿⣿⣿⣿⣧⡀⠀⠤⠤⠖⠋⠁⠀⠀⣠⠴⠊⠁⠀⣀⣤⣴⣾⣿⣿⣿⡿⠿⠛⠛⠛⠛⡟⠀⡄⠀⢀⡏⠀⡼⢀⡰⠃⣰⣿⣿⣹⡇⠀⠀⠀⠀⠀ ⠀⠈⢷⡰⠀⠀⠀⠀⠀⢠⠢⡱⣿⣟⢿⣿⣿⣷⡄⠀⠀⠀⠀⢀⡴⠚⠁⠀⣠⣴⣾⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡾⠓⠛⠛⢉⣴⣻⢧⣽⢽⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⢀⠰⡔⠈⠳⣙⣿⢎⠀⠙⣿⣿⣿⣆⠀⠀⢰⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣠⠤⠖⢚⡟⠁⠀⠀⣠⣾⠙⠲⡖⠊⣯⢢⢳⣿⣏⡶⠋⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣆⠀⠉⢙⣄⢦⡙⢦⡳⣄⠀⢊⠿⣿⣿⣧⠀⠈⠳⣄⣀⡜⢻⠿⡿⣿⡿⠁⣀⡤⠖⠊⠉⠀⣠⠴⠋⠀⠀⢀⣴⢿⣯⠁⠀⣿⡆⡞⡾⣞⡿⢋⢀⣰⠟⠀⠀⠀⠀⠀ ⠀⡄⠀⢀⣀⡽⠷⢒⢿⡻⣓⠵⢤⡙⠎⠧⣄⢝⣻⡸⢻⣷⡀⠀⠈⠳⣶⣦⣴⣴⣿⠷⠋⠁⠀⠀⣀⡤⣞⠁⠀⠀⢀⣠⢾⣿⣾⡇⠀⠀⠘⢧⠶⠋⢉⣀⣈⣹⣷⡄⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠀⠀⣰⠻⢤⣐⠈⠢⡑⢥⡉⡁⢬⣣⡍⠳⣌⠻⣽⣦⣄⡀⠈⠙⠛⠯⠤⠤⠴⠒⣒⠯⠟⠊⠁⠀⢀⣴⣿⣿⣿⣾⣿⠇⠀⠀⠀⠈⢑⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠃⠀⠀⠉⠲⣤⡉⠲⢝⠪⣷⣌⡳⣕⢪⡉⠚⠯⠭⠽⡶⠦⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣤⢾⣿⢷⢟⣿⣽⣣⡏⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠙⠲⢤⣙⡺⡑⠍⠻⢝⠦⣱⠄⡀⠀⠨⠅⢺⣑⠮⡉⠉⠙⠲⡶⠻⣟⢿⣽⣻⣯⡿⡿⢻⠟⠀⠀⢀⡴⠊⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠶⠾⠤⢭⣒⣈⣉⡡⠶⠴⠽⠷⠖⠋⠉⠙⢆⠘⠞⣿⢫⣎⡾⡿⠀⠀⢀⡰⠋⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⠉⠋⠙⠈⠀⠀⣠⠏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣨⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣇⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣀ ⢀⠄⠂⠉⠉⠁⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⣄⢐⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣀⣀⣤⣖⣋⠭⢉⡉⠐⠠⢄⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⣠⠔⠂⠉⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠉⠑⠂⢵⡀⠀⡄⠀⠀⠀⠀ ⢰⡁⠀⢀⢴⠖⢄⣴⣿⣿⡟⢹⠹⣿⣿⢳⣤⣀⠀⠉⠲⣇⠀⠀⠀⠀ ⠈⠣⡀⠻⠿⣿⣿⣿⡿⣿⠀⠀⠇⠘⣿⠀⣿⣿⣷⡀⢄⠈⠲⡀⠀⠀ ⠀⠀⠈⠂⠤⣡⡟⣿⡇⢘⢒⡂⠀⠀⡺⠯⡙⢻⡿⢷⣼⣆⠀⠈⢂⠀ ⠀⠀⠀⠀⠀⠀⠉⠺⣧⢣⣺⡏⡁⠀⢤⣫⠄⢸⣿⡆⣿⠚⠤⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠠⠁⠀⠭⠋⢠⠷⠛⠓⠒⠒⠂⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠺⣋⠀⢀⡤⠖⢟⠜⠉⠒⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡏⠀⢠⠇⠀⠀⠀⢀⠎⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠂⡲⠀⢀⡀⠀⠀⠀⠀⡠⢲⡈⠲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡛⣢⣠⣤⣼⣥⣦⣠⣦⠄⢃⠠⠯⠴⣴⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣨⢠⢃⡘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣀⣠⡯⠾⠾⠗⠯⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠤⠤⠤⠴⠯⠥⡤⠴⠶⠒⠶⣄⣀⣀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣙⢢⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⣿⢻⣿⣷⣦⣤⣦⠀⠀⠀⠀⠀⠙⠷⣄⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⡀⠼⣭⠚⡴⣠⣶⣿⣿⣿⣿⡿⠁⢹⡆⠹⣿⣿⣿⡟⣿⣶⣄⡀⠀⠀⠀⠈⠑⢿⡀⠀⠀⠀⠀⠀⠀ ⠻⣇⡀⠀⢸⣷⣶⣿⣶⣼⣿⣿⣿⣿⣿⣿⠁⠀⠀⢷⠀⠙⣿⣿⡇⠘⣿⣿⣿⣶⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠈⠳⣄⠈⠛⠛⢹⠛⣍⣷⣿⣿⡿⢸⣿⠀⠀⠀⠘⠃⠀⠈⢿⠇⢀⣸⣿⣿⣿⣿⣆⠘⢦⡀⠀⠀⠱⣄⠀⠀⠀ ⠀⠀⠀⠈⠓⠤⣄⡈⠁⣽⡿⢻⣿⡇⠀⢹⡓⠢⠄⠀⠀⠀⠰⢞⣯⣍⡐⠛⣿⣿⡿⢿⣦⢺⣳⡀⠀⠀⠈⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣆⣘⣿⡇⢰⠞⢩⣝⣦⢠⡄⠀⠀⠏⣰⣄⢻⠀⣿⣿⣤⢸⠛⣆⣛⣣⠀⠀⠀⠀⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⢿⠈⢦⣘⣋⡧⢠⠃⠀⠀⢧⣈⣡⠖⠀⣿⣿⣯⡏⡴⣛⡏⠉⠰⠶⠀⠀⣰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠉⠁⣀⠘⠂⠀⠐⠒⣺⡗⠋⢠⣿⡵⠯⠧⠤⠥⠤⠤⠤⠴⠖⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠓⠒⠒⠒⠚⠁⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⢀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣯⣿⡿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠂⠀⠉⠉⠉⡷⣦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠟⠁⠀⠀⠀⢀⣀⡤⣻⠞⣠⠟⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠒⡿⠀⢻⢶⡄⠀⠠⢺⡟⠉⠀⠋⠾⠁⠀⠀⠀⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡸⠃⠀⠀⣰⡲⠀⠀⠀⠀⠀⠀⠀⢰⠋⢠⢟⣦⡀⢘⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠛⠻⣰⢁⡌⡤⣴⣷⣁⣌⣤⡀⣠⣶⣦⡆⠘⡆⠘⢦⣋⣠⢞⡤⣾⣧⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠒⠋⠓⠉⠛⠓⠉⠘⠋⠋⠘⠚⠙⠓⠋⠀⠀⠈⠒⠒⠂⠀⠈⠉⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⡀⡀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠁⠀⠀⠉⠑⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⡔⡰⢆⠰⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣠⠀⡀⠀⠀⡞⢠⠃⠘⡆⠱⠀⠳⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⠁⢀⡰⠁⢠⣷⡇⡸⢀⣎⣀⠀⢹⡀⠳⡕⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣶⠃⣠⡿⠁⣷⡇⣼⣷⣾⣤⣤⣇⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡏⢰⠉⢀⠀⢨⣇⡟⠈⠻⢿⡿⣿⡄⡀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠃⠸⡄⢸⣀⠞⠘⢻⠀⠀⠀⠀⠘⣿⣃⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣀⡿⣾⠿⣄⣀⣡⣤⡀⠀⠀⠀⣽⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣄⠉⠈⠁⠐⡦⠠⠈⠁⢀⡾⣽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠓⠦⣀⣀⣿⣀⣠⠔⢻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⠀⠀⠀⠀⢠⣾⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢾⢹⢸⠀⠀⠀⠀⠀⠀⠀⣼⠙⡄⢸⡏⠙⠒⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⡞⠁⠀⠀⡞⢸⡘⢆⣀⠀⠀⢀⡴⠚⠃⠀⣇⠀⡷⣄⠀⠀⠘⠄⠀⠈⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣀⣈⣀⣀⡠⠼⣇⣾⣧⠀⢸⠀⠀⢸⠀⠀⣠⣾⠿⡴⠁⠈⠙⠳⣟⠛⠲⢤⡀⠀⠀⠀⢹⣳⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡎⡟⠁⣠⠞⠉⠁⢠⠎⠁⠀⠀⢹⠀⠹⣷⣈⡆⢀⡎⣠⣾⠟⠁⣠⡇⠀⠀⠀⠀⢹⡄⠀⠀⢻⠦⠤⣀⣈⠁⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⣹⠖⢺⠏⠀⠀⢠⠃⠀⠀⠀⠀⢸⠀⠀⠈⢻⣿⣾⡾⠋⠀⢀⠔⡽⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⡇⠀⠀⠉⢿⡃⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⡜⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⡟⠀⢀⡔⠁⣰⠃⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣷⠀⠀⠀⢸⠈⢧⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⣧⠤⠤⡞⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣿⠃⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠈⢟⠛⢲⠋⠀⠀⠀⢸⠀⠘⡆⠀ ⠀⠀⣠⠏⣾⠀⠀⣼⣤⢴⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣸⣿⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠻⠺⡆⠀⠀⠀⢸⡀⠀⢻⡀ ⠀⢰⠃⢠⡇⠀⢰⣅⣙⣼⠃⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⣿⣿⡇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⢺⠃⠀⠀⠀⠈⢳⠀⠀⢷ ⢀⡏⠀⣼⠀⠀⠀⡿⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣿⣿⡇⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣦⡤⣤⣴⣶⠸⣆⠀⡈ ⡼⠀⠀⡏⠀⠀⣸⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠹⡇⠉⠉⢛⡛⠁⢿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⢿⣿⣿⡍⠉⠉⠙⣿⣿⡿⡿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢧⠐⠛⠛⠋⠀⠀⠀⠀⣿⣿⣷⢡⣟⣉⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⡦⠀⠀⠟⣾⣿⣿⡿⠿⢾⣿⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠤⣤⠶⠟⠋⠀⠀⣠⡶⢿⣿⣿⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢀⡠⢾⣿⣷⣿⣿⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠀⢸⡉⠉⠛⠋⠀⢀⣠⠖⠋⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣴⢟⡫⠤⠆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⢴⠿⠗⠁⠀⠀⠀⠀⠀⠓⠒⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡷⢊⠴⠃⠀⠀⠀⠀⠀⢀⡠⠔⠒⠊⠉⠚⠛⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠐⠁⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢀⡴⠖⢰⢀⠀⠐⢣⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢲⠸⣇⠀⠀⠀⠀⢀⠜⣡⠔⣊⣉⢹⡤⠤⢼⠗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⡀⠀⠀⣰⢃⢞⡵⠋⠁⠀⠀⢧⣀⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⡄⠑⣄⠀⢷⣿⠋⠀⠀⠀⠀⠀⠘⢿⡄⠀⠱⡄⠀⠀ ⠀⣤⠖⣉⠱⡄⠀⠀⢸⠦⡉⢾⢧⠀⠀⠀⠀⣀⣠⣠⣶⠀⠀⢦⡈⢦⡈⢳⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀ ⢀⡷⣶⣿⣧⣿⠀⣰⠃⣠⡽⣿⣿⠆⠛⠂⠴⠷⠽⠟⠃⠀⠲⣄⠙⠢⣛⠛⠉⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀ ⠈⠓⠻⣿⣿⣿⣷⠃⢀⡿⣿⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣄⠉⣉⣁⣈⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠹⣿⣿⣻⣦⠘⣷⣷⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⢧⣿⣿⣯⡟⠛⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⡿⣷⢣⢣⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡁⠀⢀⡞⠉⠓⢤⣠⠔⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⢛⣿⠗⠀⠉⣿⣟⢻⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢫⣿⡿⠫⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠈⢏⠁⣠⣴⣯⣼⠃⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠉⠉⣠⠖⡉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⢤⠾⠃⠁⠀⠀⠒⣳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠕⠁⠀⠀⢀⠔⠉⠀⠀⠀⠉⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⣀⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⡜⠀⠀⠀⠀⠀⡾⡆⠀⠀⡠⡪⡂⠤⡄⠠⠃⠀⠀ ⠀⠀⠀⠀⠀⡌⢰⠁⠀⠀⠀⢀⠀⠡⡐⡄⢸⡺⠋⠀⠀⠹⡆⠑⡀⠀ ⣔⣹⣱⠀⡸⠪⣽⣆⣄⣠⣴⡴⠀⡐⢔⠬⡦⢅⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⢿⣿⣖⠁⣿⣿⠃⠀⠀⠀⠀⠀⠈⠲⣍⢒⣨⣢⡀⠀⠀⠀⠀⠀⠈ ⠀⠈⣿⣿⣧⠶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠋⢃⠜⢄⣀⠔⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠵⢒⡒⠋⢩⠀⣸⣿⡷⠟⣉⡵⠿⣟⣿⣦⣀⣸⣽⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⢠⡿⡀⣠⣾⣶⢿⢿⡿⢿⣷⣀⠀⣄⠀⠻⣿⣿⣿⠿⣿⣧⠉⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⣠⡄⢀⣴⣻⠿⣛⡭⣷⣶⣾⣞⣓⣋⣯⣍⣳⣼⣯⣦⣤⡸⠽⣶⠘⣿⣧⣙⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⡴⣶⡆⢻⣥⣾⡽⠶⠿⠖⠋⠉⠁⢠⣿⣷⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠷⠾⢿⣟⢿⡄⠸⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢳⣷⡵⠟⠋⠀⠀⠀⠀⠀⢠⡀⠀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠓⢾⣦⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⢰⣧⣀⡽⠚⠉⠀⠀⢀⣀⣀⣠⠀⠀⢸⣧⣀⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⢀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡶⣇⡿⠃⠀⠀⠀⢀⣖⡿⡻⠏⣁⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣤⣀⣀⠀⠀⠀⢀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠭⣪⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠋⢰⡇⠀⠸⣿⣿⣿⣿⠀⠙⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⠁⠀⠀⠘⢿⣿⣿⡆⠀⠈⢿⣿⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⢀⡤⢚⡛⠛⠛⢛⣿⣿⣿⣿⡿⠃⠀⠀⢸⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠈⢻⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠏⠀⠀⠀⢢⠋⢀⢏⡔⣀⣴⣿⣿⣿⣿⣿⠃⠐⠒⠤⢬⣀⠀⠀⠀⠀⠀⠈⠳⠀⠀⢀⡤⠗⠒⠚⢻⣿⢿⣿⣿⣿⣿⡟⠉⢀⢀⢀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⡶⢻⡿⡼⢻⣿⣿⣿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣿⣿⣿⣿⣿⣯⢯⢿⡟⣼⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⠀⠀⠀⠀⢸⡅⣧⣿⢡⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⣴⣶⣤⡀⠈⠀⢸⣿⣿⣿⣿⣿⡎⣾⣿⡏⡆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⢿⣿⣿⣿⠀⠀⠀⣴⡿⠋⠉⠻⡦⠀⠀⠀⡇⠀⠀⠀⠀⢾⠋⠁⠀⠘⠿⡄⠀⠀⣿⣿⣿⡟⠛⡟⣿⣿⡇⣷⡇⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⣾⣿⣿⡇⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠤⠤⠴⠤⢶⡤⠖⠀⠀⣿⣿⣿⣷⣤⣱⣺⣻⣷⡏⠙⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⡐⡂⢸⠁⣻⢛⢿⡇⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠒⠒⠦⠤⢤⣀⣠⣦⠆⠀⠀⢿⣥⣹⢛⣻⣯⣻⣳⡽⢠⠏⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠀⠀⢰⣯⢧⣧⢳⡸⡆⡇⠏⢷⣻⡀⠀⠀⠀⡶⢿⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⡼⢿⣟⣟⣤⠀⠀⠹⣧⠟⢻⣫⣫⠟⡁⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡠⠀⠘⣟⢮⣿⣧⢹⣿⢧⠀⣞⠟⡧⠀⠀⠀⢳⠀⣄⣰⣴⣾⣿⣿⢿⡿⣿⣿⡿⣿⣷⡼⣁⢶⡴⣦⠀⠀⠀⠀⣷⡰⢻⠃⠋⠘⠃⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡄⠰⢞⣮⣳⣷⢧⡻⣿⣷⢌⣙⡇⠀⠀⠀⠀⢷⣏⠉⣻⠛⣤⠉⠙⠿⣿⠋⠀⠀⢸⠿⣟⣎⡉⡁⠀⠀⠀⢀⡿⢧⣾⢀⣠⡶⠶⠚⢹⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡈⢻⡙⢮⣢⣝⣎⠻⣗⢿⣷⠀⠀⠠⣴⣄⠻⣿⣡⠤⠟⠒⠊⠉⠉⠉⠓⢶⡾⢶⡆⠙⣿⣿⣉⠉⣡⠞⢀⡬⠛⢩⢈⡁⡼⢠⠏⠀⠀⠈⠓⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠦⢭⣟⠉⠘⣻⢽⡺⢵⣾⣷⣄⠀⢿⣿⣿⢾⡛⠦⢤⣀⣀⣀⣀⠤⠖⠋⠀⠀⠀⠀⠈⣙⣧⢾⡵⠋⠑⢀⣄⢯⣦⣷⠕⠋⠀⠀⠀⠀⠀⣀⡉⠲⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠩⠿⢟⣶⣯⣟⡻⢷⠾⢭⣝⣀⣉⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣞⢿⣞⡏⢁⠞⠀⠀⢀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⠛⠃⠀⡈⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣉⣀⠘⠛⢘⠭⢥⡐⢻⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⢩⣋⣐⡁⣿⠤⠶⣾⡿⠝⢸⠿⠃⠀⠀⠀⠀⠀⠀⢠⠋⣳⠀⠀⡇⠀⣀⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⡳⣶⣒⣻⣿⠁⠈⠙⠻⢿⣿⢸⠻⣿⠿⡟⢹⣿⣶⣶⣥⣿⢀⣀⣈⣽⠟⠁⠀⠀⠀⠀⣞⡟⠀⠀⠳⠶⠟⠀⠀⠀⠀⠘⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠻⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡆⣷⣦⡅⢸⣿⡟⢠⣤⣿⣿⠋⠉⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣦⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠃⠀⢿⡇⢸⡵⣟⠃⠀⢀⣻⣉⠀⠀⣤⢦⠀⡴⣯⠳⣤⠀⠀⡞⣟⣷⠀⠁⠀⠀⠅ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠉⠑⢲⣶⣶⣾⡆⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣣⠏⣠⢿⡾⡟⠉⢳⡁⠀⢀⣙⣭⡀⣧⡘⠖⢛⡄⢰⠇⠉⢉⣄⠀⣀⠔⠀

