Breakfast Emojis & Symbols

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



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

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

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

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



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

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

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

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠈⠉⠉⠛⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⣠⠔⠛⠳⢶⣖⠒⠲⠶⠦⠤⣤⣀⡀⠀⠉⠓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡠⠊⣱⠋⠙⢦⣀⠉⠓⢦⣄⠀⠀⠀⠀⠉⠓⠦⣄⡀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡠⠋⢠⠞⢡⡶⠒⠶⢬⡙⢆⡀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠞⣁⡴⢋⡤⣤⣍⣒⠶⠶⠗⠀⣹⠀⢠⠞⠉⣷⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣰⢇⣀⠻⠤⢌⡢⣄⡀⠉⢹⡆⡤⠞⢁⡴⠃⡠⣞⣅⣄⣤⣤⣀⣀⣀⣀⣘⣆⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠓⠤⣈⡉⠒⢄⡙⠦⣍⠙⢋⡴⢃⡴⠋⣠⠞⢡⡏⡿⣠⠤⣄⣀⣤⣤⣉⣉⡉⣹⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣭⡓⠦⣈⠓⢮⣛⠋⣰⠋⣠⠞⠁⠀⢸⢠⡇⢹⠀⢠⠖⣲⣦⠀⣼⢁⡟⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⠞⣡⡾⠁⢠⣀⠙⠲⢬⣿⣡⠞⠁⠀⠀⠀⡟⢸⠀⡏⠀⠈⠳⠽⠛⠁⣿⢸⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⠸⢹⠃⠀⠸⡄⠙⠶⢤⣉⡉⠀⠀⣀⡀⢀⡇⣿⠀⡇⠀⣠⢶⣦⣄⠀⡇⡿⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⢦⣸⣄⠀⠀⠹⢤⡀⠲⠤⠍⠉⢉⣼⠇⢸⠁⡇⢰⠃⠀⠘⢤⠿⠞⠸⡇⡇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠙⠉⠳⣦⣀⠀⠉⠓⠒⠚⠋⠉⣀⡄⢸⢀⣇⡘⠒⠲⠤⠴⠦⠤⠴⠇⡇⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠻⣏⠉⠓⠒⠒⡚⠉⡹⠃⠸⠯⢭⣭⣍⣉⣉⣉⣙⣛⡛⢙⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠙⠲⠬⠯⠷⠿⠷⠤⠤⠤⠤⠤⠤⠴⠞⠛⠉⠉⢉⣩⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⡄⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠧⢢⠀⠀⠇⠂⠀⠂⠀⠀⠀⠃⠀⠒⠀⠠⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠂⠀⠀⠈⠄⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠂⠔⠐⠄⠀⢂⠀⠀⡀
⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠲⠤⣄⠈
⠀⠀⠉⠁⠀⠀⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠀⢈⣀⣀⠀⠀⠁
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢀⠋⠀⣀⣠⠴⠉⠒⠠⡀
⠀⠀⠀⠀⠀⠤⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠲⡀⠀⠀⠀⢀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⢀⡀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⣠⠤⢼⢽⡤⣦⣤⣶⡶⣆⡤⣆⣴⣦⠞⡄⠀⠽⠼⠂⠧⠼⠈⠧⠕⠨⠧⠗⠸⠬⠃
⠀⠀⠀⠀⠧⠤⢃⡤⢭⣁⠤⢤⡀⣀⣀⣀⡀⣀⠀⣠⣀⣀⠠⠤⠴⡆⠠⣤⠀⠤⢤⡤⠶⠖⣶
⠀⠀⠀⠀⠀⠀⠊⡑⢾⡇⠚⢂⠟⠠⢶⡟⢈⡜⣇⠘⢣⠂⠀⢘⣻⠄⠶⢽⠀⠘⢯⡉⠁⣿
⠀⠀⠀⠀⠀⠀⠘⠋⠼⠇⡿⡘⡷⠘⠛⣷⣰⢇⢹⣃⡎⢳⠀⠸⠀⠤⠟⠸⢟⠳⣢⠇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣄⠀⠀⠀⠐⢦⡀⠀⠠⠤⢀⠤⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡤⠀⠀⡀⠂⠀⠈⡷⠀⠀⣡⠞⢉⡆⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⣀⣄
⠀⠀⠀⠠⠀⠀⠐⠀⠀⢠⢊⣴⣕⣤⠾⠅⠀⢸⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣠⠋⠀⠀⢘⢆
⠀⡈⠀⠀⡀⠈⠄⢀⠔⣡⠟⠉⠉⠁⠀⠘⠛⠉⠁⠀⠈⠉⠂⠀⣀⣤⠔⠚⠁⠀⣠⠾⠁⠀⠀⢀⡾⠀⡄
⠀⢣⠀⠀⠘⠄⠀⢀⠜⡁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠠⠀⠈⠁⠰⢀⣠⠴⠋⠁⠈⠀⠀⣠⠞⠀⢠⠁
⠀⠀⠇⠀⠀⠈⠓⠋⠀⢧⡀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⢀⡠⠒⠊⠁⠄⠐⠀⠀⢀⡴⠋⠀⠀⠀⠃
⠀⠀⠀⠑⠄⡀⠄⣀⠀⠀⠉⠒⠦⣄⡀⠀⠀⠀⢀⡀⠤⠤⠎⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⣒⡂⠀⠀⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢋⠁

⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⡰⠁⠀⠀⠰⢤⡀⠀⠸
⠀⠀⢀⠐⠄⠀⠤⡰⣄⣀⣀⡸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠲⢦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠈⠉⠠⡈⠀⠐⠂⠒⢦⣔⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⠆⠀⢀⠄
⠀⠀⠀⢨⠓⠠⠄⠀⠀⠀⠀⠄⠀⠁⠘⠂⠀⠀⠀⠐⠒⢲⠊⣄⣀⣀⠌⠎⠀⠀⠑⠀⠐⡘⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠀⠈⠀⠀⢀⡄⠀⠀⠈⢙⠆⠀⠀⠈⠓⠼⠄⠂⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠰⣤⣀⣠⡞⠀⠀⠀⢀⠎⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⢠⡄⡠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠳⢦⣤⣠⡟⠀⠀⠞⡕⠙⢹⠿⡀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠤⠄⠄⠀⠐⠋⠀⠀⡀⠙⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⢀⣔⣤⢾⢆⠀⠀⠀⠀⢀⡀⠀⢠⣾⣡⣀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣠⡴⢻⡿⢊⣭⢾⣧⣄⠀⠀⠸⣿⣦⣀⠉⠲⣬⡙⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠘⢧⣾⡿⠴⠿⠛⠿⢷⢶⠏⡀⠀⠀⠈⠳⠍⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢎⠀⢀⡠⠂
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⢀⡆⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠊⠀⠀⠀⠘⣄⠀⠈⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⣀⣀⡲⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠠⠀⠀⢜⠳⣄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠈⠀⠀⠐⠁⠀⠀⠳⢾⠞⠁⠀⠀⠀⠢⠀⠀⠘⠥⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⡀⠦⣤⣀⡴⠟⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠀⠀⠐⣤⢀⣿⠁⠀⠨⣴⣴⣿⣻⣧⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⢶⡀⠀⠴⣠⣬⡵⣾⣿⡆⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⠀⠀⠈⢿⣸⠂⠉⢉⢉⣉⡛⢿⣦⡆⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠱⣟⡷⠈⣵⠶⢦⣐⡺⢴⡼⠊⣿⣿⠿⣿⣿⣾⢿⣷⠦⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠲⣠⠞⣋⣷⣂⠀⣤⣶⡄⠈⢳⣖⣸⠿⢋⢴⣿⡀⠀⠰⢿⣏⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠃⠀⢠⡟⠉⠉⠈⠿⠀⣼⣛⡓⣶⢨⡟⢡⣾⣧⡘⣿⣿⠷⢦⡐⢻⣅⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢡⡄⢰⣫⡶⣶⡀⠀⣻⠀⡆⢠⣤⣾⣿⣇⢒⡳⢨⣿⡜⡏⠀⣠⣾⠋⣰⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡆⣡⣈⣧⣅⣉⠳⣤⣥⣾⡗⠩⢍⠿⣿⣿⣭⣶⢟⣼⢃⡏⠘⠿⢋⡴⢫⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣽⠣⢙⣭⣬⣻⠛⠟⢨⣿⡿⢿⣏⠀⠀⢀⣽⡿⠃⣿⡟⠉⣛⣽⣿⡿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⣀⣼⣿⣡⣰⣴⣿⣧⢙⣋⣉⢀⣀⣭⠉⣀⢀⢏⣯⣾⡿⣻⣡⣶⡿⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⣬⡙⠛⠮⠼⠿⡿⣉⣉⣉⢉⡉⠙⣛⣛⣾⣿⣿⣿⠿⠿⠛⢋⣁⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣇⠈⠉⣰⠲⠶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢻⡀⠀⢡⠀⠀⠁⠀⠉⠟⡉⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⢁⢸⣇⠀⠠⢠⣷⣤⢰⢾⣿⣿⣷⣿⣿⢟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠘⣿⠆⣽⢸⣿⣶⠰⢾⣽⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⣿⢆⠚⣺⣿⣿⡉⣿⣿⣿⣸⣿⡟⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⢸⠻⡀⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢶⣦⣄⠀⣴⣶⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠻⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣾⣿⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⢿⠿⠟⢻⣿⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡆
⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀⢤⣠⣴⡶⠷⠾⠾⢶⣄⠘⣿⣶⡄
⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣈⣿⡟⠁⢤⡶⠀⠐⣂⢻⣦⢸⣿⡇
⠀⠀⠀⠉⢙⣛⣛⣿⣿⣿⣇⠀⠀⠀⠀⠀⣠⣾⣿⣟⠃⠀⠀⠀⠀⠀⠀⠈⣿⠄⢿⣷⡄
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢺⣿⣿⣿⣿⣷⠀⠀⠀⢀⣀⣀⢠⡿⠀⣿⣿⡄
⠀⠀⠉⣛⣭⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⡟⠀⠀⠀⠉⠁⠀⢸⡇⠠⣼⣿⡄
⠀⣴⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣦⣶⣾⣷⣾⣿⠉
⠀⠈⠉⠉⣩⣵⣾⣿⣿⣿⠖⡀⢀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣟⢿⣿⣿⣿⡆
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⡏⢠⣸⣿⣿⣿⣿⡟⠂⠀⠀⠀⠴⢻⠃⠸⣿⣇⢸⣷
⠀⢾⡿⠟⢋⣵⣿⣿⠟⠋⠀⢠⣇⣿⠃⣿⠹⡿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⢰⡿⠛⠉⠀⠀⠀⠀⣼⡿⠟⠀⠀⠶⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⣿⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣿⠀⡄⠘⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠁

⠀⣿⣻⣿⣿⣻⣿⣿⣻⣿⣿⣻⣿⣿⣻⣿⣿⣛⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⢿⣯⣿⢿⣯⣿⢿⣯⣿⣿⣯⣿⣿⣯⣽⣿⣿
⠀⣿⣾⡟⣿⣶⡟⣿⣾⡿⣿⣾⡟⣿⣶⡟⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⣿⣹⣿⣿⣹⣿⣿⣹⣿⣿⣹⣿⣿⣹⣿⣿⣹⣿
⠀⣿⢿⣷⣿⢿⣧⣿⠿⣧⣼⢿⣷⣾⢿⣧⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣿⣿⣏⣿⣾⣏⣿⣿⣏⣿⣾⣏⣻⣿⣟⣿⣿⣿
⠀⣷⣾⣿⣿⣼⣿⣿⣴⣿⣿⣼⣿⣿⣼⣿⣿⣶⣿⡿⠿⣿⣿⠿⢿⣿⢿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⡀
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣾⡿⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣾⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⣠⡞⠁⣠⢾⣿⣿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⢀⣴⠏⢠⡾⠁⢸⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡁⢠⡟⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡄
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠻⣷⡟⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣿⣆
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣦
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠈⣿
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣀⣾
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⡄⠀⠀⠈⣉⣁⣠⣤⣶⣾⡿⠛
⠘⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠈⠙⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⠋⢁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢟⣙⠛⣻⢛⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣥⣄⣀⣀⣤⠤⠤⠤⠤⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣛⣭⣴⣶⣶⣿⣿⣶⣶⣶⣤⣉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡿⣫⣴⣿⣿⢟⣋⣉⡀⠀⠀⠈⢉⣉⣹⣿⠗⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣫⣾⣿⣿⡏⠑⠿⠿⠟⠿⣿⡆⢸⠻⠟⢿⣏⡾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⣿⡆⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠸⣿⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡅⠠⠈⢿⣷⠀⠀⠀⠀⢠⣆⣊⠀⣠⠀⢸⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡙⣶⣶⡀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠞⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣧⠀⠀⠀⠀⠀⠚⠉⣝⣫⠀⣸⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢽⣷⡈⢻⣿⣿⣷⣦⣤⣤⠤⠶⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⣞⢿⣿⣦⣌⠛⠁⠀⠀⠠⠤⣬⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣎⢿⠈⠁⠀⠀⠀⠀⠀⢠⣿⡄⠑⠄
⠀⠀⠀⠀⠀⢀⠄⠚⣢⠀⠀⠈⢿⣿⠋⠀⢢⡀⠀⠀⠀⠀⠀⡜⠹⡟⡀⠀⠀⠲⠒⠢⣄
⠀⠀⠀⢀⠀⢀⣠⣿⣿⣧⠀⠀⣈⢹⡆⠀⠀⣨⣶⣤⣄⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠖⠉⠀⠀⠙⢟⠳⠉⠘⡁⠀⣸⡇⣀⣴⡿⠀⠻⣿⠷⡀⠀⢰⣺⠟⠓⠲⠀⣀⡄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠉⠁⠀⠀⠀⠈⠀⠹⢀⡿⠁⠀⠀⠲⠤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠐⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⣠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠋⠉⠉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⡉⠉⠉⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⢉⣀⣤⣤⠶⠶⠖⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⢦⣄⡀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⡴⠶⠛⠋⠉⠀⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠿⢿⣷⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢀⣠⡶⠛⠉⠀⠀⣀⣤⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠛⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⣼⠃
⠀⠀⠀⢀⡾⠁⠀⢠⡟⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⡾⠃
⠀⠀⠀⢸⡇⠀⠀⠘⣧⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⢀⣠⡾⠋
⠀⠀⠀⠈⢷⡀⠀⠀⠈⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠛⠋⠁⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠈⠙⠛⠳⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠖⠛⠛⠋⠉⠁⠀⠀⠀⣀⣠⡴⠶⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣛⠛⠛⠓⠒⠲⠶⠖⠒⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⢦⡤⠤⠤⢄⠀⠀⠈⠻⣿⣿⡻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⢀⣀⠀⠙⠻⢶⣤⣣⠀⠀⠀⠈⠻⢿⣤⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠲⠊⠉⡁⠀⠀⠀⠀⠀⠁⠉⠛⠒⢤⣄⠀⠀⠙⠉⢳⣬⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠙⠛⢳⣦⣤⣤⣀⠀⠀⠀⠀⠙⠛⣂⡀⠀⠀⠉⠿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⢯⣭⣅⣁⢀⡀⠀⠀⠀⠀⠀⠈⠉⠋⠑⠶⣄⡀⠀⠀⠐⠿⠶⣀⡆⠈⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠻⠿⠿⠿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠈⠀⡺⠶⣤⣜⠲⣿⣿⣾⣟⣷⣦⣝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠑⠓⠶⣶⣌⣳⣿⣿⣿⣮⣿⣿⣿⣿⠿⠛⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠙⠛⠻⠝⠿⣿⠿⡖⢂⣤⣦⡀⣀⣠⡄⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⢡⡄⠀⢉⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠐⢀⣬⣶⣮⣽⣿⣿⣿⣿⠟⠁⣄⡤⣮⡴⠿⠛⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⢤⠶⣦⣦⣤⣴⠄⣠⣤⣤⢄⢠⡤⣤⣄⣘⣟⣿⣿⣿⣿⣿⡿⠥⡤⠀⣠⡾⠋⠁⣠⣤⣄⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⢿⣿⣋⡇⡤⣼⡾⠋⠀⠀⢀⣿⣟⣿⠇⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠢⠄⢀⠲⡛⠻⣿⣷⣿⣿⡟⢡⣬⣤⡀⠙⢧⡾⣿⡁⠀⠀⠀⠀⠀⠘⠋⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⣀⡤⠄⠖⠀⠁⠀⠀⠤⠄⠤⠆⠒⠚⠋⠉⠀⠈⠉⣛⣛⠿⠀⢙⣛⣣⣿⡷⢼⡇⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠉⠁⠀⠈⠀⠀⠉⠀⠀⠀⠀⡀⡀⢠⠀⣠⢞⣴⣿⣿⣿⣿⣶⡛⠯⠿⠀⣠⡟⠁⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠂⠀⣀⡀⠀⠒⢈⣀⣤⠾⠂⠈⠀⠀⠀⡙⣫⣽⣿⣿⣿⡖⠶⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠴⠶⠿⠟⠯⠐⠃⠀⠈⠁⠀⠀⢀⣠⠀⡴⣐⡿⢿⠿⠿⣻⣿⠁⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢆⣰⠏⠀⠀⠀⠈⢀⣠⣶⣾⣿⣿⠀⠀⠃⢸⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⡵
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⣀⡀⡐⢀⣾⠿⠋⠉⠀⠀⠀⣀⡴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣀⣰⠈⠸⡻⢶⣤⣀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡴⠚⠋⠉⠀⠁⠀⠀⠐⣡⣖⡻⣟⣽⣿⣿⣿⣿⠛⠋⣿⣿⣿⣿⠟⠀⠀⠀⠀⠐⠋⠉⠛⠳⠶⢶⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠴⠿⢿⣿⣿⣿⡃⠀⠈⠁⠰⢿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⠀⠂⠐⠋⠉⠛⣻⣤⣶⠀⠀⠀⠀⠀⠈⠙⠷⣄⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢛⡕⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣠⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⢀⡤⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⡁⢡⠂
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡤⢀⠀⠀⠀⠐⠉⠁⠁⠏
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⠀⡈⡂⠢⢀⠀⠀⢆⠀⡀
⠀⠀⠀⢢⠑⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠐⠀⠂⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀
⠀⠀⠀⠀⠐⠀⠈⠢⡈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠄⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠁⠂⠄⡁⠂⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⢀⠀⠀⠀⠀⠁⠂⠠⠈⠐⠋⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠐⠠⠀⡀⠀⠀⠀⠀⠀⠐⠠⠤⢁⣀⣐⡀⠤⠤⠤⣄⣀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠀⠠⠤⣄⡀⠀⠀⠂⠄⠄⠀⠀⠄⠀⠀⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠅⡀⠀⡠⡈⡦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡈⠄⢲⠁⠀⠁⡘⢍⠐⠄
⠀⠀⠀⠄⠀⠄⠀⠤⣖⠠⠔⠖⠁⠀⢤⠂⠶⣤⠰⠑⢶⢪⠒⢬⠒⠄⠠⠀⠠
⠀⠀⠀⡁⣏⡭⠐⠉⣍⠀⠀⣉⠀⢠⣯⠋⠀⣩⠁⠀⣉⢫⣡⢩⠉⠃⣽⣃⢈
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣩⣭⣉⣤⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⣭⣍⣥⣴
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣈⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠲⢦⣄
⠀⠀⠀⠀⢀⣴⠟⠉⠀⣠⠟⠙⠷⣦
⠀⠀⠀⢀⡾⠷⣤⣴⡾⠋⠀⠀⢠⣿
⠀⠀⠀⠘⣧⠀⠀⢸⣇⣀⣠⣶⡏⢿⡄
⠀⠀⠀⠀⢸⡟⢻⠋⣡⢿⠁⢸⡇⠈⢿⡄
⠀⠀⠀⠀⣸⠃⣼⢰⣿⣾⡆⠀⢿⡀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣰⠏⠀⡇⣼⡃⣿⢷⠀⠈⢷⣆⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠚⠛⠛⠋⠉⠉⢹⣿⣦
⠀⠀⢰⡏⠀⢸⠃⢹⣆⡿⢸⡄⠀⠀⠹⣧⡀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣻⡟
⠀⢠⡟⠀⠀⣸⠀⠈⣿⠇⠈⡇⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⣠⢊⣽⠃
⠀⣸⠃⠀⠀⢻⠀⠀⢹⣇⠀⢹⡀⠀⠀⠀⠀⠙⢿⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠀⠀⠀⠜⣡⡾⠃
⠀⣿⠀⠀⠀⢸⠀⠀⠀⢿⡀⠀⢧⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣧⣤⣀⢀⡀⡀⢀⣀⣤⣤⣶⠖⣋⣩⣀⣠⣤⣄⣄⣀⣴⡾⠋
⠀⣿⠀⠀⠀⠈⡆⠀⠀⠘⣷⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠛⠷⣤
⠀⢻⡄⠀⠀⠀⠹⡀⠀⠀⠘⣧⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡆
⠀⠸⣧⠀⠀⠀⠀⢳⡀⠀⠀⠘⢷⣄⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠊⠉⠉⢁⣼⠃
⠀⠀⢻⣆⠀⠀⠀⠀⠱⡀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠙⠒⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠖⠊⠉⠀⠀⠀⢀⣠⣤⠾⠋
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠋
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠈⠉⠛⠳⠶⡦⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⢾⣿⣟⠋⠉
⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠐⣀⣨⡴⢼⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⣠⠔⣱⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣶⣶⣤⣤⣤⣤⣶⣶⡶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠿⠛⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣛⣥⡶⠂⠉⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣷⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⠰⣿⣩⣶⣿⣿⡟⠠⢶⣿⣷⠶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⣨⣿⣿⣟⠿⠀⢈⣿⢿⣿⣿⣶⣤⣀⠉⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶
⠀⠀⠀⠀⢴⠿⠿⠛⠁⠀⠀⣿⣿⣾⣿⣿⢿⣿⡉⠀⡀⣙⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣶⣿⣷⣄⠴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣋⠈⡿⠿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣤⣯⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠉⠁⠀⠀⠙⠶⢉⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿⠋⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠊⠙⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠋⠀⠶⠀⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢀⣾⠀⠀⠀⠀⣀⣤⢀⡾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⣼⣏⠀⠀⠀⢀⣿⣿⣿⣿⡄⠙⡿⣿⣿⠙⢿⣦
⠀⠀⠀⠀⢹⠋⢹⣿⣿⠁⠀⠀⢿⢿⡿⢘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣸⣿⡇⠀⠀⠀⠘⡛⠁⠘⠋⠈⠠⡟⠉⣿⠰⣿
⠀⠀⠀⠀⢸⣸⠀⣿⣿⡆⡀⠀⠀⠀⠑⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢰⣿⣿⣧⠀⠀⠀⠀⢀⣴⣟⡁⠀⠀⢠⡤⠟⠀⢸⠂
⠀⠀⠀⠀⠸⠏⠀⣿⡟⢱⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡇⠀⠀⠀⣠⡾⠃⣿⠁⠀⠀⠺⠃⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠁⠀⠀⡴⠋⠁⠐⠃⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠇⠸⠇⠀⡀⠀⠆⠈⢷⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡛⠛⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠤⠔⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡻⢿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⣠⣶⠟⠡⠿⠿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠻⢿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠉⠀⢀⣼⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠈⠻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢀⣿⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠙⣿⣯⠍⠉
⠀⠀⠀⠀⠀⠿⠋⣷⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣇⣹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⢛⠙⢶⣟⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⣿⣿⣯⠙⠃
⠀⠀⠀⠀⠀⢀⣴⣿⠧⡘⠀⠀⠀⠉⠻⢿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢿⣯
⠀⠀⠀⠀⠲⢼⡟⠻⣖⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣷⡀⣿⣧
⠀⠀⠀⠀⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⠀⣿⠉⡿⣿⡿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢹⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⡇⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣿⣿⣿⣿⣿⣿⣿⣆⢿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣡⣤⣼⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠃⢺⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⠃⠀⠈⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠿⠟⠿⠿⠻⠇⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⢠⠠⣠⣤⣄⣀⣀⣠⣤⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣾⡛⣷⡶⣾⡿⢿⣂⣏⣩⠿⠭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠪⣐⡛⠾⠯⠽⠧⠻⠿⠥⠂⠢⠀⢠⡠⠀⠀⠀⠀⢀⡀⣀⣀
⠀⠀⠀⠀⠀⢄⣀⡐⢲⣮⠩⠏⣈⠀⠀⠈⠑⠷⡶⡒⠂⠀⢀⠀⣠⠐⣿⣄⠀⠈⠉⠉⠁⡄⠉⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠼⢿⣶⣎⡉⠲⠤⠈⠁⠐⢄⠀⠀⠐⠌⣪⣵⢢⠊⡝⠛⠛⣿⣿⡾⠒⠀⠈⠁⠀⠀⠁⠀⠀⠈⢢
⠀⠀⠀⢀⣤⣕⢌⣙⠿⣷⣷⡆⡌⢓⣠⣦⡀⣁⡐⢧⣿⣯⣠⡐⠀⠠⡀⢸⣿⠙⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⢠⠧
