Delicacy Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡏⢸⡂⢻⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⢀⡞⣵⣛⠶⠀⠀⠀⠀⠀⠀⣀
⠀⠐⠚⠓⠀⢇⡗⡆⠀⠠⣭⡭⣥⠆⠀⠀⠀⢷⠘⠃⠀⡽⠀⠀⣀⡤⠀⡀⠀⠀⠴⣣⠯⣾⠟⠁⠀⠀⠀⠀⢠⡯⣹⠇
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠚⠁⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣄⣠⣀⠀⠀⠀⡀⠄⡀⠉⠀⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠄⢠⡲⠄⠀⠀⠠⣄⠻⠈⣠⠇⠀⠀⠈⠙⠛⠁⠀⠀⠀⣡⡆⠈⠐⢦⠀⠀⠘⠛⢿⡟⠉
⠀⠀⠀⠀⠶⠀⠀⠀⠠⡌⠂⣋⡀⠀⠀⠀⢀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⠶⠀⠸⠋⣀⣉⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⠒⠆⡀⠀⠀⠈⠛⠠⣤⠀⠀⠀⠀⠰⠦⠆⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠍⠙⠳⣦
⠀⠀⠀⠀⣠⣀⡀⠀⢠⡎⠀⠀⠀⠀⣴⠀⠈⠣⠀⠠⠈⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⣒⠆⠀⠀⠀⠀⠀⠀⠈⠀⣠⠔⠚⠁
⠀⠀⠀⠀⠼⣝⠇⠀⠀⠁⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠴⠆⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠠⠀⠘⢡⠀⠀⢀⠀⠆⢐⡤⠂⠀⠄⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠖⢤
⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠤⠀⠠⠦⠜⠀⠐⠒⠐⠊⠀⠀⠀⠐⠂⠂⠀⠤⠄⠀⠀⠈⠂⠄⠀⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠆⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⢠⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⢻⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠛⣼⣧⡹
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡐⠀⠀⠀⠀⠀⠀⠀⣴⡶⣲⢶⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠴⠆⠀⠠⠶⠀⠀⠀⡆⢈⢛⠀⡀⠀⠀⢠⣤⣤⡄⠰⠆
⠀⠑⢶⣦⣶⣶⠎⠀⠀⠙⠳⠿⠷⠛⠀⠀⣄⡈⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠠⢺⠏⢻⡍⣱⠀⠛⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠉
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢰⡆
⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢴⠆⠀⠀⠀⠘⢻⡟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⠆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣡⣴⡀⠀⠀⠀⠀⠀⣄⣀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠄⠈⠀⠐⠄⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⣌⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤
⠀⠀⠐⠃⡠⠾⡁⠀⠐⠒⠒⠀⠙⠀⠀⠀⣦⣽⡷⣦⡁⠀⠀⠀⢀⡆⢈⡷⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠰⠖⠒⠒⠛
⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⣤⡄⠀⠀⠀⠒⠊⠐⠃⠘⠃⠀⠀⠠⠁⠁⠭⠀⠀⠀⠈⠉⢴⠆⠻⠂⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠛⠓⠁
⠀⠀⠦⠀⢀⠀⠀⠀⠀⠀⠉⢡⡀⠀⠀⠀⣀⣤⡶⠖⠀⡀⠀⡀⠂⣀⠰⠆⠀⠀⠀⠒⠲⠂⠀⡄⠀⠀⠘⠋⠀⠠⡖⢳⡄
⠀⠀⠰⠿⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠐⢺⡗⠀⠀⠠⣤⣄⣀⣧⡔⠀⠀⠀⠀⡠⠀⠀⠁⠈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⠏⠛⣿⠉⡟⠛⣟⠟⣛⡿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠋⠉⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣠⠴⠐⢡⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⢀⡠⠀⠤⠂⠐⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠐⠒⠐⠐
⠀⠄⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆
⠀⠠⠀⠄⠀⠀⠐⠀⠨⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠐⠠⠀⠀⠀⠀⠀⠂⠐⠊⠂
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠴⠟⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⡃⠁⠀⢀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠘⠄⠰⠅
⠀⠀⠄⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠠⠓⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐
⠀⢀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡤⠦⣀⠀⠀⠄⠀⠀⠀⢀⡀⢀⣄
⠀⠘⠀⠁⠁⠑⠀⠀⠀⠀⠀⠒⠀⠋⠵⠁⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀⠐⠂⢄
⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠘⠌⠐⠚⠈⠈⠁⠸⠀⠀⠀⠀⠁⠃⠀⠈⠀⠀⠀⠀⠀⠐⠀⠒⠂⠐⠀⠒⢈
⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠬⠥⠤⠔⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠂⠀⠉

⠀⢨⡀⠀⠀⠀⠀⡠⠖⠉⠁⠀⠈⠁⠂⢄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠀⠓⡀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡄⠠⠀⠀⠀⢰⠀⠀⠀⢀⠀⣴⡄⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠘⢦⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠓⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠡⡀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⣠⠎⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠐⢤⠀⠀⠀⠈⠙⠒⠂⠀⠀⠈⡰⠋⠀⠀⠀⠀⠍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠂⣠⠖⠉⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀
⠘⢄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠤⡀⠈⠐⠂⢤⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢄⠀⢀⠖⠁
⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠔⠁⠀⠀⠀⠀⠁⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠲⠌⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⣆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠭⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⣠⣤⣤⣄⠀⢀⣤⣤⣄⡀⢠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⢰⡏⠀⠀⢹⡇⣾⠁⠀⠈⣷⢸⡇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠳⣤⣤⠾⠁⠹⢦⣤⡼⠋⠸⣧⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣀⠀⠀⣠⣄⡀⢀⢀⡀⢀⣠⣄⡀⢠⣄⡀⢀⣤⣄⠀⣀⢀⡀⣀⠀⣀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⡄⣰⠿⣆⠸⣅⢀⡀⢸⢯⡀⢺⡀⢶⡆⢸⢶⠃⢯⡀⣸⠇⣿⣸⡇⣿⠳⣿⢸⡇⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠈⠀⠈⠉⠀⠈⠀⠁⠀⠉⠉⠀⠈⠈⠁⠀⠉⠁⠀⠈⠉⠀⠉⠀⠁⠀⠉⠁

⠀⠀⣤⣀⣄
⠑⡀⢣⠶⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⠢
⡀⢠⠈⡆⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠁⡀
⠀⠠⠀⡇⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠖⠤⢀⡀⠈⠑⠢⡀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈
⠠⠔⠊⠀⠀⠀⠉⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠂⠀⠀⠀⡌⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠈⠢⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⠀⠀⠀⠀⡴⢀⠠⠀⠀⠤⣀⣀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⢡⠞⠁⠀⠀⠐⠀⠀⠀⠑⢦⡀⠀⠀⠀⠱
