Scuba Diving Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⠖⠒⠲⢜⡆
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣇⣤⣄⡀⠀⠹⡄
⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⢠⠊⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣶⣶⣾⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠈⠉⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣶⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠤⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡤⡶⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠏⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣇⠀⡀⠢⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢦⣌⠢⣄⡐⠈⠀⢌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡄⠴⠈⠀⠀⠀⠉⠓⠶⣭⣑⢮⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⢫⠿⢹⠁⠀⡀⠀⠡⠀⠀⠀⠀⠀⠙⢾⣇⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣋⣠⠏⠀⠀⠀⠀⠱⡐⠀⠀⠀⣀⡴⠯⢭⠽⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡟⠀⡴⣫⠭⣕⣦⡀⠀⣠⣿⡻⠛⠷⣦⠀⢤⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠁⢸⢱⠃⠀⣀⢻⠹⡝⣧⠁⢠⣦⠈⢊⢷⠆⠂⣲⠹⡄
⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠦⠼⠾⠷⣏⡈⡏⠳⠛⠭⢳⣌⠉⠀⠀⢊⠇⠀⢻⠀⡷
⠀⠀⢏⠈⢉⣙⣒⣒⣋⡥⠴⣶⠿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠼⠧⢤⣤⣤⠴⠒⠉⠉⢳⢳⢳⡥⠀⠠⣹⡄⢿⠇⠈⢠⠁⠁⣰⠃
⠀⠀⡼⠀⡄⠀⠠⡏⠀⠀⣸⡄⠀⠈⠳⣄⠀⠀⠀⢀⣠⡞⢳⡚⠉⠁⠀⠀⢀⡨⠗⠻⣄⣳⣍⠓⢎⡹⣜⢀⡀⣰⣞⣠⠶⠃
⠀⠀⢇⣀⣁⠒⡄⢳⡶⠋⠀⠹⡄⠀⠀⠈⠲⠖⠋⠉⠀⢣⠀⢣⠠⠄⠒⠈⠁⢀⠒⢄⠀⡷⣬⠗⠢⠤⠜⠋⠙⠓⠙
⠀⠀⠀⠀⠈⡇⢷⠟⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢢⠀⠀⠀⠀⠀⣁⣥⣞⠁⠈⠳⣄⣀⣀⣠⡴⣻⣤⣤
⠀⠀⠀⠀⠀⠥⠋⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠤⠤⢴⡤⠀⠀⢳⡀⠳⣤⠤⢖⡯⠟⠉⠈⠳⣄⠀⠀⠀⠀⠀⢹⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⡟⠉⠙⠒⠒⠒⠒⠉⠀⠀⠀⣠⠟⠙⠓⠚⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠉⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⡟⠀⣇⡀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⡤⢚⠥⠊⡼⠀⢀⡏⠉⠉⠙⠛⠒⠒⠚⠉
⠀⠀⠀⠀⠻⣄⠓⠒⡂⢇⣀⡜
⠀⠀⠀⠀⠀⢸⠀⣔⠥⠆⣽⠃
⠀⠀⠀⠀⠀⠀⠓⠛⠲⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣦⡀⠀⠀⠀⣰⢶⣶⣶⡄⠀⠀⣾⣷⣿⣿⣿⣿⡿⠇⠀⢀⣀⣀⣠⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣈⣻⣶⣾⣿⣿⠿⠿⣏⠀⠀⠀⠉⠙⢿⣿⣿⡿⡿⢿⠿⠿⠟⠛⠷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠤⠶⠛⠛⠃⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢸⣿⣿⣷⡄⠀⢀⣿⣿⣿⠁⠀⠀⢀⣠⡤⡖⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⢧⠀⠠⢾⣿⣿⢻⣿⡀⠸⣿⣿⡿⠀⠀⠈⠉⠉⠀⠀⣀⡀⠀⠀⢰⣧⡴⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠀⠈⢀⣠⣾⣿⠿⠋⠿⠃⠀⢻⣿⣇⠀⠀⠀⠀⠰⠾⠿⠋⢀⣠⣴⡾⠃⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣷⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠀⢠⣀⠀⢀⣠⣿⡟⠋⠀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠹⣦⠀⠀⠀⢀⡞⠀⠀⣿⡀⠀⣸⢿⣿⣿⠿⢻⡀⠀⠚⠉⠩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⢀⣿⡄⠀⠀⠸⡇⠀⠀⣿⠃⠀⠘⢾⠁⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠳⣄⡈⢷⡀⠀⠙⠛⠛⠁⠀⣢⠆⠀⠀⢸⡏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣷⣽⣤⠀⠀⠀⠀⠀⠀⠈⢧⡀⣷⣄⠀⠀⠀⠤⠴⣿⣶⡶⠆⠘⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⡌⠙⠳⠶⠦⣤⣤⣀⠀⠀⠈⠛⢻⣿⣿⣷⣦⡀⠀⠈⠉⠀⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⣦⣄⡀⠈⠛⠿⡿⠀⠀⠀⠉⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠃

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠛⠛⠛⠓⠒⠦⣄⢰⠋⣳⠀⢀⣀⡀⠀⠀⠀⠘⢦⣀⣀⣠⠞
⠀⠀⠀⠀⢠⡏⠁⠈⢳⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⡠⡀⠀⠀⠈⢻⡍⠁⢰⡋⠀⠙⡆⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠧⣄⣠⠞⠀⠀⠀⢸⡯⠴⢎⣀⣀⠄⡊⠀⠈⠱⡀⠀⣀⣷⡎⡢⠓⠒⠚⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠖⠒⢆⠀⠀⠀⠀⢀⣼⣷⣶⡶⠖⠚⣛⣻⢟⢿⣦⠗⠉⠁⣿⡉⣁⠀⠀⠀⠀⠀⠀⣾⠀⢸⠆
⠀⠀⠀⠘⠦⠤⠎⠀⠀⠀⠀⢸⣿⣿⠉⡔⠊⠀⠀⢐⣲⢱⢻⣇⠴⠚⣿⠟⠛⢿⣦⠀⠀⠀⠀⠈⣉⡉⠀⣠⢤
⠀⢀⡔⠒⡄⢀⣀⠀⠀⠀⠀⠀⢿⣿⣆⣱⣩⡿⢿⣦⣤⣾⡿⠁⠀⣰⣿⣶⣶⣾⣻⠶⢤⡀⠀⠘⠧⠞⠀⡈⠁
⠀⠀⠓⠖⠁⢯⣀⡇⠀⠀⠀⠀⠀⠙⠻⣟⢋⣠⣤⣍⠉⠁⢀⡠⠾⠗⠛⡖⠲⢤⡀⠀⠀⠙⢦⠀⠀⢰⠋⠉⢱
⠀⠀⠀⡠⢤⠀⢠⢄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠶⠞⠉⠀⠀⠀⢠⠁⠀⠀⢳⡄⠀⠀⢸⡆⠀⠈⠳⠤⠞
⠀⠀⠀⠈⢊⣀⣨⣥⣀⣀⠤⣄⡀⣼⣿⣿⡿⡿⠭⠭⠥⠵⠶⠶⡄⠀⢸⠀⠀⠀⠀⣷⠠⠤⢸⡇⠀⠀⠀⢠⠖⠲⡄