⠀⠀⠀⠈⠉⠛⢿⣾⣭⣝⣛⣛⠓⠛⠻⠭⢁⠙⠛⠀⠉⠻⠿⣍⣂⠤⢄⣤⣿⣶⣦⣄⠀⠀⢀⣠⡄⠈⢁⣺⣅⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠆⣀⡒⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠈⠉⠫⠑⠦⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢀⠧⠖⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢄⠀⠀⢀⠓⠀⠀⠀⣆⠀⠀⠀⣀⡼⠀⠀⠀⢀⣰⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠁⠀⠀⠀⠀⣤⠃⠀⠀⠀⢀⡀⠀⠱⠀⠀⠀⠀⠀⠀⠙⣗⢀⠀⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠤⠄⠠⢤⣕⠢⠀⢀⣀⡀⡠⠤⠐⠊⠁⠀⠀⠀⠀⢀⡷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢤⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠔⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠂⠀⠀⠉⠁⠀⠀⠀⡠
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠏⠀⢠⠂⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⡀⠀⠀⠀⠄⠀⠄⡀⠀⠀⠠⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡿⠀⢀⠏⠀⡴⠁⢀⢀⠀⠄⠀⢀⠀⠀⢁⠌⠀⠀⠆⠀⡄⠀⡀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⠀⠀⠁⠀⡸⠀⠏⠀⠀⠂⠈⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⢤⣤⣤⣤⡶⠾⠟⠋⠀⠀⠀⠀⠃⠀⡜⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣿⣿⣿⣿⣿⣿⣗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⡜⠁⠀⠐⠀⢀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡿⠿⢻⠃⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠊⠉⠀⣀⣠⠶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠽⠋⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚
⠀⠀⠀⠀⠢⠖⡈⠀⢀⠤⠄⠒⠂⠊⢠⡀⠀⠀⠀⠀⠀⠀⠐⠈⠒⠀⠤⠄⠀⠈⢀⠀⠀⠀⠀⣂⠀⠀⠉⠀⡀⣤⣤⡰⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣆⠀⠀⠠⡼⠃⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣭⣷⣴⣧⡼⠀⠀⠀⡘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠴⠶⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⠃⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠨⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠲⠊⢄⠀⠀⠀⠀⠀⠸⣉⡀⠠⠔⠀⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠶⢦⡀⢠⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠑⠦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠱⡄⠀⠠⠙⠂⠀⠀⠀⠀⠀⠀⠌⢧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⢆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠓⢄⣀⣜⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⣤⣤⣤⣤⠀⡤⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣰⢻⠃
⠀⠀⠀⠀⣶⣿⣿⣀⣿⣏⠷⠀⠘⣛⣩⡅⠰⣖⣤⠆⠀⢀⡏⣷⣄⠀⠀⠐⠀⠀⠀⠀⣠⡾⢃⡏
⠀⠀⠀⠀⠠⡹⣿⣿⣿⣿⣅⠐⠂⣾⡇⠁⠀⠈⢳⣿⠃⢰⠃⠘⣿⣦⡀⠀⠀⣀⣴⣿⠏⠀⢸
⠀⠀⠀⠀⠀⠉⠺⠿⠛⠟⠃⠞⠀⠁⠀⠀⠀⠀⢸⣏⣼⣿⠀⠀⠈⠻⣿⣶⣿⡿⠋⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⡻⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⢲⣞⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢦⣤⠞⠉⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢠⣶⡾⠟⢋⠩⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣤⣴⣶⠿⠟⡋⣃⡈⠐⢂⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠄⢀⣀⣤⣶⡿⠷⠜⠋⠡⠀⠈⠀⠀⠘⢷⡄⠈⢂⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣾⠿⢛⠉⠁⠒⠙⣶⡄⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⢆⣀⣠⣤⡶⠟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣠⣼⣿⣦⠸⢛⣩⢥⡲⣯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢀⡶⠿⣛⠫⢭⣤⠶⣾⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣤⣶⡾⠿⣛⣭⣿⡶⠿⣞⣗⣥⠬⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡐⢨⣿⣷⣾⣿⣏⡦⠽⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠾⠟⠛⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠨⣶⣿⡿⣧⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⣿⣶⣦⡿⠿⠛⠀⠀⠉⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢤⣶⣶⣬⣿⣿⡏⢬⣄⡀⠀⠐⡄⠀⠈⠋⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣽⣷⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣴⣼⣿⣿⣿⡿⠋⡏⠙⠛⠦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣿⣿⣿⣛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣄⢲⣦⢻⣰⣆⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢿⡏⣁⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⠻⠉⣹⣇⠻⡿⣾⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣀⠰⣿⣿⣿⣛⠀⠁⠘⠛⠛⠒⠚⠂⠀⠀⣤⣿⣿⠋⣹⣧⣶⣿⡟⢛⣻⣷⣾⡧
⠀⠀⠀⠀⠀⠀⢻⣶⣻⣿⣿⣿⡷⠚⠓⠀⠘⠛⠁⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⣿⡉⣿⣿⣿⣿⣏⠀⠂
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠄⢸⣤⣤⡀⢠⣤⠄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣴⣿⡇⢿⣿⣿⣿⣟⢀⠸⠇
⠀⠀⠀⠀⠀⠈⣀⣼⣿⣿⣿⣿⣿⣿⣿⠃⢀⣶⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡈⢻⣿⣿⣿⣿⣦⣦
⠀⠀⠀⠀⠸⢿⡿⠛⠛⠙⠛⠛⣿⣿⠁⠀⠀⠋⢡⣎⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⣾⣿⣿⣿⠗⣠⡶⠋⠰⢦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠛⣿⣿⣿⡋⢀⡀⢴⣾⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡾⢻⣿⡏⠙⠛⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠿⢋⣽⣿⣶⣿⣿⣋⣽⣿⠁⣸⣿⣿⣿⣿⣸⣿⣿⣏⣻⣦⣿⣿⣏⣿⣽⣯⢸⣿⣧⣾⣏⠁
⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣷⣿⡿⠏⠀⠈⠙⣹⣿⡟⣿⣿⣿⣿⣿⣿⣟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣉⣿⣿⣿⣿⠀⠀⠀⢀⣩⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⡇⠛
⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠈⢹⣿⣿⡿⠋⠀⠀⠀⠨⠝⣟⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠛⠩⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠈⢿⠛⠏⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⢿⣿⣿⣿⡿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠘⠛⠁⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣦⣤⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣲⡶⣤⡴⣶⢶⣞⣿⠛⠋⣉⣁⣀⣠⣄⣈⡉⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠨⠙⡛⢛⠛⣉⠉⠄⣤⣴⣶⠾⠿⠿⠿⠿⠷⣦⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣯⣿⣟⣿⣻⣯⡿⣿⠾⠟⠛⠛⠉⠉⠉⠙⠛⠷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠂⠠⠀⠰⠀⠂⡀⢉⣠⣤⣴⣶⣶⣶⣶⣤⣌⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⡾⣿⣿⣯⢿⡾⣿⣿⣴⣶⠾⠿⠛⠛⠛⠻⠷⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠈⡀⢃⠘⢀⠉⡀⠁⠛⠉⣉⣀⣤⣤⣤⣤⣈⡙⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣏⠙⠛⠓⠛⠚⠛⠋⣉⣠⣤⣴⣶⠶⠶⠶⢶⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣶⣤⣬⣤⣤⣤⣴⡶⠿⠛⠛⠉⣉⣉⣉⣉⠙⠻⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡟⠻⠷⠶⠶⠾⠿⠟⠛⠉⣉⣠⣤⣤⣤⣤⣤⣄⡉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣤⣈⣉⣉⣉⣁⣠⣤⣴⡶⠿⠛⠛⠛⠛⠛⠻⢷⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡿⢶⣦⣤⣤⣤⣶⡶⠿⠛⠛⠉⠉⠁⠀⠀⠉⠉⠛⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⡉⠛⠛⠛⠛⠛⠉⣁⣤⣤⣶⣶⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠈⣶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢰⠀⠀⠀⠀⠀⠀⡀⠉⣆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢃⡀⠠⢀⠀⠀⠀⠀⠈⢀⠈⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠆⠈⠙⠲⣄⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣰⠏⠀⠐⠀⠀⠀⠀⠀⠙⢢⡀⠎⠠⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠃⢈⡿⠷⠀⣀⠀⠀⠀⠀⠀⠀⢀⡜⢉⡛⢦⡀⠂⢄⠀⡤⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢿⡀⠀⠙⢦⡙⠢⡀⠀⠀⣠⠎⠠⠊⠀⠀⠈⠓⢤⣑⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⠀⡙⢦⡀⠀⠉⠒⢄⣀⡴⠃⠀⠀⣀⠀⠀⠀⠀⠄⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠈⠋⢻⠀⡉⠢⣄⠀⠀⠻⠶⢄⠀⠀⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠔⠉⢂⡀⠈⠉⢹⣠⠞⠳⣤⡁⠀⠀⠑⠂⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠄⠠⠀⡵⢢⡀⠈⠡⣴⡾⢧⡈⠓⠦⣄⡀⠘⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠞⣡⠏⡉⣄⡀⠈⠀⡸⠀⢀⣄⣀⣉⡙⠁⡟⠛
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠆⢘⠸⡟⠙⠋⠈⢁⡜⠱⠦⣷
⠀⠀⠀⠀⠀⠀⣬⡁⠠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⡁⢅⠆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠻⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⣤⣤⣤⣄⣠⣤⣤⣤⣀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠉⠋⠉⠉⠉⠉⠋⠉⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⢀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠒⠀⣬⣍⡛⢛⣩⣥⠀⠚⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⣀⠀⠀⠀⠀⣿⡿⠟⠻⢿⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣤⣤⣭⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣛⣛⠛⠛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣛⡛⢉⣉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠺⡷⠿⠟⢤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⡇⡀⠀⠀⠀⠲⣦⣄
⠀⠀⠀⠀⣿⡆⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡞⠀⠀⡄⠈⣿⣯⣦⠀⠀⠀⢾⣶⣤⣴⡿⠋⠈⠻⢦⣤⣤⣤⡿⠟
⠀⠀⠀⠀⢿⡟⠀⠃⡘⠱⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣾⠀⠀⠀⢿⠀⢸⡿⡌⡆⠀⠀⠀⠉⠉⠀⠀⢠⣴⣦⣄⠀⠀⠀⠀⠒⠂⢶⡄
⠀⠀⠀⠀⠘⣿⣄⡀⠠⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⢸⠀⢸⡇⣇⠁⠀⠀⠀⢰⣁⡀⢀⣠⣿⡿⠃⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⢠⠠⢊⡄⠀⠀⡰⠁⠀⠀⠀⠀⠠⡇⢽⠀⠀⠀⠀⠈⠀⢸⣧⣿⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠸⣧⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠖⡀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠈⡏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠈⠱⠎⡀⢡⠆⠀⠀⠀⢄⢠⡆⠀⠀⠀⠀⡟⢰⡟⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣐⣶⠧⠐⢲⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣈⢳⡄⠈⠀⠀⠀⢸⡌⣿⣦⠀⠀⢸⣷⣾⣿⡟⠀⠀⠀⠀⠀⢀⡂⠈⣽⠟⢻⣿⡿⠦⢴⣾⣏⢀⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣈⡒⠀⠀⠸⣧⣹⣿⣧⡄⣸⣿⣿⡿⠁⠀⠀⣠⣤⡀⠈⣙⣿⠇⠴⣾⣿⣦⣶⣦⣿⣿⠄⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⢿⣿⣿⣧⣿⣿⠟⠀⠀⣤⣀⡀⣼⣿⣿⣍⣥⣴⣾⣟⣿⠩⢿⣿⣯⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣄⠓⠒⠒⠒⢢⡐⠶⠒⠒⢲⡌⠉⠛⠋⠁⠀⠀⠀⠀⠈⠙⠻⢿⣶⣻⣶⣶⣽⣿⡿⠿⠿⠿⠛⠛⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠬⣿⠠⣤⠤⠤⢼⡅⢠⡤⡤⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠠⣀⠀⠀⠀⠀⠁⠀⡀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⠀⠀⠀⠀⢺⡷⠀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠠⠂⠀⠐⠁⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣏⣤⣄⠠⣄⣸⣇⣤⣀⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡⣿⠈⠉⠁⠠⣽⡆⠉⠉⠴⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⣀⡈⢿⣆⣤⣀⣄⣿⣧⣤⣤⡄⢬⠞⣦⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡎⠀⠘⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣛⣛⣛⣐⣰⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠇⠠⣄⡽⠁⠀⠀⣠⣄⡀⠀⢈⡛⠛⠛⠛⠓⠈⠹⠗⠂⣀⣄⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣞⣉⣿⣿⣿⣿⣶⣶⣶⣿⣿⡇⠠⣄⡀⣍⡁⠛⠷⠦⡹⣿⣛⠛⠛⠶⠶⢶⣤⣤⡤⣼⡿⣿⣧⡀⢀⣤⣴⣶
⠀⠀⢀⣿⣦⡀⣄⢀⣀⣿⣦⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠮⡛⠶⢿⣛⠲⣤⣀⣀⠉⠁⠐⠒⠐⢛⡋⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⠛
⠀⢀⠊⠁⠊⠛⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠢⡀⠙⠳⣴⠛⠛⠛⠛⠶⣶⣤⣄⡀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣷⣆
⠀⠠⡼⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠑⠀⡈⠻⠦⣠⣴⣶⣶⣿⣽⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⢙⣣⠄⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠠⣚⡉⠀⢀⡴⠂⠀⠀⠀⠀⠀⢸
⠀⠀⢀⣀⣀⡀⢤⣤⢄⣥⣔⣻⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣛⣧⣶⣠⣤⠄⣀⣀⠀⠀⢸
⡶⢿⣿⣿⣿⣿⣿⣶⣨⣭⣟⣻⣯⣥⣭⣛⣛⡿⢿⣿⣿⣿⣿⡿⢿⣛⣻⣥⡭⣿⣛⣿⣭⣆⣶⣿⣿⣿⣿⠷⣾
⠉⠛⠒⠿⠯⠭⣽⣯⣙⣛⣙⣻⣷⣶⣍⠛⠛⠫⠭⠤⠘⠓⠖⠛⠻⠿⣛⣋⣞⣒⣒⣒⣹⣥⣭⠭⠽⠷⠚⠋⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠉⠒⠳⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⣠⠀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠚⡡⠂⢠⠃⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠴⣊⣠⠴⠃⠀⠀⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡴⡵⠋⠁⠀⣠⢀⠤⠊⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⢀⢞⠎⠀⠀⢀⡜⡕⠁⢀⠁⠀⢰⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠔⠊⠁⠀⢀⡰⢋⠎⠀⠀⢀⠎⡸⠀⠀⡘⠀⠀⢘⠀⡇
⠀⠀⠀⠀⠀⣀⣀⡠⠔⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⡰⠃⠀⠀⢠⠎⢠⠃⠀⠀⡇⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠰⡇⠀⠐⠒⠈⠉⠉⠉⠉⠉⠉⠘⠋⠉⠀⠀⡠⠊⠀⠀⠀⡴⠃⠀⡎⠀⠀⣸⠁⠀⠀⠸⢀⠃
⠀⠀⠀⠀⠀⢸⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⢀⡴⠊⠀⠀⡸⠀⠀⢠⠇⠀⠀⢀⡇⢸
⠀⠀⠀⠀⠀⠈⢄⠀⠉⠒⣠⡤⠠⠤⠤⠒⠊⠁⠀⠀⠀⡠⠖⠁⠀⠀⠀⡰⠁⠀⢀⠎⠀⠀⠀⡸⢀⠇
⠀⠀⠀⠀⠀⠀⠈⢢⡤⠊⠀⠀⠀⣀⣀⣀⣀⠤⠔⠒⠉⠀⠀⠀⠀⣠⠎⠀⠀⢀⠎⠀⠀⠀⢀⠇⡜
⠀⠀⠀⠀⠀⢀⡞⠉⠀⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⡰⠃⠀⠀⠀⢀⡎⡰⠁
⠀⠀⠀⠀⠀⠀⠱⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⢀⡠⠊⠀⠀⠀⠀⢀⠎⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⣀⠙⠢⠄⣀⢀⣠⠤⠒⠒⠉⠁⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⢀⡴⢃⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⠤⠊⠀⢀⣠⣤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠢⠤⠤⠄⣀⠠⠤⠤⠒⢊⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠀⠐⠒⠒⠉⠁

