⣿⣿⣿⡇⢩⠘⣴⣿⣥⣤⢦⢁⠄⠉⡄⡇⠛⠛⠛⢛⣭⣾⣿⣿⡏
⣿⣿⣿⡇⠹⢇⡹⣿⣿⣛⣓⣿⡿⠞⠑⣱⠄⢀⣴⣿⣿⣿⣿⡟
⣿⣿⣿⣧⣸⡄⣿⣪⡻⣿⠿⠋⠄⠄⣀⣀⢡⣿⣿⣿⣿⡿⠋
⠘⣿⣿⣿⣿⣷⣭⣓⡽⡆⡄⢀⣤⣾⣿⣿⣿⣿⣿⡿⠋
⠄⢨⡻⡇⣿⢿⣿⣿⣭⡶⣿⣿⣿⣜⢿⡇⡿⠟⠉
⠄⠸⣷⡅⣫⣾⣿⣿⣿⣷⣙⢿⣿⣿⣷⣦⣚⡀
⠄⠄⢉⣾⡟⠙❤️⠈⢻⣿⣷⣅⢻⣿⣿⣿⣿⣿⣶⣶⡆⠄⡀
⠄⢠⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣇❤️⠄
⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣎⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠄⠄⠻⢿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣾⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⡟
⠄⠄⠄⠄⢮⣭⣍⡭⣭⡵⣾⣿⣿⣿⡎⣿⣿⣌⠻⠿⠿⠿⠟⠋
⠄⠄⠄⠄⠈⠻⣿⣿⣿⣿⣹⣿⣿⣿⡇⣿⣿⡿
⠄⠄⣀⣴⣾⣶⡞⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠃
⣠⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡟⣹⣿⣳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠔⠁⠀⠈⠒⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠣⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⠔⠀⠒⠤⠒⠛⠳⢄⠀⠀⣀⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⡤⠐⣁⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠙⡆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣾⠀⠀⠠⠀⠀⠀⣶⠀⠀⠀⠀⠀⡢⠠⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡔⠁⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⠁⠀⠀⠀⠉⠀⠀⠀⠀⠐⠌⠀⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡗⠀⠀⠀⠀⠀⠀⢈⢻⠄⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠤⠤⠤⣼⣀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠑⢒⡒⠒⠈⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠁⠀⠀⠀⠀⠀⠉⠢⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡶⠒⠒⠒⠶⠤⣀⣀⡄⠀⠀⠉⡗⢦⣄⣀⣀⡀⠀⢀⣀⣤⠔⠋⠒⢤⣀⠀⠀⠀⠀⠀⣡⠏⠀⢈⡗⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⠃⣜⠣⢎⡭⢭⡙⠯⣍⠳⢬⡙⣄⠀⠀⠙⠻⠶⠶⠒⠋⠁⠀⠀⣼⡘⠧⡜⣩⢓⣦⣀⠀⠀⠀⠀⠀⠀
⠀⡝⠋⠉⠉⠑⠒⠦⣤⠆⠐⠋⠀⣏⡙⠶⣘⠦⡹⢜⢢⠛⢦⡙⣬⠛⡶⣤⣀⡀⠀⠀⠀⢠⡴⣞⢣⡹⢜⡡⢇⡣⢖⡩⠷⣄⠀⠀⠀⠀
⠀⢆⠀⠐⢄⣀⠀⣀⡰⠀⡰⠁⣸⢥⢋⡎⡕⢮⠱⢎⢣⠛⢦⡙⣤⠛⣔⠣⣍⠇⠀⠀⠀⠈⡖⡱⢎⡴⢋⡼⢌⡵⢊⡵⢣⢍⡳⣄⠀⠀
⠀⠀⠉⠒⠤⠤⠭⠭⣴⠋⠀⣰⢏⠦⣋⠴⡙⢦⠛⣬⣧⣿⠷⣉⠦⡛⣌⠳⣌⢻⠀⠀⠀⠀⠸⣑⠮⡔⣻⡜⡬⠲⣍⠲⣍⢲⠱⣙⢦⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠺⠾⠥⠯⠝⠒⠛⠉⢹⢆⡣⣍⠶⡙⡴⢋⡴⢋⡆⠀⠀⠀⠀⡇⢞⡱⣌⡷⡑⢯⡶⣩⢒⡍⢞⡡⢏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢎⡱⢜⠲⣉⠶⣉⠶⣉⠇⠀⠀⠀⠀⢘⡣⢖⠬⣻⣹⡟⡱⢆⡫⢜⢪⡱⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡹⢌⡳⣉⠶⣉⠶⣉⠆⠀⠀⠀⠀⢸⡔⢫⡜⣼⡟⡜⢥⢣⢣⢋⡖⣱⠏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣥⠫⣔⢣⢣⡍⠶⣉⠾⠀⠀⠀⠀⢸⡜⣥⡾⠛⢧⣙⣎⠲⣍⢲⣩⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⠺⠶⣧⣼⣣⣍⣾⠀⠀⠀⠀⠀⠋⠁⠀⠀⠈⠉⠉⠛⣴⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣟⣹⠀⢠⡔⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠢⢏⣛⠶⣦⣤⣤⣄⣤⣤⣤⣤⡶⢶⡛⢯⣙⠲⣡⠾⡄⠀⠜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢳⣉⠦⣋⠴⣊⠖⣩⢆⢳⡘⢦⡙⢦⣙⠲⣌⠳⣡⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⡲⢌⡣⣍⠶⣉⠞⣡⠞⣢⣿⢣⢚⢥⠪⣕⠪⡕⢣⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣘⠲⡍⡖⡜⡲⣉⢮⡑⣎⡿⣑⠮⡱⢪⢕⠪⣕⡩⢇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢎⠵⡚⡜⡴⢣⢍⠦⣓⡾⢿⣘⠲⣍⢣⢎⠳⣌⠶⡩⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡱⢎⢣⡕⠳⣌⡓⢎⡵⣺⠁⢸⣌⢳⡘⢦⡙⠮⡔⣣⠝⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡖⢭⢲⡘⡳⠬⡜⢣⢲⠇⠀⢸⡎⣕⠪⣕⠪⢇⡳⢌⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠱⢎⡣⢖⡩⢖⡹⣘⢣⡟⠀⠀⢸⡳⢌⡳⢬⡙⢦⢃⡏⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠫⢖⡩⢖⡩⢖⣡⠓⣾⠁⠀⠀⢸⡣⣍⠶⡑⢮⡡⢏⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣌⠳⣉⠶⣉⠶⣉⠦⣻⠃⠀⠀⠀⢸⡱⢜⠲⣙⠦⡱⢎⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢌⡳⣉⠶⣉⠶⣉⣶⠏⠀⠀⠀⠀⢺⣵⣍⣞⣡⣞⣱⣎⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣥⣷⣭⡶⠛⠁⠀⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠟⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