Medical school Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠙⠛⢰⣶⣶⣶⣶⡎⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠘⠛⣛⣛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣄⠀⠀⠸⣿⣿⠇⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣷⣄⣠⣶⣶⣄⣠⣾⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠋⠛⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠛⠙⠿⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⢤⣬⣥⣤⠀⠀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⢰⣿⣟⡀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⣀⣀⠀⠸⣿⡯⠄⠀⣀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⠽⠶⣖⣚⡛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠁⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠾⠭⠭⢭⣽⣛⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠒⠒⠊⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠥⣄⡀⡔⠒⠒⠒⠒⢲⢀⣀⠬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡀⠀⠈⣇⣀⣀⣀⣀⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡤⣀⠀⠀⡏⠀⠀⢹⠀⠀⣀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠱⣄⣹⠶⠶⣏⣠⠎⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⡀⠀⠀⣀⣀⣀⡴⠓⠒⠉⡇⢸⠙⠒⠒⢦⣀⣀⣀⠀⠀⢀⣄⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣩⠥⠤⠤⢤⡀⢠⠤⠧⠼⠤⡄⢀⠤⠤⠤⠬⣍⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡖⠒⠒⠒⠁⠈⢻⠛⢛⡟⠁⠘⠒⠒⠒⢲⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣙⠢⢤⣀⣀⠀⢸⠀⠠⣇⠀⣀⣀⡤⠔⣋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢒⣠⠬⠵⠚⣒⣚⣉⡭⠥⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢩⠔⠒⡻⠉⠉⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣙⡚⠣⠤⠤⠤⣤⣌⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣉⣉⣉⣓⣒⣒⣲⠭⣑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠨⠈⠸⠰⠡⢘⠂⠀⠐⠀⠈⠀⠈⠘⠀⠂⡠⠐⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⡍⠉⠉⠉⠉⠩⠭⠭⠍⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀⣀⠀⣀⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣛⠀⢸⡇⠀⢸⠀⡇⠀⠀⡇⢸⠀⠀⣙⢘⡇⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠐⠂⠉⠀⠀⠈⠉⠓⠲⠤⣜⡀⠧⠤⠤⠇⠸⠤⠤⠟⠘⠧⠤⠼⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠿⣍⣉⡉⠉⠉⠁⠀⠀⢀⣀⣤⠔⠚⠃⠐⠒⡆⢰⠒⠒⣶⢠⡖⢒⢲⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠉⠛⠲⠤⠒⠋⠉⠀⢸⢸⠀⡇⠀⠀⡇⢸⠀⠀⣿⢸⡇⠕⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠇⢠⡧⣀⣀⣀⣀⣀⣀⣀⣀⣠⡼⢉⠀⣉⣉⣉⡁⢈⣉⣉⣉⠀⣉⣉⣉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⢰⠒⠋⠁⠀⠀⠀⠉⠉⢳⣾⢸⠀⡇⢰⡂⡇⢸⠀⠀⣿⢸⡇⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣇⠀⠀⠀⠀⠀⠀⢀⡞⢸⠸⠀⠷⠬⠴⠇⠸⠤⠤⠟⠘⠧⠤⠼⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠣⣄⣀⢀⣀⡠⠊⠀⢸⠀⠀⠀⢠⠤⠤⡤⠤⣄⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⡏⠈⠉⠁⣇⣀⣀⣸⠀⠀⠀⢸⠀⠀⡁⠀⣿⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⠲⠶⠞⠁⠀⠀⠉⠀⡀⠀⢸⠀⠀⡇⠀⣟⠀⠀⠀⠀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠚⠒⠒⠓⠒⠛⠒⠒⠒⠒⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠
⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄⠠⡀⡄⠠⡄⢀⣄⠀⡄⢠⢠⠀⠀⡄⠀⠀⡄⠂⠀⡄⠀⡄⢄⢠⠀⢄⢠⢀⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⣇⣀⠇⠆⠀⠇⡼⠚⡆⣏⡱⢸⣀⠀⣏⡀⠀⣈⡳⠀⠇⠀⠇⢃⠣⣀⡸⢸⠙⡄⠋⠁
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣿⣧⢀⣾⣿⠀⣿⡟⠛⠃⣿⡟⠻⣶⡀⣿⡇⣴⡿⠛⠷⠄⢠⣿⣷⡀⠀⣿⠀⠀⠀⠀⣰⡾⠛⠷⠆⢸⡇⠀⢸⣿⢸⣿⢸⣿⠛⢷⣦⠀⣿⠛⠛
⠀⣿⢹⣿⠏⣿⠀⣿⣛⣛⠃⣿⣇⣀⣾⠇⣿⡇⢿⣄⣀⣠⡀⣾⣧⣼⣷⠀⣿⣀⣀⠀⠀⢿⣇⡘⣻⡇⢸⣧⣀⣸⡿⢸⣿⢸⣿⣀⣠⣿⢀⣿⣛⣛
⠀⠛⠀⠋⠀⠛⠀⠛⠛⠛⠁⠙⠛⠋⠁⠀⠙⠁⠈⠙⠛⠉⠈⠋⠀⠀⠙⠁⠛⠛⠋⠀⠀⠀⠉⠛⠋⠁⠀⠙⠛⠋⠁⠈⠋⠈⠛⠛⠋⠁⠈⠛⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⠛⠛⠛⠛⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⠛⠛⠛⠛⠛⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠶⠂⠰⠶⠶⠆⠀⣿⡇⢴⣶⣶⣶⣶⣶⣿⣧⣤⣤⣤⣤⣤⣤⣿⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠠⣶⣶⣶⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢹⣏⠉⠉⠉⠉⠉⢩⣿⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣤⣀⠀⣤⣤⣤⣤⣤⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⡿⠶⢾⣿⣧⣤⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⢷⣦⣤⣀⠀⠀⠀⢀⣴⡾⠛⠋⠁⠹⣧⡀⣰⡿⠀⠉⠉⠛⠻⣶⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣤⡿⠶⠀⠻⣦⣤⣤⣿⠉⠙⠻⢷⣾⠟⠉⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⠀⣴⣾⣆⣀⣤
⠀⠀⠀⠀⠀⣾⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⣉⠉⠛⠷⣦⣄⣸⣏⣀⣤⣶⣶⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣶⠀⠀⣿⠀⠀⠀⠉⠛⠿⣶⣶⠄
⠀⠀⠀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠙⠻⠛⠋⠁⠀⠟⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠛⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⣷⣶
⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠐⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠂
⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠆
⠀⢀⣈⣉⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⣼⠟⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠛⠀⠀⠀⠀⠘⠻⣶
⣿⠀⢸⡇⠀⠀⠀⢀⣠⣶⠾⠟⠛⠿⢶⣤⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⢸⡇⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠇⣀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⢸⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠛⢣⡄⠛⠃⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿
⣿⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠰⣶⠉⢱⣶⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠿⠀⢸⡇⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢀⣀⠀⢀⣼⡇
⠶⠀⢸⡇⠀⠀⠀⠙⢷⣦⣀⣀⣀⣀⣤⣾⢿⣧⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠿⠷⣦⣄⢀⣤⡶⠿⠂⠠⡆⠀⠀⠙⠻⢾⣟⢻⣷⠟⠋
⣤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⣽⡟⠛⣿⣄⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⢲⣆⠀⠀⠈⢻⡟⠁
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⢷⣄⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⡇
⣿⠀⢸⡇⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠈⣿⣶⡿⠋⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣿⡃⠀⣹⡇⠀⠀⠀⠀⣼⡟⠀⠀⠀⢸⡇
⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠙⢿⣾⠟⠁⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡇
⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠀⠘⣿⣶⣦⣤⣤⣤⣤⠈⠻⣦⡀⠀⠈⣿⡄⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠰⡗
⣿⡀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠈⠛⠉⠉⠛⠀⠀⠈⢻⣦⡀⠈⣻⡿⠿⠷⠶⠶⠶⠶⠶⠾⠟⠋⠀⠀⠛⢣⣄
⠙⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⡿⠿⠿⠿⣿⢿⠿⣿⣿⡿⠁
⣿⣧⣤⣴⣧⣿⣴⣤⣾⣿⣄
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⣇⣠⡟⠛⠲⠶⠚⠛⠉⠻⣦⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠋⠉⠉⠙⠛⠷⣦⡈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣼⠿⣦⣄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡟⠁⠀⠀⠙⠛⠷⠶⢶⣶⡄⠸⣷⠀⣄⡀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⣿⠀⣌⠛⠶⠶⠛⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣿⠀⠉⣻⣶⢶⣟⠋⠀⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⣧⡀⠀⠀⠀⠀⣠⡿⠁⠀⠀⢻⡆⠸⠿⣄⣠⡿⢷⣼⠃⣈⣿⣉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⠀⠀⢸⡿⢦⣤⣤⡾⢿⡅⠀⠀⠀⣈⣷⠀⣠⡟⢻⣤⡾⠁⣼⠋⠈⠹⣇⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⣷⣾⣿⣀⠀⠀⠀⠀⣨⣿⢷⣿⣟⡋⠁⠀⠻⣇⣠⡟⠁⢠⡟⠀⠀⠀⣻⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⢹⡟⠀⢻⡟⠻⠶⠾⠛⣻⡟⠀⣹⣏⡙⠻⢶⡄⠹⡏⠀⠀⠀⠙⠛⠀⠛⣋⣠⣼⠇
⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣼⣇⡀⠈⣿⡀⠀⠀⢠⡿⠀⣾⠋⠉⢻⡆⠀⢿⡀⠳⠶⠶⠶⠾⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡁⢹⡷⠀⠘⣧⠀⢀⣾⠃⢸⡏⠀⠀⠈⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣧⣄⣀⠈⠛⠋⠁⠀⠀⢹⣇⣼⠇⠀⠈⠛⠛⠘⠛⣋⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⡆⡶⠀⡖⣦⢰⠂⡖⠂⣰⣆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠁⠉⠁⠈⠁⠉⠉⠁⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡥⣏⡁⡷⢺⢸⣉⡗⣏⣹⢸⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣒⣢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⠧⠤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⡴⠋⢠⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢉⡤⢧⢿⣒⢧⠮⢄⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⡏⡄⠈⠣⡧⠚⠀⡄⡇⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣀⣀⣀⣀⣃⣃⡀⠀⠃⠀⠀⣁⠃⠀⡀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣀⣀⣀⣀⣀⣀⣸⣅⡀⠀⠶⣙⡚⣻⢸⣿⢸⣛⣊⡱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣈⣧⣼⣿⣿⣹⣿⣿⣿⡅⠀⠀⠀⡴⣲⢨⣍⢄⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢵⡾⣿⠟⠚⠛⠛⠛⠛⢳⠃⠀⠀⠀⠘⣽⢾⣶⣺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡧⠟⣛⣛⣛⣛⣛⣛⣻⣇⠀⠀⢀⠴⣿⣹⣋⡱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠤⣑⣒⡢⠀⠀⠈⡇⠀⠀⡰⠃⠀⣝⣾⣿⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⡠⠤⠒⠧⠤⠈⠀⠀⠀⠈⠛⠗⠋