⣿⠟⠉⠙⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢹⣏⣿⢉⢉
⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⣀⠀⠀⠀⠐⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠈
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠠⠀⠀⠀⠰⣀⠀⠀⠀⣀⡠⠔⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠐⠀⠀⠀⠀⠂⠉⠉⠉⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠
⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠠⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠰⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠀⠀⠀⠀⠀⢰⡖⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⢁⣥⢉⣍⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠺⠻⠿⠟⠻⠸⠿⠀⠀⠀⠀⠀⠳⠤⠄⠒⠁⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠛⠿⠽⠣⠞⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠐⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠓⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠁⠐⠀⠐⠂⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠆⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠦⠤⠤⡤⠴⠐⢂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠
⠀⠀⡁⠀⠀⠀⠐⢄⣀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢧⡀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠠⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⣀⣀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⡏⠙⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠁⠀⣿⠤⡀⡆⠀⠀⠀⠀⢀⣧⢄⠀⡇⣶⡄⢸⡤⠄
⠀⠀⠀⠀⠀⠀⢸⠶⠶⢾⡶⠶⠶⡷⠖⠷⡇⠀⠀⠀⠀⢸⡷⠶⠶⣷⠷⠶⢮⠶⠶⠶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠷⠈⡟⠁⠀⡇⠀⠀⠀⠀⢸⡇⠉⠀⡿⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⡟⠛⠉⡞⡛⠛⢳⣛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⢸⡇⣚⣀⣇⣁⣂⢸⢋⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⡟⣭⠁⣙⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⣶⣶⣤⡶⠒⠃⠀⠀⠀⠀⣯⠭⠤⡭⠭⠤⣥⡤⠤⢼
⠀⢰⡀⠂⢀⣀⣤⣶⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡠⠀⢳⠀⠀⢸⠀⠀⣠⣔⠂⠁⢀⣀⣀
⠀⠖⠛⠋⠉⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡗⠒⠒⡖⠒⠒⣾⠒⠒⢺⠀⠀⠈⠙⠳⠾⠯⠙⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣭⣁⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠘⡇⢀⣀⡃⠀⠀⣻⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣿⣷⡤⠤⠽⣶⣶⠒⠛
⠀⠀⢀⣀⠀⣶⣦⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⢀⣠⡄⠀⠶⡀⣀⣹⠶⣶⡔⠀⠀⠀⠀⠘⣷⣰⣤⣤⠬⣃⠶⣶⠛⠣
⠀⠐⢿⣿⣿⣿⣿⣦⣭⣟⣛⠉⢛⡳⢐⣻⣅⡈⠻⣤⡒⠂⠈⢳⠄⣤⡜⠋⠪⣟⢀⣀⣀⠛⠋⠉⠈
⠀⠀⠀⠈⠛⢿⣯⡉⠽⠿⣿⣿⡵⠖⠉⠀⠛⠂⠀⠙⣿⣾⣝⠃⣀⣙⣆⣴⣶⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣟⣿⣟⣿⣿⣻⣿⣟⣿⣟⣻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣾⣿⣷⣿⣿⣾⢻⣾⡿⣷⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣽⡿⣯⡿⣿⣽⢿⣽⡿⣯⡿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣯⣿⣿⣽⣿⣽⣿⣯⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣻⣷⣟⣷⣿⣻⣾⣻⣷⣟⣷⣿⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠿⠷⠿⠷⠿⠿⠾⠿⠷⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠥⠤⠤⠤⠬⠭⢉⣀⣒⡒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠋⠂⢿⣍⡓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠐⠀⠀⠀⠀⠀⡴⠀⠀⢸⠧⡀⠀⠀⠀⠀⡠⢆⠠⠈⠁⠀⡀⢸⠹⡉⠳⢦⡉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⡹⠆⠀⠀⠀⠐⠈⡆⢿⠋⠉⡹⠋⠔⠈⣀⠄⠀⠀⠀⢸⠀⡇⠀⠀⠙⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡴⠁⠀⠀⠐⠂⠀⠀⠀⠀⡇⢸⢀⠼⠁⠀⠀⠀⠀⠀⠤⠀⠀⠘⣀⠇⠀⠀⠀⠀⠘⢧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠚⠁⢤⠀⠀⠀⠀⠈⠀⣀⠀⢃⢿⠣⣀⠀⠋⠀⠀⠀⠀⠀⠐⠂⠀⡏⡷⡀⠀⠀⠀⠀⠀⢳⡄⠘⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡏⠑⢤⡀⠀⠀⠀⣀⠀⠀⠀⠀⢸⢸⣦⣨⠑⢤⡀⠀⠀⠆⠀⠀⠀⠀⣇⢸⠘⡄⠀⠀⠀⠀⠀⢷⠀⠸⡆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢣⡈⠲⣗⠈⠢⣄⠀⠉⠀⠀⠀⠀⠘⡄⡧⣼⠢⣄⠉⡢⣄⠀⠀⢠⠀⠀⢹⠈⡆⠘⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡙⢦⡑⢄⡘⠑⢤⡀⠐⠃⠀⠀⡇⢳⡈⠑⢌⡑⢄⡀⠑⢤⡀⠀⠀⠸⡀⡇⠀⡄⠀⠀⠀⠀⢈⡇⠀⢸
⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⠀⠈⠣⣄⠉⠢⣌⠦⣄⠈⠢⣄⠀⡄⢷⢸⠙⠦⡀⠝⠣⣹⡢⢄⠉⠢⣌⠀⣇⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠹⡗⢏⠈⠑⢷⣝⠢⣀⠑⢦⣸⡇⠀⠀⠈⠲⣄⠈⠙⢦⡉⠢⣌⠑⢾⣇⠀⠀⠀⠀⠀⢀⡾⠀⢠⡟
⠀⠀⠀⠀⠀⠘⣄⠠⡀⠀⠀⠀⠀⠀⠙⢦⡑⠦⡠⠌⠓⢌⠱⡦⣈⡿⡄⠀⠀⠀⠀⠑⢬⡁⠈⠲⢜⣍⠺⢛⡆⠀⠀⠀⢀⡼⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠀⢄⠀⠀⠀⠀⠀⠀⠙⠢⣌⡒⢄⡈⠑⠻⣆⢥⡽⠀⠀⠀⠀⠀⠀⠈⠓⣄⡒⠩⠦⣽⠁⠀⠀⣠⡞⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠦⢄⡉⠙⣿⣀⣀⡀⠠⠄⠐⠀⠀⠀⠈⠒⠄⣻⠆⣠⠾⠋⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠛⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣉⡓⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⣁⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣬⣉⣉⣛⡒⠒⠒⠒⠚⢛⣋⣉⣉⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⡿⠿⠿⠿⡿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠉⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣦⣀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⢈⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠛⠉⠉⠀⢀⣾⣿⡿⠃⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣀⣤⣤⣶⢶⣿⣿⠟⠛⠛⠛⢛⣛⡛⠛⠛⠛⠛⣛⣻⣿⠿⠶⢶⣦⣤⣄⣀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣭⣄⣀⣀⠉⠁⠀⠿⢶⠆⠈⢩⡄⠀⠿⠃⠀⠉⠉⠻⠇⢀⣀⣀⣬⣽⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠈⠉⠙⠛⠛⢛⡻⠿⢶⡶⠶⣿⣷⠶⠶⠶⠶⠾⠿⠟⠛⠛⠛⠉⠉⠀⢀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⣦⣤⣤⣄⣘⣋⣀⡘⠛⠷⠈⠋⠀⠀⠸⠇⣀⣀⣀⣀⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⡀⢀⡀⢀⠀⢀⠀⣀⠠⢠⠀⡀⢀⡀⢀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠛⠘⠋⠘⠃⠙⠃⠛⠡⠋⠀⠀⠚⠯⡘⠃⠙⢁⠂⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢉⣄⣄⡀⢠⡦⠤⠀⡐⠀⠠⠀⠀⠀⠀⠠⠁⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁⠘⠛⠍⠿⠆⠃⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠁⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⣰⣦⣿⠅⠢⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⠸
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡠⠈⠈⢀⠁⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠈⡃⠀⠀⠁⠀⠀⠅⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢦⠰⠀⠀⠀⠀⠀⢀⠀⠴⠤⠦⠆⠀⠀⢀⢄⠀⠀⠠⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠚⣆⡀⠀⠀⠈⠂⠀⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠁⠀⠀⠀⠄⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠌⢠⠂⠀⠀⢐⣦⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠠⠀⠀⠀⠀⠐⠀⠂⠀⠀⠊⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠘⠄⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⢿⢠⣾⣽⡿⠞⣿⠀⠰⡏⠥⠀⠀⢾⣿⣿⣹⠷⠀⡷⠺

⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⡀⠰⠀⡀⠰⠀⡀⠰⠀⡀⠐⠀⡀⠐⠂⡀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠁⠠⠀⠁⠠⠀⠁⠠⠀⠁⠠⠄⠁⠠⠄⠁⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠁⢀⠀⠁⢀⠀⠁⢀⠀⠁⢀⠀⠁⠀⡄⠁⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠂⢀⠀⠂⢀⠀⠂⢀⠀⠂⢀⡀⠂⢀⡀⠒⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠆⠈⠀⠆⠀⠀⠆⠀⠀⠆⠀⠀⠆⠀⠀⠄⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣄⢠⡀⣠⣄⢀⣤⡀⣠⣄⢠⡀⠀⣠⡀⣤⣤⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣿⣼⢿⡇⣿⣾⠈⠃⡇⣿⢸⡇⠀⡿⣇⢸⡇⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠇⡿⢸⠟⣧⡿⢺⣴⠇⣧⡿⢸⣥⣴⠗⢿⢸⡇⢸⣤⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠦⠤⠤⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠄⠈⠀⡽⢇⡠⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡂⠀⠀⠀⠈⠉⠉⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀⠤⠀⠀⠀⠀⠄⠀⠀⡰⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⡞⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠒⢩⠔⠒⠞⡰⠁⢠⣟⠁⠀⠠⠤⠤⣄⢀⣰⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡴⠁⢠⠇⠀⠉⠁⠒⠐⠊⠀⠠⢙⠥⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⡖⠀⠀⠓⠂⠤⠼⠁⠀⡿⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⡀⠀⠀⠀⠁⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡶⠒⠦⢤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣶⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠠⠤⠤⣄⣀⣀⣀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⢰⡶⣿⣿⡿⣻⡿⢿⣭⣿⣿⣿⣿⣻⡿⠟⠛⠛⠛⠷⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣯⣟⡿⢿⣿⢿⣯⣿⣿⣿⣿⣟⣿⣶⣶⣶⣶⣶⣤⣌⣉⠙⠛⠋⠉⢉⣉⠙⠻⣦⣀⠀⡀
⠀⠀⠀⠀⠀⢸⣷⣟⡿⣿⢿⣷⣿⣯⣿⣿⢿⣿⣿⣻⣇⣀⣀⣤⣄⣀⡉⠛⠛⠿⠿⠟⠛⠛⠛⠳⢮⡙⠛⠓
⠀⠀⠀⠀⠀⣿⣯⣿⡿⣿⣿⣷⣾⣟⣿⣾⢿⣻⣾⣟⣿⠟⠛⠛⠛⠛⠛⠿⠶⢶⣶⣶⣶⣶⠶⠶⢦⣍⡛⠿⠆
⠀⠀⠀⠀⠀⣿⣻⢿⣿⣷⣾⡯⠾⠿⠿⢽⣿⣟⣿⣿⢿⣤⣶⣶⣶⣷⣶⣶⣦⣤⣄⣀⣀⣠⣤⣤⣤⣬⣙⠳⠶⠆
⠀⠀⠀⠀⢸⣟⣿⡿⠞⠋⠁⣀⣀⣤⣤⣀⣀⠈⠉⠙⠛⠋⠉⠀⣀⣀⣀⣀⣀⠉⠉⠉⠉⠉⠉⠉⣉⣀⣉⣙⡓⠶⠶
⠀⠀⠀⠀⠘⠉⢁⣠⣴⣾⠿⠛⠛⠛⠛⠛⠻⠿⣷⣶⣶⣶⣿⡿⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠋⢉⣙⠛⠛⠛⠂
⠀⠀⠀⢠⣶⡿⠿⠛⠉⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣶⠾⠟⠛⠛⠛⠛⠛⢛
⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠛⠉⢁⣀⣀⣀⠉⠉⠛⠛⠿⠿⠟⠛⠉⢁⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⠶⠛⠛⠛⠛⠛⠉
⠀⠀⠀⡿⠿⠛⠋⢁⣠⣤⣶⡿⠿⠛⠛⠛⠿⠿⣶⣶⣦⣤⣶⣶⠿⠟⠛⠉⠉⠉⠉⠉⠙⠛⠛⠉⠉
⠀⠀⠀⣀⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠼⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⡤⡄⢀⢤⣤⡠⣄⣀⠠⢠⣤⠄⣤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠉⠁⠁⠁⠀⠁⠀⠁⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠁⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⡶⠀⠀⠠⠤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠃⢠⠊⠢⣀⡀⢀⠂
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠧⣀⣀⢀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠣⣄⠘⠊⠱⣀⡼⠁
⠀⠀⠀⠀⠀⢀⠊⠀⠀⣄⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠉⢐⠒⠉⠘⣄
⠀⠀⠀⠀⠀⢘⡀⠀⠀⠇⠑⠤⢄⠠⠀⠀⠀⢱⠂⠀⠀⠀⠀⢸⡁⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠈⠈⠑⢦
⠀⠀⠀⠀⠀⠈⢏⢆⢀⠀⠀⠀⠀⠉⠉⠐⠖⠋⠀⠀⠀⠀⠀⠀⠏⢒⠈⠉⠁⠀⠀⠀⠣⠤⠲⠇⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠘⢥⣅⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢆⣠⡄⠀⢀⡠⠀⠀⢀⠔⠁⠘⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠒⣦⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠤⡀⠝⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠉⡦⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠇⠀⠀⠀⡜⢀⡤
⠀⠀⠀⠁⠀⢀⢤⡍⣄⠀⠂⠀⠁⠈⠀⠀⠠⠀⢸⡼⠣⣤⣤⠄⢉⣀⣀⡀⠀⠀⠬⠄⠀⠀⠀⠜⢇⣀
⠀⠄⠀⠀⠀⠙⢶⡃⠀⠀⠀⠀⠰⠀⢰⠮⣁⣀⠟⠀⠁⠀⠀⠀⠀⢨⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠆⠂⠀⠀⠀⠀⠀⠠⠤⠤⠖⠀⠀⠂⠐⢧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠐⡰⠃⠀⠒⠄⠄⠠⠴⡒⠒⠛⠒⢂
⡆⠀⠀⠀⠀⠠⠎⠀⠀⠀⠁⠀⠀⠈⠉⠈⠁⠤⢀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⠁⠰⠂
⠣⠤⢤⣤⣄⣀⠁⠀⠀⢀⣤⣀⣀⣀⣀⣀⡤⠒⠺⠭⠭⠭⠭⠭⠗⠊⠀⠀⠀⠀⠀⠤⠤⠤⠔⢃⠀⠀⠀⡀
⣆⣀⣀⣀⣀⣉⣛⣛⣚⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣛⣛⣋⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠈⢷⡄⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⠎⠐⠀⠀⠀⠀⠀⠀⠙⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣟⠈⠻⠟⠒⣶⣢⠀⠀⠀⠀⠀⠀⣠⡾⠑⠚⠋⠀⠀⠉⠉⠙⢢
⠀⠀⠀⢀⡞⠀⢀⣠⠀⠀⠠⢄⡀⠀⣿⣷⠴⢆⠀⢀⡀⢨⡀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠇⠈⢡⣤⣄⣴⣿⣿⣼⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠂
⠀⠀⠀⡜⠁⣤⡩⠀⠀⠀⠀⠀⠱⡀⢹⣿⠀⠀⠀⠈⢻⡌⠃⠀⠀⠀⠀⠀⢠⣾⣵⣤⣶⣶⣾⣿⢿⡷⠈⢛⣿⠀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢶⣯⠔
⠀⠀⢰⡇⢸⠏⠁⠀⠀⠀⠀⠀⠀⢱⠘⣧⡄⠀⠀⠀⣬⢻⡆⠀⠀⠀⣀⣴⣿⣿⡿⣿⢟⠛⢾⣿⣾⣾⣿⠿⠟⠀⠀⢸⣯⣝⣛⣃⣀⡀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⠀⡠⡿⣸⠀⠀⠀⠈⡟⣾⠉⠙⠹⠯⠘⠀⠾⢉⡿⠋⠀⠀⠀⠀⠀⠈⠻⠯⣯⣉⣟⣛⣻⠿⢶⡾⣿⡽⠁
⠀⠀⠘⡆⠀⠓⠄⠂⠀⠀⢀⣠⡴⠃⣸⣿⣗⣔⣣⢤⢴⡏⠀⠀⠀⢐⣷⣿⣆⣦⣀⣠⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠚⠛⠉
⠀⠀⠀⠈⠢⣀⠙⠛⠛⠒⠚⠉⣀⣴⣿⡿⠿⠛⢻⣻⠟⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠚⠛⠛⠛⠷⠶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣤⣤⣤⣤⣀⣈⡐⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢤⠤⠤⠤⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣛⠛⠉⠉⠀⠀⣀⣠⣭⣿⣶⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣭⣤⣶⡾⠶⢲⠷⢶⡶⠒⠲⠶⠦⢭⣿⣆⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣟⣛⣻⣿⣿⡿⢿⡋⣸⠓⢲⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡾⢫⡁⠀⢀⠄⢉⠀⢠⠆⠐⠆⣡⡴⢋⣹⢿⡆⠀⠀⠀⠈⡇⣿⡧⠭⠯⠩⠉⠉⠁⠀⠀⣼⡃⣧⠴⡫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣷⣦⣴⣓⣀⡀⣉⣀⣀⣀⣀⣤⡥⢘⣋⠴⢻⠀⠀⠀⠀⠀⠹⣜⠿⣀⠀⢰⣶⠀⠀⠀⡰⢿⡼⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢿⣿⣿⠛⠛⠛⠛⠛⠛⠛⡻⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠘⢻⣍⡳⠶⠶⣶⣒⣻⣷⠞⠁
⠀⠀⠀⠀⠀⠰⣶⡆⠤⣄⡀⠀⠀⠀⣿⣿⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛
⠀⠀⠀⠀⣴⣶⠋⠉⠓⠲⡿⣄⠀⠀⠘⢿⡷⣽⣾⣿⣷⣦⣤⣤⣤⣠⣴⠃⢠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣶⣤⣄⡀
⠀⠀⢀⡾⠟⠁⠀⠀⢀⣼⣥⣹⣛⣢⠀⠀⠙⠲⠬⣻⣿⣿⣿⣿⣿⣿⣷⠾⠟⠋⠀⠀⠀⢀⠴⠂⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀⠙⠒⠋⢹⡆
⠀⠀⣿⠏⠓⢦⡀⣠⣞⣯⣿⡿⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⣀⠀⡀⠁⡀⠑⢮⠻⣀⠀⠀⠀⠀⣽⢿⡟⠋⠁⠈⠀⠀⠉⡄
⠀⠀⣿⡇⠀⠀⠁⣿⣿⣿⢁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠻⡷⠈⢀⣷⡙⣌⣷⠟⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⢀⠜⠃
⠀⠀⣿⣇⣤⣀⠀⢸⣿⣷⣧⣤⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢿⡆⠀⢰⠈⣷⣿⡟⠀⠀⠀⠀⠐⣻⣶⠀⠀⠀⠀⢀⡾⠃
⠀⠀⣿⣿⣿⣋⠛⢿⣿⡟⠉⠉⠉⣿⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⢀⣲⠀⡀⠈⡇⢀⡟⢁⣀⣯⣠⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⠛⠳⢆⠶⠗
⠀⠀⣿⣿⠟⠝⠀⢸⣿⡇⠠⠀⠀⣿⠀⠀⢰⣯⣤⣖⣂⣉⣽⣿⣿⡆⠀⠀⢈⠁⠠⠽⢿⣧⠼⠤⠿⠉⠁⠈⠛⠉⢀⣀⣀⣀⡀
⠀⠀⣿⠋⣄⠆⠀⢸⣿⠇⠀⠈⠀⣿⠀⠀⠈⡄⡆⠀⠉⠉⢉⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠂⡚⢩⣶⣰⣯⡝⠛⠓⠲⢤⡀⠀⡐
⠀⠀⣿⠀⢀⣆⣠⢸⣿⣦⠀⠀⠀⣿⠀⠀⠀⡇⡟⠀⠀⠁⢸⣿⢸⠀⠀⠀⠀⠀⠀⢀⠔⠋⠈⣁⣤⠼⠛⣉⣉⠙⠓⠈⠉⠁⢀⣠⠤⢀⠀⠈⢶⣮⠓⢤
⠀⠀⣿⣤⣈⣿⣿⣸⣿⢿⣴⣶⠶⢿⡄⠀⠀⢻⣷⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠐⠁⠜⣠⡞⠁⠠⣾⢿⢋⢉⡿⠆⠀⠀⠀⣿⣟⠀⣸⡇⠀⢸⣿⣣⣸⣇⡀
⠀⠀⣿⡯⡿⢿⠻⣿⡟⢾⠉⠀⢀⢸⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠰⡀⠀⡗⠦⠀⠀⣙⣛⠛⠋⠡⣀⣀⣀⠀⠈⠉⠛⠋⠀⣠⡾⢛⣿⣿⡯⠁
⠀⠀⣿⡟⠿⠎⠀⣿⣇⠘⠀⢀⠛⢘⠀⠀⠀⠸⡇⠀⠀⠀⢸⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⢿⣿⡟⠻⢷⣀⠈⠩⠉⣉⣀⣠⣤⣾⡿⠟⣚⡭⠟⠉
⠀⠀⠉⠻⢷⣤⣀⢿⡿⢶⣾⡷⠚⠁⠀⠀⠀⠀⢧⣴⣶⣴⣊⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣉⣉⣉⣉⣉⣉⣭⣥⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠈⠉⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⠷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠴⠋⠀⠀⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠴⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⡀⠔⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣠⡂⠹⣄⠀⠀⠈⢻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢶⣌⢦⡀⠀⠀⠈⠛⢿⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣝⢦⡀⠀⠀⠀⠠⠊⠉⠉⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁
⡇⠘⣄⠀⠀⢀⡀⠀⠠⠤⠤⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠘⢦⣽⣶⣦⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠂⠠⡄
⠀⠀⠀⠀⠀⡠⠒⢠⠖⠒⠒⠒⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⡀⠐⠀⠀⠀⠐⠈⠁⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠁⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠉⠂⡀
⠀⠀⠑⠄⠀⠀⠀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⢀⡀⠰⠤
⠀⡀⠒⠀⠀⠀⠀⢠⠐⠀⠀⠀⠙⠄⠂⠀⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠤⠀⠀⠉⠁⠈⢡⠀⠀⠀⡘⠀⢈
⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠒⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢠⣤⢁⠀⠄⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠿⠂
⠀⠀⠁⠈⠈⡀⠀⠀⠀⠀⠀⠀⠰⢤⣤⠆⠀⠐⠂⠀⠒⢢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⡲
⠀⡀⠀⠀⠀⢀⢀⢤⢠⠀⠀⢀⣀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠉⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢶⢄⣀⠐⡒⢋⣂⠊
⠀⢀⡀⠀⣀⠜⠙⠣⡀⠀⠠⠜⢣⣈⠂⠀⠀⠀⠀⠀⠀⠒⢆⣨⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡃⠀⠉⠉⠈
⠀⠀⠀⠀⠙⠀⠀⠀⠈⠠⠀⠀⠀⡍⠈⠀⠀⠃⠀⠀⠀⠨⠉⠘⡁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢐⡀⠀⢀⠆⠀⠢⠐⠀⠴⠀⠂⠐⠞⡝⠡⠔⠲⢦⡤⢀⡠⠀⠤⠦⠈⠀⠀⠀⠄⡀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠈⠠⠤⠀⠀⠀⠈⠉⠁⠂⠀⠀⢜⠀⠀⢀⠄⠋⢇⠀⠀⠀⠉⢉⠹⠀⠉⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠂⠚⠥⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⡂
⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⢛⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣠⣄⡀⠀⠀⢀⣠⠴⢚⣋⣭⠤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⢭⢼⠖⠗⢋⢻⡶⠞⣫⡵⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠾⡖⠂⣍⣨⠷⢊⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣞⣉⣭⣥⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠶⠶⠦⠤⠤⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠫⢅⡶⠬⠖⡀⠵⢠⡤⢈⡓⠦⠄⣉⣙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⢀⣠⢞⠚⠣⡼⢑⣩⣄⢘⡀⠱⡶⠀⠆⡈⢁⡤⠤⡄⠨⢙⠊⢂⡉⡳⣆⡀
⠀⠀⢰⡶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠓⠒⠒⠶⠶⠶⠶⠾⠿⢶⡆
⠀⠀⠀⠻⣔⠂⠒⠀⠒⠀⠂⠐⠂⠒⠂⠒⠀⠐⠀⠒⠀⠒⠂⠒⠀⠒⠂⠒⠀⠒⠐⠂⢒⡾⠁
⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⠀⡘⠡⠉⠁⠁⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣯⣻⣆⠀⠀⠠⠁⠀⠀⡀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠅⠘⠟⢧⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠠⢤⣤⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⡥⣄⡉⠻⣧⠡⢀⣀⣐⣲⣾⣿⣿⣿⠶⢿⣷⠶⠾⠛⠛⠛⠛⠉⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠙⠳⠧⣘⣏⢻⣆⢣⣟⠋⠉⠉⠁⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠓⠤⣀⠀⠀⠙⢻⣆⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠐⠬⠉⠳⢮⣭⣿⡎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣤⠤⠶⠤⢄⣈⡄
⠀⠀⠀⠀⠀⣿⣿⣝⡷⢄⠀⠀⠀⠄⣒⡮⠝⠒⠻⢝⡜⣧⠀⠠⠶⠚⣛⣛⣛⣷⡮⠤⠶⠖⣒⣊⣉⣭⡭⠽⣁⠄⢄⡀
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣄⢠⣒⠉⠀⠀⠀⠀⠀⠀⡽⠾⢟⣫⣭⠭⠭⠴⠶⣒⠶⠿⠿⠩⣉⠀⠀⠀⠀⣀⠐⠀⣞⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣯⡻⢦⡀⠀⠀⣀⠤⠐⠂⡀⢷⠀⠀⣴⠺⣄⠒⠲⠈⠀⠀⠈⠑⢄⠀⣞⠁⠀⠀⠸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⡀⢀⡀⠠⡀⠈⡁⠸⠀⠀⢿⣿⣎⡳⣄⠀⠀⢀⣨⡔⣾⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠘⡃⠀⠚⠀⠀⠀⢠⡄⠀⠙⢿⣿⣦⣄⠁⣰⣆⡠⣺⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠟⠁⠸⢿⣷⣮⢡⡄

