Goofy Goober Sponge Bob Emojis & Text

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

▕╮╭┻┻╮╭┻┻╮╭▕╮╲ ▕╯┃╭╮┃┃╭╮┃╰▕╯╭▏ ▕╭┻┻┻┛┗┻┻┛ ╰▏ ▕╰━━━┓┈┈┈╭╮▕╭╮▏ ▕╭╮╰┳┳┳┳╯╰╯▕╰╯▏ ▕╰╯┈┗┛┗┛┈╭╮▕╮┈▏

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⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⠀⠒⢤⡔⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠂⢀⠂⠀⠂⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠑⠤⠀⠠⠊⠐⠤⠤⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣴⣶⣿⣿⣷⣦⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡎⠀⠀⠛⠻⠿⠿⠿⠿⠿⣿⣿⠛⠛⠛⠉⠀⢰⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⣠⠆⠀⠀⠀⠀⢁⣀⡠⢤⣼⣛⣲⣯⣭⣭⣭⠿⣆⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⡰⠃⠀⣀⡤⣖⠪⢿⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠘⡄⠀⠀⠀⠀⠀ ⣇⠀⠀⡼⣁⢴⡪⠗⠉⠀⠀⠀⠻⠟⢋⣿⣿⣿⣿⣿⡆⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠘⢤⣼⣋⠗⠁⠀⠀⠀⠀⠀⠀⠀⣤⣘⣿⣿⡿⣿⣟⣥⠖⠀⠀⢨⣿⣦⣀⠀⠀ ⠀⢸⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⡿⠟⠋⠁⠀⠀⠀⡼⠁⠀⠈⠑⢆ ⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣠⣦⡀⢠⣄⣠⠤⠷⣀⡠⠶⢄⣀⣼⣀⠀⠀⣀⣀⠜ ⠀⠀⠀⠈⠉⠒⠤⠄⣀⣰⣿⣿⣷⣿⡟⠁⠀⠀⠈⠱⡄⠀⠀⠀⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠤⢀⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤⣄⣠⢤⣄⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣾⠛⠛⠲⣼⣷⡘⠿⢿⡏⣉⡓⠶⢤⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠾⠟⠁⣤⣄⣀⣀⡀⠙⠓⠚⠷⡽⢿⣷⢀⣰⢿⣫⠿⠭⠟⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⣀⠈⣿⣶⡦⢤⣬⣉⣁⣛⣋⣀⣀⡀⠀⣶⣶⣌⠉⡿⠉⣽⣤⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠻⣿⠛⠃⣸⢻⣿⡗⠀⢸⠀⠉⠁⠀⠈⠛⠋⠀⣧⢸⣿⣿⣿⡄⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠛⠛⠛⠛⠿⠿⣦⣉⣀⣠⡾⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣿⡿⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡹⠴⣶⠟⠛⠛⠛⢳⡶⠲⢤⣙⠣⣅⠓⢩⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠰⣶⣦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⡈⠳⠤⠿⠤⠤⠤⠤⠚⠓⠒⠒⠚⠳⠬⠳⡀⢠⣤⣄⠀⠀⠀⠀⢠⠏⣏⠉⠙⠻⢿⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣙⣶⡖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⠷⠈⠉⠁⠀⠀⠀⠀⠘⣦⠈⣧⡈⠙⠲⢌⡑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡀⠀⣀⠤⠒⣋⡥⠔⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢿⣿⡆⠀⠀⡟⠒⢬⡓⢤⡀⠀⠀⠀⠀⠀ ⠀⣀⣈⠉⣤⡖⠋⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⣤⣤⡀⠀⢹⡄⠀⠈⢀⣀⠀⢷⠀⠀⠈⠳⢍⠲⣄⠀⠀⠀ ⠉⠀⠈⠙⡇⢹⠀⠀⠀⠀⠀⠀⠈⣹⣶⠤⠤⢤⣤⣶⣯⣤⣄⣀⣀⣀⣀⠈⠻⡿⠋⠀⢰⠇⠀⢀⣈⣿⡧⣼⠀⠀⠀⠀⡠⠽⡞⠓⠢⢤ ⠀⠀⠀⠀⠻⠾⠀⠀⠀⠀⠀⠀⠰⣏⣭⡀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⣩⣍⠉⢻⡏⢉⣅⡀⠀⠀⢸⡄⠀⠀⡞⣰⠊⠉⠳⡄⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣫⠵⠛⠙⠒⣾⣿⣿⣿⣿⣿⠦⢤⣀⣀⣀⣠⣿⡋⠀⣰⢃⣈⣛⣁⡤⠤⠼⠃⠀⠀⠉⠉⠀⠀⠀⠸⡌ ⠀⠀⠀⣠⣤⠤⠖⠒⠊⠁⡖⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠙⢮⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⢿⡿⠦⠔⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠈⠓⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⣨⣿⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⠖⠛⠉⠉⠛⠀⠀⠀⠸⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠋⡀⠀⠀⠐⠟⠂⠀⠀⠚⠃⠀⠀⢦⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠃⠀⠚⠃⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠏⢀⡄⠀⡠⠊⠁⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠉⠀⠈⢁⠔⠋⠁⢀⣀⣤⠤⠴⠶⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣠⡀⠀⠰⠃⢀⣴⣚⣉⡴⠋⠙⠓⢦⡀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡤⠤⢦ ⣇⠉⠀⠀⠀⡴⡿⠋⠉⠹⡇⠀⠀⠀⠀⣿⣤⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⡼ ⠹⡄⠀⠀⠘⢱⡇⠀⠀⣀⣿⡷⢺⣯⠉⠉⢹⡀⠐⣾⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣀⡀⣠⠞⠁ ⠀⠙⢦⣀⠀⠀⣷⠿⣾⡅⠀⢧⠈⢿⣧⡀⠈⡇⠐⠊⣉⣁⣈⣙⣦⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⢩⠀⠀⠀⠀⠀⢀⣤⣤⣿⠿⠛⠁⠀⠀ ⠀⠀⠀⠈⠉⠙⠻⡄⠹⣿⣄⡼⠱⢄⣙⣁⣜⣡⠔⠋⠉⠀⠀⠈⠉⠙⠓⠲⢶⠚⠉⠁⠀⢀⣀⡬⠴⠒⠋⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⣦⣌⣻⡇⠀⠀⣹⠾⠻⣀⣤⣀⡀⠀⣤⣄⡀⢀⣀⣠⡾⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣸⣀⡤⠊⠁⠀⡴⣟⢿⡟⠛⠶⠿⠿⠖⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠔⣩⠜⠁⠀⠀⡠⠊⠀⠘⣎⣧⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢲⠞⠁⠀⠀⡠⠊⠀⠀⠀⠀⡿⠉⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢃⠀⠀⢀⠜⠓⠤⣄⣀⣤⠞⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠷⣶⣾⣥⠤⠶⠚⠉⠀⢿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣀⣠⣤⣤⣀⣀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠉⠙⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣴⣶⣶⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠩⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⣠⡴⢲⣤⣤⠟⠗⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣭⣻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠟⢁⣼⡿⢡⡇⣴⣿⣿⣿⣿⣷⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⢇⡞⠁⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠻⣤⣾⣿⡿⠛⡾⡇⠀⠀⠀⠈⠙⠻⠿⠟⠛⠻⢿⣿⢲⡦⠀⠀⠀⠀⠀⢹⣿⣿⡿⠋⠀⠀⣀⡀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣯⣀⡀⢸⡟⠀⢀⠀⠀⣠⣴⣶⣤⣤⣠⣴⣿⣷⡿⠇⠀⠀⠀⠀⠸⠿⠿⠁⠀⠀⣸⠏⠉⠃⢻⡇⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡟⠋⠀⢈⣉⣲⣽⡄⠘⠆⠀⢹⡋⠉⠁⣀⡴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⣾⡇⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣀⣴⡿⠛⠉⢉⣷⡇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠖⠊⠉⢠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣶⠶⠚⡹⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⢀⡞⢠⡏⠀⠀⠀⠀⠴⠖⢯⡛⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠔⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⡞⢠⢾⡀⠀⠀⣀⠤⠤⠤⠼⠃⠀⠀⠙⢦⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣆⠀⠀⣧⠞⠺⠗⠂⠘⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⢱⡲⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡆⠀⡏⠀⠀⢀⣠⠴⢶⢒⣯⣽⣿⢿⡿⡿⣷⣶⡄⣷⡇⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣄⠹⣄⢸⣿⣶⡾⣿⢻⠙⣃⣿⣼⣶⣶⣷⣿⡇⠟⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢦⡈⠳⣽⣿⣿⣷⣾⣿⣿⠿⢻⣟⡿⠛⡼⠁⠀⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠙⣟⢮⡛⠛⠓⠚⢛⣉⣡⠴⠚⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⣆⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡒⠶⣖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠳⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢳⡀⠈⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠉⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀

twipsy takes off his clothes and whimpers "|-ls this ok?.." he asks softly and quiet. He seems to shy. As he shows his cuntboy pussy, u-uh..i hope y-y-you dont mind tho!!!!!!" as Y/N shoves Y/N's thicc veiny juicy dick up into twipsys pussy. As twipsy moans softly., ""hah..-" hh...." he whimpers and was struggling. "hah.....Mmmhm..... Y/N thrust him violently and humped twipsy. As twipsy was struggling. P-PLEASE!!-, HARDER!!!", Y/N felt the climaxing, and Y/N kept on thrusting twipsy and humping him hardly with Y/N's big veiny juicey cock.," hh h--", now. Y/N felt climazing hardly. And now bursted the hot, warm, sticky cum inside him making a bulge inside twipsy. Twipsy groaned and yelped loudly. "heh... i guess this is some humankind nature.." 💥💥

⠉⠉⠉⠀⢠⡏⢹⡿⠁⠀⢠⠊⡥⠬⡅⠀⠀⣀⣀⣼⡿⢸⣿⡏⠉⢩⡄⠀⠀⠘ ⠂⠀⠀⠀⣸⠓⢸⠗⠒⠒⡿⣞⠣⢚⡽⠉⠉⠉⣰⢹⣧⡟⠸⣇⠀⣸⣇⠀⠀⠃ ⠀⢀⠀⢠⡟⠀⣿⠀⠀⠐⠑⠚⠋⠉⠀⠀⠀⢠⠇⣸⣿⣡⣴⣿⠀⣿⣿⠀⠀⢀ ⠀⠰⠀⣾⣷⣶⣿⣦⣤⣤⣤⣤⣶⣶⣶⣶⣾⠿⣿⣿⢛⣋⣩⣿⣸⣿⣿⡀⠀⢸ ⠀⣆⢠⣿⢀⣈⣹⣉⣻⡭⣉⣁⡋⠀⢇⡠⠔⣋⢵⣿⣦⡄⠀⣿⣿⣿⣿⡇⠀⣿ ⢠⣿⢸⣿⡄⢫⠀⢷⣿⡮⠲⠆⠀⠠⠤⣬⠐⠏⠀⠙⠛⢁⣸⣿⣿⣿⣿⡇⣸⣿ ⢸⣿⣾⣿⡇⠀⠳⠬⢭⠥⠤⢤⠊⠀⠀⠛⠂⡭⠍⠙⠛⠀⢸⡟⢻⣿⣿⣷⣿⡟ ⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⡡⠊⡖⠢⡀⠀⠈⠐⢄⠀⠀⡿⠁⣼⣿⣿⣿⣿⣇ ⣿⣿⣿⣿⣿⡀⠀⠹⡖⠤⠀⠈⠻⡇⢀⠈⠢⡀⠀⢀⢠⡖⠁⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡀⠀⠹⠸⡦⡀⠀⠁⠀⠀⠀⠀⣨⡆⡜⠀⠀⠀⣿⡿⠟⢛⠉⣅ ⣿⣿⣿⣿⣿⣿⠷⡀⠄⠀⠈⢞⢦⣀⠀⣄⡖⡹⠒⠐⠱⣠⠇⢰⡇⢻⣀⠈⠋⠉ ⣹⣿⣿⣿⣿⣿⠀⠹⡌⡄⠀⠈⢎⠒⠒⢈⡜⠀⠀⢠⠧⠁⢀⢸⣷⠘⣿⡀⠀⠀ ⡏⠀⢿⣿⣿⢻⠀⢰⠹⣡⠀⠀⢈⠙⠛⠉⡀⠀⢀⠿⠀⣠⡳⣿⣿⡄⢿⣷⣤⠀ ⣷⠀⠘⣿⣿⢸⠀⠘⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢼⢃⡾⠋⢠⣿⠏⠧⣿⣿⡿⣤ ⠛⣆⠀⠹⣿⠈⠇⢸⣄⠀⠱⡄⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⣼⠏⠀⢸⢻⡞⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠤⠤⠀⠀⠤⠤⣀⠀⠀⠀⠀⠱⡀ ⠀⠀⠀⠀⠀⣀⣠⣄⡰⠁⠀⠀⠀⠀⣴⣪⣿⡍⢦⢖⣭⣍⢪⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡜⡱⢁⣖⣻⢆⡀⠀⠀⠀⢧⠸⢿⠟⢨⠸⣿⡿⢠⡗⠀⠀⠀⠀⠀ ⠀⢠⡛⡕⢣⠣⡈⡜⠩⠃⢱⡀⠀⠀⠉⠳⠤⠔⠀⠙⠶⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⣜⡀⠀⠀⠃⠙⢔⣁⣀⠼⡝⠲⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀ ⠘⠈⢧⣱⣄⠈⠀⠁⠌⠻⣯⣧⡯⠡⠘⡿⠯⠉⠉⠉⠉⠉⠉⠛⠁⠀⠀⢀⠀ ⡆⡀⠀⠘⠛⢣⡀⠀⡔⠀⣹⠿⣀⠤⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠊⠀ ⡀⠘⠳⣄⠢⠈⠙⡖⢄⣹⡏⠜⢩⣳⡼⠊⠀⠀⠀⠀⠀⠀⢀⣠⠮⠊⠀⠀⠀ ⠈⠢⡀⠀⠑⢤⣈⢐⠴⠃⠑⠼⠞⠁⠈⠉⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠂⠥⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠈⠀⢳⠀⡀⣤⡀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠸⢿⣿⠿⠻⠟⠛⠟⠛⠿⠿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠐⠒⠢⠤⣀⡀⠀ ⠀⣼⣿⣿⣟⡛⢻⣿⣟⡛⠛⠓⠓⣶⢦⡀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⣿⡿⠿⢿⣿⡟⠘⣿⣿⣿⣷⣶⣿⣼⣻⣦⠀⠈⠪⣽⡒⠠⠤⣀⣀⠀⠀⢰⡀ ⢀⠏⠙⠒⣲⢿⠀⠀⢻⡒⠖⠒⠋⠁⠀⠈⠙⠃⠀⠀⠀⢇⠀⠀⠀⠀⠈⠉⠉⠀ ⡞⠀⠀⣰⠓⠘⠄⠐⠂⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠐⠁⢀⡤⠤⠤⣀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠘⠻⠶⠶⠾⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀ ⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀ ⠀⠀⠈⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣄⠀⠀ ⠀⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢆⠀ ⠀⠀⠀⡇⠀⠀⠘⢯⠒⠤⠤⠔⠊⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄ ⠀⠀⠀⡇⠀⠀⠀⠀⠑⣄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠓⠒⠒⠒⠒⠒⠊⠒⠒⠒⠛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀

⠐⢄⠀⠘⢦⠀⡰⢘⣆⠡⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⢁⠠⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠈⠯⡂⠁⠈⣦⣧⣤⣤⣴⣾⣿⣿⣿⣦⣄⣀⠃⠀⠑⡱⡆⠀⠀⠁⠠ ⡈⠢⢑⠌⠢⡀⠑⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐⠉⡨⠂⠀⠀⠀ ⠈⠒⢄⠑⢄⢈⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠊⡠⠂⠀⠀⠀ ⠀⠢⠤⣾⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⣿⣿⣿⣷⡈⠀⠀⢀⠠⠐ ⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡟⠁⠀⠀⢹⡿⣿⣿⣿⣦⣦⣀⠀⠀ ⠀⠠⣴⣾⣿⣿⡿⣿⣽⣿⣿⠋⢸⣏⡴⠺⠆⠀⠁⣌⣉⣇⢻⣿⣟⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⡈⢱⣿⡏⠀⠀⠀⠈⣿⣦⠈⣼⣿⣿⣷⣦⠄⠀⠀ ⠀⠀⠀⠴⠾⠿⣿⣿⣿⣿⣿⡷⠲⠛⠂⠀⠀⠀⠀⠘⠳⠂⠟⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠚⠋⢁⣧⣹⡯⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣆⠀⠀⠀⠀⠀ ⠄⠀⠀⠘⣿⣶⣶⣿⣷⣿⢿⡤⡀⠀⠀⢰⣂⣘⠀⠀⢀⠜⠀⠀⠉⠂⠀⠀⠀⠀ ⠀⠘⠛⠿⢿⣿⣿⣿⣽⣯⡿⡁⠊⠕⢂⣤⣀⡠⠔⣾⣥⣄⡀⢀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣾⣿⣿⣿⠟⡉⠀⢿⣷⣶⣤⡀⠀⢰⣾⠙⡿⡟⠛⠉⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⡿⠋⠀⠇⠀⢸⣿⣿⣿⣧⣤⣼⣿⡆⠈⠌⢳⡄⠀⠀⡀⠀⠀⠀ ⠀⣠⣾⣿⢿⡿⠁⠀⢀⠀⠀⢸⣿⣿⣿⣿⡉⣻⣿⣿⡄⠈⡄⢩⢢⠑⡱⡀⠀⠀ ⠈⠉⠔⠁⢸⣏⡀⠀⡸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⣵⠀⢴⠀⢂⠑⣐⠣⡀⠀ ⠀⠀⠀⣰⢋⠜⠢⡐⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣿⣿⣄⠈⡇⠹⡄⠈⢧⠀⠀