⠀⠀⠀⠐⣶⡖⢲⣶⡶⠒⠀⠀⠂⠛⠐⠀⠀⠀⠀⡀⢀⣀⠀⠀⠐⠀⠀⠀⠈⡿⠲⣿⠂⠀⠒⠀⠀⠀⠰⠄⠐⠀⠀⠐⠲⣶⡆
⠀⠀⠀⠠⣿⡟⣼⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣦⡄⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠶⡖⠀⠀⠀⣠⣤⣼⠉⡇
⠀⠀⠀⠈⠹⣿⣿⣿⣷⠶⠐⠂⢀⠀⠀⠀⠀⢀⡀⠀⠀⠒⢄⡰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠼⠿⠟⠿⣿⡇
⠀⠀⠀⠀⠀⠙⠻⠋⠁⡀⢂⡴⠋⠀⠀⠀⣉⡉⠉⠙⠳⢤⠀⠁⠀⣀⠀⠀⠀⠀⠐⠀⠀⠐⢶⣖⣀⠀⢀⡈⠀⠀⠀⠘⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⣏⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣈⡙⠻⣿⡅⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠐⠀⠀⠀⠀⢸⡁⢸⠇⠀⠀⠀⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⢣
⠀⠀⠀⠈⠀⠀⠀⢹⡇⢸⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣱⣦⣄⠀⠀⣆⠀⠈⣷⣀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠋⠾⢿⡦⠀⠉⣇⠀⢿⣿⡷⠶⢛⣼⡇
⠀⠀⠀⠀⢰⣷⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⣿⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢠⣀⠹⡄⠸⢻⣷⣿⣿⣿⠇
⠀⠠⠋⠀⣸⣿⢇⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠟⠃⠀⠀⡼⢗⠀⠀⠀⠀⠀⠀⠈⠁⠡⣇⠀⠀⢿⣿⡿⠃
⠀⢰⣷⣾⡿⠋⠈⡿⠛⠛⠻⢿⣷⡀⠑⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠄⠀⠒⠑⠙⠀⢸⠀⠡⣄⡀
⠀⢸⣿⠏⠀⣠⡌⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠘⠀⠐⠂⠚⠛⠀⢤⡀⠠⠐⠁⠐⠀⠀⣐⣂⣶⣶⣶⣾⡀⠀⣾⠀⠀⠈⢛⠅
⠀⢸⣗⠂⠀⠻⠄⠈⠃⠀⠀⠀⣿⡇⠀⠀⠂⠀⠆⢀⡤⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⢶⣿⣯⣿⣿⣿⣿⠀⢰⡿⣽⠀⠀⣡⣶
⠀⠈⠀⠈⠀⢄⠀⢀⠔⠀⠀⠀⠁⢹⡄⠀⠃⡀⢰⠄⡋⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠁⢀⣿⠏⡷⠀⢸⣿⣿
⠀⠀⢀⠀⠂⠘⠁⠀⠠⣤⣄⠀⠀⣸⡟⢠⣱⡿⠇⢈⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉⠁⠀⢠⣾⠏⣼⠇⠠⣼⣿⡏
⠀⠀⢀⣤⡅⢶⡀⠀⠀⠈⠙⣷⠞⠉⡄⠂⠐⢁⣈⢤⣴⡶⠉⠀⠀⢠⠀⣀⣀⡀⣠⣿⣿⡄⠀⠀⣠⣶⢿⡿⢾⡟⠀⣰⢹⣿⣧
⠀⢀⡿⢻⣿⣄⢻⣾⣶⡶⠀⣀⢰⣧⣴⣶⣿⠏⣿⣿⠛⢻⣾⣭⠀⠘⠓⠿⢿⣿⣿⣿⣿⢃⡤⣮⠉⠅⠐⣱⡿⣴⣶⡿⣼⣿⣿
⠀⢸⡷⣿⣛⣛⣫⠁⣤⠐⢻⠁⣀⢤⡙⠻⣿⣀⣻⣿⡇⠘⣿⣿⣧⣤⣄⣀⣠⠛⠋⣩⣤⡞⢁⣴⢦⣶⣿⣿⣾⣿⢻⡿⣿⣿⡿
⠀⠸⠗⠹⠿⠿⠚⠤⠖⠈⠛⠀⠀⠠⢤⢀⣼⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣠⣾⣿⣙⢿⣾⣿⣿⣿⣿⣿⣿⡥⣿⣷⣸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⢤⣀⡀⢰⠒⠒⠒⠒⠒⠒⡆⠀⣀⣠⠽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡆⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠀⠀⠀⠙⢲⡖⠒⠒⢲⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠓⠲⣄⠀⠸⣆⠀⠀⣠⠇⠀⣠⠖⠚⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠈⠳⣤⠼⠛⠛⠣⣤⠞⠁⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀
⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠖⢻⡄⠀⡟⠲⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽
⠀⠀⠀⠉⠙⠉⠙⠦⠤⠴⠚⠉⠛⠋⠁⠀⠀⠀⢸⡇⢰⡇⠀⠀⠀⠈⠙⠛⠉⠑⠦⠤⠴⠋⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⣉⣉⣉⠉⢙⡆⠠⣏⣉⣉⣉⣉⣹⠄⢰⡋⢉⣉⣉⣉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣏⠉⠉⠉⠉⠀⠀⠈⡇⠀⢠⣼⠁⠀⠀⠉⠉⠉⠉⣹⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠳⠦⣄⣀⠀⠀⠀⡇⠀⠠⢼⠀⠀⠀⣀⣠⠴⠚⣁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠄⠀⣉⣡⡤⠧⠴⠖⠚⠛⣉⣉⣤⠤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣉⣡⠤⡴⠖⠒⠛⠉⢯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⣁⠀⡼⠁⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢬⣉⣙⣛⡒⠒⠶⠶⠤⠬⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣈⣉⣉⣉⣉⣛⣛⣒⣲⡤⣍⣳⠄
⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠇⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠠⠀⡄⠠⢠⠀⡄⠠⡄⢠⢠⠠⠀⢠⠀⠀⡄⠀⠤⠀⠀⣄⠄⢄⢀⡠⢠
⣀⣀⣀⣀⣀⣀⣨⣄⣧⣔⣸⣀⣇⣎⣱⣨⣽⣨⣄⣬⣄⣀⣬⣂⣀⣠⣉⣞⣤⣜⣈⣱⣨⣄⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠁⡀⠀⠁⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠠⠀⠀⠄⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠢⠤⠘⡀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠄
⠀⠀⠐⠀⠒⠀⠀⠆⠀⠆⠂⠀⠀⠀⡠⠀⠑⠤⡇⠀⣀⣤⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣄⢀⠀⠘⡴⠚⠁⠀⠀⠇⠀⠠⣀⡀⢤⠢⡀⠀⠀⠈⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠋⠀⠀⡸⡷⠿⠛⢀⠄⣠⠖⣻⠛⠋⠋⠙⢛⡓⠍⠀⠀⠀⠈⣉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠎⠀⠀⢠⡨⠀⠀⠀⠀⡞⣾⣁⣘⡇⠀⠀⠀⡀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢳⡅⠀⠐⠀⠀⣼⠁⣤⠈⡇⠀⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠄⠉⠉⠳⡇⠀⠀⠀⠀⠀⠐⡇⠀⠀⠂⠐⠂⠂⠀⠆
⠀⠠⠄⠄⠄⠀⠀⠀⠋⢧⣀⣀⡀⢉⠀⠀⠀⠀⠺⠀⠀⠁⠀⣧⣠⡀⠀⠀⡀⢺⠁
⠐⠀⠐⠀⠀⠐⠀⠀⠀⠘⡄⠀⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡀⠹⠤⠎⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢁⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⢠⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡄⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⡰⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣸⣆⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⠶⢄⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢢⠀⠀⠐⠀⠀⠀⠀⠀⡀⠊⢀⠐⠁⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠠⠀⠀⠤⠂⠀⠀⠀⠀⠑⢄⡑⠤⠄⠐⡀⠀⠀⠊⢀⠔⠁⠀⠀⠀⠰⠂⠰⠀⠰⠀⠀⠰
⠀⠀⠀⠂⠆⠀⠂⠂⠀⠆⠀⠀⠀⠀⠈⠑⠢⣀⢈⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠤⣄⠀⠀⢀⡤⠶⣤⡀⠀⢀⡠⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⢱⡀⡏⠀⠀⡿⣷⢠⠋⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⣠⣦⠀⠀⠀⠀⠀⠀⣸⠇⢹⣤⣬⣵⠃⢸⡄⠀⠀⠀⠀⠀⠀⢰⡀⠈⠓⢤⡀
⠀⠀⠀⠀⢀⡠⠖⠋⠀⣀⡴⠞⠉⣻⣄⠀⠀⠀⠀⢸⡏⠀⢸⠀⠀⢹⠀⠀⢻⠆⠀⠀⠀⠀⣠⣿⠙⢦⣄⠀⠉⠓⢤⣀
⠀⠠⢶⣚⠉⣀⣠⡴⠞⠋⢀⡤⠞⠁⣹⠗⢶⡆⠀⠀⠙⠛⢻⠀⠀⣸⠙⠛⠁⠀⠀⣶⠶⢾⡏⠙⢦⣄⠉⠳⢦⣀⠀⠈⠙⠒⣶⠄
⠀⠀⠀⠉⠉⠛⠣⠤⣴⡞⣋⣀⡴⠟⢁⣴⠟⠻⣄⡀⠀⠀⢸⠀⠀⣿⡀⠀⠀⣀⣼⠟⢦⡀⠙⢶⣄⡉⠳⣦⣄⣉⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⢷⡀⠀⠈⢙⣛⣛⢻⠀⠀⣿⣛⣛⣛⡉⠀⠀⢀⡿⠓⠒⠛⠛⠛⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠊⡁⠛⢀⣽⠀⠀⣿⣅⠀⠀⣈⠳⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⡿⢉⣰⡆⠀⣿⣈⠙⣻⠏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⠶⢽⣇⣀⣿⡤⠞⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣄⡀⠀⠀⠉⠙⠲⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠛⣷⣦⣄⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣼⠟⡇⠙⡿⣧⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠹⣄⡇⢨⣇⡼⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠓⠾⣏⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠈⠙⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠉⢻⣷⣤⡀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣧⢸⣿⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⢷⣸⡟⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠓⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢷⣦⣄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣏⢹⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⠾⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣶⣤⡈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡾⢹⣿⢻⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣼⣿⣼⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⣠⡀⣠⣀⡀⢀⠀⣠⣄⠀⣠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢿⢸⣗⡂⣿⣀⡿⢾⠸⣇⣠⣰⣯⣷⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣉⠀⣈⠀⣀⠀⣀⡈⠁⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣥⣿⢉⡁⣿⠶⣿⢾⡉⣹⢾⣏⢹⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠉⠀⠉⠈⠉⠁⠀⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠙⠓⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡟⣿⣻⡟⣿⣻⠛⣟⣻⠛⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣀⣿⢹⡇⣿⢹⡇⡏⢹⠀⡏⢹⢐⡏⣿⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠉⠉⠀⣿⢸⡇⣿⢸⡇⡏⢸⠀⡇⢸⢠⡇⣿⠀⠉⠉⠛⠺⢧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢀⣿⣸⣇⣿⣸⣇⣇⣸⣀⣇⣸⣘⣇⣿⡀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠸⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡇⠀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⡴⠞⠛⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣴⣞⡆⠀⠠⣞⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡞⣡⡴⣦⣀⣀⢉⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣆⣤⣀⣀⠘⡇⠉⠀⠀⠀⠉⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡀⠀⠉⡿⠘⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⠛⠋⠉⠀⣷⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠼⣷⠤⣾⠧⣤⡇⠀⠀⠀⠀⠀⣤⡀⠀⣻⣄⠀⣰⡀⠀⠀⢿⡀⠀⣀⡀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣀⡙⠒⢋⣠⣤⣽⣆⠀⠀⠀⠀⠘⢿⡄⠙⠧⠘⡟⠃⠀⠀⠀⠙⠛⣯⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠶⠮⣽⣿⣯⠶⠖⠛⢻⡆⠀⠀⠀⠀⠀⣤⠖⠒⠶⣄⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡃⣞⢙⡧⢹⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⡀⣸⠀⡇⢀⣀⣠⣼⠃⡀⠀⠀⠀⠈⠷⠈⣟⠁⠛⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠹⣦⣄⣀⣀⣀⣤⠙⠶⠤⠤⠤⠤⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣶⢰⣿⢰⡟⣦⣶⣴⠚⠂⣴⣦⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠘⠛⠘⠛⠉⠙⠈⠛⠉⠋⠙⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣥⡟⢙⢸⡦⣿⣾⠉⣧⣞⢙⡦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠈⠀⠉⠈⠉⠁⠈⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣞⣋⣁⣀⣀⣈⣙⣓⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢶⢶⡶⡶⣶⢶⢶⡶⡶⣶⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⢹⢸⡟⡇⣿⢻⢸⡟⡇⣿⢹⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠛⠉⠁⣿⢸⢸⡇⡇⣿⢸⢸⡇⡇⣿⢸⠈⠉⠛⠓⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⣿⣼⣼⣧⣧⣿⣼⣼⣧⣧⣿⣼⡄⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⡀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⢀⡀⠀⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡴⠋⣁⠈⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢰⡿⠟⠀⠀⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡟⠉⠓⣶⢰⡆⠀⠀⠀⠀⠒⠒⠒⠚⢻⡿⠖⠒⢸⡇⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⣤⣴⣯⣨⡇⠀⠀⠀⠀⣀⠀⠀⣦⠈⢡⡄⠀⠈⣇⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣄⣈⠓⢚⣀⣬⣷⡀⠀⠀⠀⠘⢿⡀⠻⠄⣿⠃⠀⠀⠈⠓⢿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠒⠾⡿⣿⠶⠚⠋⣿⠀⠀⠀⠀⢀⡴⣚⡒⢦⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⡰⣇⡽⢸⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠦⢤⣧⣿⠤⠶⠖⠛⠰⣄⠀⠀⠀⠙⠸⣇⠈⠀⠀⠀⠀⢀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠶⠚⠃⠈⠉⠉⠉⠉⠉⠉⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣠⣿⡇⣿⣛⡛⢸⡟⠻⣦⢸⡇⣴⠛⠻⠂⣰⠿⣆⠰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠿⢸⠇⢿⣭⡥⢸⣧⡴⠟⢸⠇⠻⣦⡴⠦⡿⠲⢿⠌⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⠀⢀⠀⠀⡀⠀⣀⣀⠀⠀⢀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣅⣼⡏⠉⠃⢸⣧⣼⣟⣼⡏⠉⣿⢰⡟⠉⢻⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠟⠘⠳⠶⠃⠸⠃⠘⠗⠘⠳⠶⠋⠈⠻⠶⠟⠁⠿⠶⠆



