Uppercase Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⡤⠤⡄⠀⠀⡤⠦⠄⠀⣤⠤⣄⠀⠀⡤⠤⠄⠀⣤⠤⠀⠀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⣴⣏⣷⠀⠀⡷⠴⣇⠀⢸⠁⠀⠀⠀⣇⠀⢸⡆⠈⡷⠶⠀⠀⣧⠤⠀⠐⡇⠠⢶
⠀⠀⠀⠀⠀⠐⠇⠀⠘⠆⠀⠳⠶⠋⠀⠈⠳⠶⠂⠀⠳⠒⠋⠀⠀⠓⠲⠀⠀⠃⠀⠀⠀⠙⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣿⠀⢸⡇⠀⢸⡇⠀⣿⡴⠋⠀⢸⠀⠀⠀⡿⣧⠀⣸⢿⠀⠠⡟⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡏⠉⢸⠀⢸⡇⢀⣸⡇⠀⣻⠹⣄⠀⢸⣄⡀⠀⣿⠘⣶⠃⢸⡄⠘⡇⠘⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⢀⡶⠒⣦⠀⠀⡶⢲⡄⠀⣠⠖⠲⡄⠀⢰⠖⢦⠀⢠⡖⠲⠀⠐⢲⡶⠂⠀⡖⠀⠀⡆
⠀⠀⠀⠀⠀⢸⡄⠀⣸⠆⠀⡷⠼⠁⠀⣿⠀⠀⡿⠀⢸⠶⣎⠀⠀⠙⢦⠀⠀⠨⡇⠀⠀⣧⠀⢀⡇
⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠋⠀⠀⠀⠈⠛⠛⠳⠀⠘⠃⠘⠂⠘⠒⠚⠀⠀⠈⠃⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⠀⢀⡀⠀⢀⠀⢀⠀⢀⠀⢀⡀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡾⠀⢸⡄⡼⣿⠀⡟⠀⠘⢦⡞⠀⠀⢧⡼⠁⠀⠉⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠃⠀⠈⣷⠇⠸⣼⠃⠀⢠⠏⢧⠀⠀⢨⡇⠀⠀⣼⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⢶⡄⠀⡴⠲⣆⠀⠔⢲⡄⠀⢠⢶⡄⢰⡶⠶⠀⢠⠶⠶⠀⠰⠶⣶⠀⣴⠒⣦⠀⡴⠲⣄⢀⡖⠲⡄
⠀⠀⠀⢸⠃⠀⠀⡴⠃⠀⠐⠺⣅⢰⣏⣸⣇⠈⠛⢳⡄⢹⠛⢳⡄⠀⡼⠁⠀⣼⠒⣧⠀⠳⠴⡇⢸⡇⢀⡇
⠀⠀⠐⠛⠓⠀⠛⠓⠂⠀⠒⠚⠁⠀⠀⠙⠁⠐⠲⠛⠀⠈⠓⠚⠁⠘⠃⠀⠀⠙⠒⠋⠀⠳⠞⠁⠀⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠈⢱⡇⠀⢠⡞⠉⢁⠀⠉⠓⣦⠀⠀⢰⠉⢀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⠀⠀⠈⡇⠀⠠⠟⠉⠉⠙⣧⠀⢸⡄⠀⠈⠉⠉⣨⠇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⡇⠀⠀⠀⠀⣀⣴⠃⠀⡼⠁⠀⠀⢰⠁⠁⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣷⠀⢀⡤⠾⠋⣀⡴⢊⣁⡀⠀⠀⠀⠉⠙⣦⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⠀⢸⡇⠀⠀⠉⠈⠁⠀⡇⠀⣿⠑⠒⠒⠁⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠒⠒⠊⠀⠈⠇⠒⠒⠒⠒⠃⠀⠁⠀⠈⠓⠲⠖⠂⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠛⡏⠀⠀⠀⡖⠒⠒⠒⠛⠳⠀⠀⠀⠀⢀⠤⠶⠒⠒⢲⡆⠀⢰⠟⠉⠛⠛⠋⠉⠉⡿⠂
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⡇⠀⠀⠀⡇⠀⢰⡒⠒⠚⠀⠀⠀⡴⠋⠀⢀⡤⠶⠾⠃⠀⠸⠶⠖⠲⠖⣶⠆⢀⡇
⠀⠀⠀⠀⠀⠀⡼⠁⢠⢿⡆⠀⣷⠀⠀⠀⡇⠀⠈⠉⠙⠢⣄⠀⢰⡇⠀⠀⠘⠛⠛⢶⣄⠀⠀⠀⠀⢀⡞⠁⢠⠟
⠀⠀⠀⠀⢀⡼⠁⠀⠧⠼⠃⠀⠙⢷⠀⠀⠉⠉⠉⢳⡄⠀⢹⡄⢸⠃⠀⢰⠚⠓⡄⠀⢿⠀⠀⠀⢀⡟⠀⢀⠏
⠀⠀⠀⠀⠸⣄⣀⣤⣤⡄⠀⠀⡶⠚⠀⢰⠶⠶⠶⠚⠁⠀⣸⠃⠈⢦⠀⠘⠲⠚⠁⢀⡟⠀⠀⠀⣼⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠸⡇⠀⠀⠘⠦⠤⠤⠴⠶⠚⠁⠀⠀⠈⠳⠤⠤⠤⠖⠋⠀⠀⠀⠀⣷⣶⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠶⠒⢦⡀⠀⠀⠀⣀⡤⠤⠤⢤⡀⠀⠀⠀⠀⡤⠖⠒⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⡴⢲⡄⠀⣱⠀⢀⡞⠁⢀⣠⡀⠀⠘⣆⠀⢀⡞⠀⢀⣄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⠓⠚⠁⣰⠃⠀⢸⠀⠀⢺⣠⠿⠀⠀⢹⠀⣼⠀⠀⡏⠸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣤⢶⡄⠈⢧⠀⠈⠷⣀⠀⠀⣀⠀⠀⡜⠀⣟⠀⠰⡇⠠⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣿⣧⡼⠃⠀⢸⠀⠀⣤⣨⣭⡽⠛⠁⣠⠇⠀⢻⡀⠀⠧⠼⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⣀⠀⠁⠀⣀⡤⠇⠀⠰⣇⣀⣀⣀⡤⠖⠁⠀⠀⠈⢷⣄⣀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⡴⣆⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠀⠀⣠⢰⡏⠁⠠⠀⠀⢰⡇⣾⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⢸⡆
⠀⠀⠘⢷⡜⢧⠀⠀⠀⣿⢸⡇⠠⠄⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠘⢿⣌⣧⠀⠀⠿⠸⠇⠀⠀⠀⠀⠀⠙⠸⣇⡀⠄⠀⠀⠸⠧⠿⠄⠀⠀⠀⠀⠿⠸⠇⠀⠀⠀⠀⠿⠸⠇


⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⠀⠑⠄⠀⠀⠀⣾⢰⡇⠀⠀⠀⠀⠀⠀⣶⢰⡆⠀⠀⠀⠀⢺⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢠⠀⠀⠀⣿⢸⡏⠀⠀⠁⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠃⢿⠀⠠⠊⠀⠀⠀⣿⣸⡇⠀⠀⠀⠀⠀⠀⣿⠸⠇⠀⠀⠦⠀⣾⠀⠃


⣿⢸⡇⠄⠈⠀⠀⠀⡏⣿⠆⠀⠀⠀⠀⠀⠲⡄⠀⠀⢾⡀⠀⠀⢸⠷⣤⣀⠀⢸⠀⢀⡄⣿⠁⠁⠢⠀⢸⡏⣿
⣿⢸⡇⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⠀⠀⠸⢷⡙⠦⢻⡈⣧⠀⠀⢘⠳⢦⣍⡛⢾⠀⢸⡇⣿⠀⠀⠀⠇⢸⡇⣿
⠿⠼⠇⠀⠀⠄⠀⠀⠧⠿⠅⠀⠄⠀⠀⠇⠀⠛⠀⠈⠧⠹⠆⠀⠸⠀⠀⠈⠙⠿⠀⠀⠁⠿⠀⠠⠊⠀⠸⠧⠿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⠂⢀⠀⠀⠀⢰⡖⣶⠀⠀⠀⠀⠀⢀⡰⣆⠀⠀⠀⠀⠀⣶⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⠂⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠘⢷⣌⢳⣄⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢸⡇⢠⡀⠁⠀⠀⢺⣇⡿⠠⠀⠀⠀⠀⠀⣀⢙⣧⠙⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⣿⢸⡇⠀⠀⠀⠈⢷⡜⢧⡀⠀⠈⠀⢻⡌⣇⠀⠰⣆⠀⠃⠀⠙⣧⠹⣆⠠⠀⠀⠈⠻⣎⠳⣄⠀⠁⠀⠀⢠⡏⣼
⠀⣿⢸⡇⠀⠀⡀⠀⠀⢻⡌⢷⠄⠀⠀⠈⣷⠹⠊⢳⡜⠟⠀⠀⠀⡸⢷⡘⢦⠀⠀⠀⠀⠘⢷⠉⠀⠀⠀⢠⡟⣸⠃
⠀⠙⠸⣇⡀⠀⠁⠀⠀⠀⢻⠆⠀⠀⠀⠀⠙⠁⠀⠀⠙⠀⠀⠀⠜⠀⠈⠻⠌⠳⠀⠀⠀⠀⠃⠀⠀⠀⠀⠟⠰⠃
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣼⣧⠀⠀⢸⣟⣻⡆⠀⢰⡟⠛⠆⠀⢸⡟⠻⣆⠀⢰⣟⣛⠃⠀⢸⣛⡋⠀⢠⡞⠛⠳
⠀⠀⠀⢸⠟⠺⡇⠀⢸⣯⣽⠇⠀⠸⢦⣤⠆⠀⢸⣧⣴⠏⠀⠸⣯⣭⡄⠀⢸⠉⠁⠀⠘⢧⣬⡽

⠀⠀⣶⣀⣶⠀⠀⣶⠀⠀⠀⢰⠀⠀⣶⣠⡾⠀⠀⣶⠀⠀⠀⢰⣶⢠⣶⡄⠀⣶⣄⢰⡆⠀⣰⠞⠳⣆
⠀⠀⣿⠉⣿⠀⠀⣿⠀⠰⣆⣼⠀⠀⣿⠙⢷⡀⠀⣿⣄⣀⠀⢸⡟⣿⢻⠇⠀⣿⠙⢾⡇⠀⠻⣄⣠⡟

⠀⠀⠀⣶⠒⣦⠀⢀⡶⠒⢦⡀⠀⣶⠒⣦⠀⠀⣴⠒⠦⠀⠐⢲⡶⠂⠀⣴⠀⢰⡆⠀⢲⡀⢰⠆
⠀⠀⠀⣿⠛⠋⠀⠸⣇⣤⣼⠃⠀⣿⠛⣯⠀⠀⣌⣙⣷⠀⠀⢸⡇⠀⠀⢻⣀⣸⠇⠀⠈⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢰⣆⢰⡆⠀⢦⣠⡆⠀⢰⡀⣴⠀⠀⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢹⣾⠀⠀⣼⢿⡄⠀⠀⢻⠃⠀⢀⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠁⠀⠉⠀⠀⠈⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⢻⣿⡿⣿⡆⠀⠈⣿⠉⠙⡆⠀⠀⣰⡟⠛⢛⣷⡀⠀⠐⠿⣿⡿⠿⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢠⣿⠋⠀⢹⣿⠀⠀⢸⠶⢾⡁⠀⠀⣿⠀⠀⠈⠉⠁⠀⠀⠀⣿⣇⠀⠀⠀⠈⢻⣇⠀⠚⣿⠛⠛⢻⡆⠀⣿⣿⠀⠀⠀⠀⠀⢿⡏
⠀⠀⠀⠀⣾⣃⣀⣀⣘⣿⠀⠀⢸⠀⠀⢹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⣠⠀⠀⠀⣿⣿
⠀⠀⠀⢸⡿⠿⠿⠿⠿⣿⡇⠀⣸⣀⣀⣸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⣿⠀⠀⣿⠛⠻⠀⠀⠀⣿⣿⣀⣀⣠⣿⡆
⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⡇⠀⠉⣉⡉⠀⣀⠀⢿⡄⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⠛⠛⠻⣿⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣧⠀⠀⢸⢀⡴⠋⠀⠸⣧⣀⣠⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⢀⠀⠀⢸⣿
⠀⠀⢀⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⢸⣿⠀⠐⠛⠒⠒⠛⠁⠀⢸⣿⠀⠀⠰⣶⠀⠀⢴⡶
⠀⢀⣸⣿⠀⠀⠀⠀⠀⢀⣿⡀⠀⢸⠈⢧⠀⠀⠰⣶⣆⠀⠀⢶⡆⠀⠀⢸⡇⠀⠀⠀⠀⢸⡿⠀⠀⣀⣤⣤⣤⣀⠀⢸⣿⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠙⠛⠛⠋⠀⠀⠀⠀⠛⠛⠛⠀⢼⡄⠈⢧⠀⠀⢺⡟⢧⡀⢸⡇⠀⣀⣼⣧⣀⣀⣤⣴⣿⠃⠀⢰⡟⠁⠀⢸⣿⠄⢸⣿⠀⠀⠀⣿⠶⠶⠾⡇
⠀⠠⣤⣤⠀⠀⠀⢤⡤⠀⢤⣤⠄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⢿⡇⠀⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⢀⣸⣿⣀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⢸⣧⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⡷⣀⡰⡇⠀⢸⡇⠀⠀⢸⡇⠀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⣿⠀⠀⠀⡇
⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⡇⠈⠀⡇⠀⢸⡇⠀⠀⢸⡇⠀⠉⣿⡏⠉⠉⠻⣷⡄⠀⠀⢸⡇⠀⣀⠀⠀⠀⢶⡶⠶⣤⡠⠿⠄⠀⠰⠷
⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣧⠀⠀⡇⠀⣸⣇⠀⠀⣸⡇⠀⠀⣿⡇⠀⠀⢀⣾⡇⠀⠀⢸⣇⠀⣿⠻⣷⠀⢸⣇⣀⣼⠇
⠀⠀⢸⡇⠀⢸⠂⢸⡇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⠉⠉⠀⠀⣿⣷⣶⡾⠿⠛⣀⣀⠀⠈⢿⣄⣀⣠⣿⠀⢸⣿⡏⠁⠀⠀⠀⣤⠤⣄
⠀⠀⢸⡇⠀⠘⠶⠞⠁⠀⢘⣿⣀⣀⣠⡆⠀⠀⠀⠀⣾⠉⠉⢻⡀⠀⠀⣿⡇⠀⠀⠀⡟⠉⠉⣿⠀⠈⠉⠛⠋⠁⠀⢸⡇⢻⡄⠀⠀⠸⣇⣀⠉
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢻⣄⠀⠀⠈⠉⢳
⠀⠀⢾⠿⠄⠀⠀⠀⢠⣴⣴⣦⠀⠀⠀⣴⣶⣤⡄⠀⣷⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⡇⠀⠀⣿⠀⠀⢀⣤⣤⣄⠀⠀⠀⣠⣤⣤⡀⢰⡖⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⢸⡇⠀⣀⣿⣇⠀⠀⠀⣷⠀⡀⣿⠀⠀⠀⠉⢻⣏⠀⠀⠀⣽⡟⠉⠀⠀⠛⠶⠚
⠀⣿⠿⢿⣿⠿⠿⣷⠀⢸⣿⠀⠀⠀⠀⠀⣿⣷⠀⠀⠹⢦⣤⠾⠁⠀⠛⠛⠛⠃⠀⠀⠹⠦⠽⢿⠄⠀⠀⠀⠀⢻⣧⠀⣼⡟
⠀⠁⠀⠘⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠰⣤⠄⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⠀⢻⣷⡟⠀⠀⢸⠛⠛⠛⣻⠇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⡄⠀⢀⡿⠀⢶⠆⠀⠀⠀⠀⢶⠆⠀⢻⡄⠀⣼⠃⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⡇⠀⠀⠸⡇⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⡟⠀⠀⠀⢷⣼⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⠀⣾⠀⠀⠀⣧⠀⣿⡇⢰⠇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣦⡏⠀⠀⠀⢹⣼⠃⢧⣼⠀⠀⠀⢀⡿⠹⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃
⠀⠀⠀⣀⣿⡀⠀⠀⠀⠀⢻⣷⣄⣀⣀⣼⣿⠇⠀⠀⠀⠈⣿⠇⠀⠀⠀⢸⣯⠀⢸⡧⠀⠀⠀⣾⠃⠀⢻⡆⠀⠀⣀⣿⣀⠀⠀⠰⣯⣤⣤⣼⠇
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠘⠛⠂⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢀⠈⢆⠀⠀⠀⢀⠆⠋⠉⠑⠢⡀⢀⡞⠁⣠⣀⡼⠀⠀⢀⠖⠋⠁⠒⠤⡀⠀⡎⠁⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠳⡀⠀⢸⠀⠀⠐⠂⢀⡆⢸⡆⠀⠡⣀⣀⣠⠀⢸⠀⠀⠰⢤⡀⠈⣆⢹⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢠⣤⣄⠀⢱⠄⡎⠀⠀⠴⠀⠀⢱⠀⠳⣄⠀⠀⠀⣰⠆⡜⠀⠀⠧⠠⠇⠀⡿⠸⠀⠀⠀⠈⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠋⠀⠈⠁⠁⠀⠧⢀⣀⣀⣀⡰⠃⠀⠀⠈⠙⠛⠛⠁⠀⣧⣀⡀⠀⢀⡠⠎⠀⠀⣇⣀⣀⣀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠖⢠⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣀⠁⢀⣀⣠⠁⠀⠀⠀⡜⠀⠀⠘⠀⠀⠀⠠⠀⢀⠀⠀⠀⡆⠀⠀⠀⠀⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⡏⠀⢿⠋⠀⡀⠸⡀⢠⠃⠀⠀⠀⠀⠀⠀⡄⠀⠈⢱⠀⠀⢇⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠟⠉⠀⠘⢧⡀⠄⠀⠀⠀⢀⠇⣸⡀⠀⡌⠑⠀⠀⢰⠀⠀⠀⡼⠁⠀⠈⣧⠀⡔⠋⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠀⠀⠀⠀⠀⡙⠒⠒⠒⠋⠉⠀⠈⠉⠉⠀⠓⠤⠤⠃⠀⠀⠀⠹⠤⠤⠶⠃⠀⢷⣤⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⢻⠁⢠⠃⠀⠀⠀⠔⠃⠐⡆⠀⠀⠂⠀⠀⠀⡴⠒⠒⢲⠀⠀⡔⠋⠑⢆⡤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠢⡀⠀⠀⢰⠀⠀⢸⠀⠀⡇⠀⠀⠀⠘⠀⢀⠀⢸⠀⢸⠀⠀⠀⠈⡀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠑⣄⠀⡇⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡎⠀⠀⠒⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⠶⠤⠤⠏⢸⣄⠂⠀⠀⡀⠀⣇⠀⢀⠀⠀⣀⠀⠀⡼⢠⣇⣀⡴⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⣀⣀⡈⠉⠁⠂⠁⠀⠈⡀⢈⣉⠉⠈⠁⠉⢁⣀⣈⡉⠀⠙⠒⠶⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠊⠁⠀⠀⠀⠐⡄⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠞⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠇⢀⠀⠀⣏⠙⡆⠀⠀⠀⠀⠀⠀⠁⠀⡠⠂⠘⢄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⡤⠐⠋⠀⠸⣄⠀⠈⠚⠃⢠⡎⢀⠄⠀⢀⠀⠀⠀⠀⠀⠜⠉⠁⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣅⣀⣤⠞⠁⠐⠦⢤⠞⠁⠀⠀⠀⠀⠈⠓⠶⣄⣀⣨⠃⠘⠳⠶⠋⢶⣄⣰⠆⠀⠷⠤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⢀⣀⡀⠀⣀⠠⡄⡰⠆⠲⠀⠀⣀⢈⡉⢀⡤⠤⣤⠀⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠄⠀⠀⢀⡍⢼⠁⠀⠄⢣⠀⠀⠆⢺⠁⠀⠰⡏⠀⠀⠇⠘⠀⠀⠰⠤⠤⠤⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢘⠉⠀⠸⡄⢀⠀⠸⠄⠀⡀⠈⢧⠀⠀⠁⠀⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⠀⠀⠀⠳⣄⠀⠀⠀⡐⠁⠀⠈⠄⠀⠀⠀⠃⠀⠀⢧⠀⠀⣠⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠓⠓⠁⠀⠀⣀⣈⣁⠀⠉⣓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠋⠁⢀⠏⢀⡔⠀⠑⡖⠋⠉⠟⠀⡏⠀⠀⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢰⡋⠀⠀⠳⡄⢀⠈⠀⡼⠀⠀⠓⢲⠆⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠱⡀⠀⠀⢹⠀⠀⠀⡇⠀⠀⣴⠃⠀⠀⠛⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠂⢠⠞⢦⡀⠀⡵⠀⠀⠸⡄⠀⢀⡇⠀⠘⡇⠀⠀⢀⣀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠛⠛⠋⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠃⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⡆⠀⠀⠀⡶⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠲⡆⠀⠀⠀⡔⠒⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠃⠀⠀⠀⠛⠒⠒⠒⢶⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠒⠚⠃⠀⠀⠀⠓⠒⠒⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽
⣿⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠔⠒⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⠀⢀⠀⠌⠀⠈⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠵⠀⠰⠋⣨⣀⡀⠈⢶⡄⣤⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠉⡩⠍⠙⠻⣶⡌⠉⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠘⡅⠀⠈⠁⠀⠠⠂⠈⠙⣦⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠁⠀⠑⣤⠄⢀⡀⠠⠊⠉⢀⠏⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡠⠂⠀⢠⠃⠀⡏⠀⠀⠘⢆⠀⠀⡈⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁⠀⠀⠆⠀⠀⠀⢀⠀⠀⠈⢳⡶⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⠀⠀⠀⡊⠀⠀⠀⢨⠃⠀⠀⠀⠀⢠⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠈⡇⠀⠀⠀⠀⢃⠀⠀⠀⠈⠀⢰⠀⠀⠀⠌⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⠀⠀⠀⠀⡰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠄⠀⠀⢀⢃⠔⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⢠⠆⠀⠀⠀⠠⠀⠀⠀⠨⠦⣠⣐⠀⡘⠀⢸⡎⠀⢀⣎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠠⡀⣈⡀⠀⡀⠀⠀⠀⠔⠒⠂⠠⣀⡈⠻⣦⣢⡆⡎⢠⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠤⠒⠉⠁⡀⠈⠼⠻⣧⣁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⢈⠛⠁⠀⠀⠒⠀⠀⠙⠓⠀⠀⠀⠀⠉⠀⠐⡠⠊⢺⠿⠯⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠩⠘⣧⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⢄⠀⠀⠀⠈⠦⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠁⠀⠀⠁⠉

