Dairy Emojis & Symbols

⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠠⢐⣀⣰⠆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠄⠀⠀⠁⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠈⠉⠠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⢀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⡀⡀⠈
⠈⠀⢈⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠀⠠⠀⠰⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡲⠀⠀⠀⢆⡀⣠⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⢠⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠠⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠐⠄⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣉⣀⣈⡉⠤⢴⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⢀⠀⠀⠀⠇⠀⠠⠄⠀⠀⠤⢀
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⢂⢀⡄⢲⠐⠀⢀⡇⠀⠀⠀⠀⠆⡐⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡈⢀⢀⠈
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⡠
⠀⠀⠀⠁⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠒⠒⠓⠒⠉⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣉⣹⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⢲⣤⣶⣶⣶⣠⣶⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠆⡆⠀⠀⢴⡾⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡩⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢄⡟⠀⠀⣔⣀⠉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⢀⡿⠁⠈⠀⠁⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠠⣤⣼⠄⠤⠴⠤⢄⡀⠀⠀⠀⠀⣴⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⢛⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠓⠛⠚⠛⠛⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇
⡖⠈⠭⠭⠭⠭⠭⠭⠥⠤⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⢀⣀⣀⣀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⢀⡠⠄⠂⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡔⠀⠉⢀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠀⠀⠀⠁⠀⠀⡄⠰⠀⠀⢃⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⠸⠀⢸⠀⠀⠀⠸⠀⠀⡸⠃
⠀⢦⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠘⠘⣾⣾⠾⠬⠽⠴⠄⠚⢊⣉⣀⣐⡀⢲
⠀⠸⣄⣀⣀⠀⢤⠏⠀⠀⠀⠀⠀⠸⡀⠀⠊⠀⠀⠀⠀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠠⡈⢉⣩⡋⢻⣽⣇⣳
⠀⠀⠀⠈⠉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡷⠀⠀⠀⢀⡓⠠⡟⢙⣿⣀⣻⡭⠇
⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠂⠛⢯⢉⡤⠛
⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⡀⠀⠀⠈⢇⠀⣀⠤⠒⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣐⣒⣒⣂⣮⣁⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠠⠤⣀⡀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠳⠶⠂⠚⠚⠀⠀⠀⣨⡍⢐⢢⣤⠈⠓⠁⡔⠒⠒⠒⠒⠒⡄⠀⠰⡉⣁⠀⠀⢀⠸⠥⠤⠼⢇⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠊⠻⠜⠂⢦⠭⢛⡀⠀⣴⠂⡰⠂⠈⠀⠀⢸⠀⠀⣠⠋⡜⠻⣆⠀⣠⠛⡀⠀⠈⠁⣠⠔⠁⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⣀⢔⡎⢡⡤⠤⠐⢒⠶⠫⣁⣤⡀⠀⠀⠉⠀⠀⠺⠀⠀⢘⠀⢰⠧⠤⠼⠾⠧⢴⠧⠤⠶⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⢘⠉⠙⠶⠚⠙⡄⠀⠘⠤⠔⣇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠢⡀⠇
⠀⠀⠘⠘⡀⠘⠒⠊⠀⠀⠀⠀⠀⢥⡠⠇⡠⣠⢤⣄⣀⠤⠔⠒⠊⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠔⠓⠉⠈⠁⠀⡔⠒⠒⠢⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠸⣼⣀⠠⠄⠒⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡴⠁⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠒⠒⠒⠀⠀⠀⠐⠒⠒⠀⢀⣤⡀⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⡠⠃⡄
⠀⠀⠀⠀⠀⢸⠀⠈⢉⢍⣑⣒⣒⣒⠒⠀⠈⠉⠉⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠸⢿⣃⣠⣮⢿⠀⠀⠀⠀⠀⠀⠀⡏⠲⢄⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⡇⢰⣦⣶⢰⢴⠀⣤⡴⠀⢽⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠈⠱⣄⠀⠀⠀⠀⠀⠀⣇⡰⠋⠉⡆⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢇⠈⠁⠉⠈⠙⠓⠉⠙⠀⣸⠀⡇
⠀⠀⠀⠀⢀⠎⠁⠒⠒⠀⢴⡦⠤⠤⠤⠷⢤⠀⠒⠂⠉⠏⠀⠀⡰⠁⢸⡀⠀⣀⠀⡀⣸⠀⢀⣀⠀⠈⠢⣈⡉⣉⣉⣉⣉⣉⣉⣉⢉⣁⠔⠁
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⢄⠀⣞⡂⢂⡴⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋⢃⠀⢠⠤⢄⠀⢙⣂⣀⣐⡃⠀⠀⠈⣇⣀⣀⣺⠁⠀⠀⢹⣂⣀⣐⡃
⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠑⠁⠀⣈⣉⣉⣉⡁⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⢨⣉⣉⣉⡇
⠀⠀⠀⠈⠑⠒⠠⢤⣇⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⡎⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠀⠀⠀⠀⠀⣆⣠⠇⠀⠀⠀⠀⢱⣀⡘⠀⠀⠀⠀⠀⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠃⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠊⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠐⠒⠚⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⡄⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠠⠠⣤⡄⠄⠀⠀⠀⠀⢠⠄⠇
⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⠤⠀⠤⠤⠤⠠⠀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠯⠠⠀⠄⠄⠀⠀⠀⠀⠠⠀⠀⠤⠀⠄⠄⠀⠠⠄⠠⠀⠀⠀⠀⠠⠅

⠀⠀⠀⡶⠛⠛⠉⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠒⠒⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠁⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣛⣷⡆
⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡁⠐⠶⣿⣧⣤⣤⣤⣤⣤⡤⠤⠤⠄⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠛⠛⠛⠶⣄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠑⢄⠈⢷
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡆⠘
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⢠
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⣼⢃⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⣠⠀⡄⡄⡄⠀⣤⠀⣿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣴⠟⢁⠎
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠊⠒⠑⠃⠁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠷⣦⣤⣄⣀⣀⣠⣤⣴⠶⠛⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠁
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠸⣧⣀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠘⢿⣷⣤⣤⣄⣀⣠⣤⣴⣾⡿⠃⠀⠀⠀⠈⠙⢷⣄⣀⢀⣀⣠⣤⣶⡶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠐⠋⠉⠀⠉⠳⣦⣄⡀
⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁
⠀⠀⢀⣀⣤⣴⣶⣛⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⠀⣴⠟⠉⠉⠉⠉⠉⠉⠒⠂⠄⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⣀⡤⣀⠀⠉⠙⠒⠶⣤⣀⠀⠀⣿⠀⠀⠙⠻⢶⣤⣀⣤⡴⠚⠋⠉⢹⡇
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⠛⠚⠀⣀⣠⠶⢢⠀⢹⡇⠀⢸⠀⠀⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⢸⠃
⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⢸⣿⠀⠀⠀⢀⡴⠋⠀⣀⣀⣤⣤⠶⠶⠛⠋⠉⠈⠙⠁⠀⢸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢸⡇⠀⢰⠆⢠⠀⠀⠀⠀⡎⠀⢸⡟⠀⢀⣴⣿⠶⠿⠛⠋⠉⠁⠀⠀⠀⠀⣰⡏⣠⡇⠀⠀⣼⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠈⣿⡀⠈⠁⠀⠳⠂⠀⠀⢝⠂⠸⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⣋⣰⠆⠘⠛⠋⠀⠀⠀⣿⠇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠞⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⡇⠀⠀⢻⣾⣛⠂⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠄⠀⠀⠀⠀⠈⠈⠉⢀⣀⣤⠞⠓⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣲⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠂⠀⠒⠒
⠀⠀⠸⣍⡴⠂⠀⠀⢀⠐⢚⠫⡍⢉⣤⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⣉⢁⡤⠐⠂⠉⡇⠀⠀⠀⠀⠀⠀⣠⣌⠿⣿⣿⣿⡄⠉⢀
⠀⠀⠀⣸⠂⡧⠀⢀⠟⠦⠄⠀⠛⢂⣉⠄⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡍⢀⣤⣴⡴⠃⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⡄⠠⡴⠒⠾⠉
⠀⠀⠘⠯⠴⠇⠀⠠⠄⠰⠖⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣅⡌⠛⢃⣩⣴⠖⠃⠀⠀⠀⠀⠀⠀⠀⡄⠈⠥⠀⠀⠤⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢐⣊⣁⣋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⢶⠖⢦⢴⠈⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⡊⠉⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡒⠶⠶⢒⣂⡴⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣉⠡⢤⡠⠀⠐⢒⣈⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⣠⡀⠀⠀⠤⠉⠭⠥⠴⠖⠚⠉⠁⠀⠀⠀⣀⠠⣠⡔⢒⠏⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢤⠤⠤⠄⠀⠀⡀
⠀⠀⢈⡿⣆⡀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠚⣿⠋⠀⡰⢿⣠⠎⠀⠀⠀⠀⠀⢸⠀⠀⠢⢽⡿⠟⢁⣶⠆⠀⡀⠀⠀⡟⠛⢛⠛⣓⣒⣒⡒⢒⠀⠁
⠀⠀⠀⢇⣹⡙⠓⠚⢋⣿⠉⠀⡸⢯⠠⠎⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠰⠋⣴⣸⠿⠋⠀⠀⡇⠀⠀⡿⠀⠸⠛⠙⠛⠋⠃⢀⠀⠸⡄
⠀⠀⠀⠀⠈⠳⠦⠴⠋⠙⠛⠋⠁⢀⣀⣠⡤⠤⠶⠶⠒⠒⠲⠤⣀⠀⠀⠀⢸⠇⠰⣤⡼⢓⣯⣚⣅⠀⢰⡇⠀⢰⠁⠀⣴⡏⠀⠒⠂⠒⠉⢧⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣄⡀⠀⠀⢀⣀⣀⣠⣤⡀⠀⠀⠀⠀⣿⡆⠘⢁⣾⣽⠿⠋⠉⠀⢸⡇⠀⣸⠀⢠⠀⠁⠀⠀⠀⠀⠀⠠⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⠯⠶⠾⠿⡿⠛⠛⠋⠡⠀⠀⠀⠀⣿⡅⢀⣉⣁⣀⣀⣀⣀⡀⢸⡇⠀⣿⠀⣇⠀⠠⣤⣤⣤⣤⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⠀⡄⢖⠉⢈⣓⣂⠀⠐⠀⠀⠀⠀⠈⠀⠚⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢻⡆⢠⠄⢀⠀⡍⢉⠩⢠⠀⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢱⠈⠂⠀⡈⢈⡀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡸⠇⠸⠀⡇⠈⡶⠸⠎⠀⠇
⠀⠀⠀⢠⠖⣒⣂⠀⢰⣲⡄⠀⠀⠀⠱⠄⠀⠀⠆⠀⠐⣉⡙⠂⠁⠀⠀⠀⠀⠀⠀⢠⣩⣭⣭⡅⠀⠀⠀⠀⠀⣖⣿⣀⣀⣀⡀
⠀⠀⠀⢈⠉⠉⠉⠉⠉⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⢭⠍⠗⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⢠⡎⠤⠀⠀⠀⠄⣼⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⣾⢁⠀⣤⣤⣄⠀⣏⠄⡇⠀⠀⢰⣖⣋⡉⠉⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⡄⢻⠀⠀⢰⣿⡿⠿⠿⠿⠿⠯⠍⠽⡗
⠀⠀⡇⢀⠈⠭⠭⣭⣉⠉⠀⡏⠀⠀⢠⣯⡿⠛⢛⣛⣛⠉⠙⣛⠈⠀⠀⠀⠀⣿⠀⠀⠠⠴⠦⠤⡀⢻⢸⠘⡇⠀⢰⣌⣙⣛⠛⠛⠒⠚⠛⠃⢡
⠀⠀⣿⡅⠀⠄⠀⠀⢹⣷⠀⡇⠀⠀⢸⡟⠃⠰⠿⠧⡼⠇⠀⠀⢠⡇⠀⠀⠀⠉⠀⠐⠀⠘⠁⠀⠐⢸⡾⣰⠁⠀⣿⡏⢉⣡⣤⣤⣀⣁⣀⠀⠈⡇
⠀⠀⢻⠘⢷⡶⠶⣒⠋⣿⠀⡇⠀⠀⢸⡇⢉⠙⢛⠛⢛⠛⠉⠁⢸⡇⠀⠀⠀⢇⢠⠀⡧⠀⠶⣀⢀⠀⠻⠃⠀⠀⣿⣰⠋⠤⠤⠄⠠⠤⠄⠙⢦⡇
⠀⠀⢸⠀⢲⡿⠻⣀⡄⣿⠀⡀⠀⠀⠸⡇⠨⠴⠒⠆⠘⠀⠠⢀⢼⡇⠀⠀⠀⢸⣞⠋⠁⠀⠈⠁⢸⠀⢠⠀⠀⠀⣿⡧⠀⠂⠂⠀⠀⠀⢂⠠⢸⡇
⠀⠀⢸⣄⣁⣀⡐⣛⣁⣿⡶⠇⠀⠀⠈⡧⠙⢓⣒⡶⠶⠶⠖⢚⢹⡇⠀⠀⠀⢸⠙⠀⣁⠀⡀⢀⡞⢀⣿⠀⠀⠀⣿⠘⢦⣐⡲⠦⠰⠚⣉⠴⢚
⠀⠀⠀⢧⡈⠉⠉⠩⠉⠅⠠⠁⠀⠀⠐⣇⣀⠙⠻⢯⣭⡽⠂⠀⠸⠃⠀⠀⠀⠀⢷⣆⣀⣋⣉⡁⢀⣠⠏⠀⠀⠀⠈⢧⣄⣈⣉⣉⣉⣉⣠⢄⣻⠆
⠀⠀⠀⠀⠉⠙⠛⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠁⠞⠉⠙⣳
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠰⡾⠷⠀⠀⠀⠀⠀⠀⠀⣿⢧⡀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧⠀⠀⠀⣠⡴⢦
⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠂⠀⠀⠀⠀⠀⠀⢷⣿⠀⠰⠐⠀⡁⠂⠀⠠⡀⠀⠀⠀⠀⠀⠠⢬⣁⠀⠀⠀⠀⠊⠀⣸
⠀⠀⠀⠀⠀⠿⡄⠀⠀⢀⠔⠀⠀⠀⢀⡰⣲⣿⠀⠀⠀⠀⠀⣠⡾⣯⣻⠂⠀⠈⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠏⠉⠙⠚⠃⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠈⠉⢉⢻⣿⠀⠀⠀⠀⢠⣿⣇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⢀⡎⣼⡿⠀⠀⠀⠀⢸⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⠀⠀⠀⣾⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠁⠀⠀⠀⠀⠈⠻⣷⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠸⡀⠠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠃

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠉⠁⠒⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠉⠑⠒⠤⠤⠀⡀⠎⠠⠚⢠⠐⠒⠒⠚⠛⠩⠭⠭⠼⠛⢲⠂
⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢰⠀⠆⠀⠆⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⠀⠐⠀⠀⢸⠀⠀⠀⡇⠀⢀⠀⢺⡀⠐⠒⠒⠒⠂⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⢸⡇⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠓⠀⠁⢓⠲⠤⠤⠤⣤⣄⣤⠤⠤⠎
⠀⠀⠀⠀⠀⠀⢸⡇⠢⡠⠂⠀⠀⠀⢸⠀⠀⢠⡇⠀⠰⣿⣶⣼⠀⢠⠆⠀⠀⠀⠀⠄⢸⠀⠀⠀⢀⡄⠐⠒⠶⠶⠤⢤⣄⣀⡀
⢀⠀⠀⠀⠀⠒⠂⣇⠀⠀⠀⠀⠘⠀⢸⠀⠀⢸⠃⠐⠷⠿⠿⠇⡄⢮⢀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠐⠂⠈⠉⠛⢲
⢛⠒⠒⠒⠂⠀⠀⣿⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠈⠀⠀⡤⠄⠞⢰⠃⣠⡶⣞⡓⠶⠞⠉⠙⢦⠀⠀⠀⠀⠀⢸⡄
⠀⠙⠒⠒⠀⠀⠀⢹⠀⠀⠉⠉⠉⠋⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⢰⠀⡴⠀⠈⠀⠀⢨⠾⡋⠀⠈⠻⣄⠀⢀⣀⠀⢳⠀⠀⠀⠀⣿⢇⣀
⠀⠈⡀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⡅⣸⠁⠀⡀⠢⠀⠀⠀⢀⡅⠀⠉⠀⠀⠀⢿⣀⠀⠁⠀⠐⠀⢀⣀⠀⠇⠨⠉⢙⠛⠛⠶⠦
⠀⠀⠑⠤⢤⡤⠤⠀⣀⠶⢠⠀⡄⢀⠀⠀⡎⠀⠀⠀⠀⢡⠇⠀⠀⠈⠒⣢⢀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠙⣧⠀⣄⡀⢳⠀⣀⠀⠉⠐⠒⠂⠼⢃⡴⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠐⠨⠀⠂⢱⠃⠀⠀⠀⡾⠀⠀⠀⠀⣎⠀⠀⠒⠶⢶⣤⣄⣉⡀⠀⠀⠀⠘⠇⠈⠁⣀⡇⢀⡉⠁⠀⠀⠀⢰⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠃⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠉⠙⠛⠷⢦⣤⡀⠐⡤⠊⠁⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣤⣤⣤⣀⣀⣉⣀⣀⣤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠶⠶⠶⠖⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠶⠒⠒⠒⠛⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠥⣀⣀⠀⠀⠳⡀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⡇⠀⠀⠀⠈⠁⠒⢻⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣟⣯⡇⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄⡇
⠀⠀⠀⠀⠀⢀⠔⠁⠈⠀⢜⠧⣄⠀⠀⠀⠀⠀⢸⢀⡄⢠⡤⡆⡖⠀⣹⣯⡀⡇
⠀⠀⠀⢀⠞⠁⡔⠀⢠⠀⠀⠑⡈⠙⢦⠀⠀⠀⢸⠀⣿⠛⠇⠇⠛⠛⠉⠁⠀⡇
⠀⠀⠀⡏⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠣⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡴⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀
⠀⠀⠀⠀⢹⡌⠉⠉⠉⠉⠉⠉⠀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠻⠿⠓⠤⣀
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠰⠾⠿⣀⠀⢠⣶⣿⠒⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠋⠛⢒⣒⠒⠒⠚⠛⠳⠦⠤⠤⠤⠬⠯⠭⣷⡄
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠿⠷⠀⢰⣾⣷⡀⠀⠀⠀⠙⢷⡄⠀⡇
⠀⠀⠀⠀⠀⣠⣤⠟⠀⠀⠀⢸⣦⡍⠓⠦⣄⡀⢸⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⣿⣶⣶⣶⣶⣿⣿⠏⠀⠀⠀⠉⠛⠶⠒⠚⠉⠉⢸⠀⠀⠀⠀⢰⣶⣶⠄⠠⣤⣄⠀⠘⠻⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠓⠶⠶⠦⠭⠿⠥⢤⣤⣀⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠗⣒⢒⢈⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠁⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⢀⠜⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠠⠄⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡄⢀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠁⠘⠄⠁⠀⠀⠃⠄⠀⡀⠀⠀⠀⢀⡤⠂⠉⠀⠀⠀⠀⠀⠈⠁⠢
⠀⠀⠀⠀⠀⠃⠄⡀⠀⠀⠀⡀⠄⠈⠁⠀⠀⠀⡎⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠢⠁⠀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⣀⡠⠄⠀⠀⠀⠐⢀⠀⡟⡉⠚⠀⠀⠈⠀⠀⠀⠀⠐⢈⠀⠀⠀⠸⡉⠒⠀⠀⠀⠀⠀⠂⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢀⡁⠀⠀⠀⠀⠀⠲⡢⠂⠀⠀⠀⠀⠑⢔⠀⠀⠀⠀⢀⣄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⡀⠁⠀⢀⡄⠀⠀⢤⠀⠀⠂⢒⠀⢀⠀⠀⠈⠉⠈⠀⠀⠀⢀⠀⠒⠂⢀⠄
⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠁⢀⠀⠀⠀⠀⠀⡏⣉⠁⠉⠹⠂⠀⠀⢸⠀⠀⠠⠈⠄⠀⠀⠀⡄⡀⠰⠪⠀⠀⠼⠆⠀⠀⠐⠅
⠀⠀⠀⠀⢀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢐⠄⢀⠤⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠡⣀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠿⠀⠀⠀⢸⠀⢀⢀⢐⠂⠃⡃⠠⠀⠀⠈⠆⠯⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠉⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠒⠒⠂⠂⠒⠒⠒⠒⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠲⠎⠉⢳⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡼⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢰⠲⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠁⠀⠀⠀⠀⠀⠀⠸⢠⣠⣤⠀⠀⠈⣇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡉⠉⢳⣎⣠⣃⣀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠃⠀⡁⠘⣉⠉⠳⡒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⢋⠭⠒⠒⣏⠀⢀⡀⠀⡁⠀⣰⠯⠭⣍⣓⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢯⠀⠀⠀⠘⠢⠤⠤⠤⠖⠋⠀⢰⣂⣐⠆⣹⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠙⠒⠶⠶⠶⠶⠶⠦⠤⠤⠤⣤⠀⡰⠊⢁⣀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣟⠑⠭⢭⣓⣒⣒⣒⡒⠲⠖⢒⣒⣒⣒⣒⣾⠁⢻⡭⠭⠴⢚⣿⠉⢻⢲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⢶⣤⣤⣀⣀⣀⣀⣀⣀⣈⣬⣭⣭⣤⣤⣬⡇⡿⠴⠖⢒⣩⡟⠀⡇⡼⢠⢷
