Guy Jeroing Emojis & Text

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

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⢼⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⠞⡝⣦⣷⣳⢿⠘⡆⢸⣀⡿⣿⣿⣷⣿⣿⣻⡿⣿⣿⡻⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⢭⡐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠈⢲⣌ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⡟⢻⢎⢿⢻⠀⣦⠂⣷⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡙⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣿⢿⣏⣲⠀⠀⠠⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣍⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢹⠀⠏⠻⠀⠀⡄⢿⣝⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡘⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡆⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠹⠑⠀⣿⣿⠻⢦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀ ⣿⣿⣿⣿⣷⡿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡆⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠿⣧⣿⣿⡹⢀⣇⣿⣿⠻⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⡑ ⣿⣽⢿⣿⣷⢿⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣫⠿⣿⣿⡇⣿⣿⡟⢹⡀⣿⣿⣿⢻⣌⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢌⣃⠠ ⣿⣯⣟⣻⣷⡽⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣾⡇⣿⣿⣿⣿⠟⡏⣿⣿⣿⣿⠿⡛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣊⠡⡔⠊⢄ ⣿⣞⢿⣯⣳⡿⢰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣶⣴⣤⣥⣂⢈⠓⡡⠔⢊⡠⠜⢂ ⣿⣞⢷⣫⢷⣞⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣥⣯⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣴⣤⣤⣀⣐⢉⠠⠘⠆⠉⡤⠎⡅⢂⡡⠔⢊⠡⢐⡨⠔⢊⡄⠈ ⣻⣷⢮⣹⡷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡷⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠃⠄⠉⠤⡘⢇⠀⢬⠓⢠⡱⢂⡡⠔⢊⡡⠆⢁⠡⢌⠀ ⣞⡹⣾⡝⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠉⠈⠈⠃⠊⠏⠙⠿⠛⠛⠛⠉⠉⢀⠠⠔⠊⢅⡈⠱⣠⠜⠣⣈⠱⣈⠰⡄⠀⢂⠄⠈⠠⠀⠀ ⣻⢭⡶⢏⡰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠕⢎⡽⣈⢧⣜⢻⣼⡾⣙⣀⣀⣄⣀⢈⠣⡔⠎⢂⡔⡊⡔⡌⠓⡄⠐⡌⠂⠈⢠⠐⠠⠀⠀⠀⠀ ⢂⡠⢌⠠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⢀⠁⡹⢶⣛⢱⡂⣝⢳⣮⣝⡾⣷⠿⠛⡉⠌⢀⠤⢂⣡⡔⢌⡒⢌⠣⣁⠢⢁⢂⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣾⠀⠇⡹⣶⡟⣏⡄⡳⢦⣹⣓⢤⠷⡙⣌⣈⣀⣀⠀⠀⠠⡐⠌⠂⢁⠠⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢸⠀⢯⡝⣮⠷⣏⠀⠀⢀⡄⠠⣀⠤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⢧⡳⣝⢳⣮⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⡓⣭⡲⡽⣳⣜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⠛⣋⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⢣⣷⠌⣳⢳⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⢯⡷⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣄⡻⢮⣳⡼⢻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⣻⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠉⠛⠛⠟⠿⡽⣭⡢⡈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢆⣎⢳⣬⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⢺⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡈⠘⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠘⣁⣳⢮⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⡍⢲⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣠⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡆⣛⠀⡡⣜⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⡘⢧⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⠅⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡛⣡⠉⠛⠛⡙⣉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣎⡁⢰⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣢⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣃⣿⣿⣿⠃⣿⣴⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⡉⠚⣿⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⠌⢈⡐⢁⡌⣷⣿⣿⣿⣿⣿⣿⣿⣾⣶⣫⣿⠿⠿⣿⣿⣿⣶⣴⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⢁⠞⣶⠶⡛⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⡿⣿⣿⣿⣿⣿⣾⣶⣷⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠂⡀⠐⠡⣄⢷⠟⠿⠷⣻⣏⢶⠷⡿⣿⣶⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣸⢉⠛⠿⠿⠿⠿⠻⠛⡛⣭⣦⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⣿⣿⣿⣿⣿⣿⣣⠟⠛⠙⡌⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠄⠂⠄⡈⠁⠠⢀⠌⠀⠈⠠⢁⠂⢀⡐⠌⡃⠄⢢⡄⠳⠈⢿⡆⠀⡗⣹⠀⡏⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⣭⣠⢀⠉⠛⡾⠃⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠐⡀⠁⠠⠂⠀⢈⠐⠈⠠⠈⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠉⢂⠄⠂⡁⠄⠈⠄⠁⡀⠂⠄⡁⠄⠈⠠⠁⠀⡘⠦⢻⡎⢸⢳⡇⢸⠈⠁⢄⡀⣀⠀⠈⣂⣀⠁⠰⠧⣀⠘⣄⣾⣵⢡⠘⡘⡼⠚⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠂⢀⠈⡐⠂⠀⢀⠌⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠌⠐⠡⣈⠄⠈⠠⠐⢂⠀⡐⠂⡀⠐⠠⠐⢈⠡⡐⠂⢡⡄⢿⣏⣇⡟⣿⢸⡀⣦⣶⣶⣷⢰⢁⠀⡁⡟⢻⣅⣄⠁⡷⣸⡆⢹⣅⢼⠌⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⠄⠀⠌⠀⠠⢁⠂⡀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠁⠂⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡈⠒⠁⢠⠐⢈⠡⢂⡀⠐⢈⠡⠂⢁⠠⠌⠁⠠⢣⡀⢘⡁⣷⢹⣷⣿⢿⠀⠣⣌⣷⣿⠸⠀⠀⡍⣮⣡⢛⠀⣿⡎⠋⣧⣾⠞⢱⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠐⢀⠂⠄⡀⠈⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⠀⠨⠐⠰⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢌⡑⠢⢈⡰⠌⠐⠡⢀⠡⠄⠈⠠⠐⠠⠌⠂⡅⠈⠱⡄⠘⡀⣷⡹⣿⣿⡸⣻⢿⠙⣄⢤⡘⠚⣿⢼⡿⣜⠸⣷⠉⡿⡏⢰⣷⣹⢀⠀⠀⠀⠀⠀⠂⢀⠄⠀⡁⠀⠠⡀⠈⠐⢀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢣⠄⡈⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡑⠢⢆⡉⠤⠎⡁⠠⡐⠐⠠⠐⢈⡐⠌⠂⢀⠰⢌⠱⠢⣌⠘⡀⣧⡟⣿⣿⡜⣿⣿⢷⠈⣸⢹⣿⣿⣸⣿⣝⡏⣓⢷⣷⠖⢡⡰⠀⠀⠀⠀⠂⠄⠀⡐⠀⢈⠠⠁⠠⢁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⠲⢩⡔⠊⢁⠤⠌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⢡⢢⠘⢢⠜⢃⡠⠔⡉⢀⠡⠄⠂⠁⢂⡀⠐⢂⠡⢤⠊⣅⠣⣌⣷⡽⣿⣿⡝⣿⢿⢿⣯⣟⡇⣿⢾⣶⣹⡿⡟⣿⢸⠕⡼⠠⠀⠀⠈⠡⢀⠌⡁⠀⠠⠁⠄⠀⠈⠠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣫⠵⣫⠔⢫⡄⠒⣈⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡑⢣⢢⡝⢃⠥⢈⡱⠌⠒⡈⠠⡐⠄⠈⠡⢀⠡⢀⠰⡌⠐⢢⡑⣎⠫⣌⣷⣿⣿⡹⣮⣿⣿⣿⣿⣻⣿⠹⢾⣨⡇⡗⠔⠇⡀⠀⠁⠄⠁⠠⠄⠈⠂⠁⢀⠠⠈⠠⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⡻⢷⣭⠾⣃⠰⢎⠀⡐⠁⠄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⡹⠱⢦⡘⠱⢣⡄⠚⡄⠘⠢⢂⡐⢂⠄⠈⡠⠐⡉⠄⠐⣈⠤⡘⠆⢌⡳⠡⣘⣦⣷⢿⣽⣦⠽⡯⡥⡽⡽⠇⡾⣦⠒⡀⠐⠈⠠⠐⡈⠐⡀⠌⠁⠠⠂⠀⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢳⣽⢮⣙⠖⢋⡄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡡⢳⣌⡙⠦⣉⠖⢃⡄⠘⢠⡘⠌⢂⠁⢠⠌⠂⡁⠄⠊⣁⠂⢡⡌⠐⢢⡌⢃⠠⠘⣁⢤⠢⠂⡔⠆⠨⠁⠀⡀⠈⡰⠄⠐⢈⠡⠄⡈⠄⠂⠀⠠⠐⢀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⢞⡹⢦⠘⢣⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢦⡓⢎⡑⢦⡙⠥⠣⢄⡘⠆⠈⡐⠌⠂⠄⠉⢀⠡⡐⠌⠂⢁⠠⠔⡉⢃⢀⠤⡈⠘⢠⠥⠂⢡⠆⠂⢅⡀⠰⣉⠄⡐⢈⠡⠄⠈⠡⠄⡀⠐⠠⢁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢿⣿⡝⢫⢅⠢⠆⡀⠔⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢮⡍⡱⢎⡑⡰⠖⡂⠐⢢⠄⡐⠂⢀⢠⠐⡄⠂⠄⠂⢀⠠⡐⠠⠐⠠⡐⢂⠄⠂⣀⠠⡐⠂⢀⢠⡐⡂⠄⠂⡀⠠⠄⠀⠠⠄⠀⠠⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠉⠛⠿⣿⣾⣶⣿⢿⠻⠛⠿⡿⣾⣶⣷⣿⠿⠛⠈⠀⠀ ⠁⡟⣾⣤⣀⠀⠀⠀⠀⡀⣄⣷⣿⠈⠀⠀⠀⠀⣀⣦⣿⠻⠀ ⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠀⠀⠀⠀⠀⠀⡄⣿⢹ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢸⠀⠀⠀⠀⠀⠀⣇⣿ ⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿ ⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⢠ ⠀⣄⣷⢿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⡿⣴⢀⠀ ⠀⠀⠀⡀⣄⣧⣿⠀⠀⠀⠀⠀⠁⠟⣿⣷⣿⣴⣠⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠇⣿⣴⢀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⣿⣸⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠉⠉⠀⠀⠀⠀⠁⠉⡏⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡟⣿⣶⣶⣷⢿⠟⡿⣾⣶⣶⣿⠻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⣀⣤⢀⠀⠀⠀⡄⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠏⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣿⠻⠉⠇⠿⠀⠋⡿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀ ⠁⠟⡿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣿⢹⠙ ⡟⣿⣿⣿⣿⣿⣿⢻⠇⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠁⡇⣿⣿⣿⣿⣿⣿⣼ ⣿⣿⣿⣿⣿⣿⣿⣸⡏⣿⣿⢰⠀⠀⠀⠀⠁⠋⠿⡌⠻⣧⣿⣿⣿⣿⣾⢀ ⡇⣿⣿⣿⣿⣿⣿⢣⣿⣿⣰⠀⠀⠉⠛⠿⣿⣿⣿⢿⡝⢷⣝⣶⣶⣴⢀⠀ ⠀⣿⣿⣿⣿⣿⣿⡍⣭⢋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣀⢀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣤⣠⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠛⠛⠻⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠂⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⣍⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⠩⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣶⣡⢛⠿⣿⣾⣶⢴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣴⢋⡿⣿⣴⣩⢟⠿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣼⢃⡿⣾⣩⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣤⣦⣿⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⠿⡾⣴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀

⠀⠀⠉⠛⠿⣿⣾⣶⣿⢿⠻⠛⠿⡿⣾⣶⣷⣿⠿⠛⠈⠀⠀ ⠁⡟⣾⣤⣀⠀⠀⠀⠀⡀⣄⣷⣿⠈⠀⠀⠀⠁⣀⣦⣿⠻⠀ ⡿⣾⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣷⢿⠀⠂⠀⠀⠀⠀⡄⣿⢹ ⣿⢸⠀⠂⠀⡀⠀⠀⠀⠁⠀⠀⡆⣿⢸⠀⠀⠄⠀⠀⠀⣇⣿ ⣿⢹⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿ ⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠏⣿⢠ ⠀⣄⣷⢿⠙⠉⠈⢀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠉⠛⡿⣴⢀⠀ ⠀⠀⠀⡀⣄⣧⣿⠀⠀⠀⠀⠀⠁⠟⣿⣷⣿⣴⣠⢀⠁⠉⠀ ⠃⢠⢀⠁⠉⡇⣿⠀⠀⠴⠀⠇⣿⣴⢀⡇⣿⠁⠈⡄⠀⡸⠀ ⡆⠈⡤⠓⠀⡇⣿⠆⠐⠀⠀⣿⣸⠀⠀⡇⣿⠀⡀⠄⡕⠒⠒ ⠒⢠⠀⠀⢏⡗⣿⡀⢯⠀⠀⠀⢣⠀⠀⡇⣿⠀⠀⠀⡆⠘⠀ ⠀⠀⠀⢸⠀⡇⣿⠀⠀⠀⠀⠀⠀⢀⠀⡇⣿⠀⠀⡇⢀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠉⠉⠀⠀⠀⠀⠁⠉⡏⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡟⣿⣶⣶⣷⢿⠟⡿⣾⣶⣶⣿⠻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⣀⣤⢀⠀⠀⠀⡄⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠏⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣿⠻⠉⠇⠿⠀⠋⡿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀

⠃⠛⠛⠛⠿⠿⠻⠀⠀⠀⠀⠀⠇⠿⠿⠿⠟⠿⠿⠿⠿⠿⠻⠙ ⠀⣀⣀⣀⣇⣿⣽⠛⠉⠀⠀⠀⡇⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣴ ⠀⠀⠀⠀⡇⣿⣿⣿⣿⠻⠛⠙⡟⣿⣿⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⢻⡇⣿⣿⢿⠀⠀⠀⠀ ⠀⠋⡿⣿⣿⣿⣿⢀⠀⢀⣷⢿⣝⣷⣿⣴⡏⣿⣿⣿⠘⠀⠀⠀ ⠀⣷⣿⣿⣿⣿⣸⠀⠀⠀⠀⣦⣿⢻⠈⠃⣿⣿⣿⣿⢰⠀⠀⠀ ⠀⡀⣤⣶⣴⣠⠀⠀⠀⠀⠀⠀⣆⣿⣿⡿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣶⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠉⠛⠿⣿⣾⣶⣿⢿⠻⠛⠿⡿⣾⣶⣷⣿⠿⠛⠈⠀⠀ ⠁⡟⣾⣤⣀⠀⠀⠀⠀⡀⣄⣷⣿⠈⠀⠀⠀⠀⣀⣦⣿⠻⠀ ⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠀⠀⠀⠀⠀⠀⡄⣿⢹ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢸⠀⠀⠀⠀⠀⠀⣇⣿ ⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿ ⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⢠ ⠀⣄⣷⢿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⡿⣴⢀⠀ ⠀⠀⠀⡀⣄⣧⣿⠀⠀⠀⠀⠀⠁⠟⣿⣷⣿⣴⣠⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠇⣿⣴⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⣿⢸⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠉⠉⠀⠀⠀⠀⠁⠉⡏⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡟⣿⣶⣶⣷⢿⠟⡿⣾⣶⣶⣿⠻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⣀⣤⢀⠀⠀⠀⡄⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⣿⠙⠀⠀⠀⠀⠀⠀⠀⠏⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣿⠻⠉⠇⠿⠀⠋⡿⣾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀ ~?uoy tnod siht fo etsat a tnaw uoy

⠀⠋⠛⠑⠋⠟⠿⠻⠙⠀⠁⠋⠛⠛⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⣼⣀⣀⣀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣼⢠⠀⠀⠀⣇⣿⣶⣷⠻⠀ ⠀⠀⠀⠀⠉⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡇⣿⠀⠀⣿⠸ ⠀⠉⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⠀⣿⢸ ⡟⣻⠿⠿⠿⣝⣮⣾⣴⣠⣀⡇⣿⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⡇⣿⢸⠀⣿⢸ ⣆⣿⣿⣿⣶⣶⢴⠀⠀⠀⠀⡏⣿⠿⣿⣿⣿⣿⣿⢿⠻⠀⠀⠀⡇⣿⢀⠀⣿⢀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣶⣶⣤⣤⣤⣤⣷⣿⣿⢸⠀⠀⡇⣿⠛⡟⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⣇⣿⢸⠀⠀⡿⣸⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠿⠿⠿⡾⣶⣴⢀⠀⠇⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠙⠉⠈⠀⠀⠁⠋⡿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀

⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⣿⣿⣿⢻⠇⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠋⡇⣿⣿⣿⠙ ⠃⠔⠤⠀⠤⠘⣿⣿⣿⣿⣿⣸⡏⣿⣿⢰⠉⠀⠀⠋⡌⠻⣧⣿⣿⣿⣿⣼ ⡀⠣⠁⠋⠋⢠⡇⣿⣿⣿⣿⢣⣿⣿⣰⠒⡤⠛⠿⣿⣿⢿⡝⢷⣝⣶⣴⢀ ⠆⣼⣤⣀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀ ⠸⠀⠀⠀⢆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣾⣶⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⡔⡠⣀⠀⣀⣤⣠⣀⢀⠀⡀⢄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠛⠿⠶⡶⣶⠶⠶⠻⠙⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⡀⣀⣀⣆⠋⠾⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⢦⢸⡎⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠒⠐⠉⠉⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠀⡀⠘⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣻⢰⠉⠉⠉⠉⠉⠉⠀⠀⠀⠁⠒⠒⠽⣧⢰⠡⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠄⣜⣤⠲⠤⠠⠀⠦⠰⠤⢃⠃⠛⡟⡈⠀⢀⡇⠈⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠢⠀⠀⠀⠀⠀⢸⠀⠈⠀⠁⡓⣶⢀⠠⡀⠦⠙⣇⢰⢠⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⠑⠀⠀⠀⢡⢣⠺⠞⣠⠔⣀⠀⡀⢄⠢⡈⢻⠸⠺⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢄⠢⠙⡸⠀⡇⢀⡀⠀⠂⠵⠬⠶⠐⡀⢼⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⣀⡤⢦⠱⠀⡤⢀⠊⠒⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⣀⣁⠈⠄⡤⣡⠔⠤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠊⡓⠔⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣖⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣊⡺⣻⣟⣻⣿⣟⣮⣝⡻⣻⡱⠱⡐⠐⠄⠄⠄⠄⠄⠁ ⣿⠻⠌⡅⣳⣧⡽⢿⣽⣿⡿⢿⣞⠝⠒⢀⠄⠄⠄⠄⠋⡿ ⣿⣿⣿⠹⣅⢚⣮⡿⣯⢽⣿⡾⣽⡳⢕⠄⠁⠉⠛⡿⣿⣿ ⣿⣿⣿⣿⠸⡸⡺⡮⣾⣟⣿⣿⣽⣻⢣⠄⡆⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠜⢆⢎⣜⣻⣿⢯⣿⣟⣯⠪⠄⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⢃⢩⣹⡷⣗⣿⣻⢿⣽⡺⢘⡆⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢹⡿⢞⣝⣟⣷⣿⣯⣟⣻⡵⠐⣧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠎⣼⡺⡯⣯⣿⣿⣿⣿⣗⡣⡀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⣊⡣⡵⣞⡿⣿⣿⣿⣿⢗⢀⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡐⡸⡽⣗⣞⣿⣟⣿⣽⣻⢨⡄⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡁⡱⡳⡧⡮⣻⣿⣷⣿⢽⢸⠄⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡀⡳⡪⢯⣗⣟⣿⣿⣾⢾⢜⠄⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢸⡅⡕⡗⢎⣻⣿⡿⣿⣿⣫⢨⠄⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢀⠆⢎⢎⣫⢵⣾⣿⣿⣯⡳⠠⠇⣿⣿ ⣿⣿⣿⣿⣿⣿⢠⡀⠄⡤⡄⡤⡲⣿⣿⣯⢕⢔⠄⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⠁⢎⡏⡯⣟⣗⠿⠋⣁⠤⢄⢀⡏⣿⣿⣿ ⣿⣿⣿⣿⣿⢰⠍⣗⡫⢷⢿⣯⢷⣿⡹⢢⠄⠃⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠄⠖⣝⡿⣿⣿⣿⣿⢷⣳⠄⠁⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠄⣜⡿⣿⣷⣿⣿⣟⣳⣠⠃⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠘⣅⣀⣧⣷⣗⣕⡰⠠⠟⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠻⠉⠉⢉⢉⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠛⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⠻⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⠐ ⡏⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣾⣴⣀⣀⣀⣀⣀⣀⠀ ⡆⣿⣿⣿⣾⠀⡀⣦⣿⣿⣿⣀⣁⣋⣞⣿⣿⣿⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣀⣀⠀⠀⠀⠀⣇⣿⢿⡿⣿⣿⢿⣯⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠋⠙⠈⣷⣿⣿⣿⣿⣴⢣⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⣿⣿⣿⣿⡸⣤⣤⣠⢀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸ ⡀⣀⣀⣀⣀⣀⣀⣄⣧⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣶⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠸⠀⡇⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⢿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⢻⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠉⠉⡉⣯⣿⣿⣿⣿⣿⣿⣶⣿⣿⣼⣋⣛⣙⣦⣿⣿⣿⣿⣿⣿⣿⢰⠀⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⣿⣿⣿⢿⡙⣦⣿⣿⣿⣿⣾⠀⠁⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠻⣌⣴⢤⠠⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠻⠈⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⢿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣶⣶⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠿⠿⠿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⢠⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡟⣐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠁⣁⠀⠀⠀⡄⢠⠀⣿⢀⠀⠀⠀⠄⠻⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠁⠚⠛⠙⠏⣶⢱⠉⠉⡉⢯⠓⠈⠀⠀⠉⣿⠀⠀⠀⠀⠄⢻⠙⠀⠀⠀⠀⠀ ⡇⢼⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⡄⣤⣤⣷⢸⡀⠰⠀⣧⢸⠀⠀⠀⠀⠋⣿⣿⠹⠀⠀⠀⠀ ⠇⢀⠀⠀⠀⠀⠛⣿⢻⠀⠀⠀⠁⢸⠀⠉⠉⠋⠐⠀⠀⠀⠀⠂⣷⠀⠀⠀⠀⠀⡇⣿⠈⠀⢅⣿⢸⠀⠀⠁⡟⣿⣾⣶⣶⢻⠀⠀⠟ ⡀⠀⠀⠀⠀⠀⡿⣿⣿⢿⠈⠃⡿⢛⠈⡠⣀⣀⣄⢶⠶⠻⠛⠿⠈⣄⠷⠿⠿⠿⡿⣿⣿⠿⡿⣿⢿⠈⠀⡟⣾⣠⠀⠀⠃⣼⠠⠃⢸ ⠀⢸⠀⠀⠀⠀⣄⣷⣀⣷⢿⣻⣿⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⡄⢷⣙⣯⣿⣿⣿⢿⠏⣾⠀⠀⠀⠀⡾⢀⡆⣿⢀ ⠁⠀⠀⠀⠀⠀⠀⡀⢰⡀⣦⣿⢿⠉⠋⠟⠻⠟⠿⠠⠉⠀⠀⠀⠀⠀⠁⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⡏⢀⠀⠀⣿⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠛⠙⠈⠀⠀⠀⡉⠟⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⢸⠀⠀⠃⢸⠀⠀⠃⣸⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⢿⠿⣿⠿⡿⣿⣿⣿⠾⠤⣤⣤⣶⣶⣶⣴⣶⣶⢿⡛⣬⣷⣿⣿⠙⠉⡈⣿⠙⠁⡾⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣶⣤⢒⣀⣀⢀⠀⡀⠀⣧⣿⢿⡴⢀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⡷⣿⣿⣿⣿⣿⡾⣧⣿⢀⠀⠀ ⠀⢳⠀⠀⠀⠀⠀⠶⠻⠟⡿⣿⣫⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣦⣀⢀⣀⢿⡾⣿⠀⠀⠀ ⠀⡀⢳⠀⠀⠀⠀⠀⠀⣄⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣿⣰⠀⠀⠀ ⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣰⠀⠀⠀⠀ ⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠛⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠁⠉⠋⠚⠒⠿⠿⣽⣦⠷⠻⠉⠉⠛⡿⣿⠻⠛⠖⠲⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠢⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⣄⣤⢦⠛⣼⣦⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠷⠪⠑⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢦⠀⡟⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠹⠀⠀⠀⠉⠉⠋⠛⠛⠛⠈⠀⡇⠉⡿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⡈⣀⠀⠀⠀⠀⡀⣀⣦⠻⣟⣀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣄⠳⠖⠴⡤⣤⣷⠿⠿⣼⣤⣧⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠑⠛⠻⠛⠙⠀⠀⡉⣛⢛⢻⠉⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⣎⣿⡿⣿⣿⢼⡿⣿⠿⣿⡿⣿⣿⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣿⣾⣠⣄⠶⡿⣶⣠⠀⠀⣄⢶⠻⠿⣾⢀⣀⣷⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⡀⣦⠻⠈⠀⠀⠀⠉⠟⣴⢀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣴⣀⣀⣄⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣴⢀⠀⠀⠁⡟⢀⠀⠀⠀⠀⠀⠀⠀⡀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣀⣷⣰⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⢷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡿⠙⠀⠀⠁⠀⠄⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⣿⡉⡆⣜⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡇⣈⠀⠄⡀⠤⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠁⢻⣸⢻⣟⠐⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣞⢠⠀⡇⣻⢹⢢⣅⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠋⣿⠿⠉⠈⠀⠀⠀⠀⠀⠀⠁⠛⡾⣤⠀⠀⠃⣿⣾⣮⢿⠙⠀⠀⠀⠀⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠿⣶⣖⣳⣶⣽⠤⠲⠀⠀⠤⠤⣀⠀⠀⠀⠁⡟⣿⣥⢞⢀⣤⣷⠳⠀⠀⠀⠄⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⢀⠀⠀⠀⠁⡒⣿⠛⠙⠉⠉⠉⠉⢉⠛⠿⣾⣴⢋⡴⢳⠀⠀⠀⡽⢻⠀⠀⠀⣇⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠠⠀⡭⣿⣛⣍⣾⣷⣽⣿⣄⣀⠂⠄⠀⠀⠀⢣⠈⠀⡆⡏⠈⠀⠀⡀⣷⡼⣹⣀⣄⣠⣀⣀⣀⣄⣶⣷⣿⣿⣿⣿⣿⣶⣶⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡀⡿⣼⣀⣄⣹⠈⢄⡲⣿⢹⠣⠀⠀⠀⠀⢆⠈⢦⠑⠈⢱⢳⡄⠙⠈⠁⣼⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⢛⠉⣀⣀⢂⠐⡀⣀⣀⣇⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣼⢀⠀⠀⣄⠱⡂⢙⡆⣞⠘⢀⠀⠀⠀⠀⢆⠘⠀⣂⡈⡳⢣⠈⣃⡿⢸⡄⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣽⠉⠍⠩⠉⠉⡏⡉⣉⣿⣿⣿⣿⣿⣿⣿ ⡿⡿⠿⠿⣿⣿⠀⠀⠀⠀⠀⡀⢦⡝⠈⣆⢟⠙⠀⠀⠀⠀⠀⡄⠱⠀⢀⠀⢦⢎⠙⢧⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⡀⣦⠻⡈⣦⢮⠙⠁⠀⠀⠀⡀⠣⠀⠀⠀⢆⡜⡿⣿⢧⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⡀⣷⠘⡀⡳⠱⠀⠀⠀⠀⠀⠳⠈⠀⠀⣄⡜⣿⡄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⢿⡈⡷⠳⠀⠀⠀⠀⠀⢆⠘⠀⠉⢣⣇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⣆⣜⠱⢦⢦⠘⠀⠀⠀⠀⢆⠈⠀⡇⡇⡄⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠒⠒⠋⠚⡆⠹⢣⠀⡄⠱⠀⠀⠀⠀⢀⠀⡆⡇⠇⢸⣿⠘⠀⠀⠉⠊⠒⠕⡬⣤⣤⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣠⣀⠀⠀⠀⠀⠀⠀⣄⠳⣏⠸⢷⠈⡞⠘⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⣿⠉⡟⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣄⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣎⡺⣦⢸⢸⠀⠀⠀⠀⠀⠀⡅⢹⡇⠘⣿⢧⣰⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⠀⢸⢸⠀⠀⠀⠀⢰⠀⡄⡜⡻⠰⣿⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿ ⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣿⠻⠀⢇⢧⡀⠘⠀⠀⠀⠀⠀⢄⣿⡟⣿⢹⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣽⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣠⠀⣄⣧⠻⣣⢿⠈⠀⠀⠀⠀⠇⠁⣏⣴⣀⣦⢻⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿ ⣿⣿⢩⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢠⠀⠀⠀⠀⣄⣦⢷⢿⠉⠉⠉⠊⡔⣠⢀⠀⠀⠀⡀⢦⠻⣟⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠁⠞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣼⡤⣤⣧⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣺⠒⠒⠒⠓⠞⡵⣾⠿⡿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⣿⣿⣵⢟⣿⣿⣿⣿⣿⣿⣾⣒⣶⣒⣒⣒⣒⣐⣆ ⣿⢠⠀⠀⠃⣰⠀⡀⣧⡜⡷⣿⣾⣿⣿⢸⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠀⠋⡿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠃⣰⠀⠀⠋⡽⢩⡉⠩⠋⣿⣿⢉⠟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⢿⣿⢁⣿⣿⣿⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⣾⠀⠋⡶⣤⣀⢀⠀⠀⠀⠀⣀⣀⣄⣦⠿⠻⠉⠀⠀⠀⠀⠀⠀⠏⠠⠀⠀⠔⣠⠀⠁⠋⠟⠾⣶⣤⣤⣤⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⢿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢷⠻⠈⠀⠀⠀⣏⠀⠀⠁⠋⠿⡶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠈⠁⣸⠁⠟⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⡿⢿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠈⠀⠀⠀⠀⡟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠦⠚⢛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠟⠼⠣⠈⠀⢸⠀⠀⠀⠀⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⢣⢺⣴⠀⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠁⠾⠣⢰⠃⢰⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⠽⠒⡒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠀⠁⠈⣄⡶⢤⣀⠋⣰⠀⠀⠀⠀⡗⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠁⠉⠉⠚⠴⢀⠀⠀⠀⠀⡃⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣷⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠹⣄⣷⢿⠻⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⡍⣏⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⢳⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣓⣿⣽⣿⣿⣿⢭⠭⠯⠷⠾⠲⠒⠛⠛⠟⠿⠯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⢦⡟⣤⣀⣄⢦⠶⠻⣛⣭⣶⣿⣿⢿⠶⠷⢻⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣛⣖⣶⣤⣠⣀⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⣆⠳⠉⠂⠀⠀⠀⣀⣧⢿⣶⣽⣭⣤⣤⠤⣤⣠⣀⣉⢋⣒⣶⣶⣲⢽⣓⣭⢻⠀⢀⠉⠞⣠⢉⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣀⣀⣄⠦⣒⠹⠉⡿⣭⣪⣔⣠⢤⠤⠤⠤⠤⣨⢀⠁⠀⠁⠈⠀⡀⢧⠺⣗⠽⣠⢉⠚⡤⢉⡖⣤⣤⣤⣶⣶⣶⣶⣷⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⡒⣂⠔⡠⣀⣏⠦⣒⢐⠍⠉⣍⠭⣬⠲⢖⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⢄⠤⠷⠿⠿⠿⠿⣿⢻⠛⠉⠀⠀⠈⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣍⠯⠛⠙⠉⠉⠉⠉⠉⠛⠼⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⢻⠉⢊⡶⢒⠒⠒⠑⠉⠈⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠈⠀⠀⠀⠀⣀⢦⡿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠴⣠⣀⣄⠦⠷⠻⠛⠈⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⣄⢳⣌⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣷⣿⣠⠀⠀⠆⡤⣀⣀⢄⠢⠀⠀⠀⣄⣿⣿⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡿⢠⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣸⠀⠀⠀⠀⡆⢈⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⡳⣯⣿⣿⣿⢸⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⣿⣿⢸⠁⠉⠉⠀⠀⢆⠛⠴⣁⠚⠠⠀⠉⠈⠀⠁⣯⢿⣇⣿⣿⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡿⣻⣿⣿⢾⠫⡿⢁⠟⣽⠲⣿⣿⣻⣯⠻⡿⢿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣺⡟⣽⣿⣧⣿⣷⣿⠁⣽⣿⣶⣱⣟⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣧⣿⣿⣿⡿⣯⣿⢭⠈⣿⣿⢇⣼⠏⣿⣿⣿⣿⣿⣼⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⢠⣿⣿⣿⢻⣹⠊⢐⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⢠⡏⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⢉⣷⢰⣧⣴⣿⣿⠃⠌⣷⣽⣾⣧⣿⣿⣿⣿⢠⠁⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈⢦⡽⠻⡋⢻⣯⡟⠚⢻⡏⣷⢹⢫⣿⣿⣾⣠⠀⡟⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠙⡀⣄⣦⣖⣿⣿⢻⠛⠟⠲⣶⣤⣄⢀⠀⠁⡟⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⠿⠛⠙⠉⠉⠉⠉⠛⠟⡿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣦⣶⣤⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ NROP TA KOOL EM TEL UFTS LLAY

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠑⠋⠟⠿⠻⠙⠀⠁⠋⠛⠛⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⣼⣀⣀⣀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣼⢠⠀⠀⠀⣇⣿⣶⣷⠻⠀ ⠀⠀⠀⠀⠉⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡇⣿⠀⠀⣿⠸ ⠀⠉⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⠀⣿⢸ ⡟⣻⠿⠿⠿⣝⣮⣾⣴⣠⣀⡇⣿⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⡇⣿⢸⠀⣿⢸ ⣆⣿⣿⣿⣶⣶⢴⠀⠀⠀⠀⡏⣿⠿⣿⣿⣿⣿⣿⢿⠻⠀⠀⠀⡇⣿⢀⠀⣿⢀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣶⣶⣤⣤⣤⣤⣷⣿⣿⢸⠀⠀⡇⣿⠛⡟⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⣇⣿⢸⠀⠀⡿⣸⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠿⠿⠿⡾⣶⣴⢀⠀⠇⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠙⠉⠈⠀⠀⠁⠋⡿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠁⠛⠿⣿⣿⣿⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣿⣿⣿⣼⠀⠁⠀ ⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢸ ⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠇⠿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⠈⣧⢿⡈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡟⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⢿⠈⣧⣿⠙⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⣄⣷⢿⠙⣄⣷⣿⣿⣿⣿⣴⢀⠀⠀⠀ ⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡿⣿⣿⣿⣴⢀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠉⣤⣷⢿⠻⡀⣀⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡉⣌⣥⣭⢉⠋⠛⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸ ⡀⣀⣀⣀⣀⣀⣀⣄⣧⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣶⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⢿⣿⣿⢿⠹⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠸⠀⡇⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠉⠈⠀⠀⡇⣿⣿⣿⣿⣿⢻⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠉⠉⡉⣯⣿⣿⣿⣿⣿⣿⣶⣿⣿⣼⣋⣛⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠄⣿⣿⣿⢿⡙⣦⣿⣿⣿⣿⣿⣰⠁⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠻⣌⣶⣶⣤⣀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠻⠈⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⢿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣶⣶⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠿⠿⠿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠏⡻⣖⣵⣟⠈⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸ ⡀⣀⣀⣀⣀⣀⣀⣄⣧⣿⣿⣿⣻⣛⣝⣭⣯⡯⣯⢸⠀⠀⠀⡇⣿⣿⣿⣿⣿⣶⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⠀⠀⠀⡇⣿⣿⣿⣿⣿⠸⠀⡇⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣴⣠⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡟⠈⠀⠀⡇⣿⣿⣿⣿⣿⢻⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠈⣿⣿⣿⡿⣿⣻⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠉⠉⡉⣯⣿⣿⣿⣿⣿⣿⣶⣿⣿⣼⣋⣛⣙⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠄⣿⣿⣿⢿⡙⣦⣿⣿⣿⣿⣿⣴⣧⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠻⣌⣶⣶⣤⣀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⠻⠈⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⢿⠘⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣤⣶⣶⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣶⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠿⠿⠿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠈⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⢿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠙⡄⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀

⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠿⠻⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠙⡄⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀

⠀⠀⠀⠀⠀⡯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⣿⠀⣳⠈⠀⠀⠀⠀⠀⡀⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠶⡭⣾⣴⣤⣀⣇⠸⠠⣇⠿⠿⠿⠿⠿⠻⠛⠉⢎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠻⠈⠂⡿⣿⢰⠀⠀⠀⠉⠉⠛⠛⠿⡿⣿⣛⠛⠞⡴⣀⠀⠀⠀⠁⡾⠀⠀⠀⡆⣾⣷⣿⣿⣿⣿⣿⣿⣾⣶⠻⠙⠀⠀⠀⠀⠀⠀⠀ ⠉⡈⣷⠏⣿⣼⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠁⠔⣠⠀⠁⠈⠀⠀⢇⠀⣀⣦⣷⣿⣿⣾⠀⠏⣿⣿⣿⠿⠙⠈⠀⠀⠀ ⣄⣷⡸⣧⣿⢠⣿⣿⣿⣿⣻⡟⣿⣿⣾⣴⢀⠀⠀⠀⠀⣽⣧⣰⠁⠀⠀⡀⣸⠀⠀⡄⠀⠀⠀⠀⣀⣦⢹⠀⣷⢹⣭⣽⣭⣽⣿⢾⠶⠛ ⠀⠀⢄⣻⣰⠧⣀⣧⡿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡄⣿⠴⢠⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣠⠀⠃⣾ ⠹⠀⠀⣧⠀⡄⢿⡿⣿⣿⣾⣠⠀⠂⠓⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⡿⠈⠀⠀⡿⠹⠀⠀⠀⠀⠆⣩⣉⣀⣤⣻⣉⣤⢳⠈⠀⣿⢼ ⡀⠀⠀⡆⠀⠀⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠸⠀⠉⠛⡿⣿⢻⠙⠏⣿⣿⠹⠀⠀⠀⠀⢦⡀⠀⠀⡀⣷⢿⠘⣀⢦⣿⠀ ⠀⠀⠀⠀⠀⠀⣧⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⢻⠈⠀⠀⡀⠀⠉⠉⠀⡄⣿⣿⠹⠀⡄⠹ ⠀⠀⠀⠀⠀⠀⡇⡆⢸⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⡏⣿⣿⣿⣬⣶⣷⣾⣶⣶⣤⣩⠞⣠⠀⠀⠀⠀⠀⠁⠐⠀⡞⣄⠻⣟⣿⣿⠘⠀⣇ ⢻⠰⠀⠘⠀⠀⡇⠏⢰⠋⠗⡾⣠⢀⠀⠀⠀⠀⠏⣰⢀⠀⠀⣀⣄⠤⠒⠔⠤⣠⣀⠀⠀⠀⠀⠀⠀⠋⡡⠃⡴⠏⢠⠆⣷⣿⣿⢸⠀⡀ ⣷⠘⠀⠀⠀⠀⡇⣾⣠⠏⣠⠀⠈⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⢏⣩⠟⣼⡝⠀⡆⢿⣌⢻⠀⠀ ⡵⢹⠀⠀⠀⠀⡇⠀⠟⢠⠀⡇⣇⢘⠀⠋⡰⠀⠋⠠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⡳⣹⡼⢃⣶⢋⡾⢃⠼⠀⣦⢹⣇⠀⠀ ⡀⣿⠈⡇⠀⠀⡄⠃⢷⠘⠀⠋⣫⡿⣽⢎⢋⡴⢀⠁⠞⡡⠛⠟⣾⠠⠀⠀⠀⠀⠀⠱⠁⠞⢀⠆⣲⠖⣶⡴⣤⢀⡦⣿⠙⠀⣿⡌⠀⠀ ⠀⡀⢷⡏⠀⠀⠀⡏⡄⢿⡟⣴⢞⣯⣣⡴⢆⡠⠒⣱⠟⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠃⠶⠤⠳⠈⠀⠀⠁⣿⣿⢿⣿⢠⠀⠀ ⠀⠀⡄⣿⠸⠀⠀⢸⠀⣿⣧⡄⠷⠕⢛⡷⠿⠿⠿⣶⣴⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⣿⣿⠿⣿⠛⠿⣿⣴⣧⣷⣿⠈⠁⠛ ⠀⠀⠀⣇⢹⠀⠀⢰⠀⣼⡇⠀⠇⣸⠀⠀⠀⠀⠀⠊⡤⠦⠳⠟⣿⠀⠀⠀⠀⠀⠀⡿⠈⠀⡀⣦⣾⣶⣶⣶⣤⣠⢀⠀⡇⣿⣘⣀⣀⠀ ⠀⠀⠀⠀⣷⠈⠀⠀⠀⢸⡇⠻⣿⠹⠀⠀⠀⠀⠇⢁⠟⠿⡿⣴⢟⢉⠀⠀⠀⠁⠈⣄⢿⠀⠀⠀⠻⠉⠉⠋⢿⠙⠀⠁⡛⢸⢸⠀⠀⠀ ⠀⠀⠀⠀⡄⢹⠀⠀⠀⢀⠀⢹⡤⣦⣶⠿⠿⠛⡿⣾⣶⣥⣛⡿⣤⣀⣠⣠⣠⢉⡜⢷⡟⠹⠀⠀⡇⡘⢀⠀⡆⣼⣿⣼⣀⢸⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠆⠹⠁⣧⠈⠀⠀⠀⡀⠿⠚⠖⡾⣴⣤⣀⡄⠻⠿⠶⡴⣀⢧⡟⣸⣷⡀⣤⣦⢸⠀⠀⠀⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠒⠰⠀⠀⠀⠀⢹⠀⠀⣷⡿⡙⢹⠃⠙⠀⡏⣀⣽⠻⠙⠉⠋⠟⡿⣿⣬⠀⠀⠀⡆⣿⢸⡀⢳⠀⠀⢸⠀⠀⠀⠇⠀⢿⣾⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⠀⡆⠘⠀⡄⣿⣸⣄⣠⣇⠾⢸⠀⣧⣿⠀⣀⣀⠀⣇⡏⢹⠀⠀⠀⠀⣿⢷⠀⡄⢻⠈⢸⠀⠀⠀⡀⠀⡇⢀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠘⠀⠀⢧⠈⠀⣇⣿⠘⠀⠀⢣⢸⠀⡇⣾⢹⠀⠀⠀⡀⣿⣿⠀⠀⠀⠀⣆⡇⠸⠀⣇⣿⢀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⢳⣄⠀⠀⡀⢷⠀⡆⣧⣌⠰⠀⠀⠀⡆⣸⢸⠀⠀⠀⠀⡀⢸⠀⡇⣿⠀⠀⠀⠃⢰⠀⡏⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠈⡀⢳⠈⠀⠀⠀⠀⠀⢰⢦⠈⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⢸⠀⡇⣹⠉⠛⠚⠶⠴⣤⣠⢀⣀⠀⠀⠀⠀

⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣸⠀⠀⣆⣿⣿⣿⣿⣿⣿ ⣿⠿⠿⠾⠴⠠⠀⠀⠀⠀⠋⡿⣿⣿⣿⢀⠀⠀⡇⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣸⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⠙⠀⠀⠀⠀⣄⣿⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⡀⣠⠀⡄⠑⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠁⠟⠙⠀⢢⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢿⠙⠉⠉⠟⣿⣿⡀⠢⠖⢠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⣀⣄⣤⢀⠀⠀⠀⠀⡀⣀⣧⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠘⠀⠀⣦⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠟⡿⣿⢻⠀⠀⠀⠀⠀⣶⠀⠀⠁⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠁⡿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠃⡿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠃⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠖⠶⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⡀⣷⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠀⠀⠁⠋⣿⣿⣿

⠀⠟⡿⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣿⣿⣿⣿⣿⣿⣿⠸⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⣿⣿⣿⣿⣿⢹⣶⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣵⣻⢿⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣵⣟⣿⣿⣿⣿⣿⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣻⣞⢠

