Ladybird Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⣤⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠛⠃⠀⠈⠁⢠⣿⣿⣟⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⣿⣦⣿⣿⡿⠃⠀⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣟⣿⡿⣿⣏⣷⡆⠀⠀⣀⡀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣽⣿⢿⣟⣾⣿⣿⡿⠁⠀⠀⠛⠃⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣟⣾⣿⡷⠯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢻⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⠙⢆⠀⠀⡠⣶⣶⡧⠄⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢿⣿⠿⠟⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣤⡀⠐
⠀⠀⠀⠀⠀⡰⠋⠡⣶⠀⠺⣿⠆⠀⠿⠈⠑⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠⣴⣶⡟⠟⠀⠀⠀⠙⠁⠀⠀⢀
⠀⠀⠠⠴⠚⠁⣀⠀⠀⢠⣤⠀⣴⡄⠀⠀⢀⠈⠒⠤⠄⠀⠀⠀⣬⣾⠿⡟⢙⡃⡀⠸⠟⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠉⠀⠈⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⡜⠁⠈⠷⡀⠀⠐⢶⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠸⠿⠀⢀⠀⠻⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠘⡆⠀⠀⠙⠢
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⠀⠀⠑⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠓


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⢩⣿⣿⣿⣿⣿⣭⣭⣉⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠬⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠿⠶⠦⣴⡊⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠙⢦⣈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢰⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠛⠙⠛⡿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠈⠐⢦⡎⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⠋⠀⠀⠀⠀⠀⢀⣾⣿⡧⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⢼
⠀⢀⡀⣀⡀⠀⠀⢀⡞⠋⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⡇
⠀⠙⠛⠉⠙⠃⢦⡈⡧⡄⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡸
⠀⠀⠀⠀⠀⠀⠀⠉⣳⡴⠀⠀⠀⠀⠀⢶⡉⠀⠀⢀⠀⠀⠀⢀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡷⢄⠈⢐⠀⠀⢸⡇⠀⠀⠈⠢⠀⡠⢂⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢌⠑⣄⣀⣀⣾⣄⣀⣀⣤⣼⡟⣾⠉⠻⡿⣦⡢⢀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠋⠁⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⡧⠀⠉⢉⡏⠉⠻⣀⠻⡍⠣⣰⣇⠴⣼⠆⢣⠈⢛⡷⣯⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⣶⠟⢛⠋⠧⣿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠄⣾⠇⠀⠀⠈⠉⠛⣧⡷⢛⡼⠃⠀⠀⠰⣯⢵⡒⠈⠉⠭⣉⡉⠉⠉⠉⠙⢦⣀⣉⠴⠊⠀⠀⠀⠀⠑⠄⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⢀⡴⠚⣡⠔⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠄⣀⢽⡳⡄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠱⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣢⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡄⣑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣹⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣧

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⠛⠛⠛⠱⣼⠀⠀⠀⠀⠀⠈⠱⣦⡀⠀⣠⣤⣤⣄⠀⢀⣤⠏⠁⠀⠀⠀⠀⢠⣇⡎⠛⠛⠛⠿⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠟⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⡴⠫⠈⣩⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠱⣄⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣿⣥⣤⣾⠿⠅⠹⠇⠻⠏⣋⠁⡿⣘⣻⣿⣦⠶⣿⣿⣤⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⣶⣾⣧⣦⣿⣴⣷⣀⣴⣿⣶⣿⣿⣿⣳⣿⣷⣬⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⣉⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠪⠉⡉⠉⠉⠉⠉⠉⠛⣛⣿⣿⣟⡛⠛⠉⡉⢩⠁⣤⠀⠀⠢⢦⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⡄⠀⠀⠀⢂⠐⣰⣾⣿⣿⣿⣿⣿⣶⣄⠡⡜⠇⠀⠀⠀⠀⠀⠛⡜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠊⠀⠄⠐⠀⠀⠀⠀⠁⠘⣿⣿⣿⣿⣿⣿⣿⠉⠇⠁⠀⠀⠀⠀⡀⠀⠀⡀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣶⠁⠀⠈⠔⠀⠀⠂⠀⠀⠀⠈⠻⢿⡏⠛⡍⠥⠡⠈⠀⠀⢆⠀⠄⠠⠀⠀⡀⠄⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣯⠀⠀⠈⠎⡀⠀⠀⠀⠀⠀⣀⡙⠾⠁⠤⢱⡚⡆⢣⠀⠀⠈⡄⠠⠀⠂⠀⠀⣠⡎⣿⡆
⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣿⣿⢸⣿⡇⠂⠈⠰⢀⠀⠀⠀⡠⠳⣲⢳⣻⠠⠘⡀⢣⢭⠀⠀⠀⠀⠱⠀⠀⠠⠀⢸⣿⡧⢹⣿⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠋⠉⠉⠙⠿⣦⣸⣿⣧⠜⠟⠁⡢⠈⠃⣌⠠⠀⠠⣻⢧⣟⢾⣿⠀⠠⣹⡌⡂⠂⠈⠀⢀⡀⠠⠆⠀⠄⠄⠛⠃⢸⣿⣇⣶⡿⠋⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⡐⠁⠋⣠⣽⣿⣿⣿⣧⡺⡿⣿⣾⠀⠱⣼⣧⣀⣴⣶⣿⣿⣿⣷⣦⣇⠘⡌⠀⠁⢸⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⡛⢸⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠌⡰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣦⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠣⡈⡆⠁⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁⠍⡙⠛⠿⠟⠻⣿⠟⠠⠷⣿⠸⣌⣟⢼⠋⡟⠛⠋⣩⢩⠉⡔⣆⢩⠐⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠈⠀⠀⠂⡖⡲⠆⠀⠴⣗⡳⢽⢪⠐⢩⣾⡿⡇⢩⠀⢣⠤⠄⢤⠤⡸⡀⠆⠰⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⡄⣄⠀⢀⠁⠄⠂⢠⡄⢨⢐⢨⠰⠀⢺⡇⠀⢁⠀⡀⡰⢦⢱⠐⡀⢀⣱⣘⢂⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠻⣿⣧⣌⠀⡃⠍⢉⡴⢸⠚⢰⢸⢩⣿⢁⠀⠈⣀⠳⢨⣏⡐⣦⣿⣿⣿⣯⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠙⣿⣿⣷⡀⠂⣡⠜⢹⢾⠨⣽⠓⡏⢸⠀⡇⢯⠸⠄⡄⢡⣿⣿⣿⡿⢃⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠈⠻⣋⠡⡄⡁⠈⢹⢘⠀⡇⡀⡇⡘⠄⠹⢨⠙⠆⣡⢨⠝⣣⠞⠁⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⠀⠀⠈⠳⢍⡁⠠⣿⢸⡀⣧⡅⠂⡋⣆⢸⠄⠲⣷⢪⡠⠞⠁⠀⠸⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠒⠿⣼⣃⡘⡇⢁⡁⠥⠘⣁⠤⠚⠉⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠉⠳⣄⠀⠀⠀⠀⡴⠛⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡾⠁⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠂⠀⠀⠀⠀⢸⡄⣸⠃⠀⠀⠀⠀⠰⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣷⣿⣧⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠁⠀⠀⢸⡇⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡴⢋⣤⣀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣠⠤⣄⠉⠲⣄⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⡰⠋⠀⣇⠀⢸⠇⠀⠀⠀⠀⠀⢸⠀⠀⢰⠋⠀⠀⠀⢳⠀⠈⢣⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡾⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣆⠀⠀⣀⠞⠀⠀⠀⢱⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢠⠖⠒⢢⡀⠀⣿⠀⠀⠀⠀⠉⠉⠁⠀⠀⣠⣄⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣠⣤⡀⠀⠸⣄⠀⣸⠃⠀⣿⠀⠀⠀⠀⣀⡀⠀⠀⡞⠀⠀⢹⣿⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠀⢠⠏⠀⠀⠈⡆⠀⠈⠉⠀⠀⠀⣿⠀⠀⠀⡞⠁⠙⡆⠀⠘⠦⠤⠊⡼⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠸⡄⠘⢦⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⡼⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣄⠀⠀⠀⢰⠃⠀⠈⡇⠀⠀⡇⠀⠀⠀⢰⠁⠀⠈⡇⠀⢀⡞⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠈⠢⣀⠀⠈⠳⠤⠔⠁⠀⢸⡇⠀⠀⠀⠈⠳⠤⠞⠁⡠⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠼⠧⠤⠤⠖⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⣀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⢿⣿⠆
⠀⠀⠀⠈⢣⡀⠀⠀⢀⣧⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⢱⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠙⠻⣿⣧
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠃⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢾⣿⠟⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⣤⣶⣿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦
⢸⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠂⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⠛⠃⠀⠀⠀⠀⣠⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢤⣀⣤⣴⣶⣤⣤⣀⡤⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⢠⠖⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒⢦⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣴⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠙⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⡼⠁⠀⣠⣤⣄⠀⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⠀⠀⣴⣶⣦⡀⠀⢻⡀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢰⠃⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⣷⠀⠀⢷⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡿⠀⠀⠈⠻⠟⠋⠀⠀⠀⠀⠈⠛⠿⠛⠋⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠸⡇⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠛⠻⠍
⠀⠀⠀⠀⠚⠩⠏⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢠⣶⣾⣶⣄⠀⢸⠀⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢻⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⢸⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⠏⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣧⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠘⣧⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣾⣦⠀⠀⠀⢰⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⢦⠈⢿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⢠⠏⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠈⢳⡀⠈⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠁⠀⠁⣠⠏⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⣀⣾⣄⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠁
⠀⠀⠀⠀⠀⠀⠘⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠟⠛⠛⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡇⢀⣿⢸⢻⠹⡎⣿⡇⡇⡇⣏⡃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠳⠘⠙⠚⠚⠀⠃⠳⠋⠳⠃⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠀⢀⣐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢾⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⢀⣤⠈⠛⢇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣾⣥⢾⣿⠭⠉⠀⠀⠀⠀⠀⠀⢀⠐⠉⣽⣯⠉⠂⡀
⠀⠀⠀⠀⠀⠀⢠⠿⠿⣄⠿⠿⢣⡴⢿⣿⢷⣀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣼⡿⣿⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⡄⠾⢢⣿⣿⡜⠇⢁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⣾⠷⠒⢛⡇⠸⣿⡟⡄⠀⠀⠀⠀⠀⠀⠓⢲⢾⡡⣾⢿⣿⣿⠏⠂⠀⠀⠀⠀⠀⠀⢿⠤⣿⣿⣟⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠈⢦⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣠⢿⠟⠁⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣶⢶⣆⣠⠞
⠀⠀⠀⠀⢉⣔⢤⣰⡈⣥⠀⣤⠀⠀⠀⢠⡄⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⢩⣯⠉⠁⢦⡀
⠀⠀⠀⠀⠀⠉⠈⢻⡿⢧⣄⣠⣀⢠⣀⣴⣤⠞⠁⠀⠀⠀⠀⠀⠀⡀⣾⣯⣟⠀⣀⠀⣦⠀⠀⠀⠀⠀⠀⣠⢫⣶⠀⠈⠉⢀⠸⣿⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡿⢿⡉⠀⠀⠀⠀⠀⠀⢠⠜⢁⡀⠉⢈⠻⢦⣍⠀⢨⠄⠀⠀⠀⠀⠈⠀⢸⣇⠘⠃⠀⠛⢃⢻⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠛⢧⣴⣶⠀⠀⠀⠀⠀⠀⠀⠿⠶⡾⣥⣤⣘⣃⣺⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⠘⢷⡀⢠⣀⠾⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣛⣙⢛⣉⣛⣿⣋⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠀⠀⠀⠀⠠⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⢀⣀⣀⣀⣠⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡾⠟⠛⠋⠉⠉⠲⢫⣾⡟⢲⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣏⣹⣄⠀⠀⡀⢠⠤⠐⠈⠁⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠳⣄⣈⡙⠛⠿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⢲⣤⣀⠙⠻⣿⣿⣿⣿⣿⣿⡇⠁⠙⠾⣇⠀⠀⠀⣸⡟⠉⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡼⡿⠿⠿⠦⢄⡉⠻⢿⣿⣿⡇⠀⠀⠀⢻⡄⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣫⣾⣿⡄⠀⠀⠀⠉⠳⣄⠙⠻⣷⣄⠀⠀⢸⡇⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣫⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢄⠈⢿⣷⣦⠈⣇⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣉⣁⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠾⠟⠉⠛⠁⠀⢠⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀
⠀⠀⢀⣠⣴⣿⠃⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠶⠦
⢀⣾⣿⡟⠉⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠋⠃⠙⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢉⡀⠉⠙⢦⡀⠀⠀⠀⢀⡴⠚⠉⢀⣠⡉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⣿⣿⠂⠀⠀⠹⣆⠀⢠⡞⠁⠀⠀⢸⣿⡿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⢹⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠿⠛⠛⠉⠉⠉⠉⠛⠻⢿⡿⠛⠛⠉⠉⠉⠉⠛⠛⠿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢿⣿⡿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢿⣿⣿⠏⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠘⠿⡿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⡿⠀⠀⠉⠙⠛⠛⠿⠿⠟⠛⠛⠉⠁⠀⣷⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⡿⠿⠿⠿⡿⢟⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⡿⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⢧⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣶⣶⣤⣤⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠉⠙⠛⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣠⣤⣶⡾⠿⠟⠛⢻⡟⠛⠻⠿⢷⣶⣤⣀⡀⢀⣿
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠟⠋⠉⠀⠀⠀⢠⡴⠾⠷⢦⣄⠀⠀⠀⠉⠙⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆
⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣤⣾⠏⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⠀⠈⠙⣷⣿⠋⠁⠀⠀⠀⣠⡴⠶⠶⣤⡀⠀⠀⠹⣷⣤⣤⣤⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⠃⠀⠀⢠⡟⠁⠀⠀⠀⠙⣷⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⢻⡆⠀⠀⠘⣿⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⢹⡆⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⠾⠃⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠈⠳⣦⣤⣤⡴⠟⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣀⣄⣀⣀
⠀⠀⣠⣶⣿⣿⠿⠿⠿⣿⣿⠀⠀⠀⠀⣠⡴⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⢸⡇⠈⣷⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣄⠀⠀⠀⠀⢿⡿⠿⠿⠿⢿⣿⣶⣄⡀
⣴⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠋⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⢿⣿
⠙⠉⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢻⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⢠⡿⠀⠀⢸⡇⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⣠⡾⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⠛⠶⠶⠟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷⠀⠀⠀⠀⠀⠙⠻⠶⠶⠟⠋⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣦⣤⣀
⠀⠀⠀⠀⣠⣾⣿⠟⠋⠉⠉⢻⣧⠀⠀⠀⢀⣴⠛⠉⠙⠻⣆⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⣴⠞⠛⠛⠳⣦⠀⠀⠀⠀⣼⡟⠉⠉⠙⠻⢿⣷⣄
⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⢻⣧⠀⠀⢸⡇⠀⠀⠀⠀⣹⠀⠀⢰⡏⠀⠀⠀⠀⠸⣧⠀⢰⡏⠀⠀⠀⠀⢸⡇⠀⠀⣼⡟⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠈⢷⣄⣀⣀⣴⠟⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠀⠀⢿⣄⣀⣀⣠⡾⠁⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠈⠉⠉⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠉⠁⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣤⣶⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⠀⠀⣴⣿⣷⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠻⠿⠟⠁⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡼⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⢠⣶⣶⡄⠀⠀⠀⣠⣶⣿⣿⣷⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⣴⣶⣶⡀⠀⠉⠛⠿⡿⠃⠀⠘⠿⠿⠃⠀⠀⣼⣿⠟⠉⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠤⡈⡀⠀⠀⢸⣿⣿⣿⡗⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠈⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⣴⣲⠀⠀⠿⠟⠈⣀
⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⢸⣿⣿⣿⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠆⠀⠌⠀⠈
⠀⠀⠂⠁⠀⠀⠀⠀⠠⠀⠀⢀⣶⣶⣦⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠁⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠈⠀⠁
⠠⠠⠤⠄⠀⠀⠠⠀⡀⢀⠀⠘⢿⣿⡿⠀⠀⠈⠻⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠈⠙⠳⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠐⠀⠀⠀⠐⠀⠄⠀⠀⠄⠀⠰⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣦⡀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢄⠂⠀⠄⠐⠂⠀⠀⠒⠐⠂⠉⠈⠑⠀⠀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠧⠒⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⣼⠗⠁⠰⠁⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠟⠁⠀⠀⢀⣀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣶⡾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⢸⣶⣾⡶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠈⠁⠂⠀⠀⢀⠀⠀⠀⠀⠄⠠⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣠⡷⢾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣀⠤⢚⠀⠀⢉⣯⣮⣻⣿⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣷⣤⣯⡀⠀⠀⣀⢢⠎⢈⢿⡥⣻⣏⡟
⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡛⢛⡟⢈⡀⠀⢘⣶⣽⣿⠇
⠀⠀⠀⠀⠀⠀⣠⠇⠀⠆⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⣒⣻⣤⠟⠁⠠⢖⣽⣟⡟
⠀⠀⠀⠀⠀⠀⣼⠀⠀⡓⢀⡂⠀⠀⠄⢰⣿⣿⣯⣿⣿⣛⢿⠋⠀⡙⣿⢿⣿⠿⠟⠋⠀⠀⠀⢀⡃⣉⢎⡠
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠓⠂⠀⠈⣐⢢⣟⢿⣿⡿⣿⣭⣤⡀⠀⠀⣘⠀⡽⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠟
⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠁⠐⠒⠤⢸⣿⣿⣿⣿⣿⠻⠋⠀⠀⢼⣿⢣⣾⡏⢳⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⣦⣦⣶⣲⢄⣤⣿⠛⣿⡄⢻⡀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⢀⣾⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢻⡇⢀⡩⠟⣿⣧⠀⠄⠀⠰⠊
⠀⠀⠀⠀⠀⠀⢈⡅⠀⢀⣼⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠒⣾⡏⠀⠀⠀⠀⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢛⠙⠡⠂⠀⡧⢸⠏⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢾⠗⣻⡆⠖⠚⠉⣿⠀⠀⠀⣀⡐⠾
⠀⠀⠀⠀⠀⠀⣸⣷⠀⣿⣿⣿⣿⣿⢿⣞⣋⠝⠁⠈⠀⠀⠀⠀⠀⢀⡤⠚⢁
⠀⠀⠀⠀⠀⣰⣿⡏⢀⣿⣿⣿⣿⣿⣯⣍⣥⡤⠤⡴⠐⠂⠀⠔⠃
⠀⠀⠀⠀⢠⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣀⣅⡤⠤⠦⠴⠃
⠀⠀⠀⠀⣾⣿⣟⠀⣿⣿⣿⣿⡿⠓⠫⠅⡀
⠀⠀⠀⢸⣿⢿⠍⢰⣿⣿⡿⠋⢁⡐⠲⠤
⠀⠀⠀⣿⣿⣏⣠⠟⣩⠊⡀⠂⠀⠈⠑
⠀⠀⢐⢿⡿⠊⠁⡐⠁
⠀⠀⢈⡛⠁⠀⠐
⠀⠀⠈⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠄⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠙⠀⠉⠉⢈⢽⢯⡭⢵⡰⠚⡈⠉⠁⠀⠀⠀⢀⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⢰⣿⡇⠀⡖⣆⣖⣶⣦⠀⠀⣼⣷⣘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢸⠀⣸⡿⠻⣿⠟⢿⣇⠀⠒⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠀⠉⠓⠒⠛⠒⠊⠉⠀⣤⡄⠐⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠄⠀⠈⢿⡆⠀⠀⠀⠐⠀⠀⠀⠸⡿⠃⢺⣦⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢺⠟⠃⠀⣀⢇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠀⠀⠑⡙⢆
⠀⠀⠀⠀⠀⠀⣀⠰⠁⠀⠀⠀⣿⠛⣼⡇⠀⢺⣿⡄⠀⠀⣿⣷⠀⠸⡇⠿⢻⡇⠀⠀⠑⣤⠧
⠀⠀⠀⠀⠀⢠⡍⠁⠀⠀⠀⠀⢀⡄⠈⠀⠀⠈⠛⠀⠀⠀⠛⠁⠀⠀⠀⢸⣯⡇⠀⠀⠀⠈⠀⠑⢄⡀
⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⢧⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣧⡃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠋⢺⢴⣦⣆⠀⠀⣀⢸⠀⣀⠀⠀⣾⢀⣾⡏⠙⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠸⣿⣅⢀⢨⠿⣸⠀⡻⢢⣰⣽⣿⠛⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢾⣿⢧⣷⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢻⠛⠛⠙⠉⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⢀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡆⠀⠀⠘⠎⡦⠤⣄⠜⠀⠀⠀⣾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢀⠀⠀⢻⣄⣄⣸⠃⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠉⠉⠛⠿⣿⣿⡿⠟⠛⠉⠉⠉⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠛⢏⠀⠀⠀⠀⠀⢀⣶⣾⣿⣶⣦⠀⠀⠀⠀⠀⢈⠛⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁⣼⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣆⠙⣧⣂
⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⢸⣿⣿⠟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⡄⠈⠻⣇⡀
⠀⠀⠀⢀⡤⠲⠛⠉⠀⠀⠀⠊⠉⠁⠀⠀⣀⣀⡀⠈⠉⠋⠉⠛⠉⠀⢀⣀⡀⠀⠀⠈⠉⠁⠀⠀⠈⠙⠳⠦⣄
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠹⠿⢿⣿⠟⠀⠀⠀⠀⠈⠿⣿⠿⠿⠋⠀⠀⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆⠀⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣷⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⢀⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠉⠛⠳⣤⡀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⠀⠀⠀⠀⠈⢷⠀⢠⡏⠀⠀⠀⠀⠀⣀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣷⡇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠿⠿⢿⡷⠿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡴⢋⠤⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡤⠶⠦⣄⠉⠳⣄⠀⠀⠀⠀⠀⢀⣴⠗
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⡴⠋⠀⢯⡀⢀⡿⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡏⠀⠀⠀⠈⡇⠀⠈⢧⡀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡾⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢧⡀⠀⢀⣠⠇⠀⠀⠀⢳⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢆⠀⠀⣿⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⣀⣀⡈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⣀⡀⠀⠀⣇⠀⠀⣸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⢹⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⢀⡞⠉⠀⠙⢦⠀⠈⠙⠋⠁⠀⠀⣿⠀⠀⠀⢰⠋⠙⢦⠀⠈⠳⣄⣠⠞⣹⠉⠉⠉⠉⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠶⠛⠛⠋⠉⢻⠀⠸⣇⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠦⡤⠞⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⣴⠚⠙⢲⡀⠀⢠⡏⠀⠀⠀⠀⡴⠋⠙⢦⠀⠀⠀⣰⠋⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠳⣄⠀⠀⠀⢧⡀⠀⣸⠇⠀⢸⡇⠀⠀⠀⠘⣇⠀⠀⣸⠃⢀⡼⠁⠀⠀⠀⠀⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠳⣄⠀⠀⠉⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠛⠓⠒⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣶⣦⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠀⢀⣠⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣇⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠀⠙⠻⣿⣿⣿⣿⣿⣁⣰⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣿⣿⣿⡟⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠟⠁⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⢧⠀⠀⣀⣠⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠀⢀⠇⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⠉
⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⡜⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠀⡜⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠛⠛⠛⢦⣄⡀
⠀⠀⠀⠀⠀⢠⣿⣿⠁⠰⠁⠀⣼⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⢰⠁⠸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀
⠀⠀⠀⠀⣠⣿⡿⠃⢀⠃⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣷⡀
⠀⠀⠀⠞⠛⠉⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠃⠀⠀⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠠⣿⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⢃⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⣰⣿⣿⣿⠀⠀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠙
⠀⠀⢀⣠⣴⣾⣿⣿⠏⠀⠀⢧⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣤⣤⣄⡜
⢀⣴⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠳⣀⣀⣀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆
⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠴⠊⠘⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⣿⣿⣿⣿⣿⡿⠿⡀⠀⠀⢠⣾⣿⡿⠿⠊⠁⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠙⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢛⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡟⠛⠋⢳⡀⠀⠀⠀⠀⠀⠀⣰⡶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠔⠀⠀⡈⣧⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣴⠀⠀⠸⡄⠀⠀⠀⠀⠘⡇⢰⡟⠻⢆⣷
⠀⠀⠀⠀⠀⠀⢸⠋⠀⢿⠙⣆⠀⠀⠀⠀⠀⠀⢹⣿⡿⠖⠀⣀⣧⠀⠀⠀⠀⠀⡇⠀⠈⣰⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠁⠘⢇⠀⠀⠀⠀⠀⠀⣿⠃⢠⡿⠻⠾⡄⠀⠀⠀⠀⣷⠀⡈⠁⣰⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠂⡀⠀⣮⢧⠀⠀⠀⠀⠀⢸⡄⠈⠀⠀⠀⢱⠀⠀⠀⠀⢸⣿⣥⠈⣿⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡷⠀⠨⠀⢳⡀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢧⠀⠀⠀⠸⠀⢀⣰⡟⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠄⠀⠀⠈⢳⡀⠀⠀⠀⢃⠀⠀⢀⡤⠴⠾⡄⠀⠀⡄⠀⡾⠋⠉⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠻⣄⠀⠀⠸⡆⢀⠊⠀⠀⠀⣧⠀⠀⡇⠀⠰⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠈⢀⡠⢀⡙⢦⠀⠀⢻⡘⡀⠀⠀⠀⢹⡀⠀⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤
⣰⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢷⢠⡟⡁⠀⠉⠈⣇⠀⠈⡇⠙⢦⣀⣀⣨⣇⣀⡇⢀⠔⠀⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠇⢀⠀⢈
⣏⢠⠂⠨⠉⢢⡀⠀⠀⠀⠀⠀⠈⢿⡀⠠⠃⠈⠀⠙⣆⣠⠁⠀⠀⠈⠍⠀⠈⠉⠀⠈⠈⢷⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⠈⠀⠨⠅⢰⠏
⠘⢦⡦⢶⣮⣿⣛⣦⣀⠀⠀⠀⠀⠈⢷⡀⠀⠁⠔⠀⠈⠁⠀⠀⢀⣠⠀⠀⣀⡀⣀⡀⠀⠘⢿⡄⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⡦⢀⣶⡖⣰⠃
⠀⠈⠳⣆⠀⠅⠀⠁⠉⠓⢦⣀⠀⠀⠈⢿⡀⠀⢿⣦⡀⠀⠀⠀⠸⠋⠁⡀⠀⠀⢤⣄⢠⣶⢁⣠⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⠟⠪⠟⣿⡿⣿⢶⠇
⠀⠀⠀⠀⠙⢦⡂⣀⠐⣶⡇⠘⠓⡤⢀⢼⠃⣀⠐⠊⠉⠀⠀⠀⠀⣤⣾⣷⣷⣦⣼⠯⢘⣿⣯⣿⠀⢠⣼⣧⡀⠀⠀⠀⠀⢠⡏⣤⢶⠨⡍⠀⢰⡞
⠀⠀⠀⠀⠀⠀⠙⢦⡾⠛⠋⠫⠌⢁⠀⣀⡀⠜⠋⡁⣀⡄⠈⢠⣾⠿⢛⣋⢉⠁⣀⡀⢰⡞⣠⠜⣦⢀⡿⣥⣹⣆⠀⠀⣠⡿⠣⡀⢦⠐⡺⣉⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡆⠴⠊⠍⠐⠛⠁⠀⠐⠀⠺⠁⡳⠎⠁⠀⠛⠟⣿⣿⢶⣡⠎⣹⢱⣬⠇⢸⣿⠄⢨⣌⠛⠻⠛⠦⠢⡬⢺⠦⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⢄⡀⢀⡤⠑⠀⠚⠀⢄⠀⢀⠀⠀⣀⠘⠛⠁⢛⣽⣖⠓⠃⡆⢘⡧⢼⢷⡚⠉⠀⢀⡁⠐⢀⡀⡿⠖⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⢹⣮⣄⡀⠀⠀⣀⡀⠐⡂⠀⠐⢿⣷⣄⠀⠻⠋⠀⠜⢃⣄⠘⠁⠘⢒⣟⢀⡧⣸⣟⡦⠀⣹⠧⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠉⠚⠠⠤⡉⢀⣉⠀⠁⠀⠀⠈⣿⢿⣷⣄⠀⠀⠤⠷⣟⡇⠠⣨⣭⣭⢾⣍⣃⡀⠀⢈⣷⣆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⣶⣾⣿⣟⠿⠀⠀⠀⠀⠛⠀⣽⡿⠇⠀⠀⠈⠉⠑⠀⠄⢀⡍⠀⣽⢻⡿⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣿⣆⠀⡆⠀⠀⠀⠀⠈⠁⠀⠒⠤⠘⢶⣺⣆⢸⡿⠀⠀⢠⣀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠋⠹⠆⠁⠁⠀⢧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠚⠅⡸⢿⡃⢀⣤⣾⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢠⡄⠶⠀⠀⠘⢤⡀⠀⠀⠈⠻⢿⠶⠜⠁⠀⠀⠁⢻⡅⠸⢿⢿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⠀⠀⠀⣀⣀⣀⠈⢠⣴⡦⠴⠦⠤⠄⠰⠆⠀⠀⠶⠿⢶⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠲⠶⣭⠽⠗⠒⠶⠖⢀⣀⣰⡖⠀⠉⠡⠴⣤⣠⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡔⠶⠿⠶⠦⠀⢀⠘⠛⠻⠛⣋⣀⣀⡀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣦⣤⠀⠠⠶⠶⠦⠀⠀⢿⡿⠍⠱⠶⠶⠶⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡈⠙⣠⠰⡐⣦⣴⣶⣶⠄⠀⠀⠀⠇⠀⠾⠛⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢲⣬⡄⡽⠅⡀⢁⡌⠀⢱⡇⢰⡄⡄⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣇⣡⣹⣇⣸⣹⣘⡃⢒⣮⡇⣸⣸⢓⣴⣿⣡⣸⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⡶⠶⢶⣾⠿⢷⣦⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠒⡒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡀
⠀⣿⠀⣥⢼⡇⠻⢺⣇⠶⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡇⢎⡰⠾⠠⣀⠠⠦⠂⠄⢖⡀⠀⢨⠀⠀⠀⢀⠀⠀⠈⠀⣀
⠀⠙⠳⠶⠚⠛⠿⠿⠟⠿⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⣀⠀⠀⠤⠤⠀⠀⡄⡠⠤⠊⠀⢀⠞⢁⠀⣆⣀⠀⠌⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠒⡁⠆⡏⠒⠢⠁
⠀⠀⠴⡇⡀⠀⠀⢀⠈⡢⠭⠥⠐⠂⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⣀⡀⠀⣀⢀⡀⠀⠄⠀⡆⠀⠀⢀⣠⡄⠀⠀⠀⡀⠀⠁⠙⠁
⠀⡎⠈⡇⠱⡄⠄⠈⡜⠄⠀⠀⠠⠘⡄⠁⡀⠀⠀⠀⢻⡗⠋⣰⠁⠁⣼⠁⠈⡧⠰⠮⠞⠀⡀⠀⠀⠋⠃⠀⠀⠀⠈⠂⠀⠃⠀⠀⠐⠁
⠀⠣⣰⡇⠐⠁⠀⠃⢡⠀⠀⠀⡀⢀⠁⠦⠀⠀⠀⠀⠀⠉⠉⠈⠙⠋⠈⠛⠋⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠁⠀⠀⠈⠀⠤⠕⡂⢉⠀⡈⡆⠐⠀⠀⡔⢀⠀⠬⠀⠀⠀⠐⡄⠀⡀⠀⠤⡀⠀⠀⠀⠀⢠⡀⠀⡀⣀⠤⠛⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠈⠉⠲⠀⠀⠀⠀⠀⣷⢀⠤⠀⠀⠠⠉⠛⠁⣸⠀⠒⢆⢹⠀⠐⠇⠀⠀⠀⠈⠉⠀⠀⠀⠠⠶⠄⠐
⢀⢰⡀⠂⡀⠀⠀⡤⠀⠄⠠⡀⠀⠀⣠⠉⠉⢢⣟⡀⠀⠀⠰⣄⠀⠀⠀⢻⠀⠀⠊⢨⠃⠀⠀⠀⣀⠤⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⡄
⠣⠔⢪⠰⠀⠀⠡⠳⠄⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠛⠁⠀⠻⠶⠒⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠰⠠⡀⠈⠀⠀⢰⣆⠀⠐
⠀⠀⢀⣤⠔⠒⠒⠒⠢⣤⡀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠉⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈
⠀⣠⡛⢿⡇⠠⠄⢚⣩⣿⣿⣦⠀⠀⠀⠀⡈⠘⠠⣍⠀⣼⠳⠹⠀⠀⠀⠡⠓⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢀⠇
⢰⠹⢛⣆⠀⠀⠰⠟⠛⠻⢿⣿⡇⠀⠀⠠⠃⠀⠈⠉⠢⠈⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⡇⢸⠒⠉
⢸⣿⣿⡏⠀⠀⢀⣾⣿⣷⣬⡛⡇⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠠⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣾⣿⣆
⠀⢯⣀⣠⡄⠀⠈⠛⠛⢿⣿⢰⠃⠀⠀⠀⠩⠀⠤⠀⠀⢰⠁⠀⠀⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛
⠀⠈⠻⣿⣿⡇⠀⠀⠀⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠑⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠀⠀⠀⠀⢀⢐⡐⢂
⠀⠀⡀⠀⠈⠁⠀⠀⠈⠀⠀⢀⠀⢀⡠⢦⡀⠚⠓⠒⠀⢠⠀⠀⠀⠀⢠⣤⠀⠀⠀⣦⠀⠀⠀⢠⡴⠦⣤⡶⢶⣦⠀⠀⠀⠀⠣⠌⠁
⠀⢸⠠⢀⠄⠤⢀⠄⢤⠀⡀⠨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⣿⣐⢃⣸⣀⣀⣿⣁⠀⠀⢀⠀⢀
⠀⠈⠒⢈⡀⠀⠉⠈⠈⠀⠁⠀⠀⠀⠀⠀⠚⠀⠀⠑⠀⠀⠀⠈⠁⠀⠀⢀⠤⠀⢰⡮⡀⠀⠀⠈⠙⢻⡟⢵⠿⡏⠻⣷⡄⠀⠀⠈⠧
⠀⠀⠀⠀⢀⠔⠂⠒⢂⣤⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠸⠀⠀⡴⠉⢁⣠⠟⠀⠄⠀⠀⢠⡴⢾⢿⡶⣾⠶⣷⡿⠁⠀⠀⠀⡆
⠀⠀⠀⢀⡦⠶⠒⠚⢉⠅⠁⠀⠀⠀⡄⡀⠀⠉⡉⠭⠁⢠⠀⠀⠀⠸⣀⡴⠚⠁⠀⠐⠀⠀⠀⢸⣇⣤⣸⣇⣷⣛⣿⡷

⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠲⣄⠀⣤⠖⠀⠀⠀⣤⣶⣤⠂⠀⠀⠀⠀⠹⣷⠀⠀⠀⡤⠊⠀⠉⠒
⠀⠀⠀⢣⣿⠇⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠁⠻⣿⠿⠀⠀⠀⢼⠇⢀⣀⣀⠀⠀⠁⠀⠀⢀⡈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠛⠒⠓⠒⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠒⠋
⠀⠀⢀⠤⡄⢄⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⡀
⠀⠀⠿⠃⢀⣾⣷⠀⠀⣺⣺⡃⣄⣄⠀⠀⣴⡿⠀⢹⡄⠀⠀⣶⢰⡖⡆⢶⠀⠀⠄⢠⣿⡇⠠⠀⠀⢛⣹⣇⣤⣀⡀
⠀⠀⠢⣛⠀⠘⠀⠀⠀⣶⠸⣦⣓⣒⠀⠀⢸⣧⢠⣼⡇⠀⠀⠁⢊⣶⡓⠚⠀⠀⠈⠀⢵⠅⠀⠀⠀⠸⠿⡏⠁⢩⡅
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⢉⡤⠀⠀⠀⠀⢠⣍⣰⡀⠀⠀⠀⠠⡦⢀⠀⠀⠀⣀⠼⢐⡡⠄⠀⠀⢠⠆⢀⠢⣄⠀⠀⠀⡄⠀⠀⡀
⠀⠀⠀⣤⢠⡀⠀⠀⠀⠀⣿⡀⠉⠁⠀⠀⣰⣿⣦⠆⠔⠀⠀⠨⠄⡧⠡⠙⠀⠀⠈⠦⣷⠫⠘⠀⠀⣾⣟⠀⣸⡿
⠀⠀⠀⠛⠟⠁⠀⠀⠀⠘⠁⠃⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠯⡇⡀⠺⠵⠀⠀⢰⣿⡿⠈⠀⠀⠀⢠⣸⣿⣿⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⡴⠀⢤⡄⠀⠀⠀⢰⡆⣴⢠⡄
⠀⠀⠀⢾⣸⠇⠀⠀⠀⢿⡟⠀⠒⠆⠀⠀⠀⢯⣉⣹⠀⠀⠀⠿⡿⠶⢿⠷⠀⠀⢿⠦⠼⠿⢾⠆⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⡄⢰⠆⠀⠀⢶⠀⡦⠀⡦⠀⠀⢀⢤⣼⡁⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠐⢼⡴⠃
⠀⠀⢰⢡⣦⠙⡄⠀⠀⠀⢸⡇⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⡇⣈⣀⠀⠀⠀⠘⢯⠁⠀⠀⠀⠀⣸⡇⠰⡗
⠀⠀⠈⠢⠥⠚⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠸⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠑⠘⠃
⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠐⢡⣧⠙⡆⠀⠀⡾⢷⠠⡾⢧⠀⠀⠀⠻⡿⠇⠀⠀⠀⡞⠁⣴⡈⢱⠀⠀⠀⣤⡼⢿⡆⠀⠀⣼⣿⡄⣿⣷
⠀⠀⠘⠄⠎⠴⠃⠀⠀⠣⣠⣿⣄⠌⠀⠀⠘⠒⠐⠛⠁⠀⠀⠳⡄⢉⣡⠞⠀⠀⠈⠋⠀⠼⠃⠀⠀⠹⣿⣇⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⠀⠐⢿⣶⣶⣿⣵⣾⣷⣦⣠⣾⣷⣮⣿⣶⣶⡾⠂⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠂⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠳⠶⣴⢀⣰⣿⣿⣿⠀⠀⠀⠀⠀⢐⡄⣦⠴⠞⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡘⡌⠙⣿⣿⡋⠀⠀⠀⠀⣴⠋⢁⢃⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠾⣿⠿⠦⢽⣿⠀⠀⠀⠀⣸⡿⠴⠿⣿⠷⠶⠤⣤⡀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⣰⠟⣶⠦⣤⣪⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣕⣦⠴⣶⠻⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠉⠈⢯⣝⡳⡏⢠⡏⢸⠇⣿⣿⣿⡇⢀⡤⠀⠀⠀⠀⣦⡀⢸⣿⣿⣿⠸⡇⢹⡆⢹⠞⣫⡭⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠟⠀⣿⠀⠿⠿⠛⠀⠘⠁⠀⠀⠀⣸⣿⠃⠀⠙⠿⠿⠀⢿⠀⠻⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣤⣾⣿⠀⠀⣾⣷⣤⣀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⡗⢤⡶⢶⡄⠲⢶⣿⣿⣿⡿⠟⠃⠀⠀⠘⠻⢿⣿⣿⣿⡶⠒⢀⡖⢶⡤⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⢻⢸⡇⢠⡀⠙⠋⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠙⠋⢀⣄⢸⣧⡾⠁⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠺⣷⠘⣿⢆⠀⢀⣾⡿⢿⡿⢿⣿⡿⢷⠀⠀⡴⠸⠇⣾⠏⠀⣴⠂
⠀⠀⠀⠀⠀⠀⢀⣤⠄⠚⡓⠀⣿⠇⠸⣿⣧⠈⠻⡶⣿⠛⠂⣿⡇⠘⠀⣾⣿⠀⣼⣿⠀⠘⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠟⠂⠉⠉⠈⠉⠀⢠⡈⢉⣀⣀⡀⠉⠀⡀⠉⣁⢀⣀⡉⢁⡐⠁⠉⠁⠈⠉⠛⠂⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠻⣿⣿⣷⠀⠃⣾⣿⣿⠟⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣌⠛⠛⠰⠆⠛⠛⣡⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⢧⣤⡀⢠⡔⣫⢍⡀⢿⣿⣿⡿⠋⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⣴⣶⣿⣿⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣍⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⣤⣏⢀⣼⣿⣿⣿⣷⠀⣠⣴⣶⣤⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠙⠳⣶⠾⠋⠉
⠀⠀⠀⠀⠀⠀⠐⠦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡶⠶⠶⠦⢤⣤⣀⡙⠻⠟⠁⠠⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⠁⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠘⠎⣇
⠀⠀⠀⠀⠀⠀⢀⣠⢿⣿⡾⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠙⠦⣀⠈⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⣏⠈⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠳⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠙⢶⣾⣿⣿⡿⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⡀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣽⢿⡃⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠘⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⠛⠁⠸⡜⣷⡄⠀⠘⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣵⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣤⣤⣴⣶⡶⠾⠟⠛⠉⠈⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣰⣾⠿⢷⣶⣶⣶⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⣰⣾⣟⠻⢫⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣷⡄⢸⣿⡟⠙⠛⠉⢸⠛⠛⠂⠙⠛⠛⢫⠉⣿⣿⡄
⠀⠀⠀⢻⣿⣿⣿⣿⣷⣾⣷⣾⣷⣼⡟⣰⣷⣶⣷⣶⡿⣰⣿⡿
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⢶⣶⣶⣶⣶⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣽⣯⣯⡿⠽⢁⠁⠈⢀⣠⣄⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⡀⠀⠈⠿⡿⠿⠃⡀⠤⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡷⣄⠀⠀⠀⠁⠐⠚⠺⢟⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠒⠉⠻⠿⣿⢿⣿⢗⠏⠉⠁⠙⠿⣿⡨⣗⢦⡀⠀⠀⠀⠘⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠤⠛⠉⠈⢀⢀⣤⣄⠀⠄⢀⠙⢿⣾⣿⣦⡀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡠⣢⠀⠀⣀⠂⡈⢀⣾⣿⣿⣆⡉⣈⣭⣵⣮⣿⣿⣿⣶⣾⠆⠻⢛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣿⣦⣻⣪⡥⣀⠠⢿⣿⣿⢟⣻⣿⣿⡻⢏⣼⣿⣻⣿⣿⣦⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣿⣿⣍⡵⣿⣯⡂⠀⠀⠙⡹⣋⣿⣻⢾⣿⣿⡿⠛⠛⠀⣼⣿⡟⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⡯⣾⣿⣿⡦⡄⠀⠀⠰⢛⣽⣿⣟⣻⡯⣷⡂⢀⣼⣿⣿⠃⢀⣙⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⣎⣉⢭⣟⣆⢅⣤⣴⣵⡻⢫⣾⣾⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣉⠦⠶⠖
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠙⠿⢷⣮⣿⣿⣿⠿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⢻⣿⠋⠁⢸⣿⣯⣥⡄⠼⢻⡟⠻⡟⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠁⠀⠀⠀⠈⠁⠞⠀⠀⠀⠓⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣿⣿⣿⣿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣩⣭⣥⡄⣤⣤⣭⣍⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠷⣤⣀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⣀⣤⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⣠⣆⠀⠀⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣄⠀⢀⣴⣄⠐⠛⠉⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⠋⠙⢻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣧⡀⠀⣠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣼⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⠟⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠰⠶⠶⠶⢶⣄
⠀⠀⠀⠀⢰⡟⠛⠛⠛⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⡇⢸⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣇⢸⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢃⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠀⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⢂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⢈⡇⠉⢑⢦⡀
⠀⠀⠀⢀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣀⠌⠀⠀⠀⠘⠤⢷
⠀⠀⠀⠄⠀⠲⣤⠂⠈⠂⠀⠀⠀⠀⣰⢋⡑⡄⠀⠀⠀⢸⠹⣠⠃⠀⡎⢆⣀⠀⠀⢨⡇
⠀⠀⠀⠈⠂⣤⣋⡤⢚⠀⠀⠀⢀⡘⠡⠎⢰⣈⢹⠀⠀⠀⢆⠀⠀⠀⢣⠀⠀⠃⣄⣼⠀⠀⠀⡠⠐⠒⡨⠋
⠀⠀⠀⠀⠈⠈⠆⠜⢣⡀⠀⡪⢀⡵⠀⠀⠀⠈⢩⢠⡀⢰⠸⠶⣄⡀⠚⠀⣀⡤⣿⢰⠀⠀⠈⠀⣠⠞⠁⡀
⠀⠀⠀⠀⢀⠀⠀⠈⢫⠃⢠⠁⢸⣱⣐⣠⠎⠃⠘⠀⡇⠀⠢⠀⠀⢩⠉⠉⠉⠀⠀⡄⠀⠀⢀⡾⠥⠄⠊
⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠘⠲⡐⠧⠋⢸⠳⠆⠀⠀⠁⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⠙⠑⠰⢐⣠⠂
⠀⠀⠀⢀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠆⠀⠰⡀⠀⠀⡄⠋