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⣄⡉⠓⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠗⠒⠋⠉⣠⡗⠺⣥⠇⣞⣼
⠀⠀⠀⠀⠀⠀⠀⠹⣗⢾⣉⠻⢭⣟⣒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠖⢒⣒⣩⣭⣛⣀⣠⣼⠾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠺⣭⣭⣛⣛⣛⣛⣓⣒⣒⣒⣒⣒⣒⣒⣻⣿⠭⠭⠭⠿⠛⠛⠋⠉⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣹⡈⣇⢣⢹⠉⣏⠉⠉⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠾⠶⠶⠾⠾⠦⠶⠶⠒⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠁⠀⠀⢀⠈⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⡠⠀⠀⣀⠤⠂⠒⠀⠉⠉⠁⠀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢢
⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠇⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠓⠒⠒⠒⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢃
⠀⠀⠀⢻⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⢸⡠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⡰⠃
⠀⠀⠀⠀⢇⠄⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠔⠈⢿⣿
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠐⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠢⣀⡀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠢⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠐⠒⠂⠤⠤⠤⠤⠤⠤⠄⠒⠂⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠀⠀⠀⡀⠀⠈⠁⠈⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠉⢉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠙⠻⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠓⢢⣄⠀⠈⠑⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠉⠲⢤⡀⠈⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⢀⡀⠁⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠁⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠲⠃⡠⠀⠀⠀⢹⠇
⠀⠀⣦⣄⠀⠀⠀⠉⠙⠛⠫⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠐⠀⠀⠀⣀⠤⠚⠀⣀⢸⠀⠀⠸⠗⠀⠀⠀⣾
⠀⢄⡉⠛⠋⠶⠴⣦⠀⣿⠒⠒⠞⠋⠀⠀⠀⣀⣀⡀⠉⠂⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⡜⠉⠀⠳⣴⠁⠀⠀⠀⡔⠁
⠀⠈⠛⠷⠶⢠⣤⣄⠠⠏⠀⠀⠀⠀⠀⠒⠂⠀⠀⢁⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢀⡤⠈⠀⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢹⣆⠻⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠉⠀⠀⠀⢀⠀⠀⠀⠐⠒⠤⠄⡀⠀⠀⠀⠀⢡⣾⡏⠁⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠓⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⢻⣿⣿⣿⠷⢤⣀⠀⠀⢀⠀⠀⢚⡄⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠛⠿⣶⣬⡟⠃⣀⡠⠤⠟⠀⠀⠀⡠⠀⢌⡁⠀⠀⠀⠘⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠠⠛⢛⡶⢶⡊⠀⢹⡄
⠀⠀⠘⢦⣀⣀⣀⡀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣠⠀⠀⠀⠘⡏⠀⠀⣸⠁
⠀⠀⠀⠀⠉⠙⠛⠓⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢄⣄⣀⣤⡑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⠙⠓⠒⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⣀⡤⠴⠒⠖⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⣤⣀⡀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣴⠒⢦⡔⠛⣷⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⡴⠋⠀⠀⠀⠀⣀⢴⡄⠀⠀⠀⠀⠀⠙⠶⣤⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠳⣄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⣰⠟⠁⠀⠀⠀⢠⣞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠇⠀⠀⠀⠈⢳⣄⠈⢷⡀
⠀⠀⠀⠀⠀⣴⠏⠀⣰⠏⠀⢀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⢾⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣷
⠀⠀⠀⠀⢰⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠐⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⠀⠸⣧
⠀⠀⠀⠀⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡇⠀⢹⡆
⠀⠀⠀⢰⡟⠀⢰⡇⠀⠀⠀⠀⠀⢠⡴⢤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⣾⠙⠶⠚⢳⠀⠀⠀⠈⣷⠀⠈⣧
⠀⠀⠀⢸⡇⠀⢸⠃⠀⢀⡀⠀⠀⢸⡄⠘⠋⣻⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠻⣄⢀⣴⠏⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣾⠇⠀⠻⠟⠀⠀⠀⠻⠶⠞⠉⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣶⠀⣿⠀⠀⢹
⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⢾⣿⠀⣿⠀⠀⣾
⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠟⠀⣿⠀⠀⣿
⠀⠀⠀⢸⡆⢸⣷⠀⠀⠀⢀⣴⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠔⢀⡿⠀⠀⣿
⠀⠀⠀⢸⡇⠀⣿⡄⠀⢾⡽⠋⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣠⡴⠛⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡇
⠀⠀⠀⠀⢷⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣼
⠀⠀⠀⠀⠘⢧⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢷⣄⠈⠻⣆⡀⠀⠘⠟⠀⠀⠀⣠⣤⡴⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣤⠖⢄⣀⡀⠀⠀⠙⠚⠀⢠⠏⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠻⣦⡀⠀⠀⠀⠸⣧⣀⡁⣼⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁⡽⠀⠀⠀⠀⢠⠏⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⠯⣽⣓⣶⣤⣄⠀⠀⠀⠀⠈⠳⠶⠚⠁⠀⠀⢀⡴⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⢶⣄⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠶⠀⠀⠀⠀⢀⣠⡴⠋⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠈⠻⢦⣄⡀⠀⠀⠻⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠉⠛⠳⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠉⠁⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢐⠒⠒⠒⢦⡀⡴⠁⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣆⡈⢦⢹⡇⢸⠀⠘⣦⠀⠀⣸⠀⣵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠁⠀⠈⠉⠙⠻⢧⣸⡄⠀⣽⣤⠾⢃⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣴⠀⠀⠀⠾⠁⠀⠀⠀⠈⠑⣄⠻⠓⠚⠳⠶⠦⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠀⠀⣠⡤⠀⠀⠛⠃⠀⠀⠈⠡⠊⠀⣰⢂⠀⢻⡟⠛⠻⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⣧⠈⠦⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣴⠀⠀⢠⠆⡀⠀⠒⣃⠄⠀⠀⢚⡡⠂⠀⣀⠀⡇⢻⢿⣦⢄⣀⢙⡂⠄⠀⠀⠀⠀⠀⠀⠀⢀⡞⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠫⠂⠀⣿⠄⢹⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣤⣀⢸⠀⣿⡜⢉
⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⢞⠄⠀⠰⢆⡄⠀⠀⠻⠷⠂⠀⠴⢖⡠⠀⢀⠄⣼⠃⠀⠂⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠈⠻⣆⠘⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠀⠁⢠⠶⣀⠀⠀⠀⢀⣈⣡⠴⣊⣵⠞⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠐⢦⣀⠀⠀⠀⠘⣧⣁⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⠁⠂⠀⠀⠀⠨⢴⣒⣺⣭⠭⠶⠞⠛⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢄⣠⠽⠛⠉⠀⠀⢀⠀⠀⠈⠻⡶⢬⡉⠉⠒⠒⣂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⡶⠊⠁⣀⠄⠀⣠⠶⠋⢀⠀⠀⢀⠹⡆⠈⡓⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⠝⢋⡠⠖⢋⣤⠶⠋⣁⣤⠖⠹⠀⠀⣸⣸⡿⠦⠤⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠁⢠⣶⣭⠶⢛⣩⠴⠒⢻⠁⠈⠁⠀⠀⢀⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⡠⠀⡤⠈⠀⠞⠀⠀⣀⣀⣠⣤⠴⠖⠋⠉⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⣤⡤⠴⠶⠶⠶⠚⠛⠛⠏⠛⠒⠈⠉⣀⢔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠤⠤⠤⠤⠤⠤⠤⠴⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠙⠛⠛⠛⠛⠻⠿⢿⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡭⠶⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠉⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠉⠁⠀⠀⠀⠛⠛⠛⠲⠶⠶⣤⣤⣀⣀⠢⣄⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣁⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠉⠁⠀⠐⠒⠛⠲⠶⢦⣤⣈⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢼⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠉⣭⣉⣙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣬⣍⣛⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠉
⠀⠀⠀⠀⠰⠋⠠⠖⠚⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣶⡄⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠓⠶⣤⣀⠈⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠷⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠔⠒⠊⠉⠉⠀⢀⣀⠀⠀⠀⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠈⠁⠀⠀⣀⣀⣤⣤⠴⣾⣮⠻⣿⡿⣄⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⠔⠒⠉⠁⠀⢀⣀⣤⡀⣶⣔⢾⡟⢿⣇⠀⠻⠧⠘⠛⠁⠉⠀⠀⣀⡠⠤⠐⠂⢙
⠀⠀⠀⠀⠀⠈⡷⢄⠀⠀⠀⠈⠻⣿⣿⡾⠛⠛⠋⠀⠁⠀⠀⣀⡠⠤⠐⠒⠉⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡏⡆⠣⡀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⡇⠘⡄⠈⡢⡄⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⡇⣿⣿⣇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠠⠋⠁⠀⠃⠀⠀⠀⠀⢀⡀⢠⡄⣶⠺⣿⠋⢹⡟⠸⠿⠃⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⣿⢾⣷⠟⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠚
⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡆⠀⠀⣀⠠⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠤⠤⣄⡀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠙⠲⢤⣙⠀⡧⠒⠉⠑⢶⣴⠞⢳⡀⠀⠀⣠⠔⠋⠉⠉⠉⣒⣦⣤⠉⠺⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡤⠛⢛⡿⠛⢀⡠⠀⠈⠀⢀⡀⠀⠠⠴⢿⣆⠀⢳⢀⡾⠁⠀⠀⢀⣴⣯⣥⣤⣤⣤⠀⠀⠘⠙⠓⠶⢤⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠰⣯⠴⢚⠏⢀⣦⠀⢱⣄⠉⢳⣶⣤⣄⣹⡆⢸⡾⠀⣀⠀⠀⠧⠀⠀⠀⢀⣞⡡⠚⡀⢸⡀⠑⢦⡄⣈⡒⢄
⠀⠀⠀⠀⢠⡏⠀⣟⡆⠀⠀⢸⣠⠏⢸⡀⢸⣨⠟⠉⠀⠉⠙⠫⣽⢸⠗⠉⠀⠉⠓⠂⠤⡀⠀⠟⢋⠀⠀⡇⢸⠈⢦⡀⠹⡌⢿⡉⠃
⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠸⠇⡴⢄⣳⠞⠉⡽⠋⢉⡠⠄⡀⠀⡀⠤⣀⠐⠒⠒⢖⡚⠻⡄⠀⢸⡄⠀⢸⣸⠀⠀⠙⢦⣿⠘⣇
⠀⠀⠀⠀⢸⡇⠀⠀⣠⢤⠀⠀⠀⠙⡼⠁⣀⠸⠷⠚⢹⠁⡰⣇⠀⠹⢦⡈⠻⡓⠶⢤⣵⡄⠙⣆⠀⠀⠀⠈⠿⠀⠀⠀⡶⠟⠀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠘⠎⠀⠀⠀⢸⠃⠀⣯⠇⠀⠀⣾⡼⠁⢹⡀⢸⠀⠻⣦⡹⡄⠀⠀⠣⠄⢹⡆⠀⡌⠀⠀⠀⠀⠀⠘⠁⠀⡿
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡤⣾⠀⠀⠀⠀⠀⠀⠘⠁⡞⡆⠳⣼⠀⠀⠈⠙⠷⢠⠄⠀⠀⢀⡇⠀⠀⠀⢰⢳⠄⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢹⡆⠀⠀⣶⢦⠀⠀⠀⠉⠀⠀⠉⠀⣖⢲⠀⠀⠈⠒⠃⠀⢸⡇⠀⠀⠀⠈⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⡵⠀⠀⠀⢿⡀⠀⠈⠃⠀⢰⢦⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠀⠀⠀⡾⠰⣉⠀⠀⠀⠀⢰⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⣀⠀⠈⣷⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢬⠃⠀⣼⠃⠀⠁⢀⠀⠀⠀⢈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠓⠀⠀⠸⣧⠀⢀⡀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⠀⢨⠇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠦⣄⣘⣧⠸⠜⠀⠀⠀⠀⠀⠈⠁⠀⠀⢾⡷⠀⣰⠏⢯⠃⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣧⡀⠀⢄⠀⠀⢀⣀⠀⠀⠀⠈⠀⣴⠷⠤⠤⠖⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠉⡀⠀⠘⠜⠀⢀⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠾⠲⢤⣄⣴⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⡿⠿⠿⢿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⠐⠒⠒⠊⠍⠀⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠠⠤⠀⠒⠒⠉⠉⠑⠒⠃⠀⡆
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠰⡀⠀⠉⠒⠂⠸⠀⠀⠀⠀⠀⠀⠑⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⠢⢤⡀
⠀⠀⠀⠀⢀⠨⣀⡀⠉⠒⠺⠦⣄⡒⠀⠀⠀⠀⠉⡶⢄⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠟⣀⡠⠗
⠀⠀⠀⠀⠑⢦⣈⠛⠷⣶⡤⣴⣀⡀⠑⠖⠦⠤⣼⣦⡀⠈⣳⢤⡔⡇⠀⠀⠀⣀⣀⠤⠴⢒⣊⡭⢴⠒⢛⠟
⠀⠀⠀⠀⠀⠀⠣⣉⠓⠦⣍⣛⠁⠉⣙⠲⢤⣀⣀⣈⢉⣶⣄⠠⠼⠗⣒⣊⢭⠤⠒⠒⠉⣉⡠⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣌⡉⠒⠦⠭⢁⣒⣭⣭⠭⠤⠖⠲⠋⠉⣁⣠⠤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢀⣀⣀⣠⠤⠔⠒⢈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣿⣟⣛⣟⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⣩⠝⠉⠀⠀⠀⠀⠉⠛⢭⡙⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣉⣤⠤⠔⠊⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⢭⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢠⠖⠚⢉⣁⡽⠀⠀⢰⠋⢳⠀⠀⠀⠀⢀⡠⠖⡄⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⠀⠀⠀⠀⢸⠀⣾⠀⠀⢀⠔⠋⣠⠖⠁⠀⠀⠀⠀⢸⢧⡀
⠀⠀⠀⠀⡰⠁⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣀⠇⠀⠀⠘⠒⠋⠀⠀⠀⢸⡉⢣⠀⠸⡆⠱⡀
⠀⠀⠀⣰⠁⢰⠁⠀⠀⠀⣏⣉⣉⣉⣁⡵⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢣⠀⢣⡀⢱⡀
⠀⠀⢀⠇⡰⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠉⠑⠒⠉⠉⠛⢆⡀⠀⠀⠀⠀⠀⠀⠑⠜⠁⠀⠈⠢⣇
⠀⠀⢸⠞⠁⠀⣇⠙⣄⠀⠀⠀⠀⢀⡴⡶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡑⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⡄
⠀⠀⡏⠀⠀⠀⠈⢦⠘⢆⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⢀⡠⠚⢁⠼⠀⠀⠀⡇
⠀⠀⣇⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢏⡠⠞⠁⠀⠀⠀⣼⡇
⠀⠀⢹⢆⠀⠀⠀⠀⠀⡠⢄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃
⠀⠀⢸⠈⢧⠀⠀⢀⡜⢁⡜⠀⠀⢸⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠞⠀⠀⠀⠀⢠⠋⣳⢸⠀⢸
⠀⠀⠈⡆⠈⡇⠀⡞⢀⠞⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠀⠀⠀⠀⢀⠏⢠⠃⠘⡄⡎
⠀⠀⠀⢹⠀⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢄⣀⡤⠤⣀⡠⠔⡿⠀⠐⣏⠙⠦⡀⠀⠸⠤⠏⠀⠀⢹⠁
⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠁⠀⠀⠀⠉⠉⣀⣀⠀⠀⠑⢦⡈⣣⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⢣⠀⣞⢉⣉⣉⣉⡱⠀⠀⠀⡠⠊⢁⠇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠉⠁⠀⡠⠖⣫⠋
⠀⠀⠀⠀⠀⠈⢣⡈⠉⠁⠀⠀⠀⠀⢠⡋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⡜⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⡒⠢⠤⢤⣀⠉⠁⠀⠀⢰⡉⠲⢤⣀⠀⠈⠣⠞⠀⠀⠀⠀⠀⢰⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠙⠢⣄⠀⠀⠉⠓⠤⣈⡵⠀⣠⠴⠒⠦⢤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠽⠦⢤⣀⣀⣀⣠⡾⠥⠤⠒⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠯⠥⢤⣱⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣀⡀⣀⠀⡀⠀⣶⠀⠲⠀⠐⢁⡠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⢲⠀⢷⠀⢸⠀⠀⡆⠀⠀⢨⢸⡁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠒⠈⠚⠈⠊⠈⠊⠀⠉⠀⠈⠋⠑⠁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⢤⣖⣒⣛⣛⣛⣛⣛⣛⣛⣒⣶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⠀⠀⢸⣤⣒⣒⠉⠛⠛⠛⠉⠑⣒⣒⣦⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠠⠭⠍⠀⡇⠀⣠⠖⠉⠉⠲⢤⣤⡤⠖⠋⠁⠀⠀⡇⠀⠀⢸⡀⠀⠉⠉⠉⠉⠉⠉⠉⢉⡁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠥⠖⠀⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣒⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠧⠤⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⢄⠒⠂⠉⣉⣉⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⢀⣀⣀⡀⠤⡇⣰⠉⠀⠀⠀⠉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠚⠂⠦⠤⢤⡚⠠⣏⠀⠀⠁⠀⠐⠀⠀⠈⠢⡤⠤⢀⣀⡀
⠀⠀⠀⠀⣀⡠⠔⠒⠉⠉⠁⠀⡰⠁⠀⠀⠠⠀⠄⠀⠈⠙⣌⠢⡀⠀⠁⠄⠀⠠⠄⠀⢸⠀⠀⠀⠀⠉⠉⠒⠢⣀
⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢂⠄⢀⠀⠁⠀⢀⡿⠢⣈⠑⠒⠂⠠⠤⠤⠔⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠤⢔⡪⠕⠁⠀⠀⢉⠗⠒⠀⠠⡔⠚⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣔⠤⢑⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢆
⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠂⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡇
⠀⠀⡌⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡆⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⣀⠔⠊⠱
⠀⠀⢰⡀⠀⠀⠈⠉⠓⠠⠭⢍⣈⡁⠉⠉⠑⠒⠣⠬⠬⢰⣁⣀⣀⣀⣀⡀⠠⠤⠤⠔⠒⠉⠁⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡰
⠀⠀⡎⠈⠓⠤⢄⣀⣀⢀⠀⠀⠀⠀⠉⠉⠁⠚⠒⠐⠒⠒⠒⠂⠀⠤⠤⠤⠤⠤⠀⠤⠤⠤⠔⠒⠊⠉⠀⠀⠀⠀⡠⠒⠉⡇
⠀⠀⡱⣄⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠔⠊⠀⠀⣴⠁
⠀⠀⢇⠈⠑⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠒⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⣀⠤⢊⡎
⠀⠀⠀⣱⢤⡀⠀⠈⠑⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠤⠤⠤⠤⠤⠤⠀⠒⠒⠈⠉⢀⡴⣋⠆
⠀⠀⡎⠸⡀⠙⢕⠢⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⠁⠀⠈⠆
⠀⠀⠱⢄⡙⠢⢄⠉⠒⠬⠕⣲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠒⠊⣁⠔⠁⠀⠀⠀⣤
⠀⠀⢠⠀⠈⠑⠂⠬⣑⡂⠤⢀⣈⠉⠉⠛⠃⠭⠄⠈⣀⣀⣀⣈⣀⣈⣉⣉⣉⠁⠤⠄⠐⠒⠒⢂⡠⠋⠀⠀⢀⡀⠔⠊⠀⡇
⠀⠀⠀⢦⠀⠀⠀⠀⠀⠈⠁⠒⠢⠬⣉⡁⠒⠒⠒⠐⠐⠒⠒⠒⠀⠀⠐⠒⠒⠒⠒⠂⠈⠉⠉⠀⠀⠀⢀⠔⠁⠀⢀⡠⠞⡃