⠀⡁⣀

⠀⠀⠀⠀⣰⣿⡀⠀⢸⡿⢷⣦⠀⠀⣠⡾⠿⠆⠀⣾⡿⣶⡄⠀⢸⡿⠷⠶⠀⢰⣷⠶⠶⠆⠀⣠⣶⣿⠀⠀⣾⡇⢠⣷⠀⠘⠻⣿⠗⠀⠀⠘⢿⡿⠂
⠀⠀⠀⢠⣿⣿⡇⠀⢸⡷⠿⣿⡀⢰⣿⠀⢀⠀⠀⣿⠀⣸⡗⠀⢸⡟⠛⠃⠀⢸⡿⠿⠆⠀⢸⡏⣤⣤⣤⠀⣿⡷⢾⣿⠀⠀⢠⣿⠀⠀⢀⣀⢸⡏
⠀⠀⠀⠿⠃⠘⠿⠀⠸⠷⠶⠟⠀⠀⠻⠿⠛⠁⠀⠿⠿⠟⠁⠀⠸⠿⠿⠆⠀⠸⠃⠀⠀⠀⠘⠷⠾⠃⠀⠀⠿⠇⠘⠟⠀⠐⠾⠿⠆⠀⠈⠻⠿⠃
⠀⠀⠀⢀⡀⠀⡀⠀⠀⣀⠀⠀⠀⢠⡀⠀⠀⣀⠀⣀⡀⠀⣀⠀⠀⢀⣠⡀⠀⠀⣠⣀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⣸⣷⣾⠋⠀⢈⣿⠀⠀⠀⣿⣷⠀⣼⣿⠀⣿⣷⣸⣿⠀⣰⡟⠉⣿⠀⢸⣿⢙⣿⠄⢰⡿⠉⣿⠀⠀⢸⡏⣻⡇⠀⢰⣿⣉⡁⠀⠈⠉⣿⠋⠁
⠀⠀⠀⣿⡏⢿⡄⠀⢸⣿⣀⣀⢰⣿⢹⣿⡏⣿⡄⣿⠙⣿⡏⠀⢿⣇⣰⡟⠀⢸⣿⠛⠋⠀⢸⣇⣻⣿⣄⠀⣸⡟⢿⡅⠀⢀⣍⣙⣿⠀⠀⠀⣿
⠀⠀⠀⠉⠁⠈⠁⠀⠈⠉⠉⠉⠈⠉⠀⠉⠀⠉⠁⠉⠀⠈⠀⠀⠈⠙⠉⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠉⠀⠈⠀⠈⠁⠀⠈⠉⠉⠁⠀⠀⠀⠉
⠀⠀⠀⣴⡄⠀⣦⠀⢰⣆⢀⣴⠀⣴⣀⣦⢀⣤⠀⢰⣆⣠⡦⠀⢴⡄⢀⣶⠀⠀⣴⣶⣶⡄
⠀⠀⠀⣿⠁⢠⣿⠀⠈⣿⣼⡏⠀⢻⣿⣿⣿⡏⠀⠀⣿⡟⠀⠀⠘⣷⣾⠃⠀⠀⢠⣾⠃
⠀⠀⠀⢻⣦⡾⠃⠀⠀⢹⡟⠀⠀⠸⡿⠸⡿⠀⠀⣾⠟⠿⠀⠀⠀⣿⠃⠀⠀⢰⣿⣷⡶

⠀⠀⠀⠀⣠⣴⡄⠀⠀⣤⣤⡀⠀⠀⢠⣤⣄⠀⠀⢀⣤⣴⡀⠀⠀⣴⣶⣶⠄⠀⠀⣠⣤⠀⠀⣤⣤⣤⡄⠀⢀⣤⣶⣄⠀⠀⣠⣶⣦⠀⠀⣠⣴⣦⡀
⠀⠀⠀⠈⠋⣿⠇⠀⠀⢉⣼⠇⠀⠀⠀⣶⣿⠀⢀⣾⣧⣿⣄⠀⠰⣿⢶⣆⠀⢀⣾⣯⣄⠀⠀⠀⣼⡟⠀⠀⣺⣷⣾⡟⠀⠸⣿⣾⡿⠀⢠⣿⠁⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠠⣿⠷⡦⠀⠀⢶⣶⠿⠀⠀⠉⠨⣿⠉⠀⢶⣤⣾⠏⠀⠘⢿⣿⠿⠀⠀⢼⠏⠀⠀⠀⠻⣧⣼⠏⠀⠀⠀⢸⡇⠀⠘⢿⣴⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣶⠶⣶⣤⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⣶⣶⣦⣄⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⢠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⣾⡟⠉⠙⠻⠃⠀⠀⢀⣿⠉⠉⢻⣧⠀⠀⠀⣿⡏⠉⠉⠁⠀⠀⠀⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣿⣧⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⣿⡆⠀⠀⣿⣷⣤⣤⡄⠀⠀⢠⣿⣷⣴⣦
⠀⠀⠀⠀⠀⢀⣿⡟⠋⠛⣿⡆⠀⠀⠀⢀⣿⠉⠙⢿⣧⠀⠀⠀⢿⣇⠀⠀⢠⣶⠀⠀⠸⣿⠀⠀⢠⣿⠃⠀⠀⣿⡟⠉⠉⠁⠀⠀⢀⣿⡏⠉⠉
⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⢻⣿⡀⠀⠀⢈⣿⣤⣤⣾⠟⠀⠀⠀⠘⣿⣷⣶⣿⠃⠀⠀⠐⣿⣦⣶⡿⠋⠀⠀⠀⣿⣷⣶⣶⡆⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣠⣄⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣤⡄⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠻⠿⠆⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⢸⣿⣇⣼⡿⠃
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣿⣿⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⢸⡟⣿⠋
⠀⠀⠀⠀⠀⠀⣿⣇⠀⢠⣤⣤⣤⠀⠀⠀⠀⣿⣿⠛⠛⣿⣿⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣯⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⢀⣴⡿⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢿⣧⣀⣸⣿⠃⠀⠀⠀⢸⣿⡏⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠻⠟⠀⠀⠛⠟⠀⠀⠀⠀⠘⠟⠿⠂⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠘⠟⠃⠀⠙⠛⠂

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⢀⣾⣿⠂⠀⠀⢸⣿⣷⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⢨⣿⡟⠛⢿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⣾⣿⣿⡇⠀⠀⢸⣿⣿⣧⠀⣿⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⡇⠀⣸⡿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⡿⢻⣿⡇⠀⠀⢸⣿⡿⣿⣧⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠙⠛⠁⢸⣿⡇⠀⠀⢸⣿⡇⠸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⢼⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠹⣿⡿⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠸⣿⠃


⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣼⡟⠉⠙⢿⡆⠀⠀⠀⠀⠀⣿⡟⠻⣷⣆⠀⠀⠀⠀⢰⣿⡿⠻⢿⠇⠀⠀⠀⠀⠿⠿⢿⣿⣿⠿⠿⠇⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⣸⡿⠀⠀⠀⠀⠸⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣇⠀⢀⣾⡏⠀⠀⠀⠀⠀⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⣀⡀⠀⣨⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⢷⠄⠀⠀⠀⠀⣿⠇⠘⢿⡄⠀⠀⠀⠀⠘⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠃


⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣠⡀⠀⠀⠀⣀⣀⠀⠀⣤⣄⠀⠀⢀⣤⡀⠀⠀⢀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⢀⣿⡏⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⣸⣿⠀⠀⠈⢻⣿⣄⢀⣼⣿⠏⠀⠀⠘⢿⣦⢀⣾⡟⠁⠀⠀⠘⠛⠛⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⣼⡿⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣧⣸⣿⠃⠀⠀⠀⠀⢸⣿⣧⣾⣿⣦⣾⡿⠀⠀⠀⠀⠀⣠⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⡟⠙⣿⣿⠇⠀⠀⠀⠀⣰⣿⠟⠙⢿⣷⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⣿⣟⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠙⠛⠀⠀⠀⠀⠘⠟⠋⠀⠀⠈⠻⠛⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠛⠛⠟⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⣭⣭⣭⡀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⡀⠀⠀⠀⠐⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣖⣢⣿⣶⣿⣿⣁⣠⡤⣤⡤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⣈⣭⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠀⠑⠝⡹⣻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢀⣀⣠⣤⣶⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠵⠫⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠿⠿⡿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⣻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣠⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡌⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢠⠔⣪⡽⠟⣋⣴⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠓⡉⠁⠚⣈⣥⣴⣿⢿⣫⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠀⠒⠊⠁⠀⠀⠐⠀⠀⣠⢀⡜⠿⣻⠭⠓⠉⠁⡈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠶⢶⠶⠶⠶⢶⢚⡛⡉⠉⠩⠁⠀⠀⠀⠀⠀⠀⡐⠰⠰⢀⣀⣡⠴⠖⠉⠀⠀⠀⠀⠠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⣛⠛⡛⢛⠙⠁⠈⠁⡉⡀⣠⢠⠀⠀⠀⠀⠀⠀⣁⣴⠥⠐⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⣲⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣛⣟⣻⡿⣗⠛⠀⠠⠘⠁⠁⠢⠀⠀⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⢀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⢀⣠⠴⠚⢋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⠋⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣩⣥⠤⣤⡀⣀⣀⣠⠤⠴⠶⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣩⡙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠶⠒⠋⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⣟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣀⣠⣤⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣀⣀⣀⡀⠀⠀⠀⠙⣿⣯⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣶⣴⣦⣀⠻⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠀⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠤⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢽⣿⣿⣿⣧⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⠀⢿⣿⣿⣿⡿⠟⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢷⢶⣶⣤⣤⣀⠀⠀⠀⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⣟⣻⣯⡽⠿⡗⠻⡿⣦⡠⠐⠁⠀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡟⢻⡏⣹⣿⡄⣅⢹⡄⠘⡜⣷⡴⢶⡄⠀⠄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠄⢴⣇⣽⣿⣷⣄⣱⣿⣾⠷⠾⣧⣾⢷⢚⣦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣸⣧⣶⠼⣿⣛⣿⣯⣿⣿⣶⣿⣿⣿⡋⠌⠌⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣷⡟⢿⣿⢿⣿⣿⣻⣽⣿⡿⢹⢹⣇⢃⢁⢊⡇⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣇⠛⣿⣦⣿⡾⣿⣿⡟⠛⠙⡄⡈⣎⣿⣾⣦⣬⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢹⠈⣁⣇⣬⣿⣷⣾⡿⢿⣿⣿⢿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⢷⣾⣻⣟⣹⣭⠿⠶⢿⠛⠛⠛⠁⢸⣯⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡏⠙⠛⠋⠁⢳⣶⣾⣿⣄⣀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣆⠀⠀⣠⣿⣿⣿⡿⡿⠛⠃⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠉⠉⠛⠿⠟⠁⠀⠀⢀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⣠⣿⣿⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣷⣾⣶⣿⣿⣿⣿⡿⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⢟⣿⠟⠻⠿⠿⢿⣿⣿⠟⠛⠛⠛⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⡟⠁⢸⠟⠀⠀⠀⠀⠀⠀⠙⠲⢷⡀⠀⢿⣄⣙⣿⣄⡿⠉⠙⢿⡟⣿⣿⣿
⣿⣿⣿⢿⣿⣿⣽⢏⣿⠏⠸⣆⠞⠀⡰⠋⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣶⣾⣿⣿⣿⣿⠁⠀⠀⠀⠹⣮⡟⢻
⠉⠉⣈⠓⠮⣿⣯⣼⣯⠀⠀⢻⢀⡼⠁⠤⠖⠒⠂⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⣷⠋
⠁⠀⠀⠀⠀⠘⣿⡏⠈⠙⠲⢼⡟⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠐⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⡆⠀⠀⠘⣧
⠀⠀⠀⣀⣀⣀⣸⣿⡄⠠⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣷⠀⠀⠀⢿
⠀⠐⠋⠉⠉⠉⠀⢿⡇⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⢿⣿⣿⣿⣿⡟⠋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⣀⣿⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⠇⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⢹⣇⠀⠀⣰⣾⣿⣿⣿⠿⠛⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣸⣦⡀
⠀⠀⠀⢘⣶⣦⣤⡄⠘⣿⡆⠀⠀⠀⠸⣿⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢰⣤⣸⣿⣿⣿⣦
⠀⠀⠀⠈⢿⣿⣧⠀⠀⢻⣷⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣿⣿⣿⣿⣶⣾⣿⣿⣏⢿⣿⣿
⠀⢤⠀⠀⢻⠁⣙⣳⣄⣸⣿⣤⣤⣶⡀⠘⢿⠀⠀⢸⡏⠀⣿⣿⣿⣿⣿⣿⠿⢿⡿⡿⠿⠛⠋⠹⣿⣿⣿⣿⣿
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠀⠀⠀⠀⠘⢩⡿⠯⠁⠀⠀⠀⠚⠋⠁⠀⠀⠐⣶⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀⠀⠀⢠⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠀⠁⠀⠀⢀⣔⡀⣀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢘⠀⠀⠀⠀⠈⠀⠈⡁⠀⠀⠀⠀⠀⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⡀⠀⣺⠞⠂⠀⠀⠁⣀⠀⠀⠀⠀⠈⠀⠀⡠⠂⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠄⠀⠘⠓⠀⠘⠛⡀⠀⠀⠀⠈⠰⠄⢀⠔⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⢠⠐⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠀⠤⡀⠀⠀⠀⢀⡄⠀⠎⡄⠀⡴⠀⠀⠘⠠⠀⠀⠀⠀⠀⠈⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠄⠀⠀⠀⠀⠀⠀⠞⡀⠀⠀⠀⠀⡠⣢⠄⠠⠀⠀⠀⠆
⠀⠀⠀⠀⢠⡄⠀⠀⠀⣤⠀⠓⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⣶⡤⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠁⠘⠂⠀⠀⢀⣤⠂⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡆⣀⢰⣷⡍⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣤⣾⡅⠀⠀⠀⢸⣿⣿⣿⣮⣿⣷⣶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣗⠄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣰⣿⣿⣿⣷⠀⠀⠀⣸⡿⠻⠿⠇⣌⠁⠁⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣿⣷⠛⠀⠀⠛⢧⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣿⡁⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⡻⣿⣿⣿⣿⣤⣿⣶⣾⢏⡂⠀⠀⠀⢮⣳⣦⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⢿⣿⣶
⠀⠀⠀⢀⡴⠒⠁⠈⠁⠀⠉⠓⠛⠿⣿⣿⡛⣿⣿⠟⠉⠀⠀⠀⠀⠙⢿⡿⣄⣀⣬⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⣿⠿⣷⠀⠀⢀⡠⠄⠂⠁
⠀⢀⡔⠁⣴⡄⠀⠒⠛⡡⣶⠔⠒⠳⣈⣿⣇⣿⣿⡄⡀⠀⠀⠀⠀⠀⢨⣷⣿⣿⣿⠙⣿⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠩⣿⣿⡷⠊⠁
⠀⢸⡇⠀⡆⢠⣶⣿⣿⣿⠃⠄⠒⠒⠈⠉⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⣿⡄⠉⣱⡀⢹⡆⠀⠀⠀⠀⠀⡨⢥⣸⠀⣀⠀⢰⠀⠀⣷⣿⣿
⠀⣸⡇⠰⠇⠘⣿⣻⣿⣿⡄⠀⠒⠠⠂⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣀⣛⣷⡞⠀⠰⣦⡶⠋⣿⠇⢨⣿⡄⠂⠁⠈⠐⠀⢟⡿⠉⠀⠀⠀⢠⠀⠨
⠀⢻⡆⠀⠀⠆⠉⠀⠈⣆⠀⢀⣀⣀⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠔⢧⡄⠧⣿⣠⠤⠀⠀⣿⢁⣀⡀⠀⢀⣿⣄⣥⣾⣷⣤⣷⣿⣧⠀⠁⣤⡶⡩⣼⣥⡄
⠀⢸⣿⠀⣸⡟⠀⣦⣀⠎⠁⠀⠸⠾⣷⡈⠁⠉⠙⠋⠁⢠⡀⣠⠄⣀⡠⠗⠀⠀⠃⠈⠀⣶⠀⣿⣶⡥⢀⠀⠀⢹⡿⠙⣿⣿⢻⣿⣏⢻⣇⠈⠉⠻⣦⣉⣛⠏
⠀⢸⣿⣆⢹⡀⢸⢻⣿⣦⠀⠀⠀⠀⠿⠿⠿⠂⠤⠀⠐⠀⠿⠷⠀⣶⣆⢀⡀⢠⡖⠀⠠⣍⠀⢸⠟⢣⣼⠷⢾⠈⠀⠞⠻⢿⣯⣥⡽⠒⢧⠀⠀⠀⠙⣿⡛
⠀⣾⣿⣿⣧⣿⠀⠉⠉⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠻⣿⠿⣛⣁⣀⠨⠅⠀⠘⠛⠒⠒⠀⠀⠀⠀⠀⠙⠓⠀⠠⢇⣀⣀⣄⠠⠎⠀⠀⠀⠀⠼⠷⠄
⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠿⠆⠀⠀⠀⠀⠀⠀⢥⡶⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣾⣿⡶⠶⠶⠶⣶⣶⣶⣶⣿⣟⣤⣤⣴⣶⣦⣂⡀
⠀⣿⣿⡿⠀⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢋⠀⠀⠀⠀⠀⠘⠛⠉⠉⠁⠁⠘⠉⠉⠁
⠀⠹⠿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⢾⡟⡧⠒⠐⠆⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⣀⣧⣠⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠈⠈⠉⠏⢻⢻⣿⡿⡿⢿⠛⠛⠛⠛⠛⠉⠟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄
⠀⠀⠐⠀⠀⠀⠀⠀⠈⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉⠙⠉⠉⠉⠋⠉⠙⠟⠛⠛⠛⠛⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⣼⣿⣦⡀⠀⢸⣆⠀⢸⣿⠀⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣹⠈⢻⣷⡄⠈⠁⠀⢸⣿⣼⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠙⠀⠀⠹⣿⣦⠀⠀⢸⣿⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣇⠀⠀⠀⠀⠀⠘⢿⠀⠀⢸⣿⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠁⠀⠀⠀⢰⣷⠀⠀⠀⠀⢾⣿⣦⣠⠀⠀⠀⠀⣾⣷⠀⠐⠿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣿⣧⡀⠀⠀⠛⢽⣿⣷⡀⢀⠀⠀⣿⣿⠀⠀⢶⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠘⠻⣿⣯⠀⠀⣿⣿⠀⠀⣠⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⠀⠙⣿⠀⠀⣿⣿⠀⠀⣨⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡀⠸⣿⡇⠀⠀⠀⠀⠀⢰⣦⠀⠀⢰⠖⠀⣶⣶⡉⠻⡆⢶⣶⡆⠀⠀⠲⡆⠀⣾⣿⠀⢲⣦⡀
⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⠀⢹⣿⡄⠀⠀⠀⠀⠙⣿⣆⠀⠉⠀⢰⣿⣿⡇⠀⠀⢸⣿⡇⠀⣠⠀⠀⠀⣽⣿⠀⢸⡿⠇
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠿⣿⣿⠀⠀⢿⣷⠀⠀⠀⠄⠀⠸⣿⣆⠀⢀⣸⣿⣿⠃⠀⠀⣼⣿⡇⠈⠻⠀⠀⠀⢿⣿⠈⠛⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠘⣿⠃⢀⡗⠀⠀⠀⠹⣿⡄⠘⢿⣿⣿⠀⠀⠀⢾⣿⡇⠀⠀⢀⣴⠀⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⣿⡂⠀⠤⣄⠀⠉⠉⣠⠜⠉⠙⠢⣄⠀⢺⣿⣧⠀⠀⠉⠋⢰⣯⢹⠖⠀⣾⡟⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠓⠀⢹⣷⡀⣼⣿⠀⠀⠀⢰⣿⣷⡜⢿⣿⣷⡀⠀⠀⠀⠈⠀⠀⢸⣿⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⢸⣿⡗⣿⣿⠆⠀⠀⠘⣿⣿⠁⠀⠻⠻⣿⣄⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⢀⣾⠟⠀⠹⣿⠶⠂⠀⠀⣿⠏⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⢰⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣭⠁⠀⠀⢠⣤⡕⠂⠰⣬⡄⠀⠰⣤⣤⠀⠀⣽⠇⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠈⣿⡇⠀⢀⣿⣿⠀⠀⠙⣿⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿⡄⠀⠀⣿⡇⠀⠘⣿⡇⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠄⢿⡟⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠊⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠈⠁⠀⠐⠛⠃⠀⠘⠛⠛⠀⠀⠂⠀⠀⠀⠻⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⢠⣷⣰⡿⠆⣿⠈⡟⢠⣷⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠁⠀⠉⠀⠁⠈⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡔⢩⡌⠱⡈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣱⣄⣋⡔⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⣖⣻⣳⣷⢿⣖⣖⣲⡆⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⢸⡿⢽⢼⣿⣾⡯⡿⣿⡇⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠻⠯⠯⠿⠏⠿⠭⠯⠿⠯⠯⠿⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⣉⠒⢠⠒⠳⡄⠶⠒⢆⡀⠀⠀⠲⣄⠤⠤⣀⡴⠚⢞⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣆⡓⢡⠌⠳⡚⠁⡎⢱⠄⢺⡀⠀⢠⠇⣤⣴⠪⠏⢪⣠⢗⢝⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠽⡥⢂⡼⠼⣇⠪⡁⢠⡞⠀⠀⠊⠙⣅⠜⢦⡤⡞⢔⡵⢋⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣠⠎⡎⠠⣖⠈⡆⢣⡁⠀⠀⠀⣠⠖⣉⠗⠋⠀⣈⡡⠔⡁⡅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡢⠧⢈⣉⡠⠧⡞⠉⢲⠀⠀⡠⠚⡡⠢⠔⢊⢈⠀⠀⡇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢢⣠⠖⠒⠧⣤⠞⠑⠆⣠⣪⣼⣸⣸⣸⣨⣤⣤⣇⣇⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⣀⡀⠤⠀⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⢀⡀
⠀⠀⠀⠀⠀⠘⠀⠰⡀⠰⠀⢀⡇⠀⠄⠃⢄⠘⠋⠁⠒⠂⠄
⠀⠀⠀⠀⠀⢰⡀⠀⠑⠲⠒⢋⠀⠀⠸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠐⣦⠀⠠⠉⡐
⠀⠀⠀⠀⠀⢸⠑⠀⠀⠀⠳⣌⠀⡠⠆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠶⠞⠇⠀⠀⠀⠳⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⡀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠂⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡠⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠰⣔⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠰⠀⠰⡄⠈⠀⠀⠀⠁⡇⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⣀⠀⠀⠀⠀⠗⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡆⠀⠈⢀⣄⠜⠁⢀⠰⠻
⠀⠀⠀⠀⠀⠀⠈⡀⠀⡜⠁⠀⠀⡠⠂⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠂⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢧⠎⢀⣀⠤⠈⠀⡄⡀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡈⢄⣀⠀⠴⠀⠀⡈⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠑⡄⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠄⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⢀⣿⠀⢑⡘⣠⡅⢤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠤⠀⠀⠀⠤⠘⡛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡙⠛⠙⢛⠋⢹⡿⠛⠛⡛⢛⢹⡇⠿⠛⠛⠛⠛⡛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⣴⣿⣾⣿⣶⣿⣿⣿⣾⣿⣶⢻⠻⠷⢾⣷⣾⣷⣿⣶⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣸⠃⡀⢻⡇⢸⡟⠛⠻⠇⠛⠲⡾⠒⠚⡇⠘⠻⣿⠟⠻⡿⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣇⣠⣤⠈⣇⠘⠃⠘⣁⡀⣾⡀⣄⠛⠀⡇⠘⢃⣤⡀⢂⣿⡀⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠉⠐⠠⡀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠈⠉⠉⠹⣧⡽⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠉⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠁
⠀⠀⠀⠠⠀⠄⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠄⠀⠀⠄⠀⠐⠒⠂
⠀⠀⠀⠀⠐⠀⢸⣿⡟⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠘⡁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠁⠀⠀⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢀⣰⠶⢶⣒⣤⣤⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠾⠁⣴⠟⠉⠉⠐⣺⣷⡶⣶⣿⣿⠁⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣾⣳⣶⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠟⡴⠂⠁⠁⠛⡿⠿⠉⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⠀⠀⠀⠀⢛⡀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢄⠀⠀⠀⠸⡀⠀⠀⠉⢾⣀⡘⢤⠘⠁⡀⠦⡀⠀⠀⠀⠀⣠⡶⢶⣦⢠⣶⢶⣶⡶⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⣈⠀⠀⠈⠢⠀⠀⠀⢿⣧⣤⡤⢻⣧⣤⣿⡇⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠢⡀⠀⠐⡄⠀⠀⠉⠉⠀⠀⠉⠉⠉⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢠⡄⠤⠤⠄⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣼⣿⣿⣿⡿⠃⣴⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣠⣾⣿⣯⣿⡟⠀⣼⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠀⡄⠀⠀⠄⠈⠀⠐⠀⠁⠈⠉⠻⣭⠊⢀⣾⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠉⠑⠀⠒⠀⠀⠀⠉⠀⠉⠀⠀⠀⠉⠁⠈⠁⠉⠁⠉⠉⠀⠂⠀⠀⢀⣾⠟⢁⡿
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡀⢄⠀⠀⠀⣠⠥⢈⠀⠀⠀⠄⠀⠠⠀⠈⢀⢀⢀⡠⠤⠄⠀⢀⡾⠁⠀⢸⠃
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⡀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⢀⡿
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡿⠁⠀⠰⢻⠇
⠀⠀⣠⣁⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋⡈⠉⢀⣈⣉⣁⣈⣀⣁⣁⣠⣾⡟⠀⠀⠀⢠⡟
⠀⠀⣨⣿⡿⠿⠿⢻⠿⠿⠟⠛⠛⠛⠙⠛⠉⣉⣉⣉⣉⣉⣭⣭⣭⠽⠿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠖⠒⠒⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣾⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⣃⣠⣴⣶⣾⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠙⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠁

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

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⢀⡤⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣠⣌⢄⣦⣞⣮⡧⢾⣦⣥⢁⡶⡆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣳⣋⡥⣌⣴⣾⡋⠻⢶⡧⠾⣟⢋⣏⡇⡴⢢⠗⡔⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡾⢋⣙⣧⡽⣷⣿⣤⡿⠹⠶⣶⣷⣶⣿⣯⡽⢿⣏⣉⡶⠉⠹⢲⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡉⢨⣿⣶⢟⡾⠿⣷⡟⢳⣤⢶⣾⣷⣿⣷⣄⣿⣇⣿⣿⡿⡧⢶⣳⣰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣉⣴⡾⠿⣿⣏⣹⣷⣿⡿⣿⢽⣿⣿⣿⣿⣤⣿⢿⣿⡿⣯⣹⡿⡞⠻⣨⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣝⣼⣲⢾⣿⣻⣧⣿⣿⣷⣘⣿⣯⣹⡟⣿⣿⣧⣞⢷⡾⠟⣱⠃⣁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⢬⣬⣇⣾⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣟⣿⣼⣳⣹⡷⣄⠆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⣿⣼⠿⣿⣯⣭⣿⣿⣿⣽⣏⣿⡿⠇⣦⢳⠺⠋⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢿⣾⣿⣤⣿⡏⣿⣿⣿⣿⣯⡖⢻⠒⠛⠩⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⢉⣏⣽⣿⣿⣷⢿⣿⣯⣿⡗⡇⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⣿⣼⣿⣿⣿⣷⣾⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢿⣻⣿⣽⠿⠿⡃⠚⢣⣿⣿⢦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡽⠟⠇⡂⠂⠈⠸⢻⣫⡻⢤⠷⠀⠀⠀⠀⢀⠀⡀⣄⣂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠁⠀⠀⢨⣻⢃⠰⣤⠀⣴⣂⢠⠾⡔⠃⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢐⡆⢲⣴⠷⣧⡸⠙⣟⠁⡄⠉⠁⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣌⣉⣨⢵⣿⣒⣩⣞⢱⣴⠒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢻⡟⠻⠯⠻⣿⣃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⠟⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⢀⠀⡀⠀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⠴⠉⢀⠀⡀⠀⠀⠀⡄⠀⣀⢀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⣀⠤⣀⢄
⢇⣀⠅⠀⢔⣈⡇⠀⢧⣀⠀⠀⠀⣀⡀⠘⣀⣠⠀⠸⣐⡂⠀⠀⠀⢂⣀⠄⠀⢸⠆⠊⠀⠀⠀⠇⠀⠄⠀⠀⠰⠁⠄⠀⠀⠅⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡇⠀⡆⠰⠁⢈⠀⢈⠀⢰⠀⢄⠀⢙⠀⠸⠀⠀⢘⠂⠄⠀⠀⠀⢄⢀⡄⠀⢂⡐⠀⠐⡐⠡⡜⠀⢀⠶⡀⠀⢣⡐⠀⢀⠀⡄⠀⡠⠊
⣀⣀⣀⣀⣈⣁⣀⣀⣈⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣜⣀⣀⣀⣤⣆⣀⣀⣀
⣿⣿⣉⢉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠐⠂⣤⣬⠒⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠁⠴⢠⠖⣀⠀⠠⠀⢸⡛⢲⣬⣏⡱⡏⢰⣃⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⣇⠀⠀⢰⣯⣿⣿⣧⠀⠀⠙⡗⠬⢿⣽⠟⠕⠊⠡⠞⣚⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠿⣿⣆⠘⣖⢿⣽⣿⣇⠀⠀⢀⣿⣞⣃⣈⠃⠾⠤⠀⢀⣝⢚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠎⠀⠉⡴⢿⡷⣄⠁⠈⢉⣉⡀⠴⠋⠉⠉⠑⢍⣻⡇⣦⢠⡄⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢔⣋⡩⢄⡟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢮⡆⠊⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⣤⠀⠀⣠⠈⠀⠀⣀⣤⠤⣤⣸⠀⠀⠛⠀⠀⡼⢲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠑⠬⣉⠉⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠖⠀⣀⣀⣀⣀⡑
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⣴⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢏⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠸⠀⡼⠐⣆⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣿⢞⣳⡆⠘⠈⠑⢠⣀⠀⠀⠀⠘⠿⡷⠒⠒⠒⠛⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡁⣠⠸⣭⡓⠐⢦⡄⠀⠙⡇⠐⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠙⡆⠙⡷⢖⠋⣴⠀⠤⠀⠀⠁⠀⠈⠙⠓⠦⠄⢤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠐⣤⠋⠈⢃⡌⢀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠒⡰⢣⣟⣈⣁⣀⠁⢀⠈⠡⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣀⣉⢘⡏⢉⡁⠓⠄⠉⢐⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣸⠃⣤⠀⠔⢃⠼⣏⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠤⠤⠠⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠉⠑⢄⠀⠀⠀⢰⠞⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠈⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⡆⠀⠀⠀⠹⠀⠀⠰⠉⠆⠀⠀⢸⡆⠀⠀⡏⠀⠀⢠⠖⠋⠉⠐⠇⠀⠀⢠⡇⠀⠀⡏⠉⠳⡆⠀⠀⢷
⠀⠀⠀⠀⢠⠀⠀⠌⣀⡀⠀⠸⡄⠀⠀⢠⠀⠀⠀⠀⠀⠰⠺⢿⡁⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢹⠀⠀⢻⡇
⠀⠀⠀⢀⡇⠀⠀⢀⣀⡀⠀⠀⢱⠀⠀⢸⠀⠀⢰⠀⢲⠄⠀⠀⡗⠀⠸⡇⠀⠀⠸⢄⡀⠀⢀⣀⠀⠀⣸⠃⠀⢸⡀⣀⡤⠞⠀⠀⣸
⠀⠀⠀⠘⠀⠀⠐⠉⠉⠉⡄⠀⠈⠃⠀⠘⠀⠀⠈⠉⠁⠀⠀⣠⠃⠀⠀⠙⢦⠀⠀⠀⠈⠉⠉⠘⠀⠀⠻⠀⠀⠈⠉⠁⠀⠀⠀⡰⠋
⠀⠀⠐⠛⠒⠒⠂⠀⠀⠀⠙⠚⠛⠃⠀⠀⠀⠀⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠀⠁⠀⠀⠈⠐⠒⠒⠒⠒⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠐⣖⠃⠀⠀⠀⠀⠰⠎⠁⠦⠀⠀⠀⠀⢤⠀⠀⠙⡣⡀⠀⠀⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡅⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡃⠀⢰⠽⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠐⠻⠆⠀⠀⠔⠀⠐⠀⠀⠀⠀⠫⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠏⠀⠀⠐⠾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣄⣰⠆⠀⠀⡴⠏⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⠄⠀⠀⠀⢀⣙⠀⠀⠀⠴⠀⢰⡏⠀⠀⠘⠀⠎⠀⠒
⠀⠀⠀⠀⠀⠠⡯⠀⠀⢸⡷⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⣸⠅⠀⠀⠀⢈⠁
⠀⠀⠀⠀⢉⡼⠂⠀⠀⠘⢿⣀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠂⠀⠀⠁⢀⡝⠃⠀⠀⠀⠉⣠⡟⠀⠀⠰⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠄⢰⡝⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠠⠆⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡐⠊
⠀⠀⠀⠀⠀⠀⣓⠃⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⢐⣗⠀⠀⠀⠀⢨⣏⠀⠀⠀⠀⠀⠀⠀⠠⣔⠠
⠀⠀⠀⠀⠀⣰⠍⠀⠀⠀⠀⠐⠀⠀⠀⠀⡗⡀⠀⠀⠐⠂⠈⢿⡀⠀⠀⠀⠘⢏⡀⠀⠀⠀⠀⠀⠖⡘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣐⠃⠀⠀⠀⠀⠀⠰⠀⢰⠊⠀⠀⠀⠀⠀⣼⡏⡄⠀⠀⠀⠀⠀⡄⢠⡎⠀⠀⠀⠤⠀⠀⡀
⠀⠀⠀⠀⠀⣘⡉⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠙⣃⠀⠀⠀⠀⠀⠀⠤⠀⣩⠁⠀⠀⠀⠀⠘⠃⠀⠹⠃⠀⠀⠰⠂⢠⠟⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⠆⡀⠀⠀⠀⠀⠀⠄⠀⢖⠏⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠅⠀⠀⠀⠀⠀⠀⢈⣁⠃⠀⠀⠀⠁⢀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢓⡇⠀⠀⠀⠀⠀⠂⣰⠟⠀⠀⠀⠀⣠⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣤⣄⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⢠⣷⣤⠉⠙⠛⠛⢻⣿⣧⠀⠀⠀⣴⣿⡿⠛⠛⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢻⣿⣇⠀⠀⠀⢸⣿⣿⣀⣤⣤⣤⣾⣿⠏⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢿⣿⡆⠀⠀⠀⣿⣿⠛⠛⠻⠿⢿⣿⣷⡄⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⠀⠀⠀⠀⢀⣿⣿⠇⠀⢸⣿⣧⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠉⠉⠁⠈⢿⡇⠀⠀⠈⢩⣴⣶⣾⣿⣿⡿⠋⠀⠀⠀⠻⣿⣷⣶⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⢠⣦⠀⣤⣲⠀⢠⠒⠀⢠⠐⣆⠀⣔⠂⠀⣖⠂⢀⡖⡀⠀⢤⣠⡄⢠⠀⠀⡄⠀⣤⡆⠀⣄⠀⠀⣦⣰⠀⢠⢤⡄
⠀⠈⠉⠀⠙⠚⠁⠈⠒⠀⠈⠒⠁⠀⠑⠂⠀⠁⠀⠀⠑⠃⠀⠈⠈⠁⠈⠀⠐⠃⠀⠁⠉⠀⠙⠂⠀⠉⠉⠀⠈⠈⠁
⠀⠀⠀⢠⠀⡆⠀⣔⡆⠀⡖⠲⠀⢠⣲⠀⠰⣇⡀⠀⡖⠀⢠⠀⡄⠠⣄⠆⠰⣠⣆⠆⠀⣶⠀⠐⣴⠂⠀⡶
⠀⠀⠀⠈⠛⠁⠀⠁⠀⠀⠉⠑⠀⠀⠈⠀⠀⠋⠁⠀⠁⠀⠈⠛⠀⠀⠉⠀⠀⠁⠈⠀⠀⠉⠁⠀⠉⠀⠈⠛

⠀⠀⠀⠀⢠⣦⠀⡖⣦⠀⡔⠀⢠⢶⠄⢠⡦⠀⢾⠀⡴⣀⠀⡶⡆⠀⡄⢠⡀⢰⡄⠀⡆⠀⡴⡔⡆⢠⠴⡄
⠀⠀⠀⠀⠈⠁⠀⠉⠁⠀⠉⠀⠀⠉⠀⠈⠁⠀⠀⠀⠘⠋⠀⠀⠀⠀⠁⠘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣤⣠⠀⣤⣦⠀⡔⡄⠀⡖⠀⢶⡀⠰⡆⢠⣀⡄⠠⣤⠀⢠⣤⡄⠀⣴⠀⢠⡄⠀⣲
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⢀⡀⠀⢀⠀⠀⣀⠀⢀⠀⠀⢀⡀⠀⣀⠀⢀⣀⠀⢠⡀⠀⢀⣠⣄⠀⢠⡀
⠀⠀⠀⢧⠟⠀⠸⠀⠠⡎⠀⢠⠷⠀⠻⠇⠈⡹⠀⠸⡷⠀⠸⠁⠰⡿⠀⠘⠾⠀⢾⠅⠀⢾⣏⡼⠀⢸⡇
⠀⠀⢀⠀⠀⡠⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡀⠀⣀⡀⠀⡉⠁
⠀⠀⠻⠇⠀⠧⠀⠐⠟⠀⠈⠿⡦⠀⡄⠀⠀⠐⠂⠀⠀⢠⠀⠘⠋⠀⠀⠁⠀⠃⠀⠿⠃⠸⠁⠘⠃⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢠⢛⡀⠀⠀⡇⢙⠆⠀⠀⡴⠉⠁⠀⠀⡏⠑⡄⠀⠀⡇⠈⠀⠀⠀⡏⠀⠁⠀⠀⡞⠉⠗⠀⢰⠃⠀⡸⠀⠀⠀⡏⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⡞⠒⡇⠀⢰⠓⠛⣆⠀⢰⠁⠀⠀⠀⠀⡇⠀⡇⠀⠀⡗⠂⠀⠀⢀⠓⠂⠀⠀⢰⠁⢠⡄⠀⢸⠖⠒⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠸⠀⠀⠙⠀⠘⠤⠔⠁⠀⠈⠢⠴⠂⠀⠀⠧⠊⠀⠀⠐⠧⠤⠀⠀⠸⠀⠀⠀⠀⠈⠦⠞⠀⠀⠘⠀⠀⠃⠀⠀⠰⠇⠀⠀⠐⠤⠜
⠀⠀⠀⢠⡄⢀⠄⠀⠀⡤⠀⠀⠀⠀⣠⠀⣤⠀⠀⡄⠀⡄⠀⠀⣠⠶⣄⠀⠀⡤⠤⡄⠀⠀⡠⠶⡄⠀⠀⡴⠤⡀⠀⠀⣠⠤⠄⠀⠀⠒⡖⠂
⠀⠀⠀⢸⡥⡏⠀⠀⠀⡇⠀⠀⠀⢀⢿⣰⢻⠀⠀⣿⡀⡇⠀⢰⠁⠀⢸⠀⠀⡇⣠⠎⠀⢰⠁⠀⣹⠀⠀⣇⣠⠇⠀⠀⠣⣄⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠁⢸⠀⠀⢰⠁⠀⠀⠀⣸⠘⡟⢸⠀⢀⡇⢷⡇⠀⠸⡀⢀⠏⠀⢠⠉⠀⠀⠀⠸⡀⣲⣇⠀⠀⡇⠹⡄⠀⠀⡀⢨⠆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⡀⠈⠀⠀⠀⠈⠁⡀⠀⠀⣀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢸⠀⠀⢸⠀⠀⡇⢠⠃⠀⣷⢰⡇⡸⠀⠀⠱⡰⠃⠀⠀⢳⡸⠁⠀⠀⠀⢠⠏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⢸⠀⠀⡆⠀⠀⣇⡞⠀⠀⢸⡞⢣⠇⠀⠀⢠⢇⠀⠀⠀⢨⠃⠀⠀⠀⣠⠃⠀⠀⠀⠒⡗⠂⠀⠀⠈⠙⠀⠀⠀⠴⠛⠄⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠢⠔⠁⠀⠀⠘⠁⠀⠀⠘⠃⠘⠀⠀⠀⠃⠘⠀⠀⠀⠏⠀⠀⠀⠰⠗⠲
⠀⠀⠀⠀⠠⠦⠀⠀⠀⠠⠲⡄⠀⠀⠔⠲⡄⠀⠀⢀⣴⠀⠀⠀⢀⠖⠒⠀⠀⢀⡴⠂⠀⠀⠒⠒⡆⠀⠀⣠⠒⢆⠀⠀⣠⠖⡆⠀⠀⣠⠖⢆
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡰⠁⠀⠀⠠⢞⠁⠀⠀⣞⣸⡀⠀⠀⠸⢦⠀⠀⠀⣞⣀⠀⠀⠀⠀⡼⠀⠀⠀⢣⣤⠊⠀⠀⠣⠴⡇⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⣇⠀⠀⠀⣰⣁⠀⠀⠀⣀⣨⠃⠀⠀⠀⡇⠀⠀⢠⣀⡸⠀⠀⠸⡁⣠⠇⠀⠀⢰⠁⠀⠀⠰⡁⣠⠇⠀⠀⠀⢰⡇⠀⠈⣆⣀⠏
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⠀⡀⠀⢀⡈⠀⣀⠀⠀⡀⠀⡀⠀⠀⢈⣀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣼⡀⠀⠀⠀⣸⠁⠀⡸⠀⠀⠀⠀⢠⠃⠀⢱⠀⢸⠀⠀⢸⠀⢸⠁⠀⣸⠀⠐⠧⠀⡗⠀⠀⠀⡇⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠖⠶⠀⠀⠀⣼⠧⠀⠀⠀⢠⠃⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⡜⠀⢸⠀⠀⢸⠀⢸⠀⠀⢸⠀⠀⠀⠞⠁⠀⠀⠀⠇⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠚⠀⠀⠀⠀⠀⠈⠃⠀⠃⠀⠘⠀⠀⠜⠀⠈⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠈⣿⡸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢉⣉⣙⠳⣄⠀⢀⣠⣿⠃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣟⠻⢄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⢷⣌⠛⠛⠋⣁⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡘⠛⡙⠁⠀⠀⢠⠦⡉⠐⠀⠀⠀⠀⢠⣆⣠⠀⠀⠀⠙⠛⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠘⠛⠀⢠⢢⠱⡀⠔⠉⠓⠁⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠢⣀⣠⣎⠀⢿⢀⣠⣄⣀⣀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⠖⠇⡔⢈⠁⢨⡀⡴⠂⠀⢹⣷⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢽⡇⣁⠀⣼⣁⡙⠂⠈⠀⢀⣴⡿⠁⠘⡆⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠘⡍⠿⠻⠿⠿⠟⠋⠀⠰⣢⣾⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠾⠥⣆⡀⠀⢹⠟⢲⠆⠀⡀⠀⡀⠀⠨⢻⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢣⠺⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⢮⢂⣺⡁⠠⠏⠺⠙⠀⢘⠕⠳⠘⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡰⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠰⣆⠀⠈⠈⠐⠚⢡⡄⠈⠧⠈⠈⠁⢠⡀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢳⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡌⢽⠂⠈⠀⠀⣠⠄⠁⠈⠳⠤⠐⠒⠉⠀⣤⠀⠀⢀⡀⠈⠷⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠶⠤⠄⢂⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⠀⠈⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢧⡀⢸⠀⠀⠀⣸⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠉⠲⠇⣀⣴⡏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠘⠋⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡞⠛⠛⠛⠛⠉⠁⣤⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⢀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢸⠃⠀⠀⠀⠀⠀⠀⠁⠈⢿⣄⡴⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡖⠛⢛⠻⠂⠀⠀⠀⠀⠉⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡐⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⠋

