Biru laut Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠆⠀⠠⣶⡷⠀⢰⣀⣿⠀⢷⣀⣴⣄⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡱⢀⢘⠆⠀⢧⠘⢰⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠦⠀⠀⠠⠀⢰⣶⣿⠟⢀⡄⣸⡀⠈⣰⢸⡇
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠁⢀⠂⠉⠙⠈⠛⠀⢻⡇⠠⢳⢨⢻⡄
⠀⠀⠰⠉⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠄⣱⣇⣼⣾⠀⠈
⠀⠀⠀⠑⣿⡽⠷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣮⠦⡀⠀⠀⠀⠀⠀⠄⢹⣿⢄⠃
⠀⠀⠀⠀⠈⠃⠰⢿⣎⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠆⠀⠄⠠⡔⠁⠀⠈⠈⢧⡀⠤⢀⡀
⠀⠀⠀⠀⠀⠠⠉⠁⡾⢷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⠀⠀⠀⡀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠿⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡗⠠⢠⠎⣡⠏⠠⠀⠀⠀⠀⠀⠀⠀⣠⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠿⢿⡱⠄⠀⠀⠀⠀⠀⠐⠈⠃⠡⠀⢞⡜⡏⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠃⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⢶⡞⢳⣌⠢⣠⠀⠀⠀⠠⠸⠊⢀⢟⣾⣾⣆⣀⣤⣀⡀⠀⢀⠇⠀⠀⠺⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠳⣞⡽⠿⠫⢦⡀⠀⠀⣀⢴⣾⣿⣿⣿⣿⣷⣾⣿⣿⣶⡼⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠴⣏⢀⠀⠀⡏⠉⠓⣘⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡏⠀⠹⠾⠀⢸⠂⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠉⠉⠉⠛⠟⡇⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⠀⠸⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⢂⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠈⡶⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣇⠀⡅⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡤⢷⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣷⠈⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠇⠀⢻⠒⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣁⢣⠱⡀⠀⠀⠀⣀⣤⣶⣦⡀⢷⠈⡏⠰⠜⠀⠀⠀⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣊⠁⣨⠿⢮⡧⠴⠖⠂⠉⠈⠻⣿⣿⣿⣌⠀⠁⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⣘⠟⡕⢐⢾⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⠈⢰⠏⢰⠀⠸⢾⢿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢠⠤⣰⣏⡻⡤⠉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡄⠀⢠
⠀⠀⣀⠀⠀⡀⢀⠆⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠋⠄⠀⠀⢰
⠀⠀⠀⠟⠰⡇⠨⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⢸⡆⢋⠉⠁⢸
⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⠇⠀⠀⢤⣄⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠙⠂⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠜⠀⠀⠐⢂⠞⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢸
⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘
⠀⡄⠀⠀⠀⠀⠠⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⣀
⠀⠀⠀⠑⠉⠐⣤⠍⠀⠔⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠟⠫⠥⠩⠉⠛⣻⣿⣿⣛⡽⠿⠛⠛⠃⠘⠛⠛⠋⠁⠢⠶⢦⠀⠐⠒⠈⠉⠉⠁
⠀⠐⠀⠀⠀⠫⠀⠀⠀⠂⠐⠂⣀⣉⠀⡀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠈⠛⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢠⣴⣆⡀⣀⠀⠀⠀⠀⠈⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠺⠛⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠠⠄⢀⡀⠀⠀⢀⣠⠤⠤
⠀⠒⠈⢁⡉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠶⠂⡀⠀⠀⠀⠀⠀⠐⠶⠶⠾⠟⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠍⠉⠁⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠉⠁⠀⠀⠀⠀⠀⠩⠀⡀⠀⠀⠀⠀⠀⠬⠉⠉⠁⠀⠀⠀⠀⠀⠀⣶⠤⠤
⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡁⠘⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠐⠃⠈⢨⢘⡛⠁⠘⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⡅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠁⠀⠀⡀⠀⠀⢀⡞⢰⡄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⡀⠀⠀⡼⢷⠀⢸⠤⢀⣞⣴⠀⢠⠀⡂⠘⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢠⠀⠀⠀⠀⠀⠠⠀⠈⢀⠘⠀⠛⠒⠘⠀⠈⠖⠀⠀⠁⢠⠋⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⢦⠀⠀⠀⠀⠄⣴⡿⠛⠛⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣀⣤⠞⠉⢣⠀⢰⠀⢸⣿⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⢇⠀⠀⠈⢣⡄⠀⠈⢿⣷⣤⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠀⠀⠀⠨⠀⠀⠀⠀⠙⠛⠛⠉⠉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠆⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⢠⣾⡃⠀⣴⣾⣹⡆⠀⠀⢠⠄⠞⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣄⣠⠟⢹⡇⠀⡟⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢢⠀⠀⠈⠛⣶⠾⠟⠋⠀⠘⠛⠉⠁⠀⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠐⠄⢤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣠⠀⠀⠀⠀⢷⠼⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠀⠀⠀⣀⢀⠈⠀⠁⢉⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢⠀⠀⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⢹⣏⣸⠒⣸⡆⡇⣸⡄⠀⠉⠗⠀⠀⠀⠀⠀⠀⠁⠀⠹⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠄⢴⠰⠀⠈⠀⠈⠉⠀⠀⠉⠁⠉⢁⠀⡄⣆⢠⡤⢶⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⠀⠰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠇⠙⠈⠋⠸⠃⠀⠀⠀⢀⠘⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡟⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠀⠠⠀⠀⠀⣐⠦⢤⣀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠈⠙⢖⠶⣦⣤⣤⣤⡤⠤⠴⢖⠒⢐⠀⠙⠛⣹⢟⠞⠋⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣱⡟⠀⠀⠀⠀⠀⠀⠳⣝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⠕⠁⠀⠀⠀⠀⠀⣽⡗⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⡀⠀⣠⢞⡽⠃⠀⠀⠀⠀⠀⠀⠀⡇⣷⡛
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠛⠚⡿⠻⡖⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⡅

⣀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣤⠀⠀⣠⣤⣤⣤⡤
⣿⣿⣿⣿⣿⠀⢀⠀⠀⢸⣿⣿⠀⠀⠀⠿⠟⠀⠀⢶⠄⠀⢠⠀⠀⠸⠟⠃⠀⠸⠃⠀⢸⣿⣿⣿⠟⢀⣴
⣿⣾⣿⣷⣿⣿⡀⠀⠐⢸⣿⡏⠀⠀⢷⡶⠀⣿⠀⡙⠀⠀⠀⠀⠻⠿⠀⣿⠇⠀⠀⠸⠿⠁⢠⣤⣴⠟⠡
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⠀⠀⠤⣀⣠⡤⠒⠁⠀⠀⠀⠙⠦⠀⣤⠄⠘⠁⠀⠀⠀⢠⡄⢿⣿⡿⣣
⠉⢻⣿⣿⣿⡇⢰⠄⠀⠀⠛⠁⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⣠⠋⠀⠀⠀⠄⠀⠀⠀⠀⠘⣫⣾⠟
⠀⢸⣿⣿⣿⡃⢸⠆⠀⠀⢀⣤⣌⠀⢄⡀⠁⠆⠀⠖⠀⠀⠀⠓⣰⠁⠀⠠⠂⢠⣶⠆⠀⠀⠀⣀⢀⡀⠐
⠀⢸⣿⣿⡟⠁⠀⠀⠀⢀⣈⠛⢁⣄⠈⡇⠀⠰⠀⠀⢀⠀⠀⠘⠁⠀⠀⠀⢀⣄⠉⣠⣄⠀⠀⣀
⠀⠸⠿⠟⠁⡁⠀⠀⠀⠘⠻⠃⠘⠛⡠⠆⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠣⣘⠛⠁⠙⠃⠀⠘⠋⠀⣀⣠
⣤⣤⢀⡀⠀⠁⠀⠀⠀⠈⠂⠠⠤⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⠉⠀⣀⠀⠀⣀⣀
⡏⠉⠀⢀⠁⠀⢀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠄
⠇⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠀⠀⡀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠰⠶⠁⢁⣤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣴⠋⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⣴⠳⠤⢀⡀⠀⠲⠂⠈⠀⠂⠂⠀⠀⠀⠀⢀⠤⠒⠠⢠⡀
⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣞⣰⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⣠⣄⠀⠊⠀⠉⠀⠉⠀⠂
⣠⣤⣄⣀⠀⣀⣀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣶⣶⣤⣤⣧⣶⣿⣿⣿⣷⠀⠀⠀⠈⠀⠐⠀⠀⢀⡐⠢⠈
⡍⠉⠉⠻⣿⡿⠇⠁⠀⠀⠐⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢄⡐⠠⠈
⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠋⠙⠉⠙⠛⠛⠛⠛⠋⢉⠉⠹⠀⠀⠀⠀⠀⠀⠀⡟⠒⢀⠂⡴
⠀⠀⠀⠀⠀⣶⣿⠆⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣶
⠀⠀⣀⣠⠺⡍⢉⠎⣡⣾⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣆⢀⡀⣀
⠉⠉⠁⠠⠀⣠⢋⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡆⠸⠃⢀⠙
⠁⠀⣀⠀⡰⣡⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗
⣶⠿⠋⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⣂⠀⠀⣤
⠁⢀⠄⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⠀⠀⣿
⢠⠊⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡌⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿
⠃⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣾⣿
⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠷⠿⣿⣿⠟⠻⠿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⡇
⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢘⠎⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠃
⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣄⣀⣠⡀⣸⣇⣤⣤⣤⣷⣦⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈
⠘⣿⣿⣿⠃⠀⠀⠀⠀⣀⠀⢻⣿⠋⢙⣿⡋⠙⣿⡟⠻⣿⣿⠙⣿⣏⡀⣹⣯⣀⣰⣦⡀
⠀⣿⣿⣿⡇⠀⠀⢀⣴⣿⡶⠿⣿⠿⠿⣿⠟⠛⢿⡿⣾⣿⡿⠿⡿⠿⠿⡿⠻⠿⣿⠟⠻⣶
⡀⢿⣿⣿⡇⠀⢀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡀
⣿⡼⣿⣿⠃⠀⣿⣷⣤⣀⣠⣤⣤⣴⣀⣄⣀⣤⣴⣶⣿⣿⣷⣤⣀⡀⢀⣀⣤⣠⣤⣄⣰⣶⣿⣿⣿⣿⡆
⠀⠀⢻⣿⡀⠐⣿⣿⣿⣿⣯⣿⣽⣯⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤⣷⣾⣷⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢻⣿⣦⣻⣿⣿⠿⠿⣟⠉⠉⣯⣿⣿⣿⣿⠿⠛⠋⠉⠛⠿⣿⣿⠿⠟⠉⠙⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⠷⣾⠑⣾⠙⡾⠹⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⢾⡋⠹⠆⢘⡀⣿⢰⣧⢴⡀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠾⢧⡀⠙⣤⡸⣾⣷⣿⣿⣟⣷⣷⠀⣇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠻⢦⡀⠁⢶⣾⣿⡿⠿⣽⣛⣷⣿⣋⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠲⡞⠓⠦⡄⣀⡻⣷⣿⣹⠇⠀⠘⠿⢭⣟⣿⣷⡆⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡙⣿⡄⢠⡴⠟⠶⡦⣠⣍⣻⣿⠆⣾⠀⠀⠀⠀⠀⠈⠙⠷⡙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠷⣦⡹⣼⣿⣾⠿⢤⡄⢀⣙⡻⣿⣿⡇⡿⡇⠀⠀⠀⠀⠀⠀⠀⠉⢦⡉⣈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⠓⠶⣽⡿⡿⠿⢦⣤⠀⣘⣿⣿⣿⣷⢀⡷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣙⣻⣿⣿⡿⣦⣤⠀⣘⣻⣿⣿⣷⡮⢈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣴⣾⣿⣿⣦⣤⠉⠰⣿⣿⣿⠟⣃⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢁⣀⣿⣤⣈⠛⢰⣿⣿⣿⣶⣼⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣙⣿⠏⣴⣿⣿⡿⢿⣛⡯⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣤⣝⣿⣫⣾⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⢶⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣛⣿⣿⢏⣄⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣹⡿⣿⣻⣗⡳⣟⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡴⢿⣽⣿⣿⣿⣿⠷⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡏⣹⢿⡟⢿⣝⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡾⠿⠾⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠀⠂⠀⠂⠰⠆⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢺⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡐⠀⣀⣀⣠⣤⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠛⠻⢻⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣌⣀⣀⠂⣴⣿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢃⡠⣶⠟⠓⠒⠚⠁⠉⠁⠈⠉⠉⠉⠉⠈⢉⠛⠛⠋⠛⢿⡿⡿⣿⣿⣛⣿⡿⢿⠿⠛⣉⢉⡉⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠈⠥⠤⠀⠈⠌⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⠀⠀⠠⢤⣄⣀⣀⣀⣀⣀⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢠⣤⣴⣀⣸⢀⡿⣦⣤⣤⣦⣤⣴⣦⣄⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣒⣲⣤⣉⣤⣤⣄⣀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢀⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠠⠄⠙⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢀⣀⣠⣄⣀⣀⣀⣀⣀⠉⠉⠉⢙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣾⣿⣶⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⢸⡿⠉⠉⠁⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⠤⣄⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤
⠀⠀⠀⠀⠀⢠⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠟
⠀⠀⠀⠀⠀⢸⡇⠀⠘⠿⣿⡿⢟⣿⣿⠿⣿⣿⣿⠿⢿⠿⠛⠿⣿⡻⣿⣿⣿⣿⣿⣾⡿⢿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⠿⠛⠇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⡿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠭⣐⠠⣣⡙⢖⢷⣀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⠄⠀⠀⠀⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡒⠤⣑⡌⠹⡌⣧⢫⠳⡄⠀⠀⠀⠀⠸⠁⠸⠴⠄⠀⠰⠆⠴⠀⠼⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣕⠬⣑⢠⡙⠄⠀⠸⠘⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡲⠦⠍⠂⠀⠀⠀⠀⢀⠇⠀⠀⠀⣀⡰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠉⠀⠀⠀⠀⠀⠀⠚⠤⣀⠀⡸⠃⠀⠂⢺⠁
⠀⠀⠀⠀⠀⠐⠲⣐⠠⢠⣖⣒⠬⣧⣤⡤⠴⠒⠚⠢⡀⠀⠀⠀⠀⠀⠄⡰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢟⠦⣤⣈⠙⠢⣝⢯⠓⢦⡀⠀⡵⠀⠀⠀⠀⠀⠀⠐⢄⠀⢀⡠⠤⢒⡦⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠈⠉⠁⠀⠀⠑⠄⠑⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠡⠖⠚⢛⡒⢄
⠀⠀⠀⠠⢤⣶⢴⣒⡒⠒⠂⠞⠲⢦⡤⣄⣨⡁⠈⠃⠀⠀⠄⣀⠎⠁⠉⠁⢲⠀⠀⠀⠀⠀⢐⠒⠒⠦⣍⣢
⠀⠺⢶⣤⣤⣄⣘⣩⣩⡥⠀⠀⠀⣠⣼⠶⠛⠁⠀⡀⠀⠞⢮⡀⠀⠀⠀⠀⠲⠀⠀⠀⢀⢢⡲⢬⣙⠲⢦⡙⢄
⠀⠀⠀⠈⠉⠙⠒⠦⠭⢥⣄⡀⠀⢠⠤⢴⡖⠛⢹⠱⠐⠃⠤⡺⡀⠀⠀⠀⠈⢣⡆⢆⡄⢳⡙⢦⣑⠮⡑⢍⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡕⡀⠀⢀⡇⠀⠈⡁⠀⡌⣄⢈⢮⠂⠀⠀⠀⠀⠘⠼⢞⣆⠻⡢⢉⡓⠦⢥⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠊⢀⡤⠊⠀⠀⠀⠇⡀⡇⠸⡎⢦⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣊⠔⠊⠉⠀⠀⠀⠀⠀⠈⢃⢳⠐⡘⡸
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣆⢡⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡆