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

)‿ˠ‿(つε ��)}O{(§łłäb ým ķçų$ yciuJ ) .͜ ㅅ .͜ ()ԅ‾⌣‾(ԅ) • () • (͞ںل ̶͞ ̶͞ ̶͞ ͞Ɑ )‿ˠ‿(.HEH ��‿�𓍆�ym kcus��ym kcus ⠀⠋⠛⠑⠋⠟⠿⠻⠙⠀⠁⠋⠛⠛⠛⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡿⣿⣿⣿⣿⣿⢿⡿⣼⣀⣀⣀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣼⢠⠀⠀⠀⣇⣿⣶⣷⠻⠀ ⠀⠀⠀⠀⠉⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡇⣿⠀⠀⣿⠸ ⠀⠉⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣠⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⠀⣿⢸ ⡟⣻⠿⠿⠿⣝⣮⣾⣴⣠⣀⡇⣿⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⡇⣿⢸⠀⣿⢸ ⣆⣿⣿⣿⣶⣶⢴⠀⠀⠀⠀⡏⣿⠿⣿⣿⣿⣿⣿⢿⠻⠀⠀⠀⡇⣿⢀⠀⣿⢀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣶⣶⣤⣤⣤⣤⣷⣿⣿⢸⠀⠀⡇⣿⠛⡟⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⣇⣿⢸⠀⠀⡿⣸⣀⣀⠀⠀ yddad kcid yciuj eht evah uoY ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⢿⠿⠿⠿⡾⣶⣴⢀⠀⠇⣿⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⠻⠙⠉⠈⠀⠀⠁⠋⡿⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀

⠄⡇⣿⣿⣿⣿⣿⣿⠈⠄⣿⣿⣿⣿⣿⣿⠄ ⠄⠄⡇⣿⣿⣿⣿⣿⣿⢿⠄⣿⣿⣿⣿⣿⣿⠸ ⠄⠄⡇⣿⣿⣿⣿⣿⣿⣿⠄⣆⣿⣿⣿⣿⣿⢸ ⠄⠄⡆⣿⣿⣿⣿⣿⣿⢁⢸⢹⣇⣿⣿⣿⣿⢸ ⠄⠄⠄⣇⣿⣿⣿⣿⢰⡿⢻⣿⠹⣧⣿⣿⣿⠄ ⠄⠄⠄⠄⣷⣿⣿⣼⡏⣿⣿⣿⣿⠸⣿⣾⢂⠹ ⠄⠄⠄⠄⡀⣧⣾⠏⣿⣿⣿⣿⣿⢿⣀⠻⢧⣜ ⠄⠄⠄⠄⠄⠄⠟⣿⣿⣿⣿⣿⣿⢸⣧⡝⢤⠄ ⠄⠄⠄⠄⠄⠁⣿⣿⣿⣿⣿⣿⣿⢸⠿⠿⠘⠄ ⠄⠄⠄⠁⠞⣴⣩⣉⣬⣦⣷⣿⣿⢻⣧⣿⣴⠄ ⠄⠄⠃⡰⠟⣿⣾⣶⣷⢿⠘⢁⠟⠿⠻⣈⠄⠄ ⠈⠄⡼⡇⣿⣿⠄⠶⠁⣿⣼⡏⣿⣿⣠⣉⠄⠄ ⣿⠻⢋⡎⣿⣿⢿⠿⣾⣡⠟⣿⣿⣿⠺⣀⠄⠄ ⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣾⣩⣛⢘⠄⠄⠄⠄ ⣶⣴⣳⣛⣚⣎⢞⡋⡺⣷⣿⣾⣴⢀⠄⠄⠄⠄ ⠄⠄⠉⣍⢷⡔⢸⣵⠮⠾⠾⠙⠄⠄⠄⠄⠄⠄ ⠄⡟⣐⠤⠄⢓⡿⣹⢍⡙⡃⡆⠸⠄⠄⠄⠄⠄ ⠄⢸⠄⠁⡇⡄⣴⠠⣤⣉⡈⢸⢿⠄⠄⠄⠄⠄ ⠄⢸⢸⡷⡇⢹⡱⣢⠰⡙⠱⣿⣿⠄⠄⠄⠄⠄ ⠄⢳⣧⡎⡹⣷⡹⡸⠹⣿⡇⣿⣼⠄⠄⠄⠄⠄ ⠄⡀⢳⢌⣗⡿⣿⡿⣿⣿⣿⣴⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⡀⣄⣤⣤⣤⣠⣀⠄⠄⠄⠄⠄⠄⠄⠄

⠀⡌⣀⣀⢇⠤⠢⠉ ⠀⢄⠃⠔⢰⠉⠉⡊ ⠀⠀⡃⠀⠀⡃⠀⠀ ⠀⠀⡇⠀⠀⡇⠀⠀ ⠀⠀⡃⠁⠈⡍⠀⠀ ⠀⠀⠀⢄⢤⢀⠀⠀ ⠂⠉⠈⠔⠨⠐⠈⠊ ⠀⠀⠀⠊⢐⠀⠀⠀

⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⢿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⠛⡿⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣩⣉⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀ �� ???..ekil os ti teg tnod uoy ti hcraes tnod uoy ti teg uoy nrop hcraes uoy .slobmys/sobmoc ijome ruoy teg dna no evom peed taht ton sti gniyrc pots gmo ekil ..tenretni eht no neve yeht era yhw ”etis siht no era sdik“

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⠻⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⡀⣀⣀⣀⣄⣤⣤⣿⣿⣿⢀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⢠⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⠀⡇⣿⣿⣿⣿⣼⣤⣤⣤⣤⣤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣾⣶⣶⣡⣛⣝⣧⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⠀⠀⠁⠋⠛⠛⡙⣈⣀⢀⠀⠀⠀⠀⣦⣿⣿⢿⣜⣷⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢸⠀⠟⣿⣿⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⠻⣈⣀⠀⠁⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⠹⠀⡟⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣴⣷⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣸⠀⠀⣄⣶⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠟⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⢀⡟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣍⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣉⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠧⠚⠒⠒⠀⠈⠒⡤⠴⠦⠻⠈⠀⠀ ⠀⠋⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀ ⠒⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⠐ ⠂⢺⠐⠀⠀⠊⠘⠀⠀⣧⠈⠀⠀⠁⣹⠈ ⠀⡄⠲⠉⠂⣸⠀⠀⠀⠀⣰⢄⠤⣀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠴⣤⣤⢤⡧⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⠀⠘⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠙⢹⡴⢀⠀⠀⠀⠀⠀

