Black magic Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⣰⡟⠠⠙⣧⡀⠀⠀⠀⠀⠀⠀⣾⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠀⠳⣤⡴⠃
⠀⠀⠀⢰⣿⠷⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠼
⠀⠀⠀⣼⣿⡆⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡆
⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⡄⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⣷⣧⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢷⣀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠐⠀⠀⠐⡀⠀⠀⠀⣠⠤⣤⠀⣠⣤⣄
⠀⠀⠀⣸⣷⣶⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠘⠚⠀⠀⠀⠀⠘⠐⠀⠀⢸⡅⠀⢀⣿⡁⠀⢹⣇⠘⡣
⠀⠀⠀⠨⠭⠙⢢⠂⠀⣠⠔⠒⢤⡀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠁⠑⠚⢒⠃⠂⢀⠈⠻⠾⠟⠉⠻⠶⠟⠁⠀⠐⡇
⠀⠀⠀⢀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢳⢸⣿⠏⢻⣷⠀⠐⠀⠂⠀⠀⠠⢀⠄⠀⠀⣳⠀⠀⢹⡄⢀⠀⠀⠀⠀⢀⡀⠀⠈⠁
⠀⠀⠀⠈⠇⠀⢆⡄⠈⠳⣄⣀⡴⢃⣿⣿⣤⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠶⠟⠁⠘⠟⠀⠀⠀⢴⣇⠆⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠀⢠⣴⣿⣿⣧⠀⢸⣿⣿⣷⣄⠀⡀⡄⢀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃
⠀⠀⠀⢠⡀⠀⣴⠀⠈⠁⢀⣿⣿⣿⣿⢏⣀⠘⢿⣿⣿⣿⡆⠉⠀⠁⠐⠃⠀⠀⠐⡀⠀⠀⠀⠀⠀⠐⠀⠀⠘⢭⠙⠀⣘
⠀⠀⠀⠘⡇⠀⠉⢼⡿⠇⣼⣿⣿⡟⠿⣿⣻⣿⠾⢿⣿⣿⣿⡄⠀⠀⠔⠊⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠫
⠀⠀⠀⠸⠧⣄⠂⠀⠀⢼⣿⣿⣿⠷⠐⠈⠉⠁⠀⠸⢿⣿⣿⣿⡀⠀⣀⣈⠀⠀⢤⡀⠀⠀⠠⡤⢆⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣤⣤⣤⣤⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⢿⡿⠂⠀⠈⡀⣀⠈⡙⡶⢋⠁⢠⣶⣄⠀⣂⠂⢸
⠀⠀⠀⣿⠀⢹⠀⣧⠈⠛⠉⠚⣲⡀⠀⠀⡊⠨⠀⢀⠀⠺⠎⠠⠀⠀⠀⠀⠤⠴⠦⣹⠇⠀⠈⠀⠁⣀⣸⣿⣿⡀⠀⠀⢸
⠀⠀⠀⢻⡇⢲⡆⢸⠀⠀⠿⢆⡈⠁⢀⠎⢠⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠂⡠⢠⠠⢤⣠⠄⣶⠸
⠀⠀⠀⠸⠷⠼⠧⠼⠃⠀⠀⠈⠁⠀⠀⠂⣶⠦⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠩⠿⠉⠇⠀⠯⠹⠏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⡄⢠⠇⡨⠟⠣⣼⣦⠞⠀⠼⠧⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢿⡼⢲⡷⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⡈⠛⠯⢀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⡔⠮⠓⠀⡀⠀⠀⠀⢠⠄⠀⠀⠻⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠭⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠠⠠⡊⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⣀⠙⠛⠛⠁
⠀⠀⡀⠀⠀⠀⠀⢠⣦⢰⣆⠙⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠐
⠀⠀⠀⢀⠀⢀⡀⠀⠁⠀⠉⠀⠀⠀⠀⢀⣀⣀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠀⢀⠀⠀⣠⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠖⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠉⠀⣿⣿⣇
⠀⠀⢠⠈⢰⠙⠄⠀⣠⡄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣴⡶⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢋⣀⠀⠀⠂⠙⣿⣿⣦
⠀⢀⡀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⢀⣠⣦⠀⠀⠀⠸⠟⠀⠀⠀⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠈⢉⣀⠀⠀⠀⠀⠀⢠⣤⡀⠻⣯⡿⠀⠀⠒
⠈⠀⠀⠀⠀⢴⡦⠈⠙⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢾⡿⠛⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀
⠐⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠁⠀⠀⠲⡶⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⣄⠀⠀⡞⢻⣉⡆⠀⠼⡓⠀⠀⠀⠀⠀⠻⠟
⠀⠀⡑⠀⢰⣿⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠻⠛⠁⠀⠙⠷⠼⠃⠀⠀⠃
⠀⠀⡐⠁⠈⢿⡾⠃⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠈⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⢂⠈
⠀⠀⠀⠀⠘⠓⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠏⠀⠘⠀⠀⠀⠈⠀⢀⠔⠊⣹⢯⠉⠑⢦⡀⠀⠀⠀⠘⡅⠘⠃⠀⡄
⣐⠂⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⢠⣧⠤⢤⡧⠬⣧⠤⢤⣵⠀⠀⠀⠄⠀⠐⠀⠀⠒⠀⠑
⠀⠅⠀⠂⠀⠰⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠓⣾⣀⠀⢘⣶⠋⢀⠂⠀⠈⠃⠀⠀⠈⢀⣐⣐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠂⠰⠃⢠⠒⠀⠃⠀⠀⢀⠀⠀⢀⢀⠐⠀⠀⠀⣄⠀⠀⠀⡾⣶
⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠲⠤⠤⠤⠤⠆⠀⢀⡔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠓⠚⠒⠒⠉⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠆⠀⠈⠁⠀⠘⠒⠀⠀⢀⣠⣖⠃⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⢙
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢊⣁⡠⠆⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣻⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡀⠀⠲⠛⠃⠀⠁⠀⠀⠀⠀⠀⡃⠀⡀⠀⠀⡩⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⢍⠀⠅⠀⠀⠀⠀⠀⠁⣡⡤⠀⠀⡀⠀⡀⡀⠀⠀⠀⠀⠃⢊⡄⢀⠙⠃⠀⠀⠀⢀⣁⠤⠴⠀⠀⠀⠀⠀⠀⢼⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣀⣀⣠⣬⡄⠡⠀⠀⠽⠿⠛⠛⠀⠀⠀⠀⠐⠌⣵⣌⠰⠀⠀⠀⠀⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⠂⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢝⠳⠃⠀⠀⠀⠀⠀⠀⢀⠶
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠄⠀⠀⠀⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⣰⣖⣲⡤⠤⠀⠀⠀⠈⠐⠐⠁⠀⠀⠀⠀⣰⠟⢲⣶⠞⢶⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⢀⠀⠈⠀⠀⢰⠀⡀⠠⡋⢛⡉⠉⠁⢤⣴⢤⡄⠀⠀⠀⠀⠀⠀⢀⠌⠀⠑⠂⠂⠒⠁
⠀⠀⠀⠈⠙⠉⠑⠲⠤⠠⠚⠉⠉⠂⠐⠁⠀⠀⠀⠈⠉⠁⠀⠀⠈⠔⠀⠀⠀⢀⠀⠰⠆⠀⠛⠂⠒⠒⠒⠒⠂⠐⠂⠘⠛⠠⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠄⠀⠀⠁⠺⢦⣤⠖⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡢⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠖⠁⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠆⠐⢀⠀⢀⡐⠶⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢘⡁⢇⠀⡰⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠰⣡⠀⠀⠀⠀⠘⣵⣼⠐⢃⠋⠀⠀⠀⠀⠀⢈⡱⣿⠆⠓⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢉⠛⠃⣈⡀⠀⠀⠀⠀⢐⢿⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠏⠙⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠟⠉⠽⠉⠷⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⠀⠀⠙⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻
⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠻⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⣀⢀⠓⠃⠐⢶⣿⡄
⠀⠀⠀⠛⠿⠿⡟⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠄⠉⣿
⠀⠀⠀⠀⢴⡀⢱⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⢀⠀⠀⠹⣧⣀⣑⣴⣤⠞⣣⡤
⠲⡀⠀⠀⠈⠛⠀⢣⠉⠀⠀⣠⠶⣶⣦⡀⠀⠀⠙⠛⠋⠁⠛⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣈⣭⣼⣿⣿⣿⡥⠔
⠲⡌⠀⠀⣠⡄⠀⠀⠀⠀⢾⣷⣦⣤⣀⣹⡀⠀⠀⠀⠀⢀⣀⠀⠀⠸⣿⣿⣦⣤⡄⠀⠞⣠⠴⠞⣻⣿⣿⣗⣾
⠀⠈⠀⠸⢿⠿⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⣾⣿⡧⠀⠀⠈⠛⠛⠉⠀⠀⢸⢁⡞⡿⠛⠻⣿⣧⡀
⠀⠀⠀⠠⠊⢠⡄⠀⢀⣀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠆⣤⣄⡀⠀⣿
⠀⠀⠀⠀⠀⣾⣯⣿⣿⣿⣿⣿⠃⠀⠀⠛⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠉⠀⠀⠀⠀⠀⠻⢶⡥⠾⠇
⣽⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡄
⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⣸⣤⠆⠀⠀⠀⠀⣴
⠟⠀⠀⠙⠿⠿⠿⠿⠿⠛⠁⠀⠀⢴⡀⠀⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣶⠀⠨⣥⠀⠘⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⣀⣤⣤⣄⠀⠀⣀⣄⠀⣶⡄
⠀⢀⣠⡀⠀⠀⠻⣂⠹⣿⣿⠟⠀⠐⠞⠀⠀⠀⠘⠻⡿⠛⠁⠀⠀⠀⠸⢿⣿⣿⡇⠀⠀⠛⠋⢰⠮⠀⠠
⠀⠸⣿⣿⣷⠀⠉⢥⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⡀⠀⠀⠀⠉⠛⠀⠀⠀⠐⠂⠀⠒
⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠘⠷⠀⡇⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣻⠆⠀⠈⢿⣷⣤
⠛⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠟⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣶⡾⠛⢉⣴⣾⠟⠀⠀⠀⠸⢿⡿
⠀⠀⠀⠀⠀⠘⠃⠏⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣦⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⣄⣀⡀⠀⠀⣴⠟⠁⠀⠀⠈⠻⣦⡀⠀⢀⣀⣠⣤⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠉⠉⢛⠻⠷⠶⠤⠀⣀⣀⣤⣤⡌⠻⣦⡙⠉⠉⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⣴⠟⣡⣴⠶⠿⠛⠋⠉⠁⠴⠶⣦⣬⣍⣀⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣥⡶⢂⣴⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⢦⠸⣧⢀⣀
⠀⠀⠀⠀⢠⣴⠶⠾⠛⠛⢉⡥⢀⣴⠟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠻⣦⡀⢿⡌⠛⠛⠷⠶⣦⡄
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣼⠇⠟⠁⠀⠀⠈⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠁⠀⠀⠈⠻⣦⡁⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⢹⣇⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠸⣿⡿⣷⠦⣀⣠⣤⣤⡄⣀⣴⣾⢿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢸⡏
⠀⠀⠀⠀⠀⠈⢋⣴⠇⣾⠃⠀⠀⠀⠀⠀⠀⠀⢿⣷⢰⡿⠟⣻⣭⡩⣾⡿⢫⣵⣜⠿⠀⠀⠀⠀⠀⠀⠀⠐⣌⠻⢂⣿⠁
⠀⠀⠀⠀⢀⣴⠟⣁⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣇⢀⣠⣮⡛⢿⣶⣄⡀⣙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢸⡏⣤⡀
⠀⠀⢀⣴⠟⠁⠀⣿⡈⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣩⣵⣿⠟⠉⠀⠀⠉⠻⢧⣿⡏⢿⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⠀⠈⠻⣦⡀
⠀⠰⣿⡁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡀⣿⡇⠿⢫⣶⠀⠀⠀⠀⠀⠀⣾⡿⠸⣷⣮⣀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢈⣿⠆
⠀⠀⠈⠻⣦⡀⠀⡄⣿⡄⠀⠀⠀⢀⣤⣾⡿⠹⠿⠀⠘⣿⡇⠀⠀⠀⠀⠸⠿⠃⢀⣾⡝⢿⣷⣤⡀⠀⠀⠀⢠⡈⣿⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠈⠛⣸⡇⠸⣧⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠷⢹⣿⡸⠿⠿⠿⠿⠿⢋⣾⡟⠼⠿⠿⠿⠿⠷⠄⠀⣼⠇⢉⣴⠟⠁
⠀⠀⠀⠀⠀⢀⣿⠡⣦⡙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣯⣇⣀⡀⣼⡿⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⠟⣡⡀
⠀⠀⠀⠀⠀⣸⡇⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⡛⢱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢹⣇
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢰⡟⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠘⠻⠶⢶⣤⣤⡘⣷⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢚⣁⣤⣤⡶⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡆⠳⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⡀⢀⣴⠟⠡⠾⢛⡛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠉⣙⡛⠻⠶⠖⣀⣀⣠⣤⣶⠶⠟⢋⣴⠟⠁⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣀⣀⣌⠻⣦⡘⠛⠛⠉⠉⠀⠒⠶⢶⣦⣥⣀⣀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠋⠉⠁⠀⠈⠻⣦⡀⠀⠀⢀⣴⠟⠀⠀⠈⠉⠙⠛⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⣀
⠀⠀⠀⠀⠀⣠⣬⡤⢤⠻⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣻⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡾⠈⠓⠋⡝
⠀⠀⠀⠀⠘⠿⣦⣤⣤⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠛⠉⠉⠙⣻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡠⣶⠀⢘⣳⡦⠄
⠀⠀⠀⠀⠀⣾⣿⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣟⣛⣛⣛⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠠⣄⣻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⡀⠀⠘⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠠⣶⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠈⠁⠈⠻⢃⠀⡄⠰⠷⠀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠤⡀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⠁⠒⢦⡙⡆⢠⢋⡴⠂⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣔⢁⡴⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠁⠀⠈⠘⣶⡆
⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣛⣒⣚⣛⣯⠁
⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⠀⠐⢶⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢠⡶⠛⠋⠩⢾⣷⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⣩⣭⡃⠀⢤⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡄⠀⣀⣹
⠀⠀⠀⢠⡿⠀⠛⠀⠀⠈⠁⢻⡄⠀⠀⠀⠀⠀⠀⠘⠛⢻⡏⣵⣦⢹⣿⣷⣿⠇⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠛⣹⡏⠀⠀⣤
⠀⠀⠀⠘⣷⠀⠀⠀⠰⠗⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⢻⢸⡟⠿⢡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⡞⣳⠄⠻⣦⠀⢠⠉
⠀⠀⠀⠀⠘⢷⣤⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡶⠶⠶⠶⣞⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣁⠘⠛⠿⠷
⠀⠀⠀⠀⢠⣽⣛⣛⣛⣛⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠰⠆
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⢰⣿⣷⣄⠀⠀⡄⠀⠀⠀⠃⢀⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⠸⢿⣿⠇
⠈⠻⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣤⡄⠀⠀⠠⢄⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⢰⣿⣷⠀⢸⣿⡆⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡠⠤⠈⠂⠉⠀⠈⠀⢄⠀⠀⠀⠙⠋⠀⠈⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆⠄⠀⠀⠀⠀⠀⣰⡆
⠀⠐⠀⠁⠀⠀⠀⠀⠁⠀⢀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠘⠀⠀⠀⠀⠰⠐⡁⠀⠐⠛⡛⢿⡄
⣤⣤⣄⠀⠁⠀⠀⠈⠀⠀⠀⠸⠿⠿⠿⠿⠂⠀⠀⠀⠈⢷⣭⠴⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⢀⡀⢀⣀⡀⠀⠁⠀⠀⠀⣰⠂
⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠳⣬⡤⠆⠀⠔⠄⣀⡠⡤⠤⠀⠀⠀⢠⣆⠀⠘⠿⠃⠴⠀⢀⠉⢀⡄⠀⠀⠀⠀⠎⠀⠀⢀⡀
⠙⠟⠉⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⢦⣄⣤⠖⠀⠀⠀⠁⠰⡆⠀⠘⠂⠀⠘⠁⣶⡄⠀⠠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠛⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠰⢤⣈⣠⡴⠂⠀⠀⠀⠀⢳⠀⠠⠀⠀⠀⠀⠉⠀⢉⠘⡌⢂⢈⣁
⠀⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠸⠆⠄⠀⠠⠖⠠⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠁⢰⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⣀⠀⠁⠀⢀⠀⠀⠀⠀⢀⡤⠖⠋⠉⣿⢿⡀⠈⠉⠙⠲⣄⡀⠠⣴⣦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠉⠙⠻⠟⠁⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢸⡇⠘⣷⡀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠍⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠛⠀⠀⠀⠀⢠⣞⣁⣀⣀⢀⣠⣾⣀⣀⣸⣷⣀⣀⣀⣀⣀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⢀⠀⠀⠀⣾⢿⣯⡉⠉⠉⢹⡏⠉⠉⠉⠙⣯⠉⠉⢉⡽⠟⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⡀⠀⠀⠀⠈⠀⢀⣾⣿⠁⠀⠠⠀⢠⠀⠀⡇⠀⠈⠙⠷⣦⣾⠀⠀⠀⠀⠀⢸⣷⡾⠋⠀⠀⢸⠀⠀⠄⡾⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠶⣿⣷
⠒⠈⠀⠀⠠⠀⠀⠀⠘⣿⣿⡀⠐⢠⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠟⠻⢶⣤⣀⣴⠟⠻⣧⠀⠀⢀⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⠀⠀⠈⠙
⡢⠀⠀⡀⠀⠀⠀⢀⠀⠙⢿⣷⣌⡁⠔⠁⠀⠀⠸⣆⠀⠀⠀⡿⠀⠀⣠⡿⠛⠷⣦⣄⢹⣧⢀⡾⠁⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣸⢃⣰⠞⠉⠀⠀⠀⠀⠙⢻⣿⠟⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡡⠄⠀⠀⡄⠀⠀⢀⠀⠀⠀⠙⠻⢿⣅⣀⣀⣀⣀⣠⡤⠖⠋⠀⡀⠈⡀⠀⠀⡀⢀⡆⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠇⣠⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠄⢀⠄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣜⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢲⣦⣤⣌⡀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠠⣌⠠⠈⠠⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠦⠄⢀⠀⣴⣿⣿⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠤⠦⠂⠐⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⠁⢠⠎⠀⠀⠀⠂⠀⠀⠲⠚⠛⠋⠁⠠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⣠⣶⡤⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣤⠤⠤⠤⣤⡀
⠀⠀⣀⣤⣿⡇⠀⠀⠙⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣁⣿⠿⣿⣿⣷⡀⠀⠈⣿⣻⡓⠲⢦⠐⢷
⢀⣿⠋⠛⠉⠀⣿⠖⡒⠻⡾⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠁⠐⣾⠿⢿⣧⣤⣴⣯⣿⣷⡄⠊⠂
⠀⢿⣦⣴⣶⠶⢶⣿⡿⠇⠘⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠻⣿⣿⣿⣾⠏⠀⠁
⠀⠀⠀⣼⣿⡖⢸⣿⣆⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡥⡤⡿⠇⠀⠀⠩⡯⠏⢀
⠀⠀⠀⠀⢀⣴⠟⢫⣿⣿⠏⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⠃⠀⠀⠀⠠
⠀⠀⠀⠀⠸⣧⣤⠾⠃⠀⠉⠟⠉⠀⠠⠀⠠⠖⢤⠀⠀⠀⠀⠀⠸⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸⠀⣠⡄⠠⠤⠀⣰⣴⠤⣷⡆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠊⠘⠀⡅⠃⠀⠀⠀⠈⠉⠉⠉⠁⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⢶⡀
⠀⠀⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡀⠀⢀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⢘⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠺⠓⠲⠒⠸⠃⠀⠸⠚⠉⠀⢀⡼⠀⠀⠀⢠⣄⣐⢚⣾⣻
⠀⠀⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣠⣠⣤⡄⠀⠀⠀⠀⡠⢉⣀⠀⠀⠀⢸⣿⣹⣟⣻⡿⠁
⠀⠀⠀⠹⠀⠀⠹⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⢀⠐⠲⠿⠛⠛⠋
⠀⠀⠀⢰⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠲⣄⣤⡤⠠⠖⠀⠐
⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠒⠒⠂⠀⠂⠀⠂⠐⠁

⢁⠄⠀⠀⣠⣿⣿⡿⠿⠛⠋⢁⠤⠖⢋⣥⣶⣶⣿⣿⣿⠟⠋⢀⣴⣾⡿⠋⢀⣠⣶⡿⠁⠀⠛⠁⢀⣼⣿
⠀⠀⠀⠞⣻⡉⠀⠀⠀⠀⠀⠀⠠⠖⠋⠉⢽⣏⠱⢦⣤⡀⠛⠿⠟⢁⣠⣴⣿⡟⠋⠀⠀⠀⠀⢠⠞⠋⠁
⣾⠋⠀⢶⠼⠟⠲⠀⠀⠀⠀⠀⠀⠀⢆⢠⡀⠈⣷⠄⣸⡿⠁⠀⠀⡈⠉⠻⠋⠁⢀⠀⡘⡃
⣁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣀⠀⢁⡾⠀⢰⡏⣾⠇⠀⠐⠀⠘⡿⠀⠀⢧⠀⠈⡏⠃⠀⠀⠀⣠⣤⡀
⠈⡷⠀⠀⣀⠀⠀⡀⢀⣿⠇⠀⠈⠀⠆⠀⠀⣻⡾⠡⡤⠄⠀⡃⠠⡄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠸⣿⣿⡿
⠟⠁⠀⠀⠙⣷⡏⠁⢸⠇⠀⢠⠀⠠⠀⠀⠚⠁⠀⠀⠁⠀⠀⠀⠐⢦⡀⢲⡀⣼⡇⠀⠀⠀⠀⣀⣌⠉
⠠⣄⣀⠘⠀⠈⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢳⠀⠣⢻⣇⠀⠰⢀⡀⠙⠉⠒⡀
⣦⡈⢻⡁⠀⢠⣤⣄⡃⠀⠀⠀⡄⠀⣆⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣆⠀⠀⢧⠸⢀⡤⣤⣤⣅⣐⣋⣀⣀
⠿⣿⣟⠛⣰⡍⡉⠈⣷⡀⠀⠀⠀⠘⢛⣻⣿⣿⣃⣠⣤⣽⣿⣿⣿⡝⢀⡀⠀⠀⣼⡇⠹⣿⣿⣿⣿⣿⣿
⣼⣿⡿⡷⢉⡀⠈⠃⠹⣧⠀⢠⠉⠃⠉⠉⠉⢩⠍⢴⠂⠿⠉⠛⢿⢿⠏⣀⠀⢠⣿⠇⠀⠹⢿⣿⡇⢻⠏
⠛⠉⣰⠃⠘⠛⠀⠀⠠⢿⣆⠸⠀⠀⠀⠀⠀⠋⠀⠀⢸⠀⣀⠤⠴⠋⠀⠟⠀⣰⣿⡦⠀⠀⠈⣿⠀⠈
⠀⣴⠃⢀⣶⣄⠈⢢⣄⠘⣿⡀⡇⠀⠀⠀⠀⠀⡀⠀⣸⡆⢸⣿⠃⠀⣤⠀⣴⣿⡿⠀⠀⠀⠀⢸
⣼⡏⠀⠸⠛⠋⠁⠀⠉⠐⢻⣷⢡⠀⠀⠀⠀⠀⠉⢻⣿⡇⠘⠛⠀⠰⠃⣠⣿⣿⠃⢀⣀⠀⣀⠀⠀⠀⠺
⡿⠀⢶⣿⡟⠀⠀⠀⠀⠀⠠⣿⡘⡀⠀⠀⠐⠲⠶⠶⢿⣷⠀⢤⡄⠀⢀⠿⠿⠏⠀⠘⠻⠧⠞⠃⠀⠖⠒
⠁⠀⣀⠙⠁⡀⠠⠁⠤⠀⠀⣘⣥⠀⢤⡀⠀⠀⠀⠛⠛⠿⠄⠻⠃⠀⣂⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⣆⠀⠋⠁⠀⠀⠀⣀⣴⠶⠛⠉⠀⠀⠀⠙⣦⣀⣀⣀⣠⡴⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣶⣤⠄⠀⢀⣀
⡄⠀⠀⢀⠤⠶⠛⠉⠀⠀⣀⠀⠀⠀⡀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣿⠯⠙⠁
⣿⠀⣀⠀⠀⠀⠀⠀⣰⣠⡟⠀⠒⢿⡷⠖⠀⠈⢻⡿⡏⢀⣤⣶⣶⣦⡁⢀⣀⣀⠘⠃⠀⠀⠀⠀⣤
⠏⠐⠋⠀⠀⡀⠀⠀⢻⠏⠁⠀⠀⠈⠀⠀⠀⠀⠀⠃⢁⣾⡿⠋⠉⣿⠟⠛⣿⣿⣧⠀⠀⠀⠀⠀⠿⠀⠠
⡀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⣾⣿⡿
⣿⣿⡿⠷⠶⠶⠀⠀⠀⠴⠧⣎⠀⠀⠀⠈⡁⠀⠀⡀⢀⣿⡟⠀⠀⢀⣴⣾⡿⠋⠀⢀⠀⠀⠀⠀⢀⡄
⡄⠀⡆⢠⡄⠀⠀⠀⠄⠀⠀⠀⢀⣠⣴⣶⠀⠀⠀⠁⣼⣯⣴⣶⠿⠟⠛⠉⠀⠀⠀⠘⠠⠄⠀⠀⠘⠇⠠
⣷⠀⠼⠀⠀⠀⢀⠀⠀⣤⣶⠿⠯⠿⠾⠛⠋⠀⠀⠚⠋⠉⣁⣤⠶⠶⠀⠀⠰⠶⠖⠚⠂
⡄⠀⠀⠀⠈⠀⠉⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⡆
⣿⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣤⣿⢿⢓
⣿⣷⡀⠀⠀⣀⢠⠄⠀⠀⡔⠉⠉⠳⡄⠀⠀⠀⠀⠐⠀⢀⠔⡂⠀⠀⠀⠙⡀⠀⠀⠈⠷⢾⠋
⣿⣿⣷⡀⠀⢹⡇⠀⠀⠈⠣⠀⠀⠀⢹⣀⡀⠀⣸⠂⠀⢌⣰⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠛⣿⣿⣷⡀⠈⠃⠀⠀⠀⠀⠀⠀⢀⡼⠓⠋⠀⠈⠈⠉⠉⠓⠀⠉⠀⠚⠙⠃⠉⠂⠀⠀⠀⣠⡴⠞⠉⠁

⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠁

⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣻⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁

⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣟⣿⣻⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣟⣿⣟⣟⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡴⠶⠀⣠⣿⢿⣷⡄⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡏⠀⠀⣴⣟⣻⣸⣟⣿⣆⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠠⠆⠀⢀⡀⠈⠇⠀⠈⣉⠉⠙⠋⠛⠛⠋⠁⠸⣄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣾⣧⠃⣠⠈⢿⡆⠀⣇⢀⣤⠶⡶⢶⣒⠲⠤⢤⡀⢹⡆⢸⡇⠀⠳⠀⠀⠰⡊⣟⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢠⠟⣝⡉⠀⠀⡸⢀⣴⠏⢹⢾⣦⣄⣱⣼⣻⣽⢾⠃⡾⠃⣼⠇⠀⠀⠀⣀⢤⣳⣼⣄⠱⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣤⠄⠀⡟⠀⠈⠁⢀⡴⠁⣾⠁⣔⠻⣤⣬⣽⣍⣉⣉⣄⣻⢄⡃⣸⣟⠀⣠⣴⣿⣷⣿⢯⡙⣿⢦⢳⡀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠳⠀⢸⠁⢠⣤⡻⢸⣇⠀⣯⠀⡇⠉⠒⠬⢭⣍⣉⣉⣉⣥⠤⢿⣅⢻⣾⣿⡿⡛⢧⡘⣦⡽⠚⢧⣽⠇⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢸⠀⣠⣿⡷⣤⠙⠆⠹⣄⠓⣶⠲⠦⢤⣤⠤⢤⣤⣄⣀⡿⠈⢳⡹⣿⢵⣙⣤⠟⠉⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⢄⢸⡔⠛⠹⠇⠀⠀⠠⡄⠈⡷⢸⡀⡖⠉⣂⠰⠂⠰⢸⡁⡴⠈⠁⡙⣞⢶⡋⠀⠀⠀⢰⢢⡴⣲⠂⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣤⠀⠀⠳⡇⠀⠀⠀⣠⠴⠶⠖⠒⠒⠚⠃⡇⠨⣤⠷⡠⡆⠸⠤⢴⣤⣬⣿⣉⣛⠁⠀⠀⣠⡴⣿⣿⠯⠑⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡟⡄⠀⠀⢷⠀⠀⢸⠃⠎⠉⣡⠟⠈⠛⠉⠀⠠⢐⣈⣠⣬⣶⣖⣒⣶⠶⠤⢬⡉⢻⠀⠀⠁⠀⢿⡌⡷⠄⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠄⠀⠀⢱⡰⠀⠀⢸⠀⠀⣼⢸⣠⣚⡑⠀⣴⣟⢻⡿⠟⢋⠥⣶⣦⡄⠀⠉⠻⢦⣴⣦⣷⢸⠆⠀⠀⠀⠘⣇⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡜⡄⠀⠀⢻⣇⠀⢸⠀⢀⡇⢸⣿⣿⡿⣿⣿⣿⣿⣿⠆⠨⣄⠙⠉⠙⠀⠀⠀⠀⢻⣿⣿⢸⠀⣀⠀⠀⠀⣿⠀⠀⢀⡞⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣜⢦⠀⢠⠹⡆⢸⣠⠎⡇⣼⢿⣿⣷⣾⠋⢰⣿⠏⠀⣠⣶⣶⣶⣦⠀⣄⠀⠀⠨⣿⣿⣼⠀⣿⠀⠀⠀⡿⠀⣠⢎⡼⠁
⠀⠀⠀⠀⠀⠀⢘⡇⠀⠈⠻⣧⣼⡇⣻⣾⢉⢤⡇⣿⢸⣿⣿⣿⣆⢀⣴⠆⣸⢿⣻⣿⣿⡿⠀⠋⠀⢠⣰⣿⡿⣿⢸⣏⠀⠀⣸⢇⣴⡷⠋
⠀⠀⠀⠀⠀⠀⠈⡏⡆⠀⠀⠈⢿⡖⠉⣿⣡⢼⡇⣿⢸⣿⣿⣿⣿⠈⠈⠀⠀⣴⣦⣀⠀⠀⢰⡆⠀⣠⡿⣹⡇⡟⢸⡏⠀⣰⣿⠟⠁⢀⡠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣼⡄⢀⣴⢻⡗⠊⢻⠀⢸⡇⣿⢸⣿⣿⣿⢹⣼⣄⣆⣴⣿⣷⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⡇⣼⠇⣴⠟⠁⣠⢔⡩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠀⢸⡇⠀⢸⡄⠈⡇⠹⣬⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣟⡿⢹⡇⣿⡿⠁⣠⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣡⠦⡈⠁⠀⠙⠦⣤⣤⣬⣉⣉⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⡼⠃⠿⠁⢐⣋⠀⠰⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⢧⣀⠘⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⣭⣭⣭⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠤⠤⠴⠋⠈⣱⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⠃⠀⡤⠠⠤⠤⠤⢤⣤⣄⣀⣀⣨⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⠤⠤⠤⠤⢄⠀⠰⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠃⠀⠀⠀⠀⠀⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣄⠀⠀⠀⠳⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠂⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠋⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⠻⣿⠟⠁⠀⠀⠈⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠒⠠⡀⠀⠀⠀⠀⢀⡤⠒⠠⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢀⣀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢰⡆⢀⠀⠀⠀⠀⠀⡀⠠⠀⠈⢀⠀⠈⠆⠀⠠⠀⡞⠠⠀⠈⠀⠀⢉⡉⣠⣅⢠⡄⠀⠀⡔⢎⠀⢸⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠍⢠⡌⢡⡄⠀⠀⠀⠻⣬⠑⡯⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠅⠀⢠⠀⠀⠡⡈⠀⠘⠀⠄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⠉⠀⠀⠀⠈⠀⠀⠀⠒⠊⠀⠀⠀⠀⢀⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠚⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⢀⡈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠀⠀⠀⠁⢸⣏⠀⠀⠀⡀⢀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠆⠐⠤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⡀⢰⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠐⢄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⢀⡁⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠈⠃⠀⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠱⣀⢀⣀⣤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠂⠉⣩⠉⠑⠠⡀⠀⠀⠀⠰⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⢄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⣐⣀⠔⠁⠀⠀⠠⢄⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠔⠉⡑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣃⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⠑⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠃⠂⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠊⡀⠀⣀⠈⠳⣄⠀⠰⠌⡤⠂⡐⡄⠀⠀⠛⠀⢠⡷⢾⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠉⠁⠢⠀⡇⠈⠋⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠇⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠁
⠀⠀⠀⢠⡀⠢⡈⠀⠀⠰⠂⠀⠀⠀⠀⠐⢁⡄⠀⠑⡈⠀⡠⠁⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠈⠒⠴⣦⣿⣔⡾⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⠈⠀⡌⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⣤⠖⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⣤
⠀⠀⠀⠀⢠⣿⡇⠐⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⢀⢠⡀⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠶⠞⠃
⠀⠀⠀⠀⣾⣿⠓⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣸⢀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⢒⠺⠓⠢⠒⠘⠏⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⣀⡀⠀⠀⡰⣴⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡤⠤⠀⠤⡴⠀⠀⢠⠂⠁⠀⢀⠔⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡛⠚⠒⠐⠢⠐⠚⠁⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠠⠇⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⠀⠀⠷⠀⠀⠀⢀⣠⠖⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠂⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢳⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠠⡴⠿⠁⠙⠉⠁⠀⠀⠀⠩⠆⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠙⠉⠃
⠀⠀⠀⠀⠀⠀⢐⠀⢓⠀⠀⠀⠀⠀⠘⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠜⡁⡐⠲⠂⠀⠀⠀⠈⠇⢀⣄⠀⠀⠀⠀⠀⠀⢰⡶⣶
⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⡀⣈⠙⠀⠀⢐⣖⣶⡞⠆⠀⠀⠀⠀⢤⠚⣁⡚⣠⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠌⣄⡀⠀⠈⠉⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠯⣣⠅⠀⠀⠀⠀⠀⠀⠀⣩⠃
⠀⠀⠀⠀⠀⠈⠛⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⢺⠠⠄⠀⠀⠀⠁⢀⣦⢤⣤⡤⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⠰⠿⠒⠛⠋⡉⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢤⡘⡛⡀⠜⠁
⠀⠀⠀⠀⠤⠴⠦⣐⡀⠁⣠⠦⠤⢀⣀⡸⠂⠘⠀⠙⠤⠖⠀⠀⠀⠛⠋⠙⠁⠀⠀⠀⢀⡀⠀⣴⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⡀⠀⠀⠆⣄⠈⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠙⣃⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠑⡐⠋⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠄⠀⠀⠀⠀⣤⢘⠃⠀⡀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⠠⣶⢈⠀⣠⢫⠄⠀⠀⠀⠀⠒⠤⢄⣀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡌⠰⠀⠀⠀⠀⠀⠲⢿⡆⣀⡌⠀⠀⠀⠀⠀⠀⠐⠘⠛⡀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⣁⢴⡂⠀⠀⠀⠀⠀⢭⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠠⢴⣶⠄⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣘⠉⠀⣚⠀⠛⣄⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⣀⣄⣄⢀⡀⠀⠀⣲⡀⠀⠀⠀⠲⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠉⠀⠀⢠⣄⠀⠙⠂⢀⠈⠀⠁⣉⠋⣷⡆⠀⠀⣬⠖⠠⣇⠀⠈⡲⠄⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣄⠀⠀⣀⠀⠀⠄⣆⢬⡼⠓⠀⢠⣰⡧⣀⣀⣻⣇⡀⠀⠀⠀⢀⠉⢀⠙⣄⠈⠉⡒⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⠀⣧⡄⡈⣥⢾⣜⡓⢉⣁⡀⠀⡀⠈⠁⠀⠀⠀⠈⢛⣁⠐⠤⠤⢀⡉⠁⠳⢽⡄⠀⡇⠀⠀⣷⣼
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⣶⣿⣦⣿⠿⢋⠁⡠⢈⣨⠍⣁⠐⠦⠀⠀⠀⠀⠀⠈⢥⡆⢀⠀⠨⡇⠢⣀⠀⣿⠢⣅⠀⠀⠹⣿⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠎⠀⣠⣿⡏⢱⢋⣴⠥⠐⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⡆⣷⢀⠈⠀⢹⠆⢺⣷⡀⢣⢹⣦⠞⢹⡆
⠀⠀⠀⢸⡄⠀⡄⠀⣸⠿⣸⠷⣿⠁⣀⢂⡂⣔⣬⣰⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⠓⠾⢬⣤⡈⢧⡑⣼⢠⣿⣦⣿⠁
⠀⠀⠈⡀⢧⣠⠓⣤⣿⢟⡟⣸⡿⠬⠋⠣⠑⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⠌⢳⣄⠸⡋⠙⢫⣷⣼⠁⢸⣿⠁⢰
⠀⢢⠀⢧⠸⣧⠑⣾⢧⡾⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠙⣿⡗⢾⣿⣊⣋⠄
⠀⠈⣧⢨⠃⠸⣿⣣⡾⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⣄⣿⣧⠸⣿⠈⣯⠆
⠀⠀⠘⣷⣀⠀⢻⣿⡡⣺⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⢻⣿⠀⣿⣇⡳⠂
⢦⡀⢰⡛⣿⣦⣾⣯⣠⣿⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠹⣿⠳⣿⣧⣟⠁
⠈⢷⡌⡾⠰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣱⣿⣧⣿⣿⠃
⠀⠈⢷⡸⡇⢸⣿⣿⠁⣀⡀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⣿⠇
⠀⠀⠘⣿⠷⣸⣿⣿⠘⡿⠛⡸⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⠀⠈⠣⣼⣿⣿⣿⣆
⠠⣼⡇⣹⣯⢸⣿⣿⡏⠀⠐⣮⣿⢅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢷⣫⣴⣶⣼⣿⣿⡇⢸
⠀⢨⣟⡵⢻⣿⣿⣿⣇⠀⢐⡫⢷⢝⡂⠀⢄⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣷⡋⠡⣼⣿⣿⡇⢸
⠀⠀⢻⣫⠌⢻⣿⣿⣿⡆⠀⢩⠽⣝⣃⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⡂⢀⣿⣿⣿⡃⣾⠀⢸⠁
⠀⠀⠈⠧⣞⢄⢹⣿⣿⣿⣄⠈⠬⣯⢲⣵⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢽⣿⠒⣾⣿⣿⣿⣶⠃⠀⠅
⠀⠀⠀⠀⠻⢎⢔⣿⣿⣿⣿⣦⠨⣧⣾⣿⢓⣂⣤⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣯⣄⠀⡄⠀⢀⣦⣄⢺⣿⣃⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢏⣿⣿⣿⣿⣿⣷⣾⣿⠻⠛⢻⣟⣿⣿⣤⣤⠀⠀⠀⢀⠀⠀⠐⡩⣻⣽⠇⡇⣇⡼⣻⠏⡽⢷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣿⣿⣷⣬⣧⣼⣽⣽⣿⣿⣀⠀⣈⣄⣄⣀⣈⡴⠖⠓⣚⡛⠛⣿⣾⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣤⣀⡀⢹⣿⣟⠁⠀⠀⠀⡀⢀⠌⠋⠙⠻⣧⡊⠁⢀⣅⠚⢻⣛⣠⣿⣿⣿⣿⣿⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⢿⣯⣭⣭⠾⢿⣤⣀⢀⠠⠊⢀⣱⡤⢶⣿⠖⡛⠛⠋⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣿⣿⣧⣼⣾⣾⠾⠷⣦⠾⡉⠐⢣⡏⠀⠀⠀⣈⡥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣙⣇⣀⣜⣁⣀⣈⣠⣎⣈⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠆⠘⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣇⠀⠀⣿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣀⣠⣦⡀⠀⢀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠙⢉⡟⠁⠀⠀⠀⠀⢤⠀⠀⠀⣷⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⢰⣤⣠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡄⠀⢰⣿⡇⠀⠀⢠⠀⠀⠀⣀⣂
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢰⠛⡚⣅⠀⠀⠀⠀⢸⣿⡯⠀⠀⡞⠃⠀⠀⣿⣧⠀⠀⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠻⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⢶⣀⠀⠀⠀⠀⠹⡿⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠄⠈⢆⡀⠀⠀⠐⢍⣣⡀⠀⠻⠿⠿⢷⣿⣽⠄⠀⠘⠀⠶⠀⠀⠀⠄⡠⠀⠀⠢⣄⣠⡆⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠁⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠖⠛⠇⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠀⢈⣴⠛⣹⣤⠀⠀⠀⣠⠖⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡩⠘⠁
⠀⠀⢠⠀⠀⠀⠀⠀⢼⣦⡄⠀⠀⠀⠀⠈⢹⡿⣿⡇⠀⠀⢀⣒⣀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠀⠀⢰⠶⠶⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠶⠦⠄⠀⠀⠀⣅
⠀⠀⠀⠀⠰⣛⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠛⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⢫⣧⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⡇⠐⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣴⣾⠋⠀⠰⠷⠈⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣋⣭⣵⣾⣯⡐⠷⠀⠀⡀⠀⣿⣿⣿⣿⣦⡀⠀⠘⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠛⠉⣿⣦⣄⠈⠁⠀⠀⠉⠛⠿⣿⣿⣶⣶⢟⣿⠇⠀⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠅⠈⠀⠃⡸⠋⡣⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣏⣀⣠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣫⣿⠃⢀⠀⠐⠜⠂⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣿⡿⢛⡛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠠⠀⠤⠜⠀⢀⡠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣌⢻⣿⣿⣿⠿⠿⢿⣦⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⡀⠀⠀⠐⠀⠀⠠⠄⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠵⡀⢄⣴⣶⣿⣿⠥⢀⠀⠄⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⡿⣏⣿⡇⠀⠀⣀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢬⣿⣿⣝⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⢰⣿⣿⠀⠻⣾⣿⣦⡀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠋⠈⢿⣝⡻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣟⢇⠀⠀⠉⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠿⠟⢻⣮⡓⠦⡤⣶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣴⡿⠟⠿⣶⡀⠙⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⣿⠃⣴⢿⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠹⠦⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⢠⣾⡿⠙⣷⠀⣀⣤⣤⡴⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣴⣿⠟⠀⢀⣿⣿⣿⠟⠁⢀⣤⣾⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⡲⠶⢶⣶⣶⠿⠟⠋⠀⢀⣠⣾⡿⠋⠀⣠⣾⣿⠟⠁⣠⣶⣿⣿⡿⠛⠁⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⣝⡶⣤⣤⣤⣤⣤⣴⣶⡿⠟⠋⣠⣴⣿⠿⠋⢁⣴⣾⣿⣿⠟⠋⠀⢀⣴⠶⠶⢤⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣛⠶⣯⣭⣍⣉⣩⣥⣤⡶⠿⠛⠉⢁⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⣾⡇⢰⣆⣼⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣍⣉⣉⣁⣀⣤⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣉⣉⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠠⠁⣀⣠⣂⠀⡤⠃⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⢀⠈⢸⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠃⠄⠀⠁⠀⠁⠏⠀⠀⡤⠂⣠⠾⠅⠀⠀⠊⠭⠋⠀⣈⠉⠛⢤⡀⣧⡀⠀⠘⣿⢃
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡟⠀⢁⠞⠁⠀⣢⠎⠀⣂⣴⡤⠊⠁⠀⠈⠈⠁⠀⠀⠀⣸⣿⣿⡧⠀⠙⢿⡄⠑⢀⣿⡈⣞
⠀⠀⠀⠀⠀⠀⡰⠃⡿⠀⢸⠃⣠⡶⢋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡄⠘⠀⠉⣷⣾⣿⣧⡿⡄
⠀⠀⠀⠀⠀⣰⠁⢰⡇⠀⣿⣟⠁⣰⣿⠡⠄⠀⠀⠀⠀⠀⠀⠒⠠⠤⣭⡽⠦⠤⡿⣿⣿⣿⣧⠀⠀⠀⣌⣿⣿⣿⡇⠘⡄⠀⡀
⠀⠀⠀⠀⢠⣿⠀⢸⣧⣰⡿⠈⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢦⡀⠀⠀⣿⣿⣿⡇⠀⢸⣠⠃
⠀⠀⠀⠀⠘⣿⠀⠀⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⣼⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⠃⠀⡊⣉⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣧⠀⢀⠀⠀⠀⠀⠀⢈⣽⡇⠀⣿⠀⠀⣄⡟⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠻⠿⡿⠶⡷⠶⠶⣤⣬⣾⣿⣸⣿⣶⡶⠿⡿⣿⠟⠋⠉⢙⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣧⣤⣤⣴⣷⣤⣧⣦⣀⠠⠬⣿⣿⠛⡲⣗⡂⢠⢠⣿⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣨⣿⣾⣿⠁⠀⠀⠴⠿⠿⢭⣭⡭⠀⠼⠿⠷⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠶⠒⠾⠖⠛

⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠀⢀⡄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢮⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⢀⠀⠈⠁⠠⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⣀⡴⡼⠁⠀⡠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⢀⠊⢹⣷⠻⡆⠸⣴⠏⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⡄⠰⠏⠀⠀⡀⠀⠀⠀⢀⠀⠀⣿⢷⣿⣿⣱⢿⣾⢷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠆⠀⠀⠀⠂⠀⠀⠁⠀⠀⢀⠈⠀⠀⡹⣾⣿⡿⠁⣾⢃⠌⣰⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⢀⡀
⠀⢸⣀⡆⠀⡀⠀⠀⠀⢀⠤⡀⠀⠑⠀⠀⠁⢿⣿⡇⢠⠛⡏⣴⠿⠒⠀⣴⠁⠀⠄⢠⠈⠀⠀⠈⠙
⠀⠐⠀⠀⠈⠇⠀⢀⠔⣋⡀⠄⠁⠷⠛⢷⡉⠷⣼⣷⡶⢻⣠⡿⣢⠴⠆⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠖⠈⣩⠖⠈⠀⠀⠀⠀⠀⠀⠚⠳⣦⣴⡬⠛⠛⠿⣵⠄⠀⠀⠛⠓⠚⣁⡴⠆⠰⢤⠤⠄
⠀⠰⡄⢰⠀⡔⠁⠀⠐⣦⡠⡄⠀⠀⠀⠀⠐⠉⣙⡕⠊⠉⠑⣖⠓⣞⡤⡶⠐⣊⠁