⠂⠀⠀⠀⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⣾⡗⠠⢃⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣿⠆⠘⢡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⠀⠸⠆
⠀⠀⠀⠀⠤⠤⠀⡀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢠⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⣠⣶⣶⠄
⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⢀⡁⠈⣈⡙⠛⡁⡀⠠⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⣀⠁⢉⣈⠛⢛
⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠀⢠⠀⠁⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡁⠈⡤⠀⠀⠂
⠀⠉⠁⠀⠀⠘⢶⡄⢠⠀⠈⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠰⣦⠀⡀⠀⠀⠰⠀⠀⠀⠀⠉⠁
⠀⠀⣠⡄⠀⢦⠀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣤⡄⠐⠦⠀⠀⢀⣀⠀⠈⠀⠘
⠀⠀⠈⠁⠀⠀⠈⠀⠘⠛⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠈⠀⠀⠀⠀⠘⠛⠀⠀⢠
⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢁⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠿⠟⠀⢀⡴⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠐⢿⠇⠀⢠⠶⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠐⠀⠀⠘⠇
⠀⠀⠀⠀⠠⠤⠀⡄⠀⠀⠒⠈⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢰⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢂⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣶⠄
⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⢀⡁⠨⢠⡙⠉⡅⠀⠠⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⣀⠁⠩⣨⠛⢩⠀⠀⠄
⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣈⣀⣰⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣁⣀⣴⣀⣀⣂⣀
⣿⣗⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⢀⣠⣴⣾⣿⡿⠿⠛⠒⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⢀⣀
⣾⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋⠀⠀⢸⡇⠺⠃⡀⠙⣆⠀⢃⡀⠱⡟⠛⠃
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠀⠛⠋⠉⠀⠘⠃⠀⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢠⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣶⡀⣏⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠻⣧⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠠⣶⣦⢀⣤⡀⠠⣤⣶⣦⠀⠀⣤⠀⡄⠀⣶⡴⣶⡄⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠿⣇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠠⣤⡀⠀⠏⠹⢦⣽⣇⣀⠀⠼⠉⡿⠃⢠⣿⢤⣤⡀⢈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣦⠀⢸⣿⣿⣿⣿⣿⠛⣿⣧⡀⠀⠀⠀⠀⠀⠶⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⣸⠋⢀⡟⠛⠿⢿⣿⣿⣿⢿⣿⣿⣄⠀⠀⠀⠀⠀⠾⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⣿⠀⢸⣿⣦⡀⠸⢻⣿⠃⣸⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⠀⠀⢻⡆⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖
⠀⠀⣾⠃⠀⣼⣿⣿⣿⣦⠾⠿⠻⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⡦⠀⠘⠁⠀⠀⣤⣤⣮⣠⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠐⠒
⠀⠀⠉⠀⢠⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⢨⣿⣿⠿⣿⡆⠀⠀⠀⠀⡄⠀⢸⡇⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⡟⢛⣿⣿⣷⣿⣿⣇⢀⣈⣿⡀⠀⠀⢰⣷⠀⢸⡇
⠀⢰⣶⠀⢸⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⡟⠛⢿⣷⠀⠀⠀⣿⡀⢸⣷
⠀⠈⡟⠀⣾⣿⣿⣧⣬⣿⣿⣿⣿⠟⢸⣿⠃⠻⠟⠀⠰⣿⠀⠀⠀⢿⢿⡄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠐⠇⢸⣿⣿⣿⣿⣿⡿⠿⣿⠁⠀⣸⣿⣷⠀⠀⣠⣴⣿⣷⠀⠀⠀⢸⡇⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⣸⣿⣿⡿⠋⠁⠀⠀⠀⠀⢀⣿⣿⣿⣷⣄⠀⢹⣿⣿⡄⠀⠀⠉⢀⣶⡄⠀⠆
⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠙⢻⣷⣼⣿⣿⣿⠀⠀⠀⢸⣿⠁
⠀⠀⢸⣿⠁⡤⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⢙⣛⣿⣿⣿⠀⠁⠀⠘⡟⢳⡀⠀⢠
⠀⠀⢸⣿⣿⢇⡀⠀⣰⠀⠀⠀⠀⢻⣿⣿⣦⣤⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⣷⣌⣁⡀
⠀⠀⢸⣿⣧⣸⣇⣼⣿⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣿⣿⡾⢂
⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡄⠀⠀⠘⢿⣿⣃⡀
⠀⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣷⣶⣿⣿⡟⠀⣿⠀⣺⣿⣿⣿
⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢋⣉⣤⣿⣾⣿⣿⣿⣿⡧⠛⢻⡀⢻⣄⢹⣿⡿⠃⠀⠀⠻⢦⡄
⣿⣿⣿⣿⣷⣶⣶⣶⣷⣶⣾⡿⢿⣿⠿⠿⠛⠛⠻⠋⢻⣿⣷⣶⠛⠁⢰⣿⣻⣿⡷⠀⠀⠀⠀⠀⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣹⣯⡉⢿⣏⠉⠉⣹⣯⣿⣄⣀⠀⢀⡀⠀⠀⢠⣄⡀⠀⠀⠈⣡⡦⠀⣾⣿⣿⠟⡀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⣿⣿⣶⠄
⠀⠈⠁⠀⠙⠇⠘⠿⠛⢿⣿⣿⡿⠟⠀⢀⣼⣿⠟⠁⠀⠀⣴⣿⣇⣰⣿⡿⠃⢸⣿⣀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠀⠉⠛⠁⠀⠂
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠉⠁⠀⠀⠈⠛⠁⠀⠀⠀⠀⠛⢻⠿⣿⣿⠃⠀⠀⠀⠉⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⢀⣴⠀⠀⢸⣿⢹⣿⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠀⠀⠀⣤⣤⣶⣦⠀⠀⠘⠃⠀⠀⢈⣿⣿⠟⠀⠀⠀⢤⡀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠃⠀⠂⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⣼⣿⣀⣀⣴⣾⣇⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿
⣀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣴⣷⠀⢰⣿⣟⣷⣄⣀⣀⣀⣽⣿⣿⣿⣽⣾⣿⣧⠀⢿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠻⣿⣿⡇⠀⠘⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣯⠀⢾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠉⠀⠀⠀⠀⠀⢀⣤⣴⡎⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣛⡀⠺⠿⠋⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⣼⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠉⠀⠀⡀⠰⠗⠀⠀⠀⠀⢠⣶⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢼⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⢿⣦⠀⠀⠀⠀⢿⣿⣿⣿
⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢹⣿⠀⢻⣿⣿⣿⣿⡟⢠⠜⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠃⢠⣶⣆⣿⣿⣿⣿
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠺⣿⠀⢰⣿⣿⣿⣿⣿⠈⠀⠻⣿⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⣤⣤⡶⠏⣀⣸⠿⣿⣿⡿
⣿⣿⣿⣿⣀⣠⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢰⣆⡻⠗⠀⢀⣄⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⢀⣴⣦⣰⣿⣿⣶⣾⣿⣷
⣿⣿⣿⣿⣿⣧⣴⣤⣴⣾⣿⠇⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⠀⣠⡜⠁⠀⠈⣿⣿⡇⢿⣇⡀⠀⠈⣿⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⣿⠛⢡⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣟⣷⣿⣿⣦⡀⠒⠀⢠⣤⠚⢛⣿⣿⣷⣾⣿⠇⠀⠀⠀⢿⣿⡇⢸⣿⣷⡄⠀⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠉⠀⠴⢯⣤⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣿⣶⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⠷⠈⣿⡟⠁⠀⠹⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢦⡼⠛⠛⠋
⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣡⣧⠀⣴⣆⠀⢻⣶⣬⣿⣷⠀⠀⣴⣧⠀⠀⣶⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⢶⣦⡜⠁⠀⢀⡀
⠿⣏⣉⣡⣤⣬⣯⣭⣭⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⡆⠘⣿⣿⣿⡏⣀⡀⠘⣿⡄⠀⠈⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣇⠘⠻⠛⠁
⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⢹⡇⠀⠹⡁⣩⣿⠋⠛⠀⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠀⣸⣿⣿⣷⣤⡀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⡜⠛⠀⢀⠙⣿⣿⣦⠀⠀⠘⣷⠀⠀⢀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠤⠀⠀⢹⣏⣨⣷⣤⠈⣾⡟⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢷⡀⠀⠸⠇⣿⣿⣿⡆⠀⣾⣿⡄⠀⢸⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⠀⠀⠘⢿⣿⡿⠷⣀⣿⣿⣿⣧⣦⡈⢻⣿⣿⣿⣿⣿⣿⡻⠿⠟⠉⡄⠀⢡⡄⢠⣷⡟⢻⣿⡇⠀⠿⠟⠁⠀⣼⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⡄⠀⠸⢿⣿⣿⣿⠟⢻⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⠃⠀⠘⠃⠘⣿⣥⣼⣿⡟⡀⠀⠀⠀⠀⠘⠗⠀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠋⠀⠀⠀⢸⣿⣿⣧⣀⣀⠀⠛⠛⠀⢸⣿⣿⣿⡟⣿⣿⣿⡷⢀⡀⠀⡆⠀⣄⠀⢿⣿⣿⣿⣿⣿⡀⢠⣾⣆⠀⠀⠀⢸⣿⡆⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⡀⢀⣀⠀⠀⣿⣿⣿⡷⢼⣿⣿⣇⣻⣿⠀⠁⠀⢹⡄⠈⢻⣿⣿⠛⣿⠇⢸⣿⡟⠀⠀⠀⠀⢙⣁⣰⣿⣟⢉⣻⠟⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⠛⠋⠀⠀⢿⣿⣿⡇⠘⢿⣿⡟⣿⣏⠀⠀⠀⢸⣿⠀⢸⠏⣿⣇⡁⠀⣸⣿⣧⣀⡀⢠⠀⠘⠟⠋⠻⣿⡟⠉⠀⠀⠀⠙⠛⣿⣿
⠀⠀⠀⣴⡆⠀⠀⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠉⠉⠀⠀⠘⣿⣷⠿⣟⠀⠀⠀⢸⣿⡇⠀⢰⣿⣿⣷⢸⣿⣿⢿⡿⠃⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⡀⠀⣸⣿⡧⠀⢀⣿⣿⣿⣯⣀⣴⣶⣄⣀⠀⠀⠀⠀⠀⠀⠙⣿⣾⢻⣆⠀⡄⢸⣿⣄⠀⢸⣿⣿⣿⡿⣿⣿⣿⣷⣬⣭⡀⠀⢀⡀⠀⠀⢀⣤⣀⠀⠀⠀⣀⣀⣿
⠇⠀⠉⠁⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣀⠀⠈⢿⣇⠀⠻⢿⠿⠛⢲⣿⠋⠙⢿⡟⠉⠀⠀⠀⠀⠰⠖⢸⣿⢻⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠻⣿⠟⢿⣿⡄⠀⠀⠀⢠⡀⣠⣿⣿⣿⣿⠛⡄⠀⣾⡟⠀⣰⣾⠀⠀⠀⠟⠀⠀⠀⠁⠀⠀⢠⣄⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠁⠃
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡣⠠⢄⡄⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢰
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠎⠲⢈⡢⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠠⢤⠶⠀⠀⠀⠀⠀⠀⠘⡄⠙⠉⠀⠛⢀⡄⠀⢼⠛⠀⠁⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠘⠐⣃⢀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠉⡀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠌⠀⠀⠀⠙⢄⢀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠰⠄⠀⠀⠀⢀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⢀⡀⠀⠀⢐⠁⠀⠀⠀⠀⠀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠄⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠈⠀⠀⠚⠗⠡⠀⢁⠨⠤⠲⡆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠠⠄
⡂⠀⠀⠘⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠄⡀⠀⠀⠀⠀⡄
⢀⢉⡥⠂⠒⢀⠻⠎⠓⠒⢄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠁⠈⠀⢀⠤⠐⠁⠁⠀⠀⠀⠀⠀⠄
⠉⠘⠟⠐⠀⠘⡅⠀⠀⠀⠈⠂⠤⠔⠁⠀⠢⣀⠀⠀⣀⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠉⠁⠀⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠠⠒⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠦⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠑⠄⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡂⠀⠡⠂⠀⠄⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⠄⠞⠂⡑⢄⠀⠀⠀⠀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠈⡀⢀⠀⠀⠀⠀⠘⢄⠁⠀⠀⠀⠈⠢⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⠄⠈⠕⠀⠀⠀⠀⠀⣬⡤⠴⠓⠀⡐⠀⠀⠠⠑⠀⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡑⢄⠂⠀⠀⢈⠢⡀⠢⡑⣌⠢⣀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣦⠀⠊⠁⢈⣣⡚⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠁⠁⢀⠀⠋⠜⠂⠈⠑⠶⠈⢢⡄⠀⡀⠤⣖⡱⠐⠀⠀⢀⠀⠰⡣⠀⠀⠨⠓⠁⠀⢀⢘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⢌⠢⢃⠂⢄⠈⠀⠀⠒⠲⠦⣤⣤⠖⠋⠁⠰⠂⠁⠘⠛⠛⠃⠁⠀⠀⠁⠘⠁⡤⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢡⣌⠓⡀⠄⠐⣊⣤⠗⠋⡙⠦⢰⢤⠂⡿⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡆⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠜⢋⡡⠶⡛⠁⠀⠀⣚⣅⢀⡉⡆⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⢻⠀⢸⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠡⠂⠀⠀⠀⠢⡙⢯⠀⠈⠁⠀⠀⠀⢠⣘⣇⠀⠀⣠⣤⡀⠀⠀⠀⠌⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠄⠀⠀⠀⠰⡏⠀⠀⣹⣿⠁⠀⢙⣷⣤⣤⣤⣤⡞⢠⠍⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠁⠈⠑⠒⠛