⠀⢀⠤⣦⡀⠀⠀⠀⠀⠀⣠⠐⢤⠀⠀⢀⡤⠒⠒⢠⡤⠀⠀⣠⠄⠐⢦⡄⠀⠀⢴⠀⠀⠀⠀⠀⣀⠤⠲⣤
⠀⢧⣀⡘⣿⡄⠀⠀⠀⠀⣿⣳⣞⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⡄⠀⢸⠤⠀⡄⠀⠀⢸⡄
⠀⠘⠞⢁⡿⣷⡀⠀⠀⠀⣿⠁⢸⠇⠀⢹⣆⠀⠀⠀⠀⠀⠀⢸⡆⠀⣠⡟⠀⠀⢸⠀⠀⠀⠀⠀⢸⡉⠙
⠀⠀⠀⣸⠁⢻⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠈⠀⠈⠁⠀⠀⠈⠁
⠀⠀⢠⣧⡤⠀⣿⡄⠀⠀⢀⠄⠀⠀⠀⠀⢠⠀⠀⢰⡆⠀⠀⠰⠀⠀⠀⠀⢰⠀⠀⡒⠀⠀⠀⠀⠀⣿
⠀⠀⡼⠀⠀⠀⠘⣷⡀⠀⠸⡄⠀⢰⠆⠀⢸⠂⠔⠸⡃⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⣿⠀⢢⠀⠀⠀⣨⠀⢀
⠀⣼⡇⠀⠀⠀⠀⣛⣳⣀⠀⠠⠓⠀⠀⠀⠼⠆⠀⠀⠃⠀⠀⠰⠄⠀⠸⠂⠁⠀⠀⠿⠀⠈⠃⠀⠀⠈⠀⠂⠁
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⡀⠀⠄⡀
⠀⣀⠄⠀⠀⠈⢹⡄⠀⠀⠀⠀⣿⡀⠈⣹⠁⠀⠀⢠⠊⠀⠀⠈⢳⡄⠀⠀⣿⡁⠀⣻⠀⢠⡟⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⣿⠻⣄⢹⠀⠀⠀⢅⠀⠀⠀⠀⢀⡇⠀⠀⣿⠋⠉⠁⠀⢸⡇⠀⠀⠀⠀⣼⠃
⠀⢀⣸⡀⠀⠂⠀⠈⠁⠀⠀⠀⠽⠄⠈⠿⠆⠀⠀⠈⠂⠄⠀⠀⠘⠀⠀⠀⠿⠄⠀⠂⠀⠀⠈⠂⠀⠀⠚⠇
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⢸⣾⠀⠈⣿⠆⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢉⣩⠛⢉⠁⠀⠀⠀⠀⡜⠁⠀⠀⢸⠁⠀⠀⢿⡄⠀⠀⡌
⠀⢸⣿⠤⣞⠋⠀⠀⠀⠀⠀⠀⠓⢷⣄⠀⠀⠀⣾⡃⠀⣺⠧⠀⠀⠀⣾⡇⠀⠀⠀⣸⡇⠀⠀⠈⣷⡀⡸
⠀⢸⣿⠀⠈⢣⣄⠠⡆⠀⠀⣄⠀⢀⡿⠀⠀⠀⠹⣧⡀⠈⢀⡔⠀⠀⠻⣧⣀⣀⠀⢹⣅⠀⠀⠀⠸⡷
⠀⠈⠉⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁
⠀⢰⠶⠆⠒⠖⠲⢠⠆⠀⢲⢰⠀⠀⠻⣿⡀⠀⠀⠶⠓⠀⠀⠀⡖⢲⡄⠀⠀⠘⣶⠂⠀⠂⠀⠐⠒⠒⣲⡜⠁
⠀⠀⢀⡾⠀⠀⢠⡏⠀⠀⢸⣿⠀⠀⠀⠘⢿⣆⡰⠂⠀⠀⠀⠘⠁⢸⢿⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⡰⡟⠁
⠀⠀⢼⣇⠀⠀⣿⡄⠀⠀⠨⣿⠀⠀⠀⠀⠈⡾⣣⡀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢠⣿⠀⠀⠀⠀⠀⣐⠍
⠀⠀⠸⣿⣄⠀⢹⣧⣀⣀⣸⣿⠀⠀⢠⠀⣜⠀⠙⣿⣄⠀⠀⢀⡀⠀⠈⠙⠛⠁⣿⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠈⠉⠁⠀⠀⠛⠋⠀⠀⠘⠚⠃⠀⠈⠋⠀⠀⠀⠀⠈⠛⠁⠀⠀⠒⠛⠛⠛⠓⠒⠃

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡏⣻⣀⡄⢲⡆⢠⡶⣦⡀⠀⠉⣿⢸⡇⢡⣄⠙⣦⢰⣶⠚⣷⣀⣀⠀⠀⢶⣦⠸⠇⠀⠀⠀⡀⠀⠀⢀⣤⣤⠀⠈
⠀⠀⠀⠀⣿⢀⣭⢹⡇⢨⡇⢻⡍⠽⠷⢀⡀⣿⠈⠇⢾⡏⠀⣿⠀⣿⢠⣟⠉⣻⡦⠀⠸⢳⡞⠛⣷⢰⣿⣽⠓⡛⣨⠶⣾⠄⣤⣤⠆⣴⣖
⠀⠀⠀⠀⠀⣼⡇⣼⣁⡀⣠⠀⣠⠶⠀⢸⣇⠋⣏⢠⣄⢀⡄⠉⠀⠛⠀⠹⢮⡽⠏⢐⡷⠸⡇⠀⠿⠈⠁⠉⢋⡁⣿⠀⠿⣄⢸⡇⣤⠷⠿⠆
⠀⠀⠀⠀⠀⣾⠀⡿⣿⠀⢸⣤⣽⣧⡀⠀⣿⡄⣿⠀⠻⢺⡇⣶⡖⠒⣷⠰⢿⡄⠀⠸⡷⢀⣷⡴⠛⣷⡀⠁⠈⢉⣉⡀⣸⠇⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⢉⣿⡀⠿⠖⠘⠗⠀⠋⠁⠀⢸⡇⠻⡾⠁⠸⣷⠹⠇⡀⠻⣆⣠⣷⠀⠸⢗⡶⢼⡇⢰⣯⡽⠆⢈⡭⢾⢳⡞⢰⡶⢆⣴⢲⣴⡆
⠀⠀⠀⠀⠀⠈⢻⣧⠶⢰⡆⣰⣿⡽⠷⡀⣨⢁⣀⡀⢠⠄⣥⡀⣀⠁⠐⣳⣶⢋⡄⠀⢼⡇⠘⠇⠘⠓⠚⠋⢨⡵⠿⢸⣧⢸⠇⠈⠙⠷⠴⠂
⠀⠀⠀⠀⢸⣇⡸⢻⡇⠘⠗⠈⠛⠖⢸⡇⠾⣦⠈⣷⠿⣶⢸⡏⠉⣿⢸⠯⣍⣠⣧⡴⢸⡷⠖⣶⠀⡶⣏⠀⣤⣤⡀⣼⣧⠄⣤⡤
⠀⠀⠀⠀⠀⢽⡧⠸⣷⠶⠆⠐⠉⠀⠈⢻⡇⡛⠐⠃⠀⣿⠘⠃⠀⣋⠀⢐⡎⠀⢸⣇⠜⣿⠀⠻⣾⣛⣛⢠⡶⢺⣧⠀⣿⠀⣿⠖⣦⣄
⠀⠀⠀⠀⠀⠘⣧⡐⣿⢀⣾⡛⠷⠖⢀⠘⣷⢰⡄⢰⠆⣶⣠⢸⡟⢙⣷⣞⡁⠀⢨⣿⣄⠋⠈⠀⠈⠉⠉⠈⢉⣉⣉⠠⡏⠀⠿⢭⣭⠅⡀
⠀⠀⠀⠀⠀⠐⣷⠀⠿⠈⠉⠛⠚⠃⢸⡇⣿⠀⢻⠟⠀⠀⣿⢸⡇⣿⣁⣉⣿⠀⣀⠁⣿⠋⣿⢠⣾⠹⠾⠇⣙⢩⣧⡀⣠⣤⠀⡤⣴⣮⡿⠆
⠀⠀⠀⠠⣶⠄⢿⡴⢶⣆⣠⣄⠀⠀⢸⡇⣭⣤⢰⡆⠰⠒⠂⠘⠃⠈⢯⣭⠋⠀⡿⢦⡏⠀⠟⠀⠘⠓⡿⠷⣿⠘⣷⡀⣿⠁⠆⠀⣙⣢
⠀⠀⠀⠀⠷⣦⢸⠇⡄⢹⡗⢚⡓⠀⠘⢳⡇⣿⣠⢱⡆⢰⣶⠛⣷⣠⠾⣧⠀⢰⡷⠔⢷⡶⢶⡄⠀⠈⠛⠛⠉⠁⣾⢹⡷⠠⡆⢀⣉⣁
⠀⠀⠀⠀⡼⢧⡆⠈⠃⠀⠉⢉⣁⡀⠀⡸⠃⢿⠇⠘⣿⠀⠟⣴⠘⣧⣠⣿⠀⠘⢻⣄⢸⡇⣴⣛⣷⡤⢘⣫⣿⣨⣿⠘⢳⡟⠁⣿⡷⠾⠇
⠀⠀⠀⢰⡟⢸⡿⠛⣧⡐⢻⡷⠾⣷⢀⡅⢠⣄⢠⣄⠈⣀⣀⡀⠐⢮⣵⣟⡀⠀⣼⠀⢸⠇⠛⠶⠶⢂⣉⠀⠀⠁⢸⡗⠘⠃⠀⠈⡿⠆
⠀⠀⠀⠘⠷⠸⠇⠀⠀⠋⢈⠋⠀⣿⡈⣿⠀⣻⠎⢹⠇⡟⠉⣷⡐⣿⠀⣹⣧⡄⣿⣤⢤⣄⢠⡄⣾⠷⠿⠶⢲⣆⠚⣿⠂⣶⢂⡤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠈⠁⠀⠘⠛⠀⠺⠘⠇⠀⠙⠃⣬⠉⠀⣿⣀⢹⡇⠀⠋⠘⠃⣭⡥⠰⢯⡭⢿⢀⡛⣾⠀⠚⢷⣍⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂⠀⠀⠂⠐⠀⠀⠂⠂⠀⠂⠂⠀⠂⠀⠀⠀⠀⠐⠀⠐⠒⠐⠂⠀⠀⠐⠂⠂⠂⠀⠂⠀⠀⠀⠀⠀⠒⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢈⠀⠈⠉⠀⡉⠀⠀⠀⠀⠀⡀⢈⠁⠈⠉⠁⠀⠀⠀⢈⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠚⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⣶⡎⣿⠹⢶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡶⠀⢀⡴⠾⠋⢻⣉⡀⠈⠛⠛⠚⠉⠀⣹⡟⠛⣦⡀⣤⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡘⡇⠠⣏⠀⠀⠀⠀⠈⠉⠓⠒⠒⠛⠛⠛⠁⠀⠀⠀⠙⣦⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢿⠤⢤⣤⣤⡀⠀⠀⠀⣀⡀⠀⣠⣤⠀⢀⣠⣴⠏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠈⠉⠉⠛⠛⠛⠛⠛⠒⠋⠉⢩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⢀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⡴⠶⠛⠁⢀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠇⠀⠀⢰⡏⢬⡄⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡀⠀⠀⠀⣉⣭⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⣀⠀⡀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⢀⡀⢀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⢀⡄⢀
⣼⣿⠀⣿⠀⠀⢠⣾⣇⠈⡇⠀⠀⢰⣿⡇⢸⡟⠀⠀⣿⣿⠀⣇⠀⠀⢠⣾⡇⠸⡟⠁⠀⣴⣿⠀⢿⠋⠀⢠⣿⡇⠸⡟⠁
⢿⣿⡄⠘⠀⠀⠀⣿⣿⠀⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⡄⢹⠀⠀⠘⣿⣷⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠸⣿⣧⠀⡀
⢸⣿⡇⠰⡆⠀⠀⢿⣿⡆⢸⡀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇⠸⡆⠀⠀⣿⣿⡀⠚⠀⠀⢸⣿⣇⠐⠃⠀⠀⣿⣿⠀⢷
⠘⣿⣿⠀⣷⠀⠀⢸⣿⣇⠘⠇⠀⠀⢻⣿⡆⠀⠀⠀⠘⣿⣷⠀⠇⠀⠀⢻⣿⡇⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⢻⣿⡆⠸⠆
⠀⣿⣿⣦⣿⡶⠀⠘⣿⣿⣶⡤⠀⠀⢸⣿⣿⣦⠄⠀⠀⣿⣿⣶⡶⠀⠀⢸⣿⣿⣦⡤⠀⠀⢿⣿⣶⠀⠀⠀⢸⣿⣿⣦⡄
⠀⠙⠛⠙⠋⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠙⠛⠋
⢀⣴⡀⢲⠀⠀⠀⢀⣶⠀⠀⠀⠀⢀⣴⡀⠀⠀⢀⣶⠀⢆⠀⠀⠀⣰⡆⠀⠀⠀⠀⢠⠀⢀⠀⣀⠀⠀⠀⠀⣠⠀⡀
⢸⣿⡇⢸⡆⠀⠀⣿⣿⡀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⡄⢸⠀⠀⢸⣿⣇⠀⠀⠀⢰⣿⡆⢸⡄⢹⠀⠀⠀⣾⣿⠀⢿
⢸⣿⣧⠈⠃⠀⠀⢸⣿⡇⠀⠀⠀⠸⣿⣧⠀⠀⢸⣿⡇⠈⠁⠀⠀⣿⣿⠀⠀⠀⢸⣿⣇⠈⡇⢸⡇⠀⠀⢻⣿⡆⢸⡄
⠀⣿⣿⠀⢷⠀⠀⢸⣿⣷⠀⠀⠀⠀⣿⣿⠀⠀⠘⣿⣿⠀⡇⠀⠀⢿⣿⡆⠀⠀⠈⣿⣿⠀⣷⠀⣧⠀⠀⢸⣿⣇⠘⡇
⠀⢻⣿⡆⢸⡄⠀⠀⣿⣿⠀⠀⠀⢀⡟⠻⠆⠀⠀⣿⣿⡀⢹⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⡄⢸⡀⢻⠀⠀⠈⣿⣿⠀⣷
⠀⢸⣿⣷⣾⣷⠆⠀⢻⣿⣷⠂⠠⣿⣿⣶⡖⠀⠀⢸⣿⣷⣾⡶⠂⠈⣿⣿⣶⠖⠀⢸⣿⣷⣾⣷⣾⡶⠂⠀⣿⣿⣶⣿⡶
⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠈⠛⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉
⠀⣠⠀⣀⠀⠀⠀⠀⣤⠀⡄⠀⠀⠀⢠⡄⢠⡀⠀⠀⠀⣠⠀⢠⠀⠀⠀⢀⡄⠀⣄⠀⠀⢠⣶⣄⠀⡀⠀⣠⣶⠀⣶
⢼⣿⡄⢸⡀⠀⠀⣾⣿⠀⣿⠀⠀⢰⣿⡇⠸⡇⠀⠀⢸⣿⡆⢸⡄⠀⠀⣾⣿⠀⠿⠁⠀⠻⣿⣿⠀⠀⠀⣿⣿⡄⢹
⢸⣿⡇⠸⡇⠀⠀⢻⣿⡆⠈⠀⠀⠘⣿⣿⠀⣧⠀⠀⢸⣿⣇⠈⠁⠀⠀⣿⣿⣆⡀⠀⠀⠀⢿⣿⡆⠀⠀⢸⣿⡇⠸⡇
⠘⣿⣿⠀⣷⠀⠀⢸⣿⡇⠈⠁⠀⠀⣿⣿⡀⢹⠀⠀⠈⣿⣿⠀⣷⠀⠀⠸⢿⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⠸⣿⣷⠀⣧
⠀⣿⣿⡄⠻⠀⠀⠘⣿⣿⠀⠀⠀⠀⢸⣿⣇⠘⠇⠀⠀⢿⣿⡀⢸⠀⠀⠀⠀⣼⠛⠇⠀⠀⠈⣿⣿⠀⠀⠀⣿⣿⡀⠻
⠀⢸⣿⣿⡶⠂⠀⠀⣿⣿⡶⠀⠀⠀⠸⣿⣿⣷⡶⠀⠀⢸⣿⣷⣾⡷⠂⠀⢾⣿⣷⡶⠀⠀⠀⢿⣿⡶⠂⠀⢹⣿⣿⡶⠂
⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣴⡆⢰⡆⠀⠀⢀⣴⡄⢸⠀⢺⠀⠀⠀⢠⣶⠀⣶⠀⠀⠀⣠⣆⠐⡇⠀⠀⢀⣶⣄⡀
⠀⠀⠀⠀⠀⢸⣿⣧⠈⡇⠀⠀⢸⣿⡇⠸⡇⢸⡆⠀⠀⣿⣿⡄⢸⡀⠀⠀⣿⣿⠀⣿⠀⠀⠹⢿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⠀⠀⠘⣿⣿⠀⣧⠀⣇⠀⠀⢸⣿⣧⠈⠁⠀⠀⢻⣿⣆⠈⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⡆⢸⡄⠀⠀⣿⣿⡀⢹⠀⢿⠀⠀⠈⣿⣷⠀⣷⠀⠀⠘⢿⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⡈⠁⠀⠀⢹⣿⣧⠈⠁⠈⠀⠀⠀⣿⣿⡀⢹⠀⠀⠀⠘⣿⣷⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠖⠀⠀⠘⢿⣿⣷⣾⡷⠂⠀⠀⢸⣿⣷⣾⡷⠂⠀⠀⣿⣿⡶⠀⠀⢸⣿⣿⣶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⣀⣀⣤⠤⠤⠤⣄⣀⣀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠩⠔⠚⠛⠳⠦⢤⣀⣀⡀⠀⠀⠈⠙⠲⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡉⠉⠙⠃⠀⠀⠈⠀⠀⠀⠀⠐⣶⣲⣄⡀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠐⠒⠐⠶⣦⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢸⡟⠉⣻⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣴⠁⣠⠖⠋⣼⢀⣤⠠⡄⠀⢹⠓⠋⠀⠀⠀⠀⠀⠀⠰⠤⠴⠚⠁⡷⢸⣿⡿⠿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⡧⠊⠁⠀⠀⢿⠋⢺⡀⠈⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣿⣿⣄⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⡟⠁⢀⣴⡀⠀⢸⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡰⢋⣾⠟⠉⠛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡼⢹⠀⢸⡇⢀⣾⣿⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⢈⣧⠴⣊⣴⣿⣿⣄⠀⣀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠘⡆⠘⡇⢸⣿⣿⠃⣰⠇⠀⢀⣤⡤⠚⠁⠀⠀⠀⠀⠀⢹⣦⣤⣶⣿⣿⡏⠉⣿⣿⣿⡿⠋⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢦⣹⣼⣿⣣⡴⠧⠤⢄⣿⣿⡇⠀⠀⠀⠀⠰⡤⣴⡿⢿⣿⣏⣹⣿⣿⣾⣿⡿⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢹⣴⣶⣦⣄⠉⠻⢷⡀⠀⠀⠀⠀⠀⠙⠋⠻⠿⠿⢛⣻⠿⠛⠁⢀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⣄⣤⣞⠿⣿⣿⡿⡷⣀⠀⠈⠀⠀⠀⢠⣤⠀⠀⠄⠀⠉⠩⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⣧⠈⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠈⠑⡄⠀⠂⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠘⡇⢸⡆⠀⣯⣿⡏⠀⢀⡀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢳⡀⠈⠿⠀⠀⡼⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣀⠀⠀⠀⣀⡤⠖⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠙⠈⣇⠁⡀⠀⢀⡼⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠑⠄⠐⢁⡴⡻⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠙⣄⠋⣇⠀⠀⠸⡐⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⢸⣰⣿⣿⣇⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢦⠀⠀⠈⠦⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠳⠂⡄⠀⠀⠀⢸⠟⢋⡁⣀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⡀⠀⠀⠙⠏⠉⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠀⢀⡇⠁⠀⠀⢀⡐⠈⠉⠉⠁⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠂⢀⣀⠀⠈⠓⠦⢬⣑⣒⠲⠶⠤⠶⠒⣋⣡⣴⠟⠃⠀⠀⣠⠎⣁⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠈⠙⠒⠲⠤⠤⠤⣭⣭⡭⠭⠭⠿⠛⠉⠀⠀⢀⣤⣾⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉

⠀⠀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⢸⣿⢟⠛⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠁⠀⠘⠀⠀⠀⠀⠉⠉⠉⠑⠨⣿⣿
⠀⢸⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⠀⠼⠛⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⡄⢀⡀⣠⣶⠋⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣦⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠀⠀⠀⠀⠀⢠
⠀⢠⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⢀⣤⣤⣴⣿⣿⠋⠀⠀⠀⠀⠀⣠⣾
⠀⢘⣛⡄⠀⢀⠀⢸⣿⣿⢃⣇⠉⠘⠂⢀⣀⣤⣤⣤⣶⣥⡄⠒⠀⣤⣶⣧⣿⣿⣿⣿⣦⡀⠀⣠⣼⠑⣿⣿
⠀⢨⣮⢷⣤⢲⢤⣾⣿⣿⣿⣿⣿⣿⣾⣾⠿⠋⣿⣿⣿⣿⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣴⢶⣿⣿⣿
⠀⢸⡗⢾⣍⣰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣟⣼⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⢸⢿⣛⣩⣯⢿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣛⣿⣿⣽⡴⣬⣛⣿⣯⣿⣥⣢⣢⡿⣻⠿⣯⣿⣿⡿⡿⣿⡟⢿⢿⠟⠿⡿⣿⡿⢿⣿⡭⣿⣿
⠀⢸⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⡋⣿⠿⣞⠿⡯⢟⣓⣷⣹⣷⣶⣮⢸⣉⣷⣛⠌⣫⣵⣿⣾⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣧⣼⣿⡿⣼⣷⣬⣅⣨⣿⡿⣭⡿⢭⣷⣿⣷⣾⣿⣿⣿⣿⡿