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⠆⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⣴⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠎⢠⡆⠀⠂
⠀⠀⠀⠀⠀⢀⣠⣴⣾⡽⠟⢹⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⠑⠀⠄⡀⠀⠀⠀⠠⠂⠉
⠀⠀⠀⠀⣾⠿⠟⡟⠃⣧⣸⠴⠇⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⢹⣀⣾⠴⠛⠉⠀⠀⠀⠀⠀⡠⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠒⠠⠀⠀⠊⠀⠀⠠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⠙⣂⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠁⡡⠮⠁⠵⠢⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠋⣣⡐⠛⣀⡐⠙⣀⡐⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠂⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⢦⠁⡡⢌⠁⠁⠀⠀⠀⠀⠀⠔⠊⠉⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡀⠀⠀⡡⠄⠒⢀⠀⠦
⠀⠀⠀⠑⠀⣠⠄⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠠⠃⠀⠀⡄⠁⠐⠨⠤⢄⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⡀⠀⠀⠀⠣⢴⡁⠀⠠⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡸⠐⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠘⡀⠀⠀⠀⠀⢀⠀⠀⠙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒

⠀⠀⠀⠀⠀⢀⣠⣴⢤⡀
⠀⠀⠀⠀⠀⡼⢩⣿⣎⡷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⢶⣶⣶⣤⣤⣄
⠀⠀⠀⠀⠀⡟⣩⣏⠛⢧⣀⣀⣠⡤⠶⠒⠋⣉⣡⣤⢶⣞⣻⠿⠿⠛⢋⣉⣩⣭⠁⠀⠀⠀⠀⠀⠀⣴⡒⠤⣀
⠀⠀⠀⠀⠀⡇⣿⣿⡆⠲⢽⣿⠷⣒⣶⣿⣿⠭⠷⠚⠋⢉⣀⣤⣶⣾⠿⠛⠉⢩⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⠑⢦
⠀⠀⠀⢀⣾⠇⠻⣿⡇⠀⠀⠉⠙⠓⠶⢶⣶⣶⣶⣶⣿⣿⠿⠛⠋⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⢢⠱⡄
⠀⠀⠀⢸⣿⠀⠀⠙⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⢡⡈⢄
⠀⠀⠀⠸⣿⠀⠀⠀⠙⣮⣝⠶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⢿⣛⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣧⠀⢣⠈⢧⣴⣷⣦
⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⢿⣿⣶⣾⣭⣭⣽⣿⣿⣽⣿⣿⡿⢟⣛⣿⠟⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⣿⣿⣿⣧⡀⣧⡼⠋⠉⠺⡆
⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠈⠻⢿⣿⣿⣫⣉⣩⣭⣡⡶⠾⠛⠉⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⡰⢁⠴⣪⡗⢰⣶⣭⣿⣿⣤⡀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠊⣾⠉⠁⢸⠃⢹⣿⠁⠉⣷⡀⠀⠀⣧
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠻⠿⣶⣦⣤⣤⣤⣠⣠⣤⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⠀⢻⣰⠀⡼⠀⣿⡟⠀⢀⡏⣷⡀⠀⢸
⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠤⣰⣶⡆⠀⠀⢿⣿⠀⠈⠛⢰⠇⢠⡏⠁⠀⣸⠡⠟⢣⡀⢈⡇
⠀⠀⠀⠀⠀⣼⡶⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣥⡾⠟⢹⠃⠀⠀⢸⣿⠀⠀⠀⡜⢠⡟⠀⠀⢠⠏⠀⠀⠀⠳⡴⣧
⠀⠀⠀⠀⠀⢻⡿⠷⣤⣀⠈⠛⠲⣤⣀⡀⠀⠀⠀⠀⣀⣀⣤⠶⠋⢁⣴⠟⠋⠀⣰⠃⠀⠀⠀⠀⣿⠀⠀⠀⣧⣾⠀⠀⣠⠟⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠘⢧⡀⠈⠙⠻⢦⣄⡀⠈⠉⠛⠛⠛⠋⠉⢁⣀⣤⡾⠋⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⢹⣿⠦⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠀⠉⠙⠓⠲⠶⠶⠶⠶⠛⠛⠉⠁⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠶⠒⠒⠒⠲⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠐⠭⠲⢤⣀
⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡖⠉⠀⠀⠀⠀⠀⠀⠑⠪⣍⡲⢤⡀
⠀⠀⡜⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠈⠉⢻⣇
⠀⠀⡇⠀⠀⠂⠀⡀⠘⠥⠄⠠⠬⠟⠁⠀⠀⠀⠀⠀⢸⠀⢠⣔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠻⣄
⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⣸⠀⠘⡇⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠰⡋⠑⠋⡠⠐⢃⡏
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠐⡰⠃⠀⠀⢏⡀⢲⠚⠀⠎⠁⠈⢁⠠⠈⠴⠂⣀⣚⣥⡭⠭⠷⠒⠛⠉
⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠘⢗⣋⣀⣤⡼⠥⠽⠓⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢶⡉⠁⡿⣦⠠⠖⢰⡾⢉⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠚⠋⠉⠉⠉⠙⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⢀⡌⠉⣷⡇⠀⢼⣿⣤⠓⢧⠀⡀⠘⠀⠎
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢦⠀⠀⢀⠴⣧⡈⠲⠈⢣⠂⠀⡿⣿⠀⠀⢣⠀⠀⠰⡄
⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡀⠀⠘⠦⡙⠻⠀⠀⠀⠄⠀⠐⣹⠄⠀⠈⠀⠀⠀⢸⡀
⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢁⡟⠀⠀⠀⠈⠲⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⣿⠀⠈⢷⣒⠄⠠⠤⠤⠄⠠⠠⠀⠒⣂⣀⣥⠺⢁⣼⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠘⡦⠄⢀⠘⠧⠉⠙⠁⠀⠀⠉⠀⠀⠄⢁⠀⠄⡋⠉⢦⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢱
⠀⠀⠀⠸⡀⠔⠣⠄⣀⣀⣀⣈⡙⠦⠄⠀⠀⠔⠧⠐⠚⢀⢤⠊⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠹⡀⠀⡀⣀⠀⠠⠤⠤⢀⠀⢀⡠⠤⠤⠀⠐⣡⠞⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠁
⠀⠀⠀⠀⠀⠈⠒⠤⢤⣀⣀⡀⠀⠀⢈⣁⣀⣤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠔⠒⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠉⠁
⣿⣿⢛⠿⢛⡛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡤⣖⣍⡆
⠙⡿⣷⡝⢄
⠀⠐⡈⡗⠈⢢⡀
⠀⠀⢰⠺⡄⡀⠉⠒⠦⢄⡀
⠀⠀⠀⠉⡜⡆⢆⠀⠀⠔⡉⢢⡀
⠀⠀⠀⠀⡥⠸⡀⠀⠀⠀⠘⢦⡑⣄
⠀⠀⢰⠀⡊⠀⠃⠁⠀⠀⠀⠀⢒⠌⢢⡀
⠀⠀⢸⠀⡀⠀⠀⢢⠀⠀⠀⠀⠀⠈⢆⠙⢄
⠀⠀⠀⡆⢁⡀⠀⠠⠣⡀⠀⠀⠀⠀⠀⠉⢂⠳⡄
⠀⠀⠀⠘⡌⠥⣂⠀⠁⢙⣆⠀⠀⠀⠀⠀⠀⠱⢈⠲⣄
⠀⠀⠀⠀⠘⢌⠱⡄⠀⠀⠒⣳⣄⠀⠀⠀⠀⠀⠀⠑⠈⡑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠢⡨⢭⠉⠤⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠀⡀⣀⡀⠀⠀⠐⠚⠉⠀⠀⠀⠈⢹⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡐⣭⠭⠄⠀⠀⢛⠢⣀⠒⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠔⠘⢀⣠⠖⢊⡻⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡘⢁⡀⢒⡀⠈⠐⠫⢦⢄⣈⠐⠑⠐⠔⠠⠠⠠⠠⢢⠠⠂⠁⣀⣠⡶⠞⡍⡄⠧⢈⠜⠁
⠀⠂⢐⠠⢐⠀⡴⠄⣂⠄⣀⠬⣢⢄⠲⠤⠭⠤⢀⠀⠈⠚⠉⢒⠶⡠⣤⢤⢤⢤⠤⠴⡖⡏⡍⡆⢆⢃⠤⢀⠔⠁
⠀⠀⠀⠈⠁⠉⠒⡩⠔⡈⠔⡪⢐⡩⠙⡢⣌⡩⢕⣒⠬⢐⡠⢔⠤⡠⠐⢄⠔⡠⡡⡱⡑⡰⡰⠑⣘⠬⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠐⠁⠂⠥⢊⠅⢋⠝⡢⢌⡐⣀⠁⠈⠀⠄⡡⢊⢔⣔⣘⣠⠅⠖⠩⠊⢀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠐⠑⠉⠋⠛⠙⠹⠻⠻⠫⠂⠔⠕⠡⠪⠔⠕⠤⠨⠂⠔⡤⠠⠨⠢⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⣴⠶⡶⢶⣤⣤⣤⣶⢶⣆⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣴⠾⠋⣉⠩⠥⣀⡀⠰⠆⠀⠐⠂⠠⢤⣀⡙⠋⠙⠿⠶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢉⠀⢛⣼⡟⠛⠛⠁⣡⠀⠛⠃⠿⠓⢀⣤⡍⠉⠓⢠⠄⡶⣄⡁⢈⡛⠻⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠟⣡⠤⠾⠑⢊⡵⣄⠈⠋⠀⠠⠶⠶⠀⠰⠆⠀⠈⣀⣠⣤⢤⡀⢠⣌⠙⠃⡈⢀⡉⢙⢻⣆⡀
⠀⠀⠀⢀⣀⣀⣀⣾⣿⣋⣐⣉⣘⣀⣘⣀⣈⣉⣡⣭⣥⣭⣤⣤⣽⣧⣤⣤⣬⣥⣤⣥⣤⣤⣤⣧⣤⣤⣬⣥⣀⣈⣁⣈⣀⣉⣻⣆⣀⣀⡀
⠀⠀⠀⠘⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠁
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠿⠿⠟⠛⠛⠛⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠻⣿⣶⡦⢤⣀
⠀⠀⠀⠀⠀⢠⡏⢸⠀⠈⢧⡙⢦⡉⠓⢦⡀
⠀⠀⠀⠀⠀⡞⠀⣿⠀⠀⠈⢷⠀⠙⢦⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠦⠤⠴⢶⣦⡀
⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠘⣇⠀⠀⠙⢦⡀⠀⠀⠉⠛⠒⠶⠤⣤⣄⣀⣀⣀⣀⣀⣤⣤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠘⡇⠀⠸⣇⠀⠀⠀⠹⡄⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⢷⠀⠀⢿⡄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠄⠂⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢸⡄⠀⠈⣷⡀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠯⢭⣭⣉⣀⣀⣀⣀⣀⣤⣤⣤⣄⣠⡴⠋
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢷⡀⠀⠀⠀⠈⢯⡙⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠻⣄⠀⠀⠀⠀⠙⢦⡀⠈⠉⠛⠒⠦⠤⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠈⠉⠓⠲⠶⣶⣚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣙⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⠿⠿⢿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣄
⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠻⣿⣆
⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⡿⠿⠿⠿⠿⠿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠹⣿⣆
⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣷⣶⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢻⣿
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠿⣿⣶⣤⡀⠀⠀⠻⡿⠃⠀⠀⠀⠈⣿
⠘⢿⣿⣶⣦⣤⣀⣀⣀⣸⣿⠁⠺⠿⣶⡄⠀⠀⣀⣀⣴⣾⡿⠷⠶⣤⡀⠀⢰⣿⡏⠀⠀⠈⠙⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠙⠛⠻⠿⣿⣿⠟⢻⣿⡄⠶⣶⣾⡇⠀⠀⠈⢿⣯⣤⣤⣄⡀⠀⠀⠀⠈⢿⣷⣀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣄⠈⣿⡇⠀⠀⣿⠁⠀⠀⠀⠈⠛⠀⠀⠀⠉⠀⠀⠀⠀⢸⣏⠙⠛⠶⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⣽⡏⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣀⣀⡀⠀⠀⠀⠈⢿⣷⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣿⣇⠀⣿⡀⠀⠀⠀⠀⣹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⡇⠀⠀⠀⠀⣸⣿⣧⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠀⠉⠛⢳⣾⠟⠛⠉⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣿⠁⢲⣤⣤⣴⣿⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣤⣤⣦⣤⣦⣤⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠁⣀⣀⣈⣉⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⣀⣀⣀⣀⣀⣈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠈⠛⣛⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠙⠋⠉⠉⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣼⣿⣠⣴⣶⣿⣿⣿⣡⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⢠⣿⣿⣿⡏⠀⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠹⣿⣷⣄⣀⡀⠀⣀⣀⣠⣤⣴⣶⣾⡿⠟⠁⠀⠀⣠⣿⡟⠻⣿⣦⣄⡀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠙⢿⣿⣷⣦⣾⡟
⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣦⣀⣀⣤⣾⣿⣿⠿⣿⡄⠀⢠⣤⠀⢿⡇⠈⠙⠁
⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣌⠛⠻⠿⠿⠛⠉⠀⠀⣼⣿⡄⠈⣿⡆⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠻⣧⡀⠀⣀⣠⣤⣴⠾⢛⣿⣷⠀⢻⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⢹⣿⡄⠈⣁⣠⣤⣶⠿⠋⣿⣇⠸⣿⠋⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⡀⠀⠀⠀⠀⣾⡇⠸⣧⠀⠀⢻⣿⣄⣀⣈⣁⣀⣠⣤⣿⣿⠀⣿⡇⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⠀⠀⣿⡇⠀⢻⣆⠀⠀⢻⣿⠛⠿⠿⠟⠛⠛⢿⣿⣿⡿⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣿⡇⠀⠈⢿⣦⣤⣿⡿⠀⠀⠀⠀⠰⣶⠌⢿⣿⣆⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣦⣄⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣬⢻⣿⣆⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠈⠁⣤⡙⣿⣆⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣶⣦⣤⣄⣛⣁⠈⠛⠆⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⡄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⢁⠈⢁⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠉⣉⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⡠⠖⠉⠁⡴⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⣠⠎⠀⠀⢀⡜⢱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⡼⠁⠀⠀⢠⠞⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡞⠀⠀⠀⢠⠏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡞⠀⠀⠀⢠⡏⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⡇⠀⣸⠁⠀⠀⠀⡞⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⠙⠓⢦⡀⣼⠀⠀⡏⠀⠀⠀⢸⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣤⣤⣤⣤⣤⣀⠀⢻⣿⠀⢸⠇⠀⠀⠀⡿⠀⣸⣴⠖⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⣾⠟⠉⠀⠀⠀⠉⢻⣷⣼⣿⠀⣼⠀⠀⠀⢀⡇⠀⡿⠃⠀⠸⠟⠛⠛⠛⠛⠓⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡿⠁⠀⠀⠀⠀⣠⡾⠛⡹⠛⠻⢤⣿⣀⡀⠀⢸⡇⢀⣹⡶⢿⡿⠻⠷⣶⣤⣀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⡾⠀⢠⡿⠁⠀⠀⠀⢠⡾⠁⢀⠜⢀⡄⢠⡾⠏⠉⠛⣦⢸⣤⠟⠁⣰⠏⠀⠀⠀⠈⢿⡙⠻⢷⣤⣀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣼⠃⢀⣿⠃⠀⠀⠀⢠⡟⠀⢠⠎⢠⡏⢠⣿⠁⠀⠀⠀⠘⣿⡏⠀⢰⠟⣷⢦⣄⣀⠀⠀⠱⣄⠀⠈⠙⠻⢦⣤⠀⠈⢷⣄
⠀⠀⠀⠀⣰⠏⢀⣾⠏⠀⠀⠀⠀⣼⠃⢀⡏⠀⣼⠀⢸⣟⠀⠐⠀⠀⠀⢻⡇⠀⠋⠀⣿⡀⠈⠉⠙⠲⣄⡙⣧⡀⠀⠀⠀⠉⠻⢶⣄⠹⣦
⠀⠀⢀⣾⠋⣠⡾⠋⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⡇⠀⣸⣯⠄⠀⠀⠀⠀⠸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠈⠻⠟⠛⠀⠀⠀⠀⠀⠀⠙⣧⠘⣧
⠀⠀⣾⠁⣼⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢠⡇⠀⣿⢻⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡄
⠀⢠⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡂⠠⡇⠀⣿⠘⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡇⢘⡇⠀⣿⠀⢹⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠸⣷
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⡈⡇⢠⡟⠀⠈⣧⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢳⣿⢸⡇⠀⠀⠸⣆⠂⠀⠀⠀⠘⣇⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠀⠀⠀⠹⡔⠀⠀⠀⠀⢹⡀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠻⣄⠀⠀⠀⠈⡇⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠸⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣠⣴⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⠄⠒⠒⠂⠀⠤⠤⠤⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣠⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣠⢞⣽⡿⠋⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢯⣿⠃
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣷⣿⠟⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠃
⠀⠀⠰⠑⠒⠀⠀⠐⠀⠀⠀⠠⠤⠤⠤⠀⣾⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣿⣿⠃
⠀⠀⡧⢀⠒⠒⠒⠒⠒⠒⠶⠆⡄⠤⡤⠄⠙⠛⢋⡈⣉⣉⣉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠶⣾⣿⣿⣿⣿⣿⠃
⠀⠀⢷⠈⠀⠀⠀⠘⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠈⠈⠁⠀⠉⠉⠙⠀⠀⠠⣻⣿⣿⣿⣿⠃
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢀
⠀⠀⠀⠧⣤⣠⣀⣀⣀⣀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⡟⠉⠁⠔⢿⣤⠤⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⣒⣾⠚⢣⠦⠦⠤⣤⣤⣤⡤⠖⢁⣇⣄⣀⣤⡿⠃⢠⣤⣾⡋⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠉⠀⠀⠑⢦⣀⣀⣀⡰⢁⠔⢁⠀⠠⠾⢅⡀⠀⠀⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⣼⣿⣿⡿⠓⢇⠀⠀⠀⠀⢤⣀⣵⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠑⠲⣤⣬⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣒⣉⠉⢩⣉⣉⣉⣛⡒⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⠤⡖⡏⡼⡰⢠⢠⢀⠀⠀⠀⠈⠉⠒⠢⠤⢍⡉⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢁⢴⠏⡏⡜⡜⡸⢱⢁⢃⢎⠎⡜⡔⣠⠀⠀⠀⠀⠀⠀⠈⠙⠢⢌⠑⠢⣀
⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠇⡜⡸⡐⡐⢰⢡⢃⣇⣎⣼⡼⠴⠵⠧⣧⣆⣄⣀⠀⠀⠀⠀⠀⠀⠉⠲⣌⠑⢦⡀
⠀⠀⠀⠀⢠⠞⢀⡔⡙⡜⡸⢰⠱⣱⠵⠓⣋⣉⣒⣒⡒⠒⠒⠒⠖⠒⠂⠀⠈⠉⠛⠶⣤⣀⠀⠃⠆⠈⠑⢄⡉⠢⣤
⠀⠀⠀⡴⠁⣠⢻⢡⢣⢱⣡⠗⣋⣀⣒⣒⣒⣒⣒⠐⠂⠐⠒⢂⣀⣀⡀⢀⠎⢭⡍⠒⡄⠘⢓⢦⡘⠀⠀⠀⠙⢦⠈⠻⡥⠤
⠀⠀⡜⠀⡔⡇⡎⣎⡶⠋⣑⣒⣒⣒⣤⣔⣉⠀⠂⠀⠀⠀⠀⢮⡐⠓⣨⠀⠳⣤⣸⠦⠃⠀⠈⠂⠉⠢⣄⠀⠀⠀⠑⡄⠘⢯⠍⠥⠄
⠀⡜⠀⣼⢃⢳⡼⠋⠀⢀⠀⣀⣰⡲⢒⠄⢺⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢰⠉⠏⠿⢱⠄⠶⠀⡔⣈⢑⢮⠳⢄⠀⠀⡌⢆⠈⢯⠭⠭⠭⠠
⢰⠁⡜⠸⣠⠞⠠⠭⠥⠤⠤⠄⠒⠊⠑⢒⠗⠒⢤⠀⠀⢠⢊⣁⢉⡒⡌⠛⠒⠀⢚⣛⠀⢘⣂⣈⠓⠓⠊⠀⣀⡑⢄⠳⠈⠆⠈⢯⡉⠉⣀⣐⡀
⣼⢠⡇⣧⠋⠬⠩⠁⠀⣭⠍⠉⠁⠁⠀⢏⠛⠀⣣⢇⠀⠈⢮⣭⡬⣔⣅⠄⣀⠲⠀⡬⠀⣏⠆⠬⣱⢠⡀⠀⠀⠬⠀⠳⡉⢸⣀⠸⡖⠒⢒⣒⣂
⡇⢸⣧⠏⣒⣒⣒⣒⣒⡒⠂⠀⠀⠀⠀⠀⠈⢛⡣⠋⠀⢀⠀⠋⠙⠋⠀⠀⣉⣀⣀⣐⠂⠀⠹⠏⢁⡔⢂⠐⡲⡄⠀⠁⠙⣜⠁⠈⡧⠤⠤⠤⠤
⡇⢸⣿⢐⡒⠒⠀⠤⠤⠤⠀⠀⡠⠒⠤⢄⠀⠀⠀⠠⠎⡫⣁⠒⠠⣆⢵⠼⣠⡐⠯⢊⡗⠛⠀⡴⡘⣾⣉⡱⢇⡼⠀⠀⠀⢸⡇⠀⣟⣉⣉⣉⣉
⣧⠸⡇⠤⠤⠬⢭⠁⠈⠁⠀⠀⢇⠀⡬⢑⡇⡄⠀⠀⠸⡫⣀⡹⠸⡼⠞⢃⣀⡭⠉⣁⠤⢄⡀⠈⠊⢉⢽⣏⠛⠢⡀⠈⠛⢰⠀⢸⡯⠤⠤⠤⠤
⢽⣆⠱⡠⠭⠍⣐⣒⣀⠀⠀⠀⠀⠉⠉⠙⠊⠀⠀⠀⠀⣬⠒⠒⡟⠉⠙⠢⡀⠀⡜⠑⠶⠰⣌⢣⢀⡸⣀⠀⠺⣣⠇⠀⠀⣜⢠⠇⣟⣀⣀⣈⣉
⢸⠘⢆⠑⣄⠒⡒⣂⣀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⡠⢀⡤⠼⣇⣹⢟⣀⡴⢁⣀⠳⣔⡇⣸⡭⠊⠈⠪⠮⠉⢉⣁⡀⢀⠞⢀⠯⣂⡗⠒⠒⠀⠤
⢸⠀⡈⠣⡈⠣⡐⢒⣒⣀⠀⢸⡷⠀⠬⣳⠀⠀⢡⡅⡏⢶⠄⢠⡈⢢⠀⢀⣿⠎⣑⠄⠀⠀⠀⠀⣠⡄⠀⠒⠈⠀⣠⠋⣠⢏⣘⣼⣉⣉⣉⣉⣉
⠈⡆⢸⡐⣙⢦⡈⠢⣄⠤⠄⠀⠉⠀⠨⠕⠁⠀⠈⢗⠕⠦⢄⡚⠥⠃⢰⠉⠾⠙⡄⡤⢚⠀⣠⣄⢤⠀⠀⠀⣠⠞⢁⡼⣻⣿⣷⡗⡒⠲⠶⠶⠏
⠀⢳⡀⢣⡐⠒⢙⣯⣘⠙⠫⣍⡂⠀⠀⠀⠀⠀⠀⠀⠑⠊⠒⠲⠄⠀⠀⠉⠀⠉⡸⣀⠻⠂⣦⠔⣼⣦⠴⠂⣠⠴⡄⣶⣾⢿⡿⠭⠭⠭⣭⡍⠃
⠀⠀⠱⣄⠱⣅⠒⣀⠈⡓⠢⢄⣉⠓⠲⠤⣴⣫⢭⡑⠲⣀⠀⠀⠀⢤⠀⠀⠀⠀⠛⢦⣭⡡⠔⠚⢉⡠⠔⡋⡅⡜⡐⡹⢁⡞⠒⢒⣒⣒⠂
⠀⠀⠀⠈⠢⣈⠳⢄⡺⠯⠀⠀⠈⠙⠒⠦⢄⣈⠍⠉⣉⠉⠒⠒⠒⠒⢒⡶⠆⠉⢉⣉⣠⠤⠖⢪⢁⠆⡜⡜⡴⣵⠟⣱⠯⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠈⠳⢄⡉⠲⢄⡉⠒⠊⠀⣀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠒⠛⠋⠉⣡⡦⡲⡲⡡⢣⢂⢎⢜⡾⢖⣡⣞⣛⣛⣀⣘⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡈⠓⠮⢍⡉⠩⠍⠁⡠⢴⡂⠔⠁⠤⠀⠀⠀⠀⢠⢞⢝⠕⡕⡱⣡⡎⢋⣩⡴⠛⠐⢒⣒⣒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠈⠉⠒⠢⠤⣄⣀⣒⣓⡒⢂⠠⠀⠀⣴⣡⣯⡾⡖⢛⣡⣴⣞⣛⣒⣒⣒⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⢄⣀⣀⠐⠀⠩⠉⠝⢑⣲⣫⣥⣥⣖⢚⡃⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠓⣒⣒⠒⠒⠂⠀⠉⠉⠉