⠀⠀⠀⠈⠳⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠠⠤⠤⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡤⠔⣁⠤⡴⠚⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠹⣑⠒⠩⢄⣒⡒⠠⠤⠤⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠂⣁⠔⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠉⠉⠁⠒⠒⠠⠤⠭⠬⠩⣭⡍⠉⢉⣉⣉⣉⣉⣉⣉⣁⣀⠠⠤⠒⠉⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠐⠒⠂⠉

⣟⣿⣿⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣻⣿⣻⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠶⢶⣶⡶⠶⠾⠿⠿⢿⢿⡿⠿⠿⠿⣷⢶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⣿⢸⡀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡏⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣀⣧⣷⣀⣀⣀⣀⣸⣠⣇⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣿⣸⣀⣀⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣤⣀⡀⣀⣀⣀⡤⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⡄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⡉⠉⠉⠉⣁⣠⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠹⣄⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠙⣦⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⢧⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠈⢳⣽⡇
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⡤⠖⠛⠓⢦⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⢠⣿⡀⠀⢀⡞⠁⠀⠀⠀⣸⠃⠀⠀⠀⡟⠀⠀⠀⠹⣄⠀⠀⠀⣴⠖⠒⢦⡀⠀⠀⠀⣿⠷⠦⣄⠀⠀⢠⠶⠒⢦⡀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⡟⠙⠛⠉⠀⠀⠀⠀⠀⠻⣄⠀⠀⣠⠇⠀⠀⠀⠀⠙⠲⠤⠞⠃⠀⠀⠀⣇⠀⠀⢸⡏⠀⢀⡟⠀⠀⢸⠀⠀⠀⡇⢀⣼⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣻⡇⠀⢸⣇⠀⣀⡼⠀⠀⠀⠉⠉⣿⠃
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⣿⢿⣆⣴⣾⡆⠀⣀⠀⠀⣿⠇⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⠈⠛⠁⢸⣇⠀⣩⡀⠀⣿⠀⠀⣿⣴⣿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠹⠇⠀⠀⠸⣿⠀⢿⠇⠠⡿⠀⠀⣿⠉⠻⣦⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣀⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠄⠀⠀⠀⠀⠈⠣⠍⠌⠄⠋⠉⢠⠀⢌⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡺⠁⠈⠂⠀⠨⡹⠀⠀⠀⢀⠄⢄⠀⠀⠈⠒⠂⠀⠈⢫⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣊⠉⠁⠀⢀⠤⡀⠀⢀⣀⠀⠀⠀⠀⠑⠀⠀⠀⠤⠒⠀⠀⠀⠀⠁⢄⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠈⠤⠃⣀⠀⠀⠑⠁⠀⠡⠼⠀⠀⠀⠀⠀⡔⠒⡀⠑⠚⠀⠀⠀⠀⠀⢀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡄⡄⠀⢸⠀⠑⡰⠀⠀⠀⠀⠀⠀⢀⡤⠒⠢⡁⠊⠀⠀⠀⠔⢠⠀⠀⠀⠣⠔⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠑⠁⠀⠀⠁⠉⠀⠀⠀⡠⠤⠤⢠⡊⠠⠠⠄⢘⠠⢀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠔⠁⠀⠀⠀⠀⠀⠈⠢⡈⠢⠀⠀⠀⢀⠔⠊⡂⠀⢠⡒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⢂⠀⠀⢘⣙⠀⠀⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠑⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠁⠁⠀⠀⠀⢀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⠀⠀⢠⠒⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⢀⠤⡀⠀⠀⠀⢇⠰⠀⠒⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⡠⠀⠀⠈⠒⠁⠀⠀⠱⡠⠃⢐
⠀⠀⠀⠀⠀⠀⠀⠰⢠⠀⠈⠒⠁⠀⠀⣀⠀⠀⠀⠀⢃⣈⠐⠤⢀⣀⣀⣀⠠⢊⠸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠣⡀⠀⠀⠀⠘⠴⠁⠀⠀⠀⡄⢄⠈⠆⣀⠄⠂⢐⠀⠊⠀⠀⠀⢆⡁⢸⠀⠀⠀⣎⢱⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡆⠀⠀⡎⢢⠀⠀⠀⡔⠱⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢔⢰⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⣀⠀⠀⠀⠈⠈⠁⠀⠰⣁⡑⠀⠐⡅⠠⠕⠀⠀⠀⢠⠂⠉⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣈⣚⠠⠀⢤⠀⠀⠀⡀⠀⠀⠀⡀⠀⢈⡉⠀⠀⠀⡰⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡇⠀⠈⠚⠀⡠⠊⠀⠀⠀⠈⠁⢀⡡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠛⠒⠀⠀⠀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠐⠀⠀⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢿⠧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⣀⣀⣀⣀⡀⢁⠶⠭⣓⠦⡀⠀⠙⠔⢅⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠖⠀⠠⠖⠛⠉⢉⡔⠣⢌⢙⠣⣍⡒⢌⠳⡄⣄⠀⠀⡀⡀⡢⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠴⠐⠁⠀⠀⠀⠀⠀⠑⠰⢯⡈⠑⠠⣁⠡⡄⢉⠀⢣⠙⣌⠳⣄⠀⠘⠄⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠑⠈⠢⠑⡇⠘⡄⠠⡀⠑⢬⣑⠲⣄⠀⠂⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⡀⠀⠘⡀⠡⡘⢤⡘⠂⡀⡀⠂⢤⡑⣌⢣⠁⡀⠈⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡁⠑⣄⠳⡜⢆⠱⢌⠢⢤⡂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⡙⢅⠈⢢⠙⠀⡑⠦⡽⠊⠀⢦⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⡀⢡⠈⠢⢌⡀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠈⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢆⡈⠑⢢⠍⠀⠀⠀⠀⠐⠀⠑⡀
⠀⠀⠀⠀⠀⠌⠀⠘⠄⠀⠀⠀⠀⠠⠀⢳⡀⢀⠀⠤⢤⠤⠂⠀⠲⠂⠰⠂⠐⠢⠄⢀⣀⠀⠀⠀⢠⠏⠢⠌⠛⠀⠀⠀⡀⠀⠀⠀⠀⠄⠈⠄
⠀⠀⠀⠀⠌⠀⡐⠀⠘⡀⠀⠀⠀⠀⡡⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠰⣏⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⢂⠈⠂
⠀⠀⠀⠐⠀⡐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠈⢄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠶⠶⠟⠛⠛⠻⠷⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣛⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠉⠙⠛⠶⣦⣤⣀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⠾⠿⠟⠛⠛⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣴⡾⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⡀⠀⠀⢿⡇⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⠁⠈⣿⡄⢠⣤⡾⠋⠀⠀⠐⢷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⠈⠁⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⣴⣦⣤⡀⠀⠀⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠈⠛⠉⣿⡇⠀⠀⢀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠆⣀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠉⠲⢦⣤⣤⣤⣤⣴⠾⠛⢀⣠⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⢀⣠⣴⣾⠿⢻⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡈⠉⠀⠀⠀⠀⣀⣠⣴⡾⠟⠛⠉⠀⠀⠀⠈⠛⠿⢿⣶⣶⣶⣶⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠀⢷⣄⠹⣷⡄⢀⣤⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁⠀⠀⣠⣿⠄⠙⠃
⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⢀⣤⣶⠿⠛⠁
⠀⢀⣤⣾⠿⠋⠁⠀⠀⢀⣠⣴⡾⠟⠋
⣴⡿⠋⠀⠀⢀⣤⣴⡾⠟⠋⠁
⢿⣷⣤⣶⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⢳⣄⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢷⣝⢦⡀⠀⠀⠀⠀⢀⡾⣏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⠙⣯⣻⣆⠀⠀⠀⣼⠁⣿⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠘⢧⡈⢿⣽⣧⡀⣸⠁⠀⢸⠀⠈⡇⢀⡤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡀⠓⢦⣿⣿⣷⡏⠀⡀⣾⣷⢰⣿⠋⡴⠁⠈⠉⣹⣭⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⣧⡁⡠⣌⢿⣿⣇⣷⣷⣿⣿⣿⠇⣼⠇⠀⣠⣾⠟⠋⠙⠳⠶⣦⠴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣶⣿⣿⣾⣿⣧⣿⣿⢟⣫⠁⣀⣈⠛⣯⣶⣖⣯⣶⣿⠗⠂⠀⣠⡔⠛⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣯⣷⣾⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣾⣿⠶⠿⠿⢿⣦⡀
⠀⠀⠀⠀⢀⣤⣶⣶⡟⠀⢰⠋⠁⣴⣥⡾⣻⣿⡟⣻⠏⣝⣿⡳⡝⢿⣿⣙⠉⠀⠂⠈⠉⢢⡀⠀⠈⠁
⠀⠀⠀⣴⣿⢝⣽⣿⡇⠀⢼⣀⠀⣿⣿⣿⢯⢿⣼⣿⣄⠈⠙⢳⡀⠀⢿⣿⣦⣴⣶⣿⣿⣶⣿⣦⣀
⠀⢀⣴⣿⡷⣋⣿⣿⣷⣴⡘⣜⡀⣿⣿⣿⠀⣾⠏⢠⠟⢦⡀⠂⢧⠀⣸⡇⠻⣶⠈⠡⠞⢷⣿⡭⢻⣷⣄
⠀⢾⣯⠵⢚⣿⣿⣙⡟⠻⠿⣮⠇⣿⣿⡸⢸⡏⠄⡀⠈⠀⠛⣆⠘⠀⡟⠀⠊⠁⠰⠆⠳⠌⠠⢞⣹⡿⠹⣆
⠀⠀⠀⠀⣾⠓⠮⠐⢇⠁⡒⠝⢷⠟⢻⣧⣸⠃⠁⣿⡆⠀⠀⢹⡄⢸⡗⠂⣿⣷⠀⢸⡇⠴⠾⣿⢯⡩⠽⠻⣆
⠀⠀⠀⣸⣿⠵⠠⠆⣾⠀⣩⡄⠙⠻⠋⠿⠏⣿⡆⠘⠁⠀⠀⠀⡙⠻⠀⢀⠁⠁⠈⢀⡀⠀⢶⣯⡀⢂⣴⡀⣿
⠀⠀⠀⡇⠐⠊⠈⢷⠄⡌⢧⣿⠀⠦⠀⠀⠀⠉⠀⠀⠐⣶⡄⠀⣁⣀⠀⠿⠇⠀⠀⠀⣄⠀⢬⡷⠢⣗⡻⠂⢻
⠀⠀⠀⣿⣾⣖⣛⠃⢨⣀⠀⠀⣠⣶⡄⠀⠀⣶⢶⠀⠈⣷⠇⠀⠘⠋⡀⠀⠀⢂⡀⠀⠛⠀⠈⠔⠃⢖⣴⡄⢻
⠀⠀⠀⢸⠀⠲⡜⢳⢸⡅⠀⠀⢿⣿⠀⠀⠀⠹⠾⠀⠀⠀⠀⢰⡀⠀⢸⣧⠀⠿⠇⠀⡄⠀⣦⡭⣀⡐⠉⠩⢼
⠀⠀⠀⠘⣧⠀⠾⠤⠀⢡⠃⣰⡄⠀⠀⣴⡄⠀⠀⢘⣷⠀⠈⡾⠃⠀⠀⠀⠀⢀⠀⠀⠠⡏⠕⢂⣛⢠⣶⢠⡗
⠀⠀⠀⠀⢿⣀⡄⢉⢲⢶⣃⣿⡷⠀⠈⢷⣿⠀⠀⠸⠿⠁⠀⠀⠀⣿⠁⠀⠘⢿⠃⠀⠀⠀⠀⣸⢂⡄⣁⢰⡇
⠀⠀⠀⠀⠈⢿⡿⠀⠘⠾⣖⡀⡀⢴⣦⠀⠀⠀⣂⠀⠀⣸⣧⠀⠀⠀⢠⣄⠀⠈⠀⠀⣰⡄⢀⣁⠈⣱⠇⣾
⠀⠀⠀⠀⠀⠈⢷⡀⣶⡔⠈⣴⡧⠘⠿⣠⠀⢰⣟⡇⠀⠻⠼⠀⠀⠀⠴⠋⢀⣰⡆⠈⠉⢡⠎⠙⠀⣈⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣎⣡⣖⠙⡿⠃⠀⣽⣷⠈⠙⠁⣴⡄⠀⠀⣼⡆⠀⠀⠈⠙⠃⣀⣠⡕⡐⡁⣸⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣏⢱⡄⢰⠔⢈⣩⣦⠀⠀⠿⠟⠀⠀⢉⠁⠀⢠⡦⠀⡀⣛⡶⠰⠷⣄⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡓⢎⠀⣤⠚⠟⠀⠀⠀⣦⠀⠀⢸⣧⠀⠛⠃⢀⡃⣠⣀⣦⣌⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡄⠻⣅⢀⣽⡆⠀⠙⠁⠀⠀⠀⠀⠀⠠⠙⡁⠻⢁⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣣⡂⠻⠯⠀⣸⣷⠀⣸⣧⠀⣷⡴⠛⠀⠿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣶⣦⠀⢈⡋⠀⢨⠅⡜⠉⠤⠰⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡀⠠⠀⢠⣾⠀⡀⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠦⢾⣥⠶⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠙⣏⠐⠀⠃⠁⠀⠀⠀⠄⠸⠧⣄⣀⣿⡵⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠶⠝⠛⠀⢠⠈⠑⠒⠂⠁⠀⠠⡽
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠷⠤⠄⠈⢀⣄⠃⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣯⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⣵⠟
⠀⠘⠀⠀⠂⡀⠀⢀⠀⠀⠀⠀⠠⠂⠁⠂⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⡼⠁⠐⣀⠤⠒⠋
⠀⠀⠀⠠⣶⢋⣀⣠⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠁
⣾⡆⠀⢠⡕⣎⢉⡀⠀⠀⡠⠀⠄⠀⠀⠁⠀⠀⠀⠀⠰⠿⠀⠀⠂⠉⠘⠛⠀⠁⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰
⠚⣁⢀⣐⣾⠛⢷⣶⠾⣎⣀⠀⠐⠄⡀⠾⠷⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⡄⠀⠑
⣄⡨⢫⠏⠸⣆⣼⠁⠀⣘⢽⣇⠀⠀⠀⠀⠠⠀⠀⡡⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⢠⡽⠂⠀⠀⢠
⠉⢁⣿⠟⡓⠀⠉⠀⠀⠅⣼⠇⠀⠤⠄⣴⠀⣰⠏⠀⠀⠸⠀⢀⡀⠀⠂⠠⠔⠀⠀⠀⢀⡀⠀⠁⠀⠀⠁
⢠⠋⠀⠀⠀⠀⠀⠡⠤⠞⠁⠀⠀⠀⠰⢷⢸⣏⣠⢖⣹⡷⠚⠭⡛⢷⡄⠀⠀⠀⠈⠂⡀⠈⢠⡄⠀⠀⠆⠀⠸⡶
⠁⠀⠀⣠⣴⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠶⢸⣿⠙⠻⡆⠀⠀⢆⠸⡇⠀⠀⠇⠀⠀⠘⣤⠀⠠⠎⠀⢀⠀⠀⠀⢀
⠀⠀⠙⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⢷⣦⠀⠀⣭⣏⠳⠶⠝⠂⠄⡀⢈⠇⠀⠀⠘⢦⡀⣀⣈⣿⡟
⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢐⠊⠀⠙⣛⢻⣤⡞⠂⠀⠀⠀⠁⠀⠀⠀⠂⠈⠈⠁⠉⠙⠛⠒⠊⠀⠀⠀⠙⠃
⠀⢸⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠉⠁⠀⠀⣠⠾⠀⢹⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠂
⡕⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⡠⠀⢸⡀⠀⢷⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⣤⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠪⣟⢳⣦⠀⡇⠀⠀⠣⡀⠀⠀⢀⣼⡃⡀⠀⠀⠀⠈⠁⠀⠐⠀⠀⢠⡴⠞
⢀⡴⠂⡀⠀⠀⠠⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠈⠥⠁⠀⡀⠀⠀⠀⠢⠄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⡇⠀⡀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡤⡀⠀⠀⠐⢀⠄⢀⠠⠤⣴⠀⢠
⡤⢂⣾⠖⠺⢛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠎⠀⠂⠀⠀⠈⠁⠀⠀⠀⠲⣾⣸⣏
⡟⠛⢿⠀⠀⠸⠁⢿⠀⠀⠀⠀⠄⠀⠠⡀⠀⠘⠛⠀⠀⠀⠀⠋⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⣤⠀⠀⠘⢀⠀⠀⡾⢹
⠳⠦⠬⠶⠠⡀⠀⣹⠀⠀⠆⠀⠐⢦⠀⢠⠄⠠⠀⡄⠀⠡⠁⠀⠀⠀⣿⠃⠀⠠⠈⠀⠀⠀⠉⠀⠀⠀⢷⣭⠄⠀⣉
⠇⠴⠲⠀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠸⠆⠨⠠⠂⠀⠂⠀⠀⠀⠀⠀⠘⠋⠈⠀⠀⠐⠀⠠⠀⠀⠠⠀⠀⠡⠸⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⢂⠀⢀⠔⠀⠀⠀⠀⠀⠀⠠

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⠀⡀⠀⢀⠢⢤⡀⠀⠀⡏⠀⢻⢀⡤⣠⠊⠉⠀⣀⠤⠄⠀⢞⢡⠀⠑⢆⠀⠐⠤⡀⠀⠀⡞⢳⡄⠀⢠⠟⠓⠦⣔⠒⠓⠦⣄⣀
⠀⠀⢀⠰⢀⠑⣄⢻⠀⡠⠓⠀⠀⠈⠓⠁⠸⡀⣀⠇⠀⢸⣇⠀⠀⠀⠈⠉⠁⠉⠁⠤⠤⠒⠳⡄⠀⣧⣸⠃⢀⡟⠀⠀⠀⠈⠙⠒⠶⢤⡈⠉⠉⢱⡀
⠀⠀⠀⠂⢢⣽⣿⡻⠋⡠⠔⠒⠉⠉⠓⠦⣀⠀⠀⠀⠀⢸⣧⠤⢄⣀⡀⠀⠀⠀⠈⢉⣀⡈⢽⡃⠀⠼⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢀⡟⡄
⠀⠀⠀⢊⢀⠔⠁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡅⢀⡀⠀⠈⣈⡉⢉⣉⣀⠀⠀⣰⠇⠀⠀⣠⠞⠀⠀⠀⠀⠁⠀⠀⣠⢎⡵⠁⠀⡼⡸
⠀⠀⠀⠀⠁⢀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⣇⠀⠙⠒⠦⠬⠤⠤⠄⠀⢀⣀⠠⠤⠘⠁⠀⠀⣧⣀⠀⠀⠐⠀⠀⠀⣰⢣⠏⠀⠀⢠⢇⡇
⠀⠀⠀⠀⠀⠸⣇⠠⡀⠀⠀⢀⡞⠁⠀⠀⠙⢦⠀⠀⡿⠀⡴⠾⠶⡆⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠀⠘⠫⢽⣲⡦⣄⠀⢠⠇⣾⣀⣀⣠⡼⢸⠁
⠀⠀⢀⣤⣄⠀⠙⢦⡀⠀⠀⠘⣇⠀⡀⢀⡄⣸⠀⢠⠇⢸⠁⠀⣰⠏⠀⢠⠒⠒⢦⡀⠀⠀⠈⣧⣀⣀⣀⣀⣀⡈⠙⠲⣝⣫⠞⠓⠶⠶⠶⠖⠋
⠀⠀⣾⠁⠈⠳⣄⠀⠉⢦⡀⠀⠈⠳⠬⠵⠞⠁⢠⠟⠀⠘⠒⠚⠁⠀⠀⠘⢮⣀⣠⡇⠀⢰⣯⣽⣏⣀⣠⣤⠤⠽⠇⠀⠀⠀⠀⠀⢠⠖⠒⠲⡄
⠀⠀⣿⡄⠀⠀⠈⠑⢤⣀⠑⢄⡀⠀⠀⢀⣠⡴⢋⣠⠴⠖⠒⢛⡓⠒⠲⢦⡀⠀⠀⠁⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⠀⠠⢹⡀
⠀⠀⠸⣷⡀⠀⢀⣤⣤⡈⠑⢦⡈⠉⠉⠉⠁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠲⢄⡀⠀⠸⣄⠤⠤⢷⡤⠤⠤⣤⡇⠀⠀⠀⢠⣾⠀⠀⠀⠀⠃⢦⡀
⠀⠀⠀⡟⣧⠀⢻⠀⠀⡝⣦⠀⢹⡄⠀⠀⡞⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⢙⡆⠀⣟⠒⠒⠚⣷⠚⠛⢉⡇⠀⠀⠀⠸⡍⢙⠋⠙⠉⠉⣩⠁
⠀⠀⠀⢿⠘⣇⠀⠳⢤⣤⠟⠀⢰⠇⠀⢰⠳⣕⠀⠘⣆⢀⣒⣒⣀⣀⣸⣇⣀⠐⣡⠞⢳⠀⢻⠀⠀⠀⠸⣆⠀⢸⠃⠀⣀⡀⠀⠙⠾⣷⣤⡤⠞⠁
⠀⠀⠀⠈⢧⣈⠳⢤⣀⣀⣠⣴⠟⠀⠀⢿⣐⣨⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢧⣀⣸⠇⠈⢧⣀⣀⣀⣉⣠⠜⠀⢯⠉⢧⠀⢀⣠⡴⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⣁⣀⣀⡀⠀⢉⣁⡀⠀⠀⠀⠸⡳⣶⣄⡇⠀⠀⠀⠀⠈⠁⢀⣴⣦⣍⡉⠉⠀⠀⠀⠀⠈⠓⠻⣄⣈⡓⠶⠴⠶⠞⠃
⠀⠀⠀⢰⡒⠦⣴⡒⠋⢉⣉⣀⠠⠀⠉⢶⡁⠀⡝⠀⠀⠀⣠⠽⠾⢿⣧⣠⠤⠤⣄⡀⠀⢸⣝⡻⠷⣯⣭⣍⣉⣉⣉⣛⠲⢤⣀⠈⠉⠓⠦⣄
⠀⠀⠀⠘⣧⠀⠱⢭⣒⣤⣀⠀⠠⠄⠀⠀⠱⡀⢨⠆⠀⣼⢡⠊⠈⠀⠈⠁⠀⠀⢠⠹⡄⠈⠻⢿⣷⣶⣶⣯⣭⣭⣽⣛⡻⠶⣌⢳⡄⠀⠀⠘⣆
⠀⠀⠀⢰⡿⡦⢤⡘⣿⣭⢻⢷⣦⣄⡀⠀⠀⠑⣌⠆⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠶⠤⢤⣉⣉⣉⣉⡉⠛⠻⢷⣼⠋⠀⠀⠀⠀⣿
⠀⠀⢀⣀⠓⢬⣒⢵⡀⠛⠉⣟⠀⠛⢿⢗⠦⣄⡈⣧⠀⠸⡆⠀⠀⠀⠏⠘⠆⠀⠀⢰⠁⠀⢸⠭⠶⠶⠶⠶⠶⠦⣭⣍⡓⠤⡉⠀⠀⢰⠋⠉⠉⣹⠂
⠀⠀⠀⠈⣳⡀⠈⠑⠮⣓⢦⣈⠉⠳⡀⢀⡙⠲⠽⠇⠀⠀⠹⣔⠤⡀⠀⠀⠀⠄⣠⠏⠀⠀⠘⠿⢿⣒⣒⣒⣒⣒⠢⠌⡙⣾⠀⠀⢠⡟⡶⠒⢲⣿
⠀⠀⠀⠑⢿⣧⣤⡠⠴⡌⠑⢬⡓⢦⣉⣁⡸⠂⠁⢀⣀⠀⠀⠈⠓⠒⠛⠓⠒⠛⠁⠀⣀⣤⠴⠶⠲⠶⠦⣄⡀⠈⠙⢦⣄⣷⠀⠀⠸⠶⢷⣬⣿⣸
⠀⠀⣠⢾⡿⠋⠛⠒⠋⠀⠀⠀⠈⠓⠖⠋⢀⡠⠞⠉⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢉⢳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠉⢁⡤⠤⠤⠄⢤⣄⣤⠤⠤⡀⠀⠀⡿⠤⠤⠤⠤⢤⡴⢦⣄⣈⣓⠲⢄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡰⡠⠃⢀⡴⠞⣻⠋⠉⠉⠉⠓⢦
⠀⠀⡎⢹⠉⣿⠛⠛⠛⠛⠛⠛⠛⡏⠀⠀⣛⣷⠀⠀⣀⠀⠙⠋⠀⠀⠉⠉⢻⠀⠈⢧⡳⢤⡀⠀⠀⠀⠀⠀⢸⠁⢀⡞⠀⢎⠉⣠⠶⢶⣄⠀⠈⢧
⠀⠀⠹⣼⣧⠘⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣯⡀⠀⠸⠽⠂⠀⣠⣤⣄⠀⠀⢳⠀⠀⠀⠙⣆⢷⠀⠀⠀⠀⠀⠘⡇⠸⡇⣠⠊⠘⣇⠀⣸⣽⠀⠀⣸
⠀⠀⠀⢠⡛⣦⣀⡀⠀⠀⠀⣠⠗⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠛⠶⠟⠀⠀⢸⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⢹⠀⢷⡸⢄⣠⣌⢉⣩⣁⡖⣲⠏
⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠙⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠳⣧⣄⣀⣠⣤⡤⠞⠀⠀⠙⠶⣤⣈⣉⣠⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠞⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢸⡆⠀⡇⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣾⠀⠀⢸⠀⠀⣿⠀⢸⡇⠀⢸⣀⣀⣧⣤⣧⡤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣸⣀⣠⣽⣤⠶⠷⠛⠛⠉⠉⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢷⡖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⣄⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢀⡼⠃⢀⣀⣤⡤⠴⠶⠚⠛⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢠⡿⠷⢿⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠿⣦
⣿⠁⠀⠀⠀⠈⠉⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⠋⠉⠁⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⢤⣀⣘⠆⣀⣀⣤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢸⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⡄⠰⡟⣷⠞⣹⠆⠸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢸⠀⠀⢰⠲⡆⠀⣾⣆⠈⣏⢿⢻⡘⡇⠀⣷⠀⢠⣏⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠙⢶⠇⠹⡆⢻⢸⣼⡇⣿⣀⣽⠀⣶⣝⢦⡀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⠀⢀⡀⢹⣼⡎⣿⣧⣈⣠⣿⣧⡽⠘⠾⠁⢸
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⡟⣧⢘⣿⣦⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠚⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⣿⠀⠀⣒⠦⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⢠⣭⣟⡒⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠈⡇⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⢹⡀⠀⢇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⣧⡀⠈⠳⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞
⠀⠀⠀⠀⠀⠉⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣤⡴⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⣸⣤⡶⠞⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠉⠀⠙⡁⠐⡖⠀⢠⠎⠉⠽⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠶⠖⠒⠒⠋⠉⠝⠁⠀⠀⠀⠈⠁⠖⠪⢼⣷⡒⣁⠀⠀⠀⠀⠙⠃⠉⠓⠲⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠂⡄⠀⠀⠀⠀⠀⠉⠑⠂⠐⠦⣤⡤⠴⠊⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣂⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⢰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠦⣄⡀⠀⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠖⠒⠛⠋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⡴⠒⠉⠙⠒⠦⡀⠀⠙⠿⣦⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⡧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠙⠷⡄⡅⡆⠰⠀⠂⠔⠀⠀⡠⠀⠀⢀⡠⠤⠤⠬⠿⣷⡢⣄⠀⠀⡇⠠⢡⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠙⠣⢳⣤⢀⢠⠀⢠⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠙⢷⣽⣶⣧⣀⠁⠀⢈⠀⠀⡀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠚⢼⣶⣠⠸⡔⢢⡤⡀⠉⠢⠄⠀⠀⠹⣿⡷⠈⢉⡗⠦⣄⣈⣠⠤⠴⠒⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠽⠏⠀⠁⠀⠀⠀⠀⠙⠲⠽⠗⠛⠛⢲⡄⠀⠉⠓⠦⣌⡀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠹⣳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣄⡀⠀⠉⠛⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠈⠙⠫⣟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢾⣧⣤⠟
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⣤⣀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠤⣀⣀⣀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡼⠀⠀⠀⣀⣤⡤⠤⠶⠤⣄⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⢺⡆⠀⠀⠀⠀⠀⢨⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠒⠒⠒⠒⢠⡀⠀⠀⠀⠀⠀⢀⡤⠼⠧⠤⠤⠤⠤⠤⠼⠼⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃
⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⢀⣀⡠⠤⠔⣊⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠐⢬⠭⠉⠉⠭⠭⠁⠤⠐⠂⠉⠀⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⡄⢀⣀⣀⡀⠤⠤⠀⠐⠒⠈⢹⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⢀⣀⣀⣀⠀⠻⣃⣟⠘⠃⠀⣠⠒⠢⠤⠭⠍⠉⠐⢲⠋⡇
⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⣤⣦⣄⠀⠀⠀⢸⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠀⠐⠃⠀⠀⡇⠀⠀⠢⠠⠐⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⢱⠀⠀⠰⣿⢿⣽⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⢀⡀⠀⠠⠤⠤⠄⠚⠃⢰
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⠟⠋⢀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣔⡉⣑⢏⡠⢶⠀⠀⠀⠀⠘⠁⢠⢰⡴⠄⠶⠦⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠐⢖⠒⠒⠂⠈⠉⠀⠀⠀⡄⠀⠀⠀⡠⠠⠤⢊⠭⠠⠕⠀⣈⠔⠨⠥⠄⠒⠤⠀⠀⠀⠀⢰⣈⡡⡀⠤⠤⠤⠤⠒⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⣀⡠⠄⠊⠀⠀⠀⠀⡗⢒⡒⢁⠔⠒⠊⠀⠀⠀⠀⣀⠀⠀⡀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠂⠑⢊⣐⢂⡮⠭⠱⢞⢄⡨⠮⡀⢴⠀⠀⠀⠀⠆⠀⠐⠒⠂⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠐⠠⣀⠀⠀⠀⠀⠀⢸⣁⢉⡈⡡⠤⠤⠊⠑⠒⠉⠑⠀⠒⠢⠼⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠤⡐⠜⠋⠁
⠀⠀⠀⠀⢀⠴⠈⠠⠤⠤⠄⠤⠤⠤⠤⠄⠤⠤⠤⠬⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠧⠤⠶⡈⢁⡀
⠀⠀⠀⠀⠘⣷⣮⡴⡤⠰⢶⣤⣤⣄⣄⣠⣡⣤⣐⣲⣶⠃⠀⠀⠀⠀⠀⠀⠀⣔⠈⡡⠄⠰⡀⠠⡤⢀⣐⠢⠤⣄⡉⢲⡄
⠀⠀⠀⠀⠀⢏⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⢋⡁⠃⠀⠀⠀⠀⠀⠀⠀⢙⠛⠠⠬⢵⣏⣘⣏⣁⣬⣡⠦⠶⠚⢛⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⡴⠋⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣷⣿
⠀⢸⡿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢟⣭⣴⢿⣿⢿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⠿⣻⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢽⣶⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣏⣽⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣄⣀⠀⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢀⣾⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⡇⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠻⣷⡀⣼⡟⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣷⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡄⢻⣶⣿⠁⣿⣿⠀⠀⢿⣿⡇⠀⢸⣿⣇⠀⠀⠀⠀⢸⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠇⠈⠻⠃⠀⣿⣿⠀⠀⢼⣿⡇⠀⢸⣿⣿⣶⣶⣶⡆⢸⣿⣇⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣧⣧⣿⣿⣿⣿⣿⣿
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠙⠉⢉⣭⣍⡙⠿⢶⣶⣶⣶⠶⠋⠉⠻⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠯⡭⠤⠤⣤⣀⡘⠻⣿⣇⠀⠈⠛⠛⠋⠠⣿⣆⢠⡀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢡⣿⠇⢠⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⣄⠀⣿⣀⠀⠀⣀⣠⣤⣤⣀⡀⠈⢆⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡄⣿⠀⠀⠉⠁⠈⠛⠛⠛⠙⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⢻⣻⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⠟⡀⠀⠀⠀⠀⠀⠀⡧⠞⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣾⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⣤⣤⣿⣧⣼⣿⣥⣤⣤⣤⣤⣤⣼⣿⣥⣤⣷⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣵⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠹⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢠⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣷⣶⣴⣶⣾⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣶⣤⣤⣤⣶⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⡿⠋
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢦⣤⣤⣀⠀⠀⢀⣴⠞⢻⣇⠀⠀⠀⠀⢀⣠⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠈⠉⠛⢦⣾⡃⠀⠀⢻⡆⠀⣀⣴⠟⠋⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠹⣷⡀⠀⠀⠀⠠⣈⢧⡀⠀⠀⣧⢞⣩⡴⠞⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠤⡄⠈⠛⢦⣄⣀⣀⣀⣑⣷⣴⣴⡷⠿⠷⠶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠳⠾⠃⠀⠀⣠⣾⠿⠋⠉⠭⢿⣿⣿⠿⣄⠉⠀⠀⠉⠻⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡔⢲⡄⠀⠀⢠⣤⣴⡿⠋⠁⠀⠀⢀⣠⡾⣿⡀⠑⢀⠑⢦⣤⣤⣤⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⠗⠋⠀⠀⠀⣀⡈⠛⠿⠷⣶⣶⠿⠟⠋⠀⠹⣷⣄⠀⠁⠈⢿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣞⢁⠇⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠘⠻⢿⣶⣤⣬⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠒⡄⠀⠀⠀⠀⠙⠉⠀⠀⠀⣼⠁⣽⠀⠀⠀⢰⡏⣹⠀⠀⠀⠀⢩⡤⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠻⠾⠃⠀⠀⠀⢀⡔⢲⡀⠀⠀⠘⠛⠁⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⢸⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⠀⠀⠸⣷⡾⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⠒⡄⠀⠈⠉⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣠⠇⠀⠀⠀⠀⣷⡴⠃⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠁⠀⠀⠀⣠⠤⡄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣀⣄⠀⠀⠀⠀⠀⣯⣴⠇⠀⠀⣠⠴⢦⠀⠀⣰⠊⣩⠂⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⡃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠞⠀⠀⠙⣋⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡉⠉⠀⢀⠔⠆⠀⠀⢀⡴⢲⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⢿⡴⠃⠀⠀⠸⠶⠞⣀⣤⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣤⣤⣶⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣩⣬⣩⣿⣹⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠓⠐⠒⠲⠤⠖⠒⠲⢤⠴⠒⠒⠒⠊⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⠀⠀⠐⠲⠶⠶⠶⠶⠒⠒⠒⠒⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⣤⠒⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠉⢧⡀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢶⣄⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠳⢦⣀⡰⠎⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠹⣆
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⡙⢇⠀⢠⠻⡆⠀⠀⢸⠋⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡉⡇⠀⣀⡤⢶⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠸⠃⠈⢷⡎⠀⠻⡀⠀⠘⠀⠇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡆⠰⠞⠁⣠⠏
⡇⠀⠀⠀⠀⠀⠀⠇⣠⢦⡀⢀⣤⡀⢣⡀⠀⡆⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⣞⠁
⡇⠀⠀⠀⠀⠀⢰⢀⡉⠀⠳⠎⠀⢳⠈⢧⠀⣇⢸⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⡇⢸⣧⠘⠦
⣿⠀⠀⠀⠀⢀⡇⡜⠁⠀⠀⠀⠀⠀⢧⡈⡇⣿⢈⠀⠀⣇⠀⠛⠛⠛⠂⠒⡄⠃⠸⠈⢧⠘⢣
⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⠇⠈⠛⠀⠀⠘⠓⠒⠲⠖⠒⠋⠀⠙⠃⠀⠈⠳⠞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠐⠒⠒⠲⠶⠶⠶⠶⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠁
⡇
⢣
⢸
⢸⡆
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟
⠀⠀⠻⣷⣶⣤⣤⢤⢤⣤⢤⣤⣤⢤⣤⣤⣤⣤⣤⡤⣤⡤⠤⣤⡤⠤⠤⢤⡤⠲⠲⠖⢶⠖⠒⣩⡟⣻⠟⠁
⠀⠀⠀⠈⢿⣀⣳⣀⠀⠳⠀⠈⠃⠀⠘⠃⠀⠉⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣞⣡⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⡞⠉
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠖⠢⠀⠐⠊⣿⠃⢠
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠴⠄⠈⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠂⣀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠃⠄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠳⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠀⠰⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡲⠀⣀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠠⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠒⢻⠷⣄⡈⠀⢐⠻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⡄⠀⠤
⠀⠀⠀⢠⢦⡤⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠐⡶
⠀⠀⠀⠀⠗⢦⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠈⠓⠠⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⢠⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣦⢀⣀⡀
⠀⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠐⠠⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠻⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡤⠀⠘⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⣠⣿⠖⢲⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣤⣄⣟⠃⠀⠀⠀⠀⠀⠀⢤⣴⣄⣁⡀
⠀⠀⢠⣍⠀⠀⠀⠀⠂⢿⠀⠀⠀⠀⠀⠀⠐⠰⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠇
⠀⠀⠘⡇⠀⠀⠀⠀⠈⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠣⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠉⠉
⠀⠀⠀⠀⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⠟⠁⢀
⠀⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡸⣿⣫⣉⣉⣛⠂
⠀⠀⠤⠞⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡅⠻⢿⣗⣳⣂⣁⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠑⠂⠀⠀⠀⠐⠀⠀⠀⡃⠀⠀⠈⠛⠶⢌⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

⣿⣿⠿⢿⡿⢿⠿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⢀⣠⣆⣬⣿⣿⣿⣦⠀⠀⠀⢀⢀⠀⠤⣤⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣓⣶⣤⣤⣖⣲⡄⠀⠈⠮⢻⠿⠟⠋⠉⠁⠀⠀⠀⠘⣜⢷⣾⣿⣿⣿⡄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠
⠅⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⢷⣾⡿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⡠⠀⠀⠐⠒⠒⠢⢤⠀⠙⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠘⣦⣄⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸
⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⠋⠀⠀⠀⠀⡐⢶⡄⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢠⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠣⡀⠀⠀⠀⠀⠇⠀⠀⡌
⢠⠀⠀⠀⣈⠀⠀⠠⠀⠀⢀⢸⡏⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⢰⣻⣭⣭⣑⠒⠶⠤⠴⣷⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⣄⠀⠀⢰⠀⠀⠀⠇
⠸⣌⠀⢀⠜⠀⢠⠁⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⡇⢿⣦⣀⠈⠳⢤⣿⣿⡿⢷⣶⣶⣿⣿⠀⠀⠀⠀⠄⣸⣷⣦⠀⠀⠀⠀⠀⣸⢿⡇⠀⠘⡄⠀⢸⠀⠀⠸
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠙⢦⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⢪⣿⡀⠀⢀⣴⣿⣿⡿⠏⠀⠀⠀⠀⣴⡿⣸⠁⠀⠀⢱
⠀⠀⡇⢁⠀⠀⡇⠀⠀⢀⣼⣿⣿⣷⣵⣄⠀⠀⠀⠀⠀⠈⠙⢮⠻⢿⣾⣿⣶⣄⣀⣀⣼⣿⣿⣾⣿⠟⠉⠁⠀⠀⠀⢀⡠⣺⡟⣡⡟⠀⠀⠀⢸⠀⠀⠀⢠⡇
⠀⠀⡇⢸⠀⠀⡇⠀⠀⢸⣿⣿⡟⢿⣿⠻⣕⡤⣀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠿⣭⡽⠟⠛⠳⣽⡇⠀⠀⠀⠀⣠⠔⣫⠾⢋⣴⣿⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⡇⠀⡆⠀⢳⠀⠀⠘⣦⣿⣿⡀⠹⣗⢄⡙⠮⣝⡒⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⣤⠤⠒⣋⡴⠞⣡⢔⣵⣿⠇⠀⠀⠀⠀⡞⠀⠃⠀⢸
⠀⠀⡇⠀⢡⠀⠈⢧⠀⠀⠈⠳⢽⣾⣄⠈⠳⢭⣒⠤⣉⠛⠶⢤⣤⣈⣉⣙⠒⠒⠒⢒⣈⣩⣭⣭⣿⣷⠖⣋⡥⢖⣩⢶⢟⣽⠋⠀⠀⠀⠀⣼⠁⢸⠀⠀⡏
⠀⠀⠀⠀⢸⡀⠀⠈⠳⡄⠀⠀⠀⠹⣿⣷⣖⢤⣉⠛⠲⢯⣕⡒⠦⠤⢍⣉⣉⣉⣉⣉⣉⣉⠿⡿⣻⣿⣯⡴⢚⡫⢞⣡⠞⠁⠀⠀⠀⢀⡾⠁⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠢⡀⠀⠀⠈⠪⠿⠷⢮⣙⠢⢤⣀⡉⠛⠓⠲⠶⠶⠒⠒⠒⠒⠛⢻⣿⣷⣿⡯⠖⣋⣴⡿⠃⠀⠀⠀⢀⣴⠏⠀⠀⢠⠇⠀⢰⡇
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠈⠙⠓⠶⠬⣭⣍⣑⣒⣒⣒⣒⣉⣉⣩⣭⣭⣵⣹⣷⣟⡿⠋⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⡸⠀⠀⢸
⠀⠀⢸⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠑⠈⢓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠗⠚⠛⠉⠁⣀⣠⢴⡺⠝⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⡀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠭⢒⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⢖⡒⠍⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣠⣄⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣲⣆⠄⠐⣊⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠸⠋⠽⠟⠉⠁⠀⠀⠐⠒⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠂⠈⢺⡄⢤⣠⢀
⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣠⡈⡀⠀⠀⠀⠈⠀⠀⠔⡻⠿⢦⣄
⠀⠀⠀⠀⢀⣠⡵⠂⠀⠀⠀⠈⠀⠒⠦⣤⣄⡀⠀⠀⠀⠀⣥⠒⠀⠀⠀⠀⢀⣀⣆⢙⡃⠀⢠⣠⣤⡀⠀⢀⡶⢿⢷⢹
⡠⢷⡀⠀⡳⠘⠿⡎⡂⠀⠀⠠⠀⠀⠀⠀⠉⠑⠢⠤⣀⠀⣧⣤⠤⠄⠒⠂⠉⠀⠀⠁⠒⠒⠋⠉⠫⡙⠓⡊⢤⠾⠀⢺
⢥⡀⠑⠬⡻⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠬⠑⠢⠔⠁
⠀⠀⠀⠀⣀⣀⣁⣀⡶⠶⠒⠒⠒⠒⠒⠲⠤⠤⢄⣀⣀⠀⠄⠀⣀⣀⠀⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣓⣛⣿⣭⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⠛⠛⠛⠉⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠘⠦⣤⣉⣉⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣀⢴⡏⠀⠀⠀⠀⠀⠈⠢⣈⠑⣆⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⣠⠞⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⡤⠞⠋⠉⠉⠓⠦⣤⣀⣀⡤⠎⠀⠀⠉⠉⠉⠀⠀⠀⠹⡆⠀⠘⣏⠛⢦⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣼⠋⠀⡏⠀⠀⣠⠖⢋⡆⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⠀⠀⠈⠣⣄⠈⣧⠀⠀⠀⠀⠀⠘⣧
⠀⣼⠇⠀⠀⢹⠀⡞⣁⡴⡋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⢶⣤⣄⣀⠀⠨⣙⠲⣄⠈⠳⣄⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢹⡆
⢸⡏⠀⠀⢀⡞⠀⠉⠁⠚⠁⠀⠀⠀⠀⠀⡇⠀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣌⠳⣌⢳⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡜⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠏⠸
⣿⠀⢀⠀⠈⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⡼⠃⡽⢠⠏
⢻⡄⠸⡆⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⢠⡖⢉⠇⠀⠀⠀⢰⣃⡼⠁⠘⡆⡰⢀
⠘⣷⠀⢷⡀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠒⠂⡄⠀⠀⠈⠙⠓⠶⠦⣤⣤⣀⣀⣀⣤⣤⠤⠶⠚⠋⠉⠀⠀⠀⢠⡏⣠⠊⠀⠀⠀⠀⠀⠀⣀⡤⠞⢱⠃⣸
⠀⠸⣧⠘⢷⡀⡞⠀⠀⠀⡞⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠃⢠⡟
⠀⠀⠘⢧⡈⢳⡹⣄⠀⣰⠇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡤⠖⢋⡽⠃⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠋⢠⡟⠁
⠀⠀⠀⠈⠻⣆⠙⢮⡉⠁⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠻⠴⠚⠁⠀⠀⠀⠀⠀⠘⠳⠦⠤⠌⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣸⠇⢀⡾⠃⣴⠏
⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠉⠉⠒⠶⠞⢋⡴⢛⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠦⣤⣤⠞⠉⠹⡄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⢚⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡼⠁⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⠤⠴⠶⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠿⣿⡿⠟⠉⠉⠉⠉⠙⢛⣿⠿⠶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠀⠀⠀⠀⣿⣅⣀⣀⣀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠉⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡾⠟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣄⣀⢹⣧⠀⠀⢠⣶⠿⠿⢷⣦⡀⠀⠀⣰⡿⠛⠉⠉⣀⣠⣴⣿⣁
⠀⠀⠀⠀⠀⠀⣠⣶⠿⠻⣧⡈⠉⠛⢻⣿⠀⠀⣿⣧⣤⣤⣤⣽⣷⣤⣴⣿⣷⠶⠾⠟⠛⠉⣁⣼⠟⠿⣶⣄