⣶⣭⣽⣿⣿⣿⣿⡏⠀⠈⢻⣧⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡁⠀⠀ ⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⡇⠀⠹⣿⣿⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⡀ ⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⢻⡀⠀⠻⣿⣇⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠙ ⢿⣿⣿⣽⣿⡿⢸⠀⠀⠀⠀⠀⠈⢣⠀⠀⠘⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡗ ⣿⣿⣿⣿⣿⡇⠀⠆⠀⠀⠀⠀⠀⠀⢆⣠⠢⠽⠹⠥⣳⢿⣿⣿⣿⣿⣟⣟⣿⣷ ⣿⣿⣿⣿⠸⣇⠀⠘⠦⠀⠀⠀⠤⠔⠝⠁⠀⠰⠿⠂⠈⠆⣿⣿⣿⣿⣿⣿⣿⣇ ⣟⣿⣿⣿⡈⢹⠝⠋⣙⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠏⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡧⠈⠁⠀⠉⠁⣠⠀⠀⠀⠀⠐⠂⡀⢒⡲⡕⠁⠀⠃⣿⠟⡫⠭⢫⠉ ⠛⠙⡏⢿⣿⡄⠐⠠⠄⠂⢰⠀⠀⠀⠀⠈⠉⠙⠀⠀⠳⠀⠀⠀⡏⡜⣀⠰⣹⠀ ⠀⠀⠁⠀⣿⢷⡀⠀⠀⠀⠀⡁⠥⠄⠐⠂⠠⠄⡀⠀⠀⠀⠀⣘⡠⠀⡘⠠⠃⠀ ⠀⠀⠀⠀⠈⢅⢵⡀⠀⠀⠨⡔⠂⠀⠉⠉⠉⢉⡩⠂⠀⢀⡔⠒⡂⠥⠂⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠹⠤⣀⠂⠀⠉⠩⠤⠤⠉⠀⢀⣠⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⣤⣀⣠⡤⠖⢛⣽⢿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠀⠀⢈⣧⠎⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⣄⣀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⣶⢀⠀⠀⠀⠀⠀⢀⠙⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠉⢹⣿⣶⣒⣒⣛⣒⣒⣢⢄⡈⠆⠀⠀⠀⠀ ⠀⠀⠀⢀⣧⢀⡞⣻⣿⣶⣶⢶⣶⣬⣄⡉⠉⠓⣤⡀⠀⠀ ⠀⢀⣔⢻⠇⣾⣿⣿⠋⢻⡿⠀⠹⣏⢻⣿⣧⡀⠸⠍⣳⡀ ⢠⡇⣿⠟⢺⣿⡏⠇⠘⢳⠋⠀⢀⠟⠀⠏⣿⡗⠀⠀⢈⢻ ⢸⣴⠋⢸⡟⡿⣧⠠⢈⡣⠃⢰⠘⢍⣡⡘⢹⡟⠂⠀⢹⠟ ⠀⠛⢄⠘⢤⣙⣧⣫⡉⠀⠘⠈⢉⣈⣭⢇⣟⡁⠴⠊⠁⠀ ⠀⠀⠀⠑⢄⠙⢍⡙⠷⣦⣄⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⡈⣉⡿⢍⠉⡹⡷⠒⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢀⠧⠿⣦⣠⣴⢧⠀⢠⣈⠒⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⣧⡝⡼⢐⣷⡬⣷⠚⡆⢈⣆⠙⣶⡙⣷⠄ ⠀⠀⠀⠀⢀⡿⡅⡿⠁⠉⣩⣿⣉⠃⣘⣿⣘⡀⠛⢻⢱⠀ ⠀⠀⠀⠀⢺⣛⣰⢿⣿⣿⣻⠒⠛⢺⡟⢿⡀⢷⠀⣸⠈⣆ ⠀⠀⠀⠀⠀⠀⠸⠛⠛⠋⠉⠀⠀⠀⠰⠸⠿⠉⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⣶⢶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠰⢰⡏⠀⢳⣳⠀⢦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣠⠇⡎⡇⠀⠀⢿⣧⢸⢧⡀⠘⢾⢆⢀⠀⠀⢧⡀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃⡀⠀⠀⠀⠀⠀⣰⢻⢸⠇⡇⠀⠀⠘⣿⡆⣆⢳⡀⠘⢟⡎⢧⠀⠀⠹⡄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡸⠃⠀⠀⠀⠀⣠⠏⣿⣸⠀⢻⠀⠀⠀⢹⣿⡟⡄⢳⡀⠸⣽⡈⣧⠀⠀⠹⡄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⠃⠀⢀⣰⠀⠀⡿⠀⣿⡇⠀⢸⡆⠀⠀⠀⣿⠙⣵⡄⢣⠀⢻⡇⠸⡄⠀⠀⢹⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣿⠀⠀⢸⡇⠀⢸⠁⠀⣿⡇⠀⠀⢷⠀⠀⠀⢹⠀⠹⣷⡈⢧⠀⣿⠀⡇⠀⠀⠀⢧⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⣿⠇⠀⡟⠀⠀⣿⡇⠀⠀⢠⣆⠀⠀⠸⠀⠀⠘⣧⠈⣆⢸⣧⢱⠀⠀⠀⡼⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⢹⠀⢰⠇⠀⠀⢿⡇⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠈⠣⠘⡆⠈⢸⡄⠀⠀⢣⢳⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⠀⡇⡇⠀⡞⣿⠀⣼⠀⣀⡤⠾⣷⠦⢤⣄⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠙⠓⣺⣧⠀⠀⠀⢸⡀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠀⢹⡇⢰⣇⢹⡆⣿⠈⠁⠀⠀⣸⡄⠀⠈⠁⠀⠀⠀⠀⠉⠀⢀⣠⣤⠤⣤⣽⣿⠀⠀⡀⠀⣇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠁⢻⠀⢸⣧⢸⢿⢾⣇⣿⢀⣴⡿⣿⣛⡿⢿⡂⠀⠀⠀⠀⠀⠀⣾⠿⣯⣿⣯⣟⢷⣿⠀⠀⡇⢸⢿⢸⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⣿⢸⡘⢸⣿⢿⠸⠋⣾⠛⢻⣿⡇⠀⠀⢀⠀⠀⠀⠀⠁⢸⣯⣸⣿⣿⡇⠙⠀⢠⠇⢸⢸⢸⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⣾⣧⡸⣿⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⢈⡇⠀⠀⠀⠀⠘⠿⣿⣿⠿⠀⢀⠀⡸⢀⣾⣾⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣧⢹⠀⠀⠤⣬⣙⣋⣩⠴⠂⠀⣼⡀⠀⠀⠀⠀⠒⠦⣤⠤⠚⠁⢸⣰⠃⣾⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠞⣿⡿⣇⠀⠘⠦⠀⠀⠀⠀⠀⠀⠈⠛⠀⣀⣀⣀⣀⣉⣀⣀⠀⢀⣿⠃⡼⣽⡏⣽⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢇⡽⡽⡄⠀⢀⡤⠶⠒⠒⠉⠉⠉⠉⠉⠉⠀⢀⣀⡀⠀⠀⣽⣿⠏⡼⢻⠷⡆⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠸⣆⡿⠽⡀⠀⢧⣤⡤⠔⠒⠚⠛⠛⠛⠉⠉⠁⠀⠉⠙⣿⢣⠇⢠⡧⣇⣴⡣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣉⡛⠻⡄⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢸⠀⣿⢤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡗⠛⣦⣄⠈⠙⠒⠤⣤⣤⣤⣤⡤⠖⠚⠁⢀⣤⣿⠀⣯⢸⣿⡀⠀⠀⠀⢀⡴⠚⠉⠙⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢧⠀⠀⣟⡎⠙⡲⣤⣀⡀⠙⠏⢉⣀⣤⣤⢶⣿⠀⣿⣟⠹⡼⣿⣷⠂⢀⡴⠋⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⣰⡿⠀⢀⡉⠈⣿⡯⣿⣿⣿⣿⣿⡟⢸⢻⡄⠹⣯⣉⠳⠾⠟⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠭⣟⠉⠾⣅⣴⣿⣤⣤⣿⠛⢿⣟⣿⡇⣿⢻⣌⣿⠟⠶⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣤⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢚⡾⠡⢄⣀⠀⠀⠈⢧⠀⠀⠀⠈⠉⢀⡏⠀⠀⠉⠛⠁⠉⠸⣆⠀⠀⠀⠀⠀⢀⡀⣀⣠⠴⠾⠲⣤⣤⡄⢀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢸⡁⠀⠀⠉⠑⠦⡄⠘⡇⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣄⣀⣤⣤⣿⣿⠉⠀⠀⠀⠀⠀⠈⠉⠙⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣠⣾⡟⠿⢭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠋⠉⢠⣿⠃⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀ ⠀⢀⡠⠖⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠘⠋⠀⢀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲ ⠴⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠲⣆⠀⠀⣠⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⠁⠈⢷⠀⢀⣾⠿⠁⠈⠙⠿⢿⣶⣤⣀⣀⠀⠀⠀⡎⠀⠀⠀⣀⣀⣤⣶⣿⣿⣟⡉⠀⠙⢿⣿⣆⣶⡿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⠃⠀⠀⢸⣾⣿⣿⣿⡇⠀⣠⣶⣿⣿⣿⣿⠿⠿⠿⠿⣿⡿⠿⠿⠿⣻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⡀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠛⢁⡐⡍⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠃⠀⣴⣿⣿⣦⣄⠀⠀⢻⣿⣿⣿⡿⢟⣠⣤⣶⣿⣦⡀⢻⡹⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠘⣶⣤⣤⣤⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀ ⠀⠀⡠⠊⣀⣤⣴⣶⣾⡏⠻⣿⣿⡻⣿⣿⣿⣿⣿⣿⣶⣄⢀⠠⠀⡀⡪⡢⢀⠊ ⠀⠌⠀⣉⣭⣿⣿⠏⢸⠀⠀⠈⠻⣷⠘⢷⡙⢿⣿⡟⣿⣿⣷⣄⠙⣄⢮⣻⠃⠀ ⠌⠀⠀⢡⣾⣿⡟⠀⠈⡇⠀⠀⠀⠹⡖⢉⣑⣀⠻⡇⠘⣿⣿⣿⣧⠘⣊⠛⠀⠀ ⠀⠀⢠⣿⣿⣿⡇⠀⠀⠈⠀⠀⠖⢀⠊⡤⠀⠀⠁⠁⠀⠸⢿⣿⣿⣧⡁⡇⠀⠀ ⠀⠀⡜⢡⣿⣿⢧⠐⡢⠤⠔⠄⠀⠈⠀⠀⠀⢀⣔⠱⠂⠀⠀⢿⢟⢛⡗⡇⠀⠀ ⡆⠀⠀⣼⡿⣿⣏⠘⠀⠉⠀⡆⠀⠀⢀⡩⠅⠃⣈⣉⣭⠀⠀⣯⡧⡘⣰⡇⠀⠀ ⠐⣀⠐⠉⠀⣼⢿⣧⡀⠒⠊⡈⠕⢈⣤⣶⡾⠟⠛⠉⡋⠁⡰⠸⢔⣵⣿⡇⠀⠀ ⠀⠑⡄⠔⡈⢽⢁⠹⣷⡄⠨⡀⠼⣿⡿⢋⡀⠄⡂⠎⠀⣴⠃⢎⢷⡿⠟⡇⠀⠀ ⠐⠀⠊⠽⡛⢤⠉⠒⡟⢝⢦⣈⠓⠾⠋⠤⠴⠞⢀⣤⣾⡿⠀⠐⢭⣶⣾⡆⠀⠀ ⠀⠀⡎⠀⠈⠐⠭⣻⡚⠶⢌⠉⡉⡶⡒⢀⡤⢶⣿⣿⠿⠃⡀⢰⣿⣿⣿⣷⠀⠀ ⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⡈⠙⠋⠀⠌⢠⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⠉⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠢ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢠⢠⠀⢠⢠⠀⠀⠀⠉⠲⡞⠹⠲⠀⡏⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠮⢂⡠⠅⠀⠠⠤⡀⠃⠁⠀⠀⠇⠀⠀⡄⡇⢸⡇ ⠀⠀⠀⠀⣠⠲⣴⠃⠀⠎⠂⡔⢡⣔⡉⢁⠚⡕⢊⢢⠰⡰⠀⢰⠀⢇⢣⠃⠘⢇ ⠀⢀⡏⢇⢏⡆⠸⡀⠀⠤⢸⢠⠙⠂⠌⢁⠊⢄⡀⡆⡆⠄⡄⠀⢣⠈⠂⠀⢀⠇ ⠀⠸⣧⠘⣼⣸⠀⡇⠀⢉⡘⡄⢆⢪⡴⠅⠓⠊⠠⠥⣁⠉⠀⢰⠊⢇⡠⠒⠁⠀ ⠀⠀⢻⡧⡈⠇⠀⢇⠀⡐⠘⢈⡶⠁⠀⠀⠀⣀⠀⠀⠀⠑⡀⢧⠵⢾⡁⠀⠀⠀ ⠀⠀⠀⠙⢦⣈⣀⠈⠁⡧⡆⡎⠀⢀⡔⠋⠉⠀⢩⢻⣶⡒⡇⡈⡶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⣿⣊⣇⢰⠔⣿⣿⠆⢴⣲⠀⢙⠛⠀⣰⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣧⣀⠀⠐⢲⢿⠾⢀⣠⡖⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢉⡵⠶⠖⠚⣿⠻⠤⡟⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣖⡝⠆⠀⠀⠀⡌⡧⡑⡱⡈⣞⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠙⡽⢷⢸⠀⠀⠀⠀⢁⢠⠐⢡⣱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠚⠀⠈⡞⠒⠒⠒⠓⠚⠊⡹⡀⠲⣡⠀⠀⠀⠀⠀ ⢀⣤⠴⠶⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⢔⣒⠆⢄⠀⢰⠁⠈⠀⠉⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⢂⠀⢹⠉⡉⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⠵⠀⠀⠨⠼⠬⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠀⡀⠀⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠖⢁⠀⣴⢱⡇⣀⠀⣄⠀⠀⠀⠘⡄⠀⠀⠀⠙⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⡽⢡⠋⣼⠃⡏⡇⣯⢆⠘⡄⠀⢀⠀⠸⡈⡆⠀⠀⠘⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡼⡽⠀⡎⡸⢹⢰⠁⢹⢻⢞⣆⢹⠀⠸⡀⢠⡇⢸⠀⢰⠀⡕⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡴⠟⣻⢁⣸⢠⠃⢸⣼⠀⠀⢫⣮⣾⣎⣇⢱⡇⢸⡟⡸⠀⣿⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣧⢸⣿⢸⠀⠘⣿⣠⣶⣫⣿⣬⣻⣿⣸⡇⣾⣇⣇⢰⢿⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡿⣾⢻⣾⡦⡄⠹⣇⢻⡏⣷⣿⣿⣿⣿⣧⣿⠿⣿⣿⡇⢰⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⣏⣿⣏⣷⣆⠙⠄⠓⠭⠽⠋⠎⢸⣿⡟⡄⠀⣰⡇⡜⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠉⢻⣞⡏⠀⠀⠀⠀⣀⡀⣠⠾⠓⠛⠤⢴⣧⢧⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠻⡉⠠⠤⢒⣚⣉⡜⠁⣀⣀⠀⠀⠀⠙⢟⢾⣦⢜⡦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠲⣌⠉⠁⢠⣧⠊⡵⢒⣻⣦⢾⡇⠀⢳⢻⡳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⢻⡇⢸⠀⡇⠀⣹⠊⠀⠀⢘⣆⠱⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢻⣸⡀⠓⠖⢁⣴⣒⣲⢾⢿⡄⠙⢆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢵⣄⣠⡿⠉⠚⠋⠸⣼⡇⠀⠀⠑⢤⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢳⣩⡿⢶⣄⡀⠀⠀⢿⠃⢀⠆⠀⠀⠈⠑⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⣿⠀⠀⠈⠫⡓⡄⠈⣆⡜⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⠒⠯⣷⣸⣃⣀⠇⢸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠲⣿⠝⢻⡧⠤⠔⠃⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡎⣤⢃⡇⠀⢳⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢭⣀⡀⠀⢱⡀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⡛⢙⣷⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢜⡆⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣙⣆⠀⠀⠀⠀⠀⠘⡄⢀⡴⠊⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠭⣙⣆⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠢⠭⣆⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⢀⡩⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢏⠉⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⡤⡞⣹⢶⢻⣿⢿⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠹⡀⣠⢔⣿⣔⣿⢶⣷⢿⠿⣾⠧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢧⠀⠀⠀⠀⠀⣯⠾⠭⣹⣿⣿⣤⣿⡷⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⣇⠀⠀⠀⠀⠸⣏⢹⢸⣹⣧⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣳⡟⡄⠀⠀⠀⠀⢳⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡛⠛⠓⠚⠒⠒⠒⠒⠚⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⠤⠤⢀⠀⠀⠒⠠⡀⠄⠀ ⠀⡰⠟⠭⠭⣐⠫⢜⢦⠀⠀⠈⡌⡀ ⢰⠃⡇⢍⠐⠠⢬⣢⠿⡇⠀⠀⠀⠁ ⠸⣞⢬⢶⣤⣾⡄⠙⡴⠻⠂⠀⠀⠀ ⠀⠑⠮⣲⣽⣦⣀⣸⡕⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣉⣼⡏⠉⢻⣶⣤⣀⠀⠀ ⠀⠀⢀⣾⣿⣿⣷⣀⣮⡿⣿⣿⣇⠀ ⠀⠀⣼⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡄ ⠀⠀⣿⣿⣯⣽⣿⣿⣿⣷⣾⣧⣜⣧ ⠀⠀⣿⣿⣃⣿⣿⣿⣿⣿⣿⣷⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡟ ⠀⠀⠉⠛⢻⡿⢿⣿⣿⣿⠿⣿⠀⠀ ⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣾⣿⠀⠀

⠀⠀⠀⢰⢕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⡵⣄⠀⠀⠀⠀⠀⢀⠔⣥⡠⢤⡬⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣵⣻⢝⢰⡄⠀⢸⢘⠀⠀⢀⣌⠇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⡀⠹⢵⣵⣋⢖⡿⣤⠚⠋⠀⠉⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢔⠎⣠⠟⠓⢒⠟⣿⢻⣂⠉⣶⡊⠁⢉⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠘⢫⡴⠀⠘⣟⣊⡻⣿⢷⠆⢏⠛⠉⡼⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠄⠀⠘⠶⣴⡿⠥⠔⠈⢂⠀⠀⣼⢸⡇⠚⢢⡔⠒⠻⠘⡌⠂⠄⡀⠀⠀⠀⠀ ⠠⠀⠀⠀⣠⡏⠀⢄⠢⡀⠘⠀⠀⡟⠈⣿⠀⠀⡁⠀⠚⠀⣿⠀⠠⠊⠂⠀⠀⠀ ⢇⢀⣠⣾⣿⣿⣦⣿⣿⣿⣦⡇⠀⢸⠀⣿⠤⢴⠗⠁⠠⠀⡏⠧⠃⠀⠘⠀⠀⠀ ⠀⠉⠉⢿⡿⡉⠉⠉⠙⣍⣿⣧⠃⠸⠀⣇⠴⢵⠤⢤⢀⡇⡇⠀⣧⣶⢦⠇⠀⠀ ⠀⠀⠀⠙⣆⠈⢄⠀⠀⢹⣿⡟⠀⡀⢠⣸⠀⢸⠀⢸⢸⣇⢃⠀⣿⣿⣷⣶⣖⡄ ⠀⠀⠀⠀⠈⠳⣌⠥⡀⠘⣉⡇⠀⠇⠸⣿⠀⢸⡀⢸⢈⠟⡠⠊⣯⠉⠈⢻⣯⠟ ⠀⠀⠀⠀⠀⠀⠑⠅⢸⢿⣿⣿⢦⡈⢆⠈⢷⣸⣈⡹⢋⣌⣤⣤⣿⢰⠀⢳⠙⢖ ⠀⠀⠀⠀⠀⠀⠀⢿⣷⢚⣟⡟⣽⠷⣤⣑⡀⠫⣎⣠⣾⠿⢟⠻⣇⠘⠀⠀⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢕⠉⠥⠥⠤⠤⠀⠀⠀⠀⡀⠴⠲⠀⠆⠄⡁⢀⡤⣬⡆

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠟⠙⠛⠶⢞⣛⣻⣽⠷⠶⣤⣴⣿⣧⣭⣹⣭⣽⣿⣿⣿⣿⣴⣿⣿⣫⢿⡇⣾⢷⢁⣠⣶⣿ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢠⠀⠐⡲⠤⣀⠀⠀⠈⠙⠧⣍⢷⡞⠁⠀⣉⠭⣙⣲⠿⢻⠧⠌⣉⣻⣟⣿⣯⠘⣷⡘⠿⣻⣿⠿⢻ ⠀⠹⡄⠀⠀⠀⠀⠀⢀⡜⠁⡖⠀⠀⢢⠀⡙⢦⡈⠑⠦⣄⠀⠀⠈⠳⣄⠀⠘⢝⡛⠟⠁⢀⣾⣤⣤⣤⣤⣴⠚⣿⣷⣿⣿⡿⠋⢹⡠⠞ ⠀⠀⠙⡄⠀⠀⠀⣠⡿⠀⠀⢹⢠⠀⠀⠱⣕⢄⡉⠢⣄⠘⢷⣶⢦⡀⠈⠳⣄⠀⠀⢀⡴⠿⠭⠐⠛⠋⢉⡠⢊⣾⢻⣟⢣⡇⡠⠊⠀⠀ ⠀⠀⠀⢳⠀⠀⣰⣿⠃⣸⠀⡜⢧⠳⡀⠀⠈⠳⣽⣦⣄⣙⠲⢌⣳⣽⣆⠀⠈⢷⣶⠯⣄⣀⣀⣀⡠⠖⢉⡴⡳⠃⢸⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⢸⠀⢰⠏⡏⢀⡿⠀⡇⠈⠳⣝⢷⢤⡀⠈⠙⠻⢿⣉⠑⠒⠿⢿⣷⡀⠀⢻⡓⣦⣄⣀⣀⣠⠞⠻⣄⠀⢠⡿⢹⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⢠⡟⢸⠁⢸⢸⣸⠁⠀⠀⠈⠛⠷⣬⡑⠒⠒⠚⠉⠀⣀⡤⠆⠙⣿⡄⠀⢳⣌⠙⠒⠚⠃⡰⠳⡈⣦⢫⠇⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⠓⡏⠀⢸⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣤⣄⣀⠈⣿⣆⠀⢻⣬⡓⢺⠂⣇⢀⡇⢸⠋⢰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⠗⢀⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠿⢿⣿⡄⠈⣏⢻⣿⡄⣯⢥⡀⢸⢀⣾⡇⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣏⣤⣿⡇⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠛⣻⡿⣏⣿⣶⢽⡆⣼⡛⣿⠀⠸⡄⠙⡇⢉⡆⡇⣼⣾⣾⡇⠀⠀⠀⠀⠀⠀ ⡯⠛⠵⡿⡫⠃⡇⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠹⠀⠻⣭⣭⣾⡾⠃⠀⢹⣧⠀⢳⠀⠉⣉⡴⡱⢡⡿⢻⡇⠀⠀⠀⠀⠀⠀ ⢿⣖⠒⠀⣠⣴⣧⠀⢹⣦⣤⣤⣴⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠁⠀⠀⠀⠀⢏⡆⠈⡆⠀⣁⣿⣿⡿⣴⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠙⣷⣾⡿⢿⣿⡀⠸⣏⢘⣿⣾⢯⣻⣎⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢱⠀⡏⡏⣼⢻⠸⣿⣉⡀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⢀⣼⣏⣇⠀⣿⣾⣏⢹⣿⣿⣏⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠘⣶⣇⠹⣟⣿⢃⡇⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡿⠟⠁⠻⡄⢸⣿⣋⡗⠶⠛⠉⠀⠙⠢⠤⠂⠀⣀⡠⠤⢤⣀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⣿⣦⣬⣿⡎⣼⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⠀⠀⢳⠈⣿⡿⣄⠀⠀⠀⠀⠀⠀⢠⡶⠛⠁⣀⣤⣴⣿⣆⠀⠀⠀⠀⠀⠘⣿⠀⣿⣿⣿⣯⣼⠀⣿⢀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠈⣆⠸⣻⣾⣦⡀⠀⠀⠀⠀⠀⢇⣤⣾⣿⣿⠟⠛⣛⡆⠀⠀⠀⠀⣴⣿⠀⣿⣿⣿⣿⣿⡆⢿⣦⡀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡄⢳⣳⣜⡹⢦⠀⠀⠀⠀⠈⢿⣿⣇⡠⠖⠋⡩⠁⠀⠀⣠⣾⣿⣿⠀⣿⣿⣿⡇⠹⣿⣸⣿⣷⣜⣿⣦⣄⣀ ⠀⠀⠀⠀⢩⡛⠀⠀⠀⠀⢱⠈⢷⣽⣇⢀⡿⣦⡀⠀⠀⠈⠻⣅⣠⠴⠊⠁⠀⣠⣼⣿⣿⣿⡏⢸⣿⣿⠟⠋⠀⢻⣿⣿⣿⣿⣿⡿⣿⣿ ⠀⠀⠀⠀⢀⠏⠀⠀⣀⣀⣀⣳⣈⡻⣿⣭⣴⡏⠙⠲⡤⣀⡀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠃⡸⠻⠏⠁⠀⠀⠀⢻⣿⣿⡿⠛⠁⣼⠿ ⠀⠀⠀⣠⠎⠀⢀⡾⠉⠀⢹⠋⠉⣿⣿⠛⢺⡇⠀⢰⡇⠈⣿⡛⢶⣻⣿⣿⡏⠉⠀⠉⣿⠇⠀⡇⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⣸⠃⢠ ⠀⠀⠀⡙⠀⢠⡞⠀⠀⡀⢸⡄⠀⣿⣇⠀⣸⢧⣠⣾⠁⢀⣿⡇⣼⣿⣿⡿⢿⠀⠀⠀⢿⠀⠀⠘⣄⠀⠀⣰⣿⠟⠁⠀⠀⠀⣰⠃⢠⣿ ⠀⠀⡠⠁⢠⠟⠀⠀⡼⢻⡌⠛⠻⣿⠿⣻⡟⢺⣿⣯⠀⣼⣿⣧⣿⢿⡿⠁⢘⠇⠀⠀⠘⢷⣄⣠⣿⣦⣾⡿⠁⠀⠀⠀⡠⣿⠏⠀⠚⠉ ⣤⣊⡀⢠⠏⠀⠀⣸⢃⣀⣿⣄⠀⠈⢿⣿⣇⣀⣯⣏⣿⣿⣿⣟⣵⣏⣀⣀⣼⣀⣀⣀⣀⣀⣹⣿⣿⣿⣋⣀⣀⣀⣠⣞⣠⡏⠀⠀⣠⡀ ⠀⠀⠀⠻⢦⣤⣴⡏⠀⠀⠀⠹⣦⣤⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠴⠟⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⡒⠒⠒⠦⢄⡀⠀⠀⠀⠉⠙⠢⡈⠳⡄⠀⠀ ⠀⠀⣴⡿⢍⣉⠛⠓⠶⢬⣐⠻⢦⣄⠀⠀⠀⠀⠘⡆⠹⡀⠀ ⢀⡾⠋⣠⢀⣉⠁⠛⠲⠤⣌⠙⠂⢻⣍⠀⠀⠀⠀⠛⠠⡇⠀ ⣾⢿⢸⡅⠀⣀⠉⠑⠢⣤⣌⣳⣤⡿⡿⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⡘⡆⠹⣄⢉⣁⠀⣰⡄⠙⠪⡇⠉⣹⣧⡄⠀⠀⠀⠀⠀⠀ ⠸⣷⡘⢶⠻⣿⣾⢶⠿⣼⠂⠀⢠⡾⠋⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⣝⣮⠳⣬⡻⣿⣔⠃⠀⢠⡟⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠮⢿⣿⣿⣷⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⣼⣿⠀⠉⠉⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣇⠀⠀⡼⣾⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⢿⣄⣸⣷⣾⡻⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⠛⣿⡿⠻⣿⣧⠀ ⠀⠀⢸⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣷⣾⣿⣊⣉⠻⣿⡆ ⠀⠀⢸⣿⣿⣿⡿⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣽⣿⡇ ⠀⠀⢸⣿⣿⣿⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⡿⠿⠟⠀ ⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣿⣿⣿⣿⣿⣿⣄⣼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⡠⢞⡟⣡⣴⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢡⠞⢠⡿⢋⣔⣡⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⣿⣿⠏⠀⠋⠐⠋⠁⠀⠀⠀⠰⠶⠶⣟⡛⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⠒⠶⠴⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠿⠂⠀⠀⡄⡴⠛⣎⣦⡀⠀⢦⡀⠀⠀⠀⠀⠀⠈⠳⣽⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⡄⠀⠀⡆⢰⣹⠃⠀⠘⣿⡷⡀⢬⣟⢆⠀⣀⠀⠀⠀⠰⣬⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⠋⡀⠀⢸⡁⣿⡏⠀⠀⠀⠘⣿⠹⣜⣾⡌⢆⠸⡄⠀⠀⠰⣌⣢⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣡⣯⡾⠁⠀⣾⢸⣿⠃⠀⠀⠀⠀⠹⣆⣽⣿⣽⡈⣆⣧⢸⠀⠀⠈⢿⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢀⡀⠀⣿⣿⢻⣄⠀⠀⢣⡀⠀⣹⠁⠹⣿⣷⣼⣿⣾⠀⠀⢳⠮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⢹⠁⠀⣿⣿⠟⢉⣍⡲⣦⣷⣜⣭⣧⠖⣻⡉⠻⣿⣿⠀⠀⣼⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣶⣿⣻⣄⠈⢛⣃⡼⠀⠀⠀⢣⡀⠙⠃⢠⡿⢿⣤⣤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⣿⣿⡇⠉⠉⠙⠉⠀⢨⡅⠀⠀⠿⠿⠿⠓⢀⣿⣏⣹⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⢿⡀⠀⠀⡀⠀⣀⣓⣁⣀⣠⠤⠀⠀⡼⢛⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠳⣀⠀⠉⠉⢩⡥⠤⠄⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢼⣿⡶⠤⣀⠀⢀⡠⠔⢺⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡤⠴⣿⠁⡼⢡⠗⡄⠀⠉⠁⠀⠀⢸⠉⢳⠈⢳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⣻⠂⠀⡆⠀⢸⠀⡇⠈⠀⢱⠀⠀⢀⣀⠼⠾⡖⠚⠛⠛⠓⠚⠻⠷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⠃⠀⠈⢹⠀⠀⡇⠀⢸⠀⢹⠤⣀⣀⠷⠺⡉⠀⠀⠀⢹⡆⣋⠀⠀⠀⠀⢀⣞⡌⠙⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⢸⡇⠀⢡⠀⠈⡇⠈⣆⠜⠉⠳⣄⠈⢧⡀⠀⠈⠓⠛⠀⠀⠀⠀⢠⠎⠀⠀⠀⣈⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢇⡔⠁⠀⠀⠀⠑⢅⢀⡡⠴⠒⠚⠛⠛⠒⠢⢤⣀⠀⠀⡠⠊⣰⠟⠹⣄⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⡴⠋⠀⡀⠀⠀⠀⠀⠆⠀⠀⠈⠑⢤⣀⣨⠖⠁⠀⠈⢆⠀⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⣰⠗⢸⠀⠀⠀⠀⡼⠶⠒⠢⢤⣀⣠⠋⠀⠀⠀⠙⢄⠀⠀⡌⠀⠀⠀⠀⠴⠋⢻⣄⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⢸⡇⠀⠀⡰⠁⠘⡟⠀⡄⠀⢀⡇⠀⠀⠀⠀⢠⠛⠦⣴⣿⡆⠀⠀⠁⠀⠁⠀⠀⠀⢀⡠⠄⠀⢿⡆⠀⠀⠀⠀⢹⠀ ⠀⠀⢀⠏⠀⠀⠀⠀⠀⢠⠇⣰⠁⠀⠀⡏⠣⠤⠤⠄⣿⢠⠞⠉⢹⠃⠀⠀⠀⠀⣀⣀⡤⠬⠥⠤⠤⢄⣸⣷⠀⣀⡠⠴⢺⠂ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⣤⠇⠀⠀⠀⡇⠀⠀⠀⠀⢻⢉⠇⠀⠼⠤⠤⠔⠚⠉⠁⢤⠀⠀⣀⣠⣄⣀⣯⣽⠀⠀⠀⠀⢸⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⣸⣿⢀⣀⣀⡄⣇⡠⢤⣤⠴⠘⡞⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣉⣀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⡇⠸⡄⠀⠀⠀⠹⡁⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠀⡇⠀⠈⠉⡓⠺⡼⠀⢤⣤⣀⣀⡏⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡷⠀⠀⠀⠀⢹⣤⡤⠴⠚⠱⣤⠀⠀⠀⠠⠔⠒⠒⠀⠀⠻⣍⣛⣒⣷⡖⠁⠀⠈⠉⢙⡟⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⢒⡞⠉⡄⣸⣿⣟⣩⠼⠿⠿⣧⣀⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⢀⣿⣦⢾⣟⢻⣿⣻⣿⢦⡘⣄⡘⠻⣿⣟⢿⣆⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⢁⣤⠰⣇⣴⣿⡭⠾⠿⠛⢛⣷⡏⠉⠉⠉⠙⠛⠓⠛⠿⢄⣿⣷⣿⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⢸⣏⠶⠛⠁⠀⠀⠀⢀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⢷⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⢹⣦⠼⠋⠁⠀⣀⣤⣤⠀⠀⢸⣦⣿⣿⣿⣿⣷⣤⣀⣀⣠⣾⠁⠀⠀⠀⠀⠀⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠾⣿⢛⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣠⡤⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠏⢸⠁⠘⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⠃⠀⢸⠀⠀⠘⢿⣿⡇⠀⠹⣿⠈⢿⣿⣿⣿⣿⣿⣿⣷⣦⡤⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⡰⠊⡅⡁⢀⣼⣿⣿⣿⠃⣀⣀⠸⠀⠀⠀⠈⠻⡇⠀⠀⢘⣆⡨⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢡⢾⣾⣾⣿⣿⣿⣿⡏⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⢹⣿⣿⣿⣦⢶⣶⣶⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⡅⠀⠀⠀⡏⣾⣿⣼⣿⣿⣿⡿⠀⠀⢀⣠⣀⡀⠀⠀⢰⠀⠀⠀⠀⣠⣤⢤⡄⠈⠈⣿⣿⣿⣿⣎⣿⣯⢧⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣹⠿⢻⣿⣿⠃⠀⢠⡟⠉⠉⠛⠀⠀⢸⡀⠀⠀⠘⠋⠀⠀⠙⠀⠀⢻⣿⣿⡋⡟⣿⣿⣸⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⠀⡄⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣁⣀⣀⣈⡉⠉⠉⣋⡁⠀⢼⠟⣿⣿⣽⣿⣿⣇⡄⠀⢀⠇⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⣰⣰⣖⢆⢇⡘⠞⣿⡄⠀⠀⢠⣴⠒⠉⠁⠀⠀⠀⠀⡀⠀⠈⢉⣿⣿⣦⡀⠈⢻⣷⢿⣿⣿⢟⠈⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠸⣄⠀⠹⡷⣿⣎⢿⣧⠰⣚⡧⠀⠀⠸⡀⣄⣴⣶⣿⣿⣿⣿⣿⠿⢶⣎⣴⣞⡆⠀⠀⠀⣧⠾⠃⠁⠉⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⠐⣵⣿⣿⢺⣿⣷⣮⣇⠀⠀⠀⠹⣯⡽⠋⣦⣀⣹⣿⣁⡀⢸⠛⢿⣯⣤⠠⠄⣰⠛⢾⡤⠶⢂⠉⡏⠙⠢⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣌⢣⡿⠿⣷⣽⣫⣿⣄⠀⢸⣷⣼⣷⣋⠁⠀⠀⠀⢀⠼⠋⠛⠀⠛⢿⣂⣴⡥⠞⠁⣶⣶⣼⠔⠁⠀⠀⠈⠳⢤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⣀⠘⢿⣿⣿⣟⠳⡾⣏⣙⠉⠀⠉⠉⠉⠉⠁⠀⢀⣠⣶⣶⡎⠹⠃⠀⢀⣽⣾⡟⠁⠀⠀⠀⠀⠐⠛⠀⠙⠳⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢬⣁⣈⠋⠛⢥⠐⣿⣿⣿⣿⣏⣿⣿⣿⣿⣯⣙⣁⣠⡇⠴⢾⡏⣡⠟⠃⠀⠀⡀⠀⢠⢋⡆⠀⠀⠀⡈⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢽⣿⣿⣿⠇⠀⠉⠙⠛⠻⣿⡛⠇⢹⣿⠟⠛⣧⡶⢶⠟⠁⠀⠀⠀⠺⠇⠀⠈⠛⠁⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠈⢹⡿⠀⠀⠀⠀⠀⠀⢻⣿⡇⢸⣿⢸⣻⡿⠁⠈⣦⠀⠀⣀⡀⢠⣤⣄⠀⠀⣴⣤⠀⠀⠀⡈ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠒⣤⣴⣾⡎⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⠜⣡⣷⡶⠚⣏⠁⢀⣛⡁⢫⡱⠜⡇⢰⠉⠙⡀⠀⡀⠀