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⡄⠀⠀⠠⠀⠀⠈⢢⠀⠈⠢⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠡⠀⠀⠙⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀⠀⢀⣠⣤⣤⣄⡀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡟⠋⠉⠉⠙⢻⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣟⠀⠀⠀⠀⠀⠀⣻⣇⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⡾⠟⠛⠻⠿⠶⠶⠿⠟⠛⠻⢷⣄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣠⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣾⠿⣶⣤⣄⣀⡀⠀⠀⣀⣀⣠⣤⣶⠿⣷⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠉⠉⠛⠛⢻⡟⠛⠛⠉⠉⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⣰⡾⠿⣶⡀⢸⡇⢀⣴⠿⢷⣦⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢿⣆⣠⣿⠇⢸⡇⠸⣿⣄⣰⡿⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣄⡀⠉⠉⠁⠀⢸⡇⠀⠈⠉⠉⢀⣠⣄⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣿⠀⣿⠋⠙⣿⡄⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⠋⠙⣿⠀⣿⡟⢷⣦⡀
⠀⠀⣤⣤⣀⣠⣾⠋⠀⠘⣿⠀⠻⢷⡾⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠻⢷⡾⠟⠀⣿⠃⠀⠙⣷⣄⣀⣤⣤
⠀⠀⠈⠉⠉⠛⠃⠀⠀⠀⢻⣇⠀⠀⠀⢀⣤⣤⣀⠀⢸⡇⠀⣀⣤⣤⡀⠀⠀⠀⣸⡟⠀⠀⠀⠘⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣆⠀⠀⣿⡋⠉⣿⡆⢸⡇⢰⣿⠉⢙⣿⠀⠀⣰⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠻⣷⡀⠙⠿⠾⠟⠁⢸⡇⠈⠻⠷⠿⠋⢀⣾⠟⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⢸⡇⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⣀⣠⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣄⣀
⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠰⣤⣤⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠙⢶⣾⣏⢹⣿⣷⣾⣿⣷⠈⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⡈⢳⣶⣿⡋⢘⣉⣻⣿⣿⠻⣧⣴⣾⣿⣶⣶⡎⢛⣀⣁⣤⣤
⠀⠀⠀⠀⠀⢶⣄⣀⣤⣿⣿⣿⠿⠻⣿⣧⡌⠉⠋⢰⣿⣾⠻⠇⢙⡿⠛⠿⣿⡿⢿⣿⣿⠿⣷⣶⣦⡀
⠀⠀⠀⠘⢇⣀⣿⣿⣿⠿⠀⠈⠃⢀⠰⣿⡁⠘⠃⠀⢰⣿⡄⠚⠛⠁⣀⣼⠸⣷⣌⣿⡆⠘⣻⣿⠛⣿⣀⠑
⠀⠀⠀⠀⠈⢻⣿⣿⠿⣀⠲⢼⣷⣾⣷⣟⠛⢶⡄⠀⢼⣿⣿⠂⢐⠃⡍⠀⡀⢠⣄⡸⢿⡏⢻⠷⣾⣿⣿⣤⣤⣄
⠀⠀⠀⢷⣀⠀⣿⣿⣶⠉⣷⣾⠛⠟⣳⣾⠂⠈⢁⠀⠈⠻⠇⢰⣾⠀⠉⠀⢳⠆⢻⣷⣬⣿⢺⣶⡿⢉⣠⣋⠙⠡⣄
⠀⠀⠀⠀⠈⠁⢿⣿⣿⣷⣿⣿⣿⡶⠌⠻⢿⡃⠈⢷⣶⠰⠃⡛⢸⡶⠀⢰⢴⡗⠙⣿⠟⢿⣿⣏⣠⣾⣿⣯⡈⢷⡄
⠀⠀⠀⠘⠃⠀⢸⣿⣿⣿⠋⠉⢩⣥⣤⣦⣼⣷⡇⢰⣿⣶⣾⣿⢰⠆⠁⠺⠈⠛⣮⡷⢠⣬⡟⠙⣧⣼⣿⣿⠃⡀⠉
⠀⠀⢠⡀⢻⣤⣼⣿⣿⠆⡿⠓⢴⣦⢙⣿⣿⣿⢷⣿⡟⣻⣧⡍⣘⠀⢛⣀⣎⡐⢿⣀⢸⡛⠷⠴⢦⡀⣼⣿⡦⠋
⠠⠆⠈⣿⣤⣾⣿⣿⠁⠘⠃⢀⣾⣿⣿⣿⡹⣿⣾⡟⣾⣿⣿⡶⠛⠀⠈⣩⣽⡗⠈⠁⠀⠀⢀⣀⣀⠁⢈⣿⡗
⠀⠀⣾⣿⣿⣿⣿⣿⡁⢸⡅⠺⠻⢡⣿⣿⣷⡼⠇⣸⣿⠻⣿⣤⣇⠘⣷⣿⣿⣠⣶⣇⠀⠀⠈⠁⠈⠑⢾⢿⣿⣶⡄
⠀⢚⣿⣿⣿⣏⢣⢀⣿⠄⢹⣆⠠⢈⣿⣾⣿⣧⢰⣿⣿⣴⣿⣶⣿⢰⣿⣿⣻⣿⣩⡏⣼⡗⠀⢀⡿⣧⣾⣶⣿⣏⠁
⠀⢿⣿⡟⢋⡉⠛⠁⠉⠠⣼⡿⢿⣽⡟⡿⢻⣿⡌⣿⣿⣿⣿⢻⣿⣿⣿⠳⡿⢿⣿⣿⠇⡹⢦⠘⢣⣄⠘⣿⠛⠿
⠀⢻⡟⣿⣿⣧⣶⣜⠃⠰⠈⠁⣤⡜⠻⣿⠿⣿⣷⠸⣿⣿⣿⢸⣿⣿⢃⣴⣾⣿⣿⢻⡾⣷⠀⡀⢼⡉⢠⣿⣗
⠀⠀⡀⠘⠋⢙⣿⣟⠁⠘⠂⠘⣅⢀⡾⠛⢾⣿⣿⣇⢻⣿⣿⡼⠟⣡⣾⣿⣿⣿⠃⣼⣷⡀⢲⡀⠈⣷⣿⡇⢸
⠀⠀⣠⠐⠃⡘⢿⣿⣦⣠⣤⠾⡇⠀⣠⣾⡾⢿⣿⣿⡌⣿⡿⢃⡴⠿⠿⢻⣯⣽⣿⣿⣿⡟⢻⣟⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣯⣀⣶⣀⣿⣶⣧⣼⣿⣿⣇⠘⢠⡾⠗⠀⠘⠋⠉⣿⣿⣿⣿⣿⡟⢹⣿⡋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⣿⣿⡿⢿⡻⣿⡏⠹⣿⣏⠀⣿⣷⣿⣧⣴⣿⣿⣿⣿⠿⢿⡏⢹⡇⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠊⣻⣟⠁⣄⣿⡏⢸⣯⣿⡏⢹⡏⣹⠙⡿⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⢿⣿⠃⢸⡿⠋⠉⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠉⢲⣤⡟⢡⠟⠁⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢻⣿⠡⠟⢀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⢌⣿⠀⠀⢸⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢷⣮⣻⠇⠀⠀⣿⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠠⡟⠛⠓⠿⠾⠷⢦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠶⣿⣶⣶⣶⣤⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⡾⡟⠏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⠀⠀⢒⣿⣿⠀⠀⢀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠟⡿⠻⢿⣽⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠀⠈⠀⢛⣿⠀⠀⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣤⢺⡏⠀⣦⡇⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⣿⣸⡇⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣄⣀⣼⣿⣹⣧⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⣿⢹⡋⢹⣿⣿⡀⢸⡏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡁⠘⡇⠘⡇⣟⠁⠈⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠇⢸⠁⢰⠇⣼⡇⢀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⠾⢀⡿⠦⣿⠀⢿⡇⢨⢠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⣷⠘⡇⢠⠀⠀⣿⠃⠀⣈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠙⣿⣿⣟⣷⢄⣿⠇⢠⡏⠸⣿⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠿⠾⠿⠟⢻⣿⣫⣴⠿⢷⣦⣿⣿⣷⡿⠿⠶⠶⠤⠠⣤⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⢤⣸⢤⣤⡴⡄⣴⡄⣧⣴⡦
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠩⠏⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠼⠸⠻⠿⠼⠇⠇⠯⠇⠷⠾⠷
⠀⠀⠀⠀⠀⠰⠉⠁⠀⠀⢀⡀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢸⣧⣶⣦⣖⠶⠀⢧⡶⣶⣶⠖⣶⣀⡆
⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠋⠁⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠒⠚⠉⠉⠉⠙⠋⠛⠒⠶⢤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣄⢀⣠⠔⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠙⢫⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⣿⣿⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⢰⠃⠌⠀⠀⠀⠀⠀⠃⣿⣿⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠅⠀⠀⠀⠀⡀⠀⠀⠀⢿⢄⠙⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⢀⠀⠀⠐⠂⠀⠀⠀⠘⣾⣿⢆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢠⠟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⣦⠀⠠⠀⠀⠂⠀⢿⠁⢠⢰⠀⡔⠀⠀⣼⡚⠀⠀⠀⠀⢠⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢰⣼⣆⠈⠀⠸⠉⠘⠼⠌⠀⠂⠈⠈⢷⠀⠀⠂⠀⡾⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣹⡏⢆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢻⢸⢧⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠈⣧⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢐⠸⠀⢳⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢴⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡰⠂⠀⠀⢠⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⡜⢀⠞⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⠀⠀⠀⠀⠀⠆⢃⠀⠀⠀⠀⢀⠔⠀⠃⠀⠀⠀⠀⢀⠎⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣡⡇⠀⠀⠀⢀⡴⣀⡇⠀⠀⣴⣖⣩⠖⠁⠀⠀⠀⠰⠿⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠒⢤⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠈⠉⠳⣤⡀⠀⠀⠀⠀⠑⣦⣤⣤⣤⣤⣤⣴⣶⣭⠄⠀⠀⠀⠀⢀⣠⣤⡶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⢀⠼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣍⠙⢦⠀⠀⣸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢀⣴⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠖⠐⠀⠀⢀⣠⣴⣿⣿⣷⣦⡀⠀⠀⠊⠉⠰⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠿⡿⠿⠃⠀⠀⠀⠀⠀⢰⢸⣧
⠀⠀⣀⣀⣀⣠⣿⣿⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀
⠛⠉⠛⠉⠉⠀⠀⡟⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⣶⣷⣶⠦⠀⠀⠀⠰⣧⠀⠀⣠⣶⣿⣿⣷⡀⠀⠀⠙⠛⡟⢻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⣿⣿⣿⢷⡀⠀⢸⣇⠀⠀⣽⣿⣿⣿⡿⠃⠀⠀⠀⠠⡇⠀⠉⠉⠛⠻⠷⢤
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠙⠻⠛⠋⠁⠀⠈⡏⠀⠀⠙⠻⠟⠟⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣠⣤⡀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢿⣿⣿⣶⡄⠀⠀⠀⠀⠸⡏⡆⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡌⠙⢿⡿⠟⠂⠀⠢⢾⣿⣿⣿⣷⡤⠤⠼⡿⣿⡿⠃⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⠀⠉⠢⣄⠀⠀⠀⠉⣯⠀⠀⠀⣀⡤⠖⠉⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠉⠒⠤⠼⠛⠦⠔⠛⠁⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⣠⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⣶⣶⠶⠶⢶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠙⠳⣄⠀⠀⠀⠀⣠⠞⠋⠉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⡆⠀⠘⡆⠀⠀⢰⠃⠀⢰⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⣀⣿⣤⣤⣿⣀⠀⠈⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠟⢻⠛⢻⣿⣿⣿⡉⢻⡿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⡿⠿⠻⠿⣾⢷⣞⣿⣿⣈⣙⣶⣿⣷⠞⠛⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢳⣯⣤⡴⠲⡄⠈⢧⢸⣿⣿⣏⣡⠟⡟⢯⡙⠛⢯⡉⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣿⡿⠁⡇⠻⣿⠟⠓⣎⣿⣿⣿⣿⠃⣰⣧⠈⣿⢶⣤⠷⠶⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⡟⠙⢦⣧⠞⠹⣦⣴⣏⢹⣿⣿⡿⢶⣋⡼⢦⢿⡞⢰⠋⣳⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣈⡿⠙⠦⣤⣇⡴⠚⢻⣇⣸⣿⣿⣿⣿⣠⣿⠷⢾⣾⠀⠘⢦⣥⣴⡋⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢀⡗⠦⣄⣈⣇⣠⡤⠾⡇⠀⣿⣿⣿⣿⠀⣇⡴⠋⣸⣏⣹⡞⣡⢤⡙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⡷⠤⣄⣉⣏⣠⡤⠴⣷⣾⣿⣏⢹⣿⡶⠛⠛⢒⡟⠛⢷⡇⢧⣒⣣⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⣄⣀⠈⡏⢀⣠⣾⡇⣽⣿⢻⣼⣿⣿⠛⢒⣾⣷⡤⠞⠹⣴⠋⠉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢿⡘⣯⠟⠛⣯⠏⣼⣶⣿⡿⠯⣄⢹⣿⣶⠞⢧⣸⣇⠀⠀⠘⡗⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣸⡄⠀⣿⣴⣿⣿⣿⢤⣀⣈⣙⣿⣿⣦⣰⣇⣸⣷⠋⢻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣸⣿⣿⣿⡿⠛⣋⣽⠟⠁⡼⠹⣿⣿⣭⡟⣻⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠿⠿⢿⣯⣽⣾⣀⣰⣧⡴⠿⠻⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡉
⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠄⢀⣾⣿⡶⡁⠀⠀⣀⣀⣀⠀⠀⡆⡀⠀⢠⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠠⠀⠄⠉⠀⠾⠂⠀⠒⠋⠉⠉⠀⢀⢨⡄⠒⠀⠁⢀⠤⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠘⣶⠠⢄
⠀⠀⠀⠀⣀⡀⠀⡀⢠⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣙⡇⠀⠀⣸⠂⠈⠳⣄⠀⠀⠀⣂⠀⡀
⠀⠀⠀⠀⠀⠛⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⡄⠀⠀⠀⠀⠄⠀⢾⢁⡄⠂⠀⠁⢿⠀⠁⠸⠋⠀⠀⠀⠘⢧⣄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⣇⡠⠔⠂⠀⠠⣤⡀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠉⠀⡠⠔⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⣦⠀⠀⢀⡀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠠⠄⢾⣁⣤⣀⡄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢦⣀⢀⡀⠀⠀⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠠⢀⣴⡀⠀⠀⠄⠀⠀⠴⠄⠰⠆⠀⠀⠀⠀⠀⠀⠐⠚⠓⠀⠈⠁⠑⢦⠤⠤⠤⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠲⣞⠿⠤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠆⠄⢀⣁⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠣⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠶⠶⠶⣞⠙⠉⠉⢉⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡇⠰⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒


⠀⠀⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠘⠋⠛⠋⠛⠃⠂⠘⠙⠛⠉⠙⠁⠘⠙⠋⠛⠀⡙⠉⠉⠋⠛⠈⠋⠙⠛⠛⠙⠉⠛⠛⡛⠀⠀⠀⠀⣀⡀
⠀⠘⠛⠛⠛⠀⠛⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠐⠛⠓⠛⠛⠛⠃⠘⠛⠓⠘⠛⠃⠛⠛⠛⠻⠇⠘⠛⠛⠛⠀⠛⠛⠛⠛⠓⠛⠛⠛⠃⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣄⡀⠀⠀⠀⢀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣀⠀⠀⣰⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣏⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠈⠻⣿⣿⣿⣿⣟⣉⣽⣿⣿⠿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢴⣿⣿⣿⠇⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡟⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠛⠿⠿⠿⠿⠿⠿⠛⠳⣀⣀⣤⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⢫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⢰⣿⣿⠃⡰⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⡎⢀⣤⣶⣤⡀⠀⠀⠀⠀⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣾⣿⠇⢠⠁⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠻⢿⣿⠟⠁⢰⠁⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤
⠀⠀⠀⠀⣰⣿⠟⢀⡇⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⠿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣷⡀
⠀⠀⠠⠾⠛⠁⠀⢸⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠃⠀⢠⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⣴⣶⣶⡄⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⢀⣿⣿⠿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣼⣿⡟⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠻⣷
⠀⠀⠀⠀⣀⣼⣿⣿⠀⢣⡀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⣼⣿⣿⡇⠀⢸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⣠⣶⣿⡿⠿⠛⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⣠⣾⣿⣷⡃
⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠻⢿⣿⣿⣿⣿⡿⢧⡀⠀⠀⣴⣿⣿⠷⠚⠁⠀⠀⣿⣿⠇