⠀⠀⣠⣾⣿⠿⠾⠷⣿⣋⡓⠦⣝⠳⢿⣿⠃⡄⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⣿⢠⣬⢼⡇⠀⠀⠀⠹⣄⣠⠎
⣀⠾⣷⣿⢶⠀⠀⠸⣟⠦⣭⣙⡂⠀⠀⠛⢄⢉⡉⠉⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⠀⣿⢚⣻⣻⡇⠀⢠⢤
⠣⠋⠛⡅⢸⡀⠀⠀⠈⣹⠖⠂⠤⢄⣀⠀⠸⠀⠈⡋⠐⠂⠠⠤⢀⣀⣘⠀⠀⠀⠀⣯⢭⡉⠉⡇⠀⠈⠊
⢚⡉⣈⣦⠀⠙⢛⡛⢯⡉⠀⠀⠀⢠⣿⣿⡿⢃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣱⠀⡇⠀⢠⠤⡀
⠀⠹⣿⣷⣤⣀⠼⠃⢀⡇⠀⠀⣰⠋⣿⣿⣇⠀⠀⠈⠐⠂⠤⢀⣀⠀⠀⠀⠀⠀⣠⣯⠔⠁⠀⡇⠀⠈⠚⠁
⠀⠀⠈⠙⠻⠿⠶⠶⠾⠓⠒⠋⠁⠀⢻⣿⣿⡂⠀⠄⠠⠠⣤⣤⢤⡾⢛⠷⣶⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣷⣶⣟⠥⣬⢽⠀⠀⠀⣿⠿⡩⢻⡉⠉⠁⣿⠀⠀⠀⠀⢀⣠⠞⠛⠨⡙⣆
⠀⠀⠀⠀⠀⠳⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠭⣉⠙⠒⠀⠚⠳⠶⠞⡣⠊⠀⠘⡇⠀⠀⣿⠀⠀⢀⡴⢏⠉⠑⡄⠀⢁⣽⡄
⠀⠀⠀⠀⠀⠠⡦⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠉⠒⠤⣀⠀⠀⠌⠀⠀⠀⠀⢷⠀⠀⣿⢀⡴⠋⠀⠀⢈⣿⣤⣤⣾⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣆⠀⠀⠀⠀⠉⢚⠀⠀⠀⠀⠀⢸⡦⣠⡾⠋⠀⠀⢀⡴⠉⡏⢸⢩⠁⢰⠈⣧
⠀⠀⠀⠀⣞⢹⠀⠉⢉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢿⠋⠀⠀⢀⡴⠋⠀⢠⡇⢸⠈⣦⠈⡀⠸
⠀⠀⠀⠀⠈⠁⠀⢈⣿⣧⡤⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠀⠀⣠⠏⠀⠀⠀⢸⡇⡘⠀⢿⠀⢃
⠀⠀⠀⠀⠀⣦⠀⠘⣿⢞⣃⠀⠀⢀⣀⣬⣾⣵⠆⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⠁⡃⠀⢸⡆⠸
⠀⠀⠀⠀⠀⠀⠚⣧⣾⣵⡮⠁⠀⢺⣯⡤⠛⠋⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠑⢤⡤⠴⠊⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢸⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠛⣧⣽⡇⠀⢰⣿⡿⠀⠀⣿⣶⡿⡆⠀⠀⠀⠀⠈⠷⣄⣀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣁⡀⢸⡇⠀⢃
⠀⠀⠀⠀⠀⣤⢤⠀⠉⠿⣷⣄⣿⢷⣳⢐⢾⠻⣞⠻⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠙⣾⡟⠉⠻

⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡄⣤
⠀⠀⠀⠉⠻⢿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣶⣿⣷⣿⣦⡀⢐⣤⣀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⢀⣨⣿⣙⠻⢿⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢀⡠⠤⠖⠛⠉⠉⠛⢿⣶⣿⣿⣿⣦⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣶⣦⡀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠛⠃⠀⠀⢸⣿⡿⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣼⡟⠹⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣬⡿⢿⣿⣿⣿⣿⣿⣷⣾⣿⠁⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠙⠻⢿⣿⣉⡉⠙⠉⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣤⣠⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⠂⠀⠀⠈⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠏⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⡿⠟⠙⣿⣿⣿⠛⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣴⣶⡿⠟⠛⠉⠉⠁⠀⠀⠀⢘⣿⣿⠆⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡀
⠀⠀⣼⣿⠋⠀⠀⠀⠀⢀⣴⣿⣷⣾⣿⡿⠿⢿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣏⡀
⠀⣾⣿⠏⠀⠀⠀⠤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦
⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⡿⠉⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣿
⠀⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡟⠿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⢸⣿⣿
⠳⣾⣷⣄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣤⣈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⢸⣿⡿
⠀⠀⠀⠙⠿⠏⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠋⠙⠛⠿⣿⣷⣤⣄⣠⣤⣾⠟⠁⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠏⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡛⣽⢳⣴⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣗⡹⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡿⠟⢯⣿⣿⣿⣿⣿⣿⣿⣧⠇⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣤⡴⣚⢻⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⢍⣜⢿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠇⣵⠀⢀⣿⠃⠈⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⠋⢀⣼⣿⠀⠀⠀⠀⠈⠉⠀⠉⠙⢷⣄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⡀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⢀⣴⡿⠋⠀⣰⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