Bilberry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡀⠀⠂⠙⡇⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠚⠀⠀⠀⠙⠲⢤⣀⣀⡠⢤⠊⠀⠀⠀⠀⠃⢀⣭⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠀⠀⠀⣢⡈⠁⡀
⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⡀⠁⡇⠀⠀⠉⠒⠤⢰⣤⡄⣒⣀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⣉⠉⢉⠕
⠀⠀⠐⠒⠀⠀⠀⣠⡤⠤⠷⠶⡶⠊⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠰⡖⠦⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢀⡤⠀⣠⡴⠚⠋⠀⠀⠀⠀⠀⢀⣀⣠⢊⣧⠀⠀⠀⠀⠀⠀⢀⡄⢳⡀⠀⠀⠀⠀⠀⠐⠶⣄⠀⠠⠄
⠀⠠⠰⠋⠀⠀⠀⠀⠀⠀⢠⢀⣰⣿⠃⠀⠈⢣⠀⠀⠀⠀⣠⠋⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠦⠄⠀⠀⠀⠀⠀⠀⠐⠘⡇⠔⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⢀⠀⣸⠃⠀⠀⠀⠀⠓⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠐⠢⡏⠀⠀⠀⠀⠀⠀⣄⣉⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢾⠏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠀⣤⠔⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡤⠀⢤⠄⡀⠀⢑⠀⠀⠀⠔⠚⠁⠂⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⣀⠴⠿⠦⠀⠀⢀⡟⠉⠉⠂⠀⠀⠀⡀⠀⠀⠀⢄⡀⠢⠀⠀⠀⢀⠀⠀⠀⠈⣴⣖⠀⠄⠀⣀⣠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠓⠶⣄⡈⠀⠀⢀⠞⢁⣀⣀⡀
⠀⠀⠀⠀⠈⠀⡀⣀⣀⣀⣀⣀⣠⠖⢧⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⠀⠨⠗⢄⠀⠀⣀⣁⢀⣄⠀⠉⠁⣠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⢠⠎⠁⠀⠈⠢⠀⣤⢰⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠋⠁⠀⠀⠈⠉⠉⠐⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠲⣄⠀⡎⠀⠀⠀⠀⠀⠂⠀⢀⡀⢄
⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠇⠀⠀⠀⠀⠀⠀⠘⡦⠾⣦⣄⢈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢙⣥⣟⠳⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠻⣋⣨⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⣸⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣢⣤⣤⣖⣒⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠸⣠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠘⠁
⠀⡀⣈⠁⣀⣀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⠀⠀⠀⠀⠀⠀⠀⠒⠢⠌⣾⠁⠀⠀⠀⠀⠀⠀⢸⠀⡠⠾⠁⡀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣈⢓⢆⠀⠄⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⢣⣀⡀⠀⠀⠀⠀⣸⣾⠧⠤⠴⠶⠊
⠀⠀⠈⠀⠐⠀⠂⠀⠀⢀⡼⠋⠘⠛⠀⠀⠀⡀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⢷⡈⢑⡶⠀⠒⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠜⣙⡏⠀⠀⠀⠀⢹⡗⣀
⠀⠀⠀⠀⠀⠀⠀⠾⠧⠀⠐⠀⠀⠀⠀⢀⣴⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠀⠀⠀⠈⠂⠉⢇⠐⢤⣤⢶⡶⢡⠁
⠀⠀⠀⠀⠀⠀⠀⡿⠂⠀⠀⠀⠀⣤⠀⠉⣤⣀⠐⠳⢤⠄⠀⠀⠀⠀⠀⠀⠀⠙⠹⡄⠀⠀⠀⠀⡇⠈⠑⢺⠇⢴⡗⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣷⠀⠀⠻⠋⡀⠀⠀⠳⠀⠈⠀⠀⠀⠀⠀⠀⠳⡏⠑⠀⠀⠈⠁⠀⠀⡸⠂⠚⠻⠲⠤⣀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠠⠄⠈⠉⠀⠀⢠⠠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡉⠁⠉⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡽⠀⠄⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡏⢠⡄⠀⠀⠀⠀⠀⠙⢦⡀⢀⠀⠀⢀⡀⠄⠀⢀⣤⣤⢤⠆
⠀⠀⠀⠀⠸⣆⠀⠀⠀⢹⡀⠲⢶⡔⠇⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠓⠚⠋⠀⠎⠚⡅⠰⠀⠋
⠀⠀⠀⠀⠀⠙⠺⠀⠠⠚⡆⠀⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣀⠘⡆⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣠⠂⠀⠀⠀⠀⠀⢦⣸⣀⠀⡀⠀⢸⡄⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠁⠨⠷⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⢀⣰⡌⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠉⠁⠀⠲⣜⠁⠀⠀⠀⢢⣠⠔⠒⠂⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢘⠃⠀⠀⠀⠀⠇
⠀⠀⢀⡤⠀⣀⠐⠁⠀⠀⢀⡀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⣀⠤⢤⡀⠀⡼⣷⠀⠀⠐⢾⠀⠀⠀⢀
⠀⣄⠈⠀⠀⠀⠐⠒⠐⠂⠂⠀⠓⠂⠉⠁⠁⠘⠀⠀⠀⠀⠀⠀⠈⠑⠀⠚⠀⠛⠛⠀⠀⠡⠀⠀⠘⠢⣤⣴⠤⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⣰⡀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢠⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡰⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⣀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠐⠂⠒⠀⠂⠀⢠⣀⣀⠈⢳⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡜⠛⠒⠒⠂⠀⠀⢠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⡫⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣟⣂⣠⣤⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠀⠚⠉⠁⠀⠀⠹⣏⠙⠲⠤⣄⡀⣀⣀⣴⣟⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⣠⠞⠉⠀⠀⠀⠉⢿⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠏⣏⢹⡗⠀⠀⠀⠀⠀⠀⠈⣷⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠹⡀⢸⠸⡀⠠⢀⣀⢀⢀⣤⣠⡿⢰⡛⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡖⠀⠀⠀⠀⠀⠀⢱⢸⠀⠳⣄⠀⢼⣾⠙⠉⠿⢁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢿⡄⠄⠀⠀⠀⠀⠀⢸⠀⠀⠈⠛⢬⠝⠒⢾⢾⠉⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⡟⣘⠦⠀⠀⠀⡘⠙⠂⡀⠀⠀⢸⣤⠤⠾⣦⣷⣤⣀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⢀⣤⠴⠊⠀⠀⠀⠀⢦⣰⠃⠀⠀⠀⠀⠀⠀⠉⠹⣶⠤⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⢀⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⡀⢣⣀⣀⣠⣴⠗⢀⠲⣄⢠⢜⠛⠛⠿⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠛⠙⠉⠁⠀⢸⠁⠈⠹⡆⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠸⣤⠄⠐⠒⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠈⠙⠳⢤⣟⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⡀⠀⠀⠀⠀⡄⢀⡧⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢞⠱⢲⣦⠰⣎⡄⠈⠉⠀⠠⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⢠⡠⠀⠀⠄⠀⠀⠀⢀⡴⢀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⠳⠎⠀⠀⠀⠀⠀⠀⠀⢼⣱⠋
⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠠⢴⡀⣈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠲⠀⠀⠀⠀⠈⠛⠓⢳⣤⡀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠒⣦⡀
⠀⠀⠀⠀⠀⠐⠦⡀⠐⣄⠈⢯⣰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⠓⠈⡓⢦⡔⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠞⠢⠼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠠⠄⠀⠀⠂⠘⣇⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠈⠉⠤⠀⢀⣤⣠⡵⠞⣳⣄⡀⠀⠀⠀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠛⢏⢻⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⣠⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠄⠀⠀⢠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠀⠙⠀⠀⠀⠀⠀⠐⠲⣶⣆⠐⠦⠀⠢⣄⠀⠀⠀⢁⠠⡀⠟⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⣄⠀⠈⠑⢆⠀⠀⠱⣽⡇⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡇⠀⠰⡄⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠨⠷⣤⡄⠀⠹⡄⠀⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⡦⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠙⣄⠀⠧⢀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣧⠐⡎⠀⠀⠀⠀⣤⠄⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⣿⣿⡯⣿⣗⡶⠄⠀⠀⠀⠀⠀⣿⢮⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⡔⠛⣀⣍⡻⢽⣀⣀⡑⠄⠀⠀⠀⡛⠋⠛⠠⣙⣯⡉⠻⢿⣿⣶⣶⣶⠖⠶⠶⢶⣄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠐⠂⢄⣀⣀⠀⠀⠀⢸⢳⠋⠳⡠⣿⣻⠷⢘⠛⠻⢯⣻⡄⢀⣼⠁⠀⠀⠀⠉⢉⣀⡀⠀⠈⢫⠙⢦⣤⣄⣀⣀⡈⠆
⠀⠀⢀⢔⠅⠀⠀⠀⠀⠀⠀⠀⢈⣡⣿⣄⡀⠀⢸⠃⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⣹⠴⠞⠀⣤⣄⡀⠀⠀⠀⠹⠆⠀⠀⠀⡄⠀⠉⠀⡀⠀⠀⠙
⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣹⣡⠏⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠄⠀⠀⠀⠀⠈⠉⠑⢄⠀⠀⠀⠀⠀⠀⢱
⠀⢸⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣩⡿⠀⠀⠘⢧⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙
⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠙⠒⠦⠴⠒⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⢘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠉⠁⠙⢤⣄⠀⠀⣀⣤⡤⠤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢢⣼⣦⡤
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠚⠻⢡⣦⡜⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⡀⠀⣤⠂
⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠈⣃⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢧⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠤⠼⢻⡀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢀⣀⡤⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠢⣀⠀⠀⠀⠀⣾⣠⠖⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡸⣷⣀⡬⠓⠀⠰⢾⡛⠛⠛⠲⠶⠶⠖⠂⠛⠁
⠀⠀⠀⠀⠀⠀⣾⣤⠀⠀⠀⠈⢱⠀⣧⠟⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⢸⠉⡄⠰⣄⣀⣠⢀⡇⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠹⡎⠘⠀⠀⠀⢤⠃⠀⠙⢄⣿⡉⡹⣃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢰⠛⠐⠖⠂⠀⠀⠀⡀⢀⡮⠤⣸⣋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⠙⠱⢆⠀⠀⡠⠘⠁⠀⠀⣄⠀⠘⠉⠈⠻⠐
⠀⠀⠀⠀⠀⠀⠀⠙⡦⢂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠁⠀⠀⠀⠒⠀⠀⠀⠀⢀⡠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⢡⠰⣄⡤⠶⢤⠤⡠⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠘⡆⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢀⣠⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠢⣀⡗⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠺⡆⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⠑⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢑⣦⠀⡠⠂⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠂⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢸⠀⠻⣄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠐⢀⡀⠀⢀⠀⢳⡀⠀⠈⡆⠀⣀⠀⢀⣀⠀⠑⣄⣈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠁⠄⠀⠀⠉⢦⠈⢆⠐⠻⣀⠀⢧⠊⠀⢀⢀⣈⡗⠉⠀⠀⠀⠈⣿⠀⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠑⢤⣀⠀⠈⠄⠨⡀⠀⣉⣲⣬⣓⢼⣶⠿⠛⠉⠸⡇⠰⡚⢲⠀⠀⣿⡠⠤⠖⠛⠙⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠑⠶⠖⢲⣷⢛⠟⠋⢸⣑⣀⡋⠀⠀⠀⠀⠳⣄⣈⣁⣠⠾⠃⡎⠀⠀⠀⠀⠀⠈⠐⢄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠤⠚⢁⢼⠏⠀⢠⠞⠉⠀⠈⠑⢄⠀⠺⡻⠁⡸⠁⢀⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⢀⢢⡏⠀⠀⠞⠀⠀⠀⠀⠀⡸⠊⠉⠀⠀⣃⣤⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⠁⠀⡀⠀⠢⣄⣫⣽⠼⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡇⠐⠀⢀⡀⡤⠄⠒⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠈⠉⠒⢄⠀⠀⠐⠋⠀⢀⣀⠄
⠀⠀⠀⠠⠄⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠃⠀⣄⡀⠀⠀⡆⠀⠀⢀⠄⣀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⢢⣠⠔⠉⠉⠉⠒⢤⢎⡥⢒⡆⠀⠙⣄⢀⠌⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⢦⠀⠀⢣⡐⠀⠁⢀⡼⠃⠀⢠⠃⠢⠐⠁⠀⠘
⠀⠀⠀⠀⠀⠁⢠⠃⠀⡠⠄⡄⢀⡿⠐⠛⠦⣄⡀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠛⠉⠀⠀⠀⠘⣄⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠣⠤⢲⠎⠀⠀⠀⠀⠀⠑⣴⠟⠢⠄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠒⠦⣄⠀⠀⢀⠤⠀⠠⢈⠓⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣤⣾⡀⠀⠛⢦⠀⠀⢰⣏⠀⠤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⡆⠰⠁⢀⡀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣁⢁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⣬⠇⢰⠀⠙⠤⠃⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠛⠁⠀⠀⠙⠶⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠆⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⡀⠘⢢⣄⣀⣀⠀⢨⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠙⠳⢼⡇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠈⠀⠰⣾⡅⠀⠀⠀⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⢆⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠙⢉⠀⠀⠀⠀⠀⠀⠄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡀⢀⣤⣩⣄⡀⠀⠀⠀⠀⠀⠀⣨⣷⡀⠀⠀⠈⢙⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⢀⠀⠀⠀⠀⠀⠀⣠⠞⠈⠀⠀⠀⠀⠈⠙⢧⡄⠀⠀⠀⠀⠅⠀⠑⠦⠽⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⣄⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣦⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⡤⠠⠜⢣⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⢸⠇⠀⠁⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠚⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠴⠂⠂⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⡀⠚⠀⠈⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⣀⣀⣠⡴⠖⢊⡥⠾⠏⠠⣄⣘⠒
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠁⠀⠀⠎⠀⠀⠀⠀⠁⠝⣷⠀⢠⡤
