Hand over mouth Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠓⠶⡄⠒⠒⠂⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣠⠤⠀⠀⢸⢀⡀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠡⠤⠒⠀⠀⢸⡇⣠⠖⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣠⣒⠩⠥⡄⠀⠀⣗⠥⢒⣀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠡⠔⠒⣉⣁⣠⠴⠳⣿⣿⣟⣒⡀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠞⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠏⠐⠉⠉⠉⠛⠲⠶⠦⠀⠀⠀⠀⠀⠀⢠⣤⠶⠶⠒⠛⠓⢼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆⠀⠀⢠⡤⠖⡶⢄⠀⠀⢀⠀⠀⠀⡀⠀⠠⠤⠤⣄⡀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⠀⠢⣼⠿⠀⠅⠀⠀⠆⠀⠀⠀⠀⢀⣾⣧⡀⠄⠀⢸⡆⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⠴⠤⢀⠀⣚⠍⠢⣀⠀⠀⠀⠀⡔⢓⢠⡄⢀⡀⠀⠀⠀⢸⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⢶⡃⠀⠙⠻⢄⠀⠈⠓⠲⠤⠤⠥⣀⣀⠀⠈⠉⠢⣀⠀⡏⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡉⠢⣀⠀⠀⠱⣤⡖⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠤⠙⣇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⡌⢢⡈⠑⢴⡀⠀⠉⠓⠲⢤⣀⣀⡀⠀⢀⠀⠀⠀⠀⢸⡄⠀⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢰⠀⠸⡀⠙⢦⡏⠀⠁⠠⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠘⢸⠀⠀⠙⣦⠀⠙⢶⢄⡀⠀⠑⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠹⡀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣸⡄⠀⢰⠀⠑⢄⠈⠃⠍⠀⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⣸⠀⠀⠀⠙⠢⢤⣱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⠿⠿⣿⣟⠛⢙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⠁⠀⠀⠀⠈⠑⠂⠉⠳⣄⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣤⣠⠤⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⣀⠐⠲⠦⣄⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡠⣺⠷⠋⠁⠀⢀⣤⣄⠁⣷⡌⢱⣆⡀⠀⠀⠀⠀⠈⠉⠓⠤⡀⠉⠒⢄⠈⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠘⠁⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠁⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⡿⠁⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠘⠳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣄⢢⡑⣄⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿
⣿⣿⣿⢻⢹⡿⣿⠇⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢘⢆⢳⡈⠧⠀⠀⠀⠸⡄⠀⢸⣿⣿
⡟⣿⣿⢸⠈⣿⡟⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠈⢷⣄⠀⠀⠃⠂⠹⣗⡄⠀⠀⠀⠹⡄⠀⣿⣿
⡇⣿⣿⢸⣾⡿⠁⠀⠀⢸⣿⠠⠒⠶⣤⣄⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠈⠁⠀⠙⢷⡀⠀⠐⠀⠘⢆⠀⠀⠀⠀⠘⠄⠹⣿
⡇⡏⣿⣾⡿⠁⠀⠀⠀⣿⣿⠀⢀⣤⣀⠉⠉⠀⠀⠀⠀⢀⠒⣿⢾⣷⣦⣴⣄⠀⠀⠀⠈⠻⣦⡀⠈⢄⠈⠃⠀⠀⠀⠀⠂⠀⠹
⡇⡇⣿⣿⠃⠀⠀⠰⠀⠹⡝⣿⣿⣿⡏⣙⠂⠀⡆⠀⠀⠋⠰⠿⠾⢤⡤⠿⠃⠀⠀⠀⠀⠀⠹⣷⡀⠀⢢
⡇⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠘⠋⠋⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢣⠀⠀⠀⠀⠀⢀
⡇⠀⡇⣿⡄⠀⠀⡀⠀⠂⠀⢸⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠆
⡇⠀⡇⠈⣷⡀⠀⠱⡀⠀⠀⢸⡄⠀⠀⠀⢸⣆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣎⠀⠀⣠⡏⠀⢸
⠀⠀⡇⠀⠈⢷⡀⠀⠙⢄⠀⠈⣧⠀⠀⠀⠀⠉⡉⢏⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠅⠚⠋⠀⢀⡏⣠⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠑⠀⠹⡆⢀⠄⣸⣆⠉⠺⣇⠈⠙⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⢶⣿⠟⣁⢔⣀⣠⠆⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⡀⠀⠹⡄⢳⡬⠝⢆⠀⠈⠳⡀⠀⠈⢢⡀⠀⠀⠀⡀⠀⠀⢀⠄⣹⣶⣄⡈⠉⠉⠉⠀⢀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⠉⠀⠀⠱⡀⣢⠀⠀⠣⡀⠀⠈⢦⡀⠀⠙⢦⠀⡰⠓⢀⣰⡏⠀⢹⣿⣿⣿⣟⡓⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠱⣌⢣⡀⠀⠈⢢⡀⠀⠑⣄⠀⠀⠑⠇⠀⢻⣿⣇⠀⠘⢿⣿⣿⣷⣭⣍⣉⣁⣠⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣶⣂⣨⠈⠀⠄⠀⠀⠱⡄⠀⠈⠓⠀⠀⠀⠀⠀⢿⣿⣆⠀⠈⠙⠿⣿⣿⣿⠿⡿⠷⠒⠂
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠉⣿⣿⣿⣿⣿⣿⣧⠀⠀⢄⠀⠀⠙⣦⠀⠀⠈⠀⠀⠀⠀⢦⠻⣿⣧⡀⠀⠀⠀⠉⠉
⠀⠀⠀⣠⣶⠿⠛⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠙⣿⣿⣆
⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆
⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⢀⡀⠠⠉
⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⢠⣤⣩⠙⠁⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⣀⡀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢿⠀⠀⡤⠀⠀⠩⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡀⡞⣆⠀⠀⣤⢔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇⡇⠸⠴⠊⠵⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠀⣇⠀⠀⠀⢈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠻⡄⠈⠢⣸⠀⠀⢰⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠙⢄⠀⣸⠤⠤⢼⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡯⠤⠤⢼⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⠲⣄⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠑⢇⠀⠀⠀⣾⠀⠀⠀⠀⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢄⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣿⠀⠀⠀⠀⡇⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⣸⣿⣀⣠⠤⠤⠧⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⠛⠦⢄⣀⣀⠔⠙⡄⠀⠀⠀⠀⠀⠈⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡆⢀⣀⡠⠖⢳⠦⠾⢤⡤⣄⣀⣀⣠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⡅⡏⠀⠀⠀⢸⡀⠀⣸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠁⠀⠀⠀⠀⠹⡼⠁⠀⠀⠀⠀⠇
⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠀⠀⠀⠀⠀⠀⠰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢹⡇
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⣦⡀⠀⠀⢀⣼⠋⠀⠀⠀⢀⡾⠃⠀⠀⣠⡴⠟⠋⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠈⣷⠀⣠⡞⠁⠀⠀⠀⢠⡾⠁⢀⣤⠞⠋⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣴⠏⠀⠀⠀⠀⣰⠟⢀⡴⠛⠁⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢰⡿⠃⠀⠀⠀⢀⣼⣫⡾⠋⠀⠀⠀⠀⢀⣤⠞⠋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠟⠁⠀⠀⠀⣠⣿⠟⠉⠀⠀⠀⠀⣠⡴⣋⣥⠶⠛⠉⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠁⠀⠀⠀⢀⣤⣾⡿⠞⠋⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣭⡴⠶⠶⠶⣄⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠁⠀⠀⠀⠀⣀⡼⠂⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⢞⣛⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣭⡥⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣀⣤⠶⠟⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢈⡀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡟⠁⠀⣀⠴⢚⡫⢵⠖⢤⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡎⠀⡠⠊⠵⢊⡥⠖⠁⠀⠀⠈⢦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠐⠁⣠⣾⡅⠀⠀⠀⣰⣶⠶⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠀⣰⠋⠘⠃⠀⠀⠀⠉⠚⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⢠⡟⠀⠀⠀⠀⡄⢤⠀⠀⠀⠀⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣥⠀⠀⠰⣆⣀⡀⠠⡀⠀⠐⣿⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢐⡛⠛⠦⠈⠲⠀⢟⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢹⢿⣾⡚⠛⣛⡛⠀⠀⠀⠀⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢹⣌⠢⣼⢷⣍⣉⠁⠀⠀⠀⠀⠘⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡄⠀⣿⠁⠀⣼⢻⣿⣄⣤⣤⣽⣷⣄⠀⠀⠀⠀⠘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠁⠀⣿⡀⢠⠃⢸⠹⡇⠈⠉⠉⠛⣻⣷⣷⡦⢤⡀⢈⣻⣷⢲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠢⠀⠈⠳⠀⠀⣼⠀⡟⠀⠀⠀⠋⠉⠀⢹⣿⣮⡿⣫⡁⠈⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢷⣦⠀⠀⣾⢏⣴⣿⡆⠤⠤⠀⠀⠀⣼⠉⢿⣧⡹⣿⣶⢆⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⡟⠡⠴⠛⠉⠐⣉⣵⠿⢯⡀⠱⡀⠀⠀⠀⣰⠇⢀⠞⢿⣿⡟⣿⠁⠀⠀⠹⣎⡳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⡄⠹⣄⠀⠀⠉⠉⠀⠀⠀⠀⠙⢆⡙⢆⠀⣰⣏⠔⠁⠀⠘⢿⣿⣿⢶⣾⡆⠀⠈⠙⠢⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⠻⣦⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣷⠟⠁⠀⠀⠀⠀⠈⢿⣿⣆⢿⣷⠀⢀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠐⠠⣉⣦⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣎⢿⣇⠀⢣⡀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡷⢿⣷⣬⣿⣦⡀⠀⠀⡿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣸⣿⠋⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠙⠛⣿⣿⣿⣶⣼⡷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠙⣿⣿⠁⠀⠈⣿⣿⣦⣀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣼⣿⠃⠀⠀⠈⠙⠛⠛⠛⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⣴⣿⣿⠀⠀⠀⣾⣿⡿⢿⣿⣶⣾⠿⠛⠛⢉⡁⠀⠀⠀⠉⠙⠛⠛⠿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣰⣾⣿⡿⠃⠀⠀⢠⣿⣿⣧⣤⣭⡥⠤⠄⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠲⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢷⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⣠⠔⢊⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⡴⢁⡀⠀⠀⠀⠀⠹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠀⠀⠀⠀⣀⣤⣴⣆⣤⠴⣺⣟⣡⠴⠖⠋⠱⢒⣟⡡⢶⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⠁⠀⣠⡔⠋⠁⢈⡉⠀⠤⢤⠀⠀⠀⢠⠦⠤⠤⢤⣅⡀⠸⢷⣄⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⢨⡇⢀⠞⣁⡤⠤⠒⠋⠀⠀⠀⠈⠒⠤⠤⢄⣀⠹⡄⠘⣿⠀⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢸⠇⢴⠊⢁⠤⠄⠀⠀⠀⠀⠀⠀⠐⠒⠒⠠⠈⠙⠇⠀⢹⡀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⢼⠀⠀⠀⠀⢤⣴⡶⠖⠀⠀⠀⠀⠒⠲⠶⠖⠤⠀⠀⠀⢸⡟⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣸⠀⠀⠀⠒⠆⠀⠂⠀⠀⠀⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⢸⣧⡞⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢹⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢀⣠⡔⠂⠀⠀⠀⠀⠀⢸⡿⡏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢺⡆⠀⠀⠀⠀⠀⠀⠉⠙⢛⣛⣉⠁⣀⡀⠈⠀⠀⠀⠀⢸⡗⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⣇⠀⠀⠠⠀⠀⢰⣟⣋⣉⣉⣹⠟⠉⣿⡔⠋⣧⠀⠀⣸⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡖⢦⡀⠀⢸⣃⡤⢶⡾⠁⢀⡼⠋⠀⡰⠟⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢳⠀⣿⢃⡴⠋⠀⣠⠞⠀⣠⠞⠁⣰⠃⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⢸⢀⡿⠋⠀⢠⠞⠁⢀⡴⠃⠀⣼⢥⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣠⠞⠋⠀⠀⠰⠋⠀⢠⠞⠀⣠⠞⢁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠁⠀⠀⠀⠀⠀⠀⠐⠃⠀⣴⠋⢠⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣴⠋⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠹⣗⠲⢶⢶⡤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠁⣾⢸⠇⠀⠀⠉⠙⠓⢦⣄
⠀⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⣠⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣾⢯⣙⠲⠤⣤⣀⣀⣀⣀⣀⣤⠴⢚⣡⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠉⠙⠒⠶⠤⠭⠭⠥⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠠⠯⠀⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⡴⠶⢶⣴⢶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣷⣶⣾⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⣉⣉⣉⣽⣿⡟⠛⠁⠀⠀⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠠⠔⣊⣉⣩⣭⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠶⠛⠉⣉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣋⣠⠴⠒⠋⣉⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣛⣋⣁⣤⣴⡾⢿⣟⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⣋⣡⣴⣿⣿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣵⣶⣿⣿⣿⣛⣉⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣶⡶⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡙⢏⣿⣿⡛⠖⠛⠋⠀⠀⠀⠀⠀⢀⡶⢛⣡⣾⣿⣿⠃⠐⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡘⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠛⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠙⠋⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣾⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⣶⣴⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢺⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣼⠿⡯⠋⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣤⡀⠀⠀⢠⣾⢛⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠛⢏⠙⠌⠋⠻⣯⡀⠀⠀⠀⠈⠙⢷⣤⣀⠀⣀⠀⡀⢤⣀⠀⠀⠹⣿⣦⡀⠹⣷⠀⠀⣹⡯⠀⠀⢹⠶⣄⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢿⡣⠕⠨⠢⠁⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⠪⡦⡆⣽⣿⣿⣿⣿⣿⣷⡀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢀⣾⣿⢿⡳⢝⠢⡈⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠨⣟⢿⣶⣶⣿⡟⠛⠉⠉⠈⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣼⡿⣙⠦⡉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⡀⠀⠀⠀⠀⡠⢋⣴⣿⠿⣿⡇⠀⠀⠀⠀⣿⣿⡷⠛⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⣸⡟⠑⢮⡃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣄⠀⠀⣰⣿⣿⠗⣋⣽⡇⠀⠀⠀⠀⣿⣿⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣭⣟⠿⣿⣾⣿⣿⣿⣯⣵⣾⠃⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠉⠀⠈⠛⣿⣿⡿⠟⢻⡇⠀⠀⠀⢠⣶⣾⣿⣿⡀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢋⣠⠖⠛⣧⠀⠀⢰⣿⣿⣿⠿⠿⠿⠶⣶⣤⣄⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⠀⠀⠹⡄⢰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁
⣿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠣⠀⠄⠀⡀⠈⠀⠀⠀⠐⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣦⡁⠐⠉⠂⠀⠀⠀⠄⠀⠀⠀⢀⣴⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣆⠀⠠⠀⠀⠀⡈⠀⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⡋⠀⢀⣸⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠠⣐⢾⣿⣿⣿⣿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡎⠉⠉⠁⠈⠛⠛⠋⠉⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⢹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⠀⠀⠀⠀⠴⠶⢶⣶⣤⡄⠀⣤⣴⡶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠻⡆⠛⠀⠀⠀⠀⠁⠚⠋⠉⠉⠀⠀⠋⠉⠉⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⣀⡠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠘⣋⠐⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣄⠀⣸⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠈⠻⡿⡿⠀⢀⡽⠋⢉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠉⣠⠖⠉⣀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠚⠛⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠘⢄⠀⠀⠀⠙⠲⢤⣠⡏⠀⠀⠀⠀⢠⣴⡇⣠⠏⠑⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠞⡿⠀⠀⠀⠀⠀⠼⣿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢆⠀⢰⠃⠀⠀⠀⠀⠈⣴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⢀⠞⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠄⠛⠉⠉⠀⠀⠀⠀⠘⠛⣿⣦⡌⠙⠶⣤⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⣁⠙⣿⣔⡐⠚⠛⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⣀⣀⠀⠤⠤⠤⠶⢋⡡⡢⢝⣿⣤⣀⣈⡁⠚⣦⡀⠀⠀⠀⠀⠀⣠⠞
⠀⠜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⡴⠁⠀⡀⠐⠂⠉⣀⣀⠀⠁⣒⣒⣂⣭⣉⣷⣾⣿⣭⣤⣤⡄⣀⠈⢳⡄⠀⠀⣠⠔⠁⠠
⠈⠈⠌⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠟⠀⠀⠀⠀⠀⢈⡁⢠⣤⣴⣶⣿⠿⠟⠛⠉⠉⠙⠻⢿⣿⣧⠄⠀⠁⠀⠹⣤⠊⠉
⠀⠀⡐⠀⠀⢉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢰⠏⠀⠀⠀⡀⠔⠃⠈⣡⡴⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⢱⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠂⠀⠀⠀⠀⣠⠇⢀⠃⠀⠀⢀⠂⡠⢔⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⢇
⠀⠠⠠⠀⠄⠀⠄⠀⠀⠡⠠⠀⠌⡼⠉⠉⢣⣠⡏⠀⠀⢀⠀⣰⡗⣩⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⢂⠸⡧
⠀⢡⢡⠉⡌⠈⠌⠀⠀⠁⠠⠉⡜⡵⡤⠠⢼⣿⠁⠀⠀⡌⢠⣟⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⢢⠈⡄⣿⠀⠀⠈
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡐⠀⠀⣾⣭⣄⡀⢰⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣆⢃⣰⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡿⣅⢀⡸⡀⣿⣿⠃⣤⠶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⣠⠴⠾⠛⠛⠉⠛⠒⠀⠀⠀⠀⢸⣿⣿⡎⢹⣾⡇
⠀⠌⠌⠀⠡⠡⠡⠀⠀⠌⠌⠤⠡⠡⠀⢸⣷⠀⠀⠀⢱⣿⣿⡀⠀⣠⣴⣦⣤⡢⠀⠀⠀⠀⠀⠀⠀⣠⡶⡶⠿⣷⣦⡀⠀⠀⠀⠀⠸⠹⣿⣷⠈⣿⡉
⠀⡈⡈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢡⠀⠀⢠⣼⡆⠀⠀⠸⢹⣿⡇⠘⠛⠯⡭⠀⠉⠶⠀⠀⠀⠀⠀⠘⠙⠲⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⡀⣿⠟
⠀⠐⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⢂⠂⠀⠀⣸⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣾⣿⣧⣸⡇
⠠⠡⠡⠈⠄⠄⠌⠀⠀⠠⠠⠀⠌⡄⠄⣀⣸⣇⡿⢀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠀⠀⠀⠹⣿⣷⣶
⠀⢁⢃⠈⠀⠀⠀⠀⠀⠀⠂⣀⣼⣾⣿⣿⣿⣿⡇⠰⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⢰⠀⠀⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠉⠻⣿⣿⣷⣦⡀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠐⠂⠀⠀⢸⠀⠀⣿⣿
⠀⠄⠄⠠⠀⠠⠠⠀⢀⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⣿⣿⣿⣧⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠃⠀⡀⠀⠀⠸⠀⠀⠘⠀⢰⣿⡇
⠀⠈⠈⠀⠁⠀⠁⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⢹⣿⣿⣿⣧⡀⠀⠀⠀⠈⠛⠿⠷⠾⠋⠁⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡆⠀⡀⠀⣸⣿⡇⣾
⠀⡀⡐⣀⠀⢀⢂⠀⣿⣿⡇⠀⠀⣄⠘⣆⠀⠀⢻⣿⣿⣇⡈⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠸⢀⣥⣾⣿⣿⣰⡿
⠀⡸⡀⠀⠀⠀⠀⠰⣿⣿⡇⠀⠀⠸⣦⠘⣧⠀⠀⢿⣿⣿⡠⠀⠀⠈⡹⢿⣿⣿⣷⡀⠀⣀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡗⠂⠸⣿⣿⣿⣿⡇
⠀⠽⠡⠀⠄⠄⠀⢸⣿⣿⡇⠀⠀⠀⢹⣧⡹⣷⡀⠸⣿⣿⣧⢂⠀⠀⠈⠙⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⡟⣿⡟⡀⠘⠀⢿⣿⣿⣿⣷
⠀⢱⢣⠉⠈⠈⡌⢸⣿⣿⡇⠀⣤⠀⠀⢻⣷⣿⣷⠀⣿⣿⣿⣟⣦⠀⠀⠀⠸⡞⣹⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⢠⣾⣇⣀⠀⠂⢻⣧⠇⠀⠁⠈⠹⣿⣿⣿
⠀⢃⢂⠀⠀⠐⡀⢸⣿⣿⡇⠀⣿⣿⣄⠈⢿⣿⣿⣧⢸⣿⣿⣿⣿⣧⢆⠐⡀⢻⣣⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢿⣿⣼⣰⠃⠸⣧⠈⠀⠀⠀⠀⠹⣿⣿
⠀⢚⠆⠀⠀⠀⠀⢸⣿⣿⡇⣀⢹⣿⣿⣷⣜⣿⣿⣿⣿⣿⠙⣿⣿⣿⣾⣦⢳⡈⣿⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣼⠀⣿⣆⠐⠀⡄⠀⠀⢿⣿
⠀⠜⠄⠀⠠⠠⠠⢸⣿⣿⡇⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⣿⣿⣿⣿⡎⣷⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡞⣼⣿⣆⢠⣷⠀⡆⢸⣿
⠀⣼⡌⠀⠀⠠⠀⢸⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆⢻⣿⢿⣿⣷⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣿⣶⣧⣼⣿
⠐⡸⡐⠂⠂⠂⠂⢺⣿⣿⣧⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⣼⠃⢠⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣶⣤⣀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠉⠁⠀⠉⠛⠿⣿⣿⣿⡿⠟⠉⠁⠀⠉⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣦⣄⡀
⣠⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦
⣿⣿⡉⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠈⣻⣿