⣄⣈⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠉⢻⣿⣿⣿⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⣵⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀ ⣿⣿⣞⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⣿⢹⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀ ⣿⢸⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⢟⣵⣿⣿⣿⣿⡟⣑⣵⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⣿⢸⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠘⢿⣿⢋⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡏⣿⣭⣽⣽⣿⠿⣿⣄ ⣿⢽⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠈⠘⣿⣿⣿⣿⡄⠘⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⡄⠀⠉ ⣿⢸⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠈⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢻⣿⣿⣿⣿⢯⣿⣦⡀ ⣿⢸⣘⣻⣿⣛⣛⣵⣿⣿⣿⣿⡟⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠈⢿⢟⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢳⣿⣿⣿⣿⢿⣿⡿⢿⢿⡿⣿⣿⡙⠛ ⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣷⣮⣝⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣀⠴⠚⣙⣿⣟⣿⡟⠀⠹⣷⢸⣿⣿⣿⣿⣮⣭⣽⣾⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⡗ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⢞⡥⠒⠋⠉⠘⡇⠉⠉⠓⠲⣽⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣴⣻⣾⣿⣿⣿⢳ ⣜⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⠞⠁⠀⠀⠀⠀⢠⣶⣶⣆⠀⠀⠈⢻⡀⢩⣿⡿⣿⣿⡿⠿⣿⣿⡷⣫⣿⣿⣿⣿⡿⣏⠉ ⣿⣎⢿⣿⣿⣿⣿⣿⡆⠀⢿⣿⡆⠀⠀⠀⠀⠻⡝⠆⠀⠀⠀⠀⠀⠀⠓⠶⠟⠁⣠⠏⠀⠀⠀⠀⠀⠀⠸⠿⠿⠋⠀⠀⠀⠈⠳⡀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣤ ⣿⣿⣯⢿⣿⣿⣿⣿⡇⠒⠚⢿⡗⠒⢒⣶⣴⢶⣶⣤⢤⡀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⣿⣿⣿ ⡿⣫⣶⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⡔⠋⠉⠀⠀⡀⠉⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⢀⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣾⣆⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢠⠄⠀⠀⠀⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⠻⢿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠀⠁⠈⠀⠀⠀⠈⠉⠁⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠶⠒⠒⠉⢱⣤⠴⠛⠀⠀⠀⠀⠟⠀⣿⣿⣿⡿⠋⢉⣠⠥⡀⠻⡌⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣳⣤⠤⠖⠛⠁⠻⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⢀⡴⠋⠀⠀⢹⠀⡇⠀⠀ ⣿⠟⠋⠀⣿⠋⠻⣿⣿⣿⣿⡄⠀⠀⠦⢤⣀⣀⣀⠤⠞⠁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠐⡺⣗⠀⠀⠀⠀⠀⢀⣿⠃⢠⠟⠀⠀⠀⠀⡟⠀⡇⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠟⢠⡿⠒⠒⢦⡀⠀⢱⣿⠇⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⢻⣹⣽⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠁⢀⣀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇⠀⠀⢸⠇⠀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢦⢹⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⠴⠚⠁⢀⡴⠋⠀⣠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⠸⡟⣧⠀⠀⠀⠀⢀⠀⠀⢰⠋⢀⣀⡠⠤⠤⠤⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠚⣷⠀⠀⠀⠀⠀⠀⢀⣾⣁⣠⣤⠤⠖⠋⢀⡠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⢿⣧⠁⠀⠀⠀⢀⠀⠘⢿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠁⠀⠀⠀⠀⢀⣴⢋⠉⠉⠉⣁⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣷⡝⢷⡀⠀⠀⠀⠲⡄⠀⠉⠓⠒⠢⠤⠤⢤⣤⣤⣤⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠿⢶⣔⢄⡀⠈⠀⠀⠀⠀⠀⠐⠶⠤⠤⠤⠴⠶⠂⠀⠀⠀⠀⠀⢀⣴⣾⣷⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣽⢟⣿⣷⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣤⣀⣀⠀⠀⣀⣠⣴⣾⢻⠟⠫⢍⣶⣞⣿⢷⡿⢀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠙⠻⠿⣟⣻⡿⠃⠉⠁⠀⠀⡼⣿⡝⠁⢰⠇⠸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠓⠀⠀⠀⠀⠀⠃⣷⠁⣠⠃⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠲⠋⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⢹⣻⠶⣤⣤⣀⡀⠀⠀⠀

⣶⣧⡜⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⡿⠀⡼⢰⡀⠀⠀⠀⡄⠤⢧⠤⢦⡀⠀⠀⠠⠄⠀⠀⠀⠀⢀⣆⣴⣀⡄⠀⠀ ⣿⡇⢸⠃⠸⠇⠀⢠⠊⠐⢄⠀⠑⠀⠉⢣⠀⠀⠀⠀⠀⠀⡴⢏⠀⠑⠀⠙⠢⡀ ⣿⠀⡟⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡇⢠⡄⡜⠀⠀⠁⠀⠀⠀⠀⢱ ⣿⠀⡇⠀⠀⠀⣷⡆⠀⠀⠀⠀⣶⡆⠀⠀⠇⠀⠀⠘⣄⡇⠀⠀⠀⠀⣴⡄⠀⢸ ⣿⣰⠧⠀⠀⠀⠘⠿⣄⡀⠀⠀⠀⠀⡀⠌⠀⠀⠀⠀⠈⠛⠢⠤⠤⠤⠤⠀⠐⠛ ⠋⠁⠀⢀⣀⠀⠀⠀⠈⠉⠉⠐⠈⠉⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠄⢀⡤⠤⠤⠤⠀⠀⠀⡴⢶ ⠀⠀⢸⡉⠢⢄⠀⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⢀⢹⠀⡌⢡⠀⠀⠀⢀⠄⠊⢀⠞ ⠁⠀⠈⠙⠢⣀⠈⠒⠤⣀⠀⠈⠑⠂⠤⠄⣀⡈⠈⣄⣉⣁⡠⠔⠊⢁⠤⠊⢁⠌ ⠀⠀⠀⠀⠀⠈⠑⠢⢀⡀⠉⠐⠢⠤⣀⣀⣀⡇⠀⢱⣀⣠⠴⠖⠊⠁⡠⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣀⡀⠀⠀⠙⠒⠉⠀⣀⣀⠤⠐⠉⠀⠀⠀⠐ ⣖⣢⣤⢤⡀⣀⡀⠀⠀⠀⠀⢀⠔⠈⡀⣽⠿⠋⠉⠙⠻⢿⡉⠳⠄⠀⠀⠀⠀⢀ ⣿⡿⣷⣾⣷⣿⣯⡾⠅⠀⣦⠊⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣴⣶⣴⣷⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠐⡂⠉⠀⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠎⢄⣎⠇⡦⢡⠀⠀⢡⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⡏⡌⡞⡞⠘⣿⣇⢇⣠⢰⣼⢀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⢸⡞⡇⠀⢧⢤⣻⣽⣿⣿⣸⣈⣸⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣷⡜⠌⠜⠿⠿⣿⣿⠙⣻⡘⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠋⣻⠇⠀⣀⠠⡠⠛⠛⠲⢿⣆⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠁⠑⢍⠂⢹⡔⠔⣶⣴⠎⢫⡏⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠽⣼⠸⡤⢃⣤⣸⡎⢂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣴⠋⠉⠹⡗⠀⠑⠌⣂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⡏⠙⢖⠀⢃⠄⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⢬⡷⣇⢘⠜⠈⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⡜⠇⠐⡄⠀⠀⢡⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣖⣲⠀⠀⠀⠣⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡑⢣⠀⠀⠀⠱⠀⢀⠄⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⠥⡄⠀⠀⢋⠀⠀⠈⠑