⠀⠀⠄⡌⡀⠀⠀⠀⠀⠈⠻⣶⣃⡀⠀⠀⠀⠀⡿⠀⠴⠀⠛⠹⡆⣉⢷⡄⢀⢈⠙⠢⣀⠀⠀⠀⣠⠄⠶⠀⡄⠀⠀⠀⠄
⠀⠰⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⢀⡝⠳⡄⠰⠟⠀⢿⣸⠎⠷⠆⢘⣋⡄⢹⠗⠂⠉⠐⠖⠒⠈⠀⢠⠾⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠀⠉⠒⣰⣷⡶⠟⠊⣠⣔⣻⣧⢈⣁⣙⣧⠳⣄⢦⣄⠠⠀⠉⣸⢇⣀⡀
⠀⢰⠆⡄⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⣼⠆⣠⣤⡀⢠⠞⢢⣴⢇⣼⠿⠿⡄⣉⡻⣹⡆⠈⠴⣉⣦⡰⠞⠁⠀⠈⢉⠆
⠀⢨⡂⡇⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⡧⠴⠇⠀⠳⢶⣢⣶⣶⣿⣷⠄⣀⠿⢿⠙⢦⣛⡶⡘⠗⣤⠸⣄⠀⠰⠆⠈
⠀⢠⠍⠀⠀⠈⠷⢀⠀⠀⠀⠀⠀⠈⢉⠅⡲⣓⢛⠶⠹⠃⠌⢹⡄⣀⠙⠶⡫⠄⠰⢇⠠⡏⢳⠚⣤⠀⠙⢿⡓⠳⣄
⠀⢠⠀⣆⠐⠀⣄⠀⠙⠙⠢⠄⣠⣖⣁⡴⢉⠋⡽⢛⢄⣼⢳⣷⡾⠙⠥⠀⡿⣤⡚⠁⠀⠿⠀⠃⢻⡉⠩⣈⠣⢤⣁
⠀⠈⠀⠉⠠⡀⠈⠀⠀⢀⠀⠉⠉⣠⠞⣴⠋⣼⠳⠟⣘⡣⠙⠁⢀⡐⠂⠤⠭⢙⣡⡴⠂⠀⠀⠙⢮⣹⠶⠺⢿⠂⣉⠓⡀
⠀⠀⢀⠀⠰⠁⠀⠀⠴⣿⠀⠀⠀⠀⠘⠀⠢⠙⠒⠎⠁⠴⠣⠾⣦⡀⠀⠀⠀⠈⠳⠶⢞⡉⣤⡄⡀⠈⢷⡒⠦⠀⢉⡜
⠀⠀⠈⠂⠀⠀⠀⠀⢠⣄⠙⠆⣰⡆⠀⠂⠀⠀⠈⠀⠀⠀⢰⡞⢻⣿⡧⠀⠀⠀⠀⠀⠈⡡⠟⠐⣻⣿⡀⠘⢦⠁⠈⠓
⠀⠈⠀⢀⠄⢰⡆⠀⠰⣿⠀⠘⠉⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠⡿⢇⣈⣿⣀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠏⠿⣄⠈⠼
⠀⠀⠀⠈⢀⣈⠹⠀⡀⠁⣾⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⢷⣄⣤⠙⣟⠻⡶⣦⣤⣄⣰⡁⠀⢸⣿⣿⠛⡇⢠⠀⠀⠀⡀
⠀⠀⡄⠀⠈⠟⠀⢠⡁⠢⠘⠄⠀⠀⠐⣦⠠⡀⠀⢀⠀⠀⠀⠀⢠⡁⣘⣇⠠⡏⡹⢏⡿⢻⢦⡏⠀⠀⠀⡀
⠀⠀⠁⢀⡈⠀⣀⣾⠑⠊⠀⠀⠀⠀⠈⠈⡠⡏⠀⠘⠀⠀⠀⠀⠀⣉⣹⠟⢻⡷⠇⠈⠱⡟⢬⣿⣶⠟⣿⣀
⠀⠀⠀⠸⠓⠁⠙⢉⠀⠀⠠⢦⠀⢠⡀⠄⠡⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⣼⢁⢦⡀⠆⢻⡆⣿⠻⣿⣽⣯⣶⡖⠀⠠
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⣇⠄⠻⢠⠀⢈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠤⠜⣡⡜⠀⠈⠀⡌⢛⣦⡁⠈⠉⢻⡎⣠⠀⠇
⠀⠀⠀⠀⢳⡤⠤⣄⡈⠀⠀⠈⠀⡀⣦⠈⢀⣊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠁⠻⡄⠀⠀⠸⡇⠙⠻⣦⣡⣤⢹⡗⠀⡀
⠀⠠⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠞⠉⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠙⠄⠀⠀⣷⢀⡀⠟⣀⠀⠀⠀⠀⠁
⠀⢰⣤⠐⠒⣋⠟⣚⣡⡾⠲⣟⣵⠞⣍⣓⣶⣤⣼⡵⠦⠠⠀⢠⠀⠠⠄⠠⠤⠆⠤⠤⠔⠉⣉⣠⣾⠷⢦⠟⠷⣦⡄
⠀⢸⡟⠛⠛⠟⠛⠉⠏⠑⠛⠋⠉⠀⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠙⠋⠴⠁
⠀⠸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀⡀⢘⡀⢀⠐⠀⡀
⠀⢠⡀⡀⢀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠁⠁⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣬⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣋⣴⣿⣿⣿⣿⣿⢟⣿⣯⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣽⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣒⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣟⠋⡽⠋⠉⢻⣿⡿⠿⣿⡿⠛⣿⣿⣿⣿⣿⡟⣭⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣓⣽⣿⣿⣿⣿⣇⠀⠀⣼⡿⠁⠀⢈⡇⢀⣼⡷⠿⢿⣿⣿⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠋⠈⠙⣿⣷⣾⣿⣷⣿⣿⠿⠿⠿⠋⢀⡴⢊⣽⣿⣿⡿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⣠⠴⠚⠙⠻⣿⣿⣿⣿⣿⣷⣶⡶⠋⠉⠉⠁⢿⣿⣿⣆⣣⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠠⠀⠀⠀⠀⡠⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⣀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠊⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠓⠠⠀⠨⠄⠂
⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⡠⠒⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡀⠤⠀⠀⠈⠐⠀⠀⠈⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠂⠀⠁⠉⠉⠀⡀⠠⠔⣈⡀⠀⡀⠀⠠⠄⢂⢠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠤⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⢾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠨⠤⢄⣤⣬⣥⣤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠠⢔⣽⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⣀⠀⠉⠐⠒⠀⠄⠠⠤⠀⠀⠀⠀⠤⠄⠐⠷⢤⣤⣀⣀⣀⣀⣐⣐⣨⡧⢀⠠⣊⠔⠒⠉⠉⠉⠙⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠒⠠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⠀⡀⠀⡴⠃⢀⠠⠀⠀⠄⠠⢌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⢧⡔⡥⠚⠉⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⠀⠀⠀⠀⠠⠀⠐⡀⠔⡯⠥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣟⠒⠤⠤⣤⠭⢤⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⡀⠉⠉⠙⠛⠛⠛⠛⠛⢑⣂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠶⠖⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠄⠠⠈⠠⠀⠀⠠⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡀⠀⣠⣤⣤⣄⡀⠙⠏⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⣸⣧⡀⠙⠛⠛⠛⠁⠈⠋⠀⣀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠈⢻⡟⠉⠀⠀⠀⠰⠶⠀⠀⠀⠙⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠀⠃⠀⠈⠁⢀⣤⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⡀⠀⠀⠉⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠉⠁⠉⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⠀⠈⠋⠀⢰⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀⣀⣤⣤⣄⣤⠤⠀⠀⠀⣀⠄⠘⠛⠉⠹⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠈⠛⠟⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⠤⠤⠤⠄⠀⠀⠀⠠⠄⠤⠄⣤⠤⠀⡘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣾⡗⠒⠒⠒⠲⠒⠒⠒⠒⠲⠶⠒⠒⠖⠿⠖⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢸⣾⠇⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠧⠀⠀⠀⠀⠤⠶⠒⢢⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠷⠶⣴⠤⠤⠤⠤⠴⠤⠦⠤⠤⠤⠤⠶⠤⠤⠤⠴⢦⡼⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤⣤⣤⣴⣶⣶⣶⣦⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⣤⣤⣤⣦⣤⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠽⠶⠶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠤⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣧⣀⣠⣤⣤⣤⣤⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣐
⠀⠀⠀⠀⠀⠀⢁⠤⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⠀⠒⠒⠂⠀⠀⠀⠂⠒⠀⠀⠀⢲⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠤⠤⠶⠤⠦⠤⠶⠶⠦⠶⠶⠶⠶⠶⠶⠧

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⠀⣀⡀⢀⠀⠀⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⢖⠀⠀⠑⢡⠀⠠⡄⠀⠀⠀⢀⠀⠀⠀⠂⠄⠀⡈⠀⡀⠀⠀⢀⠈⠶⠅⠄⠈⠂⠑⠈⠀⠀⡀⠈⡁⠠⠆
⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠁⠈⠀⠅⢈⠂⠀⠁⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠐⢀⢈⠂⠂⠀⣟⠂⠐⣀⠆
⠀⠀⠈⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠔⠠⠀⠀⠄⠀⠆⠀⢲⠀⣀⠀⠀⠀⠐⠀⠢⠄⢎⠀⡐⠐⢄⠀⠈⠉
⠀⠈⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠠⠄⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⡀⣀⠀⠄⢎⠀⡑⠰⡀⠒⣦⣀⠀⢆⢄⡀
⠀⠐⠀⡀⠀⠀⡀⢀⠀⠐⠾⠠⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠈⠉⠀⠀⠀⠀⠀⠁⢀⣀⣀⣃⣀⡀⠀⢀⣀⠀⠂⠈⠻⠆⠐⠤⠃
⠀⠀⠀⠧⡈⢀⢁⢸⠀⠀⠈⠋⠁⠀⠐⠉⠑⠀⡛⢣⠼⠆⠀⠓⠃⡀⠀⣀⠀⠀⠀⠀⠄⠀⠒⡒⡒⣒⡒⠓⠀⠐⠀⠀⠡⠂⠀⠀⣀
⠀⠀⠁⢀⡤⠀⣬⡀⠀⠀⠀⠀⠀⠨⢅⠆⠀⡀⠙⠮⠞⢁⡀⠆⠆⠈⠀⡉⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀
⠀⡰⠒⢂⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⢣⡄⠠⡃⡂⠠⢂⡀⠰⠠⠌⠁⠐⠁⠀⠀⠀⠂⠐⠀⠀⣰⣆⡰⠿⠚⠇⠀⠀⠦⢂⣤⠀⡀⠨⢀
⠀⡁⠤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⢠⠀⠈⠀⠀⠀⡁⠀⠀⠀⢈⡃⠀⢢⠀⢀⣀⠐⠀⣀⠈⢉⣩⠔⢉⡀⠀⠠⢐⠂⠩⣆⠀⠂
⠀⠈⠒⠁⠀⠀⠐⡄⠁⠀⠀⠒⠒⠒⠂⠈⢀⡀⠀⡀⠀⡡⠀⠠⠀⠀⠁⠀⠀⠄⠈⠋⠀⠀⠍⠁⠉⠀⠠⠀⠀⠀⢴⡆⠀⠀⠀⠐⠸⠆⠁
⠀⠀⡟⠄⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⠛⠀⠀⠀⡀⠀⡐⠀⠀⡎⠀⠑⠀⠄⠡⡡⢀⠀⠄⠈⠁⢸⠂⠉⠀⠀⠀⠐⡁
⠀⠀⠋⠁⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠀⠁⠀⠀⢀⠠⣠⣄⢈⠄⠀⠐⠀⠀⠈⠒⠪⠀⠀⡐⠐⡐⠀⢀⠄⠀⠐⠀⠀⠀⡐
⢀⣐⢢⠢⢠⠀⠀⠀⠀⠀⠙⢹⠀⠁⠆⣠⠂⠈⠀⠐⠈⠨⠚⠋⠉⠆⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⡠⡀⠁⠀⠀⠀⠁⠀⠘⠠⢠⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠱⠊⠀⠠⠆⠈⠒⠇⠘⠄⠀⠁⠔⢀⠀⠀⡄⠢⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠈⠀⠀⠋⠃⠀⠀⠀⠄⠀⠀⠬⠄⠀⠀⠀⠀⠀⢂⠂⡀⠒⢐⠀⠀⠁⢀⠀⠅⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⡀⠋⠶⠴⠴⣄⡄⠀⠀⠧⢀⠀⡀⠑⢖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠒⠂⢠⢀⣤⠀⠀⣰⠀⠘⣧⡄⠐⠛⠁⠛⠄⠀⣅⠂⠬⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠠⡔⡖⢻⢀⠠⠒⣄⢼⠝⠏⠋⠀⠀⠶⠋⠑⠒⠚⠷⠂⢀⣀⠀⠂⠰⣌⣆⠀⡀⠈⢹⣄⡄
⠀⠀⠀⠀⠀⠀⢠⠹⣦⣼⣧⣶⡿⠟⠉⠀⢓⡳⠂⠡⣄⠀⠀⠀⠀⠘⣧⠀⠀⢉⡧⢀⠀⢹⡦⣀⠀⠈⢿⡇⠀⡀
⠀⠀⠀⡀⢸⠀⠎⢀⣸⣿⢳⣏⣤⠤⠚⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢇⣆⣷⢀⠁⠘⡧⢸⣦⡀⠎⢷⡴⢻⡆
⠀⠀⠀⣧⠀⡆⠀⡸⢋⡿⣾⣉⣆⢠⢠⡠⣴⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢿⠳⠷⣧⡄⣣⡑⡄⢼⣷⣾⠁
⠀⠀⢀⠸⡔⡉⢶⡟⣹⣱⡟⠓⠁⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠂⠳⣄⣏⠘⠻⢷⣿⣀⣿⡃⣨
⠀⢳⠈⡦⢻⣦⡟⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢸⣿⡝⣿⡷⡴⠂
⠀⠈⢷⡄⠈⢿⣾⢃⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⣿⡇⢻⣇⢽⠄
⣄⠀⣸⢿⣆⣼⣟⣱⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⢻⡷⣼⣿⣷
⠘⣧⡽⣎⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣸⣿⣼⣿⠏
⠀⠘⣧⣿⢸⣿⣿⢀⣄⠀⢠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⡏
⠀⢀⢹⣾⢾⣿⣿⣨⠋⠡⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣀⠀⡓⢾⣿⣿⢳
⠐⢾⡤⣿⣤⣿⣿⡄⠀⢸⣿⣫⡀⠀⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⡻⡟⣾⣿⣿⢸⠇
⠀⠸⣿⢏⢿⣿⣿⣧⠀⢒⢸⣟⡆⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡇⢈⣿⣿⡇⢸⠀⠠
⠀⠀⢹⡥⡂⢻⣿⣿⣧⠀⢖⣿⢩⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣿⠥⣼⣿⣿⣇⡏⠀⠏
⠀⠀⠀⠘⢷⡈⣿⣿⣿⣷⡨⣯⣾⣿⢘⣠⣀⡆⠀⠀⠀⠀⠀⠀⠀⢶⣷⣆⡀⠀⠈⢀⣤⡸⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣛⠛⣿⣻⣿⣶⣄⢀⠀⢀⠀⠀⠘⢝⢯⣇⢆⣇⡞⣿⠩⢿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⣿⣷⣾⠼⠿⠿⠿⠯⣄⣠⣤⡄⢠⠴⠓⢉⣩⣍⠙⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠦⠤⣼⣿⣥⠤⠄⣨⡤⠐⠀⠀⢈⠗⣅⠀⣲⣊⣹⣥⣾⣿⣿⣿⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡏⠉⢻⣿⣟⣩⣹⣷⣶⣊⣠⠶⢻⣯⠟⠉⠀⠀⢤⣤⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠿⠏⠀⠊⠁⠐⢤⠞⠂⠀⠐⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠉⠀⠀⠀⣈⣙⡦⠀⠀⠀⠀⠀⠀⠀⡔⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡏⠉⢢⡐⢋⡥⣄⠀⠈⠂⠘⠀⠀⠀⠀⠀⢐⠌⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠙⠒⠷⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠉⠐⠒
⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⢜⡠⠀⠀⠀⠀⠈⣄⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠈⠊
⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠓⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡔⠈⠹⠄⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠘⠢⠤⠤⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠃⠀⠀⠀⣈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠰⠀⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀
⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠤⠀⠀⢠⡎⠁⠀⠀⠀⢑⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠒⠶⠶⠚⠋⠀⠀⠀⠀⠁⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣝⣁⣀⣀⡀
⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠈⢁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠧⢤⡤⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠉⣲⣤⡀⠀⠀⠀⠀⢠⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⢀⣠⠴⠾⢦⣤⣄⣰⠟⣥⣾⣿⡳⣄⠀⠀⢸⡆⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⢤⣄⣀⡀⠄⠴⢿⣖⢲⣀⣀⣄⣴⣿⣾⣯⠄⠀⠀⠀⠈⠙⢏⠈⣇⠁⣯⡾⢍⡑⢄⣸⣧⠏⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣛⠒⠀⠀⠄⢀⡈⣙⣿⣷⣄⠀⠀⠈⠉⠀⠀⢹⣿⡃⠟⠿⠆⠀⠀⠀⠀⠈⣆⣿⠀⣌⣿⣤⠉⢾⠉⠀⣠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠲⠄⠀⠀⠀⠀⠊⠉⠉⣿⣿⣿⣂⡰⠞⠚⠛⠓⢺⡏⠑⣀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠃⣹⣿⠟⠀⢸⡗⣺⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣿⣿⠋⠀⠀⠀⠀⢀⣼⠃⠀⠈⣻⣶⣦⣤⣀⡀⠀⠉⠿⠾⠟⠋⠀⣀⣼⠂⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠛⠲⠿⣷⣮⡀⠀⠀⢸⣿⠃⠀⠀⠀⣴⠞⠻⣧⡴⠚⠛⠉⠉⣿⢻⡿⠿⢿⣿⣿⡶⠿⠿⢿⡛⠛⠋⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⣷⣄⣼⠃⠀⠀⢀⣾⠁⠀⠀⠈⢻⡷⠄⠀⣰⠁⢸⡇⠀⠀⠙⣿⣝⠢⠀⠀⠈⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣦⡀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⢀⣾⡏⠀⠀⠀⠀⡼⠻⠶⣾⡧⠀⣼⠃⠀⠀⠀⠸⡌⠀⠀⠀⠀⣤⣤⡾⠁