⣴⠿⠋⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠈⠁⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⢄⠀⠈⠓⢿⡦⢔⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠠⠤⠤⠀⠐⠒⠐⠒⠒⠒⠒⠛⠚⠢⢄⡀⣂⠌⠀⠀⠘⢣⢋⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢗⡀⡠⠀⠀⠀⠀⠀⠀⠀⠐⡤⠄⣀⠀⠀⠀⠀⠀⡰⠙⡁⠀⠀⠀⠰⡀⢉⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⡔⠉⠀⠀⡠⠊⠉⠒⠒⠉⠀⠀⠰⣠⠐⠉⠒⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⣄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⡩⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁
⠀⢀⣀⠠⠤⠤⠤⠤⠤⠀⠀⠠⠤⠀⠀⠠⡄⠠⠤⠀⠒⠂⠀⠉⠐⠒⠂⠩⠁⠀⠀⠀⡰⠁⠀⠀⠰⡀⠀⠀⠀⠀⢀⣀⠤⠐⡢⠂
⡎⠁⡠⠤⠄⠐⠒⠒⠒⠂⠀⠐⠄⠀⠀⣈⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⢠⠀⠀⡠⠊⠀⠀⠀⠀⠀⣱⠄⠒⠈⢁⠔⢁⡠⠊
⠱⡀⠢⠀⠀⠀⠀⠀⠀⠀⣀⣴⠮⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⡠⠚⢡⡄⠀⠐⡁⠔⠁
⠀⠸⠀⠇⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠠⢀⣀⠔⠉⠀⠀⣞⣷⡠⠜
⠀⠘⣀⣑⡠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⡁⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡉⠔⠉⠉⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢁⡠⠊⠀⠀⠀⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠔⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠤⢀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⠡⣀⢌⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠶⣦⣄⣀
⠀⠀⠀⠈⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠉⣻⣷⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣀⣠⡄
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦
⢀⣀⣤⣴⣾⣿⠟⠋⠉⠉⠉⠙⠿⢿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠈⠙⠛⠛⠻⠿⣿⢿⣿⠋⠉⠉⠛⠋⠉⠛⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⠀⠀⠸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠗






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣴⣶⣶⣶⣶⣶⣦⣶⣶⡤⢄⣤⣄
⠀⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣄⣹⣿⣷⡀
⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣏⢻⣿⣿⣿⣗⣀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣝⠺⣿⣷⣤⣶⣄
⠀⣌⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣌⣻⣿⣧⣀
⠐⠛⠿⣷⢹⣿⣿⣿⣗⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⡅
⢀⣄⣠⣿⣶⣤⣝⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⡃
⠀⠙⠿⣿⣍⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠳⣀⡀⠀⣀⠀⠀⠀⠀⣶⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴
⠐⣾⡷⡎⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣶⣦⡰⣄⣿⣿⣿⣿⣶⠀⠀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠈⠠⢀⣬⣿⣿⣿⣿⣿⣿⣻⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣤⣬⣿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡼⢾⣿⣿⣤⣿⣿⣿⣿⣿⣟⣽⡾⣷⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣤⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣤⣀
⢀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣁⡿⢤⡙⢿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠑
⠀⠈⠉⠙⠳⢶⣤⣀⡀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠈⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣾⠃⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡳⢤⡀⠀⣸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣈⣻⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡴⠚⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣦⣀⣀⣤⣤⣶⣶⣶⡶⠾⠛⠛⠛⠛⠻⠿⠿⣿⣿⣛⠛⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣦⡀⡱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢤⠀⠓⠲⠤⠀⢈⡀⠠⠄