⠀⠀⠀⠀⠀⠈⠉⣙⡒⣀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢶⠒⣆⠀⠀⠀⠀⠀⠀⢠⠀⣸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠔⠀⠀⠀⠉⠳⡄⠀⠀⣀⡤⢞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠋⠛⠛⢆⠀⠀⠀⠀⠀⣘⣸⠏⠀⠀⠀⠀⠠
⠀⠀⠀⣄⠙⠀⠀⠀⠀⠀⢀⡟⠋⠉⠁⠔⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⣳⠖⠚⠉⠙⠛⠷⣤⠀⠀⠀⠠⡄
⠀⠀⠀⠈⢦⣄⣀⡀⠀⠐⢫⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠈⢲⣤⣤⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣠⡀⠀⣀⣤⠴⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣠⠤⡀⣠⠀⠀⠀⠀⣠⠄⠄⡀⠀⠘⡏⠛⠂⠀⡀
⠀⠀⠀⢰⠟⠛⠛⠋⠈⠀⠀⠀⣱⠊⠀⠁⠀⠀⠀⠀⠄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠛⢛⣈⣻⣤⠀⠀⣸⠱⠟⠃⠀⠀⡀⠁⠀⠀⠀⢃
⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠆⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠘⢇⡀⠀⠀⠀⠀⢴⠋⠀⠀⠠⢎⡀
⠀⠀⠀⠘⣧⣚⠦⠀⠀⠀⠀⣠⣷⡀⢐⢀⡐⢲⠔⠃⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠀⠀⠀⠁⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠻⢶⣷⣿⣶⣿⠿⠋⠙⠻⣿⣷⣶⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⠠⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀⣼⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠰⣌⢷⡄⠀⣿⣿⢸⡿⠟⠓⠛⠒⠂⠀⠀⠀⢀⢀⠀⠀⠄⢸⣠⣴⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠈⠙⠃⢀⡩⠭⠴⠦⠄⠀⠀⡄⠀⠀⠀⠀⣈⣿⢀⡠⢒⣉⡁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢄⠀⠈⠁⠰⣎⡥⢀⠲⣶⣤⡀⠈⠳⠀⠀⠘⣦⣬⣾⠷⣤⠁⠀⠀⠀⠑⠆
⠀⠀⠀⠀⢀⣀⡀⡠⢑⡤⢕⢿⡿⢿⣤⣨⡀⠁⠈⣿⠃⠀⡄⣀⣤⣿⣜⣿⣧⣼⣷⡷⠆⠀⠀⠀⠘⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠚⠉⠉⢀⢣⣾⣧⠀⠁⠉⠫⠛⠋⠀⠀⠀⠁⠀⠀⠻⠿⠟⠜⣛⡹⠀⣬⡥⠤⠀⣆⠀⠀⠠⠔
⠀⠀⠀⠀⠀⣠⣤⠀⢿⣷⣿⣿⣦⡄⢀⠗⢗⠒⠀⠀⠀⠐⠂⠀⠉⠀⣤⡌⢛⡻⣶⣦⣰⣠⠀⠁⢢⡀⠀⣀⣀
⠀⠀⠀⣠⡿⠃⠉⢦⣋⠙⣿⡞⠉⠉⠁⢠⠈⢂⠰⠲⠀⠒⠲⠤⠖⡰⢿⣷⣿⣦⣿⣿⠿⠉⡄⠀⠀⠀⠢⠀⠈⠛⢟
⠀⠀⠀⣿⠁⠀⠀⠀⢻⣿⠿⣧⠀⠀⢀⠈⠀⡀⠙⠲⣌⠁⠀⠀⠀⠟⠾⢛⣿⣥⣼⣿⡵⠋⠃⠀⠀⠘⡄⠓⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠟⠈⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⢈⣳⣒⡀⠀⠀⣾⠟⠛⠉⢻⡇⠀⢀⣾⣆⢰⠇⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣧⠈⠉⠑⠀⠸⠋⠀⠀⠀⠀⠀⢠⠟⠉⠙⠋⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠄⠀⠀⠀⠆⠀⢀⠀⢐⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣆⠈⡄⠀⠸⠐⠀⠘⠐⣼⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢹⡀⠸⠀⠰⠀⠠⠀⣰⠃⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠑⢄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⡇⢰⠀⠀⢳⣠⠞⠃⠀⠀⣀⡠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢄⠈⢢⠀⠀⢀⡠⠐⠒⠨⣦⡸⢴⣷⣾⠿⣛⣫⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢸⡇⢈⠀⠀⡎⢀⢠⣄⣶⣿⡏⠹⢳⣄⡀⠠⠉⠛⠢⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢸⣣⠞⠂⠉⠙⢯⠋⠁⠀⠀⢈⠊⠁⠀⠈⠑⠷⢀⠀⠈⠳⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⠔⢢⠀⣧⠀⠀⠀⢨⠀⠀⠀⣀⠀⣸⠀⠁⠒⠰⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠙⢆⠀⠈⠒⠋⣠⠟⠽⢋⡤⠜⠦⣄⣘⣱⠷⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡤⠔⠺⣑⠖⢒⠊⠉⠑⠄⡀
⠀⠀⠀⠀⠀⠀⢰⡗⠁⠀⠀⠀⠀⠙⠳⠽⠵⠶⠶⠛
⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁
⠀⠀⠀⠐⠐⠀⠀⡀⠈⡄⡁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠡⠄⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡔⠉⡄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣠⠏⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠾⠄⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠠⢄⣀⠀⠈⠹⣆⠀⠀⠀⠀⢀⡴⠂⠀⠲⢦
⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⡖⠈⢡⣆⠀⠓⠦⠀⠀⠀⠀⠊⠍⠀⠀⠘⠅⠀⠀⠀⠈⢑⠒⠀⢲⡋⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⢀⠈⠃⡄⠀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠚⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠉⠆⠁⠀⠀⠀⢳⢀⠀⠈⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⠶⠖⠢⣀
⠀⠀⠀⠠⡄⠀⠀⠘⡂⠠⢬⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠂⠀⠰⢧⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡔⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢘⢺⠀⠀⠀⠀⢘⠇⡰
⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠊⠀⠀⠉⠢⣀⣄⠀⠚⠻⣁⠀⠀⠀⣦
⠀⠀⣠⠒⠁⠠⠘⠀⠀⠀⠀⠤⢠⡂⠀⣀⡀⡄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⢠⠁⠀⠀⣠⠠⠀⢱⡀⠀⠉
⠐⡀⠁⠀⠀⠀⠐⠃⠁⠁⠈⠀⠀⠉⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⡀⠀⠁⠙⠓⠀⣀⣾⡀⠀⠀⠝⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠓⣤⣀⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠠⡟⠃⠀⠀⢤⠄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⡄⠚⠀⠀⠀⠀⢄⠀⡔⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠑⠄⠀⠀⠀⡄⠈⠠⠀⠀⠀⠐⠓⠐⠃⠐⠂⠀⠛⠃⠀⠈⠈⠁⠈⠘
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⠃⠀⠀⠀⠰⡁⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠉⠷⠂⠀⠓⢂⠀⠀⠀⠀⢓⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⡤⠒⠦⢤⣴⣎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡤⡐⠀⠀⠀⠀⠘⠚⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣰⡄⡀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠔⠚⠐⠾⡁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⢰⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠉⠏⠀⠀⠀⠀⠀⠠⠀⢱⣄⠀⠀⠀⠀⠀⠀⣄⣧
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⠀⢀⠖⠋⢀⣰⡎⠉⢲⠄⠀⠀⠀⠐⣷⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⡀⠟⠁⠀⢸⡀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠓⡤⠂⠀⠀⠈⠒⠄⣀⡤
⠀⠀⠈⣈⢙⡖⢙⡦⢄⠀⠀⠀⠄⠘⡉⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣇
⠀⠈⣉⣈⣩⡝⠋⠁⠀⢳⠀⠀⠄⠠⠆⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠱⠛⠁⢠⠉⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣀⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡾⠑⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠍⠐⠄⠀⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄


⠀⢀⡀⢀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⣠⠁⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⢨⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⡀⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢹⠽⡿⢷⣲⢾⡃⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠙⢧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡙⠁⠤⠌⡙⠮⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠃⠀⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀⠀⠀⠀⠀⠀⠈⠉⠐⢾⠁⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⣄⡈⠦⠀⠀⠣⡀⠀⠀⠀⡬⢠⡇⠀⠀⠀⠀⠀⠰⣷⠄⠀⠀⠀⠀⠀⠀⠙⠣⠐⠀⢬⡄⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⡄⠀⠀⠀⢠⣦⠤⠞⠀⢊⠀⠀⠀⠀⠀⢀⠲⠷⠀⢀⣀⣤⡐⠆⠈⠒⠠⢄⡀⠘⠿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠸⡄⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠦⠤⡄⠈⢆⢸⠀⠀⠀⡤⠀⠈⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠋⠀⠀⣀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠛⣦⠛⠀⣀⣀⣄⣠⣤⣀⠐⠀⠀⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡟⠋⠉⠑⠀⠀⠀⠀⠀⠑⠁
⠀⠀⠀⠄⠈⢀⣠⠶⠂⠈⠁⠀⠈⠃⡘⠊⠁⢹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⢿⣿⣁⣐⢀⡀⠀⡇⠀⠀⠀⠉⠳⠀⠀⠈⠆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⢠⣦⠋⠀⠀⠀⠀⠀⠀⢀⠁⡟⢰⣾⡦⠛⠉⠛⢷⡼⠀⠶⠒⠒⠤
⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠜⠚⠃⠀⠀⠀⠀⠀⠀⠀⠸⡏⠈⠁⠉⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣁⣠⠴⠦⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠔⢶⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠒⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⣸⠆⢀⣄⡒⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⠁⠀⠀⠀⣼⢇⠔⠋⠉⠙⠁⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠘⢿⡷⠖⠚⠦⣿⣆⠀⠀⠀⠀⠀⠀⡳⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡆⠀⠈⠋⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⣀⣄⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⣭⣤⠀⠀⢀⣼⡟⠋⠉⠻⣦⠑⠢⠤⣌⠤⣤⡀⠀⣀⣀⣠⠤⠄⠒⠒⠊⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⡝⠁⠀⠉⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣀⣀⡤⣤⣾⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣗⡘⢾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠌⠃⢷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂
⠀⠀⠀⠀⠀⠀⠀⡐⢀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠦⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠁⣄⠤⠀⠉⠀⠀⠀⠀⠿⠁⢀⣀⠠⠀⠀⠄⡀⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠈⠒⠂⢈⢀⠁⠀⠄⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠐⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢷⠄⠒⠛⠛⠋
⠀⠀⠀⣠⠴⠂⠀⠀⠉⠘⠀⠘⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢶⠿⡿⣁⣤⡄⠈⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢠⠃⠘⠏⠀⠀⠝⠁⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠈⠤⠀⡀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠈⠀⠀⠀⠀⢀⢀⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠃⠠⠬⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣦⠤⢤⣯⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠱⣀⣀⣀⢄⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢞⠄⠀⠚⠃⠀⠈⢃⠁⠀⠈⠐⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣀⡤⢤⢆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠌⠫
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠀⠃⠀⠀⠀⠀⢠⠞⠁⠀⠀⣀⣹⠗⣄
⠀⠀⠀⣧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠐⠀⠐⠧⠀⠀⠀⢰⠁⢠⡖⡈
⠀⠀⠐⢌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠦⣅⡀⠂
⠀⠀⢦⡈⠙⣆⠀⠀⠈⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣀⠞⠉⡙
⠀⠀⢀⡉⠳⣄⣀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⣀⣠⠎⠀⠛⠿⠿⣭⡤⠴⠊
⠀⠀⠀⠙⠄⣌⣻⣄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⣀⢩⠿⠶⣾⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠂
⠀⠀⢀⢐⡻⠟⢻⡲⡄⠀⠑⣴⣇⠔⠒⠁⠀⠉⠉⠉⠹⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠏⢹⣇⠺⠿⠀⠁⠀⠀⠈⣷⢀⣀⢀⣀⠀⠠
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛
⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⡦⠆⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠉⠀⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⢀⢀⡀⢀⣴⣟⣡⠶⠖⠓⠒⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡟⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠘⠏⠰⣈⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢦⠀⠀⡎⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠐⢆⠀⠉⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⣺⡾⠟⠻⢤⣀⣀⣀⠰⠛⠁⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠚⠀⠀⠀⠀⠈⠢⠀⡀⠀⠀⢀⡠⠔⠳⠤⣤⣤⣤⠶⡿⠁⠀⠀⠀⠀⠈⠉⠛⠃⠤⢤⣤⡀⠀⠢⠄
⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠠⠟⠶⠦⠴⠶⣖⣖⣋⡽⠋⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⡤⠄
⠀⢠⠼⣥⠤⠀⠀⢀⡀⠀⠀⠀⠈⢿⣦⡠⠤⢄⡀⣀⠄⠀⠀⠀⢀⡴⠋⢉⠘⠉⠋⠦⣰⠇
⠀⣧⣼⠀⠀⠀⠀⠈⠙⡦⠤⠤⠤⠖⣁⠀⠀⠀⠙⠳⢤⣀⣀⣠⢋⢠⡰⡃⠀⠀⠀⠀⢻
⠀⢯⣡⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⣞⡁⠀⠀⠀⠀⠀⠀⢻⠀⠸⡞⠛⣷⡀⠀⠀⠀⠀⢸⣦⡀
⠀⠈⠃⠑⠂⠀⠀⣰⣇⣠⡴⠚⠋⠙⢲⠄⠀⠀⠀⠀⠀⣼⠗⢾⣗⢢⣾⣋⠀⢀⣀⣤⡿⠉⢿⣿⡋⠉⠉⠉⠐⠢⠄
⠀⠀⠀⠟⠛⠃⠀⠀⠈⠈⠃⠀⠘⠃⣸⡇⠀⠀⠀⠀⠐⣹⠃⠀⠸⢦⠄⣉⣙⣩⠽⠋⠀⠀⢸⡏⠙⠣⣄⠀⠀⠀⠀⠈⢀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢚⠀⠀⠙⢤⣏⣀⢀⡀⠀⣨⠋⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠸⣷⠀⢠⠉⢷⡄
⠀⠀⠈⢷⣀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡑⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠁⠉⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢇⣠⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠨⠛⠲⢄⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⣰⣃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⠈⠉⢒⠄
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡠⠃⣠⠴⠛⠉⠉⠉⠙⠓⢦⣀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⢀⡇⡿⠶⠤⠤⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢝⠳⣤
⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡹⣄⣾⡟⠁⠀⠀⠀⢸⠀⠀⠀⠀⣀⣠⣤⣶⠋⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡓⢻
⠀⠀⠈⠑⢦⣤⣤⡖⠚⠛⠛⠛⠻⢶⣄⣀⣀⣽⢿⣿⢀⣀⡀⠀⠀⠈⢀⠴⠒⠋⠉⠀⠈⢎⣧⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛
⠀⠀⠀⣀⣼⢫⡏⢷⡀⠀⠀⠀⠀⠀⠙⣯⡀⠀⠀⡻⡇⠉⠛⢷⡶⣷⠁⣀⣠⣤⣶⣶⣶⣬⣞⠷⣤⣤⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣯⡈⠉⠁⠀⠻⣦⣄⠀⠀⠀⠀⢸⡇⠀⠀⣷⡹⣄⠀⠀⠉⣾⠟⠉⠁⠀⠀⠀⠀⠈⠙⣷⡖⢆⢿⡛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⢾⣅⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⣼⣇⡠⢞⡽⢳⣌⡳⣦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢢⣧⣀⣙⣳⣦⣄⣀⣀⣤⡴⠟⠁