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

⠀⠀⡄⠀⠰⠂⠀⠀⠂⠀⢀⣀⠀⠀⠀⠄⠲⠀⠀⠀⠀⡀⠀⣠⠆⠀⠀⠆⠀⢀⠀⠀⢀⠀⠀⠀⠰⠀⠀⡠⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⡀⠁⠀⠀⠁⠓⠀⠀⠁⡄⢀⠆⡰⢡⣷⣊⡄⠀⠔⠀⢀⠀⠀⠀⠄⠈⠀⠐⢤⣄⠀⠀⠀⠐⠈⠁⠀⢀
⠀⠀⠈⣄⡠⠁⠀⠀⠉⠀⠃⠀⡄⠀⡇⢰⠃⠈⢠⣶⡪⠥⠂⠀⠃⠀⠠⠀⠐⠀⠀⠔⠠⠠⠄⠀⠀⠉⠓⠤⡄⠀⠀⠀⠉
⠀⠈⠁⠀⠁⠀⠠⠤⠀⡀⢰⠀⠙⠸⠀⡀⢠⣶⠋⠄⠄⠒⠂⠐⢁⠀⠀⠀⠠⠆⠀⠀⠀⠠⣠⠎⢀⠀⠀⠀⠀⠺⢆⠀⠈
⠈⠀⣄⠀⠀⠀⠀⢰⠀⡇⠈⠀⡆⢸⡰⠷⠇⠀⠀⠀⠒⠒⠀⡀⠀⠀⢀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠀⢠⠂⠘⠃
⠀⠀⠀⢄⠀⡆⠀⢀⡀⠀⢰⠀⣧⣈⣉⠓⠂⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠠⠀⢀
⠀⡀⠰⠸⠀⢇⠀⠀⡇⢻⣘⠁⠀⠀⠀⠁⠀⠉⢉⡁⠀⣀⠀⠀⠄⠀⠀⠀⠀⠟⠂⠀⠀⠐⠀⠀⠀⠈⠂⠀⠀⠀⠂⠐⣄
⠀⠓⠀⠀⠀⢸⠀⠀⠣⠤⣬⡉⢀⠁⠒⠦⠄⠀⠞⠙⢦⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⣇⠘⣤⣘⣓⠒⠂⠠⠤⣈⠛⢂⡤⢨⢥⠛⡀⣁⠐⠆⠀⠀⠀⢀⠆⢀⠀⠀⠊⠀⠀⠐⠒⠀⠀⠿⠄⠀⠀⠀⢁
⠀⠀⠀⠀⠐⠓⠒⠀⠠⢄⣈⡑⠂⠀⠀⣉⠝⣇⠈⠆⠁⣨⠀⠘⠃⠈⡡⠄⢀⠀⠀⠈⠀⣀⠄⠀⠀⠀⠛⠀⠑⡄⠀⠀⠈
⠀⡠⠂⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠈⠁⠀⢠⠀⠺⠀⠀⠀⠀⠀⠼⠃⠈⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐
⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠘⠀⠘⠀⠀⠀⡠⠚⠀⠀⠀⠀⢀⠠⠋⢀
⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣢⡄⠉⠀⠀⠀⠀⠄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⣰⠦⠤⠄⠀⠀⠀⠤⠀⡀⠄⡀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠈⠁⣀⠜⢏
⠀⠀⠀⢀⣀⠄⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⡜⠓⠀⠂⠀⢀⣀⠐⠀⠐⠃⢀⡠⠀⢰⠀⠁⠀⢀⡠⠀⠀⠰⠀⣠⠒⠀⠘
⠠⠤⠒⠊⠉⠀⠀⠈⢀⠀⠈⠀⠐⠄⠀⣴⣋⡁⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⠔⠋⠀⠂⠀⠔⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠂⠀⠀⠰⠯⠀⠀⠀⡀⠀⡋⠀⠀⠂⠀⠀⠱⠀⠀⢠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡲⠄⠀⠰
⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢣⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠦⡀⠀⠊⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠜⠊⠀⠀⡀⠀⠀⢀⠔⣴⣾⣿⣿⡿⣿⣿⣿⣿⣷⣦
⠀⠀⠁⡀⠀⣐⠆⠂⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠡⠐⠀⠊⠀⠀⢆⠀⠀⠈⡠⠀⠁⢸⣿⣿⡿⢿⡷⣿⣿⡿⣿⢿⣿
⠀⠀⠃⠀⠀⠀⠿⠰⠙⠀⠒⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⢸⣿⢸⡇⣻⡇⢹⠃⡆⣿⡸⣿
⠀⠀⠀⢀⠠⠊⠀⠄⠀⠀⠀⠀⠀⢠⠀⣤⢀⣀⣐⠀⠀⠀⠀⠀⠀⠈⠁⡠⢐⠊⠔⠃⠀⠘⣿⣼⣧⣻⣴⣾⣴⣇⣿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⢆⠀⠀⠀⠀⠀⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢃⠀⠀⠀⡸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠁⢸⠀⠀⢠⡇⠀⡀⠀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢰⡄⡏⠀⠀⢸⠀⠀⡇⠀⣿⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠻⣅⠀⠀⠸⡆⠀⠁⠀⣿⠀⢠⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠸⡇⠀⠀⠡⡈⠓⠲⠤⠷⡀⢀⠰⡏⡆⠸⡀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠁⠀⠀⢧⠀⠀⠀⠹⣦⣄⣀⡀⠀⠀⠈⠃⡘⣄⢳⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⠀⠀⠀⠈⢧⠀⠁⡀⠘⢦⡉⠉⣏⠙⢦⠀⠐⠈⢦⣇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠣⡀⠀⠀⠀⠱⢄⡈⢀⠀⠱⡄⢹⠀⢸⠇⢠⣦⠀⠙⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠢⣀⠀⠀⠀⠙⠲⣄⠀⢳⡼⢀⠞⢀⣞⣠⠗⠁⠐⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠉⠒⠒⠒⠢⢌⣆⡼⠟⡩⠐⠉⣁⣤⣴⡿⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⡀⠀⡟⢀⣾⡵⠊⢁⡠⠤⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢚⠋⠉⠉⠉⠙⣧⢸⡧⠚⣁⣉⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠑⢀⠀⠀⠀⠈⢇⠀⠀⠀⢈⡧⠔⠖⠚⠶⠶⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⡀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠲⠤⠤⢤⣤⣤⠶⠋⠙⠲⠤⠤⠤⢤⣄⣀⣀⣠⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⢿⠛⡟⢿⡟⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⢌⠀⠰⡘⢃⠀⠀⠋⣰⠟⣱⡿⣻⣿⡟⠀⠀⣰⣿⣿⣿⣄⠀⠘⢀⢀⡄⠐⣶⣌⣿⣿⣿⠿⠟⠋⠁⣿
⡮⣑⣇⠀⠀⠈⠀⠀⠘⠃⠀⠋⣈⣼⣿⣀⣀⣀⣿⣿⣿⡻⡿⢷⣦⠀⠳⣿⣶⣾⣝⣿⣿⡇⠀⠀⠀⠀⠻
⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⡿⣿⡝⢿⡄⠈⡯⠳⠀⠀⠉⠛⠿⢿⣿⡏
⠀⠉⠢⠄⣈⢦⡀⠀⠀⠀⠠⠒⠁⠈⣦⣍⠙⠻⣷⠈⢿⡄⠀⠀⠀⠀⠤⠀⠀⣠⣄⠀⠈⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⢦⣄⡀⠀⠘⢯⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⢙⣧⣤⣄⣠⣼⣿⡿⢷
⠀⠀⠐⠂⠀⠀⠀⠀⠀⢠⣐⡽⠃⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠲⢿⣿⣿⡷⢞⡫⠅
⠂⠀⠀⠀⢐⣤⠀⢀⢨⣦⣿⡆⠀⣠⣶⣬⡄⣀⣀⠀⣀⠠⠔⠒⡫⠉⠁⠀⠀⠀⠀⠈⣉⠭⣭⡶⠋⢴⣿
⣴⠋⠀⡄⢹⣿⣦⣇⢿⣿⠟⠀⠀⠒⠂⢀⡬⢔⣈⠝⠀⢀⠀⠎⠀⠀⠀⡀⠀⠀⠸⣿⣿⡿⠋⠀⠀⣰⠟
⠇⣀⣴⣃⢀⡉⠙⠛⠈⠁⠀⠀⠀⠀⠐⠻⠶⠿⠟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠦⡄⠀⠀⣼⡇⣿
⣾⣿⣿⡿⡼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⢠⢀⢠⣀⡄⠀⢧⡀⠀⣿⠀⠀⠘⠛⠛
⠟⠸⠁⠃⠀⣿⣿⠀⠞⠙⠙⢣⣶⣶⣤⣀⠀⠀⠀⠀⠀⢿⢏⡿⣿⢸⡘⣿⠷⣦⢲⣽⣷⣾⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠍⠁⠀⠤⠤⠞⠫⠪⠫⣾⠇⠀⠀⠀⠀⡀⣤⣾⣷⢿⠜⠗⠀⠀⠘⢷⣗⣽⠇⠀⠀⠀⠈⠻
⠀⢀⠀⠀⠀⢀⡀⠀⠀⠤⣤⣾⠛⠉⣟⢿⡗⣄⡀⣠⡹⡌⣇⣿⣾⣦⠀⠀⠀⠀⠀⠀⣈⣠⠤⠀⠐⠂
⠀⢸⡇⡀⠀⠀⠀⠀⠀⠐⣛⣛⣡⣴⣷⣿⣛⠌⠻⢿⣷⠸⠸⢹⡿⠏⠀⠀⠀⢀⣤⣾⣿⠋⠙
⠀⠀⡇⠈⢢⠀⠐⠶⣬⣴⣒⡶⣶⣖⢰⡀⠉⠳⡄⠈⠁⠀⠀⠈⠃⠀⠀⠀⠸⡿⢏⡝⠁⣀⡍⣀⣠
⠀⠀⢡⠀⠈⠂⠀⠈⢺⣿⣿⠝⠛⠉⠈⠳⠦⠀⠀⠀⠀⠠⠀⠀⠀⡔⠁⠀⣘⢤⠩⠂⡴⢶⣞⣉⡀
⠄⠀⠞⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦⠀⠀⠀⠀⠀⠘⣀⠴⠊⠀⠀⠠⢀⣀⣠⡿⠋⣠⢀⣼
⠄⣶⠀⢷⢹⡿⠀⣀⣴⣿⣦⡀⠀⠀⢠⡿⠭⢉⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠛⠻⢿⣵⣾⠷⠟⠁
⢸⡟⡄⠀⠻⢁⣾⡟⢸⣿⣿⣧⣀⣠⣤⣿⣿⣿⡦⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠿⣦⡀
⠎⣿⠡⠄⠠⡿⠘⠁⠼⠿⢻⡿⢿⢿⢿⣿⠛⠻⠿⢿⡕⣠⠞⠀⠀⠀⠀⠀⠀⠻⣦⡈⠿⡿⣷⣶⣶
⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣦⣄⣹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠇⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢿⣾⣿⣿⡿⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠋⠉⠁⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣾⣿⣿⣿⣿⠂⠰⣿⣿⣿⣿⣿⣿⣿⣿⠛⣒⢒⡘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣦⣤⠼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⣴⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠸⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡏⠀⠀⠻⠋⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⠀⠠⢄⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⠀⠀⡀⠛⣍⠈⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠄⠀⠀⠀⠀⠀⠀⢢⡀⠘⣿⠁⠀⠔⠁
⠀⠀⠀⠀⡀⠀⠀⠸⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣿⠁⠁⠀⠊
⠀⠀⠀⠀⠙⠀⠂⠠⢸⡂⠠⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⣿⡤
⠀⠀⠀⠀⠀⠂⣀⠀⠌⣇⢀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠚⠲⠒⠓⠚⠀⠛⠒⠓⠒⠒⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠠⡀⢠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⠀⣸⠅⠀⠀⠀⢤⠠⠀⠙⠀⠀⠁⠉⠃⠀⡀
⠀⠀⠂⠀⠀⠀⢲⡆⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠃⠀⠀⠉⠀⠀⠀⠳⢤⡄⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠠⠤⠤⢴⣾⡿⠃⠈⠉⠂⠀⠁⠀⠀⠀⢠⡼⠄⠀⠀⠀⠀⠀⠈⡓⠀⠈⠈⣙⡦⣄⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⠐⠉⠹⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣭⣭⣭⣥⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⢸⣿⣿⣿⣿⣷⣿⣟⣿⠿⠿⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⠿⠿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⢩⣿⡿⠹⣆⠉⠉⠙⢿⣷⣄⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣸⣿⣧⡀⢹⣆⠀⠀⠀⠹⣿⣦⣬⣍⣿⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣧⣄⣿⣿⣷⣶⣦⣽⣧⠀⠀⡴⠿⠛⠛⣿⣿⣿⣿⣿⡛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢫⣾⣿⣿⣿⣿⣿⣿⣇⡈⠙⢿⣆⠀⠀⣠⣶⠟⢻⣿⣿⣿⣷⣿⡄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣼⣿⣿⣿⣿⣿⠿⣍⠙⢿⣄⠀⠻⣆⠰⠏⠀⡴⠁⢻⡏⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣿⣿⢹⣿⠀⠘⢦⠀⠙⠀⠀⢹⡆⠀⣼⠁⠀⣿⠀⣼⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠈⢹⡇⠀⢿⡆⠀⠈⢧⠀⠀⠀⠀⣿⠀⡇⠀⠘⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠙⠀⠀⠘⣇⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠙⠶⣶⣦⣄⠀⢀⣤⢀⠀⠀⠀⣀⣨⣥⠴⢖⣄⣀⣀⣻⡄⠀⠀⣿⠀⣧⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠒⠻⠿⠿⠿⠟⠛⠛⠋⠀⠐⠋⠉⠉⠛⠉⠉⠀⠀⠈⠉⠁⠀⠀⠈⠀⠉⠉⠹⡇⠀⠀⣽⠉⡿⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢾⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣠⣄⠀⣠⣤⣠⡄⢀⣤⣿⣀⣠⣾⣿⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣿⡿⠍⠉⢉⣉⣛⣛⣻⠿⠿⠟⠙⠙⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣤⣴⣦⣤⡄⠀⠀⢐⠒⠒⠂⣀⡀⠀⠀⠀⢀⣰⣾⣾⡆⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⣠⣾⣧⣠⠂
⠀⠘⠿⠿⠿⠿⠇⠀⠀⠘⠀⠀⠣⠀⠀⠀⠀⠻⡿⠛⠻⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠄⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾
⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠀⠀⠀⠚⠁⠟⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣾⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠠⢨⡂⠀⠀⠀⠀⢸⡇⣶⣿⣿⠀⠀⠀⠀⠀⣠⡺⠟⠁
⠀⠀⢹⣿⣾⡿⠀⠀⠀⠀⢠⢏⠷⡄⠀⠀⠀⠈⣇⣻⣿⡟⠀⠀⠀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⡦
⠀⠀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⡇⢥⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⣛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣖⣫⠭⠵⠼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢲⡄⣿⠁⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣒⣲⣾⣧⡿⠀⠀⠀⢀⣀⣸⣧⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⢀⣀⣿⡷⠶⢞⣛⣉⣉⣀⣀⣠⣤⣤⣤⣤⣤⣤⣽⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣰⡏⠉⣟⣛⣉⣩⣭⣭⢤⢤⢴⢶⢶⣶⣶⣶⣶⣶⣶⣦⣤⣭⣭⣉⠙⡇
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠶⠖⠒⡛⠋⠉⢹⠇⠀⡿⠷⠷⠓⢛⣛⣛⣋⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣙⣛⣛⣤⠇
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣁⣁⣬⠤⠤⠖⣒⣿⢀⠉⡟⢛⣛⣉⣉⣉⣭⣥⢤⡤⣤⢤⡤⡤⡤⣤⢤⢤⣤⣤⣭⣽⡇
⠀⠀⠀⠀⠀⣯⣭⣭⣶⠶⠶⠶⠾⢟⣛⣛⡿⠀⠤⣿⢹⡏⡇⢸⣀⣇⣸⣸⣇⣿⣸⣤⣧⣇⣿⣸⣸⣯⣧⠷⠿⠗⠒⠲⣦⡀
⠀⢀⣤⣴⠚⠓⢒⠒⡈⠉⢉⡉⣉⠉⠀⠠⠀⠆⢀⡟⠚⠛⠋⠉⢉⣉⣀⣤⣤⡤⠶⠶⠒⠛⠋⠉⠉⠀⠀⠀⠀⣀⣀⣀⣎⣿⠆
⠀⠘⠦⣤⠤⠥⠬⠤⠥⠤⠤⠶⠶⠖⠒⠒⠛⠉⠉⠙⠒⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⠚⠋⠉⠉⣀⣸⡿⠃
⠀⠀⠀⣇⣀⡀⠀⠀⠀⠀⠠⠐⠀⠀⠂⠀⠀⣀⣁⣈⣀⣠⣤⠤⠤⠴⠖⠒⢚⣉⣉⣉⣤⠤⠤⠶⠖⢾⣿⡿⠉⠉⠉⡿⠁
⠀⢀⣀⢸⡟⠛⠻⠿⠭⠭⠯⠭⠭⠭⠭⠭⠭⠭⠥⠶⠶⠒⠒⠒⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠣⡈⢯⣀⡄⠀⢸⠇
⠈⠉⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡿
⠚⢉⣓⣢⣾⣻⡶⠲⢶⣤⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⢤⣤⠖⠢
⠚⠁⠀⠈⠑⠤⣀⢀⡞⠙⠳⢖⡲⠶⠋⢉⡽⠿⠭⣭⣽⠛⠳⢶⣒⠒⢒⡶⠶⣖⠒⠲⠲⡶⣶⡒⠒⠒⣺⠿⢭⣿⠛⠳⣤⣀⣀
⠀⠀⣠⢤⣀⡀⠀⠉⠀⠀⠀⠀⣉⡓⠒⠋⠀⠀⠀⠀⢈⣉⠒⠒⠚⠛⠛⢀⡀⠈⠓⠶⠴⠇⠀⠉⠳⢬⣍⣽⠂⠈⡦⠦⣄⡉⠁
⠉⠉⠁⠀⠀⠈⣉⣉⣐⠒⠒⠚⠉⠉⠙⠲⠤⢤⣀⡠⠞⠉⠉⠓⠲⠤⢤⠜⠉⠙⠒⠤⣄⣀⣠⡟⠑⠲⠤⣄⣀⠴⠃⠀⠀⠙⢦
⠀⢀⣠⣴⠖⠋⠁⠀⠈⠉⠑⠲⠤⣀⡀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠙⠒⠲⠤⢄⣀⡀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠙⠒⠲⠤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠿⡻⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⠉⣨⣴⣿⣿⣿⣿⣿⡟⢿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣶⣼⣾⣷⡟⢩⣿⣿⣿⣛⢛⣭⣿⠎⣉⡠⢧⡃⠉⢻⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⣟⣟⣭⣭⣽⢻⣬⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣭⠤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠁⢁⣬⣶⣿⣿⣿⣿⣿⢿⣯⢿⣿⢿⣿⣿⣦⡥⢿⣿⢿⣿⣿⣿⡿⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡟⣼⣿⣿⢿⣹⣿⣟⣻⣿⢹⢿⣿⣿⣿⣿⢸⢻⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠷⣼⣿⣿⣿⣆⣻⣿⣿⣖⢿⡜⠘⠏⢹⣿⣿⣌⡀⠀⠹⠛
⠀⠀⠀⠀⠀⣼⠿⠟⠏⠈⢠⣿⣿⡝⠯⡧⢹⣿⣯⡓⠸⣷⠀⠀⠏⢿⢿⡓⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡿⡝⠆⠀⢸⣿⣦⡉⠀⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠑⠈⠀⠀⠀⠻⠇⣩⣶⣿⡝⢿⣿⡿⣶⣤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⡿⣫⠵⢿⣹⡇⠀⠀⠹⡄⢹⠷⠄⠀⣀⣙⠿⣔⣲⣤⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠛⠛⣿⣷⣾⣖⣲⣤⣄⣿⡗⠛⠛⠓⠂⢲⣶⡼⠶⢦⣸⣷⣶⡿⠿⠿⠿⠛⠛⠛⠻
⠀⠀⠀⠀⠛⠉⠛⠒⠒⠒⠚⣁⣤⣤⠤⠤⠌⠈⠉⠒⠒⣿⡇⠉⢁⣷⡆⢠⠈⣡⠈⣋⣉⣣⠤⠴⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡾⢸⢻⢃⣮⢞⢥⠀⠠⠤⠭⣭⣿⣿⣯⣈⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣬⡏⢀⡟⣯⣈⣬⡃⢻⣾⣯⣀⠀⠐⣾⠿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠊⠉⢛⡽⠋⠋⠀⠸⠘⠹⠉⠳⠈⠙⠛⠿⠿⢽⣿⠿⠿⠓⠒⠓⠂

⣄⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⣻⣷⣷⣾⣷⣿⣾⣷
⣿⡿⣡⡶⡠⣂⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡽⡿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⡉⠫⡽⣙⠛⢿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣝⢧⠙⢄⠙⢆⠙⢜⣧⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠋⠁⢹⣿⣿⣿⣿⣿⣿
⣯⣍⢷⡍⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠘⠁⠀⠀⠀⠘⠋⢻
⠙⠛⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣁⣤⠤⠤⠤⢤⠈⣠⣿⣀⠘⢱⠙⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠀⠀⠀⠀⣀⣀⣀⣀⠀⡔⠛⢛⣟⠀⢸⡇⠀⡀⠀⠀⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⡀⠀⠙⠉⠁⠀⢀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⢿⣣⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠠⠀⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠄⠐⣒⠨⣽⠁
⠀⠀⠀⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢯⣤⣴⣦⠘⣿⣿⣶⠶⠂⠠⠀⠀⡄
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠥⠀⠀⡀⢀⣀⠄⠃⠀⠀⢀⣠

⠀⠀⠀⠀⠀⢀⡀⡠⠐⣲⣷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⠭⠁
⠀⠀⠀⠀⡴⠛⣻⣟⣿⣡⢾⠏⠚⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣷⠏⣯⡉⠀⠀⣠⣶⡒⣂⣤⣤⡀
⠀⠀⠀⠀⠀⢸⠟⠹⠓⡹⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⡙⢀⠀⠀⠋⠘⢷⠈⠋⠗
⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⡀⠀⠑⠠⡀
⠀⠀⠀⡠⠃⠀⡠⠋⠀⠤⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡈⠑⠀⡀
⠀⠰⠞⢁⣴⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠗
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⢿⠿⡿⡿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⣀⣀⣀⣀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠀⣠⠖⠋⠉⠀⠀⠀⠉⠛⢦⡀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣠⠖⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣀⡀
⠀⣠⠴⠶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠶⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠙⠲⠤⢤⣤⡤⠴⠞⢉⠀⠀⠈⠉⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⢶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⡀
⠀⡇⠀⠀⠀⠀⠀⠠⠤⠤⠀⢀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣀⣠⡿⢏⠉⠈⠉⠉⢳⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⡇⢀⣰⣿⣿⠁⠀⠘⣶⢶⠆⠀⢸⠳⣄⠀⠀⠀⠀⠀⠉⠛⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⢀⡠⠊⠀⡞⠍⠀⠈⢁⣀⠤⠀⡴⠋⠀⠀⢸⣀⡤⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⢀⡴⠋⠀⠀⣼⠉⠒⢲⠤⢠⣤⠤⠊⠀⠀⠀⠀⠹⡍⠀⣀⣤⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣧⣴⠾⣏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣠⠄⠹⡞⠉⠁⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠳⢶⣤⡀⠀⠀⢸⡇
⠀⡟⢳⡄⠈⠓⠶⠦⠤⠤⠤⣬⡙⠂⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠈⠉⠀⠉⠀⠀⠀⠈⠙⠛⠲⢾⡇
⠀⡇⠀⠙⢦⡀⠀⠀⠀⢀⣠⠴⠛⢆⠀⠀⠒⠊⠁⠀⠀⠀⠀⣀⣤⠴⠶⠛⠦⣄⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⣰⢦⣶⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠙⢦⣤⠶⠋⠁⣀⡤⠞⠳⡄⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⡆⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠸⡎⠀⠛⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠳⣄⡴⠚⠉⠀⠀⠀⠙⢶⣄⠀⡰⠋⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢉⠿⠛⠦⣄⡀⠀⠀⠉⠓⢤⣀⢸⠇⢀⠀⣼⠁⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀⠀⠀⠀⠘⢷⢶⣤⡀⣰⣿⣤⡀⠀⠀⠉⠛⠓⠶⠶⠤⢬⡟⠀⠋⣰⠏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⠌⠳⢤⡀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⣤⣷⣌⠙⠛⠋⠈⠳⠶⠦⠤⠤⠤⠤⢤⣤⡀⠀⠀⢰⡏⠳⢤⡀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠻⣆⠀⣼⠋⠉⠲⡟⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠁⠀⠀⠉⠲⢄⡀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠈⠻⠿⣄⠀⠀⠱⣄⣰⠎⠙⠉⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠈⣧⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠘⣇⠀⠀⣿⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠳⢦⣼⡀⠀⠀⢹⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠈⠹⢦⣤⡼⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠐⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⡤⢠⠤⣤⠄⣤⣼⣧

⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⢀⡀⠀⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠀⠀⣠
⠀⡾⡄⠀⣼⣧⣤⡄⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⡀⠀⠉⣓⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠉⢿⠇⠀⠀⢀⡄⠀⠈⠙⣀⠀⠀⠀⣰⢾⣤⡀⠀⠘⠿⠂⠀⠱⢤⡀⠈⠉⣵⣾⡧⠀⠁⡄⠘⠋⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⢿⡁⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢀⠝⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠞⢋⡀⠀⠘⠉⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠶⠿⠛⠒⠺⠿⢶⣷⣴⣷⣶⣦⡄⠀⢀⢀⢀⠀⠀⠀⠀⠐⠶⣤⣤⣀⣀
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠾⠿⣿⠗⢀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⠶⢦⣤⣄⣀⣀⡀⢀⣀
⠀⠀⠀⠦⠀⠤⠀⠈⠂⠐⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣘⣷⣤⣧⣾⡻⠋⠉⠙⠛⠲⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣣⠅⠼⠘⠞⠒⠝⠸⠞⢀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣬⣭⣻⣿⣿⠵⠾⠿⠿⠒⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⢾⡿⢛⡿⣯⣛⠟⠻⣶⣤⡈⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠞⣵⣿⡆⣇⠙⣦⡀⠈⠙⠆⠙⠅⠀⠀⠀⠀⣠⣼⣷⡛⣚⠷⠦⠀⢀⣳⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⡄⣤⢻⣿⡄⠹⢶⣽⣿⣄⠀⠀⠀⠐⡀⠀⠐⣣⢞⢿⣷⣬⠈⢳⢤⣴⠞⣻⣿⠛⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢡⠻⠘⣿⡇⠘⠀⢹⡷⠙⠐⠆⠀⠀⠀⠀⣸⠧⠈⠈⣿⣟⢷⡀⢸⡏⢺⡏⢌⠓⣆⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⢠⡀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠸⣿⡁⠀⠀⠀⠁⠂⠰⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣄⡀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠠⡀⠀⠈⠙⢦⣀⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠤⠬⠯⠿⠿⠤⠴⠖⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣆⣤⡀⠀⠀⠹⣿⡄⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢈⣉⡀⣠⣤⠴⠚⠋⠀⠀⢠⢴⠖⠈⠀⠀⠤⠐⠂⠙⢿⣯⢦⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣤⡤⠶⠶⠶⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠈⠐⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣯⣷⡀⠀⠈⠳
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡤⠤⢤⠤⣤⡤⠂⢀⡤⠖⠲⠿⠟⠛⠋⢀⡾⠀⠀⠀⠀⠀⢀⣤⠖⠒⠈⠁⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⢞⣋⣩⣥⣤⡤⣶⢶⡶⠶⢶⣦⣤⣄⣀⣀⣀⣠⣤⡤⡶⠚⠋⠀⠀⣀⣀⠤⠚⢉⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠠⠤⠤⠤⠤⠴⠶⠖⠒⠒⠂⠉⠉⠉⠉⠀⣀⣀⡤⠨⠀⠀⠴⠒⠊⠁⢀⡀⠄⠚⠁⠈⠀⠀⢀⣜⠛⣋⣲⣆⣤⡤⠟⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢉⣉⠥⠀⠀⠀⠀⣀⠠⠄⠀⠲⠉⠀⠀⠀⠀⠀⣠⡖⣥⣦⡾⢸⡞⠈⢙⡓⠢⠄⠀⠀⠀⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠚⠉⠀⣠⠴⠒⠋⠉⠀⠐⠂⠀⠠⠂⠀⢀⠤⠐⠛⠱⠋⠽⠇⠀⠙⠋⠙⠛⠑⠃⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣄⠀⠀⠀⠘⢿⣿⣦⡀⠀⢀⣠⣤⣄⠀⠀⠀⠰⣾⣷⣦
⠀⠀⠀⢀⣠⣤⣦⣤⡀⢠⣿⡿⠋⠉⠀⠀⠀⣀⣤⣤⣬⡛⣿⡴⠿⠿⠛⠋⠁⠀⢀⣀⣈⣉⣻⣧⣴⣶⣶⣶⣆
⠀⠀⠀⠘⠛⠿⠛⣛⣻⣾⣿⣾⣿⣷⣄⠀⠀⠙⠛⠛⠋⠉⣿⣟⢻⣷⣦⡀⠀⠰⠿⠿⠟⠛⡛⢻⣍⠉⠛⠛⠛
⠀⠀⠀⠀⠀⣴⣿⣿⢯⣿⠱⡄⠈⠹⣿⡆⠀⠀⠀⢀⠄⠀⣿⣿⣇⠙⠻⠇⠀⠀⠀⠀⠀⡜⠀⠀⣿⣷⡄
⠀⠀⠀⠀⠈⣿⡿⠋⢾⣿⡄⠹⡄⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠙⠻⠇
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠹⠇⠀⢹⡄⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢠⣿⠃⠀⠀⢀⣴⣶⣦⣀⡀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣄⢰⣆⣾⡇⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⣿⣿⣧⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⡤⠀⣾⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿
⠀⣠⣴⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣄
⣿⣿⣯⠽⣿⣛⣋⣭⣝⣓⡿⢽⣛⣿⠿⣿⣿⣿⠿⠿⣿⣿⡿⠿⠿⣿⣿⣿⣿⡿⠿⣛⣫⣽⣶⣶⣾⣿⣿⣿⣶⣶⣿
⣿⣿⣿⡿⠿⣶⣛⣛⣛⣿⡿⠶⢾⣿⣯⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠾⠟⢛⡻⠿⢿⣿⣿⣿⣿⣿⠿⣛⣻⠿
⠿⠿⠶⣿⣿⣿⣛⣛⣛⡻⠿⢿⣿⣶⣮⣝⣻⡿⠿⢛⣛⣛⣛⣛⣛⡻⠤⠶⣞⣭⣿⣿⣯⣷⣒⣢⣭⣭⡿⠿⠷⣶⠿
⣿⣿⣿⣶⣶⣬⣿⠿⠿⠿⢿⣿⣟⡛⣛⣭⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠿⠿⠿⠿⣭⣭⣶⣶⣿⣿⣿⣿⣿
⣿⣿⠿⣛⣭⣴⣶⣿⣿⣿⣷⣶⣭⣭⣛⣛⠿⢿⣿⣿⣿⣿⣿⡿⠟⣋⣭⣶⣾⣿⣿⣿⣿⣿⣶⣶⣭⣝⣛⡻⠿⠿⣿

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠀⠀⠈
⡈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢠⡡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣧⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣆⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⠳⣻⡵⡃⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠐
⠀⠦⡆⠘⢄⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠈⠯⢳⡵⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢰⡄⠙⠠⠂⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⢰⠀⠀⠁⠘⢃⠉⣀⡀⠛⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⣨⠃⠀⢲⣁⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⡴⠂⠈⠈⣌⠁⢋⣠⠆⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⢐⠀⠱⠀⠈⢑⠀⠈⠉⠀⠀⠠⠖⡄⠀⠞⠀⠀⠀⠀⠈⣄⠩⠖⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠾
⠠⠀⡀⠀⠀⣨⠆⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠤⠀⢀⣄⠸⠀⠀⠀⣤⣶⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠻⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢰⡖⢰⣶⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡽⠟⠛⠘⡅⢆⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤
⢀⡌⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠐⡀⠀⠀⠀⠀⠐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠦⣄⠀⠄
⣿⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠄
⠋⠀⠘⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢄⠀⠠⠀⡀⠀⠑⠩⣢⡀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀
⠈⠀⠀⣦⡈⡢⠄⡀⠀⠀⠀⠀⠀⢉⣉⣙⡛⠙⠋⠀⠀⠀⠀⠐⠠⢀⠀⡠⡀⠰⡃⠀⠠⠎⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠂⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢶⢶⣦⣃⡀⠀⣤⣀⣉⣩⣭⣍⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠲⣆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹
⠀⠀⠀⡃⠸⣿⢿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠁⠘⣄⠀⠄⠀⢀⡀⠀⠀⠀⢀⠀⠂⠁⠠⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⢀⠀⠀⠘⠛⢿⣏⣛⠙⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⡁⠀⢀⡀⠈⠧⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⢤⢀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠐⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠰⠂
⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣦⡀⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠘⣣⠈⠓⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⠀⠀⠀⠀⠢⠀⠐⢄⠐⠀⠀⠀⠘⠋⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠄⠘⡀⣄⢀⢃⠀⠀⠀⠀⠁⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⢠⠼⠏⡐⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠈⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡈⠀⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠰⣟⣿⣿⣿⡿⠟⡻⠶⠖⠲⢆⣀⣀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠃
⠀⠀⠀⠀⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣄⠀⠀⠀⠀⠀⠃⢠
⠀⠀⠂⢄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠘⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉
⠀⠀⠀⠀⠀⠙⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠔⣩⠖⠈⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢠⣶⠠⠀⠀⠀⠀⠀⠁⠠⢁⠎⠀⢀⠔⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⢋⠞⡴⠁⢀
⠉⠀⠀⠀⠀⣘⠿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠐⠀⢠⠃⡠⢀
⠀⠁⠀⠀⠀⠉⠲⠠⠄⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠂⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢁⠂
⠀⠀⠀⠀⠀⢀⡄⣧⠀⠀⠁⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⢸⠇⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⡠⠂⠀⠀⠀⡀⠀⠂⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⢀⣵⠀⠀⠰⡄⠃⠀⠀⠘⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠠⣀
⣠⣄⣀⢀⡔⢡⠌⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡧⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⣴⠐⠀⠉⠀⣼⣷⡀⠀⠈
⠀⠰⢦⣺⡔⠷⣶⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⢀⣰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡿⢻⣤⡀
⠰⡞⠁⠚⢟⠐⢮⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠑⣄⠴⠁⡜⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡜⡀⠸⠍⡤
⠀⡧⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠤⠤⢀⢁⣸⢀⢊⡀⡨⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢰⠀⠣⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡶⠉⣰⣷⠈⣦⠁⠛⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠠⠆⠏⠸⠆⢸⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⣶⣶⣶⣶⡶⠁⠂⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⡁⣶⣠⣖⣀⢰⠄⠂⠀⠀⠀⢀⠀⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⡇⠐⣖⣶⡶⠶⠶⢤
⠿⢿⡟⠋⠀⣐⠀⡍⠹⣷⣈⡀⠛⠉⠽⠭⠉⠿⣿⣿⡀⠉⡉⢠⢤⣴⣼⣀⡃⡈⠐⢂⣸⠘⣿⣿⣿⣭⣿⣿⣿⣷⣾⣉⡡⢈⡀⠲⣻⠿⢾⣿⠏
⠀⠀⠀⠀⠀⢀⠀⡇⠀⠈⠁⠀⠀⠀⠠⠴⠒⠀⠀⠰⠀⠙⠏⠉⠉⠽⠞⠋⣭⡤⠐⠳⠖⠚⠛⠉⠙⠛⠛⠀⠉⠉⠐⠀⠸⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠂⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠾⠑⡂⠈⠉⠀⠤⠴⠿⠀⠀⡀⠀⠀⠀⠀⡶⠀⠀⠨⠉⠁⠀⠐⠂
⠰⠂⢀⠐⠂⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠂⠂⠀⠀⠀⠉⠑
⣤⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁


⡀⠀⠀⢀⣴⣶⣶⢶⡐⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⣀
⠀⡳⠘⠸⣿⣯⡤⠾⢿⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠛⢿⣷⡄⠁⠘⢰⠂
⠀⠀⠀⠀⠿⣶⣦⡄⠺⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣠⠉⠙⠛⠿⠃⠐⠀⡇
⠀⠀⠙⠂⣄⠀⠹⣆⢀⡜⠓⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⠉⠁⠠⠔⠁⠀⠀⠴⠁
⠀⢀⢀⠈⢿⣷⣄⣍⣙⡟⢘⣟⢚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⢰⠞⢷⠤⡔⠏⠠⠀⡀⠁⠀⡀
⠀⠀⠀⠑⠈⠈⢟⠋⣹⡋⣹⣏⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣽⣙⣗⢺⠛⠟⠀⢀⡜⠘⠴⠪⠂
⠀⠀⠀⠀⠀⠈⢡⢁⠘⠋⣽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢉⡟⠙⠷⠟⠀⢊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠲⣍⠀⠀⠄⠐⢤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⡀⠀⠀⠘⠛⠟⡡⢂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡄⠉⠀⠀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠈⠘⠃⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠀⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠲⡤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⢎⠳⡄⠀⢀⣤⠒⠉⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡈⢆⢸⢔⠟⠡⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣒⠂⠉⠉⡙⠲⢦⣧⡈⢇⠎⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠛⣛⣲⣦⡴⣮⠺⡴⠿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⢈⡩⠞⠋⠉⢀⣠⡿⠠⡈⢳⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡠⠔⠋⣿⢋⢼⡇⡀⠷⠀⣿⠲⢤⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠖⠁⠀⠀⢐⡕⠁⠈⡄⢹⠂⢇⠏⠀⠈⠳⣄⠸⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠱⡸⠀⠸⠁⠀⠀⠀⠈⠢⡟⢼⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣜⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠋⡝⠉⠉⠣⣄⠀⠉⠙⠲⢅⠒⠤⢀⡀⠀⠀⠀⠈⠫⡸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠕⠁⠀⠀⡰⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠙⠢⡀⠈⠑⠢⣀⠀⠀⠑⣜⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⢠⠎⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⢦⡀⠈⢶⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢀⠀⠀⢃⢀⡤⢄⡒⠒⠠⢵⣤⣮⠥⣄⣙⣂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠀⠀⠀⡎⠀⢀⣀⣀⠀⢰⠀⡠⠒⠙⡝⡍⠉⠑⠼⡫⠶⠅⠘⠓⢢⣴⠭⡍⠀⣩⢁⣼⣷⣗
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡔⠉⠁⠀⠉⠙⢺⡖⠉⠁⠀⠀⠉⠺⠊⠀⠀⠀⢡⢡⢀⡔⠊⠁⠀⠘⠉⠀⠐⠉⠃⠘⣄⠀⠀⣻⡟⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠇⠈⠉⠀⢈⡴⢠⣤⢬⠭⣭⠭⣥⡍⠉⠉⠩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡸⡀⠀⣰⣿⢃⢆⠎⡜⢠⠃⣴⠏⠀⠀⠀⠐⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢧⢣⡼⣣⢣⢊⠎⡰⢡⢂⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡳⢖⠕⡡⢋⠜⡰⣣⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣲⡒⢒⣊⠥⢊⠥⣊⠔⣡⠞⣴⠋⠀⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠙⠑⢾⢥⡞⢁⣾⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢨⡼⣾⡟⠛⠙⠲⠦⢾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠳⠲⢤⣤⣀⠀⣴⠏⠀⠀⢀⡤⢦⣤⡀⠉⠁
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠃⠀⠀⢠⣡⢊⠟⢦⠘⡄
⠀⠀⠀⠀⠀⠀⠐⠤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢧⣸⣀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠁⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠀⡇⠀⠞⠁
⠀⠀⠀⠀⢀⡠⠴⠒⠚⡯⡀⠐⠒⠒⠒⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠞⠉⠉⠑⡄⢠⡤⠤
⠀⠀⢠⠞⠉⠀⠀⣀⠈⠀⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠘⢆⡀⠀⣠⠃
⠀⢰⠃⠀⠀⢀⠜⠁⠀⠀⠀⠀⠁⠀⠀⢀⡠⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⠁⠉⠲⠄
⢀⠇⠀⠀⠀⠋⠀⠀⠀⠀⣀⡤⠤⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠈⠓⠒⠢⡤⠔⠒⠒⠒⠒⢹⣧⠀⠀⢀⡠⠖⠚⠉⠉⠉⣑⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⠀⢰⠋⠀⠀⢀⣠⣶⣿⣿⣿⣧⣷⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢀⠘⠃⠀⠀⠞⡳⣤⠞⠛⠛⢿⣿⣿⣽⠅⠙⠿⣿⣹⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⢫⠆
⠀⠀⠀⠀⠀⠀⠀⡖⠛⠛⢉⡟⢛⣝⡦⢀⡈⠙⣛⣉⣑⣶⠶⠟⠹⠤⠶⠖⠒⠒⠲⢤⡤⠤⠤⣤⣀⣀⣤⣿⢻⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⣸⡕⠿⠭⢤⣒⠯⢍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣤⣤⠏⠉⠉⠉⢹⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⣇⠈⠉⠉⠁⠀⠀⠈⠑⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣀⣀⡼⠿⠟⠛⠛⠛⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠚⠉⠁⠀⠉