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣟⣋⣉⣀⣀⣀⣀⣀⣀⣈⣙⣛⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣿⠉⣿⣩⣿⢹⣯⣹⡏⢹⣏⣽⡏⣿⣉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡏⣿⠀⣿⠉⣿⢸⡏⢹⡇⢸⡏⢹⡇⣿⠉⣿⠀⢀⡀
⠀⠀⠀⠀⢠⣄⣤⣿⠶⠞⠛⠋⢸⡇⣿⠀⣿⠀⣿⢸⡇⢸⡇⢸⡇⢸⡇⣿⠀⣿⠈⠛⠻⠾⢷⣤⣦⡀
⠀⠀⢠⡴⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⠀⣿⢀⡇⢸⡇⢸⡇⢸⡇⣿⠀⣿⠀⠀⠀⠀⠀⠀⠉⠛⢿⣄⡀
⠀⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⣿⣤⣿⣤⣿⣼⣧⣼⣧⣼⣧⣼⣧⣿⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢻⡄⠀⢀⣤⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣤⠀⠀⠀⣴⢦
⠀⠺⠷⣰⠟⠁⢀⡀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⢺⡟⠶⠟⠀⠀⠀⠻⠾
⠀⠀⢰⡟⢰⡶⠛⠻⣦⣴⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡿⣧⣼⣧⣤⣤⠄⢸⡇
⠀⠀⣼⠇⠸⣇⠀⠀⠀⣸⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰
⠀⠀⣿⣄⣤⣿⣦⣤⣴⣿⣤⣠⡿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⢷⡄⠀⠀⣶⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸
⠀⣰⡟⠉⠀⠘⢧⣤⡾⠃⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⢹⣿⡆⠈⢿⣏⠀⣿⠿⠀⠀⠀⠀⠙⠳⠶⣾⣛⣷⠶⠛
⣴⣿⣛⣛⠳⠶⣤⣀⣴⠶⠟⣛⣛⣿⣤⠀⠀⠀⠀⠀⠀⠉⠛⠂⣀⣉⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁
⣿⠈⠉⠙⠛⠻⣾⠿⣷⠛⠛⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⣴⠟⣋⣉⡙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡏⢸⡏⠉⣿⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠈⢿⣌⠛⣿⠋⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠉⠙⠛⠳⠶⠶⣿⣴⣿⠶⠶⠛⠛⠋⠉⠘⢷⣄⠀⠀⠀⠀⠀⠁⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣶⣤⣤⡴⠾⡟⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣶⣦⢰⡿⡀⠀⣽⡄⠀⠀⠀⠀⢠⣀⣠⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣼⣿⣷⡼⣿⠇⠄⣹⠇⠀⠀⠀⠀⠈⢻⣟⣿⣿⣷⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣠⣶⣸⡿⣫⣅⣛⣛⡷⢚⠓⠚⠻⠅⠀⡀⢰⣿⣿⣯⣿⣿⡄⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢻⣾⣿⡿⠻⣿⣝⣿⣿⣛⣋⡐⡄⠀⠛⡿⠿⣿⠛⣿⣿⡧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠆⢀⣴⢰⣿⣿⣿⣷⣤⡾⠋⠉⠀⢣⠈⠈⠉⠑⡛⠐⠏⣡⡜⢻⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣴⢛⣉⡙⡾⣫⣤⣿⣿⡅⡀⠴⠿⣿⡿⣷⣶⠶⠖⠒⠚⢻⣧⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠧⣤⠶⢺⣏⠀⣰⡿⠋⢀⡄⠀⠈⣧⢙⡿⠀⣀⢀⡤⠞⠻⣟⠋⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢸⣷⡟⠛⠋⠀⢁⣾⣷⢠⣬⡇⠀⠀⢹⡿⠿⠛⠋⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠶⠛⠣⠉⠀⠐⠋⢸⣿⠰⡿⡏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡆⠳⢃⡀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣫⡎⣡⠀⠛⠋⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⢆⢶⣶⣶⣦⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣸⡟⣾⣖⣇⣾⣾⣷⣶⢾⣷⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣚⣛⣛⣻⣿⣿⣿⣶⢥⣻⢾⡷⣿⢾⣷⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⣾⣭⣟⣿⣻⣭⡇⣶⡏⣿⢿⡿⠿⢸⡿⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⢯⣉⣭⣭⣭⣉⠃⣿⣏⣽⣽⣯⣭⣹⣯⣭⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⡿⡴⣯⣯⣿⣽⣯⣿⣽⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢹⣿⡍⣾⡇⣿⣿⡏⣶⣴⡎⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣮⣿⣵⣿⣷⣿⢿⡇⣿⢸⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣪⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⣛⣿⣟⣻⣟⡞⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣦⣀⣿⣁⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣛⣿⣛⣻⣟⡃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠛⠋⢽⠙⠛⠿⠿⠿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠂⠀⣾⠂⠀⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣾⣿⣷⣷⣲⣽⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣢⣤⣿⡤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣿⢿⣶⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⣸⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⣿⣿⠙⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣥⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⢿⣿⢿⣿⡏⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣻⣿⣿⣿⠧⠤⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡿⠟⠁⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡈⠻⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣿⠈⠻⣦⣈⣻⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⣷⣄⠙⢷⠌⠉⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠻⣯⡙⠃⣿⡏⠻⠿⠛⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣄⠰⣶⣾⡄⢻⣤⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡋⠻⣦⡈⠻⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢶⣄⠙⢷⣌⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡈⠻⣦⣨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⡙⢷⣄⠙⠷⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⣶⣤⣸⣿⢠⣌⣻⣦⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠛⠛⣧⠘⡿⠿⠆⠙⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⣯⡉⠻⣦⡀⣿⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣀⡐⢷⣄⠙⢿⠀⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣦⡈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⢷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⣀⣀⠀⣀⡀⠀⣀⡀⢀⣀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢾⡇⣿⣒⢸⣇⣹⠆⣿⠰⣏⢀⢠⣯⣧⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠉⠀⠉⠁⠀⠉⠁⠈⠉⠈⠀⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠆⣿⠭⠰⣯⡇⣾⠭⠀⣾⣧⢸⣏⡷⢰⡏⠙⢸⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠃⠛⠒⠘⠚⠃⠙⠓⠘⠉⠙⠈⠃⠙⠈⠛⠋⠘⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⡯⢽⡏⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡘⡇⠀⣿⢸⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⢒⠖⢳⡝⠶⣇⣸⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⢻⡒⠋⠓⡾⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⣀⡤⠤⢶⡻⣖⡾⡷⠤⢤⣀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⢸⠁⡀⠀⠀⠑⠦⠞⠁⠀⠀⡈⢷⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠤⢶⠦⣄⠀⠀⠀⠀⠀⠐⣁⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡫⣶⠒⠒⢮⡳⡄⠀⢀⡽⠿⠿⠯⠀⢰⢡⠚⢢⠀⠈⣧⠀⠀⠀⣴⡛⢬⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠛⣯⠝⣳⡄⢹⢹⠠⠎⢀⣐⣒⣀⠀⠸⡜⠿⠃⠾⢂⡏⢀⣴⢊⠠⢙⣦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣄⠙⠺⢷⣗⡞⡜⣀⡀⠘⢻⣤⣟⠀⠀⠈⠓⠒⠒⠋⢠⣻⣌⠢⣴⣯⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢽⣒⣺⠽⢾⡷⢤⡈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠯⠛⠁⠈⢦⣸⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡄⠀⠀⠀⠙⢦⡙⢦⠈⡇⢦⠀⠀⠀⢀⠀⣴⣒⣒⣒⣶⠀⢀⣀⣸⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡙⢤⣀⠀⠀⠀⠙⢋⣴⠇⠀⠳⣄⡰⠋⠀⠀⠼⣧⡷⣒⠒⠛⢲⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣒⠮⠭⠤⠴⣒⡽⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⢴⣛⣒⣒⣒⣚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢦⠀⠀⠀⠑⢦⣁⠚⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⠀⠘⡐⠓⡀⠀⠀⠀⢻⠻⣄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠂⠀⠂⠀⠋⠀⠀⠀⠀⠀⢿⠏⠳⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡔⠈⠂⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠠⠀⠀⠀⠁⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢰⣄⠀⠀⠁⠂⠀⡀
⠀⠀⠀⠀⠀⣱⡀⠜⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠓⢀⠀⠀⠈⠉⠰⠆
⠀⠀⠀⠀⠀⠀⢉⠀⢄⠀⠀⠀⠀⠀⠀⠉⢀⡀⠄⠀⠘
⠀⠀⠀⠀⠀⠀⢸⡀⢈⡆⠀⠀⠀⠀⠠⡄⠀⢛⣆⠀⠸⣅⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠇⠈⠁⠀⠀⠀⠀⠈⢠⠄⠘⢀⠱⡀⠀⢰⠄⠀⠀⠀⠀⢐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠙⣷⠀⠀⠐⠁⠀⠁⠈⠀⠀⠄⠀⠀⠲⣄⠀⠀⢐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠳⣮⣾⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠙⣆⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣴⠏⠳⣄⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣂⣀⣀⣀⣈⣁⣀⣀⣀⣀⣠⣚⣁⣀⣀⣌⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⡉⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢀⠰⠀⠒⠄⠀⠀⠀⠀⠀⠠⠰⠀⠀⠄⠆⢀
⠀⠀⠀⠀⠀⠀⠸⠤⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⢃⢀⠞⡍⠌⣂⠄⡀⠀⠀⠀⠀⠐⢯⢨⠭⠅⠭⠝⠹⡆
⠀⠀⠀⠀⠀⠓⠖⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⡤⢁⡀⣤⠀⠀⡖⠒⠀⠀⠀⠀⠀⢀⠉⠲⡠⠔⣇⡄⠴⠀⠀⠀⠀⠀⠇⡀⠀⢆⠂⠀⠠⠇
⠀⠀⠀⠀⠀⠰⠉⠈⠉⠡⠀⠀⠀⠀⠀⠀⠀⠨⠀⠨⠤⠄⠅⠀⠑⠀⠀⠀⠀⠀⠀⠈⠚⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠀⠀⠈⠀⠠⢀⠄⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠛⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⢥⠄⠀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠊⠀⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠰⣤⠚⡖⣰⠒⠀⠀⠀⠀⠀⠀⢠⣾⠒⢠⡘⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠠⡢⠀⣠⠀⡔⠄⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠈⢬⡱⡀⠰⠹⠀⠀⠀⠀⡔⠁⠀⠈⣤⡀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠄⣈⠉⠀⡀⠡⠂⠀⠀⠀⠀⡄⠀⣠⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡠⢀⠁⠐⢄⠀⡠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⢦⠀⢤⠂⠀⠀⠀⠀⠀⠀⢀⡔⠓⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⢠⡤⠄⡤⢤⡀⣤⢀⡤⠤⢀⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠿⠸⠯⠄⠧⠼⠃⠿⠘⠧⠤⠾⠻⠆⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢠⣤⢀⣠⡄⢠⣤⠀⣠⡀⢠⣤⡀⣠⣤⢀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⢯⢸⣯⠀⣝⡷⢸⣏⢰⠿⢷⢸⠻⡇⢿⣤⠸⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣖⣿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⠀⢸⡇⣿⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠤⠬⢮⠳⣼⡃⣿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⢱⠖⠛⠒⡾⠈⠲⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⢀⣠⡤⢤⡷⣖⠾⡧⠤⣤⡀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢀⡏⡀⠀⠀⠑⠶⠚⠀⠀⢀⠘⡆⠀⠀⠀⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⣭⣀⠀⠀⠀⣠⢤⣤⣤⠀⠀⡴⠒⠒⠲⣄⠀⠀⠀⠀⣘⣥⡔⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣕⣯⣉⡉⢺⡳⡀⢀⡼⠛⣛⠛⠀⢼⢸⣉⡇⣀⠘⡆⠀⢀⡼⢏⠳⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣷⣫⢿⣀⡇⡇⠋⢀⣚⡛⣒⠀⠘⢮⣋⠈⣋⠜⢠⡶⣏⠈⣠⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⣌⣉⣽⢟⣽⡁⠶⢤⡘⠒⠚⠀⠀⠀⠈⠉⠁⠀⠻⣳⣬⡿⠳⡟⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠒⠚⠉⠹⣍⠢⡀⠙⣆⡀⠀⠀⠀⠀⠀⣀⣀⣀⣙⡁⠀⠀⢸⡞⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢇⠀⠀⠀⠈⠳⡼⢂⡇⠙⢦⠀⢀⠖⠘⠓⣷⣳⣎⣁⣴⣒⡚⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢝⣒⣂⣀⣠⢴⡿⠃⠀⠀⠱⠋⠀⠀⠀⠉⡿⠼⠧⠤⠤⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⡴⠋⠀⢸⢸⠀⣨⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡇⢸⢸⠀⡇⠀⠀⠀⡼⠁⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⢰⠃⠀⠀⢸⠈⣫⠴⠊⢹
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢠⢣⡄⠀⠀⡿⡄⢶⣄⠈⢇⠀⠀⡀⡇⠀⠘⣆⣤⡀⠘⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢸⢸⠁⠀⢸⣷⣟⢼⣎⣗⣾⡄⠀⡇⢸⠀⠀⢿⠀⣗⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠴⠧⠾⠼⠴⠷⠧⠼⠾⠤⠧⠄⠀⢸⢸⡀⢀⣇⣘⣠⠋⢧⣘⣀⣇⠀⡇⢸⠀⣴⣚⣈⣓⡍⠉⠁⠀⠀⠀⠀⢰⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⢧⣸⣆⠀⢀⣐⣀⠀⢀⠿⡀⣇⡞⠀⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⡷⣄⠀⠀⠀⠀⠘⢮⡟⣨⡳⡤⣉⡡⡴⢋⣤⣱⡟⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠓⣤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣀⡉⠙⡇⠀⠀⠀⠀⠀⠈⠁⣹⠇⠀⠀⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠯⠇⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⡠⠖⠒⠦⣼⠀⠶⠶⠆⠀⡇⠀⠀⣠⠖⠚⠻⣋⢷⠀⠀⠊⢱⢋⡻⠒⠲⠤⣀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⣀⣈⣉⣁⣀⡇⠀⡜⠁⠀⠀⠀⠈⠹⡖⠦⠶⡞⠉⠀⠀⠀⠀⠘⡆⠀⠀⢸⣉⣉⣉⣉⣉⣉⣿⣏⣹
⠀⠀⠀⠀⢀⡹⠀⠀⠀⡆⠀⠀⠈⣇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢃⠀⢀⠃⠀⠀⠀⣤⠀⠀⢹⠀⠀⢸⠀⠀⠀⡴⠦⡄⠀⠀⢸
⠀⠀⠀⠀⡎⠀⠀⠈⠳⡷⠊⠀⠀⠈⢧⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠸⡄⡼⠀⠀⠀⠀⣇⠀⠀⠀⣇⠀⢸⠀⠀⠀⠳⠶⠧⠀⠀⢸
⠀⠀⠀⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⡠⠏⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⣿⠀⠀⠀⢹⡀⢸⠀⣒⣒⣒⣒⡒⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠸⣤⣤⣤⣤⣤⣤⣤⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠦⣾⠀⠀⠀⠀⠀⠷⠇⠀⠀⠀⠀⣯⡤⠤⠶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣲⣿⠭⢬⣣⣴⠃⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣼⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⣽⣷⡾⠋⠀⠀⠀⡵⣝⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠧⠤⠤⠴⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⢠⡄⠂⠀⠀⠤⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⢀⣼⡅⠀⠀⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣮⣽⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⣾⡇⣧⡄⠀⠀⠀⠀⠀⠀⡛⠛⠛⠒⠢
⢸⡇⢄⢸⡇⢠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠠⣿⠇⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠄


⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣰⡾⠛⠙⠻⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣽⠖⠲⡿⢦⠀⠀⠀⠀⠀⢀⣞⣉⡇⢹⠱
⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣟⣽⣿⣿⠅⠀⠀⠀⠀⢸⣸⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣲⢖⡃⡺⢄
⠘⢿⣶⣴⣾⠗⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⢯⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢩⣷⣻⠗


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣤⣤⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⡆⢀⢈⣿⢀⠄⠀⠀⠀⠀⣠⡀⢁⢂⣠⣶⡤⠢⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢
⣿⣿⣧⣤⣾⣿⡇⠀⠀⠀⠀⠀⢻⡇⠈⠘⡿⢀⠀⠀⠀⠀⠀⠸⠱⣦⡦⢫⢔⠔⠳⠄⠀⠀⠀⣯⣱⣾⣿⣶⣶
⠛⠛⠛⠻⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠛


⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢀⣀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⡇⣠⠿⢿⡃⠀⠀⠀⠀⢨⣭⢨⣭⠈⠉⠁⠀⠀⠀⠀⠀⢀⡀⣴⢰⣿⢸
⢿⣿⣯⣽⣿⣿⠇⠀⠀⠀⠀⠀⡿⠛⢾⣿⣦⣾⡇⠀⠀⠀⠀⠰⠶⠰⠶⠰⠶⠲⠶⠆⠀⠀⠀⢸⡇⣿⠨⣿⢸
⠀⠏⢀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠿⠶⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠛⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠀⠋⠘
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠙⠛⠸⠸⠕⠍⠊⠐⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠸⠕⠍⠪⠰⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠨⠝⠩⠋⠐⠗⠤
⠀⠠⢐⠆⠴⠴⠰⠆⠆⠆⠤⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠶⠰⠄⠆⠴⠴⠦⠆⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠦⠄⢴⠰⠒⠀⠀⠆⠴⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢠⣐⠒⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⡋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢻⣀⣉⡀
⠀⠀⠀⠀⠀⠄⠨⢀⣠⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣨⣀⣥⣍⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠄⠀⠀⠀⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠘⠂⠄⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣁⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠒⠒⠒⠒⠒⠒⠃
⠀⠀⠀⢀⣀⠀⡄⠘⠀⢀⣃⣉⠀⣼⣽⠁⠀⠀⠀⠀⠀⢀⡞⣣⡌⢳⠀⢊⣁⠀⠼⠥⠤⢀⡀⠋⡽⠀⠀⠀⠀⠀⠀⠀⢸⠈⠄⠀⠁⠙⢀⠀⠀⠀⠀⠰⠆⠠
⠀⠀⠒⠄⠀⠎⠁⠀⠀⠀⠀⢀⣨⣡⢸⠂⠀⠀⠀⠀⠀⠀⠣⠌⠿⢯⠀⠈⠉⠀⠀⠀⠀⠹⠗⠚⠁⡀⠀⠀⠀⠀⠀⠀⢼⢸⡗⣿⡇⠀⢸⠀⡀⠀⠑⠊⠐⠂⠄
⠀⠀⠐⠓⠚⠁⠐⠄⠀⠐⡞⠁⠀⡀⣸⠁⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⢠⡕⠀⡀⠀⠻⣾⠂⠤⠈⠁⠀⠀⠀⠀⠀⠀⢺⠀⠥⠄⠀⢈⢸⠀⡀⠀⠀⢦⡀
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠓⠚⠒⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠉⠒⠓⠒⠋⠀⠀⠁⠀⠀⠛⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠘⠒⠐⠒⠒⠃⠘⠀⠁⠀⠀⠀⠙

⠀⠀⠀⠚⠛⠸⠘⠐⠂⠃⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠘⠘⠂⠂⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠘⠐⠐⠃⠐⠗⠂
⠀⠀⠀⠰⠐⠦⠐⠘⠒⠰⠶⠖⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠰⠄⠶⠐⠒⠆⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢶⠰⠂⠆⠂⠒⠲⠒

⠀⠀⠀⠀⠀⠀⠀⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⡀⢂⡄⠀⣠⠙
⠀⠀⠀⠀⠀⠀⠀⣡⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠔⠂⡈⠒⢀⠘
⠀⠀⠀⠀⠀⢸⢴⠃⠁⠤⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣀⠀⠀⣈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠈⠀⠁⠀⠀⠰⠀⠀⢀
⠀⠀⠠⢤⠤⢀⠠⡄⠀⠀⠀⢀⡀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣤⢀⣀⠈⠉⠉⠉⠉⠀⣈⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠈⠂⣀⠀⠀⢀⡀
⠀⠂⠀⠈⢑⠂⠐⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⢹⠆⠀⠀⠀⠀⠀⠉⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠀⠀⠀⠀⠑⠉⠋⢇⠙⠙
⢀⠆⠔⢀⠒⠀⠀⡄⠀⢠⡤⠆⡰⢣⡌⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⠈⠶⠆⡀⠀⢠⣤⣀⠶⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⡶⣤⠶⠂⠀⠀⠐⣧⡶⣼
⠋⠀⠀⠀⠈⠀⡹⢃⠀⡀⠐⠂⠐⠂⠆⠀⠀⠀⠀⠀⠀⠀⡁⢠⠀⣥⠀⠀⠘⠀⠱⢶⠓⠒⠒⠓⠶⡎⠀⠀⠀⠀⠀⠀⠠⣉⣦⣎⣤⣝⣱⣀⠀⠂⠀⣧⣿⡞
⠁⠐⠒⠒⠊⠙⠁⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠐⠈⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠲⠶⠺⠰⠰⠆⠦⠀⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠶⠰⠐⠀⠆⠰⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢶⠐⠰⠰⠆⠰⠖⠤
⠀⠀⠀⠀⠀⠂⣔⡦⣠⢄⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⣦⢠⢀⣲⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⢶⡤⣰⢤⡆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠛⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⣬⠺⡄⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⡉⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠰⠂⠶⣶⡞⠓
⠀⠀⠄⠂⠀⢠⠄⠀⣶⠀⣟⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⡐⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣦⡼⠻⠛⠿⢹⠀⠢⢀
⠀⠀⠄⠀⠀⠸⠆⠀⠹⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠶⠦⠤⠄⠪⠰⠀⠀⠈
⠀⡀⠚⣘⡟⠈⠀⢀⠔⠒⠢⡠⠖⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⣀⠂⠀⠀⠀⠂⠀⠀⣂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠁⠀⠀⠀⠀⣳⢒⣀⣐⡒⣚⣌
⠀⠉⠈⢽⡇⠠⠀⢸⣄⣀⠤⠤⢄⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠰⠃⠀⢂⡐⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣠⡀⡀⠀⠀⣹⣭⣽⣭⣭⡍⣭
⠀⠲⡴⠈⡇⠀⠀⠤⢀⠤⣄⠐⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠨⠀⡼⢀⠀⢠⡏⠀⠀⠰⢠⡀⠀⠀⠀⠀⠀⢀⡞⠂⢸⡿⠃⠀⠡⠀⣠⢷⣠⢧⣤⢷⠞
⠀⠀⠇⠀⠃⠀⠀⠀⠈⠓⠁⠀⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠡⠾⠧⠶⠤⠂⠠⠃⠀⠀⠀⠀⠀⠀⠣⢀⣀⠗⠐⢄⠒⠀⠁⠀⠈⠉⠀⠉⠁
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢶⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⢇⠈⢧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣧⠈⢇⠈⢆⠈⢇⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠠⣦⠘⢇⠘⣇⠘⣇⠙⢧⠈⢆⠈⢆⠈⢆⠈⣦⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⣈⣿⣿⣿⣿⣿⣿⡙⡇⠘⣄⠈⣆⠘⣆⠈⣆⠸⡧⠸⠇⠸⠇⠸⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠛⠋⠈⠛⠛⠿⣿⣿⣿⣿⣧⠘⡄⠈⡄⠘⡄⠈⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⢋⣬⠐⡄⠘⣄⠸⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⡷⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡠⠞⠋⠁⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⣀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⢶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠛⣋⡉⠉⠉⠉⠙⠛⠒⠒⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⠻⣤⡀⠀⠀⠸⡉⢇⠀⠀⠀⠀⠀⠀⡠⠤⠄⡀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⡴⠞⠍⠻⣅⡴⠋⣹⢦⠀⡔⢻⡿⡆⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⣠⢞⠩⠀⠀⠀⠈⠻⣾⠁⢸⠀⠱⡝⣧⢘⠄⠀⠀⡎⠈⢣⡀⠀⢀⢠⢱⠀⠀⠀⠀⠀⠀⢨⡻⣷⣦⣀
⠀⠀⠀⣰⠯⠐⠀⠀⠀⠀⠀⠀⢈⣥⠀⢠⣞⠭⡏⠉⠀⠀⠀⠧⡀⣴⣧⣿⣼⣼⡾⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣷⣄⣀⡀
⠀⠀⢠⣟⠭⠀⠀⠀⠀⢀⠠⡄⢏⠇⢰⠉⠀⠀⡆⠀⠀⠀⣀⣤⢧⢀⠽⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣻⣯⠿⡻⣷
⠀⠀⢸⢒⠀⠀⠀⠀⢸⠹⠊⠁⠀⠀⢸⠀⠀⠀⡇⣀⣤⣾⠋⣼⢾⣡⢎⡔⠉⠓⣄⠀⠀⠀⢀⣠⢾⣻⠯⠑⠋⠉⠀⠀⠑⢍⡪
⠀⠀⢺⠀⠀⠀⠀⡠⠼⣇⠀⠀⠀⠀⢸⠀⠀⠀⣋⣥⣿⡿⢠⡟⣀⠕⢫⠒⠃⣪⣭⣦⣶⠿⠟⠛⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⠌
⠀⠀⢸⡄⠀⠀⠀⢯⣉⣛⣧⠀⠀⠀⠘⣄⣴⣾⣿⣿⣿⡇⢸⠚⢁⠴⠚⠀⠀⠉⢻⡿⣀⣀⣀⣀⣀⣀⣀⡼⣿⠛⢿⡷⡄
⠀⠀⣠⢛⣉⣽⣿⣾⣷⡤⠼⣇⠀⠀⠀⠙⠛⠛⠉⢹⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⣧⡏⠉⠉⠃⠀⢸⢸⣣⠀⢤⡀⢙⡇
⠀⠀⡇⣿⣿⠟⠻⡟⢻⣻⠒⠛⠒⢒⣦⣤⠀⢀⡀⣼⡿⠈⠀⠀⠀⠀⢀⡜⣧⠀⢀⣿⣷⠀⠀⠀⢠⠸⠼⢏⣢⣤⠼⠃⢙⢦
⠀⢀⣽⣯⡅⠠⠀⢀⣿⠃⡇⠀⠀⠋⠁⢈⣷⣋⡽⠿⡇⠀⠀⠀⠀⣀⡼⠤⠇⠠⣽⣿⣸⢀⣀⣀⣸⡇⠀⡸⠃⢠⢶⠚⠛⠛⠓
⢠⣿⣿⣧⢼⡶⣴⣿⣯⢤⣿⠀⡀⠀⠀⢸⠁⠀⢀⠀⢹⠒⢒⢛⠁⢀⣠⣤⣴⢞⠯⣾⡯⢝⣂⣀⣉⣧⠜⢁⡼⡏⠀⢹⣶⣶⣶
⣿⣿⡿⠧⣤⣸⣿⣿⣾⠀⠈⠀⢸⡀⠀⠀⡇⠀⠘⢿⣷⣤⣾⣼⡀⣞⣯⡝⠊⠁⠀⣿⣷⢿⠁⠀⡿⠋⢠⣾⣹⠁⢀⣿⣏⠢⡀
⢻⣿⠀⢰⣿⡙⢿⣿⣿⠀⠀⠀⢠⣷⡤⠤⢳⣀⣀⣠⣤⣿⣿⣿⣿⣿⠟⡇⠀⠀⢀⣿⣿⡼⠀⠀⣇⣴⡿⢷⠇⠀⣸⣿⡪⠕⠘
⠈⣿⠀⢸⣿⣿⢈⣻⣿⡄⠀⣠⣾⡿⠗⠛⢹⠁⢸⣿⡿⠟⠛⠉⠀⠀⠀⢳⠀⢠⣿⣿⡿⢿⠀⠰⣏⠀⠀⡼⠀⢠⣿⣗⠯⠀⢠
⠀⢸⣄⣈⣿⣿⣼⣿⡿⠓⡏⠉⠀⣀⣠⣤⣾⢤⣸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠛⢍⠀⠀⠈⠳⠤⣴⣿⡆⢨⡢⠾⢯⣓⠅⠀⣼
⠀⢸⣿⠋⠀⠀⣿⠉⠉⠓⠛⢻⡿⣿⣟⣫⣵⡿⣿⠉⠉⠉⠛⠓⠒⠛⣿⠋⠀⠀⠀⠑⢄⡀⠀⠀⠈⠉⠁⠈⣿⣿⣷⣯⣓⢶⣿
⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⢶⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣫⣵⣶⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣡⣿⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡜⣿⣯⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⡜⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠸⣿⣿⡿⠗⣽⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⢾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠉⠑⢞⣣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣵⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⢒⡒⢒⣒⣂⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠀⠀⣀⣠⣾⠿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣶⣶⣶⣶⣶⣶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠘⠋⣡⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢈⣤⡀⠈⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡼⠟⠿⣿⡀⠈⠑
⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⢠⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣈⣥⡦
⠀⠀⠀⠀⢀⡀⡁⠀⠀⠠⠿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣄⠋⠁⠀⠀⠻
⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⡂⠀⠀⠀⠀⠀⠀⠃⠻⠀⠀⠀⠀⠀⢰⣶