⠀⠀⠘⣿⣴⠶⣶⡟⠛⠁⠀⠀⠀⠀⣰⠿⠷⠚⠉⠀⠀⢹⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠟⠋⠉⠉⠉⠛⢿⣏
⠀⠀⠀⠹⣧⣀⠈⠀⠀⠀⠀⠀⣠⡼⠋⣀⣤⠴⠶⠶⠾⢿⣆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣶⣾⣿⣷⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣮⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⢀⡤⠖⠂⠀⣠⣴⠋⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⠛⠻⠶⠶⠶⠿⠟⠋⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⢀⡴⠋⠀⠀⢀⠞⠁⣾⠀⢸⡀⠀⣶⡿⢻⡟⠶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⢀⡀⠀⠀⢀⣿⡀
⠀⢠⠏⠀⠀⠀⣰⠋⠀⢰⡇⠀⠀⢷⡀⡾⠀⠀⠁⢤⣿⡆⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢥⣀⣴⣤⡿⠿⠃
⠀⡎⠀⠀⠀⢰⠃⠀⢀⣿⠁⠀⠀⠀⠙⢿⣦⣤⣶⠺⠟⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁
⢰⡇⠀⠀⠀⠇⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉
⠘⡇⠀⠀⠈⠀⢀⣾⠏
⠀⢳⡀⠀⠀⣠⡿⠃
⠀⠀⠻⡴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⣹⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠏⠀⣿⠀⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠁⠀⠀⢀⣼⠀⠸⣄⢹⠹⠟⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠊⢈⡇⠀⠈⠻⣦⣶⣴⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡠⠀⣶⣿⣿⠾⠣⡀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠙⠻⠃⠀⠀⣴⣾⡄⠻⡿⠂⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡇⠀⠁⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠛⠛⠛⠷⢦⣤⣴⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢀⠅⢀⠠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡀⠀⠀⠀⠐⠂⠐⠀⠀⠘⠂⠀⠀⠁⠐⠂⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡴⠁⣀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠔⠁
⠀⠀⠀⠀⠐⡄⠳⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⣤⣤⡤⢼⣧⣇⠀⠀⠀⠀⢀⡠⡾⠁⠓⠦⠀⠠⠤
⠀⠀⠀⠀⠰⠈⢢⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠓⠀⠲⢏⠁⣼⡇
⠀⠀⠀⠀⢀⣈⠳⣇⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠈⢿⡉⢢⠤⠤
⠀⠀⠠⢢⡜⣋⡃⡀⠁⢀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠱⣴⣤⣄⠔⢀⠎⡇⠄⠀⠀⠀⠀⢠⣠
⠀⠀⡀⠈⠁⠉⠁⠀⠀⢸⠏⠀⠀⠀⠉⠑⡦⠀⠀⠀⢀⠀⠀⠀⠀⠘⠲⣥⡤⢿⡰⠋⠀⢡⡀⠀⠀⢀⣠⢛⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⢴⠾⠒⠰⢇⠀⠀⠈⠁⠀⢀⠁⣈⠟
⠀⠀⠀⠈⠂⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠎⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⠈⠁⢙⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⠀⠀⠀⠀⡃⠀⠀⢀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠰⠂⠛⠦⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠣⠛⡉⢑⡤⠎⡆⠙⠒⠒⠂⠘⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⢀⠀⠀⢀⡼⠀⠀⣇
⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡌⡁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡧⠊⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠈⢓⠶⠀⠨⠛⢀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⡠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠛⠲⠴⠶⠧⠀⠀⠀⠀⠀⠈⠐⠆⠀⠘⠁⠠⣆⣴⡂⠛⠁⠀⠀⠀⠀⠀⠀⡠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠠⠈⠀⠀⠚⣣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠵⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢠⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠠⢊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠉⠉⠂⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣮⣭⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣤⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠄
⠀⠀⠀⠐⢰⣖⣦⣼⣤⠀⠰⣵⣦⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢀⠄⠐⠂
⠀⠀⠀⠀⢸⣿⣿⡟⢏⠀⣸⣿⠟⠀⠀⣿⣿⡠⠤⠀⠂⠀⠀⠀⠀⣼⣿⡷⠈⠀⠀⠀⠀⠐⠒⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠙⣿⣦⠀⠘⠿⣿⣶⠀⠀⠀⠀⠀⣾⣷⢦⣯⡄⠀⠀⠀⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⣶⡆⢰⣾⠟⠃⠀⠰⠀⠀⠉⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠲⠀⠀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣈⠘⠂
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣀⠄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠃⠈⠋⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚⠁⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⡀⢀⡀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠠⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠂⢠⡄⠄⠀⠀⠀⠀⢤⠄⠈⠒⠃⡠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠖⢹⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⠺⢴⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢃⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⡴⠄⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⢧⡆⡔⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢭⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀
⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠈⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠂⠐⠲⠒⠈⠉⠉⡉⠁
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣾⣏⢻⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⢰
⡀⠀⠀⠀⣡⣴⢒⡤⠐⠀⣴⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻⣿⣿⠿⠃⠀⢀⠀⠀⠀⡀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣶⣶⣦⡀⡀⠸⡟
⡏⠀⠀⠠⠯⠴⠿⠃⠀⠸⣿⣿⠏⠀⠀⠀⠀⠠⢄⡢⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⢼⣿⠋⣩⣿⠟⠻⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠘⡵⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠘⣿⣶⠟⢿⠗
⣠⡄⠀⠀⠘⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠆⠦⠀⠀⠀⠀⢀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠴⠀⠈⠦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣌⢀⠀⠀⠀⠀⠀⠐
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠈⠀⠈⡉⠈⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉⠛
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠉⠙⠲⠦⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⣀⡴⠞⠋⠉⠁⠀⠈⠉⠙⠶⣄⠀⡠⠖⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⡜⣀⡴⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠙⢧⡀⠆⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣀⣼⠭⠤⠤⠄⠀⠀⠀⢀⡟
⠀⠀⠀⣀⡤⠖⠒⠒⠒⠻⡄⠀⠀⠀⠀⠙⠺⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣁⣰⠐⠀⠢⠤⠀⠀⠀⡾
⢶⠋⠉⠁⠀⠀⠀⠀⠀⡀⠘⢦⠀⠀⠒⠒⠒⠚⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠉⠒⢮⡞⠁
⠀⠑⢤⡀⠀⠐⠢⢤⣦⡈⢢⡀⠑⢄⠀⠀⠀⠀⠀⢳⣀⡤⠖⠚⠛⠛⠛⠓⠲⢦⣄⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠉⠲⣄⡀⠀⠉⠉⠓⠛⢶⣤⢽⣦⣄⡀⢀⣾⢡⡤⠤⣀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⡉⠁⠀⠀⠀⠈⣹⠋⠀⠁⠀⠆⡽⡆⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠲⣶⣯⠄⢄⠀⢔⡼⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢷⣬⡴⣋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠳⣤⣀⠀⠀⠀⠀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⢶⣾⢶⣷⣾⣶⡔⢸⣷⠷⠿⣾⠟⠛⠃⠀⠀⠀⢮⡷⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣶⣦⣤
⠀⠀⠈⠓⠴⠥⠝⠁⠀⠀⠒⠉⠑⠂⣠⣶⣦⡀⢀⣀⠀⠀⠀⠀⢜⢹⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠜⣿⣞⢦⠀⢀⡄⣰⢻⡦⠀⠀⢼⣿⣿⣟⣿
⠀⠀⠀⠀⡠⠀⠁⠀⠀⣀⢀⠀⠀⡀⠻⣿⣿⠷⣫⣁⣽⠉⡲⢄⠀⠉⣠⣤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⠜⢿⣷⢠⣿⠱⡇⢽⣇⠀⠀⠘⢿⣿⣿⣿
⣀⠀⣤⠞⣔⠆⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠄⠘⢿⢿⣿⣿⣿⡅⠀⠀⠻⠶⠃⠀⣾⣳⠀⢀⡄⠀⠠⣤⣆⣀⣁⣀⣼⠋⠀⠹⡾⢿⡆⢀⡀⠀⠈⠉
⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣦⠙⠂⠤⠈⢙⣿⣧⡀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠩⢉⣙⣻⣧⣬⣳⠷⣾⣷⣾⠿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣾⣿⡆⠀⠹⠿⡿⢠⣾⣆⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣲⠀⠀⢾⣿⣿⢿⣯⣿⣼⣶⣿⣗⢻⣿⣃⢀
⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠉⠉⠁⠀⣠⣄⠀⠸⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣾⠟⡡⠞⠉⠙⠽⠛⢷⣾⣟⡿⢻⣾
⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⣀⡀⠀⠰⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠀⠀⢀⣀⣀⠀⠀⠉⠀⢐⣿⣟
⣀⠀⠉⠋⠉⠀⠀⣠⣶⣿⣿⣿⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣼⣧⣶⣤⣤⣤⣉⠢⠀⠀⣾⡿
⠈⠯⣴⣀⠄⠀⠀⢿⣿⠊⢻⣿⡇⠀⠀⠀⠀⠀⣿⣹⡆⢺⣉⡁⢸⣉⡷⢸⣏⣻⠀⡇⢸⣍⡁⠰⣏⣁⠀⠀⠀⠀⠙⢦⣈⡉⠙⠙⠻⢿⣷⣄⠀⠙⣯
⡤⡀⠙⠇⣢⠆⠀⠀⠉⠓⠺⠿⠃⠀⠀⠀⠀⠀⠻⠖⠃⠘⠶⠆⠘⠈⠃⠘⠃⠓⠀⠃⠘⠶⠆⠐⠶⠛⠀⠀⠻⠛⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠀⠀⢉
⠓⠃⢠⠀⠁⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠁⠒⠒
⠠⣀⠀⠀⠀⠀⣀⠀⠙⠦⣰⠟⣁⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⢀⠂⠟⠉⠻⡽⠀⠁⣴⣪⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣯⣟⣿⣿⣿⣿⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⡄⠀⠀⣺⣿⣯
⡀⠀⠀⠊⢠⣄⣀⠀⠀⠀⠀⠉⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠟⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⢿⣿⣿
⠻⣤⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠰⠿⠻⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢄⡀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠤⣀⠀⠀⠀⠈⢿⣿⡏⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠰⢯⡔⣀⣌⢁⣴⣤⠀⠀⠀⠀⠀⠀⣾⠛⣿⡆⠹⣆⠀⠀⢀⠔⠁⠀⠀⠀⢀⣨⣆⣲⣆⡀⠈⠉⢀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠛⠀⠙⠁⢀⡤⠐⠒⣀⣰⣿⡄⣿⣿⠀⠸⠀⠀⠎⠀⠀⠀⠀⠀⢠⣾⡿⡿⢿⣿⡆⠀⣯⣿⡿⣿⡾⠇⢸
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠄⠀⠘⢳⡶⠀⠀⠀⠔⣡⣴⣾⣿⣿⣿⣿⠷⢿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣧⣄⣸⡇⠀⢿⡿⣷⡿⢦⡄⣺
⠀⠀⠀⠀⢀⠀⠂⠈⠁⠀⠀⠸⠷⠂⢈⣷⣄⠀⢨⠾⠟⠻⠛⠟⠙⣛⣿⣶⣾⡆⠀⠀⠀⠀⠠⠂⠉⠈⣰⣄⣀⠈⠙⠿⣿⡿⠀⣀⣀⠑⠋⠉⠊⢊⣁
⠀⠀⣤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠓⠶⠶⠶⣿⢿⣿⣿⠧⢠⠄⠀⠀⠀⠁⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⢠⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡤⡀⠀⠀⠀⠀⠀⠀⠸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣪⢓⠄⠀⠀⠀⠀⠀⣧⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠫⠈⢀⠀⠀⠀⣰⣿⡿⣧⣀⠤⠴⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣞⣿⣸⠃⠸⠀⠀⠀⢸⣿⣡⠞⣿⠖⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢫⣼⣏⠀⣼⡇⢀⠄⠚⢻⣅⣀⡀⣀⠀⠐⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠶⢽⣷⣼⣿⣿⣷⣤⠂⢀⢿⡏⢀⡀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣿⣿⣯⣿⣿⣿⣵⣏⠀⠙⠲⠶⣶⣥⡶⢿⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣤⣤⣬⣿⣿⣿⣿⣿⠏⢹⣿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡀⠉⠃⠐⠀⢰⣾⠿⠛⠉⠉⠙⣻⣧⡾⠟⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⣁⠤⠀⠀⣠⠔⠋⠀⠀⠀⠀⢤⣸⣿⣿⣿⣿⠃⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⡿⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡝⣋⡏⢨⡀⠠⣠⣾⣠⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠲⣼⣯⣙⣿⣟⣿⣿⣿⣿⡿⠁⠀⢰⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠀⠀⠀⠀⠀⠈⠿⣿⣹⣿⣏⣠⣿⠿⠀⠀⠀⡄⠛⢿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⡴⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠻⡁⠀⠀⠀⠀⠁⣴⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣀⠢⠀⠀⠀⠀⠠⣾⣿⣿⣧⠀⠀⢀⠀⠴⢦⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣷⣿⣖⣲⣴⣾⣵⣟⣈⡿⠧⣀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢬⣩⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢉⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⢀⣿⣿⡃⠀⠀⠀⠀⠈⢹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣥⣶⠿⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣏⣽⣦⣼⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⡀⠀⢦⠀⠀⡇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⢦⣄⣸⡰⠄⠐⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠐⠒⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣧⠀⠀⢀⠀⠀⠐⢾⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠇⢘⡷⠂⠎⠀⠀⠀⠈⠧⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣑⣦⣀⡤⠊⠉⠉⠛⢗⠌⡀⠀⠀⠀⢀⡘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠒⠈⠁⠉⢩⠉⣠⠟⠉⢸⡄⠀⠀⠀⣇⢸⠄⠈⠛⠀⠀⠉⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠞⠃⠀⠀⠘⢟⠆⣰⡟⢹⠗⢄⣀⣀⠀⠀⠀⠀⢀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⠞⢛⡶⠁⠀⠉⠉⠑⢤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢰⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⢀⡄⢠⠧⠀⠂⢠⠞⢁⠹⡀⠀⠝⠉⠁⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⡀⠚⢴⠀⠀⠀⠀⣏⡅