⡀⠀⢹⡄⠀⠀⠀⢀⡀⡂⠀⠀⠀⣠⡄⠊⠀⠀⠀⡀⠈⢿⣇⠀⠃⢀⣀⠀⠛⠻⣐⠿⢤⠔⠒⠤⠄⣿⡾⠟⠀⢊⣿⣿⣿⠏⠈⣯⡐⢀⠀⠀⠀⠈⠒⠤⣤
⠁⠀⠀⠙⡄⠀⠀⣤⡀⠡⠶⢶⣼⣯⠕⠀⠀⢂⠀⠀⡀⣸⡿⠀⠘⠀⢩⣄⠀⠀⠎⣤⢤⡴⠶⠟⠘⠈⠀⠀⢀⣌⢶⡟⡻⣄⠀⠋⠐⢦⣣⣄⡀⠀⠀⢀⣀
⡀⠀⢀⠀⠙⠂⠒⢿⡈⠳⢤⡈⠛⠻⠀⡀⠠⡤⠀⠀⠀⡿⠃⠐⠀⠀⢾⠋⡥⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠋⠑⠫⡀⠀⠀⠈⠉⠻⠻⠆⠉⠉
⡇⠀⠸⣆⠀⠀⡀⢈⣷⡀⠀⠙⠣⢀⠈⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣇⢀⠀⠘⡆⠀⣇⠀⢿⠛⠢⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠟⡌⠀⠀⠋⠂⠄⠀⢠⡀⠀⠈⠓⢆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠠
⠀⡀⠀⠀⠠⠀⠀⠀⠀⠈⠒⠄⡀⠀⠉⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣘⠀⠀⠀⢀⠀⢂⡐
⠟⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠠⡀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣦⣤⣀⠉⢷
⠀⠀⠀⠀⠃⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠈⣉⣙⠛⠶⢬
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢠⡤
⢆⠀⠀⠀⣶⣠⣥⡀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⡀
⡛⣷⠀⠀⣮⣽⣷⠞⠁⡀⠀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠤⠄⠀⠀⠀⢀
⡻⣾⡇⢸⣿⣯⣿⠀⣸⠗⠊⠖⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠘⠓⠲
⣿⠿⣿⣼⡇⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢹⢶⣽⠙⣷⣿⣥⣄⣤⡴⣆⠀⢰⠴⣦⠠⢄⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠠⡀⢀⣦⠀⠀⠀⠠⠀⣴⣟⠉
⠀⣿⣽⣷⡌⠻⠟⠛⠉⠁⠀⠀⡀⢅⣨⣤⡀⠀⠀⠀⠀⢀⠃⠀⠀⠂⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⣃⠀⠀⠀⠀⢀⠀⠈⠻
⠂⢿⡏⠙⠟⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⡜⠀⡠⠀⣼⠏⠀⠀⢀⡤⠤⠎⠀⠀⠀⠀⠀⠁⠀⢀⡅⠀⠀⠀⠀⠀⠀⢰⡖⠒⠁⠊⢄⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢞⠢⠄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠂⠀⡔⠠⠠⠺⠂⠀⠢⡈⠂
⠀⣀⡀⡀⠀⠀⡌⠀⠀⡰⠁⠐⠒⠒⠒⠒⠒⠶⠒⠆⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠐⣇⠀⢘⠁⠈⠙⠀⠀⠀⠐⠄⠀⡠⠃⢄⣠⠦⡀
⢡⠀⠀⠀⠀⠀⠰⡀⠐⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⠀⠀⠀⠀⠉⠐⢺⠀⠀⠤⠀⠀⠀⠘⠕⢀⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⡀⠶⡄⠀⠈⢢
⠀⢆⠀⠀⠀⠀⠀⠀⠀⢒⠒⠒⠂⠀⠀⠀⢤⡌⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⡉⠐⠀⠈⠢⡀⠀⠑⢄
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠈⣄⣀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢀⣀⠀⠁⠀⢀⡠⡇⠀⠀⠀⠣⡀
⠀⠀⠘⡀⠀⠀⠀⠀⢀⠔⠀⢸⠀⠀⠀⠀⢀⣀⠐⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠠⠤⠐⡆⠉⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⢦
⠀⠀⠀⠡⠀⠀⠀⢠⠂⠀⢀⠦⠀⠀⠀⣀⢢⠠⠵⠀⠀⠀⠀⢀⠠⠄⠚⠒⢲⠀⠉⠁⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠑
⠀⠀⠀⠀⢃⠀⠀⠆⠀⢠⠂⠐⠃⠈⢁⡀⠤⠤⢄⣃⣠⡔⠊⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⣈⡦⠠⠤⠀⠀⠒⠚⠒⠀⠉⠉
⠀⠀⠀⠀⠈⠆⠀⠢⠀⠀⠐⠂⠘⡇⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣀⡀⠀⠠⠤⠄⠚⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠤⠄⠐⠂⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡀⠤⠵⠀⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠁⢒⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⢠⣎⣀⠀⠀⠀⠀⢀⠔⠉⠀⢛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⢝⠂⠀⠀⠈⠙⢲⡀⢠⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡉⠉⠋⠀⠀⠀⠀⠀⠀⢱⣇⣀⡀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⡰⣖⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⣸⠋⠑⢄⠀⡇⢀⠀⡾⠀⠀⠀⠀⠀⠀⠠⣀⡳⠜⠀⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⢀⡀⠀⠀⠀⣰⠃⠀⠀⠈⠷⠋⡠⠈⠴⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤⠠⠒⣓⡄⢠⢀⠤⢡⠒⠢⢴⠃⠀⡠⠀⢀⡠⠊⡱⠷⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠈⠖⢥⠀⠀⢠⠃⠀⠀⠀⠑⡏⣀⠴⢋⠔⠙⠦⠤⠊⢀⡀⠀⠀⠀⢀⠔⢲⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢽⡖⠨⡷⠔⠂⠄⠀⠀⡾⠀⠀⠀⢀⣠⢼⡥⢚⡁⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡠⠎⢳⣀⣠⠗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠠⡀⠔⠀⠐⢦⣀⣇⠀⡠⠞⠉⠀⢀⡟⡉⢁⡀⠀⠀⠒⠀⠀⠀⠢⡀
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡿⠀⠄⠉⠋⠀⠑⠀⡇⠀⣏⠀⠀⠀⠀⣼⠁⡀⠄⠩⡒⠀⠒⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠒
⠀⢀⡗⡁⠀⠀⠀⣀⣂⣀⣃⣤⣼⢥⣿⣿⣱⠁⣠⣨⣁⡖⡀⣉⣞⣀⣑⣤⡠⠾⠷⠏⠘⠚⣢⠈⠂⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣳⡜⢻⡄
⠀⡌⠁⠁⢠⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠙⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠉⠂
⠀⡃⠀⠘⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇
⠀⠿⠲⢶⠃⠀⠀⣠⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏
⡴⠛⠈⠚⠲⡀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣠⣇⣀
⡇⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡆⡴⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⢈⠀⠀⠃
⠘⠠⠄⣀⠴⣧⠃⠀⠘⢀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡠⠀⢁⢧⠀⠀⠀⡰⠃⠰⠄⠉⢹⡂⠘⠆⠁⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⡤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠈⡏⠍⠉⣉⢱⠀⡔⠀⠀⠠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⡀⠀⠀⠀⠀⠀⠀⡼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⢰⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⡆⠀⠀⠀⢀⡎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠂⢇⠀⠀⠀⡼⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠀⡆⠀⠀⢠⡇⠀⠀⠀⢸⣴⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⢰⠇⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠻⣄⠀⠀⠀⡇⠀⠸⠀⢸⣇⠀⢸⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⢿⠀⠀⠀⠣⡈⠙⠒⠦⠼⠄⣀⡄⢼⠸⡀⢸⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠇⠀⠀⠸⡄⠀⢂⠀⠹⣦⣄⣀⠀⠀⠀⠈⠙⠠⠱⡀⢧⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⡄⠀⠀⠀⠹⡄⠀⢂⠀⠙⢦⡉⠉⢻⠙⢶⡀⠀⢡⠙⢮⣇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠣⡀⠀⠀⠀⠘⢦⡀⠁⠀⠀⢳⡄⢸⡆⠈⣷⠀⢸⡄⠀⠹⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠙⢦⡀⠀⠀⠀⠙⠲⢬⡀⠀⢳⣸⠇⣠⠇⢀⡎⣹⡦⠂⢠⠊⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠉⠒⠤⢤⣤⣀⣀⡙⡆⢘⣿⠴⢋⠴⠛⠋⢉⡠⣶⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢄⣀⠀⠀⠉⣻⠋⢡⡖⣡⠤⠒⠊⠉⠉⠉⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠬⠽⠦⢠⣭⠀⡿⢋⡤⠠⠔⠈⠙⢿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠑⠠⡀⠀⠀⠀⠀⠻⣶⠛⠓⠒⠒⢦⠀⠂⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⠂⠀⠀⠀⠀⠹⡀⠀⠀⢀⡼⠛⠉⠉⠉⠉⠹⠉⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠡⠀⠀⡀⠀⠘⣄⡴⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⠀⠐⢄⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠶⠤⠤⢤⠴⠟⠋⠈⠓⠒⠶⠶⠦⠤⠤⣀⣀⣠⠶⠊⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠈⠀⠀⠀⠁⠈⠀⠀⠀⠁⠈⠀⠀⠈⠁⠁⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠱⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⣤⠴⣤⡁⠂⢄⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⡤⢾⣦⡰⡟⠻⡉⠉⠙⢦⢌⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⠁⠈⠁⠈⠛⠒⣻⢏⠎⣂⢰⠀⠀⣼⠀⠑⡈⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠒⡄⠀⠀⠀⠀⠎⢀⠇⠯⡀⠘⠔⠁⠀⠀⠀⠈⡄⢂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⠀⠀⠀⠀⠉⠀⠖⠺⠀⠀⠀⠀⠀⠸⣮⠿⡀⡀⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⢀⠀⠀⢄⠀⠀⢀⣀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢐⠵⠾⡇⠁
⠀⠀⠀⠀⡀⠨⠰⠉⠉⠉⣷⠨⠀⡀⠈⠓⢄⣇⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡄⡀⢀
⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⡉⡄⠀⠀⠀⠙⠶⠒⠂⠀⢀⠀⠀⠀⠀⠀⠑⠂⢲⢁⠁⠈
⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠵⠤⠤⠤⠤⠤⡧⠾⠴⠓⠲⢟⣚⡛⢍⠉⠙⠛⠛⢋⠆
⠀⠀⢰⠀⠘⠠⡷⠀⠀⠀⠰⡧⠈⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠈⢻⡆⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⠄⠁⠰⢢⢀⠀⠀⠀⠀⠰⠀⠀⡠⢄⠙⠒⠚⠁⠃⠀⠀⠀⠀⡔
⠀⠀⡄⠀⡠⠐⠒⠒⠒⠒⠒⠒⠠⠀⠀⡷⢤⡁⡐⠂⠀⠒⠀⠒⣘⡜⡠⠀⠡⠄⠀⠬⠅⠀⠀⠈⢆⠀⠀⠠⠀⠀⠀⠀⠀⡠⠂
⣆⠀⠀⠀⠃⠤⠤⠤⠤⠤⠤⠤⠄⡆⠀⠂⢀⠧⠀⢀⡀⠀⠀⡀⠠⠖⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠦⠀⡖⠐⠀⠂⠈⠀⠠
⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠰⠠⠀⣠⠑⠶⣷⣴⡀⠀⠀⠀⠀⠀⡔
⠣⣘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡠⠂⠐⠒⠓⠒⠒⠓⠒⠀⢀⠀⠀⠀⠀⠀⢀⡤⠊⠈⠁⠐⠃⠀⡀
⣀⣈⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣌⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣎⣶⣶⣶⣦⣬⣤⣦⣤⣖⣒⣒⣚⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢
⠀⠀⠀⠀⢘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠪⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⣄⠀⠀⠀⢀⡀
⠀⠘⠷⣄⠂⠈⢽⣇⡕⠏⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠳⠲⠄
⠀⢠⣄⠙⢻⡀⠱⢃⣴⣤⣧⣦⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⣀⡀
⠀⠀⠨⢧⠈⢥⣠⢀⣌⡀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠑⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠈⣣⠜⣉⡁⠙⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡜⢲⠟⠛⠷⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⡆⠃⢀⢠⠇⡄⢠⠃⡄⢀⠄⠀⠀⠀⠀⠂⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡰⣌⢆⠣⢱⣠⣘⣘⡰⠡⢃⠎⡰⢋⠀⠀⣀⠀⠀⠀⢀⠀⡀⠀⢀
⠀⠀⠀⠠⠔⠀⢀⠀⠈⣇⠀⠀⠀⠐⠦⣄⡐⠦⣀⠦⡑⢌⠾⠋⠉⠀⠀⠀⠉⠓⢮⢊⠴⣋⠴⠊⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⢈⠳⠀⡿⠒⠒⠒⠠⠤⣀⣉⠓⠬⡑⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠵⢚⣁
⠀⠀⠀⠀⠁⠀⠈⠂⢧⢈⡉⠓⠶⠆⠀⠠⠬⢭⡑⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠭⠤⠒⠒⠉⠁
⠀⠀⠀⠛⠀⠀⠀⠨⠶⢦⡉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈
⠀⠀⠐⠂⠀⠈