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣋⣍⣹⣟⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⢒⡒⠒⠒⠒⠆⠀⠀⠀⢠⠒⠒⠒⠒⠒⢦⠀⠀⠀⠀⠀⡴⠲⠿⠖⢢⠀⠀⠀⠀⠀⢠⣶⣿⡷⠐⠄
⠀⠀⠀⠻⠷⠀⠀⠀⡆⠀⠀⠀⢸⠀⠤⠤⢾⠉⣛⠀⠀⠀⠀⠀⡟⠿⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣣⣄⣈
⠀⠀⠼⠿⠿⠽⠿⠿⠧⠀⠀⠀⠈⠉⠩⠿⠏⠉⠙⠂⠀⠀⠀⠀⣧⣤⣤⣶⣸⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⠶⡶⢦⡀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠆
⠀⠀⡇⠀⣄⢀⣄⡀⣿⠀⠀⠀⠀⣿⠒⣿⢚⡇⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤
⠀⠀⣇⣺⣛⣟⣟⣇⡿⠀⠀⠀⠀⠈⠓⠛⠛⢧⡀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠋⠀⠀⠀⠀⠀⠀⠺⠛⠒⠛⠻
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣤⣀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣠⡀
⠀⠀⣀⣰⣋⡠⠿⣶⡶⠀⠀⠀⠀⣰⠏⠁⠀⢛⢳⡄⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠴⢒⣄
⠀⠀⠉⠉⠻⠥⠴⢇⠀⠀⠀⠀⠀⢿⡠⠶⠴⠿⣸⠇⠀⠀⠀⠀⠸⠴⢤⡤⠦⠄⠀⠀⠀⠀⠀⡟⢖⣛⣜
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠰⠾⠷⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠶⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡿⠿⠿⠿⠿⠿⣟⠀⠀⠀⠀⡞⠉⣩⡿⡆⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⠀⠀⠀⠀⠀⡠⡼⠩⠍⢧⢄
⠀⠀⡤⣤⣤⣔⣩⣕⣾⠀⠀⠀⠀⢷⣛⣛⣳⡃⠀⠀⠀⠀⠀⠀⣿⣁⣉⣀⣿⠀⠀⠀⠀⠀⠂⡇⠐⡂⡰⠐
⠀⠀⠦⠤⠤⠬⠵⠭⠮⠀⠀⠀⠀⠀⠈⠉⠀⠹⣦⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⠭⣈⣣⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠇⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⡆⠀⣿⠀⠀⠀⠀⣠⣾⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣠⣾⠟⣳⠀⠀⣰⡾⣛⣭⣽⡻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡄⠀⣿⡇⠀⣿⠀⠀⠀⣸⣿⣿⣿⢟⣭⡻⣿⣿⡄⠀⠀⠀⣿⡿⠿⠿⠿⣿⣫⣾⠟⠁⠚⠁⠀⢰⣿⣸⣿⣿⣿⣿⡞⣿
⠀⠀⠀⢰⡆⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⠀⢻⣿⣿⣿⠻⠿⢇⣼⣿⣶⠀⠀⠀⣿⡿⠿⠿⣿⣣⣬⣷⠀⠀⠀⠀⠀⠘⣿⡜⣿⣿⣿⡿⣳⡿
⠀⠀⠀⢸⠇⠀⢿⠀⠸⡇⠀⢿⠇⠀⠿⠀⠀⠀⠈⢿⢟⣵⣿⣿⣿⢟⣱⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣷⠾⢛⣵⣤⡀
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠙⠓⠲⠚⠋⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⣷⢸⣟⣛⢸⡟⠛⣦⢸⡇⣴⠛⠻⠂⣸⢿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠻⠋⠿⠸⡯⠥⠸⠧⠴⠟⠸⠇⠻⢦⡴⠢⠿⠚⠿⠼⢷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀⢀⣀⡀⢀⣀⣀⠀⢀⣀⠀⢀⣀⣀⠀⢀⣀⣀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠇⣿⢭⠅⠿⣯⣅⢸⣯⡭⢀⣿⢻⡆⢸⣯⣽⠇⣿⠉⠉⢰⣷⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠻⠂⠿⠶⠆⠻⠶⠛⠸⠷⠖⠺⠋⠙⠛⠸⠃⠻⠂⠙⠷⠟⠘⠇⠀⠻


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣉⣥⣤⠦⠶⢦⣤⣍⡙⠓⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣴⠟⠉⠀⠀⢤⠄⠀⢀⠈⠙⢷⣄⠁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠠⠄⠀⠚⠂⠀⠀⢤⡀⠀⣾⢷⣄⠀⠙⢷⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡆⠀⠀⠀⠰⠆⢀⣠⣤⠶⣿⣦⣽⣷⠄⠘⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⢦⠀⢴⠄⢠⣿⡉⠻⣦⣼⡇⠀⠀⠰⡄⢹⡆⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠷⠞⠃⢸⡇⢻⡄⠀⢀⣀⣀⣸⡏⠻⣦⣨⠟⠠⣄⠀⢠⡄⣼⠃⣿⠀⠛⠷⢶⣦⣀⡀
⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠘⣧⠘⣧⠀⠙⢿⣍⢹⡟⠋⠉⠁⠀⢀⠀⠀⠀⢠⡟⢰⡏⠀⠀⠀⠀⠈⠙⢿⣄⡀
⠀⠀⠀⠰⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⡘⢷⡀⠀⠙⢿⠇⠀⠀⠰⠆⠙⠁⠀⣰⠟⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⢴⡏⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠳⣄⡙⢷⣤⣀⡀⠙⠂⠀⣀⣠⣴⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⢹⣿⠀⠀⠀⠈⠻⢶⣬⣉⣙⡛⠛⣛⣉⣩⣴⠾⠋⠀⠀⠀⠀⠀⣠⡶⢶⣄⠀⠀⢸⡟⠁
⠀⠀⠀⠀⢸⣧⡀⠀⣀⣿⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠁⠀⠀⠀⠀⣠⣄⣠⡾⠋⠀⢀⣿⠀⣠⠟⠃
⠀⠀⠀⠀⢀⣠⡴⢾⣏⣹⡇⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠙⠿⣄⢀⡴⢟⣡⡾⠛⠃
⠀⠀⣠⡴⠟⢁⣠⡶⠛⣿⣀⣀⣸⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠈⢿⡄⠋⠉⠉
⣾⠛⣿⠀⣰⠟⠁⠀⠀⢹⣏⣉⣿⠁⠀⣿⣉⣉⣩⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⠟⠷⠞⠁⠀⢀⣀
⢹⡟⠋⢰⡏⠀⠀⠀⠀⠀⣿⣼⡯⠀⠀⢹⠏⠉⢹⡇⠀⠀⠀⠀⠀⣠⡾⠛⠛⢛⣿⠟⠁⠀⢀⣴⠾⠛⠛⠉⠛⣿⢦⣄
⢸⡇⠀⠛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣼⡇⠀⠀⠀⠀⣰⠏⠀⢀⣴⠟⢡⣶⡀⢠⡟⠁⠀⠀⣀⣤⣤⣿⣄⣹⣧
⠈⢷⡀⣼⠋⠉⠹⣆⠀⠀⣤⣤⣤⣤⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢿⣤⠞⠛⠁⢀⣿⡉⠀⣿⠀⠀⢠⣟⠙⢷⣄⣹⠉⠉⢹
⠀⠈⠻⣿⣧⣤⣾⣧⣤⣼⣧⣤⣤⣤⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⣾⠋⠁⠀⣿⠀⠀⣿⠙⢷⣄⣸⡟⠀⠀⢸
⠀⠀⢠⣾⣧⣤⣤⣤⣤⣤⣤⣤⣴⣿⡄⠘⠷⠶⠾⠁⠀⠀⠀⠀⣰⠟⣧⢀⣾⠋⠁⠀⠀⠹⣿⠛⢻⡟⠛⠛⠉⠀⠀⢠⡿
⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⠐⢷⣄⡀⠀⠀⣿⣀⣼⠇⠀⠀⠀⠀⠀⠀⠈⠳⣾⣇⣀⣀⣀⠀⠆⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣿⣃⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⣿⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⢿⣿⣿⣿⠀⠀⠀⠋⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣌⣉⣉⣀⣤⡴⠟⠉⢳⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣤⣤⣉⣉⡁⠀⢠⣾⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣦⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠘⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡖⠒⢲⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠂⢐⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⢰⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⢁⠞⠁⡠⠄⠈⠢⠑⡄⠀⠀⠀⠀⠀⡀⠤⡀⡀⠿⠸⠸⢂⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠠⢤
⠀⠀⠀⠀⠀⡂⡯⠭⢽⠀⠒⠒⡆⠀⠀⠀⠀⢘⠁⡆⠀⡠⠄⡇⠀⠀⠀⠀⠀⡼⠤⠂⠘⡈⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠠⠠⠤⠠⠤
⠀⠀⠀⠀⠀⠄⣏⠉⣿⢰⣄⣠⡇⠀⠀⠐⡈⢮⡀⠅⠀⣇⡴⢠⠂⠀⠀⠀⠀⠈⣄⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠑⠂⠠⣄⠔⡱
⠀⠀⢸⠈⢹⠅⠏⠉⡿⠸⡏⢀⠇⠀⠀⠀⠈⠢⠍⣁⡉⠡⠴⡣⠑⠄⠀⠀⡔⠁⠀⠎⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠗⠠⠀⣈⣀⠠⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠈⠀⠈⠈
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠔⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⡒⠀⠀⠀⠠⠂⠀⠀⠀⡠⡀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠄⣒⣂⠠⣀⠆⠸
⠀⠀⠀⠋⠀⠊⠀⡄⡂⣀⢇⠀⠀⠀⠀⠀⠀⢀⠔⣉⠢⠔⡠⠲⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⣇⣠⠃⠀⠀⠀⠀⠀⡐⡐⢁⢄⢀⠐⡌⠎⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡆⠆⠀⠀⠀⠀⠴⡡⠊⠀⠑⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠜⢌⠀⠃⠁⠗⠀⠀⠀⠀⠀⡁⢇⠔⠢⡥⠊⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠊⠤⠌⣜⢀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⢄⠙⠪⣂⠀⠀⣊⡔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠤⠤⠧⠠⠤⠸⠤⠤⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠁

⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢩⢩⡍⣭⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠐⠂⠐⠒⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣔⡄⢀⡢⠈⠀⠀⠀⠀⠰⠒⠒⠒⠒⠖⠶⠲⠖⠲⡁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠰⠳⠣⠇⠶⢰⠐⠞⢆
⠀⠀⠀⠀⠀⠙⠀⠘⠝⠀⢀⠀⠀⠀⠀⢀⣘⣈⣃⣛⠄⠀⠠⡐⣄⠇⠀⠀⠀⢀⣀⣀⡀⠁⣀⣀⣀⠀⠀⠀⠀⠆⠤⠴⠤⢤⢔⠢⢑⠾
⠀⠀⠀⢆⣀⣀⣀⣄⣀⣄⣀⠲⠀⠀⠀⠀⢤⠠⠄⠈⠀⡀⠀⠐⡈⡆⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠡⡴⡤⡄⣼⢀⠀⠀⡁⠁
⠀⠀⢘⠘⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠈⠀⠀⠀⠓⠉⠒⠐⠚⢝⠇⠀⠀⡏⠉⠈⢰⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⠈⠳⠥⠬⠶⠥⠄⠪⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠁⠁⠈⠁⠈
⠀⠀⠀⢀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠈⠔⠈⠉⠁⢢⠀⠀⠀⠀⠀⠀⠱⠆⠒⠀⠂⠒⠀⠐⠂⠶⠃⠀⠀⠈⡤⠤⠄⠠⠤⠤⢬⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⢀
⠀⠀⢠⠤⠥⠔⠠⡀⢰⠠⠖⢄⡀⠀⠀⠀⠀⣀⣀⠉⠀⠀⠔⡄⠀⠀⠀⠀⠀⠀⠀⡄⢀⢄⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⣽⢛⣙⣫
⠀⠀⠘⠒⠒⠢⠐⠁⢠⠒⠦⠊⠁⠀⠀⠀⠀⣃⣸⣀⣖⣲⣀⡇⠀⠀⠀⠀⠀⠔⡆⡇⠀⣄⡀⢌⠘⠀⠀⠀⠀⡄⠀⠀⢤⠀⠀⠠⠠⠀⠠
⠀⠀⠀⠀⠢⠠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠤⠤⠤⠤⠎⠀⠀⠀⠀⠈⠁⠁⠘⠝⠛⠫⡞⢄⠀⠀⠀⣇⣋⣀⣸⠈⠁⢃⣉⣀⣀
⠀⠀⠀⠠⠄⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠤⠈⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠎⠁⠉⠱⠀⠀⠰⠉⠈⠱