⠀⠀⠀⠀⠠⠆⢄⣀⣀⡀⣀⡀⣀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠰⣄⠐⠒⠋
⠀⠀⠀⢠⡀⠚⠉⠀⠀⠀⠀⠀⠈⠓⠂⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⣠⣶⠶⢸⠁⠀⠀⠀⠀⠻⡂⠓⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⡀⠀⠀⣸⡀⠀⠀⠀⢀⣀⡏⠓⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠛⠁⠀⠀⠀⠂⠁⢀⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣒⠀⡄⠀⢰⠀⠀⠀⠀⢠⡸⡶⠋⠀⠀⠀⡀⠀⠈⠂
⠀⠀⡀⠀⠀⠀⠀⠈⠁⠉⠃⠀⢀⣤⣄⠀⠠⠤⠾⠃⠀⠀⠀⠀⠀⠈⠠⠀⠀⠡
⠀⠀⠀⠀⠈⠑⠢⢤⣠⢤⠖⠈⠋⠀⠀⠁
⠀⠀⠀⠀⢀⠄⠈⠀⠀⠈⢁⡀⠀⠀⢀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⣁⢰⠀⠀⢰⢈⢀⡁⢈⢠⠅⣨⠀⢈⠰⡁⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠶⠂⠉⠁⠀⠀⠀⠀⠥⠺⠀⠠⠜⠨⠠⠔⠫⠘⠂⠙⠀⠨⠀⠵⠀⠀⠀⠀⠀⣀⡀⠈⠓⢾⡷⠧⠦
⠀⠀⠀⠀⠀⠀⢴⠀⠀⠂⠀⢦⣁⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⢿⡆⣁⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⠊⠬⠙
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣄⠀⠀⠠⠃⠀⠀⠁⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⡸⢁⡶⢷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠁⠛⠉⠁⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣩⣠⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣦⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢧⡀⠀⣋⣀⣀⣀
⠀⠀⠀⠐⠂⠤⠄⢀⠈⠀⡄⠁⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠡⠃⠉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣣⡈⠁⠀⠷⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⢣⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⣠⣾⡟⢸⣿⡷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠆⠐⠂⣉⡟⠃⢀⢸⢸⡇⠀⠉⠉⠒⠲⠦⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⢀⣴⠋⠀⠀⢈⡞⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣴⠟⡇⠀⠀⠀⣼⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⡀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⢀⣴⡿⠁⠀⠆⠀⠀⣀⠏⠀⣬⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠉⢻⠶⣤⣤⠀⠈⠉⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠄⠀⢡⠏⠀⠀⣠⡦⠶⣾⣁⠀⠀⣿⠀⣌⡀⠀⠀⠀⠀⢲⠄⠀⠀⠀⢘⣷⡤⠄⠙⣦⡙⢿⣦⣄⡀⠘⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡎⡀⠀⠉⠀⠀⠀⠀⠉⠓⣼⣿⠾⠿⠿⣷⣦⣤⣄⣤⣾⠀⠀⡀⠸⣿⣿⡀⠀⠈⠛⣎⢣⠈⠛⢍⠀⠛⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠁⠀⠀⠙⢷⡀⠉⠉⠂⠀⡇⢀⠏⣿⣯⣄⢀⣐⣻⡀⢣⡀⠀⠹⣦⡀⢠⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠟⡇⠀⠀⠀⠈⠀⠀⠀⠀⠘⢸⡀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠰⣷⡎⠀⠹⢿⣷⡀⠈⠙⣧⢠⠑⢦⣦⡬⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⠈⠁⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣿⡄⠀⠀⢸⡿⣷⡀⠀⢹⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⡀⠃⠀⣀⣀⡤⠾⢧⣀⠀⠀⠀⠞⢸⣷⡶⢶⣦⡼⣿⠁⠀⠀⠇⠀⢿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢻⣿⡟⠉⠀⠀⠀⠀⠈⠙⢶⣢⡴⠋⠉⠈⠉⢮⠱⡘⡄⠀⢠⠀⠀⢸⡗⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⠈⠈⠃⣤⠘⢾⣾⠀⠀⢸⠃⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣦⣤⣾⠀⠀⠀⠀⠀⠠⠀⠀⢰⣿⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠉⠂⡠⣿⡇⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⠀⠈⠀⡑⡆⠀⠀⢀⡀⠀⣰⠛⠂⠀⠀⠀⠀⠁⣰⠃⠀⠀⠀⠀⠹⣿⠘⣄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢄⠈⠀⠲⣶⣤⠀⠀⠉⠳⠂⠀⣀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⠚⠷⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠄⡄⠘⡔⡠⡄⢊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⡶⠂⡀⢰⠀⠀⡀
⠀⠀⠀⠀⣰⠐⡋⡈⠳⡠⠒⠃⠰⢈⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠃⠺⣀⠴⢂⠋⠀⡐⢠
⠀⠀⠀⠀⠸⣈⡇⠑⠒⠶⠀⡅⢘⠘⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠞⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢒⠈⠈⠄⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁⠠⢄⢠⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠊⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⣀⡰⠎⣡⠀⠀⠀⠁⠀⠀⠀⠀⢢⣎⠀⡄⢀⠀⠀⠀⠀⠁⢠⡄⢀⠀⢈
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡆⠈⢅⡀⣖⠙⠇⢀⣄⣠⢨⡇⠈⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠏⠲⠄⠀⠁⠊⠀⠙⠒⠂⣠⠗⠀⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠓⠀⠁⠀⠀⠀⠀⢠⠎⠁⠀⠀⣀⣹⠗⡄
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠁⢀⣖⠈
⠀⠀⠐⣌⣆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢢⣅⣀⠂
⠀⠀⢦⡈⠹⣆⠀⠀⠀⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀⠀⡀⠔⠉⠹
⠀⠀⢠⡉⠓⢀⣀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⠞⠀⠛⠿⢦⣭⣤⠤⠂
⠀⠀⠀⠙⠠⣈⣻⡄⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⣀⠩⠿⠦⣶⠀⠀⠀⠀⠀⠀⠀⢀⢀⠐⠂
⠀⠀⢀⠔⠻⠟⠻⣂⡆⠀⠑⣴⣣⠔⠒⠀⠀⠉⠉⠁⠩⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠎⣸⣇⠺⠿⠀⠁⠀⠀⠈⡧⢀⣀⠀⡀⠀⠠⠄
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠛
⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⡤⠄⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠉⠀⠤⠀⠤⠤⠚⠁⠀⠀⠀⠀⠀⢀⣀⠀⢀⣴⣟⣡⠶⠖⠓⠂⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡎⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠙⠏⠀⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⠀⠎⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⠠⢇⠀⠉⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠘⣪⡾⠟⠻⢤⣀⣀⣀⠠⠛⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠒⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⣠⠔⠣⠤⣀⣠⣤⠶⡿⠁⠀⠀⠀⠀⠈⠉⠛⠃⠤⣤⣄⡀⠀⠀⠄
⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠗⠤⠤⠤⠤⢔⣒⣈⡽⠋⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠠⡄
⠀⠠⠼⣣⠄⠀⠀⠀⡀⠀⠀⠀⠈⢿⣆⠀⣄⣀⠀⢀⠤⠀⠀⠀⢠⡴⠊⢁⠈⠉⠛⠦⣠⠇
⠀⣦⣴⠀⠀⠀⠀⠈⠙⡤⠤⠤⠤⠄⣁⠀⠀⠀⠛⠳⢄⣀⣀⣠⢋⢀⡰⠃⠀⠀⠀⠀⢛
⠀⢿⣡⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣞⡁⠀⠀⠀⠀⠀⠀⢻⠉⠹⠾⠚⣷⡀⠀⠀⠀⠀⢸⣆⡀
⠀⠈⠃⠑⠂⠀⠀⣠⣇⣠⡤⠞⠋⠈⢲⠄⠀⠀⠀⠀⠀⣸⠖⣺⡶⢠⣼⡏⠀⠀⣀⣤⡾⠉⢿⣿⡛⠉⠉⠙⠀⠂
⠀⠀⠀⠞⠒⠂⠀⠀⠈⠈⠁⠀⠘⠃⣸⡇⠀⠀⠀⠀⠐⣻⠃⠀⠸⢦⣌⣈⡙⣉⠽⠚⠁⠀⠸⡎⠙⠢⣀⠀⠀⠀⠀⠈
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢤⣅⡀⠀⠀⠀⣨⠋⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢰⣇⠀⠀⠙⢷⡄
⠀⠀⠈⡷⡀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢿⠀⠐⠀⠀⠉⠠⡄
⠀⠀⠀⠀⠁⠐⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⠙⠦⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⢿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢤⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡴⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⢦⣠⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⡴⠂
⠀⠄⠒⠀⠐⠦⠦⠀⠀⡀⠀⠈⢄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⢀⡜⠙⠀⠀⠀⣠⠴⠂
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠠⣁⠝⣀⡠⠂⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡠⠔⠃⠹⡦⢄⣀⠀⠀⠀⢀⡿⠿⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡶⠋⠀⠉⠁⠂⠀⠠⠄⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢀⡽⠒⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠠⡇⠀⠀⠀⠀⠀⠀⢀⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠌⢉⣿⠀⠀⠀⠀⠀⢸⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⣦⠄⠀⠀⠀⠀⠀⠀⢀⣴⠃⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⢢⢈⠻⡈⠢⣄⣤⢶⡶⢁⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⢠⡤⠒⠋⣬⠀⠀⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣧⠀⠀⠀⠀⠀⡆⠀⠙⠦⣹⠧⢬⡵⠛⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠊⢥⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⡟⠀⠀⠀⠳⣄⠀⠐⠀⠀⠀⠀⠀⠀⠰⣼⠃⠢⠀⠀⡐⠛⠀⠀⠀⡷⠄⠺⢶⠦⣄⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠚⠃⡤⣄⠀⢇⡇⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⠶⠂⠀⠀⠀⢱⡞⠀⠀⠀⠀⠀⠀⠹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠌⠀⠀⠀⠀⠉⠈⠻⠎⠁⠆⠀⠀⠀⠹⡦⣀⠀⠀⠀⠀⠀⠀⠘⢧⡄⠀⠀⠀⠀⠀⣏⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⢿⠀⠈⣙⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠃⠀⠀⠀⠀⠀⠀⠈⠛⢦⡐⣄⣀⣤⡟⢈⢂⣠⠜⢛⠛⡩⠃
⠀⠀⠀⠀⠀⠹⡤⡀⠀⠀⢸⡆⠀⠉⠛⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⢨⠀⠈⢣⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠉⣧⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠒⠤⣘⡇⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠻⣤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢦⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢻⣄⡄⠀⠀⠀⠀⠀⠁⠰⣄⠆⣀⠀⢀⠄⢸⡆⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠽⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡄⠀⠀⠀⠀⠀⢧⠁⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠚⠋⠉⠁⠠⢄⡞⠁⠀⠀⠀⠀⠀⣠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠐⡆
⠀⠀⠀⠀⢂⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡀⠀⠀⠀⣸⡇⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠠⠎⠁⠀⠂⣁⣀⢀⡀⡐⠂⢸⣡⠀⠤⡀⡄⢠⣀⠄⠀⠀⠀⠀⠀⠳⢤⠒⣁⠝⢳⣤⡼⠉⠛⠂⠀⠀⠘⣅⠀⠰⡄⠊⠁⠁
⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠰⢂⠠⡀⠀⠀⣤⣼⢸⣿⣷⠄⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠣⣙⡆⠀⢿⣿⠸⠟⠋⠉⠉⠙⠀⠀⠀⠀⣄⡄⠀⠀⣠⠤⠶⠿⠶⢄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⡀⠈⢁⡠⠒⣒⠋⠑⠂⢀⡐⠂⠀⣄⠀⠠⣿⠃⠔⠨⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠙⢆⣠⣤⣤⠓⠲⠲⠍⠻⣷⡄⠀⠙⠀⢀⡼⣿⣿⠋⣿⣃⡀⠀⠀⠀⢁
⠀⠀⢀⣠⠴⠶⢀⠃⣼⠓⠾⠿⡽⣿⣶⠇⠀⠀⠟⠀⠠⣥⣾⡿⣷⣾⡟⠻⠿⠛⠙⠀⠀⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡈⢻⣿⣣⣤⡄⠈⠀⣤⣄⣀⠀⠀⠀⢀⡉⠉⠄⠐⠒⢥⣼⣏⡉⠀⠓⠂⠄⡀⠁
⠀⠀⠀⢀⣴⠛⢃⣠⠿⣿⣿⠿⠷⠔⠁⡑⡄⢀⣀⠀⣠⣄⢀⡅⣘⣿⣰⡆⢼⣿⣷⠟⠁⠀⠈⠃⠀⠚⠳⣴⠄
⠀⠀⠀⣿⠃⠀⠀⢻⣦⣼⣷⠀⠀⠀⠸⠀⠐⠢⣄⠠⠀⠈⠉⢠⣧⣽⣿⣟⣛⣿⢇⡴⢡⠀⠀⢠⠈⡄⠀⠀⠡
⠀⠀⠀⠃⠀⠀⠀⠀⢻⠗⠛⠁⠀⠀⠀⢠⠃⠀⠀⠑⠠⢤⠄⠈⠀⢀⣾⠿⠟⢻⡏⠀⠀⣴⡄⢠⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡏⠛⠛⠆⠀⡼⠃⠀⠀⠀⠃⠀⡴⠛⠻⠞⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⢀⣟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⣠⣴⣒⡶⠖⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⢀⣴⣶⣶⣶⣇
⠀⠀⠀⠀⣠⢿⠉⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⣹⣿⣦⡀⠀⠀⠀⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾⣹⣿⠋⠙⢿⣷
⠀⠀⠀⢠⡏⡏⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣀⣤⡾⠏⠉⠀⢿⡇⣷⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⣦⣄⠀⠀⠀⢘⣿⣇⢀⢀⣿⡟
⠀⠀⠀⣸⣴⠃⠀⠀⣀⣄⣾⠛⢦⡀⠀⠈⠉⠉⠀⣀⣄⣸⣾⡇⠸⣼⠇⠀⣀⡤⣤⣀⣴⣶⡶⢦⡄⠀⡀⡎⠀⢼⣿⣿⣛⠓⢤⣀⠉⠛⠿⠋⠁
⠀⠀⠀⠿⠁⠀⠀⡼⠟⣿⣼⠃⠀⢿⠀⠀⠀⣴⢿⣿⡿⠛⢿⡄⠀⠉⢠⣶⡟⠀⠀⣿⣿⣿⣧⣀⣿⣋⠟⢢⣀⣈⣙⢹⠿⣦⠤⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡗⣦⣾⣁⢀⣠⡏⠀⠀⢰⣇⣿⣿⡁⠀⣸⡇⠀⠀⠘⣿⣿⣶⣶⣿⣱⡽⣿⣿⣿⣿⣤⣾⠏⠉⢿⣿⡄⠘⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠑⠬⣹⡿⠟⠋⠀⠀⡀⠀⠻⢿⣿⣿⣶⡏⠀⠀⠀⠀⠉⠻⣿⣿⡛⠛⢻⣿⡿⣤⣴⣿⣿⣷⣤⣾⣿⣷⡀⠈⠯⡀⠀⠨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣼⣯⣼⢟⣯⣿⢿⣿⣿⣿⣯⠻⣇⢄⡄⠑⢆⡀⣿
⠀⠀⠀⠀⠀⠀⣠⣤⠶⠦⣄⣀⣠⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⣶⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠛⠿⠿⢷⣿⡅⠀⢹⣿⡇⠀⠙⠷⢷⣤⡙⢿⡆⠀⡠
⠀⠀⠀⠀⠀⢰⣿⣟⣦⣀⣸⣧⣠⢆⡀⠀⠀⠀⢰⡟⣻⣿⡛⠛⠻⡆⠀⠀⠀⠀⣀⣈⣉⡱⣻⣶⠶⢶⣌⠻⣷⣤⡾⡏⠀⠀⠀⠀⠀⠈⠁⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠘⣿⣾⣻⣿⣿⣿⣧⢤⣽⣆⠀⠀⢸⣿⣿⣿⣅⠀⢠⡇⠀⠀⢠⣾⣿⠿⠿⣿⣿⣧⣤⣼⣿⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠤⣠⣼⡿⠁
⠀⠀⢀⣤⣤⣴⣩⡿⠿⣶⣿⣿⣟⠻⢿⡟⠀⠀⠀⠙⠻⠿⠿⠾⠋⠀⠀⠀⢼⣿⡁⠀⣴⣿⣽⣿⣿⣿⡿⠁⠀⠀⠀⠀⡠⠔⠈⠀⣼⡿⢏⡿⠃
⠀⢠⡿⠁⠀⢸⣯⣄⣀⣿⣿⣿⡿⠿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠛⠿⢿⣿⡟⠛⢻⣿⡇⠀⠀⠀⠀⣀⣈⠂⠀⣬⣭⢛⣰⡿⠃
⠀⠘⣿⣀⣶⣾⣿⣿⣿⣽⣧⣾⣀⣀⠘⣿⠀⠀⠀⠀⠀⠀⣰⣏⣥⣦⣈⠛⣆⠀⠀⠸⣿⣅⠀⢀⣿⠏⠀⠀⠀⠚⠁⠀⣐⡾⠋⣀⣾⠟⠁
⠀⠀⠻⣿⣿⣿⠿⠋⠛⠛⢻⣻⣿⣿⣯⡿⠂⠀⠀⠀⠀⢰⣿⡟⠿⣿⣿⠆⢻⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⣰⡦⢀⡤⠚⢁⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⢻⣻⣷⣿⣧⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣯⣼⣽⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠂⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡌⠀⢀⡞⠁