⠀⠀⠀⠀⡀⠀⢀⡾⠀⠀⠀⠈⢻⣄⠀⢀⡠⠛⡽⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠃⠀⢀⣿⣧⢠⡏⠀⠀⠀⠀⠀⣇⣀⣤⣴⠾⠟⠉
⠀⠀⠀⢰⣧⣄⣸⠣⠀⠀⠀⠀⠀⠹⠁⠁⠀⠀⣧⣀⢠⠀⠀⣾⡇⠀⠀⠀⠀⠰⠀⠀⣼⣿⡏⡾⠀⠀⠀⠀⠀⣼⠛⠉⠉
⠀⠀⢀⣼⡿⠛⠻⣄⢐⣶⣦⣴⣄⡀⣧⠀⠀⠰⢻⣿⣿⣿⣿⠟⠀⠀⡀⢀⠀⢸⡀⢰⡿⠹⡿⠁⠀⠀⠀⢀⡼⠃
⠀⢠⠊⢸⠀⠀⠀⠀⠙⠉⠁⠈⠉⠻⢿⣷⢶⣶⣧⣼⠩⢻⠏⠀⢰⣼⣴⣿⣦⣦⣳⣜⡇⠀⠁⠤⣤⣤⡶⠋
⠀⡜⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠈⢻⣷⠈⠑⢿⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⠛⠛⠻⠶⠶⠶⠾⠋
⠀⡇⠀⢸⡆⢠⠀⠀⢳⣤⠀⠀⣸⠁⠀⠀⠿⠀⠀⠈⣦⠀⢤⣶⠟⠁⠀⠈⠙⠛⠶⢦⣤⣤⡤⠤⠂
⠀⢷⡀⢸⣇⠘⣷⣄⣀⠙⣷⣤⣟⠀⠀⠀⠀⠀⠀⣠⠟⣠⠼⠋
⠀⠘⠙⣺⣷⠀⣼⠋⠉⠋⠙⠿⠟⠢⠤⠤⠤⠐⠚⠋⠉
⠀⢴⣼⣿⣿⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⠶⣄⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⡀⢈⡆⠀⣠⠾⣻⠟⠋⢀⣀⣀⣀⣀⣀⡤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⡦⠾⣁⠈⣻⠛⠻⣟⣡⢾⡗⠋⠸⠛⢚⣿⣶⠶⣾⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⣾⠁⠀⢹⣟⣻⣦⣤⡿⠛⠿⣿⣿⡛⢿⣯⠛⠉⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢷⣤⣤⣾⡟⠋⠛⣿⠋⠁⢀⡷⣤⣤⡼⢿⣗⡤⢽⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣴⠚⠿⠛⣄⣒⣴⡿⠿⠿⢿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢹⣷⣤⣾⣿⠿⢿⡉⠳⣤⡠⠈⠙⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢬⣿⠟⣱⢻⡧⢀⣸⡇⠀⠀⢹⡶⣆⠒⠂⠀⠀⠘⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡾⠟⢰⢋⣽⣫⣾⡇⠜⠓⢶⡿⣷⡀⡆⠀⠃⢈⡳⣞⠃⠀⠀⠈⠙⢓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡯⣔⠀⣿⡿⠋⠁⡇⠙⣦⠀⠁⠂⢸⡻⣧⠀⠀⠈⣇⠈⢻⣌⠉⠀⠀⠀⠉⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡘⣡⣾⢿⡇⠀⠀⣇⠀⣯⡀⠀⣠⠧⢋⢻⣦⡠⠀⠀⠀⠀⣏⠿⣟⠓⠒⠀⠀⠘⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡿⠃⢸⡁⠀⡆⣽⡀⠀⣹⠆⣠⠂⠘⢾⡇⠙⢦⡀⠀⠀⠙⢸⠀⠳⣖⠒⠀⠀⠐⠺⣆
⠀⠀⠀⠀⠀⠀⢀⡤⠾⣿⠙⣇⠀⠀⣇⠀⠰⢻⣏⠘⠧⡜⠁⠀⠐⠈⣝⣆⠀⢳⣄⣀⣤⡀⠀⠀⠩⠳⣦⡰⠂⠀⣘⣆
⠀⠀⠀⠀⠀⢰⢏⡄⠠⣿⠀⠘⢦⠀⠈⣷⡀⠀⠸⣷⠄⣿⣤⣐⡿⠀⣈⢻⡀⠀⠈⠉⠉⠉⠳⣄⠈⠀⠈⠙⠦⣄⠉⠹⡆
⠀⠀⠀⠀⠀⢸⢸⠃⢰⣿⠀⠐⠘⣆⠀⠀⠹⣴⡀⠟⣷⣌⢧⡘⢦⣤⣇⣆⠹⡄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠒⠚⠿⣦⣿⡄
⠀⠀⠀⠀⠀⠸⣆⠀⠘⠉⣦⠀⢀⠘⢦⡀⠀⠀⠛⠦⠼⣽⣎⣧⠀⠈⠉⠙⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣿⣧⡀⠀⠂⠹⡄⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢳⡴⠀⠙⠉⢳⡄⠈⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⣴⠀⣿⡄⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢷⡸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢿⣿⡄⠀⠀⠀⣰⠞⠛⢿⣤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠾⠟⠛⠛⠋

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⡥⠒⠉⠀⢀⡤⢲⠎⢀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣟⠀⠀⠙⣆⠠⡇⡇⢀⡔⠁
⠀⠀⠀⠀⡀⠀⣸⠃⢀⠀⢰⠁⢀⣀⣰⣋⣠⣤⡴⠧⠒⠀⠀⢀⡠⠤⠒⣀⠀⠀⠐⠂⢀⡂⠄⠀⡀⠀⠀⣿⠀⠀⠀⠘⣿⣷⢷⣞⡀⠀⢀
⠀⢘⡐⢰⠃⡰⠃⢀⠈⡠⠃⠀⠘⠁⡝⠁⠀⢀⣄⠤⠀⢀⡴⣋⠀⠀⠀⠰⠋⣩⠟⠉⠉⠉⠉⠛⠧⣄⠀⢸⡇⠀⠀⠀⠸⣿⡾⡁⠀⣠⠋
⠀⢸⡇⣿⠞⠁⠶⢉⡼⠀⠀⣈⠀⡼⠁⣄⠐⣠⠃⣀⡶⠫⠤⠅⡦⠤⠖⢊⡉⠀⠀⠀⣰⣷⣶⣶⡊⠈⠳⣌⣇⠓⠠⣄⠈⣿⡇⢧⡴⠁
⢠⡞⣸⡏⠀⣀⡰⠋⠀⠀⣀⡵⠊⠁⣀⣭⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠃⠀⠀⡈⠻⣦⣀⠉⢠⣿⣧⠘⡇
⠏⢰⡿⠀⠀⣽⠁⢀⣴⠟⢉⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠈⠉⠐⠀⣹⣷⣿⣿⣿⣆⡿⣄
⠀⢸⡇⠀⢰⣿⡾⠋⠀⣰⣿⢋⣤⡁⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣉⣉⣉⣙⣳⣤⣀⣘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡈⢹⣿⣿⣿⣿⠇⠙⣆
⠀⢸⡇⠀⣼⣿⠱⠆⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣤⠤⠤⠤⠞⠋⠉⠁⠈⠉⠉⠛⠻⣿⣿⣿⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⠀⠀⠸
⠀⢸⣿⣰⣿⡏⢀⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠙⢶⣄⠀⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣿⣿⣿⡆⠀⣸
⠀⢸⣿⣿⣿⣿⡏⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⣰⡟
⠀⠈⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⢷⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠍⢸⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣃⡤⠾⡟⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧⠀⢰⣯⠄⠀⠀⡞⣼⠃⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⣤⣦⣤⣀⣀⠀⢀⢒⣻⣷⡒⣶⣻⣧⣤⣤⣿⣿⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⠟⠉⢹⣿⡏⣿⣿⡃⠀⠈⠉⠉⡿⡉⠉⡏⢹⠛⠛⠻⠷⠭⣽⣯⣷⣿⠿⣿⠟⠛⠛⡛⢻⡿⠁⠀⠀⠀⣠⣿⣿⠿⠛⠛⠛⠻⠿⠿
⠛⠉⠀⠀⠀⠀⢿⣷⣜⢿⣷⣦⣤⣤⣴⣷⣷⣶⣷⣾⣤⣀⠀⠶⠶⣿⣿⡛⢛⡛⣟⣋⡁⢰⡇⣼⣇⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣿⣷⣾⣿⡏⠀⠈⠉⣉⣽⣿⣿⣝⣋⣛⣏⡁⢀⣼⣷⢿⣿⣤⣤⣄

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡸⠀⠘⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⢀⠄⠑⡶⠏⡁⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠸⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠩⠠⠄⠷⠀⡰⣘⠗⠃⠙⡀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠍⠑⠀⠔⠂⠀⠀⠀⠐⡀
⠀⠀⠀⠀⡀⠃⠀⠀⠀⢀⠎⠀⠋⠀⠁⠀⠡⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠄⠈⠀⠀⠀⠀⠀⠄⢠⠳
⠀⠀⠀⠂⠃⢢⡀⢸⠀⡞⠂⠁⠈⠀⡀⠀⠆⢠⠄⢀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⡀⠀⠐⡂⣤⣠⠀⠀⢀⡃
⠀⠀⠀⠀⠘⠀⠑⠈⢆⢿⠀⠄⠀⠀⠀⣤⠏⠄⣌⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢾⠃⢘⠁⡼⣵⡿⠘⡱⢿⠡⡟⢹⢘⡃
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠚⢄⢰⠜⢠⠾⠃⡈⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠥⠀⠀⢀⡪⠍⠀⠀⠠⠈⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠐⣐⡝⠤⠠⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠫⠀⠀⠐⠍⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⡄⠀⠀⠀⠢⠐⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣤⣄⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⡏⠐⠤⡀⢀⠄⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⠡⢭⠯⢽⡐⢤⡀
⠀⠀⠀⠀⢀⣼⢁⠄⠴⠢⠃⠋⠘⡾⢣⠚⠓⡻⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠀⠀⠀⠀⢰⢋⡠⠉⠂⠤⢄⡒⠼⠄⢳
⠀⠀⠀⠀⠚⠈⠀⣀⠈⠠⠈⣀⠐⡀⠄⠡⠊⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⢹⠂⢠⣀⠀⢸⡀⠂⠖⣑⣦⣴⣥⣖⠄⡸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠐⠉⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⢃⡰⣚⢉⠩⡅⠻⢴⡋⢩⡈⡙⠉⢺⠞⠁⢰⢐⠀⠉⠉⢀
⠀⠀⡴⣻⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⢠⠅⠀⠀⠀⠸⡭⣄⣅⣂⣓⡒⠠⣐⢈⠒⡄⡀⠀⢣⣀⠐⠀⡀⠈⠀⠄⠘⡆
⠀⡸⢠⠛⡝⠀⠦⠢⢤⡀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠁⠀⢰⡜⢀⢾⠀⠀⠀⣽⣼⠟⠛⠿⣽⣷⣬⠳⡍⠄⠁⠈⠩⠫⠖⠑⠒⠮⣅⡊⠰⠃
⠀⡄⢨⡆⠐⣤⣀⡔⠀⠱⠀⠀⠀⠀⢀⠘⠁⠠⠠⠐⢠⠿⠱⠀⡸⠀⠀⠀⠉⠿⠂⠀⠀⠈⠻⣟⢷⣎⡲⢄⣀⣰⠇⠀⡀⠀⠀⠈⠻
⠀⠱⠰⡙⣀⠘⢎⡉⠃⠹⠆⠀⠀⠀⢨⠈⠀⠀⢀⣴⡃⠀⣠⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⢣⡂⢅⡀⣆⡈⠀⢠⡀⠀⡀
⠀⠀⠀⠊⠸⢄⠙⡵⠇⡀⢐⠀⠀⠀⠸⣄⣰⠟⢉⣐⣈⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣈⠀⠀⠀⢏⡀⢋⡁⢠⡿
⠀⠀⠀⠀⠀⠈⠈⠳⠂⠙⠚⠃⠀⠶⠒⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣐⡹⠴⠊
⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⡀⡸⡟⡃⠀⠀⠀⠀⡺⣿⡇⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠂⡸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡝⠻⢧⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⡏⢠⡎⠹⡆⠀⠀⠋⠒⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠡⡘⢷⣠⡇⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⠸⣿⡀⠀⠈⡢⣝⠛⠧⢀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⠾⠮⣅⣉⡒⣤⣀⠁⠓⠺⢅⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⠞⠟⠓⣲⣦⣤⣄⡀⠈⠙⠺⣟⡲⣦⡂⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⢀⣽⡿⠛⠉⠈⠹⣆⠀⠀⠀⠹⡄⠙⢦⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⣸⣟⠂⠀⠀⠀⢠⡿⠀⠀⠀⠀⡇⠈⠈⢷⣁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⡋⠉⠙⢻⠒⢤⣾⡟⠁⠀⠀⣠⠞⠀⢀⠀⢸⣿⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢄⡈⢿⡻⠶⠃⠀⠃⢈⢿⠿⢷⣿⣅⡀⠀⠈⢀⣾⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⢹⡿⢽⣶⣄⣀⠀⠈⠁⠀⠀⠀⠈⠉⠓⠶⢮⣈⡴⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠙⣿⠁⠄⠈⠹⣿⣭⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⣦⡀⠀⠀⠻⣷⡙⢦⡉⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⢈⡄⠀⠈⡆⠉⢳⠢⠄⡘⢷⡼⠟⠋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⣝⢦⠈⠳⢤⣀⠀⠀⠀⢇⡀⠀⢱⣀⣨⠦⠖⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠈⠓⢄⣀⠼⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⢀⠴⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⡗⣊⣉⣦⢠⠤⠤⠤⠀⠛⠚⠉⠙⠛⠓⠒⠠⠤⠤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣭⣭⡵⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⠐⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⢰⠆⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠃⠀⠀⠀⠀⠀⢤⢰⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⢀⡎⠠⠀⢸⡁⠀⠀⠀⠀⠀⣄⠀⠺⢢⠚⠃⢀⡄⠀⠀⠀⠲⠀⣀⣀⠐⠃⠀⠀⠀⠠⠴⠀⣀⠄⠀⠀⠤⠀⠒⠂⠀⠀⠀⠈⡟⢻⠀⢐
⠀⠀⢶⣶⠟⡇⡏⠀⠀⠀⠀⠀⠘⡗⣬⣿⡹⡄⡯⠁⠀⢀⣐⠀⠃⢴⣄⠘⡁⢂⡀⠀⣰⣦⠀⣤⠟⠀⠚⡴⠂⠈⠀⠀⠀⠑⢘⣓⣘⡣⠊
⠀⠀⠨⣐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠗⠉⠀⠀⠀⠀⠀⠠⠧⣙⣁⠴⠑⠂⠀⠈⠘⠁⠀⠀⠉⣀⡘⠁⠀⠀⠀⢠⠀⠀⠀⠏⠹⠄⠀⠀⢀⡀
⠀⠀⠀⢿⡵⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠘⠖⠀⠀⠀⡀⠀⠀⠀⠀⢭⡥⠀⠀⠀⠀⣡⢣⠀⠀⢀⣀⠀⢠⠌⠙⠆
⠀⠀⠀⣘⢠⠀⠀⠀⢀⡷⢯⡀⠀⠀⠀⢀⢀⠀⠀⣀⠤⠄⡄⡀⠀⠸⠗⠀⠀⡀⠠⠀⡁⠠⠀⠀⠀⢰⡆⠀⢀⠀⡘⠔⢥⡏⠀⠨⠍⠀⢰⢚⠀⠈⠀⠀⡀
⠀⠀⠀⢸⡖⠀⠠⣁⠁⣷⣯⡇⠀⠤⠀⠘⢉⠀⠮⢰⡶⠳⣶⠹⡄⠀⡂⠀⠀⠀⠛⠀⡅⠘⠃⠀⠀⠈⣷⠒⠋⠀⠀⣄⣢⠀⠀⢀⣆⠀⠀⠙⠶⣀⡈⠟⠁
⠀⠀⠀⢰⢺⠀⢄⡅⢰⢾⠿⡇⠤⠄⠀⠸⠚⠀⣇⢹⣦⣤⣟⢁⠃⠈⠋⠀⠠⠀⣀⠈⠂⢀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠰⠖⠀⠀⠘⡞⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢬⡷⣾⠔⠡⠀⠀⢰⣠⠀⠀⠃⠠⡅⠄⠋⠀⠀⠀⠀⠀⠐⠁⠀⡀⠸⠁⠂⠀⠀⡟⠀⠀⠀⠀⠈⡏⠀⠀⢀⢦⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣴⠄⠀⢐⣸⠀⠐⠀⠀⢠⠀⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠰⠇⠀⠀⠀⡏⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢐⠀⠀⠀⠘⠿⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⠀⠀⠘⠦⠆⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⡄⡄⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⡆⠀⠀⢠⠉⠄⠀⠀⠀⠘
⠀⠀⠀⢸⢉⠀⠀⠀⠖⠐⢠⠁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠷⡆⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢦⡆⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢐⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠰⠀⢠⢠⠄⢄⠄⠀⠀⠀⠀⠀⠀⢠⢠⠄⠀⢀⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠰⠒⠚⠀⠀⠀⠀⠀⠞⠀⠐⠀⠰⠠⠀⡀

⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣰⠀⢰⠀⠀⠀⢀⠀⠶⢀⡀⠀⠀⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⢰⡀⠀⠀⢠⡀⠀⢠
⠀⠀⡅⠉⡄⠈⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠃⢠⠞⠉⠂⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢉⠀⠠⡐⠋⠘⠃⠈⠀⠏⠀⠈⠒⢀⠀⢨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠾⠒⠲⣄⠈⠳⡀⠀⣠⡄⠀⠀⠀⠀⠀⣄⠀⠀⠉⣤⣀⡂⠐⢤⣄⠀⠀⠘⠋⠁⠘
⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⡾⠃⠀⣤⢀⠁⠀⠀⢿⡆⠘⠀⠀⠀⠀⠠⠒⠉⠀⢠⠻⠋⣉⣹⣶⠀⠙⣷⠀⠀⠋⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠐⣏⠀⠀⠀⢱⠀⠀⠀⠀⠈⢡⠃⠀⠀⠰⠃⣠⠜⠀⠀⠚⠀⠷⠀⢷⡀⠀⢠⠀⠰⠛⢐⠤⠀⠀⠀⠀⠉⠀⢸⣧⠀⢸⡇⠀⠖⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⡤⠂⡲⣘⠛⣗⣤⠘⠣⠀⠙⠀⢀⣄⠙⠃⠀⠠⡀⠀⣠⡄⣠⡏⠀⣸⠃⠀⢤⡄⣩
⠀⠀⡇⢠⠆⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⠀⠘⣠⠂⣠⠟⠁⠈⢁⣈⠁⠐⢀⡆⠀⠀⠛⢁⠑⡶⠀⠀⣿⡛⠿⠿⠋⢀⣰⠏⠀⠀⣀⡸⢿
⠀⠀⡇⠉⡆⠀⠀⠀⠰⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣥⠀⠐⠃⢰⣯⠀⠀⠀⠀⠀⢀⣶⡄⣥⠀⠀⠀⠈⠣⡀⣀⠀⠀⠑⠒⠲⠚⠛⠁⠀⠤⡀⠸⣀⣈
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠦⠀⡄⠀⠀⠀⢀⠀⣀⣾⠇⠀⠛⠇⠀⠐⠿⣿⡇⢸⣇⠀⣿⢆⣠⠀⠉⣀⠴⡂⢀⠂⡄⠀⣷⠀⡜⠋⠛⠉⡸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡖⠁⠀⠀⠀⠀⣰⣧⡟⢰⠄⠀⠀⡀⠄⠠⣿⢠⡇⣿⠀⠑⠈⠉⠂⡀⠋⣤⠈⣸⡇⣧⡜⠀⠐⠶⣠⣶⣾⢷
⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⠀⢀⡀⠀⠀⢀⡶⠀⠘⠀⠀⢠⡟⠁⢃⣼⡀⠀⠀⠀⠀⣸⣷⡌⢃⠘⡆⢻⣏⣀⣀⡀⠚⠛⣦⠀⣤⡈⠁⣦⣽⣦⠟⢻⡇⢘
⠀⠀⡅⠀⠀⠈⠃⠀⠀⠀⠘⠄⠀⣠⣶⡏⠀⠀⠀⠰⡄⠁⣰⣶⠚⢅⠱⢦⣀⣤⣴⡉⠏⣛⠉⠴⣣⠀⢉⠉⠀⣄⢹⠀⠘⢦⠛⡧⠘⠃⠙⠃⢴⣬⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡶⠀⢻⣿⡌⠛⠂⠀⡀⢾⠀⣀⠀⠘⠋⢼⣿⠀⣉⣤⢷⡆⢸⡍⠛⣀⠙⢆⡀⠁⠀⢿⣥⡄⠀⡀⠀⠇⠘⠀⠀⢀⠾⢋⡀⢸
⠀⠀⣯⠀⠀⠀⠀⢈⡷⠀⡴⠀⠀⣀⣤⠐⠒⠋⢤⡈⠀⡀⠉⠀⠀⠀⢻⡇⠀⣨⡼⣷⣾⠕⠊⡙⠰⠚⠉⢂⡀⠀⠀⠰⣶⡅⡀⠀⠀⠀⠀⠈⢰⡾⠃⢸
⠀⠀⠉⠀⠀⠀⠀⠈⠁⠸⢧⠄⠒⠂⢠⠀⠳⢄⠀⠹⣆⠀⠀⠀⠈⠂⢸⣇⠀⢈⠀⢻⡃⠀⣹⡍⠂⢀⡤⠚⠡⣄⠀⠘⣶⣴⡍⠆⠀⠀⠀⠀⢩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡼⠖⠀⠀⠀⢋⣶⡄⠓⡀⠉⠳⢦⡁⢀⠀⢸⡟⠀⠈⠀⣸⠁⡂⢹⣇⡀⠂⣠⡈⣰⠛⣀⠀⠿⣤⠀⢄⠀⠀⠀⣠⠞⠁⡄⣠
⠀⠀⡄⠀⠀⠀⠀⡾⢠⣾⠃⢲⣶⣟⠀⠈⠁⣿⠀⠀⣠⣤⣄⠙⢦⡀⢨⡗⠂⠔⠸⢷⣈⣱⡞⢋⠀⣤⠼⠈⢉⡴⢇⠀⠂⠀⠀⢸⠁⠀⣐⠁⠀⠈⠓⠹
⠀⠀⡧⠤⠔⠀⠤⢇⣼⠟⠀⣿⢿⣿⠚⣤⠀⠙⣧⡀⢀⠋⠀⠛⠲⠷⣌⡛⠛⠛⠛⠂⡉⢡⡀⣹⣶⠏⠠⢠⡾⡇⠀⢣⡾⠦⣀⠈⣦⠀⡉⠠⠤⠤⠄⣸
⠀⠀⠃⠀⠀⠀⣴⣾⠇⠀⠀⣹⢿⣿⠐⢸⡄⠀⠈⢷⡀⠻⣷⣄⡀⠀⠈⠙⠛⠧⠼⠶⠷⠾⠿⠿⠟⠓⣐⠿⡄⠈⠒⡋⠀⠞⠛⠛⡤⠟⠀⠀⠀⠀⠀⢿
⠀⠀⡆⠀⠀⠈⢻⠋⠀⣤⠀⠇⢸⣿⠀⠈⠀⠀⠀⠈⠳⣄⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠚⠟⣇⠈⡖⠀⠀⣾⠀⠘⣾⠤⠀⠦⠀⠀⠀⠀⣸
⠀⠀⡇⢠⠀⠀⠇⢀⡴⠉⠀⠃⣼⠇⠀⠀⢸⡀⠀⡀⠀⠻⣆⣀⠈⠛⢿⣶⣄⡀⠀⠀⠤⠄⢀⣀⣀⡀⠀⡈⠓⠀⡀⢸⣿⣧⣀⡀⠀⠋⠀⠀⠀⢀⠀⢨
⠀⠀⡁⠘⠆⠀⣀⡌⠁⠀⠁⠀⣿⠀⠀⠄⠀⣷⠀⠹⡀⠀⠙⢾⡦⠀⠈⠻⣿⣿⣷⣤⣤⣤⣴⡾⠋⣡⡞⠃⣠⡾⠃⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⢼
⠀⠀⠟⠃⠘⠃⢸⠀⢀⣿⣠⡄⢩⣷⡄⠀⠀⠘⣧⠀⠀⡀⠀⠈⠷⡼⢆⡀⠈⠙⠷⠾⠟⠉⠁⢀⣼⡟⠀⣠⠁⠘⠃⠸⣿⣿⠏⠠⠖⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠎⠀⠈⠁⠀⠶⠾⢻⣿⢀⡄⢻⣷⠀⠀⠀⢹⣄⠀⠘⠀⠀⠀⠈⠺⢏⠂⡀⠀⠀⠀⡀⠀⢠⡿⠀⡄⢙⡂⠀⠀⠁⠈⢡⣤⡀⢀⠀⠀⠀⠞⠁⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣹⣿⣆⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠈⠀⠉⠀⠈⠀⣈⣡⠏⠱⠀⠀⠀⣠⣌⠟⠻⢮⣧⣆⣰⠇⠀⢀⣿
⠀⠀⠇⠀⠀⠀⠠⠀⠀⣰⠊⠙⢿⣿⣿⡟⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⡏⠀⢠⠀⢠⡎⠁⢈⣅⢠⣼⠋⠙⢿⡎⢉⠉⢻
⠀⠀⠄⠀⠀⢠⠆⣠⠎⡉⠁⠀⠀⠙⢿⡇⠀⢆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠒⠋⣠⣼⠟⠀⢠⡞⠂⠺⣁⠀⠸⢧⣸⣧⡀⢀⠸⢅⣸⣇⣤
⠀⠀⠆⠀⢸⡅⠀⠹⡄⠁⠤⠀⠘⠇⣠⠀⠀⠘⢄⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠠⡾⢂⠀⠛⣷⣤⣤⣠⡄⠀⠀⠀⢤⡄⠀⠆⢸
⠀⠀⠂⠀⠃⠰⣦⡄⠈⢑⣆⣠⣤⡄⢸⠀⠀⠀⠀⢂⠀⠀⠀⠄⡀⠀⠀⠀⠀⠈⠉⠿⠿⠛⠉⠀⠀⣠⠀⣷⠈⡆⠀⠸⠁⢘⡁⢀⠀⠄⠀⠀⠉⡀⠀⢘
⠀⠀⠁⠐⠂⠄⠘⢷⠟⠛⠋⠉⠀⠀⢸⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢱⡄⠀⣦⠎⠁⠐⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⢾⣧⣀⡀⣀⣄⠀⠀⠸⢂⡀⠀⠀⢮⠀⣤⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⢀⡜⠀⠀⢸⠖⢲⠆⠀⠐⠛⠁⠀⠀⠀⣦⡀⠀⡤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠉⠁⠀⢠⡆⠈⠷⠀⠀⠆⠀⡏⠑⣄⣀⢀⠀⠀⠀⠢⠀⠀⠀⣠⡞⠀⠀⠀⡞⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠂⢀⡄⠀⠀⠸⠁⠀⠀⢆⠀⠐⠀⡇⠸⠟⠉⠉⠻⠷⣤⣀⠀⠀⠈⠀⠀⠀⢀⡰⢿⠄⠀⡅⠀⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡄⠀⠀⠀⠐⡀⠀⠀⣀⣴⡄⠀⡇⠀⣿⡟⠳⠦⣤⣤⡾⠛⠙⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⣁⣀⣀⠀⠠⠤⠤⠤⠀⠀⠀⢰⣿⣟⠀⢱⡄⣠⠀⠀⢹⣿⠀⢀⠀⠀⠿⣿⠀⠀⠘⠁⡇⠀⢸⡆⠘⣷⠀⠀⡀⠤⠛⠀⠓⠀⠀⠤⠤⠤⢀⡀⠀⢨
⠀⠀⣙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠁⠈⠁⠀⠦⠀⠀⠛⠀⠸⠀⠀⠂⣿⠀⠀⠀⠀⢱⠀⢸⡇⠀⢻⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠄⠀⠀⠀⢳⣄⠀⠀⠄⡇⠀⠀⢹⡀⠀⠀⠀⢸⡀⠈⣷⠀⠀⢻⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠒⣰⣤⡀⠀⠀⢸⣿⠟⠉⠀⣷⠀⠰⣿⣧⠀⠀⠀⢸⠃⠀⣹⣦⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠞⠛⠁⠙⠁⠶⠚⠛⠦⠤⠴⠿⠀⠀⠿⠗⠀⠀⠐⠚⠓⠘⠛⠹⠶⢶⡴⠆⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡋⢙⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣽⣿⣷⣄⠀⠀⠀⠘⠛⠛⠛⠛⢿⠟⠛⢻⡟⠉⠉⠉⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣀⣀⡀⣼⠀⠀⢸⡇⢀⣴⣿⡿⠟⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⠀⢀⣴⣿⠟⣿⣿⣿⡀⠀⢸⣧⣾⣿⣿⣿⣦⣿⣿⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡍⠙⡏⠉⠉⠀⣴⣿⣿⣷⣦⣾⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⣄⠀⠈⡇⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣷⣼⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣾⣿⣦⠀⣷⠀⢻⠀⣼⣿⣿⣿⣿⣯⡸⣿⣿⣿⣿⣿⡇⡿⠛⠛⣻⠛⠛⠛⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣙⣿⣟⣡⣿⣿⣷⡰⡇⠘⠀⠘⠛⠛⠛⠻⡿⠿⠿⣿⠿⠿⠟⢡⡇⠀⠀⡏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⠉⠉⠀⣃⣄⣀⣾⠂⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⠠⢸⠇⠀⢸⠱⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠁⢣⠀⠙⡆⠀⠀⠀⢰⡇⠀⢠⡇⠀⢀⡀⣾⠀⢀⡏⠁⢀⣴⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣴⣶⣦⡘⡆⠀⢸⡀⠀⠀⢸⠀⠀⠘⣡⡾⣿⣿⡆⠀⡼⠀⢠⣾⣟⣿⣅⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣷⠀⠈⡇⠀⠀⡞⠀⢰⣾⣿⣿⡿⣿⣿⡌⠁⠀⠘⣻⠛⠿⠿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⠿⡟⠋⡇⠀⢸⣶⣶⡇⠀⢸⡟⣻⠛⢻⠿⢿⠇⠀⠀⢠⠇⡌⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⢹⡄⢹⢀⣿⣧⣿⣿⠆⢸⠁⠇⠀⣾⡴⠃⠀⠀⢠⠏⣸⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣄⢧⠘⢷⡘⡆⠀⡏⢸⠁⠀⣿⡜⠀⣴⠋⠀⠀⡠⣠⢳⣌⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣼⣟⠈⢆⠀⢳⣇⠀⡇⢸⠀⢠⡿⠁⢰⡏⠀⣠⢞⡴⠇⡁⠈⢳⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠈⢦⠘⣆⠀⠙⣄⡷⢸⠀⡼⠁⢀⡞⠀⡪⣐⢩⠴⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣄⠀⠀⠈⠣⡈⠧⠈⢧⠀⠈⠃⠘⠋⠀⠀⠚⠋⠉⠈⠀⠀⣠⠔⠋⠀⠀⢠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠆⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠰⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⡀⠀⣼⣿⣿⣿⣿⣷⠀⢀⠀⠸⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠀⠟⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡶⠶⣄⠘⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⡿⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠉⠋⠀⣘⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⠆⠀⠀⡴⠉⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢶⣦⢰⣶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠉⡙⠻⣤⣠⣤⣤⣠⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢲⣶⠚⣿⠉⠙⠋⣿⡇⠈⠋⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢠⠀⣉⠀⠋⡤⢠⡞⠁⣘⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⢻⣦⣀⣀⠜⢠⣾⣿⣟⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⡀⠀⠙⢷⣦⣿⠛⠟⣉⠀⠀⣤⡜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⠻⠂⠘⠃⢾⡆⠀⠀⠘⢿⣦⣭⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢁⣼⠟⠛⢷⣶⠀⠀⠀⠀⣶⣉⡉⢹⡄⢰⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⢸⡃⠀⠀⢀⡽⢇⠀⠀⣿⠀⠙⣁⢸⣧⠈⠁⠿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣸⢷⣄⠀⡼⠃⣾⠀⣾⠀⠀⣤⠟⠋⠀⠙⢻⣦⠙⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠉⠀⠀⠸⢆⣿⠀⣼⠋⠀⢰⡞⠁⠀⣿⡇⠛⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠀⣿⠀⠀⠸⢷⣴⠾⣏⡀⠶⠀⠀⠀⠀⢾⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢻⡶⠶⣤⡹⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢁⡸⠇⢠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡜⢻⡖⢻⣿⠿⣿⡀⠀⡀⠀⠀⠀⢀⣠⣤⡀⠀⠀⣀⠐⠛⠛⢷⣤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣧⠘⢻⣾⠿⠛⣷⣾⣿⡍⢉⠛⣤⣤⣀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⣏⣠⡞⢣⣤⣿⣷⣞⠛⣷⠶⢻⡟⠀⠀⢶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠻⢿⡿⠇⡸⠃⠠⠼⣿⣀⣿⣄⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠱⡀⣠⠗⠂⠀⠈⠿⠧⣱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⢰⣿⣦⣄⣼⠃⠀⣠⠐⣤⠀⢀⡅⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣿⡟⠛⠙⠛⢿⣿⣿⣶⣤⠔⠋⠁⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣶⢠⣿⠘⢧⡀⠃⠚⣁⣼⠿⣷⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠗⢉⣀⣉⡀⠹⣷⣄⠹⠶⠚⠛⢉⣴⣿⠈⠉⠁⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⣴⡞⢋⡉⠻⢶⣄⠉⢳⣶⠶⠿⠟⠉⣿⢀⣴⣿⣻⣶⠛⢁⡀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡶⣏⠀⠈⣉⠀⠀⢹⣷⠀⠀⣠⣤⠀⠀⣿⠈⠛⠛⢋⡀⠠⣿⠃⠀⠛⠁⠀⢲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠻⠟⠃⠀⠀⢈⣿⢠⡼⢃⣽⠃⠀⣿⠀⠀⢀⠸⠷⡀⠛⠂⠚⠃⣤⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠶⣢⣤⡀⠀⢸⡟⢸⣿⢻⣿⠀⣶⣅⣠⣼⠟⢀⣤⠟⢣⣴⣶⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⢀⣴⢿⠟⢷⡄⠀⣸⡟⠙⣿⡀⢸⡇⠸⣿⡟⣣⡿⠉⠛⠋⢉⣠⡾⠻⠤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣼⣿⢈⣁⣨⡿⠀⠘⠿⢿⣿⣧⡈⠇⣀⣠⡾⠋⣀⣀⠿⣦⠙⣿⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣿⣎⠉⠉⠀⠀⠀⠀⠀⠀⣉⣡⣄⣽⣯⣴⠄⠛⢋⣤⡌⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠠⠀⠈⢹⡇⠀⢀⣾⣦⣤⣤⡾⠟⣉⠙⠻⣯⡁⠻⠷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠁⢀⡁⣠⡿⠋⣩⠉⣩⠿⢶⣄⠐⢀⣼⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⣿⣧⠼⣀⣠⣤⣶⣦⣜⠳⣾⣿⠉⣤⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⡄⢻⡏⠀⣼⡿⠛⠿⠉⠙⢻⡇⢸⡿⣦⡀⠙⠣⣄⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⢨⣇⣸⣇⠀⢿⣿⠛⠶⠃⠀⠀⠀⠾⠃⠈⣳⡀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⢉⡹⢿⣷⣀⠙⠷⣤⣄⠀⠑⣾⡆⠀⢰⣿⣠⣾⠇⠀⢠⣾⠁⠀⠀⢠⡘⠿⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢸⡇⢸⡇⠀⠀⠀⠉⠉⠻⠿⡈⠀⢠⣾⣿⣿⣥⣴⣾⡿⠁⠀⠀⠀⠈⠁⠀⠲⣮⠋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⢸⡇⠈⢿⣧⡐⣤⠀⠀⠀⡰⠟⢰⠟⢻⡈⣿⡏⠉⠁⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⢺⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣦⣄⡈⠻⣦⣄⠙⣿⣿⣿⡷⠿⢣⡄⠀⣠⠎⢠⣿⠇⢀⣴⠟⠋⠁⠀⠀⠀⠉⠻⣿⣷⡀⠘⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠛⢿⣷⣦⡀⠈⠉⣥⣿⠙⢷⣦⣀⣠⡾⠃⣠⣿⡿⣶⡟⠁⠀⠀⠀⢀⣀⡀⠀⠀⠙⣿⣿⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⢷⣄⠉⠻⠿⣿⠿⠟⢿⣦⣄⡈⠙⠋⣠⣾⣿⠟⣿⠏⠀⠀⠀⠀⢰⡞⠉⠁⠀⠀⠀⣿⣿⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡹⢷⡄⠀⠀⠀⠀⠀⠛⣿⣿⠿⢿⣿⡟⠁⣾⡇⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⣰⣿⡟⠀⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠓⣆⣱⠂⠀⠀⠀⣴⠟⠉⣿⠀⠀⠈⠁⣴⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⡿⠋⠀⠰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢴⣿⣿⡆⠀⠀⢰⠁⢸⡿⢩⡇⠀⠀⣾⡟⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡾⠿⠟⠁⠀⠀⠀⢠⣶⡇⠸⠇⠀⢠⣿⠃⠀⢿⡏⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠀⠀⢿⣿⡿⠀⠀⠀⢸⡟⠀⠀⠀⢀⣼⠟⠀⢴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠙⣿⡿⣿⣷⣶⡄⠀⠈⠛⣀⠀⠀⢀⣾⣇⠰⠶⠶⠿⣧⣀⠳⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣌⡛⢿⣿⣿⡿⠇⠀⠚⢿⣆⠀⣸⡟⠁⠀⠀⠀⣀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⣧⣰⡿⠀⠀⠀⠀⢾⡀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡟⠛⠿⠟⠛⠿⠟⠛⠿⠟⠛⣼⠟⠛⠻⠿⠟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⣿⣏⣉⣉⣉⣉⣉⣩⣏⣿⣿⣿⣟⣛⡛⠛⠛⠛⠛⢛⣛⣻⣿
⣿⣿⣶⣿⣷⣶⣾⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢲⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿
⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⣴⣿⣿⣷⣾⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣼⠟⢒⡆⠀⠀⠀⠀⣀⣀⣄⣀⣤⣾⡷⢿⣿⣿⡿⠟⠉⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣄
⡟⠀⣿⣵⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣄⣨⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⢿⡿⣷⡀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣟⠛⠛⠛⢙⡃⠀⠀⢁⣿⣿⣿⣶⣶⠶⠆
⠀⢠⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣟⠁
⣴⡾⡗⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀
⣽⠟⢿⣶⡆⠀⠀⠀⠀⠀⠀⢸⣟⣹⣿⣟⠁⠛⣿⡏⠉⠻⣿⣿⣿⣧⣀⡴⢾⣿⣷⣴⣾⢿⡿⣿⣿⣿⡿⠛⠹⢿⣟⢾⣿⣿⡇⠀⠀⠀⠀⠀⢦⡻⠄
⡟⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣾⣽⣶⣤⣭⣳⣠⣼⠺⣿⡟⣹⣿⡦⣴⣿⣴⠿⠇⣯⣿⣿⣫⣯⣤⠠⣤⣶⣛⡮⣿⡻⠀⠀⠀⠀⠀⠀⢾⣷⡀
⠤⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⢠⣽⣿⣿⡿⣏⣾⡟⢿⣧⣿⣻⣾⡀⢈⣛⢿⣿⣿⣿⣿⠿⢫⣙⢿⣿⡿⢛⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄
⡿⠂⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣟⣺⡿⢧⣌⢁⡀⠀⢿⢿⣿⣿⣶⣾⣿⣿⣟⡍⣤⣴⣿⣿⢛⣅⣀⣿⣧⣆⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠓⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡽⠧⢥⠡⣟⢢⣙⣿⣿⣿⣿⡿⣿⣿⣿⠿⠯⢽⣿⣿⣿⣿⣿⣈⣮⣿⠵⠼⣿⠵⠶⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣌⣸⣶⣠⣿⡶⠿⣿⠿⠛⢛⣉⡉⢰⣿⣿⣿⣿⣿⡷⠀⠀⠙⠻⠿⠷⣷⣿⣾⣮⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣿⣿⡿⢀⣴⣇⠀⠀⠀⠀⢙⣿⣿⣋⣉⣁⣸⣟⡏⠀⠘⣛⡏⠀⢀⣉⣭⣿⣿⣿⣿⣿⣶⣄⢠⣀⣈⣿⣿⣻⣿⡿⣿⣾⣿⣿⠓