⠀⠀⡀⡀
⣤⣤⣉⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣴⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠐⠛⠛⠳⣾⣿⣿⣥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⣴⠏⠀⣀⡤⠀⠀⢀⣤⢾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣿⡾⠋⠁⠀⠀⠀⠈⢱⢟⣽⣿⠯⡟⣿⣿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⣿⣿⣟⠙⠓⠦⠀⠀⠀⠈⢸⡏⡟⠸⠃⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣼⠃⢩⡟⣿⢰⡀⣿⠀⠀⠀⠀⠈⡌⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠡⠇⣀⣀⣳⣿⣶⣋⣁⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣨⡽⣿⣿⣿⣿⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢁⡴⡻⠁⢹⡉⡇⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢰⠁⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡤⢤⠧⠠⢤⢤⣾⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣶⡾⠶⢶⡶⠾⣏⠀⠀⠀⠈⠉⠉⠉⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠶⠒⠒⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛⢿⣦⣼⣇⣴⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣽⣿⣿⣿⣿⠶⠛⠛⢻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⣻⡿⣿⢿⠻⡌⣛⣷⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⢸⠌⡇⢿⠁⠟⡙⡏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠶⠶⠶⠶⠴⠶⠤⠄⠀⠀⠀⠀⠀⢀⡖⠙⣷⣬⡀⠠⢾⣧⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣷⢀⣠⣁⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠛⠛⠛⠛
⢀⠀⡀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀
⣿⣏⢽⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡠⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠂
⠀⡤⢊⠄⠀⠀⠀⡀⠠⠀⠀⠀⡡
⠀⠄⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠀⡆⠄
⠀⠠⠀⠀⠀⠀⠀⠈⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⣿⣿⣿⣿⣿⡇⡄⠀⢀⣶⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣷⠁⠀⠀⢿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡾⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠟⠃⠢⡤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠘⠀⠻⣷⣦⠀⠈⠛⠿⢿⡿⠿⠖⢉⣠⣴⣾⣿⣿⣿⡟⠐
⠀⠀⠀⠀⠀⢄⠘⢿⣿⣿⡒⠒⠀⣀⣤⣾⣿⣿⣿⣿⣧⣽⣛⡷⠀⠄⠀⠀⠀⠀⢤⣤
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠛⠿⢿⣿⣿⡿⠿⣿⣿⣉⣿⣧⠩⠽⠁⠀⢠⠦⠀⠀⠀⠈⢻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠤⣄⣠⣾⣿⣽⡿⠃⠀⠀⠀⠀⠈⣲⠗⠀⠀⠀⠀⢻⡷⠖⠀⠀⠀⠀⠠⠊⠀⠀⠘⠀⢹⣛
⠀⠀⠀⣀⣀⣄⠀⠀⠀⡴⠀⢀⢀⢀⡀⣹⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠰⠀⠀⣀⠀⢀⣀⡼⣿
⠀⠀⢤⣏⣹⡟⠂⠀⠀⠀⠈⠁⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠉⠒⠀⠀⠀⠀⠀⠚⠀⣻⣿⣧⣿⣿
⠀⠀⠘⠋⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡠⠤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢐⣨⣿⣿⡒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡡⠊⣽⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣧⠀⠰⠟⢃⣁⣿⣿⠡⠦⡄⠀⠀⠀⠀⠀⡴⠛⠃⠲⢶⢎⣽⠿⣙⣕⡊⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠈⢷⡙⣉⢷⡤⢻⡆⠀⠀⠠⠂⣀⢀⣀⡀⠀⠀⠑⠂⣾⠉⡙⢲⢄⡴⡳⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠲⢭⣫⡾⠇⠘⢴⣶⡤⠀⠘⣿⢿⡿⣇⠀⠀⠀⣀⠙⠳⣄⠤⡚⣿⢦⣯
⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠉⠉⡿⠁⣠⡀⠛⠁⢿⡷⢲⠟⠈⣀⠉⠀⡀⠀⠿⠀⠈⠁⠀⠉⠓⠛⠿
⠛⠛⢿⡷⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⣄⠀⠁⡴⠋⠁⠀⠀⠀⣿⣾⡇⢀⡧⢶⡆
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢀⣠⣤⢚⣀⣀⠲⠀⠀⡌⠀⠀⠀⠀⠀⢘⣿⣿⢿⣟⡅⢰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⢸⡇⠀⠀⠀⠰⡼⠀⠀⠀⠀⢠⡤⣴⣤⡄⠈⠀⠠⡾⠁⠀⠀⠀⡠⠶⠾⣻⠇⠀⠀⠀⠛⠺⠃⠁⣀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠘⠃⠺⣷⠀⠀⠤⠀⣀⡀⠀⠀⢸⣄⣭⠃⢠⠀⠠⠄⠀⠀⠀⠬⠔⠃⠀⢻⠀⠀⢀⠔⠒⠀⠀⠈⠁⠻⢖⣶⠲⣦⣠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⠶⣶⣿⠏⠘⢠⣦⠆⢀⡀⠀⣸⢀⡧⠀⠀⣠⠎⠀⠀⠁⢀⡤⠒⠀⠀⠀⠀⠈⠛⠳⣿⠟⣡⣼
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡛⢚⠰⠃⠀⠀⠈⠉⠲⠁⠁⠀⠀⠀⢀⠟⠀⡴⠀⠀⠀⠀⠀⠀⠈⢣⡾⠟⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠁⠀⠀⠀⠀⠀⠀⠈⠋⢠⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠘⠀⠆⠀⢲⡔⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⣧⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢋⣛⡾⠁⣠⢠⣴⣬
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⣷⠟⠁⠀⠈⠛
⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⢧⠀⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⠀⣠⡏⠠⠀⠠⢄
⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠐⠊⠀⢐⣼⡿⠟⠠⢤⠤⣲⣄⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣴⣄⠀⠀⠀⣠⣤
⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⠴⠿⠃⠀⠀⠀⠙⢠⡸⢇⠀⠁⠀⠀⠿⠃⠀⠀⠀⠀⢀⣤⡀⠀⠀⠙⠻⢿⣿⣿⡄⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠐⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⡤⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠊⣹⠂⠀⠀⠀⠀⠀⠀⠀⠐⠊⣀⣀⡙⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⢠⣾⣿
⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠩⡝⠀⠠⠶⠈⠁⠀⠻⠃⠀⠀⡄⢠⡄⠀⠀⠈⠉⠏⠁⠀⠀⠀⠀⠀⠒⠋⠉⠙⠳⣦⠀⠀⠉⠻
⠀⠀⢰⢣⡄⢠⡙⢦⣄⣀⣤⢷⣶⣤⣴⣶⣿⣤⣤⣤⣄⣘⣄⢳⣶⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠘⢯⣧⣈⠛⠀⠈⠉⠀⡴⠋⠙⠛⠛⠉⠉⠀⠀⠂⡟⢩⣶⢿⣿⠃⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⢀⣴⠇
⣦⡀⠀⣿⣿⡋⠐⠷⠂⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⢺⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠺⢿⠆⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣿⣷⡈⠛⠛⠣⠴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⢰⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠉⠙⢶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⣴⣀⠀⠀⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢓⠳⣤⠀⡀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⣿⣆⣿⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡘⠷⣧⣴⡂⣀⠻⡇⠀⠀⠀⠀⠘⠠⡀⠀⠘⠶⢦⣴⣿⡧⠔⠁⠀⠀⢳⣸⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⠻⣥⣈⣻⣿⣿⡾⠀⢠⠤⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣗⠀⠀⠀⠀⢹⣿⣃⡠⠉⠙⠋
⠀⠀⠀⠀⠀⢠⢁⡤⠴⠆⠶⠶⠿⣿⠿⣿⣧⡠⣷⠀⢀⠀⠀⠁⠀⣠⣤⠶⠋⠀⠀⠛⢆⡀⠀⣤⣾⣿⢻⣍⢛⠠⢄
⠀⠀⠀⠀⠀⠈⠈⠒⠤⠀⢀⣤⠤⠾⣄⠀⠉⠧⢿⣄⡽⠒⠀⠂⠀⠑⢆⠀⠀⠀⠀⠀⠈⠁⠀⠘⠿⠿⠏⠉⠙⠷⠬⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣟⢠⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⡀⢀⠀⡀⢀⠄⡄⡄
⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢣⠈⣄⠀⠀⠀⡞⠀⡄
⠀⠀⠀⠀⠁⢀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⣼⡀
⠀⠀⣀⠀⠀⠈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⢨⣀⣴⣿⠷⣠⠀⣠⠔
⠀⠈⠀⠀⣀⠀⠀⢧⠀⠀⠀⠀⠐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⢀⣄⠤⣙⣿⣿⣿⣷⣶⡈⠀⠀⠂
⠀⢀⡠⠜⠁⠀⠀⠼⡖⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡇⣆⡏⠀⡀⠀⠀⠀⠐⠂⠀⠉⠿⡿⠟⠿⠿⣿⡂
⠀⠸⠀⠀⣄⠍⠀⠀⠉⠀⡀⠀⠀⠲⠄⠀⠀⠀⢀⡃⢀⠹⣿⣠⣨⣾⡶⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠁⠀⠀⢀⠀⢁⠉⠚⠉⠀⠀⠀⠀⠀⠰⢄⡪⣤⣰⢳⣿⣿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠠⣄⠈⣑⢿⡻⡘⣿⣗⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡇⠀⢸⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⡰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠘⣿⠇⢇⠘⢻⣃⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⡀
⠀⠀⠀⠀⣤⡀⠆⠸⠀⢐⡤⠂⢐⠀⠀⠀⠀⠀⠠⠄⠉⠙⢳⠄⢧⡘⡵⢊⠤⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠠⣸⣿⣰⠁⡠
⠀⠀⠂⠀⠨⣍⠳⡟⢤⣠⣦⠄⠚⠚⠀⠘⠁⠀⠀⠀⠄⠚⣉⡥⠄⢣⣘⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡟⣿⣇⠎
⠀⠀⠀⠀⢢⣝⣦⣶⠈⣿⣡⣴⣷⡶⠂⢀⠀⡀⠀⠀⠀⠈⠐⠚⠿⠶⣛⠅⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⢈⣻⣷⣿⠃
⠠⠀⠀⠀⠀⢉⡽⠿⠿⣿⡿⠑⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠬⢝⣿⡏
⠀⠀⠀⠀⠀⠨⣀⠀⠠⡿⠛⣦⣤⣴⣶⣍⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠴⠾⢿⡦⠂
⠀⠀⠀⠀⠀⠀⣦⠀⠀⣏⠉⣡⠋⠯⠙⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⣤⣤⣤⣤⣤⣤⣬⣤⣤⣥⣤⣤⣤⣤⣤⣦⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⣻⣿⣶⣿⣯⣵⣖⡂⢤⣄⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠈⠁⠚⠴⡱⣙⡟⠛⢿⣿⣿⣷⣀⠝⠉⢒⠿⢭⣷⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠈⡻⠿⢦⣤⣙⣿⣿⣿⠀⢀⠎⠀⡼⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠈⢖⢠⡀⠀⠀⠙⠛⢻⠟⠋⠁⠉⠀⠘⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡰⢡⠀⢀⢿⠓⠋⠂⡴⢂⣡⠷⠒⠁⠀⠀⢀⣴⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢎⠜⡰⡡⢠⡖⢺⠀⠀⢀⣊⡹⠃⠀⠀⠀⢠⠔⡝⢹⠘
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠑⡀⠒⠄⡀⠀⡠⢣⣪⢊⢴⣿⠞⢷⣮⢔⣠⠾⡟⠁⣠⠄⠚⢡⢎⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠡⢁⠀⠀⠈⠲⢵⠿⢷⣧⢤⣷⣄⣠⣧⣀⣷⡄⠀⡠⠋⠀⣰⢃⠮⢄⣀⡤⢓⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢃⠀⠀⠀⠀⠀⠢⣼⣧⣀⣹⡏⠙⣟⠁⠻⠇⠀⠁⢀⡼⢣⠊⡩⢖⡡⡎⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢻⠉⢻⡟⠻⣿⣦⣴⡟⠁⡠⡻⣡⠗⡫⠔⠁⠀⠣⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣦⣾⡆⢀⣼⡡⠋⣠⢎⡔⣱⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢩⡗⠄⠀⠀⠀⠀⠀⢸⠛⢙⡿⠋⣀⡴⢛⠝⡔⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣌⠆⠀⠈⢎⠑⠫⣒⣦⣤⠀⠈⠒⢁⣠⢞⡩⢒⢏⡜
⠀⠀⠀⠀⠀⠀⡄⠀⠰⣯⠣⡀⠄⢊⠆⠀⠀⠑⠪⢝⣦⠖⡫⠔⠉⢠⢊⠎
⠀⠀⠀⠀⠀⡠⠁⠀⣾⡫⠤⠒⠪⣑⠢⣀⠀⠀⠀⠸⠕⠊⠀⠀⢠⢣⠊
⡤⠐⠆⠘⠉⠀⠀⢴⠀⠀⠀⠀⠀⠀⠉⠢⢕⠢⢄⠀⠀⠀⠀⡰⢡⠃
⠉⠀⠒⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡢⢄⡴⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠐⣶⣤⡄⠀⠀⣀⢰⡶⣾⣶⠀⠀⠀⢠⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⢀⣆⡀
⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⠀⡀⢿⣼⢟⣿⣛⡆⠀⣤⢹⣼⣿⣿⡩⠄⣠⣴⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⡿⡃⠀⠀⠐⢿⣷⡄
⠀⠀⠀⠀⠀⠲⣿⠂⠀⠀⠀⠀⠻⣾⣫⣾⠿⢦⠀⢰⣸⣿⣿⣽⣿⡗⠀⣿⣿⣿⣿⣿⣷⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣯⣴⡶⠂⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡟⢯⠷⠀⠀⠀⠉⠙⠿⠟⠃⠀⠀⠻⢿⣿⣧⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠙⣿⡓⠀⠀⠀⠠⣾⣿⡇
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡡⠄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠹⢿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⢠⣿⠂⠀⠀⠀⠀⢀⡴⡛⠈⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⡀⣄⣀⠀⠀⢠⣄⠀⠀⠀⠀⣀
⠀⠀⠸⢿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⣿⡟⢁⣴⡿⠀⠀⢀⠎⡀⠁⠀⡀⠄⠀⢸⣿⡆⠀⠉⠀⠠⣉⣻⡥⢆⡀⠘⣿⣷⠀⣠⣾⣿⠀⠀⠀⢀
⠀⠀⢻⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⢬⣷⡿⣋⣤⡤⠀⠀⠘⠁⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⢐⠲⠶⣽⠋⠩⠀⠀⠈⠛⠃⣿⣿⠟
⠀⠀⠻⣿⣿⣿⡗⠀⣤⣤⠀⣼⣷⠀⣠⣤⠸⠿⡶⠦⣿⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠀⠀⠠⠭⢭⣯⠴⠞⣋⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠁
⠀⠀⠈⢿⣿⠆⠀⠀⡻⣿⣷⣿⣿⣾⠿⠋⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠘⠀⠀⡀⠀⠀⢠⠀⠐⣻⡭⠀⠠⣤⣀⡒⣶⣚⣯⠗
⠀⠀⢠⣀⠀⠀⠀⠘⠿⠿⣿⣿⣿⡷⠿⠷⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠐⢢⡤⠙⠀⠄⠀⠀⠀⢻⡯⠀⠲⠦⣤⣄⣋⣡⠴⠚
⠀⠀⠸⣿⣿⣦⠀⠀⠀⠰⠿⠛⠻⠿⠀⣴⣄⢠⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠂⠐⠠⠀⠀⠀⠁⠀⠑⠶⢦⣄⣉⣴⠾⠋⠀⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⢰⠀⠀⠀⣬⣽⠿⡇⠀⠀⠀⠀⠀⠀⣾⡆⠾⠡⡤⠆⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠁⠀⠀⠀⠛⠏
⠀⠀⠀⠀⠈⠉⠁⠀⢠⡀⣴⠀⢁⣀⣠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣦⡘⠳⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⡀⠀⢰⣴⡀⠀⣄⠀⠀⣶⡧
⠀⠀⠀⠀⠀⣀⠸⣆⢸⠇⣯⣴⣿⡉⠁⠀⠀⢀⡄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠛⠀⢼⣯⠄⠈⠉⠀⠀⠿⢀⡀⠈⠁⠀⢠⡐⣴⢃
⠀⠀⠀⠀⢦⡙⢦⠻⣼⣿⠯⠄⠀⢀⢠⣶⠶⠘⣿⣖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢀⣀⡙⠶⣋⣤⠄⠀⠀⠲⣝⣗⣫⣔
⠀⠀⠀⠳⣮⡻⣦⣍⣛⡛⠁⠀⠠⢜⠛⠁⣀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⡇⠀⢠⣛⠯⢈⠥⠶⡂⠀⣈⡻⢮⡭⢟⡋
⠀⠀⠐⠲⣞⣿⡓⢦⡄⠀⠀⠀⠀⠀⣶⡿⣿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⡿⠇⠀⠀⢭⣍⡀⢚⡋⠁⠀⠠⣭⣹⣛⡭
⠀⠀⠀⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠱⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣯⣤⣭⣥⣦⣭⣷⣥⣿⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⢠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣶⣤⠀⢀⣴⣾⠿⡿⣿⣦⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣿⠏⠀⠀⠀⠦⠹⣿⡆⠀⣾⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⡀⣿⣧⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⢻⣿⠀⠀⠀⠀⠠⢁⣿⡏⠀⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢿⣷⣤⣉⣤⣤⣾⡟⠁⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠉⠛⣛⠛⠛⠁⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⣼⡿⠀⠀⣿⡇⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠰⣿⠇⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⡿⢿⣿⣿⠛⠿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢿⣿⠋⠀⠀⠙⣿⣿⣦⣄⠈⠙⠛⠿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢻⣿⡀⠀⠀⣰⣿⠏⠙⣿⣷⠄⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⠻⠿⠿⠿⠿⣋⣴⣾⠿⠋⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠻⣿⣦⠀⠀⠀⣀⣠⣴⡿⠟⠻⢿⣶⣶⣶⣾⠿⠛⠁⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠿⠿⢿⣿⣶⣶⣿⣿⣶⣶⣾⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢾⣦⠀⠀⣠⣤⣤⣿⡏⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠸⣿⣷⣤⣬⣭⣭⣭⣥⣴⣶⣶⣶⣿⣷⣤⣤⣤⣤⣤⣶⣾⡿⠛⠁⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⠉⠉⠉⠉⠉⠉⠉⣉⣁⣀⣈⣉⣭⣭⣭⣽⣿⣿⣿⣶⣶⣾⣿⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣾⡿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠘⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠤⡤⠒⠒⠒⠒⠂⠐⡖⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠖⠂⢩⠶⠿⠙⠉⠀⠀⠘⠟⠛⠙⠉⠀⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢂⡀⡄⠈⠀⠤⠤⢤⡤⠤⠤⣤⢤⡀⡆⠈⠀⣉⠁⠐⠂⠳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⡄⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠰⢀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡠⠀⠀⠀⠃⠈⠀⠉⠈⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠀⠁⠀⠀⢀⠠⠓⠖⠁⡀⠉⠀⠀⠀⠀⠀⢀⡀⠤⢀⡤⠶⡶⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠊⠀⠀⠀⠀⢀⠄⠈⠀⣠⠞⠁⠀⠂⠀⠀⠀⠙⢦⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠃⠀⠀⠀⠀⡰⠁⠀⠀⡜⠁⠀⠀⠌⠀⠀⠀⠈⠀⠀⢣⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠂⠀⡀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠑⠂⠀⠘⠀⠀⠀⠰⠄⢀⣀⡀⣀⠀⠀⠀⡇⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠰⢷⡴⠻⡿⠿⠦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠐⠦⠤⠀⣀⣀⠁⠀⠀⠈⠁⠐⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⠼⣦⡀⣿⠉⢹⣿⠗⠀⠢⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⠘⣡⠆⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣈⠙⠉⠘⣿⣷⣼⡋⠈⠋⢀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀⠇⠀⡾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⠀⠙⠶⠶⠶⠛⠿⠿⠷⠦⢀⠀⠁⡀⠀⠀⣤⠀⠑⠀⠞⡈⠀⠀⠀⡀⠀⢘⡄⣪⠃⡜⠁⢙⠃⢆⠅
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⣌⣉⡀⢈⠀⠀⠈⠀⠀⠀⠀⠑⡄⢋⠜⢁⡞⠁⡠⢞⡴⠁
⠀⠀⠀⠀⠀⠀⢀⠂⠐⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠁⠀⠀⠀⠀⠐⠶⣀⠀⢞⣐⡭⠞⢟⣤⠞⠁⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠂⠀⠀⠀⠀⡀⠠⢼⢝⠳⢯⡐⠦⣞⣪⠦
⠀⠀⠀⠀⠀⠀⠐⢀⡃⠐⠀⢲⡎⠉⠉⣶⡎⠉⠙⣦⣀⣤⣤⣤⣤⣤⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡬⠑⠂⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⠒⠊⠉⠙⠒⠺⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⡿⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣘⣛⣛⣙⣛⠛⠛⠛⠛⠂⡃⠚⠛⠒⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣉⣍⣉⣉⡉⠉⢉⠛⠛⠛⠋⠙⠛⠋⠉⠉⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⡄⠀⠀⠀⠀⠀⠀⠚⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠓⠛⠟⠛⠲⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢼⡅⠀⠀⢠⣔⣀⠀⣀⣤⣀⢀⢠⠀⡄⢀⠀⠀⠀⣠⡀⣀⢀⢠⣄⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣅⠐⠀⠀⠀⠀⠓⣌⠋⣿⠋⠙⡟⠀⠀⠈⠀⠀⠀⠀⠉⠈⠁⠉⠁⠀⠈⠉⠉⠁⠙⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠈⡃⢈⡀⠀⢀⠀⠀⠜⠀⠈⠀⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⡄⢨⠀⠀⠀⠀⠀⠀⡧⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣾⡤⣡⠁⡀⠀⠀⠀⠀⠀⠠⡅⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠠⡤⠀⠀⠀⠀⠠⠀⠀⡀⠀⣘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠽⠦⠄⠈⠤⠀⠟
⠀⠀⠀⣀⡤⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠤⡇⠈⠐⠓⠶⠚⠃⠀⠀⠀⠠⠟⠛⠚⠓⠒⠒⠒⠒⠒⠒⠚⠓⠓
⢀⣀⠾⢉⡠⠤⠄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠀⠇⠀⠀⠀⠀⠠⢘⡀
⠀⠁⠐⠋⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠛⠗
⠀⠀⠀⠀⠀⠀⠀⢻⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠗⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣛⠈⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣤⣤⣾⢋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠘⠖⠛⠟
⣤⣤⣤⣤⣤⣤⣤⣼⣯⣥⣬⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢠⣿⣦⣍⡛⠿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏⣰⣿⣿⣿⣿⣿⣦⣌⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⡿⠟⠋⠁⠀⣤⣀⣴⣄⣠⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⡄⠙⠋⠀⠀⠀⢠⣴⠟⠋⠉⠉⠙⢷⣤
⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⢠⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠈⣷⣤
⠀⠀⠉⠁⠀⠀⠉⠉⠙⠁⠛⠁⠀⠀⠀⢠⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡀⠀⠀⠀⠀⣰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠷⣶⡶⢾⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⡈⠻⠿⡿⢟⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣷⣠⣾⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠻⣿⣿⣄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣁⣀⣀⣈⣻⣿⣷⣄⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁



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

⠀⠀⠀⠀⠀⣰⡦⢴⢴⢄⠴⣴⡦⣶⡄⠀⠀⠀⠀⠀⠀⢀⠀⣀⡠⡤⢀⠀⣤⢄⡀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⣽⣿⣗⠀⢸⠀⢄⡮⣛⡇⠀⠀⠀⠀⠀⢸⣾⢿⣿⢧⣳⣽⢠⣟⡞⣷⡏⡿⡇⠀⠀⠀⠀⣼⡻⠤⠽⠷⢾⣿⠴⠿⠥⠴⣟⡀
⠀⠀⠀⠀⠀⢹⣖⠍⠀⢸⠁⢐⣭⣶⡂⠀⠀⠀⠀⠀⢸⡜⡜⣟⢯⣻⣿⣿⣯⡞⡽⣱⣱⠆⠀⠀⠀⠀⣿⠅⠀⠉⠍⢹⣿⠉⠩⠥⠬⢽⡇
⠀⠀⠀⠀⠀⢿⣛⡫⠁⢸⡄⠉⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡝⣌⢳⡙⣿⣿⣫⢞⡵⢣⢿⠃⠀⠀⠀⠀⣿⡛⣛⣛⣒⣻⣿⣛⣛⣛⡓⣻⡇
⠀⠀⠀⠀⠀⣿⣿⣓⠂⢸⡇⣐⣿⣿⡃⠀⠀⠀⠀⠀⢨⢳⡹⣌⢳⣽⣿⣿⣣⢞⣵⢋⢎⠂⠀⠀⠀⠀⣿⠄⠀⠠⠤⢾⣿⠤⠤⠤⠄⢽⡇
⠀⠀⠀⠀⠀⣲⣿⠿⠗⢸⡇⠾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣧⣳⣌⢷⣽⣿⣿⣫⠟⣡⢟⣾⠇⠀⠀⠀⠀⣿⡍⠉⠩⠭⢽⣿⢭⣭⠍⢩⣽⡇
⠀⠀⠀⠀⠀⣸⡷⢏⠁⢸⡇⠨⣿⣿⡇⠀⠀⠀⠀⠀⢸⣧⠳⣽⣦⡙⢿⡿⣡⣾⣿⢋⢾⠇⠀⠀⠀⠀⣿⣄⣒⣒⣒⣚⣿⣒⣒⣒⣒⣺⡇
⠀⠀⠀⠀⠀⣻⠽⡣⠂⢸⠀⢔⣽⣿⠃⠀⠀⠀⠀⠀⠀⢧⠳⣬⡳⣽⣿⣿⡵⣛⣵⢏⡞⡀⠀⠀⠀⠀⣿⣒⠲⠶⠶⢺⣿⠒⠒⠒⢒⣺⡇
⠀⠀⠀⠀⠀⣼⣭⡶⠀⢸⠂⢨⣒⣿⡇⠀⠀⠀⠀⠀⢸⡘⠷⢮⣽⣿⣿⣿⣞⣯⠵⠟⣡⡇⠀⠀⠀⠀⣿⠧⠤⠭⠭⢭⣿⠭⠭⠭⠴⢿⡃
⠀⠀⠀⠀⠀⣾⣿⣡⣀⡸⣠⣤⣝⣿⡅⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠻⢿⡿⠖⠒⠚⠻⠟⠁⠀⠀⠀⠀⠛⠁⠀⠀⠈⠸⠿⠘⠛⠁⠈⠙⠃
⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠈⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣆⣴⡾⠷⠢⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣬⣝⣿⣿⡷⡶⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⢏⡽⡛⣝⠙⠷⣦⠠⡀⠀⠀⠀⠀⢠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠀⣿⡇⢱⣘⣷⡀⠀⠁⠀⠀⠀⠠⣸⣿⣏⠀⢍⠁⣠⢾⣶⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⢹⡗⠀⠈⣿⠙⠠⠀⠀⠀⠀⡾⠉⠘⣿⣧⡈⢸⠳⡟⢹⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠉⢿⡅⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢄⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠓⡂⣂⣀⣲⢄⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢻⠛⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠳⣄⡀⠀⠘⢦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⡀⡀⠀⠙⣶⠄⢴⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠲⣀⠹⣷⣄⢀⡈⠈⣲⣄⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠆⠀⠀⠀⠀⢀⣠⡴⠞⠊⠉⢉⡽⠥⣑⣌⠿⣹⡽⣟⣠⣶⠉⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣴⠾⠉⠀⡄⠀⣴⠖⡀⡄⢠⣆⠹⣿⣇⣤⡀⠘⢙⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢋⣭⢏⣴⣾⢐⡋⢡⢰⣷⡷⡿⠿⢿⠿⠿⠿⠿⢷⣄⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⠛⠿⠿⠷⠿⠷⠿⠋⠃⠀⠀⠀⠀⠀⠑⠀⠐⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢄⠀⠀⠄⠐⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢵⠆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠂⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠌⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⢠⠏⠀⠄⣀⠤⠀⠀⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠀⢠⠏⠀⠀⠸⡠⣤⠄⣠⡀⠘⡀⠀⠘⡄
⠀⢀⡤⠐⠀⡀⠀⠀⠀⠱⡅⠰⠀⠀⠀⠀⠈⠈⢁
⡔⠁⠀⠀⠀⢡⠀⠀⠀⠐⠐⢠⣆⠀⠀⣀⠀⠀⠀⠑⢤⠐⠒⣄
⡆⠀⠀⠀⠀⠀⢧⠀⠀⠠⠀⠁⡜⠀⠈⣠⠇⠀⠀⠀⠈⡆⢡⠸
⢀⠀⠀⠀⢀⠠⠘⠞⠁⠀⠀⠀⢇⠀⢰⠁⠀⠙⠒⠤⠴⠃⠀⢹⡀
⠈⣄⡴⠺⣟⠀⠂⠀⡠⠀⠀⠀⢬⠠⣸⠀⠀⠂⠀⠀⠀⡠⠔⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠋⠀⠀⠀⠉⠉⠁⠈⠑⢄⢢⡘⣄⡏⠀⠀⠀⠐⠔⠁⠀⠈⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠛⠁⢀⠀⠠⠁⠈⢂⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠚⠐⠁⠀⠐⠀⠑⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠀⠜⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠂⠀⠈⠳⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠤⠤⠔⠂⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠢⡀⠁⡀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡘⠢⣀⠑⢆⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⠳⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⢀⣠⠖⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣽⣿⣯⣽⣯⣭⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢀⡐⠈⠏⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⡰⠁⠀⠀⠀⢀⠘⢝⣂⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⠂⠍⠀⣵⣀⠀⠀⠀⠈⠿⠁⠀⠂⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠚⢀⣼⣿⣿⣿⣦⣄⣠⠂⠣⡈⡴⠑⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⠀⡀⢄⠔⠥⠂⠰⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠑⠢⡀⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⢠⠀⠀⠂⠀⠀⠹⠤⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠺⠟⣿⡀⠘⡟⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣐⠀⠈⠶⢤⠢⡀⠀⠆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢸⠇⠤⡉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠉⠓⢁⣀⣘⡆⠀⠘⢀⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠀⠀⠉⠚⠠⠟⠀⠀⠟⠛⠉⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⠎⠉⢹⣿⡖⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢂⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⢁⠀⠀⠆⠀⢠⣤⠀⠀⡻⢃⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠁⠀⠀⠀⠈⠀⠀⢢⠀⡇⠀⣠⠀⠀⢀⠠⡀⠈⡄⠀⢦⠀⠀⠐⠶⠔⠁⠸⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⢊⠠⠀⠀⠂⢠⠀⠀⠀⠀⠀⢈⢢⠁⠞⠁⠀⢀⠌⠀⢳⡀⠀⠀⠀⠇⠀⡌⢀⠐⠀⢀⡄⠀⢠⣃⣠
⠀⠀⣀⣤⣤⣤⠃⠀⢠⣼⣀⠇⠀⠀⠀⢀⠀⣮⡜⠀⠀⠀⠀⡌⠀⠀⠀⠱⡄⢀⡀⣀⠐⠀⣰⠀⠀⢀⢙⣈⢉⣴⠟
⠀⠘⠻⠿⠿⣧⣤⣶⣿⣿⣿⠀⠒⣻⣿⠁⢀⣿⡇⠀⠀⠀⣼⣿⣷⣦⡀⠀⣈⠃⡈⠀⡤⠊⠑⢄⣀⣤⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢠⣿⣷⠀⢾⣿⡇⠀⠀⢰⣿⣿⣿⣟⡁⠀⠀⠀⠀⠂⠋⡆⢠⠞⠛⢿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠻⢷⣾⠛⠇⠀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠴⠃⠘⠀⣠⠂⠈⡁⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠢⣄⠒⣾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠁⢀⠀⠈⠲⢤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡁⠰⠃⡡⠄⠀⠀⠀⠀⠑⣄⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣱⠀⠤⠄⠁⠀⠀⠀⠀⠀⠏⠠⠃