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣏
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢜⣳⠖⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣬⣗⣿⣷⣺⣩⢞⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡟⣿⢩⡿⣷⣿⣿⣺⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢦⣛⢴⡻⡞⠵⣷⣿⣾⣿⣿⣿⡿⣿⣿⣷⢿⣷⣶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠳⢭⣃⣬⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⢿⡿⣷⣻⣿⣿⣛⣷⣦
⠀⢀⣠⡄⡄⣠⢀⣀⡀⠀⠀⢀⡀⠐⣺⡼⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣿⣯⣿⣽⣷⣿⣿⣿⣿⢶⡢
⠈⠘⢿⢻⡇⡟⡹⣸⣿⣷⣮⣿⣷⣾⣿⣷⣿⣽⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠙
⠀⠀⠸⣼⢙⡃⣛⡿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠟⠛⠋⢹⡿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⠁
⠀⠀⢰⡏⣶⣬⣦⣷⡿⠛⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣾⣿⣿⡿⡿⠁⠀⠀⣿⣿⡿⠃
⠀⢠⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠋⠀⠀⠀⣸⡻⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⡷⣶⠀⣶⣾⣻⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣯⣏⣁⣀⣈⢻⣯⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣏⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⢰⣿⡟⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⢿⡦⣦⠀⣦⣼⢿⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⢁⣧⣽⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠁⠀⠙⢿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡆⣺⣿⣟⣿⡿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣻⣟⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡍⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠋⠛⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⡀⣀⢀⣴⣴⣦⡀⠀⣀⣄
⠀⠀⠀⠀⠀⠠⣤⣾⣦⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⡿⣤⣤⣠⣤⣀
⢀⣠⣄⡶⠐⣘⣿⣿⣟⠟⠻⣝⣿⣿⣿⣿⢫⣿⣿⡿⣉⣟⠿⡿⠿⣶⣿⣿⣿⣿⡳⢶⣶⣀
⢿⣟⣿⣴⣟⣯⣿⣿⡿⠀⠴⣾⣿⣿⢼⣟⣿⣿⢏⣴⠯⣿⣷⠧⢠⣴⣟⠉⢉⠛⠻⣶⣦⡝⢣⠶⣳⡦⢄⣀⣀⣀⡀
⢸⣿⣿⣿⣿⡿⣿⣧⡅⠠⢼⣿⣿⠇⣾⢻⣿⣫⣟⣦⣧⣿⢣⣿⣧⠀⣿⠰⣿⣴⡈⣁⡬⢄⣠⡬⢛⣾⣿⣟⣻⣿⣭⣁⣄⡀
⠀⣿⣿⣿⣿⣯⣿⡿⣇⣵⣿⣿⣇⢰⣟⣾⣿⠙⣿⣿⣿⣿⣿⣿⣿⣠⡿⣶⣿⣿⣿⡿⣱⢫⣍⣴⣶⣵⣿⣿⣿⣿⡟⣻⣯⣿⠗⣰⡄
⠀⣹⣿⣿⣿⣾⣿⠠⣩⣿⣿⢿⡀⢸⣯⠸⣿⡮⣿⣿⣿⣿⣿⣿⣿⡟⢿⣾⣿⣿⣿⣿⣿⠿⣼⠿⠟⡿⢿⣿⣿⣿⣿⣠⣤⢀⣿⣟⢤
⠀⢹⣿⣿⡿⣿⡻⡷⣾⣿⣿⣡⠤⣶⣿⣸⣿⣷⣿⣿⣿⣿⠛⠻⣿⣿⣶⣿⣿⣿⣿⣿⣯⣀⢴⣶⣦⢵⢶⣺⣿⣷⣿⣿⣿⡿⠿⠟⠋
⠀⣼⣿⠿⣿⣿⢢⣘⣿⣿⣷⠻⠴⠸⢟⠟⣾⣿⣿⣿⣿⣿⣿⣃⣤⣿⣿⡿⣿⣿⡿⣿⣿⣿⣦⣀⣠⣾⣿⣿⣿⠖⠈⠁
⠀⠛⠁⠀⠀⠉⠛⠚⠻⠿⠿⠤⠤⠶⠬⠷⠯⠿⢿⣽⣿⣿⣿⡟⠛⠉⠁⠀⠈⠷⣤⣼⣻⣿⣿⣿⣿⣿⣿⣿⣷⣆⣰⣶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠈⢹⡿⠷⢮⠙⠛⠯⡉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣴⣿⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡝⢯⣷⠵⣯⣍⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⠈
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠋⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠳⠤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢀⣀⣀⣀⣀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠋⠉⠉⠙⠛⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣀⣠⣤⣴⠶⣶⡶⢶⣦⣤⣄⡀⠀⠀⣿
⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⠟⠋⠉⠀⢀⣤⠾⢦⣄⠀⠈⠉⠛⠷⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣾⠋⠀⢀⡴⠛⠉⠙⢳⡄⠀⠀⠀⣿⡇⠀⠀⠀⣰⠞⠉⠉⠳⣆⠀⠈⢻⣷⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⡇⠀⠀⠀⠀⡷⠀⠀⠀⡟⣧⠀⠀⠀⣏⠀⠀⠀⠀⣹⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠳⣤⣀⣤⠾⠁⠀⠀⢸⡇⣿⠀⠀⠀⠙⢦⣄⣠⡴⠋⠀⠀⠀⠈⣿⡀
⠀⠀⠀⢀⣠⣤⣤⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣀⡀
⢀⣤⣾⠿⠛⠋⠉⢻⣿⠀⠀⢀⡴⠚⠋⠙⠳⣄⠀⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⢀⡴⠚⠛⠛⠲⣄⠀⠀⢸⣿⠉⠉⠙⠻⢿⣶⣄
⠿⠟⠁⠀⠀⠀⠀⢸⣧⠀⠀⣼⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⡆⠀⢀⣿⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣆⠀⠀⠀⢀⣼⠃⠀⠀⠀⡿⠀⠀⣧⠀⠀⠀⠹⣄⠀⠀⠀⢀⣼⠃⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠈⠛⠒⠒⠋⠁⠀⠀⠀⢰⡇⠀⠀⢿⠀⠀⠀⠀⠈⠓⠶⠖⠋⠁⠀⠀⣼⠇
⠀⠀⠀⠀⢀⣴⣶⣿⢿⣷⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢸⠇⠀⠀⢸⡆⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⢰⣿⣿⣷⣦⣄
⠀⠀⠀⣴⣿⠋⠁⠀⠀⠹⣧⠀⠀⢰⠏⠀⠀⠈⣷⠀⠀⣿⠀⠀⠀⠈⣇⠀⢰⠏⠁⠀⠙⣦⠀⠀⢠⡿⠁⠀⠀⠉⠻⣷⡄
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠙⣷⡀⠸⣆⡀⠀⣠⡟⠀⢀⡏⠀⠀⠀⠀⢿⠀⠸⣆⠀⠀⢀⡟⠀⣰⡟⠁⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠉⠋⠉⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⠈⠛⠛⠉⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣾⣧⣄⣀⣀⣀⣀⣠⣽⡶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣄⠀⠀⠀⠳⠤⣀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⠀⠀⠀⢰⡌⣄⣀⣠⣊⡷⠀⠀⠀⣶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢀⠀⠀⣾⣻⣿⣏⣷⠄⠀⢄⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣴⣇⣠⣠⣿⣟⣿⣿⣿⣤⣤⣼⣦⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣞⡍⠐⠁⠙⣇⣈⣙⣿⣿⣿⣉⢡⡴⠋⠀⠀⠻⢷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢠⣿⡏⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⣿⣇⢻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢠⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡄⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣾⣿⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⡀⠈⢻⣧⣀
⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠙⠙⡿⠉⠹⠏⠋⠀⠀⣀⡀⠀⠀⠈⢹⠟⡇⠀⠀⠈⠛⠻⠶⣤⡀
⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⢸⡇⢸⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠐⠀⣼⣿⣿⣿⣿⣿⣿⠀⢠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠘⡤⠀⢘⣿⣿⣿⣿⣿⣿⢠⠀⢨⠀⢿⣿⣿⣿⣿⡿⠋⠀⠌⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⢿⣇⠣⠀⠀⠙⠻⠿⠿⠟⠋⠸⠀⢸⠀⠀⠙⠻⠋⠙⠁⠀⢀⠃⡾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢿⣮⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⡄⡞⢁⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠈⢻⣿⣿⣿⣿⣦⡀⠀⠀⢸⢠⢸⡀⠀⢀⣾⣿⣿⣿⣿⡟⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠙⢿⣿⣿⣿⣿⣀⠀⢴⢸⠈⠄⠀⣾⣿⣿⣿⡿⠋⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠉⠻⢿⡻⠿⣷⣯⢸⡈⡇⣴⣬⣯⠝⠋⠀⠀⠰⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠉⠑⠒⠿⠚⠳⠛⠛⠉⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣠⣿⣿⣿⣿⡿⠋⠁⣿⠛⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣘⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣄⠸⣆⡴⠛⣡⣤⣤⣼⣿⠟⢻⠽⠻⣟⣿⣿⣛⣭⣙⣻⣿⣷⣾⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⠿⣿⣿⡟⠋⠀⢿⡀⠀⢿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣷⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣀⡁⠈⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣇⠈⠉⢻⡿⠛⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⢸⣇⣾⡟⢃⢀⣼⢿⣿⣟⣋⣉⣉⣭⣙⢛⣛⣿⣿⡋
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢀⡾⢫⡏⠀⢀⣿⣿⡾⠛⠙⢿⣿⡿⠿⠿⠿⠛⠛⠛⠁⠀⠀⣠⠖⠢⢄⡀
⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⠟⢡⡟⠀⢀⡾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢦⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⢛⠿⢧⣄⣀⣀⠀⠀⠀⠀⢀⡿⠀⢀⣾⠀⣠⠟⣼⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣎⠀⠀⠀⠘⣇⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠑⠄⠈⠙⠿⣍⡲⢄⡀⢸⡇⢠⠏⣿⢾⣱⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠈⠙⠲⣤⣀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣉⣿⢠⠏⢀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣒⣒⡚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⠎⠀⢀⣿⣏⡀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⣌⣽⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠄⠀⠌⣾⠙⠛⠶⣤⡔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⢠⣿⣴⣼⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⣶⡀⡖⠀⠀⠀⣴⡄⠀⢸⡇⠀⠀⣰⣿⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⢀⣾⡆⣀⣀⣾⣷⣶⣾⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⢨⣿⣶⣇⣼⡇⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⣤⣀⣼⣟⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⣿⣿⣿⡟⢡⣬⣿⣿⣿⣿⡇⣰⣿⣽⠇⢀⢀⣠⣤⣿⣾⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣇⣾⢻⢷⣿⣿⣴⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣳⣿⣿⣿⡆⠀⣀⡀
⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⠡⣳⣿⣿⣿⣿⠧⣸⣿⣧⣦⠀⠀⠀⢀⣠⣶⣦⣴⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣰⡆
⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠈⢹⡏⢘⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣦⣾⣿⣿⣿⣿⣿⡆⠀⣰⣿⣷⠀⠀⣀⠀⣸⣿⣶⣿⣿⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⢠⣿⡥⣣⣃⣿⠁⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡾⡿⡐⣵⣽⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣭⡞⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡛⠛⢛⣿⡿⣛⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣽⢻⣿⣿⣿⣷⡟⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⡇
⠀⠀⠀⠀⠀⢸⢹⢳⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⢁⢺⣿⣿⣿⡜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣐⡒⠀⠀⢀⣐⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⡤⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⣯⡟
⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣟⣿⣿⠿⣿⣿⣿⣽⡿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣯⣿⣿⣿⣾⣿⣟⣽⣿⣿⠇
⠀⠀⠀⠀⢐⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⡟⣿⡝⣿⡀⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⣿⣿⡟⣯⣿⢦⢻⣧⠠⡿⡿⣿⡍⣸⣷⣷⣿⣭⣿⣿⣧⣿⠃
⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣱⣾⣿⡹⣿⣻⣧⣌⠉⠽⢿⣎⣿⣿⣿⣟⣿⣿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣶⣤⣄⠓⠶⡾⣿⡿⠁
⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢯⡝⢿⡿⣿⣿⣿⣿⣿⣿⣿⢗⣾⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢢⣽⣿⣿⣿⣿⣿⠟⣡⣿⣿
⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣽⣿⣿⣟⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⣷⣿⣿⣿⣿⠁⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠘⣿⣾⣻⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⡟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⡀⠀⣿⣿⣿⣿⣿⣷⣤⣀⡀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣟⣿⣛⢿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣛⣻⣿⣶⡿⢿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣟⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⡿⠇⠀⠀⠈⠉⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⡿⠿⠟⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣄⡀⠀⠀⠀⢀⣤⣤⡤⣤⡀⠀⠀⠀⢀⣠⣤⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⣀⣰⣿⡼⠧⠸⠧⣿⣦⣀⢀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠞⠛⠁⣿⠂⢀⡀⠐⣿⠈⠛⠳⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣧⣤⣤⣴⣿⢤⣾⣷⡐⣿⣦⣄⣤⣼⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠁⠀⠉⠛⠻⠿⣿⣧⣹⣏⣼⣿⠿⠟⠛⠉⠀⠈⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣤⣤⣴⣮⣩⣯⣿⠏⢹⣿⣿⣯⣷⣦⣤⣤⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠸⡏⠉⢻⢿⠛⠋⠉⠀⠀⠈⠙⠛⠛⡟⠉⣸⠃⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⡀⢸⣶⣶⣶⣶⡆⢴⣶⣾⣿⣿⡇⢀⣿⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⡿⢸⣏⠁⠀⠐⡄⠀⢁⠈⢈⣿⡇⢾⡏⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣶⠇⢸⣿⣿⣿⣿⡃⢘⣿⣿⣿⣿⡇⠸⣷⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⡾⠚⢀⣼⢋⠉⠉⠙⠋⠈⠋⠙⠋⣛⣧⣀⠛⢷⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣁⣈⡾⠿⣿⣾⣤⣤⣤⣦⣴⣤⣿⣿⡿⢿⣗⣌⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⠋⠀⠐⡟⠉⠉⠙⢹⡟⠛⠙⠛⣻⠃⠀⠙⣷⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⢧⡀⠀⢿⣶⣶⣤⣸⣇⣴⣶⣶⡿⠀⢀⡼⠃⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⢷⡄⠘⣏⠙⠛⢻⡏⠋⠉⣻⠃⢀⡾⠁⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⣻⡀⠹⣿⣿⣿⣿⣾⣿⠏⢀⣿⠃⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⣺⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣗⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⢰⡞⣉⡉⢠⣦⣀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡀⡀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⡿⠀⠸⠟⠁⠊⣉⠁⢠⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⣱⣇⣀⣤⠎