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

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⠁⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⢿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠟⠿⠻⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠉⠌⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡿⣿⣿⣿⠙⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡈⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣀⣦⣿⣿⣿⠹⣆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠻⣌⣷⣿⣿⢻⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⣿⣿⣿⣿⣴⢀⠀⠀⠀⠇⣿⣿⠙⣌⣤⣡⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡿⣿⣿⣿⢿⠻⠙⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣦⣿⣿⣿⣿⣿⠻⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣶⢠⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⣷⣿⣿⣿⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠁⡟⣿⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣿⣿⣿⣿⠿⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠈⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠃⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣧⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⡼⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⡿⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⢽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⣿⠉⠋⠒⠒⠒⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢰⠀⠀⠁⠾⣠⢀⠀⠀⠀⠀⠀⠀⣀⠦⠙⠀⠀⠀⠀⠋⠖⡴⣀⣀⣀⣀⣀⢤⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠃⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀ ⠀⠀⠀⠀⡇⢰⠀⠀⡼⠀⠀⠈⠉⠀⣄⠀⠀⠀⠀⠀⠀⠀⡀⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⡆⢹ ⠀⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠈⣿ ⠀⠀⠀⠏⢠⠀⠀⠀⢳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢃⣼ ⠀⠀⠃⣰⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀ ⠀⠀⣼⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⠀⠀ ⠀⡏⢀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣰⣇⠸⠀⠀ ⠛⣼⠀⠀⠀⠀⠀⠀⠀⡄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⢀⠀⠀⢸⠀⠀ ⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠀⠀⢹⢸⠀ ⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀ ⠀⡀⢢⠙⠀⠀⠀⠀⠀⠀⠉⠉⡉⣿⠛⠛⠒⠚⠒⠒⠴⠀⠓⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀ ⠀⠀⠀⠀⣄⢾⠿⠛⠙⣀⢀⠀⡀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣟⢲⠚⠤⠿⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠉⡼⣟⣧⣧⣸⢄⠳⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠘⠁⠋⠟⡸⣀⢀⡞⢀⠏⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⣹⢸⡇⢸⠀⣼⣅⠻⠃⣿⠀⠀⠀⠀⠀⠀⡟⠴⣀⡇⣮⢀⠋⡼⢀⠇⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⣿⢀⡀⢸⠀⢸⡿⠀⣿⢰⠀⠀⠀⠀⠁⠛⣴⠤⠳⡍⢰⠇⣿⣧⠻⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣻⣹⠀⠀⡇⠈⢿⣟⠀⣿⠀⠀⠁⠚⡴⣀⠀⠀⠀⠀⡀⣄⡳⢹⠀⣷⣄⠱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⠸⠀⡄⢹⡇⣈⠀⣹⠀⠆⣠⢀⠀⠀⠁⠉⠋⠒⠒⠀⠀⣀⠦⡟⠘⡀⢷⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⢿⠈⠀⡇⠘⢰⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡷⠈⠀⠀⡄⢻⠀⠀⢧⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢸⠀⡀⢿⠁⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠉⠙⠀⡄⠙⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⡇⣱⣼⣆⠀⠀⠆⠇⠿⠿⠾⠀⠀⠀⠀⠀⡞⢿⡿⠳⠛⣏⠻⠀⡄⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠛⣽⠇⢸⠀⢻⠀⠾⡇⣿⢾⣷⠉⠙⠀⠀⠀⠀⣷⣿⠩⣛⣿⡆⢸⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡀⢻⢸⠀⡇⣼⢶⠟⡛⢿⠾⣶⣀⠀⠀⠀⠁⠉⠉⡉⣿⢿⡴⣇⠀⡇⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣶⠻⣿⢸⠀⣄⣷⠛⡉⣿⢀⠁⠉⠛⢾⢠⠀⠀⡀⣏⣿⣼⢠⠀⡇⢸⡇⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡀⣄⢻⠀⠀⡀⢧⡇⣿⣄⣤⣠⣀⠀⠀⠀⠃⠞⣣⣼⠀⠀⠀⡇⢠⡏⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⣇⠀⠀⠀⡀⣧⣿⠘⠀⠀⠀⠁⠋⡴⣡⠞⣠⠀⠀⠀⠁⡼⠃⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⡆⢷⠊⠶⡴⣀⠉⠖⣠⠀⠀⠀⠀⠀⡶⢣⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠤⠤⠶⠶⠶⠤⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣇⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⡀⣏⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⣤⣶⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⡿⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣤⣊⣗⡿⣶⣠⢀⠀⣄⠶⠙⣌⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠗⠿⣴⢀⠠⠀⠀⠀⠀⠀⠀⣄⠦⣟⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠆⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⢿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⢿⡘⣀⢤⠢⠒⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⣿⣿⣿⣿⠻⠈⠀⠀⠀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠶⠤⠤⡀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣠⣀⣷⣿⠿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⢹⠆⡿⣿⣾⣿⣿⣿⠿⠭⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⢠⡷⣅⣮⣷⣿⣿⠿⠻⠒⠛⠛⠙⠉⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣿⣿⢿⣒⣽⣮⣶⢶⠷⠛⠐⣤⣀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣠⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⠸⠀⣀⢤⠤⠲⣒⢒⠐⠋⠛⠒⠒⠴⠤⣀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠻⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠋⡶⠿⣿⣿⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⣀⣤⣦⣴⠷⣜⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣠⢄⠦⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣰⠀⠀⠀⠀⡀⣄⠦⠓⠉⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈ ⠀⠉⠉⠉⠛⠟⠿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀ ⡀⣄⣦⣿⣿⣴⣤⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠛⠿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠀⠀⠀⠀⣀⣦⣶⣷⣿⣿⢻⠈ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⠿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠀⠂⢳⡖⠔⠠⠀⠀⠐⠒⠒⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣦⣿⡹⣬⢻⣘⠀⠆⠂⠐⠇⠛⡿⣿ ⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣯⢹⠀⠀⠉⡿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣽⠉⣍⡤ ⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⢸ ⢻⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠯⣿⣿⣤⡄ ⣿⠘⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣻⡈⢋⢁⠈ ⣶⢸⠈⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣁⡮⣿ ⣀⢻⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡽⣿⣿ ⠀⡇⢳⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿ ⣿⣿⡞⠀⡏⣯⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢽⠀⣀⢻⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣙ ⢹⣏⢹⠘⢳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡆⠘⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣭ ⣠⣀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢹⠀⠀⢧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀ ⠀⠃⡈⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠂⠘⣇⠀⢰⠘⣆⡙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿ ⠀⡀⣤⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡾⠀⢧⡁⡏⡇⢀⠀⡀⢦⡙⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣻ ⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⢰⠀⡀⠸⢱⣸⠀⠀⠀⠀⡀⢦⠳⢌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢻ ⠀⠀⠀⠀⠀⡄⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢫⣰⠀⠀⠀⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠁⡿⣿⣷⣿ ⠀⠀⠀⠀⠀⠀⡀⣿⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡵⣞⢀⠀⠀⠀⠀⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠁⡟⢿⠘⣿⢿ ⠀⠂⠐⠀⠀⠀⠦⣦⢧⡙⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣋⢴⣀⠀⠀⠀⠀⠀⠇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠁⠟⣼⣿⢶⠶⣰⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣄⠳⡉⣅⠤⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⡠⣀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡼⢀⠀⣰⢁⠀⠀⠀ ⠀⠀⠄⠦⠒⠒⠉⠈⠀⠀⠀⠀⡀⣤⣳⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣶⢾⠐⡶⠼⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠢⠗⠩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⡶⣼⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠤⠲⠒⠙⠉⠉⠉⠀⠀⠁⠈⠀⠀⠀⣄⠠⣀⠤⠤⠀⠀⠀⠀⠀⠂⠐⠤⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠤⠲⠓⠉⠀⠀⠈⠀⠀⡀⣀⠁⠉⠚⠴⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰ ⠀⣄⠳⠉⠉⠉⠉⠉⠚⠒⠒⠛⠴⠦⠼⣤⣀⢤⢸⠀⠀⡆⣸⣤⢤⠧⠴⠦⠺⠒⠒⠒⠒⠓⠉⠉⠋⠴⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠀⠀⠇⢰⠀⠀⠀⢸⠀⠀⡇⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⡄⠳⠉⠁⠞⣠⠀⠀⠀⢀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢈⠀⠀⠀⠀⠀⠀⡀⣹⠀⠀⠀⠀⠀⠀⡇⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣄⠸⠀⠀⡀⢠⠀⠀⡇⠀⡄⣤⠀⠀⠇⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣿⠈⠀⣿⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡟⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠟⠿⡿⣙⡋⣶⣠⢦⠺⡖⠹⠈⠀⠉⠛⡴⢦⠙⠉⠀⠉⠋⢶⠧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⣤⣠⣀⠀⠀⠀⠀⠀⢧⠛⠙⣞⣤⣧⢻⠛⠛⡿⣼⣤⣳⠉⠋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⡿⣿⣿⣤⣠⣀⣀⠄⠶⠶⡀⣀⣀⣄⡤⣿⣿⠿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⢀⠁⣿⢹⠉⠋⠛⠙⠉⠀⠀⠛⠛⠓⠙⠉⡏⣿⠀⡀⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⡿⣼⢀⠟⣿⣿⡛⢸⠀⠀⡇⢛⣿⣿⠻⣀⣧⢻⠉⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⢽⡤⣤⣀⣋⣼⠀⠁⠈⠀⣧⣉⣀⣤⢤⡿⣾⣶⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠉⡏⣿⢿⠿⡧⣿⠿⠿⣸⣆⠿⠿⣿⢼⠿⡿⣿⢹⠉⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⡟⣿⣻⣟⠀⠀⣻⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⠈⠀⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⣀⣿⣼⣤⣤⣧⣿⢀⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⡇⢸⠀⠀⡇⢸⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⡏⢸⠀⠀⡇⢹⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⡟⣿⣿⣿⣿⣿⣶⣴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿ ⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢷⠼⠾⠶⠶⠷⠿⠿⠤⣤⣯⣿⡋⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇ ⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⣿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⣿ ⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⡟⣿⣠⢀ ⣶⣷⢿⠘⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⠿⣾⣶⣴⣤⣠⣤⣦⣿⣿⠙⠀ ⠀⠀⣿⣿⣿⣾⣶⣶⣿⣿⠿⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠻⠒⠀⠀⠉⠛⡿⣾⣴⣦⢸⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⠈ ⠀⡏⣿⣼⢀⠀⠀⠀⠀⠀⡀⣾⣤⣶⣿⠿⠛⠙⠈⠀⠀⠂⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⣠⢉⠋⠟⠿⣶⣤⣧⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸ ⠀⣿⣾⠀⠀⠀⠀⠀⠀⠼⡦⢸⠀⢹⠀⡀⣀⣤⣦⢷⠿⠛⠛⡉⣤⢳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠛⠈⡁⢛⠿⣾⣴⣠⣇⠙⠀⠉⣿⢰⠀⠀⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸ ⡇⣿⢸⠀⠀⠀⠀⠀⠀⣧⠸⢧⠈⣆⢻⠈⠀⠀⠀⠀⠁⣏⣤⣧⣿⠿⠙⠟⣿⢸⠀⠀⠀⠀⠀⣄⣶⣿⣿⣴⣆⠻⠈⠀⠀⣀⣀⣀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠃⡴⡏⣿⢀ ⠀⣿⢽⠳⠈⠀⠀⠀⠀⡇⢸⠀⣄⠳⡉⣤⠶⠲⠞⠶⣤⢁⠋⣴⠀⡄⣷⣿⣀⠀⠀⠀⠀⠀⠀⠀⠇⣿⢰⠀⠀⣄⣦⠳⠙⠉⠉⠛⠖⡴⣠⠀⠀⠀⠀⠀⠀⠀⠁⠞⢠⠋⣿⣸⠋ ⠘⣇⣿⠘⢦⠘⡆⢶⠷⡾⢿⠾⠶⠰⡀⣄⢤⠶⠶⠴⡤⣠⢀⠀⠀⠀⡇⣿⠸⠀⠀⠀⠀⠀⠀⠀⡆⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣀⠀⠟⣿⣽⠟⣿ ⢿⠈⣷⣿⠙⡀⠢⠀⡿⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⣠⠀⠀⠋⡿⣿⣿⣿⣿⣿ ⣿⣿⠻⣮⣿⠻⠈⠀⣄⢶⡗⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠐⢏⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⢻⠉⠀⠀⠀⠀⠀⠀⠀⠄⡠⣀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⡀⣀⢤⠤⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⠿⠛⠙⠉⠉⠉⠉⠉⠋⠛⠿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠛⠉⠉⠀⠀⠀⠁⠉⠋⠛⠿⣿⣽⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠛⠾⣤⣤⣤⣤⣶⣶⣷⣭⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⠀⣀⣀⣤⢤⠤⠦⠴⠀⠀⠀⠀⠀⠀⡤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠋⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠀⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⣀⢤⠤⠦⠓⠚⠓⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠤⠤⡠⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⡀⣀⣀⣀⣀⣇⣀⣀⣄⢸⠀⠀⠀⠄⡸⣀⣒⣀⣀⣀⢀⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⢄⠑⠀⠀⠋⠖⠤⣀⣀⣀⢄⠢⠙⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⣀⢀⠀⡀⣀⠤⠒⠈⠀⠀⢅⡴⢀⠀⠀⠁⠊⠒⠀⠀⠒⣎⢿⠉⠟⡶⣤⠢⠟⠿⠛⠔⢀⠀⠀⠀⠀⠉⠂⠒⠒⠒⠓⠈⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢤⠢⡿⠀⠀⠁⠜⢀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠚⠠⣀⠀⠀⣀⠦⠈⠀⠁⠔⣀⠀⠀⠃⡴⠀⠀⣄⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣧⢤⠒⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠛⣰⠀⠀⠀⠎⢠⠀⠀⠀⠀⢇ ⠀⠆⠈⠀⠀⠀⠀⠟⣶⣸⠀⢄⠳⡏⠘⠀⠀⡀⣀⢤⠦⠒⠒⠙⠉⡏⢸⡀⠣⠙⠀⠀⠀⠀⠀⡟⣿⢴⠳⠀⡇⢀⠀⠀⠀⠀⠁⣸ ⠀⠀⡀⠦⠙⠉⡉⣸⠀⢆⠉⠉⠉⣖⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣄⣤⠤⠤⠤⠤⣿⢀⠀⡏⠁⡟⠀⠀⠀⠀⠁⡴⠀ ⠀⠀⠀⠀⣄⢹⡀⣆⠙⠀⡇⢰⠁⠞⣠⠀⠀⠀⠁⠾⠴⣠⣀⡀⢀⣼⣀⠦⠓⠈⠀⠀⠀⠀⠀⣿⠉⡔⢀⡀⣿⢶⠙⠉⠜⣀⠀⠀ ⠀⠀⠀⠀⠀⡀⠳⠀⣇⢾⡠⠃⣠⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠏⢀⠀⠞⡠⡀⢄⠢⠈⠀⠀⣦⢹⠈⠁⠋⣾⠀⣏⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢣⡈⢹⠀⢰⠀⠀⠋⠔⣀⠀⠀⠀⠀⠀⠃⡼⣿⠀⡇⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⡀⣄⣽⠀⠏⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⠻⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠟⣾⢀⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⢄⠑⠀⠀⠀⡄⣿⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣘⢢⠙⠀⠀⠀⠀⠀⠀⠁⡟⣿⢸⠀⡄⢳⢹⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠙⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⣀⢄⠦⠽⠤⠠⡂⣿⣧⠸⠀⠀⡀⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢏⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠑⠉⠛⡖⠤⠤⠤⣿⠻⠘⣀⢀⠤⡧⣿⢾⠓⠉⠈⠀⠀⠁⠉⠚⡯⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣨⣀⣄⠹⠊⠔⡦⣿⢶⠶⠶⠷⣿⣴⢀⡀⡀⣦⣽⣀⣷⣿⣈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣠⣆⢻⠈⠀⡞⠀⠀⠀⠀⣀⣞⣤⣯⣠⠀⠁⠚⠐⠀⡀⢧⡟⡾⣶⣤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠚⠒⠒⡖⠻⠈⠀⡄⢿⡿⢲⠛⠓⠑⠈⡴⠃⡴⢁⠊⡴⢀⠀⠀⠀⠀⠀⣄⢿⠉⠟⢻⠒⠙⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡿⣾⢤⣠⣀⢀⢀⡀⢯⣾⣠⣿⣿⣿⣝⠻⣅⠾⣡⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⠈⠀⠤⠤⣤⢷⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣦⠘⠀⠀⠁⠉⠿⠿⣿⢹⡍⣿⣿⣿⢿⡟⣴⠎⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⡏⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢄⠯⣶⣲⣷⣾⣶⣶⣶⣶⣶⣿⣴⢁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠓⠛⠖⡤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠞⣠⢁⠊⡴⣀⠀⠀⠀⠀⠁⡞⢠⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢿⠀⡓⢿⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡼⠁⠞⣠⠀⠀⠀⠀⠀⠀⠏⣠⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡀⣄⢿⠘⠀⠀⠀⠀ ⠀⠀⠀⠁⣿⠛⡰⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀ ⠀⠀⠀⡇⣾⢠⠂⠴⢀⠀⠀⠁⠊⡦⢙⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⢸⠀⠀⠀⡀⠢⠈⡆⢸⠀⠀⠀ ⠀⠀⠀⡆⢲⠓⠉⠊⠒⠔⡤⣀⠀⠀⡀⢦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡴⢀⠀⣀⠤⠲⠛⠉⠉⡉⠋⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠉⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢡⠊⣴⣀⣀⠀⠃⢔⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⡠⠀⠈⠉⠉⠖⣤⢤⠤⠤⠠⠙⠀⠀⠀⠀⠀ ⢤⠙⡈⢀⠀⠀⠀⠀⠀⠂⠒⠁⡈⢿⠴⠁⠚⠀ ⠀⢡⣣⢀⠢⠛⠁⠉⠉⠀⠀⠀⠅⡯⡒⢒⠉⢯ ⠀⡀⠘⢆⠘⣸⡿⣿⣸⠸⠀⠀⠎⢄⠤⠂⡑⢸ ⠀⠀⡆⠘⣇⢠⡦⠓⡄⢺⠟⡩⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⡇⠂⠀⠀⣀⢧⠂⠁⠀⣅⠘⠀⠀⠀ ⠀⠀⠉⡖⢹⠛⠤⠥⢳⡈⠰⡎⠀⠃⢠⠀⠀⠀ ⠀⠆⢸⠀⣄⠈⠆⠠⠀⢻⣞⢀⠁⠰⠀⠀⠀⠀ ⠀⠀⡀⠠⠛⡋⠢⠀⡇⣆⢀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣢⠑⣠⡁⢄⠠⠼⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠠⠤⡔⠈⠇⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣟⣿⣜⡸⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣦⡿⣼⡯⢮⢵⠂⠈⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠆⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣶⣤⣤⣤⣤⣶⣷⠉⠴⢯⡟⣾⣶⣴⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⡜⠱⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿ ⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣽⣀ ⠀⣄⢸⠀⠀⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⢀ ⠳⠀⢷⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠉⠉⠉⠉⠁⠉⠛⡷⣸⠋⡠ ⠀⣄⠲⢻⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⣹⣤⣿⢠⠋⣿⣿⢿⣾⡿⠙⠀ ⠀⠀⠀⠀⢆⠑⠀⠀⡀⣀⠀⠀⠧⠿⣟⣿⣿⣾⣿⡶⢁⡻⣆⢺⡄⠹⠄⢸⡇⠹ ⣀⠄⠢⠑⠈⠀⢄⠐⠈⠁⠉⠞⣷⣿⣿⣿⣽⢿⢡⠊⣴⣆⠑⡅⢻⣆⠿⢸⠀⢿ ⠀⠀⠀⠀⡀⣀⠤⠤⠦⣿⢻⠛⣦⣿⣿⣻⣿⡾⣶⣵⠴⠤⡿⣽⣻⢳⣿⢸⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠿⠹⠀⠀⠉⠀⠀⠨⢸⠀⠀⣿⡇⣿⣽⣸⠹⠁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣾⣟⣿⢽⢈⠀⠀⠎⣢⢷⠀⠀⡀⢶⡖⣠⢰⣄⣤⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⣣⣿⣿⣹⢄⠃⡼⠆⢠⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣼⣿⣿⣿⣿⣿⠿⠠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣿⣿⣿⣿⣿⠺⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣕⣾⣿⣾⣾⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠋⠀⠀⡆⢸⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⡀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀ ⠈⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢸⠀⠀⢣⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠷⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⣼⣇⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⡀⠸⠀⠃⣠⠀⠀⠀⠀⢄⠲⠉⡎⣻⠘⠀⠀⠈⠀⠀⠉⠊⠒ ⠀⢿⡿⠈⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠀⡇⠉⣸⠀⠀⠀⠀⠀⠀⠀⠁⣏⣈⢤⠤⠤⢤⣠⣍⠀⠀⣀ ⠀⣇⣾⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢻⠀⠀⠁⠋⠖⢤⠤⠤⠤ ⠀⡇⢹⠀⠀⡿⣤⣀⣄⣤⣄⠤⠒⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠲⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠎⣠⠋⠿⣴⣀⠀⠀ ⠀⡇⣿⠟⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠂⠒⠉⠀⠀⠀⡄⣼⠀⡏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⢨⢹⡟⣴⣠⠀⠀⠀⠀ ⠀⡇⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⣼⣄⣦⢵⠛⣈⠳⠀⠀⠀⠀⠀⠀⡀⣆⢸⡆⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠘⠀⣄⣷⠙⢧⠙⠀⠀⠀⠀⠀⠃⢸⠀⣄⠙⠀⠁⠀⠀⠀ ⠀⠀⠀⣆⠻⠙⠈⠀⠆⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⣶⡇⠀⢀⠀⠀⠀⠀⡏⢸⠀⠀⡇⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⣇⢄⢻⠀⠀⡀⣿⠿⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣇⢰⠀⠀⡄⡀⣿⢿⠘⠀ ⠀⠀⠀⠀⠀⢻⣾⠠⠀⠀⡇⣾⠀⠁⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⢿⠀⠀⠀⠀⠁⡸⠀⠀⠀⠀⠀⣿⣿⢿⠀ ⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⣰⢉⠖⣦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠊⣠⠀⠀⠀⠀⠃⡀⣷⣾⣧⠀ ⠀⠄⠤⣀⡁⣾⣑⣊⣶⣻⣉⡛⣾⠹⠁⡚⠶⠒⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⡶⢧⣸⠀⠀⠀⠀⠁⠉⡚⠖⣥⠛⣽⠀ ⠀⠀⠀⠀⡄⢷⡸⢂⠓⣿⣿⣹⠀⡀⣷⠀⠀⠀⠀⣀⢤⠑⠈⠀⠀⠀⠀⠊⣼⠀⠁⠞⣀⠀⠀⣿⣮⣐⣀⣀⣀⢁⠘⠀⠀⡀⣦⣿⠀ ⠀⠀⠀⠀⠀⠀⢄⠤⠄⣶⣽⡞⠘⠀⠀⢄⠛⠀⠀⠀⠀⠆⣶⢿⠸⠒⠓⠒⠚⠤⣄⠢⠑⠁⡿⣿⣀⠀⠀⠀⠀⡋⢿⠺⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⣦⡘⠢⠈⠀⡄⠹⠀⠀⠀⠀⠀⠈⢸⠀⡇⠞⢀⠀⠀⠀⠀⣄⠢⠉⠀⠀⠀⠀⠏⣸⣏⢸⠀⠀⠅⣿⠚ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣄⠙⡇⠉⠉⡏⠳⠈⠀⠀⠀⡇⣴⠤⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⡶⣒⢒⠒⠖⠤⡠⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠔⣡⣿⣤⣁⢚⠑⢇⠀⠁⠟⢡⠉⠚⢶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⢀⡇⣻⣿⣶⠓⣛⣻⡿⠾⣶⣿⣽⢀⠋⠒⡄⢣⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⠹⡀⣦⣾⣴⠀⠀⠀⠀⠁⠛⡟⣿⣿⠿⠶⠻⢈⣠⣈⢤⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⢿⠙⡏⠓⠉⠋⠉⠉⠋⣿⡏⣠⢀⠤⠂⠁⣌⠢⡉⠀⠇⡘⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣯⣵⣻⣿⢻⡿⣾⢀⠀⣷⠚⠉⡉⣈⣤⣦⠱⡈⠱⠀⢶⠘⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡀⠀⡄⣠⠀⢻⠈⠀⡏⢷⠈⠻⡀⣄⠧⠑⠈⠀⢣⠚⡖⠱⠉⢫⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢶⡤⣴⢤⠁⠋⠇⣼⢶⡴⢹⡏⢹⡉⢏⠉⡉⢯⡈⠢⠀⢳⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⡙⣍⣋⣞⢺⢠⠀⠀⠀⠀⣀⣄⠦⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠇⠀⠀⡇⠀⠀⠉⠀⠁⢠⠙⠀⡇⠀⠈⠒⠒⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠈⡆⠠⢀⠀⠀⡉⠔⣀⠁⡀⡞⠀⠀⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⡠⠀⠀⢄⠀⠀⡞⣠⠛⠹⡀⢄⣷⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀ ⠀⢰⠀⠁⠉⠛⠟⡿⢿⣿⣿⣶⢿⠉⡁⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀ ⠀⠿⡿⣿⣿⣴⣠⣀⠀⠀⠀⠀⡄⣿⠸⣆⣹⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠇⣿⣿⣴⠀⠀⠉⠉⠉⠋⡜⣯⣿⣿⢀⠀⡇⢼⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣴⢀⠀⠀⡀⠀⠀⠗⡿⡶⣷⣾⢀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠋⠀⠊⠶⣠⠒⠀⡀⢰⠁⠁⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⢩⡴⠒⠀⠈⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠳⠈⠀⠀⠀⠀⠀⠀⠀ ⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠈⠂⠒⠒⠔⠦⠶⠗⢸⠀⣄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠈⠒⠥⠦⣶⣤⣤⣤⣀⣀⣀⣀⢤⠤⠒⠑⠈⠁⠉⠊⣠⢇⠀⠀⡄⠱⠀⠀⠀⠀⠀ ⠀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⣤⠢⠑⠉⠀⠸⠀⠀⡄⠘⠀⠀⠀⠀ ⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⢸⡇⠘⣀⢦⠑⠀⠀⡆⠘⠀⠀⠀ ⠀⠀⠀⣀⠤⠤⠒⠒⠒⠒⠓⠚⠒⠗⠤⠀⠀⠀⡀⠄⠢⠐⠆⣡⢀⠀⠀⠀⢄⠙⠀⢇⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠱⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠋⢰⠀⠀⠀⠋⠞⠀⠀⠉⠛⠙⠀⠀⠀⠀⠀⠀⡀⠸⠀⠱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠞⢲⠑⠈⠀⠀⠀⠂⠼⣀⡀⣳⣷⠘⠀⠀⠀⠀⠀⠀⡆⠈⡆⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡸⠆⠶⠀⢋⠀⠤⢤⠦⠘⠀⠀⡀⡿⣼⠙⠀⠀⠀⠀⠀⠀⢧⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⣆⠲⠈⠀⣠⠀⠀⠃⣿⣼⠀⠀⠀⡇⢼⡀⠳⠀⠀⠀⠀⠀⠀⢱⡇ ⠀⠀⠀⠀⠀⠀⠀⡟⢨⠀⠀⠉⠒⠏⠻⠙⠈⡶⣴⢾⠀⠀⠀⡇⢸⠀⠀⢆⠙⠀⠀⠀⠀⡀⡇ ⠀⠀⠀⠀⠀⠀⠇⢸⣼⠤⣀⠤⡠⣤⣤⣤⡠⢦⡟⢾⠀⠀⠀⡇⢼⠀⠀⠀⡀⢦⠙⠀⠀⠋⡼ ⠀⠀⠀⠀⠀⠉⣏⢹⠇⡏⣛⣿⢹⠀⠀⠇⠟⠿⡅⢻⠈⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣄⡠⢀⠀ ⠀⠀⠁⠔⣀⠀⡇⣌⡿⣿⣿⣾⢴⠤⣥⣯⣿⣿⣷⣿⢿⠈⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠀⠀⠀⠀⢣⡀⣀⣀⣄⡤⣤⣤⣀⠀⠋⣾⢠⡼⢸⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠈⠀⠉⠞⣷⢻⠉⠀⠀⠀⠀⡋⠶⣤⣠⠀⠀⢿⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⢀⠀⠀⣦⣝⢶⠓⠉⡈⢐⠀⠀⠉⠚⡥⢸⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⣀⣀⣀⣀⣄⢱⢇⡴⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡀⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⠁⢀⠀⠀⠀⠀⠀ ⠀⠀⣸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡈⠀⠀⠀⠀⠀⠠ ⠀⠀⡇⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⡹⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡰⣿⠘⠀⠀⠀⠀⠀ ⠀⠁⡾⣔⣀⢄⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⣀⣯⠈⠀⠀⠀⠀ ⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠀⠀⢰⠀ ⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⠀ ⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠹⠸⢀⠀ ⡄⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢸⣇⢸⠸⠀ ⠀⠀⠀⢧⠷⠉⠒⠐⠉⠉⠁⠉⠉⠀⠉⠈⠀⠀⠀⠁⠉⢊⣠⠍⣿⢝⠀⠀ ⠀⠀⠀⠀⠱⢆⠻⠙⠉⣀⠄⠢⣟⣾⢰⠁⠈⣀⢐⠉⠉⠋⠟⣶⣠⡄⠀⠀ ⠀⠀⠀⠀⠀⣄⣼⣿⠈⠁⣍⡼⣀⢵⠶⠷⠯⣟⣶⣿⣴⣬⢀⠁⠚⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡛⠋⠛⠙⠒⠑⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⡛⠛⡟⣿⣿⢹⠉⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⠡⠍⠠⠋⠚⡽⠭⠀⢸⠇⣹⠏⠸⣇⠈⢰⡇⣤⠄⣹⠇⡋⣴⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⡀⠶⣶⠶⢶⠶⢶⡲⠶⣤⣀⣀⣀⣀⣀⣀⣼⣄⠦⢶⡶⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠉⡟⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠾⠶⣤⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠿⣴⣠⢀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡞⣴⢉⡀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠿⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢐⠀⠋⡼⠛⣴⠀⠀⠀⠀⠀⠀⣾⣿⢠⠀⠀⠀⠀⠓⠛⠟⠓⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠏⣼⠀⠀⠟⣰⠏⣰⠀⠀⠀⠀⠀⠀⡇⢿⣸⠀⠀⠀⠀⠏⡾⣤⣤⣤⣤⠳⠀⠛⠴⣿⣺⣒⣓⢽⠶⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠀⡏⣠⠇⣼⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⠀⠟⡿⣾⣾⢡⠈⠀⢀⠃⡰⢀⠟⣼⢀⠀⠀⠀⡀⢶⡝⢳⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢴⠀⠁⣿⠀⡿⠀⠀⠀⠀⠀⠀⠁⡿⣿⢠⠀⠀⡾⣰⡄⣿⣠⢀⠀⠀⡇⠀⡇⣿⢀⠀⠀⠁⠉⠀⠀⡆⢷⣎⠙⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠉⣿⠉⠈⠀⣷⠈⣿⠘⠀⠀⠀⠀⠁⣿⣿⢿⠀⠀⠞⢀⡇⣿⣭⠻⠘⠀⠀⡇⠀⡀⣿⠀⠀⢷⠙⡀⢦⠙⠀⡆⢳⣧⠘⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⣿⣾⣾⣷⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠸⠀⠀⠋⡿⣿⢠⠀⠀⠰⠋⠟⣿⣿⣼⢀⠀⠀⠆⣹⠀⠀⣿⠀⠀⠀⣄⢻⠈⣆⢹⠀⡇⠈⢷⠀⠀ ⡶⣫⢟⡿⣼⣏⠰⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⡿⣸⣟⣸⠀⠀⠆⣿⣿⣟⣿⣿⣿⣴⢠⡀⠀⣷⠘⠀⣧⢸⠀⠀⠀⡀⢿⠀⣧⠀⡆⢶⡼⢹⠀ ⣿⣿⡿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⠿⣼⠀⠀⠀⠀⣿⠈⠀⣀⣄⣷⠻⠂⠀⠀⡆⢿⠀⡀⢿⠀⠀⠀⠀⣧⠃⡆⢸⠀⠀⣾⣷⠀ ⣿⣿⣚⣿⣿⣩⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⡀⣇⣿⣿⣿⣿⣿⠀⠁⠋⠉⠀⣀⣦⠹⠈⠀⡀⣶⢻⠉⠀⠀⣷⢩⠀⡆⢻⠀⠀⠀⡆⡸⠈⢿⠀⠀⣧⡇⢸ ⣿⣿⣭⣿⣙⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣼⠀⡏⣼⣼⣤⢷⠛⡈⣦⠻⠀⠀⡄⣷⢹⠀⡀⣿⠈⠀⣿⢸⠀⠀⠀⢸⢧⣸⠀⠀⡇⡇⢠ ⣿⣶⣷⣟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣿⣿⣾⠀⠀⣿⢀⣿⠰⡄⣷⣧⠙⡀⢧⠙⠀⠀⣄⢻⠈⡄⣿⠀⡇⠸⠀⠀⠁⢸⡀⢸⠀⠀⡿⣿⠀ ⣯⠹⠭⡛⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠿⣿⣿⣿⣿⣿⣿⢰⠀⡇⣸⡟⣠⠀⠀⡀⣄⣷⠻⠀⣦⠸⠈⠀⠀⢀⡄⣿⠀⡇⢸⠀⠀⡇⢸⠀⢸⠀⠀⣿⣼⠀ ⣡⣬⣦⠶⠶⠶⠶⠶⠶⠶⠶⡶⣶⣶⠶⠶⠶⠶⠶⠶⠲⡟⣿⣿⣿⣿⣿⣼⠀⠀⣶⢷⣻⠙⠉⠉⠉⠞⡀⣷⢻⠀⡀⣤⢳⠙⠀⠁⣼⠀⡟⢰⠀⠀⡟⢠⠀⢸⠀⠀⡇⢰⠀ ⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣦⣿⢸⠀⠀⠀⠦⠳⠙⣉⠉⡉⣍⣬⢦⣿⢮⠙⠀⠓⡉⣤⣠⠀⠏⣴⠀⠀⠇⣿⠁⡟⢰⠀⠃⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣀⣄⣠⣀⣓⣼⢷⠛⢈⣦⣿⠐⣀⢶⠿⣬⣀⠀⠀⠀⡟⢀⡏⣴⠀⠄⡟⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣛⣧⠻⣌⠳⡈⠠⡁⣌⠶⠛⠛⠟⢸⠇⣸⠀⠀⠇⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡌⢿⠹⣄⢦⠷⣽⢣⠙⡇⠙⠀⡄⣀⣦⠻⡌⢈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣮⠳⠈⠀⣄⢷⣮⠙⠀⠀⠀⠀⠀⠀⢻⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣤⢶⠛⠉⡌⢦⠐⠀⠁⠛⠟⣿⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣤⢤⡶⠿⣻⣞⣴⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠋⡿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣷⣎⣿⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣐⠋⡾⣫⡾⣤⢀⠁⠉⠛⠛⠶⠶⠹⠀⠀⣂⣤⣿⣾⣴⢀⡼⠀⣆⣿⣿⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣸⠟⣫⡾⣠⠋⠟⡶⣤⣀⢁⠛⠖⠤⠀⠉⠛⠶⣤⣀⠀⠉⠟⢸⠀⠀⡀⣤⣷⣿⠿⠛⠛⠛⠛⠛⠛⠟⠿⣿⣿⣴⣤⣤⣤⠳⠈⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡞⢟⣿⠾⣴⣀⠀⠉⠉⠉⠉⠛⠽⡯⣹⢉⠛⠛⠟⠿⣿⣾⣠⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣶⣶⣴⣤⣠⢋⡿⢘⠀⠀⠀⠀⡀⢠⠀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣠⣀⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡴⢀⡈⢿⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠖⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣾⣠⣄⣀⣷⣽⣉⢋⣛⣛⣛⣛⣿⣾⣴⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⠠⠀⠄⣷⣾⣶⣶⣷⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠻⠛⠙⠉⠉⠀⠀⠀⣀⣿⠿⠌⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠀⠀⠉⠀⠀⠀⠁⠉⠛⠖⡤⣠⢀⠀⠀⣆⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡆⣿⣿⣾⡇⣿⢿⠻⠛⠟⣾⣧⣿⣿⠀⠀⠀⠀⠀⠄⠲⠀⠀⠀⠏⣾⠶⣻⠛⠙⠗⡿⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⠻⠉⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣆⣿⣿⡟⣴⠈⠏⣿⣴⠋⣿⣿⣿⢿⠻⠛⠁⠉⠉⠉⠉⠋⡴⣠⠀⠀⠀⠀⣀⣧⢸⠀⠀⠀⠀⠁⠛⠿⡶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣄⣿⣸⠀⠟⣼⢋⡟⣿⣴⣀⠀⡀⣄⣦⠻⡛⠙⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠟⣾⣠⠉⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⠈⠀⡀⣤⠷⣽⠏⣿⣿⢴⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⢿⠻⠙⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⡟⣼⣿⢾⣙⣄⠲⠛⠒⠑⠞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣿⠙⠀⠀⠘⣇⣭⣶⣳⠉⠀⠀⠀⠀⠀⠀⠀⠉⣯⣼⣿⣿⣿⣤⠿⠬⡿⣴⢀⠀⠀⠀⢩⣿⠀⠢⣆⡻⣍⢦⠰⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣦⣯⣿⣿⣿⣿⣿⣿⣿ ⠉⣿⣿⠻⠈⣄⣿⣮⡟⢸⡟⣿⣿⢥⠀⠇⠿⣿⣟⣿⣿⣾⣠⡏⠿⣸⢀⠀⠀⠀⠀⠁⠉⡟⣿⡿⢿⠿⠻⠛⠛⠾⠶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢹⣧⣿⠿⡿⢿⡙⣮⣿⣿⣿⣿⠉⡿⣼⣿⣿⣿⣴⢁⡟⣿⣏⠸⠀⠀⠀⠀⠀⡀⠋⠻⣿⠘⠀⡄⣿⢸⡀⣄⢦⡛⡋⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠻⣀⢦⣙⣤⣶⠿⡛⣏⣼⣷⣿⣿⣷⣿⣾⢁⠞⣡⢟⣿⣿⢻⠈⡀⠈⠀⠀⡇⣼⣤⣷⢹⠀⠁⣿⢠⠀⠀⠀⡀⣅⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠻⠙⢉⠈⠀⣀⣄⣶⣿⡛⣯⠹⣇⠿⣵⢞⣾⣷⣿⣿⣿⣽⠀⠀⠀⠀⡀⢳⠈⡀⣧⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠐⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣙⣀⣄⢤⠿⠶⠛⣙⣿⣿⣻⡍⣿⣾⠶⠀⡀⣦⣷⣟⣿⠲⠒⠙⠉⠀⣄⢦⠓⢈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⡎⠘⣛⣛⣛⣿⣿⡿⣾⢷⠈⠀⠀⠀⡀⣶⢠⠀⠀⠀⡀⣀⣤⠦⠒⣗⣯⣿⠈⡀⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⣿⣿⣿⣿⣿⣾⢀⠀⣇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠲⠛⠙⠉⠈⠀⠀⠀⠀⠀⡇⣿⡇⣿⢸⡅⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣸⣽⣀⣴⣿⣤⣶⣵⣤⣠⣀⣀⣦⣶⣦⣿⣴⠖⠠⠋⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢦⠶⠿⠛⡛⣿⠉⣿⢨⡀⡰⣷⣿⣿⣿⣿⣿⣿