⠠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡝⠂⠀⠈⠆⠀⠀⡀⣴⣬⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢰⣴⠼⣾⡗⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⢻⣿⠿⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠿⠵⠤⠤⠼⠅⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⡘⠀⠟⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⢰⠟⣸⣇⣿⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⣤⠶⠛⠛⠛⠉⠉⠉⠉⠙⠛⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠾⠶⠒⠶⠒⠲⠿⠗⠚⣶⠶⠞⠛⠛⠛⠷⣤⣤⣄⣀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⣤⣄⠙⢳⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣦⣴⣿⣶⣶⣤⢤⣄⡀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠳⣽⣄⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠋⠀⠀⠀⠀⠀⢀⣤⡄⣠⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠻⣿⠘⢿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠈⠛⠷⣄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⡀⠀⠀⠀⢀⡀⠸⢷⡞⠉⠼⣀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⢻⣇⠈⢻⣿⣿⣿⣿⠙⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡇⠀⠀⠀⢸⣿⡶⣾⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⣿⡀⠈⠻⣿⣿⣿⠀⠘⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣇⡀⠀⠸⠿⡇⡏⢻⢿⠟⣏⣿⣿⣿⣿⠋⣿⣿⠀⠀⠀⠀⠘⣷⠀⠀⠹⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣦⠀⠀⣄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⢷⡘⣷⣿⣿⣿⣿⣿⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣤⠴⠾⣿⡿⣿⣿⣿⣿⣷⡀⢘⣷⡀⠀⠀⠀⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⢠⣿⡿⠋⣿⣿⣿⠀⠀⢸⣍⣙⠓⠂⠀⠀⠀⠀⠚⢫⡽⠶⢦⡀⠉⠁⣿⣿⡿⠻⣿⣷⡘⡏⣷⠀⠀⠀⠀⠀⠙⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣶⡀⢻⣿⣿⠀⣴⠟⢉⣯⢻⣆⢀⣄⠀⠀⠀⠏⢀⣶⣄⢹⡆⠀⣿⣿⣡⡦⣸⠛⣧⣙⣋⣃⠀⠀⠀⠀⠀⠈⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣏⣿⡀⠻⣄⠘⠿⢫⣋⠀⡿⠀⠀⠀⣦⡈⠉⣁⡴⠁⠀⣿⣿⣻⣳⡟⣠⡿⢿⠛⠋⢠⣦⡄⠀⠀⢀⣼⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⣧⠀⠙⠲⠾⠛⠁⢸⡃⠀⠀⢀⣈⣙⣿⣹⡧⠆⢀⣿⢟⣫⢿⠃⠉⠶⠛⠀⠀⠀⠉⣀⣀⣴⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⣤⡀⠉⠀⠀⠈⢉⣩⡿⠁⠀⠀⣾⣶⡿⠓⠚⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠀⠀⣠⡾⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⡀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣦⣤⢴⣶⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢾⣼⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠇⠀⠀⠀⠀⠀⠀⡿⣷⠦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣤⢿⡴⠋⣰⡟⠷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣿⠃⢿⣧⣀⠀⠀⠀⢀⣤⣶⡿⠋⠁⣿⢁⡴⠋⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠁⠀⠋⠀⠀⣿⠙⠇⠀⠀⠁⢸⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⡗⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣫⡉⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠟⠀⠀⠀⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡞⣻⢦⡀⠀⣻⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⢿⢀⡍⢀⡈⣀⣄⣼⣷⠋⢀⢳⣀⠀⠀⣠⣴⣄⣤⠀⢻⠀⠀⣧⡹⠊⢀⣠⢟⣠⣴⢟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡴⣿⡠⢾⣵⣏⡽⠟⢻⣷⣿⠿⢻⣧⠾⣿⣿⠟⠁⠀⠈⠷⣀⣈⣉⠛⠉⠁⠿⠾⠿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⠀⡀⢀⢀⠀⡀⢀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⢖⢠⣤⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠊⡠⠊⠀⠀⠀⠀⡠⣒⣹⣣⣶⣽⣦⢹⡵⣗⢌⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⡑⠀⠀⠀⠀⢀⣞⢿⡗⠂⠀⠀⠈⠉⠘⠁⠁⢣⢳⢶⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⡼⣿⣯⠀⡇⠀⢠⠀⢀⡠⢄⣀⠀⠊⡧⣧⣹⡀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⢀⡿⣿⣂⠠⣀⡗⠒⠲⢤⠈⡨⠂⡸⢣⣷⢍⣷⡃⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⡸⣰⣷⢟⣮⡴⠿⣷⣦⣴⡯⣷⢟⡒⢿⣿⣱⣿⡇⠀⠀⠀⠀⠇⠀ ⠀⡇⠀⠀⢠⠇⡟⢿⡨⠻⡛⠏⠃⡙⠀⠐⡜⠍⣁⢸⠓⣿⣽⠇⠀⠀⠀⠀⠀⠀ ⠀⡆⠀⠀⣡⡀⡿⣟⡆⠀⣈⣯⣁⣀⣠⡤⣔⡀⠴⣼⣤⢙⣿⡎⠢⠤⡀⠀⣨⡀ ⠀⢃⠤⢡⡊⢱⣗⢟⢶⣾⡟⠗⠒⣀⣀⣠⣥⣭⣀⣈⢇⢸⣟⢟⡳⣴⡓⠒⠢⡱ ⢨⠟⠀⡼⣱⡋⠁⣿⢿⡜⠋⢾⠟⠉⢀⣀⣀⠉⢙⢏⢘⣿⢠⢇⢼⢃⣾⡆⠀⢸ ⣏⠀⠀⢣⣳⣄⠳⡜⣬⢻⡢⣑⢝⣃⣀⣐⣒⣂⢥⡆⣼⢸⣮⣦⠈⣿⡏⡕⠀⢸ ⢿⡄⠀⠈⢯⠶⡟⣏⣿⡌⢷⠙⠀⠸⠁⢸⢁⠁⠄⡸⢿⣾⣯⣼⠎⠝⡰⠁⢠⠊ ⢍⡺⠶⢄⡈⠣⡈⢶⣧⡇⢠⠀⠈⠚⠘⠚⠘⠂⠈⢠⡟⣯⡏⣟⢊⡴⠁⡠⣡⢮ ⠤⠔⡎⡹⠙⣷⣶⣄⢹⡔⠘⢇⠀⠀⠀⡀⠀⢰⣠⣼⡞⢡⡿⢣⠎⣠⣎⣶⠟⠁ ⠀⢀⣀⣀⣴⣻⣿⣿⠐⢽⣆⠀⠑⣷⣶⣼⣶⣿⣿⠃⠈⣸⢡⢯⡾⢋⡴⠋⣠⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣟⣲⣷⣾⣧⣲⣾⣉⠳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣿⣿⣿⣿⡟⠉⡿⣿⣿⡶⢤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣩⣾⣿⣏⣿⠏⠀⢰⣃⣿⢿⣿⣅⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠈⠙⣽⣇⠇⠩⠓⠀⠈⢡⡄⢹⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠔⠛⢿⡀⠀⠈⠀⠃⠀⡑⢸⡟⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣒⠚⠥⡒⢤⣀⣀⠑⣄⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⣄⡉⠐⠸⢷⡦⣾⠓⠘⠻⣷⣬⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⣿⣿⢗⣀⠗⢀⣰⣯⡙⢯⡹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠋⠀⢀⣠⣴⣾⡿⠼⢛⡀⢁⣚⣿⣷⣿⣿⡷⣽⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣞⣡⣤⠴⠾⠛⠉⢁⣤⣴⣾⣿⣿⣿⣿⣿⡿⢻⠹⢿⣿⡌⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠚⠉⠀⢀⣀⣤⣴⢶⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣉⣽⣳⡧⡘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⣾⣷⣂⣴⣿⣿⠿⣛⡿⢿⣿⣴⣿⣿⣿⣿⣟⣿⣿⣉⣁⠀⠀⠙⣿⣷⣧⡈⢿⣦⡀⠀⠀⠀⠀⠀ ⠙⠿⠭⠷⣯⠵⠚⠁⠀⢨⠻⠿⢛⣿⣿⣿⣿⣿⣿⣿⡺⣝⠲⢦⣾⡟⢹⣧⡀⡙⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣴⣿⣿⣿⢿⠏⠸⠿⠿⠷⣨⣷⣾⡟⠶⠾⣿⢿⣝⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣭⣿⢫⡿⠃⣾⠀⢀⣀⣠⣧⣀⣿⢻⣧⡄⠀⣿⠈⣿⡎⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⣿⡿⢣⣿⣷⡾⣿⠀⠈⠉⠁⣏⣭⣿⢸⣿⣷⠆⣿⠀⣾⡿⢸⣻⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⡰⢁⣾⠟⢡⣿⣿⣿⢂⣿⣷⡄⣀⣠⣯⣽⣿⡏⢿⣄⢠⡿⣰⣿⡇⣸⡏⢿⣷⠀ ⠀⠀⠀⠀⠀⣜⣷⠟⠁⣠⣿⣿⡿⠋⣼⡿⣿⣿⡦⣾⢿⡟⠻⢿⣸⣿⠟⣷⡟⣋⣬⣽⣷⡈⢻⡀ ⠀⠀⠀⢀⡼⠛⢁⣚⣿⣿⠟⢁⣄⣴⡏⡟⣾⠧⣜⣟⣦⣷⣦⣴⣿⣏⡴⣿⣿⣿⣯⣽⣿⠃⢸⠇ ⠀⣠⠾⢥⣤⣭⣿⠿⠋⠀⠀⠈⠉⡼⣠⡇⣽⣶⡶⢿⡯⠙⣿⣿⡿⠉⢰⡉⢻⣿⣿⡿⠋⣤⠋⠀ ⡞⠋⠉⠛⠻⢿⣧⠀⠀⠀⠀⠀⣼⣿⡿⠟⠛⢛⣿⣾⡶⠾⠿⡇⣶⠇⢼⣿⣾⢿⠏⣠⡼⠁⠀⠀ ⠹⣆⠀⠀⢀⡴⠋⠳⣦⡀⢀⣾⣿⣵⣶⣶⣾⣿⣷⣾⣷⣾⡄⠀⢿⣦⣬⠆⠈⣡⣾⣿⠃⠀⠀⠀ ⠀⠈⠓⠶⠞⠁⠀⠀⢹⣿⠟⢩⡿⠿⢛⣛⣛⡿⠿⢿⡿⠿⣧⣴⡦⣿⣿⣷⣾⣷⡮⠳⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠤⠤⠴⠶⠶⠶⠶⠤⠄⠀⠇⠀⠈⠠⠿⠶⠶⠾⠿⠿⠿⠷⠼⠿⠆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠈⣿⣶⣦⣤⣀⣴⣶⣿⣿⣷⣶⣶⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⡄⠀⠀⠀⡠ ⠀⠀⠀⢀⠞⠁⣀⣤⣶⣾⣿⣿⣿⡿⣿⡏⠀⠉⠻⣿⣿⣿⡙⢿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢄⠀⡰⠀⠠⡀⠨⣧⣌⣆⢀⠎⠀ ⠀⠀⡰⠃⠀⠋⠉⢉⣩⣿⣿⣿⡟⠀⢿⠁⠀⠀⠀⠈⢿⣿⣷⠈⠻⣷⡌⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣄⠀⠑⡷⡈⢦⡙⡅⣽⠏⠀⠀ ⠀⡼⠀⠠⠤⣴⠾⢿⣿⣿⣿⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⣿⡇⠀⢈⣿⡄⠈⢻⣿⣿⡇⠹⣿⣿⣿⣿⣿⣷⡀⠘⣗⡜⢟⣌⡟⠀⠀⠀ ⣰⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢙⣿⠊⠁⠀⠑⡄⠀⠙⢿⣿⠀⠘⣿⣿⣿⣿⣿⣿⡄⠈⡳⡌⢻⠃⠀⠀⠀ ⡅⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡤⠋⠘⡤⠚⠉⠉⠉⠉⠲⢌⠏⠀⠀⠸⣿⣿⣿⣿⣿⣿⡆⢹⠘⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⡎⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣿⣿⣿⣿⣿⣄⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠋⣸⣿⣿⣿⣿⣀⡠⠴⠒⠒⠒⠤⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡜⢠⡴⠃⠀⠈⠀⢻⣿⣿⡿⢿⣿⡤⡟⠀⠀⠀⠀ ⠀⠀⠀⠸⠃⠀⣿⣿⣿⣿⡟⣇⠀⡔⠊⣩⣍⠑⠈⡆⠀⠀⠀⠀⠠⣀⣀⣀⢤⡴⢿⣒⣋⣤⣄⠀⠀⠀⢨⡿⣡⠒⠲⡙⡆⡇⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢰⣿⡿⢻⣿⣧⠀⠘⡀⠀⠉⠁⠀⢰⠁⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⢀⣀⣌⣸⠁⠀⠀⢸⢻⣷⢄⠠⠃⣷⡇⠀⠀⠀⠀ ⠸⡄⠀⠀⣠⠿⠋⠀⠈⣿⣿⣷⡄⠀⠀⠀⢀⡠⠊⠓⠂⣀⠤⠒⠈⢁⣀⣤⣶⣾⣿⣿⣿⣿⡟⠂⠀⢀⡎⢸⠁⢨⠃⣸⡿⣧⠀⠀⠀⠀ ⠀⢱⣀⠀⠁⠀⠀⡠⣰⣿⡿⣿⣿⣦⠀⠉⠁⠀⢀⠴⠊⠁⣀⣴⣾⣿⣿⡿⠟⠋⠁⠀⠀⣠⠃⠀⠀⡼⠤⠾⠖⣡⣾⣻⣿⣿⠀⠀⠀⠀ ⠀⠀⠳⡀⠀⢐⡄⠙⢞⣿⡇⠙⢿⣿⣧⡀⠀⢰⠁⠀⢠⣾⣿⣿⣿⡿⠋⠀⢀⡀⠤⢐⡶⠁⠀⢀⣾⠓⢦⠒⣟⡼⣿⣿⠟⢻⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⣀⣨⣦⡢⠹⣵⣄⠡⢝⣿⣷⣄⠈⠣⣤⣈⠙⠛⣿⣏⡠⠖⠋⠁⢀⡴⠋⠀⠀⣠⣿⡿⠀⠘⡇⢹⡷⠟⠡⣤⠋⠀⠀⠀⠀ ⠀⠦⠄⠒⠉⣩⣛⠑⢯⡡⡀⠈⢱⣶⠿⣜⢿⣦⡀⠈⠛⠿⣿⣋⣁⠀⣤⣴⠾⠃⠀⢀⣤⣾⣿⣿⠇⠀⠀⠙⢥⣴⣶⣶⣾⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠈⠑⢦⡙⠪⣾⢶⣝⣷⡊⡑⠻⠭⠷⠦⢤⣀⣀⣀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠓⠪⢗⣍⣉⢋⣲⠗⡀⠀⣼⠈⠿⣦⢈⣉⡹⣟⠻⣿⣿⣿⣿⡟⠛⠁⠀⡠⠊⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠚⠉⠉⠉⠉⠀⠀⠈⡆⠹⠛⠽⠿⠃⠀⡠⠊⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⡈⢳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⢀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠤ ⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⣀⡀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀ ⣀⡤⢰⣴⠁⠀⠀⢀⠀⠀⠀⠀⢸⠂⡐⣄⠀ ⠻⡇⠚⣟⠀⢀⡀⠿⡿⠇⢀⣀⢸⣴⢣⡽⠃ ⠀⠈⢹⠞⣉⠠⣄⠶⠶⢖⣠⠴⢌⢻⢏⠀⠀ ⠀⠀⣿⠋⢱⢹⣿⡇⠀⢸⣿⡏⠄⠙⡼⠀⠀ ⠀⠀⠈⠂⣤⠷⣍⠠⠹⣠⣀⠌⠄⠚⠁⠀⠀ ⠀⠀⠀⠀⣳⣶⢂⠈⠉⢁⡔⠕⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⣀⠉⠀⠉⢀⣸⢆⢑⡀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⣠⡝⢻⠀⢈⠉⢣⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⢄⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠟⠈⢸⣿⣷⢾⣓⣚⣛⣛⣒⠒⢲⣤⣄⡀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⡼⠿⣿⣯⣭⣭⣭⣭⣍⣉⡉⠉⠙⠛⠺⢆⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣾⠇⣸⣧⣶⣿⠿⣿⣿⡏⠻⣿⣿⢿⣿⣦⣄⠀⠀⣿⠷⣄⠀⠀ ⠀⢀⣴⣯⣀⡏⢰⣿⣿⣿⡯⣀⠙⣿⠁⠀⠘⣿⡌⢿⢿⣿⣆⠀⠘⠃⠨⣷⡄ ⢀⣾⢠⣯⡟⠙⢻⣿⣿⠹⠀⠘⠻⡉⠁⠀⢀⠟⠃⠺⠈⣿⣿⠃⠀⠀⢀⠈⣻ ⠸⣇⣸⠋⢀⣿⠿⣿⣿⠀⣀⠘⢃⡇⠀⣇⠨⣙⠃⣀⠿⢻⣿⠳⠀⠀⠸⣿⠏ ⠀⠻⣇⠀⢸⡏⠀⢧⡏⢰⠤⠭⠍⠤⠤⠭⠤⠬⠿⠿⡇⣼⡼⠀⢀⡤⠖⠃⠀ ⠀⠀⠈⠳⣄⠙⢷⣦⣽⣦⣷⡆⠤⠤⠤⠤⠒⠒⢚⣿⣼⠯⠔⠚⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠙⠦⣀⠙⠿⣷⣦⣤⣤⣴⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⢹⣿⣏⠀⠈⣹⣷⠖⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢈⣉⣿⣌⠁⡀⢁⣼⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⡾⣸⣉⣻⡳⢿⣟⢉⡇⠀⢹⡗⢦⣈⠙⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡧⣾⣡⠇⢠⣿⢶⡺⣿⡌⠹⣄⣦⢧⠀⠈⣿⡌⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡥⣼⠏⠀⠈⠉⣽⣯⡁⠉⢀⣹⣿⣈⣇⠘⠛⢻⠙⡄⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⢡⣼⣷⣿⣿⢿⣯⠽⠿⢭⣽⡿⣿⠈⣿⡆⠀⢈⠇⢳⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⡿⠾⠗⠀⠀⠸⠙⡆⢻⣷⠴⠃⠀⢿⣦⣼⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠛⠃⠀⠀⠀⠉⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⠉⠙⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣀⣤⡶⠖⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠘⢿⣿⣿⣿⣿⣿ ⣿⣿⡿⠁⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠛⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠻⣿⣿⣿⣿ ⣿⡿⠁⠀⢀⡞⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⡟⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠁⠀⠹⣿⣿⣿ ⣿⠃⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⣛⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢸⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠹⣿⣿ ⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⣦⠀⠹⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠋⢹⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠈⠁⠀⢿ ⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠰⢛⣿⣿⣿⣿⣿⣿⠏⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠹⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠓⠂⠀⠀⠀⠀⢸ ⡇⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠉⠙⠲⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⣿⠁⠀⠀⠀⢻⠀⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠠⡀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠃⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠀⠀⢠⡴⠾⠓⠒⠦⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠠⠔⠒⠲⠶⣦⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢹⣿⣿⡟⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡛⠓⠀⠀⠀⢸ ⣿⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⢸⡿⠿⠿⣿⣿⣿⣿⣆⠀⠀⠀⣼ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢋⡙⢧⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠄⠐⠒⠒⠒⠒⠒⠒⠀⠤⠤⠄⠀⢀⣀⣀⣠⡄⠀⠀⠈⠀⠀⢄⠘⣿⡏⠀⠉⠀⠀⢠⣿ ⣿⣿⣇⠀⠠⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⡀⠀⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠃⠂⠄⠘⢠⣿⠁⠀⠀⡄⠀⣾⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡭⠐⠀⢩⠀⠀⠀⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⡜⠀⢰⡄⠀⠀⢠⣿⠃⠀⠀⠸⠀⣸⣿⣿ ⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⡀⢁⠀⢿⣦⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣾⠃⠀⠀⠀⠀⠰⢻⡇⠀⠀⠀⠀⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣄⠈⠳⣄⠀⠀⠀⠀⠀⠈⠢⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠈⠂⠁⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠁⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠻⣟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠋⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣀⣀⡀⠀⠀⢀⣀⠤⠒⢉⡠⠖⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠈⠉⠉⠉⠉⠉⡀⠤⠲⠉⠀⠀⠀⠤⠒⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣭⣭⣭⣭⣭⣭⣭⣟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣯⣭⣷⣶⣶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣼⣿