Bump off Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⢸⠀⢀⡖
⠀⠀⠀⠈⠉⠙⠲⠶⠶⠦⠤⢤⣤⣀⣀⣀⠀⠈⠃⠈⠀⠛⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠤⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⡄⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⡏
⠤⠴⠶⠒⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⡇⢸⠃⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣒⣶⡤⢶⣄⣠⠀⠀⣷⣿⡇⡿⠀⠀⠀⣺⠟⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠈⠉⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣈⡀⠀⠀⣿⣿⠁⠓⠶⠶⡾⠃⠀⠀⣀⡴⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢯⣽⠟⠋⠁⣀⠀⠀⠀⢧⣀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣿⠀⠸⣄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⠀⠀⠙

⠀⢀⣀
⠀⠀⠉⠛⠶⢶⣤⣤⣤⣀⣤⣤⣤⣴⠶⠾⠟⠛⠻⠷⢶⣤⣤⣤⣴⠶⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠋⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⣿⡞⠁⠀⠀⢀⣤⠄⠀⠀⠘⣷⣀⣤⣤⣴⠋⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡏⠙⣦⠀⣰⠟⠁⠀⠀⠀⠀⢻⡏⠀⢰⣏⡆⢀⠇⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢘⣿⡃⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢉⣿⠛⠛⠀⠀⢸⡷⠶⠶⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⠉⠻⣦⣄⠀⠀⠀⠀⣸⡇⠉⠙⠋⢸⡧⠀⠀⠀⣸⡇
⠀⠰⣄⠀⠀⠀⠀⠀⠈⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠂⠀⠀⠀⣿⠙⠲⠤⠤⢾⡅⠀⠀⠰⠋
⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⠀⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⢠⣿⢦⣄⣀⣠⣷⡃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠾⠛⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣤⣀⣤⡾⠻⢤⣀⣠⣼⢿⣇⣀⣠⣴⣿⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⣠⣴⠏⠉⠉⠉⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠲⢶⣛⣥⢾⣄⣀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⣏⢉⣠⣾⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄⠙⠀⠀⠀⠀⢸⡄⠀⢹⠀⢀⡆⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣄⠀⠀⠀⣸⠻⡄⠀⠀⣼⣇⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣷⠈⠛⠦⣤⠏⠀⠙⢦⡴⠃⠹⣄⣀⡤⠞⣹⠁⠀⠀⢠⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁⢦⣤⣤⣏⠰⣷⡤⠤⠔⠉⠲⠤⠤⠒⢄⣈⣁⣤⠤⢯⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡥⠖⠒⠋⠁⠀⠀⠀⠈⣏⡍⠙⠲⣤⡴⠚⠉⣍⡏⠀⠀⠀⡀⠉⠒⠒⠤⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⡞⠀⠀⠀⢀⠃⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠈⠛⠲⠾⠿⠶⠶⡏⠀⠀⠀⠀⠑⢴⢇⠀⠀⠀⢸⡆⠀⢀⣴⠋⣳⣄⠀⠀⡇⠀⠀⠀⢀⢷⠔⠁⠀⠀⠀⠈⡷⠿⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠾⣤⣀⣀⡼⠷⠒⠋⠀⣿⡁⠈⠓⠲⠷⣄⣀⣠⡾⣎⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⣟⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⢤⠟⠒⠳⠶⠶⠒⠒⠛⠉⠀⣾⡄⠈⠙⠒⠒⠲⠶⠶⠓⠛⢦⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢦⣀⣀⠀⣀⣀⣀⣀⡤⣞⠁⢹⠦⣄⣀⣀⣀⡀⢀⣀⣠⠞
⠀⠀⠰⠖⠒⠒⠚⠛⠛⠚⣧⡀⠀⠀⠀⢾⠀⠉⠉⠉⠉⠉⠀⢀⡿⠀⢸⡄⠀⠈⠉⠉⠉⠉⠁⢸⠀⠀⠀⠀⣠⠗⠚⠿⢿⣓⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠁⠀⢉⠶⠤⢤⡬⠷⢴⣤⣤⣤⣤⣴⡋⠓⢋⣁⣉⠳⢤⡤⣤⣤⡴⠴⢯⡤⠤⠐⠚⠤⢄⡠⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠂⠈⡇⠈⣠⣄⡈⠶⠋⣠⣄⠙⠚⢠⡟⠛⠲⣤⣘⣇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠁⠪⠀⠀⣧⠞⠁⡈⢷⠀⣸⠃⠈⠳⣄⢸⡇⠀⠀⠀⡉⠻⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠀⠇⠈⣧⡏⠀⠀⠀⠈⢻⡇⠀⠀⠀⠙⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀⢀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠸⠁⠀⠀⢸⡀⠀⠁⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠒⠀⠀⠐⠄⠀⠀⢀⣴⣾⣯⣶⡴⡠⣠⣰⣜⠂⠀⠀⠀⠀⠀⢐⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣳⠙⠈⠀⠐⠑⠻⠋⣿⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢿⢻⠟⠀⢀⡠⠀⠀⡀⠃⢠⣿⣿⠀⠒⢐⠀⠀⠀⡄⠀⣀⡤⠏
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠞⠀⠀⠀⠀⡨⣨⡄⠀⠀⣀⠀⠀⠂⠡⣾⣿⣿⠀⠀⠁⠀⠀⣀⠟⠯⣁
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢀⡠⢇⣠⣄⡀⠀⣀⣀⣀⡈⠱⠅⢣⡀⢀⣬⠉⠀⠀⣠⣿⣿⣃⣠⡀⠀⠰⠄⠀⠀⠀⠀⠂⡁
⢠⡄⠀⣀⢐⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢫⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠨⠢⣭⡤⠀⠺⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠐⠄⠀⢸⡅
⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⢿⣿⣿⣟⣻⣿⣿⣿⡿⢋⣀⢉⡗⢠⠙⣄⠀⢀⣿⠀⢿⣿⣧⣤⣠⣴⣤⣢⣤⣴⣠⣤⣤⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢹⡆⢰⡏⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠁⠈⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠙⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⣀⡄⠀⢸⡗⠲⡄⠀⠀⢠⠖⢺⡇⠀⢠⣀⡄⠀⠀⠙⢦⡀
⠀⠀⢀⡖⠶⠶⠖⠋⠀⠀⠀⠀⠀⣿⠀⠀⣾⣤⣤⠃⠀⠀⠘⣤⣤⣷⠀⠀⣿⠀⠀⠀⠀⠀⠙⠲⠶⠶⢶⡄
⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣤⡼⠁⠀⠈⡇⠀⠀⢸⠁⠀⠈⢧⡤⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠐⠋⢰⡋⠉⠙⠛⠒⢾⠁⠀⠀⠈⡷⠒⠛⠋⠉⢙⡆⠙⠂⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠒⠶⢤⣤⠞⠀⠀⠀⠀⠳⣤⡤⠶⠒⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠉⠉⠓⠦⢤⣄⣀⣀⣈⣳⣤⣀⡼⠃⠀⠀⠀⠀⠀⠀⠘⢧⣀⣤⣞⣁⣀⣀⣤⡤⠴⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡀⢀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣸⠇⠸⣇⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢿⠀⠀⠈

⠀⠀⠸⣿⣤⣿⣿⠀⠈⠁⠀⠀⠀⡀⠈
⠀⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠐
⡾⠿⠋⠉⠁

⠂
⠿⠗⠂⠀⠀⢀⡀
⠛
⠀⠀⢠⠎⠀⠀⠄⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⣠⣶⠀⠀⠆⠀⠀⠀⠀⠀⠈⠁⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠋⠁⡀⠀⠀⠀⠀⠀⣤⡆⠀⠀⣾⠃
⠓⠿⠃⣀⠀⠀⠀⠈⡉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄
⣶⣶⣾⣿⣦⣹⡦⣾⣿⡟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣯⣿⣿⣿⣹⣧⣿⣿⡿⢿⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠁
⣿⣿⣿⣿⣿⡏⢉⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠛⠙⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠃⣤⠀⠤⢤⣴⡆⠀⣀⣤⣾⣿⡖⠒⢠⣤⡀⢀⣶⣤⣤⣌⢁⠘⠻⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣧⡀⠄⠁⢀⣶⣿⣿⣿⣿⣿⣦⣾⠏⢻⣿⠙⡿⢿⣉⠻⡃⣀⡴⠛⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣧⣰⠿⠈⢿⡟⠻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⠘⠛⠀⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣳⣾⣆⠀⠓⢶⡼⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠐⢿⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣤⡀⠛⠛⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣷⣾⠟⣳⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋
⢽⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠹⢿⣿⣿⣿⣿⣼⣿⣶⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠈⠛⠓⠟⠋⠁⠙⢿⡛⠻⣿⡀⠀⠀⠈⢿⣿⣿⣯⣤⣿⣷⠻⢟⡋
⠀⠀⣶⠆⠀⠿⠀⠠⠌⠀⠀⠉⠁⢤⡀⠀⠀⠙⠋⠀⠈⢿⣿⠀⠙⣿
⠓⠄⠹⠶⠀⡀⠀⠀⣴⡄⠀⣶⠂⠀⠉⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠋
⠀⢀⠆⠀⠈⠁⠀⠀⢈⡠⠄⠈⠲⠛⠒⠀⠐
⠒⠿⢶⣤⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⢀⣀⡀

⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠠⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣦⣀⣶⣼⣿⣿⡿⠺⠷⠀⠀⠂
⣉⡷⠦⣴⣿⣙⣿⣿⠋⢾⣿⣭⣿⣿⡉⠛⠁⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⣉⠳⣶⣆⣸⠿⢿⠿⠃⠀⠉⠉⠉⠁⠀⠀⣀⣀⣀⡀⠀⢤⡔⠋⠉⠉
⠛⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⠉⠘⠟⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠾⣿⠿⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣴⣶⣿⢟⣁⣀⣤⡟
⠀⠀⠀⠀⠀⠻⠿⠇⠸⠟⠉⠙⠷⣤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠘⠛⢶⣟⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠉⠁⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠆⠀⠈⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠂
⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⡀⠀⣀⠀⠀⢀⣀⠀⢀⠐⠒⠀⢀⣠⣴⣿⡀⣀⠀⠀⠀⣠⣤⣀⣴⣶⣿⣦⡀⠀⣴⡀⠀⠀⢀
⠀⠀⠀⠀⠼⠉⠀⠉⠁⠉⠡⠤⠀⠾⠁⠀⠋⠁⣠⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⢀⣶⣾⣿⣉⣏⣽⣿⣿⣿⠁⢸⡍⠁
⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣄⣀⠀⠀⣿⣅⣠⣿⠋⠉⣻⣿⣿⠿⠿⠏⣿⠀⣿⡇
⠀⠀⢠⣶⣿⣿⣷⣶⣤⣤⣄⣠⣤⣤⣶⣤⢠⣶⣶⣿⣿⣿⣿⣿⣄⣴⣿⣿⠿⠁⠀⣰⣿⣿⣷⣶⠶⣾⡿⢠⣿⠃
⣿⣶⣾⣿⣿⣿⡉⠉⠉⠉⠁⠙⠋⠉⠉⢉⡟⠉⠉⠉⠉⢻⣿⣿⡿⠛⢻⣿⠀⣠⣼⣿⡏⠀⢸⡆⠀⢾⡇⣸⡏
⠿⠿⣷⣾⣿⣿⣷⣴⣶⣾⣶⣶⣆⣴⠖⣾⣿⣶⣶⣦⣤⣼⡿⠋⢠⡔⢃⣠⣴⠟⠉⢰⡿⢠⣄⠀⢰⡞⠀⣿⡇
⣶⣾⣿⣭⣿⣿⠿⢿⠿⠛⢻⣿⣿⡏⠐⠟⢻⣿⣿⣿⣿⠛⠟⠛⠛⠿⣿⣿⡅⠀⠘⠿⠀⠨⠉⠀⠻⠃⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣧⣀⣀⣠⣼⣷⣤⡜⠛⣰⣿⡿⠿⣿⠗⢀⠀⢹⣿⣿⡿⠋⠀⠀⠀⠀⠸⣿⣤⠀⠀⢠⣆⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⠛⠛⢻⣿⠟⠁⠀⠀⠀⣤⡀⠀⠀⠈⠁⣤⡾⠀⠀⠀⠀⠀⠛⠛⠳⣤⠀⠀⠀⠀⠘⠀⠀⠈
⠉⣙⣻⣾⣿⡷⢾⣿⣿⣷⠶⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⣿⡻⢿⣼⣿⣤⠈⠉⠀⠀⣀⣼⣿⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠀⣄
⣽⣿⣄⣹⣿⠟⠀⠀⢀⣼⠟⠻⣿⠁⠉⠳⠀⠀⠀⠀⠀⠀⢰⣀⣀⣴⣶⣿⠛⠻⠀⠈⣿⣀⣀⠀⢠⡆
⠿⢧⣿⡿⠁⢀⡀⣠⣿⡷⠒⠐⣿⣷⠀⠀⠀⢀⣀⣠⣤⡴⠟⠛⠉⠉⠛⠿⠀⠀⠀⠀⠀⠀⠉⠀⠘⠁
⣴⣞⣿⣿⠗⠿⣿⣿⣿⣷⣤⣤⣿⣿⣦⠶⠿⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠿
⣿⣿⣿⣿⠀⠀⠀⠈⢿⣶⣿⡿⣇⠀⣿⠀⠀⠀⠀⠀⢠⣄⣠⣤⣶⠖⢿⣆⠀⠀⠀⠀⠀⡶
⠟⠋⢹⣿⡀⢀⣼⣶⣾⣿⡍⢀⠀⠈⠻⣷⠀⠀⠀⠀⠀⢹⣿⠀⣹⠀⠈⠻⠀⠀⡀
⣴⣶⠤⠿⢿⣿⣿⣷⠉⠹⢿⡀⠴⢄⢰⣿⠀⠀⠀⠀⠀⢸⡷⢠⣿⠀⠀⢰⡄⠈⠻⣤⡀⠀⠀⠃
⢀⣠⠾⠶⠾⣿⣯⠉⠻⣦⡀⠙⢶⣄⣼⣿⠀⠀⠀⠀⠀⢈⣤⠾⠋⠠⣀⠐⠀⣀⠀⠈⠃⠀⢠⠄
⠸⣿⣄⣀⣠⣿⣿⠛⠳⠾⢻⣶⣄⠉⠳⢿⡄⠀⢠⡶⢶⣞⠁⠀⠻⠶⣟⠀⠀⣿
⢿⣦⣭⣏⠙⠿⠿⠦⢀⣠⡌⣾⠿⣷⠆⣀⠀⠂⣀⠀⢨⣅⣰⠄⠀⠐⠟⠀⠀⡿⢠⡄⠀⠀⡿
⠀⠀⢸⣿⣷⣄⠀⢀⠸⢏⣹⡿⠐⠛⠀⣹⣶⣤⡀⠙⢿⣥⣀⠀⠀⠀⠀⠀⢀⣀⣸⠇⠀⢠⡷
⣾⠿⠿⢿⣿⢿⣦⠈⠀⠿⠿⠃⠀⣶⡞⠛⢋⠀⠀⠰⠀⠀⠹⡗⠀⣀⠀⠰⣦⡀⠛⠀⠀⡏⠀⠀⠀⢠⣄
⠀⣠⣄⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠉⢳⣾⠛⠀⠀⠀⠈⠛⣾⠄⠀⠙⣀⣤⣤⡀⡶⠀⠀⣱⣤⣠⣤⡤⠁⠀⠠⠄
⣿⡏⠉⠛⠛⠋⠉⠉⠉⠛⠋⠈⠙⠛⡼⠿⣤⣀⣀⣀⣀⣤⣴⡟⠀⠀⠉⠛⠻⣿⠄⠀⠈⠛⠻⣷⣿⣷⣄⠀⠀⠀⠀⠀⡀
⣿⡷⠀⣾⣷⣶⣿⣶⣾⣿⣿⠂⣿⣿⣿⠄⠿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⠦⠀⠀⣿⠀⠀⠀⠈⠻⣿⣷⣦⡄⠀⠀⠀⠀⠒⠺⠷⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠤⠴⠤⡖⠏⠀⠴⠶⠆⠠⠲⠲⠲⠂⠄
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⡀⢠⣀⠠⠤⠀⠰⠤⠴⠀⠆⠀⡤⢤⢰⡄⢠⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣭⡻⣶⣤⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡾⣿⣿⠀⠀⡀⣹⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠙⠀⠀⡙⢿⢿⠀⠨⠭⢸⣿⣿⣦⠐⠒⠚⠛⠛⠉⠛⠉⠋⠉⠋⠉⠉⡉⠻⣿⣿⡄
⠀⣼⣿⡿⠿⢿⠿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⣿⠑⢄⠚⣹⣯⡖⠢⣄⡀⠊⣯⣿⡟⠀⠦⠶⠦⠶⠶⠾⠸⠀⢻⠰⠒⠂⠿⠘⡇⠶⠆
⠀⣿⣿⣇⠐⠒⠂⣿⣿⣿⠀⠀⣿⡦⣤⣤⣤⣼⠀⢠⡌⠓⢦⣳⡟⢹⣯⢢⡘⣀⠞⠁⣿⡏⠙⠦⣀⡀⠀⠖⠶⠰⠒⠼⡖⠀⠀⣠⡾⠁⠁
⠀⣿⣿⡯⠀⠀⠄⢻⣿⣿⠀⠀⠙⡧⢯⡧⣿⢿⠀⠀⣇⠀⠀⢻⡇⢸⣿⡆⠱⣟⠀⠀⡏⠁⡚⠀⠿⠿⣿⣷⠒⠖⠦⢴⣶⣿⣿⣧⠄⠀⠀⡀
⠀⣿⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⠐⠥⣬⣧⣽⢸⣇⠀⠹⣆⡀⠈⡷⠀⣿⡇⠀⣿⠀⡎⠀⣐⣂⣰⠦⠫⠿⠇⠠⠆⠀⠈⠉⠛⠛⠛⠀⠀⠀⠁
⠀⢘⣉⣧⣴⢤⣦⣎⣠⣬⣥⠹⣭⡬⣽⢉⣭⢸⠙⠰⠞⠉⠙⡄⣡⠀⢙⡁⠐⢋⣀⠃⠉⠁⠀⢀⠀⠀⠀⠀⠀⣄⡀⠀⢀⣀⡀⠀⣀⣀⣀⡀
⠀⢀⣤⣤⣤⡬⣥⣀⣀⣀⣀⣈⠉⠁⠁⠈⠉⠙⠀⠀⠀⠀⠀⠀⢹⡀⠘⡃⣽⡙⢚⡀⣀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠈⠉⠁⠀⠉⠉⠉⠉
⠀⢻⣿⣿⣽⠶⠟⠛⣩⣭⣭⠝⢋⣛⠿⠟⡲⢾⠀⠀⠀⠀⠀⠀⢸⠁⠈⡇⢹⡋⠏⡇⠅⢛⠒⠒⠂⠐⠈⠁
⠀⠐⠊⠁⠀⠀⠴⢓⣀⠤⢐⣪⡽⠖⠚⣁⠤⠈⠢⡤⣤⣤⡤⣤⠚⠉⣿⠁⠘⡄⠀⠉⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⢰⠶⡄
⠀⠀⠀⠀⠠⢐⡨⠵⢖⡋⠽⠿⣒⣡⠤⠔⢚⡩⠥⢂⣻⠀⠀⣿⡆⠀⣿⣆⣶⡅⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠾⣇⣳⣶⡦
⠀⠀⠻⠶⠶⣶⣦⣥⣤⣔⢒⡉⠩⠐⠒⣈⡤⠖⣚⣭⣽⠀⠀⢿⡇⣀⡻⣿⣿⠿⠛⠛⣲⣾⣿⠷⠒⠲⢶⣒⣶⣾⣿⣿⣿⡟⣩⢅⣀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⣷⣦⣤⣍⣉⣛⣉⡿⠷⠾⢿⣿⣯⠭⢿⠤⠖⢋⣛⣣⣤⣶⠾⠿⠛⠛⠉⠁⠀⢸⡟⡇⠹⠞⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠶⢶⣿⣼⣿⣾⣿⠶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⣧⠜⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠘

⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⢴⡄⠀⠀⠀⣶⠀⢶⡟⠳⢶⣤⠀⠀⢠⡾⠛⢷
⠀⠀⠀⢹⡇⠀⠀⠻⠀⠀⠀⠘⠻⠄⠀⠀⠘⠛⠀⠀⠀⠉⠀⠈⠀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⢸⡇⠀⠀⣤⡄⠀⠠⣦⠀⠀⠀⢠⣤⠀⠀⠀⢻⣆⠀⠀⠈⠿⠀⢿⠋⠉⠛⠒⠀⠀⠸⠋⠈⠛
⠀⠀⠀⠘⣇⡀⠀⢹⡇⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⣀⡀⠀⠀⠀⣤⠀⣤⣤⢤⣄⡀⠀⠀⢀⣴⠶⣦
⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⢺⡆⠀⠀⣿⠀⠀⠀⢸⣿⡀⠀⠀⢸⣷⡄⠀⠀⣿⠀⢸⡇⠀⠈⠹⣦⠀⢸⡇⠀⠈
⠀⠀⠀⠀⣿⠀⠀⢸⣷⠆⠀⢸⡇⠀⠀⢿⠀⠀⠀⣾⠈⣇⠀⠀⠘⡇⠹⣄⠀⢸⠀⢸⡇⠀⠀⠀⠸⣇⠈⢻⣆
⠀⠀⠀⠀⣿⠀⠀⠈⡇⠀⠀⠘⡇⠀⠀⣸⡄⠀⠀⡟⠀⢹⡄⠀⠀⣧⠀⠹⣆⢸⡇⢸⡇⠀⠀⠀⠀⣿⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠙⠁⠀⠀⣿⠀⠀⠀⣿⠛⠛⢻⡇⠀⢸⡇⠀⠈⣧⠀⠀⣿⠀⠀⠘⢿⡇⠘⡇⠀⠀⠀⠀⣿⠀⠀⠀⠈⣿
⠀⠀⢀⣴⠒⠲⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⣸⠧⠶⠶⢿⡄⠀⣿⠀⠀⠀⢸⡇⠀⣷⠀⢀⡤⣶⣇⣀⠀⠀⠀⣸⠇
⠀⠀⡿⠙⣆⠀⠀⠀⣀⠀⠀⠀⣿⠀⠀⢸⡇⣀⣿⡀⠀⢠⡼⣧⡀⣹⡀⠀⠀⢠⣷⢀⣿⣤⣾⠶⢋⠎⠛⠷⣤⠶⠏
⠀⠀⢿⡀⠀⠀⣰⣏⠉⠙⠀⠀⠿⠇⠀⠘⢿⠋⠛⣽⢠⡏⠀⢸⠇⠉⠁⢀⡤⢴⣿⣶⠤⣼⠤⠖⠋⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠉⠀⠀⡇⠈⠳⠀⠀⣠⡤⣄⡀⢀⣿⣠⡴⢃⣸⣥⠴⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⢻⣴⠞⢳⠀⠀⠀⢠⡞⢁⡟⠀⢀
⠀⠀⠀⠀⠀⠀⠻⢤⠀⠀⣼⠻⡀⠀⣧⠈⣿⠀⠀⠀⣸⡅⠀⠀⢠⠆⠀⠀⠀⣿⠀⠀⢀⢾⡁⠀⢸⠀⠀⣠⠾⡟⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⢳⡟⠚⣿⣤⠴⠞⢹⡷⡖⠚⠉⠀⠀⠀⠀⠹⠦⠖⠋⠘⠃⠀⠈⠓⠚⠁⠀⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠚⠋⠀⠀⢹⡈⢧⠀⠈⡇⠹⡄
⠀⠀⠀⠀⠀⣀⡀⠀⢸⣇⠀⠀⣤⠀⠀⠀⠈⠧⠜⠀⠀⠙⠶⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣤⢀⣀⣀⡀
⠀⠀⠀⠠⢒⣾⡽⠃⠘⠋⠀⠀⢹⠀⠀⠀⢶⠦⣄⠀⠐⣿⠀⠀⠀⠈⣿⠁⠉⣿⡄⠀⠀⠀⣼⣇⠀⣿⠈⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⣄⡀⣸⣦⠀⠀⢸⡀⠈⣧⠀⣿⠀⠀⠀⠀⢸⡄⠀⣿⢻⡄⠀⣸⠇⣿⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠸⠿⠎⠀⠈⠀⠀⠀⢸⡇⢀⡿⠀⢻⠀⠀⠀⠀⢸⡇⠀⣿⠀⢻⣠⡟⠀⣿⠀⢻⣀⡴⠇⠀⠀⠀⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣝⢲⠤⢸⡟⠻⣄⠀⢸⡆⠀⠀⠀⠸⡇⠀⣿⠀⠀⠻⠁⠀⢹⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠈⡇⠀⠘⣧⢸⡇⠀⠀⠀⢠⡇⠀⢻⠀⠀⠀⠀⠀⢸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡇⠀⢠⡟⠈⣷⠀⠀⠀⣸⠇⠀⣸⡀⠀⠀⠀⠀⢸⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠷⠞⠋⠀⠀⠈⠛⠛⠛⠋⠀⠀⠙⠃⠀⠀⠀⢀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣄⢶⡀⣄⠀⠀⠀⠀⠀⠀⣰⢦⡿⣼⠷⣟⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠼⠋⡾⢻⠟⢹⠃⠈⢴⣤⠄⠈⠻⠈⠛⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⣲⡄⣠⠖⠒⠒⣄
⠀⠀⠀⢀⡀⢀⠞⠁⠀⣠⠊⠉⠉⠁⢀⡄⠀⢘⡉⠑⠒⣄
⠀⠀⠀⠀⠈⣋⠀⣠⡞⠁⠀⠀⠀⢀⣼⣅⠀⢸⠧⠤⣴⠇
⠀⠀⠀⠀⠀⠈⠛⠋⠙⠲⢤⡄⠀⠈⢻⡿⠶⠾⠄⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⠛⠂⠤⣀⣾⡤⠤⠤⠤⢤⣤⣤⠖⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣅⣀⣀⣼⢋⠄⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠑⠲⡚⠉⠉⢳⢘⡦⠴⠶⠶⣾⠏⠀⡇⠀⢀⣆⠄⠀⠀⠹⡄⣤⠶⠒⢒⢦⡀
⠀⠀⠀⠀⠤⡴⠒⢲⣤⡞⠀⢠⡀⠀⠘⡶⠒⠛⣾⠠⠀⠀⠐⢧⣤⡎⣀⣪⡞⠁⠀⠀⠀⠀⢻⠛⢷⠃⠀⠑⢻⡋⠁
⠀⠀⠀⠀⡼⠁⠀⡎⠀⠁⠀⠀⣷⣤⣀⡷⠤⠠⣟⣤⠤⠤⠤⠤⠤⠭⣾⣿⣇⠀⠀⠀⠀⠀⠊⠀⠸⣧⡔⠂⣢⣷
⠀⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠈⠉⠻⣭⠄⠠⠤⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣕⣏⡘⡇
⠀⠀⠤⠤⣄⠀⡾⠦⠦⠴⢦⣀⡀⠀⠰⠀⠀⣠⢾⠗⠒⠒⠒⠒⠛⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣊⣉⡧⢷
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⢉⡽⠻⣤⢸⡄⠀⢀⣀⣠⡴⠏⠀⠀⠀⠀⢀⣤⠆⣿⣀⣀⣀⣼⣷⢀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣎⡀⢀⡜⠉⢻⡶⢤⣀⣀⣀⣀⣀⣀⣀⣠⡭⠶⠛⠉⠉⠉⠉⢯⣽⣸⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠈⠙⢦⡴⠊⠙⣆⡀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⠳⣤⣦⣾⣀⡀⠉⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢲⡾⠃⠀⠀⠘⠋⠉⠉⠦⢐⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠺⡇⠀⢳⡀⠀⠀⠀⣀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢳⣄⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⣻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣭⣭⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠉⠉⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⠀⠀⡠⢊⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡑⢄
⠀⠀⠀⡠⢊⣴⠟⠁⠀⣿⣿⣿⣿⣿⣶⣄⠀⠀⢰⣿⡇⠀⠀⠀⢰⣿⡇⠀⠀⣾⣿⡆⠀⠀⠀⢀⣾⣿⠀⠀⠀⣿⣿⣿⣿⣿⣶⣦⡈⠻⣦⡑⢄
⠀⡠⢊⣴⠟⠁⠀⠀⠀⣿⣏⠀⠀⠀⢹⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⡄⠀⠀⣼⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠙⣿⣷⠀⠈⠻⣦⡑⢄
⡞⣴⡟⠁⠀⠀⠀⠀⠀⣿⣷⣤⣤⣶⣿⠟⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⡀⣼⣿⣿⣿⠀⠀⠀⣿⣿⣤⣤⣴⣾⣿⠃⠀⠀⠀⠈⢻⣦
⢧⠻⣧⡀⠀⠀⠀⠀⠀⣿⣟⠉⠉⠉⢻⣿⡄⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⠘⣿⣿⣿⡏⢸⣿⠀⠀⠀⣿⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠑⢌⠻⣦⡀⠀⠀⠀⣿⣟⣀⣀⣀⣠⣿⡇⠀⠈⣿⣷⣀⠀⢀⣼⣿⠃⠀⠀⣿⣿⠀⠸⣿⡟⠀⢸⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠓⢌⠻⣦⡀⠀⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠻⠿⣿⡿⠟⠁⠀⠀⠀⠿⠿⠀⠀⠹⠁⠀⠸⠿⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠑⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣦⣀⣀⣴⠟⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣛⣛⡥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣒⠂⠀⠀⠀⡈⠁⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠉⡱⠀⠀⡆⢹⠀⠀⠀⠈⠁⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠤⠤⠊⠀⣠⠞⢡⣦⠆⣠⠆⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⢦⣀⣀⣐⣊⣡⣶⠿⣿⣷⣧⣾⠀⢀⣀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⡆⣬⠉⠉⠉⠉⠀⠀⠈⠻⣿⡿⠋⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⢠⡀⠀⠰⠃⠃⠀⠀⠀⠀⠀⣠⡀⣀⣸⠁⠀⢀⣤⣤⣤⡀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⢳⠒⢤⡠⠛⠓⠀⠐⠒⠒⠲⠶⠷⠾⠿⣿⣿⡇⠀⠀⣾⠛⠋⠉⠙⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡰⠁⠀⢧⣧⠰⡊⡹⡆⢄⠃⠀⠀⠀⣇⢀⠆⠀⠀⠀⠀⠀⢀⢹⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⡇⠀⠀⠀⠈⣷⣚⠾⠖⠙⢆⠀⠀⢠⣿⣗⠀⠀⠀⠀⠀⢀⣾⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠑⠀⠀⠀⣠⣿⠀⠀⠀⢈⣨⡿⠖⠛⡉⠉⠉⠙⠛⠛⠛⠛⠛⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠉⠉⢈⠉⠉⠉⠀⠀⡇⠀⠀⠘⡆⡓⠀⠀⠀⠀⠀⢠⢸⣏⠙⠓⡒⠒⠒⠂⠀⠀⣀⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣄⠀⠀⠀⠘⣷⠤⠤⠤⠚⢧⠀⠀⠰⣣⣷⣄⣀⣀⣀⣴⣿⡟⠻⣄⠀⠉⠑⠒⠶⠖⠊⠁⠀⠀⡆⠀⢠⡀
⠀⠀⠉⠉⠁⠒⠒⠒⠒⠒⠚⠛⠛⠛⠒⠒⠚⠛⠒⠤⠁⠤⢺⡟⠒⠛⠋⠉⣉⠉⠁⠀⠀⢠⠘⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⠆⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢴⡿⠷⠆⠈⣀⣀⣤⡾⠟⠁⠀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠭⣛⠻⣟⣀⣀⣴⣦⣴⣿⣴⣷⠶⠿⠿⠿⠿⣿⣿⣿⣧⣄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⣀
⣿⡟⠠⣐⡄⢹⣿⣯⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦
⣿⣿⣄⣉⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡆
⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⢸⢀⠿⠀⠀⢠⢏⡼⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢦⣀⠘⠆⢸⠓⢀⢀⠎⠀⠀⢠⠟⠁⠀⠀⠀⠀⢈⡄⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠃⠁⠂⠴⠀⣀⠁⡠⠂⢈⡁⠄⠄⢰⡀⠄⠊⠙⠀⠀⠠⢋⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠚⠦⢄⡀⠀⠈⠳⡒⡤⠄⠐⠄⠈⠀⠔⠠⢬⡠⠒⢤⠄⠢⠈⠁⠠⠀⠀⢄⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠀⢀⣰⠀⠀⠀⠀⠀⠀⢘⡂⠀⠀⠀⠀⠀⠀⣦⡀⠀⠗⣄⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣄⣤⡴⠁⠀⠀⠙⢻⣄⢎⠀⠐⠂⠒⠻⠟⠂⠐⠀⠀⡱⣰⡟⠋⠀⠀⠈⢦⣾⣛⣉⣁⣀⣀⣀⣀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣽⣍⣁⣀⣀⣀⣀⡰⢄⣀⣀⣀⣀⣈⣉⣿⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢀⡴⠛⣏⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣹⠛⢦⡀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠈⠀⠈⠀⠸⣏⠉⠁⠒⠒⢖⠁⠀⡲⠒⠒⠈⠉⣹⠇⠀⠁⠀⠁⣆⡀
⠀⠀⠀⠀⠀⣀⠀⠄⠒⠂⠉⠉⠙⠒⠠⢄⡀⠀⠀⢑⠂⡤⠔⢈⠢⠄⠙⠢⢤⢐⡊⠀⠀⣀⡠⠄⠒⠻⠉⠉⠐⠒⠠⠀⣀
⠀⠀⠀⠈⠉⠀⠀⠐⢂⡀⠀⢀⡤⠂⠀⠀⠀⠉⢈⡈⢂⡠⠂⡍⠑⠄⢈⡀⠂⠀⠉⠁⠐⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠚⠁⠀⠀⣐⡠⢤⠎⠀⠀⠀⢀⢼⠋⢢⣀⠀⠘⡆⢄⡀⠀⠀⢦⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡴⠃⠀⠀⠀⡖⠡⣿⠀⠀⠛⠀⡄⢹⣆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠲

⠀⠀⢀⣀⡀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣀⡀⠀⣀⣀
⠀⠀⣿⣯⣬⣉⣉⣥⣾⠗⠚⠛⠀⠀⠀⠀⠀⠰⠄⠀⠀⢻⡏⢉⠀⢼⣇⣦⠀⣿⡅⢻⠁⣺⠏⢍⠈⣯⣔⠢
⠀⠀⠛⠛⠛⠛⣛⣋⣡⡄⠀⠀⠀⠀⠀⠀⠐⣦⡄⠀⠀⠈⣿⡶⢀⣼⣧⣦⡀⢸⡇⠞⡀⢻⣾⡟⠂⢬⣝⣿⡀
⠀⠀⠀⠀⠀⣻⣷⡿⠿⠷⠶⠒⠐⠒⠒⡐⠀⠉⠀⣤⡆⠀⠛⠉⠀⠈⠁⠈⢩⠀⠉⠋⠁⠀⠉⠋⠀⠈⠛⠋⠁
⠀⠀⠦⠃⠀⠀⠀⠀⡀⢄⡀⡀⠀⠘⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⡀⡀⠀⠨⠀⠀⠀⠀⣰⣎⠑⠠⢾⡿
⠀⠀⠂⠉⠀⠑⠀⠉⠉⠁⠀⠀⠀⠀⢰⣻⣿⣿⣻⣿⣿⣧⡁⣈⣑⣖⡀⠀⢠⣴⡄⠀⢉⣀⠶⠴⠊⠀⡄⠒⠠⠇
⠀⠀⠀⠀⣼⠄⠀⠀⠀⠉⠉⠁⠉⠉⠈⠛⠛⠛⠛⠿⠿⠷⠦⡯⠝⠋⠀⠀⠺⠞⠀⠀⢰⠯⠇⣠⣤⣄⠈⡅⠀⡀
⠀⠀⣶⡀⣿⠀⣠⡆⠀⠀⠀⠀⢒⣈⡉⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⡀⢀⠀⣄⠀⠀⠀⠀⢀⣠⣈⠉⠉⠉⠀⢀⡰⠠⠤
⠀⢠⣽⣷⣿⣾⣿⣶⠏⠀⠀⠀⠉⠠⠂⠀⠀⠀⢀⡴⠋⠉⠀⠉⢙⣃⣘⠷⣌⣙⠀⠀⣾⣿⣿⡿⠀⠀⣾⡓⠊
⠀⠀⣙⣿⣿⣿⣿⣭⡄⠀⠀⠀⣤⣾⠻⣼⡄⢀⡎⠀⢠⠤⣤⢤⣿⣿⣻⣷⡍⠋⠀⠀⠀⠋⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠙⢿⣦⣉⣛⡿⠁⠀⠀⠀⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀⢠⠂⠒
⠀⠀⠀⠀⡄⠀⢀⣶⣄⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣿⠈⠟⠟⠟⢋⣠⡾⠋⠀⠀⠀⠀⢱⠤⠄⣴⣶⢃
⠀⠀⠀⠀⠀⠀⡘⣿⣽⢉⣼⠟⠆⠀⠀⣼⠉⠢⠀⠀⠀⣿⡿⠀⠀⣠⠀⠀⠉⠑⠀⠐⠈⠀⡀⠁⠀⠀⠈⠉⠹⣆
⠀⢠⣬⡀⡀⠈⣛⢻⡿⣿⠁⢀⠀⠀⣨⡍⡆⢠⠦⡀⠀⠿⠃⠀⠀⠀⠄⡀⠠⠀⡀⠀⠀⠀⢳⡀⠀⠀⠀⡀⢀⠜⠉⠉
⠀⠘⠿⠷⠖⠀⢹⣟⠀⠈⠻⡿⠃⠀⢹⣶⡷⢏⡇⠀⠀⠀⠀⠀⠀⠆⠆⠉⠠⠘⠁⠀⠀⠀⢾⡗⠐⠶⢾⣷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠿⠿⠿⠛⠛⠘⠓⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠻⣿⣶⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠈⠙⠻⣿⣿⣟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣦⣄⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠻⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⣿⠏
⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡿⠿⠿⠶⠶⠾⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡏⠻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣤⣴⣿⠟⢸⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣄⡀⠉⠛⠿⢿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣽⣿⡿⠋⠁⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠁⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠉⠛⠒⠒⠶⠤⠴⠤⠶⠶⠖⠚⠛⠃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠢⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡠⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣧⢸⡇⠀⢾⣉⣈⢿⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⣇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢀⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀⠉⠉⠉⠉⠀⠀⡷⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⣴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠒⠲⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠛⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡙⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤
⡞⠋⠉⡟⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⠹⠉⠓⢦⡀
⠉⠒⠲⠦⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠁⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⣭⠇⠀⠀⡼⠁⠀⠀⣸⠞⠁

⠀⠀⠀⠀⠀⣀⠤⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⣤⢤⡴⡄⣬⣤⢭⣧⢤⢤⣤⣤⡤⣤
⠀⠀⠢⠖⠡⠀⠀⢠⠀⠀⠐⠈⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⠉⠩⠉⠉⠨⠍⠛⠛⠋⠙⠉⠛⠙⠋⠙⠙⡟
⠀⡁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⣄⡀⠀⠀⠀⠀⡇⡇⠘⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠂⠀⠘⠀⠀⡧
⡟⢀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⡇⢀⣈⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⣿
⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⠀⡏⠀⠀⠀⣿⢓⣶⣦⣐⣖⣀⣶⣆⣶⣶⣾⣆⣶⣶⣳⣶⣶⣷
⠰⡔⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠉⠈⠉⠈⠀⠀⠁
⠀⠙⢌⠢⠈⠀⠀⠀⠀⠀⠄⡀⢌⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠉⠒⠤⢭⣠⣤⠬⠅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡍⠉⢡⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠃⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⢔⡢⠖⠊⢹⡄⠉⠛⠷⣠
⠀⠀⠀⠀⠀⠀⢀⡆⠈⠈⢰⠄⠈⠉⣏⣉⠁⠀⢰⡂⠁⠠⡀⠀⠀⠠⡞⠛⠓⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⢺⠋⠀⠀⠀⢾⡗⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠘⢲⡀⠖⣠⠔⠉⠀⠠⠀⠀⢉⠂⡝⢶⢀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢈⠀⠀⣀⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⡼⠁⢠⣄⠀⠀⠀⢀⡀⠑⠘⡀⠁⠀⠀⠀⠀⣷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡈⠁⠀⠀⠀⠘⠁⠉⠋⠁⠀⠉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠀⠉⠳⣦⡞⠋⠀⠠⠀⠁⠀⠀⠀⠀⠀⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠫⢄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⣐⡅⣀⡀⣀⡠⢦⣔⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠠⠀⠀⠄⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠿⡟⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠒⠒⠂⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠙⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠛⠳⢶⣄⠀⠀⠀⠀⠀⢸⣻⠞⠁⠀⠀⠀⠀⢀⠀⠤⠀⠁⠼⠤⠥⢈⣀⣤⣀⡀
⠸⠧⠥⠴⠦⠤⠄⠄⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠀⠀⠀⠀⠙⢦⣀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠰⠾⠿⠾⠿⠿⠿⠷⠶⠶⠶⠶⠶⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⡄⠀⠀⠀⠀⠀⢻⡇⢀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠘⣇⣾⡿⠁⠀⠀⠀⠀⠀⠈⠉⠏⢈⠁⠁⠀⡀⢀⠀⠀⠀⠙⢏⠁
⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣿⣶⠄⠀⠀⢠⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡅⠀⠈⠂⠀⢀⢸
⠀⠀⠈⠐⠄⠂⠂⠈⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡧⠐⠾⢿⡗⢦⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⡀⠀⠀⢀⡀⠀⣀⠀⠠⢸⠈
⠀⠀⠀⡀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⣰⠀⠠⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠈⠈⠀⢸⠸
⠀⠠⢁⠄⠀⠀⠀⠐⠀⠑⡄⠀⠀⠀⠀⠀⢀⡎⠀⠀⢀⣔⠁⠀⠼⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠠⠄⢀⠠⡀⠀⠀⡀
⠀⢃⠇⠀⠀⠀⠀⠀⠀⠱⢡⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⡏⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠂⠀⡞⢹⡏⠙⠂⠈⠀⠀⡀⡆
⠀⡀⠃⠀⠀⠀⠀⠀⠀⢈⢨⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠇⠉⣠⢂⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠇⡈⠡⠀⠀⠀⠀⠀⠀⠇
⢠⣗⣐⣒⣆⣓⡒⠚⠒⠒⠚⠆⠀⠀⠀⠀⠈⠠⣈⣀⣠⣤⣼⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⢭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣭⣭⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⠙⠳⠦⢤⣤⣄⣀⣀⣀⣀⣉⣁⣀⣠⣤⡤⠾⠛⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⡶⢶⣶⣦⣤⣤⣭⣭⣭⣥⣤⣤⣴⣶⡶⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣧⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣼⣧⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠷⢶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⣿⡇⠀⠀⠀⠀⢀⣴⠟⡽⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣶⣦⣤⣄⡀⠀⠀⢸⣿⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣿⣇⠀⠀⠀⣰⡿⠛⠳⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⠒⠲⠍⣿⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠄⠀⣿⡀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣶⣦⣶⠟⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢿⡟⠛⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠉⢹⡇⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠛⠋⠙⠛⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣀⠀⠀⠰⠆⠀⠀⢀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠈⠁⠀⢸⡇⠀⠀⠋⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⢀⣴⠟⠁⠀⠀⠀⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣠⠈⠁⠀⠀⠀⠀⣀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠁⠀⠀⢰⡆⠀⠀⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⡴⠞⠋





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠶⠶⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠚⠋⢿⡄⠉⠉⠋⠛⠓⠒⠒⠒⡖⠒⠒⠛⠋⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠈⠳⣄⠈⢳⠶⢤⣤⣄⣀⣀⣀⣀⣃⣀⣥⣤⠴⡞⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢷⣸⡄⣀⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣷⣞⠉⠉⠉⠉⣙⣷
⠀⠀⠀⠀⠀⣀⣴⠷⠛⢿⡓⢦⠀⠀⠀⠀⠈⢿⡇⠀⠉⠉⢙⣛⠛⠛⣷⠀⠀⠀⢀⣿⣈⣉⣉⣉⣉⣉⡼
⠀⠀⠀⠀⣰⢫⠇⠀⠀⠀⠹⡌⢷⡀⠀⠀⠀⠘⡇⠀⠀⠀⣯⡬⢃⠀⣿⠀⠀⠀⢰⠏⠀⠉⠉⠉⠉⠀⠙⡖⠶⢤⣀
⠀⠀⠀⠀⡇⢸⠀⠀⡠⠖⠲⣿⠈⣇⠀⠀⠀⠀⡇⠀⠀⠀⠉⠽⠫⠀⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⣇⠸⡆⢀⡵⠶⣞⢹⠀⡟⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠉⠒⠶⠶⠶⠶⠖⠋⣿⠀⠀⠀⠀⢠⠞⠉⢳
⠀⠀⠀⠀⠸⣆⢿⡁⣠⠟⢉⡟⣸⠃⠀⠀⠀⠀⣿⠲⢤⣀⣀⣀⣀⣀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡖⠀⢀⡎⢠⠂⠛⢢⡄
⠀⠀⠀⠀⠀⠈⠳⠯⠿⠶⠿⡚⠁⠀⠀⠀⠀⠀⣻⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣇⡇⢸⠀⢻⣄⣰⣷⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠬⣟⠲⠶⠶⠖⠛⠉⠉⠓⠦⢤⣤⣤⣤⡤⠤⠖⠋⠹⣶⠤⣀⣀⣀⣀⣀⣴⠏⠀⠈⠙⠛⠓⠋⠀⠉⠁⠀⠈⠙⠲⠦⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣋⠀⢘⣀⡼⠁⠀⠀⠀⠀⠀⠀⣠⣒⣲⠶⢦⡀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠶⠷⠚⠉⠀⠀⢀⣤⠤⠤⢤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢧⣀⣀⠃⠀⠈⢻⠉⠁⠀⠀⠀⡠⠴⢶⠶⢤⣟⠲⠤⠤⢞⢇⣠⠶⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡇⠀⠉⡧
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⢸⠆⣀⣎⣀⡴⡏⠉⠛⢋⠟⠋⠉⢆⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠓⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠶⠚⠁⠀⠀⣯⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣩⡛⣉⣝⣙⣯⣏⣿⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠀⠀⠀⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣷⡄⠀⢤⣤⣠⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠛⣁⣀⣸⣀⡙⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⣩⣷⡾⠟⠛⠛⠛⠛⠛⠿⢶⣿⣙⠛⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡄⠀⠀⠈⠙⢢⣦⡄⠀⠤⠤⠄⢤⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠉⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⠷⣶⣶⣶⣶⡶⠿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠒⠒⠲⠦⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢿⠒⠦⠤⠤⡤⡤⡤⢤⠤⠴⢾
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠙⢦⡘⡶⠤⠤⢤⣀⣄⣤⣤⠤⢴⢋⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣯⣤⣄⠀⠀⠀⠱⣟⠐⠤⠤⠤⠤⣄⠀⠀⢸⡿⠤⠤⠤⢽⡆
⠀⠀⠀⡜⡏⠀⠈⢣⢳⡀⠀⠀⢻⠀⠀⢰⡵⡀⣿⠀⠀⡸⠋⠙⠛⠋⠙⡶⠤⣀⡀
⠀⠀⢸⡀⡇⠠⣊⡹⡇⡇⠀⠀⢸⠀⠀⠀⠊⠁⢸⠀⠀⡧⢀⣀⣀⣀⣀⢼⠀⠀⠉⢑⠦⡀
⠀⠀⠀⢧⢳⢈⡼⢳⢣⠇⠀⠀⢸⠦⣄⣀⣀⣀⣸⠀⠀⡇⠀⠀⠉⠁⠀⢸⢠⠀⢠⢃⠄⠧⡀
⠀⠀⠀⠀⠙⠛⠛⠻⣅⣀⠀⣀⣨⢦⣀⠀⠉⠁⠀⠀⣀⣇⠀⠀⠀⠀⠀⡽⠾⢤⣼⣸⠦⠾⠳⢤⣀
⠀⠀⢀⣀⣀⣠⠒⢋⣹⠈⠉⠁⠀⠀⣈⢭⣭⡙⠉⠉⠀⠙⠿⠷⠶⠶⠟⠃⠀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠒
⠀⠀⠧⢄⣅⣈⣹⠉⠀⠀⡠⠐⡖⠲⣟⣒⣖⣧⣤⠒⣦⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⢀⣆⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣒⣓⡾⠃⠀⡜⠁⢀⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠋⠉⠉⠉⠉⠉⠉⠑⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣀⡤⠴⠒⢚⣉⣉⣉⣉⣉⣉⣉⡙⠒⠲⠤⣄⡈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⡠⠖⢋⡡⠔⠚⠉⠉⠀⠀⡄⠀⠤⣄⠀⠈⠉⠙⠒⠤⣉⠓⠦⣀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⣀⠔⢉⡴⠊⡅⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⢠⡄⠉⠢⣌⠑⢤⡈⠳⣄
⠀⠀⠀⠀⣠⠋⢀⠜⢁⠔⠁⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⢄⠙⢆⠈⠣⡀
⠀⠀⠀⡼⠁⡰⠃⡴⠁⠀⠀⠀⠀⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠱⣄⠳⡀⠙⡄
⠀⠀⡜⠀⡼⢁⠞⢠⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⢆⠹⡄⠘⡄
⠀⡼⠀⡼⢁⠎⠀⢸⠀⣯⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠹⡄⠸⡄
⢠⠃⢠⠃⡞⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⡆⢳⠀⢳
⡼⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢳⠘⡆⠸
⡇⠀⡇⢸⠀⢀⠄⢦⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⣀⣀⣤⠤⠤⠶⠒⠒⠻⠖⠉⠀⠐⠦⠀⢸⠀⡇
⡇⠀⡇⢸⠀⠈⢃⠟⠛⠧⠼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢄⡼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢘⠀⡇
⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⡇
⢫⠀⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠇⢰
⠘⡄⠘⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠃⡼⠀⡜
⠀⢳⠀⢱⡈⢇⠀⠀⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠗⢀⠏⣰⠃⢰⠃
⠀⠀⢣⠀⠳⡈⢦⠀⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⠃⢠⠃
⠀⠀⠀⢳⡀⠱⣄⠳⡄⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⡴⢃⡴⠁⣰⠃
⠀⠀⠀⠀⠙⣄⠈⠢⡈⠢⣀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⢀⡠⠊⡠⠊⢀⡜⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠈⠢⣌⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡤⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠑⠢⣌⡑⠲⠤⣄⣀⡀⠀⠀⠣⠘⠀⠀⣀⣀⡤⠴⠒⣉⡤⠖⠉⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡉⠑⠒⠤⠤⣍⣉⣉⣉⣉⣉⣉⡥⠤⠔⠒⠉⢁⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⢤⣀⣀⣀⣀⣀⣀⠤⠤⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢸⡀⣸⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⠀⠀⠙⠊⠁⠁⠚⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⡴⠋⠀⠀⠈⠙⣦⢤⡀⠀⠀⢀⡀⣠⣶⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹⠤⠊⠀⠀⣠⢾⡇⠀⣼⣠⡇⠀⠀⠸⠗⣿⣿⠇⡙⢿⣿⣷⣄⡀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠠⡏⠳⢤⠇⠀⣹⠀⠀⢿⣿⣜⣫⣶⢸⣿⣿⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⠀⠀⠀⠀⠠⡏⠉⠉⠉⠉⡇⠀⠀⢰⣶⣶⣶⣶⢼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣀⠀⠀⠀⠠⡏⠉⠉⢙⡏⠁⠀⠀⠀⢠⣶⣶⣶⢸⣿⣿⣿⡿⠟⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋⠈⠉⠙⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢱⠆⢦⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⢀⡤⠤⠦⠴⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⢸⣉⣉⣀⣉⣉⡇⠀⠀⠀⠀⠀⢸⣃⣀⣀⣀⣀⣀⢀⣻⠀⠀⠀⠔⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢼⡁⠀⠀⠀⠀⢀⡴⠃⠈⠀⠀⠀⠀⠈⠳⢄⠀⠸⡣⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠒⡂⡐⠈⡇⠀⠉⠒⠦⠤⠤⠒⠋
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠆⡬⠀⠙⠒⠐⠀⠀⡀⡀⡇⠀⡴⠒⠒⠛⠛⠻⣿⣿⣿⣶⣆
⠀⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⡇⠄⡋⠀⣀⣾⣆⡀⠀⡘⠀⡇⠸⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠠⠃⠀⠉⢿⠏⠁⠀⠅⠂⡇⠀⠉⠛⠒⠒⠒⠛⠛⠛⠛⠉
⠀⠀⠀⣼⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠙⠤⠤⡠⠤⡠⠔⠁⠂⡇⠀⡔⠋⠉⠉⠉⠉⠉⠉⠉⠒⡄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠈⠓⠖⢂⡈⠡⡃⠂⠀⡇⠘⡅⠀⠀⠀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣻⠀⠀⠀⠀⢶⣿⠶⠀⠀⠀⠀⡇⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠀⠈⠉⠛⠓⠒⠒⠒⠒⠋⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠤⠲⠤⠠⠴⠲⡤⠤⠶⠒⠖⠲⠖⠒⢲⠲⠶⠒⠒⡶⠦⡀
⠀⠀⠀⣿⣶⢶⣦⣶⣦⣤⣤⣶⣶⣶⣖⡇⠀⠀⢀⡞⢡⣀⠀⠛⣄⡀⠈⠃⢥⡄⠀⠉⢠⣤⠀⠈⠀⢦⠀⠀⠁⡼
⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⢀⠎⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡄⢀⠀⠀⣠⠀⠠⠀⠀⣀⠀⡰⠁
⠀⠀⠀⢻⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⢟⠇⢠⠋⢠⣤⠀⠋⢤⠄⠈⠁⢢⡆⠀⠀⠰⠖⠈⠈⠀⠲⡖⠈⠈⣰⠃
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠒⠒⠛⠉⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⠴⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣚⠉⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⠵⠊⠁⠀⠀⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⠥⢖⡩⠔⢀⠀⠀⢀⣠⢴⡺⠟⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢀⡤⠖⠋⠀⠀⣁⡴⣚⠽⠊⠁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡫⠀⢀⡤⠞⠉⠀⠀⣀⣴⡾⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⡠⢞⡩⠖⢋⠤⠚⢉⠤⢊⣠⣴⡾⠛⠁⠀⠀⠀⢀⠀⠀⠀⢠⡞⠋⠉⢳⡄⠈⢧⡀
⠀⠀⠀⡞⠉⠐⠉⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣇⣀⣠⡼⡷⠀⠀⠹⣦⡀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⣀⡤⠤⣄⣀⣤⣤⣀⡤⢶⠿⣿⠷⠊⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠙⣦⡴⡪⠟⠁⠀⠀⠀⠀⠀⠀⡞⠢⠤⢤⣌⣿⠀⠀⣾⠀⢸⠀⢸⡏⠙⣢⠤⠤⣄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣄⣀⣠⡴⣿⣤⠖⢿⣦⣼⣦⡞⢡⡎⠉⠲⣤⡾⡆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡼⡏⠣⡈⠙⣦⢰⡇⢿⡴⠋⣷⠀⠘⣬⠿⠿⢾⣋⣩⠴⡧⠶⠶⣄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢷⠳⣄⡙⢆⡿⠈⣧⣈⣳⣤⠟⠀⣾⠓⠲⢖⣰⢿⠀⢸⡄⠀⠀⣸⡇⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠳⠮⠽⠟⢡⠾⡀⠉⢍⢱⣴⡟⠻⣿⣭⣭⠵⠋⠀⠘⠮⣭⣭⡽⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠈⢧⣉⠓⢶⣿⡘⢿⢦⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣽⡉⠁⠀⢸⡆⠑⠿⠞⠃⠀⢀⠤⠶⢤⡀⠀⠀⠀⠀⢀⣴⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢧⣙⡲⢶⡿⠁⠀⠀⠀⠀⢠⣇⠀⠀⣨⡇⠀⠀⠀⢐⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠉⠀⣠⠴⡶⢤⡀⠈⠻⢿⡭⠟⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢰⡇⠀⡇⢀⣿⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠸⣿⣶⣷⣻⠏⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠉⠉⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡽⢿⣿⣿⣿⣿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⡿⢯⣿⣿⣧⣀
⠀⠀⠀⣶⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣶
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣨⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠉⢀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⡀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⣰⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⢠⣷⣶⣤⣤⠀⠀⠀⣀⣀⣠⡀⠀⠀⢠⣾⡿⠿⠿⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⡿⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠒⣶⠒⠦⣤⣀⠀⠀⢰⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⣀⡔⠾⣀⠀⠉⠀⠀⠀⠙⢷⣄⣈⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢤⣀⣬⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠹⣿⠂⠀⠀⡱⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⣸⣿⣿⣿⣿⡌⠉⠀⠀⠀⠀⠀⠀⠀⢡⢴⣿⣶⠐⠃⠱⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⣠⣠⣶⣿⢏⣿⣿⣿⡆⢀⡀⠀⢀⠠⠤⠾⣞⠁⠀⠀⢿⡅⠆⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡤⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣾⡓⠀⠀⠀⠀⠀⢫⠀⠀⠉⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣀⣠⣿⣖⣻⣿⣾⣿⣟⣿⣿⣿⣿⣿⣶⡦⠀⠀⠀⠘⠄⠀⢢⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠸⣶⠀⢸⣦⡾⣿⣤⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠛⠛⠋⠀⠈⠉⠉⠉⣉⣉⣭⣽⣿⣬⣽⠙⠓⠒⠒⠛⠛⠁⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⣿⡀⢀⣿⠃⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠙⠃⠘⠏⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠁⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⡀⣠⠀⠀⢸⡟⠛⢦⡀⠀⠀⢀⡴⠛⢻⡃⠀⠀⣄⢀⡄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⣤⣤⣤⣤⡴⠛⠁⠀⠀⠀⠀⠈⢿⠃⠀⠀⣼⠁⢀⣸⠃⠀⠀⠘⣇⡀⠈⣧⠀⠀⠘⡿⠁⠀⠀⠀⠀⠈⠛⢦⣤⣤⣤⣤⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⣸⠋⠉⠉⢳⡀⠀⠀⢀⡞⠉⠉⠙⣇⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣻⣽⣷⣋⣀⣀⢀⡼⠃⠀⠀⠘⢧⣀⣀⣀⣙⣾⣯⣟⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⡇⠀⠀⠀⠉⠉⠹⡇⠀⠀⠀⠀⢸⠏⠉⠉⠀⠀⠀⣸⠇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠛⠲⠶⢤⣤⡼⠃⠀⠀⠀⠀⠘⢧⣤⡤⠶⠖⠛⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⠛⠛⠛⠳⢦⣄⣀⣀⠀⠀⠀⠘⢳⣄⡀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⢀⣠⡞⠃⠀⠀⠀⣀⣀⣠⡴⠚⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⣰⡄⢠⣄⠘⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⢠⣿⠁⠈⣿⡀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣵⢂⠀⠀⠀⠀⡈⠀⠘⢶⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠃⠀⠀⠀⠀⠶⣀⠻⠟⢂⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠂⠀⠀⡀⢠⡤⠜⠛⢯⡉⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢆⠀⠠⠀⣀⡀⠀⠀⠰⠂⠉⠀⡄⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣪⢀⠀⢀⠉⠀⠐⠀⠀⠀⢠⠀⣠⡄⠀⠀⡠⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⣁⡨⠀⠀⢀⡁⢀⣤⣄⠀⠀⠀⠙⡃⡀⢠⡙⠧⠘⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠤⠈⠀⠈⡂⠒⢨⠁⠘⣹⣦⡂⠀⠀⠀⠠⠌⢦⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠒⠛⠟⢻⣿⣿⣶⣿⣷⣶⣿⣤⡉⢠⣄⠊⢡⡄⠀⠀⠀⠀⠀⠓⠀⠀⣠
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣽⠱⣄⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⡟⢸⡟⠁⠄⠀⠐⠀⠒
⠀⠀⠀⠀⣠⠞⠉⠻⣿⡁⠀⠑⣌⠣⡀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⠛⣥⡠⠶⠀⡀⠀⡀
⠀⠀⣠⠊⠀⠀⠀⠀⠙⢿⣆⠀⠈⠳⣌⠢⡀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣾⣃⡁⠀⠂
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠈⠳⣌⠢⡀⠀⠀⠀⢈⣿⣿⣿⣿⣮⡑
⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⢷⣝⢆⠀⢀⣹⡿⣿⣿⣿⣋⡑
⠀⢸⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠙⢷⣟⠉⠀⢐⣿⣿⣯⠼⠀⠓
⠀⠈⢧⡀⠉⠒⠤⠀⣀⡀⠀⠀⠀⣀⡀⠹⣧⢀⣠⠤⠛⠀⢀⣴⣿⠟⠅
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠉⠀⠀⠀⡀⠀⠠⠄⠀⢀⠀⠀⠈⠉⠙⠛⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⡀⠄⠒⠀⠀⠀⠀⠠⣤⠀⠠⠄⢦⡄⠀⠈⠀⠃⠠⠀⠀⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠀⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⠄⠈⠀⠀⢻⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⠀⢀⣀⣋⣀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⢤⠀⠙⢿⣷⡀
⠀⠀⠀⠀⢀⣼⡿⠋⠀⠄⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⣦
⠀⠀⠀⢠⣾⡟⠁⠠⠀⠀⠀⠀⠀⠀⠀⠼⠇⠀⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⢿⣷⡀
⠀⠀⢠⣿⠏⠀⠦⠀⢠⣤⠀⠀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠆⠀⢻⣷⡀
⠀⢀⣿⡏⠀⡠⠀⠀⢸⡏⠀⣸⡃⠀⢸⡇⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠤⠀⢻⣷
⠀⣼⡟⠀⢠⠀⠀⠀⢸⣇⠀⢹⡇⠀⢸⠇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⡀⠈⣿⣇
⢰⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠚⠛⠀⠀⠀⢀⠀⢸⣿
⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⣿⡇⠀⠀⠀⣠⠂⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠃⠀⢿
⣿⡇⠀⠆⠀⠙⠶⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣬⡀⠀⠀⠶⠀⢹
⣿⡇⠀⢀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣕⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⡄⠀⣿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠐⣿⣿⣿⡟⠁⢀⠀⠀⣿
⠸⣿⡄⠀⠀⠀⠀⠀⢀⡀⢀⡐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⣤⣴⣶⣾⣿⣿⣿⣦⣈⠀⢸⣿
⠀⢻⣷⠀⠙⡀⠀⠀⠸⣆⣠⠃⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⡏
⠀⠈⢿⣇⠀⠐⠀⠀⣴⠉⠙⣷⣰⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠘⣿⣦⠀⠖⠀⠈⠓⠚⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠈⢿⣧⡀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣷⣄⠀⠲⠀⠀⠀⠈⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⣿⡧
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠃⢀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⠠⣿⣿⣿⣿⣿⣿⣿⢠⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠁⢾⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⡇⠈⢻⡆⠀⠀⠀⠀⠀⠘⠂⠈⠁⢠⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠓⠀⠚⠁⠀⠀⠀⢀⠀⠤⠐⠈⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣧⠁⠉⠀⠘⠂⠀⠉⠀⠀⢀⣀⣠⣤⣶⡿⠟⠋⠁⣼⣿⣿⣿⢿⣿⣿⡏⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⡿⣷⣶⣶⣶⣶⣾⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣏⣻⣿⣦⣈⣏⣙⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣑⣾⣿⣛⣿⣁⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣦⠀⠀⢠⢏⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠙⠀⠸⠆⠀⢘⡆⠀⠀⢀⡎⠊⠁⠀⠀⠀⠊⡁⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⠈⠉⠂⠀⢀⠀⠈⠊⢣⢄⠘⠁⠠⠀⢀⢀⠀⠔⠛⠀⠀⠠⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠐⣶⣤⣶⠴⠾⠉⠁⣤⣠⣁⠐⠁⢢⢀⣡⣄⡀⠉⠹⠶⢴⣦⣤⡀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢾⠉⠁⣡⣴⡀⡀⠀⠋⠉⢉⠍⢱⠉⢍⠉⠙⠃⢀⡀⣰⣤⡁⠉⢹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣷⣿⡂⠀⠿⣿⣧⡖⠀⠙⣿⠿⠾⣏⠾⠾⢿⡟⠉⠐⣦⣿⡿⠗⠀⣺⣿⣷⣖⠒