⡿⢿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣀⣀⣀⣀⣀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⢶⣶⡶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣤⣤⣬⣥⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⣩⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣉⣩⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⠋⠛⠛⠋⣛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣼⣿⣿⡀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣻⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⣿⣿⡅
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣽⣿⡇⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⠉⠉⠉⠉⣽⣿⡇⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⡖⣖⣢⣦⣖⢂⣶⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⢠⡅⣬⠅⣄⢨⣤⣠⠄⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠛⠐⠛⠛⠛⠛⠛⠙⠙⠒⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠭⢓⠚⠭⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠐⡀⢀⣀⣷⣌⢳⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢸⢸⠀⠐⢰⢯⣳⠏⠀⡂⡇⡧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⢏⢆⠙⢿⠋⢁⠠⠀⡼⡹⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢠⣤⠈⠳⢕⡢⠬⠤⣔⡫⠞⠁⠀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣴⣯⠹⡆⠀⠀⠈⠉⠉⠁⠀⢠⡲⣎⣠⣏⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⢋⠕⠋⣷⣲⠃⣖⣲⡄⠀⠀⠀⡠⠊⣹⢮⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢾⣀⠀⠘⠋⠀⣯⣸⠀⠀⢠⠎⣩⢟⡁⡴⠋⣉⣹⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣯⣨⣇⣴⣒⡂⡇⢸⠀⠀⠙⡋⢁⡞⠸⣁⣸⢯⣳⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠬⠭⠭⠭⠗⠈⠋⣄⣀⢸⣱⠊⠀⠀⠹⢽⣉⡁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣠⣤⣤⣄⠀⢀⡀⣀⣠⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣿⣟⣿⣷⣿⡇⠘⠓⠛⠛⠚⠐⢠⣺⣷⡄⡀⠀⠀⠀⠰⢆⣂⣂⠈⠀⢀⣀⣠⡶⠋⠀⠀⠠⣀⠀⠀⠀⠀⠳⢎⡸⠀⠀⠀⠀⠄
⠀⠀⠈⠛⠿⠟⢿⠋⠀⠀⠀⣠⠶⢄⠀⠀⠉⠉⠀⠀⠀⠲⢣⣞⠁⠈⢻⣛⣆⠛⠋⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠸⠟⠻⠇⠀⣠⡄
⠀⠀⠀⣠⣴⣤⣌⡀⠀⣀⡤⣷⣤⡾⠃⠀⡀⠀⢠⠀⠀⠀⢾⣿⡄⠀⠈⣿⡏⡇⣰⠆⣠⡦⠀⡴⡄⠀⠀⢠⡶⣦⢠⣶⣦⡸⣧⣸⣿⡀
⠀⠀⢰⠻⣿⣿⡿⠟⠋⠑⠀⡼⠁⡀⠐⡤⡾⣿⡯⠑⢏⠀⠘⢏⡁⣠⣤⣍⡠⠃⠋⠊⠁⠀⠐⣃⡀⢠⣦⠘⢷⡿⢻⣧⣴⣷⠘⠋⠹⣧
⠀⠀⡏⠀⠘⣯⣠⣄⣀⣀⣾⣇⠀⣧⠈⠳⢤⣮⣦⠴⠋⠀⠀⠀⠉⠙⠛⡉⣠⡄⢠⣠⣦⢠⣿⠛⣿⡌⣿⣤⣴⡆⠀⠻⢿⠿⠀⣀⡀⢀⡄
⠀⠀⢿⠀⢤⠁⠉⠻⢮⣿⣿⣿⡇⠈⠷⣶⣆⠀⠀⠀⢤⣰⠚⢣⣤⣄⣺⣧⣸⣷⢻⣿⣿⣎⣿⣦⣿⠇⠻⠿⠛⠋⠀⠀⢰⣾⣿⢿⡇⠈⠇
⠀⠀⠈⢷⣤⡀⠀⠀⠀⣈⡽⠟⠁⠀⠀⠉⠀⣀⣤⣴⡄⠈⣀⣿⡏⠙⠛⣿⡏⢿⡞⡿⠙⠟⠈⡉⠁⠀⠀⠀⣧⠀⠀⠀⣸⣷⣤⣄⣧⣀⡀
⠀⣤⣶⣾⣍⣛⣻⣿⡛⠉⢀⢤⡒⠄⣇⡀⠹⠛⣿⡏⢺⣿⣽⡜⢿⣶⣿⠻⠗⠈⠀⠀⠀⡀⠛⠁⠲⠄⠀⠤⠞⠀⠀⠘⣿⣷⣾⣿⣿⣿⠃
⠀⣿⣟⠛⠛⠛⠛⠛⢻⠃⡜⠀⠀⠀⠀⠂⢀⠀⢹⣿⡘⣿⣷⠶⠀⠉⢁⠀⠀⠀⢹⡀⠀⠸⡄⢠⠤⠒⠀⣀⣠⣤⣤⣀⠀⠙⢿⣿⣿⠃
⠀⣿⠿⡀⠀⠀⠀⢀⡏⠀⢷⠀⠀⠀⠀⢈⡆⠀⠀⠉⠀⣀⡀⠀⠀⢰⣬⣟⣲⠤⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣟⣿⣿⡟⠀⢠⡀⠙⠁
⠀⠻⣧⣇⣀⣀⣀⡼⠁⡀⠀⠑⠂⠔⠐⠀⢀⣠⠤⠒⠉⠙⣁⣀⣤⣼⣿⣿⡿⢿⣿⣶⡆⠀⡁⠀⠀⠈⠙⢿⣿⣿⣿⠀⠰⡏⠘⠳⠆⣀⡀
⠀⠀⠀⠉⠉⠉⠁⠀⢄⠀⠠⣀⡀⠰⠞⠛⢉⣀⣤⣶⣺⣿⣿⣿⣻⣿⣿⣾⣿⣿⡿⠃⠈⡥⠁⠀⠀⠀⢀⡀⠈⣵⡆⠀⣼⣿⣦⣦⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⡔⠀⠸⣃⣤⣶⣾⣿⣽⣿⠿⠿⠟⠛⠛⠛⠉⠹⣿⡿⠋⠀⠂⡠⠔⠉⡁⠀⢤⣿⣷⡄⢸⡆⠀⠻⠿⠛⠁⠐⣿⠂
⠀⠀⠀⠃⠁⡔⠀⠀⠉⠉⠀⠈⠛⣛⠋⠉⠉⠀⠀⠀⠀⠀⢈⣶⠃⠀⠀⠉⠈⠆⡆⠀⠀⣀⣀⢿⡿⠄⢉⣩⠥⠔⠧⢄⡀⠀⠀⠀⠬⡁
⠀⠀⠀⠂⠀⠀⠀⠀⠂⣤⡞⢉⣻⣅⣈⠑⣤⠢⠐⠀⠻⢷⣾⠋⠀⠀⠑⠈⠢⣠⠖⣆⠀⡇⠈⡎⠁⣰⠋⣠⣶⣶⣶⣦⣙⡄⠀⠠⣤⣄
⠀⠀⠀⠀⡀⠰⡆⠀⣾⣤⣾⣿⣽⠶⠶⠟⠾⠷⣉⡴⠠⠐⠀⠀⠀⣤⣦⣤⣤⡘⣦⣈⠛⣷⣤⠇⢰⡇⣬⣿⣿⣿⣿⣿⣿⣇⠀⢨⣷⣾
⠀⠀⣠⣾⣷⡀⠉⠘⡿⢋⠉⠀⢻⡀⠀⠀⢤⣤⢸⣷⡀⠐⡅⢰⣟⣛⣿⠻⡟⣿⣎⠙⢻⣿⣿⣆⠈⣧⠸⣿⣿⣿⣿⣿⠏⢹⡀⠘⠿⠟⠂
⠀⠀⠛⣿⡟⠓⠀⢸⣿⡾⠆⢠⣾⣿⣷⣦⣄⣀⠞⠙⣿⡀⢇⢸⣿⣛⣿⣠⣇⣿⣿⠀⠘⣏⡕⡻⣷⣿⡦⠄⣉⣉⣉⡤⠒⠉⢿⡵⣦⡀
⠀⠀⠀⣿⡇⠀⢠⣿⠉⠓⢦⣾⣿⣿⢿⣿⠟⢅⠀⠀⢸⣧⢪⢸⣿⢙⠏⡿⡏⣿⣿⠀⠀⠙⣾⣱⣹⣿⢴⢒⣍⣩⣭⡍⡭⣽⠸⣿⣒⣳
⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠘⢯⣛⣛⠛⣋⡠⠆⠀⠀⣴⣛⢦⡀⣿⡞⡿⣷⣗⢿⣿⡆⢰⠄⠈⠛⠿⣿⡸⣙⠞⠙⢿⠇⢉⡼⠀⣿⣿⣾⡆
⠀⠀⢀⣿⡇⣴⠋⢿⣳⡄⠀⠀⢨⠏⠛⠂⢲⠀⠀⢸⣿⡦⡌⢷⢹⣷⣤⢿⡼⠼⣿⣧⠘⡄⠀⠀⠀⢸⣦⣄⣉⣘⣛⣋⣥⣴⣾⣿⡿⠙
⠀⠀⢸⣿⡇⢹⡀⡏⢿⡷⠀⠀⣸⣀⠀⠀⡇⠀⠀⠈⠛⠓⠘⠉⣿⣿⡆⣾⡿⠾⣿⣿⡙⡄⠀⠀⠀⠈⣿⠿⠿⢿⣿⣿⡿⢟⣹⡞⢷⣰
⠀⠀⣾⣹⣷⠀⠉⢡⣴⣶⠆⠀⠀⢸⠁⠀⢉⠇⢀⣀⣾⣀⡀⠀⣾⡿⣻⢻⡟⢿⢻⣿⡧⡇⠀⠀⠀⢀⣿⣭⣭⣭⣧⢸⣿⣿⣶⡷⣶⣄
⠀⢰⣿⣹⣿⣧⡀⢀⡏⠀⣾⠆⠠⠚⠚⣧⠎⠀⠀⢹⢿⡏⠁⠀⢻⣷⠹⢿⡇⣆⢘⣿⠇⡸⠀⠀⢰⣯⣛⣿⣿⣿⣿⠸⣿⣿⡿⠿⠿⢿⡆
⠀⠈⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠁⠀⠀⠈⠛⠿⠿⠿⠿⠿⠋⠀⠁⠀⠀⠘⠋⠋⠛⠛⠛⠉⠀⠉⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣒⠒⡖⣢⠨⣡⣶⡔⠦⠃⢀⠀⠂⠀⡤⠀⠒⠒⣂⣀⡐⠒⠒⠂
⠀⠀⠀⠀⣀⠤⣺⠁⢠⣤⣤⣤⣶⣶⣶⣾⠀⠀⣾⣦⣴⣿⣿⡧⠀⠨⢎⠌⠜⡼⠠⣖⡻⠷⣔⠃⡎⠀⠀⡀⢰⣷⠀⠁⢻⣿⡇⠀⠿⠿⠿⠿⠗⠐
⠀⠀⠀⠸⢐⠥⠚⡁⢸⣿⣿⣛⣟⣻⣿⣿⠀⠀⠙⢿⣿⣿⡟⠁⠀⣐⣠⣂⣊⣾⡀⠢⠄⠉⣹⡶⣄⠀⢀⠁⠸⠿⠀⢠⠘⠛⣁⣤⣤⣦⣤⣄⠀⠀⡀
⠀⠀⠀⡋⠤⢂⠥⡇⠈⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠄⠙⠉⠀⠀⣸⡿⠿⠿⠿⢿⣧⣀⠀⢀⡟⠃⠙⠆⠘⠀⢠⣶⣦⠸⠀⣼⣿⢟⣩⣍⡝⠻⣿⣄⠁
⠀⠀⠀⡇⠊⡡⠔⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⣼⡟⠁⠀⢀⡀⠀⡉⢻⣧⠈⠁⠆⠀⠀⠀⠀⠈⠻⠋⠀⢸⣿⡇⣾⣿⣿⣿⣇⢹⣿
⠀⠀⠀⡇⣈⠔⣊⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠹⣿⣇⠀⠀⢘⡁⠉⠁⣸⡟⠀⠀⡃⠀⠀⠀⠀⠀⠀⢠⠀⠘⣿⣧⡹⠿⣿⠿⣣⣿⡟⡀
⠀⠀⠀⣋⡠⢊⠅⠘⠼⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⠀⠀⠙⢿⣷⣤⣨⣁⣠⣴⠟⠁⠀⠀⠃⠀⠀⢠⠀⠀⠀⠈⠀⠀⠈⠻⢿⣷⣶⣿⠿⠋⠀⠂
⠀⠀⠀⠧⢈⣤⢊⣠⡀⠀⠀⠀⠀⠀⢀⢼⠀⠀⡒⠄⡁⠠⠐⠀⠀⠈⢻⡻⠻⠟⣿⠀⠀⠀⠀⡆⠀⠀⠀⢄⣀⣀⣀⣠⡄⣠⡠⠠⠤⠤⠤⠤⢠⠲
⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠐⠊⠀⠀⠈⠢⣿⠤⠚⠀⠀⠀⠘⠒⠀⠒⠞⢀⡴⣤⠀⠘⠀⠠⡶⣦⠈⠓⠓⠚⠓⠒⠒⠂⠋⠂⠈⠈⠁
⠀⠀⠀⠋⠀⠀⠀⣀⠄⣆⣂⣖⡠⡀⠀⠀⠀⡌⠁⡀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠿⠂
⠀⠀⠀⠀⠀⠠⡎⢰⠊⠉⠙⢿⣿⣮⣢⠀⠈⠀⠁⠠⣿⡴⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣥⣥⣤⣤⡀⢱⡀⠀⡊⠁⠰⠈⠀⣧⢀
⠀⠀⠀⠀⣐⢃⡡⠁⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⣠⣤⣿⢀⡀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⣉⣉⡉⠉⠙⠛⢻⣿⡇⢸⡇⠀⠀⡀⠀⠀⣰⠏
⠀⠀⠀⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢷⣆⠀⢸⣿⡇⢸⡇⠀⢀⠀⢠⡴⠃
⠀⠀⠀⢠⡁⣈⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠈⠛⠛⠁⠀⠀⢀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠀⠸⣿⡇⢸⡇⢀⠀⠀⣸⣿⠀⠻⠃
⠀⠀⠀⠀⡁⢌⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠀⢠⣄⣰⡆⢀⠀⣿⣿⠀⠀⠀⠀⠐⠘⢿⣷⣿⣽⣿⡛⠋⠀⠀⣿⡇⢨⡇⢸⠀⠀⣿⣿⡆
⠀⠀⠀⠀⢅⠈⣭⣉⠛⢶⣄⠠⠐⠂⢩⣙⢻⣿⡄⠀⠈⢿⡿⠃⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⡇⢠⡇⠸⠂⠀⣿⣼⠇
⠀⠀⠀⠘⠂⠁⠈⢿⣷⣄⠻⣧⠔⢠⣿⣿⡆⣿⣷⠀⠀⠀⠀⠀⠀⢄⠻⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣾⠿⠿⠿⢃⣸⠇⠀⠀⠄⠀⡀
⠀⠀⠀⠀⢰⣾⣿⣆⠻⣿⡄⢻⣇⣿⣿⣿⡇⣿⣿⠀⠁⠀⠀⠀⠄⠂⠀⠀⠈⠉⠁⠁⠈⠻⢿⣿⣿⣷⣾⣟⣃⣉⣀⣀⣉⣑⣒⡄⠀⠀⠸⠀⠰⠁
⠀⠀⠀⠀⣿⣿⣿⣿⡆⢹⣷⢸⣿⣿⡿⠏⣰⣿⡟⠀⠀⠠⠀⠀⢷⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠠⠀⠐⠀⠈
⠀⠀⠀⠀⠻⣿⣿⣿⡏⢨⣟⣿⣧⣤⣴⣾⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⣲⠄⣀⡲⠄⢠⠰⠤⠀⣀⣀⡀⠀⠀⠀⢀⠠⠐⣒⣒⣒⡀⠄⠁
⠀⠀⠀⠀⠄⠈⠛⠛⠴⠛⠋⠀⢀⠉⠁⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠘⠛⠀⠀⢹⣿⣷⠀⠁⠀⠓⣿⣿⠿⣿⣿⠿⢷⣾⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢠⠂⠚⠀⠠⡎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡆⠀⠀⠀⣿⡇⠀⣿⡏⠀⣾⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠡⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⢹⣷⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠒⣴⣶⣶⢽⣿⢿⡍⠃⣉⣶⣶⣿⡙⠻⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠀⢀⣿⠀⣸⣿⠀⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣼⣿⣽⡧⠧⣿⣿⣿⣿⡷⠀⠀⢐⢂⠀⠀⠀⠀⠀⠉⠉⠈⣈⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣴⣾⣧⣀⣿⣧⣸⣿⣷⣦⡀
⠀⠀⠀⠀⢀⠀⠀⠙⠛⠛⡉⢩⣉⣠⡂⠙⠻⠿⠛⠁⢠⠀⠈⠀⠀⠀⡦⠠⠤⠀⠤⠤⠤⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠂⠂⠒⠒⠒⠓⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠂⠀⢀⠀⠀⠀⠀⠀⠘⢣⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠉⠉⠀⠂⠀⠀⠠⢄⣀⠤⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢤⣀⠡⠄⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡠⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠒⠛⠂⠐⢢⣀⢈⢁⡒⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠭⠀⠀⠀⠀⠄⠐⠀⠒⠐⠶⢶⢎⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠉⠙⣫⣍⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⡦⠄⠠⠠⢠⣄⡀⠀⠀⠀⠀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣔⣤⣀⣩⠥⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠦⠉⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠚⠋⠁⠐⠶⣀⠂⢀⢙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⠥⠌⠀⠀⠀⠸⠀⠀⠈⠠⡥⡍⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡠⠟⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢹⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⣃⣥⡠⠤⠤⠀⠀⢀⡤⠔⠋⢠⠤⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⣔⣓⡶⠒⠒⠀⠀⡄⠄⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⢀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠰⣯⡽⠇⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠓⠒⠐⢊⠔⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢉⢣⡀⠀⠀⠀⠀⢀⠈⠒⠄⠠⠀⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠒⢆⠀⠀⠀⠀⠀⠀⠁⠀⠲⢜⡀⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣚⡂⣀⣀⢀⣀⡀⠀⠀⠀⢙⡓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠕⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠶⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⠆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠀⣿⠀⠈⢻⡀⠀⠀⠀⣤⠀⠀⠀⠉⠙⢧⡀⠀⠀⠀⣸⣏⣹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⣴⠟⠳⢦⣼⠇⠀⠀⠀⣿⠀⣤⣤⣤⠀⢨⡟⢳⡶⠛⠉⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢾⣅⣀⣠⡴⠋⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⢀⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⣿⠀⡿⠀⣿⠀⣿⠀⣿⠀⣾⠛⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⣤⣤⡤⠠⣤⣤⣤⡄⠀⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡽⠋⠉⠉⠉⠉⠉⠉⢿⡍⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡯⠈⠀⣾⣧⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠇⣨⡝⠂⣸⣿⡏⠀⠀⠀⢋⠁⢤⠤⠒⢂⣷
⠀⠀⠀⢀⡀⠀⠀⠐⠀⢠⠥⠄⢹⣿⣿⣿⣿⣿⡿⠀⠀⠒⣞⠀⠈⡀⢠⣿⣿⠁⠤⢤⣄⡐⢠⢯⢐⣦⣍⡿
⠀⠀⠘⡄⠀⠀⠀⢀⣂⣀⣭⣵⣀⣿⡿⠟⠋⠁⣀⣀⣀⣀⠈⠉⠒⠋⠚⠛⠁⠀⠀⠀⠀⠫⠉⠭⠜⠛⠉
⠀⠀⠀⠙⠛⡛⢛⡻⠛⠉⠀⣹⠛⠛⢋⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠀⠀⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⢠⠉⣐⢎⠐⠁⠀⠀⠀⠀⡇⢠⣿⣿⣷⣶⣶⣶⣶⣦⣤⣬⣤⣤⡀⠀⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢸⢰
⠀⡼⠣⢍⡁⢱⠀⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠟⠻⣧⣐⣲⣆⡼⣸
⡘⢠⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣨⠛⣙⣤⣶⣿⣿⣿⢟⡠⠋⠔⠁
⠇⢸⡀⠀⠀⠀⠀⢀⣀⡀⣸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢾⣟⠁⣿⣿⣿⣿⡟⠉
⠈⠀⢱⢤⡒⣈⣭⣤⠄⠀⢀⠗⠘⠛⢛⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣶⣿⣿⣿⢤⣤
⠀⡔⠁⠀⠚⠛⠋⣁⡤⠖⠉⠛⢶⣤⣤⣀⣈⣉⠉⠙⢌⠻⣿⣿⣿⣥⠖⣺⣿⣿⣿⢿⣫⣷⣿⣿⠀⣀⡀
⠀⠈⠒⠒⠒⠛⠛⠳⠤⠄⠀⣶⠻⠿⣒⣚⠛⠛⠛⠓⣚⣓⣍⠻⣿⣿⣷⠞⠛⣫⣵⣿⣿⣿⣿⣿⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣐⡒⠫⠉⠩⠉⣙⣓⠒⠓⠾⠛⠿⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠠⠬⠥⢉⣑⣒⠒⠂⠨⠥⠄⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠠⢍⣉⠑⠒⠒⠤⠬⣭⣉⣉⣉⠀⢻⣿⣿⣿⠟⠁⣀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣈⣉⠛⠓⠶⠤⣤⣄⣀⣀⠀⠀⠉⠁⠀⢸⣿⡿⢃⡴⠊⠑⣢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⡂⠭⢉⡓⠒⠦⠤⢤⣉⣉⡙⠛⠻⠶⠶⠾⠋⠠⡏⠑⢢⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣚⠁⠀⠀⠈⢉⠚⠂⠀⠨⠉⠐⠂⠀⠀⠉⣍⣩⢿⠒⠒⢂⡄⠈⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣀⣀⡉⠒⠒⠀⠀⠀⣠⢮⢟⣰⢃⢞⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣦⣤⣽⣷⣶⡖⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠴⣶⠤⣄⣠⠞⠛⠛⠛⠨⠛⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡞⠁⠀⣿⠀⠞⢳⡀⠀⠀⠀⠈⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠛⠒⠒⢺⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣄⡈⠳⣄⣠⠞⠀⠀⠀⣶⣶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠛⠚⠛⠛⠂⣦⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣽⡉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡆⡆⡆⡆⡦⢴⠀⠀⠀⠀⠀⠀⠀⠠⢔⠄⠀⠀⠀⠀⠀⠲⠀⠀⡖⠂⠀⠀⠀⠀⡀⠀⡐⠒⡀⠠⡀
⠀⠀⠀⠀⢀⣇⣀⡇⣀⣇⣸⠀⠀⠀⠀⠀⢀⢔⡕⠈⡄⠀⠀⠀⠀⢴⣶⠄⢰⠷⡆⠀⠀⠀⠀⠱⣠⠟⡛⢇⡀
⠀⠀⠀⠀⠰⠄⠤⠄⠤⡤⢰⠀⠀⠀⠀⠀⠀⠁⡄⡔⠀⠀⠀⠀⠀⠀⢠⠀⢀⣭⣀⠀⠀⠀⠀⡔⢙⡣⢴⡏⠑⡀
⠀⠀⠀⠀⠀⠂⠀⠒⠂⠓⠊⠀⠀⠀⠀⠘⠀⠈⠁⠉⠃⠀⠀⠀⠀⠀⠒⠀⠂⠀⠑⠀⠀⠀⠀⠈⠁⠁⠀⠁⠉