⠀⠀⠀⠀⢀⣴⣿⡅⢀⣤⡘⠿⠃⣼⠿⠈⢛⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⠋⠉⠉⠁⠢⢄⣀
⠀⠀⠀⠀⠈⠉⠻⠤⠈⠟⠃⣴⡿⠛⠿⣿⣶⡧⠀⠀⠀⠀⠀⠀⢹⣿⠁⡀⠀⠀⠍⣿⣆⠙⠻⢶⠈⠉⠉
⠀⠀⠀⠀⠀⢀⣀⡠⠖⠀⣻⡋⠐⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠀⠀⠀⠀⠉⠀⠙⠂⠈⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠲⠋⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣔⢠⣶⡄⠀⠀⠀⢦⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⢀⠼⠿⠗⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠍⠉⠀⠒⠴⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⢀⣴⡤⢀
⠀⠀⠀⡀⠀⠀⣠⣤⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠈⠙⠁⠀⠱⣄
⠀⠀⠀⣷⠀⠀⠿⠇⠠⢄⠀⢿⣿⣿⡞⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⣄⡀⠀⣴⣦⠀⢀⡀⠐⣿⣆
⠀⠀⠀⠿⣈⠐⠂⣄⠀⠀⠀⠀⣻⣿⣿⠀⣂⣠⠂⠀⠀⠀⠀⢀⠰⠆⠉⢿⣿⣶⠟⢋⠑⢈⣋⣄⢌⠻
⠀⠀⠀⠘⢻⣿⣤⡛⢁⣄⣀⣼⣿⡿⢻⣗⣩⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡿⣶⣤⣬⣽⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⠋⠉⠙⠳⠾⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠙⠛⢿⣏⢉⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠿⣿⣅⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⢀⣀⣠⠀⠐⢆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⠒⠆
⠀⠀⣰⣷⣾⣿⣿⣿⣯⡉⠶⢤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⠀⠘⠿⠟⠀⠀⠘⠶
⠀⠀⠀⢭⠿⢿⣿⣿⡟⣏⠀⡀⠈⢙⡂⢁⠀⠂⠀⠀⠀⠀⠀⠀⢳⣿⣄⠀⣴⣶⡅⠀⠀⢀⣰⣯
⠀⠀⠀⠁⠀⡯⢻⣿⣿⣿⡑⠯⡀⠥⡆⠀⠀⠀⣄⠀⠀⣡⠀⠀⢠⠀⠀⠀⠘⠛⠁⠀⠀⢸⣷⡏⢁⣦⠔
⠀⠀⠀⠀⠘⠀⠈⢼⣿⣿⠇⠀⠀⠉⠁⠀⠀⠀⠒⠈⠉⠁⠀⠀⠘⢧⠀⠸⠦⠤⠀⣠⣤⠀⢀⣀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣄⣀⡙⢻⠟⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣾⢀⣤⣰⣧⣄⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⣿⣿⣿⣯⣸⣿⡗⠛⣼⠛⣥⣾⡇⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠻⣿⣿⡿⢨⣭⣭⣈⠛⣱⣆⢈⢸⣿⡿⣃⠉⣵⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⡁⣠⡍⣴⣄⠻⣿⣿⣿⣿⡿⣿⠆⣡⣾⣇⣴⣿⡿⢣⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⡿⣯⣿⣅⣿⠇⠹⣿⠇⣮⠉⢛⡍⣶⠛⠃⣻⣟⢁⡍⠉⣐⣤⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡣⠙⡿⠿⢧⡲⢿⣿⣷⢯⣰⣿⠇⢸⣇⣴⣯⣥⣟⡃⢀⣿⣿⣟⢁⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣾⣿⢇⣚⢳⣤⣀⣿⣄⣘⢿⣷⢿⡄⣦⣾⡟⣁⣠⣾⣯⣷⠿⣹⣿⠀⠸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠛⢹⣿⡿⠇⢰⠟⠉⠉⠛⠿⣷⣾⣷⣾⣿⡿⠋⠉⠀⠈⠛⠃⠻⣿⣧⠀⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠿⢿⢿⣿⣦⣄⣀⠀⠀⣀⣀⢠⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢻⣽⣭⣶⣾⡿⢿⣁⡦⠉⠉⠙⠿⣿⣿⣿⣿⣇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⣶⣿⣿⣿⣿⣿⡿⠇⣠⣤⣀⠀⠀⠀⠈⠻⣿⡿⠀⠰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣡⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⠉⠙⠛⠟⠳⠆⠀⠀⠘⢷⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢈⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⢿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⡆⠀⠀⠀⠀⢀⣼⣿⣿⡇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⡇⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⡾⣹⣿⡿⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠀⠀⠋⠻⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠀⠀⢸⠷⢿⣿⣿⣿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⢟⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣤⣬⣥⣤⣵⠶⠛⠉⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣿⡟⣿⠏⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⡠⠐⠠⢀⠀⠀⠀⠀⢰⣿⠟⡤⣄⠀⠀⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⡀⠀⣠⣧⡀⠀⡀⠀⠀⠀⣿⠛⠛⠻⣷
⠀⠀⠀⠀⠐⡀⣿⡿⢀⠂⠀⠀⠀⢸⠁⡾⡷⢈⡇⠀⠀⠀⠀⢸⣤⣰⡇⠀⠀⠀⠀⠿⡇⣾⢽⡴⡿⠁⠀⠀⠀⣿⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠐⠠⠐⠀⠀⠀⠀⠀⠈⠢⢤⠥⠞⠀⠀⠀⠀⠰⠾⠿⠿⠷⠄⠀⠀⠀⠀⠛⠊⠘⠚⠂⠀⠀⠀⠀⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⡀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠐⣜⡔⢮⡵⢦⣣⠂⠀⠀⣠⠴⠋⠙⢦⡀⠀⠀⠀⢰⢻⠟⠀⠹⡆⠀⠀⠀⠴⣿⢫⡝⢿⠦⠀⠀⠀⠀⢞⣗⣗⣻
⠀⠀⠀⢀⡟⣆⡜⢇⣸⢳⠀⠀⠀⢧⣀⣀⣀⣠⠟⠀⠀⠀⠘⣄⢸⠗⡠⠃⠀⠀⠀⠀⣯⣍⣽⣼⡀⠀⠀⠀⠀⠒⢒⣖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣬⡍⠀⠀⠀⠀⠀⠀⠀⣠⡜⠂⠀⠀⠀⠀⣰⡖⠒⠒⢲⣄⠀⠀⠀⢠⣶⠿⠿⣶⡄⠀⠀⠀⠀⢀⡎⠉⢣
⠀⠀⠀⠀⠀⠈⢸⡟⠂⠀⠀⠀⢀⡤⢜⢻⣉⡥⢄⠀⠀⠀⠉⡷⣶⣶⢾⠁⠀⠀⠀⢸⣿⢤⡤⣿⡿⠀⠀⠀⠀⣼⢷⣶⣾⡆
⠀⠀⠀⠀⠀⠠⠎⠹⡄⠀⠀⠀⠘⠦⠜⠈⠙⠤⠜⠀⠀⠀⠀⠟⠉⠉⠛⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠜⠛⠛⠙⠆

⠀⠀⠀⠀⠀⠀⡴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠸⣿⠿⠿⣿⠃⠀⠀⠀⢠⣎⣉⣉⣧⠄⠀⠀⠀⢀⠀⣿⣷⢀⡀⠀⠀⠀⢠⣿⠟⠻⣿⡄⠀⠀⠀⠀⣀⠛⠘⢷⡀
⠀⠀⠀⠀⠀⣧⡻⢧⣽⠀⠀⠀⠀⣾⣿⡥⣽⣿⡇⠀⠀⠀⢸⣏⣻⣟⣹⡇⠀⠀⠀⠘⠻⡄⢠⠟⠃⠀⠀⠀⠰⢯⣤⢠⣬⣿
⠀⠀⠀⠀⠀⠙⠉⠉⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂

⠀⠀⠀⠀⢀⢰⣸⣴⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠠⡆⠠⡶⠀⠀⠀⠀⠀⠤⣄⡤⠤⣀⠤⠀⠀⠀⠀⠀⡤⡤⡤
⠀⠀⠀⠀⠘⣿⡿⢿⣧⡖⠀⠀⠀⠺⣿⣦⠛⠛⠁⠀⠀⠀⠀⠙⢲⣶⣶⠀⠀⠀⠀⢦⣉⡊⠙⡉⡰⠀⠀⠀⠀⣦⣴⣿⣤⣄
⠀⠀⠀⠀⠀⠹⣤⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠈⠙⠇⠸⠏⠁⠀⠀⠀⠀⠁⠈⠉⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡶⢾⣿⣷⡷⢶⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣀⡤⢾⣿⣷⣾⣿⣿⣷⣾⣿⡷⢤⣀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣠⣶⣿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣶⣄⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣧⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡶⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠉⠉⠉⠙⢛⣿⣿⣿⣿⡛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⣿⠁⠀⣴⣿⣿⡆⠀⠀⠀⠀⠈⠛⠻⢿⡿⠟⠛⠁⠀⠀⠀⠀⢰⣿⣿⣦⠀⠈⣿⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢰⡟⠀⠰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⠀⢻⡆⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⡇⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢸⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⠀⠀⢸⡇⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠏⠀⠀⢸⡇⠀⠀⠹⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣸⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⢿⡄⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⣶⣶⠀⠀⢠⡿⠁⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⠻⣦⠀⠻⢿⣿⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⠟⠀⣴⠟⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠀⣠⡾⠋⠀⠀⠀⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣾⣷⡶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣾⣿⣿⣶⣶⣿⣿⣶⣾⣶⣠⣀⣀
⠀⠀⢠⣤⠴⣀⣹⣿⡟⠙⢿⣿⣿⣯⣿⡿⣫⣝⣛⠿⢾⡿⣿⣿⡲⢦⡄⢀
⠀⠀⢸⣿⣿⣿⣿⣯⠃⣨⣿⡿⣹⣿⣟⣴⣃⣿⣫⣔⢺⡄⣤⡈⠛⡓⠈⣱⢯⣵⣶⣶⣤⣀
⠀⠀⠈⣿⣿⡿⣽⡿⣦⣾⣿⠁⣟⣿⣟⣿⣿⣿⣿⣿⣸⢷⣿⣷⣿⣵⢍⣵⣮⣿⣿⣿⡛⣿⣷⢂⠄
⠀⠀⠀⢿⣿⣿⣿⣄⣼⣿⠓⢀⣷⢹⣯⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠏⢚⣋⣹⣛⣿⣿⣷⣶⣬⣿⡖
⠀⠀⠀⣾⡿⣿⡇⣹⣿⣿⠃⠘⢿⢾⣿⣿⣿⣿⣖⣨⣿⡿⣿⣿⣿⣿⣯⣉⣹⣿⣿⠭⠙⠉⠁
⠀⠀⠀⠉⠀⠀⠉⠉⠛⠛⠒⠚⠒⠛⠛⢻⣿⣿⣿⠉⠁⠀⠈⠲⢾⡿⠿⠿⠿⣿⣿⢶⣶⣶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠹⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠭⣿⠭⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⠀⠠⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⢻⡿⠂
⠀⠀⠀⠈⢣⡀⠀⣀⣵⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⠋⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠈⢿⡿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣾⣿⣦⡄⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁
⠀⠀⢀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀
⢠⣾⡿⠿⠿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠈⠉⠀⠀⠀⠀⠀⢀⣠⣶⣷⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠀⢀⣴⣾⣿⠿⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣴⣾⣿⣿⣦⡀
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢃⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⡟⠁⣰⠇⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡼⢻⣀⡄⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠈⣇⣾⡟⢠⡯⠊⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⠀⡀⠀⠀⠀⠈⢛⣤⣰⣶⣿⣟⣠⡿⡤⢃⠤⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠮⣅⣀⠀⠀⠀⠡⠉⠛⣮⣮⡉⡄⡐⢺⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠖⠾⢖⠷⣾⣿⣿⡞⢀⡧⠂⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠳⣴⡄⠠⢀⠠⣤⡄⣼⠛⢀⣾⠖⠀⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⣀⣈⠳⣄⡀⠁⠈⣻⡇⠀⢰⡇⠀⣺⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣇⠱⢢⡀⠀⠙⠫⠉⠛⠒⢦⣹⡄⣠⣿⣇⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⣿⣄⡌⠀⢁⡀⠀⠀⠉⠓⣺⡟⠉⠁⢙⣉⢈⣿⣶⣶⣿⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢿⡟⢾⠘⠀⢀⠀⠀⣼⣿⣿⣶⣶⡶⠶⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠙⢿⡅⢾⠘⢷⡀⣿⡿⠍⣿⡿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣄⠹⣷⡄⣾⡵⣿⡧⢰⣟⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢻⣿⣇⢿⣧⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡙⢿⣾⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠒⠖⠲⢾⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣧⡄⠀⠀⠀⣄⣀⣠⡾⠛⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣥⡀⣀⢠⣿⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠋⣸⡟⠂⠛⢻⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⢾⠿⠁⠀⣠⠎
⠀⠀⢀⠱⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⠀⢀⡼⠃
⠀⠀⠲⣿⣭⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⣀⢷⡏⠁
⠀⠀⢩⣿⣿⣿⣿⣿⣟⣷⣦⣄⠀⠀⣰⠿⠿⣿⣧⠀⢀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠐⠉
⠀⠀⠀⢻⣧⣾⣿⣿⣧⣿⣿⣿⣿⣾⣷⡀⠨⢿⡟⠛⠉⠉
⠀⠀⠀⠀⠙⠟⣿⣿⠿⣿⣿⣿⣿⣿⣿⢷⠆
⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃⠘⠋⢸⣿⡟⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⣷⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠐⣦⠴⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣶⣶⣦⢀⡀⡀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣇⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣠⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠳⠀⠁⡠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⢹⣯⣀⣀⣀⣀⠹⢿⣿⣿⣿⣿⣿⣿⣶⣶⠒⢡⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⣿⣿⣿⣷⣦⣼⣿⠿⢿⡟⠃⠘⢿⠀⢊⣌⠀⣰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠿⢻⣆⡀⠀⢠⣿⣷⣿⡿⢷⡟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣿⣿⣿⣿⣿⠟⣉⣰⣿⣿⣶⡟⠁⣛⠽⣿⢋⠁⢹⣷⠄⠙⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣈⣿⣟⣡⣤⣾⣿⣛⢭⡅⢚⣁⣾⣿⠶⣟⠻⢄⡊⣩⡈⠁⢤⣄⣀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣻⣿⣷⣶⣷⣹⣷⣮⣿⣿⣿⣷⣾⣿⡿⠟⠛⠳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢁⣿⠃⠹⠈⠉⢰⡿⢿⣏⣟⣿⣿⣿⣿⢹⣿⣿⡿⣿⣿⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠘⠇⠀⠠⣼⠉⢿⡏⣿⠜⣿⠿⠛⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢿⠀⠈⠁⠈⠳⠈⠃⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠐⡠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠒⠐⠒⠚⢐⣶⣬⣭⣧⠠⠔⠈⠉⠉⠉⠀⠀⠀⢠⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠁⠀⠀⡀⠀⠀⠀⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢰⣾⡅⠀⡦⡄⡦⣤⣴⠀⠀⢡⣶⠀⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏⣛⠁⢰⣷⣷⣷⡿⣿⣆⠀⢸⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠿⠇⣠⣿⣤⠼⠛⠂⢈⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⠀⢻⣷⡀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡿⢨⣬⠉⢴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠄⠉⢪⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⣯⠇⠀⠻⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠈⡴⠋⠀⠀⢰⣮⡆⣠⡄⠀⣴⣦⠀⠀⠀⣴⣦⠀⢠⣤⢠⣏⣦⠀⠀⠐⡌⢣⡀
⠀⠀⠀⠀⠀⠀⠶⠦⠁⠀⠀⠀⠈⠏⠄⠻⠃⠀⠹⣿⠃⠀⠀⣿⡟⠀⠀⠋⠈⡧⣿⠀⠀⠀⠈⠎⠣⡄