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⠛⣚⡓⠛⡛⠛⠛⠛⠚⠓⢸⡅⢩⡍⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⣿⢸⡿⡟⡏⠂⢶⠸⠁⠀⢸⠀⠀⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀ ⣀⢁⡋⢈⡇⠀⣷⣘⡇⢰⢼⠶⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀ ⠿⣭⣳⠈⡇⠘⣿⢀⡇⢠⢸⠁⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⣹⡉⣉⢮⡷⠄⣤⠉⣸⠀⢸⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣭⢄⣤⢀⡇⠙⡞⢀⣇⠘⢸⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢛⠛⠙⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀ ⣶⣶⠶⣦⡇⣦⡴⣁⣄⢠⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⣿⣿⣾⣠⣀⣧⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠿⠙⠈⠀⠃⠛⠙⠛⠙⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣶⣶⣿⣼⢀⠀⠀⠀⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣿⢀⠀⠀⡇⣾⣿⢿⠘⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⠀⡀⣿⠙⠋⠞⠤⡧⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀ ⣿⣼⠻⠀⡆⣸⣇⣹⢩⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⠟⡿⣿⢹⢋⠖⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣾⢸⢸⠀⠃⢈⣀⠀⠀⣟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⠀⡇⣿⣷⣾⣤⢀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠻⠉⠛⠀⡇⢤⡤⣦⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀⡀⣦⡾⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⢀⣇⣿⢨⡇⠀⠉⠈⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠚⡒⡒⢶⡶⠓⣛⣛⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀ ⣿⣿⣿⢸⡇⠀⣛⣃⣟⢸⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀ ⣤⣥⣭⢩⡟⠛⣻⡉⣿⢸⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠋⠐ ⠀⣿⣿⣴⣠⣄⢦⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠾⣠⢀⠀ ⠿⣿⢠⠀⠀⠀⠀⡀⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀ ⣶⣸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠚⠒⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠽⠤⠤⠤⠶⠒⠛⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠟⠶⠴⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⢄⠤⠤⠦⠶⠒⠒⠓⠉⠉⠉⠉⠈⠉⠛⠿⠿⠭⠦⠶⠻⡈⣻⠈⠀ ⠀⠋⠟⠿⣷⣞⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠖⣤⣷⣏⣿⣥⣀⣷⣿⢿⣿⣿⣄⢻⠀ ⠏⢲⠑⣋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠽⣿⣠⠀⠀⠀⠂⣍⣷⠈⠀⣇⣯⣿⣾⢀⠀⡇⠘ ⣦⣿⠽⠙⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⣠⣀⣀⠁⠚⡴⣤⣷⠀⠀⠁⡒⣖⡶⢶⢯⠀⠀⣄⣶⢀⠀⠀⡏⣾ ⠀⣄⣦⡿⣛⢮⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⡿⣉⠈⠀⠀⡇⠀⠃⣰⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠂⣾⣤⣀ ⠀⠀⠀⠀⣀⢤⡤⣦⠶⠷⠓⠛⠛⠛⠒⠗⠼⡤⣀⠀⠀⠀⠀⡀⣄⢷⠿⡬⠻⡟⠈⠀⠀⠀⠀⠀⠁⣟⢹⠀⠀⠀⣝⠹⠀ ⣀⣀⢤⠦⠲⠛⠛⠖⠴⡠⣀⣉⠚⠐⠁⡰⠀⠀⠀⠄⠤⠘⠀⠀⠀⠀⣧⡼⣀⢀⣦⠘⠀⠀⠀⠎⣿⣿⣿⠿⠙⠀⡄⣿⠀ ⠀⠀⠁⠚⡴⣀⠀⠀⠊⡠⣀⠀⠀⠀⡁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇⢰⠚⠷⠭⣎⢳⠈⡜⠀⡄⣿⣿⣶⡽⢾⡴⢀⠀ ⠞⡭⢀⠀⠀⠀⠀⠇⢀⠀⠀⠁⠊⡴⢀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠀⠀⡜⠀⠀⠀⣄⠳⠈⣆⢸⠉⠋⣴⡤⣀⠀⠀⠀⠀⠀ ⠈⠒⣔⠲⠉⠀⠀⡀⠁⠊⠔⣠⠀⠀⠀⠀⠀⠀⠃⣾⢠⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⡇⢸⠀⣄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢄⠑⡬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠃⣰⠀⠉⠉⠀⠀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠀⠀⠀⠀⠀⢄⠱⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⡽⠋⠴⣀⢀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠱⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⡞⣠⢀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢢⠈⠀⠀⠀⠀⠀⣄⢷⠿⠺⠶⡟⢰⠀⠀⠀⠀⠏⢠⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠙⠉⠀⠀⠀⠀⠀⣄⠳⠏⢰⠀⠀⠀⠀⠇⣰⠁⠉⠉⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⡷⠸⠀⠀⠀⠀⠀⡀⣦⠸⠀⠀⠀⢿⣰⠀⣸⠀⡝⢹⠉⠒⣴⣧⢽⠻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢰⠀⠀⠀⠀⠓⠈⠀⡇⠘⠀⠀⣼⠀⠏⢹⠉⡿⣴⠀⠀⠁⣾⣥⣊⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⡄⢸⠀⡇⢰⠀⡇⢘⠎⢀⡟⣿⣠⠀⠀⠀⡀⣋⣻⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠃⣲⣾⢀⠀⣿⣰⠀⠀⠀⠀⠓⣿⣟⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠃⣠⡞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣄⣷⣹⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠏⣨⡞⢀⠀⠀⠀⡇⠐⠋⠙⠈⠀⠁⢀⠀⣄⣦⢳⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠁⣹⡴⢀⢆⢳⠀⠗⠺⠀⠀⡃⣭⣷⣿⢿⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⣰⠀⠀⠀⡀⢦⠉⠊⠠⠰⡟⡀⣮⣿⣿⢠⠀⠀⠀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⢠⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⣿⡞⣶⣧⢰⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⢶⡷⢻⣾⢸⠀⠀⠀⠀⠀⠀⡀⢳⠏⠖⣠⠀⠀⠀⠀⠀⠀⡏⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⣰⣀⠀⡀⢿⢻⠛⠤⠤⠛⠉⠉⠉⠀⠁⠉⠈⠀⠀⠀⠀⠀⠞⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠇⣴⠸⠀⠀⠃⣰⡀⣇⣵⣠⠁⠞⣀⠀⡃⣻⢔⠠⠀⠀⠈⠋⡰⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⡾⢠⠀⠀⠃⢰⠇⢀⠀⠀⡼⠀⠀⡟⢠⠇⣴⠀⠀⠗⣸⠀⠀⠀⠀⠁⣾⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⣀⠀⠀⠀⠁⡹⡼⢀⠀⠀⠏⢀⠀⠇⢸⠀⡘⠀⠀⠀⡼⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⡾⣧⢀⠀⠀⠀⣾⠀⠀⡇⢀⠀⢸⠀⠀⠁⢸⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠃⢰⡇⠀⠀⠀⡇⢀⠀⠀⡇⢸⠀⢇⠀⠀⡄⢸⠀⠀⠀⠏⣰⠤⠑⠉⠀⠀⠁⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⡗⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⣧⠈⡀⢲⠀⠀⢸⠀⠁⡞⢀⠀⠀⠀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⣧⠃⢰⠀⠀⠀⢸⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⢸⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠀⡇⡸⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⢄⠙⠀⠁⢿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⡇⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠉⠘⠁⡏⢀⠁⠰⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣵⠁⡹⣰⢿⡨⠏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⢀⠀⠀⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠁⠀⠀⡇⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⡋⣸⡀⠀⠀⠟⣠⢀⠀⠀⠀⠀⠀⡀⣷⣻⣟⣙⣼⣀⢳⣇⡉⣄⣳⣮⠘⠀⠀⠀⠀⠇⣦⢸⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⠀⠀⠀⠀ ⠀⣤⠀⠀⡜⠀⡇⣼⠀⠀⠀⠀⠀⠀⠋⡞⣶⠀⠆⠉⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⠀⣀⣄⠠⡄⠻⣛⢿⠛⣌⣝⠙⠀⠀⠀⡟⠀⢻⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠄⠀⠀⠀⠀ ⠀⡇⠀⠇⢠⠀⡇⢸⠀⠀⠀⠀⠋⡶⣠⠀⠀⡄⠣⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣀⣤⣳⣿⡟⣬⠹⠀⠀⣿⠀⡆⠘⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⠀⡴⠀⠀⡿⢀⠀⠁⠊⡴⢀⠀⠀⠀⡧⡿⢟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣿⠹⠀⣧⠀⠀⣧⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀ ⠀⢰⠈⠀⠀⠏⢰⠁⠞⣠⠀⠀⠀⠀⠀⠃⣸⣀⢷⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⡏⠀⠀⠀⢧⠈⠀⠀⠀⠀⢸⠀⠀⠀⢠⠊⠾⣠ ⠀⠜⢀⠀⠃⣿⠞⣠⠀⠀⠀⠀⢀⠀⠀⡏⢀⠀⡇⠹⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠟⢠⣿⠀⠀⠀⠀⡀⣤⠠⠀⠉⠉⠀⠀⠀⡀⣧⠸⠀⠀⡀⣳⢦⠙⠀⠇⢸⠀⠀⠀⠀⡜⠀⠀ ⠜⠀⠀⠁⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣦⣶⢴⣤⣤⣀⣀⣤⢤⠤⣥⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⠯⠛⠈⠀⣧⠘⠀⠀⡀⢷⡈⢷⡏⠀⠀⠀⠀⠁⢀⠀⠀ ⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡅⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣝⠦⡙⣿⠘⠁⠀⡀⢷⡎⣿⠀⠀⠀⠀⡌⠀⠀⠀ ⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⡤⣧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⣄⢦⡐⣤⣿⠈⢷⠈⠀⣧⣿⠀⠀⠀⠀⢸⠀⠀⠉ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣰⣦⠛⠛⠛⠛⠞⠴⡤⣁⣛⣖⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⣠⠀⠀⠀⠀⠀⠈⡀⢧⠙⢷⠘⡇⣸⠀⠀⠀⠀⢿⠀⠀⠀ ⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠲⠒⠛⠚⠓⠒⠒⠤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣋⠠⠀⠀⠀⠀⠀⠀⡄⠹⠀⣄⣷⣿⡿⢀⠀⠀⠀⠀⣸⠀⠁⠠ ⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡾⣶⡠⢀⠀⠀⠀⠀⠀⡷⠻⠙⣍⢳⠈⡀⣧⣽⠀⠀⠀⠀⠀⢀⠀⡄⠀ ⠇⣿⢸⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⡀⣦⣿⡿⣯⢿⠀⠀⣿⠀⠀⠀⠋⠠⠀⠄⠀⠀ ⣧⣿⢻⠄⡀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣶⡤⣤⣦⢷⠛⠈⠀⠀⠀⡀⣶⢾⣿⢻⠀⡆⢸⠀⠀⢠⡀⠘⠀⠀⢣ ⣧⣴⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣴⢋⡴⣄⠦⠓⠉⣆⢻⠘⠀⠀⠀⠀⣇⣽⣿⢹⠀⢣⠀⠀⠀⠂⠀⠀⠀⡆ ⡌⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠻⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⣸⠀⠀⠀⠀⣄⠿⣿⢸⠀⠀⠀⠀⡇⣻⣻⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢰⠃⠿⠠⠀⠀⠀⠃⡿⣠⢁⠚⠛⠉⣀⣦⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⢹⠈⠋⠿⠛⠟⣿⣿⢠⠀⠀⠀⠛⡽⣿⣿⣾⢸⠀⠀⠀⠀⠀⠸⠀⠃⠀ ⠀⠀⡇⠘⡿⣾⠀⠀⠀⠀⡇⢻⡿⡾⠀⠀⡀⢦⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⡀⣦⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠋⡿⣿⣿⣾⣡⠟⣾⠀⠀⠀⠀⠀⡀⢜⡀⠀ ⠀⠀⡇⢿⣿⢸⠀⠀⠀⠀⡇⢿⣿⢸⠀⠁⠉⠀⡏⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⠻⡛⣝⣿⣮⣶⣠⢉⠋⠟⡿⣿⣽⢋⣿⢓⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠦⠘ ⠀⠀⡇⣿⣿⢸⠀⠀⠀⠀⡄⣿⣿⣿⠿⣿⣿⣿⣿⣿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⡾⣓⣻⣯⣿⣿⣿⣻⣟⣿⣿⣾⣶⣿⣙⣏⢀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⡄⣿⣿⣿⣼⢤⡿⠀⠀⠀⣄⣶⣿⣿⣿⣿⣾⣫⡾⢱⠛⠟⠋⠓⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣷⣿⣿⣼⣷⠞⠤⣀⡇⡈⣴⠀⠀⣿⠀⠀⠀⠀⠠⠄⠒⠉⡇ ⠀⠀⠀⣿⣿⣿⢸⠀⣿⠉⠉⠉⠛⠒⠖⣷⣿⠿⡿⣵⢞⣫⣰⣆⢰⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⠤⢹⠀⣧⡟⢸⠀⣆⠹⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⣇ ⠀⠀⠀⡆⣻⣏⠀⠀⣿⣿⣿⣿⢰⠀⠀⡟⣿⣿⣶⣠⠃⣼⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⣷⢀⠀⠀⣆⠸⠀⢸⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⣿⣆⢸⠀⣧⣍⣧⣼⠀⠀⠀⣽⣀⢀⠁⠛⡼⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⠀⠀⠸⣧⠉⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠹⢸⠀⡇⣸⣇⢀⠀⠀⠀⣼⣤⡤⣀⠇⢸⠀⠀⠀⠀⡏⢀⠀⠀⠃⡷⢰⠀⠀⠀⠀⠀⠉⠈⠀⠀⡆⠸⠀⠀⠀⠀⠉⣿⣯⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢄⠲⠘⠀⠀⣧⢸⠀⠀⢳⡾⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠇⠠⠀⣿⠀⠀⠃⣴⣿⠀⠀⠀⠀⠀⠀⡄⣂⢷⠽⡯⢺⠒⠷⠿⣲⢤⣷⡀⣿⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢦⠙⠀⣧⠈⠀⡆⢿⠀⠀⢸⠀⢸⠀⠀⠀⡇⢸⠀⣸⠀⠀⢸⠀⠃⣰⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⣟⠀⣾⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⡀⣷⡻⢰⠀⠀⣇⠘⠀⢸⠀⢧⠓⠛⠞⡷⣸⠀⢸⠀⠀⢸⠁⡼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⢰⠀⠀⠀⡞⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀ ⣆⠹⠀⠀⠀⠀⣀⢧⠈⠀⠀⢀⠀⣧⠀⡇⠘⠀⠀⡆⢸⡇⢨⠀⠀⢹⡏⢠⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣞⠢⠈⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠃ ⠝⡄⢱⠀⠀⠀⠀⠀⣦⠻⠀⠀⠀⡇⠀⡀⢻⠀⠀⠀⢸⡇⢸⠀⡇⣿⣸⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢽⠋⢰⠀⡀⠦⢹⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠸ ⡹⢦⡜⠻⠀⠀⠀⠀⠀⣄⢷⠈⠀⠀⢻⠀⣆⠘⠀⠀⡇⠁⢸⠀⡇⣿⢠⠀⡇⢸⠀⠈⠀⠀⠀⠀⠉⠀⠁⠋⠛⣿⣹⣼⠀⠀⠀⠃⡀⢤⠳⠈⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡟⢰ ⡄⠘⡄⡷⢞⠘⠀⠀⠀⠀⡀⣦⠙⠀⡄⠘⠀⢳⠈⠀⡇⡌⢹⠀⡄⣿⠀⠀⡏⢿⡿⢟⠾⠉⠟⡴⣽⠞⣫⣿⢏⣿⣼⠀⠀⠀⠞⣠⢧⠈⠀⣀⢷⠉⠉⡞⢀⠀⠀⠀⠀⠀⡟⣾⠀

⠀⠀⣢⣈⢀⠋⡨⠭⠼⠤⠦⠤⠤⠇⢿⠘⠈⠀⠥⠐ ⠀⠐⠈⠃⠀⣦⣤⣀⠁⠀⠀⢀⠐⡀⢦⠿⢐⠃⢀⠀ ⡂⢁⠩⣀⠐⠄⠁⠔⢀⠀⠀⠠⡀⠂⠈⠠⠀⠰⠀⠀ ⠀⠀⠇⠘⠚⠵⢭⠲⠁⠁⠊⠠⠉⠄⡁⠠⡰⠀⠀⠀ ⠀⠀⠀⣦⡓⠛⠞⠃⠀⡁⢌⠛⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠃⡟⡻⢽⠭⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⣤⡀⣀⣄⢻⠉⢋⢀⠁⠀⠈⠀ ⠀⠀⠀⠀⠃⡿⢠⡈⢀⠺⣴⣥⣷⠹⡉⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣿⣝⣎⠁⡋⣛⢟⡴⣄⣇⢂⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢿⠻⣿⢰⣃⣿⠹⠏⣠⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣶⣶⡶⣾⣷⣀⠳⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠀⠀⣄⠀⠀⠀⠀