⠀⠀⠀⠀⢠⡾⠋⠀⠀⢸⣟⠛⠷⣶⣬⣿⣄⣸⣟⠀⠀⠉⠉⠉⠉⠈⠁⣀⣀⣀⣤⣤⣶⠾⠛⣻⡆⠀⠀⠙⢷⡄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣶⣤⣀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⣀⣤⣶⠟⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠉⠛⠛⠿⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⡶⠶⠿⠛⠛⠉⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢉⣉⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣧
⠀⠀⠀⢼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡿⠀⢿⡄⠀⠀⢀⣠⡴⠶⠶⠲⠶⠶⣤⡀
⠀⠀⠀⢸⡈⠛⠶⣤⣄⡀⠀⠀⣠⡴⠖⠛⠛⠳⢦⣼⠛⠦⣄⣼⣁⠀⠘⣧⢀⣴⠟⠉⠀⠀⠀⠀⡀⠀⠀⢙⣧
⠀⠀⠀⠘⣧⠀⠀⠀⠈⠉⣹⣞⡁⠀⠀⠀⠒⠢⣄⣿⠀⠀⠀⠈⠉⠙⠓⢿⣿⠃⠀⠀⠀⢀⡴⠋⠀⣠⣶⡋⠁
⠀⠀⠀⠀⠘⢷⣄⡀⠀⠐⠋⠉⠙⠳⣦⡀⠀⠀⠀⠙⢦⡀⠀⠑⢦⡀⠀⠀⠙⢧⣀⣠⠴⠋⠀⣠⡾⣯⣀⠙⠲⠦⠤⠴⠶⣶⠟
⠰⣶⡶⠶⠶⠶⠾⠛⠛⠛⢋⣉⣡⡤⠾⠿⣷⣤⣄⣀⣀⣹⣆⠀⠀⠙⣦⠀⠀⠈⢿⣁⣠⡴⠞⠻⠶⠶⢦⣤⣤⣤⠴⠶⠛⠁
⠀⠈⠛⠶⢦⣤⣤⣀⣀⣈⣀⣉⣠⣤⠶⠛⠉⠀⠉⠉⠉⠉⠻⣦⣄⣀⣹⣆⣤⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢀⡶⠋⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠳⡄
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⢹⣄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠢⠀⠀⠀⠀⠀⠀⢿
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠤⢀⠆⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⣿⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠎⠂⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢀⠀⡓⠀⣸
⢸⡇⠀⠐⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢰⢒⡄⠀⠀⣠⡀⠀⠐⠀⠀⡀⠤⠀⠀⠀⠀⠆⠀⢀⠐⠀⠈⠀⠃⢠⡿
⠀⢿⡄⠄⠀⠀⠀⠇⠀⢐⡂⠀⠀⠀⠣⡼⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠀⡜⠐⢁⡤⠀⢀⣿⠃
⠀⠈⢷⡈⠀⠀⠄⠀⠠⢈⠁⠀⠀⡀⠀⠀⠀⠀⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠚⠀⠀⣾⠃
⠀⠀⠈⢻⣄⠈⠂⠀⠀⢫⡇⠀⠀⢰⠳⡀⠀⠀⠀⣧⣹⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⢠⡌⠄⠀⠔⠃⠀⠈⠂⠀⣼⠇
⠀⠀⠀⠀⠹⣦⠀⠀⠀⡄⠀⠀⠀⠀⠓⠃⠀⠠⢄⡈⠁⠀⠀⠀⠁⠈⠠⠀⠘⠲⠃⢀⡀⠀⠀⡀⠀⠠⠄⠀⠠⢄⣽⠃
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⠀⠀⠀⠰⡄⠀⠀⠈⠰⠇⠀⠠⠤⣄⠀⠀⠀⣠⠔⠂⠘⠁⠀⠀⠀⠀⠀⠃⣡⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⠀⠀⠑⠁⠀⠀⠒⢤⠀⠀⠀⠐⠈⠁⠀⠘⠀⠃⠀⡴⠓⠀⠀⢀⠒⠀⠈⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠀⠀⠀⢄⠀⠠⡀⠘⠀⠀⠀⠒⡄⠀⠔⡒⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢢⡈⠀⠀⢁⠀⠀⠒⣀⠈⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠁⢀⠤⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡁⠀⠀⠄⠀⡀⢀⠁⠀⠀⠈⠉⠑⠀⢀⣀⠀⠀⠀⠀⠃⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⡄⠀⠀⠁⠀⠉⠀⠀⠀⡀⠑⠀⠀⠋⠠⠄⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠙⡀⠀⠀⠠⠂⠈⠀⠀⠒⠂⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠠⣄⠀⠐⠒⢄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣤⡶⠾⠛⠁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣤⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⣀⣀⠤⠄⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡔⢲⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠓⠲⢄⠀⡀⠤⠒⠒⡲⠦⣀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠋⠀⠑⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠁⠀⠀⠀⠀⠀⠘⣦⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢠⠀⠀⠀⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠠⠀⠛⠺⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣀⡀⣀⡀⠻⠗⠀⣣⠈⠀⠀⠀⠑⠄⣀⢀⠀⠀⠀⠀⠀⣴⠋⠊⢉⠉⠣⣀⠀⠀⡀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠁⣠⢄⠹⢶⠤⠾⠃⠦⡀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣰⣾⡀⠀⠀⠈⠀⠀⡤⠑⠛⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⣀⡩⠞⣼⠁⠀⣠⠀⠘⢂⡤⠐⠒⠀⠐⠒⠠⢄⣹⡞⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡠⠄⠠⣄⠸⡀⣶⢌⢁⣠⡞⠉⣠⠀⠐⠀⡒⠀⠀⠀⠉⢧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢸⡆⢧⣅⣀⢀⡀⠀⠀⠈⠣⠈⠀⠁⠔⠁⠀⠀⠈⣳⣦⠤⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠥⠎⠀⡟⠁⠀⠈⡇⠀⣀⡈⠁⠀⠀⠀⠐⢂⠨⠓⠝⠋⠀⠀⠀⠀⢘⠀⡠⠂⠀⠀⠉⠒⠤⠤⣀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣇⠸⠖⠀⣣⠀⠀⠤⠂⠀⡐⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠾⠀⠓⠒⠒⠙⢄⠀⢂⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣡⠀⠀⠀⠤⠐⢞⠈⠑⠤⣀⣀⠀⣀⣳⡀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢿⠁⠁⠀⠠⣄⠀⠀⠀⠀⠀⢨⠀⠀⠈⠢⠵⠀⣠⣄⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⡀⠀⠉⠉⠳⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⠐⠂⢤⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⢀⣀⠤⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠐⢄⣀⣀⣀⠠⠜⢗⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣁⠠⠊⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⣠⠴⠖⠒⠉⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠁



⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣷⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠚⢻⠛⠉⢹⠉⠉⠏⠉⢹⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣤⠼⠦⠶⠾⠖⠒⠛⣛⣋⣉⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⠽⢦⡀⠀⠀⠀⠀⠀⣾⡏⠀⠙⡆⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠚⠁⠀⠈⠳⣄⠀⠀⠀⠀⠻⣿⣦⠾⠁⠀⠀⢀⣈⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠛⠛⠛⠛⠒⠶⠶⠿⣶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡤⠤⠶⠶⠖⠒⢹⡇
⠀⠀⠀⢠⣟⣛⠓⠒⢶⣄⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⠖⠒⠒⠢⠤⣀⣀⣇⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⢧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡜⣷⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⢀⡇⠀⣄⣀⣀⠠⠄⣶⢸⣿⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⢾⡇⠀⠀⠀⢸⡇⢸⡏⠉⢹⡜⠇⠙⠈⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣧⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠉⠙⠒⠒⠒⠊⠉⠉⠉⡏⣿⠀⠀⠀⠀⢸⡇⠀⠀⢠⠖⠳⣄⡰⠃⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠉⢆⠀⡴⢺⡏⢦⣀⠜⠀⠀⠈⠀⣀⠀⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⢸⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡟⠉⠓⠶⢤⣄⣸⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣭⣒⣒⣒⣤⡤⢤⣔⣚⣥⠞⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⢠⠔⣒⡲⢄⡀
⠀⠀⠀⠀⢻⡘⡀⠈⠐⠝⠦⡀
⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠉⠒⠤⣀⡀⠀⠀⣀⡤⠖⠊⠉⠉⠉⠉⠉⠉⠁⠀⠀⡉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡄⠀⠈⠑⠫⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢎⣁⣳⣄⣀⣀⡀⣀⣉⡒⢤⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⢸⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⠑⠢⢄⣱⠀⠀⠀⠀⡰⠃⠀⠉⠉⠉⠉⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠈⢲⡀⣠⠊⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⢀⣀⠤⠒⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠟⠒⠒⠒⣺⠞⠁⠀⠀⠀⢀⡴⠋
⠀⠲⠮⠭⢤⣄⣀⣀⣀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⣄⡠⠴⠚⠒⢒⣒⣋⣀⣀⣠⣤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠴⢥⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⢠⡐⠉⠙⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠀⠀⢺⠀⠀⠀⠘⠀⠐⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠘⠒⠊⡁⠀⠈⢹⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣭⣍⣛⣛⡻⠿⠷⠶⠶⠶⠒⠒⠀⠀⠐⠉⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⣈⡉⠉⠛⠛⠿⠿⠷⠒⠚⠛⠃⠀⠀⠀⢴⠿⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣮⣉⡙⠛⠛⠿⠷⠶⠆⠀⢒⠀⠀⠀⠀⠐⠈⠀⡴⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢤⣉⠛⠛⠻⠷⠶⠶⢶⣤⣤⡤⠀⠀⠀⠒⠀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠙⠻⠶⣶⣶⣤⣤⣤⣤⡤⠤⠄⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⣛⣭⣭⣛⣛⣒⠶⢤⣄⡀⠀⠀⢀⣠⡤⠶⣒⣛⣛⣭⣭⣛⣓⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢭⣓⣚⡭⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⠉⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠘⡇⣷
⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢆⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠛⠀⣇⠀⠃⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣀⡔⠹⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠛⠋⠉⠀⠀⠈⠙⠛⠉⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⣀⡤⢶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡶⢤⣀
⠀⠀⠀⣠⠞⠁⣠⢼⠇⡇⠀⠀⠠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣄⠈⠳⣄
⠀⠀⣼⠁⢀⡞⠁⢸⢰⡇⠀⠀⠈⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⡇⠈⢳⡀⠈⣧
⠀⢠⡇⠀⢸⠀⠀⢸⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠀⢸⡄
⠀⠘⡁⠀⠸⢦⡀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢀⡴⠃⠀⢈⠃
⢀⡞⠁⠀⠀⠀⢧⣀⣳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣞⣠⡼⠀⠀⠀⠈⢳
⣼⠀⢀⣴⡦⣄⣀⣠⠇⠙⢮⣑⡢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢔⣫⡵⠋⠸⣄⣀⣠⢴⣦⡀
⡇⠀⢸⠇⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⠶⡶⢶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠚⠋⠉⠁⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣷⣶⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⠛⠉⠉⠉⠈⣻⣟⣻⣿⣿⠿⠛⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣟⠾⡅⠓⣶⡿⡯⠽⣏⣹⣟⣥⣬⣶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠲⢭⣽⣼⣉⣉⣉⣩⣽⣿⣶⠿⠛⣩⢜⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢮⣅⣺⣾⡇⠤⠤⠤⠽⠾⠿⣾⣻⣽⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠷⣌⠹⣿⣿⠭⠭⠭⠿⠿⠟⠋⣋⣊⡭⣛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠤⣈⢹⢿⡷⠬⣭⣭⣙⣭⣬⣭⣷⣶⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠳⢮⣍⣿⣧⣤⣤⣬⣵⣶⡿⠷⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣶⠤⢤⡟⡟⠉⠩⠉⠉⢭⣒⡫⢵⣾⣿⣧⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠐⠁⠀⢀⠴⢾⣿⣔⠝⠒⡿⣯⣭⣭⣉⣭⣥⣴⡾⣛⣭⣿⢿⡋⠒⢄⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣰⢼⡄⠙⠿⣿⣾⡧⠤⠤⠬⢭⣯⣭⣵⣾⣿⣿⣿⣗⡰⣎
⠀⠀⠀⠀⢀⠀⠀⠀⠲⣷⣿⣿⣶⣤⡾⣹⣏⣉⣛⣛⣛⣭⠽⢶⣻⣽⣿⣿⣿⡶⠋⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⢻⢿⣟⠨⠿⢿⣿⣶⣶⢶⣾⡿⢿⢿⡿⠟⠋⠉⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠉⠓⠛⠛⠛⠛⠛⠒⠒⠚⠉⠉⠁⠀⠀⠀⣀⡠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠶⠶⠶⠤⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠙⠂⠀⠀⢦⡄⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠛⠉⠁⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠛⠉⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⢤⣤⣄⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣅⡀⠀⠀⠈⠙⣦⣀⡴⠋⠀⢀⡀⠀⠀⠀⠈⠳⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣷⠀⠘⢷⣄⣠⡴⠛⠻⡆⠀⠀⠀⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠒⠶⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⣇⢀⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⣠⠤⠦⠤⠴⠞⠁⣾
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢸⡇⠀⢀⡞⠁⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠈⠳⠶⠟⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⢹⡏⠉⠁⠀⢈⡽⡅⠀⠀⢿⣯⠉⠉⠉⢉⡟⡏⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣿⠀⠀⠀⠀⡇⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⣤⣤⣤⣴⣷⣧⣤⣤⣼⣷⣤⣤⣤⣼⣷⣧⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣿⢦⣄⣀⣀⣤⠴⡎⣿⠀⠀⠀⠀⠀⠀⠀⣼⢳⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣤⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠱⡄⠀⣷
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⣆⢹⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⢮⣷
⠀⠀⠀⠀⢠⡏⠀⠀⣠⠖⠋⠙⣆⠀⠀⠀⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⢸⡧⢤⠴⠁⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠹⣄⣀⣠⠋⠉⠑⡄⠀⢀⡟⠉⢳⠀⠀⡞⠉⢱⡄⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠓⠤⢼⡇⠀⣏⠀⢀⡇⠀⠈⠓⢺⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠉⠉⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣴⣦⠀⣠⡄⠀⠀⠀⣶⠀⢠⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⠘⠟⢹⡇⠐⣃⠀⣿⠀⢸⣤⡾⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠃⠀⠀⠿⠀⠟⠀⠟⠀⢸⠏⠻⣆⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⠶⠟⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠾⠛⠋⠉
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⢛⣓⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⣀⣀⡤⠤⠼⠓⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠖⠋⠁⣀⣠⠤⠖⠒⠋⠉⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠛⢓⣢⣤⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠠⠾⠕⠒⠚⠉⠁⠀⠀⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⣀⣠⠴⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⢤⣀
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠛⠒⠒⠮⠷⣄
⠀⠀⠀⠀⠀⢻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠽⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣀⣀⣠⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠶⠦⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣀⠤⠀⣠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢶⣇⣔⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣥⣔⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠧⣄⣤⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠺⠷⠶⠶⠶⠾⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀
⠀⠀⠀⠀⠀⠈⠰⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠄⢤⣀⠀⠀⠀⠈⠑⠢⢄⣠⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠨⢙⠳⢦⣄⣀⣠⢴⠞⠋⠀⠀⠀⢨⣦⠀⠀⠀⠀⠀⠀⠉⠒⢄⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠭⣙⠦⢤⣄⡀⣀⣠⡴⠋⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⢀⣤⠤⠖⠒⠒⠀⠐⠒⠂⠤⣄⠀⠀⠀⠀⠀⢷⡀⠀⣠⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⡐⣧⢻⡁⠀⠀⠀⠠⡤⠞⠂⠀⠤⣿⡗⣀⠀⠀⠀⠀⠹⣄⠒⢵⠲⠤⢾⠛⠁⠈⠢⡀
⠀⠀⠀⠀⠉⠛⣦⣌⠓⠒⠤⠤⠤⠤⠴⠞⢛⣁⡴⠛⢃⡄⠀⠀⠀⠙⣆⠀⠉⠐⠂⢀⣀⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠳⣌⠉⠁⠐⠒⠒⠒⠚⠋⢉⣱⠖⠚⠋⠀⠀⠀⠀⠀⠈⢷⡶⠾⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⠏⠀⠀⣀⣤⡴⠖⠛⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡆⠀⠀⠀⣠⠞⠋⣰⢏⣠⡶⠛⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠃⠀⢀⡾⠁⠀⢰⡿⠟⠁⠀⠀⠀⣠⣴⠟⠛⠓⠲⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⣿⡸⡇⠀⡼⠁⠀⣰⠟⣠⠖⢁⣠⠶⢛⣉⣀⣀⣀⠀⠀⠀⠀⣈⡟⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⠻⢿⣇⢳⡼⠃⠀⡼⢁⡼⠁⠰⠿⠛⠛⠉⠉⠉⠉⠉⠉⠙⢋⣩⡟⠱⣦⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣠⣿⣎⢷⡄⢸⢃⣾⠁⣠⡶⠚⠉⠉⣀⣀⣠⣤⣴⡶⠾⠛⠁⠀⠀⠉⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⢉⣁⣀⣿⣆⠹⣆⢸⣷⠟⠁⣠⠴⠖⠛⠋⠉⠁⢠⣄⠀⠀⠀⣦⡀⠀⠀⢠⣄⠀⢸⣇
⠀⠀⠀⠀⣠⠞⠁⢠⠴⠛⠉⠉⣉⡥⢹⡿⠛⠘⠁⠀⠀⣿⠀⢀⡀⠀⠀⠀⠈⠻⠂⠀⠀⠙⠁⠀⠀⠘⠿⠀⠀⣿⡄
⠀⠀⠀⢰⠏⠀⢀⣠⣴⠶⣺⡿⢋⡴⠋⠀⡖⠀⠀⠀⠀⣿⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢠⢏⣴⠾⠋⡿⠁⣰⠏⢠⠞⠀⢀⡾⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⡀⠀⠀⢸⣆⠀⣿⡇
⠀⣠⣿⠟⠁⠀⣼⠃⢰⡏⠀⠘⠀⣠⠏⠀⢿⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠘⣿⡄⠀⠀⠋⠀⢻⣧