⠀⠀⣠⠶⠚⠛⠲⢦⡀⠀⠀⠀⣠⠖⠚⠛⠲⣤⡀⠀⠀⠀⣠⠖⠚⠓⠲⣄⠀⠀⠀⠀⣠⠖⠛⠓⠶⣄⠀⠀⠀⢀⣤⠖⠛⠓⠶⣄⠀⠀⠀⢀⡴⠖⠛⠓⠶⣄
⠀⢸⠃⠀⣼⢣⠀⠈⢷⠀⠀⣼⠃⢰⣏⣙⡆⠈⢷⠀⠀⣼⠃⣰⠋⠉⠆⠈⣧⠀⠀⣼⠁⢰⠋⠑⣆⠈⣧⠀⠀⡾⠁⢸⣉⡉⠁⠘⣧⠀⠀⡾⠁⢸⣉⡉⠀⠘⡇
⠀⢻⡀⢰⠟⠚⢧⠀⣼⠀⠀⢿⡀⢸⣏⣉⡷⠀⣼⠀⠀⢿⡀⢻⣀⢀⡤⠀⡾⠀⠀⢷⠀⢸⣀⣠⠏⢀⡿⠀⠀⣧⠀⢸⣉⣉⠀⢀⡟⠀⠀⣧⠀⢸⠉⠉⠀⢀⡏
⠀⠀⠻⢦⣄⣀⣤⠞⠁⠀⠀⠈⠳⢤⣌⣀⣤⠞⠁⠀⠀⠈⠳⢤⣈⣁⡤⠞⠁⠀⠀⠈⠳⢤⣀⣀⡤⠞⠁⠀⠀⠈⠳⢤⣀⣈⡤⠞⠁⠀⠀⠈⠳⢤⣀⣠⡴⠟

⠀⠀⣠⠖⠛⠛⠲⢦⡀⠀⠀⠀⣠⠖⠛⠛⠲⢦⡀⠀⠀⠀⣠⠖⠛⠛⠲⢤⠀⠀⠀⢀⡤⠖⠛⠛⠲⣤⠀⠀⠀⢀⡴⠞⠛⠛⠲⣄⠀⠀⠀⢀⡴⠖⠛⠛⠲⣄
⠀⣸⠃⣰⠋⠉⠳⠀⢳⠀⠀⣼⠁⢸⣀⣀⣿⠈⢷⠀⠀⣼⠁⠀⢸⡇⠀⠈⢷⠀⠀⣼⠁⠀⠀⢸⠀⠈⣧⠀⠀⡾⠁⢸⣠⠞⠁⠈⣧⠀⠀⡾⠀⠀⡇⠀⠀⠘⡇
⠀⢹⡀⠹⣄⣈⣿⠀⣼⠀⠀⢻⡀⢸⠉⠉⣿⠀⣾⠀⠀⢿⡀⠀⢸⡇⠀⠀⡾⠀⠀⢷⠀⠠⣄⡼⠀⢀⡟⠀⠀⢷⠀⢸⠉⢳⡀⢀⡟⠀⠀⣧⠀⠀⣇⣀⠀⢀⡏
⠀⠀⠛⢦⣤⣥⡤⠞⠁⠀⠀⠈⠻⢦⣤⣤⡤⠞⠁⠀⠀⠈⠳⢦⣤⣤⡴⠞⠁⠀⠀⠈⠳⢦⣬⣤⡴⠞⠁⠀⠀⠈⠳⢤⣤⣤⡴⠞⠀⠀⠀⠈⠳⢤⣤⣤⡴⠛

⠀⠀⣠⠞⠛⠛⠓⢦⡀⠀⠀⠀⣤⠞⠛⠛⠳⢦⡀⠀⠀⠀⣴⠞⠛⠛⠳⢦⡀⠀⠀⢀⡴⠞⠛⠛⠳⣦⠀⠀⠀⢀⡴⠞⣛⡛⠳⣤⠀⠀⠀⢀⡴⠚⠛⠛⠳⣄
⠀⣸⠁⣾⣇⠀⣾⡄⢷⠀⠀⣼⠁⢸⢧⡀⣿⠈⢿⠀⠀⣼⠁⡴⠉⠉⢧⠈⢷⠀⠀⡾⠁⢸⡋⢉⡧⠈⣧⠀⠀⡾⠁⡞⠉⠉⣦⠈⣧⠀⠀⡾⠁⣿⣉⣹⠆⠈⡇
⠀⢹⡀⢿⠹⡜⢸⠅⣼⠀⠀⢻⡀⢸⠀⠳⣿⢀⡾⠀⠀⢻⡀⠳⣀⣀⡞⢀⡾⠀⠀⢳⡀⢸⠉⠉⠀⢀⡟⠀⠀⢷⡀⠧⣀⣤⡟⢀⡟⠀⠀⣷⠀⡯⠈⠳⡄⢀⡏
⠀⠀⠙⠦⣤⣤⡤⠞⠁⠀⠀⠀⠛⢦⣤⣤⡤⠞⠁⠀⠀⠀⠻⢦⣤⣤⡴⠞⠁⠀⠀⠈⠳⢦⣤⣤⡴⠟⠀⠀⠀⠈⠳⢦⣤⣤⡴⠛⠀⠀⠀⠈⠳⢤⣤⣤⠴⠋

⠀⠀⣠⠞⠛⡛⠛⢦⡀⠀⠀⢀⣴⠞⠛⠛⠓⢦⡀⠀⠀⢀⡴⠞⠛⠛⠓⢦⡀⠀⠀⢀⡴⠚⠛⠛⠳⣦⡀⠀⠀⢀⡴⠚⠛⠛⠳⣤⡀⠀⠀⢀⡴⠚⠛⠛⠳⣤
⠀⣸⠁⠰⣏⣉⠃⠀⢻⠀⠀⣼⠁⠀⠉⡏⠁⠀⢷⠀⠀⣾⠁⢸⠀⠀⡇⠀⢷⠀⠀⡾⠁⢹⡄⢀⡏⠈⢋⠀⠀⠙⢻⡄⣾⣧⢰⡟⣷⠀⢠⣿⠁⠙⣧⡾⠃⠘⣷
⠀⢸⡄⠰⣄⣈⡷⠀⡾⠀⠀⢻⡄⠀⠀⡇⠀⢀⡾⠀⠀⢻⡀⠸⣄⣠⠇⢀⡾⠀⠀⢻⡀⠀⢳⡞⠀⢀⣟⠀⠀⣋⡈⣭⠁⢙⡍⢠⡟⠀⠈⣟⡀⣴⠏⢻⡄⣰⡿
⠀⠀⠙⠦⣤⣤⠴⠞⠁⠀⠀⠀⠙⠦⣤⣤⠴⠞⠁⠀⠀⠀⠛⠦⣤⣤⠴⠟⠁⠀⠀⠈⠳⠦⣤⣤⠴⠛⠁⠀⠀⠈⠻⠦⣤⣤⠴⠋⠀⠀⠀⠈⠻⢤⣤⡤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠓⢦⡀⠀⠀⢀⡴⠚⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠘⢦⡰⠃⠀⢷⠀⠀⡾⠀⠀⢉⡽⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⡇⠀⢀⡞⠀⠀⢻⡀⢠⣏⣀⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⠴⠋⠀⠀⠀⠀⠛⠦⣤⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠐⠀⡸⢸⠀⠘⡉⢁⡀⢸⠀⢠⢄⠈⠆⠣⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠳⣄⣀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡠⠂⣀⣄⠠⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⡼⠀⡇⠀⠋⠀⠀⢁⢰⠀⠀⠀⠀⠀⠀⠀⢙⡀⠰⡄⠀⣠⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠧⡤⠃⠀⠀⠙⠦⠤⠤⠔⠋⠘⠀⠀⠀⠀⠰⠀⠀⢸⣀⣀⠖⢰⣅⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠒⠀⠃⠀⠀⠔⠀⡄⠀⠀⠀⠀⠠⠒⠒⡀⠀⠔⠒⢠⠤⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣀⣠⠂⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⢀⡄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⢀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠉⠁⠘⠒⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠐⠰⠃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠂⠀⠦⠴⠃⠀⠀⠀⠙⠒⢤⡠⠇⠘⠒⠊⠢⠤⠄⠀⠦⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠄⡴⠀⠢⠃⠈⢀⠔⠀⢀⠖⠀⠂⡔⠀⠆⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⢀⠖⠁⠃⠀⠠⠇⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⠀⠀⠘⠆⠀⣀⠴⠀⠀⠀⢀⡀⠀⠀⠰⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠠⠀⢀⠔⠂⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢰⠁⠈⢦⠀⠀⢀⠂⠀⠦⠤⠈⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠂⠀⠀⠇⠀⠸⠀⠀⠎⠀⠀⠁⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⡀⠀⠀⣀⣀⠀⠀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⣴⣿⡆⠀⢰⡾⠛⢻⡆⠀⣼⡏⢹⣧⠀⢹⣿⠛⠛⠻⡆⠀⣾⡇⠀⠀⠀⣿⠀⠀⠀⣾⡏⠛⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⣸⣿⢿⣷⠀⣸⣧⣴⣿⡁⠀⣿⡇⠘⠙⠀⢸⣿⠀⠀⢀⣿⠀⣿⡷⠀⠀⢰⣿⠂⠀⢸⣿⠁⠀⠀⠀⣿⡷⠒⢾⣿
⠀⠀⢰⣿⠟⢿⣿⠀⢽⡇⠉⠉⣻⠀⣿⡇⢰⡆⠀⢸⣿⢀⣴⡿⠁⠀⢿⣇⠀⠀⠸⣿⠀⠀⢸⣿⡀⣸⣶⠀⢸⣿⠀⢸⣿
⠀⠀⠺⠿⠀⠈⣿⠀⠘⠳⣶⡾⠟⠀⠸⠿⠿⠃⠀⢸⡿⠛⠁⠀⠀⠀⠸⠿⠀⠀⠀⠛⠃⠀⠀⠻⠗⠛⣿⡄⠘⠛⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⣤⡀⠀⠀⣁⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠲⠿⢻⣷⠀⠀⣾⡆⠀⣶⠆⠀⢸⣷⠀⠀⠀⠀⣿⣷⡀⣼⣿⣇⠀⠀⣿⣿⣤⣿⡇⢀⣾⠋⢁⠀⣾⡟⠉⢉⣿
⠀⠀⣄⡄⠀⠀⠀⠀⣿⡆⠀⣿⣇⣼⠟⠀⠀⣾⡏⠀⠀⠀⠀⣿⣿⣷⣿⢿⣿⠀⠀⡏⣿⣿⣿⠀⣾⡏⠀⢸⡇⣿⣇⣴⡿⠃
⠀⠀⣿⡇⠀⢀⡀⠀⣿⡇⠀⣿⡇⠹⣷⠀⠀⣿⡇⠀⠀⠀⢠⣿⠛⣿⣿⠘⣿⡀⢰⡇⣿⣿⡟⠀⣿⡇⠀⣿⠀⢿⡟⠋
⠀⠀⢻⣿⠀⠘⣿⣀⡿⠀⠀⢿⣇⠀⢻⡆⠀⢹⣧⣀⣀⡄⠘⠟⠀⠿⠟⠀⣿⡇⠸⠇⠈⠿⠇⠀⠻⣧⣰⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⡖⢂⡀⠀⢰⣶⠟⠳⣤⡀⠀⢰⠿⢳⡄⠀⢴⣶⣾⡿⠿⠿⠿⢰⣶⠀⢰⣶⠀⢷⣆⢀⣾⠀⢶⣦⠀⣴⣶⡀⣸⠃
⠀⠀⢀⡟⠀⢸⣷⠀⣸⣟⣠⣾⠟⠁⠠⣾⠀⢸⠇⠀⠈⠁⣿⡇⠀⠀⠀⢸⣿⠀⢸⣿⠀⢸⣿⣸⡇⠀⢸⣿⣰⡟⢿⣷⡟
⠀⠀⢸⡇⠀⢸⡇⠀⣿⡏⠙⢧⡀⠀⠈⢿⡄⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⢀⣾⣿⠀⠀⣿⣿⠀⠀⠀⣿⣿⡇⠘⣿⡇
⠀⠀⢻⣇⣘⣿⡅⠀⢸⣧⠀⢸⣿⠀⠀⢈⣻⣦⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿⣘⠛⠛⠃⠀⢹⣿⠀⠀⠀⢿⡿⠀⠀⠛⠃
⠀⠀⠀⠉⠉⠉⠛⠂⠀⠀⠀⠈⠉⠀⠀⠈⠛⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣄⡀⢀⡴⠂⠀⢤⣀⠀⢀⣦⡀⠀⠴⣶⣶⣦⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣾⠿⣷⡄⠀⠀⣦⡄⠀⠀⠀⣴⡿⠿⣦
⠀⠀⠀⠹⣿⣾⠃⠀⠀⠘⣿⣆⣼⡿⠀⠀⠀⢠⣾⠟⠁⠀⠘⠻⣿⡿⠇⠀⠀⢸⣿⣴⠟⠁⠀⢸⣿⠃⠀⠀⠀⣿⠃⢀⣿⠇
⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⣴⡯⠋⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣼⠟⠃⠀⡀⠀⢸⣿⠀⠀⣤⡀⠈⢀⣾⠏
⠀⠀⢠⣿⠏⢿⡄⠀⠀⠀⣰⣿⠃⠀⠀⣼⣿⣥⣤⣤⣄⠀⢴⣶⣶⣶⣶⠀⢼⡏⠀⢀⡜⠁⠀⢘⠛⠀⠀⠉⠀⠀⠸⠟
⠀⠀⠉⠉⠀⠈⠁⠀⠀⠀⠉⠃⠀⠀⠀⠈⠋⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠛⠁⠀⠀⠘⠛⠀⢀⣿⠇⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⣿⡇⠀⣿⣿⠈⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⣿⡇⢠⣿⣿⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣿⡇⣿⠀⠹⣆⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⣿⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠛⣿⡧⠀⢸⣿⡇⠛⣿⣿⠛⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⣿⡇⠀⢸⣿⡇⠀⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠤⢿⣧⠀⢸⣿⡇⢰⡿⠿⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⣿⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠀⠀⠐⠖⠒⠀⠀⠀⠙⠒⠀⠀⠀⠀⠐⠊⠂⠀⠀⠈⠋⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠃⠈⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠐⠉⠀⠀⠀⠐⠚⠂⠀⠀⢄⠒
⠀⠀⠀⠐⠒⠀⠀⠚⠀⠈⠒⠚⠁⠀⠀⠈⠒⠂⠀⠀⠓⠒⠚⠉⠀⠀⠐⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢏⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⡂⠀⠀⠀⢢⡀⠆
⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄⠀⠤⠇⠠⢀⠴⠃⠀⠤⠄⠀⠧⠀⠤⠥⣤⡄⠀⠜⠢⠼⠃⠤⠀⠀⠄⠀⢄⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠨⢀⣤⠀⠀⡐⠉⡀⠀⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⠀⠀⠀⠐⠉⠀⠀⠐⠄⠀⣠⠆⠀⠀⠐⠀⢁⠀⠀⠈⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠒⠃⠀⠉⠁⠈⠉⠀⠀⠉⠉⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⡤⠀⠀⠀⠀⢀⠀⠀⠤⡬⢉⡆
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠐⢀⠄⠀⠀⠀⠁⡄⠈⢠⠀⠀⠀⢀⠸⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠠⠤⠖⠀⠀⠀⠀⠚⠀⠀⠀⠠⠴⠀⠠⠎⠀⠀⠤⠋⠀⠸⠀⠀⠀⠤⠀⠀⠠⠤⠥⠠⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣠⢤⣀⣤⣤⣤⣴⣶⣶⡶⣶⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣼⣤⣦⣤⣤⣦⣼⣯⣤⣴⣤⣼⣧⣩⣤⣤⣤⣦⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⢻⡏⣿⠿⢿⡏⠿⣤⠦⠼⡏⠿⢿⡿⠿⡿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣁⣤⡘⣇⠻⠐⣂⡀⣶⢠⡘⡂⡃⡒⣠⣄⢀⣿⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠹⠼⠋⠉⠉⠉⠛⠛⠋⠉⠁⠈⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠎⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣳⠀⡰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⣰⠰⠐⠃⢊⡶⢁⡌⠈⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⠀⠀⠀⢰⣿⣏⠐⡀⠁⢖⣃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⢯⣄⢀⣾⠟⢿⣿⣿⠀⣿⣴⣿⣿⡦⣴⣿⣿⡆⣿⠟⣿⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠻⢿⡿⢃⠀⠀⡼⠏⠀⠻⠷⢿⡏⠻⠾⠿⠙⠷⠾⠃⠙⠷⠾⠂⠿⠀⠿⠇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠢⡀⠀⠂⠀⠀⠀⠀⠉⡜⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⣿⣀⣀⠀⢀⣀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⠐⠐⠀⠜⠑⠂⠖⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⣻⡷⣿⡿⢿⠳⣿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠈⠛⠛⠁⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠢⠈⠀⠀⠒⠈⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢠⠀⠐⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠠⠄⠐⠂⠊⠁⠀⣤⠤⡤⠁⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣦⡤⠀⠀⠀⠈⠏⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣰⣶⡶⠶⢶⣿⡛⠉⠙⢷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠠⢿⣿⣔⣢⣿⣿⠀⠀⢀⡀⠀⠀⢀⠀⢠⠤⠐⠂⠂⠀⠀⠀⢀⠃⠀⠙⣄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢸⣯⢶⡠⣤⢠⣶⣾⣿⢿⣿⣿⡀⢸⣧⡶⣭⡷⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⠓⠀⠀⠙⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠘⣷⣌⣷⢠⠆⠀⠈⠫⠉⠘⣿⣿⣿⠛⠷⠧⠋⡀⠀⡄⢀⢺⡇⡀⠀⠀⠀⠙⢦⡀⡄⢠⢄
⠀⠀⠀⠀⠀⠘⣿⢠⡽⣎⠀⠀⠀⢀⡀⢙⡿⡿⠋⠀⠰⠒⢢⡀⣀⡀⠄⠘⣇⣈⠉⠀⠄⠀⠀⠙⢢⠿⠮⠃⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠻⣤⠟⠈⢳⡶⠶⢶⡾⢨⡿⠁⠀⠀⠀⠀⠀⡄⠠⠄⠂⢠⡅⠉⠣⠀⠀⠐⠆⢀⠚⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢈⣤⣇⠀⠀⠂⠰⠇⣰⢃⣀⠀⠀⠀⠀⠘⠂⠀⠀⠆⢾⠀⠳⠄⣀⣀⠦⠀⠀⠓⠤⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⡄⠀⠀⠁⢠⣏⢨⡏⡐⠀⠀⠀⠀⠀⠀⢠⠂⠁⠀⠂⠀⢤⡤⠀⠀⣶⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠒⠀⠉⢘⡇⠈⠀⢦⢀⣀⠴⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠁⠁⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣈⠰⠆⠀⠠⢴⡛⠀⠀⠀⠙⠂⡄⠀⠀⠀⠐⠀⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠐⠃⠐⢁⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⡡⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⡦⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠶⠋






⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠲⠶⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⡿⠆
⣄⡀⠀⢀⣀⡀⢀⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣀⣀⡀⠀⠀⠀⠈⠙⠛⠉
⣿⡟⠀⢸⣷⣶⣾⣿⣿⣿⣥⡄⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⠗⣻⣿⣿⣷⠦
⣧⠀⠀⠈⠙⠿⠿⠟⠋⠈⢁⠤⠀⠀⢀⣀⣀⣀⣈⣉⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⣹⠃⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠷⢤⣀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠶⠋⠁⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠳⡄
⠀⠀⠀⠀⢰⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⣿⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠲⣄
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⡅⠠⣄⡀⠀⠀⢀⣴⠋⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢢⣄⠈⢳⡄⢀⣴⢿⠀⠀⠈⢟⢆⢠⢻⢃⢎⣏⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢸⡀⠛⢶⣤⡑⢯⣹⠑⡄⢻⣊⣃⣸⣀⣀⡀⠈⢪⠃⣎⠎⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⢸⡇⠲⢦⣝⢝⢺⣿⡷⠋⠉⠉⠉⢀⠌⠙⢿⡗⡞⢸⡏⢠⠏⣿⡿⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⢧⣀⡤⠽⠮⣧⣻⠁⠀⠀⠀⠀⠉⠀⠀⠀⢻⡆⢸⡇⣬⣼⣽⣧⣧⠤⣄⠀⠀⡇⠀⠀⠀⠀⢀⡤⠟
⠀⠀⠀⠀⠀⠀⢯⣀⣂⣀⡹⠻⢤⣀⣀⣀⣀⣤⣤⡤⠴⠿⢧⡼⢿⣅⠀⢀⣠⣇⣀⣼⣄⣠⣧⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣦⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡿⠾⣧⢾⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣷⢸⣇⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠆⣿⣨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢠⡶⢶⡄⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠆⣴⠆
⠀⠀⠀⠀⠀⠀⢸⣇⣠⡟⢾⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⢸⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⡴⠲⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⣠⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣄
⠀⠀⠀⠀⠀⠀⠸⣇⣘⡷⢰⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡴⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣄⡿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣧⠀⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⣤⠀⣤⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⡀⠀⣀
⠀⠀⠀⠀⠀⠰⣿⣿⢿⢰⡏⣻⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⠁⡏⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣸⠇⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣴⢶⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢶⡄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠚⠁⣿⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣽⠃⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢾⡁⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣭⣛⣧⢘⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⣸⠇⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢹⣶⠏⠸⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⢻⡿⠘⣶⢿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⣤⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠻⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣃⠀⣹⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢟⣉⣻⡿⠿⠿⢿⠿⠿⢿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣮⣈⣿⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠞⢁⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠊⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⡀⠀⠀⠀⠀⠀⡼⣿⢠⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡬⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠿⢃⠀⠀⠀⠀⡔⠁⢹⡿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠃⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢣⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠦⢄⣠⠄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⢀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⠀⠀⠂⣠⠊⠀⠀⡸⠁⠈
⠀⠀⠀⠀⠀⠀⢰⠇⠀⡀⠈⠆⠀⠈⠓⢄⡀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠐⣤⠃⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠦⠀⠈⠢⡀⠀⠀⠌⠣⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠈⢈⠆⠈⡇⢀⠞
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡀⠙⡆⠀⠀⠀⠀⢱⣄⠀⠀⣀⠀⠀⢀⣀⣀⣀⡀⢀⠄⠀⠀⠀⠌⠀⠀⢛⡡⢤⠌
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⠜⠚⠀⠀⠀⢠⠀⠀⠢⠍⠁⠀⠀⠀⠀⠀⠀⠀⡱⠋⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⢂⠀⣠⠅⠀⠀⠈⠢⠐⠀⠀⢀⡀⠀⠀⠂⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁⠀⡀⠀⢀⡀⠀⠀⠀⠀⡐⠁⠐⠀⠐⠒⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠇⠀⠀⡠⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⣉⢁⠀⠀⡀⡠⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠖⠉⠃⠄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠠⡠⠁⠀⢁⡤⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣀⠆⠀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠜⠁⠀⠴⠋⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⢢⣵⣐⡄⠈⢢⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⢀⡞⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡄⠉⡁⠀⠀⡟⠀⠀⡆⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠂⠀⠀⠂⠀⠀⠁⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠐⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⠃⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⡠⠆⠀⠀⢀⠇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⡀⠀⠈⢀⠀⠀⠡⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⡄⠀⠊⠉⠀⠒⠃⠀⠀⣀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠖⠈⠉⠁⠀⠳⡄⠀⢘
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠂⠈⠄⣀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠌⠀⠀⠀⠀⣠⠤⠦⠤⣤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠒⠊⠛⠁⠠⠤⠔⠊⠁