⠀⠀⠤⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⢣⣁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠠⡀⠀⠀⢱⡀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⢷⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⣀⡴⠶⠯⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠤⠤⠴⠎⠋⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢀⣠⣶⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠢⣀⠀⠀⠀⠀⠀⠀⣾⢀⡤⠞⠛⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⢳⣤⠀⣀⣀⡼⠿⠿⠯⢤⣤⣤⣀⣀⣀⠐⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠀⠚⠲⢄⡠⠋⡍⣷⡎⠉⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡿⢾⠁⠀⠀⠀⠀⠀⡇⢀⢳⠟⠀⠀⠀⠀⠀⠀⠈⡿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⠀⠀⠀⠀⠀⠀⠀⡘⠀⡆⠈⠢⠄⣀⣀⡄⣸⠇⣩⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠞⠙⢦⠀⠀⠀⢀⣠⠃⠀⠸⣆⠸⣽⠉⢉⢿⠃⡰⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⣀⣀⡀⠔⠁⠑⢀⠀⠀⢀⡗⠉⢰⡾⡖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⡂⣠⠜⠓⠒⠺⣧⣇⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠄⣀⣀⢰⣄⡨⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠈⠂⠛⢦⡀⠀⢀⠔⠈⠁⠀⠀⠐⣦⡝⠀⠉⡆⠀⠉⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⠐⡆⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠗⠂⠀⠈⠀⠀⠀⢰⠒⠁⠀⠄⠀⠁⠀⣀⣤⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠻⠷⠶⠶⠟⢀⢢⠀⡀⢀⣀⣀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠳⣏⠁⣉⠙⣋⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢰⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢫⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡢⢤⣾⡋⠙⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠋⠀⠈⠳⡀⣸⠓⠀⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡿⠚⣷⡈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⡄⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⡖⠋⢦⠐⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⢓⣀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣽⣧⣱⡎⠀⠘⠇⠀⠀⢀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠶⣆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⣀⣀
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢂⣠⣤⢤⣤⠤⠤⣄⣐⣄⡀⠀⠀⢀⠠⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡽⠋
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡄⠂⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠒⠉⠁⢠⠇⠀⠀⠈⢆⠀⠀⢠⠀⠀⠀⠀⢀⣴⠁⠄
⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⣀⣀⠴⡏⠀⠀⠀⠀⠀⠙⢲⣆⡀⣤⡀⠐⠉
⠀⠀⠙⠦⣤⣀⠀⣀⡠⠈⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⡶⢋⡠⠴⡿⠛⠉⠺⡅⠀⠀⠀⠀⠀⠀⠀⠙⣤⡂⠄⠑⠊⠁
⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⡠⣀⠀⣷⠀⠀⠀⠀⠀⠠⠶⠭⣀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⢀⣀⢠⡃⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢿⢆⡀⠀⠀⠀⡀⣀⣘⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣴⠖⠉⠀⠀⠀⠀⢠⠔⠋⠁⢘⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡙⠒⠤⣼⡄⠙⠉⠰⠁⠀⢀⠁⠀⠀⢀⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⠬⠃⠀⠈⠀⠀⠀⢈⢠⠁⣘⣁⠀⠦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣄⣙⡶⠏⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠈⠃⠉⠙⠧⠀⠘⠀⣠⣀⡀⠀⠀⢀⡄⣸⡟⠃⠀⠀⠀⡀⠀⠀⠀⠈⠀⡀⠀⠀⠈⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠂⠰⠦⣄⠀⠀⠀⠀⠀⣠⠤⢤⠞⠁⠈⠙⠆⠈⠁⠈⠐⠀⠀⠀⣠⢀⡗⡴⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⣉⠷⠶⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⠄⠈⠁⠀⠀⠀⠸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠶⠴⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠖⠶⠦⣄⡀⠀⠀⢑⣾⠷⠲⠂⠄⢀
⠀⠀⠀⣰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠨⢶⡄⠉⠀⠀⠀⠀⠀⠀⠡
⠀⠀⢀⠤⠂⢀⠠⠊⠀⠀⠀⢀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢴⡶⢏⢠⠲⠐⠀⠀⠀⠀⠀⠀⠳
⢠⠀⠋⠀⠀⡀⠠⠶⠤⠰⠂⠤⠀⠘⠶⠀⠈⠃⠘⠀⠒⠔⠀⠠⣀⣤⠤⢒⡶⠛⢉⠤⠋⠁⠞⠁⢰⣟⡃⣳⡇⠀⠀⠀⠀⠀⠀⡇
⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⡔⠋⡠⠶⠊⠀⠀⠘⡏⢡⣥⡤⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠑⠀⠀⠀⠠⠖
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣰⢦⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠔⢁⣆⣸⠀⡀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⠃⣔⡯⠔⠁⡀⠜⢋⢰⢀⡀⠀⠀⣀⡀⠀⠒⠶⡈⣯⠰⡆⠀⡤⢤⠀⢲⡄⠀⣠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡇⠀⠈⠀⡄⠈⠀⣠⠆⠰⠾⠔⠧⠘⠛⠐⠚⠇⠒⠁⠙⠛⠉⠉⠀⠈⠉⠉⠁⠈⠉⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠙⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢀⠁⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠈⢣⡼⢃⠀⣀⡈⠲⡀
⠀⠀⠀⠀⠀⠀⠙⣭⡄⡀⠀⠀⠀⠀⠘⣷⠈⠀⠀⠈⢱⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠒⢧⡝⣢⣁⠀⠀⣀⣀⣼⠁⠀⠀⠀⠀⢀⣠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠂
⠀⢀⠀⠀⠀⠀⠈⣹⠟⠉⠁⡠⠞⠙⠻⣀⠀⠀⠀⠀⢠⣿⠐⠆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣨⡆⠀⠀⠀⡸⠉⠀⠀⣀⠀⠀⠀⠀⢸⣇⣀⠠⠔⠋⠁⠔⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠈⠧⠰⠀⣀⣷⠀⠈⠡⣮⠓⡀⠀⠠⢸⡏⢻⠾⠖⠺⠙⠄⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⢀⢀⠁⡀⣆
⠀⠀⠀⠀⠀⠈⠉⠁⠀⡀⠈⠈⠁⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⡈⠛⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠢⠠⠤⠔⣻⣿⡀⠀⡀⢀⡠⠄⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠹⠃⢩⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠏⠈⠁⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⣰⡿⠧⡔⠓⠋⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠤⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠁⠀⡰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠈⠀⠀⠉⢈⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣠⣦⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠉⠻⢦⣀⡀⠀⠀⠀⠀⢠⡘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⣄⠀⢠⠀⠀⠀⠀⠀⠈⠉⠙⠻⣋⠋⠀⠘⢇⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠀⠀⠘⢿⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠣⠀⢶⣄⣀⡀⣀⣀⣠⡼⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⡒⠐⠀⠀⠀⠀⠈⣤⣀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡄⠀⠸⡆⠈⠋⠉⠛⠃⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡇⠐⠀⠀⠀⠀⠀⠸⣿⠒⠄⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣄⠀⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⡿⠗⠐⠂⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⡿⠛⠀⢀⠴⠉⠀⡄⠀⠀⠀⠀⠘⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠙⣿⣿⠀⢀⣰⠉⠀⠀⢀⣿⣦⡄⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠐⠿⣿⣿⣿⢧⣤⣟⠀⠀⠀⢀⣾⣯⣿⠗⠀⣼⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣆⠀⠑⠂⣠⣾⣿⠋⠀⢸⣿⣿⣀⡴⠋⠁⠉⠉⠐⠿⣿⣧⣶⣖⣄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⢉⣿⣆⣀⡤⣿⣿⣿⣦⣴⣾⣿⣿⣿⠶⠖⠖⠒⠀⠲⢀⣽⣿⠿⢿⣿⣿⡏⢀⠀⠘⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣤⣶⡦⣤⣶⣿⣿⣿⣶⣾⣿⣿⣷⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠶⠺⣿⣿⡏⠉⢹⣿⡟⣉⣩⣽⣿⣮⠙⠉⢠⠞⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠩⣿⢷⣴⣾⣿⣇⢻⣿⣿⡟⠁⢠⣴⣿⡄⢀⣿⣤⣠⣿⣏⣿⣿⡏⠉⣻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠻⣿⣿⡏⠙⢧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢷⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣾⡇⣰⠟⣽⣧⠘⣴⣿⣿⡏⠙⣿⣿⣿⣶⡾⣿⠻⣲⡤⡀⠙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⣿⣇⣾⡟⠉⣠⡾⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣧⣀⡀⠉⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣄⣀⡀⠀⠀⠁⢠⣾⣿⣋⣁⣸⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣅⣈⠛⢿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⣿⣿⡿⠀⠀⠀⠉⣙⣿⣿⣽⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣆⣀⣀⣥⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠂⠁⣀⠸⣿⣿⣿⣿⡿⠃⠀⢀⡤⡶⠋⢉⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⠟⡙⠤⡀⠁⠄
⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⣈⣿⣿⡟⢁⠄⠈⠀⠀⣠⣴⣿⢿⣟⣿⠟⠻⣿⣿⣿⣿⣿⣿⣤⣾⣿⠄⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠻⢿⣧⣤⣤⣶⣶⣶⣿⠋⠀⣸⣿⣿⣦⣴⣿⢿⣿⣿⣿⣿⡟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⠯⣿⣿⣿⣿⠟⡛⠻⣷⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣿⣿⣿⣿⡏⠉⣿⣿⣿⣉⣾⢟⠁⠀⠀⢠⠍⠙⠀⠐⠀⠸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⢻⣿⣿⣿⣿⣷⣶⣿⣿⡗⠁⠁⠈⠁⣄⠀⡀⠀⠀⠀⠀⠀⠸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠉⡐⠋⠛⢻⠻⢿⠇⢀⣰⠀⠀⠂⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡁⢸⡟⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠒⠀⠀⠀⠀⠀⠛⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂

⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⢳⠒⠒⢶⡀⢄⠲⢆⠚⠙⡻⣤⠀⠈⠀⠙⣏⠒⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢂⠀⠀⠱⡄⠁⠊⠳⡀⠀⠀⠳⡀⠀⠀⠘⡆⠀⠹⣇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠓⣬⣆⠀⠀⠹⠀⠀⠀⠉⠀⡀⢀⣐⣀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⡉⠲⠒⠦⠶⢤⠖⠒⡟⠉⠉⢀⠏⠀⢆⣀⠀⢻⠀⠀⠌⡀⠧
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣀⠀⠀⠀⠈⠀⡀⠊⠀⠀⢠⠂⠀⡠⠂⣁⣀⡀⠉⠈⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁⢀⣼⠡⠋⠀⠀⠈⠷⠸⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠰⠶⠁⠀⠒⠀⠉⠁⠀⠀⠀⠀⠀⢂⡴⢄⠑⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⠃⠀⠉⠒⠨⠭⣀⠘⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠓⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣨⡜⠱⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⢳⠂⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣀⠀⢀⡤⠖⠀⠒⢲⢀⡤⠶⢶⡉⡇⠉⠓⢟⠳⡄⠀⠀⠀⠀⢹⡆⠀⠘⠈⠶⢦⣀⠀⠀⠀⠀⠀⠈⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠁⠀⠀⠀⠀⣠⠞⠀⠀⠀⢡⡇⠀⠀⠀⠱⡙⢄⠀⠀⠀⠀⠳⣄⡆⠀⠈⠀⠉⠉⠙⠋⡓⠐⡂⠀⠬⠶⣤⣤
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡀⠘⠁⠀⠀⠔⣁⠸⡆⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠈⠳⢤⣄⠀⡀⠀⠀⠀⠁⡀⠰⡀⢀⡄
⠀⠀⡇⠠⡞⡿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠠⢸⡇⠠⢄⠈⠀⠀⠀⠀⠀⠜⠉⠣⡘⠄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠉⠓⠾⠴⣄⠈⠦⠴⠄⠚⠉
⠀⠀⡇⠀⠙⢷⠀⠘⣷⠀⠀⠀⠀⠀⢠⣴⠷⠛⠁⠈⠁⠒⠐⠲⠿⣧⣀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⢷⠀⠀⠰⠦⠠⠝⠁⡀⠀⢀⡖⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠈⢧⡀⠀⠀⠀⡈⠃⠀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣆⠀⠀⠀⠀⢀⠜⠛⠁⠀⠀⠉⠉⠉⠙⠳⢦⣄
⠀⠀⠀⠈⠳⣤⣄⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠁⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⡇⠀⠀⠀⠀⠀⠠⢒⣰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢂⣠⣤⠖⢃⡾⣧⡘⠂⠀⠀⠀⠀⠀⠀⠀⢺⠀⡾⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⠶⢤⣄⠌⠈⠀⣙⡳⠀⠀⠀⠀⠀⠀⢐⠟⢸⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⢤⢤⡄⠀⠀⠀⢘⠇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠄⠈⣿⣀⣰⠉⡀⠅⠀⠀⠀⠀⣠⡿⠀⠘⣇⠀⠄⡀⠀⠀⠈⡘⠛⠛⠉⠀⢀⣿⠁⠀⠀⠀⠌
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣄⡁⡀⡔⢄⠀⠀⠀⣠⠞⠋⠁⠀⠀⠹⣦⡀⡀⠀⠀⠈⣽⣀⣀⡦⠖⢊⠡⢈⠀⡠⠊
⠀⠀⠀⠈⠳⣄⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠛⣿⠖⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣀⠀⠀⠈⠁⠄⡆⠀⢂⠁⠀⠈
⠀⠀⠀⠀⠀⠸⢮⣙⠓⠶⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢱⠖⠒⠒⠓⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁⢀⠀⠀⠀⠀⣀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠁⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠄⡀⠀⢘⡙⠷⠒⠋⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠘⠛⠲⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⣀⠂⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⡤⠒⠒⡶⢏⠀⠀⠀⠀⠀⠀⠘⠄⠀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢭⠣⡐⠀⠀⠀⢠⠃⠀⠀⠀⠀⠐⠶⠲⠒⠂⣄⢀⢀⠄⢀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠙⠖⠛⢓⣡⡄⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢁⡀⢠⠤⠇⠀⠀⠀⠀⠀⠉⠀⢩⡚⠀⠁⠈⠛
⠀⠀⠀⠀⠒⠳⡄⠀⠀⠠⠚⣄⠀⠼⡅⠳⠋⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢠⢠⠀⠁⡤⠤⠆
⠀⠄⠀⠀⠂⠂⠘⠛⠉⠙⠛⠙⠃⡈⠀⠉⡄⠀⢈⠤⠠⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⠈⠂⠀⢀⠄⣠⡤⠑⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠈⠠⡄⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⣰⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⣲⠤⡀⣀⡠⠚⠀⠀⠀⠀⡔⠞⠀⠀⠀⠀⠉⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠃⠀⠀⠀⠈⠁⠀⠉⠙⠤⢀⠀⠀⡠⠒⠒⢢⠀⠀⠀⠉⣏⡀⠀⠀⠀⠀⠀⡄⠐⡒⠁⠀⠀⠀⠀⡀⠀⢠
⠀⠒⠂⠀⣀⣑⡀⣠⡂⡀⠀⠀⢀⠀⠀⠀⠇⠀⠀⢈⢋⠀⠀⠀⠀⠀⠀⠱⠀⠤⠖⠉⠀⢀⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣔
⠀⠀⠀⠀⠈⡽⡀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠀⢰⠴⠒⠁⠀⠀⠐⠶⠖⠆⠀⠀⠐⠀⠀⢠⠎⠀⠀⠙⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠑⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⢀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⠀⠀⠀⠂⠀⠘⢢⠀⡀⠀⠄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢀⠀⠂⠀⢂⠀⠄⠀⠀⢈⡠⠊⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠄⢀⡀⠠⠒⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠄⠲⠀⠘⠀⠀⠀⡤⠀⠒⠒⠈⠉⠁⠀⠐⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠂⢂⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠞⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠉⠀⠨⠁⠒⠂⠐⠢⢄⣹⡒⢤⡀⠀⢀⡀⢤⠤⠖⠒⠠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠈⢉⠁⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠀⡀⢀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠱⣄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢘⠀⠀⠂⠀⠀⠀⠀⠀⡎⠀⠔⠀⠀⢠⡀⠀⠀⠱⡄⠀⠀⠀⠀⠉⠀⠀⢀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠄⠀⠀⠀⠀⢃⠘⠁⠀⣀⠁⡁⠠⢄⣜⡅⠀⠀⠀⠀⠀⢃⡄⠀⠀⢈⣦⠔⠉⠠⢀⣠⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⢶⡡⣤⢁⠿⢄⡜⠈⠀⠀⠀⢀⠠⠀⠈⢌⠁⠢⠼⣘⡄⠔⡁⠋⢰⠖⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⢁⠌⠓⠨⣳⡂⠀⢵⠂⠀⠀⢐⠃⠆⠠⠂⢈⠕⠒⠒⢬⠽⠏⢬⠀⠺⢅⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⢣⡀⠀⢀⠈⠈⠉⡹⠢⠥⠶⢄⠁⢠⢓⠆⠺⠄⣀⣠⡆⠀⠀⡰⢄⠀⢀⣧⠃⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⢲⣀⢠⠉⠉⢩⠉⠒⢶⢅⡀⢠⡃⢀⡀⠘⠬⠄⢸⡀⠀⣠⠋⠙⡁⠀⢀⠿⡁⠀⢱⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⡄⠀⡱⡖⠈⢦⣠⠼⠀⠈⣡⡃⢠⠁⠠⡀⢸⠉⡗⠉⠣⡀⣀⠝⠲⠁⠀⠈⡒⢣⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣀⡈⢩⡀⠘⢲⡂⠑⢄⣉⡝⢁⣜⠃⠀⠀⢱⠚⢆⡸⠦⣤⠌⠑⢄⣠⠖⠐⡎⠀⣰⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠈⠙⡈⢋⠧⡈⣈⢇⣀⣌⣡⠏⠀⠀⠀⠈⢦⣘⢤⡠⠶⣀⣀⡴⠓⣄⠴⢛⠋⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣙⡀⠀⣠⠄⢢⡀⢾⠔⠁⠀⠀⠀⠀⠀⠀⠡⡀⠱⣄⣈⡆⠀⢐⡀⡠⢛⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠄⠓⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⠬⠯⢁⣉⠽⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⡄⠀⠀⠠⠀⠀⠀⢀⡔⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣿⡛⠒⠀⠀⠀⠀⠀⠀⠁⢾⣵⠋
⠀⠀⠀⢀⠀⠤⣤⣀⠀⠀⠀⠰⢧⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠙⠀⠀⠀⠀⠀⠉⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⢀⡲⣄⠀⠀⢰⢦⡀
⠀⠀⠀⠀⠀⠈⠳⠄⠘⣄⠈⢧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠁⠀⠙⣦⡀⠀⠙⡀
⠀⠀⠀⠀⠀⢀⡠⠀⠈⠉⠓⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠐⠂⠀⠴⠶⠖⢛⣭⣷⣤⡀⠀⠀⠠⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠙⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⢠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢨⡀⠀⠀⠀⠀⢀⡀⣀⡀⢀⡀⠀⠀⠀⠘⠌⠀⠀⠀⢺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠻⢷⣀⠑⠀⠙⠦⣄⠀⠀⠠⡰⣼⡀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⢶⣄⠀⠈⠳⣄⠀⠸⣿⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠑⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠉⠛⢆⠀⠸⠀⢰⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢷⡀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⡆⣠⣤⣀⠀⠀⠀⠀⠀⢈⣧⠱⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⡿⠉⠣⢿⢷⠋⠁⢦⠀⠀⠀⠀⡿⠾⠋⠛⢿⠒⠦⣤⣄⡀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡴⢿⠀⣸⣿⣧⠸⠿⣷⡲⣤⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢀⡀⠀⠀⠈⠁
⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠙⣸⡇⠀⠀⠘⡇⠀⠀⠁⠙⠋⠀⠀⠀⠀⠈⢻⣠⡼⠁⣀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠄⠀⠑⠉⠀⠀⠀⠦
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⡟⡱⠂⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠈⠉⠛⠐⢄⡀⠀⠀⠀⠀⠀⢸⡄
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⣳⡆⠀⠘⢧⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰
⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡅⠀⠀⠀⠈⠓⠤⢄⡄⠤⠚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠛⠉⠳⣄⡀⠀⠀⢀⣀⡤⢢⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠀⠄⣤⣶⣄⡀
⠀⠀⠀⠀⠀⠈⠙⠻⠶⠭⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⢰⣦⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⡿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⠈⠲⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠂⡀⠀⠀⠀⠀⠀⡠⠤⡄⠁⢈⡠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠲⠀⠀⢀⠔⠉⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡒⠃⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠋⠁⠐⠐⠀⠀⢰⡠⠉⠀⠀⠀⠀⠈⠅
⠀⠀⠀⠀⠀⠀⢠⠐⠐⠏⠈⠀⠟⠀⠐⠄⡄⠀⠀⢀⡄⠀⠀⠀⢀⣖⡖⠀⠀⢀⣌⠀⠀⠀⠀⠀⠀⠹⠂
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⢐⣤⠀⠀⠠⠐⠁⠈⠠⠀⠠⠀⠈⡨⡇⠀⣤⠁⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⣠⡀⠀⠑⠰⠀⠀⠀⠀⢠⠤⠒⠈⠀⠘⠓⠤⣶⠀⠂⣴⣳⣠⢠⠁⠀⠀⠀⠀⠐⡆⠀⠀⠀⢤⠀⠀⠀⣀
⠀⠀⠀⠀⠁⠄⡀⠀⠀⠀⠀⠒⠞⡁⠀⠀⠀⠀⠀⠀⠀⠌⠳⣆⠉⢀⠎⡬⠀⠀⣀⢀⣻⠌⠵⠊⠀⠀⠈⠀⠀⠀⠛⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⢠⡂⠀⠀⠀⠐⠀⠀⠠⠀⠀⡤⠀⠈⠳⣞⠒⣻⣦⠞⠁⠂⠀⠀⠀⣤⠂⠀⠀⠀⠀⢀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠘⣟⠻⢣⠀⠀⠀⠀⠀⠈⠀⠀⠩⠀⠐⠚⠠⢄⠀⠀⣀⠀⠀⠚⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢀⠀⢗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠂⠀⠐⠀⠀⠐⠀⠀⠠⠀⢀⡄⢀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠈⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⣄⠠⠘
⠀⠀⠀⠀⠀⠀⢦⡀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⢀⠡⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠃⠀⠄⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠐⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⠤⠤⣤⡴⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⡰⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠳⣼⡃⠀⠀⠀⠀⢀⡄⠀⠀⠀⠉⠀⣀⡀⣤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣇⡠⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠐⠀⠀⠀⠀⠏⠀⠀⠀⢠⠀⠀⠀⠁⠁⠀⠤⠃⠾⢀⠀⠀⠂⠠⡤
⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⠀⢀⠁⠀⠀⡴⢼⣀⡴⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠈⠀⠙⣄⣀⣠⣀⣁⢦⡀⢀⡓⠂⡍⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⢰⠐⠀⠀⠐⠒⠉⠡⣀
⠀⠂⠀⠀⠁⠀⠀⠈⠉⠀⠀⠉⠄⠁⠀⡀⠀⠐⠀⠀⠀⠒⠀⠢⠄⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⠀⠁⠀⢀⡄⠀⠶⠖⠈⠉⠂⠤⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢂⠀⠀⠀⡅⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢒⠥⢤⠀⣀⡠⠋⠀⠀⠀⠀⣠⠚⠃⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠉⠀⠐⠉⠝⠠⠀⠀⠀⠀⠰⠂⠂⢦⠀⠀⠀⠈⢹⡃⠀⡀⠀⠀⠀⠀⣀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠶⠤⠄⠀⠈⢂⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠛⠁⠀⠈⠀⠀⠀⠀⢣⠀⢀⡤⠞⠉⠁⡀⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠋⠈⠠⣇⠂
⠀⠀⠀⠀⠈⢙⡏⠀⠉⠓⠀⠀⠀⠰⠂⠀⠀⠀⠀⢠⣀⠤⠔⠁⢀⠀⢤⣀⡤⡄⠀⠀⠘⠀⠀⠀⣀⠙⠀⠀⠻⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠨⣜⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠞⠛⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠏⠀⠀⠁
⠀⠀⢀⡀⠉⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣹⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠘⠐⠂⠒⠀⠘⠓⠛⠂⠀⠀⢀⡀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣘⠢⡘⣇⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠐⠊⠀⠠⢄⡄⠀⠀⠀⠀⠀⠀⠀⣩⠟⠀⠼⠞⢣⣀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⢀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠛⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⠀⠀⠀⣶⠋⠀⠀⢁⣷⢄⡠⠈⠛⠳⡴⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠸⣷⠖⠃⠀⠀⠀⠈⢦⡀⠀⠉⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⠅⡀⠀⠀⠘⠃⢠⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡀⠀⠤⠒⠈⠀⠀⠀⠀⠙⠢⣘⢁⡿⠄⠀⠀⠀⠀⠀⠻⣄⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠀⠀⠀⠀⠀⠀⣿⠢⣀
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⠈⠖⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠇
⠀⠀⠀⠀⠀⠀⠐⠿⡂⠀⠀⠀⠀⠀⠈⣆⠀⠘⠺⢷⡄⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢥⡀⠀⠀⢀⣠⣏⠀⠀⠀⠈⣥⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⢻⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡛⢧⣀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⢋⠙⠦⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠀⠃⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁
⠀⠀⠀⠐⠒⠀⠀⠀⠰⢈⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠠⠀⠀⠀⢀⡰⠆⠲⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⢁
⠀⠀⠀⠀⠀⠀⢰⠈⠱⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⡸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣗⠂⠀⠀⠀⢀⣠⠞⠀⣀⠀⠀⠀⠀⠀⢠⣖⠒⠒⣤⡌⠀⠀⠹⣄⡀⠀⠀⢀⠴⠃⠀⠙⠲⡀
⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⢘⠁⠀⣷⠄⠉⠑⣀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⠀⠀⠀⡉⠁⠈⠅⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠚⠀⠄⡈⢠⠀⠀⠈⣄⠀⠀⢀⠀⠀⠀⢀⠟⠀⠀⠀⠈⠀⠀⠀⠀⡦⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣹⠀⠄⡀⠀⠀⠈⠀⠀⠀⠀⢸⠂⡄⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠢
⠀⠀⠀⠘⣆⠀⠀⢉⡄⠐⠦⠃⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠉⣇⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢆⡌⠀⠀⠀⠀⣼⢀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠖⠀⠓⠧⡀⠀⠀⠠⢧⡟⠀⠀⠀⣀
⠀⠀⢀⠥⠄⡀⠔⠁⠀⠀⢀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢋⡀⠀⠀⠀⡸⠉⠀⠀⡀⠉⢢⠀⠠⠙
⠀⠀⠉⠀⠀⠀⠴⠰⠐⠂⠂⠀⠓⠂⠈⠁⠘⠀⠓⠂⠀⠀⠀⠀⠈⠀⠊⠷⠄⠀⢨⡇⠀⠀⠘⠗⠀⠘⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠒⠚⠋⠘⢄⡀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣸⠿⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠤⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣬⡓⡄⠀⠀⠀⠀⠀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⢃⠘⢀⠀⠀⠀⣸⣿⡿⣧⣀⠤⠴⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣞⣿⣰⠆⠸⠀⠀⠀⢹⣿⢣⠞⣿⠖⠀⠀⠑⠎⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢫⣽⡗⠀⣸⡇⢀⡄⠚⢿⣀⣀⡀⠀⠀⠐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠶⢿⣿⣼⣿⣿⣷⣠⠀⢈⢿⡏⠁⠀⠂⠈⠀⠁⣼⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣿⣿⣯⣿⣿⣻⣴⡇⠀⠙⠲⠶⣶⣤⡴⢿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣤⣤⣬⣿⣿⣿⣿⣿⠋⢻⣿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠉⠁⠂⠀⢠⣾⠿⠛⠛⠋⠛⣻⣧⡿⠧⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⣉⠤⠀⠀⣠⠔⠋⠀⠀⠀⠀⢠⢸⣿⣿⣿⣿⠃⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠓⠒⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⡿⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡽⠟⠋⣁⠀⢀⢠⣾⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢦⣼⣯⣛⡿⣿⣿⣿⣽⣾⡿⠁⠀⢨⣟⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⢿⣯⣹⣿⣏⢡⣿⣿⠀⠀⠀⡈⠛⢿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⣌⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠻⠉⠀⠀⠀⠀⠁⣶⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣀⢦⠀⢀⠀⠀⢠⣼⣿⣿⣇⠀⠀⠀⠀⠠⠤⣺⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣧⣶⡖⢖⣤⣾⣿⡟⣈⣿⣧⣀⠀⠀⠒⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⢍⣩⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈⢙⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⣿⠆⠀⠀⠀⠀⠈⢳⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣭⣴⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⣵⣆⣴⣯⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢿⣿⡿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣤⣰⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠄⡀⠀⢀⣀⣤⡠⢄⣀⡀
⠀⠀⠀⠀⠉⢻⠁⠀⠉⠳⣀⡤⠂⠢⢷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢀⠜⠛⠝⠓⠀⡓⠶⠂⡀
⠀⠀⠀⠀⠀⠈⠳⠤⣀⡴⠃⠀⠀⠀⢨⣿⡭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣄⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⠉⢿⣠⢠⣴⣾⠦⣬⠍⠱⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠞⣩⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠄⠀⣸⠁⢼⡇⠀⢡⠈⠳⣒⡀
⠀⠀⠀⠀⠀⠄⠠⢀⠠⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⣤⣄⣀⡠⠋⠀⣾⡄⠀⠀⠢⠀⡍⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡟⠿⣦⡀⢠⡾⡿⡀⢹⡆⠀⠀⠀⠛⠉⠁⠀⠀⠁⠉⠚⠦⠄⣤⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠄⠀⣻⠇⠸⣿⣀⣁⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡻⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣀⠀⣧⠀⠙⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠈⠹⡍⢛⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⡆⢀⣀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣠⣼⡃⠀⣿⣶⢶⣖⠞⠳⠞⢋⠧⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠒⢎⠢⡔⣿⠟⢻⠧⠞⠛⠋
⠀⠀⠀⡴⠾⡀⠀⣿⣿⣿⣷⡀⣼⠄⢦⡂⠸⠋⠁⠀⠀⠀⠀⠀⠀⣸⣭⣽⡽⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⢸⣿⣤⡼⣿⣡⡼⣅⣻⡊⠉⣷⡄