⠴⠋⠀⠀⠀⢠⡟⠀⢼⡇⠀⠀⣴⠃⠀⠀⠈⠻⣦⣀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣸⠏⠀⠀⠸⣷⠀⠈⠙⣷⡈⡇⠀⠀⢸⣷⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣄⠀⠸⣿⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢷⡀⡿⠀⠀⠀⠀⠈⠀⠀⠀⠈⠻⣿⠀⠀⠀⠉⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠘⠿⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢿⡇⢷⡄⠘⣿⡇⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠸⣿⡈⠟⠀⢻⠀⠀⣀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠘⠀⠀⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠰⣷⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠻⣶⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⢼⣦⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣦⣤⣀⡀⠀⠈⠛⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠸⣷⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠂⡠⠤⠀⠀⠀⠄⠀⠀⠑⡄⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣄⣀⡄⠠⠀⠀⠀⠀⠇⠀⠐⠁⠀⠠⠰⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⢀⠈⡁⠈⠛⠓⠛⠛⠁⠀⠓⠛⠛⠇⠈⠛⠁⠀⠀⣢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠐⠀⠀⠈⠛⠋⠤⢄⣀⡀⠀⣀⣀⣐⣂⣀⡀⠊⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁⠒⠢⠤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠐⣒⣀⠔⠊⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠅⣀⣀⡀⠀⠀⠀⠈⠉⠙⠀⠉⠉⠉⠉⠉⠉⠉⠀⣂⡴⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠈⠉⠉⠛⠚⠒⠒⠆⠀⠲⠶⠶⠒⠚⠚⠉⠉⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣤⣀⣀⡇⠀⠀⣀⣀⣠⣤⣤⠤⠴⠒⠋⢁⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⣀⡀⠀⠀⠈⠀⡀⢀⣉⣉⣁⣤⣤⡤⠶⠖⠛⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠲⠤⣄⣀⠈⠉⠉⠉⠉⠉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠤⣤⣀⣀⣀⠀⠈⠉⠛⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⠉⠉⣀⣀⣀⡤⠄⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠩⠭⢉⣛⡓⡒⢒⣒⣒⣒⡒⠒⣒⣻⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣶⠶⠚⠋⠉⠉⠛⠲⢶⣤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⡁⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⡈⠙⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠋⠉⠉⠉⠁⠀⣀⣠⣤⠴⠖⠒⢦⠀⠀⠀⠀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⣀⣀⡤⠴⠋⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢳⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⣠⠞⠋⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⢿⢷⡀
⠀⠀⠀⠀⡴⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠸⣇⣠⡴⠋⠁⠀⠀⠀⣰⠞⢲⡄⠀⠀⢸⡄⠹⡄
⠀⠀⠀⡼⠁⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⡄⠀⠸⡇⠀⠹⡆
⠀⠀⣼⠁⠀⣸⠁⠀⠀⠀⠀⢸⡋⠀⠀⢀⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢹⡄⠀⢻⡄⠀⢹⡄
⠀⢰⠇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣴⡿⠿⠛⠓⠦⠤⠴⠚⠛⠯⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡿⠀⠀⠙⠲⣄⢷
⠀⡟⢀⡞⠁⢀⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢻⡆
⢸⣷⠋⠀⠀⠘⢇⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻
⣼⠁⠀⠀⠀⠀⠘⢧⠀⠘⣆⠀⠀⠀⠀⠀⢰⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠃⠀⠀⠀⠀⠀⢀⡴⠚⠁⢨⡇⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠈⢷⡀⢘⡇⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⠖⠋⠀⣠⠞⠉⠀⠀⠀⠀⢰
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠻⣄⡴⠋⠁⠀⠀⠀⠀⠀⣰⢿
⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢸
⢸⡇⢳⡀⠀⠀⠀⠀⠀⢀⡞⠉⢹⠄⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠇⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣼⠁⠀⣿
⠀⡇⠀⠹⡄⠀⠀⠀⢠⠟⠀⣰⠏⠀⠀⠀⠀⣏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠂⣿⠀⢀⡇
⠀⢻⠀⠀⢻⠀⠀⣠⠏⠀⣰⠃⠀⠀⠀⠀⠀⠉⠳⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢠⠏⠀⢹⡀⢸⠃
⠀⠸⡇⠀⢸⠀⠀⠘⠦⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⣴⠖⢦⡀⠀⠀⠀⠀⣼⠁⢠⡟⠀⠀⠈⣧⡟
⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣓⢶⣤⡴⠖⠓⠶⢤⣶⠚⢉⡼⠁⠀⠀⠻⢄⠀⠉⠢⣄⠀⠀⠙⠶⠛⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⢻⡀⠀⢀⡤⠤⠶⠶⠶⠶⠶⣤⠀⠀⠀⠀⠀⢀⣤⠞⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣷⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⢀⣠⠴⣾⠋
⠀⠀⠀⠀⠀⢧⠀⠸⢄⣤⣤⣤⣤⡤⠤⠞⠀⠀⠀⢀⡴⠋⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⣠⠶⢦⣄⡀⠀⠀⠀⠀⠸⣇⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣉⠉⠉⠛⠲⠦⣄⠀⠀⠀⠀⠀⠹⢤⣀⠈⠙⠓⠦⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠈⠙⠲⣤⣀⣸⠇⠀⢀⡴⠖⠒⠒⠶⢤⣤⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣌⣙⣦⣄⡀⠀⠀⠀⠀⠉⠁⣠⠞⠉⣀⣀⣤⠴⠞⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣓⣶⣶⣶⣶⣞⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢢
⠀⠀⡆⠀⠉⠉⠀⠀⠈⢣⢀⠔⠒⠒⢄⠀⡏⠀⠈⠁⠀⠀⠀⠀⢇⠀⡰⠒⠒⠀⠒⡄⠀⡀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⢀⡼⡎⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⢸⡜⠀⠀⠠⠀⣤⠃⠀⢹⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠫⡅⣸⠀⠀⠀⠁⠀⢳⠉⠁⡆⠀⠀⠀⠘⠋⠁⠱⣀⣀⣀⠀⠈⠣⠀⠸⠀⠀⡞
⠀⠀⡇⠀⠀⠀⠠⠴⢃⠇⠀⠰⠟⠀⠀⠈⡆⠀⢀⠈⠀⠀⢠⠀⠀⡠⠒⠒⠒⢵⡄⠀⣇⠀⠣⢤⠇
⠀⠀⡇⠀⠀⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⠀⡀⠀⢸⠀⢠⠇⠀⠠⠂⠐⠁⠀⢸⠀⡞⠉⣢
⠀⠀⠑⢲⢀⠤⠞⠰⣅⣀⡀⡰⢃⠀⠀⢀⠜⠀⢸⡀⠀⣀⡜⠀⠈⠧⡀⠀⠀⠀⠈⢀⠆⠀⠙⠚⠁
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡘⠃⠈⣧⠒⠋⠀⠀⠀⢿⠉⠉⠀⠀⠀⢀⡙⠙⡄⡰⠂⠉⠀⠀⠰⠄
⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠛⠀⠀⣬⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠈⠁⢠⠈⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠔⠒⠒⠒⠲⠤⢄⣙⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄
⠀⠀⠀⣀⡠⠴⠒⡃⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⡔⠋⡍⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤
⠈⠢⢀⠐⠠⢀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠠⠀⠂⠙⡇⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⢀
⠀⠀⠀⠙⠢⢄⡈⠒⠤⣀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡢⣄⠀⣀⠴⡉⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠘⢍⠑⠠⢀⠁⠂⠄⡀⠀⠈⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠆⠒⡒⠇⠈⠉⠀⠀⢀⠧⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡈⠐⠤⣀⠁⠒⠄⠀⠀⠀⠉⠐⢒⠃⠁⠐⡊⠭⠐⠀⠁⠀⠀⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡉⠂⠀⡀⠉⠐⠂⠉⡀⠀⠂⠁⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣁⢲⡈⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣉⣲⣦⣤⣴⣎⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣉⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠼⠤⢠⣄⣠⣰⡀⡇⣰⣶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⠁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠐⠔⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠋⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠳⣄⣀⠠⠤⠖⠒⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣠⡠⠤⠔⠒⠈⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠀⠀⠈⠉⠉⢉⡍⢹⠀⢀⡀⠀⡄⠀⡟⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣀⡀⢀⠀⢀⠀⢸⠀⢸⡇⣼⠁⠀⠇⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠸⠁⠃⢸⠀⣿⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠈⠀⠛⠀⢸⠋⢷⡄⢀⡀⠀⣠⡠⠴⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠄⠒⠒⠒⠒⠒⠒⠒⠀⠁⠀⠀⠬⠭⢼⠗⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠓⠒⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⡄⠒⠂⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣈⡥⠆⠀⠀⢄⣀⣀⣠⡀⠈⠀⢤⡄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠄⠀⡀⢀⠄⠚⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢵⠀⢠⣄⣀⣹⠀⠀⣠⣄⣒⡂⠤⠭⠍⠐⠒⠊⠉⢢⢀⡠⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⢀⣀⣀⡀⡉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠒⢟⡈⢀⡨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢀⣀⠁⠀⠀⠀⠈⢱⡀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⠀⠑⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢄⣉⠀⠀⠐⠒⠂⠶⡇⠠⠤⠤⠒⠒⠒⠋⠉⠉⠁⢀⣀⡗⠐⠈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣭⠈⠒⠒⠒⠒⠶⣇⠠⠤⠤⠤⠔⠒⠒⠊⠉⠉⠀⢀⡠⠔⠊⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡓⠤⣀⡈⠑⠒⠒⠒⠂⠆⠀⠠⠤⠤⠤⠤⠔⠒⠚⠉⠽⣧⡀⠀⢀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⢃⠢⢄⡉⢁⠒⠶⠦⠄⣴⠀⣀⣀⣠⣤⠤⠤⠤⠴⡶⠋⠀⠁⠀⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⠋⠁⠀⠙⠶⣼⠁⠀⠀⠰⢤⡤⠤⠤⠤⠤⠤⠤⠴⠶⣶⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⢄⣀⠤⣉⠀⠀⣀⠠⢄⣀⣀⠠⠝⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⠠⣀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⠛⢛⠒⠢⠤⡀⠀⠀⠀⠀⠀⣠⡤⠶⠲⢤⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣀⣠⣤⣨⡾⠳⠦⣄⠀⣏⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣈⣆⠀⢀⡤⠻⢿⡄⠀⠀⢸⡿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⢿⡦⡊⠁⠀⠉⠟⠛⠀⡀⢀⠸⡆⠸⣷⠇⠀⢠⣴⣟⣗⡆⠀⠀⢨⣽⣿⠋⢀⡾⠆⠀⠀⠃⠀⠀⢸⠀⠀⣠⡿⡄
⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠀⡸⢀⠀⠀⠈⠳⣿⠂⠀⢨⠀⠀⠀⠈⠏⠁⠀⠀⠀⠀⣹⠏⠀⣎⠀⣈⡶⠤⠾⠶⠶⠛⠒⠾⢧⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣠⣜⣇⣑⣐⣀⣤⠟⠀⠀⠘⠳⢤⣤⣴⠀⢀⣀⣠⣤⡬⠏⠀⠀⠰⠜⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣴⣾⠛⢻⣿⣮⡵⣄
⠀⠀⠀⠀⠀⢀⡤⠤⡤⠀⡶⢤⣤⠖⠒⣶⢶⣶⠶⠋⢉⣩⣟⡲⠚⠉⣹⢒⣳⣶⠾⠉⠓⠒⢆⠀⢠⠓⠒⠉⠉⢻⣿⡟⠉⠙⠇⠀⢷
⠀⠀⠀⠀⠀⣏⡀⠠⠴⠋⠛⠁⠤⠒⠛⠛⠉⠀⠐⠚⠙⠉⡉⢀⣒⢉⡋⢉⡉⠀⢀⠀⣀⢄⡼⠀⠸⡀⠀⠀⠀⠟⠀⠙⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠙⠛⠛⠒⠓⠒⠓⠻⠿⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠶⣤⣤⣀⣤⣤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⢒⡲⠶⠶⠖⢒⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⠤⣤⣀⣀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⢀⣷⡦⣰⣯⣄⣀⡴⣮⢬⣉⣀⣀⣀⣱⡄⠀⠀⢀⠤⠂⠉⢡⣫⠟⠋⢁⣴⡫⠿⡋⢀⡴⡿⠟⠋⠁⠢⡀
⠀⠀⠀⠀⠀⠀⣾⢸⡟⠻⣆⠙⠽⢧⡌⠛⠷⣌⣀⠈⠳⢤⡈⠉⠙⢦⠀⢺⣠⠀⠀⠟⠁⠀⠀⣸⡿⠁⠀⠀⠚⠉⠂⠀⠀⡀⠩⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⣘⣤⣄⠈⠻⡀⠀⠈⠛⢅⡂⠀⣙⣦⠴⠋⠀⠀⠙⠷⣆⣀⠀⢀⣤⡅⠀⠀⢀⣀⣀⠀⣀⣤⣯⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠒⠚⠑⠒⠛⠚⠉⠉⠉⠁⣀⣀⣀⣀⣠⣤⣀⡈⠉⠉⠙⠛⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠒⢗⠖⢛⠍⡭⠊⢡⠔⠂⠈⠛⡆⠀⠀⠀⠀⠀⣀⣤⡤⠀⡒⢢⣤⢄⡀
⠀⠀⠀⠀⠀⠀⣰⢇⡴⠊⠛⢄⠙⣆⠀⠀⠀⢀⠎⢰⠫⠊⡠⣣⣿⣴⠞⠁⠀⠀⠁⢠⠃⠀⠀⢀⢔⠟⢛⣽⠛⡄⡦⢠⢘⡦⠙⣆
⠀⠀⠀⠀⠀⠀⡏⣼⢇⣀⡤⠤⠶⢿⡀⠀⠀⣾⢾⡇⣾⠸⡃⡇⠘⣷⠀⠂⠀⠀⠂⠘⠀⠀⣴⠃⡆⢠⡋⣂⡬⢔⡥⠂⢼⡗⠀⢼
⠀⠀⠀⠀⠀⠀⣇⠸⡃⣌⣉⣓⣶⠶⡈⢦⠀⠹⣌⠣⡱⠄⠳⡘⢷⡝⡆⠀⠠⠀⠀⢰⠀⢸⠁⡀⠑⢀⣀⣀⣠⠵⠂⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢦⢷⣅⠙⠈⠀⠀⢸⠋⢧⠀⠈⠱⡌⣎⢆⠘⡀⠃⡇⠀⠀⠀⢁⡎⠀⠘⣷⡈⠲⣦⣤⣤⣤⣤⡤⢴⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡁⠗⠰⠖⢁⡰⠃⠀⠀⠀⠸⣌⣘⡄⡇⡄⢿⡄⠀⡠⠊⠀⠀⠀⠈⠑⠲⠼⠿⠾⠷⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣠⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠈⠛⠤⣤⣤⣤⣤⣀⠀⠀⣠⣤⣶⠏⠁⢀⡤⠞⠁⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⢿⣧⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠂⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠉⠛⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠄⠀⢀⠀⠀⠀⠀⠐⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣤⣦⣃⠀⠀⠀⢀⠐⠀⠀⢤⣄⣀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣴⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣼⢄⡀⠉⠉⠛⠶⢤⣿⡀⠀⠀⡦⠭⠉⣝⣓⣦⣄⣀⡦⣆⣀⣄⣀⣠⣤⡶⣞⣻⣯⣵⠶⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠛⠷⣧⣈⠀⠀⠀⠀⠀⠀⠋⠃⠘⠛⠒⠿⠿⣿⣿⣿⡗⣿⠿⠿⠿⠟⠛⠛⠉⢉⣁⡤⡾⢻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⡀⠈⠉⠛⠻⠷⣶⣀⣾⣤⣤⣀⠀⠀⠤⠀⠀⠀⢠⠀⡀⠀⠀⢀⣀⣠⣤⣼⣿⣽⠷⠾⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⣙⠳⢤⣤⣄⣠⡀⣎⡴⢈⠉⠉⠛⠳⠶⠶⠶⠴⠞⢠⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⢀⣰⣶⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠻⠾⣷⡀⠀⠀⠈⡉⢉⡟⠛⠲⠶⠤⢄⣑⣀⡀⠀⢐⠊⡀⣀⣀⣀⣠⣦⡴⠴⠶⠚⠋⠉⣹⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠉⠑⠶⡆⢰⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠀⣀⣀⣀⣤⡤⠶⠛⠉⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⠿⢦⣀⡒⢀⣀⢃⠀⢡⠈⠉⠉⠛⠲⠲⠦⠤⠤⠄⠒⠶⠖⠒⠒⠋⠉⠁⠀⢀⡀⠀⢀⣄⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣤⡉⠙⠻⠿⠾⢧⣼⣠⣈⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⣉⣀⣠⣶⠶⢿⣛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣤⣀⣈⡙⠛⢿⣟⢿⣾⢶⣶⣴⣤⣤⢤⣶⠶⠶⣾⡿⠿⢋⣡⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠉⠉⠛⠛⠿⠷⠶⢦⣭⣭⣭⣤⣬⣥⣭⣭⠤⠖⠓⠛⠉
⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁
⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠾
⠀⠀⠀⠂⠘⠛⠋⣿⣿⣿⣿⣿⣿⡿⠿⠿⠤
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⡤⠐⠒⣒⣶⣤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⡠⣺⠉⣀⠔⡪⢁⡠⢤⣤⣤⣄⣀⣀⡒⠋⢉⣉⠤⠬⢭⣶⠤⣀
⠀⠀⠀⠀⡀⣼⢃⠞⡱⠊⡔⠁⠼⡳⠄⢒⣒⣒⣚⣛⡳⠦⣄⣐⠀⠀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⢇⠀⠁⠊⠀⢸⠀⠀⠤⠒⠉⠁⠀⠀⢀⡠⠤⠤⠤⠬⠍⣒⣤⣀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠸⠀⠀⠀⠀⠤⠶⠤⠤⠒⠒⠉⢉⣉⣉⠀⠠⢀⣈⡑⠦⡁
⠀⠀⠀⠀⢀⠤⢀⠔⠀⠐⠢⣀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⠤⠒⠒⠉⠉⠉⠛⠋⠺⠶⣄
⠀⠀⠀⠀⠇⢠⡁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠈⠁⠀⠀⠀⢀⡠⠤⠀⠀⢈⣉⣁⣒⠢⢬⡳⡄
⠀⠀⠀⠀⢗⡸⣈⠑⠢⣄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠘⠋⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠚⢆
⠀⠀⠀⠀⠀⠑⢨⡛⠓⠺⣗⠤⠤⠤⠤⣔⡇⠠⢄⡀⠀⠀⠀⠀⠀⠀⠶⠶⢀⣀⣈⣉⡁⠒⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⣟⠿⠿⢭⣴⠞⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠔⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣚⣯⣍⣉⠉⠉⠛⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣚⣉⣀⣠⠞⠁⠀⠀⠈⠙⠒⠋⠉⠉⠻⡟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⠉⠈⠉⠀⢰⡆⠀⠑⠦⠀⠹⡄⠀⠀⠀⠻⢤⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣠⠞⠀⢤⡀⠀⠀⠘⠃⠀⠀⢀⣀⠀⠀⣠⠖⠀⠀⡄⠈⠳⡌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠉⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠰⠇⠀⠀⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣇⠀⢀⠤⠖⠂⢀⡇⠀⢀⣽⠶⠒⠒⠒⠶⣄⠀⠘⠓⠂⠀⡀⠀⢧⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠃⠀⠀⠀⠀⠀⠘⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⡀⠀⠙⠆⠀⠙⣆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠲⠦⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠋⠀⡀⠀⠀⣹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⢲⡀⠀⠀⠀⢦⡀⠈⣇⠀⠀⠀⠀⠀⠀⢀⡾⠀⠰⠋⠀⠀⣇⠀⢠⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡆⠀⠁⠀⣶⠀⠀⠁⠀⠘⠳⣄⣀⣀⣀⣤⠞⠁⡀⠀⢠⠞⠀⠈⠀⢸⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢧⣀⠀⢠⡇⠀⠀⠀⢲⠀⠀⣠⠍⠉⣉⣀⠀⠀⡇⠀⠀⠀⠲⡄⠀⠈⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢳⡀⠀⢠⣀⠀⠈⠃⠐⠃⠀⠀⠈⠉⠀⠀⠀⡤⠀⠀⠀⠀⣠⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢧⡀⠀⠈⠀⠀⠀⠰⣄⠀⠀⠲⡄⠀⠀⠸⠁⠀⠐⠲⢾⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⡛⠓⠦⣄⠀⠀⠘⢃⣀⡀⠙⠀⠀⠀⣠⠴⣲⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣬⣝⣓⣚⣉⣉⣉⣳⣶⣤⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠖⠒⠒⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⣀⠀⠀⢀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢠⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡅
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⣿⣿⣷⣦⡀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠸⠿⣿⡇⢰⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⠟⠋⠁⠀⠀⢀⣤⡀⠀⠘⡇⢸⠁⠒⠀⠤⠤⠤⠤⠤⠀⠚⠉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡦⠀⠈⠁⠀⠀⠀⠀⠀⣼⣿⣟⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⣿⣆⠀⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢀⣤⣄⡈⠛⠿⠻⠿⣿⡿⠃⠀⡆⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⠀⢀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠸⢿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⢛⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⢀⠜⠀⠀⢸⣰⢀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠢⠤⠤⠼⠿⠿⠟⠛⠒⠁⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠖⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⢳⣄⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⡀
⠀⠀⠀⠀⣠⠶⠞⣋⣥⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⡀
⠀⠀⠀⠀⣷⣄⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣀⣤⡿
⠀⠀⠀⠀⠻⣬⡉⠛⠶⢤⣤⣀⣀⣀⣠⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣈⣉⣉⣩⣥⡴⠞⠋⣩⣼⡃
⠀⠀⠀⠀⠀⢰⡟⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣉⣉⠉⠛⠛⠛⠛⠉⢉⣉⣉⣀⣀⣀⣀⣀⣀⣠⣤⡴⠖⠋⠁⠉⠙⢳⡄