⠀⠀⠀⠀⠀⡌⠉⠁⠑⠀⠀⠀⠀⡀⠐⠓⠓⠂⠢⢀⠀⠀⠀⢠⠴⠒⠂⠐⠒⠠⠀⠀⠀⡞⠛⠁⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⢆⠀⠀⠀⡇⠀⠠⡀⠄⠀⠈⣇⠀⠀⠏⠀⠀⡤⠒⠒⠸⠀⠀⢀⡇⠀⢰⠛⠢⡄⠀⠹⡄
⠀⠀⠀⢀⠀⠀⠇⣠⠀⠈⡄⠀⠀⡄⠀⠀⠀⠀⠔⠺⣇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠀⠀⢹⠀⠀⡿
⠀⠀⠀⡌⠀⠀⣀⣠⡀⠀⠸⡀⠀⡇⠀⠐⣀⠱⠀⠀⢸⠀⠸⡄⠀⠈⠢⢄⣀⡠⡄⠀⣸⠁⠀⢧⣠⠴⠋⠀⢀⡇
⠀⠀⢠⣁⣀⡈⠀⠀⠰⣀⣀⡁⠀⠁⡀⣀⣀⣀⣠⠴⠃⠀⠀⠈⠦⣀⣀⣀⣀⢠⠁⠀⠸⣀⣀⣀⣀⣀⣠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣰⢳⠀⠀⠀⠀⢳⣵⡟⣷⣦⠀⠀⢀⣶⡿⠛⢻⡆⠀⠈⢻⣿⠟⠲⣦⡀⠀⠀⠛⣿⡟⠛⣷⠀⠀⠙⣿⡿⢛⣷
⠀⠀⢠⣿⣿⣧⠀⠀⠀⢸⣿⡷⢿⣏⠀⠀⣾⣿⠀⠀⠀⠁⠀⠀⢸⣿⠀⠀⣿⣷⠀⠀⠀⣿⡷⣿⠀⠀⠀⠀⣿⣿⣿⠁
⠀⣠⣽⡁⣀⣿⣆⡀⠀⣸⣿⣇⣼⣿⠇⠀⠘⢿⣦⣠⣼⠇⠀⢀⣼⣿⣤⣴⣿⠏⠀⠀⣠⣿⣇⣩⣾⡇⠀⣠⣿⣧⡈
⠀⠈⠀⠁⠈⠁⠉⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠈⠈⠀⠁⠉⠀⠀⠀⠁⠈
⠀⠀⠀⣠⣤⣤⣤⣤⠀⠀⠠⣤⣤⡤⢤⣤⣤⠄⠀⢤⣤⣤⡄⠀⠠⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⠀⠀⢤⣤⣤⡄
⠀⠀⢰⣿⠏⠀⠈⠿⠀⠀⠀⣨⣿⣀⣀⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⣼⣿⠀⠀⠀⣷⡿⠾⠋⠀⠀⠀⠀⣿⡏
⠀⠀⠸⣿⡄⠘⣿⣿⠆⠀⠀⣿⣿⠉⢉⣿⡇⠀⠀⠀⣿⣇⠀⠀⠀⣿⣿⠀⠀⠀⣽⣿⠻⣧⡀⠀⠀⠀⣿⡇⠀⣰⡆
⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠘⠛⠛⠓⠛⠛⠛⠂⠀⠙⠛⠛⠂⠰⣦⣿⡟⠀⠀⠘⠛⠚⠛⠛⠛⠃⠀⠙⠛⠛⠛⠛⠃
⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠈⣿⣿⡄⢀⣾⣿⠋⠀⠀⢹⣿⣦⠈⢻⡏⠀⠀⢠⢾⠟⠉⠹⣦⡀⠀⠈⢹⣿⠛⣻⣦⠀⠀⣴⡿⠋⠉⢷⣄
⠀⠀⠀⣽⢿⣿⣾⢿⣿⠀⠀⠀⢸⡇⠙⣷⣾⡇⠀⠀⢻⢿⠀⠀⢀⢿⡇⠀⠀⢸⣿⠾⠟⠃⠀⠈⣿⡇⠀⠀⣸⣿
⠀⠀⠠⣿⣦⠻⠿⣾⣿⣤⠀⠠⣼⣧⡄⠈⢻⠇⠀⠀⠈⠻⢦⣤⡾⠟⠁⠀⠠⣼⣿⣤⠀⠀⠀⠀⠙⠿⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠐⢶⣶⠶⣦⡀⠀⠀⠀⣴⠶⢶⡄⠀⠀⣶⡶⣶⣶⠶⣶⠀⠀⠶⣶⡶⠄⢶⣶⠆⠀⠰⢶⣶⠆⢲⣶⠆
⠀⠀⠀⠀⢸⣿⣴⣿⠇⠀⠀⠀⢨⣶⢌⡃⠀⠀⠉⠀⡿⣿⠀⠙⠀⠀⠀⣿⡇⠀⢨⣿⠀⠀⠀⠘⣿⣆⣼⠇
⠀⠀⠀⢀⣼⣿⡙⣿⣆⠀⠀⢰⣆⢈⢿⡇⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⣿⡇⣀⣰⡟⠀⠀⠀⠀⠸⣿⡏
⠀⠀⠀⠈⠉⠉⠉⠈⠙⠁⠀⠈⠉⠙⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣠⣀⣀⣤⣀⠀⠀⣀⣄⣀⣠⣀⣀⠀⠀⣀⣀⣀⣀⣄⣀⠀⠀⣠⣄⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠱⣿⡅⣸⣿⣇⢨⡿⠁⠀⠀⠈⠻⣧⣾⠏⠁⠀⠀⠈⠻⣿⣠⡿⠋⠀⠀⠹⠋⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠹⣾⣿⠁⠀⠀⠀⢀⣴⡿⣷⡄⠀⠀⠀⠀⠀⣹⣿⠁⠀⠀⠀⢀⣾⡿⠃⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠻⠃⠀⠀⠀⠐⠿⠿⠔⠾⠿⠶⠀⠀⠀⠐⠿⠿⠦⠀⠀⠀⠻⠿⠷⠾⠿⠇

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

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⣀⠀⠀⡄⠀⠀⠀⡆⠀⢰⠐⠂⢰⠀⠀⠐⡆⠀⠀⠀⡆⠀⠀⢤⠀⠀⡄⠀⠀⠄⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠈⠛⠀⠑⠀⠀⠀⠃⠀⠘⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠛⠀⠀⠘⠀⠀⠇⠂⠐⠇⠀⠀⠇⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠢⡀⠀⠇⠀⠇⠀⢸⡀⠘⠀⠀⠙⡄⠀⠀⠓⠄
⠀⠀⡀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⠤⣤⣤⣤⣄⣠
⠀⠀⣻⢿⣧⣿⣽⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣾⣷⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠋⢸⣛⣿⣟⣻⠈⠓⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢸⣭⣿⣯⣽⡇⠀⠀⠀⠈⠀⠁⠈⠀⠈⠈⠈⠈⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠸⣯⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡿⣿⣾⡇⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠒⠀⠐
⠀⠀⠀⠀⣿⣷⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⡄⠀⠄⠆⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣿⣿⣾⣠⣀⣠⡀⠀⠀⠀⠀⠚⠙⠋⠋⠀⠀⠀⠀⢀⣴⣦⣼⠻⣧⣹⣿⡇⠀⠀⠀⠁⢀⠀⠄⠀⡀⠆⢀
⠀⠀⠀⠰⣧⣭⣭⢼⡟⢿⡿⠆⠀⠀⠀⣀⣀⠀⢀⣤⣀⣀⣰⣞⣽⣟⣹⢦⣭⣭⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣿⣿⣿⣦⣭⣬⠿⢶⠯⣧⢹⡿⣿⣿⣿⢻⡏⣿⠿⠿⠿⢶⠆⢴⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⣩⣼⣿⣃⣨⠭⣭⠭⠭⠯⠼⢾⠿⠽⠿⡿⠧⠭⠭⠭⢭⠥⢤⣀⣉⣛⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⣿⣭⣭⣭⣿⣾⣟⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣹⣷⣶⣯⣭⢭⡍⡇⠀⠀⠐⠂⠀⠀⠄⠀⠄⠠⠀⠀⠀⠠
⠀⠀⠀⠀⣽⣿⠀⢿⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣯⣿⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⢻⣿⠀⢸⢸⠀⠀⠀⠀⠀⠀⢲⡶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢸⡇⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣾⡆⠀⠀⠀⠀⠀⢺⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⡇⡇⠀⠀⠈⠀⠀⠉⠀⠁
⠀⠀⠀⠀⢸⣛⣛⣛⣸⡇⠀⠀⠀⠀⠀⠘⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣇⠛⠚⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣴⣼⣥⣿⣯⣽⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣧⠀⠀⠠⠄⠄⠀⠆⠀⠀⠀⠄⠀⠠
⠀⠀⠀⢹⣼⣿⣻⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣿⠿⣿⡀⠀⠀⢀⡀⠀⡀⠀⡀⠀⠀⢀
⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠙⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⢀⡀⠀⡀

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠍⠛⠙⢣⣜⠋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠙⠳⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠈⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠀⡏⠀⠀⠀⠀⠀⠀⢀⠇⢻⣷⢲⡖⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡈⠛⣿⡦⠠⡅⠀⠀⠀⠀⠀⠠⠀⠀⠘⣿⡀⢣⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣼⡇⣼⣿⡇⣦⡀⠀⠀⠀⠀⠀⣏⣈⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣿⢉⣿⠇⣿⣝⢣⠀⠀⠀⠀⢰⣿⢏⠀⠀⢻⡇⠀⢀⡀⠀⢠⡜⢣⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣿⣾⣋⠀⠹⣿⡄⠀⠀⠀⠀⠚⣱⣿⠃⡀⣿⣷⣄⣾⡷⢦⠼⣿⣿⣿⣿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⡈⣿⡟⢁⠶⣀⣿⠁⠀⠀⠀⢦⣀⠻⣄⣼⡏⣿⡇⢹⡟⠀⠀⠀⠉⠀⠛⠯⣇⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡝⡿⣿⣴⣯⠾⡁⠘⠀⠈⢤⢧⡤⡽⠂⠌⠃⢠⣿⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣧⡤⣸⠄⠀⠀⢸⢷⡼⠃⠛⠀⠀⢀⣾⠏⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠓⠦⣤⣶⣿⣾⡃⠉⠀⣠⡔⣿⣟⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠿⣿⣿⣽⣏⣤⣶⠿⣿⢛⡯⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠛⣿⣿⡛⣫⡟⠛⣛⣛⣛⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣿⣾⣿⣿⣷⣿⣿⣿⠿⠛⢯⡁⠀⣚⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠉⠹⡏⡇⠉⠀⠀⠀⣀⣤⠗⠈⠁⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠚⠓⠳⠰⠐⠂⠀⠁⠀⢲⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠙⣶⠀⠀⠠⠀⠇⠀⠀⠀⠀⠸⠆⡀⠠⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢰⠀⠀⠀⠀⠠⢚⡡⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠧⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⠣⣄⡀⣴⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡠⠔⠋⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠋⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠴⢶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠠⠴⠂⠰⠞⠋⠉⢀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡿⢴⡇
⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠈⠠⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⡷⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡼⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⣧⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣞⣱⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⢤⣤⡤⠴⠒⠈⣨⠤⢆⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⡦⢰⣯⡤⠴⠒⠋⠁⠈⣉⣛⣳⡄⢦⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠛⠉⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠛⠶⠶⠦⡠⡖⠛⠉⣙⣉⣁⣹⡌⢣⣬⣉⣭⡙⣦
⠀⠀⠀⠀⠀⡠⡶⠛⠉⠁⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣍⣛⣛⣛⠛⠛⠛⠻⣿⣿⠯⠭⢶⠋
⠀⠀⠀⠀⠀⡄⠈⠓⠲⠶⠤⣴⣎⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠙⣇⠀⠀⠠⠤⠤⠤⠤⠤⠤⠔⠂⡾
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠶⠲⡒⠋⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣁⣀⣀⣀⣀⣠⠴⠚⠹⡇⠀⠀⠤⠤⠄⣤⠾⠛⠓⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢛⣳⡶⠛⠉⢁⢄⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⣟⠛⠶⠶⠦⢤⣼⣥⣄⣀⣀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠈⢦⠱⡄⠀⠀⠀⠀⠀⠀⢀⡴⢻⣀⣤⠶⠶⣾⠒⠒⠶⢬⡉⠉⠉⢓⠦
⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢳⡝⣆⠀⠀⣠⠴⢚⣩⣶⡟⠋⠀⠀⠁⠲⠚⠀⠀⠀⢹⣦⠴⠋⢸
⠀⠀⠀⠀⢠⡾⣏⣁⣹⣤⣈⣉⣙⡛⠛⠛⠲⠶⠶⠶⠶⣿⢌⡄⢪⡵⠚⣛⣿⡏⡰⠁⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠛⠛⠛⠛⠿⠿⠶⠶⣶⣶⣶⣿⣿⣟⣁⣼⣞⣣⡼⡇⠁⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⠉⣍⢳⡄⠀⠀⠀⠀⢀⣈⣉⣉⠉⠛⠛⠳⠷⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼
⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⢠⠚⠁⡼⠁⠈⠀⠀⠀⠀⠀⢀⡔⠐⣼⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠙⠶⠤⣤⣰⢡⠀⠘⢇⣀⣀⣀⣀⠀⢀⣠⡞⠁⣰⠃⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⣒⣒⣀⡀⠀⠀⠉⠉⢁⣠⡾⢃⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠛⠋⠁⠀⠀⠉⠉⠙⠓⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠷⠆⢀⣾⣿⡄⠀⣿⠛⢻⡆⣿⡇⠛⣿⡟⠃⢠⣿⣷⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣠⡀⣼⣧⣼⣷⠀⣿⠛⠛⠁⣿⡇⠀⣿⡇⢀⣿⣧⣿⣧⢸⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠈⠉⠀⠀⠉⠁⠉⠀⠀⠀⠉⠁⠀⠉⠁⠈⠉⠀⠈⠉⠈⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠿⠻⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣰⣆⣀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⡋⠉⠉⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠛⣷⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⣧⠀⠀⠛⢿⡟⠋⠀⠀⣰⡟⠀⠀⠀⠀⠚⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⡿⠛⠁⠀⠙⢷⣦⣄⣈⣁⣠⣴⡾⠋⠀⠀⢀⣀⣠⣾⠟⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣶⣤⣼⡿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣡⣄⠀⣀⣠⣿⣋⣿⡇⣀⣴⣆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡶⠿⠛⠛⠉⠉⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢀⣾⣏⣹⡟⠋⠉⠉⠛⠋⠀⠈⠉⠛⠛⠿⢷⣤⣤⡄
⠀⠀⠀⠀⠀⣸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⣿⣷⣤⣤⣶⣦⣶⠟⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣤
⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⠟⠉⣉⠁⠀⠈⢻⣧⣾⠇⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀
⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⡿⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢿⠀⠀⠀⠀⢿⠇⠀⠀⠀⢸⠇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⠟⠁
⣀⣀⣀⣀⣀⣉⣀⣀⠀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠛⢷⣄⠀⠀⢀⣼⠟⠻⠷⣶⣄
⣿⠉⠉⡉⢉⡉⣉⠉⡀⢉⣀⢈⣉⣉⣉⣉⡉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⣸⡏
⣿⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡇⠰⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⣤⠀⠴⣶⣦⣤⣀⠀⠘⠻⣦⡀⣀⣀⣄
⣿⠀⠸⡷⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶⣶⡿⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⢶⠟⠁⣠⣶⠟⢀⣀⠀⣀⡀⠀⣈⡙⠻⣦⡀⠈⠛⠛⠉⢹⣧
⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⡇⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣴⡟⠁⠀⢸⣿⠛⠋⠛⠛⣿⠃⠀⠈⢿⡆⠀⠀⠀⣠⣿
⣿⠀⣻⡇⠀⠀⠀⠀⠀⣿⡃⢠⣄⢀⣄⠀⣿⢀⣿⡷⠟⠛⠻⠷⣦⣀⠀⠀⠀⠀⠘⠷⣦⡄⠀⢰⡿⠀⠀⠀⣠⣿⠶⠶⠶⢾⣿⣀⠀⠀⠈⣿⡀⠀⣿⠋⠁
⣿⠀⣸⡇⠰⠶⠶⠷⠀⣿⡁⢈⣿⣿⣅⠀⣿⡿⠁⣠⡶⣶⡶⣦⡈⢻⣦⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣠⡾⠋⠀⢀⣴⣦⣄⠈⠻⣷⡀⠀⢹⡇⠀⣿
⣿⠀⣼⣇⣀⣀⣀⣀⣀⣿⣇⣈⣁⣈⣉⣀⣿⠁⣼⣯⣤⣿⠆⠘⣷⠀⣿⡆⠀⠀⠀⠀⣸⣷⠀⢸⣧⢠⣿⠁⠀⠀⣿⣍⣉⠁⠀⠀⠘⣿⠀⣿⠃⠀⠛⢷⣦
⣿⠀⢼⡟⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⣿⡄⠹⣯⡉⠉⢀⣰⡟⢀⣿⠃⠀⠀⢰⡿⠋⠁⠀⠀⢻⣾⣿⠀⠀⠀⣈⣉⣹⣷⠀⠀⠀⣿⣾⠏⠀⠀⠀⢠⣿
⣿⠀⢸⡇⠘⠻⠛⠟⠀⣿⡅⢠⣼⣧⣄⠀⣿⢿⣦⡈⠛⠻⠛⢋⣠⡾⠋⠀⠀⠀⠈⢿⣄⣀⣀⣄⠀⠙⢿⣦⡀⠀⠛⠻⠟⠁⠀⣀⣼⡿⠋⢀⣴⣶⣦⣾⠃
⣿⠀⣸⡇⠰⠾⠶⠷⠀⣿⡇⠈⠹⠏⠁⠀⣿⠀⣿⡟⠿⠷⠿⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠙⢷⣄⡀⠉⠛⠿⢶⣶⣶⠶⠿⠛⠁⠀⣴⡿⠋
⣿⠀⢹⣷⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⡿⠀⣿⡇⠀⠀⠈⣿⣶⣤⣀⣀⣀⣠⣤⣾⡟⠀⠀⠀⠀⣽⡇⠀⠀⠀⣀⣀⣀⣠⣄⠀⠀⠀⢻⡆
⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠈⠀⠉⠿⠉⠙⠟⠁⠈⠁⠀⠀⠀⠀⠿⢷⣤⣄⣼⡟⠉⠉⠉⠻⣧⣀⣤⡾⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣯⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠠⢄⡐⢤⡀
⠀⠀⠀⡇⠀⠀⢠⣾⠋⠉⠀⠀⠉⠹⠆⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢹⣆⢳
⠀⠀⠀⠁⠀⠀⢨⡇⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠉⠉⠢⠀⠀⠀⢀⡾⠚⠋⠉⠉⠛⢦⠀⠀⠀⣽⠈⠇
⠀⠀⠀⠀⣤⣤⣼⡇⠠⣀⣀⣀⠀⠽⠅⠀⠀⠀⢲⡀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢽⠀⢥
⠀⠀⠀⠀⣿⠉⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⡀⣐⠼⠁⠀⠀⢠⡼⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢘⡀⢰
⠀⠀⠀⡆⠉⠀⢸⡦⠀⠀⠀⠀⠀⠀⡢⠚⠉⠀⢤⡀⠀⠀⢸⡇⠀⠀⠀⢀⠴⣄⣺⠅⠀⠀⠀⢸⡇⢸
⠀⠀⠀⡇⠀⠀⠸⣿⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠘⣯⠀⠙⠀⠀⠀⠀⢨⡇⢸
⠀⠀⠀⠁⠀⠀⢈⣿⠀⠀⠀⠀⠐⣇⠀⠈⠢⢴⡾⠗⠀⠀⠈⣧⠀⠀⢢⣤⣘⡇⠀⠀⢦⡀⠀⢸⣟⢸⡄
⠀⠀⠀⡆⠀⠀⠀⠿⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠲⠤⠀⠁⠈⠢⣄⢀⢈⢉⡠⢄⠀⠈⢻⡷⢸⣿⢻⡇
⠀⠀⠀⢘⢦⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⣼⡿⣿⠇
⠀⠀⠀⠈⠦⣍⣙⠒⠒⠒⠒⠒⠒⠂⠂⠂⠤⠀⠒⠀⠂⠂⠈⠩⠤⠤⠤⠶⠴⣤⣠⣄⣀⣀⣨⡞⢠
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠊⠒⠛⠛⠛⠉⠚⠚⠓⠒⠒⠊⠚⠚⠐⠂⠒⠐⠒⠂⠴⠶⠄⠤⠠⠘

⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⡇⠸⡟⠩⢹⡉⠉⣹⠉⢙⡏⣝⠩⠽⢉⢹⡏⠙⡋⡉⣻⡇⠸⣟⠉⢹⡀⣥⢸⠋⡉⡏⣩⠉⢹⣿⡁⠶⡇⢸⢸⠩⠍⣿⡏⠀⢿⢩⡅⢼⣿
⣿⣿⣿⣶⣿⣶⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣾⣾⣷⣿⣿⣾⣿⣿⣶⣿⣷⣿⣷⣿⣾⣿⣾⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣴⣾⣿⣿⣿⣾⣾⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⠅⢿⡇⠈⠍⠏⢙⠫⡏⠹⣿⠃⠙⣿⡌⡈⣅⠉⡏⡅⡟⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⢀⡀
⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⢀⢸⠀⢄⡆⠀⠀⠀⠀⠀⠀⣀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⢀
⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇
⡇⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠘⠂⠀⠈⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⣷⡄⢠⣤⠠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄⣤⡄⢠⣤
⣯⡽⢯⣨⠿⣭⡇⠀⠀⠀⣿⠿⢲⡖⣶⣦⣶⣶⣶⣴⣲⢼⣗⡇⣶⣦⣶⡾⠀⣿⣯⣴⣰⢴⣖⣴⣖⣴⣶⣴⣶⣰⣶⣸⠃⠀⠀⠀⡿⣏⡽⢯⣨
⣿⣷⣾⣹⣶⣛⣧⣤⣤⣤⣬⣤⣬⣥⣬⣥⣬⣭⣬⣬⣭⣬⣭⣥⣥⣥⣿⣿⣤⣭⣥⣬⣭⣤⣭⣬⣭⣬⣭⣤⣭⣤⣭⣬⣤⣤⣤⣴⣷⣏⣳⣾⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡀⠀⠀⣿⠉⢻⠄⠀⢠⡟⠉⠙⠀⢠⡟⠉⠳⡄⠀⢰⡏⠉⠁⠀⢸⡟⠉⠀⠀⡶⠋⠉⠙
⠀⠀⠀⠀⠀⠀⠀⣼⠷⠾⣧⠀⠀⣿⠛⢻⡆⠀⢸⡄⠀⠀⠀⠀⡇⠀⢠⡯⠀⢸⡟⠋⠀⠀⢸⡗⠛⠀⠀⢿⠀⠙⢻
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠂⠀⠘⠒⠛⠁⠀⠀⠙⠓⠋⠀⠀⠛⠛⠋⠀⠀⠐⠛⠛⠂⠀⠈⠃⠀⠀⠀⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢰⡏⠀⠀⢾⠃⠀⢸⣆⡴⠃⠀⢸⡃⠀⠀⠀⣿⣆⠀⢀⣾⣟⠀⠀⡟⣧⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⣿⠀⠘⣇⠀⠀⢸⡄⠀⢸⡛⣆⠀⠀⢸⡇⠀⠀⠀⡇⠹⣄⡼⠁⣿⠀⠀⡇⠘⣆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠻⠀⠀⠏⠈⠷⠞⠁⠀⠘⠃⠘⠇⠀⠘⠟⠗⠀⠀⠃⠀⠹⠃⠀⠻⠀⠀⠷⠀⠘⠿