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠁⠈⠉⠙⠓⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⡀⢠⣄⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣮⡙⠁⠀⠀⠺⣷⡄⠀⠀⠀⠀⠈⠉⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⣰⡇⣤⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣎⡉⠀⠀⠀⢀⡿⢿⡟⠀⢀⣀⣤⣀⡀⠀⠀⠉⠛⠷⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡶⠶⠎⠁⠺⢡⠞⠉⠀⠀⠀⠙⡖⡆⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣟⠛⣂⡤⢤⣟⠀⠀⢀⣀⣀⡼⠷⡧⢾⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⠁⠀⠀⠈⣦⡠⠼⠿⠋⢀⡼⠃⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⣤⣀⣠⠟⢲⠿⠗⠚⠉⠀⣰⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣒⡛⠋⠁⣠⠞⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣫⠉⣁⣠⣤⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠸⡏⠙⠛⠛⠛⠛⠩⠤⠴⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣂⣉⣁⣒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⡚⠝⠛⠒⠢⡀⠀⢎⣒⣊⣒⣪⠇⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠊⠀⠀⠀⠀⠀⢈⡍⠀⠀⠀⠀⠀⠉⢇⡀⠀⠀⠑⢦⠀⠀⠀⠀ ⠀⠀⢀⡴⣇⣀⣀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢱⠀⠀⠀ ⠀⣤⣮⡄⠀⠀⠸⠉⢑⡞⠁⠀⠀⠀⣀⠔⠋⠉⠉⠉⢢⠀⠀⢸⠢⠄⠠⡄⠀⠀ ⡰⠈⣿⡇⢀⡠⠁⡠⠊⠑⣄⠀⢀⣜⣁⣀⣀⡉⠉⢉⣈⢣⢀⡎⠀⠀⠀⡷⣦⠀ ⠇⠀⠈⠉⠉⠑⡉⠀⠀⠀⠈⠑⣇⣀⡀⠀⠀⠀⠀⠀⠀⢸⡊⢉⠒⢖⠺⡬⠃⢃ ⢸⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⣸⠠⠉⠢⢄⠀⠉⠀⠈⢉⠏⡇⠘⣆⠀⢀⣀⠀⠘ ⢀⣀⢀⢀⡴⡏⠀⠀⠀⢀⠔⠉⠝⠒⢄⡀⠁⠢⠄⠒⠁⡠⠫⠑⢌⠲⣿⣽⡙⣦ ⠸⡅⠁⢹⣀⣬⠇⠀⠀⣼⠀⡌⠀⠀⠈⠝⢆⣀⣀⢴⢊⠂⠀⠀⠈⡶⣯⢓⢐⠋ ⠀⠹⠷⠯⠾⠃⠀⠀⠀⢸⡀⡇⠀⠀⠀⠰⢸⠸⡀⢸⡄⠀⠀⠀⡰⠁⠀⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣣⠤⡀⠀⡤⠊⠀⠱⡜⡄⠀⡠⢾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠓⠾⢷⠚⠀⠀⠀⠀⡎⠉⠉⠉⠉⠣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡴⠖⢢⣠⠔⠁⠀⠀⠀⠀⠀⠈⠲⢄⡆⠍⠫⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣿⣿⣷⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⣀⣠⣤⣶⣶⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠛⠁⢀⣤⣾⣿⡿⠟⠋⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⣿⣿⣿⣿⡿⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣴⣾⣿⡿⠟⠁⣠⣶⡿⠿⠿⠿⠿⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⣠⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡟⢁⣴⡿⠿⠟⠋⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⢿⣿⣿⠋⢹⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡁⠀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣧⠀⢿⣿⡿⠟⠁⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣇⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣤⣀⣀⣀⣀⣀⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⡿⠛⠉⠁⠉⠉⠙⠿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠏⠀⣠⣴⣶⣶⣶⣤⡀⠀⠹⣿⣆⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠶⠶⠶⠿⠟⠛⠛⠛⣿⣿⠃⢀⣼⣿⣏⣀⣀⠈⠙⣿⡆⠀⠘⣿⡄ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢀⣼⡿⢿⣿⠻⣿⣿⣿⣿⣿⡀⠀⣿⡇ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢸⣿⣧⣾⣿⣴⣿⣶⣿⣿⣿⡇⠀⣿⡇ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⣿⠅⠀⠀⠀⠀⠀⠀⠈⣿⡇⢰⣿⠀ ⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⡏⠀ ⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⠇⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡟⠀⠀⠀⠀⠀⠀⣾⣿⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣼⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⠀⣿⡟⢀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣧⠀⠘⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⠁⢸⣿⡿⠶⠶⣤⣄⡀⠀⢹⣿⡀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣸⡟⠀⠀⠀⠀⠙⢻⣦⠀⣿⡇⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣦⣄⡀⠀⠀⠀⠀⢸⣿⠃⠀⣿⣇⣤⣀⣀⣀⣤⣤⣽⣿⣿⡇⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⠀⠀⢸⣿⠀⠀⣿⣏⠙⣿⠋⣿⡟⣿⡏⣹⣿⠁⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣿⣿⠀⠀⢹⣿⣿⠿⠿⠿⣷⣿⣷⣿⠏⠀⢠⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠻⣿⣤⣀⣀⣀⣽⣿⠋⠀⢀⣾⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠺⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⣠⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠉⠛⠒⠦⠄⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⣀⣀⣀⣀⣀⣤⣾⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⣀⡀⣀⣀⢀⣀⠀⣀⠀⢸⠀⠠⢆⢰⣄⣀⣀⡀⢀⣀⣀⠀⠀⣶⣲⢄⣀⣀⡀⢰⢀⡀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠈⠸⠬⠁⠀⠟⠥⠜⠧⠜⠏⠈⠭⠵⠂⢸⠀⠰⠈⠻⠼⠥⠏⠧⠼⠹⠀⠇⠀⠏⠀⠸⠘⠧⠍⢐⠲⠬⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀ ⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⣧⣿⣿⣿⣿⣿⣿⠁⢻⣿⣿⣿⡿⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⣸⠛⢿⣿⣿⠿⣿⡇⠀⠀⢻⣿⣁⡀⠀⠀⠀⠀⠻⢤⣄⣀⠙⠲⣤⠀⠀⠀⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢻⠀⠀⠙⢿⣿⣿⡇⠀⠀⠘⡆⠈⠙⠒⠒⠒⠒⠦⣄⡀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠿⠿⢧⣀⡀⠀⠋⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠻⣿⡇⠀⠀⠀⢷⢠⠔⢲⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠾⣟⠻⠶⠀⠀⠀⠀⠀⠀⠸⠿⣶⡦⠀⠀⠈⠙⠲⠇⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠹⡇⠀⠀⠀⢸⠁⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⣤⣀⡀⠀⠀⠀⢠⡤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠺⢿⣦⡀⣀⣴⡳⣄⣀⣀⣾⠀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣙⡒⠦⠬⣽⣶⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠈⠹⣅⣿⣹⠏⠉⠉⠉⢩⣷⡒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⣀⡀⠀⠀⢀⣠ ⠙⢲⣤⣀⡀⢸⠃⠀⢠⡖⠛⠒⠚⠻⢤⡀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢉⡹⠗⠊⠉⠀ ⠒⠉⠉⠉⠉⢹⡀⣤⣾⠀⠀⠀⠀⠀⠀⠉⠳⣿⠛⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⠟⠋⠀⠀⠀⠀⢀ ⠠⠤⣤⣤⣤⡴⣟⠛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⣳⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⢄⣀⣀⣀⡀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣠⣾ ⠀⢀⡿⠋⠁⠀⢘⣆⠀⠨⠷⣄⡀⠀⠀⠀⠀⠀⠀⢳⡛⠟⠙⠦⠤⠴⠒⣻⣯⠋⢀⣀⣰⣾⡇⠀⠀⢠⡽⡿⠻⢤⣀⢀⣀⣠⠴⠟⠛⠉ ⠰⠿⢤⣤⠒⠚⠉⠈⠓⢤⣀⠀⠉⠓⠲⠤⡤⡤⠶⠚⠁⢠⣶⣦⠀⠀⣠⠟⠛⠉⠉⠉⠁⠈⠉⠉⠛⠒⠿⣄⡀⠀⣬⣭⠀⢹⡀⠀⠀⠀ ⠀⠀⠸⣿⣀⠀⠀⠀⠀⢀⡞⠉⠉⠉⠑⠒⠷⠷⣠⣤⠤⠤⣍⠁⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠘⠛⣡⠤⠖⠓⠶⠶⣛ ⠀⢀⡤⠿⠯⠛⢢⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠈⠳⣄⢀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⣰⣇⣀⡀⠀⠀⠀⠀ ⠀⣾⠷⠤⠀⠤⠾⡄⠀⠀⠈⠑⠲⠤⠤⠤⠤⠐⠒⠉⠁⠀⠀⠀⠈⠻⢏⡀⠉⠓⠶⠤⢤⡤⠤⠤⠖⠋⠁⠀⣠⠞⠁⠀⠙⢯⣉⣳⠖⠢ ⠀⠙⣦⠄⢀⠠⠴⡇⠀⠀⠀⢀⡀⠠⢤⣤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣸⣿⣇⣀⣀⡠⣤⠖⠋⠙⣗⣦⣄⡀⠀⠈⠻⣄⠀ ⠀⠀⠧⣄⣀⣠⠴⠁⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢠⠋⣹⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠘⣿⣿⡏⢳⡦⢄⣘⣦ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠉⠒⠃⠰⣁⡀⠀⢨⠓⢄⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠀⢘⡷⢄⡀⢹⠏⣰⠟⠁⠀⠀⠉ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⢤⡀⠀⠈⠙⠃⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⣸⠀⠀⣠⡟⠁⣠⣭⠉⣼⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠸⣄⣀⠴⠃⠀⣰⠏⣀⠴⢿⡏⢰⠇⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠣⡀⠈⠉⠓⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠊⠁⠀⠀⢹⠋⠀⠘⣇⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⠿⠟⠻⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡆⠀⠀⠀ ⠀⠀⠀⣀⣠⡾⠿⢥⡴⠖⠒⠚⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀ ⠀⡼⠏⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⠛⢷⣄⠀⠀⠀⠀⡾⠀⣿⡆⠀⠀ ⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⣀⣸⠇⠀⢹⣇⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⡀⠀⡈⣿⠀⠀ ⠘⢿⣦⣤⠶⠦⣤⣴⠶⠶⠒⠒⠒⠒⠾⣖⠒⣲⣶⠶⠒⠒⠛⠛⢷⣦⠶⣟⣦⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣿⠀⠀ ⠀⢰⡟⠁⠀⢀⡾⠁⠀⠀⠀⣀⣤⣄⠀⢽⣿⠁⣠⣤⣀⠀⠀⠀⠀⠹⣆⠈⠙⠋⢉⡽⠷⢶⣦⡄⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀ ⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⢰⡏⣿⣿⣷⢸⡁⢸⣷⣿⡾⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡁⠀⠀⣙⢿⣦⣤⡀⠀⠀⣰⡟⢠⡟⠀⠀ ⠀⠸⣷⠀⠀⠀⢻⣆⡀⠀⠀⠻⠾⠶⠛⢘⣿⡈⠳⢿⠿⠋⣠⣤⣤⣺⠏⠀⠀⠀⠈⢧⠀⢀⡴⠾⢄⢘⣿⡾⠻⠟⠀⢸⡇⠀⠀ ⠀⠀⠸⣧⠀⠙⣏⠈⠙⠛⠶⠤⣄⣠⣴⠟⠉⠻⢦⣄⣠⡞⠹⠶⡟⢛⣻⠆⠀⠀⠀⡸⠀⢸⠀⠀⢸⡄⢸⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⢠⡿⠀⠀⠙⠳⠦⣤⣤⣤⣤⡿⠭⠁⠀⠀⠀⠉⠙⠃⣴⣿⡏⠙⠁⠀⠀⠀⣸⠃⠀⠘⢧⣀⡼⠁⣾⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⢸⣧⠀⠀⠀⠀⠠⠴⢾⣿⣤⣤⣤⣤⣤⣤⣤⠴⠖⠛⠉⠀⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢠⣾⣻⣶⠶⠶⣶⣿⣧⡀⠀ ⠀⠀⠀⢹⣷⠖⠒⠲⡄⠀⠀⢹⣄⣀⡇⢸⣄⣀⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣴⡿⠶⠶⡄⠀⠀⣾⣷⡏⠀⠀⠀⠀⠀⠸⣷⡀ ⠀⠀⢀⣿⡇⠀⠀⠀⣹⠀⠀⠀⠀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢿⠀⠀⢀⡇⠀⣰⣿⣼⠇⠀⠀⠀⠀⠀⠀⢾⡇ ⠀⠀⠀⣿⡹⣆⣀⡠⠋⠀⠀⠀⠀⠸⣆⠀⣠⠖⠛⠉⠽⠛⠉⣹⠇⢠⠤⣄⠀⣸⠓⠒⠋⢀⣼⡏⠈⠻⣷⠀⠀⠀⣀⣀⣴⡿⠃ ⠀⠀⠀⢻⡇⠈⠉⣠⠲⣄⠀⠀⠀⡄⠛⠾⣥⣤⣤⣤⣤⡴⠚⣁⣴⠁⠀⢘⣶⡇⠀⠀⣠⡟⠉⣷⡀⠀⠙⠻⣶⠾⠛⠛⠋⠀⠀ ⠀⠀⠀⣺⣧⣀⠀⠻⡶⣋⣀⣤⣤⣙⡲⠶⠞⠛⠛⠲⢦⣶⠞⠁⠈⠳⣤⣞⣹⡇⠀⢀⡿⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣭⣻⣿⣿⣏⣭⣻⣭⣉⣻⡷⠶⢶⣤⣶⣾⣿⣛⣛⣷⣶⣿⣛⣿⣳⣾⣿⣷⣶⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠤⠤⠤⠤⠬⠁⠈⠩⣽⡇⣉⣹⡯⠭⠭⠿⠿⠿⠿⠿⠿⢿⣿⠟⠿⠟⠛⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡗⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢰⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣷⣶⣟⣠⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣀⣠⣴⣿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⣨⣿⡻⡇⠀⠹⣇⣈⠉⠉⣹⡏⠉⠉⠉⠉⠉⠉⣿⡍⠉⠉⢛⢛⣿⠁⡴⠏⠈⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣶⠋⣇⣷⣿⠀⠀⠈⠉⢻⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⡖⡞⠋⠁⠀⠷⣿⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠷⠟⠛⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇⠀⠀⠀⠀⠻⠾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠛⠁⠀⠹⣆⠀⠀⠀⠀⠀⢀⣀⣰⡾⠷⠞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠤⢀⣀⣠⣤⣴⡿⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣙⢶⣤⣤⣤⠶⢛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠿⣆⠀⠀⢸⣇⢤⣼⣏⣴⡾⠟⠉⢿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⢠⣿⡇⠀⢸⣿⣿⣿⡏⠁⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠇⠀⠀⠀⡾⣿⠁⠀⢸⡏⢹⢿⡇⠀⠹⢦⣀⣸⣇⣀⡀⢀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣸⣳⡏⠀⠀⢸⡇⠶⢸⡇⠀⠀⠀⠉⣿⣿⣯⣵⣦⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣦⣤⢇⣿⣄⡀⠀⢸⣇⢠⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣃⣀⣀⣀⡀⢀⣀⣀⣈⣿⣿⣿⣿⣿⡟⠁⢈⣷⡀⢸⣇⣸⣾⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⡁⠉⣡⣬⠙⠋⠉⠉⠉⠉⠉⠉⠙⠉⠉⠛⠛⠛⢻⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡾⠁⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢂⡾⠁⠻⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠘⣷⠘⠋⢁⣤⠖⠋⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⢸⡇⣠⣦⣄⠙⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣉⣁⣼⣄⣠⣴⣿⠏⢶⡴⠋⠀⣀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⣾⠁⢻⣿⣿⡇⠀⢙⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠤⠤⠤⢴⠶⢶⣶⣶⣶⣶⣶⣖⣶⣟⡛⠋⠉⠉⠉⠉⠉⠉⠉⠉⢴⡿⣿⡇⣼⠁⠀⠘⠋⠀⠀⠀⠀⣿⠆⠀⠸⡆⠀⠀⠘⡇⠀⠀⠙⠛⠃⢠⣾⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠐⠀⠀⣴⣿⡿⠿⠿⠿⣿⣿⣿⣛⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡇⠀⣀⠀⠀⣰⡦⠀⠀⠀⠀⠀⠀⣷⠀⢠⣼⠃⠀⣠⣀⠀⢀⣼⣇⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⡇⠈⢫⡀⠀⠀⠀⠀⢀⡷⠆⠀⢀⡏⠀⢸⣇⡀⠀⠘⠿⠃⣸⣿⠍⠙⠿⠤⠀⠀⠀⠙⣻⣷⣶ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢿⡀⠈⠳⢤⣤⡤⠴⠋⠀⠀⢀⡾⢀⢀⡾⣿⣿⣷⡀⠀⣴⠟⠛⣿⣯⣴⡶⠶⠶⠶⢶⣿⣿⣷ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⢺⡃⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⣾⣿⢿⡇⠘⠿⠿⠇⢀⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣤⣤⣀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣦⣾⣧⣾⣿⠇⠈⠓⠲⠤⠤⠤⠖⠋⠁⠀⠙⢁⡾⠃⠀⣀⢠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠉⠉⠀⢸⣟⣻⣦⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢺⡇⢀⡞⠉⢿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣸⡇⠀⠀⠀⢸⣿⠟⠛⠚⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣯⣉⠙⠓⠚⠛⠦⠤⠴⠦⢤⣤⣼⢧⣤⣾⣀⣾⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠞⠋⠁⡇⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠲⠦⢤⣤⣀⣀⠀⠀⠀⣾⠋⠀⠙⢶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⢀⡇⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠦⣤⣼⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣴⣿⡇⠀⠀⠀⢸⣿⡏⠉⠉⠉⠉⠉⠻⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠟⠃⣷⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠿⠛⢿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣤⣀⡀⠀⠀⠀⠀ ⠁⠀⠀⠀⢻⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡵⢀⡞⠺⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⢿⣅⠉⡾⠀⡄⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⡤⠤⠤⣀⡀⢀⡠⠤⠼⠷⠾⠿⣿⣃⡀⡇⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣧⣄⣀⣠⠚⡁⢀⠀⠀⠀⠀⠀⠀⠉⠪⡉⠓⢄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡠⠋⠉⠑⠄⠀⣀⠦⠧⡠⠀⠈⡄⠀⢱⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡅⠀⣾⡧⠘⢰⣤⣤⠀⠈⡆⠀⢀⠀⠀⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠙⠖⠢⠔⡁⠘⢍⠉⢀⠔⡱⠂⠸⠀⠀⣾⢦⠀ ⣿⣿⣿⣿⣿⣿⣿⢻⠀⢠⡜⣌⡑⠒⠂⠀⠀⣉⡇⠚⠀⠀⡀⡠⡀⡿⢸⡆ ⣿⣿⣿⣿⣿⣿⣿⡼⠀⠈⠫⡃⡧⢽⣉⡉⡇⣗⠟⠀⠀⠀⡿⠀⢰⡇⢸⡇ ⠭⠍⠩⠭⠩⠭⣭⣇⠀⠀⠀⠈⢑⡂⠘⠒⠉⠀⠀⠀⠀⠀⠃⡤⢼⠇⣸⠁ ⠀⠀⠀⣀⣑⣕⣔⠿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣟⣾⠀⡏⠀ ⠒⠒⠚⠓⠒⠲⣯⠀⣦⣀⣙⢍⠕⣶⠖⢖⡢⠄⠀⠀⠐⡗⡞⠘⡏⣸⠀⠀ ⣉⣉⣉⣉⣙⣉⣙⣶⣿⡛⠛⠹⢿⠁⣷⣾⡖⢲⣶⣶⢲⣿⡆⢸⣧⠃⠀⠀ ⣿⣿⣿⣿⣿⣿⡏⣿⣽⠿⡍⢱⣮⣋⣀⣠⣴⣢⣤⣠⣷⣺⡿⢻⡞⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠛⠉⠁⠀⠀⠉⠀⠀⠈⠙⠻⣿⡿⡟⠁⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⠄⡀⣀⣀⣀⠀⠀⠀⠀⣠⣾⣿⡙⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣥⣴⢿⣿⠷⡷⣖⣦⣤⣴⡛⣉⣉⣻⣿⢿⣿⣿⣿ ⣿⣿⡿⠋⠡⡀⠈⠙⠁⣀⠀⠀⢹⠭⠄⠐⠓⢊⣓⣊⣯⠑⣒⣒⠛⢛⣻⣏⡁⠙ ⡿⠋⡠⠐⠄⠁⠀⠀⠀⠑⢄⠐⠓⠂⠀⠀⠀⠀⠒⢍⣉⠉⢁⣀⡠⠘⡠⠋⠰⣶ ⣷⠀⣁⢀⠆⡇⠀⠀⣠⡀⠀⠈⠐⠀⠤⠤⠀⣀⣀⣀⡀⠠⡤⠄⠒⠁⠀⠀⣰⣿ ⣿⠀⠀⠀⠀⠐⡄⠀⠓⠁⠀⠀⠄⠐⠢⠖⠰⢄⠐⠒⠒⠔⠫⠁⠀⠀⠀⠀⣿⣿ ⣿⡇⢴⡆⠀⠀⡇⠀⠀⠀⠀⠈⣄⠀⠀⣀⠠⠂⠀⠠⠄⢀⡠⠔⠁⠀⠀⠀⢸⣿ ⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⡄⠀⠄⢄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠸⣿ ⣿⣿⡇⢸⣀⡘⠸⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⠇⢠⣿ ⣿⣿⡇⠀⠀⠀⢰⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠀⢸⣿ ⣿⣿⣷⠀⠀⠀⢸⠀⠀⡄⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢸⣿ ⣿⣿⣿⣇⠀⠀⠈⡀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣷⣶⣶⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣆⠀⠘⣎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣇⢀⠈⢾⣧⡀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⣉⣲⣞⣿⡙⠋⠀⠀⣿⡏⠉⣉⣭⠁⠀⠉⠉⠁⠀⠄⠈⢁⣠⠞⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡴⠚⠉⠀⢉⣉⡛⠉⠉⢲⣶⣾⠟⣿⠀⢠⣒⠒⠒⢢⠄⠀⠀⠀⣀⡞⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠾⢅⣀⣀⠤⠤⣄⣉⣀⡠⠔⠋⠀⢀⣴⠯⢤⣀⣈⡩⠥⠤⣀⡠⠤⣞⠁⠀⢀⠤⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣄⠀⠠⢴⡄⠀⠀⠀⠈⠷⣆⣐⣶⠟⠁⠀⠀⠀⣀⣤⠖⠒⡦⢄⡀⢘⡆⢀⠏⠀⡷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⢨⣷⢁⣸⠄⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡨⠧⠴⢇⡀⠉⠸⡀⠈⠣⠴⠃⠀⢷⡀⠀⠀⠀⠀⠀⡠⢚⡅⡇⠀⠀⠀ ⠀⣧⣞⣩⣤⡀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⡈⢆⠀⠱⡄⠀⠀⣤⡆⠀⢻⣿⠟⠉⠛⢿⣤⣿⠀⡇⣀⣀⠀ ⠀⢸⢾⣿⣿⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠸⣿⣿⣿⡼⠀⠀⢸⠀⠀⠙⠃⠀⣸⠃⠀⠀⠀⢀⣿⡏⢀⣿⣿⠹⢳ ⠀⠈⠲⢍⡁⢀⣀⠴⠋⡠⢂⡄⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣨⠽⢛⡁⠀⠀⠘⣆⠀⠀⢠⣾⡇⠀⠀⢀⣤⣾⣿⡇⢸⠛⡧⢆⡎ ⠀⠀⠀⠀⠹⣏⣁⠴⠊⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠊⠉⠀⠀⠈⠀⠈⢢⠀⣿⠘⡷⠒⠒⠻⢷⣾⣿⣇⠘⠋⣀⡎⠀ ⠀⠀⠀⠀⣴⠉⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠛⠁⠀⣴⡀⠀⡇⠀⣿⣿⣟⠙⣿⠀ ⠀⠀⠀⠀⠈⠒⠚⡏⠁⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠈⠓⣄⠀⠀⠉⠀⠀⣣⠀⢸⣿⣿⣶⣿⠇ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡾⣿⠿⠛⠋⣁⣀⠤⠤⠒⠃⠀⠀⠣⠄⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⢧⠀⠀⣿⠿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡰⠻⣉⠠⠔⠚⠯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠀⠀⢱⣴⣴⡾⠖⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢰⠁⠀⠀⠀⠀⠀⢀⣤⣿⣶⣶⣦⣤⠖⠒⠒⠒⠒⠒⠒⠒⢲⣶⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⢈⡿⢋⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⢋⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠒⠲⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠛⠛⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⡴⠊⠁⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠉⠑⢤⡀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠋⠀⠀⠀⠀⠀⡠⠂⠁⠢⡈⢢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠎⢁⡈⢢⠱⡄ ⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡁⢰⣿⡆⢱⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠘⡀⠸⠿⢠⠀⢳ ⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠣⣀⠉⣁⠏⠀⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠑⠠⠄⠊⠀⣸ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⡞⠀⠀⢠⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⠴⠁⠀ ⢰⠃⠀⠀⢺⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⠤⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠓⠒⢺⠏⠁⠀⠀⠀ ⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀ ⡇⠀⢰⣿⣿⡆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀ ⣷⠀⠸⣿⣿⡇⠀⢠⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀ ⢹⠀⠀⠈⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢱⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⠀⢸⡀⠀⠀⠀⠀⠀⠀⡏⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⢿⣿⣧⣀⣠⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡄⠈⣇⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡆⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠘⡇⠀⢻⠀⠀⠀⠀⠀⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⢰⠁⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢿⠀⠀⣷⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⡾⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣄⠀⠀⠀⠀⢸⠀⠀⠀⢱⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠀⠀⠀⠀⢇⠀⢰⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠙⠛⠛⠒⠊⠋⠀⠀⠀⠀⠈⠲⠾⠶⠦⢼⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠴⠶⠒⠒⠒⠒⠒⠺⠿⠿⣿⣿⣁⣀⣀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣴⡋⠉⠉⠉⠙⠦⣤⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠚⠉⠉⠉⠉⠒⠒⠤⠤⠤⠤⠤⠄⠂⠁⠈⠛⠒⢶⠄ ⠀⠀⠀⠀⠉⠛⠒⠒⠺⣦⣀⡀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣀⣀⣠⠖⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠻⠶⢤⣤⡤⠤⠶⠖⠛⠉⠛⠷⠶⠶⠖⠛⠋⠉⠛⠳⢦⣤⣤⡤⠤⠒⠒⠛⠛⠶⠶⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠉⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⣧⠀⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⠠⢶⡿⣉⣀⣽⡉⠭⣉⡉⠀⠁⠉⡩⠊⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠞⣁⠠⠄⣒⡠⠜⠉⣱⠇⣉⠲⠬⠀⠤⡂⠁⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢠⠔⡂⡄⠀⠑⠀⠛⠁⠀⡀⢲⣉⡗⠠⡅⢨⣀⠃⡇⠀⠀⠀⢀⠄⡄⠀⠀ ⠀⣽⣭⡄⠉⢂⠀⠀⠀⠀⢠⠊⠁⣠⣬⢂⠐⠄⠀⡤⠘⡶⠂⠒⣵⡇⣇⣠⠀ ⠀⠫⣛⢃⡠⢊⢄⠀⠀⠀⠘⢄⣀⣙⠻⡂⠀⢠⠀⢀⣴⠁⠀⣠⣿⢠⢿⢌⠃ ⠀⠀⠈⠫⠐⢁⠌⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢡⠸⠼⠀⡉⢳⠻⣄⡡⣎⠀ ⠀⠀⠈⠒⡒⠁⠀⠀⢀⣤⣶⡶⠿⠖⠀⠀⡀⠀⠈⠒⡄⠀⠃⢘⠀⢿⣧⡿⠀ ⠀⠀⠀⠀⢃⠀⠀⣰⣙⡩⢅⡒⠀⠈⠀⠈⠁⠀⠠⠠⠐⠒⣄⣈⡤⠘⠉⠀⠀ ⠀⠀⠀⠀⠈⢄⡐⠀⠀⠀⠠⣼⣶⣶⡖⠒⠒⠒⠀⢰⣶⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢔⣵⡉⠉⠀⠀⠀⠀⠀⠀⣇⡉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⡿⠀⠀⠀⠀⠀⠀⠉⠉⣭⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠏⠀⠀⠀⠀⠀

⠀⠀⢰⠋⢓⠊⠉⠉⠂⠉⠉⠀⠈⠉⠁⠈⠉⠐⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠻⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⢀⣀⠀⠘⠀⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡆⠠⠀⢠⠁⢀⠄⠉⢲⡖⡨⠭⡀⠐⡀⠀⠀⡜⠀⠀⢀⡀⡀⠀⠀ ⠀⠀⠀⡇⠀⠀⠐⠀⠠⠙⠜⡸⠢⠆⠃⠃⢀⠃⠀⠀⡧⠲⡪⠕⠲⠸⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠌⠂⠀⠂⠃⡠⠑⠀⠐⠀⠀⠀⢸⢀⣠⠃⠀⡄⠃⠓⠄ ⠀⢀⠔⠚⠀⠀⠀⠹⠿⢏⣷⡄⠀⠀⠀⠀⠀⣀⡀⢸⠁⠀⠀⠀⠸⡡⠠⠂ ⠀⣇⢀⠀⡄⢆⣀⡀⠀⠂⠈⠁⠂⠀⠀⠀⠀⠛⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢃⣂⠨⢑⡀⠀⣤⡤⠠⢤⣀⢤⠤⠄⣀⠤⢌⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠐⠒⠈⢹⢉⣐⣀⢀⣀⣀⠆⢂⣁⡀⢀⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣈⣢⣌⣉⡁⠘⣍⣩⡍⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⢤⢤⣣⡀⠀⠀⠀⠈⠑⠢⠤⡟⣹⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣘⠬⡿⣇⠀⠀⠀⠀⠀⠀⢼⣿⣟⠡⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣿⣿⡄⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⣠⣾⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣤⣤⣶⣶⣿⡿⠿⡷⣶⣶⣾⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣶⣶⠶⠿⣿⣷⣦⣄⣀⣰⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⡀⠀⠀⠀⢀⣤⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀ ⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀ ⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⢉⣉⣉⡛⢿⣆⠀⠀⢹⡇⠀⠀⢀⣴⡿⠟⢋⣋⣙⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣠⣾⣿⣿⣿⣿⣮⣿⡆⠀⢸⣷⠀⠀⣾⡏⢠⣾⣿⣿⣿⣿⣆⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡏⠀⠀⣿⡇⢿⣿⣿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣈⠻⢿⣿⠿⢟⣹⡟⠀⢀⣾⠇⠀⠀⠘⣷⣄⠻⠿⣿⡿⠟⢁⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀ ⢸⣿⣿⣄⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠛⠷⣶⣶⠶⠟⠋⠀⢀⣼⣿⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣄⡀⠀ ⠈⣿⡿⠛⠹⣯⠉⠛⠛⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠛⠉⠉⠉⠉⢻⡆ ⠀⣿⠀⠀⠀⠀⠀⣴⡄⠀⠻⠋⠛⢿⣦⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⡇ ⠀⠻⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣤⣴⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣶⡶⠶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇ ⠀⠀⠀⠀⠐⠛⢻⣿⡿⠶⣆⠀⠀⢰⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⢻⣿⡟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠉⠛⠗⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠌⠛⠒⠦⠶⣞⠛⠋⠛⣓⠦⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣛⡁⠀⠴⣦⣤⡄⠈⠉⠉⠚⠛⠧⠤⣭⡵⠞⠛⠋⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡝⢦⣾⣿⡏⣻⣶⣶⠒⢶⠤⠖⠀⠀⠀⠀⢸⡇⣾⠻⣆⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡷⠮⠷⠶⣧⣉⠉⣀⣼⠁⠀⠀⠀⠀⠀⠀⡵⠹⣆⡸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣖⣾⣟⣿⣶⣶⣶⣲⣤⣍⠻⢍⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⣀⠀⣶⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣽⣛⡻⠛⠛⠛⠛⠋⠉⠉⠛⠢⠱⡄⠀⠀⠀⠀⠀⠀⢸⠻⣍⠉⣓⠤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠀⠘⡇⢨⣄⠈⠑⢾⣝⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣶⣖⠛⠓⢶⣶⡿⠛⠉⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⡇⠈⠛⠃⠀⢸⡏⠙⠺⢿⣦⣄⠀⠀⠀⠀⠀ ⢿⣞⡩⠞⠉⠉⠙⡎⢷⠀⠀⠀⠀⠀⠙⣷⠦⠤⠤⣤⣞⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣓⣀⡇⠀⠀⠀⣈⡯⠷⠤⢄⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⢸⣯⣅⠀⢺⡏⠀⠈⡿⠀⠀⠉⠉⠀⠀⠀⠈⡏⠉⣭⠉⠁⠀⡇⠀⢠⣏⡟⠉⠳⣦⢠⡿⣷ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⣴⠾⠟⠙⠛⢛⡿⡃⠀⠀⣟⠛⠲⠤⠴⣶⣤⣤⣠⣷⣶⡤⣴⠒⠚⠁⠀⠀⠉⠀⠀⠀⠹⣏⡿⠾ ⠀⠀⠀⠀⠀⠀⣾⠿⣉⣉⡁⣼⠇⠀⠀⠀⠀⠘⠻⠷⠶⣾⡟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣷⣜⠷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀ ⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣤⣀⡉⠙⣲⡦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠛⠁⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⣞⠀⣰⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣼⢻⣞⡌⣱⡿⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⢿⣳⣀⠀⢠⣿⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣯⣤⣼⣿⣿⣿⣾⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠉⠉⠉⠛⠲⠦⣤⣀⠴⠖⠛⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣶⠦⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣽⣤⣄⣀⡀⢀⣴⠚⢁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⠷⠶⠿⢤⡤⠀⠀⠀⠀⣤⠀⣶⠄⠀⠀⠀⠙⢆⠀⠀⠙⢷⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⡞⠁⠀⠀⠀⠀⠹⡄⠀⢀⡤⠛⠛⠛⠳⢾⠁⠀⠀⠘⣇⠀⠀⠈⢿⡄⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣸⡁⠀⠀⣾⣿⣷⠀⡿⢠⡏⣠⣤⣄⠀⠀⠈⢷⠀⠀⠀⢿⠀⠀⠀⠸⣧⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⢧⡀⢀⠙⠛⠋⡰⠃⠸⡇⢿⣿⡿⠀⠀⢀⣸⣄⣀⠀⢸⠀⠀⠀⠀⣿⣆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢧⠀⡿⡏⠉⠲⠯⣤⠀⠀⠑⢄⡀⠀⢀⣴⠋⢀⠼⠋⠀⢸⠀⠀⠀⠀⣿⠹⣧⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⢀⣵⣁⠈⠓⠦⠤⠤⠀⠀⠀⠀⠉⠉⣿⠢⠴⠁⠀⠀⠀⣾⠀⢀⠀⢰⣿⠀⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠀⠀⠘⣿⢇⣸⠙⣶⠤⣤⣤⣀⣀⣤⡤⢴⠚⣿⡄⠀⠀⠀⠀⠀⡿⡴⠉⢳⠈⣿⠀⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⠀⠀⠀⠈⠣⣏⠓⡿⠤⣼⣀⣸⣇⣼⡧⢾⣻⠟⠙⠀⠀⠀⠀⢀⣿⠁⠀⠈⣧⡿⠀⣾⡟ ⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠈⠑⠳⠤⣟⣀⣸⣤⠼⠗⠋⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣠⣿⡇⠀⣽⡇ ⠉⠉⠁⠁⠉⠍⠭⡌⢯⡩⢯⢿⣿⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢹⢻⣿⠃⢰⣿⠀ ⠠⠀⠀⠀⢰⣄⣀⣙⣦⣱⣄⣻⡿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⢸⣾⡿⠀⣾⠇⠀ ⣂⣒⣀⣐⣶⣿⣛⣛⣛⣛⣻⠏⠀⣯⠉⠙⠛⢖⡲⠶⠤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣼⣁⣤⡏⣾⣿⠇⢰⡟⠀⠀ ⣀⣀⣀⣀⣀⣈⣁⣀⣒⣙⣷⣏⠀⢾⣷⣶⣤⢤⣝⣶⣋⣘⣷⣞⠀⠳⡭⠟⠛⠉⠉⠉⠉⠉⠉⡿⣠⠟⠀⢸⣿⢀⣾⠁⠀⠀ ⠛⠛⠛⠉⠛⠛⠙⠻⠛⠉⠋⠻⣶⢾⣿⡻⠿⠿⠏⢿⣿⡟⠀⢻⣿⣿⣗⣒⠒⣶⣶⣶⣶⠶⣾⣿⣷⡏⠀⣾⣿⣼⠇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣷⣤⠤⣤⣄⠈⢷⣤⠞⠉⠙⠛⠃⠀⠛⠛⠛⠟⢰⡟⣻⣿⣥⣷⡿⢻⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣷⣿⠿⢳⡄⢀⣼⣷⣶⣥⣤⣤⣤⣶⣿⣛⣛⣿⣦⠴⣿⣿⣯⣾⡟⣋⢸⡿⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠿⠛⠛⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡶⠋⠀⢀⣀⣀⣤⣤⣤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀ ⠀⣤⢴⠞⠋⠑⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠒⠒⠲⢤⣤⣀⠀⠀⠀⢀⠈⣷⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⢀⡼⠀⢻⡄⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⠀⢸⡇⠀ ⠈⢻⠖⠛⢳⡞⠋⠉⠉⠉⠉⢻⣭⠟⠋⠉⠉⠉⠙⢿⡛⠿⡶⠶⣦⣀⡀⠀⠀⠀⠀⠈⢆⢸⡇⠀ ⠀⡟⠀⠀⢿⠀⠀⠀⡴⣿⣷⣼⡏⣰⣿⣷⡆⠀⠀⠈⡇⠀⠀⢸⠉⠉⠻⣦⣀⡀⠀⠀⡾⢸⡇⠀ ⠀⢻⡄⠀⣘⣦⣀⠀⠙⠻⠟⢉⣷⡜⠻⠟⢃⣤⢤⣼⡃⠀⠀⠈⡆⢀⡜⠺⡉⢷⠖⠛⠁⢸⡇⠀ ⠀⠀⣷⠀⠹⣄⡈⠉⠓⠲⣶⠏⠀⠙⠳⢤⡏⣉⣿⣭⠟⠀⠀⢠⠃⠸⡄⠀⡇⣸⠀⠀⠀⣾⠁⠀ ⠀⠀⣯⠀⠀⠀⢉⣹⣿⣉⣉⣀⣀⣀⣀⡤⠴⠋⣧⠀⠀⠀⠀⣾⠀⠀⠙⠊⣠⣿⣤⣤⣤⣿⣀⠀ ⠀⠀⢹⡶⠒⠒⡄⠀⢸⣄⣸⠅⣇⣈⡇⠀⠀⠀⢹⠀⠀⠀⣠⠧⠒⢄⠀⢠⣿⡏⠁⠀⠀⠀⢻⡄ ⠀⠀⣾⣇⠀⠀⡼⠀⠀⠀⢼⠀⠀⣀⡠⢤⣀⠤⣼⠀⠀⠀⢹⣀⣀⠎⢠⡾⢿⡇⠀⠀⠀⠀⣸⡷ ⠀⠀⢽⡎⠓⢊⣀⡀⠀⢀⡘⢦⣎⣁⣀⣈⣠⠴⢋⡜⠉⢆⡜⠀⠀⡴⠻⣇⠀⠿⢦⣤⠶⠶⠋⠀ ⠀⠀⢸⣧⣀⠘⣴⣃⣠⣄⣳⡤⠜⠛⠛⠥⣤⡊⠉⠳⣤⣏⣇⢀⣸⠃⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⡿⠿⠿⠿⠿⠷⢬⣿⠛⣶⣶⣾⣿⣭⣽⣿⣿⣽⣯⣿⣿⣷⢶⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡏⠉⠉⠉⠀⠀⠈⡏⢀⣿⠁⠉⠉⠉⠉⠉⠉⢻⠃⠉⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣤⣤⣄⣀⣀⣠⣷⣶⣛⣀⣀⣀⣀⣀⣀⣀⣸⣀⣠⣴⡏⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣧⣾⢿⣇⠈⠷⠤⣀⣬⠏⠀⠀⠀⠀⠉⣯⣉⣉⣯⡿⢠⣛⡀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⣼⡾⠟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣹⠁⠀⠀⠹⣥⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⢷⡀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡉⠉⠁⠀⢀⣷⠀⠀⠀⣠⠴⠒⠋⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢛⡛⠋⠉⠉⠁⠀⠀⠀⡻⣤⣤⣤⡴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠙⠒⠒⠚⠉⠁⠈⠉⠙⠋⠉⠉⠁⠉⠉⠒⠦⠤⠖⠚⠛⠲⢤⣀⣠⠖⠋⠓⠲⣄⣀⡤⠤⣄⠀ ⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀ ⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⣿⣀⢀⡶⠀⠀⠀⣴⣀⣀⣾⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⠜⠋⠁⡠⢚⣛⡳⡄⠀⡠⠊⠉⠀⠀⠈⠙⢣⡀⠀⠀⠀⠀⠀⠀⣰⠟⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣇⠻⡿⢇⡜⣾⠁⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⢧⡀⠀ ⠀⠸⣆⠀⠀⠀⠀⠀⢸⡀⣀⣀⣀⣈⣑⣒⡈⡔⠉⠙⣾⣭⡅⢦⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣼⠇⠀ ⠀⠀⢈⡇⠀⠀⠀⠀⠺⠥⠄⠀⠀⠒⠂⠀⠈⣇⠀⠀⣟⠛⣁⠞⠀⠀⢠⠎⠀⠀⠀⠀⠀⢿⡀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣰⠛⠣⠤⠤⠐⠚⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠹⣿⣿⠿⡋⠓⢄⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀ ⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣷⣄⡀⠀⡸⠃⠀⠀⠀⠀⡾⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⡁⣟⡀⠀⠀⣀⡀⠀⠀⣀⣀⣤⣀⠀⠀⠀⢁⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣻⢸⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⡤⣿⠉⠉⠀⠈⠛⠉⠙⠳⢤⣈⡹⣖⣺⣏⣉⡿⠖⠒⠒⠋⠉⠓⠲⢾⣥⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⢸⠦⣤⣤⢤⡶⠦⣤⣤⠤⠼⢦⠏⠹⣾⣷⣦⣤⠤⠤⣤⣤⢤⡤⡞⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣼⡄⠛⠛⠛⠃⠀⠛⠛⠛⠋⢿⣀⣠⠟⠛⠛⠛⠁⠘⠛⠛⠛⢠⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⢓⣶⠶⠤⣤⣄⣀⣀⣀⣀⣀⣙⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣧⠘⣿⡆⠀⠈⠓⢶⡗⢿⠋⠀⠀⠀⠀⠉⢻⠻⡟⠛⠋⠉⢱⡏⡈⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡌⢶⡿⣵⠀⠀⠀⠀⣇⠘⡄⠀⠀⠀⠀⢠⣇⣸⠀⠀⠀⢰⣿⣷⠃⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⠿⠋⠀⠀⠀⠀⢹⠉⡇⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⠘⠿⠥⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣞⠀⣸⠀⠀⠀⠀⣸⣀⣳⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠛⠛⠋⢙⠛⠋⠀⠀⠀⠀⠀⠙⠃⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⡿⠻⣿⣿⠿⠿⠋⠉⠙⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀ ⡎⠻⣿⣿⡇⠀⢛⠣⢄⣀⣀⡓⠠⠭⠶⠀⠀⠉⠛⠛⠻⢿⣿⣿⡄⠀⠸⠀⠀⠀ ⢰⠀⠈⢻⡇⠀⠸⡠⠲⠀⠀⠈⠑⠒⠂⠶⣲⠄⠀⠀⠀⠲⠶⠄⠈⠑⠴⠀⠀⠀ ⠤⢧⡀⢀⠧⡀⢠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠤⣀⣘⠯⢔⣢⡄⠀⠀⠀ ⢄⡀⠈⢾⠙⢀⠀⢹⡇⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⢤⡠⠔ ⠒⠉⠁⢃⣠⡇⠀⠀⠈⠑⢾⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠂⠁⠀⢀ ⠉⡵⠒⠈⣄⠑⢄⡀⠀⠀⠀⢡⠴⠢⠀⠠⢤⡒⠒⢠⡄⠐⢒⢦⠎⡀⢀⣀⠴⠟ ⠚⢲⡆⠉⠀⠑⡤⠬⠑⣲⡖⠊⠀⠾⠆⡠⠊⠉⠀⠀⠀⠈⠙⠳⡄⠴⠆⣡⣀⡀ ⠀⡬⠋⠒⡀⠘⢄⠀⠀⠀⠀⢉⡠⠛⢄⣸⡤⡀⠀⠀⠀⠀⢀⠤⠁⡰⢅⣀⡀⠈ ⠘⣍⣀⡈⡇⠀⠀⣈⣉⣉⣁⡀⠀⠀⠀⠈⠢⠄⣉⣽⣉⣉⣠⠔⢺⢄⡀⠑⢾⠉ ⠀⠑⢠⠐⠁⠀⠀⢀⠐⠤⢀⠊⠍⠒⣄⠀⠀⠀⠀⢀⡀⠀⠈⢆⠀⢻⠏⡵⠂⠵ ⠀⠀⢸⠀⠀⠀⠀⠀⠑⠀⠀⢄⡉⠒⡁⠑⠀⠀⡐⠁⠸⠀⡠⠃⣭⢂⢾⠀⠀⠀ ⠀⠀⢸⡲⡒⠂⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁⣰⠕⠈⠙⡞⠈⡆⠀⠀

⠀⠀⠀⠀⠀⣠⡤⡶⠶⡖⠠⢄⡀⠀⠀⢀⠤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⣢⢋⡎⠀⠀⠙⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⢖⣒⣒⣒⣒⣂⡤⢀⣴⣿⣏⣼⣀⡀⠀⢰⣃⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠔⠒⠀⠠⠄⠀⠀⠵⡫⠐⣊⣃⣻⣞⣿⢗⣒⣲⣒⣿⣷⡦⠀⠠⡀ ⠀⡠⠊⣀⡈⠄⠀⠀⠐⡖⢂⠤⢋⣁⠀⠀⣀⡀⠬⠇⠤⠐⠊⢉⠝⡻⠁⡠⠃ ⢻⠀⢸⠁⡅⡆⠀⠀⠀⠈⠒⠤⢀⣀⠀⠀⠀⠀⠀⠒⠒⢒⡈⠕⠊⠀⠀⡇⠀ ⠀⡀⠈⠉⠀⠡⠀⠐⠜⠀⠀⠂⠈⠇⡤⠌⡏⠉⠭⠭⡡⠶⠀⠀⠀⠀⢸⠀⠀ ⠀⢃⢀⡄⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠠⠔⠀⠠⢀⣀⠠⠊⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⡠⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀ ⠀⠀⠇⠸⡠⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠎⢰⠀⠀ ⠀⠀⠸⠀⠀⠀⢡⠀⠀⡠⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀ ⠀⠀⠀⠠⢂⡀⢈⠀⢰⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀ ⠀⠀⠀⣷⠁⠘⡌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⡇⢠⠀ ⠀⠀⠀⡧⣄⡀⠏⠖⠒⠀⠁⠐⠂⠘⠩⡉⡩⢯⣹⠫⣁⠔⠋⠁⠀⠉⢷⠁⠀ ⠀⠀⠀⣿⡇⣷⣦⠤⠤⣤⣤⣤⣤⠔⢲⣶⣶⡾⠳⣶⣶⠒⣲⣶⣶⣾⢺⠀⠀ ⠀⠀⠀⣿⡇⡟⢻⠀⠀⠙⠉⠉⠉⠀⠈⠉⠹⡁⢀⡿⠉⠀⠀⠀⠀⢸⢸⠀⠀ ⠀⠀⠀⢈⠇⢷⣼⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠋⢀⣀⣀⠀⣀⢤⠼⠸⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⠉⠐⠒⠒⠂⠒⠶⣄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠤⠦⠤⢄⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀ ⠒⠂⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⠒⡇⠀⡆⢠⠄⢀⡠⠖⠒⠳⠤⣠⠀⠐⣄⡠⠤⣀⡀⡀⠀⠀⣤⠀⠀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣇⢀⡞⠁⡰⠋⢀⣤⣤⣄⠀⠈⡷⠊⣀⣀⠀⠀⠉⠣⡀⠀⠻⣀⠀⢹⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀ ⠛⢇⠙⢦⠀⠀⠀⠁⣀⠀⠀⠀⣠⠶⡏⢿⠇⢀⡇⠀⢺⢸⣿⣏⡇⢰⠁⡾⣿⣶⣷⠀⠀⠀⢣⠀⠀⠈⠃⡼⣧⣹⠀⠀⡇⠀⠀⠀⠀⠀ ⠑⢄⠳⣤⠳⣄⡠⠞⣧⢀⡤⠚⠁⢸⠁⠀⠀⢈⡷⢄⡈⠓⠚⠋⠀⠘⡄⠙⠿⠿⠋⠀⠀⢀⡜⠀⠀⠀⡜⠁⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀ ⠣⡀⠛⢀⡀⠈⠁⣰⡿⠋⠀⠀⠀⠀⠇⠀⠀⠹⡀⠀⠈⠑⠦⣤⣤⠚⠙⢄⡀⠀⠀⡰⢾⠉⢓⣄⠀⠀⡇⠀⢀⣦⠀⡼⠁⠀⠀⠀⠀⡠ ⡀⠙⣄⠀⠙⠆⣰⠋⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢈⣱⠆⠤⠤⢤⡀⠀⠀⠀⠈⠉⠉⠃⣠⣿⠆⠸⠀⡼⠁⠀⠘⠛⡜⢹⡋⢦⠀⡠⠊⠀ ⣶⣦⣤⣷⡆⠀⣿⣿⣿⣭⣭⣭⣭⣿⡀⢀⡄⠀⠈⠉⠒⢦⠤⢤⣀⣀⡤⢤⣤⣴⣶⣿⣿⠏⠀⠀⠀⣇⡴⢆⠀⠀⣧⠤⣧⠈⠋⠀⠀⠀ ⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠛⠉⠁⠀⢣⠘⠓⢀⠀⠀⠀⢸⣀⣀⣿⡁⠀⢸⠟⠛⢛⡿⠁⢀⡀⠀⣠⢻⡀⣸⠀⢠⣷⣶⣾⣆⠀⠀⠀⢀ ⣿⣿⣿⣿⡇⠀⠿⠿⠟⠛⠊⣧⠀⢀⠏⢀⠞⠉⢣⠀⠀⠈⠻⣟⣁⣉⣁⣉⠤⠖⠉⠀⣰⠋⠙⡄⡇⠈⣿⠟⠒⠲⢿⣿⣿⣿⠀⠀⣴⣿ ⣿⣿⣿⣿⣧⣀⣀⣤⣤⣶⣾⣅⣠⣼⡀⠸⡄⢀⠎⠀⠀⠑⠤⠀⠠⠤⠄⣀⣀⡠⠄⠀⠻⠤⠞⠀⡧⠀⠹⡀⠀⠀⠀⡙⣿⣿⠀⢀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⡰⠃⠀⠀⠱⡀⢠⢏⠙⠻⡿⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠒⠢⠤⣤⠖⠦⣄⡀⢀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⡇⠀⠀⠀⣀⣿⣦⣴⣷⣄⠀⠀⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⠤⠤⠬⣷⣴⣋⡿⣏⣙⣤⣜⡛⠉⠀⠀⠉⠒⢺⠋⠉⣓⣫⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿ ⠒⠚⠛⠿⠯⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⡀⢸⣿⣟⠀⢹⣿⣿⡏⢉⣭⣿⣿⣟⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠒⠚⠛⠿⠷⠤⠽⠿⠿⣿⣄⣿⣿⣍⣀⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀

⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠚⠛⠛⢿⡀⠀⠀⠀⠀⣠⡿⠟⠛⠓⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢴⣶⣦⡹⡄⠀⠀⢰⠏⣴⣿⡿⠆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠸⣿⣿⡿⢣⡇⠀⠐⢸⡄⢿⣿⣿⣿⠀⢠⡟⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢶⡖⠒⠛⠉⠀⠀⠀⠀⠙⠶⢬⣭⣤⡶⠋⠀⣠⠞⠋⠁⠀⠀⠀⠈⠙⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠀⢀⣦⣤⣄⣀⣀⣀⡀⢠⣼⠀⣿⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⣀⣾⠟⠋⠉⠉⠉⠻⣿⣾⠇⢰⣿⡄⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢸⠟⠁⠀⠀⠀⠀⠀⢠⡾⠃⢀⣾⣿⠗⣿⡇⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣶⠋⣠⣤⣤⠤⠤⢤⡀⠀⠀⢀⣾⣿⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⢀⡀⡀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡟⣡⣾⠗⠓⢻⡼⠗⠳⣿⢦⠀⠈⠀⠹⣦⣠⡾⢋⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠚⠻⣿⠟⢰⣏⣮⠀⣾⣾⣡⣦⠀⢸⡞⡇⠀⠀⢀⣽⣯⡴⠿⠥⠽⠷⠤⣄⣀⣀⣤⠴⠿⠷⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⣸⠘⠮⢽⣿⠛⠻⠭⢤⠞⠀⣇⠀⠰⣿⠟⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠘⣆⠀⢺⣓⣶⣲⠤⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡞⣽⠫⠀⠀⠀⠀⠈⠳⢤⣒⣚⣛⣂⣤⠞⠁⠀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠀⠀⠀⣽⠇⠀⣰⠚⠓⣦⣄⣀⠀⠉⠉⠉⢁⣀⣤⠶⡖⠛⢶⡄⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⡟⠀⠀⠀⠀⢰⡏⠀⠀⠹⣦⣠⠇⠀⣹⠛⠛⡟⠛⢻⡇⠀⠀⣇⠀⣸⡧⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⣾⣇⡀⠀⠀⠙⠿⣦⣀⡇⠀⠀⡇⠀⠘⡇⠀⢀⣸⡾⠋⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⣷⠻⣧⡀⠀⠀⠀⠀⠘⠿⢶⡾⠤⠤⠤⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣽⡤⠾⠛⠷⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⡿⢶⠶⠶⠤⠤⢤⣶⡶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠈⣇⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣤⣴⣿⣿⠀⠀⠀⠀⠀⣗⡇⠀⡝⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠

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