⠀⠀⠀⠀⠀⣸⡷⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣿⠃
⠀⠀⠀⢀⣞⠉⠙⠶⣤⣉⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋⣁⣤⣾⠋
⠀⠀⠀⠀⣿⠳⠦⣤⣀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣄⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⢖⣻⡿⠿⢻⡏
⠀⠀⠀⠀⢈⣿⢦⣄⣉⠛⠛⠒⠒⠒⠒⠒⠒⠲⠶⠶⠤⣤⣤⣤⣤⡤⠴⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⢋⣁⣤⠾⠿⣤⡀
⠀⣀⡤⠶⢻⣧⣀⡀⠉⠛⠛⠒⠒⠒⠒⠒⠒⠲⠶⠶⢤⣤⣤⣤⣤⣤⠴⠶⠶⠒⠒⠒⠒⠒⠒⠚⠛⠋⠁⠀⢀⣠⣼⡷⠦⣄⡀
⣾⠉⠀⠀⠈⢷⣌⡉⠛⠶⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⢉⣥⠟⠀⠀⠈⢹
⠙⠷⣄⣀⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣉⣉⠉⠙⠛⠛⠋⠉⣉⣉⣀⣀⣠⣀⣀⣀⣠⣤⣤⠶⠚⠋⠁⠀⢀⣠⡴⠟
⠀⠀⠀⠉⠛⠓⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠖⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣽⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣭⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢻⠇⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣀⡃⠀⠸⡀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⢀⡴⣊⠀⠈⣿⢆⣿⡇⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⢶⡀⠀⠀⡄
⠀⠀⠀⢀⡴⢀⠄⠁⠀⠀⠀⢀⣠⣠⣏⣾⣿⣿⣿⣵⣿⣿⣧⢀⠞⠛⠀⠀⠀⠀⠀⠰⢆⠘⣿⣄⣀⣀⠀⠀⠁
⠀⠀⢀⣿⣵⠏⠀⡄⠀⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠠⠕⡌⠻⣿⣿⡆⠀⠒
⠀⠀⢸⣿⣄⡁⠀⠣⢀⡀⠤⠊⠁⠀⢀⠈⠀⠈⠀⡠⠚⠋⠀⢀⠜⠝⢿⣶⣄⠲⡀⠀⣳⣼⣧⠀⠈⠉⠁⠀⡄⠀⡀
⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⢸⣿⣿⣦⠀⣤⣔⣿⡿⠀⢀⡀
⠀⠀⠀⠀⠮⣻⢿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠟⣿⣿⡛⢾⣿⢷⡄
⠀⠀⠀⠱⣆⠀⠀⠫⠛⠻⠿⠿⠿⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉⠉⠀⠀⠀⣠⡾⣫⣿⣿⡟⠀⠙⡄
⠀⠀⠀⠀⠈⠙⠒⠄⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠚⠉⠀⠙⠟⠉⠁⠀⠀⠈⠒⠂⠠⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠶⠶⠶⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢦⡔⢀⠎⠀⣤⢀⠄⠀⡱⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠁⠊⠀⢀⠁⠈⠀⢀⠅⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⢤⣡⠎⠀⢀⠀⠄⠀⢀⢎⠜⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡄⠀⢀⡖⠀⠀⠀⡠⠂⠀⢀⠔⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡃⢐⠎⠀⢀⠊⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠐⠀⠀⠀⠀⠁⠀⠠⠔⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⡀⠀⠀⠀⡁⠀⢀⢂⠅⢄⠈⠒⠀⢠⠄⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⡀⢖⠁⠄⠀⠀⠁⠀⢨⡌⠓⠃⠀⠀⠀⠈⠡⠂⠀⠀⠇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⠸⠒⢁⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⡄⠤⢉⢀⡔⠘⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠈⡀⠀⠀⣰⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⡀⢉⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⢀⠄⠉⠁⠻⣚⠠⠧⠄⣄⠀⠘⢆⠀⠀⠀⠀⣀⠀⠁⠈
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⡠⠇⠀⠀⠀⡁⠀⠀⢄⡀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠴⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡇
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠍
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠎
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⢄⡀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣻⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡤⡤⠤⣀
⠀⠀⠀⠀⠀⡀⢤⠒⠋⢹⡖⠂⠈⢳⡌⢂⠙⣿⠣⡀⠀⠀⠐⡟⠡⠔⣛⣫⣶⣦⠀⠀⢀⠎⠀⣀⠤⠜⠀⠧⣀⠀⠡⡀
⠀⠀⡠⠒⣭⢄⠸⡍⠳⡈⢳⡀⠀⠀⢻⡌⡄⠘⣄⡇⠀⢸⠀⠃⢠⠊⠉⠉⢉⣈⣁⠀⣸⡀⠚⠀⠀⡄⢠⠀⠀⠱⠀⡧
⠀⠰⠁⠀⢿⠀⠂⠹⣆⢱⡈⢷⡀⠀⠘⡇⣧⣶⠟⠀⠀⠘⢧⡀⠐⠔⠒⠉⠉⢉⡟⠀⢿⣧⡀⠀⠀⠸⠂⠀⠀⣀⣴⠇
⠀⢠⡀⠀⠈⠓⠄⣦⣘⢦⣧⣀⣷⣶⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⠴⠚⠁⠀⠈⠻⣿⣷⣶⣶⣶⣾⣿⡿⠋
⠀⠀⠉⠛⠓⠒⠛⠛⠛⠛⠛⠋⠉⠀⡠⠒⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢉⡩⠭⠟⠫⢤⣀⣀
⠀⠀⣠⠒⠫⣅⠉⠉⠱⣶⢤⠀⠀⡌⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠀⠀⠙⡿⠉⠱⡀⠀⠀⢀⣴⡙⠀⠀⠀⠀⢨⠀⢨⣉⠵
⢀⣞⠣⠄⢈⢮⡀⠀⣠⡇⢠⠳⡄⡇⠁⠀⠀⠀⠀⠀⣸⠀⣸⠶⢦⣄⡰⠁⠀⠀⣷⠀⣰⡋⠀⠘⢎⢂⠀⠀⣸⠀⠊⠁
⠠⠁⠀⠉⣷⣿⣿⡾⠛⠶⠾⢤⠁⠘⢄⣀⣀⣀⣠⠴⠃⠀⡇⠀⠀⠘⡇⠀⠤⠞⡿⠠⠀⠬⢷⣤⠼⠿⠶⠛⠁
⠘⠦⠒⠛⣉⣁⠀⠄⡠⠠⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⣤⡀⠀⠰⣄⠀⠚⠀⠀⠀⠀⠤⠶⠾⠥⣄⡀⠈⠙⠲⣄
⠀⠀⣴⠍⠁⠀⠀⠀⠀⠀⠛⣯⠀⠀⠀⠀⠀⠀⠀⠤⡤⢤⣤⣤⣭⣉⠉⠁⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠙⢲⡀⠀⠈⡆
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⠈⠢⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢲⣧⡤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⡱⠀⠀⠠⠁⠀⢀⠀⠀⠀⠀⠀⢹⠁⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣸
⠀⠀⠀⠙⠢⠤⠴⠄⠂⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠘⠓⠢⠤⠤⣄⣀⡀⠀⡼⠖⠉
⡶⠒⢶⢶⡶⠶⠶⣶⢶⠶⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⠶⠶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠃⠴⡟⡁⠀⠀⠐⠒⠢⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣾⣷⡀⠀⠀⡴⡠⠀⠀⠀⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠂⠉⠁⠀⠀⠒⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢄⡀⠈⠙⠓⠲⠶⠶⠤⠤⣤⡤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠒⠚⠋⠁⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠂⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠙⠒⠶⠤⠤⣬⣭⣉⣁⣀⣀⣠⡤⠤⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠓⠤⣀⣀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢀⠀⠄⢀⣀⣀⣤⠤⠴⠒⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠉⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠁⡀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠉⠓⠲⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠶⠖⠒⠛⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠙⠦⣄⡀⠈⠉⠛⠓⠷⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠶⠖⠛⠊⠉⠀⠀⢀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠛⠓⠶⢶⣤⣤⣤⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠀⠉⠉⠁⠀⢀⣀⡤⠶⠛⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⡀⠀⠀⠀⠀⠉⠛⠒⠶⢤⣤⣤⣤⣤⣄⣀⣤⣀⢤⣀⣀⣀⣤⣤⠴⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⣀⡀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣠⡤⠤⢶⣖⡖⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠚⠦⠤⠤⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠤⠴⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠊⠀⠂⠠⢶⠂
⠀⠀⠀⠀⠀⢀⠀⠀⢖⣿⡀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠠⠀⠐⠚⠉⠁⠀⠂⠀⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠀⠈⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣴⠥⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠂

⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣆⠄⢀⠀⠀⠀⢰⠀⣰⠀⠀⠀⢰
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠏⠾⠈⠳⠁⠼⠸⠇⠘⠠⠿⠑⠼⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠱⡀⠈⠁⣀⣼⢀⡀⠜⠀⠀⠀⠀⠀⠀⠇⢀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀⠀⠀⠀⠈⠉⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠
⢀⡀⠀⢰⢁⡈⢀⡶⢾⣹⡾⡿⠂⠀⠀⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐⣒⠀⠂
⠈⠻⠀⠈⠁⠠⢭⣙⣤⣄⣘⣭⡼⠶⠞⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠪⢙⠒⠀⠤⠤⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠂⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠒⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢠⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⡷⠦⠤⢾⠧⢴⠚⠻⠛⠶⠤⠤⠤⢤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠠⠀⡸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠳⢤⡤⠃⠀⡎⠠⠀⡤⠄⠰⣄⣠⡀⠀⠙⣆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⡀⣤⠔⢀⣀⢴⠾⠀⠙⠀⠓⡘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡷⡇⠘⠛⠋⡀⢀⠀⢀⠀⠀⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⡼⠂⠀⠘⢛⠘⢻⡀⢋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⡇⠳⡄⠀⠈⠈⠁⠉⠉⠉⠁⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠇⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⡀⠀⠀⡇⠘⢄⡀⠀⠀⡠⠻⣀⣀⡠⠏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢄⠀⠀⠑⠢⠄⣀⠀⠀⠀⠀⣾⠈⠭⠍⠩⠍⠁⠀⡇⠀⣀⢀⢉⣉⣀⡀⠀⣀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠠⡀⠀⠀⠀⠉⠁⠐⠾⠿⢀⣟⡀⠘⠓⠀⣠⠀⠀⢩⡄⣬⠩⠉⠁⠁⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣀⣀⡑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠧⠰⠴⠶⠶⠶⣦
⠀⢀⡴⠛⠛⠙⠋⠁⠉⠙⢶⣄⠀⠀⣿⠶⠛⠋⠉⠉⠉⠙⠲⢬⡒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡌⠀⠀⣀⣠⡀⢸
⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠉⠉⠙⠂⠚⠉⠉⢀⠀⢻⠋⠀⠀⠈⢋⣉⡡⠼
⡏⠀⠀⠀⠀⣰⠋⠉⠙⢳⣶⡿⠘⠁⠀⣠⠖⠓⠉⠙⢦⡀⠀⢀⣀⡿⠷⠤⠴⠆⠀⠲⠒⠴⠶⠦⠤⢤⣴⡟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⡀
⠃⠀⠀⠀⠀⠇⠀⠰⠊⣸⡏⠀⠀⠀⠀⠻⣀⡀⣀⡤⠞⠋⠉⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠉⠙⠒⠤⣀⠀⠀⠀⢀⡴⣋⡿⠷⢦⡀
⠰⡄⠀⠀⠀⠈⠓⠲⠟⠛⢧⠀⠀⠀⠀⠀⡼⠛⠁⠀⣀⡤⠖⠊⠉⢈⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠒⠦⢄⡀⠀⠀⠑⠢⣴⣩⡟⣹⠤⠖⣶⠟⢧⣀
⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⡷⢦⣀⡰⠋⠀⠀⡠⠊⡥⢤⣀⡔⠊⠉⠙⣿⠯⢤⣞⣿⡾⣻⣏⢉⡵⣶⢦⣀⠀⠉⠒⣄⠀⠀⠈⠻⣿⡧⣶⠋⢉⣽⠛⢯⣧
⠀⠀⠀⠀⠉⠑⠒⠒⠒⠚⠉⠀⠀⡟⠀⠀⢀⠞⠀⢀⡴⠾⠿⡆⠀⠀⣴⠃⠀⢠⠋⠉⠉⢉⠏⠀⠀⠘⡟⠋⠑⢦⠀⠀⢳⡀⠀⠀⠹⣿⣛⣻⣋⣉⣩⠟⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡎⠀⣰⢻⠀⠀⠀⣸⣏⣉⣽⣇⡴⡞⠀⢀⡰⠛⢳⡤⡤⣾⠥⠤⢄⡠⢳⡄⠀⢷⠀⠀⠀⢋⣸⣏⣋⡽⠉⠙⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢠⣏⠙⠤⡤⠴⠛⠌⢻⡶⣏⠀⠈⠉⣁⣹⣀⣸⣄⠑⣷⠀⠀⠘⡷⠋⡿⣄⢸⠀⠀⠀⢸⣇⣀⣝⠹⢓⡶⠧⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢯⠹⡏⠹⢶⣿⣻⣦⠀⣀⣽⠛⢋⣩⣿⣏⣿⢯⢤⠀⣑⡛⡶⡖⣾⣁⣼⣾⣇⡎⠀⠀⠀⣾⣻⣏⡉⣹⢿⢦⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣀⣀⣈⣿⣷⡧⠴⢟⡛⣛⣉⠉⣉⡀⠘⠻⠾⠀⠈⠁⣼⣼⣭⡟⠓⢻⣁⠀⠀⣸⠟⠀⠀⠀⣼⠉⠑⣴⡙⠙⢳⣾⣁⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⢉⣩⢭⣭⣵⠶⠒⠛⢿⣍⠁⢽⠁⠀⠈⠛⡿⠟⠉⠒⠒⠚⡄⠀⠀⣷⠤⠿⣯⡷⠛⠁⠀⠀⣠⣞⠛⢳⢶⠋⢉⠟⢧⣀⡝⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠒⢄⡀⠀⠈⠑⠂⠕⣶⣿⠞⢣⣜⠄⠒⠒⢲⣧⣄⡴⠥⠔⠊⠁⠀⢀⣠⣴⠿⡁⢈⠷⣅⢀⡽⠧⢤⣀⠟⠦⣤⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠄⠀⣀⠀⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⢀⣀⠠⠤⠒⢊⠉⠉⠑⣤⡜⢧⣀⣼⢋⠛⢣⡴⠛⣆⡠⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠒⠒⠀⠉⠉⣁⡀⠀⠀⠀⢮⣋⠆⠀⠈⠣⣤⣏⡽⣻⡔⠛⢧⡠⠚⢷⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣈⡼⢟⠻⢳⠀⣡⠦⡄⠀⠀⠀⠀⠟⠉⣀⡡⠋⠉⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣩⠟⠓⠋⠉⠁⠀⠛⠴⠀⠀⠀⠀⠀⠱⣴⠿⠧⣄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠒⡂⠐⠒⠦⠤⣋⣉⠉⠩⠉⠙⠒⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣚⣋⡀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⢦⣀⣀⠀⢄⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠌⠠⠒⠔⠲⠈⠍⠩⠉⠙⠛⠛⠛⠛⠒⠒⠤⣌⡀⠠⡀⠉⠁⠀⠈⠙⠲⣄⢀⠀⡴⠐⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡈⣀⢈⣥⣤⣀⡀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⢠⡈⠛⠀⡠⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠽⠚⠁⠉⠀⠀⠐⠉⠍⠉⠉⠙⣛⠓⠚⠣⠦⣄⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⢀⠀⠀⠀⠨⢆
⠀⠀⠀⠀⠀⠀⡰⡷⠁⠀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠑⠫⣢⡀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠅⢪⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠠⠀⠤⠉⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠅⠀⠀⣀⠊⠀⢈⡹⣷⣌⠂⠄⠀⢁⠀⠀⠆⠄⠆⠀⢁⡨⠀⠀⠀⠀⣿⣓⣒⡀⡀
⠀⠀⠀⠀⢀⣀⣴⠿⠿⣦⣄⣈⡀⠀⠀⠀⠄⠠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠻⣦⠀⡀⢂⡴⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⣴⡋⠐⠂⠠⠀⢀⡀
⠀⢀⣴⡾⠛⠉⠉⠉⠨⠉⣉⠉⠈⠛⠀⠛⠷⢶⢤⢬⣀⡀⠁⠀⠀⠠⠀⠐⠂⠀⠀⡀⢂⠂⠠⢳⡧⠐⠃⠀⠀⠐⠀⠂⠀⠀⢀⢀⡨⠞⢁⣀⠀⠐⠀⠀⠉
⢠⣨⠁⠀⡀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠅⢀⠀⠀⠨⠍⠐⠛⠿⢶⣤⡀⠀⠀⢀⠀⠀⠀⡩⠂⣾⠷⠔⠐⠶⠳⠶⠾⠶⣶⣷⣶⣾⣿⣶⣶⠶⣶⣶⣶⣷⣶⠖⠂
⢺⠉⠙⠳⢦⣤⣐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⢛⢶⡀⠈⠡⠀⠀⢀⣴⡽⠲⠲⠒⢒⠳⠶⠖⠛⠛⠻⠿⠏⢻⣿⣿⣿⣿⣿⠟⠋⠉
⠈⠉⠁⠶⢄⡀⠉⠛⠶⢤⣀⠀⠁⠀⠐⡀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠄⢳⣿⡻⣷⠖⣞⣿⢫⠾⠟⠛⠛⠿⠏⣛⣛⠛⠛⠛⠒⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⠈⠉⠓⠶⣠⡀⠀⠀⠀⠀⠀⠀⠆⠈⠤⠀⣀⣎⣼⠤⠩⠀⠀⠉⠑⠒⠒⠢⠥⠒⠒⠠⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣤⣀⣙⠣⠗⠶⠒⢒⣲⣖⣼⡿⡛⣡⡮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠶⠤⢴⣂⣲⣧⣴⠟⠛⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢷⡿⣷⣄⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⣜⣿⣿⣿⣧⠀⢸⣟⠹⡇⠀⠀⢠⣶⣿⣥⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣉⠳⡄⡇⢀⡇⣠⣶⣿⠏⡽⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣤⣶⣤⣀⣀⣈⡻⣌⣻⣿⠿⢿⠷⠧⣤⣿⣿⣯⣄⠄⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⢿⡿⠋⠙⣛⢻⡟⣿⡽⢻⣿⣿⢚⣼⠟⠻⠦⣾⠿⠭⣬⣹⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠑⢀⡄⢟⣾⣿⡌⣄⢠⣶⠺⣿⣧⣼⠿⣴⡟⣶⣾⣇⢠⣶⣉⣽⠤⡈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡦⠀⡼⢣⠗⣿⣿⠏⠿⣿⠼⣿⣧⣿⡏⢿⣶⣿⣿⣿⣯⢹⡇⣍⣻⣧⢤⣝⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠃⡀⠙⢻⣶⡼⠉⡸⣿⣿⣶⣿⣏⢿⣿⣿⣿⢿⣿⣸⣿⣿⣇⡙⢋⢻⡟⣏⢻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢁⡘⠻⢸⢧⡝⣿⣞⠟⣆⣿⣶⣾⣿⣿⣿⠿⣿⣾⣿⣿⣿⢿⣏⣿⣘⣿⣯⣿⡜⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⠀⢸⣇⢀⣌⠻⢃⡟⢯⡛⡿⡛⢿⣿⠿⣿⣿⣿⣿⣿⣿⠛⣿⣼⣿⣽⣿⣱⣿⣏⣻⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣄⢱⣦⡸⣇⣈⡓⢾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣻⣷⣽⣿⣛⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⢻⢦⣝⠋⢘⠧⠿⢰⢦⢘⣿⣶⣌⣿⣿⣡⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢺⡻⠇⣿⠵⡶⢹⢟⣤⣘⢻⣿⣯⣹⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡀⠿⣆⢈⡛⢿⠄⡈⢷⣽⣿⠿⢿⣿⣿⣗⣎⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡿⠆⠁⠻⣿⠆⣤⣿⡷⢹⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⠼⣦⢶⡦⡍⠛⢿⣟⣿⡟⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢾⣏⣿⣇⠸⣿⢿⡽⣘⣿⣿⠛⣿⣿⣬⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠹⣿⣙⡾⠎⠉⣴⣯⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠿⣝⠆⡻⠷⢮⣿⣯⣭⢿⣿⣿⣿⣿⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡸⠦⠻⢆⠻⣧⡹⣿⠿⢿⣿⣭⣿⣿⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡘⢟⣿⢿⣧⣼⣻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣟⠻⣽⣿⣝⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠤⠴⠶⠦⠤⠤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⡠⢄⠀⠀⠀⠀⠘⠧⢭⣉⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⠀⠀⠀⠀⠀⠑⢦⣙⡆⠀⣀⣤⣀⡀⠀⠀⠀⠀⢀⠤⣤⣀⣤⠴⠶⢤⡀⠀⠀⣀⡀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⡼⠁⠀⢀⣀⠀⠀⠀⠀⠈⡰⠚⠁⠀⠀⠉⠓⠶⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢣⡙⠳⣄⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢀⡾⠁⠘⡇⢀⠔⢋⡴⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠒⠤⣀⠈⢧⠀⠀⠙⠢⠼⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠃⠀⢀⠟⠘⠚⠽⠂⠀⠀⠀⠀⡇⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠶⣌⡑⢌⠳⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⢠⡏⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠃⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡞⢸⡇
⠀⠀⠀⢸⡇⢀⡀⠈⠂⠤⣀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠔⠁⣀⠀⠀⠀⠀⡜⢁⠇⡞⠀⠀⣷
⠀⠀⠀⠀⣷⠀⣇⠀⠀⠀⣸⠃⠀⠀⠀⢀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠁⣠⠎⠉⠀⠀⠀⠸⠱⠋⠀⡵⡐⢠⡇
⠀⠀⠀⠀⠸⣇⠸⡄⠀⡔⠁⠀⡠⠀⠊⠁⠀⡀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠧⠔⠀⠀⠀⠀⠀⣠⠖⠉⣰⠃⣾⠁
⠀⠀⠀⠀⠀⠙⣦⠹⣆⢇⠀⢀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡤⠖⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣰⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣌⠫⡙⠋⠀⠀⠀⠀⠀⠘⠲⣄⠀⠸⠥⠖⠉⠀⠀⠀⠀⠐⠭⠭⠝⠂⠀⠀⢀⡀⢀⠀⠀⠀⢀⡇⢀⡼⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠒⠒⣋⡴⢋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⠴⠊⠁⠹⡄⠀⡞⠁⠀⠀⠀⠀⠀⠀⢀⣉⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⣀⣀⣠⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠚⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⡀