⠀⠀⠀⠀⠀⠀⢠⡞⠋⠻⣦⠀⠀⣿⠛⣦⠀⠀⣴⠛⠉⢷⡀⠀⢸⡋⠻⡆⠀⢰⡋⠙⠂⠀⠛⣻⠟⠃⠀⣾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⠴⠏⠀⠀⣷⠀⠀⢸⠇⠀⢸⠶⣾⠁⠀⠀⠙⢶⡀⠀⠀⢸⡆⠀⠀⢹⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠳⠶⠾⠃⠀⠀⠿⠀⠀⠀⠀⠉⠳⠖⠻⣄⠀⠸⠇⠈⠧⠀⠳⠶⠞⠁⠀⠀⠸⠇⠀⠀⠈⠳⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⢠⡆⠀⣶⠀⢰⣷⡀⢀⡆⠀⢰⡄⢀⡶⠀⠰⡆⠀⡴⠀⠰⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣼⠁⠀⢸⡄⡾⢸⡄⣸⠃⠀⠀⣹⣾⠀⠀⠀⠹⡾⠁⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠏⠀⠀⠀⣿⠇⠈⢷⡟⠀⠀⢰⠏⠘⢦⠀⠀⠀⡇⠀⠀⢰⣿⣤⣤

⠀⠀⠀⣠⣶⠀⠀⣠⡴⣦⡄⠀⡴⠶⣄⠀⠀⢀⣴⡄⠀⣶⠶⠦⠀⢀⣤⠶⡦⠀⢴⣶⣶⡆⢀⡴⠶⣤⠀⣠⠶⢦⡀⠀⡴⠶⣆
⠀⠀⠀⠁⣿⠀⠀⠀⠀⣼⠃⠀⢤⣴⣏⠀⢰⠏⢸⡇⠀⠻⠶⣤⠀⢸⣷⢶⣄⠀⠀⣰⠟⠁⢈⣷⠴⣏⠀⢻⣄⣼⡇⢸⡇⠀⣸
⠀⠀⠀⣠⣿⣄⠀⣠⣾⣡⡀⠀⣄⣠⡿⠂⠙⠛⣿⡟⠀⣄⣀⣿⠃⠘⣆⣠⡿⠀⢰⡏⠀⠀⠸⣧⣀⡿⠀⣤⣀⣼⠃⠘⣧⣠⡟
⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡀⢀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⣠⠀⠀⠀⠀⡄⠀⠀⠀⢠⠄⠀⠀⠀⢤⠀⣀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⠀⠈⢸⢃⣎⠀⣸⠁⠀⠐⠁⡾⠈⣦⠀⣯⡀⠀⠀⢀⡇⠀⠀⠀⣿⢀⡆⠀⠀⣼⣰⠇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡇⡀⢀⡾⠀⢸⠃⣿⠀⠀⠀⢰⠇⠀⡟⢸⠈⠁⠀⠀⢸⠗⠀⠀⠀⠈⢸⠀⠀⢠⠇⡏⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠂⠀⠈⠀⠀⠀⠉⠀⠈⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠡⠋⠀⠀⠈⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⡴⢂⠀⠀⠀⠀⢠⡆⠀⠀⠀⢠⡄⠀⡤⠀⠀⠀⠀⡀⠀⠀⠀⣠⠄⠀⠀⢰⡄⢠⡀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣧⡄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠠⢳⡠⡇⠀⠀⠀⠀⢳⡀⠀⢠⡏⠀⠀⠀⢸⡇⡼⠁⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠼⠁⢿⠀⠀⠀⡰⠏⠀⠠⣄⡀⠁⠾⠀⠷⠀⠈⠀⠀⢸⠇⠀⠘⡇⠀⠀⠀⡼⠀⠀⠀⠻⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⠀⠀⢰⡇⠀⠀⢸⠀⠂⠀⢸⠆⡴⠀⠀⣽⠀⠂⠔⠐⠙⡆⣶⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⡇⠀⠀⠈⡇⠀⠀⢸⠇⠀⠀⡿⢰⡇⠀⠀⢿⡀⠀⠀⠀⠀⣷⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠙⠂⠀⠘⠁⠀⠀⠞⠀⠀⠀⠃⠈⠓⠀⠀⠘⠁⠀⠀⠀⠀⠟⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡄⠀⠀⡄⠀⢀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇⠈⠁⠁⢸⠃⣧⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠘⠀⡟⠀⣠⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠞⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡟⠀⣀⠀⢀⣰⠇⠀⢀⡀⠀⣿⠀⠀⡀⠀⠀⡟⠀⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⡿⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⢸⡃⢸⡇⠀⣟⢼⠀⠀⡿⠀⢠⡇⠀⢸⢷⡀⢸⣇⡇⠀⡟⠀⠀⡇⠀⣷⡔⠁⠰⡇⠀⠀⡿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠆⠀⠀⠁⠀⠀⠀⢰⠇⠀⠁⠧⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⢠⡀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⡀⠀⢀⠀⠀⠀⠀⣀⡀⠀⢠⡀⠀⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⢿⡇⠀⢾⠹⠀⣸⢧⡿⠀⢼⣽⠇⠀⢰⡋⠀⢨⡇⠸⡇⠀⢸⣣⡗⠀⣾⠀⠀⣿⣶⠀⢀⣸⡏⠀⢸⡷⡆⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠁

⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⢿⣀⡀⢻⣧⠀⠀⠀⠀⠀⢸⡟⡷⡋⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢹⡆⠀⠐⣧⠤⢀⡆⠀⠀⠀⣿
⠀⠀⠘⡽⠁⣸⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠓
⠀⠀⠀⠀⢀⡟⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⣿⠀⠀⢀⠀⠀⢸⡇⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⢀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠻⢄⡀⢸⠇⠀⢸⡏⠘⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡸⠁⠀⢰⡇⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠽⢦⡀⠀⠚⠁⠈⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠀⠀⠀⠀⠘⠛⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠰⠏⣵⡄⠀⠀⠀⠀⠈⣿⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢷⡇⢀⠈⡷⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⣿⢷⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢨⡿⠓⠚⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣿⡇⠀⢰⡆⠀⠀⠛
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢰⣲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⡤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢰⠂
⠀⠀⠸⣿⠀⠀⢸⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣷⠀⠀⢀⠇
⠀⠀⠀⣿⠒⢶⣋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢼⣢⠀⠀⠀⢰⣿⠀⠀⡽⠓⠢⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣇⢀⠎
⠀⠀⠸⠿⠀⠀⠙⢵⣄⠀⠆⠀⠀⢠⡀⠀⢀⡿⠀⠀⠀⠀⠻⣆⡀⠈⠀⣠⠁⠀⠀⢻⣷⠀⠀⣀⠄⣿⠂⠀⠀⠀⠀⢿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢠⡤⠀⠀⢶⡆⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⢦⠀⠀⠀⢤⠄⠲⠤⠠⠤⠄⠰⠂
⠀⠀⠀⠀⠠⠎⠀⠁⢀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠙⢀⣄⠀⠠⠂⠀⠀⠀⠀⠐⠀⢿⣧⠀⠀⠀⢸⡇⠀⠀⠀⠈⠂⠀⠀⣰⠇
⠀⠀⠀⢠⣤⠀⠀⠀⣾⠃⠀⠀⠀⢼⡇⠀⠀⠀⠀⠘⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⡰⡽⠃
⠀⠀⠀⢸⣿⠀⠀⠘⣿⡄⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⡼⠣⣷⣄⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⡠⢿⡇⠀⠀⠀⠀⠀⣰⡎⠁
⠀⠀⠀⠀⠛⠓⠀⡀⠙⠓⠀⠀⠀⠟⠓⠀⠀⠐⠂⠘⠁⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠓⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠝⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡀⠄⠀⠠⢀⡄⠀⢀⣀⢠⡀⠈⢰⠀⠀⠀⢸⡧⠄⠀⠠⢀⠀⠀⠀⠀⠀⣀⢄⡒⠤⠤⠔⡠
⠀⠀⢔⠕⠈⠀⠀⠀⠁⠢⠁⠀⠀⢵⡇⠀⢀⠀⠀⠀⠥⠊⠀⠀⠀⠑⠨⢢⠀⠀⣜⠕⠁⠀⠀⠀⠀⠈⠢⡣⡀
⠀⠘⠌⠀⠀⠀⡠⣀⠄⠀⠀⠀⠀⢸⠁⠀⠃⠀⠀⠀⠀⡠⣀⡠⡀⠀⠀⢡⢷⠘⠌⠀⠀⠀⡠⣒⣒⣀⣪⡶⠇
⠀⡇⠀⠀⠀⡌⡿⠋⠑⢡⠀⠀⢰⢸⠀⠀⠀⡇⠀⠀⠈⢼⠋⠉⠚⠄⠀⠀⣼⣇⠀⠀⠀⢸⢸⠋⠀⠉⠈
⠀⢠⠂⠀⠀⠡⠣⣀⠰⡌⠀⠀⠈⢸⠀⠀⠀⠁⠀⠀⠀⡹⢄⠠⡪⠀⠀⢠⢹⠻⣡⠀⠀⠈⢜⠆⡀⢔⣂⡤⣀
⠀⠀⠪⡢⡀⠀⠈⠀⢁⠤⠀⠀⠀⡘⡆⠀⠰⠀⠀⠀⢄⠈⠉⠉⠀⠀⡠⣢⡟⠀⠱⡣⣀⠀⠀⠉⠉⢁⡰⣱⡏
⠀⠀⠀⠈⠺⢥⣤⣤⠵⢮⣶⣶⣖⣃⣷⠀⢦⣶⣶⣾⣴⠥⣴⣶⣤⡬⠺⠋⠀⠀⠀⠈⠒⠥⣤⣲⣄⣵⠾⠋

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢄⠀⠀⢀⡀⠠⠄⣀⣒⣒⣂⡠⠄⡀⠀⠀⠀⠀⡠⠤⠤⢄⣀⡠⠄⢀⡀
⠀⠀⠀⢀⠤⡪⠂⠁⠉⢹⢸⡇⠀⠃⡆⠈⠁⠀⠀⠀⠀⠀⠁⠺⡕⣄⠀⠀⡜⡉⠀⠀⠀⠀⠉⠁⠪⡰⣄
⠀⠀⠀⠸⢈⠀⠀⠀⠀⢸⢸⡇⠀⢸⠠⢠⣐⣔⣤⣔⢄⠀⠀⠀⠘⢸⡄⠀⠡⣓⣢⣄⣔⢄⠀⠀⠀⠘⢸⡄
⠀⠀⠀⠀⢜⡀⠄⠀⠀⢘⢸⡇⠀⠀⠙⠋⠉⠀⠀⢈⢸⠀⠀⠀⡘⣾⠃⠀⠀⡨⠥⣀⢐⠝⠀⠀⢀⢜⡼⠇
⠀⠀⠀⠀⠀⢩⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⠀⠀⢀⢎⠂⠀⢀⢜⣼⠏⠀⠀⠀⡇⠅⠀⢀⡀⠀⠀⠣⡚⢎
⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⢀⢔⡁⠁⢀⠔⣡⣫⠊⠤⡀⠀⠀⠈⠛⠛⠓⢲⢡⠀⠀⠈⠎⣇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⢸⡇⠀⠠⢒⠭⠒⠁⠀⠀⠘⠒⠂⠈⠉⠁⣿⠀⠀⡌⠆⠩⠭⠑⠂⠀⠀⢀⢆⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⢸⡇⠀⠈⡰⣀⣀⣀⣀⣀⠀⠀⠀⠀⡀⡀⣿⠀⢠⢸⡀⠀⠀⠀⠀⡀⢄⣪⡾⠃
⠀⠀⠀⠀⠀⠑⠶⠶⠶⠶⠾⠃⠀⠀⠙⠒⠒⠒⠒⠒⠒⠖⠶⠶⠶⠶⠿⠀⠈⠒⠲⠶⠭⠵⠶⠾⠛⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣦⣤⣤⣶⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⢟⡋⣉⡙⠛⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠛⠛⠿⠿⢿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣁⠀⠤⠾⣿⡭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⣴⣿⣯⣿⣻⣿⠛⢃⣀⣀⣠⣤⣤⣤⣤⣴⣶⠶⠶⠶⠶⠦⢤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠿⣶⣀
⠀⠀⠀⠀⠀⠀⣠⢊⡱⢎⣉⣿⣿⣿⣿⣿⡟⠛⠉⠉⢉⣁⣀⣠⣀⣀⣀⣀⣠⣤⣤⡤⣤⣄⣀⣀⣀⣀⣉⣉⠉⠛⠛⠳⠶⣦⣄⣀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⣼⠃⠶⢾⣿⣿⣭⣿⣷⣾⣧⠥⢤⣗⣒⡲⡿⠩⠭⠁⠤⠴⠶⠶⠆⠸⠥⠿⠿⠿⣿⣿⣿⣿⡟⠳⢶⣧⣤⣆⣀⣈⠉⠛⠷⣦⣄⢻⣄
⠀⠀⠀⠀⡼⠁⢀⣼⣿⠿⣟⣛⣻⣿⡿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣿⣷⡶⠤⡉⠉⠻⡆
⠀⠀⠀⣸⠁⢀⣿⡿⠿⢛⣋⣭⡥⠶⠒⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⣷⣮⣧⡀⢻⡄
⠀⠀⢰⡇⠀⠨⠛⣚⣉⠭⠔⠒⢂⣉⣀⣤⣴⣶⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⠙⠯⠸⣇
⠀⠀⣼⠀⠀⠚⢋⣀⣤⣴⣶⠿⠿⠛⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣦⣤⣄⠀⠀⠀⣿
⠀⠀⣿⠀⣴⣶⣿⣿⣯⠭⣖⣒⠿⠭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣶⡄⣿
⠀⢸⡟⠀⠋⠉⣿⣱⢾⣿⠤⠘⠛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿
⠀⠐⣷⠀⠀⠙⠒⣉⡥⠤⠒⣊⡩⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⣧⠀⠀⠀⠋⣡⠴⠚⠉⣁⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠸⣇⠀⠀⠁⠀⠄⠚⢉⣠⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢸⡄⣤⣬⠀⠀⠞⠃⠀⣠⣤⣤⣤⡤⠶⠶⠒⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠻⣟⠿⢿⠄⣠⣴⣾⣿⡿⠁⣒⠂⢀⣀⣀⡠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⣤⣀⣀⡀⠀⠈⠉⠙⠛⠿⣿⣷⣦⣄⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠹⣆⠀⠘⠙⠟⣉⣻⣷⡿⣿⣿⣏⠉⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠋⠻⠙⢻⣶⣶⣤⣄⡀⠀⠉⠛⠻⢿⣶⠾⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣄⠐⠋⠉⣻⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣩⣖⣶⣦⣤⣄⣈⡉⠛⠻⢿⣶⣦⣄⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣀⡛⠿⣿⣻⣭⣭⣵⡿⠶⠖⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠉⠉⠛⠛⠿⢷⣦⣤⡈⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡴⠾⢿⣭⣤⣶⣶⣾⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠒⠒⠊⠩⢭⡿⢶⣶⣤⣄⣀⠀⠉⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⣹⣿⣿⣿⡿⠟⠛⠛⢉⡁⠀⠀⠀⠀⠀⠀⠀⠬⠉⢉⣙⣛⣶⣶⣤⣄⣈⡉⠙⠛⠿⣿⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣥⡔⠒⢈⣈⣉⣤⣤⠤⠤⠄⠀⠀⠒⠶⣆⡀⢤⣤⣤⣤⣄⣉⣉⠙⠛⠛⠿⣶⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠞⢻⠿⠟⠛⠛⢂⣀⣀⣀⣀⣀⠀⢀⣀⠀⠐⠚⠛⠛⠩⠿⠿⣷⣦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡶⠶⢛⡛⠉⡭⠄⠀⠀⠀⠈⠛⠛⠛⠛⠛⠿⠻⢷⣶⣦⣄⡰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣦⣈⠤⠶⢒⣛⡚⠛⠒⣒⣒⣒⣲⣶⡶⠶⢤⣄⡉⠹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠞⠛⠛⣷⣶⣶⣶⣤⣤⣤⣤⣄⣈⠉⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡖⠋⣉⣉⣀⣀⣈⣉⣉⣉⣉⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣏⣉⣉⣩⣍⣉⣙⣛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠃⣀⣀⣈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣹⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠛⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣠⠇⠀⣷⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣤⡄⠹⣆⠀⠀⡇⠀⠉⠒⣄⠀⠀⢠⠋⢠⣤⣽⡆⠀⢠⠋⢰⣦⠀⣿⠀⠀⢰⠋⣤⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢴⡦⠀⣿⠀⠀⢂⠀⠿⠃⣸⡇⠀⠸⡀⠸⡧⢄⡀⠀⠈⢆⠘⠏⠀⣿⠀⠀⢡⠀⣤⠴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠿⠀⠀⠙⠶⠶⠾⠟⠀⠀⠀⠘⠲⠶⠾⠃⠀⠀⠈⠛⠲⠾⠟⠀⠀⠀⠓⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⡄⠀⠀⠀⠀⣰⠒⣄⠀⠀⠀⢀⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡾⠇⠀⢀⠔⠒⠢⡀⠀⠀⢀⠀⢸⣇⣀⠀⠀⠀⣸⠒⣿⠀⠀⠀⢈⠖⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣼⠆⠀⡏⠀⣿⡆⢸⡆⠀⠀⠀⢀⡀⠈⣧⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⠀⠀⠱⣄⣛⠁⢸⡇⠀⠀⡆⢸⡇⢀⡟⠀⠀⢿⠀⣿⠀⠀⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⢯⣉⣀⣾⠇⠀⠀⠈⠛⠉⠛⠁⠀⠀⠈⠙⠋⠀⠀⢯⣉⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣦⠀⠀⠀⠀⡖⠒⣦⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠟⣩⣦⠀⠀⡇⠀⣿⠀⠀⢸⠉⠙⠓⠂⠒⢢⡀⠀⢸⠉⠙⠒⢢⡀⠀⢀⠖⢉⡙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⡁⠀⠀⡇⠀⣿⠀⠀⢼⠀⣶⠀⢰⠀⢈⡇⠀⢸⠀⢰⡆⢸⡇⠀⢸⠀⣿⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣦⣤⣷⠀⠀⢇⣀⣹⡄⠀⠸⣀⣿⣀⣼⣀⣸⡇⠀⠸⣀⣸⣅⣸⡇⠀⠈⠢⣬⣡⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠈⠉⠈⠉⠀⠀⠀⠈⠉⠉⠉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣰⠁⢸⣆⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣈⠉⢦⠀⢀⠞⢁⣀⠀⣷⠀⠀⡇⠘⠋⣱⡄⠀⡜⠁⣤⣩⣦⠀⠘⢤⠀⢠⣼⠇⠀⡇⢸⣿⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⢀⣾⠃⠘⣄⠘⠛⠀⣿⠀⠀⡇⠀⣾⠟⠁⠀⣈⢶⡄⠙⣆⠀⠀⢀⠀⢸⡇⠀⠀⣇⠸⡿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠛⠁⠀⠀⠈⠛⠆⠀⣿⠀⠀⠣⣴⠿⠀⠀⠀⠘⠲⢤⡾⠟⠀⠀⠈⠦⣼⠇⠀⠀⠈⠢⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠟⠀⠀⠀⠀⠀⠀⠙⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣀⠤⢤⠀⢀⡤⢤⡤⣤⠤⣄⠀⠀⡤⢤⡤⢤⡀⠀⡤⢤⡠⠤⣄⠀⢠⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⡟⠀⣿⠁⠈⡀⠸⠀⠹⠀⣿⠁⠀⢣⠀⢀⣾⠃⠀⢱⠈⠃⢰⡟⠀⠈⢲⠂⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣸⡏⠀⠀⠇⠀⣠⡀⢀⣿⠀⠀⡜⢀⠀⢻⡀⠀⠈⡇⠀⣼⠇⠀⢠⠃⠀⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠈⠛⠛⠙⠛⠋⠀⠀⠙⠛⠛⠛⠃⠀⢠⠁⣰⡟⠀⠀⠈⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠆⣀⠀⡆⢲⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⣷⡇⣼⣿⢸⢸⠁⡇
⠀⠀⠀⠀⠀⠀⠰⣄⠄⣄⢀⢀⢁⠀⡰⡙⣘⢂⢀⣣⡀⡀⡄
⠀⠀⠀⠀⠀⠀⠰⠊⠳⡇⢧⢸⢿⠀⡇⡇⣿⢸⢸⠀⡇⣇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠉⠘⠀⠀⠐⠋⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠠⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡀⠀⠂⠀⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡡⠁⢀⡀⠶⠀⠁⠐⣄⡀⠝⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⠘⠁⢠⠁⢀⣿⠵⠤⣀⣈⡻⡐⢏⣀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠁⣧⡀⠀⢀⡤⠒⠀⠉⠻⢷⡄⠐⡄⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠒⢹⠀⠀⠈⠀⠀⠀⠂⢉⡈⠙⣶⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠌⠀⠂⠱⣤⠄⢀⡀⠀⡜⢩⠀⣠⠃⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⠄⠁⢀⡠⠀⠀⠇⠀⠠⠘⢦⠀⠀⠀⡍⠀⠀⠀⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠃⢀⠀⢸⠀⠀⠀⠀⢀⠀⡀⠈⠣⣄⡜⠀⠀⠀⠀⡂⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢻⠁⠀⡀⠀⠀⠂⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠀⡠⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⢀⠁⠂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠆⠂⢀⠏⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⡔⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠃⠀⠘⠁⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⡇⠀⠃⠀⠀⡴⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢢⡐⠀⠘⠀⡇⠀⢠⢃⠔⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠻⣰⠇⠀⠀⠀⠀⡄⠀⠀⠀⠬⠦⢙⣌⡢⡡⡁⠀⣸⡎⠀⠀⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢜⠂⣁⠃⠀⠀⠀⢀⠀⠀⠀⢀⡰⠖⠂⠀⣀⠁⠙⢿⣄⠋⡅⡜⢁⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⠈⠉⠉⠀⠀⠀⡠⠀⠀⠀⢀⡤⠖⠚⠉⠉⣑⣻⠿⣧⡰⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠴⠤⠀⠀⠠⠤⠀⠀⠤⠴⢆⡈⣁⠀⠠⠐⠊⠀⡠⢀⠴⣍⣿⣦⡀⠈⠁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⡀⠃⠀⢸⠊⠀⢙⡒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠈⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⠁⡌⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢳⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⢀⠠⡀⡁⠀⠀⠘⠒⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠊⠀⠀⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠜⡆⠀⠀⠀⠀⠀⠀⠀⢶⣚⣉⡉⠉⠉⠉⡁⢀⣈⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠉⠉⠉⠉⡍⠈⢩⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠖⠀⢚⣤⠼⣷⠀⠀⠀⠀⠀⠀⡜⠀⠀⡄⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡⠀⠀⠀⣀⠀⠀⠀⡰⢀
⠀⠀⠀⠀⠀⠀⠘⢀⡀⠞⠿⣤⢦⣼⠄⠀⠀⢀⡜⠀⠀⡰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⣄⣥⢐⣤⡜
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⡍⣦⠀⢀⠎⠀⠀⡰⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡍⡻⠛⣿⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠚⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡄⠀⠴⠠⡿⠂⠁⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡞⠀⠀⣠⠞⠀⠀⠀⠀⡀⠀⠀⠈⢻⡟⢀⠀⣀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠁⠀⡀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠇⠀⠀⠀⡞⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠸⡁⠀⠠⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⡀⠁⠀⡰⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠧⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠔⠪⠂⠀⠢⢿⠀⠠⠃⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡰⠀⡇⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢉⠓⠀⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠇⠀⠀⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡞⠀⠀⠞⠀⠀⡠⠒⢤⣀⣀⠀⡀⠀⠀⢠⠜⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠞⡅⠀⠀⠐⠰⠚⠁⠠⠆⠸⠁⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠠⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠐⠀⠔⠀⠀⠀⠀⠀⢰⡟⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠑⠢⠤⠀⠠⠀⠀⣠⠇⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠰⠂⠀⡀⠉⠁⠈⠑⠒⠒⠦⠤⢤⣄⣤⠟⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠂⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋⠉⢻⣿⣷⣴⣾⣿⣿⠉⠉⣿⣿⠉⠉⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⡿⠛⢹⣿⣿⠀⠀⣿⣿⠀⠀⢻⣿⡏⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⣏⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⡟⠀⢸⣿⣿⠀⠀⣿⣿⡆⠀⢸⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣇⢠⣼⡿⠿⠿⠿⣿⣿⡃⠀⢸⣿⣿⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⢻⣷⠀⢸⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⡄⢸⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⣿⣿⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠁⠀⢂⠆⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⢰⠀⠱⢄⠀⠀⡀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠁⠀⠀⠀⠀⠇⠌
⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⢠⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢂⠀⠄⢠⢸
⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠑⠀⠣⡼
⠀⠀⠀⠀⠀⠀⢀⡄⢠⢠⠆⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠠⠂⠀⠀⠀⠦⠃⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡄⢠⠊⠀⠤⠀⠀⠀⠁⠀⠒⠒⠊⠏⠀⠀⠀⠀⠀⠤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠠⣤⠀⠀⠀⠀⢥⠀⠈⡇⠀⢀⠀⠁⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⠀⠀⢠⠆⠀⠁⠀⠀⠀⠀⠀⠈⠓⠰⡀⠄⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠑⠂⠄⠀⠋
⠀⠀⠀⠀⠀⠀⡀⠀⢠⠖⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠔⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠂⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠤⠂⠈⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⡆⠈⠴⣠⡀⡀⠀⠀⣀⣀⣈⡁⠤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⣶⣶⣿⣦⠀⠀⢀⣶⡿⠆⠀⢰⣶⣾⣶⡄⠀⢰⣶⣾⣷⠀⠀⠀⣶⣿⣿⡇⠀⢠⣾⣿⠖
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⣿⣿⢿⣟⠀⠀⣼⣿⠁⠀⠀⢸⣿⣿⣿⡇⠀⠘⣿⣷⣶⠄⠀⠀⣿⣇⣀⠀⠀⣿⣿⢁⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⢹⣿⣿⣿⡇⠀⢻⣿⡀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣤⡄⠀⠀⣿⡟⠉⠀⠀⢿⣿⡘⢻⡇
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠃⠀⠸⠿⠛⠛⠁⠀⠈⠻⠿⠂⠀⠘⠟⠛⠋⠀⠀⠀⠻⠟⠛⠃⠀⠀⠿⠇⠀⠀⠀⠈⠻⠿⠾⠃