⠀⠀⠀⠀⠀⣀⠓⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣀⣌⡇⢄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⢰⣷⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠀⠇⣿⣾⠇⠀⢠⣤⢸⠀⣴⡀⢰⠛⢃⣹⠛⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠹⣿⢦⣤⣸⡛⣼⣀⣼⣱⣼⣬⣭⠝⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠟⢿⣷⣿⢻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠻⠝⠉⠈⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣀⣀⣀⣤⣶⣶⣶⣶⣤⣀⣀⣠⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⡿⠋⠉⠀⠀⠉⠙⢿⣿⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣤⣤⣄⣀⣤⣤⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣠⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣄⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⠋⠀⠈⠙⠛⠿⠿⠿⣿⣿⣾⣿⠿⠿⠿⠛⠋⠁⠀⠙⢿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢀⣀⣄⣀⠀⠀⣿⣿⠀⠀⣀⣠⣀⡀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⣰⣿⠟⠛⢿⣧⠀⣿⣿⠀⣼⡿⠛⠻⣿⣆⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢻⣿⣄⣀⣾⡿⠀⣿⣿⠀⢿⣧⣀⣠⣿⡏⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡀⠀⠙⠛⠛⠋⠀⠀⣿⣿⠀⠀⠙⠛⠛⠋⠀⢀⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠀⢠⣾⡿⠿⣷⣆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣰⣾⠿⢿⣷⡄⠀⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⢹⣿⠀⢿⣿⡀⠀⣼⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣇⠀⢀⣽⡿⠀⣿⡏⠉⠻⣿⣆
⠀⠀⢠⣶⣦⣤⣄⣼⣿⠃⠀⠀⠸⣿⡆⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⢸⣿⡇⠀⠀⠙⣿⣷⣤⣤⣶⣶⡆
⠀⠀⠀⠈⠉⠉⠛⠛⠃⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⣿⣿⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⢀⣹⣏⠁⠀⠀⠀⠈⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣧⠀⠀⠀⣰⣿⠛⠛⢿⣧⠀⣿⣿⠀⣼⡿⠛⠻⣿⣆⠀⠀⠀⣼⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⢿⣧⡀⠀⢻⣿⣄⣠⣾⡿⠀⣿⣿⠀⢿⣧⣄⣠⣿⡟⠀⢀⣾⡿⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠻⣿⣦⡀⠉⠛⠛⠋⠀⠀⣿⣿⠀⠀⠙⠛⠛⠉⢀⣴⣿⠟⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣿⣿⣶⣾⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡀
⠀⠀⠀⠀⠀⢾⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⢿⠷⣶⣾⣿⣴⣾⣿⣿⠶⠶⣤⡀⢀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡤⠖⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⡋⢻⣿⣿⣿⣧⣀⠀⠀⢹⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣾⡏⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠸⣿⣿⣿⡿⠋⣿⣿⣿⣿⣧⣀⣤⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠛⣿⣿⡆⢀⣽⡞⣿⠗⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣰⡿⠋⠀⢀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡟⠿⣧⠉⠁⢠⣿⣿⣿⡿⠀⠉⢻⡟⠁⠈⠛⠷⠆⠖⠚⠁
⠀⠀⠀⠀⣰⣿⠀⠀⠀⠸⣿⣿⠟⠁⠀⠀⠀⡀⠄⡒⠁⣿⣿⣿⣯⣿⠟⠁⠐⠙⢷⡀⠀⠀⠀⠉⠁⠀⢀⣾⠃
⠀⠀⠀⢠⣿⣟⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⡩⠒⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⢤⣀⣈⣖⣿⠏
⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣀⡤⢚⡥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠛⠿⠿⠋
⠀⠀⠀⢸⣿⠣⠀⠀⣠⢞⡭⠚⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⠷⢶⣤⠤⠶⠶⠚⠓⢦
⠀⠀⠀⠘⣿⠇⣠⣾⠕⠃⠀⠀⠀⠀⢸⣿⢿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣴⣾⣿⡆⠀⠀⠘⠳⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠹⣠⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⡼⠟⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠻⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠙⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⢀⡀⢠⣴⣴⠿⠋⠁⠀⠀⠉⠛⠷⣦⣤⡀⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣟⣤⣤⣶⣴⡶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠤⢤⡤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠈⣤⠄⠀⠙⠀⡀⡀⠂⠆⠀⠜⠃⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠈⠀⢀⣀⡨⠡⡤⠰⠀⠄⠁⠀⢀⠀⠀⣈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡁⠀⠀⠀⠀⠀⠁⠈⡁⠀⠤⡔⠀⠀⠀⠀⠓⠐⠀⠂⠁⠀⠲⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⡆⡠⠄⣀⠀⠀⠀⠈⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢀⠧
⠀⠀⠀⠀⠀⢠⣀⡀⠀⠐⢀⡜⠀⣁⡀⠀⠈⡂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠃⠀⢀⢀⣳⣾⣧⠀⠠⠤⠄⠒⠒
⠀⠀⠀⠀⠀⠀⡀⢌⠁⠒⠒⠧⢀⡙⠛⠮⡀⠑⠀⠀⠠⢀⠀⡂⢄⠀⡀⠀⠔⠀⡠⠂⢀⠴⠓⠉⠀⠀⠀⠀⠀⠀⠊⠘
⠀⠀⠀⠀⠀⠀⡇⢀⡱⡀⠀⠀⠀⠀⠉⠒⠽⣇⢜⠚⡀⢁⠈⠂⠕⠈⡀⠐⠐⣡⢾⠖⠁⠀⢀⠀⠀⠀⠀⠀⡐⠁⡊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⠑⢮⡂⠑⠈⡂⠀⠄⠦⠰⣋⠖⠁⠀⠀⡎⠀⡑⠀⠀⢀⠊⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀⠙⢄⠀⡪⡰⢘⢅⡢⠉⠠⡀⠀⠘⡄⠀⢃⣄⠔⠁⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠙⢀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢢⠞⠀⠇⢀⡜⠀⠀⠈⢛⠟⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠍⠀⠀⠀⣑⢄⠀⠀⠀⠀⠀⠀⢹⣴⠋⠀⠀⠀⠉⠀⠀⠠⠂⠁⠀⠀⠀⠄⣀⡠⠃⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠠⠀⠀⠂⢀⡹⠦⡀⠀⢀⠀⠀⡇⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⡀⠄⡥⠖⠉⠀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⠚⠉⠉⠉⠉⠙⠓⠒⠂⠤⠤⠄⠤⠖⠛⠈⠉⢙⢂⣀⡤⠖⠉⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠇⡠⡸⠁⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⡀⠀⠀⠕⠊⠀⠀⠀⠂⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠁⠀⠐⠀⠐⠒⠀⠀⠀⠀⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁

⠀⠀⠀⡠⠐⠲⢌⡙⠗⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣠⠔⣂⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠶⠶⡦⠄⣀⡀
⠀⠀⡄⠀⢰⡖⠀⠙⢢⣄⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣞⠁⠀⠙⠿⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣷⣶⡾⣿⣦⢀
⠀⠀⡃⠀⠀⠀⠀⠀⠘⢻⠷⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠼⣟⠋⠀⠀⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⣶⣿⣯⣤⠛⠿⠶
⢠⡼⠑⣀⠸⠆⠀⠀⢠⣧⣦⣿⣿⣝⡆⠀⠀⠀⠀⠀⠀⠜⣿⣁⣤⣾⣿⣄⠀⠀⠻⢃⣤⠆⠀⠀⠀⠀⢰⣷⠀⠀⠈⣉⡴⡾⠋⠻⠉⠹⠳⡄
⠀⠀⠀⠀⠁⠒⢦⡴⢿⡟⣉⣿⣿⡟⢧⣥⠀⠀⠀⢀⣄⣰⣿⣿⣿⡉⢻⣿⠶⠖⠉⠋⠀⠀⠀⠀⠀⠀⠀⠑⣷⢒⡾⠏⡼⠁
⠀⠀⠀⠀⠀⢠⠏⠀⠈⠓⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠬⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠊
⠀⣀⠀⠀⠀⠰⡀⠀⡰⠀⠀⠀⢀
⠀⠉⠳⡄⠀⢴⣿⣿⡶⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⠖⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠰⢄⡀⣠⣴⣦⣄⠀⣠⠂⡀
⠀⠀⠀⠹⠿⠿⣟⣻⠿⠾⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⣤⡙⢿⣿⣿⣿⠋⣬⡀⠻⠆
⠀⢀⣶⡀⠀⠀⢿⡿⠀⠐⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣎⣉⣙⣦⡀⠀⠐⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠻⠟⠀⠘⣿⣿⠃⠀⠻⠟
⢀⡞⠿⠁⣴⣷⠰⠀⣾⡆⠀⢻⠳⣄⠀⠀⠀⠀⡀⢰⠾⣿⣿⣿⠿⢿⣷⣄⠀⠨⠤⠾⢦⠀⠀⠀⠀⠀⠘⡄⢶⡄⠀⠀⢠⣿⣿⡆⠀⠀⢠⣦⡀
⠉⠀⣤⡀⠈⠋⢸⡇⠉⠁⠀⢤⡀⠈⠀⠀⠀⠀⠠⣽⣟⢻⣿⠷⢠⡜⠉⠙⠛⠳⣆⠀⠈⠓⠒⠀⠀⠀⠀⠈⢆⡀⠀⣠⣼⠛⠻⣧⣀⠀⡨⠊
⠀⢀⡇⠲⣄⠀⠸⡇⠀⢠⡾⣿⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠉⢦⢈⡟⠀⠀⠀⠀⠹⠦⣤⡀⠀⠀⠀⠀⠀⠀⣠⠜⢾⠟⢿⣷⣾⣿⢿⣿⡀
⠰⠋⠀⠀⠈⠂⠤⠣⠆⠊⠀⠙⡄⠀⠀⠀⠀⠊⠁⠀⠀⠀⢀⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠺⣿⣿⣇⠿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣞⡛⢻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⠙⣻⢿⣝⣛⣯⡛⠩⢟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣷⠶⣾⣱⣛⣮⣉⣎⣿⣻⢿⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠠⣾⡇⢉⢿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣾⢼⡃⠀⠀⣴⡻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡾⣣⣄⠀⣸⣻⣿⡔⠀⢻⣿⣿⣿⣿⣿⣿⢡⣿⠃⣼⣿⣤⡾⢯⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣫⢞⣾⣿⡏⣿⣯⠀⠈⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⡿⡇⠸⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣛⣻⣾⣿⠇⠀⢰⣿⣿⣿⣿⣿⣷⠸⣻⡄⢩⡵⣌⠢⢍⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡉⠛⠛⠛⠛⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣦⠹⣹⣆⡘⠣⠿⢸⡟⣧⢀⣀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣳⡶⣦⣼⣿⣿⣶⣦⣤⣤⣴⢞⡽⠋⠁⣿⢻⢻⡇⠈⢙⢷⣈⡚⠽⣖⣶⣤⢤⣬⡝⣷⣻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢯⣿⣿⣿⣿⣿⣿⣿⣷⡋⢀⣴⣾⡟⢸⠘⣿⣷⣄⠠⢻⣿⣷⣮⣭⣥⣥⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠖⣭⣛⢿⣿⣿⢫⠀⣾⣿⣿⠃⢸⠀⢻⣿⣿⡆⢢⣿⣿⡿⢛⣻⣭⡿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠲⣄⢻⣧⠹⣿⣿⠘⣿⣿⠏⠀⣸⡄⠘⣿⣿⠇⡘⣿⢫⣾⠿⠋⢁⣠⣷⢢⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣖⣿⡙⣷⢸⡇⣚⡇⣿⣿⡆⢹⡟⠀⠀⣺⡇⠀⠸⣷⣀⣿⠇⣿⡏⠀⣴⣻⡷⠧⢿⣽⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠿⠚⢡⡟⣰⡇⣺⠇⣿⣿⣿⡿⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⡇⣿⡅⠀⣿⣿⡜⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢋⡴⢏⣼⣿⣿⡿⠁⠀⠀⠀⢸⡇⠀⠀⠀⠙⣿⣷⠘⣷⡀⠹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣴⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⢿⣷⣌⠻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠠⢸⣿⣿⡄⠀⠀⠀⠀⠀⠙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⡀⠀⠀⠀⣾⣿⣿⣧⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⣸⠟⠛⠛⠻⣎⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⢰⠏⠀⠀⠀⠀⠹⡇⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⢀⣀⡤⢤⣀⡀⠀⣀⡰⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠋⠀⠀⠀⠀⠙⣏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⣀⣇⡀⠀⠀⠀⠀⢀⣸⣀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣠⠞⠁⠀⠉⠉⠙⠋⠉⠉⠀⠈⠳⣄⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠉⠙⠲⠤⠤⣤⣀⣀⣤⠤⠴⠒⠋⠉⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣀⡀⠀⢸⡇⠀⢀⣀⡀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢰⠋⠀⢹⠄⢸⡇⠠⡏⠀⠙⡆⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠓⠖⠋⠀⢸⡇⠀⠙⠲⠚⠁⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢼⠀⢀⡔⠒⢦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡴⠒⢢⡀⠀⡧⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⢸⡀⠘⢆⣀⡼⠁⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⣀⡰⠃⢀⡇⠀⠙⢦
⠀⠀⠈⠙⠓⠚⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⢠⠋⠉⢳⡀⢸⡇⢀⡞⠉⠹⡄⠀⠀⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠘⢦⡀⠈⠧⠤⠞⠀⢸⡇⠀⠳⠤⠜⠁⢀⡴⠃⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠾⠧⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⣀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⣠⠃⠰⡧⠒⠐⣭⣸⣛⢟⡛⣧⣄⡶⠒⠲⢄⠀⡇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠊⠁⡠⠟⠀⠀⡰⠉⠀⢹⡟⠉⠛⢿⣷⡄⠀⠀⠑⠷⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠊⠀⠀⠀⠜⠀⠀⠀⠀⠼⢄⠀⠀⠈⠻⣧⡀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⠀⠀⡰⠊⠀⠀⢀⠎⢀⠀⠀⠙⢆⠀⠀⠈⠙⠷⠶⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠐⢊⣄⠀⠀⡔⠁⠀⠀⠑⢦⠀⠀⠑⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣡⠤⢞⡂⠀⠠⠗⠀⢀⣁⣤⣤⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣾⠿⠿⠿⠟⠋⠉⠉⠉⠉⠉⠻⠛⠛⠿⣿⣿⣿⣿⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠖⠶⡅⣽⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⢻⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⣤⣀⣸⣷⣾⣷⣷⣿⣿⣥⣰⣶⣤⡀⠀⠀⠀⠠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠻⠿⠟⠛⢻⡟⠙⠛⠿⠿⠛⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠀⠀⢀⣀⣾⣿⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣶⣦⣦⣤⣤⣅⣤⣤⣶⣿⣟⠫⠅⢤⣤⣤⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣯⣿⢿⡿⢿⣯⣽⣿⣾⠎⠀⠀⠀⠀⠈⠟⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⡎⣷⠻⣗⡿⠁⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢿⡀⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⠁⠀⠀⠀⠀⠀⠀⢀⣔⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣗⢶⡂⠀⠀⠀⠀⣠⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠑⠀⣀⣠⣴⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢿⠗⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⡼⢟⠁⠉⠳⣦⠀⠀⠀⠀⠐⢛⡥⢲⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡾⢧⠄⠀⠀⠀⠀⡤⢚⠋⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀
⠀⠀⢀⣤⣉⠁⣴⡆⠀⠀⠀⠀⠀⠀⢿⠟⣿⣿⣿⡟⣿⠀⠀⠀⠀⢀⣴⣿⢋⡉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠙⠛⠃⠉⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠦⠆⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠴⣿⣿⣁⣨⣿⣿⠦⠀⠀⠀⠀⠀⠈⠃⣤⠈⠁⠀⠀⠀⠀⠀⠀⣾⢿⣧⣸⣶⣆⠀⠀⠀⠀⠀⠀⠙⢯⣅⠸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡇
⠀⠀⠐⢿⣿⠟⠿⣿⡿⠂⠀⠀⠀⠀⠘⢷⣘⣿⣣⡾⠁⠀⠀⠀⠀⢀⣻⣶⣛⣛⣫⣝⡀⠀⠀⠀⠀⠀⠢⢈⢃⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⢿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣤⣴⣦⣠⣶⣦⡀⠀⠀⠀⠀⣠⡶⠿⠿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢾⡆⠀⠀⠀⠀⠀⠀⠀⢶⣼⣧⡴⠆
⠀⠀⠺⢫⡄⠀⠻⣿⣿⡿⠀⠀⠀⠀⠈⣧⣦⣆⣿⣸⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⡘⠀⠀⠀⠀⠀⠀⣼⣏⣿⡿⠿⡏⣤⠀⠀⠀⠀⠀⠀⢠⡉⠉
⠀⠀⠠⠀⠀⠼⠇⠬⠁⠀⠀⠀⠀⠀⠀⢯⡿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠁⠀⠀⠀⠀⠀⠀⢾⣿⣿⣤⣾⣿⣿⠆⠀⠀⠀⠀⢀⠠⠄⠀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈

⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢏⣶⣿⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣠⡄⠀⠀⠀⠀⠀⠈⣿⣄⠸⣿⡷
⠀⠀⠀⠋⠝⢷⣺⡵⠟⠀⠀⠀⠀⠀⠀⡾⠿⣻⠛⣧⠀⠀⠀⠀⠀⠀⠀⢘⢷⣤⢦⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⠾⣶⣤
⠀⠀⠀⠐⠠⠆⡁⠔⠂⠀⠀⠀⠀⠀⠈⣷⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⡐⠻⠸⠃⡈⠂⠀⠀⠀⠀⠀⠀⠞⢈⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢐⠛⠓⠛⠓⠛⡀⠀⠀⠀⠀⠀⢸⠉⠍⠉⠍⠹⠀⠀⠀⠀⠀⠀⡄⣶⣿⣶⠘⠋⠀⠀⠀⠀⠀⠀⠉⢠⣾⣁⣀⡀
⠀⠀⠀⠘⠛⠀⢡⣤⣄⠀⠀⠀⠀⠀⠨⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣘⣀⢾⣶⠞⢀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⡟⠻⣿⡇
⠀⠀⠀⠀⠀⠐⠘⠳⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠀⠀⠀⠀⠀⠈⠻⠿⠆⠉⠀⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣶⣶⣾⢰⢲⢶⠰⣶⣼⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠛⠛⠛⠚⠘⠘⠘⠚⠛⠓⠛⠃
⠀⠀⠀⠀⠀⣄⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⡇⠀⢿⠿⠖⢶⣎⢼⡆
⠀⠀⠀⠀⢀⣿⠟⢹⢿⠷⣼⢳⡦⣤⡄⣀⣀⣀
⠀⠀⠀⠀⡖⠉⠶⡻⠻⠂⠻⠃⡁⠉⠃⠇⡏⡆⢻⢷⣦⣄⣀⣀⣀⣀⣀⣀⣠⣤⢤⣶⢶⡶⣤⢤⣄⡀
⠀⠀⠀⢰⡤⠚⠁⢈⡠⢠⠂⣥⣷⠀⢀⠀⠃⠑⠸⠘⣸⢰⡟⢟⣯⣻⣿⠹⣽⠸⡜⣿⢸⣼⠃⡏⣼⣛⣶⣄
⠀⠀⠀⠈⠛⠛⠏⠀⢔⣡⠴⠋⣷⢀⠌⠀⠀⡆⣰⢠⠌⠘⢣⣇⣿⢿⡝⢸⡸⡇⣇⣟⡜⣻⣰⣧⣿⣿⠟⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⠃⡎⡀⢠⠀⠁⣇⣸⠀⠀⣸⣿⡀⠘⣿⡈⢇⢃⡿⡄⢸⠸⡇⢸⣿⣿⢣⠞⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡔⠁⡎⠘⠰⢿⠈⣳⠄⢰⠹⡄⠘⡏⠋⠄⠠⠻⣧⡟⢸⠃⢸⡏⢿⣼⣎⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠾⡁⠀⠀⠈⠀⣭⡏⢸⠀⡀⠀⣁⣠⠼⠤⣆⢻⢧⣿⠞⠸⡧⣰⡇⡧⠴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠁⠀⠀⡤⢀⠻⠶⠓⠘⠃⠈⠉⠀⠀⠀⠐⡆⢞⣵⣿⡶⠀⡟⠂⣷⢺⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠜⢀⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢖⣋⡴⣺⣟⡠⢘⠚⣛⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣬⠋⠀⠰⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣻⠾⠽⡏⡄⠸⣛⣭⢆⢀⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠄⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡰⢁⠄⢀⠹⢄⣾⠁⡷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠆⢰⡖⡋⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠊⣀⠜⠀⠐⠒⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠙⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⢙⡆⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣞⢙⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠶⠒⠒⠲⠾⢧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣤⣤⣤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣇⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠉⢡⠃⢀⣀⠤⠔⠚⠉⢹⡏⠉⠓⠢⠤⣀⡀⠘⡌⠉⠙⠛⢷⣦⣄
⠀⠀⠀⠀⢀⣴⠞⠋⠀⠈⠂⠒⣊⠵⠚⣉⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣉⠓⠮⣑⠒⠂⠁⠀⠙⠳⣦⡀
⠀⠀⠀⣠⡟⠁⣀⠄⠀⢠⣴⠊⠁⠰⠋⠀⠀⠀⠑⠄⠀⣿⣿⠀⢠⠊⠀⠀⠀⠉⢆⠈⠑⢦⡄⠀⠠⣀⠈⢻⣄
⠀⠀⣰⠏⠀⡐⠁⢀⡴⠋⠈⢂⠀⠇⠀⠀⠀⠀⠀⡘⢠⡟⢻⡆⢂⠀⠀⠀⠀⠀⠸⠀⡐⠁⠉⢢⡀⠈⢃⠀⠹⣦
⠀⢰⡏⠀⠀⢣⡰⠋⠀⠀⠀⡜⠀⠈⠢⢀⣀⡠⠔⠁⣼⠃⠘⣷⠈⠢⢄⣀⡀⠔⠁⠀⢡⠀⠀⠀⠙⢆⡘⠀⠀⢹⡆
⢀⣿⠀⠀⢀⡜⠑⠢⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠄⠊⢳⡀⠀⠀⣿
⢸⡇⠀⢀⠎⠀⠀⡠⠔⠒⠂⢄⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⡠⠔⠒⠢⢄⠀⠀⠱⡀⠀⢸
⣼⡃⢀⠎⠀⠀⡘⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢣⠀⠀⠱⡀⢈
⣿⠀⡜⠑⢆⠀⠡⡀⠀⠀⠀⢀⡌⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢡⡀⠀⠀⠀⢀⡌⠀⡰⠊⢣
⣿⣸⠁⠀⢈⠀⠀⠉⠒⠀⠒⠉⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠙⠒⠀⠒⠉⠀⠀⡁⠀⠀⣇
⣿⡇⠀⡠⠊⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠀⠑⢄⡀⢸
⢻⣧⣤⡶⠶⠶⠛⠛⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠛⠛⠶⠶⢶⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣤⣤⣤⣤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⡤⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠺⣿⣿⣿⠿⠿⠶⠶⠀⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢰⣾⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡧⢤⣴⠒⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣶⣆⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠑⢦⣸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢠⠄⡀⠀⡸⠁⠄⠀⠀⠀⠀⠀⠀⠀⠹⡋⠉⠉⡟⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⣀⣀⢧
⠀⠀⠀⠀⠀⠀⠀⠈⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⣴⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡸
⠀⣶⡶⠶⢤⣀⠀⡏⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠇
⠀⠀⠀⠀⠀⠈⠃⣯⢁⠀⠀⠀⠐⢄⠄⠀⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠿⢛⠌
⠀⠀⠀⠀⠀⠀⠀⠘⡧⣀⠂⠄⠀⠈⡇⠀⠀⠐⠄⠀⡠⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⠢⣁⢀⣰⣇⣀⣀⣀⣸⠮⡖⠹⣿⣦⡦⡀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠛⠁⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡼⡇⠈⠉⣻⠉⠙⢅⡻⡍⢯⢸⣠⢦⡧⠱⠈⢛⡶⣥⣆⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⡶⢛⠏⠯⣗⠳⢄
⠀⠀⠀⠀⠀⠀⠈⠉⠁⡠⣠⠟⠀⠀⠀⠉⢛⣧⠖⣡⠎⠀⠀⠐⠿⢭⣁⠘⠉⠍⣉⡉⠉⠁⠙⢦⣈⡵⠊⠀⠀⠀⠀⠑⠂⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣠⠖⢋⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠠⢘⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠺⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⡄⣀⣀⠀⣀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣧⡏⣿⣿⡏⣿⣯⣿⢿⢹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣦⣤⡄⠶⠄⢰⣤⣤⡤⠤⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⢶⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣶⣶⣶⢲⣶⣿⡧⠊⠉⠀⠈⢳⠉⢀⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⠉⠛⠦⣄
⠀⠀⠀⠀⢰⣿⣦⡄⠘⣿⣿⣟⡷⣦⠀⠀⠀⠀⠑⠙⠿⠿⠟⡻⠿⠿⠛⠃⠀⠀⠀⠀⠀⣴⡀⠈⠳⣄
⠀⠀⠠⣦⣬⣿⣿⣁⣀⣷⣿⣿⣧⡯⠐⢀⠀⠄⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⢟⣿⣿⡶⡼⣆
⠀⠀⠀⠈⠙⠋⠉⠉⠉⠉⠉⠛⢿⣌⣆⣀⣴⣶⣾⣡⣄⣀⣐⠊⠮⠶⣤⣞⣲⣛⣃⣀⣒⣾⣿⢿⣿⣵⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣾⣿⠟⠈⢻⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣾⣿⣿⣿⡇⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣶⣿⣿⡿⠛⠀⢀⣠⣤⣿⣿⠋⠀⢀⣤⣤⣼⣿⣟⣹⣿⣿⡿⠀⠀⠹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠉⠉⠉⠛⠿⠿⠟⠋⠀⠀⠀⠀⠈⠙⠁






⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠰⣦⣀⠀⠀⢀⣤⣶⣦⣤⣶⣶⣾⠂⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠧⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⠛⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⢇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠙⠻⣿⡿⢹⣿⣿⡟⠉⡆⠀⢸⡿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣷⣶⣶⣶⣶⠒⠋⠉⠁⠈⠉⠉⠛⣴⣷⠶⠿⠿⠿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠚⠛⠿⣟⣿⣿⠀⠀⢀⣾⣷⣄⠀⠀⢸⡿⢲⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠠⠀⠄⡐⢹⣾⣿⠀⠀⣿⣿⣿⣿⡀⠀⢸⡇⢸⡇⣸⢨⡇⠐⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢀⢸⣿⠀⢸⣿⣿⣿⣿⡇⠀⢸⣇⢸⡇⡛⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢴⣤⣀⣀⣸⣿⣀⠈⠛⠿⠿⠟⠁⣀⣼⡇⢸⡇⣿⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠛⠿⠿⢿⢷⡿⠿⠛⠋⠀⢸⡇⣽⢸⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣇⣛⣘⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣠⣰⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⣀⡀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠙⣿⣿⣿⠀⢠⣿⡿⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠛⠉⣰⣿⡟⠀⠀⠐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣷⣶⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⢉⣩⣭⡉⠻⢿⣿⣿⣿⠟⢋⣩⣭⣉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⣼⣿⣿⣿⠁⣰⣿⣇⠀⣹⣦⠈⢿⣿⠃⢠⣿⣏⠀⣸⣧⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⢿⣿⣿⣿⣿⣿⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠈⠿⣿⣿⠿⠃⣠⣿⣿⣧⠈⠻⢿⣿⠿⠋⢀⣾⣿
⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⡿
⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠃
⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣍⣛⡛⢛⣛⣫⣥⣾⣿⣿⡟⠁
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⢀⠇⠀⠀⢀⣤⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠈⠙⠻⠿⠿⣿⠿⠿⠟⠛⠉⠘⡄
⣸⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠓⠒⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⡀⠀⡀⠀⢀⠀⠀⢀⠀⠀⢀⠠⢤⡁⠂⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⣤⡷⠓⠉⠉⠀⠀⠀⠀⠀⢉⢀⡰⡋⣒⠛⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡐⢦⡴⡋⠻⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠀⠊⢘⠁⠧⡠⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⠃⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⢨⢐⣷⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡠⢔⣱⣤⠠⡀⠀⠀⠀⠀⢠⠄⢰⠴⣤⡀⠀⠌⠣⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠠⠚⡅⢾⣯⠞⠀⠀⠀⠀⠀⠐⠷⡾⠞⠐⡄⠀⢶⠳⢄⠀⠀⠐⠟
⠀⠀⠀⠀⡄⣶⠘⢺⠀⠀⠀⠈⠀⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢚⠁⠀⠐⠊⡄
⠀⠀⠀⠠⡛⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣁
⠀⠀⠀⠀⠈⠃⢰⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠜
⠀⠀⢀⠠⠤⠠⠌⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⡀⣶⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠁⠙⡄⠀⢀⣴⠀⠀⠀⠀⢀⣀⣀⠰⠾⢫⠃⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⣀⠼⠏⠀⠀⠀⢀⠀⠒⠒⠴⢤⣠⡤⢊⣧⠥⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂⠀⠡⣴⣤⣄⠔⠀⣈⡴⠛⡉⠙⢹⣯⣀⢌⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠⣤⣤⣤⣯⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣦⠉⣦⠌⠁⢙⣷⠟⣹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣷⣿⡙⠫⠿⡷⢶⣿⣿⣿⡖⣿⣿⣿⡏⢉⣿⣿⡋⡽⣿⣿⣿⣿⣿⣭⠁⠀⠾⣛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠒⣉⡷⠄⠀⠁⠈⠏⣿⠋⣽⠿⣿⡿⢛⠏⡠⣖⠀⠐⠀⢿⠛⡟⠫⢷⠿⠃⣸⠿⡇
⠀⠀⠀⠀⠀⠀⢤⣄⣼⠛⠳⣿⣶⠄⡀⠀⠙⢶⣶⡇⠀⡔⣯⢀⡏⣠⡾⠋⠉⠋⣳⣬⣶⡡⡞⠉⠙⠝⠀⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⡀⠀⠹⠄⣙⡂⣀⠀⣸⣗⢸⠀⠈⣿⣾⠉⠀⠀⢠⡎⢠⡾⢀⣋⣀⡤⠴⣦⣼⡶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢒⠄⠐⢤⠀⢀⠔⠐⠒⠿⣾⡇⢰⡿⠁⠀⠀⢀⣞⣁⣀⣽⠉⣉⣵⢯⣿⠿⢿⡿⣿⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⠀⠀⠸⣤⣌⣀⠀⠀⣰⢿⡄⢸⣧⠀⢠⡴⢛⡵⣶⠏⠉⠻⢭⣤⣈⣁⣀⣼⡿⠋⡟⡜⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡇⠈⠻⣿⣿⣶⢿⣶⣿⡿⠛⠶⠶⢶⣯⣽⣍⠥⠅⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⢸⣿⣷⡿⠋⠁⠀⠀⠀⠀⠘⢻⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣶⣶⣶⣤⣾⣿⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡆⠀⣀⣀⣀⢠
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣦⠀⢀⡘⣀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣰⣶⡄⠀⢾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠋⠀⣀⣙⣩⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⢈⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣌⢂
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣁⡴⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⣀⣈⢢⣆
⠀⠀⠀⠀⣰⠂⢰⠀⠀⠀⠀⠀⠀⠠⡀⣦⢉⢉⠀⠀⠀⠀⠀⠀⠀⢀⢉⡸⠄⠀⠀⢀⠤⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⡀
⠀⠀⠀⣤⡇⡠⠊⣤⣄⠀⠄⢠⠀⠀⠀⠸⠛⠋⠀⠀⠀⠐⠀⠀⠀⢰⠯⠄⠊⠀⠀⠁⠉⠉⠛⠻⠿⣿⣿⣉⠪⠀⠀⡰⠁⠃⠀⠀⠸⣷⣾⣷
⠀⠀⠀⠘⠟⠀⠀⠿⠋⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣠⣤⠀⢠⣤⣮⠙⢿
⠀⠀⣿⡷⠀⢠⡶⠀⠀⠀⠄⠠⡤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠛⠉⠀⠀⠈⢙⠀⣀⡤
⠀⠀⠏⠀⠀⠈⠈⠀⠀⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠠⠳⣶⡖⠀⠀⠀⠀⢀⣝⣿⣶⣀⠀⠂⠀⠈⡇⠀⠐⢷
⠀⢄⡥⠀⡀⠀⠀⠀⣼⠁⠰⠀⢠⠀⢰⠢⠰⣶⡦⠀⠀⠀⠀⠀⠀⢀⠀⡐⠀⠀⠀⠀⠀⠃⠉⠉⢰⠀⠀⠈⠉⠉⠒⠈⡟⠀⠀⠀⠘⠁⣀⣖⢄
⠀⢬⡴⠀⠀⠢⠭⠼⠃⠀⠀⠀⢃⠐⢱⡰⠁⠀⠀⠀⠀⠀⠀⢀⠓⢤⣑⢤⣤⠀⠀⠀⠀⠀⡀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣶⠈⡒⢻⣼⠲
⠀⠶⣴⠇⠀⠀⣰⡆⠠⠀⣠⢤⣤⢀⡿⠁⠀⠀⠁⠀⠀⠀⢀⣦⣞⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⢁⠔⠀⠀⠀⠀⠑⠀⠻⠂
⠀⠰⢦⡴⠀⠀⠙⢣⡇⠂⠈⠉⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠸⠈⠛⢇⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠄⠀⠀⠠⠀⠀⠀⠀⠀⢠⣤⣤⡶⠆
⠀⠐⠶⠆⠀⠀⠀⠀⠭⠳⢖⠂⠀⡄⠉⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⠹⣥⡀⠈⠀⠐⣀⠄⠀⠀⢠⠜⠀⡐⠠⡀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠉⠉⠀⣄⠂
⠀⠀⡛⠀⠀⠀⠀⠠⠤⠤⠤⠸⠧⠶⠀⠀⢀⣦⠀⠀⠀⠀⠀⠁⠈⢣⢫⠀⠀⠕⠀⢀⡀⠤⠖⠡⣈⡤⠃⣠⠤⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⠹⠖
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀⠃⠀⠀⢄⠛⠁⣼⣻⡤⢀⠀⠀⠀⢋⢦⣀⠀⠀⠀⠀⢀⣤⡾⠷⠒⠋⠁⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⢈⡆⠈⠹⠛⠃⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⢰⡏⠤⠒⠋⠉⠉⠙⡟⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠐⠶⠒⠋