⠀⠀⠀⠀⠠⣄⣈⣿⣀⣰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢠⢣⣿⣿⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⣤⣦⣾⣿⣷⣿⡄
⠀⠀⢀⡴⠏⡏⠙⢻⢿⣿⡷⣤⣤⠀⠰⣐⣼⣎⡌⡆⡀⠀⠀⢠⠇⡄⣸⣿⡥⢾⡇⠀⠀⢯⡿⡇⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⢟⣽⣦⣤⡀
⠀⠀⣾⠶⠘⡃⣧⠳⣺⣿⣿⡄⠀⠀⢀⠒⠚⢻⣷⣇⣷⠁⢸⣿⢰⣷⡯⠤⠖⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⠖⠀⢈⢿⣿⣯⣻⡆
⠀⢰⡴⠘⠁⣱⢾⣿⣿⣿⣿⡇⠀⠀⠘⢻⣃⣩⣭⢿⣿⡄⢸⣷⣿⡟⠛⠉⠠⠀⠀⠀⣀⢀⣄⠀⠀⣀⠀⡠⠊⠀⠀⠀⠀⠀⡴⣫⣿⣿⡍⠛
⠀⠘⡷⢤⡇⣸⣿⣿⣿⢿⠍⠁⠀⠀⠀⠀⠁⠐⠂⠀⠈⠁⢬⣀⣀⣀⠠⠀⠀⠀⠀⢰⣻⣾⣭⡖⠶⢹⣶⣄⡤⠀⣀⡤⠀⠀⡴⢣⣿⠿⡈
⠀⠀⠱⣷⣾⣿⡿⠶⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢻⣿⣿⡭⠤⢥⡀⠀⠘⠛⣻⠿⡤⣶⢺⡿⣿⣾⣿⣯⣦⣄⠀⠀⠐⠷⡄
⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠸⡿⣿⡯⢜⡂⠀⠀⠀⡟⡐⡎⢷⡟⢳⣿⡿⣯⡉⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠰⣦⣴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠃⠋⢋⠀⠙⠀⠀⠀⣟⣱⢿⣿⣧⠬⠘⠟⠋⢹⣿⣿⡿⠀⠀⠀⣄⠢⠶⠆
⠀⠀⠀⣈⡽⣷⢦⣿⣿⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⣿⡿⠿⠖⢀⡌⣴⣿⣿⣿⠃⠀⠀⣿⣋⡟
⠀⢠⢾⡍⢴⠈⢢⡌⣽⣿⣦⡀⢀⡀⢔⠳⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣖⣀⡄⠀⠀⠀⠀⠀⠀⣠⠖⣀⡀⠀⠂⠭⣿⠟⠁⠀⠀⠀⢛⠋⠃⠐⠃
⠀⢸⣏⠰⠂⠶⡀⣶⣿⣿⣿⡇⢨⣏⢺⣿⣤⠈⠤⠀⠀⣀⣸⣷⣿⣿⣯⢤⣤⡀⠀⠀⣤⣠⣠⣿⠏⠭⠙⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠸⣿⣇⠺⣺⣯⣿⣿⣿⣿⠃⠀⠹⠂⢽⣿⣶⡼⠀⠀⣠⠾⠍⠻⠛⠁⠉⣉⠿⡆⠐⠛⠉⢉⠁⢴⣆⠈⠤⠸⡆⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠙⢯⣅⣹⣯⣿⣿⠟⠁⠀⠀⠀⠀⠉⠻⢿⠃⠀⠀⡏⠀⠃⠀⢦⡇⠀⡀⠀⣿⠀⣧⠀⠈⠠⠀⠤⠀⠐⠀⠸
⠀⠀⠀⠈⠛⠾⠿⠛⠁⠀⠀⠀⠀⢀⣤⣶⡶⠊⠀⠀⠀⠹⡄⠀⠃⠀⠃⠠⠀⢀⡇⠀⠉⡻⠶⣦⣤⣤⣤⣤⣤⠔⢀⣠⠶⣷⣦⣀⠤⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⡀⠈⠁⠀⠀⠀⠀⠀⠙⠦⣄⡁⠀⠀⢀⡟⠀⠀⠀⠈⠓⠚⠯⠝⠛⠋⠁⠀⠀⠹⣾⣿⣾⠛⣰⡶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠙⠞⠟⠁

⣿⣿⡟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡠⠶⠂⠀⠀⠀⠀⠀⠀⢠⣧⠆⠀⠀⠀⠀⠀⣠⠤⠀⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠈⠣⠄⠠⡆⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘
⠀⠀⠀⠀⠀⢠⠀⠀⠐⠦⠀⠀⣷⠀⢀⠀⠀⠘⠁⠀⠐⠋⠀⠀⠙⡆⠀⠀⠀⠀⢸⣠⠂⠀⠀⢀⠀⢀⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⠀⠀⠛⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠐⠁⠀⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⡀⢀⡤⠀⠀⢧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⢀⡄⡀⠀⠰⣦⡤⠊⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠻⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣀⡆⠀⠀⢿⣇⣀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠻⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⢤⡠⠄⠀⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠐⢄⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠠⠀⠀⠰⠆⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡀⣠⠀⠀⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⣿⣿⢛⠿⠛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⢣⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠖⠂⠹⣋⠁⠠⠀⣈⡋⠹⠉⠉⠉⡭⠽⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣉⠠⠄⠀⠁⡠⠔⠒⡄⠉⡩⠄⠲⢤⠀⠀⠀⢉⣉⠉⠉⣹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡁⣀⣀⠠⠯⠀⠀⡔⡠⢄⢣⠤⠄⠀⣇⠀⡜⠉⠈⢣⢸⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⡿⠍⣙⣗⠀⠠⠰⡀⡇⢸⠀⠆⠀⠒⢇⣴⡇⠌⠉⢸⠸⣀⡟
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⢏⡒⠼⢨⣉⣉⣁⣳⡇⠚⢛⣂⣉⣉⠁⠸⠱⠀⠐⣚⠀⣯⣤⣀⣀⡀
⠀⣠⠴⠒⠋⠉⠁⠀⠘⡇⢰⡀⠱⠼⠒⠂⠠⠶⢹⠄⠄⠀⠀⠒⠂⡆⢸⠂⢁⡨⠟⢷⡄⠀⠈⠉⠉⠓⠢⢤⡀
⣟⣄⠀⠀⠀⠀⢀⠤⠴⢷⡸⠨⠍⠀⠒⠒⠒⣧⡔⠒⠒⣒⠒⠒⠒⠣⠜⠍⠁⢒⣁⠴⠣⠤⡀⠀⠀⠀⠀⢐⢝
⠈⠻⠵⣒⣢⠤⠬⢒⣂⡀⠙⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠖⠒⠛⠛⠉⠁⣀⣀⣀⠡⠤⣤⣒⡪⠝⠊
⠀⠀⠀⠀⠉⠉⠓⠲⠦⠤⣄⣀⣀⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣀⣠⠥⠤⠶⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⢋⣍⢉⡉⠓⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣀⣠⣤⣤⣀⡀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡴⣫⣅⢄⣰⠠⠈⠝⢦⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡞⢼⣊⠊⠜⠇⠁⠈⠁⠦⢹⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠓⠱⡠⠁⡅⠂⡀⠀⠈⢠⠷⠶⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⣇⠀⠀⠀⢳⡄⠔⠈⣈⢄⠐⠊⠌⣀⣼⠟⠛⠁⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⣤⠤⠴⠶⠶⣶⣶⣶⣤⣄⣀⠀⠀⠉⠒⢤⡀⢸⣄⠀⠀⠀⠙⠶⣼⣂⡪⣁⣮⡵⠛⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣤⣶⣿⡛⠓⢦⣤⡄⠸⣷⢄⠐⢈⢻⡈⠙⠲⣄⠀⠘⢉⡻⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⣠⠊⠀⠀⣠⣶⡏⠀⣹⠛⠻⠶⢿⣤⡇⠀⠙⢮⡧⠄⠁⠑⢦⡀⠀⠙⢦⡈⠁⠈⢻⣿⡶⢄⣀⡀⠰⠆⠖⠀⣀⣠⠔⠋
⠀⠀⡴⠁⠀⢀⣼⠿⣽⡧⢤⣿⠦⣦⡄⢀⡍⠛⢓⢆⠈⢷⡂⢡⡀⠠⠙⡆⠀⠀⠑⣄⠀⠀⠹⡇⠀⠈⠉⠉⠉⠉⠉⠁
⠀⡸⠁⠀⢠⡏⣸⣠⡇⢀⣠⡃⢀⣼⣽⣷⠲⡀⠄⠉⠛⠶⣿⣿⣬⡤⠀⢹⣦⡀⠀⠘⣆⠀⠀⠹⡀
⢰⠃⠀⢀⣿⣧⠋⠉⣹⠁⠀⣿⣏⠀⣼⣃⠀⠈⠻⢧⣙⣶⢤⡘⠻⢦⡀⠀⠀⠻⡄⠀⠘⣆⠀⠀⢧⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠓⠒⠤⣄
⡾⠀⠀⣸⡿⠻⣤⠼⢻⠶⠚⠋⠉⠉⠙⠛⠛⠦⢤⣀⠀⠉⠛⢿⣴⠄⣗⠄⠒⠀⢹⣄⣀⣿⠀⠀⠸⣄⣀⡴⣪⠅⠀⠀⣀⣀⣤⠴⠚⠉⣹⠀⢠⠶⡝⠦⡀
⡇⠀⠀⣿⣇⡀⣸⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⠄⠈⠙⠶⣽⣦⡂⡄⠀⠳⡽⠟⢦⡀⠀⡿⠋⠘⠁⣠⠖⢋⡽⠋⠁⠀⠀⢠⠟⢿⠏⠀⢹⠀⠈⢦
⡇⠀⠀⣿⠉⢿⠋⠀⠀⠀⠀⣠⠴⠖⠒⠒⢦⠀⠀⠂⢸⡙⠂⠀⠀⠀⠀⠈⢷⡘⡆⠀⢻⣿⣫⠇⠀⡇⠀⣠⣾⡵⠚⠁⠀⠀⠀⠀⢀⠏⢠⠏⠀⠀⠸⡇⠀⠀⢳
⢷⠀⠀⢿⠙⣿⡀⠀⠀⠀⡾⢱⠀⠀⠄⢂⢘⣇⡴⠒⠚⡛⠛⠉⠓⢦⠀⠀⠀⢹⡄⠠⠀⣿⠃⠀⢰⠁⢸⡟⠁⠀⠀⠀⠀⠀⠀⢀⡎⢀⠏⠀⠀⠀⠀⣷⡀
⠸⡄⠀⠸⡇⠜⣧⠀⠀⠀⢷⡈⠀⡀⠆⢀⣸⠟⢀⡤⠥⠦⣤⡀⠀⠀⢳⣀⠀⠸⣌⣅⣠⡟⠀⠀⡜⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⡼⢀⡞⠀⠀⠀⠀⠀⢹⣇
⠀⢱⡀⠀⠙⣦⣈⣦⡀⠀⠀⠈⠓⢳⡿⠛⠁⣰⠯⡀⠀⠐⠠⠙⣆⠀⠀⢹⣆⠂⡈⣹⠟⠀⠀⣰⠁⠘⣯⣿⣇⠀⠀⠀⠀⠀⡜⢁⡜⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢳⡀⠀⠘⢖⡐⡛⡄⠀⠀⠀⢸⠀⠀⠀⢿⡣⠐⠠⠐⢀⠂⡿⠀⠀⠈⢷⣬⣶⠋⠀⠀⣰⣷⠀⠀⢹⣽⣿⡀⠀⠀⠀⣰⢗⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠙⢄⢀⡈⠳⣄⠿⢦⣀⣀⣼⣧⠀⠀⠈⠳⣤⣁⣵⣥⠖⠁⠀⠀⠀⠈⢿⠁⠀⢀⠞⠁⠙⡆⠀⠀⢻⣷⣹⡄⠀⢰⡏⡼⠁⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⢰
⠀⠀⠀⠀⠀⠻⢵⡆⠈⠑⠦⣈⠉⠀⠈⠣⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⣀⠔⠁⠀⠀⠀⠘⢆⠀⠀⠙⣧⣇⢠⣯⣥⠃⠀⠀⣀⣀⣠⣴⡾⠟⡡⠆⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠉⠑⠲⠤⠶⢭⣽⠷⠶⠶⠦⠤⠤⠖⠊⣉⡥⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠿⠿⢾⣷⣶⣶⣿⠧⠴⠚⠉⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠔⠊⠁

⠀⠀⠀⠀⠀⠐⠦⣀⢀⡀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠈⠦⠈⠙⢤⣀⠀⠀⢀⠀⠀⢀⣠⠴⠞⠓⠀⠀⢀⠀⠠⠖⠀⠉⠀⠘⠋⠀⠀⣐⠣⠤⠛⣄⠂⢀
⠀⠀⠀⠀⠀⠀⢄⠀⠀⡀⠙⢳⣦⣄⠈⡏⠁⠀⠀⠀⠀⠀⠐⢄⠠⣿⡀⠀⠀⠀⡂⠀⠀⠀⠀⣀⣀⡤⠿⣓⣤⠇
⠀⠀⠀⠀⠀⠒⠂⠳⠤⣤⣀⣉⢈⠻⣮⠑⠢⢤⣐⠂⠀⠀⠀⠀⠀⠈⠑⠂⢄⣼⠧⣀⣐⣚⡭⠅⠒⠀⠉⠁
⠀⠀⠀⠀⡂⠉⠒⠲⠤⢤⣏⣉⣭⡏⠀⠀⠀⠀⠈⠁⣢⣄⠀⠀⠀⠀⠀⠀⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠗⠃⠁⠀⠀⠀⠀⠀⠀⠀⢈⡥
⠀⠀⠀⠀⢠⠂⠉⠉⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀
⠀⠀⠀⠀⡆⠄⠀⢠⠞⠛⢿⡶⡅⠀⠀⠀⠀⡠⠄⢄⢀⢐⣀⡀⢀⡆⠀⡀⠒⠀⠀⡔⠉⠀⠀⠐⣩⠴⡔⠂⢲⡆
⠀⠀⠀⠀⠹⣦⣀⠸⠴⠿⠆⠻⢴⡄⠀⠀⡐⠀⠀⣠⣾⡇⢈⣧⢞⠀⠀⢠⠀⠀⠘⠀⠀⠀⠀⣠⠞⣷⡅⠀⢀⠇
⠀⠀⠀⠀⠀⠈⠙⠢⠑⠂⠀⠀⠀⠀⠀⠍⠹⣄⣰⠷⢊⣠⢞⠛⠉⠒⣈⣀⡷⠀⢠⡀⠀⠠⣴⣋⣀⠜⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⠍⠃⠭⠗⠂⠩⠭⣁⣀⣨⠇⠀⠈⠳⣴⡀⣿⠉⢁⣠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣀⣠⠼⠶⠒⠉⠉⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠒⠂⣤⡉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠒⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣔⠶⣈⠀⠀⠀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠰⣶⣦⣤⡠⣪⡿⠀⠀⠀⠉⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠐⢷⣄⣲⠄⠀⠈⢲⢢⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣂⠗⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠞⠀⠢⡀
⠀⠀⠀⠀⡠⢂⠄⣠⢀⣽⠇⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣽⠇⠀⠀⠀⠀⠀⠀⠀⢰⠢⡀⡀⠀⠀⠀⠀⣤⡘⠄
⠀⠀⠀⡰⠁⠎⠀⠛⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠏⠀⠀⠀⢼⡾⠀⠘⠆
⠀⠀⣀⠡⣄⠀⠀⠀⢰⢸⠆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⢰
⠀⠠⡥⠞⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣾⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣶⠀⠆
⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠲⡅⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂⠀⠀⠀⠀⠀⡀⠸
⠀⠰⡀⠀⠀⠀⢰⣽⢳⣶⠿⠿⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠄⠤⠄⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⡿⠀⢀⠀⠀⢠⣾⢁⠇
⠀⠀⢆⠰⢶⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢗⣿
⠀⠘⢌⣄⡈⠻⣷⣤⣀⠀⢠⠄⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⢐⣀⣠⠀⠀⠀⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⢛⣵⣿⡟
⠀⠀⠸⠛⢿⣷⡙⣿⣿⠳⢬⣟⠖⠃⠀⠀⣰⣹⠃⣀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⢴⣿⣾⣽⡟⠁⢰⣿⣿⣿⠃
⠀⠀⠀⢆⠀⠙⢻⣮⣭⣀⠀⠨⣤⣦⡄⢠⢌⣥⣾⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣤⣜⣻⠯⠍⠁⢀⣠⣿⣿⡿⠃
⠀⠀⠀⠈⠢⡀⠀⠈⠻⢿⣦⣀⣀⣉⣉⠁⠈⠉⠛⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⣊⣭⡉⠉⠉⠙⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠈⠛⠛⠿⠿⢿⣿⣷⣄⡀⠉⠉⠛⠉⣡⣤⣶⣶⣶⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠛⠟⢿⣦⣠⣤⡾⠿⠿⠿⢻⠿⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⣄⣀⠀⠈⠁⠉⡠⢤⣶⣖⣻⣿⣿⢿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⢂⡀⠈⣣⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠑⢺⡧⠈⡀⠐⠈⠀⠀⠰⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠤⠐⠒⠀⢰⠛⠓⠆⠀⠄⣿⣧⠌⣤⣤⠄⣤⡷⢀⡠⠄⠀⡀⠐⠒⠠⠶⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢉⠁⠀⠀⠀⠀⠀⢀⡘⡀⢀⡀⠂⠀⠀⠙⡿⠛⡁⠀⠉⠙⣯⠁⠀⠀⠘⠳⠶⢤⣀⠐⠂⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠀⠀⣠⠴⠚⠋⠉⢙⣬⠉⠵⣐⠀⠀⣼⠃⠀⠄⡁⠀⠀⢸⣇⠴⠛⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⣀⠀⢀⡞⠁⠀⠀⠀⠐⠒⠺⣧⣐⢢⣨⣶⣛⣆⠀⠁⠀⠀⢔⣬⢯⠉⠁⠀⠀⠀⠀⠀⠀⡄⢳⡄⢀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⢿⠑⢤⣀⠉⠀⡼⠀⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠻⠿⠦⠌⠛⠛⠁⠀⠀⠀⠀⠀⠤⠤⢔⠃⠀⢸⠇⠉⠀⠀⣠⡴⠛⡇
⠀⠀⠀⠀⠀⠀⡸⢧⠀⠈⠻⣦⣱⠀⢈⡐⠒⠒⢈⡉⠤⠤⠤⠄⠀⠀⠀⠀⠀⣐⣢⣭⣭⣽⣦⣶⣤⣤⣄⡀⠀⠀⠀⢠⢏⣀⡤⠖⠋⠉⢀⣼⣅
⠀⠀⠀⠀⠀⢸⡇⠈⢷⣤⡀⠀⠉⢆⠀⠈⠀⠀⣠⣴⣶⣿⣶⣤⡁⠀⢀⣴⠛⠩⠅⠀⣂⣀⣒⠤⠤⠤⠭⢿⣦⠀⢰⠟⠋⠁⠀⢀⣠⡴⠟⢁⢸⣧
⠀⠀⠀⠀⠀⢹⡙⢦⣀⠈⠛⠷⣦⣬⣥⠀⠀⢰⠏⠀⠀⠀⠀⠀⢣⠀⣼⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣽⣤⣴⠶⠟⡋⠁⠀⣀⣤⠏⣿
⠀⠀⠀⠀⠀⠘⣧⠀⠙⠻⢦⡀⠀⠉⠙⡀⠀⡿⠿⠶⠶⣶⣶⣶⣾⠀⢻⣦⣤⣤⣶⣶⣶⠶⠶⠶⠾⠿⠟⠛⠻⣦⡿⠁⠀⢀⡠⠥⠒⠛⠉⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠙⠶⢦⣼⠀⢰⡁⠈⠀⠀⠀⠀⠀⢸⠄⠸⡇⠀⠤⠀⠀⠀⠀⠀⠠⠀⢀⣀⣤⣤⠤⠶⠶⠚⠁⠀⠀⢀⣠⣴⠟⠁⢸⣧
⠀⠀⠀⠀⠀⠀⢘⢿⡙⠻⢶⣤⣄⡀⢸⡆⠀⡟⠛⠒⠒⠒⠒⠲⣾⠀⠀⡷⠒⠒⠒⠲⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠉⠀⠀⣠⠎⣿
⠀⠀⠀⣀⡤⠒⢹⡆⠳⢦⣤⡈⠉⠛⠻⣷⠀⢹⣤⣤⣄⣀⣀⣀⣿⣀⣴⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⠶⠞⠛⠉⠁⠀⠀⢀⣠⡴⠛⢁⣼⡛⠳⢤⡀
⠀⣴⠞⠉⠀⢀⣾⠻⣄⠀⠀⠙⢦⣀⠁⢸⡇⣼⠁⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠁⣀⣠⡴⠟⠋⠁⢀⣤⠞⠉⣷⡀⠀⠙⢦
⣾⠁⠀⠀⠀⢨⢳⡀⠈⠳⢦⣀⠀⠈⠋⢻⠁⣿⠒⠶⣤⣄⣀⣤⣤⣤⣤⣄⣀⣀⣀⡁⣀⣀⣀⣤⡤⠶⠶⠖⠛⠛⠛⠋⠉⠁⣀⣠⣤⠾⠋⠁⢄⣰⢿⡇
⢿⡄⠀⠀⠀⠸⣆⠙⢦⣄⡀⠉⠛⠷⣶⡇⠀⢿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠟⠛⠉⠀⢦⣠⠴⠛⢁⣼⠇
⠈⢻⣄⠀⠀⠀⠙⢷⣄⡀⠉⠓⢦⣄⠸⣧⣤⡿⠛⠿⠿⠶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⠶⠶⠿⠛⠛⠉⠉⠀⠀⠀⢀⣀⣤⠖⠋⠁⢀⣤⠾⠋⠀⠀⣠⡾
⠀⠀⠈⠻⢦⣀⠀⠀⠙⠻⣶⣤⣀⠈⠙⠢⢤⣀⣀⣘⣂⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⡤⠔⠚⠛⠛⠛⠛⠋⠉⢀⣠⣴⠾⠛⠁⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠉⠳⠶⣤⣀⡀⠉⠙⠻⠷⣶⣤⣤⣄⣀⣀⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣤⣤⣴⠶⠟⠋⠉⢀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣤⣤⣈⣉⡙⠛⠛⠛⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠋⣉⣉⣠⣤⣤⣶⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢭⣭⣛⣛⠛⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⣛⣉⣩⣥⠴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⠉⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠉⠛⠛⠳⢾⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠶⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣽⣶⣿⣭⣭⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢚⡉⠉⠐⠃⠀⠐⠂⠀⠚⠀⠀⣀⠉⠳⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠠⠀⢀⡤⠖⢚⣉⣉⣉⣹⡆⢤⠀⠀⣀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠠⠆⡀⠀⠀⠸⢴⣞⣩⣥⠤⠖⠋⡀⠀⠀⠀⠁⣰⠒⠋⢻
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⣏⡀⠀⠀⠀⠠⡄⠀⠀⠀⣠⠄⠀⠀⠀⢁⣀⣀⠀⣠⠏⠀⠀⢸⡇⠀⠀⠐⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠴⠦⡄⠀⢀⠀⠀⣀⣀⣀⡀⠀⠀⣰⠋⠛⠛⠉⠓⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠙⢦⣌⣠⡞⠁⠐⠒⠽⠿⠫⠅⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠓⠦⢤⣄⣄⣀⣀⣀⣠⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡆⢀⣀⡀⠀⣀⣤⡀⢀⡀⠀⣄⢀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣀⣠⡼⢳⡏⠁⢹⡆⡏⠀⢹⡸⡇⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠛⠒⠛⠀⠃⠀⠘⠀⠙⠞⠙⠂⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⣤⡥⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠤⠖⠂⠀⠀⢀⠀⠀⠀⠀⠀⢀⣞⣡⠄⢻⣿⡣⡁⠀⠘⣿⣂⠀⠀⠀⠐⠂⠘
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠀⠀⠰⢆⡀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠰⠔⡅⠞⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⢠⠀⠡⠀⠀⠀⠊⠀⠀⢳⡄⠀⠀⠀⠀⠀⢩⢠⠈⠤⠓⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠐⠁⠂⠄⠁⠀⡞⡶⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⣄⣀⣆⣀⠔⠀⠀⠀⡀
⠀⠀⠀⠀⠈⡀⠀⠐⡀⠀⠂⠀⡀⠠⠁⠖⠂⠀⠀⠰⢤⣄⡬⢐⠴⠚⠘⠀⠄⠀⠁⠹⠁⣄
⠀⠀⠀⠀⡀⠁⢀⠀⠁⠐⠀⡀⠀⠀⠁⠀⠀⠀⢛⠄⡐⢨⢉⠁⠀⠂⠀⠃⠀⡀⠁⠀⠁⢀
⠀⠀⠀⠀⠠⠂⢀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠁⠀⢛⠈⠀⠂⠨⠀⠀⠁⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⡉⠉⠀⠠⠀⠠⠀⠈⠀⠃⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠃⠘⠀⡄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠐⠊⡚⠂⠠⠔⡄⠀⠀⠀⣀
⠀⠀⠀⠁⠀⠐⠒⠀⠛⠋⠋⠙⠀⠁⠀⠀⠀⠀⠀⢀⠰⣶⡆⢀⠀⠀⠉⠉⠲⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⠀⠀⠀⠗⠀⠰⠊⠆⠀⠠⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠛⡿⡄⠶⣀⣟⠦⠒⠄⣀⠃⡁⠆⠀⠀⢀⠀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢀⡀⢾⠀⠘⠢⡡⢙⠘⠈⢀⠠⠠⠘⠁⢶⠘⠛⢿⡗⡄⢠⢾⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡁⠀⠐⡀⠀⠑⡈⠀⠀⠀⠠⠆⠀⠐⢀⢐⣀⢐⢇⡷⠀⣌⠘⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢘⠀⡀⡀⢠⠁⠀⠀⠀⠀⠀⠀⢋⠀⠔⡀⠂⠚⠆⠃⠄⣅⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠉⠀⠀⠘⠈⣀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡢⡀⠀⠀⠀⠄
⠀⠀⠀⠀⢠⠁⠀⠀⠀⢠⠔⠀⠀⠀⠀⢸⠷⣀⠀⠀⠀⠀⠀⢂⢘⡿⠂⠀⣀⡄⠀⠀⠀⠀⠀⠀⠸⣄⡀⡺⡟⡿⠄⠀⡀⠀⢀
⠀⠀⠀⠘⠺⠄⡀⠀⠀⢸⡂⣀⠤⣀⣥⠶⠛⠁⠀⠀⠀⠀⠀⠪⣑⣚⡴⠟⠉⠀⠀⠀⠀⠀⣄⠀⠀⢿⡿⣝⡋⢀⡠⠞⢀⡀⡾
⠀⠀⠀⠀⠉⠓⠲⠬⣌⣉⣩⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠓⠦⠅⢠⡤⠀⠠⠐⣈⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⠤⠒⠚⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡉⣱⡗⠠⡀⣐⡆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠀⠈⠀⠀⠉⠀⠀⠈⠉
⠀⠀⢀⡀⢀⣠⡴⠒⠋⠁⠀⠀⠀⠐⠄⡀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢢⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣄⠤⠒⣉⠁⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣿⣷⠖⠩⣦⣀⠤⢄⣀
⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠈⠁⠁⡢⡄⠀⠀⠀⠀⠀⠀⠤⠀⣠⠴⠊⠁⠈⠙⠿⣤⣬⠓⠀⠉⠀⠠
⠀⠀⠀⢄⣐⣿⣇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢰⣀⠀⢾⢿⠤⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠊
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣛⣁⢀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⢆⠀⠀⠀⠐⠠⠀⠀⠄⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠰
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠄⠀⠀⠠⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠂⠀⠄⢠⠄⠂⠊⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣊⠠⠁⠀⠀⠀⠐⢘⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠡⢉⠀⢀⡀⠀⠀⠀⡀⠈⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡈⠀⠆⡈⠂⠄⡁⠀⢔⠀⡑⠀⡐⡂⠘⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠒⢄
⠀⠀⠀⠈⡄⣆⢱⠀⠀⠀⠀⠀⠀⡄⠁⠀⢠⠀⠈⠀⠈⠚⠋⠄⠉⢉⠁⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠃⢱⠘⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠐⠃⠀⠚⠉⠉⠉⡉⠉⠉⠉⠐⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠀⠀⠌⠀⠀⠀⠊⠀⠀⠀⢀⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠤⠒⠂⠀⠀⢠⠏⠉⠉⡁⠀⠀⠀⠠⠀⠈⠉⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡘⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⠰⠀⠒⠂⢀⣶⠚⠈⠉⠉⠉⠉⠉⠉⠂⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⡞⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠠⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢷⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠠⠬⠙⠶⠤⠤⠤⠤⠤⠤⠔