⢱⡄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠑⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠁⠀⠀⠹⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠐⠀⠸⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢂⡀
⠸⣄⠀⠀⠱⡀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠉⠢⣄
⠀⠸⣇⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠡⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠘⢦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠀⢒⠆⠙⣦
⡅⠀⠀⠀⠀⠀⠻⣄⠈⣆⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⠈⠀⠀⠀⠀⠀⠂
⠘⢦⠀⠀⠀⠀⠀⠹⣆⠘⡄⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠊⠁⠀⠀⠔
⠀⠀⠳⡀⠀⠀⠀⠀⠘⢆⠹⠀⠀⡂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠿⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀
⠐⠀⠀⢀⠀⠀⠈⢧⡀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠁⠠⠌⢷⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⢀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠘⢿⡌⣿⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠪⣷⡟⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠠⡀⠀⠀⠀⠀⠈⠠⡀⠀⢹⡇⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⢸⡇⠐⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣟⠉⣿⣻⣛⣛⣛⣟⣛⣛⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣻⣟⣛⣛⣻

⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣤⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⡿⣿⠿⠷⢬⡀⠤⣽⡿⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⢸⢃⠀⠈⠃⢰⠋⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠁⠀⠀⠀⢇⠀⠀⠈⠀⢸⠀⠴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⢿⡋⠒⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⢡⡀⠀⠀⠀⠀⠀⢳⠀⠀⣀⣿⣄⣦⣤⣀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣙⣶⣆⣶⣶⣶⣼⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣛⡛⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠀⠀⠀⢀⣀⡄⢀⡉⠉⠑⠒⢒⣒⣂⠠⠄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⢒⣒⠒⠀⠠⣤⣄⠀⣀⣀⣀⢉⣉⣉⣉⣀⣀⣤⣤⡶⠞⠋⣉⠁⠀⠀⢐⢒⡟⠉
⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣐⣠⣬⡥⠶⠶⠶⣾⣻⠻⠿⠟⠛⠛⠋⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠈⠁⢲⣶⡤⣄⠀⠁⢠
⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣶⣶⣶⠿⠟⠛⠉⠀⡾⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⢛⣉⣉⣉⣥⣤⣤⣤⣤⣤⣤⡀⡀⠀⠈⠀⠀⠀⢀⣀⣠⣤⠶⢻⡅⠀⠀⠀⢀⡠⠔⢋
⠀⠀⣶⠀⠐⠒⢀⣉⣉⣙⣋⣉⣭⠭⠤⠶⠞⠛⠛⠋⠉⠁⠛⠙⣋⣁⣀⣉⣉⡽⠟⢛⠛⠛⢛⡭⠍⠑⠊⠉⠒⠺⠿⠖⣒⠉⠀⠀⣀⣈⡦
⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠋⠩⠍⠐⠊⠉⠀⠂⣉⡠⠖⠋⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⢺⣷⡞⣶⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠀⠀⣀⣠⡤⠖⠒⠉⠔⠈⢂⠀⡀⠀⠀⠀⢀⡤⢺⣼⣮⡿⠯⣵⣿⠁⣤⣴⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠋⠉⠉⠁⠀⠠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠈⠉⢀⡛⠴⠞⠃⠀⠀⠉⠀⠉⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠀⠈⠉⠉⠀⠐⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠄⠰⠄⠈⡄⠁⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠐⠁⢈⣠⠤⠤⠄⣤⣤⠒⠜⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠠⠤⠐⠒⠛⠁⠀⠀⠀⠀⠈⠠⠈⠁⠁⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⢀⠄⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠗⠀⠀⠀⢀⠴⠋⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠃⠐⠀⠀⢀
⠀⠀⢀⡄⠀⠀⠀⠅⠀⢰⠶⠓⠊⠉⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⢀⠠⠐⠁⠀⠈⠀⠀⠡⠀⠀⠀⠀⠈⠀⠀⠀⢤
⠰⣔⠊⠀⣀⡀⠀⢠⠀⠀⠏⠢⡀⠈⠀⢠⣤⠀⠀⡀⢣⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢠⠎⠰⡌⠉⠀⠀⠘⠐⠂⠱⣀⠈⠐⠀⠀⠄⠄⣁⠀⠔⠩⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠊
⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠘⠅⠐⡀⣿⠄⡴⠛⡂⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡐⢎⡃⠀⠀⠀⠀⠀⠀⡂⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⣠⠴⠒⠖⠚⠓⠒⠤⣀⠀⠀⠀⣆⡑⢨⡹⠄⠀⠀⠂⠀⠀⡅
⠀⢀⠔⠋⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⣆⡉⡍⠙⡷⠀⠈⠏⢀⠀⠈⠀⣰⠀⢸⠕⢀⡼
⢀⠉⠀⠀⠀⠈⠉⠀⠀⠸⠕⢂⡀⢀⠈⢧⣰⠀⡦⠈⠆⢘⢀⠀⠀⠀⠀⠶⠦⣄⠠⠄
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢛⡀⠀⠰⡆⠃⠑⢈⠃⠌⠀⠀⠀⠀⠀⢀⠀⠉
⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠀⡇⠀⠀⡰⣆⠀⠀⠀⢀⡀⣀⠔
⢘⡀⠀⠀⢄⠀⠀⠀⠀⠀⠈⣀⠄⠀⠀⢰⣁⠤⠾⠇⠒⠂⠈⠉⠀⡀⠠⠄
⠀⠻⡀⠀⠀⠁⠀⠀⢀⠀⠰⠁⠀⠀⣠⠋⠀⠄⠀⠀⠂⠀⠁⠈
⠀⠀⠉⠢⣄⡀⠀⠀⠀⠂⠀⣡⡤⠚⠁
⣤⣤⣤⣤⣤⣬⣵⣶⣶⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣛⡻⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣟⣛⣛⠻⠿⣷⣦⣍⡛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣯⣟⣛⣭⣙⠛⠿⣷⣦⣌⡙⠿⣷⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠾⠿⢿⢻⡆⠘⢿⣷⣌⡉⠙⠻⢷⣶⣬⣍⡙⠛⠷⣮⣝⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠯⢭⣉⠛⣾⠘⢿⣆⠀⠙⠿⣿⣷⣤⡀⠈⠙⠻⣿⣷⣦⡀⠉⠻⣦⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⡉⠒⠬⡑⡘⣧⠈⠻⣷⣄⠀⠈⠛⢿⣿⣶⣄⡀⠀⠉⠻⣿⣷⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⡴⣻⣄⠁⠀⠐⢌⠳⣄⡈⠻⢿⣦⣀⠀⠈⠛⢿⣿⣦⣄⠀⠈⢻⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣙⣁⡺⠽⣫⢘⠀⠀⠀⠉⠂⠙⠲⢤⣉⠛⠷⢦⣄⣀⠈⠙⠻⢷⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠘⡀⣠⠤⠶⠋⣡⢃⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠄⠙⡋⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⣆⢣⠀⠀⡴⠚⠁⢊⠀⢀⠀⢠⡀⠠⠀⡀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠈⠀⣠⠀⢰⡏⠀⣿⡀⠘⠷⣄⡈⠓⠢⠤⣭⣈⡡⠄⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⣥⠀⢿⡄⠘⢷⣄⠈⠻⢦⣄⣈⠙⠓⠲⠶⠦⠖⣒⣩⠀⠀⡀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠉⠢⣀⠀⣐⡢⣌⠳⢄⣙⠶⢤⣉⠛⠶⢤⣌⣉⣙⣛⣒⡾⡭⣭⣶⡒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠛⠓⠚⠛⠒⠒⠻⢿⣷⣶⣶⣿⣿⣿⣿⣿⣿⡋⠥⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢱⡀⠂⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣿⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⡆
⠈⠠⠡⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠂⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠐⠀⠀⠀⠀⠀⢠⠠⡅⠇
⠀⠀⠀⠂⠀⠀⠀⠀⠀⢘⢰⡆⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠲⣾⠗⡛
⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠈⠉⡽⠙⠆
⠀⠀⠀⢀⡄
⠀⠀⠂⠠⠇⠀⠀⡔⠀⠀⢀
⠀⠀⠈⠀⢈⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢂⠀⠈
⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠤⠀⠀⠐⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⣉⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⢀⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠿⠿⠛⠉⠉⠙⠻⠷⠟⢋⣉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣻⣟⣤⣠⣤⣤⣤⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠛⢛⡛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠀⠒⣒⠒⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⢿⣿⣿⣿⣿⢏⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣾⣿⣿⣿⣿
⠛⠉⠉⠀⠀⠠⠤⠔⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿
⠀⣴⡖⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣈⣤⣄⣀⣈⣴⣶⡄⠀⠀⠀⢀⣀⣀⠀⠀⠀⢠⣀⣀⣄⠀⣀⣀⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣟⣣⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢛⠿⠛⠛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⢻⢀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⡄⠒⢶⠀⠁⢨⡍⠙⢷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⣾⣦⠀⠀⡟⠆⠀⠀⠀⠀⠀⠀⢀⠀⣸⡲⣄⢞⡟
⠀⠀⠀⠀⠀⠠⠀⠀⠈⡸⢹⣿⠇⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠂⠤⡑⣯⡾⢶⠒⠆⠀⢀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡞⠡⠚⣟⠳⣹⡓⣆⣌⣧⡤⣔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡅⠀⠀⠸⡆⠉⢉⠜⡡⣿⡿⡌⡅⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⠋⣸⠉⠁⠉
⠀⠀⠀⠀⢉⣉⠀⢈⠠⠀⠉⠁⠀⠀⠐⠂⠀⠀⠀⠀⢀⠉⠉⠁⠒⠀⠀⠀⠘⡇⠰⠆⡗⠒⠈⠉⠀⢤⣘⠁
⠀⠀⠐⣢⢈⣉⡙⢃⠐⠛⠿⠀⠀⠀⠐⠛⠲⠆⢀⣁⢀⠀⠀⠀⠐⠠⠈⠱⠤⠷⠄⢸⠁⣈⣡⣀⡀⠉⠉
⠀⠀⠀⣽⣍⠉⠁⠸⠀⠀⠤⣴⣦⡶⡰⣤⠄⠀⠈⠙⠛⠋⠁⠠⠤⠶⣤⣄⣀⢐⠀⣘⣀⢀⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠚⠐⠆⠄⠔⠠⠤⠤⠀⠈⠀⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⣇⡠
⠀⠀⠀⠀⠀⠀⠀⣠⣇⣀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣴⣾⣿⣿⣿⠟⠁⢀⠀⢸⣶⡎⣉⠙⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢱⠄⠀⠀⣠⠀⣤⣴⣄
⣰⣿⣿⡿⠛⠫⠃⠀⠀⣀⣴⠟⣹⣀⣿⠻⣿⣇⡀⠈⡆⢀⠠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣰⣟⠺⣣⣷⡄⠸⡂⠀⠀⡉⣻⣿⣿⣿⡦
⣿⡿⠙⠂⠐⡠⣸⢀⣴⠏⠁⡄⢀⣤⣁⠀⠘⠻⠃⠀⠀⠈⠻⣷⡀⠀⠀⠀⢀⠠⠀⢀⣾⣿⠇⠀⠘⢰⣟⠀⠠⡄⠀⢛⡉⢿⣿⣿⣧⡀
⠟⠁⠀⠄⠀⢁⣿⠟⠁⠀⠠⠄⣞⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⣠⣿⠏⠈⠀⠀⢸⡞⠈⠀⠀⠷⠀⠈⠛⢞⣿⣿⣫⣸⡄
⠀⠀⡌⢜⣠⡾⠋⠀⠀⢸⠆⣠⣤⡅⠀⠀⠀⠀⠈⠰⡵⠀⠄⠀⠘⢿⡀⠀⡀⢰⠟⠁⠀⠀⠀⠀⠀⠏⠀⢀⡄⢸⣷⠶⠀⠸⣯⣻⡿⢷⡇
⠀⢰⢠⡞⠁⠀⠀⠀⡀⠄⢠⣿⠎⠀⠀⠀⠀⠀⠀⠀⣧⣔⠀⠀⠀⠘⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢣⣀⠀⠀⠸⣿⣷⣯⣷
⠀⢰⠋⠀⠀⠀⠀⠀⠉⢠⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢾⣏⠀⠀⠀⠙⣿⣯⣿
⠀⠈⠀⠀⠀⠀⠀⠸⠶⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⡰⠀⢀⣠⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣠⣬⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⢀⣀⣀⠦⠠⢰⣿⣥⣤⣤⣀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⣴⢟⠁⠀⠠⡄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⠀⠀⢀⠄⢈⡀⠛⣤⣤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠈⠆⠀⣴⡇
⠀⠀⠀⠀⢸⠀⢀⣮⣾⢯⡀⠀⠈⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢀⠀⠀⣀⡀⡉⠣⣻⣄⠀⠀⠣⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣶⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢋⡀
⠀⠀⠀⢰⠀⢠⣿⣾⠁⠀⠈⠛⢷⣦⣀⠙⠦⣀⠀⠉⠲⠤⣀⣀⠀⢀⡤⠤⠖⣚⣭⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇
⠀⠀⢀⠈⢀⡈⠙⠋⠀⠀⠀⠀⠀⠈⠙⠻⢦⣬⣝⣶⣤⢤⣤⣤⣤⢶⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢦⡆
⠀⡀⢸⠀⠘⣿⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇
⠀⢣⣏⣤⠀⣸⣿⣶⡾⠕⠊⠁⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢄⠀⠠⠼⠁⣀⣤⡶
⢆⢸⡚⠰⠁⠛⡿⡣⠂⢤⡔⢦⠐⢶⡧⠀⢀⠆⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⣀⠠⠓⢈⣀⠀⠴⣊⠙⢷⠽
⢺⣷⡼⢂⢓⡗⣪⠴⠒⣠⣿⣤⠞⠛⠁⠙⠃⠐⠐⠴⠂⠀⠀⠀⠐⠂⠀⠉⠁⠀⠒⠀⠀⠀⠀⠐⠀⠒⠒⠀⠁⠀⢀⣈⠅⠐⠶⠈⢠⣤⠼
⠿⠿⠥⠞⠋⠉⠟⠃⠛⠶⠀⠒⠤⠇⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠦
⠀⠀⠀⠀⠀⠀⢠⢆⣄⠸⣿⣧⣀⠀⣠⣮⣂⣤⣾⠟
⠀⠀⠀⢀⣠⣤⣬⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣷⡶⠶⠖
⠀⠀⠈⠉⢉⣉⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⣊⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⡀⠀⠉⠉
⢀⣴⠿⠿⠟⠟⢛⣩⣽⡿⢟⡿⠻⣿⣿⣿⠿⣿⣾⣯⡕⠄
⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⣸⡇⠀⠙⢽⣿⣷⣌⠙⠋⠁
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⣿⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⣴⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⣿⣿⣿⡿⠿⠋⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠻⠟⠋⠉⠀⢀⣶⣿⣿⡷⠀⠀⣴⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣄⡀⠀⠀⠀⠿⣹⣿⣇⣀⣠⡿⠟⢀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⢾⣿⣿⣶⣄⡀⠀⣿⣿⣿⣿⣷⣤⣀⣾⣿⡏⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠙⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠈⣻⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡛⠛⠃
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤
⠀⠀⠀⠀⠤⠀⡈⡀⠎⠀⠉⠙⠙⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠲⣤⡀⠈⢇⠇
⠀⠀⠀⢀⠔⡺⠷⠼⠦⣶⣿⣷⣦⢴⣿⣧⡀⠀⠀⠀⠀⠀⠈⠳⡤⢄⠈⠣⡘⠡⡀⠈⣾⣄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠋⢹⢻⣿⣾⠖⠹⣆⠀⠀⣀⡀⠀⠀⢌⠢⡣⣀⢻⡦⣌⢲⣜⣟⠄
⠀⠀⠀⠀⠹⢠⠀⢀⢀⡀⠀⠀⠈⠛⢳⣷⡀⠩⠄⠀⠀⢍⡑⠠⢀⣲⣬⡻⣗⣏⣾⢸⡼⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠷⣶⣤⢄⠀⡘⣿⣏⢸⠧⠀⠀⠀⣀⠭⢛⡟⡟⡇⢸⡏⠸⣈⡁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠐⣽⡈⠐⠀⠀⠀⠈⠀⢀⠄⢀⠇⠀⢠⠱⡄⠙⣷⠀⠸⡄
⠀⠀⠀⢀⣀⡀⠀⢀⡄⣤⣦⣤⣄⡀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠋⠀⠎⢠⢧⠏⠀⠁⠐⠉⠀⠀⠁
⠀⠀⠤⠀⢠⣼⠇⣶⡷⢺⡌⠆⡽⡿⠲⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⣀⠀⡀
⠀⠀⢠⣾⠟⠁⣼⠏⠀⡼⠀⢀⠁⠀⠀⠀⠀⠀⣀⠙⣓⣲⢶⣶⣶⣶⠼⠾⠟⠙⠟⠂⢄⠓⠷⢤⣤⣤
⠀⠔⡝⡏⠀⠸⡟⠀⡰⠃⢰⢸⠀⢱⠀⠘⡄⠀⠈⢱⣎⡙⠿⠷⢶⣶⣶⣴⣦⣤⣶⣯⣷⣤⣶⣶⣶⣿⠂
⠀⠀⠈⠀⠀⠀⠇⠀⠁⠀⠸⢸⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡈⡁⠉⠉⠛⠉⡁⢈⣩⣤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠡⠁⠞⠁⠘⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠁⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⢶⣦⣤⣄⡀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠘⣧⣀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⡙⠁⠀⢠⠀⣈⢙⠛⠿⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡀⠼⠞⠒⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣚⡁⠀⠀⠠⠌⠐⢄⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⣀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣼⠀⠨⠀⠀⠉⠃⢤⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠂⠀⠀⢆⡄⠀⢀⣈⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣅⡼⠃⢠⠐⠃⠀⠀⢀⣿⡖⠁⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠗⡐⠀⠀⠀⠀⠘⠙⢢⢀⣄⠈⡄⠶⡀⠀⢀⠚⠁⠀⡀⠐⠀⠀⢀⣀⣤⡠⠛⢂⡀⠀⠚⠁⠀⠰⡖⠠⠦⠀⠀⣠⠜⢋⡿⠂
⠀⠀⠀⠀⠀⠀⢀⠆⠭⠀⠈⠀⠀⠠⠔⠀⠀⢁⣤⠾⠯⢤⡨⠀⠉⣵⡆⠀⠀⠘⠿⠂⣶⠠⠛⠁⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠿⠃⠰⠀⡈⣥⠞⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠠⠎⠀⠀⠀⣰⢫⠁⠀⠀⠀⢹⠀⠀⠀⠈⢂⡀⠀⠐⠀⣀⠀⠀⠀⠀⠐⢀⠤⠀⡄⡀⡤⠀⠈⠠⢉⡀⠆⣀⠘⠠⠀⢠⡀⢠⠼⣍
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⠀⠠⣲⠶⡯⠀⠠⡄⣦⣄⣚⠤⠀⠀⠀⠀⠁⢠⠀⠀⠀⢡⠀⠀⢀⣀⢈⠱⠚⠁⠀⠀⢀⠀⠀⠰⠃⠀⠉⢎⣀⡊⣉⠁⠁
⠀⠀⢀⠄⠒⠒⣀⠉⠋⠀⠀⠔⠈⠁⣀⠄⡤⠄⠀⠈⠋⠤⢧⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢠⠇⠸⠡⠀⠒⣃⠀⠃⠉⠀⠪⢀⠈⡀⠀⠀⢴⠶⠁⠀⠀⠆
⠀⣀⠛⠛⠋⠱⠚⠄⠀⠀⡠⠞⢹⠶⠋⠀⢀⣶⡆⠀⣴⣶⠇⠕⠀⠀⠀⠀⠀⠀⠀⠘⠌⠃⠈⠁⠉⠩⡑⠀⢀⠀⠀⠀⠈⠐⠀⠀⠀⠃
⢀⠀⣐⡀⠀⠀⠀⢰⡔⡀⠑⠠⢀⠦⡀⠀⠈⠉⠄⠀⢁⠘⠉⠐⠂⠀⠴⠤⣤⠦⠴⠂⠀⠀⠀⠀⠀⠀⠈⠂⢠⡑⢄⡀⠀⡹⠄⠀⠁⡠⠀⠀⠀⠀⢀⠌
⡔⠀⠀⡥⣀⣌⠉⠆⠀⠀⠀⠀⠀⠉⠈⠐⠠⡄⠀⠆⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣷⣶⣞⠒⣶⣯⣽⣖⣉⣭⡵⡆
⢐⠀⠐⠀⠀⠐⠂⠁⠀⠀⠀⠂⠀⢠⠀⠘⢟⠲⡦⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠀⠀⠀⠀⠉⠉⠁⠀⠻⣿⣯⢉⣫⣶⠶⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⣠⠀⠈⠀⠐⠷⠔⠲⠤⣄⡀⠀⠀⡀⠀⠀⠀⠀⡠⠄⠉⠀⠀⣀⣠⣰⡞⠛⢂⠀⠀⠀⠀⠀⠀⠀⠿⡅⠂⠰⠚⠁
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣬⠡⠙⠙⢿⢙⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣤⡬⡷⡀⠠⡊⠀⠈⠿⣤⡤⠉⠀⣀⢠⡄⠀⠡⡀⠀⡀⠀⠀⠠⠈
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠓⠬⣅⣀⣉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡚⠛⢋⡙⠠⡌⢣⠀⠀⠀⠀⠀⢀⡠⠅⢲⡤⠀⣄⠠⠄⠑
⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠙⠧⠘⠃⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢉⡀⠀⠁⢤⡄⢳⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣄⣤⣄⣌⢠⠀⠩⠄⢰⠅⠈⢹⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡀⠐
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠠⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⠛⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⣠⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡃⠁⠀⠈⢆⠰⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠂⠀⠀⢆⡈⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠁⠄⢄⢂⠄⠘⠠⠬⣃⡑⣀⣀⠿⢉⣤⢤⠤⢤⠀⢸⡟⠝⠛⠛⡏⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠦⣞⡦⠔⣂⠴⠚⠩⡦⠀⠀⣀⣤⣀⠀⠀⡾⠉⠈⢄⣠⡄⠀⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⢠⠔⠂⠀⠐⠉⢄⠀⠀⠀⠀⠀⠃⣧⣀⣼⠀⣰⣿⡤⠖⢊⠁⠐⣰⡧⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠘⣿⠠⠓⣀⡥⠖⠋⣿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠲⣦⣅⣀⡀⢰⡇⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠁⠰⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⠀⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⡀⠀⢂⢸⡀
⠀⠀⠀⢰⡖⠛⠓⠲⠶⠦⠤⠤⡤⣤⠤⠤⠖⠋⠀⠀⠀⠄⠀⠠⢀⢳⡀
⠀⠀⠀⠈⠳⣤⡀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠈⡠⠀⠀⠀⠀⡀⠀⠄⢁⠝⠢⢤⣤⣀⣀⣀⣀⣤⣤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠙⠦⣄⡠⢈⠐⠀⠂⢠⡤⡀⠠⡄⠀⠀⠂⠀⠀⠀⠀⠢⠀⠑⠀⠂⠂⠀⡀⡀⠀⢀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢖⡀⠀⠀⠈⠀⠐⠆⣠⡀⠀⠀⠠⠀⠀⠆⠂⠀⢀⠓⡁⠤⢀⣈⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡘⠰⡉⠨⠀⠂⠀⠀⠀⠀⡀⣴⠄⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⠀⠀⢀⠞⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠌⠐⠐⡅⠀⠀⠀⢹⡄⠀⠈⢞⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⢀⠀⠆⡀⡑⠀⠀⠇⠀⠀⠀⣄⠁⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⠀⣈⡀⠲⣠⠵⠒⠋⠙⢦⣀⠀⠈⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠐⠋⢀⣨⠖⠋⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⢀⣠⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣢⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠋⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣧⡀⠀⣰⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⢈⣵⣆⣠⣄⣠⡆⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠞⠛⠋⢿⣿⠋⠀⢀⣴⠏⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠠⠾⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⡔⠀⢀⡄⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⣿⣿⣿⡇⣠⠄⠀⠀⢠⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣷⡏⠀⠀⢀⡞⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠀⠀⠀⠁⠀⠀⠙⡟⠀⠀⢀⡞⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⢀⣠⢾⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠛⠋⠁⠀⠠⠆⠀⠀⠀⢀⣠⡴⠞⠋⠁⣀⣤⠖⠋⠀⣼⡆⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⢀⣤⠄⠀⠀⠀⢀⣤⡶⠛⠁⠀⣠⡴⠚⠉⠀⠀⠀⠀⢽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠴⠟⠁⠀⠀⢀⡴⠟⠁⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⠒⠲⠶⠄⠀⠀⣀⣀⣴⠏⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠖⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⡟⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠶⣄⣠⣄⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢀⣧⣬⡳⠟⣿⡇⣤⢉⣾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠹⡜⣿⣀⡀⠰⢋⠂⠉⡳⠢⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠆
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⢭⣧⠾⢦⣀⠀⡸⠟⢻⡞⣦⣄⠀⠀⢀⡴⢒⣒⣒⣤⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠙⣆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⢷⣉⠬⠭⠟⠛⠛⠋⠉⠉⢋⡝⠋⠁⣳⣀⣀⣠⠤⢤⡴⠋⠁
⠀⠀⢀⡻⠉⠀⠀⠈⠳⣄⠀⠀⠀⢀⣠⠤⢤⣄⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠙⠀⠀⠀⠀⠀⢸⣤⡎⠉⠋⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡤⠤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣲⣄⡀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⣀⣠⡤⣴⢶⡶⡏⠉⠉⠀⠀⢀⣀⣀⣀⣀⠀⢠⠇⠀⠀⠀⢀⣀⣀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⡶⣶⠟⢛⣻⣤⠿⠤⠛⠓⠈⠉⠉⠁⠀⠀⠚⠻⠉⠁⣸⢀⣀⣀⣠⠏⠀⠀⠋
⠀⠈⢲⣄⠤⠤⠤⣄⠀⠀⠀⣰⠏⠀⠉⣀⡼⠗⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⢇⣀⣰⣿⣏⠀⠀⠈⢳⣀⡀⠀⣀
⠀⠀⠀⠁⢠⠞⣧⠈⢳⡴⠊⢉⣥⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠕⠒⣀⡀⠒⢌⡇⠀⠀⠀⠀⠀⠁⠀⠈⠛⠁
⠀⠀⠀⢴⠋⠀⡏⢧⡈⠀⠐⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣡⠁⠶⠃⠀⠘⠂⠘⣏⢉⣉⣽⡽⠛
⠀⠀⠀⢸⣀⣴⣧⠀⢳⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⡇⣈⣴⣊⣵⡦⠀⠘⢒⡒⡆⢃⡀
⠀⠀⠀⠈⢿⠉⠀⢇⣘⠸⠓⠿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡟⢛⣿⠇⠉⠏⠉⢴⡗⡀⠉⣀⣼⠉⠙⢦⡠⢤⡀
⠀⠀⠀⢀⠼⡇⠀⠘⣯⠃⠀⢠⡤⠬⢈⣉⡐⠢⠤⣀⠀⠀⠀⠀⠀⠘⠦⣤⣼⢏⣩⠉⠙⠲⢸⠳⢽⠋⢹⡇⠀⠀⠀⠀⠀⠈⣇
⠀⠉⠙⠇⢀⣿⠀⠀⣿⡔⣠⢔⣪⣭⣭⣭⣥⣌⡑⠦⣍⠑⠢⣤⣤⡤⠤⣞⠀⠊⠁⠐⠒⠆⠙⢀⠟⢳⡘⡇⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⣼⢀⡄⠀⢸⣿⣵⠟⢋⠀⠤⠀⠀⡉⣹⠷⡌⣷⣀⣀⠙⠻⡞⢹⣀⣀⣀⡀⣀⡀⣼⡇⠀⠈⢻⠛⠛
⠀⠀⠀⠀⢻⣬⣇⠀⠘⡿⠛⠁⠀⠀⠀⠀⠠⠀⠙⠲⠴⠋⠉⠙⡷⣤⡜⢡⢴⣵⠉⣉⠀⠀⡨⠿⢾⠁⠘⢇⣠⣄
⠀⠀⠀⠀⠀⠹⣿⡀⠀⢃⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠⡁⠸⡄⣧⣄⠑⢤⢂⣁⣺⣦⠀⠀⠃⠀⢸⣭⡟
⠀⠀⠀⠀⠀⠀⢹⣧⠀⠘⡀⠁⠀⡀⠤⠤⠄⢀⠀⠀⠐⢄⠀⠂⠀⢀⣷⣍⡛⠿⣋⣜⠳⣌⡤⠤⠤⠷⣾⠿⠞⣷
⣤⡦⠀⠀⠀⠀⠀⢻⣧⢆⢦⡐⠀⢀⠠⣤⣤⣤⣄⡀⠀⢄⠀⠀⠄⠸⢿⣾⣦⣋⠋⢉⠛⠶⣭⣗⣶⠾⠇⢒⣪⡟⠀⠀⠀⣀
⢘⣧⣀⡀⠀⣀⢴⠟⢛⣿⣿⣧⢈⡴⠋⠀⠀⢀⢬⠹⡂⠄⠁⠀⢀⡀⠂⠉⠋⠈⠀⠀⡀⠀⣤⣬⣿⣿⠉⠏⣾⠀⠀⠀⠀⢅⡷
⣎⠼⠯⠿⢛⣵⣏⣷⣾⡟⢿⣿⡟⢀⡴⠒⠠⣾⢌⣔⠋⣢⡀⠀⠄⠀⠀⠀⠀⠀⠈⠂⠀⢠⣿⣶⡖⠓⠀⢰⡟⢹⣉⠖⡶⢮⡀
⠈⠉⢉⡽⠯⢤⠀⣏⢠⡍⢈⡟⠀⢹⡇⠀⠈⠀⢸⡈⣣⡏⢠⠂⡒⣄⠒⠀⠀⡀⠀⠄⠀⠒⠀⠀⠀⠀⠠⣿⠓⣒⣵⢾⣤⠇⡷
⠀⠀⢸⡴⣄⣸⡧⠼⢛⡝⠀⠁⠠⣤⠷⠤⣄⡀⠀⡟⠁⠈⠙⢚⠗⢉⢢⡐⠠⢴⡓⢶⠀⢀⣤⣄⢀⣺⠋⠀⢿⣧⢸⠆⠀⠈⠁
⠀⠀⠈⠻⠦⣤⣤⣴⠟⠄⢀⡀⡀⠈⠀⠀⣀⡉⠳⣄⠀⠀⠀⠙⠂⠙⠚⠉⠳⠦⡿⠀⠿⠋⠤⠝⠛⢁⠀⠀⣴⠲⣻
⠀⠀⠀⠀⠀⠀⠀⢷⣔⣃⣮⣐⣊⡴⠞⠛⠉⣿⠓⣹⠦⣄⣀⣀⣠⡴⠞⠻⠦⣤⣀⠀⠀⣀⡤⠞⠛⠶⠶⠞⠉⠛⠁

⠀⠐⠀⠀⡔⢛⡷⢆⠀⠑⢄⠈⠒⠦⣀⠰⠖⠚⡻⢛⠟⣿⢞⠿⣦⡜⣾⣴⠎⠁⠐⠊⠓⠈⠀⠉⢳⡀⠘⣿⢡
⠀⠀⢀⣀⠤⢽⡇⠈⢧⠀⢀⡑⢦⡀⠢⠁⠀⠚⣤⠋⠀⣧⠾⠚⣡⠔⢋⡽⣷⣗⣖⠐⠒⠀⠰⣶⣾⣷⣀⠀⠈
⠀⠔⠋⣩⡏⠸⣷⡀⠀⡳⠀⠉⠢⠌⠀⠀⠢⡀⠁⠀⠘⠋⠋⠐⠡⢠⠊⠠⠋⡻⢿⡀⠈⠃⡸⠛⡀⠈⠉⠓
⠀⣀⠄⢵⣧⠀⠻⡷⡄⠈⠢⠀⢀⣠⣤⣴⡶⠟⠛⠳⣦⡀⠀⠘⠀⠸⠀⢸⡀⢳⠈⠻⡆⣸⠁⣰⡁⠀⠀⠀⢠
⣀⣀⡀⠸⢿⣆⠀⠙⠈⠢⠀⠀⣮⠇⢀⣧⣿⣆⡀⣰⠌⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⠏⣍⠲⢦⡀
⣡⠔⠁⠀⡎⠎⠂⠀⠀⠀⠀⠀⠀⠀⠙⣥⣍⠈⣣⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠈⠓⠦⠽⣆
⢳⣄⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⡙⠳⠄⠀⠀⢳⡴⠚⣓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢧⠀⣿⡎⠀⢈
⣵⠀⠀⢸⣦⣾⠷⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡟⣷⣀
⠿⣤⣶⣷⠄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠷⡯⠽⡿⣅⡀
⣿⣣⡼⣾⣒⠫⣤⡶⠖⢢⡀⠀⠀⠠⠰⠀⠔⠲⠀⠀⠰⠀⠰⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠁⠊⠁⠋⠁⠀⠐⠉
⡇⠐⣿⠏⠻⢷⡺⠗⠀⠉⢉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⡿⠛
⣿⢡⠇⢳⠘⠂⠄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⢿⠟⠹⣿
⠟⠀⠀⠘⠀⠀⢰⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠈⠀⠀⠁⠰⠶
⠀⠀⣄⠀⢸⣓⢻⠷⣾⠏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢠⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⢤⡄
⠀⠀⠈⠿⣿⡏⣟⣷⣿⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⣄⠙⠦⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡐⣦⣌
⠀⠀⠠⢞⠉⠙⠺⠟⠉⠲⠀⠀⠀⢠⢀⢀⣷⠀⠀⠀⠀⠀⠑⠪⢭⣂⢴⡆⣶⣀⡤⠤⢶⣶⠖⠂⠀⡏⠠⡁⠸
⠀⠀⠀⠉⠀⡀⠀⠘⠀⠀⠀⠀⣦⡆⣯⣸⢫⣄⠀⠀⣀⣀⡤⠖⡻⠟⣻⠿⠋⣁⣤⠶⠋⠁⠀⡌⠛⠢⠤⣿⣷
⠀⠀⠀⠸⡀⣰⣴⠀⣀⠀⠀⡰⡙⢲⣿⣯⠘⠫⢾⣀⠀⠀⣄⡀⠀⢰⣿⠶⠛⠉⠁⠀⣀⣴⠀⠙⠋⢶⣴⠿⠿
⠰⣄⠈⢠⣻⡿⠛⣉⣁⠀⠀⣿⠀⢺⢿⣇⠀⠀⠘⢿⣷⣀⡈⠀⠀⠘⠃⠀⠀⠰⠊⢫⡷⠀⠀⠀⠀⠚⠀⢀⣤
⠠⡠⠱⡤⢯⠟⠉⠁⠀⠀⠀⠯⠴⢶⣿⣷⠇⠀⠀⠀⠰⠟⡴⠀⠀⠼⢤⠀⠀⠀⠶⠿⠁⠀⠀⠀⠀⠀⠲⣾⠗