⠀⠀⠀⡰⣾⠈⣻⢇⢀⡨⠁⠁⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣾⣷⣾⣟⣿⣿⣿⡆⠀⠀⠀⠀⠷⠤⠟⣴⠻⣿⣦⣼⡏⠻⠿⠛
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠗⢿⣯⣯⣿⣯⡿⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠛⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠙⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡟⣉⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣿⣼⣏⣉⣡⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢬⢠⡘⣏
⠀⠀⠀⠀⠀⠀⢀⠄⡤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣉⣻⣟⠉⣛⣿⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⣠⠄⠸⠸⠋⡉⢀⠠⠄
⠀⠀⠀⢰⣄⡀⠈⠈⡤⢠⠄⠀⠀⠀⠀⠀⠘⠿⠯⠿⠋⠻⢶⠽⠟⢹⣳⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⢰⡖⢫⡿⢻⣦⡀⠀⠀⠀⠈⠰⡶⢐⠢⠝⡆⢣⠌
⠀⠀⠀⣸⣿⢦⠠⠀⠄⠶⠘⠂⣀⠀⠀⠀⠀⠀⠀⠤⠀⠔⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⣭⡦⢦⣀⣼⣏⣸⡇⡨⣼⠁⠀⠀⠀⠀⠀⠉⠈⠉⠙⠈
⠀⠀⠀⣿⣿⠈⡆⣗⡄⠚⡃⢛⠋⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⣟⣟⣯⡅⠈⠻⢾⡿⠞⠋
⠀⠀⠀⠹⣿⣶⠁⠈⠁⠀⠀⠨⡆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣈⡖⠋⠉⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⡻⣟⡷⠀⠀⢀⠀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠟⠋⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢃⠀⢳⡀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠄⡀⠀⠰⠀⠘⡆⠀⠀⠹⠀⠀⢀⣀⣀⡀⠈⠢⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢤⡀⠁⢠⠀⠰⢌⢢⡀⠣⡀⠹⣆⠀⠀⣦⠊⠁⣀⣀⢙⡖⠊⠉⠀⠈⠙⣷⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠑⢆⡆⠁⠀⢆⠀⠅⠀⠉⠂⣤⡳⣰⣷⣶⡦⠟⠛⢹⡁⢠⠔⢤⠀⠀⣿⣀⣀⡬⠿⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠉⠛⢤⡤⠤⣼⡶⢾⠿⠛⡝⢇⢙⠋⠀⠀⠀⠈⢧⣈⠑⠋⢀⡴⠏⡵⠀⠀⠀⠀⠀⠉⠣⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡠⠞⢱⣷⠣⡀⢠⠟⠋⠉⠑⢦⡀⠀⠶⣶⠋⡹⠋⠁⡌⡶⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠊⠁⠀⣰⣱⠋⠀⢥⡇⠀⠀⠀⠀⠀⠷⠐⠚⠁⠀⠃⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡟⠀⠀⠄⠡⣀⠠⢒⣦⡴⠃⠀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⢀⠌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠌⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢄⡀⠃⠀⢀⡤⠒⠉⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡀⣒⠈
⠀⠀⠀⠀⠉⠠⡀⠈⢑⡦⠤⠤⢄⡀⢀⠴⢒⡈⠒⠲⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⡀⠀⠀⡄⢀⠛⠆⠀⢀⡇⠀⠀⡰⡋⢐⡆⠈⠱⡀
⠀⠁⠀⠀⠀⢀⠘⡶⠁⠀⠀⠀⠀⢹⠋⣪⡥⠚⠀⠀⠘⣆⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠹⠄⠀⠘⠦⣤⣠⡴⠞⠀⠀⠀⡇⠈⠁⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠰⡁⠀⢴⠁⢒⣠⠞⠁⠀⠈⠙⠢⡀⣰⣏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⣀⣤⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣀⠈⠙⢁⡇⠀⣀⣀⠀⠀⠀⣹⠟⠉⠉⢀⠤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠁⠀⠉⠢⡀⠀⡰⠊⠀⠉⠐⢄⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢇⠀⢄⠘⠂⠀⢠⡟⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⢘⠀⢠⠒⢄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣠⡾⠃⠘⣄⡈⠐⠉⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣀⡀⡠⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠫⣵⠀⠀⠀⠀⡀⠈⠀⠘⢋⣀⣀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠚⡧⠤⢴⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠂⠀⠀⠘⠀⢀⣠⠄⠁⠀⠈⠀⠚⢲⡴⠀⠒⠠⠄
⠀⠀⠀⠠⠦⡀⠀⠀⠠⡄⠀⢾⡛⠖⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠓⢁⠀⠀⢀⠠⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⠋⠉⠛⠉⠃⡀⠀⠄⠀⢨⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠁⠀⠀⡄⢠⡴⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠐⠀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠋⠛⠐⠤⠖⠡⢤⠀⠀⠒⠁⡀⢀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀
⠀⣄⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⠆⠀⠊⠀⠀⠡⡀⢀⡠⠗⠀⠀⠀⠀⠈⠈⠒⠀⠀⠀⠀⠖⠀⢸⡄
⠀⠀⠀⠉⣻⡁⠉⠀⠀⠀⠂⠀⠀⠀⠰⠤⠔⠀⠀⠠⠤⠤⠀⠀⠨⠀⠀⡠⠁⠀⠓⠀⠀⠀⠀⠠⡄⠀⠀⠀⢸⡏
⠀⠀⠀⠀⢓⠁⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡒⣽⠠⠠⣯⡁⣨⠆⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⣤⡎⠀⢠⣀⡀⡋⢁⡀⠀⠀⠙⢆⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠠⡀⠉⣱⠦⠥⠼⠬⠭⣡⠤⠀⠀⢸⣤⡤⠊⠁⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡩⠋⠀⠀⢀⡤⠂⢲⡆⢀⢱⡄⠘⠀⠀⢱⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠁⠀⠀⠀⠀⢷⡀⠋⠀⠈⠺⡚⠓⢄⡀⠀⠁⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡙⠑⢴⠄⠠⣦⢤⣲⠁⠀⢀⢀⠃⠀⢢⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠻⡇⠀⠀⠀⠀⠀⠀⠑⠤⠔⡇⠲⣏⠀⢹⡆⢀⠞⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠤⠊⠉⢁⣏⡁⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠉⠒⠤⣄⡀⠀⠀⠀⢱
⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⡨⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⢠⣀⡀⠀⠀⠉⠁⠀⠀⠀⠉⠙⠒⢲⠔⠒⠚⠉⠉⠢⢄⡀⣀⡀⢀⠀⣀⠀⠠⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠑⠦⠀⣀⣀⣀⣠⠤⠔⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠌⠆⠢⠐⢁⠂⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡀⠔⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠋⢀⠜
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⢸⡀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⣳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⣀⣀⡿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⣀⠠⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠦⡀⠀⠀⠀⠀⠀⡾⢀⡤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠈⣳⣄⠀⣀⡴⠿⠿⠦⣤⣤⣀⣀⠠⠶⠆
⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠁⠢⡔⢱⣹⡏⠁⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠙⢽⠀⠀⠀⠀⠀⠇⡼⢋⠠⣄⠀⠀⠀⢠⡿⠇
⠀⠀⠀⠀⠀⠀⢲⣼⠢⡀⠀⠀⠀⢱⠁⠸⣆⢸⡾⠖⣷⠎⡱⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣷⠄⣀⡀⠠⠊⠃⠀⠀⠈⡖⠓⣶⠶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⢰⣠⠞⠁⠘⠻⡶⣄⠀⠀⠀⠀⢠⠄⠀⠀⠀⡀⢠⡤⠠⣆⡇⡀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠈⢳⣄⡀⠆⠀⠀⠀⣀⠓⢂⠀⠸⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣦⣤⣤⡴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠑⣾⠈⡙⢳⡱⠎⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⡞⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣀⠀⢸⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠴⢏⢙⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⣼⠃⠀⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠿⠐⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣽⣆⣢⡊⠀⢿⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠈⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠁⠀⠅⠀⢀⠀⡠⠉⡀⠓⡀
⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠄⠤⣄⢣⢃⡀⣷⠀⡰⠰⠁⠠⠂⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⢀⠠⠄⠊⠙⠛⠿⡄⠀⠀⠀⠀⡆⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠁⠀⠉⣷⣴⣄⣸⣵⣿⣿⣭⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣴⠖⠀⣼⣿⣿⣥⡄⠈⢉⣿⣿⣧⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣟⡛⠛⠉⠛⢿⣦⡴⣯⣦⠰⢦⠈⢻⡄⠀⣠⣲⠞⣩⠟⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣿⣿⠏⠰⢦⡀⠀⢈⣿⣿⣿⣿⠿⠓⠒⠛⠁⢾⣿⣷⣿⡉⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⣟⣷⢹⣠⣄⡏⠻⣿⣿⣅⡀⣀⡰⠂⢈⢿⣿⣿⣧⠤⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣼⠿⠋⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠙⠾⠿⠿⠟⠋

⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⣀⣀⣀⣀⣄⣤⠖⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣠⣤⣾⠀⢀⣉⣉⣉⣉⣁⣀⣀⡀⠘⠻⣶⣦⣤⡴⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⢈⡭⠗⠛⠋⠉⠉⠀⠀⠀⠈⠉⠙⠓⢦⡀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⣿⠙⢷⣄
⠀⠀⠀⠀⠀⠺⣍⠉⠉⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠈⠲⢄⣙⢦⡀
⠀⠀⠀⠀⠀⢀⣾⠛⢦⠀⠀⠀⠈⠛⠶⢤⣤⣤⣀⣠⣤⣤⡤⠴⠶⠚⠋⠀⠀⠀⢀⣠⠤⠴⠶⠞⠋⢳⡀
⠀⠀⠀⠀⠀⣼⠃⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡘⣇⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢰⡏⠾⠯⠶⠒⠛⠉⣱⠀⣀⡤⠖⢲⡄⠀⣀⡤⠶⠦⢄⡀⠀⣾⠁⠀⠈⠉⠛⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠸⠿⠋⠁⠀⠀⠸⣧⠞⠋⠀⠀⠀⠀⠙⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣶⣶⣶⣤⣴⣶⣶⣾⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⡀
⠀⡉⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣗⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠙⣏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⠯⠴⠛⠉⠀⠀⠀⠀⠀⠈⢆⠀⢰⢁⠴⠃⠀⠀⣀⡀
⠀⢀⣄⡰⠒⠦⠄⠀⠀⠀⠀⠿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢈⡀⠐⠁⠀⠀⠀⠀⡆⠀⠀⠀⢈⣱⠟⠋⠒⠶⠦⡤⢀⢀⡀⠀⠠
⠰⠏⣈⠁⠀⠀⠐⢄⣀⣀⣠⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⣁⠀⠀⠀⠑⠀⠀⠀⠀⠠⠔⠓⢢⣴⠖⠻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠻⢆⡉⠀⠀⠀⠀⠸⠘⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠘⠒⠂⢀⡰⠿⠾⢥⣀⡆
⠀⠘⠧⣀⣀⡀⠄⠀⠀⠘⠀⠂⠀⢠⡖⡁⠀⠀⠀⠀⠀⠘⢷⠄⠄⠠⣠⠀⠀⠀⢴⠃⡰⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⡏⠀⠀⠈⠑⡖⠒⠒⡢⠂⠀⠀⠀⠉⠲⠈⠳⠛⣧⡀⠀⠀⢀⡷⣤⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠄⠀⠀⠀⡐⠁⣀⠴⠓⢄⠀⠀⠀⠀⢰⡖⠻⣔⠾⠧⠤⢴⡾⠁⠘⡟⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠛⠛⠃⠀⠂⠸⠂⠀⠀⠀⢸⠃⠀⠉⠁⠐⢇⠁⠀⠀⠀⢿⠀⠉⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠑⠂⠀⠀⢤⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡀⠀⠀⠀⠉⠑⠢⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠉⠀⠀⠀⠀⠀⠔⠈⠀⢈⢹⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣤⣤⣀
⠀⠘⠌⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣤⣄⣀⡰⠿⠋⠰⠂⠎⡙⠻⣇
⠀⠢⣄⠰⡄⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣰⠶⡄⠀⣴⠿⠛⠙⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠋
⠀⢢⡈⠁⣤⡀⠀⠀⣸⠀⠀⠀⠀⣄⣀⣀⡀⣀⠤⠋⠱⠶⢄⡩⠤⠀⠀⢸⠫⠆⠀⠀⠀⠀⠐⣄⡀⢀⣀⣀⡴⠃
⠀⠀⠉⠐⠦⣷⡀⡀⠃⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣀⢀⣀⡠⠏⠀⠉⠉⠹⡀
⠀⢀⣤⣴⣶⣉⡙⠋⡀⢀⠀⠀⠀⠀⠠⢄⡌⣃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠄⠱⡀
⢠⠢⡆⢡⣴⠂⠆⠀⠈⢻⡊⠁⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⢳⠒⠓⠒⠒⠛⢄
⢀⠆⠙⠀⠀⠀⠀⠀⠀⠘⠁⠒⠖⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠑⠂⡀
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⣀
⠀⠘⠀⣀⣀⣀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡇⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢸⡇⣠⡤⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⡷⠋⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣠⠖⠀⢸⣧⠶⠚⡋⠉⠉⠛⠓⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣋⠉⡛⠳⢼⣷⠋⠀⣰⠏⠀⠀⢠⡇⣠⡴⠞⠋⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⠏⠉⢿⡄⠀⠹⡆⣼⠃⠀⢀⣠⠟⠋⠉⠉⠙⢂⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠷⠦⡿⠁⠀⠀⢻⣧⠶⠛⠉⠉⠙⠳⢦⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⢠⡶⠖⣆⠀⠹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣠⠖⠛⠉⠉⠛⠶⣄⠀⠻⣆⣀⡾⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⡞⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠁⠈⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢠⣤⣤⡄⠀⠀⠀⠈⡇⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⢿⡀⢀⡿⠂⠀⠀⢰⠗⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡈⠋⠙⠁⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠖⠚⠋

⣾⣿⠀⠀⠀⡀⠀⢛⡀⠀⣀⠿⣦⣀⡠⠷⡀⠀⠀⠀⠀⡀⠈⢉⠩⢛⡗⠀⠀⠀⠈⠲⠽⠾⠿⠃⠀⠀⢿⣣
⠋⠀⠀⣀⠀⠸⣖⠶⠛⣘⠃⠀⠀⡍⠀⠀⣿⡆⠀⠀⠀⠀⠀⡦⡆⠉⣳⡔⠐⣆⣤⣄⠀⠀⠀⠀⠀⠀⠈⠻⠼⠿⠿
⣴⢦⡀⠁⠤⠞⠋⢧⡀⢀⣼⠶⠾⠟⠲⠶⠞⠁⠀⠀⢀⠀⠚⢿⣷⣦⣴⠋⠙⡿⣯⣽⣷⠀⠀⠀⠠⠄⢠⣤⣀
⠡⠞⠁⠀⠀⠀⠀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣖⣿⣿⡏⠉⣷⣿⣟⠛⠛⠃⠀⠀⠀⠀⢠⡀⠙⢮⢹
⠀⣀⡀⠀⠀⠈⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣭⣿⣴⣿⣿⣋⣿⡇⠀⠀⠂⢀⠤⠒⠈⣳⣄⠸⠏
⠳⡈⠉⢦⠀⠙⠛⠉⡀⠀⠀⠀⡀⢀⡱⠴⠒⠒⢒⣦⡄⠀⠀⡁⠲⣾⢤⣿⠟⠉⠀⠀⡠⠀⠀⠀⢀⣀⣿⠏
⠀⢡⠀⢸⠇⠀⠀⣸⣆⠀⠀⠀⠳⠀⠀⠀⠀⠈⠉⠀⠉⠦⠀⠳⠿⠟⠀⠀⠀⠀⠀⠈⠀⠈⠙⠛⠛⠋⡁
⠀⠸⠀⡝⠀⠀⠀⠙⢿⣶⣄⣤⡶⠀⠀⠀⢴⣶⣄⠀⠀⠀⠀⠀⠠⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡠⣄⠄⠀⠀⠢
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⣿⣄⣘⣿⠀⠀⠀⠀⠁⠂⠀⠉⠳⣻⠄⠀⠀⠀⠀⠀⢤⡉⡉⣋⣶⣤⣀⠄
⠀⠀⠃⠀⠀⢠⣄⣤⣴⠄⠛⠉⠀⠀⠀⠈⠙⠋⠁⠀⠀⢀⡇⠀⠀⠀⠀⣐⣿⡇⠀⠀⣦⠀⠸⡀⣀⡰⣼⣾⡏⠐⠚
⢀⠀⠀⠀⢠⡅⠩⠋⠉⠙⢶⣂⣤⣀⡤⠀⠀⠀⣀⡀⠀⠨⣷⣷⣶⣶⣾⡿⠋⠀⡠⠀⠁⠀⠀⠙⠿⠿⠟⢿⣧⣢⣼
⠀⠢⣄⣠⣴⠇⠀⠀⡱⠤⠈⠙⠓⠂⠀⠀⣴⡄⢅⣻⣆⠀⠈⠉⠉⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠉
⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⡛⣡⡅⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢋⣷⣀
⣿⠂⠀⠀⠀⠀⠀⠐⠀⢀⡄⠀⠀⠀⠀⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⡀⠀⠙⠐⢂⠀⢸⣤⠀⣤⠀⠀⠀⠈⠓⠚⢻
⠁⠀⠀⠀⠀⣐⡀⢤⡂⠸⢧⠆⠀⠀⠀⠀⠠⠐⠤⠄⠀⠀⠀⠀⠘⣟⡒⠤⣄⡾⣀⠼⠷⣶⢶⡄⠃⠀⠀⠀⠀⣠⣽
⠀⣀⠀⠀⠀⠘⠻⣽⣯⣷⢶⠠⠀⠀⢀⠄⢄⠈⠀⢀⡐⠀⠣⠀⠀⠈⠉⠉⠉⠀⣧⣀⣠⣿⠇⡿⠃⠀⠀⠈⢺⢲⣛