⠘⢿⣿⣶⣄⠀⠀⠀⠻⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠈⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠃⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⠀⠀⢻⣿⣧⣤⣴⣶⣶⣿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣾⣿⡿⠋⠉⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⢻⣿⣧⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣶⣶⣿⣿⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⡀⠔⢮⢴⠠⡰⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢽⣹⠞⡁⢸⡘⣿⠚⡵⢟⣿⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣟⣓⣇⠈⠸⣦⠀⢰⡄⢤⠈⠀⣍⠉⠭⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡀⠄⠀⡉⠖⠁⠀⠘⠈⠈⢁⠘⣆⠁⠸⣀⣋⠤⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢈⠄⡐⡘⠂⠉⠀⣘⠈⠀⠃⠈⠀⠉⠀⠀⠀⡐⡂⠀⣈⢇⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢏⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠌⠠⢀⠆⡥⠑⠀⠁⢲⣽⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠘⣫⠀⡀⠀⠀⠁⠸⠀⠊⠈⠈⠈⣑⢠⡔⣆⠘⣼⢻⣶⡂⠗⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠷⠌⠉⢀⡠⣤⠠⣴⠞⣰⢿⢶⡾⠲⠎⠀⢩⠟⠝⣧⡑⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠺⣞⢂⡇⠧⢪⣀⣾⣾⣼⣪⣷⠟⣦⠀⢩⠆⠲⣆⠡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⠆⡳⣯⡯⣞⢿⣻⠽⡖⠟⢏⠱⢧⣘⣧⣼⡛⠓⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠀⠀⠐⠳⠛⣯⢎⠰⢇⢃⡴⡴⣚⣷⣯⠌⡁⠀⠀⠀⠀⠑⠪⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⡍⢁⣏⣈⢡⣞⣿⡵⣶⣮⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣭⢭⣽⠙⣝⠌⡶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣝⢏⢴⡥⡔⢦⣴⣚⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣚⣻⡯⠄⠈⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠉⣉⣁⣤⠴⠖⢋⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣉⣁⣤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⣄⠀⡀
⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠁⠉⠙⠓⢦⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢤⡦⠟⡶⠄⠙⠒⠤⣆⡀⣰⠀⠀⠀⣠
⠸⣄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⣳⣌⠀⠉⠘⡀⠀⠀⠉⠉⠹⠔⡦⢊⡏
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⠖⢦⠀⠀⠀⠀⠀⠀⠀⠴⠶⢄⠈⠁⠀⢀⣄⣤⣾⣄⣄⣀⠀⠀⡰⡇
⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡴⠃⡜⠁⢠⠎⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⡏⡷⠤⠚⠉⠀⠀⠈⠉⣻⣦⡄⠸⢤⡄
⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠊⠉⠀⠀⠣⠔⠁⠀⡌⠀⡜⢀⠊⡇⠠⡲⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⡁⠀⠧⣀
⠀⠀⠀⠈⠳⠤⣄⣀⣀⣀⣠⡶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠊⠀⠀⠀⡰⠋⠀⠀⠤⣀⠀⠀⠀⠀⢀⣿⡟⠛⠂⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠰⢦⣀⡈⡙⠀⠀⢀⣸⠋⠁⢰⡚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠸⢮⣁⡬⠃⠀⡴⣋⣉⣠⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣩⡀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣡⣦⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⠈⠀⠠⡀⠀⠀⡠⠤⠴⠃⠁⠈⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠐⢄⠀⠀⠐⡀⠀⡀⠘⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣄⠀⠀⠉⠉⠓⠃⠀⣧⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠉⠉⠓⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⣀⠴⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠉⠁⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⢾⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⡉⠁⠀⠀⡼⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠹⢄⣀⣠⠾⡁⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⠀⢠⠜⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣐⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⠀⠙⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣄⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣠⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠰⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⣦⣤⣤⡘⠿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠿⡿⠿⠛⠉⢻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⣠⡴⠛⠛⠻⢶⣶⠀⠀⠀⣠⣴⣶⡿⠛⠛⠒⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡗⠡⣤⡶⢶⡶⢶⣌⣷⠀⠀⢼⣷⡶⢶⡿⢧⣄⡀⠸⢣⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢘⣇⠀⠀⠀⠈⠙⠀⠉⣿⠀⠀⠀⠨⠀⠈⠁⠀⠈⠁⣀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⡄⠀⠀⠀⢠⠞⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡝⢀⠀⠀⠀⠀⠈⠓⠲⢦⡴⠞⠚⠛⠀⠀⠀⠋⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⣠⡀⢄⣠⣄⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⠋⣽⠀⠈⠉⠀⠉⠑⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣶⠀⢰⠆⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⢰⠃⠀⠰⠀⠀⠀⢀⣴⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⡇⠀⢰⠀⢀⣠⣿⡟⠁⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢩⣿⠁⠿⣿⣿⡇⠀⠀⣶⡿⠿⠋⠀⢀⡷⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⢻⡇⠀⠀⢹⠇⡀⠄⠉⢠⣀⢀⣀⣀⡁⢒⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠹⣷⠛⠀⢠⡋⢀⠀⣀⠴⠋⡉⠉⠉⠙⠃⢉⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⢦⠀⠀⠀⠈⠑⠢⣼⡗⠀⠉⠁⢀⣴⠟⠛⠛⠲⠦⠀⠀⠀⡼⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⢸⣷⣄⠀⠒⠋⠀⢰⣶⣶⣴⠂⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀
⠀⢀⣠⡤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠈⣿⣿⣦⠀⠀⢻⡿⠿⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⡀
⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⣹⢿⡆⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣦⠂⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢷⠀⠠⣀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠈⣿⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠘⣴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣶⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠋⠻⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠈⠻⠛⠃⠈⠛⠟⠁⣽⣿⣿⣿⡇⠀⣠⣶⣤⠀⠨⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠿⠁⠀⢀⣀⣀⡀⠀⠈⠻⠿⢿⣿⡆⠀⠻⣿⡿⠀⠠⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⣴⣾⣿⣷⣆⣠⡀⣀⣰⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣷⡄⠀⠀⠉⠉⠀⠀⢠⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣶⣶⡄⢠⣴⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠾⠿⠷⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠦⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄
⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣆
⠀⠀⠀⣸⡟⠀⣀⡀⠀⠀⢀⣴⠟⠁⣿⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢀⣼⣏⣴⣾⠏⠀⠀⢀⡾⠃⠀⠀⠸⣇⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣿⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠰⠿⠿⠋⢹⡟⠀⠀⢀⡿⠁⠀⠀⠀⠀⠹⣦⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⣼⡇⣀⠀⣾⠃⠀⠀⠀⣤⠾⠷⠙⢷⣄⠀⠘⢷⣄⠐⠛⢿⣷⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⣿⡿⢿⣷⡏⠀⠀⠀⠈⠋⠀⠀⠀⠀⠉⠻⠶⣦⣽⣿⣶⣾⡟⠁⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠻⠇⢸⣿⡇⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⢻⣷⠟⢻⣆⣰⡟
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠈⠻⣦⣀⠀⠀⠀⠀⠀⢤⠤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠙⠛⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⢿⡁⠀⠀⠀⣀⣀⣤⣶⠶⠶⠶⠶⢶⣤⣀
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⢹⡟⠳⠶⠶⠾⠛⠋⠁⠀⠀⠘⠷⣶⡾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠘⠷⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠉⠻⣶⡄⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⣤⣤⣤⣤⣤⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠈⠉⠉⣹⡟⠉⠉
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡾⠁⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣼⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⣼⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⣤⣤⣾⡃⠀⠀⢀⣿⠛⠷⠶⠶⠶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠉⠉⠻⣷⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣻⣶⣶⣶⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣶⣿⣿⣻⣿⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢴⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣚⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠐⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤
⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠂
⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠄⠀⠙⢷⡄⠀⠀⡴⠾⠛⠛⠛⠓⠄⣿⣿⣿⣿⣿⡿⡁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠃⠰⠶⠀⠀⠀⠀⠀⠀⠐⠶⠂⠈⠄⢀⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠰⠒⣟⣻⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⠶⠁
⠀⠀⠀⠀⠀⠀⠐⢎⠻⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣸⣿⣟⠽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠩⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡎⠩⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⡿⣦⣄⠀⠀⠀⠀⠀⢀⣴⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢛⢒⠀⢐⢛⣋⠁⢸⡀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⢀⡀⠤⠤⢠⠀⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⢸⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⡠⠀⢄⠸⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⣰⠃⠀⠀⠀⠀⠰⡅⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠉⠀⠁⠸⠀⠀⠀⢠⠄⠀⠢⡀⠀⠀⢧⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⡶⠒⢲⠶⡶⠒⠶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡄⠀⠠⠁⠀⠀⠸⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠟⠛⠛⠛⠒⠛⠚⠟⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠗⠶⠶⠶⠴⠴⣿⡩⢽⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣟⣽⠀⠀⠀⠠⠤⠄⠀⢰⠀⠀⠀⢈⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⠀⠀⣯⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣏⢼⡀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠒⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⣀⠀⢀⡀⣀⣀⠠⠔⠊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⡏⠈⠈⠉⡉⡉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣩⣩⡩⡍⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣓⣓⣂⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡼⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⡁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣰⡻⢤⣀⣀⣀⢀⣀⣀⣀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⢹⡇
⠀⠀⢀⣀⣀⣀⣤⣤⣼⣧⣿⣯⣼⣯⣥⣴⣮⣽⣯⣽⣫⣋⣝⣩⣉⣙⣽⣫⣪⣗⣡⣠⣟⣕⣽⣟⢙⢁⡽⡭⣫⠿⡿⣩⠞⠕⣽⠁
⠀⠀⠸⣆⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠂
⠀⠀⠀⠈⠉⠉⠉⠉⠙⠚⠛⠛⠓⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠚⠚⠓⠚⠛⠛⠒⠛⠛⠓⠛⠛⠓⠚⠒⠒⠒⠲⠶⠶⠴⠶⠴⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣀⡀⠀⣠⠤⠤⣄⠀⠀⠀⣀⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠞⠁⠀⠀⠀⠈⠟⠁⠀⠀⠀⠹⠉⠹⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠀⠀⠀⠀⠀⢀⠤⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣀⣀⡀⠀⠀⠠⠃⠀⠀⠀⠀⠟⠒⠀⠀⢄⡀⠠⢀⡀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⠙⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠊⠙⠀⠀⠀⠰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⡆⠀⠀⠀⡷⡄
⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⡄⠂⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠣⡄
⠀⠀⠀⠀⠀⠀⢨⠦⠄⠘⣄⠀⠀⡀⠀⠀⡵⠦⠖⠃⠀⠈⠓⠒⠳⣄⠀⠀⢀⡼⠤⠔⢣⠔⠁⠀⠀⠢⡀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠸⣄⡄⠀⠁⠀⠀⢉⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⢀⠇⠀⣴⠃