⠀⠀⠀⠀⠀⣶⣶⠀⣶⣶⠀⠀⣶⣶⠂⠀⠀⢲⣿⠃⠀⢰⣿⡇⣠⠞⠀⠀⣾⡆⠀⠀⢰⣶⣶⣶⣶⣶⡆⠀⠀⣶⣦⠀⢰⣶⣶
⠀⠀⠀⠀⠀⣽⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⡏⠀⠀⠀⣿⡇⠀⠀⢸⣿⢿⣿⡟⢹⡇⠀⢸⣿⡿⣧⣸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠛⣿⣿⠀⠀⢻⣿⠀⠀⣀⢸⣿⠀⠀⢸⣿⡟⢿⣦⡀⠀⣿⣇⣀⡀⢸⣿⠈⠛⠀⣿⡇⠀⢸⣿⡇⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠻⠟⠀⠿⠟⠀⠐⠿⠿⠗⠀⠙⠿⠟⠀⠀⠸⠿⠇⠀⠙⠛⠂⠻⠿⠿⠃⠸⠟⠀⠀⠀⠿⠇⠀⠘⠿⠇⠀⠘⠿⠟

⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡄⠀⢸⣿⣶⣆⠀⣰⣾⣿⣷⣄⠀⠀⣾⣿⣷⡆⠀⠀⣶⣿⡿⠆⠀⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⠇⠀⠀⢿⣿⣶⡄⠀⠉⢿⣿⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⢸⣿⣿⠟⠀⢹⣿⣿⣿⣿⣄⠀⢻⣿⠿⣆⠀⠀⣀⣸⣿⠇⠀⠀⢸⣿⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠘⠛⠂⠀⠀⠀⠙⠛⠛⠉⠋⠀⠘⠛⠃⠙⠃⠀⠛⠛⠋⠀⠀⠀⠘⠟⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⣿⣿⠀⢸⣷⠀⢠⡄⠀⣾⣿⠃⠐⣶⣶⣦⣶⣶⠆⠀⣶⣶⣶⣶⣶⠆⠀⠒⢚⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⡇⠀⠈⣿⡇⣼⣿⢰⣿⡟⠀⠀⠘⣿⣿⣿⠏⠀⠀⠈⢿⣿⣿⠋⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣆⠀⠀⠀⠀⣿⡏⠀⠀⠀⢠⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠈⠿⠿⠿⠿⠿⠀⠀⠸⠿⠿⠉⠻⠿⠇⠀⠀⠀⠿⠗⠀⠀⠀⠘⠿⠿⠿⠗

⠀⠀⠀⠀⣤⠀⠀⡄⢠⠀⣠⠀⠠⠀⡄⢠⡀⢠⠀⠤⠀⡴⢠⠀⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠
⠀⠀⠀⡐⠘⣆⠀⣇⣹⠄⢣⡀⡀⢸⣇⢰⠇⢸⠛⣠⠀⡟⠃⠘⠆⢀⡔⠀⠀⣇⡄⢸⠀⠆⢠⣈⠰⠀⡇⠰⣘⠀⡇⢘⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁
⠀⠀⠀⢰⡂⢰⠀⢰⠂⠀⡔⠀⣄⡠⠂⠀⡄⠀⠀⠴⡄⠰⡖⠀⠦⡀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⢀⣀⢀⠀⠀⢀
⠀⠀⠀⠸⡁⢸⡀⢸⡀⠄⡇⠀⣏⠑⣄⠀⠅⢠⠀⡄⠙⠀⣇⠀⠀⠹⡇⠀⠀⠀⠁⠀⠀⣳⠈⡛⣄⠨⠄⢈⠸⡀⡇⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⡔⠀⢢⡀⠰⢀⠀⡀⠀⢠⠀⢰⢀⡆⠠⣀⠆⠀⢰⠐⠀⡆⠀⠆⠀⠀⠀⡀⢀⣀⡀⢀⢀⠀⢀⣀⠀⡀⠠⡀
⠀⠀⠀⠱⠀⠘⠁⠸⠀⠀⠡⢀⠸⠀⠠⠈⠄⠠⡀⠇⠀⠸⠀⠀⠣⠠⠀⠀⠀⠀⠆⢸⠠⠇⠠⠰⠀⠨⠀⢌⠆⠸⠄⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⡀⠐⠀⠰⡀⣾⣀⠃⠀⢦⠀⠀⠲⣀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⣠⠀⢀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠏⠀⠤⠀⠧⠄⠀⠧⠀⠠⠥⠤⠀⠀⠀⠀⠀⠀⠀⠟⠀⠘⠁⠏⠀⠌⠄⠈⡇⠀⠮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⢰⠀⠀⠀⡄⠀⠀⢀⠀⠀⢀⠰⠀⠀⡀⠀⠀⠀⢠⠀⠀⠄⡀⠀⢀⠠⡀⠀⠀⠄
⠀⠀⠀⠀⠀⢸⠸⠀⠀⢨⡀⠀⢠⣎⡀⠀⡀⠓⠀⠀⢼⠆⠀⡀⠹⠀⠘⣅⡇⠀⠀⡆⠀⠀⡈⡳⠀⢈⡴⠃⠀⠇⠸

⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠝⠀⠸⠀⠀⣦⣀⠀⠀⠀⠀⢶⢃⠄⢀⠊⡠⡄⢂⠀⠻⣝⠀⠰⠇⡐⢁⠀⠀⠾⠂⠈⡆
⠀⠀⠀⠀⢹⡀⠰⠀⢰⠀⠐⠂⠀⠐⠀⠀⠃⠀⠈⠉⠀⠳⠞⠿⠂⠘⢌⠓⠗⡢⠀⠶⠟⠀⠀⠎⠀⠳⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣧⠀⠀⠀⢠⠇⠹⡀⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢿⣿⣿⡆⠀⠀⡈⠡⠄⣇⠞⣁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠘⣿⣿⣿⡄⠀⠀⢠⡞⢃⠜⢉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢹⣿⣛⣓⠎⣔⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢸⣿⣿⣟⣆⠈⡅⠶⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠂⢄⣉⣁⡿⠿⠷⢨⠭⣍⠲⣍⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⣿⡇⠀⣈⡁⣤⠘⡠⠃⡸⢇⡤⠺⡁⠀⠈⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⢹⣿⣥⣠⣝⣀⣉⡹⠉⠙⣀⣨⣿⣀⡖⢁⣁⡹⢻⣶⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡲⠀⠈⣺⣿⣟⣿⢻⡛⠻⠛⠷⣏⣙⠩⣟⣿⣿⣿⣿⠿⠛⣺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠞⠋⠈⣿⡏⢱⠘⠁⠉⠀⠀⠀⠀⠐⠛⠧⣽⣿⣿⣿⡄⠉⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢠⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⣔⠆⠏⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠸⠛⢄⠌⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠽⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⠀⠑⠂⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠿⠿⠷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠴⠿⠿⠿⠿⠿⠦⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣠⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐
⣿⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⡃⠀⢸⣇⣤⣄⠀⠀⢸⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢀⣠⣄⣿⠁⠀⠀⠀⠀⢀⣀⣀
⣿⠀⠀⠀⠀⣾⠏⢹⣿⠀⠀⡇⠀⢸⡏⠉⢹⣧⠀⢸⠀⠀⣾⠋⠉⠉⠀⠀⠀⠀⣿⠋⠉⣿⠀⠀⠀⠀⢰⣿⣭⡿⠃
⣿⠀⠀⠀⠀⠻⣦⣴⣿⡄⠀⡃⠀⢸⣷⣶⡾⠃⠀⢸⠀⠀⠿⣦⣴⠶⠀⠀⠀⠀⠻⢶⡶⠿⠀⠀⠀⠀⠘⠿⣶⡶⠆⠀⠨
⣿⠀⠐⠒⠒⠒⠒⣒⣒⠐⠐⠖⠒⠒⠒⠒⠒⠒⠂⢺⠒⠒⣒⠂⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠂⠖⠐⠒⠒⠒⠂⠒⠒⠺
⣿⠀⠀⠀⠀⠀⣸⣟⡉⠀⠀⡇⠀⢀⣴⠶⢶⡄⠀⢸⠀⠀⣿⢀⣀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⢈⣇
⣿⠀⠀⠀⠀⠛⣿⡟⠋⠀⠀⡀⠀⢸⣿⢀⣼⡇⠀⢸⠀⠀⣿⠟⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡀⠀⠀⡙⢛⣿⠇⠀⢸⠀⠠⣿⠀⢸⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣀⣿⠀⠀⠐
⣿⠀⠀⠤⠤⠤⠭⠥⠤⠤⠤⡦⠤⠬⠿⠿⠭⠤⠤⢼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠿⠯⠤⠤⢬
⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠂⠀⠀⠀⣿⠀⠀⠀⢸⠀⣀⢀⣀⣀⣀
⣿⠀⠀⠀⠀⣿⣧⣾⠟⠀⠀⡃⠀⠀⠀⣿⠀⠀⠀⢸⠀⣿⡟⣿⡟⢻⡇⠀⠀⠀⣺⣷⠿⣷⠀⠀⠀⠀⢀⣶⠿⣷⡄
⣿⠀⠀⠀⠀⣿⡏⢿⣦⠀⠀⠂⠀⠀⠀⣿⠀⠀⠀⢸⠀⣿⠀⢸⡇⠸⣿⠀⠀⠀⣿⡇⠈⣿⠀⠀⠀⠀⠸⣧⣀⣾⠇⠀⠐
⣿⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠅⠀⠀⠀⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠉⠀⠀⠤⠀⠀⠈⠉⠁⠀⠀⠠
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠉⠉⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠲⡚
⠀⠀⠀⢀⣀⠀⢢⠀⠀⠀⠸⠄⠂⠀⢄⠀⠀⠀⢀⢀⣀⠆⠀⠀⢀⣀⠀⠀⠃⠀⠀⠴⠂⢙⡆⠀⢀⠏⠙⠁⠀⠀⠄⡄
⠀⠀⠐⠚⠀⡀⢠⡀⠀⠀⠀⡔⠒⠀⠈⠁⠀⠀⠆⠈⠉⠀⢀⠀⠐⠀⠀⠸⠀⠀⠘⠉⠉⠈⠁⠀⠈⠀⠀⠀⠠⠐⠀⢀
⠀⠀⠀⠀⠊⢁⠀⢱⠀⠀⠀⠃⠀⠀⡰⠀⠀⢄⡀⣀⡠⠜⠀⠑⠒⠒⠦⡄⠃⠑⠤⠀⠤⠈⠀⢠⣤⡄⠀⠰⠄⠀⠄⠈⢆
⠀⠀⠀⠙⠋⠁⠈⠋⠀⠐⠊⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠖⠊
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡀⢠⡄⠀⠠⡀
⠀⠀⠀⠀⡧⠀⠠⡄⠀⠛⢷⠀⠀⠀⠘⢶⠁⠀⠀⠀⠄⠀⠀⡄⠀⠀⢀⠀⠀⠀⠈⠁⠀⠈⠀⠀⢸⠀⠀⠀⡠⠄⠀⠁⠀⠀⣀⠀⢠
⠀⠀⠀⠀⢀⠴⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠔⡀⠘⠀⠀⠀⢘⠀⠀⠀⠀⡞⠁⠀⡈⠁⡌⠀⠀⠀⠀⠀⢀⡇⠀⠠⠥⠀⠨
⠀⠀⠀⡀⡌⠀⣀⣀⠀⠀⢰⠀⠄⡄⠀⠀⠃⠀⠀⠀⠖⠁⠀⠀⠀⡀⠀⠀⡆⠀⡀⠤⠠⠤⠇⣀⣠⠀⠰⠴⠆⠲⠴⠇⠰⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠁⢄⠁⠀⠀⠀⠀⠐⠒⠛⠀⠘⠊⠁⠉⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⢀⢀⡀⠀⠈⠱⠀⠀⠠⠀⠀⠠⠀⠄⠠⠀⠀⠀⠄⢀⠀⢄⠀⠠⡀
⠀⠀⠀⠂⠁⡐⠄⠙⡀⠀⠀⢀⠀⢨⠀⠀⠀⢀⠤⢀⠈⢀⠀⠠⡆⡄⠀⠁⠀⡏⠉⠀⠀⠀⠀⠀⢰⠀⠂⠀⡇⠀⠈⠀⠀⠀⡜⠀⠠⠇⠀⡀
⠀⠀⠀⠀⠀⠂⠀⠰⠀⡀⠐⠀⠀⢘⠀⠀⠀⡀⠀⠀⠀⠀⠑⠢⡄⠀⢢⠀⠀⠃⠠⠀⠀⠀⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠉⠒⠒⠀⢨⠀⠠⡠⡅⠀⠀⠀⢠⠀⠁⠀⣀⠌⠠⣄⠀⠰⠄⠈⠛⠉⠛⠙⠃⠘⠛⠛⠇⠀⠀⠳⠾⠿⠻⠾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉
⠀⠀⠠⠄⠴⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬⠀⢤⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠒⠀⢀⠀⠀⡒⠀⠀⠀⠀⡀⠁⠀⠅⠀⠀⠀⡀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠐⢤⠅⠠⣤⠁⠀⠠⣄⠃⢰⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠘⠁⠀⠊⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⡆⠀⠀⠀⡀⠄⠈⠣⠀⠐⠈⢃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡂⠀⠀⠀⠀⠀⠀⠮⠁⠀⠁⡀⠐⢄⡈⢀⣀⠄⠀⠀⣀⠈⢁⠀⢈⡀
⠀⠀⢤⠀⢢⠘⢠⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⠂⠤⠔⠳⠆⠁⠀⠀⠈⠉⠀⠀⠀⠀⠈⠑⠊⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀

⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⡏⠹⡟⣉
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠟⣆⡸⠿⠿⠿⠿⠿⠿⠿⠿⠷⠛⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾⠷⠶⠷⠶


⠀⠀⠀⢀⡀
⠀⠀⠀⢁⠆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣒⡀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡔⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠸⣿⡿⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡯⢼⣉⣧⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠻⣽⡶⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂



⠀⠀⢠⠄⠠⠵
⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠐⠈
⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⢠⠀⡄⢀⠀⡀⠠⡄⢀⠀⡀⢀⠀⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣡⣈⣤⣡⣌⣠⣁⣤⣤⣈⣤⣵⣞⣤⣉⣿⣧⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⡷⠖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣚⣮⣶⣤⣄⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣷⣾⣿⣿⣿⣿⣿⣷⣤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⠀⠓⣼⣾⣿⣿⣿⣿⣿⡿⣿⢿⣿⣽⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢹⣿⣗⣮⣽⣿⣿⣾⣿⣿⣿⣿⢿⣳⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣧⢻⣿⣿⣿⣿⡿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣻⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣥⣿⣿⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠺⢿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⡿⣾⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠾⠐⠰⢤⣤⠔⠻⣿⠏⠻⣿⣿⣻⣽⣞⣟⣿⣿⣿⣿⣿⣿⢷⣙⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⡁⠀⠀⠀⠸⠿⢿⣥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠐⠒⠈⠀⠀⠠⢀⣼⠿⢿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠄⠀⢀⣠⣶⠾⠓⠈⠀⠀⠀⠀⠹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣀⣲⡀⠀⣤⡀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⣤⣠⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠛⡿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇
⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣛⡿⣿⡟
⠀⠀⠀⢀⣿⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠈⣁⣤⣄⣤⠴⣿⣭⡾⠋
⠀⠀⠀⢠⣿⣿⣿⣿⠋⡄⠰⠖⢀⣤⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⢀⠀⠀⠀⢀⢩⡍⢀⣶⣶⣿⣿⣿⣇
⠠⠄⠀⠀⣿⣿⣿⡇⢠⣷⣀⠀⡈⠈⠀⠀⣀⣤⣶⣶⣲⣶⣿⣿⣶⡖⠀⠉⠁⠂⢾⣴⣟⣗⣫⣵⣾⣿⣿⣿⣿⣷⣄⠀⠀⡰⠠
⠲⠧⠰⡰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣽⣾⣿⡿⠟⢹⣿⣿⡻⢟⣿⡀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣏⡻⣈⢛⢉⣿⣇⢰⡦
⠄⢒⣲⣟⡉⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠴⠄⠌⠻⣿⣷⣬⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣅⣽⣿⣿⣧⣿⣿⣤
⢀⠺⢾⡅⢷⠾⢺⣯⢽⣿⣿⣿⣿⣿⣿⠯⣬⢕⣍⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣌⠵⠖⢈⡽⡏⢾⡌⢿⣷⣿⠭⣯⣽⣶⣇⠁⣀⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡅⣾⡶⠋⡟⢉⡐⠈⣀⣱⠷⠶⢯⡖⠙⢨⢉⡁⢲⣾⣿⢿⠿⠿⢻⣿⢿⣿⣿⠿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿
⢤⣬⠿⢖⣲⢶⡂⣻⣤⣤⡼⣿⡚⢟⣻⠗⡰⢆⣾⡌⡃⠬⠍⢈⠲⠆⠬⠿⣗⠙⠛⠻⣞⢃⠈⠒⣛⣃⠈⡝⠙⡁⢹⠛⠙⠛⢟