⠈⣿⡷⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡙⣦⢤⣄⠀⠀⠀⢀⠆⠀⠘⠻⠿⠿⠞⠁⠀⠀⠀⠀⡀⠈⢻
⠻⡉⢷⣬⡿⠃⠀⠀⠀⠀⠀⢀⣉⢠⠀⢶⣬⣄⣀⡿⠿⣏⡀⣻⣧⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⢤⠔⠒⢦⠀⠈⠐⠚
⣾⠝⣶⡄⠀⠀⠀⠀⠀⣀⣶⣴⡋⣿⠟⠻⣧⣨⣿⣧⡀⣙⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠸⣷⣆⣼⡃
⠂⠴⠟⠉⠀⢀⠀⠐⠶⢿⣈⡏⠙⠛⠿⣤⠟⠉⢀⠙⡛⠛⠋⠋⠁⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠈⠉⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⣠⣤⠠⣶⡀⠀⢀⠀⡀⡤⠠
⠂⠀⠀⠀⠀⠀⠀⠀⠀⣘⠃⡀⠀⣦⠀⠀⠀⠀⠀⠀⠤⡀⠀⠂⢀⣧⣆⠘⠀⠀⠢⠤⠠⡔⢚⡇⠀⠀⣽⡿⠆⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠋⠉⠈⢉⣿⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⡰⣣⠄
⠀⠀⠀⣀⣘⡈⢡⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⢸⠁⠁⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠠⠀⠛⠀⠀⠀⠀⠀⠠⢄⠀⠻⡄⠀⠀⠀⠈⠀⠢⣩⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠚
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⡼⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⡀⣀⡴⠊⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⠉⠛⠦⡀⠀⠀⠀⡀⢼⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⠙⠛⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⡠⠽⠞⠒⠦⣀
⠀⠀⠀⠀⠀⣀⠀⢀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢖⢚⣲⠖⠶⠒⠀⣲⡦⢴⣦⣴⠋⢁⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡤⠶⠊⠉⢀⠠⠚⠁⣲⣴⣏⡉⠂⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⢠⡿⡧⢠⣿⠃⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠰⢦⡤⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣄⣠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢡⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠐⠚⠇⢹⠻⠏⠙⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣦⣀⣀
⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⣀⡴⠿⠒⠈⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠈⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠚⡁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⢀⡀⠜⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⣆⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠻⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⡄⣉⠙⠢⠀⠲⣄⠀⠀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠻⠛⠛⠛⠋⠛⠯⢽⡇⠀⠀⠀⠀⠀⣳⣄⣀⠀⡟⣻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠈⠁⣠⠄⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢐⠛⢀⡅⢹⡷⢪⡿⣦⣤⣀⣤⣀⠀⣀⡠⠄
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣠⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢥⠀⠀⠀⠀⡎⠀⠋⢀⣨⣿⡟⠠⡄⠉⣦⡀⡀
⠀⡀⡀⠤⠔⠂⠀⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⣾⠻⣽⠁⠀⠰⡄⠈⠆⠈⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢿⠀⠘⡆⠀⠀⠀⠐⠢⠀⢠⠄⠀⠘⠀⠀⠀⠀⠀⢻⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡰⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⢀⣐⣁⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣀⢨⣿⡿⠇⠒⠀⠘⡿⠦⡀⠀⠀⠀⠀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢘⡉⠁⠀⢰⡀⠀⠘⠁⠀⠀⠀⠀⠀⠰⣃⠻⠁⡀⣫⢕⣪⠁⠀⠀⠈⢛⡖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠐⢀⡤⢉⠱⣄⠀⠀⠀⠀⠀⠀⠀⢠⢠⠂⠄⢋⡐⠃⠁⠀⡀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠔⠀⠈⠀⢀⠀⠈⠀⡀⠐⢹⠆⠀⠀⠀⠀⠀⠀⠰⢴⠆⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠠⠃⠀⠁⠈⠠⠂⠀⠀⡎⢸⠑⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠤⠮⣤⣔⣁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⡀⠀⠐⢀⠀⠐⠁⢀⡀⠐⡀⢢⠓⠀⠀⠀⠰⠤⣆⡤⢌⡫⠚⠉⠉⠀⠰⠀⠁⠀⠏⠠⡄
⠀⠀⠀⠀⠀⡈⠀⢀⡀⠁⠠⠂⠀⡈⠀⠀⠁⠀⠀⠀⠐⣃⠄⡴⢈⢙⠋⠀⠰⠀⠀⠇⠀⡀⠈⠀⠘⠐⠄⠂
⠀⠀⠀⠀⡈⣠⠀⢉⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢈⢡⠠⢿⠘⠀⢠⠀⢀⠀⠀⠂⠀⠀⠀⠀⠁⢼
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠂⠞⠂⠀⡈⠀⠠⠀⠰⠀⢰⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠀⡃⠀⠀⠀⠁⠀⡄⠀⡄⢠⠄⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⢀⠄⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈⠰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣘⢃⡀⠀⠀⠀⣐⠋⠨⠍⠉⠐⠌⠆⠀⠀⠀⠄⢄⣀
⠀⠀⠀⠈⠀⠀⠀⠉⠀⠉⠁⠉⠁⠉⠀⠀⠀⡀⠀⠀⠀⠀⢐⠲⣷⣦⢄⡀⠀⠀⠀⠉⠛⢿⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡠⣠⠅⠀⠀⠰⠆⠁⢠⠊⠡⠀⠀⠬⠁⠀⠀⠀⠀⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠿⡿⡃⢰⡄⠰⠖⡄⠶⡀⠀⠊⢐⢰⠄⠀⠀⠀⠀⠘⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡖⠁⠀⣼⠁⢸⠄⠘⠉⠗⢤⠰⠀⢘⠀⡘⡖⠀⣤⢴⡾⣵⣾⡄⠀⢀⣵⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠐⢥⠘⢀⠀⠆⠩⡅⠾⠀⠐⠝⠈⣀⠁⠀⣀⠉⢠⠀⢉⣻⢸⣁⠋⠹⢹⡝⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠘⠀⢠⠀⢠⠀⡀⠰⠆⠀⠀⠀⠈⠁⠀⢠⡄⠄⠠⠐⡠⣑⡾⢣⡘⠇⡌⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠠⡄⠂⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠋⣤⠁⠉⠘⡈⢁⠃⠆⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣂⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠁⠈⡔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⡀⢠⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠈⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⡈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⡗⠿⢛⣗⢻⣇⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢆⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠲⠂⣌⠓⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠦⡀⠀⠀⢀⠀⠀⠀⠀⠙⠄⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠑⢤⠈⠂⠀⠈⠆⠀⠀⢀⠐⢠⠎⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣶⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠱⡀⠀⠀⢀⣿⠖⠋⠀⠑⠀⠀⠀⠀⠀⠰⠙⠛⠀⠀⠠⣦⣌⠂⡈⠉⠒⠠⡄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠓⢀⡈⢀⡃⠀⠀⠔⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠋⠀⠀⡤⠒⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠙⣦⣀⠤⣴⠖⠲⠶⠖⠈⢀
⠀⠀⠀⠀⠠⠀⠀⣀⡀⠀⠀⠀⢤⠀⣏⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠄⡀⠀⠀⢹⠁⠀⠀⠠⣀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠂⠀⠴⠚⠉⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠀⠀⠀⠀⠀⠀⠀⠚⡿⢋⣛⠳⣤⣦⢶⡀⡘⢀⣀⣀⠀⠈⠁⠀⠀⠙
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠂⠀⠀⠀⠀⠀⠀⢰⡼⠣⠘⠿⠃⠀⠀⢨⠛⠁⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠁⠉⠛⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⣀⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⢠⣼⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⡄⠀⠀⠤⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⢠⡏⣀⠜⠟⠳⠢⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⢾⣷⣤⠤⢤⣿⡌⠀⠀⠀⠀⠀⠈⡏⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠞⠁⠀⠀⠀⠈⠛⢆⠀⠀⠀⠀⡀⠃⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⡀⠀⣐⣢⠀⠀⠀⢸⡗⠒⠚⠷⡍⠦⠄⢀⣁⣀⣀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠘⡱⠃⠀⠈⠉⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⠀⣀⣤⣴⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠈⠀⠘⢷⠘⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡒⢋⡁⡀⠑⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡼⠋⢈⡟⠈⠳⠅⢠⣾⡃⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣷⠎⠒⢛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠃⢤⠐⠉⠉⠈⢳⠀⢨⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠀⢀⠠⠠⠤⠄⢠⡔⠈⠀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢰⡇⠀⠀⠀⠀⠀⠀⠙⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⡉⢤⡀
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡾⠁⠐⠀⠀⠀⠀⠀⠀⠂⢼⣇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⡤⠃⣤
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠒⠐⠤⢤⡀⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣀⡀⠀⣀⡠⢘⡃⠀⠀⠀⠀⠀⠀⢱⡌⠁⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠨⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣀⠴⠋⠀⠠⠔⠚⠉⢡⠀⠀⠀⠀⠀⠀⠈⢉⣿⠁
⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⣈⡱⣤⣀⠀⠀⢀⣢⠞⠃⠀⠀⠀⠁
⠀⠦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠉⠛⠛⠻⡷⣆
⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉
⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡆⠤⠼⠷⠴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⠁⠀⠀⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠒⠲⢦⣄⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠰⣄⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⡀⠀⠀⠀⠀⠈⠑⣮⠀⢈⠀⠀⠀⠀⠐⠂⠀⣦⡀⠀⠀⠀⠀⡀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢠⠒⢰⠏
⠀⠀⠀⠀⠀⠀⠠⠘⢶⡆⠀⣀⠀⠀⠀⠀⢀⣀⣼⠧⣄⣶⠖⠶⠞⠁⠀⠀⢎⡱⣄⠀⠀⠀⠀⢰⢀⡀⠀⠘⠤⣄⣀⡀⠄
⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠈⠁⠀⠀⠀⣰⠋⠉⣷⣀⣠⣾⣤⣮⠤⣀⡄⠀⡀⠉⠚⢷⡀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠈⠀⡿⢄⡤⠄⠀⠀⣾⠃⠀⠀⠀⠈⠓⣤⣃⣱⣀⣨⠀⠀⠉⠙⠲⢤⢉⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⢀⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠘⠄⠀⠀⠑⢦⡄⣈⡙⢧⣄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠒⢲⣊⠁
⠀⠀⠀⠂⢀⡴⠲⠂⠘⢛⡷⠆⠀⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣑⡿⠷⠾⠇⣀⢀⡆⣠⠔⠁
⠀⠒⠒⠉⠀⠀⠀⠠⠋⠁⢠⠞⠁⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠶⡷⢒⠆⠀⠀⠙⢿⡇⠀⠀⠀⣀⠀⠀⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠃⠀⠈⠂⠠⠄⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣌⢡⡋⢡⣼⡅⠊⠀⠀⠀⠀⠿⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣨⠷⢄⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢀⠀⠀⠀⠀⠀⢀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⢰⣦⣀
⠀⠀⠀⠀⠀⠀⢸⠃⠈⠉⠓⠒⠂⢦⠀⠄⠲⢆⠚⠙⡻⣤⠀⠈⠀⠙⣏⠒⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠱⡄⠀⠊⠳⡀⠀⠀⠃⠀⠀⠀⠘⡆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠓⢠⣄⠀⠀⠰⠀⠀⠀⠉⠀⠀⢀⣐⡀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠉⠰⠒⠤⠶⢤⠒⠒⡛⠉⠉⢀⠊⠀⠀⣀⠀⢸⠀⠀⠌⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠂⠀⡠⠀⣁⣀⡀⠁⠀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⢀⣼⠡⠊⠀⠀⠈⠳⠸⠌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠰⠂⠀⠀⠒⠀⠉⠁⠀⠀⠀⠀⠀⢀⡴⢄⠐⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠃⠀⠉⠂⠈⠭⣀⠘⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠓⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⡜⠱⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⢀⡤⠖⠀⠒⢲⢀⡄⠶⢶⡉⡇⠈⠓⢏⠳⡀⠀⠀⠀⠀⢹⡆⠀⠐⠈⠶⢦⣀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠁⠀⠀⠀⠀⣠⠞⠀⠀⠀⢡⡇⠀⠀⠀⠁⠙⢄⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠉⠉⠑⠋⠓⠐⠂⠀⠌⠶⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡀⠘⠁⠀⠀⠔⣁⠸⡆⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠈⠳⢤⣀⠀⡀⠀⠀⠀⠀⡀⠠⡀⢀⠄
⠀⠀⡃⠀⡞⡿⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⢄⠀⠀⠀⠀⠀⠀⠘⠉⠢⠘⠄⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠉⠓⠾⠤⠄⠈⠦⠰⠄⠘⠉
⠀⠀⡇⠀⠙⠷⠀⠘⣷⠀⠀⠀⠀⠀⢀⣴⠶⠛⠁⠈⠁⠒⠐⠲⠿⣧⣀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⢷⠀⠀⠰⠦⠠⠕⠁⠀⠀⢀⡖⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠸⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠈⢧⡀⠀⠀⠀⡈⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣆⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠈⠉⠉⠙⠒⢦⣄
⠀⠀⠀⠈⠳⣤⣄⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠃⠒⠛⡇⠀⠀⠀⠀⠀⠠⢀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠂⣠⣤⠖⢃⡾⣧⡈⠂⠀⠀⠀⠀⠀⠀⠀⢺⠀⡾⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⠶⢤⣄⠈⠈⠀⣙⡳⠀⠀⠀⠀⠀⠀⢐⠏⢸⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⢤⢤⡄⠀⠀⠀⢘⠇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⣯⣀⣰⠉⡀⠀⠀⠀⠀⠀⣠⡿⠀⠘⣇⠀⠄⠀⠀⠀⠀⡘⠛⠛⠉⠀⢀⣾⠁⠀⠀⠀⠌
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣄⡁⠀⡔⠄⠀⠀⠀⣠⠜⠋⠀⠀⠀⠹⣦⡀⠀⠀⠀⠈⢽⣀⣀⠦⠖⠊⠁⢈⠀⡀
⠀⠀⠀⠈⠳⣄⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠛⣿⠖⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣀⠀⠀⠈⠁⠀⠂⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⢮⣉⠓⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢱⠖⠀⠒⠂⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⢀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠄⡀⠀⢘⠙⠷⠒⠋⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠘⠓⠲⠐⠃