⢸⣿⣿⠇⣾⣿⡿⠀⠀⠀⠀⠀⠉⠛⢿⣟⠻⣿⣷⣶⡶⣶⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠋⠀⣭⡉⠉⠉⢁⣘⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀
⣾⣿⣿⣸⣿⣿⠇⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⢿⣿⣷⣗⣷⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⢀⣤⣤⣤⣤⣤⡿⣿⣿⠋⠟⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⣿⢿⣯⢹⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⡿⠿⣿⡟⣹⣶⣿⠟⠁⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠀⠰⠆⠀⠀⣿⠀⡙⢾⣿⠟⣿⣿⠁⡘⣿⢿⠋⣼⣯⣴⣷⡟⠩⣿⣿⣿⠀⠐⠋⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢶⡦⠀⠀⣠⠀⣿⠀⣀⣼⣿⣿⣿⣿⣾⡇⢹⠘⡀⣸⣽⣿⣿⣿⡿⠋⢹⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠤⠀⠻⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣱⣿⣿⣿⣿⣿⠄⠀⢸⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⣶⣿⡄⠈⢹⣿⣿⣿⡿⣿⣿⣿⠀⢿⣿⣿⠟⠉⠃⠀⠀⣸⣿⠈⠛⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿
⣿⣿⣿⣿⡇⢀⣴⣦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠻⡿⠃⠀⠘⣿⣿⣿⡇⠘⣿⣿⣶⣾⡿⠁⠀⠀⢀⠀⠀⣻⡿⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟
⣿⣿⣿⣿⣧⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⣿⣿⣿⡇⠀⣿⢿⣿⠏⣹⣷⣷⡞⠁⠀⠀⠿⠁⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⣿⡇⠀⣿⡇⠁⠀⠹⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠉⠉⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⠰⠂⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⡀⠀⠰
⠀⠀⠀⠀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠄⠀⠤⠀⡰⡳⠀⠀⠀⠀⠀⢘⠂⠆⠁⠄⢰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠲⠄⠀⠀⠂⠈⠀⠒⠀⠚⠁
⠀⠀⠂⠀⠀⠀⠓⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡐⣂⠂⠀⠀⠀⠀⠀⠈⠢⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⠀⠀⠀⠒⠈⠀⠀⠀⠀⠂⠀⠀⠨⠈⡡⠀⠀⠁⠀⠀⠐⠊⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠄⠈⡐⠀⠀⢁
⠀⠀⠀⠄⠀⠀⠀⠀⢀⡄⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠠⡀⢠⠀⠁⠉⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠘⠁⠀⠀⢀⢀⠠⠀⠀⠀⠠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⢡⠸⠄⠀⠊⡄⠂⠀⢄
⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠁⠈⠁⠊⠀⠀⣀⣀⣀⣃⣀⣀⡀⠀⠀⠁⠀⣠⡀⢠⡄⠀⠀⠀⠀⠀⢀⠀⠀⠁⠈⠂
⠀⠀⠃⠁⠀⠑⠿⡀⠾⠦⠀⠀⠄⣀⡀⠀⠄⠐⠀⡀⠀⠰⢓⠒⠶⠒⠒⠒⠣⠀⠀⠂⠀⠁⠀⠀⠉⠁⡀⠀⠈⡀⡂⢐⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⢄⣁⠴⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠐⠀⠉⠠
⠀⡰⠀⠑⡄⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⢶⠆⠀⡴⠲⣦⠀⣴⠀⠀⢀⡴⠲⣦⠀⣠⠖⠶⠄⠐⣆⠀⣴⠀⠀⠀⠀⠁⠊⠀⠀⢠⠂⢰
⠀⠇⢀⠀⠰⠰⠀⠿⠈⠂⠀⢸⡷⣏⠀⢸⠀⢸⡇⠀⢸⠄⣿⠀⠀⢸⡇⠀⣹⠀⡿⠀⠰⡤⠀⠘⣾⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠉
⠀⠀⠤⠄⠁⠀⠀⡀⠀⠀⠀⠸⠧⠞⠀⠾⠆⠈⠷⠶⠛⠀⠻⠶⠶⠈⠷⠶⠛⠀⠻⠶⠾⠃⠀⠰⠏⠀⠀⠠⠀⠀⠀⠀⠂⠂⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠰⡆⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⡁⠀⠀⠁⠀⠀⠀⣴⠀⠰⣿⡇⠹⠃⠀⠀⠀⢀⠃⠠
⠀⡠⡆⠀⠐⠀⠀⣤⡀⠀⠁⠀⠨⣗⠀⠀⠀⡀⠐⠀⠀⠀⠘⠒⠀⠀⠀⠉⡁⠀⠀⠀⢀⠁⠈⠋⠉⢉⣀⠄⠉⠀⠀⠀⠐⠁⠀⠐⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⠀⠐⠸⠀⠀⠀⠖⠉⠀⠀⠊⠁⠀⠠⡀
⠀⡤⡙⡀⠠⠠⡄⠀⠀⣀⠑⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠠⠠⠀⠀⠀⠈⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⡉⠉⢀⢀⡠⡀
⠀⠀⠀⠁⡀⡀⠁⠀⠀⢀⠆⢠⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠂⠈⠀⠀⠀⠀⠀⠒⠒⢀⢀⡘⠀⠂
⠀⠀⠈⠆⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠐⡊⠠⠀⠠⠰⡤⠀⠀⠀⠀⠀⠂⠀⠠⢀⠠⠌⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠂⠀⡄⠐⠀⠀⠀⠀⢄⡁⠀⠀⠣⠤⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠄⡀⠈⠀⠐⠀⣅⠀⠀⠈
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠲⠀⠀⠀⡀⠀⠘⠃⠀⠠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠈⠀⠐⠀⠀⠀⢀⠄⠀⠁
⠀⠀⠰⢀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠘⠃⠀⣀⠣⠀⠁⠀⠀⠂⠂⠀⠀⠀⠅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢀
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠾⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠁⠀⠀⠀⠔⢂⣈⡭⠥⠤⢤⣀⡐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡷⠋⠀⠀⣀⣤⠴⠄⠒⠋⠉⠁⠀⠀⡄⠀⠀⢉⠛⠆⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡛⡴⠖⠒⠉⣁⣀⣀⣤⣴⣦⣾⣴⣿⣿⣿⣷⣷⠟⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠯⢱⣤⠐⢠⡉⢹⣿⠟⠉⠉⠀⠉⠉⠋⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣷⠂⠀⠀⡜⠁⠀⣀⠤⠴⠤⢄⠀⠀⠒⢓⣛⣒⣒⣚⣛⡒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣒⣸⡆⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠛⠋⡩⡭⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣨⢿⠞⢫⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠰⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⡿⠀⢀⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⡄⠀⠀⠀⠀⢀⡾⠀⢰⣧⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⡿⠟⠿⠷⠷⠼⢼⠟⠁⠈⢨⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠂⠀⠀⠀⠀⠀⠘⠀⠈⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⡂⠀⠀⠀⣀⣠⡄⠀⠀⢠⣄⣀⠀⠀⠀⢐⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠑⠒⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠒⠊⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠐⢄⣠⣄⡠⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠀⢀⠀⠀⠁⠛⠛⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠰⢶⣉⡉⠊⠈⣉⣱⠶⠏⠉⠀⠈⠀⠀⠀⠀⢀⡤⠞⠛⠳⠄⠂⠱⠁⠂⠴⠓⠂⠠

⠀⠀⠀⠀⠀⠆⣠⠤⠤⢤⡜⣠⠤⠤⢤⣐⣦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠂⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡠⠀⠀⠀⠈⠀⠀⠀⠠⣀⠀⠀⠀⢀
⠀⠀⠀⠉⠉⠛⠉⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠓⠒⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢝⡓⠒⠋

⠀⠀⠀⠀⢀⣠⠤⠴⡂⠀⠀⠀⠐⠲⠦⢤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠶⣦⣄⣠⡔⠀⠒
⠀⠑⠒⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⠦⠠⠒⠋⠡⠛⠓⠲⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡐⠲⢄⡀⠸⣆⠠⠀⠀⡀⠠⠀⣀⠤⠒⣁⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠐⠀⢀⣀⠀⠂⣀
⠀⠂⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠈⠑⠊⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠚⠏⠀⠀⠀⣄⣀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠛⠿⣶⣄⠀⠀⠀⠚⠻⠁⠀⠀⠠⠴⢿⡟
⠀⠀⣠⡾⠛⠉⠀⠀⢀⣠⡤⠶⠚⠛⣋⣉⣩⣭⣭⣭⣛⣦⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠁
⢠⣾⠋⠀⠀⢀⡴⠞⠉⢀⡤⢖⣪⠭⠒⠒⢋⣩⡭⠿⠛⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠏
⣿⠃⡎⣖⡆⡞⠀⢠⠞⡡⠚⠁⢀⣠⠶⠛⠉⠀⠀⠀⠀⢀⣀⣠⣤⣶⠟⠁⠀⠀⢀⡾⣻⠏
⣿⡄⢣⠳⠃⠳⢤⣏⣞⣀⡤⠞⠋⠀⠀⠀⠀⣀⣤⣶⠟⢛⣿⠉⠁⠀⠀⠀⠀⢀⡞⣰⠃
⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠁⣠⢎⣿⡄⠀⠀⠀⠀⢠⡞⣴⠃⢀⣸⣦⠄
⠀⠈⠻⢷⣤⣀⣀⠀⠀⢀⣀⣠⣴⡾⠛⠉⢀⣠⠴⢊⡵⢋⠘⣧⠀⠀⠀⢠⠟⡼⠃⠀⠀⠀⠙
⠀⠀⠀⠀⠈⠉⠛⣿⣛⠿⠿⠯⠗⢒⣒⣉⠥⠔⠊⡥⢖⡡⠂⠹⣆⠀⢠⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⡩⠔⣡⠀⢻⣴⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⣢⣴⢃⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠚⣵⢣⡞
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣠⣤⡴⠶⠛⡿⢡⠏⠀⠀⣰⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣾⣿⠏⠀⠀⠈⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠸⠃⡇⣨⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⡇⢨⡷
⠘⠉⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⠸⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢰⠀⢠⠀⠀⠀⠀⠀⠀⠘⠑⠚
⠀⠀⠀⠀⠀⠀⠘⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⢠⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⢀⠀⣀⣀
⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡤⡀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡤⡀⠀⠀⠀⠀⠀⣄⠀⣀
⠟⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠄⠀⠀⠈⠓⠈⠓⠃⠀⠀⠀⠀⠀⡟⣤⢻⠰⣏⠟⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠈⠓⠈⠓⠃⠀⠀⠀⠀⠀⡿⣴⢿⢰
⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠸⣟⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⢰⣖⡦⡦⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠱⠀⠀⠀⠀⠀⠀⢰⣖⡦⡦⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠌⠱
⠈⠁⠀⠓⠀⠀⠀⠀⠀⠰⡇⠀⠐⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠓⠀⠀⠀⠀⠀⠸⡇⠀⠐⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠸⠳⡇⢨⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⡇⢨⡷
⠘⠉⠀⠀⠀⠀⢰⠆⢠⠀⠀⠀⠀⠀⠀⠸⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠸⠑⠚
⠀⠀⠀⠀⠀⠀⠘⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠘
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠄⠀⠀⠀⠀⠀⢠⠀⣀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⡤⡀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⡤⡄⠀⠀⠀⠀⠀⣄⠀⣀
⠟⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠄⠀⠀⠈⠓⠀⠓⠃⠀⠀⠀⠀⠀⡿⣤⢻⠰⣏⠟⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠈⠓⠈⠓⠃⠀⠀⠀⠀⠀⡟⣤⢿⠰
⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠸⣏⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠸
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⣒⡦⡦⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠱⠀⠀⠀⠀⠀⠀⢰⣖⡦⡦⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠌⠑
⠈⠁⠀⠓⠀⠀⠀⠀⠀⠰⡇⠀⠐⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠓⠀⠀⠀⠀⠀⠰⡇⠀⠐⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠂⢁⢀⠀⠠⠀⠀⠀⠀⠄⡕⠀⠀⠀⠀⡐⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢀⠀⠄⠈⠀⠀⠀⠀⠀⡠⠀⠈⡦⠄⠀⠀⠀⠀⠀⠀⠀⡠⠂⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠊⠀⠁⠀⠂⠁⠀⣀⠄⠁⡀⠀⠀⠐⠈⠀⠀⠀⠠⡆⠠⡆⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠁⢠⡠⠐⠆
⠀⠀⠀⠀⠀⠀⠊⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠠⠀⠉
⠀⠀⠀⠀⢀⡄⠂⠀⠀⡄⠀⠂⠁⠀⠀⢠⠆⠀⠐⠖⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠒⢃⠀⠀⠀⠘⠀⠀⠀⠀⠐⠃⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠙⡂⠀⠠⠀⠀⠀⠀⠴⡄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠴⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠢⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠠⣀⠀⠤⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⡀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠉⠀⠨⠭⠍⠁⠉⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡦⠀⠀⠀⠀⠈⠙⠀⠀⢀⡀⠀⠀⠀⠀⠀⠨⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⡀⡀⠀⠀⡅⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠆⢀⠈⠁⢀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠒⠀⣀⣐⠀⠸⠄⠀⠂⠁⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠰⠄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⠄⠈⠑⠀⠀⠰⠀⠀⠀⢐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠱⢄⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠄⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠁⠈⠂⠠⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠖⠀⠀⢀⡔⠀⠀⠀⠠⠈⠇