⢀⣶⣶⣶⣶⣾⣯⣿⡿⠿⠿⣻⡿⣙⣿⠯⠀⢰⣿⠛⠿⣶⣶⢁⡴⢀⣨⡀⠐⣄⢑⣶⡾⠟⢻⣷⠀⠨⢿⣟⡹⣿⡛⠿⠿⣿⣿⣿⣶⣶⣶⣶⣆
⢈⣉⣉⣥⡄⣀⡉⠉⠶⠾⠻⢻⣷⣿⣷⠀⢀⣿⣿⠷⠖⠶⠒⠒⠒⠟⢇⠛⠗⠒⠒⠶⠖⠶⢿⣿⣃⠀⢰⣿⣿⣿⠻⠻⠶⡎⠉⣁⡀⣤⣍⣉⣉
⠏⠙⠀⠀⠀⡀⣠⣤⣴⣶⣴⢎⢏⢻⣟⣠⣿⣿⣿⣷⣶⣤⣤⣴⣦⣤⠽⢧⣴⣶⣤⣤⣴⣶⣿⣿⣿⣇⣉⣻⢋⣏⢶⣴⣴⣤⣤⡀⡀⠀⠀⠘⠉
⠀⣦⣶⡾⠿⠿⠿⢛⣯⣥⣿⣾⣿⣶⡃⠉⠡⠻⠿⣧⣀⣉⠉⠙⠉⠉⢆⠈⠋⠙⠉⢉⣁⣠⣿⠟⠣⠉⠁⣲⣾⣿⣾⣷⣭⣟⠻⠿⠿⠿⣶⣦⡦
⠀⠀⢤⣶⣶⠾⠛⠛⠉⠩⠝⠉⠉⠉⣻⠶⠤⣤⠤⠌⠩⡭⠿⠒⠂⡉⠠⠄⢒⠒⠞⢫⠭⠉⠤⠠⣤⠴⠞⠋⠉⠉⠁⠉⠈⠙⠛⠿⢶⣶⣦⠄
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠊⠁⠰⠋⠁⠀⢠⢀⢠⠖⠁⠱⠀⢁⢴⠋⢀⢀⠊⢱⡄⡈⠀⠀⠐⣄⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⣱⠋⠀⠀⢀⡴⠡⣿⠀⠀⠿⠀⡀⢳⡌⠃⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣴⣶⣼⣧⣶⣶⣶⣶⣦⣦⣴⣶⣶⣤⣶⣧⣾⣥⣴⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀⣀⣈⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠙⠻⢷⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⡟⠀⠀⠀⠀⠀⢤⣤⣤⣄⣀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡘⠀⠀⠀⡰⢻⣆⣌⢛⣦⠀⠘⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢰⣧⣶⣠⣦⣷⣿⣼⣿⣿⣿⠀⢈⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣦⠀⢸⡏⠸⡏⠀⢹⣿⣿⡇⠐⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡇⠀⡇⠀⢸⣿⣿⣷⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣅⣤⣡⣤⣬⣭⣭⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠋⠻⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠾⠷⠒⠒⠛⠛⠛⠛⠿⠦⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠒⠂⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠴⠊⠀⠀⠀⠀⣠⠔⠚⡛⠥⠐⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⢐⠵⠁⠀⠀⠀⡀⠐⢉⠤⠂⠁⠐⠂⠀⠀⠀⠀⡶⠀⡷⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣀⡀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⣠⡖⠡⠀⠐⣄⢳⡀⠀⠀⠀⠀⢠⡄⣿⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠙⢷⣝⢦⡀⠀⠀⠈⢿⣆
⠀⠀⠀⡰⠁⠀⠀⠀⣴⢃⡴⠃⠈⠀⠀⠀⠈⠳⣳⡀⠀⠀⠀⠘⠓⠛⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡙⢶⣿⣦⡀⠄⠈⢿⣆
⠀⠀⡴⠀⠀⠀⢀⡾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠔⠈⠀⠈⢻⣿⣿⣶⣆⠀⢿⣆
⠀⢠⠃⠀⠀⠀⠞⠠⠀⠀⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⣴⠿⠛⠀⠀⢻⣿⣿⣿⣶⠘⣿⡄
⠀⡄⠀⠀⠀⡘⢀⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⣠⠖⠉⠀⠘⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⢻⣧
⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠸⣿
⠃⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣦⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⣿⡇⢿⡇⠐⣿
⠀⠀⠀⠐⣼⡇⠰⠀⠬⠍⠉⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠿⢀⡀⣿⣟⢸⣷⡀⣿
⠀⠀⠀⠘⡎⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡿⣌⠧⠀⣿
⢠⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣸⣿⡇⢟⠁⢀⣿
⠈⡤⠀⠀⢹⡿⢣⠀⠀⢀⣄⢖⣫⢱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠠⣄⠀⠀⠀⠀⠀⠀⣾⣿⣶⣤⣦⡀⠀⢠⣿⡻⠼⠞⠀⣸⡏
⠀⠐⢀⠀⠘⣷⡉⣧⡀⡈⠻⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠉⠛⠶⠙⠀⢠⡿⡷⢡⠚⠀⣸⡟
⠀⠀⠀⢂⠀⢻⣷⡹⢿⡇⠀⠋⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⠀⢘⣧⡀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣏⡟⣡⠎⠀⣰⡟⠁
⠀⠀⠀⠀⡣⡈⣿⣿⣌⠢⣾⣦⠀⠀⠀⢀⣤⠏⠗⠀⠀⠘⠃⠈⠛⠉⠀⠀⠀⠈⠀⠻⣄⠀⠀⠠⠄⣠⣾⣯⢏⣴⠁⠀⣰⠟
⠀⠀⠀⠀⠘⢷⠈⢿⣿⣷⣝⠿⣷⣄⠀⠈⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⠂⢀⣤⣾⣯⠟⣡⠟⠁⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢂⠉⢿⣿⣿⣮⡝⢷⣦⢄⡀⡀⠀⠀⠀⠘⠂⠰⡆⡀⠀⠠⠀⡀⣠⡴⣞⠿⠟⢋⣴⡟⠉⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⢻⣿⣿⣿⣷⣮⣘⣤⠉⡀⠐⠒⠂⠤⣤⣤⣶⣶⣶⣿⣿⠿⢞⣋⣴⣶⡿⠗⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣍⣉⣁⣀⣠⣤⣤⣶⣶⣿⢿⢛⣉⢤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠻⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣥⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⢠⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⢷⣿⠀⠀⠁⠑⡀⠠⠋⠑⠢⢀⡀
⠀⠀⠀⠀⠤⣤⣄⣀⣀⣀⣀⣀⣴⠃⠀⠀⠀⠀⠀⠀⡴⠋⠉⠑⠀⠀⠘⡉⢢⠷⠤⣀⠀⠉⠑⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⡧⠴⠴⠆⠠⠤⠤⢠⣽⠀⠀⠀⠑⢶⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠋⠢⡀⠀⠀⠀⠀⠰⡗⠀⠀⠀⠀⠀⠆⠀⡏⠍⠑⠢⠤⣼⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠑⠒⠂⠀⠠⢤⣴⠷⠀⢀⣀⠀⡘⠀⠀⠀⠀⠈⣿⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⠿⠤⣀⡀⠀⠀⠀⠀⣽⣀⡀⠀⠀⢨⡅⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⠀⠀⠀⠀⠀⠀⠸⡀⠂⠀⠉⠑⠲⣤⠴⠋⠀⠉⠉⡻⠃⠀⠀⠀⠀⠀⠔⣴
⠀⠀⠀⠒⠒⠒⠚⠛⠛⠛⠛⠛⠳⠦⣄⣀⠀⠀⠀⠙⠶⠤⡀⠀⣠⠟⠀⠀⠉⠓⠲⠤⢤⣄⣀⣀⣀⡤⣾⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠖⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢛⡻⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣶⣿⣿⡿⠛⠉⠀⠀⠀⠰⢦⣌⡙⢿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⠋⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⡿⠉⠀⠀⠀⠘⢶⣄⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄
⠀⠀⠀⢀⣴⣿⣿⡿⠟⠋⠉⠉⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⡀
⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⣿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣼⣿⡟⢀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⡇
⠀⣿⣿⡇⣸⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡿⠀⣿⣿⣷
⠀⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⡇⠀⣿⣿⣿
⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠇⢸⣿⣿⣿
⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⣿⡇
⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣾⠉⣿⣿⣿⡀
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⠘⣿⣿⣧
⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⡇⠀⠀⢹⣿⣿⡄
⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠈⠁⠀⠀⠀⣿⣿⣷
⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠻⣿⣿⣷⣶⣦⣤⣤⣾⣿⣿⣦⣖⡲⠶⠶⠖⠛⣡⣿⣿⣦⣀⣀⣀⣀⣀⣠⣤⣴⣿⡿⠿⣿⣿⣿⣭⣉⣉⣁⣀⣀⣠⣤⣾⠟⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣿⣿⣛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⣿⣿⡇⠀⡟⠁⠈⠉⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣼⠃⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⣄⣀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣤⠶⣞⣷⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣿⣧⡀⠀⢀⡆⠀⠀⠀⢸⠇⠀⠀⠀⠀⠐⣋⣥⣶⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣾⣷⣀⠀⠀⠎⠀⢀⣠⣴⣶⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠶⠤⠤⠤⠤⡴⣶⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣤⣤⢤⡄⣤⣥⣾⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣮⣭⣵⣿⣭⣍⣩⠼⣯⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⠉⠀⠐⠃⠉⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠣⠄⠁⠀⣤⣀⠀⠈⠐⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⠁⠀⠈⠉⠀⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠟⠛⢳⡖⢂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡔⠀⠀⠀⣸⢿⢈⡽⠓⠶⣤⡴⠆⢀⣐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠷⣴⣉⡠⠈⠸⠊⠁⢀⠔⠁⠀⣀⣽⣯⣽⡷⣷⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣤⣉⣁⠓⢤⣰⣶⠃⠀⠀⠚⠿⣿⡿⣉⣃⡈⠑⡀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠿⠍⠉⣙⠁⠰⣶⣿⢰⠀⠛⠁⣀⠘⢿⣿⣭⣿⣿⡟⠛⣤⡀⠜⡿⣾⣇⠀⠀⢀
⠀⠀⠀⠀⢠⣶⣾⣿⣯⡖⠶⠓⠒⢒⣼⠿⢿⣥⣠⣮⢹⣶⣆⠀⣩⡗⠐⠀⣸⣿⡿⣷⡿⢅⡥⠂⣠⢞⣿⡆
⠀⠀⠀⠀⠈⢲⣭⣭⣭⣭⣭⣭⣥⣤⣴⡖⠁⠀⠉⠻⡞⢿⡙⣧⠍⠉⠐⢀⣈⣽⠛⣡⠛⠿⣧⣽⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⡛⡛⠩⠍⠙⠀⠀⠀⠀⠀⠘⠂⢛⢿⣄⡰⢶⣆⣍⡠⠊⠁⣡⢞⣽⢿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠰⠛⠠⣼⠀⡘⠑⠛⠉⠐⡛⠛⢹⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⢀⡄⡙⠒⠇⣀⣰⡛⠋⠁⣰⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣀⡠⢾⠿⣋⡄⣶⣾⣿⠧⣼⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡔⠛⠛⢡⡾⠿⠿⠚⣿⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠏⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣬⣍⣈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⠟⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠏⠀⠀⢠⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠸⠋⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠛⠀⠀⠛⠀⢀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠒⠶⣾⣧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣷⣾⣿⣿⣾⣭⣍⠛⣦⠰⣧⣤⣼⠇⢾⣁⣀⣴⣾⣿⣿⣿⣿⣿⣷⣄⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⡄⢀⡞⣽⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣀⣿⣄⣀⣀⣈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡟⣧⠀⢿⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡿⠀⡾⠀⣿⣿⣿⣿⣿⡟⣉⣤⠶⣛⣫⣭⣭⣿⣿⣿⣿⣿⣷⣶⣿⡟⠻⣿⣿⣿⡇⢸⠄⢸⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇⠀⢿⣿⡿⢋⡽⠛⣩⣶⣿⠿⠛⠛⢉⣉⠉⠉⠛⠻⠿⣿⣿⣿⣷⣄⠉⠛⠧⡿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠻⣤⠞⠁⣰⠋⣠⣾⡿⢋⡅⠀⠀⠀⢸⣿⠀⠀⠀⠀⠖⠈⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣾⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣾⡿⢡⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠴⠶⠀⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢿⣸⣿⡄⠛⠃⠀⠀⠀⠀⠀⠀⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢗⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⡀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡾⢸⣿⠁⢠⡏⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⣇⠀⠹⣿⣿⣧⠀⡤⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢡⣿⠏⢀⡾⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣦⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⠞⣱⣿⠋⢠⠞⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢳⡀⠈⢻⣿⣿⣷⣤⣘⠃⠀⠀⠀⣿⠄⠀⠀⣀⣤⠞⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢻⣿⣿⣿⣿⣶⣶⣶⣶⠶⣖⣛⣭⣴⡿⢿⣯⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠋⠛⠻⠿⢿⣿⣿⠿⠿⠟⠛⠉⠀⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋

⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⡿⠻⣿⠛⡿⢿⠿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠋⠉⠉⠉⣉⠉⠉⠛⠲⡄⠀⢠⠖⠒⠒⠒⠒⠳⠆⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠓⠦⢤⣸⡉⠉⠻⡄⠀⣇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⢄⡀⠀⠈⡳⠦⣎⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠖⠚⠁⠰⡙⣮⡁⠙⠒⠲⡶⠋⠀⢸⡁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡴⠿⣆⠙⠓⠒⣺⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠤⠤⠴⠶⠓⠻⣆⠈⠙⣋⠟⠀⠀⠀⠀⠀⠑⠦⢤⣄⣀⣀⣀⣀⣀⡠⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⢠⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠓






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⠀⠀⣤⡴⠶⠔⠿⠃⡀⢠⢠⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⡀⠀⢠⡄⠀⢦⣠⣆⠀⠀⠰⠁⠀⠀⠶⠋⢁⡀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠸⠟⡃⠄⢰⣶⠿⢈⣉⣭⣤⣤⣦⣴⣤⣿⣧⣀⡺⠻⣦⣤⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡈⠁⢀⣠⣴⣾⠛⠛⣻⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⣦⣄⡀⢠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠶⠀⠈⣁⣿⣿⣿⣿⣧⣄⡨⣽⣿⣿⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⣠⡦⢀⣶⣿⣿⣿⣿⣿⣹⣿⡇⠋⠈⠛⠛⠋⠙⠛⠻⣿⣿⣼⣿⣿⣿⣿⣿⣷⣠⣬⠁⠀⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⢀⣾⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿⣿⣿⣿⣿⣿⣿⡄⢘⡁⠀⠀⢾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠘⠀⠀⠺⢦⣾⣿⣿⣿⣿⣿⣿⣿⢸⣟⠠⣠⣤⣤⣤⣤⣤⣤⣤⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣞⣁⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠙⢿⣿⣿⣿⣿⡿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡻⠇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⡄⠀⠙⢿⠿⠉⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡎⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡹⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣙⣿⣿⠀⠀⠈⠀⠀⢠⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢠⠆⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣷⠀⠀⠀⠠⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣟⣈⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣞⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⡈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⢶⠄⠘⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⢀⣴⣦⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⢋⡄⣿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠐⢤⡄⠈⢻⣿⣿⣿⣿⣿⢿⣿⣧⣀⣴⣿⣿⡿⢿⣦⣠⣿⣿⢿⣿⣿⣿⣿⣿⡿⠋⢘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡄⠙⠿⣿⣿⣿⣾⠟⠿⢧⣶⣿⣿⣷⠒⠿⠿⢿⣿⣾⣿⣿⣿⡿⠋⣄⡀⢊⡙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠟⢴⣌⣻⢿⣿⣤⣈⣿⣿⣿⣿⣿⣭⣥⣤⣿⣿⣿⡿⠟⠉⠠⣶⡈⡁⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢨⡿⠻⢂⣤⠉⡙⢻⢻⠿⠿⡿⡿⠟⠛⣛⠉⢡⡄⢀⠛⠀⠂⢀⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⢰⣶⡄⠻⠆⠛⢃⣈⡁⠀⠀⣿⣿⠶⣿⠁⠈⠁⣿⠁⠛⠀⠙⠋
⠀⠀⠀⠀⠀⠐⠀⢱⡜⢂⣀⣀⣠⣄⠱⣆⠀⣄⠀⣰⠃⠀⡙⠁⠾⠂⠠⠚⠛⠋⢰⣿⠀⠁⢴⡷⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⢀⣡⣼⣿⣿⣿⡏⣩⣦⣦⣶⣿⣿⡟⠀⠢⠉⠀⠀⠀⠀⠀⡀⠀⠀⠁⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⣤⣀⡀⠀⢀⠀⢀⣼⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢰⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⣸⢳⡖⠀⠀⠉⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣀⡤⠚⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⠉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡀⠓⠋⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠒⣼⠶⠴⠚⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⡿⠇⠀⠀⠱⣈⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⣀⣠⣴⣧⠀⠀⠈⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠐⠤⣄⢶⡾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢹⣛⣛⣯⡅⠀⢢⠁⣠⠄
⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⢻⣋⠙⠻⠿⢿⡄⠂⠈⠚⠁⠀⠀⡀
⠀⠀⠀⠤⠤⠂⠀⠀⠀⡀⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠞⣿⢽⣯⣷⡄⠀⠀⢉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⠁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⣇⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⢀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢇⠀⠀⠀⠀⣿⡀⠀⢺⠀⠀⡄⠀⠀⢀⠞⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠈⢷⣄⠀⠀⠀⠀⣿⢷⡀⠘⠀⢰⣧⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢸⡎⠳⢦⣀⣠⠇⠈⢳⣄⣠⠏⢹⡄⠀⢀⣤⠞⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠙⢀⡀⠀⣸⠇⣠⢄⣈⣉⡠⠲⢄⡈⢁⣠⡀⠙⠛⠋⠀⣸⠃⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣁⣈⡭⠟⠋⠉⠉⠙⢢⠥⠤⠤⣀⣉⣉⡤⠬⠷⣾⠛⠉⠉⠑⠒⠦⣄⣀⡈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⢀⡄⠀⠀⠀⢸⠛⠀⠀⠈⢿⠋⠀⠀⠘⢷⠀⠀⠀⠐⣄⠀⠀⠀⠉⠳⣎
⠤⣄⣀⢠⣄⣀⣀⡰⠃⠀⠀⠀⢠⡀⣸⠀⠀⠀⠀⢸⠀⠀⠀⢀⣾⣄⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⣠⠀⠀⠀⠈⢣⣀⡀⠀⠀⢐⣒
⠀⠀⠉⠉⠛⠉⠹⠃⠀⠀⠀⠀⠀⠙⣟⡆⠀⠀⠀⢸⣀⣀⡴⠻⣤⡜⠳⣄⣀⣼⠀⠀⠀⠀⣎⡏⠁⠀⠀⠀⠀⠀⠋⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠲⠶⠒⠋⠉⠁⠀⠀⣿⡂⠀⠀⠉⠉⠓⠶⠶⠚⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⢸⣀⢀⠀⠀⠀⢀⣀⣀⡤⠞⣷⠛⢦⣄⣀⡀⠀⠀⠀⢠⢀⣸⠀⠀⠀⠀⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡏⠉⠉⠛⠋⠉⠉⠉⠁⠀⢀⡿⣆⠀⠀⠉⠉⠉⠉⠛⠋⠉⠙⡗
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢑⡦⣤⣀⣀⣀⣤⣤⡤⠖⣯⠀⢨⡗⠦⣤⣤⣄⣀⣀⣤⡤⡞⠁⠀⠀⠀⠀⡄
⠒⠚⠛⠛⠋⣉⠉⢉⠳⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡴⠋⠛⠛⠿⠍⠙⠛
⠀⠀⠀⠈⠋⠀⡀⠁⠀⠈⠕⠒⠦⡤⠽⠶⣦⣤⠤⣤⣴⣞⡉⠙⢉⣠⣌⡙⠶⡤⠤⣤⠤⠶⠚⣥⠀⠐⠚⠓⠠⠄⡠⠂⠀⠢
⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⢁⠀⡘⠀⢸⡄⢀⣠⣄⠈⠶⠋⣠⣄⠈⠚⠀⡞⠉⠓⠦⣄⣸⡀⠀⠀⢀⡀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠐⠅⠀⢸⣷⠋⠁⠈⢧⠀⣸⠃⠈⠻⣆⠀⡇⠀⠀⠀⢈⠙⠇⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠁⡠⠸⠇⠘⣧⡏⠀⠀⠀⠈⠳⣇⠀⠀⠀⠈⢧⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠇⠀⠀⠀⢹⠃⠀⠀⠘⡄⠀⠉⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠤⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣑⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣤⣄⣂⣀⣀⣀
⣿⣿⣉⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠀⠈⠉⠉⠛⠒⠲⠤⠤⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠉⠲⠤⣄⣀⠀⠀⠀⣠⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢌⡃⠀⡀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⠀⢧⡉⠒⢍⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⠒⢬⡲⢤⣭⠢⡍⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡐⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡛⡆⡈⠑⠯⣛⠾⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡈⠂⠄⡀⠀⠀⠀⠀⢉⢁⢢⢃⢠⣆⢨⠙⠢⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣁⠃⡀⠀⠀⠀⠸⡄⢸⡈⡀⡈⡄⡔⡈⡓⢤⡀⢤⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⠭⠳⢤⣙⠢⠀⠆⡇⠀⠇⠁⠁⢃⢠⢡⢱⢂⢍⠲⣌⠧⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠤⠬⠭⠭⠓⢦⣀⠃⠀⠸⠀⣸⠸⡘⠈⡈⡘⠘⡼⢨⠑⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣀⡀⠀⠨⠭⠄⣰⠟⠢⣅⠃⠅⡆⠇⠃⢡⠃⢃⠣⠇⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠐⠒⠒⣂⡀⣽⠋⠀⠀⠀⠙⠾⣵⢰⠸⠸⠐⠸⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠠⠤⠤⠤⢠⡖⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣇⣆⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠤⠉⠀⢠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠄⠉⠉⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢒⡒⢪⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⠀⠀⠀⣀⣒⡒⠒⢒⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠐⠒⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠁⠀⠀⠀⠤⠀⠀⠩⣭⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠂⠀⠀⠀⣀⡁⢐⡀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⠈⠀⠀⠀⢀⠀⠲⠂⠐⢂⡾⠁
⠀⠀⠀⠀⠀⠀⡰⠁⠔⠀⠀⠀⠀⠠⠤⠤⠤⠤⢤⡟⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢈⣀⣒⣒⡂⣀⡞
⠀⠀⠀⠀⠀⠈⢦⡀⠀⢀⡐⠒⠒⠀⠀⠐⣐⠞
⠀⠀⠀⠀⠀⠀⠀⠑⢶⡀⠠⠤⠍⠥⠀⣒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢭⣭⣭⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⡠⢐⡡⢉⡤⣊⠕⡣⠔⡠⢒⡠⠊⡡⠒⡡⠐⡠⠔⡡⢖⡠⢖⡠⢂⡠⢂⡠⠄⡠⢀⡠⢀⡄⠀⠀⢀
⠀⠀⠀⠀⠈⠐⠀⠈⠔⢩⠔⣡⢔⡡⢊⠕⢋⠔⡩⠔⣁⠔⢉⠔⢋⠔⢊⠔⣋⠔⣩⠔⣉⠔⢉⠔⢉⠔⢊⠔⣉⢔⡡⣪⢞⡵⢋⠔⡡⢊⠔⡡⢀⢔⡠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⠈⠀⠘⠁⠈⠁⠈⠁⠀⠁⠈⠁⠈⠁⠘⠁⠈⠁⠘⠁⠘⠁⠚⠁⠉⠘⠁⠉⠀⠁⠈⠀⠁⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣀⣀⣠⣤⣤⠤⠤⠴⠶⠶⠦⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⣀⡀⣠⣤⠴⠶⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆⠀⠀⠀⠀⠀⡄⠀⠀⣠⠀⠈⢹⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⣀⣠⣤⠄
⠀⠀⠀⠀⠀⢴⡾⠿⠛⠛⠳⡖⠚⣏⠸⠋⠀⢠⠃⢠⢀⢸⠇⠀⠀⡻⠛⠂⠀⠀⠀⠀⠀⣾⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣌⠲⣶⣖⣁⣠⠃⡸⢸⠀⠀⢈⠃⠀⠀⠀⣠⣄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠱⠲⠶⡞⠓⠛⠦⡔⢁⣸⣶⡶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠴⠇⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠣⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠉⠉⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⡆⠀⠀⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣧⡀⠀⠀⠀⠀⠉⠻⢷⣤⠀⣀⠔⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⣾⡃
⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣧⡀⠀⠀⠀⠀⠀⠀⢙⠶⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠊
⣾⠃⠀⠀⠱⡄⠀⢀⣀⡀⠀⠀⠀⠸⡆⠙⠿⡄⠀⠀⢀⡤⠊⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠃⠀⠀⠀⠈
⢷⡀⠂⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⢦⣀⣀⣤⣄⣤⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠂
⠈⢷⡀⢠⡀⠀⣱⡀⠀⠀⠀⠀⠀⠀⡖⣤⠀⠀⠀⢀⣠⣀⠀⠀⢀⡀⠀⠀⠀⢘⡜⠛⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠋⠀⠀⠀⠀⠀⢠
⠀⠈⢷⣴⣿⠉⣿⣿⡄⠀⠀⠀⠀⣸⡿⣾⢀⡴⠢⠎⠝⢭⢗⣶⣴⢾⣥⣶⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠟⢋⣩⡄⠀⠀⠀⠀⣀⣤⠟
⠀⠀⠘⣿⣿⣧⠈⢿⣿⡄⠠⠤⠴⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠛⠻⠻⣛⣤⠀⠀⠀⠀⠀⠀⠀⣏⢉⣁⣤⣾⣿⣿⣧⣤⡴⠖⠋⠉
⠀⠀⠀⠘⣿⣾⣧⠘⣿⣿⠀⠀⠈⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢠⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠘⢿⣿⣿⡁⠋⢠⠆⠄⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢠⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠑⣼⣿⣷⣄⠀⠀⠐⠒⠒⠒⠛⠋⠁⠀⠀⢀⢴⣿⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢄⡈⠛⢶⣤⣿⡏⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠻⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢷⣤⣤⣀⣀⡀⠠⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢄⠉⠻⣿⣷⣆⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⡄⠀⠈⠛⢿⣿⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰
⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠸⠷⢤⣀⣠⢀⡀⣠⠔⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢧⣽⣿⣷⣴⣼⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣶⣿⠆⣿⣿⣿⣿⡏⠉⠁⠉⠁⠈⠀⠉⠉⠉⠁⠉⠁⠉⢹⣷⣶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠿⢿⢧⣿⣟⣛⡿⣧⣤⡤⠤⠤⠤⠤⠤⠴⠤⣤⣄⣠⣤⣼⣿⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡇⢸⠷⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠿⠙⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⡈⠋⠀⠀⠀⠀⠀⢶⣾⠡⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢄⠀⠀⠀⠀⢀⡾⠁⠁⠀⢀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣾⣿⠀⠀⠀⠀⠀⢄⠀⢀⡮⠊⠀⠀⠀⠈⠷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⢿⣷⠀⠀⠀⠀⡀⠈⢸⠀⠑⠀⠀⠀⠀⠀⡾⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠈⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⡀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠣⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠀⠈⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⡃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠑⢾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡇⣸⣦⢤⣤⡤⠀⠀⠀⠀⠀⠠⠧⣴⣃⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣾⣾⡞⣿⣯⣽⣷⡟⠛⠳⠒⠒⠒⠒⠲⠖⠒⠛⠋⠑⠛⢻⣷⣶⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠿⣿⢆⣿⣿⣿⣿⣇⡀⠀⠀⡀⢀⠀⠀⢀⡀⣀⣀⣀⣀⣸⣿⠿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣽⣿⡁
⠀⠘⠛⠛⠛⠉⠉⠉⠉⠁⣀⡄⠀⠀⠈⠉⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣇⠀⠀⠀⠀⠀⣠⠀⠀⠀⠙⠛⢳⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣄⣶⣶⣾⣯⡴⠄⢰⡟⢠⣌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⢿⠿⠛⠋⠉⠉⠙⣿⣿⣿⣿⣿⣇⣠⣶⡿⣀⣾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡇⠀⠀⠀⠈⢿⣿⡿⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⠤⠤⠄
⠀⢠⣤⣤⡤⠴⠶⠶⠶⠒⠚⠛⠛⠛⠒⠶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢢⡄⣀⡀⢀⣤⣤⠶⠖⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠘⢹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⣴⣾⡿⠿⠷⣦⣤⠤⢶⠖⣲⠗⠊⠀⢸⠃⢠⠀⢸⡿⠀⠀⠐⢷⣦⡦⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠈⠳⣄⠈⢇⣀⡀⢀⡴⠁⢀⠏⢰⢸⡇⠀⠈⠰⡏⠄⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⣝⠿⣟⠦⠴⠋⢠⡟⣸⡇⠀⣠⠔⢁⡀⠀⠀⣰⣿⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣘⠉⠙⢻⡏⠉⠁⠙⠰⠃⢠⣾⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠾⠃⠀⠀⠀⠀⠀⠀⠛⠉



⣿⣟⢽⣟⠻⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠙⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠋⠀⠀⠈⠉⠙⠢⣄⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡾⠁
⠀⢀⡤⠶⠶⠶⠦⢤⣄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⢰⡏⠀⢠⡀⠀⢄⠀⠈⠙⠲⣼⡟⠛⠒⠒⠚⠛⠛⠉⠉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⣿⢇⠀⠀⠙⢢⡀⠱⣄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⢿⠈⢆⠀⠀⠀⠈⠢⡈⠳⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⣴⠃
⠘⢧⠈⠳⡄⠐⠠⠀⠈⠳⣌⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⢀⡼⠃
⠀⠈⠳⣄⠈⠲⢄⣀⠀⠀⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠈⠙⠦⣄⣈⡉⠛⢛⣋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠉⠁⠀⠀⣀⣠⣤⠤⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢀⣤⠞⠋⣉⠀⠀⢀⡠⠖⠋⣀⠽⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⢀⣴⠋⠀⠀⠀⠀⡠⠖⠉⣀⠴⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⢤⣤⣄⣀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠔⠁⢀⡤⠚⠁⠠⠂⠀⣠⢺
⠀⠀⠀⠀⣠⡞⠛⠳⢤⣀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢴⣎⠁⢀⡴⠋⠀⢀⣀⡤⠔⠋⣠⡞
⠀⠀⠀⡾⠁⠉⠓⠦⣄⡈⠙⠲⢤⣀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡈⠉⢉⣉⣉⣉⣀⣤⠴⠞⠉
⠀⠀⠀⣷⣄⠀⠀⠀⠀⠉⠓⠦⣄⡈⠙⠲⢤⣀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⢻⡌⠑⠢⢄⣀⠀⠀⠀⠀⠉⠓⠦⣄⡈⠙⣲⠞⢻⡆
⠀⠀⠀⠀⠻⣄⠀⠀⠈⠉⠒⠒⠲⠶⠶⠖⠚⠋⠉⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣓⣶⣶⣦⣶⣶⣖⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠿⠿⠿⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠿⠛⠉⠀⠀⠀⠀⣿⢸⡀⠀⠀⠈⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⢦⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⡴⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡞⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠤⠴⠄⠀⠀⢀⣀⣤⣤⣤⣤⣴⡛⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡼⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⡜⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠋⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠁⣀⡴⣫⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⣀⠀⠀⠘⠃⠀⢀⣀⣠⣴⣾⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡄⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠃⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢢⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠸⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⢋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣼⠀⠀⢀⠄⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢱⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡄⠐⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡐⠛⢦⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠑⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠙⡆⠈⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠏⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⡸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠚⠋⠉⠉⠑⠒⠲⠦⠤⠤⣄⣀⣈⠉⠉⣛⣻⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣾⣛⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⠿⢻⠉⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣟⣉⣀⣀⣀⣀⠀⠀⠉⠉⠉⠙⠓⠒⠢⠤⢤⣤⣤⠶⠛⠉⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡟⠉⠁⢹⠁⠀⠀⠀⠈⠉⠉⠉⠉⢙⣻⣷⣶⣶⣶⣦⣤⣶⣟⡉⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⣤⣾⣯⣥⣤⣿⣽⣶⣿⣿⠀⠈⠹⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠀⢀⣠⣴⣞⣋⣥⣸⣿⣷⣶⣖⣺⣿⣿⠿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⣠⠶⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡿⠟⠋⠁⣾⠭⠤⣀⣈⣹⣧⣴⠛⠛⠛⠛⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⣦⣤⣄⣀⣉⣛⣒⠶⠖⠛⠙⠷⢭⣭⣭⡭⠾⣿⠀⠀⠀⣿⠀⣀⡴⠞⠉⠀⠀⠀⠀⢀⣠⠶⠛⢉⣉⣛⢦⣄
⠀⠀⠀⠀⠀⠀⠸⣇⣠⠶⠛⠁⠻⣿⣿⡻⠛⣿⡟⣿⠛⠲⠶⠶⣤⡴⠞⣿⠀⠀⠀⣿⠞⠋⠀⠀⠀⠀⣠⡴⠞⠋⢁⣤⠶⢿⣿⣿⡇⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⠤⣤⣤⣀⣈⣉⠉⠉⠀⠈⠛⠛⠛⢛⣫⠴⠛⣿⠀⠀⢀⡿⠀⠀⢀⣠⠶⠛⠁⢠⡞⢛⣻⡿⠿⠟⢉⣡⣶⣒⣲⡮⠙⣦
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠲⠶⠚⠋⠛⠒⣲⡿⡴⠶⠛⢁⣠⠶⠋⠁⣠⡴⠶⣾⡿⠿⠛⢁⣠⣾⣯⣝⣿⠟⠋⣡⡶⠋
⠀⠀⠀⢰⠛⠛⠛⠓⠶⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⢀⣠⠶⣋⣡⣤⣀⣸⡧⠴⣖⣿⣁⣀⣰⣯⣥⣤⣿⠏⢁⣴⠞⠉
⠀⠀⠀⠸⠧⢤⣤⣀⣀⡀⠀⠀⠈⠉⠛⠓⠶⣤⣀⠀⠀⠀⣠⠞⠉⠀⢀⡴⠛⠁⣾⣋⣀⣀⣭⣿⠉⠉⣹⣟⠉⢉⣹⡏⠉⢉⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠶⣤⣤⣀⣀⠈⢷⣠⡾⠋⠀⠀⠀⠀⠻⣦⡀⠛⠶⠶⢶⣿⠷⠶⠶⣾⠿⠿⠿⠟⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣶⠖⠶⢦⣌⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⢿⡳⠤⠶⣚⡿⠀⢀⣤⠞⠉
⠀⠂⠀⠀⠀⠀⠀⠀⣾⠧⣄⣀⣏⣇⡤⠔⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠉⠛⠋⠉⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⣤⠶⠞⠋⠀⣠⡴⢶⣶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠥⠤⠧⠿⠴⢒⣩⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡄
⠀⢠⣤⣤⡶⠶⠶⠶⠖⠛⠛⠛⠳⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠉⠓⣶⢤⣄⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣧⣠⣤⣦⣴⣏⣤⠀⣴⠀⡘⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⢸⡿⠿⠛⠉⠙⢻⣿⣿⣿⣿⣏⣠⣶⡏⣰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠛⠛⠻⢿⣿⣿⣿⣿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠀⠀⠀⠘⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⢀⣀⣀⣀⣀⣤⣤⡤⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠒⠚⠋⠉⠉⠉⠉⠁
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀⠀⢀⣀⣤⡤⠴⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠁⠘⢻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⣴⣾⠿⠿⠷⣦⠤⠶⡆⢸⠖⠁⢀⠎⢀⠆⢸⡏⠀⡀⠸⡷⠶⠀⠀⠀⠀⠀⢀⣼⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠳⣄⠓⢤⣄⡠⠊⢀⡞⢰⢸⡇⠀⠀⠺⠐⠀⠀⠀⣀⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡙⢯⣅⣋⣠⣯⠼⣇⢀⠖⠀⣤⣄⣠⡾⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⣀⣷⠀⠀⠀⠙⡀⢺⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⡠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⣶⠆⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠈⣿⡇⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠛⠁⣀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡠⢀⠐⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠟⠂⠀⠰⠟⠶⠲⠾⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠠⡀⢄
⠀⠀⠀⠀⠀⠜⡠⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠣
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠠
⠀⠀⠀⠄⡐⠀⠀⢀⡀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢂
⠀⠀⠀⠐⠀⠀⠀⢸⡇⠀⣠⣟⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠘⣿⠀⠀⠀⠂⠀⡀
⠀⡀⠀⠁⠀⠀⠀⢸⡇⠀⢸⡿⢿⣿⣎⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠞⠁
⢀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠈⠿⠄⠙⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢦⣤⣄⡀⠀⠀⠀⠀⢸⣿
⡇⠀⠀⠀⢠⡄⠐⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣀⠀⢈⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⡀
⡇⠀⠀⠀⣿⡀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⣷⣦⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠇
⡇⠀⠀⠀⢈⡝⠂⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠻⣿⣿⠟⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⣶
⠇⠀⠀⠀⠈⠃⠀⠚⠁⠀⠀⠀⠀⠀⠀⠠⠄⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠤⠼⠋
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠈⠀⠀⠀⠀⠀⠀⣠⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠃⠀⡀⠀⠀⠀⢿⣦⣀⡘⠀⠀⠁⠂⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠠⠀⠀⢰⠃⠀⠈⢻⡆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⣿⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠃⠀⠈⠓⠀⠀⠛⠁⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⡈
⠀⠀⠀⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰
⠀⠀⠀⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⣼⡟⣴⠶⠶⠶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡔
⠀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⠀⢸⣿⠃⢀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⢦⣄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠢⡀⠀⢼⡿⠀⢈⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣰⣏⡀⢈⡉⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⢀⣽⠀⠀⠀⠀⠀⠐⢁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⠀⠀⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⠛⠐⠋⠁⠀⠀⡠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢂⡁⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣪⠭⠭⠭⢑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡸⢇⠸⢄⣀⣀⡠⠜⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠀⠒⠒⠈⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠒⠒⠒⠒⠊⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠒⢬⡑⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠴⢒⢤⠀⠱⡘
⠀⠀⠀⠀⠀⠀⡗⢦⡀⠀⠀⠀⠀⠀⢀⣀⠤⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣠⣾⡵⢻⠇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠂⢬⡉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⠀⡠⠚⣡⣴⡿⠟⣋⠴⣁⣀⣠⠗
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢉⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠉⠲⡝⢦⣾⠟⢋⡤⠊⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣗⠠⣀⠇⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠧⠚⠉⠉⠉⠑⢄⠘⡞⣧⠔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⢀⣀⠴⣪⠃⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢍⣉⣉⣉⣉⡡⠤⠊⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠈⠉⠢⡀⠀⠀⢀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠐⠒⢄⠀⠀⢱⠀⠀⣨⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡍⠢⣀⠜⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠖⠛⠊⠁⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⢀⡠⣞⠵⠊
⠀⠀⠀⠀⡠⢖⡽⠊
⠀⣀⢔⡫⠖⠁
⣾⠕⠋

⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠲⠶⣤⣀
⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠤⠄⡀⠀⠀⡀⣀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦⣄⠀⠸⣿⣿⣿⣄⡀
⠀⣰⠏⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠂⠀⠈⢻⣷⣄⠉⠿⣿⣿⣿⣆
⢠⡏⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⣿⣿⣿⡀
⣾⠀⠠⢄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠈⠞⢑⠀⠸⡇⠙⠿⠟⣿⣿⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣲⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣿⣿⣿⡀
⣿⠀⠀⠐⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⠀⠀⢀⠠⠄⠀⢠⡇⠀⠀⣠⣾⣿⣿⣿⡇
⢸⡆⠀⠓⠒⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣸⠁⣰⣿⣿⣿⠿⣿⣿⣷
⠀⢻⡄⠀⠀⠀⠠⣄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⣰⠇⠸⣿⣿⠋⠀⠀⠹⣿⣿⣆
⠀⠀⠹⣄⠀⠘⠓⠲⠀⠀⣀⠀⠀⠀⢀⡀⡀⠀⠀⠁⠈⠡⢀⡼⠃⠀⠀⢻⣿⣇⠀⠀⠀⠙⢿⣿⣷⣦⡀
⠀⠀⠀⠈⠳⣤⡀⠀⠀⠨⠬⠑⠀⠀⠐⠪⠍⠀⠀⠀⣀⡴⠛⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⣀⡀⠀⢀⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⢀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢉⣿⠿
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣴⣾⠟⠋⠉⠉⠙⢿⣦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⢸⡏⠀⡗⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠹⣇
⠀⠀⠀⠀⣾⡧⠀⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⣼⡿⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣼
⠀⢀⣾⠟⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⡟
⠀⢸⣿⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⡾⠁
⠀⠸⣿⣦⡀⠀⠀⠀⠈⠻⠶⠶⠶⠶⣶⣾⣿⣥⣀⣀⣀⣀⣠⣼⣿⣄⣀⣀⣠⣤⣿⠀⠀⠀⣠⡾⠁
⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠿⠿⠿⠟⠛⠋⠀⠉⠙⠛⠋⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⢠⠀⠀⠠⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣤⣼⣷⣆⡀⠰⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠿⠿⠿⠿⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣤⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠈⠉⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⣾⡟⠃⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢸⣿⡿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⣿⡟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣴⣿⠟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⣾⣿⠋⠀⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⡂⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⣾⠃
⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣤⣤⣤⣤⣶⣿⣿⣭⣀⠀⠀⠀⠀⠐⢒⣈⣽⣿⣅⡀⠀⠀⠀⣀⣒⣾⠧⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠻⠿⢿⡿⠿⠿⠿⢿⣷⣶⣶⣶⡾⠟⠁
⠀⠀⠀⠀⠹⣿⣿⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣾⠀⠀⠀⠀⠀⢠⡎⡀⠀⠐⢄⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⣀⣀⣼⣷⣼⡄⠀⠀⢂⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠛⠛⠛⠶⣦⣬⣶⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣲⡖⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⣿⣂⠘⠁⡰⠷⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⠟⠊⠀⠀⠀⠀⠀⠀⠻⣐⠒⢐⣗⠠⠿⠅⢰⡇⠀⠀⠀⠀⠀⠀⡔⠉⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣎⣡⣒⣁⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠅⠒⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠥⢬⠁⠀⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠈⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⣀⠀⢀⠀⠀⠀⠀⣀⠦⢒⣂⣠⣤⣤⣀⣒⠠⢇⡀⠀⠀⠀⠀⠀⠀⡯⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⠖⠋⠉⠀⠀⢰⠀⠀⠈⠉⠓⢮⡑⢄⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣡⠞⠁⠀⠙⠀⠀⠀⠘⠀⠀⠀⠘⠁⠀⠈⢢⡱⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠐⠂⡜⣴⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⠄⢱⡜⡄⠒⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⢰⠃⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢳⢠⠀⠀⠀⠀⠀⢀⠔⡣⠎⣴⣉⠙⡦⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢸⠀⣀⡀⠀⠀⠀⠀⠈⠓⢤⠖⠁⠀⠀⠀⠀⠀⣀⡀⢸⠌⠀⠀⠀⠀⠀⡒⢰⠥⣰⡀⢸⠉⠓⢲
⠀⠀⠀⣸⣷⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠦⢼⢀⡇⢀⠋⢐⠗⡼
⠀⠀⢠⣉⣀⣀⣶⣶⣶⣶⣎⣁⣉⡆⠀⠀⠀⡈⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡎⡈⠀⠀⠀⠀⠀⠈⠲⣤⣁⣍⡱⣓⠔⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠒⠉⠑⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡐⠉⠑⠂⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⡳⣄⠀⠖⠀⠀⠀⢰⠀⠀⠀⠐⠆⢀⡴⡫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠢⢝⠲⠤⣤⣀⣈⣀⣀⡤⠴⣚⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠓⡽⡂⠀⠀⠀⠀⢀⠋⠁⠒⠂⠀⠀⠒⠂⠉⢃⠀⠀⠀⠀⠀⠀⠀⡠⡺⡉⢱⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣎⠵⣳⣚⠳⡲⠽⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠅⠸⣗⠀⠇⢣⣬⠫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣄⠀⡈⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⣖⠒⢒⣶⣒⠀⠀⠀⠀⠀⠀⠀⢀⢖⡭⠚⠂⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠣⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡆⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠃⠐⣶⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠶⠶⠴⠭⠯⠯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢬⣿⡛⠳⢿⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠛⠀⠈⠁⠀⠀⠀⠀⠻⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⣀⠤⠔⠒⠒⠀⠐⠒⠒⠠⢄⣀⠀⠀⠀⣴⡏⠤⠄⠒⠂⠀⠂⠤⠄⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⢀⣾⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠘⢁⣤⠴⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠙⠶⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣀⠈⠳⡀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⣿⣿⣄⡄⢳⠀⠀⠀⠀⢰⡇⢰⣾⣿⣇⣀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢻⣄⡀
⠀⠀⣼⠁⢸⡇⠀⠀⠘⠉⠉⠛⠻⢤⡀⠀⠀⠻⣿⣿⡿⠃⣸⠀⠀⠀⠀⢸⡇⠹⣿⣿⣿⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣺⠉⣷
⠀⠀⢹⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢄⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠻⣄⣀⣉⣀⣠⣤⠖⠋⠉⠉⠛⠒⠀⠀⠀⣿⢀⣿
⠀⠀⠀⠙⠶⣿⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣄⣰⠟⠉⠱⡄⠀⠀⠉⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠾⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣴⣟⣻⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⣼⠐⢻⣶⣈⢉⢩⡏⢹⡆⢀⣠⡤⠖⢳⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣷⣶⣿⣼⣼⣼⣿⣾⣼⣗⣺⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⣤⠶⠚⠋⣉⣀⠤⠤⠤⠤⠤⢄⣈⡉⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠾⠋⠁⠀⠊⠉⠀⠀⠀⠂⠀⠀⠀⢀⠆⠈⠉⠒⠄⠈⠛⢦⡀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡀⠀⠀⠀⠀⠲⣄⠙⢶⡾⢧⣄⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠋⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠚⠈⢢⡈⠻⣤⠿⠻⣷⣿⡿⣆
⠀⠀⠀⠀⣠⡾⢋⣾⠁⡰⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢹⣆⠀⢹⣿⢿⣿⡄
⠀⠀⣠⠞⠁⠀⣼⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡱⠀⢿⣄⣠⡿⠈⠉⠙⢦⡀
⢀⡾⠃⣴⠛⠛⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣿⠷⢶⣄⠀⠀⠀⠻
⣾⠁⠘⣃⣀⣴⡋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⢹
⠹⢦⣀⢠⡟⠁⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣴⠟⠛⣿⠋⠀⠀⣠⡴
⠀⠀⠉⠛⢻⣤⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣀⣀⣼⠷⠞⠛⠉
⠀⠀⠀⠀⢿⡀⠀⣿⠰⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼⠋⠙⣧
⠀⠀⠀⠀⠈⠛⠛⢿⡀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠠⢄⢠⠃⣰⠿⠦⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠱⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡠⠊⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠑⠢⣄⣀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡤⠒⠁⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣄⣀⡙⠀⠒⠂⠶⠆⠳⠀⠚⢉⣀⣤⣶⠛⠁⠸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠉⢻⡟⠓⠶⠶⠶⠶⠛⠛⠋⠉⠀⣿⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⠳⣄⡀