⠀⠝⠈⠡⠀⠀⠁⠀⠀⠀⠈⠂⠒⠐⠈⢡⠀⠀⢇⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⢑⠀⠀⢆⠹⠜⢀⠀⠜⣀⠀⠀⠀⠀⡀⡦⠊⠒⡔⠂⠙⢸⠀⠀⠀⠀⠀⠀ ⠀⢆⠚⡪⢣⢏⠀⡇⠀⠀⠀⠀⠀⠀⠣⠀⣇⠠⢀⠀⡀⣧⠲⠙⠀⠙⠀⠀ ⠀⠀⣡⠱⠀⣤⡤⡶⢕⠠⠀⡠⢀⠔⡟⠒⠐⢼⡏⡼⠠⠸⢆⡩⢿⡟⠹⠀ ⠀⠀⡀⠘⠂⠈⠀⠀⠀⡀⠣⠈⠀⠀⡈⠉⠈⣄⡟⠀⠀⢾⠈⢇⣿⢻⡎⠸ ⠀⠀⠀⠃⠀⡀⠡⠀⠀⠁⡡⢧⠀⠃⢀⣤⢀⠀⢸⠀⠀⣸⡈⡀⣷⣧⢠⢠ ⠀⠀⠀⠀⠳⠉⠉⢇⠍⢔⢀⠀⠁⠨⢀⠥⠑⠀⣄⠀⠄⢼⠐⠈⡆⡜⡎⠈ ⠀⠀⠀⠀⡄⢑⠁⣈⣊⠢⠋⠚⠋⢶⠤⠤⠠⡊⠳⠈⠁⢰⠀⡄⠐⢿⢨⢰ ⠀⠀⠀⠀⠀⠀⣀⢀⠄⠈⡇⠆⢫⠐⠝⠪⠀⡋⠜⣄⣀⣄⠱⠀⡄⢸⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⣿⢼⠥⣰⠆⠤⣤⡤⠶⠀⣀⣧⠀⡇⢂⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣥⢈⣀⠀⠀⢄⠤⢀⠁⠴⣐⣌⠀⡴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠎⠑⠈⠀⠀⠁⠆⠈⡇⠀⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠂⠠⣁⣀⣁⣀⢀⢅⠻⠀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠅⢡⠀⠁⢘⠀⠀⣄⠖⢠⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⠆⣠⣀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢁⠘⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠋⡰⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢡⠞⢀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠍⠫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢃⡼⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠔⣠⠋⠿⣾⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠁⡰⠀⠀⠀⠀⠊⡠⠀⠋⠰⠀⠀⠀⠀⠀⠁⠕⣾⣴⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡸⠀⠀⠀⠀⠀⠀⠁⠜⢀⠀⠀⠀⠀⠋⡿⣴⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡎⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠁⠀⠋⡞⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⡎⢀⠀⠀⠀⠀⠋⡠⠁⠀⠁⠔⣫⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢷⠁⢰⠀⠀⠀⠁⡔⢀⠎⣡⠔⢋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⣸⡀⠀⠀⠀⠙⡼⠀⠑⠟⣾⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣎⠀⠀⠀⠁⡴⠀⠈⠋⡾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠀⠧⠤⡠⣄⣱⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣷⢱⠀⠁⠘⠀⠀⠁⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢱⠀⠀⡀⠀⣧⡻⢻⠀⠀⠀⠀⠀⠀⠀⡇⣸⡎⠀⡜⠀⠀⠏⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠙⠉⠈⡄⠘⠀⠀⠀⡉⣻⣯⠿⠈⠀⠀⠀⠀⠀⣾⢇⢰⡏⢀⠁⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣷⣿⣿⣷⠹⠁⡿⣲⠙⠉⣛⣿⠻⠙⠉⠀⠋⢸⡘⠃⢠⠗⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⢡⠩⡟⣰⠀⠀⠏⣤⣤⠶⠁⡻⣿⣧⣿⢻⢉⡼⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⢠⡄⣯⣰⠀⠀⠃⢠⠀⠀⠃⡤⣐⠀⠀⣇⢿⡼⢣⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠟⣸⠀⠀⠎⢠⠀⠀⠁⢰⠀⠀⣀⠀⡇⣿⢻⡿⣿⠘⠯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠈⠀⡴⠀⠀⠀⠀⡼⠀⠀⠁⠋⠿⣿⣶⣾⣤⣄⢲⡝⢻⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡞⠀⠀⠔⣧⣴⣠⢀⠀⡀⠀⠁⠋⣶⣂⢤⠻⠒⠒⠙⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⡏⢀⠀⠀⠏⢠⠀⠀⠀⠀⠉⠞⣠⢄⠀⠀⠀⡆⠙⠘⠋⣴⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⠀⠀⠃⣿⢿⠻⠈⠀⠀⠞⢀⠀⠀⠀⠀⠇⣰⠈⠀⠀⠉⠊⠘⠀⠀⠀⢸⠀⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠹⣿⣾⣿⣼⢻⠈⠀⢠⠀⠀⠀⠀⠀⣺⡠⢃⠴⣀⢀⠀⡖⠈⠀⡆⠁⠴⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣿⣿⢿⣿⢸⡇⣿⣿⢿⠹⡀⠤⠀⠀⠁⠟⣶⣶⣵⢠⠀⠀⢇⠈⠃⢠⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠘⠈⠀⠀⣿⣿⣿⣟⣿⡇⣿⣿⣿⣿⣿⠿⠿⡿⣽⠲⠩⠛⠈⠀⠀⠀⠀⢄⡦⠙⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢦⣝⠐⠀⣾⣷⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣷⣿⣿⢷⣾⣧⣿⠸⠀⠀⠀⠀⠀⡀⢄⠳⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⡋⢿⠿⢻⠙⣿⣿⣿⢻⣇⣿⣿⣿⣿⣿⣿⣿⣽⣯⢿⣿⣿⢿⠘⡇⢰⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣌⣷⣿⣿⣿⣿⣿⣿⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠏⣿⠽⣿⠚⡾⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣶⠿⡛⣛⣝⣭⣭⢹⠂⠐⣧⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣻⢿⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣋⣟⣿⠙⠂⠐⣷⣿⣿⠘⣯⣿⣿⣿⣿⣿⢂⣿⣿⣿⣿⠏⣿⣿⣿⣿⣟⣠⡟⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠟⣿⣽⣿⣴⣏⠿⠿⡿⣷⣿⣿⣿⣿⣘⣀⡀⢁⡞⣤⡿⣿⣿⣾⣷⣿⣶⣶⢶⡷⣽⢯⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣿⣿⣿⣵⢟⡿⣾⣠⢀⠀⠀⣄⣶⣿⣿⢿⠽⠈⣠⠉⠔⢀⣭⣚⠤⣠⢉⠚⠚⡭⣿⣿⣿⢹⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣻⠿⣿⣶⣱⠈⠀⠀⠀⠀⠀⠀⡀⣄⣿⣷⠿⡺⢖⠴⣠⢀⠀⠁⡉⢚⠴⣀⣄⠦⡙⣌⣦⠹⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣀⠀⠀⠀⣇⢼⠲⠉⠈⠀⠁⠋⠟⣼⢀⠀⣀⣀⠤⠤⠤⣰⣤⠀⠀⠀⠀⢸⠀⠀⢆⠜⡅⠹⡀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠁⡁⢀⠲⠓⠀⠃⠖⠸⢁⠀⠉⠀⠀⠐ ⠀⠀⠀⡅⠐⢀⡀⠑⠐⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⡘⠣⠀⠠⠀⠀⠠⠃⡀⠀⠀⠀⠀⠀ ⠗⠶⡄⣀⡼⠃⠓⡨⠫⠓⠔⡰⠀⠀⠀⠀⠀ ⠀⠀⠂⠴⣿⢠⣀⣤⣠⢀⣇⢼⠲⠀⠀⠀⠀ ⠀⠀⠃⠶⢸⣤⣬⠁⡄⣼⢠⣾⠳⢘⠀⠀⠀ ⠀⠀⠗⠿⣿⣻⣿⢨⣥⣿⣿⢿⠿⢸⠀⠀⠀ ⠀⠀⡄⣷⣿⣿⣿⢻⣿⣿⣿⣿⣴⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣮⣷⣿⣿⣶⣮⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢄⡏⠀⡇⠎⢀⠀⠀⠀⠀⠀⠀

⢡⠀⢀⠂⢀⠀⠀⠊⠀⠀⣶⣳⣿⣾⣷⣿⣮⣜⣤⣷⣿⣿⣿⠀⣁⢸⠟⣾⢺⠥ ⠀⠀⠔⢀⠁⠔⡠⠀⠁⠉⠉⠔⠂⡈⢀⣤⢷⡈⠻⠈⣆⣿⣿⣿⡿⣿⢧⣇⢿⣼ ⠀⠀⠀⠔⢀⠀⠀⡱⠔⠴⢀⠀⠀⡄⠘⠀⠀⣄⡵⣻⠧⣿⡇⣿⣿⠎⡿⣿⣿⢸ ⠠⠀⡀⠀⠀⠀⡇⣽⠀⢢⠒⠇⢉⠉⠠⠀⠀⠀⡀⣧⢿⣝⡷⣿⣿⢹⣷⣿⣿⢸ ⠘⠠⠀⠀⠀⠀⡇⢹⠀⠀⠀⡇⠶⢠⠀⠀⠀⠀⠀⡸⣆⣿⢧⡙⣦⣿⡜⣿⣿⢸ ⣿⠀⠀⠀⠀⠀⠀⣢⢥⠭⠦⣔⢀⠀⠀⠀⠀⠀⠀⠈⠀⣇⢻⣆⢿⡝⢿⣎⣿⢻ ⣿⠘⠀⠢⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠈⡀⣆⠈⣄⣿⣿⢫⣧⣿ ⣿⢸⠀⠇⡲⣮⠻⠟⠘⠀⠀⠀⠀⠀⠀⠀⠁⠊⠰⢺⡀⠠⠈⢁⡀⣟⣿⣿⢻⣧ ⡏⢻⠀⡢⣴⠥⡄⡹⢧⠀⠀⠀⠀⠀⠀⠃⡿⣚⣟⠿⠀⠸⣇⡿⠙⡆⣯⣷⣿⡟ ⣷⣿⡟⠀⠇⢿⠦⡿⢻⢦⠙⠀⠀⠀⠆⡿⣿⢿⣿⣿⠛⢽⣶⣩⢹⣀⢿⡄⣿⣹ ⡀⣿⣿⠿⡟⣿⣿⣶⣦⢻⣐⢢⠈⠀⠄⣢⣐⣀⣠⣒⣧⢠⠀⡄⣿⠀⡇⠀⣧⣿ ⠉⡄⠘⡆⣤⣤⠤⣀⠢⡘⣨⠹⢆⠜⢀⢀⠈⠒⠀⠀⠀⠈⠀⢸⣿⡀⡟⠇⡇⣿ ⣸⠰⢃⠀⠀⠀⠀⠀⠀⡦⣧⡎⡿⢼⠜⡀⠀⠀⠀⠈⠀⢸⠁⠀⣿⠀⣟⡏⡇⣼ ⡞⡌⠘⠣⠀⠀⠀⠀⠀⠀⡶⢸⣿⣿⢞⠀⠀⠀⢀⡀⠘⢸⠆⠇⣿⢀⡖⣼⡇⢇ ⡌⢿⡎⠻⢊⠉⠙⠀⠀⠀⠃⣧⣗⣿⢿⢡⠀⠀⠀⡀⢎⢸⠀⡇⣼⠇⡇⢺⢱⡞ ⠗⡘⣧⣟⢿⢿⣿⠀⠀⠀⠊⡸⡿⣿⣿⢸⢻⢹⠀⠉⡏⠘⠀⣿⢠⡿⣿⢁⡛⡶ ⠀⡀⢧⣿⣻⣿⣏⣿⣽⡤⣧⣇⣿⣿⣿⣿⣆⣿⡿⣿⣮⢸⡇⣰⡟⣾⢪⡠⢸⠳ ⠀⠀⠀⡄⡧⣷⣵⣯⣿⣿⣿⡉⣿⣿⣿⣿⡼⡄⣶⣸⣧⢪⣱⡟⣿⣠⠀⠇⠇⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠌⠐⠀⠀⠀⠀ ⠀⠈⠐⠦⠠⠤⠤⡤⣤⣠⠐⠉⠈⠔⢀⠀⠡⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣘⠤⠂⠀⠀⠡⠀⠀ ⠀⠀⠤⠀⠀⠈⠄⠠⠀⠀⠀⠠⡄⢈⠀⠀⠢⡀⠐⠀ ⠀⠀⠀⠀⠁⢀⠀⢀⠀⠂⠀⠁⠛⠈⠀⠀⠀⢂⡄⠈ ⠀⠀⠀⠀⡘⡌⢀⠀⠀⠀⡰⠀⠄⢯⠀⠀⠀⠀⢡⠃ ⠀⠀⠀⠃⢠⢄⠀⡁⠀⠏⣿⠀⠀⣧⠀⠐⠀⠀⡀⡐ ⠀⠀⠀⣼⠠⠄⡠⣤⢤⠀⡿⠀⠀⠋⠀⠀⢄⠐⠈⠔ ⠀⠄⡄⢾⣿⣿⢶⠁⡿⢿⣿⠹⠀⢸⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⢋⣈⣀⣀⣀⢋⡖⢠⣾⠂⢀⠀⠀⠀⠀⠀⠀ ⡀⠀⢀⡀⡶⢩⠙⡭⠉⠋⠅⢰⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠀⠀⠀⠂⠀⠀⠀⠀⠀

⠀⠀⡀⢀⠀⠧⠤⠀⠒⠒⠒⠐⠘⠁⠈⠀⠀⠊⠒⠒⠒⠐⠇⠤⠀⡀⢀⠀⠀ ⠀⠁⠈⠁⠈⠀⢄⠁⠁⠔⠠⠀⢤⠂⢹⠀⠁⠸⢀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢅⠒⠃⢀⠁⠔⡀⢀⡀⡄⠼⣁⣐⣠⣤⢑⠀⠊⠤⡀⣊⣀⠢⠀ ⠁⠀⠀⠀⠋⡜⠑⡄⢄⡠⠒⠁⠉⠀⠀⢸⢱⠀⠀⠀⠁⢿⠉⠀⡜⠀⠀⠀⠰ ⠀⠠⠙⡇⢈⢢⠈⣖⢪⠠⠀⠀⠉⡈⣁⢉⡀⢤⠤⠤⡧⣠⡊⠃⠈⠀⠁⡔⠀ ⠀⠀⡀⠑⢇⠒⢣⡠⠀⠁⠔⣀⠀⠀⡌⠀⢐⠠⠑⠀⡆⠼⢀⡏⣀⠾⢀⠀⠀ ⠀⠀⠀⡀⠡⠹⢩⠊⠄⢀⠀⠀⠁⡼⢸⡀⠀⠀⠀⢄⠈⠀⢀⢱⠞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣣⠢⠁⠈⠀⠀⠋⣿⠀⠆⠘⠀⠀⠀⠀⠀⠢⠉⡌⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⠁⠉⢎⠒⡗⣝⠀⠂⣗⠺⠉⠀⠀⠁⠊⡞⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠛⠗⢘⣄⠜⡠⣦⠵⠮⣾⢀⠀⣄⣑⣥⣛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠓⡋⠺⠉⣏⠟⠛⠚⠁⠣⡡⠒⡠⠀⠀⠀⣦⠘⡲⠒⠁⠀⠀⠀⠀ ⠀⠀⡆⣨⠀⠁⠛⡟⢹⡿⣿⡹⡴⢜⢀⠀⠀⠀⠀⠀⠀⢇⠈⠀⡀⢾⠀⠀⠀ ⠀⠀⠀⠁⢔⢥⡶⣤⣤⣤⣾⢡⡰⠀⠀⠀⠀⠀⠀⠀⠀⡇⢬⠶⣈⠀⠀⠀⠀ ⠀⠀⠎⢃⠔⢀⠀⠀⠁⡰⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⣄⠹⠀⠀⠀ ⠀⠁⢾⢁⠔⠀⠀⠂⢨⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⠀⠄⠑⣄⠈⠀⠀ ⠀⡄⢤⠀⠤⠠⢀⠀⡀⠢⠁⠀⠀⠀⠀⠀⠀⠁⠂⡠⠀⡀⡄⠢⠒⢒⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠈⠀⠀⠀⡀⠦⠑⠉⣀⣦⠀⠀⠀⡏⣡⣯⠑⣀⠠⢕⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠺⠀⠐⠀⠀⠀⠀⢄⠸⠀⠀⠀⢀⣰⡀⣀⢄⠌⡘⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⣸⠄⠠⠓⡄⠄⠂⠛⠠⠀⠀⡄⠀⠈⠀⠀⠀⢧⢀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠅⡀⣀⢸⠀⠁⠔⢰⠀⠀⠀⠀⠀⢂⠀⠀⡆⢨⠉⠊⠒⢑⠈⠀ ⠀⠀⠀⠁⠉⡇⠀⠃⠂⡠⢀⠀⠀⠀⠀⠀⡆⠈⠃⡎⢙⠋⣾⣠⠀⡘⠦⡘⠢ ⠀⠀⠀⠀⠁⣔⡠⠄⠐⠀⠀⠁⠀⠀⠀⠗⢥⠠⢣⠖⣷⣽⠉⠈⠁⢩⠈⡂⠻ ⠀⠀⠀⠂⢰⠀⠃⠀⡀⠬⠒⠂⡙⠤⠃⢠⠨⠂⠄⢰⢱⡉⣂⣆⣲⡏⡀⢻⡄ ⠀⠀⠀⠀⠀⠁⠪⡠⢀⠀⡀⢄⠊⣰⣿⠈⢆⠀⡏⠁⠓⢛⠈⠗⠟⢸⠀⡇⠀ ⠡⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⡞⢌⠀⣄⢌⠀⠇⠸⡷⠛⣾⢀⠀⣳⣿⠂⢠⠀ ⠀⢄⠢⣒⠚⠐⠠⢇⢉⠂⡰⡠⠀⠀⠀⠎⠤⠐⢠⠔⣶⠵⠲⠎⣺⢠⢸⠀⠀ ⠀⠀⠀⠃⣰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠇⢠⠀⠀ ⠀⠀⠀⡆⢸⠐⠀⢆⠈⠀⠀⠀⠀⠀⠀⠁⢌⠃⠉⠀⠀⠊⠠⠁⠂⢃⠘⠀⠀ ⠀⠀⠀⠀⢂⠲⠙⠀⠀⠂⠁⠈⠀⠀⠀⡥⠲⠒⡐⣠⣦⡦⣧⠀⠇⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣀⠄⠤⠤⢀⠀⠀⠀⣀⢢⡹⠺⠁⠉⡉⡐⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢉⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣼⢿⠚⠔⠤⡀⣀⣀⣦⠱⠀⠀⠀⠀⠎⡴⢤⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠶⣠⢀⠀⠀⠀⠀⠀⠀⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣬⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⡅⠬⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣀⠄⠤⠤⣀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣲⠙⠉⠀⠀⠀⠀⠁⠋⠒⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⣀⠢⠀⠴⢀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⡴⢦⠓⠙⠀⠀⠀⠀⠁⠊⡠⢀⠆⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⢆⠑⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⣆⢰⠀⠋⠴⢀⠀⠀⠀⠀⡄⠽⢲⠛⠛⠛⠾⠀⢷⠿⠛⠟⠿⡴⢀⠀⠀⠀⢄⠲⠈⠀⢆⠞⣠⠀⠀⣀⢤⠑⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠋⠶⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣼⣇⠊⠶⣶⠷⣻⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⢄⠙ ⠀⠀⠀⠀⠁⠂⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣶⢹⢄⠙⠛⠻⢈⣏⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠑⠈⠀⠀⠀⠀⡀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⡎⠿⣿⣀⣧⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠒⠉⠀⠀ ⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡈⣄⢱⠀⣻⠞⣦⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣞⢤⡦⠤⣠⣄⠦⡗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠁⠀⠀⠖⠴⣠⣈⢇⠟⡳⣾⢀⠁⣿⣿⣿⣿⣿⣿⣿⠿⠛⠈⠀⠀⠀⠀⢀⠀⢀⣤⢙⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁⠋⡐⣀⠀⠀⠀⣀⠀⢀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠑⡞⡤⣀⣯⣸⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠉⠀⠀⠀⠀⠀⡁⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢏⣾⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠁⡟⣠⣆⠝⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠀⢀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⡪⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⣿⢠⠀⠀⣄⠹⠀⠀⣄⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠉⠀⠀⢦⠙⠀⠀⠀⠀⠆⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀ ⠀⠀⠀⠀⠀⠃⠀⠀⠞⢯⢠⠀⠀⠀⠀⡄⠻⠀⠀⡀⢦⡳⣝⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⠉⡄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⠸⠦⢷⠸⠀⠀⠀⠉⡔⢀⠁ ⠀⠀⠀⠀⠀⡇⠁⡜⢇⢰⠀⠀⠀⠈⠀⠀⡄⠹⠀⠀⠀⠀⣀⣤⠦⣛⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠯⠙⠀⠀⠀⠀⠀⠀⠀⡍⣼⢤⠒⡑⢸⠍⠤⣠⢁⠋⠿⢟ ⠀⠀⠀⠀⠀⣿⡼⠃⢸⠀⠀⠀⡤⣏⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠃⣶⣷⡹⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠂⠒⠶⠥⣉⠉⠟⠿⣸⣄⢀⡀⣿⣿⣿⣴⣀⠀ ⠀⠀⠀⠀⠀⣾⠀⡼⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠋⡽⠟⡙⣷⢶⠙⠀⣄⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣀⣀⣀⢀⠀⡀⣿⣿⢸⠁⠋⡷⣿⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⠸⠀⠉⠞⡴⣤⡶⠓⣏⢰⠀⡀⢡⠈⠀⠀⡀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣠⠀⡞⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⢻⠈⠀⠀⠀⠀⠀⠀⠁⠏⣿⣿⣿⢿⡴⣀⠀⠀⠀⠀⠃⣸⠀⠀⠀⡠⢧⠙⠀⠀⠀⠀⡀⣤⣦⣿⣿⣿⣰⠀⠆⡿⠹⠟⠾⠀⠀⡆⣿⣷⠸⠁⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⣄⠦⠙⠀⠀⠀⠃⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠋⡿⣴⠀⠀⠀⠀⠀⡀⡀⣄⠿⠼⠶⠴⠤⣧⣈⣀⣠⠀⠀⠀⣇⡛⣛⢛⠀⠋⡾⣏⡆⢸⡇⢠⢀⠀⠂⠙⠀⠀ ⠀⠀⠀⠀⡆⢀⠀⠀⠃⣿⣿⠿⠟⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⡗⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⣄⠶⠙⠉⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⣽⠆⣿⠀⢦⡄⠀⠀⠀⠀⡀⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠁⠀⠀⠀⠀⠀⠀⣦⠈⠀⠀⠀⣀⢦⠳⣯⠻⠈⠀⠀⠀⠀⠀⠀⢸⣄⣧⠾⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠌⢠⠀⠀⠀⠀⠁⠋⠟⢻⠈⠀⠀⠀⠀⠀⡀⣄⣷⠹⠀⠀⠀⠀⠀⢠⡿⣄⢲⠙⠈⠀⣄⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠳⠙⠈⠉⠟⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠘⠀⠀⠀⡟⣿⣧⠫⠛⣿⠘⠀⣆⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠁⡿⣿⣿⡇⣛⠀⠀⣾⠀⠀⣿⠛⠛⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣾⡇⣿⠀⡆⢶⡴⣠⣏⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⡄⢸⢸⠀⠀⠃⣾⢒⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⠘⢀⢳⠀⠄⠷⠿⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⠳⡝⠨⠀⡄⣧⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠞⡠⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣾⠙⣀⠦⠙⡆⢸⠀⠀⠀⠏ ⠀⣿⢰⠀⠀⠀⠃⡾⢀⠀⠇⢰⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣾⠹⠀⡀⢦⢸⠀⠀⠀⢲ ⠀⢰⠀⠀⠀⠇⣼⢀⠀⠀⡼⠀⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⡿⠘⠀⣆⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠀⠀⠀⠃⢰⠏⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⡹⣄⠲⠙⠀⣿⠸⠀⠀⠀⠏⠴⣽⣫⣍⠿⠙⠀⠀⠀⣇⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⡇⠏⣯⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⡝⠸⠀⡀⢄⣗⣆⠘⡄⢷⣿⣭⣋⣟⣿⣿⣿⢻⠛⠟⡿⣿⣿⣿⣿⣧⣈⠀⠀⠀⠀ ⠀⠀⠀⠟⢀⠀⠀⠀⠀⡟⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠹⠀⠀⠀⠀⣄⠹⠀⡀⣦⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⢙⣧⣿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡿⢰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡶⣠⣋⠟⠻⠈⠀⠉⠀⠀⠓⠈⠀⡀⣧⢮⠙⠀⠀⠀⡀⢢⠈⠀⠀⣀⣀⢀⣄⠳⠈⣀⣀⠀⠀⡜⡇⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⢇⢸⠀⢸⠀⠀⠀⠁⠹⠀⠀⠁⠏⣾⢶⠶⣷⣿⣿⣿⢿⣼⢀⠀⠀⡀⣧⠦⠘⠇⢧⡜⠹⠀⠀⠀⠀⡀⠢⠉⠀⠀⡀⣄⣶⣷⠹⠀⠀⠁⢰⡌⢸⡆⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢀⡾⠀⡇⢈⠀⠀⠋⣿⣿⣿⡿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣶⠠⠉⠚⠤⠀⡀⢸⣄⣷⡈⢧⡀⠘⠀⠀⠀⠀⠀⣄⢷⠛⠉⠀⠀⠀⣣⢯⠈⡆⠀⢷⢸⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠙⡏⣿⠿⡿⣦⣙⣀⣒⣟⣿⣽⣭⣭⣿⣾⣤⣤⠤⡤⣠⣀⠁⠚⠀⠀⣧⠀⡀⢳⡀⢻⢣⠈⠀⠀⠀⠀⠀⠀⣦⡹⣦⣻⣀⣄⣹⣦⣜⠤⡧⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⣈⣦⢿⣙⢷⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⡴⣠⠀⠀⠀⡆⠸⠀⡀⢳⡀⣱⢳⠀⠀⠀⠀⠀⠀⠀⣆⠻⠈⣄⠙⡏⠈⢧⠈⡏⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⡀⣳⢳⣮⢮⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢿⠪⠐⡆⠘⡆⡈⢹⠀⠀⠀⠀⠀⠀⠀⡄⢿⠀⡀⣦⢸⠀⢷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⣄⣿⡘⢷⢸⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⡴⣠⣀⣄⠀⠀⠀⠀⢷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠀⠀⣧⠘⡀⣿⠀⠀⠀⠀⠀⠀