⠀⠀⠀⠀⠀⠙⠀⠀⠈⠃⠄⣀⠀⡀⠀⠀⠀⠊⣀⠀⠠⡀⠘⠁⠀⢁⠰⢦⠐⠝⠶⠂⠀⠀⢀⡠⢎⠁⠀⠀⠀⠀⠐⠀⠐⠂⠂⠁⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠉⠁⠺⣄⠀⠀⠀⠀⠀⠕⠀⠀⢄⠨⠁⠀⠀⠠⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠂⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠔⠈⠅
⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⡀⠀⠀⠀⠐⠃⠀⠀⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⠊⢀⠀⠀⠀⠀⠐⠠⠂⠐⠈⠢⠀⠀⠀⠀⡀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠄⠀⣀⢀⣀⣠⠀⠄⠈⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠄⡀⡀⠀⠀⠙⢀⠇⠁⢀⠀⠂⠁⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠀⠀⠀⠀⣇⡀⠂⢐
⠀⠀⠀⠀⠀⢰⠁⠐⠠⠁⠀⠒⠀⠀⠠⠐⠃⠀⠈⠃⢀⣀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⡘⠀⠀⡠⠆⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠙⢠⠒⣆⠉⠄⠀⠀⠀⠀⠀⠈⠁⢀⠐⠒⠂⠀⢀⠄⠀⠁⠀⠀⠉⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠘⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠤⠄⠀⠒⠂⣠⣻⡄
⠀⠀⢀⡀⠤⠄⠐⠒⠀⠉⠀⢀⣀⠀⠠⠤⠄⠀⠀⠒⢾⠈⠪⡇
⣠⣔⠡⠤⠀⠂⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡢⢺
⠁⠀⡠⡐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢀⢔⣧⢤⠄⣀⣀⡀
⢠⠀⢆⠣⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠕⠁⣻⣛⡿⢥⠛⣓⡩⠯⠟⣀⣰⠆⡤⢠⢄⣀
⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣠⢤⠤⡤⡤⣀⠀⠀⠀⠀⠀⠘⡅⠪⣺⣽⣠⢿⡚⣹⢧⠎⡞⡰⠃⠊⢁⣁⠔⡸⢉⣼⣵⣲⣦⡀
⠀⢀⠀⠀⠀⠀⠀⠀⡴⡛⠑⣠⠪⣪⡨⡨⢓⠄⠀⠀⠀⠀⣧⡪⠪⣿⢯⡞⢙⣃⡾⢾⡤⢤⠎⡝⢁⠞⠐⢁⣁⡼⢷⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡫⡢⠎⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⢸⣪⡆⣿⣴⠶⢮⡭⡽⢙⣣⡶⡚⢀⠅⡰⢁⣋⡘⢸⣳⠃
⠀⠀⠀⠀⠀⠀⠀⢨⡎⢜⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠊⢸⣧⠟⡟⢀⡧⠟⡙⡿⠋⡎⢀⠧⠎⢉⣠⣷⠃
⠀⠀⢠⠀⠀⠀⠀⠀⣗⢕⢧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⢔⢝⣍⡀⡟⢻⣜⣽⠋⣇⢠⡓⣮⡠⢤⣃⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣕⢝⢆⠀⠀⢀⣼⢿⢽⠀⠀⠀⠀⠀⢸⡕⠡⣯⢫⢹⣬⡇⢸⣸⡍⣛⣵⠛⡧⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣵⡠⠋⢪⡫⡢⣱⠃⠀⠀⠀⠀⠀⠀⡧⡪⣺⣦⢾⠀⣦⣼⣩⣬⣋⣷⣜⣷⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠚⠚⠁⠀⠀⠀⠀⠀⠀⠀⢿⡪⢪⣿⢨⣧⢟⣧⣬⢠⣬⢿⣭⡬⣽⡟
⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢄⣀⠀⣀⢀⡤⠄⠀⠀⠀⢸⡊⡊⣿⠶⢫⣼⠇⣶⡶⣶⣶⠀⣶⣶⣶⣤⢄
⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠐⣛⠘⠁⠸⠤⠉⠒⠀⠀⠀⠀⠀⠀⠈⣋⠀⢿⢴⢻⠠⣤⡷⣴⠇⣅⣠⣿⣾⣿⣽⣽⣿⣿⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⡀⢠⠀⠄⠀⠀⠀⠀⠀⢿⢐⢽⡹⣸⡻⣪⣼⡀⣶⠿⣭⣿⣿⡿⣻⣿⣿⢷⡾⡏
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠇⢩⡁⠀⠣⠜⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⣻⣷⣏⣠⠾⡀⡿⢇⣷⢷⣾⣷⣾⣿⠷⣻⣿⠾⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠼⠾⠅⠭⠭⠙⣛⣛⣿⠿⠽⠾⢿⣿⣻⣿⣿⡷⠉⣩⣀⡤⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠸⣀⣀⣀⣀⣠⣤⣄⣐⣲⡒⠒⠒⠨⠭⠍⠩⠭⠉⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑
⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠰⢶⠱⣾⡄⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢸⣆⠀⠠⡄⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⣦⡈⡵⡞⣧⠀⠀⠀⠌⠉⠉⠀⠀⠀⠀⠀⢸⠛⠀⠘⠃⠸⠛⣧⠀⠐⠀⠀⠀⠀⠀⢀⣆⠀⠐⣇⠀⠀⠀⠀⡆⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⢈⢶⠀⠀⢠⣏⠀⢡⠞⣷⣿⡆⠀⠐⣢⣤⣴⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⠛⠀⠀⠈⣄⢀⣀⣠⢼⣿⣆⠠⠀⠀⣷⣇⠀⢃⣷⣿⣿⣿
⠀⠀⠀⠀⢘⡷⠰⠁⡁⠀⢸⠏⣷⣌⣘⠻⠂⢙⠀⡀⣹⣷⣯⡼⣦⠀⠀⠀⢸⠀⠀⠀⠀⠘⡯⠄⠀⣷⢦⣿⡏⠏⡌⠉⣿⠉⠟⠚⠈⢉⣵⠀⠈⠙⢻⣿⣿
⠀⠀⠀⠀⠉⠱⠀⢀⣿⠀⣿⣀⠫⠹⡿⣏⣼⣿⠀⣶⣿⣟⢁⡀⣻⣅⠀⠀⢸⠀⠀⠒⠒⢀⣭⣦⡴⠁⣴⡶⡀⠀⠁⠈⠀⠀⠀⣀⡠⣾⣿⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⢍⡀⠈⠀⠡⠿⣽⢻⠀⠿⣿⠛⡏⠻⠿⣿⣷⠀⢸⠀⣴⡂⢰⡏⠉⣾⣋⡁⣿⣿⡇⠀⢸⣆⠀⠀⠀⠀⢠⣿⢿⠀⠀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠉⠃⢀⠀⠉⠆⠀⠠⢠⠤⢥⢰⠀⠀⠀⠛⠙⠀⢸⡀⠛⢁⠈⠃⣴⠅⢸⣽⣿⣿⡿⠀⠀⠈⢷⡀⢀⣺⠖⣏⣿⡇⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⠇⠀⡀⠋⠀⢀⣶⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣼⡤⠆⠀⠠⠙⣯⣾⣿⡄⠀⠀⠀⣸⣿⡆⠀⠀⢸⣿⠅⠀⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⢸⡇⠈⠀⣤⣄⣴⣶⣾⣿⣿⣿⣀⢀⣤⣾⠿⠋⠀⠀⠀⠈⠁⠀⠰⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠠⡄⠀⣀⡀
⠀⠀⠀⢀⡀⡴⠂⠀⠀⠀⣤⣴⣶⣦⡄⠀⢠⡤⠀⠲⠀⠄⠀⠠⠀⠀⢀⠀⠀⢰⢸⠄⠂⠽⠀⠓⠀⠀⠀⠒⣀⢀⡀
⠀⠀⠀⠉⣰⠀⠀⠀⠁⠀⣿⣌⡹⢿⠷⢄⢀⠀⠘⠜⠀⠀⠈⠀⠀⡸⠂⠘⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡆⠑
⠀⠀⠀⢀⠋⠀⠀⠀⠀⠠⠿⠿⢿⣆⡀⠀⢀⠀⢘⢂⠀⠀⢘⠐⠀⠁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢬⡟⠂⠀⠠⡤⠀⡀⠀⠀⠂⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡄⠀⠰⠂⠠⠀⡴⠒⠀⣠⠀⠀⣠⣿⣆
⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠄⠀⢸⣷⣤⣴⣿⣿⡿⣿⠿⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠒⠀⠀⠀⠀⠀⢹⡿⠿⠁⢹⠟⠀⠈⠀⠟
⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠊⠀⠀⠀⠂⢠⠀⠀⠈⠃⠀⠀⠉⡰⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠠⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢲⠁⡆⠀⣠⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡤⠀⠖⠅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠂⢴⣶⣦⣄⣀⣤⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣀⠀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠀⠤⠄⠀⢄⠘⠉⠉⢻⣿⠛⠛⣿⠋⠉⣛⣩⠄⠀⠀⠄⠀⠀⠀⠀⠌⠀⠊⠁⠀⠈⠁

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⣧⡉⠙⣀
⠀⠀⠀⢸⠃⠁⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⠠⣽⠁⠰⡅⣄
⠀⠀⠀⠸⡃⠐⢶⠄⠶⠐⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢀⣸⡅⠈⠀⠀⠀⠀⠠⡴⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣧⠦⠀⠀⢤⣦⡀⣼
⠀⠀⠄⠀⠘⠆⠰⣦⠀⠀⢄⠀⠀⠀⠀⠀⠀⠻⡀⠀⣾⣟⠁⣀⠂⢀⣀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡁⣰⣾⣿⣷⡟⠈
⠤⠤⢍⠀⠘⡇⠀⠛⠀⠀⡎⠒⠀⠀⠀⠀⠀⠀⠱⡀⠹⡿⢠⣄⡈⢋⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣴⢷⠿⠟⠀⠈⡀⢠
⠀⠠⣴⣆⡄⠇⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⣀⣤⣴⣄⠀⢈⢋⡅⠙⡿⢷⠒⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⢸⡟⠍⠀⠀⠀⠀⠘⠂⠙
⠙⣷⢬⢽⣿⡀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠙⠢⣹⣿⣀⠴⣷⠞⣷⣤⠀⠀⠀⠀⠀⠘⠁⢀⣠⡌⢷⠢⢂⠀⠀⠀⣠⣤
⣀⣾⣿⠈⠄⠁⠀⢀⡸⠃⠀⠀⣠⡾⢇⣠⠈⢋⡀⠀⠲⠀⡟⣷⡍⠁⠀⠀⢘⣦⠀⠀⠀⡆⢠⣠⣶⣿⠟⢁⢈⡀⣸⠀⢀⠀⠹⠟⢰
⢨⣿⡿⠀⠈⠀⠀⠋⠰⠃⠀⠀⣿⣿⣾⣿⠀⠏⢀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠠⢿⠀⠀⠀⢃⣾⣷⣭⣤⣤⡴⣻⡆⢸⣶⡘⠆⠁⠀⠴
⣻⣿⣷⠖⠖⠃⠀⠀⡘⠀⢴⣾⣿⣿⡟⣿⠀⣶⣿⡀⠀⣼⡇⣿⠀⠀⢰⠀⠀⣾⠀⠀⢀⣿⣿⣿⣿⡇⣭⠀⠈⣷⣆⠹⠿⢿⣧⣄⣐
⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⣴⣿⡟⠉⠁⢹⠀⣻⡿⠻⠾⠿⠗⠛⠀⠀⠀⠀⠀⠿⠀⠀⣿⡏⢻⠟⡏⠃⢹⡇⠀⠶⣿⡇⠀⠀⡈⠙⢻
⣿⣿⠿⠃⠀⠀⠀⠃⠀⠸⢻⣿⡗⡞⠀⢸⠀⠂⢀⠀⠀⣰⡄⢲⣄⠀⠀⠀⠀⢆⠀⠀⣿⠥⠄⠀⠁⠀⠈⠀⠀⢰⠈⢻⡆⠀⠁⠀⣸
⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠉⢼⡇⠀⢀⣾⠀⠁⠀⢠⣸⣿⠀⠸⣏⣶⡀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠺⠂⠘⠷⠸⢷⡀⣀⠀⣻
⣀⠀⣀⣀⠀⠀⠀⢀⠀⣀⠀⢰⡗⠀⠰⠸⠀⠀⣦⠈⢹⣿⡀⣶⣿⡇⢱⡆⠀⠸⣷⠀⠃⠀⠀⠀⠀⣰⡃⠙⠢⡄⢠⣄⣤⣿⠟⠋⣭
⣿⠀⣿⠀⣀⠋⠉⠄⠀⠛⠘⢋⠀⠀⠀⢠⠀⡀⠘⠆⢠⣿⠁⣦⢹⡇⠈⠀⠀⠀⢻⠀⣠⣠⣤⡤⢰⣿⠏⠀⠀⠀⣬⡖⠙⣷⣶⣂⠙
⣽⠰⢩⠀⠂⠀⠀⠀⠀⠀⠀⠈⣷⣀⡄⢸⢘⣿⢓⣄⢨⡿⡄⢹⣿⠁⢀⡀⠰⡔⢆⠀⠀⣥⡤⠄⣾⡏⢀⣾⠁⠀⠸⠃⠀⠀⣄⢿⠠
⣿⠉⢺⡬⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠈⣿⠺⣿⡾⣧⢣⡾⠃⠀⡀⢿⣆⠙⢄⠁⠀⢸⡇⢸⡟⠀⣸⣟⠀⠀⠀⡄⠀⠀⢀⠈⠐
⢿⢀⣸⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⢀⠈⠀⡈⣁⣿⣿⣜⡾⠃⠀⢧⢧⢧⠻⣄⠀⠀⠀⠀⣿⠸⠀⠀⣿⡏⠀⠀⣶⡇⠀⠄⠛⠃⠈
⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠁⠈⠸⣧⢹⣿⣸⣿⡇⠀⣄⠀⠘⣯⠃⠙⢦⡀⠁⣁⣤⠀⠀⣴⣾⣷⣾⣿⣿⣤⣀⣤⠘⠷⢒
⡀⠘⣿⡇⠀⠀⠀⠀⢷⡀⠀⠀⠈⠃⠀⠀⢰⣿⡆⢻⣿⣿⡇⠀⠹⣆⠀⠘⣧⠀⠀⠉⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠘⠏⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠈⣿⣿⣄⠹⣿⠇⣴⡀⠹⣦⠀⠈⢷⣄⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢻⣿⠋⠀⣠
⣦⠀⠀⠀⠀⠀⠀⠀⣠⠘⠀⠚⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠸⣿⣷⡆⠘⢷⣄⠀⠙⢦⡅⠀⠀⣤⠀⢻⣿⣿⣿⣿⣿⠁⠀⢹⣧⠀⠟
⢻⣆⠀⠀⠀⠀⠀⢠⡷⡀⠄⠁⠀⠀⠀⠀⠀⢻⣿⣻⣿⠀⣆⠈⠛⠀⠀⠈⢻⣦⡀⠀⠁⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⢻⣶⣀
⠀⢻⡄⠀⠀⠀⠀⠸⡅⠟⠁⢰⠇⠀⠀⠀⠀⠀⠹⣿⣿⠸⣿⣷⣄⠀⠀⠙⢦⡙⣿⣶⡆⠀⠀⠰⠃⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿
⠀⠀⢻⡆⠀⠀⠀⠀⠙⢮⡷⠋⠀⠀⠀⠀⠐⣇⠀⣹⢛⣿⣛⢿⣿⣷⠀⢲⣤⡈⠨⡛⠇⡀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠈⣿⣶⡏⢸⣿⣿⣷⣏⠈⢶⣄⠉⠙⢂⡈⡅⠀⠀⠀⣴⡀⢽⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠂⡀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠂⠀⠀⡀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣾⢶⠀⢀⡔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠊⠻⠶⠥⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣰⣿⣿⣿⣿⣟⠿⣿⣧⠀⠀⢰⣿⣿⣯⣽⡿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⡿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⣖⣿⣷⢻⣿⣿⣮⢟⡽
⠀⠀⠀⠀⠀⠀⠹⣿⣋⣽⢿⣿⣿⣿⠏⠀⠀⠀⠹⠁⠛⣿⡿⢫⣭⣾⡟⠀⠀⠹⣿⣯⣥⣼⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠙⠀⠙⠚⠉⠋⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⡠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠄⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠤⠀⠀⠈⢆⠀⠀⠀⠀⢠⡞⠈⠐⠠⠁⠀⠐⠚⠷⠀⠚⠃⢀⠀⠀⠀⢈⣀⠖⠘⢤⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠰⡆⠀⠀⠀⠀⠆⠰⠀⠚⠀⠀⠐⠀⠀⠀⠀⠀⡌⢀⠚⠀⠉⠀⠀⠀⠀⠠⠶⠀⢾⣿⠈⠛⠃⠀⠀⣫⠘⣄⢁⠼⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠐⠃⡴⠆⢀⢷⠀⠀⠀⠀⠁⠻⠆⠬⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⠀⠀⠆⢀⠀⣤⠀⠀⠈⠄⠀⠀⠉⠀⠔⠀⢀⠔⠀⠀⠀⠨⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠈⠁⠀⠀⠀⠀⠑⠠⠠⠤⠶⠒⠁⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡘⠈⠆⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⢣⡀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⢀⠐⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⡄⠀⠀⠀⢤⠀⣜⡤⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠐⣂⠈⠀⢀⠆⠂⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⣿⠔⠀⠀⠀⠠⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠙⠀⠀⠒⠉⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⡠⠀⠰⠀⢀⠀⠠⠀⠀⠰⠂⡗⠀⠀⠀⠐⡍⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⡐⣁⠈⠳⡀⠀⠀⠈
⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⢀⠀⠃⠀⠀⠀⠀⠙⠃⠀⠀⣄⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠀⠁⠀⠁⠀⠀⠀⡀
⠀⠀⠄⠀⠀⠄⠀⠀⠀⠹⢀⠄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢀⠇⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⡅⠇⠀⠀⠀⠀⠀⠀⠘⢧⠂⠀⠀⠀⣀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠇⡠⠊⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⡓⠀⠀⠀⠉⠐⠚⠋⠉⠀⠀⠀⠀⠀⠀⡀⠤⠤⠠⠤⢀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⣀⠴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡀⠺⠆⠀⠀⠙⡆⠀⠀⠀⠀⠈⢀⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⣂⠥⠔⠀⠀⠀⠀⠀⠐⠢⠂⠀⠀⠀⠀⠀⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⡠⠊⢉⠲⡄
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠢⣀⠰⠐⢀⠀⠁⠀⠉⢃⠄⠀⠀⠀⠀⠀⠀⣄⠀⠑⠄⠀⠈⢂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠆⠞⠰⠀⠀⠂
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠠⠂⠈⠉⠐⠪⣄⡆⠀⠀⣄⠠⠀⣀⠀⡀⠀⠀⠁⢶⠆⠀⠀⣤⣠⡆⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡺
⠀⠀⠀⠀⠀⠈⠈⠃⠄⠀⠀⠀⠀⠐⠀⠐⠓⢀⡈⠹⢤⣀⠉⠁⡟⠀⣄⡸⠀⠀⠀⠀⠀⠀⢺⣏⣻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠑⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⠀⢧⠀⠵⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠈⠳⡀⠃⠀⠃⢠⠆⠀⠀⠀⠀⠀⢰⠃⣀⠀⠀⠑⣸⠀⢀⡜
⠀⠀⠀⠢⢤⣁⣄⣹⣆⣠⣴⠆⠀⠀⠀⠀⠀⠀⠈⠄⠁⠄⠀⠀⣿⠐⠉⣉⠱⠀⠀⠀⠀⠀⠀⠈⠀⢈
⠀⠀⠀⠀⠀⠀⠙⠶⠶⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠠⡘⠱⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