⠁⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠁⠀⠐⠀⠙⣴⡀⠀⢶⠼⣇⣀⣀⡀⠰⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢐⡀⠄⠞⡩⢷⡂⠘⡆⢨⣀⡀⠙⠟⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠡⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠀⠂⠠⠐⠀⠈⡲⡷⣴⠼⡉⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢂⢀⠀⢀⡤⠒⠉⠉⠝⠢⠀⠀⠀⠀⠸⠀⠀⢠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠠⠉⠂⠀⠊⠀⠀⠀⠀⡶⡀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠆⠴⠀⠀⠐⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⠠⠊⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡰⠋
⠀⠀⠀⢀⠀⠄⢂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣤⣤⣄⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣥⣤⣭⣭⣿⣿⣧⣶⠾⠶⢷⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⡿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣠⣾⡟⠁⠀⢀⣠⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⢻⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣾⠋⢀⣾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣏⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣹⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠟⠉⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡿⠋
⠀⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⣀⡈⠙⠛⠛⠻⣿⣇⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⡆⣠⣤⣀
⠈⠻⢦⣄⣀⣀⣀⠹⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠉⠛⠿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠁⢢
⠀⠀⠀⢀⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⠄⡐⠂⢨⡥⠀⠚⠠
⠀⠀⠠⠁⠀⠀⠀⠉⠒⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⣁⣀⢠⠀⠀⠀⠤⠀⢰⠔⠦⡀
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠉⠐⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠁⠀⢄⢄⠀⠒⣠⠏⠀⠀⡨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡁⢀⠔⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠁⠑⢉⣡⢖⠀⠉
⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⠗⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢤⠀⢄⢘⠩⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡄⠀⠢⢠⠞⠳⠂⠐⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢆⠀⠑⣄⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠊⡂⢠⠀⠀⠈⡄⠀⠀⠀⠀⠠⠡⠊⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠄⣀⠬⠃⡀⠀⠀⠀⠃⠀⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠦⠀⠨⠐⠀⢣⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⠑⠦⣀⠀⠀⠀⠀⠠⠃⠀⠣⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠀⡁⠀⠀⠀⢈⠵⠶⢤⣄⣈⣹⡈⠙⢄⠀⠀⠀⠀⠀⠀⠉⢓⡶⠶⠶⠒⠂⠁⠀⠠⠠⠂⠈⡂
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠠⠁⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⢉⠟⠉⠀⠀⠁⠐⠀⠀⠀⠲⢾⠉⠀⠀⠀⠀⠁⠀⢒⠁⠀⠚⠭⠁
⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⠔⠛⡀⠈⠀⠄
⡠⠐⠉⠀⢀⠔⠀⠀⡠⠊⠀⠀⠀⠈⠉⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢁⠀⠀⠊⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠢⡀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠸⠂⠦⡤⠀⢉⠀⠡⠄
⠁⠀⠀⠀⠀⠘⠠⠀⣀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠃⠀⠑⠀⠐⣂⡍⠀⣠⣔⣿⣀⢀⡀⠀⠴⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⡀⠄⣀⠁⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⠀⠀⠀⠀⠀⠈⠀⡠⠠⠞⠻⡤⠀⢣⠀⡏⠀⠉⠳⡺⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠄⠀⠀⠀⠰⢆⠁⠀⠀⠀⠀⠀⠀⢀⢀⠠⠐⠁⠐⠀⠈⠄⠈⠲⣼⣄⣌⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢄⠀⠀⠈⡀⠀⠀⠀⣀⠤⠒⠚⠺⠅⠀⠀⠀⡇⢀⡆⠀⠀⣈⠌⠈⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⢀⠚⠀⠈⠕⠀⠀⠀⠐⢤⠂⠀⠀⠀⠠⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⢀⠌⠀⠀⠀⠀⠀⡊⢁⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠐⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠉
⠀⠀⣀⠠⠀⢂⡡⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠀⠰⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⣴⡾⠿⣶⣀⣀⣤⡾⠿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⠞⠉⠀⠀⠀⠀⡍⠉⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣤⡾⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⣠⡾⠁⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡾⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⠶⠀⣠⠶⠆⣸⠟⠁⠀⣰⠟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠞⢁⣠⠞⠁⠀⠀⡴⠃⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡜⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠋⢠⣴⣞⡉⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢠⡴⢿⣥⣀⠀⠈⠉⠙⠳⠶⣤⣾⣿⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠰⣮⣥⣤⡀⠈⠙⢷⣶⣶⡶⠶⠾⢿⡋⠀⠀⣠⣼⠷⢶⣤⣤⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠀⠉⠙⠛⣶⣿⣿⠋⠀⠀⢀⣾⣿⠟⠛⢉⣤⣶⣿⠿⠿⠛⠻⣷⡄⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⢰⣿⣿⠁⠀⠀⣠⣿⣿⠋⢀⣾⠿⠟⠋⠁⠀⠀⢀⣠⣼⣿⡄⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⡏⠀⠀⢠⣿⣿⣧⠞⠋⠁⠀⠀⢀⣠⣴⣾⣿⣿⠟⢻⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⣤⣤⣾⡿⠉⠀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠋⠁⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣾⣿⣿⠿⠿⠛⠉⠁⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣶⣦⣤⣤⣤⣶⣶⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠛⠛⠛⠿⠛⠉⠁⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣶⣤⣤⢀⣠⡤⠀⠀⠀⠀⢀⣴⠟⠋⣉⣤⣀⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠛⠛⠋⠑⠋⠁⠀⠀⠀⠀⣴⠟⠁⣠⠞⢛⡝⠋⠀⣈⣤⣄
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣤⣀⣀⣀⣤⣤⣤⣶⡇⠀⠀⠀⣼⠇⠀⠘⠁⠐⠊⠀⣰⣾⠋⠉⠹⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠰⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣶⣠⡟⠁⠀⠀⠀⢀⣀⣀⠀⢀⡀⣸⣇
⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣀⣀⣀⣀⡠⠤⠠⢶⣾⣿⣿⣿⡟⠀⠁⠔⠀⠰⠏⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⢻⠋⡩⠽⣇⠀⠀⠀⠀⠀⠀⢤⣤⠂⠀⠐⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠉⠉⠉⠙⣄⡀⠀⠀⠱⣾⢀⡐⠀⡌⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⢙⣦
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣴⣿⡇⠀⠀⠀⢹⣿⣷⣄⠁⠀⠀⠀⣰⠿⠋⠉⠀⠀⠰⠟⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠿⢿⡇⠀⠀⠀⠀⠛⠀⣿⠃⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⡜⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣾⣇⠀⠀⠀⠀⣷⣶⣿⣇⠀⠀⠀⠀⠈⠳⢄⣀⣀⠴⠛⣠⡟
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇⠀⠀⠙⢷⣄⡀⠀⠀⠀⠛⠉⠉⣠⡾⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⣅⠀⠀⠀⠀⠙⣿⠛⢷⡖⠒⠒⠉
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢹⣆⠀⠀⠀⢸⣿⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠹⣧⠀⠀⢰⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢻⡀⠀⠀⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠿⠀⠀⣀⡤⠤⠒⠛⢋⠉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⡇⠀⠀⢻⣇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠌⠀⠒⢛⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢠⠀⠀⠈⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣈⣁⣤⡤⠒⠒⠉⠉⠀⡉⠈⠉⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⡇⠀⠀⢙⡇⠀⣇⣰⠶⡆
⠀⣤⡤⠶⠖⠋⠉⠁⠀⢀⣀⣤⣴⣶⣾⣿⣶⣦⣄⣀⠀⠉⠻⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣤⡴⠲⠻⢧⣤⠿⠋⢸⣧⡴⠛⣿
⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈⠀⠀⠀⣀⣠⣤⠶⢋⣁⠴⠞⠁
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⢇⠀⠀⢰⠋