⠀⠀⠀⠀⠀⢠⢢⠀⠀⡔⠢⠀⠀⠀⠀⠀⢀⠄⡀⡒⢄⠀⠀⠀⠀⠒⠒⠒⠒⣒⠲⠀⠀⠀⠀⡖⢲⠀⣖⠒⡆
⠀⠀⠀⠀⠀⠀⠉⡖⠐⡋⠈⠀⠀⠀⠀⠀⠀⠎⠀⠈⡆⠆⠀⠀⠀⠀⠡⡇⡸⠤⢣⠀⠀⠀⠀⡇⢸⠀⠤⠀⡇
⠀⠀⠀⠀⠈⠡⠀⠌⢊⣁⠀⠀⠀⠀⠀⡀⢾⠮⠐⠪⠊⠀⠀⠀⠀⠀⠀⠂⠊⠀⢐⠀⠀⠀⠀⠉⢹⢀⠋⠉⣡
⠀⠀⠀⠀⠠⠔⠒⠨⠍⠒⠈⠀⠀⠀⠐⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠫⠬⠄⠙⠚⠹⠀⠀⠀⠀⠢⠘⠢⠤⠤⠤⠆

⠀⠀⠀⠀⢀⡠⠔⠠⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣒⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢
⠀⠀⠀⠀⠀⢈⠍⠩⠅⡇⠛⠀⠀⠀⠀⠀⢀⢔⢆⡓⠉⠀⠀⠀⠀⢀⡀⠸⡀⢸⠘⡆⠀⠀⠀⡔⠈⠘⠄⢀⣠⠃
⠀⠀⠀⠀⠀⠐⡂⠐⠂⡇⣀⠀⠀⠀⠀⣀⢼⠤⠕⠁⠀⠀⠀⠀⢀⠃⠀⠀⠀⠿⠐⡇⠀⠀⠀⠣⠀⠠⢢⠂⠰⡀
⠀⠀⠀⠀⠠⠬⠤⠤⠤⠇⠲⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠬⠃⠤⠁⠀⠀⠀⠀⠀⠀⠈⠢⠐⠄

⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⣄⠀⠀⠀⠀⠀⠀⡠⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⡀⡄⠀⠀⠀⢀⠀⡀⠀⡄⠤
⠀⠀⠀⠀⠀⠀⠀⢸⢹⢀⡀⠀⠀⠀⢀⠔⠀⡖⢲⠀⠣⠀⠀⠀⢨⠘⠸⡤⢠⠤⠌⡆⠀⠀⠀⢸⡂⡅⠀⡇⡀
⠀⠀⠀⠀⠀⠐⠒⢨⠰⣀⠀⠀⠀⠀⠈⠠⠄⠧⢼⠠⠔⠁⠀⠀⢸⠀⠘⠄⠔⠰⠆⡇⠀⠀⠀⠯⠤⡭⠬⠥⠭⠆
⠀⠀⠀⠀⠸⠀⠀⠺⠂⠀⠸⠀⠀⠀⠀⠀⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠨⠇⠨⠅⠀⠀⠀⠀⠀⠏⠀⠁⠈⠁⠉⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢻⣦⣤⣀⠀⠀⠀⠀⢠⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠁⠀⠈⠳⣄⠀⠀⢻⣄⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⢹⡷⢦⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠉⠉⠉⢷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⣄⠀⠈⠙⠋⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸⣧⣤⡟⠀⠀⠀⠀⢀⣸⣀⣀⣀⣸⣀⣀⣀⣸⣇⣀⣀⣸⣃⡀⠀⠀⠀⠀⠘⢷⣤⡿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠉⣻⠀⠀⠀⡇⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦⠀⠀⠀⠀⠀⡇⠀⠀⢼⡋⢙⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠋⠀⠀⠀⠓⠒⠒⠒⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠃⠀⠀⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⢀⡀⢀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⣨⡷⠒⠒⠒⠒⠒⠒⠒⠲⣿⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⡘⠃⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠒⠒⣿⣀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣻⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⠀⠀⢿⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⠸⠧⠤⢴⡏⢉⣷⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣦⣀⣀⣠⠞⠁⠀⠀⣾⠋⢹⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠟⠀⠀⠁⠀⠀⠀⠀⠘⠛⠛⠁⠀⠈⠳⣄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠺⣇⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⠶⠶⠶⣶⣶⠶⠶⣶⠶⠶⢶