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠉⢻⠀⠀⢠⠔⢊⣰⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠒⣄⠘⣄⣀⡔⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢆⡀⡀⠀⠀⢀⡞⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢹⡀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⠀⠉⣗⠀⠀⠐⠢⠉⠔⢄⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐⠄⠀⢸⠓⠒⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡔⢒⣿⠀⠀⠂⠸⠶⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠀⠐⠀⢸⡤⢤⡀⢄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⡆⠁⢹⠀⠀⠀⠂⠀⠂⠁⠀⠀⢀⣄⠀⠀⠀⠑⠂⠀⠐⠁⠀⣼⠒⠀⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣸⡀⠀⠀⠀⠀⠀⠀⢀⠔⡞⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠘⢎⡇⢸⣉⠏⠀⠀⠀⠀⠀⠀⣠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡴⠶⠤⠤⡇⢸⡅⠀⠀⢀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⢒⡀⠀⠀⠀⡏⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁⢤⠀⠀⠀⡧⠤⣼⠦⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠙⢲⠃⠀⠀⢠⡏⠉⠁⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⣆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⡀⠀⠀⢸⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢳⡇⠀⠀⠈⡇⠀⣀⠴⠋⢳⡃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢿⠉⠀⠀⠀⠀⢿⣅⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠸⠀⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⡀⠀⠀⣢⠠⢄⡀⠀⠀⠠⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠠⢠⣀⠀⢀⣤⢠⡄⠆⢄⡀⡨⠃⢠⡰⠌⠖⠆⢀⠀⢀⡃⠉
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⡀⠀⠈⠐⠀⡠⢊⣭⡭⣒⠏⣤⣤⢓⣬⡆⣷⡂⣦⠄⡠⣸⠤⠼⡂⠈⠈⢊⠀⢀⡀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⣀⣦⣯⡷⡱⣧⠾⣭⣓⡻⠎⣓⣛⡵⣧⢞⡕⣹⢫⡞⣅⢢⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠉⠙⠛⠛⠙⠓⠚⠛⠲⠻⠻⠙⠛⠚⠛⠳⠿⣯⣶⠿⠿⠟⠓⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠠⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⢂⠀⠀⠀⠀⠂⢀⠁⠀⢄⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠐
⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⡆⠀⠈⠁⠀⠀⢀⠎⠀⠀⠀⡀⠊⠁
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⡅⠦⠠⡀⢠⠄⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⠒⠶⠒⢊⡁⠴⡀⠀⠀⠙⠂⠦⠈⠀⠀⠀⠀⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠀⣤⠄⠐⠠⠊⠀⠸⠴⠦⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠂⠐⠂⠁⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠦⣤⣀⠀⠀⠀⣀⡤⠴⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⢀⣀⠀⢤⠴⠤⠀⠀⣀⡀⠠⠴⠤⠤⠤⣀⡆⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⣠⣴⣾⣧⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣽⣷⣤⣄⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡤⠚⠁⢀⣤⣾⣿⣿⠟⠛⠛⠛⠻⠷⢶⣤⣤⣾⣶⣤⣴⡶⠿⠛⠛⠉⠉⠙⠻⣿⣶⣌⡀⠈⠓⢦
⠀⠀⠀⠈⣇⠀⠒⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡗⠀⣼⠃
⠀⠀⠀⠀⠘⣆⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⢠⠏
⠀⠀⠀⠀⠀⢹⡄⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⡴⠚⠋⠀⠀⠀⠀⠛⠠⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠙⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⠖⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⡀⢀⡀⠀⠀⠀⠀⢀⠀⠐⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⣀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡿⡿⠿⠿⠿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⣀⡙⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣶⣤⣤⣶⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡏⠁⠈⠉⠙⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡉⢻⣿⣿⠏⠀⠀⠀⢀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣷⡄⢹⡿⠀⠀⠀⠀⠈⣀⡀⠉⠛⠋⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠃⠈⠁⠀⠀⠀⢠⠟⠻⠟⠳⣦⣦⡄⠀⠀⣰⡿⠉⠉⠉⠛⠂⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⣿⠻⠿⠟⢳⡄⠀⣨⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠂⢀⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣇⣀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠓⠤⠞⠋⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⡴⠶⠶⠶⠶⢦⣄⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣤⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣨⠛⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠈⠑⠶⠶⠶⠶⢤⣶⡿⠟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡾⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⣀⡠⠴⠞⠋⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠉⠁⠀⢻⡀⠀⠀⠀⠀⢉⣷⣶⣶⣿⡇⠉⠁⠀⠀⠀⠀⢀⡿⠉⢻⣄⡀
⠀⠀⠀⢀⣤⠖⠀⠁⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⠁⠉⠻⠶⣤⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢠⡟⠛⢿⣿⣿⣿⠟⢿⡄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠃⠀⣸⣿⣿⣿⠀⠀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⢿⡏⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⣰⣄⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣴⣶⣿⣿⣿⣿⣦⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣦⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠑⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣿⡇⠀⣀⣠⣤⣀⢀⠴⠚⠉⠙⠀⡠⠊⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠙⠎⠀⠀⠀⠀⠛⠀⢀⡠⠔⠋⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠁⠀⠈⠉⠛⠻⠶⠶⠟⠛⠋⠉⠀⠀⠀⠉⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⣉⣁⣤⠤⠤⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣤⣤⡴⠶⠶⠶⠶⠶⣦⣤⣙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⡄⠀⣀⣠⠤⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠉⠉⢉⣯⠁⠀⠀⠀⠀⠸⣇⠀⠀⠈⠙⠳⣮⣙⠂⠀⠀⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⢷⣤⡶⠻⣧⣀⣀⡀⠀⠀⣀⣀⣁⠀⠀⠀⠀⣀⣀⣼⣧⣀⣀⣠⠳⣄⡴⠀⠉⠛⠛⢿⡖
⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉⠙⠛⠋⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⡰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⢈⣭⣴⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⠤⣴⣞⠁⠀⠙⢿⡄⠀⠀⢀⣾⠏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢸⠀⠀⠀⠹⡏⠉⠉⠙⣿⠷⠶⠶⢷⡟⠁⠀⠀⠈⠓⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠁⠀⠀⠀⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣀⣠⡴⠟⠋⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠉⠀⠀⠈⠉⠓⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⣤⠖⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠙⠓⠶⠻⣆⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⢸⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰⠶⠛⠁⠸⠿⠿⠛⠗⠀⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠀⣧⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣹⠂⢀⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣆⣧⣤⣤⣄⡀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣯⣞⡁⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⢻⣍⠀⠀⠀⠈⢹⠻⡟⠛⠛⠛⠛⣻⠟⠉⣹⠁⠀⠀⠤⠤⡼⣿⠇⠀⠀⠀⠀⠲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡑⠀⠀⢀⡏⠀⣿⠀⠀⣠⠞⠁⣠⠞⠃⢀⣀⣀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠶⠆⠀⠀⠐⢸⡇⠀⢀⡞⠀⣸⢏⣠⠞⢁⡴⢞⣁⡴⠞⢋⣁⡽⠀⠀⣾⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⠏⠀⠀⠈⠉⠀⠐⠿⠖⢋⣡⡴⠞⠋⠁⠀⠀⠀⣿⠀⠀⠀⢀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⡥⠴⠶⠶⣦⠀⠀⣄⠸⣧⠀⠀⠫⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣛⣛⣛⣛⠉⣠⡶⣾⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠶⠮⣭⣻⡟⠛⠉⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠁⠠⠄




⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠄⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠄⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠔⠀⠀⠐⠄⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⣀⠜⠀⠀⠀⠀⠚⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⡊⠁⠀⠂⢰⠀⠐⠀⠈⢁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠄⠊⠀⠈⢃⠀⠔⠝⡡⠶⣆⡰⠁⡀⠑⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⠀⠀⢀⣀⢈⢀⢈⠳⡐⢹⠘⣅⣀⡈⠐⠤⢀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠜⠀⠀⠀⠀⠃⠰⠙⠅⢳⡈⠌⠀⡰⡠⠀⠀⠀⠀⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠁⠀⠀⠏⠀⠀⠀⠀⠀⠀⢃⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠁⠀⠀⠀⠀⠀⡠⠊⠀⠑⢼⡖⠉⠀⠘⢄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢆⠔⠁⠀⠀⠀⠌⢡⠀⠀⠀⠀⠢⠰⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⡘⠀⠈⢂⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁⠀⠀⠀⠀⠐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢅⠠⠟⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠲⠂⠀⠀⠘⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⡄⠀⣤⠀⠡⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢢⡀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠴⣒⡶⠑⢄⠀⠀⠁⢀⣀⠠⢞⢷⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠀⠀⠀⠹⣀⠀⠀⢙⠋⠉⠀⢀⣴⣷⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠹⣷⡀⠀⠀⠈⠉⠐⢸⠀⠀⢸⠁⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⠀⠀⠀⡟⢷⡄⠀⠀⠀⠀⢸⠀⠀⠀⢇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⡇⠈⢻⣆⠀⠀⠀⢸⠀⠀⠀⠘⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠲⠤⣀⠴⢛⠳⢤⡀⢸⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠸⡀⠀⠀⠀⠀⢀⢐⠢⠭⣾⡇⠘⡄⠀⠀⠀⡸
⠀⠀⠀⡎⣉⠭⠛⠉⠉⠉⠀⠀⠉⠉⠙⠻⣒⠒⠒⠒⠚⠪⠽⠿⠋⠻⠉⠉⠙⠒⢞⡓⠒⠐⠒⠒⠀⠀⠂⠀⠀⠀⠲⢄⡀
⠀⠀⢸⠈⠁⠒⠢⠤⠐⠒⠈⠉⠉⠀⠒⠒⠢⠷⠤⠤⠐⠒⠒⠒⠂⠀⠉⠉⠉⠉⠒⠚⠓⠀⠀⠀⣀⡠⢤⡢⠀⠀⠀⠀⠙⠢⣀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣒⠭⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣢⣄
⠀⠫⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠁⠀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣁⠀⠀⠀⡀⠀⠀⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣾⣿⣿⣶⣄⠀⠀⣀⣀⣀⡀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠒⠚⠉⠀⠙⠋⠻⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⣾⡀⠀⣀⣰⡏⠁⠀⠀⡘⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣼⣿⣿⣇⠀⡄⠀⠙⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⠕⠶⠶⠂⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⠀⠀⠀⢹⣿⣩⣔⠒⠶⠶⠄⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢰⣦⣀⢰⡀⢛⣴⡀⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠶⣶⣤⣤⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠀⠀⠈⠙⣿⣿⣷⣿⣌⣿⠀⣅⣽⡜⢷⣤⣼⠿⣿⣿⣆⠀⠀⠀⠉⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣄⣴⡆⠀⢉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢻⣎⣿⣿⠀⠈⠻⣿⣶⠀⠀⣼⠋⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⢻⣿⠗⠊⠙⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠷⣈⠛⠲⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣤⠄⠈⠁⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠙⢶⣷⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠙⢿⣿⣿⣿⣷⣶⣠⣤⣾⣿⣿⣿⠟⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⡿⠿⢿⡿⡁⢀⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⡿⠟⠉⠀⠀⢈⠁⣠⡄⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⢸⣴⠀⠀⠀⠀⠀⠀⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⣀⣀⠀⣧⣴⣿⡏⢠⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢄⢰⡆⠀⠀⠀⠀⣙⣿⣿⣿⣾⣶⣶⣶⣆⡀⠀⡀⠠⠦⠀⢠⡇⠀⠻⣿⣿⣿⣿⣿⣱⣮⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⢀⡀⢀⣦⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠿⣞⠛⣧⣴⣿⣿⣵⣤⣤⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⠀⠀⠀⠘⢷⣽⣿⣿⠿⢛⠛⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣯⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠁⢀⣦⠐⢦⣈⣾⣿⣴⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣰⣿⣿⣧⣿⠿⠛⣡⣿⣿⣿⣿⣿⣿⣿⡿⠇⠠⣿⠏⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠻⣿⣾⣿⣧⣄⠀⠀⢼⣿⣿⣿⣿⣿⡿⢀⣶⣾⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⣿⠀⠙⠋⠁⠀⠚⢿⣿⣿⣿⣿⣷⡏⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⢯⡀⠀⠀⣸⣤⡄⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⡤⠀⠀⠀⢉⡥⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣄⠀⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣠⣤⡜⠻⠟⣻⣿⣶⠶⠀⠀⢹⣿⡟⢿⣿⣿⣿⣿⣿⣀⡈⠙⠂⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠈⠄⠀⠈⠛⠛⠀⠀⠀⠀⢈⠟⢡⣦⣨⣿⣿⣿⣿⣿⣿⣶⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⢤⣼⡃⠁⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⡗⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⣿⡧⠀⠀⠠⣶⡄⠀⢀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⠛⢿⣿⣿⣿⣟⣷⠙⢷⣄⣀⡀