⠀⠂
⣶⣶⣶⣶⠶⢶⣶⣀⣴⣶⣶⣶⠒⠲⣶⣶⣶⣶⣶⣤⣀⣀⣀⣀
⣛⡛⠙⣿⣶⣼⣿⣿⣿⣏⣈⣿⣿⣾⣿⠟⢿⣷⣤⣿⣿⡿⠿⠿⠿⠿⣷⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⣹⣿⣿⣿⡿⢿⣿⣤⣼⣿⣿⣿⡏⢙⣿⣶⣾⣿⠿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠒⠂⠀⠀⠀⠀⠒
⣿⣿⠛⢻⣧⣴⣿⣿⣿⣯⣉⣽⣿⣿⣿⠛⢻⣿⡶⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀
⣈⣿⣿⣾⣿⠟⠛⢀⣤⣭⣭⣭⣍⣈⣽⣿⣭⣅⠀⣤⣤⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠷⣶⣶⣦⣤
⣿⣿⡟⠛⣿⣶⣾⣿⠿⣿⣤⣼⣿⣿⣿⣏⣙⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⢀
⣅⣨⣿⣿⣿⠟⢿⣷⣦⣿⡿⢿⣿⣤⣽⣿⣿⣿⣉⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⣿⣿
⣿⣿⣿⠛⢻⣷⣾⣿⠟⢿⣷⣶⣿⡿⣿⣧⣴⣿⡿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠉⠉⠙⠛⠋⠙⠙⠛⠤⠬⠭⠭⠽⠶⠾⠿⠿⠿⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡄⠀⠀⣀
⣤⠄⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⡶⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠉⠙⠛⠛⠿⠿⠿⠿⠿⠋⠱⠶⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀
⠻⠿⠿⢿⣿⣿⣻⣿⡿⠿⠟⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡋⠆⢃⢀⢣⠋⠆⠀⢀⡀⠀⡞⠉⠆⡇⠐⡔⠑⠀⠀⣀⠀⠀⣊⣕⢀⠊⠑⣠⠊⢱⠀⢐⠏⢰⢸⠉⡆⡇
⠀⠀⠀⠀⠀⠌⠆⠘⠞⠘⠮⠗⠀⠈⠀⠀⠟⠈⠐⠉⠆⠱⠼⠂⠀⠈⠀⠀⠄⠜⠁⠦⠔⠘⠤⠜⠀⠘⠤⠎⠸⠐⠁⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠈⠁⢀⠀⠀⠀⠀⢀⢤⠀⡆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣉⣉⡤⢬⣉⡉⠉⢉⣡⣈⡷⠁⠀⠀⠈⠒⠒⠦⠤⠦⠀⢶⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡀⠀⢀⣠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠙⣿⣁⢄⣒⢐⡄⠐⠊⠀⠀⠀⠀⠠⠄⠈⠑⣀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠉⣭⢄⣀⡀⠀⠀⠀⠀⢠⡄⢠⣅⡬⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⢠⡉⢩⠀⠠⠀⠄⢉⡐⡀⠀⠀⠀⠙⡜⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠈⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠘⣬⣆⠀⠔⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡠⠂⠊⡀⠀⠰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣴⡺⠟
⠀⠀⠀⠀⠀⠀⠀⡅⠒⢢⣀⠙⢁⠀⠐⠺⣶⢤⠚⠗⠁⠀⠀⠀⠤⠄⣪⠀⠐⢒⡩⠂⠀⠀⠀⠀⠀⠀⠠⡤⠄⢀⠐⡀⠠⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠷⠤⠴⠛⠚⠛⠒⠚⠀⠀⠀⠀⠀⠀⢰⠡⣤⣴⠒⣭⠄⠲⠖⢤⠀⠀⠀⠀⠀⠇⡀⠀⠈⠙⠖⠲⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢢⣖⣀⡠⠴⠃⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⣁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠃⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢃⠀⠀⠀⠀⠰⠈⡀⢄⡀⠤⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⡐⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⡄⠀⣀⡠⠠⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠰⠆⠀⠀⠀⢀⢠⣤⡀⠉⠰⠂⣀⠀⢂⣰⠄⠀⠀⠀⠀⢀⡓⢀⡠⠴⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠀⠀⠀⡀⠀⠀⠈⢃⠀⢈⢉⠰⠶⠤⠄⠊⠛⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⣀⡌⠗⠀⠀⠀⠨⠀⢠⣤⠠⠀⠴⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠔⠂⠲⡌⠉⠉⢀⠙⠆⣀⣀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⡄⠉⠀⠀⠱⣄⣀⣤⣤⠴⣴⠖⠛⠛⠙⢧⡀⠠⠀⢐⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⢰⡀⠀⠀⠀⢠⡖⠠⠀⢤⢀⡀⠀⠀⠀⠀⠀⠙⡆⣀⣠⣤⠽⡶⠖⠛⠋⠛⠉⠀⠄⠀⢙⡄⢀⡠⠴⠌⠓⠒⠛⠉⢉⡄
⠀⠀⠀⠀⠐⡈⠑⠒⢀⡌⢀⡃⠀⠀⠀⠀⢀⢠⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⡜⡅⠀⠀⠀⠰⡀⢀⣠⠤⠴⠄⠐⠚⠋⣉⢀⣤⠆⠠⠴⠚⠐⠂⠈
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡽⡙⠚⠲⢿⠆⠉⠀⠀⠀⠀⠀⠹⣠⠔⠒⠛⠉⣉⣀⢠⡦⠤⠠⠖⠂⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⡂⠁⠀⠀⠀⠀⠀⠀⠙⠤⠐⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⡀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⣸⠶⠿⠋⡡⠜⠶⠆⠀⠱⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⠞⢉⣀⣤⡸⢷⠀⠛⠀⠀⠘⠑⠢⢀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣨⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠘⠄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⢀⣼⢫⠁⠄⠀⠰⢀⠀⡔⠋⠁⠀⠐⠄⠈⢣⠀⠀⠀⠀⠰
⠀⠀⡜⠀⠀⠀⠀⠀⢀⠀⠀⣀⣻⣾⠁⠀⠀⣾⣡⡔⠀⠀⡀⠑⠀⠀⠐⠀⠀⠀⠀⡼⠀⠌⠀⠀⠀⠀⠀⡄
⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⣶⣿⠇⠀⠀⢰⡿⠁⠃⠀⠀⠀⠀⠂⠀⠀⠠⠀⠠⠜⠁⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⣷⠀⠀⠀⣻⡇⢌⡇⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⢀⣀⡟⣄⢀⣵⠏⢹⣷⠇⢶⡖⠢⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⡇
⠀⠀⢱⠀⠀⠀⠀⠀⠀⠓⠴⠋⡡⠀⠈⠀⢲⠀⠉⠉⠉⠠⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢰⡇
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠸⣀⠀⠀⢦⢀⠜⢁⠀⢄⡀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠢⢤⡀⠀⠀⠀⠀⡾
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠸⢀⢄⠀⡐⠋⠛⠠⡡⠰⠸⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠀⠘⠀⡁⠁⠀⠀⠀⡃⠁⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⣤⣤⣄⣀⣀⣀⣀⣤⠄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡾⠀⠈⠳⣄⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣠⠞⠁⠀⠈⣧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢦⣾⡾⠁⢀⣤⠴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢤⣄⠘⣿⣷⣶⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠛⠁⣀⣰⡋⠙⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⣼⣦⣬⣙⣲⣄
⠀⠀⠀⠀⢀⣾⡶⣚⣫⡽⠟⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠙⠲⢬⣭⣿⣆
⠀⠀⠀⠀⣼⠉⢯⡉⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣴⠋⢻
⠀⠀⠀⠀⣿⠀⠈⠳⣄⠀⣾⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠞⠁⠀⣸
⠀⠀⠀⠀⢸⡄⠀⠀⠈⣻⠃⠀⠀⠀⠀⠀⠀⡿⠈⠳⢦⣄⣀⣉⣳⣦⣄⡀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠹⣤⣄⠀⣿
⠀⠀⠀⠀⠈⣧⢀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣉⣭⠉⠀⠀⣩⣍⠛⠋⠉⠁⠈⠛⢦⣀⡀⠀⠀⠀⢀⣠⠟⢰⡇
⠀⠀⠀⠀⠀⢹⡌⠻⣦⣤⣤⣤⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠉⣠⠀⠀⠀⣠⡈⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⡏⢻⡀⣾
⠀⠀⠀⠀⠀⠈⣧⣾⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣀⣀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿
⠀⠀⠀⠀⠀⠀⣼⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢻⡀
⠀⠀⢰⣤⠤⠾⠃⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠳⠤⢤⡶
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣶⣤⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⣀⣙⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣻⣿⣿⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠳⢦⣀⠀⠀⠀⢀⡿⣷⣶⣶⣚⣻⡇⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠶⢼⡇⠉⠉⠉⠉⠃⣧⣠⣤⡤⠶⢺⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢺⡿⠶⢤⣽⣦⡀⠀⣠⣞⣁⣀⣀⣤⡴⠾⣷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣸⠃⠀⠀⠀⠈⢻⢰⠋⠉⠉⠉⠁⠀⠀⠀⢻⡄⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡿⠀⠀⠀⢀⣀⣼⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠴⢾⣧⣤⠖⠛⠉⠉⣿⣘⣇⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⢉⣩⣧⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣉⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⡀⠀⠸⣇⠀⠀⣀⠀⠀⣸⠟⠛⠳⣆⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⠏⠛⣛⣋⣿⠋⠉⠻⡟⢻⣄⣀⣠⠟⠓⢲⣿⣿⣗⠶⣤⣹⣤⠞⢁⡿⢧
⠀⠀⠀⠀⠀⢀⡴⠦⠶⠤⢶⣾⣍⣹⡿⢿⣫⡽⠋⠹⣦⣤⣴⠇⠀⠈⠉⠁⠀⠀⣏⠀⠀⢹⡆⠈⠻⣿⣷⣾⢧⣾⣷⠶⠶⠶⠶⢦⡄
⠀⠀⠀⠀⢀⡾⠁⠀⣠⠶⠋⠁⣙⣿⣹⣿⡇⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠋⠀⣠⣤⠏⢀⡟⣷⣀⡉⠳⢦⡀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠁⠀⣾⠃⠀⠀⢸⡿⣿⡷⣴⣿⣛⣋⣥⣼⣇⠀⣀⣴⠟⣿⣷⣄⣀⣠⠾⠟⠛⠶⠋⣠⡴⢻⣟⠉⣨⠏⠀⠀⢻⡄⠀⠈⢷
⠀⠀⠀⣸⠃⠀⠀⢻⣄⠀⠀⠈⢷⣄⠙⠳⠦⣭⣍⣉⣛⡛⠛⠛⠉⠉⠉⠉⣁⣉⣀⣠⣤⡴⠖⠛⢉⣴⣿⡙⡏⠁⠀⠀⢀⣼⠃⠀⠀⠘⣧
⠀⠀⣰⠇⠀⠀⠀⠀⠙⠳⣤⣀⠀⠈⠛⠶⢦⣤⣈⣉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⣉⣁⣠⣤⠶⠚⠉⠀⠀⠙⠃⢀⣠⡴⠛⠁⠀⠀⠀⠀⠘⣇
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣄⣉⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⢀⣀⣀⣀⣤⣤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣀⡀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠈⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠐⡀⠀⢰⣿⣿⡿⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠢⠄⠠⢀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠁⠀⠀⠈⠀⠀⠐⣯⠁⠀⠀⠈⠱⡕⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⡰⠀⠀⠀⠀⠠⠐⠛⠒⠒⠒⠒⠚⠓⠠⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⣃⠀⠀⣀⡀⣒⠨⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢰⡀⢀⠀⠠⠄⠀⠐⠊⡃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⠃⠇⠂⠀⡤⠒⠤⠄⠀⠀⠞⠃
⠀⠀⠀⠰⠀⠀⢠⣶⣶⣦⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠑⠂⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠘⠿⠿⠟⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢠⡊⣢⠀⠀⠀⠖⢀⢀⣈⢩⠅⠀⠈
⠀⠀⠀⠀⠈⢒⠒⠂⠀⠀⠁⢀⠀⠀⠀⠤⠄⡂⠤⢔⠀⠩⠉⠡⠐⠐⠀⠀⠀⢀⠨⠤⠤⠤⠄⠚
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠂⠁⠀⠀⠀⢉⠉⢔⠀⡁⡀⠄⣀⠄⢄⠐⡄⠀⠀⢀⠀⠀⡀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⡀⠀⠀⠀⠀⠖⢀⠐⡀⠀⠅⠠⠑⠣⠩⠄⡁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠁⠂⠠⢀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠴⠒⠉⠁
⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⠀⠀⠀⠀⠀⠀⡠⠀⢀⡒⢒⠒⢛⡂⠀⠤⡀
⠀⠀⠀⠸⠛⠻⠷⠾⠿⠿⠿⠟⠛⠛⠛⡣⠀⠀⠀⠀⠀⠸⠲⠉⢲⣖⣸⣒⣑⣪⠹⠴⠚
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠤⠤⠄⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠒⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⣯⠀⣤⣶⣶⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣉⣉⣉⣉⣉⣩⣿⣿⠉⣉⣉⣉⣉⣉⣩⣿⡄⠀⢿⡀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠁⢀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠳⢾⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠈⠃⣵⠈⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢼⠃⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠂⠀⢀⠸⡀⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡈⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⣤⣄⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⠁⣤⣤⣤⣤⣤⣤⣿⣿⠀⣤⣤⣤⣤⣤⣴⣿⣿⢠⣤⣤⣤⣤⣤⣼⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⡋⠉⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠙⡰⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⢸⣀⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣟⣸⣿⣿⣿⣿⣿⣿⣿⠀⣄⡛⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢋⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠛⠿⢷⣶⣶⣶⣶⣶⣶⣿⣿⠀⣶⣶⣶⣶⣶⣾⣿⣿⢠⣶⣶⣶⣶⣶⣾⣿⠶⢾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢌⡙⠛⠿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠿⠛⠋⣉⡤⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠓⢶⣤⣭⣟⡿⠉⠉⠉⢀⠀⠀⢈⠉⠁⠠⠒⠒⠋⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⠓⠶⠦⣤⢤⣀⣉⣠⣤⣤⠀⠋⠛⠛⠛⠳⠶⠚⠛⠁⠀⠀⢠⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣿⣷⣿⣶⣾⣷⣿⣷⣶⣷⣿⣶⣿⣿⣶⣷⣶⣷⣶⣶⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣶⣶⣶⣶⣿
⣿⣿⣯⣁⣌⣹⣁⣬⣉⣹⣍⣠⣿⣋⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠠⢠⠀⠀⠀⠀⠀⠈⣷⣦⣦⣤⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⢈⠃⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡐⠀⠀⠀⢸⡄⣠⠞⠠⠀⡴⠂⠀⡀⠀⡀⠀⣠⠄⣢
⠀⠀⠀⠀⠀⠠⢶⡄⠀⠀⠀⠀⠀⠀⠀⠈⢞⠁⠀⠀⠀⡇⠀⠀⡇⠀⣹⠀⠻⠈⠁⠀⠀⠼⠈⠃⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⡦⠈⢆⠀⠀⠀⡇⠀⠀⠛⢠⠏⢀⠀⠀⢆⠀⢀⣤⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⡀⠀⠐⠃⠀⠐⠃⠠⠤⠵⠀⠤⠖⠉⠀⠀⢁⣠⠞⠀⠀⣿⣅⣠⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣄⠀⢰⡄⠀⡤⠴⠆⢢⠀⠀⡖⢠⡆⠀⡆⠀⠀⢿⣦⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⣴⠀⡇⠀⣡⠆⠀⢨⢦⠀⡇⢸⠀⠀⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⣸⡇⠀⢀⡇⣀⣃⡤⢀⡸⠀⣀⡇⠈⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡈⠀⠀⠀⠀⢰⠁⠀⠛⠟⠀⢀⢀⣄⠀⠀⠀⠀⠉⠑⠂⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⡄⠁⠀⠾⠿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢸⣁⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⣤⠄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣀⡗⠀⠀⠘⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣿⠏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡆⠀⠀⠘⢧⡀⠀⠀⢀⡤⠟⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠃⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠀⠀⠀⢀⣀⡗⠀⠀⠀⠓⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠠⠴⠞⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⡤⠖⠒⠲⢤⣀⣀⣀⣀⣀⡴⠚⠛⠓⢦⣀⣀⣼⠀⠀⣼⣁⣀⣀⡀
⠀⠀⠀⠀⡿⠿⠯⠭⠭⠤⠼⢥⣤⠄⢤⣬⣧⣤⣤⣤⣼⣥⣤⣤⣤⣤⣷⣤⠧⠤⠼⠧⠤⠭⠭⠿⠟⢷
⠀⠀⠀⠀⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣸
⠀⠀⠀⠀⣷⠀⡞⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢹⠀⡟
⠀⠀⠀⠀⢹⡀⠹⠤⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⡴⠚⢲⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⢰⠇
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠘⣆⠀⢰⠋⠻⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⡴⠁⠀⠀⠀⠀⠀⠀⢰⠋⠛⡆⢀⡞
⠀⠀⠀⠀⠀⠀⠈⢧⡈⠲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⢰⣋⣳⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⡇⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠙⢿⣿⣿⣶⣌⣛⢿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣤⣭⣙⢿⣿⣿⣷⣯⣻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣤⣀⡈⠛⠛⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡗⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀⢿⣯⡙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⣿⡟⢿⣿⣿⣦⡛⣿⣶⡙⣷⡌⣛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣷⣷⣶⣦⣄⣀⣹⣽⣿⣿⠻⠿⣿⣷⣮⣛⠻⣿⣆⡻⣷⡘⣷⡘⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣍⣉⠿⠷⣜⡋⠁⠉⠆⡰⢆⡉⠺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣷⡶⣯⡭⠀⠘⠈⠶⢶⣀⣀⣠⣼⣯⣥⣀⣘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣾⣷⣴⣿⣯⣤⣠⣴⣶⣿⡿⠿⣭⣥⣤⣸⣀⡌⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠛⢻⣿⣿⣿⡏⢻⣿⣗⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠈⠹⣿⣿⣿⠁⠀⠀⠁⠀⡶⠟⠁⢘⣷⠀⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⢉⣩⣼⣿⣿⣿⣿⣟⣵⣿⡀⠀⡀⣰⣿⣿⣿⣿⣶⣶⣶⠄⠀⡨⣾⣉⠹⠀⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣷⣶⣾⣿⣿⣿⣿⣿⢿⣿⣧⢀⡞⠁⠈⠛⢻⡟⢻⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⢋⣽⣿⣿⣿⣿⣿⣿⣾⡟⢡⡇⢹⣿⣿⣿⣿⣯⣰⢸⡟⣫⣂⡠⠤⠶⠮⢥⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⣻⣿⣿⣿⣿⣿⣤⠀⠇⢸⣿⣿⣿⣿⣿⣿⣾⣷⣿⣴⣶⠿⠿⠿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢋⣡⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠘⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⠹⣿⣿⣿⣿⣿⣿⡿⢿⣿⣉⣤⣿⣿⡿⢿⣿⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠚⠋⢿⣿⣿⣿⣿⠁⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣷⣤⡛⠉⢸⣿⣿⣇⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⡄⡄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣿⣿⠇⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⣀⠀⣿⡏⠀⠉⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⢿⠂⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣿⣧⠀⠈⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠉

⢦⡀
⠸⣟⢦
⠀⠻⣾⡇
⠀⠀⠈⢷⣀
⠀⠀⣠⡟⢿⣿⣷⣶⣤⣤⣀⡀
⠀⢸⡃⢇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀
⠀⠀⢧⠈⢤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠻⠿⠷⠶⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠈⠣⡀⠛⢾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠷⠶⣶⣦⣤⣤⣄⣀⣀⣈⠉⠉⠙⠛⠛⠿⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⠛⠿⢾⣿⣽⣿⣿⣿⣿⣿⡷⢤⣤⣤⣀⣈⣉⡉⠙⠛⠛⠛⠿⠶⠶⣶⣤⣤⣀⣉⠙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠳⠶⣤⣌⣉⡙⠛⠷⣙⣷⣬⣿⣿⣟⣉⠛⠛⠛⠻⠿⠶⠶⣶⣤⣤⣤⣈⣉⠙⠛⠷⢶⣤⣉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⢦⣤⣈⣉⠛⠛⠶⡇⠈⢋⣉⣋⣭⠙⠛⠛⠛⠶⠶⠶⢦⣤⣤⣤⣉⣉⡙⠛⠻⠶⢦⣤⣉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣉⠙⠛⠳⠶⠦⣤⣻⣿⣟⠻⣿⡛⠛⠷⠶⠶⢶⣤⣤⣤⣄⣉⣉⠙⠛⠳⠶⢦⣬⣉⡛⠶⣦⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⣀⣽⣿⣍⡛⠻⠷⢶⣤⣾⠏⠀⣽⣿⡿⣾⡿⠿⠶⢶⣦⣤⣤⣤⣀⣉⣉⠉⠛⠛⠳⠶⢦⣤⣉⡙⠓⠦⣌⡛⠧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢞⠯⠽⠿⣿⡖⠄⠀⢠⣿⡏⢀⣾⣯⡾⢸⣿⣷⣦⣤⣤⣄⣀⣀⣉⠉⠉⠛⠛⠛⠿⠶⢶⣤⣤⣉⡙⠳⠶⣤⣉⠳⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⢀⠀⣻⣶⣤⣾⣿⡇⣼⣿⣾⡇⣿⣿⣿⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠷⠶⣶⣤⣤⣄⣈⡉⠛⠳⢶⣤⣉⠻⢶
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⠓⠈⠀⠈⣿⣿⣿⣿⣿⣧⣿⣿⣿⡇⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢶⣦⣄⡉⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⢀⡀⠀⠀⢻⣿⣿⣟⠛⣿⡿⢟⣯⣤⣬⡟⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣏⢰⡄⡴⢹⣏⠁⠉⠉⢴⣿⣿⣿⠿⣿⣿⣤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⣭⠛⢿⡬⠤⠥⣾⢻⣶⣟⢻⣿⣿⢻⣿⠳⣌⢿⣿⣿⣄⠀⠀⢀⣴⣛⣭⠶⠾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣀⠴⣿⠀⢸⢿⣶⣶⣿⣆⠻⣿⡆⣿⡇⣾⠃⠀⢠⣷⣿⣿⣿⣷⣶⣿⣵⣿⣾⣿⣿⣻⠿⢿⣿⣿⣿⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⢸⣿⣿⣿⣿⣷⣬⣵⣿⣧⣿⠀⢀⣾⣿⣿⠀⣿⣿⣿⣿⣿⣿⠛⠿⣿⣿⣿⣷⣶⣶⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠉⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡀⠸⣿⣿⣿⡆⢸⡿⣿⣿⣿⣿⡆⠀⠈⠙⢿⣿⣿⣿⣿⡿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠋⣠⡿⠛⣽⢿⣿⣿⣾⣿⣿⣁⣠⡿⣿⠿⠇⢸⠃⠘⣿⣿⣿⣷⠀⠀⠀⠀⠉⠛⢿⣿⡛⠦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡹⢦⣄⣌⣁⣀⣬⣶⣿⣿⣿⣿⣿⣿⣯⠀⢀⣼⣦⣤⣾⠀⠀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⢀⣿⡄⣿⠀⠙⠟⠛⢉⣽⣿⣿⣿⣿⣿⣿⣿⠛⣿⣻⡀⢻⣿⣿⠀⢐⣿⣿⣿⡿
⠀⡤⠆⠒⠒⠚⠛⣿⣷⡾⠛⡑⠒⠲⠾⣿⣿⣿⠟⠋⣰⣿⡟⢠⣿⣿⣧⣨⣿⣿⡆⠀⣿⣿⣿⣧⠀⠀⢀⡀
⣸⢁⣶⠲⠤⣄⣲⣿⣿⡁⣚⣡⣤⣀⠐⠺⢿⣷⠶⣚⣿⡟⢠⣾⣿⠿⣙⢇⡼⠉⢷⡀⢻⣿⣿⣿⣀⣴⣿⣿
⠸⣿⡏⠀⠀⠀⠀⠀⠀⣧⡟⠻⠟⠛⠿⠶⠤⠶⠾⠿⢿⡶⠿⠿⣷⣾⡟⠋⠀⠀⠀⠻⣄⠹⣿⣿⣿⡿⢻⣿
⠀⠸⣷⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠸⣿
⠀⠀⢻⣇⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠘⣿⣦⠀⠀⠀⠀⠙⢿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣄
⠀⠀⠀⠹⣿⣶⡄⠀⠀⠀⠈⢿⠟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣛⠿
⣀⣀⣀⣀⣫⣭⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡁⠀⠀⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠠⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠂⢀⠌⢂
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⢀⡯⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠸⠯⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢸⠆⠐
⠀⠀⠀⠀⠀⠀⠠⡿⠄⢘⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⡔⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢘⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣠⣟⠂⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡀⠂⠶⢆⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⣄⡀⠀⠀⠤⠆⠀⣠⠎⠄⠩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢰⠀⠀⠓⠘⢗⣦⢤⣤⠀⠘⠁⠀⠀⠀⠀⠀⠀⡿⠖⠛⢃⡼⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⡴⠴⣯⠀⠀⠀⠀⠀⠀⠀⣀⡴⢤⡄⠀⠀⠀⠀⠀⢁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠤⣀⠀⠀⠀⠀⠀⠀⠒⠔⠀⠀⡀⠁⠀⡀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠒⠙⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