⠟⣿⣴⣠⢀⠀⠀⠀⠀⠀⠃⠚⠉⠁⠉⠋⠛⠿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇ ⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⣰ ⣀⢻⠶⠶⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠉⠛⠶⣧⣀⠀⠀⣆⠸ ⡇⢠⠀⠀⠤⢀⣸⣄⠦⠲⣛⢮⠀⠈⠀⠀⠓⠉⢞⡴⣦⢉⡴⠁⡼⠀⠀⠀⠁⣼ ⡇⠺⠈⠉⡏⠉⡢⠥⠭⡨⠔⣀⣷⢀⠀⠀⠀⣸⠀⢄⠠⠐⠤⣠⠀⠀⠁⠀⢟⢫ ⢻⢿⡘⠄⢹⠰⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⡠⠋⡿⣿⣿ ⣿⣿⣿⠻⠙⡈⠀⠀⠀⠉⠛⣴⢀⠀⠀⠀⠀⠀⡀⣭⠶⠓⠛⠛⠿⣯⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⣈⣃⣉⢉⠀⠀⠀⠀⠁⠀⠉⢉⠋⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠤⣀⣀⠀⡀⣀⠤⠑⠀⠀⠀⠀⠀⡎⠐⠒⠐⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠈⠁⠔⢀⠀⠀⠀⠀⠀⡀⢦⠈⠀ ⠀⠀⠀⠀⠀⡸⠀⠄⠀⠀⡀⠠⠀⠀⠀⠀⠀⢇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘ ⠀⠀⠀⠀⠁⢸⠀⠄⠑⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀ ⠀⠀⠀⠁⠀⠀⡀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀ ⠀⠀⠀⠀⢣⠈⠀⣀⠀⠄⢠⠒⠈⠀⠁⠜⢀⢂⠀⠀⠀⠀⠀⠀⠉⠒⡠⢸⠀⠀ ⠙⠀⠁⠀⠀⢡⠀⠀⠀⡀⣀⣁⢲⠁⢈⠀⠀⠀⢀⠀⠁⠖⡐⣀⣂⠐⠁⢀⠀⠀ ⡋⠀⠀⣀⠄⠒⢀⡌⣀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣞⣦⣶⡚⠘⠁⠾⢤⢠⠀⠀⠀ ⡄⢑⠀⡀⣀⠀⡤⢖⠙⠶⠤⠢⠋⠞⠴⣤⣀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠣⠝⠀⠄⠤⠭⡯⠀⠀⠁⣲⠈⠐⠇⠐⠉⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠤⡦⠬⢀⠁⠹⢀⠁⢞⢾⣠⢁⣉⠾⢨⢀⡁⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠤⣳⠀⢧⢁⡠⠀⠀⢤⠅⣶⣈⠢⡌⢇⠒⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⢸⠀⠀⠀⠠⠀⠀⠀⠁⢋⠀⢡⡀⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡿⢩⠙⠀⡟⠿⠯⠈⣄⣤⣶⢻⡆⠸⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢣⡇⣾⢿⣇⣶⣠⠀⠀⠀⠀⡇⠀⢻⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⡀⣦⢳⣯⠀⠀⠣⠚⠚⠑⠈⠠⠄⣌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⠀⡀⢄⠒⠒⠇⢀⠀⠒⡢⡠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠋⠠⢀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠤⠤⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣦⣲⢛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠓⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠄⠿ ⢶⠶⠷⠼⠶⠦⣾⠶⠿⠤⠤⠧⠾⠷⡼⣤⣤⣿⠶⠿⠤⠤⠦⠛⠛⠛⠛⠛⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣤⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞ ⠀⠁⡟⢸⠀⠀⣿⠀⣿⠀⠀⡄⢸⠀⢸⠀⠀⣧⠀⣇⠀⠀⠀⣿⠀⠇⢰⡀⢳⠀⠀⠀⠄⠿⠴⡤⣭⣭⣬⢤⠤⠤⡤⣤⠤⠤⠦⠶⠒⠓⣟⢾⠒⠒⠛⠙⠉⢉⠉⠉⠉⠛⠛⠛⠿ ⠁⣟⣿⢸⠀⠀⣿⠁⡟⠀⠀⡇⢸⠁⢸⠀⠀⡿⠀⡏⠀⠀⠃⣺⠟⣴⠀⠀⡇⠀⠀⠀⠇⢸⠀⠀⠀⠀⡀⣀⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣰⣀⠀⠀⡤⣤⣿⢹⠋⠋⣿⠛⡼⠀⠀⠏⢹⠟⣰⠀⠋⡿⣽⢉⠉⠉⠋⡟⢿⠶⠤⣤⣤⠹⠀⠀⠀⠀⠀⠀⠀⣄⡲⠙⠉⠀⠂⠙⠉⠈⠀⠀⠀⠀⣼⠃⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠀⠀⠀⠋⠿⣿⣴⣠⠀⡀⣀⣄⢤⠤⡿⣿⣾⣠⡀⣤⣶⣿⡻⣉⣉⣉⠉⣿⢿⠙⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⠷⡛⣧⢸⠀⠁⠈⡅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠒⡤⣣⣴⢀⠀⠀⠀⠀⠀⠀⠃⠃⣿⣼⢦⠿⠛⣠⠀⠀⡀⣀⣀⣀⣀⣼⣠⣄⠹⠀⠀⠁⠀⠀⣄⠳⠈⠀⠀⠀⠀⠏⣷⣿⡿⣿⡀⢦⣷⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⠀⠀⠖⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠏⣴⣦⡿⢹⡉⣼⠦⠶⠒⠛⠉⠉⡞⠀⠀⠀⡄⠙⠉⠋⢾⠒⠑⠉⣈⠦⠙⠉⠞⣫⣿⣿⣿⢠⠀⠀⠀⣄⣧⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⡟⣻⠈⠀⠀⣀⣄⠦⠲⠓⠙⠉⠉⡟⢰⠀⡀⢄⠦⡷⢀⠀⢸⠀⠀⠀⡀⣧⣠⣄⣶⣻⡿⣾⢠⠀⠀⠀⠀⠀⠀⣧⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⢀⠀⠀⠈⠈⠀⠀⣿⣿⣿⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⣀⣄⠦⠓⠀⠀⠀⠀⠀⡏⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡆⢀⠀⡄⡿⠺⢯⢣⠃⣰⣄⣶⣿⢨⡀⣄⢤⠦⠶⠶⠶⠿⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠟⣤⢸⡇⣾⣤⣠⣀⣄⣿⣾⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣷⣿⡿⠛⠴⢀⠀⣀⣤⣦⠶⠒⠒⠖⡷⣤⢹⠀⠀⠀⠀⠀⠁⢸⡠⠉⠛⡿⣿⡎⠶⠛⡉⢯⠉⠉⠉⠛⠔⡤⣀⣀⣀⣆⠘⢸⡇⠀⠋⠀⠀⣤⡤⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⣼⠀⠀⠀⠁⠛⡿⢟⣿⣿⣿⣿⣿⣿⢿⠻⣛⣝⣩⣀⠒⠈⡙⠦⠙⠀⢧⠋⣷⢻⠞⣧⢫⠐⠀⠀⠀⣇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⢰⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⡀⡄⠘⡄⢿⡃⢫⣿⢴⠏⣿⢠⠛⠀⠁⡿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⡇⣼⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⢠⠀⡀⣻⣾⢀⠏⢨⣿⣤⣦⠷⡿⠀⣄⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠛⡽⣽⣫⣿⣿⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⢀⠀⣀⢻⣆⠘⠀⡿⢰⠀⠃⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⣁⣋⡴⣠⠃⡿⣿⣻⡛⢉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⢿⠏⣠⠀⠁⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠏⣾⣧⠻⠈⠀⠀⠀⠀⠀⡟⣻⣟⣶⢀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⣇⠀⠀⠀⡀⠰⡄⣼⠀⠁⡿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⢼⠀⣷⣿⢿⠻⠛⠖⣤⣀⢀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠙⠈⠀⠀⡀⢻⠈⠀⠀⠀⠃⢰⠋⡿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⣿⣿⣿⢠⠀⠀⠀⠀⠁⠟⣼⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸⠀⡀⣄⠦⠛⠛⡉⣿⠻⠛⠛⡿⣿⣿⣿⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⣿⣿⣼⠀⠀⠁⠟⣿⣿⣟⢟⢠⣌⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢠⠀⠀⠀⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⣾⢀⠀⠀⡏⣾⣠⣀⣀⣷⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣿⣴⢀⠀⠀⠃⣿⣿⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡴⢀⠋⣿⣰⠂⠀⠀⠋⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠇⣿⠸⡦⣶⣶⣷⣿⠀⠀⠀⠀⡇⣿⣿⢷⣿⣿⣿⣿⣿⠺ ⠀⠀⠀⡇⣿⢿⠀⠀⠀⡏⣿⣿⢿⠉⠉⡇⣿⢿⡆⣿⣿⣈⣀⣀⢀ ⠀⠀⠀⡄⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⢸⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠸⠋⠛⡛⣈⢁⠉⡍⣿⡻⣾⣴⢃⣿⣿⢿⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⢾⣿⣿⣿⣿⡆⣶⣴⣀⣧⢿⠘⡿⣿⣿⣼⠀⠀⠀ ⠀⠁⠟⣿⣿⣿⢸⣄⣤⣤⢠⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⢀⠀⠀⠀ ⠋⡿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⢸⠀⠀⠀⠀ ⣆⣿⡿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣍⣬⣠⠀⠀⠀⠀⠀ ⠀⣄⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⡉⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣶⣶⢀⠀⠀⠀⠀⠀ ⠀⡟⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣶⣶⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠇⡬⣠⣀⣂⣀⠇⠀⠀⠋⠞⣡⣗⣈⠚⠒⠒⠓⠉⠋⠛⠓⠙⠉⠀⠋⠷⠾⠓⠀⠀⠃⠶⠒⠒⠓⠉⠈ ⠀⠀⠀⠀⠀⣄⠳⠘⠀⠀⡆⠛⡿⣹⠀⡃⠿⣯⠀⠀⠀⠀⡀⢱⠀⠀⠀⡀⢦⣟⡼⣌⡔⠸⠀⣿⠀⠀⠀⠀⠋⣴ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣷⣿⣿⢿⡮⣤⢠⠀⠀⠀⠀⠀⡄⠦⠛⠀⠀⠀⡄⡿⣽⠋⡟⡟⢴⠀⠀⠃⣰⠀⠀ ⠀⠂⡾⣀⣅⣇⢀⡇⠘⠀⠀⡄⣾⣠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⡀⣦⣿⣸⢠⠀⠀⡼⠀⠀⠀ ⠇⡞⣤⠲⠉⠈⠖⠒⢻⠀⠀⠀⢇⠀⠀⠀⠁⠊⡤⠀⠀⠀⡀⠐⠂⠀⡄⢦⠙⠀⠀⠀⠀⣞⠀⠀⠀⠇⢠⠀⠀⠀ ⠀⢤⠓⠉⠉⠈⠀⠀⡄⠘⠀⠀⡀⢠⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡀⢆⠑⠈⡆⢀⠀⠀⠁⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⢈⠀⢣⠈⠀⠁⠟⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠉⣄⠳⠈⠀⠁⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢨⠗⠤⣦⣓⢉⠈⣀⣿⢼⠑⠈⠀⠀⠀⠋⡼⢀⠀⠀⠉⡔⣠⠀⠁⠀⣀⢦⣘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⢻⡌⠲⠒⠙⠀⣁⢸⢸⢣⠀⣀⣀⣃⣷⠳⡀⢧⠬⣠⢀⠀⠀⠀⠀⢄⠀⠀⡀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣿⠷⠛⠉⢍⣋⠞⢸⡇⠀⠀⠀⡇⡄⠀⢧⠉⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡄⣧⠛⢸⡀⠺⣂⠐⠀⠀⢸⡀⣧⣿⣤⠦⠓⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⡆⢸⠀⢀⠀⠀⠀⠀⢃⠉⡉⣋⢿⠟⣿⣿⣨⣀⢯⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠃⠷⠀⠇⠛⡿⣶⣷⣿⣽⣤⣤⣤⣦⣘⣦⣾⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢚⠴⣤⣀⣀⠀⠀⠀⠀⣦⣿⠸⠀⠀⠀⣆⠘⠀⠀⠀⠉⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣾⣠⠉⠋⠰⠀⠀⠁⠉⠋⠛⠓⣟⣿⣾⣶⣶⣶⢻⠀⠀⠀⣤⠀⠀⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣼⠀⠀⣀⢀⠀⠟⡴⣁⣿⣶⣴⡥⢸⣷⣿⠈⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢻⠓⠿⠻⠀⠀⡄⣱⢈⠀⠁⠋⡴⠀⡇⣿⢿⠖⠿⠿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣾⡟⢹⠖⣠⣃⠰⠀⠀⠀⣁⣋⣙⠄⡿⣼⣤⢀⣀⣴⣧⣿⠉⠉⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣻⣿⠺⠛⡴⠁⠋⠟⡼⣷⣿⣿⠻⣿⣠⠀⠀⠁⠉⡏⣿⠀⣄⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⠿⠹⣇⣿⣶⢸⡀⣡⣟⣿⣿⢿⠰⠀⠅⡿⣸⣧⠙⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣷⣿⣿⣿⢿⣿⡼⢡⠀⠀⠟⣿⣿⣿⢾⠋⡿⣸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣻⣿⣿⣿⢻⠟⣿⣿⣿⣿⣼⣠⡀⣷⠻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣤⣷⣹⣀⡇⢸⠀⠀⠀⣆⢿⣿⠙⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⡈⢿⠂⠀⠀⠀⡀⣧⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⡌⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠚⠚⠑⠀⡇⠑⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⣠⢢⠈⢄⢸⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡼⠡⡀⠱⠉⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀ ⠄⠢⠁⠀⠂⠀⠀⠀⠀⠄⠠⠰⠀⠀⠦⡷⣒⢖⠈⢢⢫⠈⡀⠥⠃⠈⠀⠀⠀⠀ ⠀⠀⠀⡀⢠⠑⡇⠉⠉⠛⠛⡞⠐⠀⠀⠀⡀⣄⢶⠙⢆⢹⣁⠹⢄⣷⠘⠀⠀⠀ ⢀⠩⠐⠉⠀⠀⣀⣦⣿⢰⢀⠡⠀⡀⠄⠠⠑⠀⠌⢑⣡⡌⢻⡨⠘⡏⣀⠙⠀⠀ ⡃⢒⠷⠶⣼⠓⠀⠀⡄⠀⠄⠟⣶⣴⠻⠘⠀⠢⣫⠱⡣⢹⡄⠘⠇⣶⠀⣿⠺⠈ ⢶⡤⠐⣼⠙⡏⠠⠀⠀⠀⠀⣹⠀⠏⣿⣿⠀⠀⠀⠀⣃⣾⠱⡀⡐⠱⠁⣸⠛⣌ ⡄⣬⣶⣦⡯⣿⢸⠀⠀⠃⠀⡅⣦⣶⣴⣠⠀⠀⠋⡿⣶⠱⡚⠹⡀⠐⡱⠟⣏⢰ ⢄⠦⠡⡄⢹⡀⣤⠀⠘⠱⢕⡸⠀⠂⠠⠀⠠⠢⣟⣵⠹⡐⣀⡑⠱⡆⡆⢴⢀⠀ ⠀⠀⣇⡏⣤⠹⠋⠆⡛⠫⣫⢱⠉⠛⠿⠱⠇⢆⢁⡀⢱⠃⠿⠿⣿⠘⢹⠳⠈⠀ ⠀⠀⡇⠀⢄⡾⣷⢭⡦⣿⣄⣄⣹⢙⠈⡆⣾⠹⠀⠢⡀⡐⣧⣿⣟⢮⡏⠀⢄⠑ ⠀⠀⡇⠀⡎⢘⠀⡀⢤⡛⢮⢾⡈⢤⠉⠀⣟⣬⢢⠈⢀⡀⣣⣧⡘⣁⡿⠙⠀⡄ ⠀⠀⡏⠆⡀⠀⠀⠀⠀⠀⣄⠵⡦⠲⡉⡦⣿⣿⠿⡙⠉⠉⠒⣟⢟⣴⠀⠀⠀⡀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠵⣈⡤⢳⣧⣶⢠⠋⡾⢤⢀⠀⠀⠀⠀⠀ ⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⢀⡤⣦⠤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⣆⣽⠀⠀⣀⣯⢻⠾⣶⣴⣤⢀⠀⠀⠀⣀⣁⠞⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠙⠟⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠇⠾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠞⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⢿⠻⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣶⣠⣀⣀⣄⣠⣀⣀⣀⣀⣄⣤⠾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⠀⠀⠀⠀⡿⣶⠤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠉⠉⠀⠀⠀⣇⣿⣿⣚⣴⠤⠦⠛⠙⠀⠀⠀ ⠀⠀⠃⣹⣄⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢶⠉⠀⣿⣸⠀⠋⠗⠾⣦⣲⢙⠀⠀ ⠀⠀⡄⣾⠀⣧⢀⡀⣄⢦⠳⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⣷⢹⠉⡋⠙⠈⠀⠀⢦⢗⠙ ⠀⠀⠀⣆⠘⡀⢷⠈⠀⠀⡀⣧⣿⣤⣥⠿⠻⠒⠚⠛⠚⠓⠘⠀⠀⠀⠀⠄⠤⡾⣤⣠⣀⡀⣤⢦⠷⠚⠚⣶ ⠀⠀⠀⠀⣷⠘⠀⣦⠹⠀⠀⡇⣼⢇⣿⣿⣿⡿⢻⡄⠸⠀⠀⠀⠀⠀⠀⠃⡿⢋⠒⠷⡽⢉⠀⠀⡀⣧⢸⠀ ⠀⠀⠀⠀⡀⢻⠈⠀⡀⢻⠈⡇⢀⡄⣿⣿⣶⣶⢻⠃⣼⠀⠀⠀⠀⠁⠟⣤⣀⠀⠀⠀⠀⣀⣄⠦⠳⡙⢸⠀ ⠀⠀⠀⠀⠀⡆⠻⠀⠀⡆⣿⣿⠘⠿⣿⣿⠀⠀⡄⣿⢸⠀⠀⠁⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀ ⠀⠀⠀⠀⠀⠀⣧⠾⠀⠀⣇⣸⠀⡁⣄⣶⠿⡤⠀⡆⣾⠾⠿⣿⢻⠛⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⡟⢸⠀⡟⠀⠀⡀⣥⠶⠓⣟⢨⠘⠀⡀⣀⢀⡄⣄⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⣿⠀⠇⢠⠀⠀⠀⣿⠀⠀⣄⣸⢤⠲⠙⠉⠀⠀⠀⠀⣅⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢠⠀⡀⠀⠀⠀⠀⣄⠸⠀⠀⣇⠈⠀⠀⣇⢼⠤⠤⠤⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⣟⢹⠀⠁⠞⠴⣠⣀⣄⠦⣷⠻⠈⡀⢷⠈⠀⣾⢠⠀⠀⠁⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡿⢤⢠⠀⣗⠿⣾⣴⣀⣁⣈⣄⠤⡐⣧⣿⠠⡁⢹⡟⢀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣿⢹⠀⠀⠀⠀⣇⢈⠀⠀⡿⢽⠀⠀⠀⠀⣿⢻⡅⣿⣰⠀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣷⠈⠀⠀⠀⠀⢦⠈⠀⡀⢀⠀⠀⠀⠃⣿⣿⡟⣰⠀⠀⠀⠐⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠲⠙⠈⠀⠀⡄⠲⠉⠀⠀⠀⠇⣽⣧⣿⢠⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠿⡝⠩⡈⠠⠀⠀⣇⣽⡀⣠⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⡹⣦⢻⢀⡡⣄⠢⠒⣆⠶⠙⠉⠉⠉⠛⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠓⡿⠀⠀⠂⠈⠀⠀⣀⣀⣏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡄⠿⠼⠤⠧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣸⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⣇⢪⠈⠀⣇⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣸⢀⡴⣄⠲⡽⢌⠀⠀⡆⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠻⠙⠉⠉⠉⡋⣛⣿⠻⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣡⣀⣿⣿⢻⡈⣧⡿⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣶⣷⢿⢹⢸⡇⢸⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢿⡿⣿⣽⣸⠑⣯⣿⠿⣻⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⢜⠩⡿⣿⠘⣄⣤⢳⡈⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡰⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣰⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⡇⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢠⡞⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⡿⢹⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⢰⡇⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⣾⣤⣤⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠖⡤⣤⣤⣤⣤⣤⣷⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠟⣴⣠⠀⠀⠀⠀⠀⠀⣀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣷⢻⠀⠀⠀⠀⠃⠀⠀ ⠃⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠸⠀⠀⠀⡇⠀⠀ ⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⡇⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠘⠀⡸⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⢿⠀⢸⠀⠀ ⣷⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢁⣷⣿⠀⠀⠀⠀ ⡀⣄⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⢺⠠⡇⣿⠀⢼⠀⠀ ⠀⠀⠀⠀⣄⠿⠛⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡟⣴⢀⠎⣿⣼⠏⢀⠀⠀ ⠀⠀⠀⠀⠀⡆⣬⢶⠻⡐⣀⣀⢤⠦⠷⠟⠮⠶⠻⠛⠛⠛⠛⠛⠚⠐⠀⠁⠉⠉⠉⠀⠒⠓⠾⣴⢀⠀⡟⢟⣿⣼⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠘⡀⢿⠛⠉⠀⠀⠀⠀⣀⢤⠦⠛⡛⣿⣿⣹⠀⠀⡀⣀⢉⠉⠀⠀⠐⠀⠁⠉⠋⠟⣿⣾⣠⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠻⡟⣿⣿⣿⢈⠄⠄⠷⠛⠋⡟⣷⣿⢙⠉⠉⣉⣉⣋⠛⠛⠟⠿⣿⣿⣿⣿⣾⣤⢀⠀⠀⠏⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣧⣿⢸⠀⠒⠛⣛⣼⢀⠁⣄⣳⣭⣶⣷⣩⠟⡿⣶⣤⣧⣾⣤⣀⣸⠀⠀⠀⠗⠴⢀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⣄⢦⠛⢈⣏⠻⡟⠭⢻⠉⠙⣉⠤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠁⠋⠖⣩⢛⠟⠴⣤⣀⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀ ⠠⠀⠀⠀⠀⠀⠃⠛⠙⡏⣶⣶⠙⡝⢤⣤⣤⠤⡦⣶⣶⠶⠶⡶⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠾⠴⠤⢧⣿⣾⣶⣴⣤⣠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀ ⣄⢿⠿⡿⣿⣽⢀⣧⣿⣽⠮⠛⣿⣼⠲⠙⠈⠀⠀⠀⠀⠀⠀⠁⠚⡀⣄⢦⡛⣉⣤⣦⣶⣿⣭⢉⠟⡽⣩⣈⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⡄⢀⣀⣤⣼⢆⣻⣿⣿⣿⣸⣤⣦⣷⣾⡶⣿⠿⠙⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⣉⣙⣭⠿⠿⡲⣙⡿⣻⠛⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠉⠀ ⠀⠄⠻⠀⢸⠀⣷⢧⡿⣿⣽⠳⠈⡀⢦⠘⠀⣦⣿⢻⠀⠃⣰⠀⠀⠀⠁⠍⣫⠛⠉⠉⠀⡀⣄⡶⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣱⠋⡴⢀⠉ ⠀⠀⣇⢿⢛⠀⠃⡀⣿⣿⣿⡻⣿⠹⠀⣿⢸⠀⡆⣿⠀⣀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⡤⣀⠀⠀⠀⠁⠾⣠ ⠀⠀⡇⡀⣦⢹⠀⠀⡂⣷⣿⣿⣿⣿⠿⣿⣿⠉⠀⣿⠀⠸⠀⠀⠋⣿⣿⣿⣤⣠⣀⠀⠀⠀⣀⣀⣀⢤⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⡿⣩⣀⢉⣭⢀⠀⠀⠀⠁⠋⠖⣠⠀⠀ ⠀⠀⠀⠀⠏⣿⢳⠙⠀⠀⣄⣿⣿⣿⣿⣿⣿⣽⢀⣿⠀⢧⠁⠏⣿⣿⣿⣤⡤⣋⣀⣀⣀⢄⠤⠤⠤⠲⠓⠛⠛⠛⠘⠀⠀⠀⠀⠀⠃⡟⣿⣘⢧⠙⣀⣀⢤⠧⣬⣾⠹⠀⠀⠀⠀ ⠀⠀⠀⠆⣿⣿⠰⣆⠉⡀⠹⡀⣿⣿⣿⣿⣿⣿⠀⣿⠀⡿⡟⣿⣾⣠⢀⠀⠀⡠⢄⠵⠿⠴⣤⣀⣋⣾⣶⢀⠀⠀⠋⣗⣿⣿⣸⣆⣿⡟⣿⢿⠀⣧⢻⠀⠀⠀⢆⣇⣇⠘⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⢹⠛⠛⠛⡟⢿⡞⣷⣼⣾⣿⣰⠀⣤⡦⣿⣾⣠⠀⠀⠀⠀⠁⢡⢟⣰⢀⠀⠐⡤⣉⠚⠒⠴⡤⣤⢀⠘⡀⣷⣿⡿⣿⣿⣿⣿⠀⠳⣽⠸⠀⠀⠀⣿⡟⢿⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⣿⣿⣼⣷⣿⣿⢻⡿⢋⣿⢹⠉⠉⠉⠉⣼⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠋⠔⣡⣿⣿⠈⠀⠀⠀⠀⠤⠲⠙⣏⣿⣿⣿⣿⣿⠘⡇⡏⣿⠀⠀⠁⣿⢸⣾⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⣿⣿⣿⡏⣽⣿⣿⣾⣿⣶⣿⣿⣾⣣⣷⢸⠀⠀⠀⠀⠉⠈⡇⣿⠃⠶⣠⠀⠁⡿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⣦⣿⣯⣿⣿⣿⢹⣿⣸⣿⢸⠁⡿⣴⡇⢰⠀⠀⠉ ⢿⠈⠀⠀⠀⠀⡄⣼⣿⣿⣿⣿⣿⢸⢹⠀⡏⣿⢠⡿⣼⠀⠀⠃⠕⡨⣀⠀⡆⣿⠛⠉⠛⠿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⣧⣿⣤⣦⣿⣿⢿⡟⣼⠀⡴⠋⠚⡤⣤ ⣿⢿⠘⠀⠀⠀⠀⢿⣟⣿⣿⣿⢼⢘⣿⣤⣦⢠⡞⣿⢠⠁⠋⡾⣠⣀⠀⠀⠃⣶⣷⣿⣿⣿⣶⣴⣤⣩⣎⢲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⣿⢹⠈⣧⣿⣿⣷⠐⠃⡾⣀⠀⠀⠀ ⣿⡀⣧⠹⠀⠀⠀⣦⣿⣿⣿⣿⢈⣿⢩⠘⠀⡏⣯⣾⠟⣷⣿⢀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣄⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠙⣇⣿⣿⣺⣆⣿⣿⣿⣿⣿⠛⣰⠀⠀⠀⠀⠀ ⣿⠈⡄⣿⠹⡄⠈⠀⠃⡆⣿⣿⢸⣠⣆⣸⠃⣷⣿⢿⢰⡟⣰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡉⣿⣿⣿⢿⠿⣿⡿⣿⣿⡿⣿⢿⠘⠀⠀⠀⠀ ⣿⢸⠀⡆⣿⠹⠀⠀⠀⠀⣆⣿⢸⠇⠀⢿⡿⣼⡇⣿⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠛⠟⠿⣶⣶⣶⣤⣤⣧⣿⢀⠀⡖⣷⣿⣿⣿⣿⣿⢹⣿⡄⣿⠘⠀⠀⠀ ⣿⣿⠀⠀⣧⣿⠘⠂⠀⠀⠀⣧⣿⡌⠀⣧⣿⠀⡇⣿⢹⠋⠛⠛⠛⠟⠿⠿⠿⡿⣿⣿⣿⣶⣤⣷⣿⣠⣀⣀⠉⠋⠀⠀⠀⠀⡤⣤⠀⠀⠉⡏⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⠀⠀ ⡈⣷⢹⠀⠀⣷⣿⠫⠀⠀⠀⠀⣷⢹⠀⣿⣾⠀⡀⣿⣿⣿⣿⣶⣷⣿⣾⣠⣀⣐⠀⡇⣿⠀⠀⠀⣦⠐⠀⡇⣴⣀⠀⠁⠈⠀⠃⠿⠘⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⣿⠸⠸⠀ ⢉⠛⣞⢿⠙⡄⣿⢻⠀⢠⠀⠀⡄⣻⠀⣧⠸⠀⠃⣿⣾⢀⠀⠀⡀⣀⢀⠀⠏⠸⠀⡇⣿⠀⠀⠙⠀⠀⠀⠇⡾⢰⠀⡀⢠⠀⡇⣿⢻⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢹⢸⠀ ⣷⣘⠅⠀⢀⠘⡀⣿⢱⠀⠀⠀⠀⣇⠸⡇⣿⡿⣤⣤⢠⠀⠀⠀⠁⡿⢚⠃⡿⢰⠀⡆⣴⠀⠀⣿⠻⠈⠉⠉⠋⠛⠿⠿⣿⣿⣿⣽⣩⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⡇⣿⠈⠀ ⠀⠀⠤⠤⢁⠨⠂⡀⡰⠐⠃⠀⠀⡀⣿⡏⣶⣷⢳⠛⡟⠀⠀⠛⡬⢠⠀⣿⢁⠉⠉⠋⠛⠛⠿⣿⣿⣿⣷⣿⣴⣯⣿⢹⠁⣿⣿⣿⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠿⡿⣼⢸⠀ ⠶⠶⠶⠶⠷⣿⠻⣹⠈⠀⠀⠡⠱⠈⡆⣹⡀⠀⣿⣿⣿⠉⠋⡟⢿⠿⡿⣿⣿⣿⣾⣶⣿⣴⣠⣣⢘⠀⡇⣿⠀⣷⣿⣿⡽⣍⣟⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣤⣷⢛⠉⠓ ⣤⠲⠙⠉⠀⡀⣿⣿⣽⣤⠿⠿⡀⢷⠐⣧⠘⠇⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⢙⠉⠉⠛⣿⢼⠦⣿⢿⠷⡆⣿⣤⠩⣿⣿⣿⣶⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣷⣾⣤⣦⣶⢲ ⠀⢹⡀⣄⢷⠙⢀⣼⣮⢿⡘⣷⣿⣻⢿⡿⣿⡝⣷⣴⣧⣿⢿⠘⠈⣇⣿⣿⣟⠘⡄⠸⣿⢿⠀⣿⣿⡿⠀⣿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣟⣿⣼⠀⠀⠀⠀⠀ ⠀⡄⠘⠀⡠⣷⢿⠛⡈⡀⢷⠉⣧⣿⣿⣿⣿⣿⡈⢆⡌⣷⣿⣿⣿⡻⣿⣿⣿⣿⠉⢹⣿⣿⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡟⣿⣠⠁⠈⠀⠀⠀⠀ ⠀⠀⡄⠳⡀⡠⣷⣿⢿⠿⠉⡈⠁⣏⣿⣿⣿⣿⢿⠀⠟⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣳⠛⡿⣴⢫⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠳⡀⣧⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⣉⠛⠿⡿⣱⣟⣴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠳⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⠿⣿⣿⣿⣾⣿⣲⡙⢎⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⢿⡟⣿⣾⣤⡟⣏⣿⠟⣿⣿⣿⣿⣿⣿⣿⣻⣴⣠⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣟⣻⣉⣍⣿⢻⣉⣿⠻⣿⠿⠻⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠖⣶⠶⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣻⠀⠀⣄⠷⠝⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣡⠋⠞⣴⣤⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠢⠍⠐⠈⠀⠀⠀⠀⡉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠑⢄⠘⠄⣇⣽⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⢉⠛⠻⣍⢐⣀⢷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀ ⠀⠀⠀⠀⠀⠀⡄⡄⣾⣿⢰⠀⠛⣴⠣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀ ⠀⠀⠀⠀⠀⡁⡾⠛⢢⣿⠀⠆⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠙⠜⣜⣀⣄⠣⡿⡟⢰⠢⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⠀⠀⡀⢳⠀⠀⠀⠀⣇⣉⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠃⠛⠾⡥⠲⠈⠀⠀⠀⠀⠀⠀⠀⠈⠗⣣⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⣠⠎⠁⢤⠄⣀⠤⠒⠛⠒⠐⠠⡀⠁⡰⣀⠱⠑⠀⠀⠀ ⠢⠉⠀⠀⠀⠀⠇⣻⠀⠀⡆⠀⠀⠀⠀⠀⣿⢹⠈⠀⠇⢶⠀⠀⡇⡼⠰⠀⠀ ⠀⠀⡀⣆⣈⣞⣠⣷⠈⠀⠀⠀⠀⠀⠀⠌⣠⠀⠀⠤⠑⢇⠀⠋⡥⡖⠠⠀⠀ ⠀⠀⠀⡀⠏⣶⠤⢤⠦⠑⠀⠀⠀⠁⡚⠑⠛⠈⠀⠀⠀⣄⠼⠔⣤⣤⠐⠀⠀ ⠀⠀⠀⡀⡢⣁⢀⠄⠀⠒⡁⠌⠦⡟⢂⢾⠶⠈⠀⠀⠀⠀⣄⠤⠒⠈⠀⠀⠀ ⠀⠀⠀⠀⠉⠂⣄⠤⠚⠁⠀⡀⠄⡑⠩⢃⡹⢉⠈⠀⠁⠈⠀⠀⠀⠀⢄⠑⠈ ⠀⠀⠀⡸⠀⠀⠀⠀⣠⣂⡠⠄⠐⠈⣄⢳⣧⡏⣀⣤⣀⣄⢿⠣⠐⠁⠀⡇⢰ ⠀⠀⠀⠀⣀⣀⣀⢁⠎⢀⠀⠁⠔⣓⠻⡑⠹⣧⠟⠳⣸⣿⠀⡰⠀⠀⠁⡰⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⢿⠄⡠⣀⠱⠀⣧⢎⠉⡇⢰⣠⢋⣾⡞⠀⠀⠃⡠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠈⠀⡀⠑⠀⣄⢤⢦⠿⠶⢒⠔⢀⠀⠔⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⠀⠀⣁⠆⠤⡤⠆⠠⠀⠀⠁⡠⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠏⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠸⠀⠀⠃⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡆⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⡜⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⢰⠀⠀⠀⣄⠙⠀⠀⠀⠀⡀⢠⠀⠀⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠑⠀⠀⠀⠀⠀⠐⠀⣾⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⡽⠉⠒⠒⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢠⠀⠁⡴⣀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠋⠴⣠⢀⠀⠀⣀⢤⠑⠀⠀ ⠀⠀⠀⠀⣾⠀⠁⣰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢷⠀ ⠀⠀⠀⠇⢀⠀⡇⠀⠀⠵⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⡀⢸ ⠀⠀⠀⡸⠀⠀⡄⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡂⣠⠇⢠ ⠀⠀⡎⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀ ⠀⠇⢠⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠘⠀⠀ ⠃⡼⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⢸⠀⠀ ⡆⢹⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⠀⠀ ⠀⡄⠑⠀⠀⠀⠀⠀⠀⡀⣧⠉⠉⠉⠉⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀ ⠀⠀⠀⣀⠯⠿⠛⡈⣀⣀⣀⢻⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⢞⠓⠔⠾⡠⢀⠀⠀⠀ ⠀⠀⠀⡞⢏⣎⣇⣀⢯⠑⠀⣿⠀⠀⠀⠀⠀⠟⠊⠟⡼⢀⠋⣠⠎⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⢰⡇⠀⢸⡞⢣⣼⠀⠀⠀⠀⡇⣹⠈⠷⢀⠟⢳⠏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⣿⠀⡀⠸⢻⢸⡇⢀⠀⠁⠖⡠⢀⠀⡀⢄⡶⣟⡀⡼⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠸⠀⢇⡆⢘⡇⠀⡤⢀⠀⠀⠂⠒⠶⠰⠈⡀⢦⢻⠀⢦⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠈⡀⢹⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⠀⡄⠘⠀⢇⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⠀⣇⡽⣴⠘⠀⠐⠛⠛⠐⠀⠀⠀⣀⣻⢟⠉⣏⠹⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⣹⡇⠀⢣⠋⠸⣷⢼⢱⠛⠀⠀⠀⡦⣶⡛⣾⡇⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⠈⣿⠀⡅⣹⣤⢿⣶⣤⢀⠙⠘⠀⠆⠓⡟⣾⣠⢳⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⣄⣧⠈⠀⣆⣸⡿⠢⠶⣤⣠⠀⠀⠋⡳⣰⠀⠀⡎⠇⢾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⡄⣗⠘⠀⠀⠉⠚⡥⢚⣠⠀⠀⠁⢸⡞⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⡀⢦⠤⣠⢀⠴⣠⠀⠀⠀⠀⡥⡞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠁⠉⠚⠴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣉⣯⡿⣿⣿⣿⣿⢈⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢤⠤⠦⠶⠹⠀⠀⠀⠀⠀⡟⠀⡆⠹⠀⢳⠀⢸⠀⢸⠀⠀ ⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⣀⠀⣄⣿⣿⣿⣻⠉⠀⡀⣀⣤⣤⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⡀⢳⠘⠀⠀⠀⡇⢿⠀⡀⠀⡇⠀⢳⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣄⣶⣶⣶⢿⠙⠀⠀⠞⢧⠀⠀⠀⣦⣿⣿⣿⢿⡙⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⣄⣿⠹⠀⠀⢧⢯⢎⠀⡆⠘⡇⠙⢸⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠉⠒⠀⠋⠔⠤⣥⣬⢤⡤⢥⠒⠒⠓⠙⠉⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⠈⠀⠀⠀⡀⣦⠻⠀⠀⢧⣟⠈⠀⢿⡏⣀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠀⠉⡴⢀⠁⡔⢀⠀⠀⡇⢋⠀⠀⡆⠇⠈⠀⡀⣀⣄⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⡄⢳⠈⠀⣧⢹⠀⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⣀⠁⡜⢀⠀⠀⠀⠀⠁⣸⢧⠈⠀⡀⢳⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⣄⠸⣣⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠞⣠⠀⠀⣀⢀⠀⠋⡴⢀⠀⡀⣄⠶⡐⠹⠈⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣓⣉⢦⠛⠈⠀⠀⣆⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠻⠈⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⠠⡂⢿⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠆⠙⠢⡈⠢⡈⢻⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⣇⣞⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠒⠒⠒⠓⠛⠙⠉⠉⠉⣼⣄⢀⠀⠀⠀⠀⠀⡇⢹⠀⠁⠀⠀⠀⠀⡄⠸⣼⡧⢓⣼⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠼⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠀⠀⡀⣀⡏⢀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⡄⠸⠀⠀⠀⠀⢻⣷⡿⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⡿⣿⢻⠈⠀⠀⠀⠀⠀⠀ ⣿⢻⠊⠓⠛⠉⠉⠉⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⣏⣿⠿⠿⠏⣿⡇⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠻⠈⠀⠀⠀⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠻⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣼⣤⣤⣤⣥⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⢹⡏⣿⣿⣿⣿⣿⣿⢻⠴⠤⣀⠤ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠧⠿⣻⠋⠛⠛⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢹⡉⣿⣿⣿⣿⠘⠀⠀⠀⠀⣤⠦⣒⣽⠮⠒⠛⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣅⣯⣿⡽⣩⢀⠁⠟⣿⣴⢀⡄⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⠀⠀⡁⢯⠛⠉⠉⠉⠈⠈⡄⠅⣯⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⣴⢀⠀⣉⣟⣿⣿⣴⣀⣀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣽⣯⣿⣿⣟⣿⣿⠹⠟⣽⢈⠀⡋⣾⣤⣤⣷⣽⢫⠸⠀⠁⠀⠀⠀⠀⠀⠀⠤⠿⠛⡿⢿⠿⠿⣿⣶⣵⣛⢴⣠⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡴⣤⣿⣿⣿⠿⠿⠿⠿⣿⣼⢀⠛⠛⠙⠉⣉⣈⠂⠁⠘⠟⣴⣀⣟⣶⡴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡀⢈⠀⠀⣀⣖⢴⡠⣀⠁⠘⣀⣀⠄⠠⠠⣤⣠⣀⠀⢀⠆⠹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿ ⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⢀⠈⠀⠀⠀⠂⠒⠒⡤⠀⠀⠀⠄⢽⠐⠀⠀⠀⠀⠀⠀⡀⢤⠒⠒⠒⠤⠀⠀⠁⠊⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿ ⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠈⣀⢤⠢⠓⠉⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡴⣠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⡇⢿⠛⠛⠙⠀⣀⣄⠶⠻⠙⠀⠀⠀⠀⠀⢇⠀⠀⠙⠈⠉⠉⠉⠛⠿⣿⣿⢁⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿ ⠀⡇⣿⣿⣿⣿⣿⣾⣿⣿⢀⠀⠀⡂⣿⣿⣿⣿⢿⠿⠻⠙⡉⣍⣶⠤⠀⠀⠀⠀⢠⡖⣶⡴⣀⣤⣴⣠⢃⡿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠸⠏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣝⠷⠻⠙⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⠙⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⣄ ⣤⠳⠈⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⣿⣿⣿⣿⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠉ ⠀⠀⣄⠳⠉⠀⣄⣦⣷⣿⣿⣿⣿⣿⠙⡀⣥⣿⣿⢻⡟⣿⡿⣛⣝⣿⣾⣶⣷⣿⣿⣿⣿⣿⣝⣿⢿⡌⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣠⢀⠀⠀⠀⠁⠖⣠⢀ ⠀⠀⠀⠀⡀⣤⠦⠶⠴⣤⣀⣄⣤⣶⣶⢿⠻⣌⡲⣞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠲⠙⠈⣀⣄⣤⣥⣾⣤⣦⣶⣶⣶⣷⣶⣿⣿⣿⣿⣶⣶⣶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀

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