⠀⠀⠀⠀⢠⡖⠶⠞⠾⠟⠻⠝⠁⠤⠀⠛⠿⠿⡤⠶⠀⠀⠀⠀⠀⢀⠙⢦⣄⣀⠀⠀⠀⠚⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢸⣦⡕⠠⠀⣀⡀⠄⢤⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣄⠉⠻⣶⣷⣼⠿⠋⠀⠀⠀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶
⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣤⣤⣬⣝⣛⣙⣿⡿⣿⣷⡆⢀⣸⣟⣿⣿⠛⢿⣦⣤⣤⡤⢶⣦⣶⣶⣶⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣾⣼⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠃

⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠸⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⠇
⠀⠀⠀⠀⠀⠀⠑⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣦⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠠⢤⡏⠀⢸⡤⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢄⠀⠀⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⠀⢀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡀⠀⠀⢸⠀⠀⠸⣆⣀⣀⡴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠙⠶⢤⣼⢀⡤⠞⠉⠀⠈⢧⣀⡀⠸⣄
⠀⠀⠀⠀⠀⢀⣠⠴⠒⢹⡏⠀⠀⠀⠀⠀⢀⣴⣚⠭⠔⠒⠉⠉⠙⢻⠁⢘⣦⠙⡏⠓⠦⣄⡀
⠀⣀⡤⠖⠋⠉⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠉⠙⢺⣄⠀⠀⢹⠃⠀⠀⠀⠈⠙⠲⢤⣀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢾⠀⠀⠀⠀⠀⠀⢧⣠⠼⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠋⠉⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠛⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⠛



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠉⠉⠉⠋⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⢿⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢹⡓⢄⠀⠀⠀⠘⠈⠂⠀⠐⠒⠃⠀⠀⠀⠀⠔⣻⠇⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⠄⠀⣀⣴⠀⣀⡀⠀⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠁⠀⠀⢒⠃⠀⡗⠂⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠀⢈⠋⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠑⢤⡀⠰⠀⠀⣸⠀⠀⠀⢀⡠⠞⠁⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠈⢷⣄⢙⠇⠀⠀⣴⣤⠴⣞⠋⠀⢠⠞⠩⡙⢦⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢸⡇⠀⢀⡹⠿⠒⠚⠉⠁⠀⠀⠘⢦⡴⠃⠀⠀⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⡇⠀⠀⠀⣀⠴⢚⡿⠁⠀⠀⠘⡇⢰⠋⠀⠀⠠⠤⠤⠤⠤⠀⠀⠈⣷⠠⡀⠀⡇⢀⠀⠀⠙⢦⠀⡀⠀⠀⢸
⠀⠀⠀⠀⣧⠴⠒⠋⠁⢀⡞⠀⠀⢠⠇⠀⢹⡏⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⠸⣤⠃⠀⡇⠀⢦⡀⠀⠈⠳⡈⠓⢄⣸
⠀⠀⠀⠀⣧⠀⠀⠀⢀⠏⠀⠀⢀⡞⠀⠀⢸⠁⠀⠀⠀⠈⠉⠉⠉⠓⢆⠀⢸⡄⣧⡀⠀⣧⠀⠀⠙⢦⡀⢀⠝⠀⠀⣼
⠀⠀⠀⠀⢸⡀⠀⠀⠈⠒⠦⢄⠞⠁⠀⢀⡏⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠂⠀⡃⠁⠈⣦⡿⠀⠀⠀⠀⠙⢧⡀⠀⢀⡇
⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⡿⢿⠋⣀⠀⣠⢸⠅⠀⠔⡧⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼
⠀⠀⠀⠀⠀⠈⢧⠀⢰⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡏⠀⢀⡴⠋⠀⡇⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢳⡀⢳⡀⠄⢠⠞⠁⠀⠀⠀⠀⠀⠀⣇⡴⠋⠀⠀⠀⢻⠸⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡴⠃⡇⠀⠀⠀⠀⠈⠀⢷⠀⠀⡇⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠱⡄⢀⣀⡤⣞⠁⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢠⡇⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣈⢢⠊⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⢸⡆⢸⣁⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣷⣠⣇⣀⣀⣀⣀⣠⠤⠼⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠂⠠⠀⡀⠀⠀⠀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⣘⡿⠃⠀⠠⠀⠉⣀⢀⣤⣄⠠
⠀⠀⠀⠀⠀⠀⠄⢰⠾⣷⠀⠀⠀⠠⠀⠀⣸⡋⡿⢀⣿⠂⠂⠸⣉⠛⠁⡧⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⠀⠈⠂⢌⣉⠁⠿⡿⠀⠘⠄⠈⠛⠞⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠢⠄⡀⠀⠽⠄⢀⣦⣄⡀⣠⠺⠏⠀⠀⠀⠂⠀⠘⡀⡀⢤⣤⠂⠈⠀⠀⠀⡀⠤⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠀⠉⢱⡶⠛⠁⠀⠀⠢⡀⠀⠀⠀⠀⠈⠩⠀⠀⠰⠀⠀⠀⠰⠆⠉⣆⡡
⠀⠠⠄⠀⠀⠀⠂⠢⠀⠀⠬⠀⠀⠀⠈⠦⡂⠤⡀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⢘⡠⠴⡏⠉⠓⡢⠤⢀⣀
⠀⠀⠀⢸⣶⣧⣤⡄⣤⢦⣘⠶⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠜⡴⠷⡀⠀⢀⠀⠰⠿⡀⠀⠀⣀⠀⠐⢀⣄⢡⠀⢠⠁
⠀⠀⠀⠘⢿⣿⣿⠀⠋⠁⠀⠀⢂⣣⢀⡀⣠⠊⡀⠀⠀⠀⠀⡀⠇⠀⠀⠐⢠⣦⡀⠀⠉⠉⠀⡌⠀⠀⣦⡴⠊⠀⠄
⠀⠀⠰⠀⠀⠀⠀⠒⠁⠀⠀⡀⢈⡴⠆⢀⠁⣜⡛⡽⣩⣤⣭⡝⢎⠭⢜⡶⡀⢰⢡⣀⠀⠀⠐⠄⣀⡀⠛⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠇⢈⠁⠊⠘⡀⢏⣱⣌⡁⣴⣃⠾⠷⠴⢋⠙⢀⠏⡘⠉⠀⡂⠄⠀⡸⠋⠀⠀⠀⠁
⠀⠀⡀⠔⠈⠉⢀⢀⡄⡈⠉⡐⢶⡶⣦⠲⣴⠦⣭⣥⠃⠈⠀⡿⣖⣘⣿⣶⡵⢾⢃⠒⠀⠈⠉⠁⢠⠀⠐⡒⠂⠀⠉⠉⠂
⢔⠁⠀⡀⠠⡀⠀⢻⠁⠀⠀⠈⠐⠍⣚⣀⢃⠴⠂⣡⢃⠤⣐⣡⡌⢒⠉⠙⢟⢉⣬⢊⣤⠀⢀⣠⣾⠀⠶⠀⠇⣠⠂⣠⠄
⠀⢂⠈⠀⠀⠀⠀⠀⠣⠀⠀⢀⡀⢀⣾⣻⡗⠻⡷⣡⣾⣷⣬⠻⣷⣾⠳⣿⣽⢀⣿⣯⡉⢒⠀⠀⠀⡀⠀⠀⢮⠐⠓
⠀⠀⢀⠀⡀⠄⠂⠁⠀⠀⠀⡈⠉⠒⠩⠙⡛⠻⠶⠧⢿⣥⣾⣴⣿⣼⡧⠿⠧⠾⠛⠋⠀⡈⠀⠀⠀⢇⠀⠰⠾⠤⠄⠀⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢠⠆⠀⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⢕⡄⠃⡷⠊⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠁⠀⠀⡠⠦⣀⣬⢵⢄⠀⠀⠀⠀⠀⠀⣠⣦⣤⣤⣠⣄⠈⠀⣧⣚⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢈⠀⢰⠋⠀⠀⠀⠑⠌⡉⠑⡀⠔⠁⢀⠀⠀⡄⠘⠡⡉⢛⡛⢈⠝⠀⠀⡇⠘⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠜⣇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠺⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠃⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⢤⠶⠞⠥⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠂⣁⣢⠔⠂⠒⢄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠯⢥⣤⠤⣠⣀⣉⣁⣚⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠢⡈⠓⠒⠒⠚⠚⠉⠉⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠈⠐⠤⠤⡤⠒⠀⠀⠀⠀⠀⢂⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠴⠑⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠳⢄⣀⠀⠀⠀⠀⡠⠠⢀⡾⠁⠄⠐⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠒⠒⠒⠉⠀⠀⠀⢀⢜⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠢
⠀⠀⠀⠀⡀⢠⡄⢀⠄⡠⢥⣤⣠⢄⣤⣤⣤⡤⣠⢤⡤⣤⣤⣤⡤⣤⢠⣤⡤⣤⣤⣤⡤⡤⣤⣷⠄⢀