⠈⠛⠛⠋⠈⠛⠿⣿⣿⠿⠟⠛⠛⠉⠁⠀⣀⡀⠀⠤⠤⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣀⠘⣇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠖⠛⠀⠀⢀⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⡀⢰⠉⡄⢻⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⢸⠀⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢾⣀⣧⣤⣽⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠋⠉⠛⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣴⣦⣴⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣾⣤⡝⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣾⣿⣿⣏⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠙⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢨⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⢁⣀⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡏⢀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⣤⣆⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣖⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠙⠁⠀⠀⢉⡙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡹⣦⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢹⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⣠⠔⣆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⡇⠀⠀⠀⠀⢰⣦⠀⣹⠀⠀⠀⠻⠷⠏⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣄⠀⠀⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠼⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣠⠔⠀⠋⠀⠈⠱⣶⠊⢀⡀⠀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠛⠓⠒⠊⠉⢈⠇⠀⠀⠀⠐⣦⡀⠈⠒⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⣀⣄⣀⣀⣀⠀⠀⣀⡼⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⡤⡄⠀⣾⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠚⠉⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⢺
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡔⠁⠀⠀⣠⠶⠒⠲⣶⠒⠴⠶⠚⠉⠢⡤⣤⡄⡤⠔⠻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⡰⠊⠉⠈⠳⡄⠈⠙⠓⠶⠶⣄⠀⠀⠀⠀⣠⡄⠀⠘⢆⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠱⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠙⣆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⢠⠶⡄⠀⠐⢀⡴⠋⠀⠀⠀⠙⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣡⣤⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⢀⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⢀⣴⡿⠡⠆⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⡄⠀⠀⣸⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⢠⣾⡟⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⠏⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⣼⠻⡴⢋⣰⣿⠟⠀⠀⠙⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡼⠃⠀⠀⠀⠀⠛⠀⠈⠻⢦⣀⠀⣸⡿⠀⠙⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⡏⠀⠀⠀⡰⠚⠛⢦⠀⠀⠀⠀⠙⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠞⣻⡷⠀⠀⠀⢀⡠⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠊⠀⠁⠀⠄⠀⠀⠀⣎⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠀⠀⠀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⠟⡻⢻⡿⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣦⣤⣶⣿⣶⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣃⡈⠁⠛⠿⣿⡀⣥⠀⠠⡀⠀⠈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣠⣴⣼⠾⠁⠈⢿⣿⠗⣲⠲⢾⡇⢩⠂⠐⡃⠀⠀⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⣠⣤⣬⡾⠿⠏⡀⢀⢄⠀⣣⣼⡿⠓⠃⠈⢂⡀⢀⣽⠊⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠛⠉⠉⠠⢁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⡌⠳⢫⣿⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⡀⠀⠀⣠⣿⣻⣿⣶⣤⡤⢀⣀⣤⣤⣶⢍⣐⣠⣿⡏⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢸⣠⣾⣿⣿⣿⡿⠟⠋⠀⠀⢉⡁⠀⠁⠛⠛⠛⠋⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠒⠁⠀⠀⡴⢾⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⣀⣀⣀⣠⡤⡤⠤⠊⠀⠀⢙⡿⠟⠁⠀⠀⠀⣀⣀⣤⡄⠀⠀⠘
⠀⠀⠲⠀⠀⠀⠀⠉⠀⠀⣤⣤⡖⠊⠀⠈⠉⠉⠁⠉⠀⠀⢀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠘⠂
⠀⠀⠀⠈⢆⢹⣦⣄⣀⣴⢿⣥⠖⠃⠙⠒⠒⠒⠒⠂⠐⠈
⠀⠀⠀⠀⢠⡯⣿⣿⢋⣴⠟⠁
⠀⠀⠀⢀⣎⣀⡿⠟⠋⠁

⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠏⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡴⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢠⠞⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣰⠏⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡟⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠚⢠⠏⢀⡶⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣴⠋⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⣤⣤⣤⡀⡞⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢡⠞⠁⠀⠙⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠋⠁⠀⠋⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⢀⣠⡶⠾⠛⠛⠛⠻⢶⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀
⠀⠀⠀⠀⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⢸⣿⣿⣿⡷
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠒⢶⠀⢸⣿⣿⡿⠁
⠀⠀⠸⠀⠀⠀⠀⣀⣀⠤⠤⠤⣄⡀⠀⠀⠀⢷⠀⣿⡀⠸⡟⠉
⠀⠀⠀⠀⣠⠖⠉⢧⣀⣀⡴⠒⠋⠙⠶⣄⠀⢸⡇⠀⣹⠂⣿
⠀⠀⣧⠘⠁⠀⠀⠀⠉⠉⠀⣀⣠⠀⠀⠘⢆⠸⣇⠼⠃⠀⣿
⠀⠀⠸⣇⠀⢀⣀⡀⠀⠀⠙⠁⣀⠀⠀⠀⠘⣠⠃⠀⠀⠀⣿
⠀⠀⣀⠙⠷⡈⢉⡉⢣⠀⠀⠀⠉⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿
⠀⠀⠉⠛⢤⢅⠈⠉⠀⠀⠀⢀⣀⣤⠀⠀⠀⡿⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⣌⠁⠤⣀⣐⠛⠿⠿⠋⠀⢀⡼⠃⠀⠀⢠⡟
⠀⠀⠀⠀⢀⡏⠀⠀⢸⡏⠈⠁⠒⠒⠚⢁⠃⠀⠀⢀⡿
⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⡞⠀⠀⢀⡾⠁
⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⠀⠀⢀⡞⠀⠀⢠⡟
⠀⠀⠀⠀⠈⡇⠀⠀⣿⠀⠀⠀⢀⠎⠀⠀⡠⠋
⠀⠀⠀⠀⠀⣷⠀⠀⡏⠀⠀⣠⠋⠀⢀⡞⠁
⠀⠀⠀⠀⠀⢻⡀⠀⣇⣴⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠸⣧⣦⡅⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠹⣎⣠⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣧⣤
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠳⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡋⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣿⣟⠿⠇
⠀⠀⠀⠀⢰⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣿⣿⣧
⠀⠀⠀⠀⢸⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠿⣯⡉⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠻⣷⡶⠖⠚⠛⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠸⣧⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣴⣄⣾⣿⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢰⠉⠉⠻⠿⠟⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣤
⠀⠀⢀⡿⣿⣿⣿⣿⣿⣯⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⣾⣿⣿⣿⣿⣿⡻⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣏⠹⡀
⠀⠉⠛⠛⠀⠹⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⣿⠻⣿⠈⠃
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⣿⡿⠿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠀⣣⠀⠀⠀⠀⠀⠀⣀⡴⠇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⢴⡿⠋⠀⠀⠀⠀⢻⣷

⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣠⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣀⣤⣤⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣴⣾⣿⠟⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⣀⣴⣿⣿⠟⠁⠀⠀⠀⢀⣠⣾⣿⣦⡀
⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⣀⣴⣾⣿⣿⡿⠟⠛⢿⣿⣦⣠⣤⣤⣀⣀
⠀⠉⠻⣿⠟⠹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠈⣿⡏⠛⠻⠿⡿⠿⠿⠿⢿⣿⣿⡿⠛⠛⠿⠿⠿⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠂⢄⠀⢀⣶⠋⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣬⣦⣄⣙⣿⣿⣿⣇⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⣠⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠋⢀⣀⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⢰⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⠟⠀⠐⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠴⠟⠛⢦⣀⡤⠾⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣴⠶⠶⠤⠶⠈⠀⠀⠀⠀⡠⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠙⠂⠉⠀⠀⠀⠀⠀⢀⠄⠀⣴⠞⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠥⠀⠀⢀⣀⢀⣠⡖⠁⢀⡾⠃⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⢁⡠⠞⣩⡼⠋⠀⣠⡟⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣡⠞⠁⠀⠀⣰⠏⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡾⠁⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⣏⠀⠈⠙⠓⠲⢤⣄⣤⣶⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢤⣆⣈⡀⠉⠛⢷⣶⣶⣶⠤⣾⡟⠉⠀⢀⣨⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⡀⠀⠀⠈⠉⠙⠓⢶⣾⣿⠋⠀⠀⣼⣿⡷⠞⢋⣡⣴⣿⣿⡿⠿⢶⣄⠀⠀⠀⢸⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⣀⢠⣿⣿⠃⠀⢀⣾⣿⠏⢀⣴⡿⠟⠉⠁⠀⠀⢀⣼⣿⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡏⠀⠀⣼⣿⡧⠒⠋⠁⠀⠀⣀⣠⣴⣾⣿⠟⢻⡿⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠧⠤⢴⡿⠋⠀⣀⣠⣤⣶⣿⣿⣿⠿⠛⠁⠀⣸⠇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣶⣿⠿⠿⠟⠋⠉⠁⠀⠀⠀⣀⣼⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣸⠇⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠈⠉⠉⠀⠀⠉⠁⠀⠀⢀⣠⡴⠤⠤⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⠿⣧⠶⠛⠀⠀⠀⢀⣾⠟⢁⣤⣶⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢠⡿⠁⠰⠋⢠⠊⠀⣠⡴⠶⠦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠉⠉⠉⠉⠉⠁⠀⠀⢀⣧⣀⡼⠋⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⠀⢤⣶⣾⣿⣿⡿⠁⢋⡄⠀⡴⠋⠈⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⠛⠉⠿⢇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠈⠹⢀⡀⠀⠀⢢⢀⡀⠐⡬⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠘⢻⡄
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣤⣴⣿⡆⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠜⠏⠀⠀⠀⠀⠟⠛⠘⡏
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠛⢻⡇⠀⠀⠀⡇⠀⣯⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⠄⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⡇⠀⠀⠀⣿⠿⠿⣆⠀⠀⠀⠀⠈⣓⠀⠀⠐⠉⣠⠏
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⡁⠀⠀⠈⠳⣤⣄⣀⣀⣉⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢧⡀⠀⠀⠀⢸⣏⠉⢻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢳⡄⠀⠀⢸⣿⠀⠈⣧
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢷⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⣀⣤⠤⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⢸⡇⠀⠈⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠀⢀⣀⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⠀⢻⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠒⠉⠉⡏⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣿⠀⠀⠘⣿⠀⣿⢠⣤⡄
⠀⠠⠤⠔⠒⠋⠉⠁⢀⣀⣠⣤⣴⣶⣿⣶⣤⣀⡀⠉⠛⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣤⡤⠶⢿⣤⣿⠞⢺⣃⣠⠖⣶
⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠉⠀⠀⢀⠀⡀⠴⢛⣩⡤⠞⠋
⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡀⠀⢰⠋
⠀⠈⠉⠀⠀⠉⠻⠿⠟⠛⠉⠁⠀⢀⣀⣠⠄⠐⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⡄⡦⢰⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡇⢸⢀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢷⡾⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⢤⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠐⠁⠀⠀⢀⠄⣨⠁⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡧⢁⠁⠀⠀⠀⠀⣈⠴⣶⠎⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠠⠁⠀⣠⣤⡾⠿⠕⠊⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⡤⠴⡂⠈⠀⠀⠀⠠⠐⠈⠄⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⢀⣤⡶⠆⡀⠀⠀⠀⠀⠀⠀⠀⡰⢭⡃⠀⠀⠉⠙⠒⠂⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠠⠂⠀⠠⠀⠀⠀⠀⠠⣸⢉⠋⠓⢂⢀⡀⠀⠀⠀⠀⠘⠛⢯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⢠⠁⠀⠐⣀⣠⣤⣀⠀⠀⢹⠉⢉⣩⢌⡤⠀⠀⠀⠀⠀⠀⠀⠈⡥⠱⡄⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠉⠥⠠⠀⠀⡀⢲⣶⠡⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠇⠀⠀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠄⠀⢄⣲⣤⣄⡼⠗⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⠛
⠀⠀⠔⠉⠀⡏⠀⠀⠀⠁⢶⣹⠆⠘⠁⠀⠀⠀⠀⠀⡁⠀⠀⢀⠠⠐⠁
⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⡄⠀⠄
⠀⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠋
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠁⠴⠀⠁
⠀⠀⠀⡤⣀
⠀⢀⣜⣿⡟⠁
⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