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠿⠿⠭⠷⠧⠽⠧⠿⠾⠧⠿⠿⠾⠾⠿⠿⠮⠿
⠀⢀⡰⢢⣠⠄⠀⠀⢠⠶⠶⡄⢀⣀⡠⠀⠀⠀⠀⠀⠂⣐⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⣴⣶⣿⣦
⠀⠀⡅⣇⣆⡇⠀⠀⠻⣄⣠⣏⠘⠿⠳⣅⠀⠀⠀⠈⠸⠤⠇⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠘⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⢀⡐⠆⠐⠇⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⢠⣾⠿⣷⣄⠀⠀⠀⠀⠀⣠⡄⣿⡇
⠀⠈⢁⠻⠿⡀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠷⢠⣤⠾⠆⠀⠀⠀⢹⣧⣀⣼⡿⠀⠀⠀⣿⡇⣿⡇⣿⡇
⠀⠀⠙⠀⠀⠉⠀⠀⠀⠀⠃⠈⠃⠘⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢠⠤⠤⡄⠀⠀⠀⠀⢰⣶⢀⣀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⣠⣲⣂⠄
⠀⠀⢉⡏⢥⡄⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⣿⢸⣿⢸⣷⠀⠀⠀⠸⠿⣿⠿⠇⠀⠀⠀⠈⣹⣿⣿⣮
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠚⠛⠚⠛⠚⠛⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠚⠂⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠘⠛⠛⡷⠤⠀⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⠀⢠⣋⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠖⢂⡐⠶
⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠣⠤⠴⣅⠀⠀⠀⠀⠀⣐⣖⣯⡇⠀⠀⠀⠀⣆⡘⢃⣤
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡷⡧⠘⡆⠀⠀⠀⠀⢀⡄⠀⠠⠆⠀⠀⠀⠀⡔⢉⡙⢆⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⡐⢈⡐⠂
⠀⠀⣇⣄⣼⡃⠀⠀⠀⠘⠃⠁⠶⠀⠀⠀⠀⠀⠀⠣⣄⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠡⢈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⢺⠓⡀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⢀⢬⠝⠀⠀⠀⠀⠀⠀⠤⠤⡀⣃⠀⢠⠔⢓⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠾⡄⠀⠀⠀⠀⠀⠀⠈⠢⢻⣟⡔⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡚⣇⠴⠃⠀⠀⠀⠀⠀⠀⢀⣧⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⢏⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣖⣲⠖⢒⣒⡒⠲⣲⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⠲⣆⠀⠘⢆⠹⣤⠤⠤⠤⢤⣤⠋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠿⠃⡸⢀⣠⡈⠓⢌⡻⣦⠼⢛⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⠛⢧⡏⡹⠁⠀⡴⢛⡴⢎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⠤⣿⠃⢠⠞⣴⡯⠠⢤⣵⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠠⢼⣤⠋⣼⢉⠉⠉⢉⣉⣙⣆⢹⡀⠀⠀⢀⣨⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢨⠓⠛⠛⠒⠒⠒⠚⢻⡄⡗⢦⣀⠜⣡⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⡇⠤⠒⠨⠀⠀⠲⣾⠃⡇⠸⢡⣾⣩⣾⢄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠱⣤⠤⠤⠤⢤⣴⠇⡼⡡⠖⠣⡀⠳⠵⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢬⡙⢮⠽⢋⡤⠞⠊⢱⡂⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡥⢆⠛⢄⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⠿⠅⠨⠷⣌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣓⣲⠖⠒⢲⡾⣆⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⠁⠀⠀⠀⠀⠀⠀⠘⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢲⠾⡀⠀⠀⠀⠀⠀⠀⠀⠰⠟⡴⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣦⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠊⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⠦⠦⡍⠃⠀⠀⠀⠀⠀⠀⠀⠘⢢⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣂⠓⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⣤⡄⣤⢤⡀⣤⢀⡤⠄⢠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠃⠿⠅⠻⠔⠃⠿⠘⠦⠆⠛⠛⠸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⢀⣤⡄⣴⡆⣤⣤⢀⣤⠀⣤⣤⢠⠴⠄⣄⣠⢠⣤⢠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠊⠓⠂⠚⠛⠛⠒⠘⠙⠃⠋⠓⠘⠒⠂⠃⠙⠘⠓⠘⠋⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡁⠶⢀⣄⣹⢷⡄⣈⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⢌⣿⡤⣴⣵⢋⣁⣰⢟⣤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡘⠿⢉⣉⣀⡡⣼⣿⠋⢿⣌⢠⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠈⢗⢤⡸⠟⢹⡿⢠⡅⠀⢀⠴⡻⠁⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠑⠬⣑⣒⣒⣒⣒⣩⠕⠊⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣱⢄⣀⡀⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣼⣯⡿⡼⣯⢯⡿⣽⢧⡖⡆⠀⠀⡇⣀⣼⡀⠀⢀⠞⡴⠂⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢹⡏⣽⢹⠋⡏⢹⠉⡏⡇⡇⠀⠀⢇⣓⣶⣃⠰⣁⣤⣟⠉⠉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⣹⢸⠍⡇⢸⠀⡇⡇⡇⠀⠀⠸⡘⠥⣤⡙⠲⣉⢀⣝⡩⠈⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠉⣽⢸⠄⡇⢸⠒⡇⡇⡇⠀⠀⢀⢵⠴⠃⠙⣆⡈⢉⣇⡠⠤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢾⣼⣆⣿⣸⣆⣇⣾⣴⣧⡷⢧⣄⡰⠋⠀⢹⣭⠏⠀⠉⢹⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠈⠉⠀⠀⠀⠘⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⡣⢿⡄⣼⣿⡄⢸⡇⡄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⡀⢠⣾⣿⣿⠀⢸⣧⢸⣿⣿⢧⡄⣿⣷⣶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠈⠀⣬⠉⣀⣻⣿⣿⣿⡿⣤⣷⣿⣯⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⣣⡄⠀⠈⢀⣸⣿⣿⣿⣿⠙⢻⣧⣿⣧⣿⢯
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠓⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠒⣀⣮⣿⣿⣿⣻⣿⣿⡘⣿⣯⡿⢿⣿⣿
⠀⠀⠀⠀⠈⣿⣤⡀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠤⡐⠻⠟⠉⠻⠆⢾⣿⣿⣿⣽⣿⡏⣻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣌⠉⠲⣶⣤⣤⣀⣀⡀⠹⣷⣤⠀⠀⠀⣀⠀⠀⠀⠘⠀⠀⠀⠀⣠⠁⠀⠀⠘⠃⠀⢠⣤⡼⠃⠀⣨⣽⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⢿⡟⠳⣦⣤⣬⣤⣭⣬⣭⣽⣿⣿⠿⣶⣶⡦⠼⢦⣄⣀⣀⣀⣘⡃⠈⠁⠀⣠⣤⣀⡀⠈⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿
⠀⠀⠀⠀⠀⠘⢿⣶⣾⣾⣿⣿⣾⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢱⣿⣿⣿⡿⠿⣿⣿⣿⣀⣤⣤⣸⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡼⣿⣿⡁⡀⢠⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠆⠀⠞⠀⣤⣤⠀⢰⣿⣿⣧⡀⣁⠀⠙⠿⢀⣤⣴⣶⣾⣿⣿⣷⣿⣿⣷⣿⣷⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠂⠀⠀⢠⡦⡀⣀⡀⠁⠀⠸⣿⣯⣷⣿⣯⡈⣹⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠺⠗⠀⠁⠇⠀⡰⠂⣶⠢⣿⣿⣿⣿⣿⡏⠹⣿⣿⣿⣿⠿⣿⢷⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠛⠋⠙⠉⠿⠷⠈⢿⡿⠿⠿⠆⣿⣵⣿⣿⣿⣟⣿⡟⣿⣙⣿
⣿⠿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠰⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⢋⣭⡝⣿⣦⠀⠀⠀⠀⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⣿⢃⣾⡿⢡⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡅⢿⣷⣥⣾⡿⣡⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⡿⣃⣬⣍⠻⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣎⢻⣿⡿⣡⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⢰⣿⣿⣿⣷⠘⠻⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣭⣵⣿⣿⣿⠟⣡⣤⣀⠀⠀⣿⣿⣿⣦⡛⠿⠟⠁⠀⠀⠀⠈⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣙⣛⣋⣭⣴⣾⣿⣿⣿⣿⣶⣝⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⣫⣥⣤⣭⡻⣿⣿⣷⡙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣡⣦⡻⣿⣿⡿⠿⠿⠟⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣡⣾⣿⣿⣿⡎⣡⣾⣿⡷⢦⡹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⠡⣿⡿⢋⣴⣿⡇⣹⣿⣿⡇⣀⣀⣀⣀⣠⠀⣠⣾⣿⣿⢡⡎⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡙⢿⣿⣿⠟⣡⡹⢶⣿⣿⠟⣡⣿⣿⡿⠐⠛⠛⠛⠛⣡⣾⣿⣿⣿⣿⣷⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣶⣾⣿⣿⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⢈⠠⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠈⠁⡐⠀⠄⠀⢀⠀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⣀⣀⡈⠀⢠⠂⠀⡀⠈⠤⠀⠀⠀⠎⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠲⠀⢸⡆⠚⠒⠓⠂⠀⠈⠀⠂⠘⡀⡀⠂⠀⠠⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠸⠆⠭⠭⠅⠀⠀⠐⠀⠁⠈⠂⡀⠁⠈⠀⠆⠀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠊⠀⠀⠴⠄⠠⠤
⠀⠀⠀⠀⠀⠀⡄⠀⠨⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠉⠉⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⡇⢈⣉⠀⢘⡁⣉⡁⠀⠐⠀⣀⢠⣄⠁⠀⠀⠀⠀⠣⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠂⡃⠀⠀⠰⠀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢈⠑⠀⠀⠀⠀⠀⠀⠀⢠⠍⠈⢅⠀⠀⠀⠀⠀⠀⠄⢄⣀⠂⡀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠌⠀⠠⠀⠆⠰⠀⠀⠰⠀⠀⠦⠆⠆⠆⠀⠠⠀⠐⠀⠈⠂⠠⠊⠊⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⡆⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠆⠐⠀⠀⡀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠄⠀⠉⠈⢀⣄⠀⣀⠀⢀⡀⠀⣀⡀⠠⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁

⡿⠟⠋⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⠀⠀⢀⠤⠾⠿⠿⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣄⣀
⠀⣠⣴⣾⠿⠋⠀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⣽⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷
⣿⠟⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠁⠀⡿⠟⠋⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣋⣽⣿⣿⣿⡿⠟⢿⣷⣶⣤⣀
⣿⣿⣿⣿⣿⣾⠉⠉⠛⠻⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢈⠍⢺⣿⡇⠀⢸⣿⠟⠉⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣠⣶
⣿⣿⣿⣿⣿⣿⣦⣤⣶⡾⠛⠃⣀⠖⢶⣄⠀⠀⠀⣤⠿⠟⠃⣰⣄⣀⣴⡾⠛⣁⠀⠛⠃⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣦⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣿⡿⠄⠀⢿⢿⡾⢛⣽⠟⢶⣴⠿⠀⠐⢋⣠⣍⣿⠏⢀⣼⠋⠑⠂⠀⢀⣬⣿⠶⢦⣤⣼⣿⠏⠁⢸⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡘⠁⡿⢣⣾⠿⠁⠰⠿⣶⠛⠋⢀⣄⣉⣿⠿⣿⣷⣾⣿⣿⡧⢠⣾⣿⣦⣄⣠⣿⣦⡾⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⣃⠀⠀⢠⣤⣉⣷⣶⣾⡿⣿⠷⣶⣤⣾⠋⠀⣉⡳⢾⠛⢍⣙⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣩⣿⣷⣶⠎⣛⢉⣩⡿⠀⠀⠤⢱⡌⠛⠁⣧⣀⢨⣶⡿⣷⣶⣀⣻⣿⣷⣦⣤⣩⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣭⠤⣿⣦⣩⣶⣿⢤⠄⠀⣻⡀⠈⣥⣼⣿⣭⠟⠻⠟⢋⣿⣿⣿⣿⣿⣿⡿⢻⣷⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣷⣿⣽⠶⣿⣉⢛⣿⣿⡟⣯⣾⠿⣿⣿⣿⣽⣯⣀⣀⠀⠀⠀⢉⣿⣿⣦⣭⣿⣿⡟⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⡳⡝⠲⣶⣬⣽⠟⠁⣠⣵⣏⡃⠺⣦⠟⢈⣿⠉⣿⣿⣿⣴⣾⣿⣿⣿⣿⡿⢷⣼⣿⣷⣾
⣋⠿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡳⠏⣧⣉⣙⣷⣶⠿⠷⣶⣾⣿⣿⣤⣙⢛⣛⣶⣿⠟⣷⣿⣽⣿⣿⣿⠻⠖⣿⣿⣷⣿⡋⠘⣿⣿