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⢠⡞⠋⠉⠀⠉⠙⠳⣄⠀⢀⠃⠀⠀⠀⠀⠀⠄⠒⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠺⠃⠈⠀⠀⠀⡸⠀⠠⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡄⠀⡁⠀⠈⠢⢄⡀⠀⠀⣀⡠⠔⠁⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠂⠉⠉⠁⠀⠀⠀⠈⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⣀⣠⡤⡤⠶⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣤⣤⣤⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⠊⠹⡇⠀⠀⠀⠀⠀⠰⠦⠤⢄⡀⠀⠉⠛⠦⡀⠀⠀⠈⠀⠀⠀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣤⣄⣀⡀⠀⠀⠈⠛⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢠⡇⠀⡄⠉⠈⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⡜⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡴⠖⠛⠉⠀⠀⠀⠈⠳⢤⣤⣄⣤⣤⣤⣤⣤⣴⡶⠾⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠀⠐⠉⣷⠄
⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠏⠀⠀⠀⠀⢀⣭
⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⢠⣀⣀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⡀⠀⠀⡀⠀⠀⢀⡜⠉⠁⢠⡆⠀⠀⠀⠐⡟
⠀⠀⢰⣦⣀⠀⠀⠀⠀⠀⠙⠛⠲⠷⠶⢠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠈⠁⠀⠀⢀⣠⠤⠚⠁⠀⣠⢸⠀⠀⠀⠛⠃⠀⠀⠀⢾⠇
⠀⢄⠉⠙⠛⠫⠷⠰⣶⠄⠘⡟⠒⠛⠿⠛⠁⠀⠀⠀⣀⣀⡀⠉⠑⠂⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⢠⡏⠉⠀⡳⢣⡎⠀⠀⠀⠀⡰⠋
⠀⠈⠻⠷⣶⣤⢀⣀⣀⠀⣸⠃⠀⠀⠀⠀⠀⠰⠦⠄⠀⠀⠉⢀⢀⣀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⣁⠌⠁⠀⠀⠰⣶⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠓⠒⠀⠀⠀⠀⠄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⣿⠆⣾⠁⠀⠀⠀⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⡤⠶⠖⠛⠁⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⣽⡶⠆⠀⠀⠠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠉⠙⠒⠤⡀⠀⠀⠀⠀⠻⣿⠄⢀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢄⠀⠀⠀⠻⢿⣿⣽⣻⠷⢤⣄⠀⠀⢀⡀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣀⡤⠤⡤⢄⣀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⠙⠻⢿⣦⣬⡟⠋⢀⣀⣠⠤⠟⠁⠀⠀⠀⡠⠠⢈⡃⠀⠀⠀⠀⠘⣦⣀
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⡬⠀⠀⢀⡽⠗⢲⢶⣦⠞⠁⠙⣧
⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢀⠀⠀⠀⠉⢲⡾⠁⠀⠀⡿
⠀⠀⠀⠀⠙⠶⣶⣶⣖⠀⠠⠶⣶⣶⠶⠟⠁⠀⠀⠀⠀⠀⠈⠐⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⠀⠀⠀⠀⠘⢇⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠆⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠴⠾⠷⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣠⠴⠐⢁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⡠⠀⠤⠂⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠐⠒
⠀⠄⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠆
⠀⠠⠀⠀⠀⠀⠀⠀⠨⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠀⠀⠀⠀⠀⠀⠂⠐⠊⠂
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠴⠏⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠁⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠘⠄⠰⠅
⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡤⠢⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄
⠀⠘⠀⠁⠁⠑⠀⠀⠀⠀⢀⠒⠀⠃⠴⠁⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀⠐⠂⢄
⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠐⠌⠀⠚⠈⠈⠀⠸⠀⠀⠀⠀⠁⠃⠀⠈⠀⠀⠀⠀⠀⠐⠀⠐⠂⠐⠀⠒⢈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠐⠠⠤⠥⠤⠔
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠂⠠⠄⣀⡼⢀⠆
⠀⢀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⡄⠤⣃⡠⡤⠐⠲⠀⠠
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡈⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⢀⠀⣈⠀⠐⠀⠀⠈⠉⠁⠬
⠀⠀⠈⠀⠀⠀⠀⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠐⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠉⠙⠲⡆⠀⣀⠀⠠⡃⠀⠁
⠑⢄⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠤⠠⠀⢄⡀⠀⠀⠄⠀⠀⢀⠀⠀⠈⠁⠄⢢⠤⣌⠡⠄⠀⠠⠆
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠓⠤
⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⢀⣾⣦⣀
⠀⠀⠀⡠⡀⣀⡀⠈⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⢎⡰⡓⡾⢠⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠤⣄⡀⠀⠀⠀⠈
⠀⠈⡌⢕⡺⢞⠄⡗⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⢀⠎⠀⢤⠀⡄⠈⠂⠠⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠈⠢⠴⠊⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⢠⠀⠄⠠⠟⠂⡈⠸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⡡⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⡁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡠⠃⠀⠀⠀⢀⠀⠤⠐⠒⠊⠀⠀⠀⠀⠀⠂⠈⠀⢀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠉⠐⠂⠈⡁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠄⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⠁⣀⣄⠀⣀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠠⣾⣿⠟⠀⠁
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠤⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠁⠄⠀⡀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠐⣩⣶⢠⡁⠀⠐⢈⠀⠈⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣬⢒⣢⡀⠀⠀⠀⠉⠁⢺⡆⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠
⠀⠠⢁⡄⠡⠃⡿⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠂⢀⡀⡄⠀⠀⠀⠀⠀⠈⠀⠑⢎⡁⠤⠒⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢀⡄⢀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠈⠡⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⣖⠁⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⣾⣟⣿⠑⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠇⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠐⠀⠀⠀⠀⠻⢠⣌⢀⢀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠋⠀⠀⠀⠰⢀⠀⠀⠐⠈⠈⢂⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⢰⡖⠒
⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⣀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⢂⡘⠀⠀⠀⢠⡆⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠰⠀⠀⠀⠀⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠃⠑⠠⠀⠀⠀⠀⠀⠀⠀⠈⠠⠦⠀⠃
⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⡀⢠⣆⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠢⠤⠀⠀⠀⠀⢀⢐⡦
⠀⠀⠀⢰⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⣾⣬⣻⢵⠂⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠅⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠶⠟⣻⣈⢵⣚⡜⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠂⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠

⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠤⠄⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠘⠀⠀⠀⠀⠀⠈⢄⠀⠰⠁⢀⠀⠉⠆⠀⠀⠌⠠⠊⠠⠀⠟⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⠡⣈⢀⡄⠐⠰⣲
⠀⠀⠐⠀⠐⠀⠀⢉⠣⠀⠀⠣⡀⠈⠀⠈⠆⠈⢠⠴⡀⠊⠀⠀⠀⠂⠀⠠⠀⠄⠀⠁⠀⠀⡠⠁⠀⠒⠄⠀⠉⠉⠀⢐
⠀⢀⠀⣋⡀⠀⠀⠀⠈⣀⢀⢀⠈⠒⠈⠄⢀⡴⠀⡯⢚⠁⠀⠀⢠⠐⠂⡐⠠⢀⢀⠀⢀⠜⠀⢣⢄⣀⡀⠀⠀⠀⠤
⠀⠘⠀⠀⡆⠀⡠⠊⡁⠀⠃⠂⢌⡑⢄⠀⠸⠋⠀⢸⡵⠀⠀⢸⠃⠀⢀⡅⡀⠘⠄⠐⠁⢀⠀⠠⣀⡀⠀⡀⠠
⠀⢠⠖⢦⠀⢄⣠⠒⡂⢜⣊⠼⠓⢊⠁⢠⠒⠒⠤⡀⠃⠀⠀⠀⠁⠨⠉⠁⠀⠀⠀⠀⠠⠂⢤⠀⠠⠀⠀⠁⠀⠈
⠀⠀⡆⣈⢂⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⡌⠀⠀⢰⠀⠰⢠⠀⠀⠂⠆⠀⢀⣴⣶⢻⣟⣳⡆⠀⡀⠀⢀⠀⢀⡰⠉⡘
⠀⠀⡄⠂⢠⠀⠀⠀⢖⠒⠀⠠⠀⢲⠆⠑⠀⠲⠈⠀⠀⠁⠃⠀⠀⠀⠀⢀⢀⠽⠉⠉⠉⠉⠀⠀⡀⠐⠀⠀⠉⠉
⠀⠀⠈⠉⠁⠔⢄⠀⡄⠉⠀⠒⠀⠁⢀⠀⣴⡢⡄⠀⠠⠀⠀⠀⢀⠖⡆⠀⠀⠀⠀⠍⠀⠁⠀⡀⠃⠀⠀⡔⠉⢆⠁⢠
⠀⠦⠀⠀⠈⠀⠀⠀⠀⢀⠀⢈⠈⠡⠏⠓⢉⠠⠣⢶⠠⢅⢤⡤⠀⠀⠀⡀⠈⣁⠀⠈⠈⠀⠂⠀⠀⠀⠨⠀⡠⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠂⠈⢀⣐⣃⡠⠤⠗⢉⠀⠀⠀⠀⠰⠀⠀⡀⠼⢑⠀⠉⡂⠲⢀⠑⢀⡱
⠀⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠈⠉⣤⠀⠀⢘⠭⠁⣀⠀⠐⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠎
⠀⠐⠂⠀⠀⡠⠄⠀⠀⠊⢟⠀⠀⢠⠶⠛⠉⠐⢹⣶⠄⠈⡠⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⠀⠀⠀⠀⣡⠀⠀⠘⠀⠂⠄
⠀⠰⠠⠍⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢈⠠⠒⠀⠀⠀⠀⠉⠉⠉⠈⠐⠡⠄⢀⣀⠀⠂
⠀⢠⠀⠀⡀⠄⠈⡆⡕⠀⠈⠀⠐⠀⠀⠠⠒⠃⠀⠀⠀⢰⠀⠀⠀⠌⠀⠀⠄⠠⠏⠀⡀⠀⢀⠠⠀⠀⠙⠇
⠀⠀⠀⡀⢀⡄⠀⢡⠁⢀⡀⠌⠀⡄⠂⠂⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠒⢅⡀⢀⠰
⠀⠠⠐⠊⠸⠈⠆⠈⢀⠡⠀⠀⠦⠠⢖⠀⠀⠀⠈⠁⠀⠈⠀⠐⠀⡄⠀⢠⠂⠉⠀⠀⠀⠈⠀⢀⠜⡀⠀⠀⢻⠧⠂⠁
⠀⠀⠠⠨⠄⠀⠂⠀⠀⠒⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠒⠃⠀⠀⣀⠀⢌⢀⠢⠤⠬⠔⡀⠤⠔⢊⠈⠃⡀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠠⠂⠀⣀⡀⡔⠒⠒⡆⠀⢢⠀⠐⠀⠀⠁⠀⠈⠀⠠⡈⡀⢄⠀⠠⠀⠈⠀⠀⠀⠀⠐⠁
⠀⢀⡀⠐⠀⠀⠀⠀⠂⠄⠁⠀⠀⠘⠄⠂⢘⣀⣸⠀⠀⡀⠀⠐⠄⢤⠆⠀⠀⠈⠚⠁⠡⠊⠈⠠⠁⠀⠤⠀⠐⠀⠒⢤
⠀⠀⣠⡶⢀⡶⠀⢀⠀⠃⡀⠂⠈⠠⠀⠀⡀⠄⠠⣀⠀⠀⠘⠀⢀⠀⠀⠀⠃⠀⠠⣀⣠⣤⠄⠀⠀⠀⢄⠀⠀⠀⠀⠔
⠀⢸⣆⠅⠊⠀⡀⠁⠀⡂⠀⠀⡀⢊⠀⠌⡠⠊⢉⡉⠠⠀⠈⠠⠊⠀⠀⠀⠁⠀⢀⠜⠈⠡⡀⠀⠀⠀⡈⠀⠈⠁⠁⢠
⠀⠀⠁⠂⠀⠀⠃⠀⠀⠈⠀⠉⠀⠈⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠂
⠀⠀⠤⠔⢀⠀⠁⢀⡎⠈⠓⠀⠀⠀⠀⠀⠀⢀⠄⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠠⠀⠁⠒⠄
⠀⢡⡀⠦⠀⢈⣒⣀⠀⢤⡆⠀⠠⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⢇⣤⡍⠉⠀⠀⠀⡀
⠀⠈⢜⠧⡀⠀⠀⠀⠐⠀⠠⠀⡭⡐⢢⠀⠀⠀⢀⡀⠀⠠⠀⠀⡠⢔⠐⠀⠀⠀⠀⠀⠈⠉⡉⠀⠘⡄⠐⠆
⠀⠀⠐⠷⣌⣀⠓⡀⢀⢣⣤⣼⡭⠝⠋⠀⠀⠐⠏⢀⢄⠎⠥⣀⡈⣛⡛⠉⠉⠀⠀⠀⠀⡐⢀⡔⢀⠅⠀⡁
⠀⠀⠀⠄⠀⠉⠉⠀⠠⠈⠀⠀⠠⠄⠀⠀⠀⠈⠀⡇⢼⠁⠀⠀⢀⠉⠀⠀⢀⠀⢀⣠⠚⡀⠁⢠⠞
⠀⠀⠀⠀⠤⠂⢴⣂⣔⡒⡠⠀⠀⠀⠀⡀⠀⠀⠑⠃⣏⠀⠀⠀⠀⠀⣀⣀⣤⡶⢊⠡⢻⡥⠖⢁⢀⠴
⠀⠀⠀⠐⢦⠀⠀⠀⠙⢾⡁⠩⠢⡀⠀⠀⠀⢠⣄⡇⠁⠀⠘⠋⢉⡥⠡⠛⢈⠒⠀⠐⠂⠐⠂⢁⠔⠀⠀⠀⢀
⠀⠀⠀⢄⠀⠀⠀⠈⠐⠀⢱⠀⢟⡃⠀⠀⠀⠀⠁⠹⣤⣈⣙⣋⢁⣀⡤⠚⠷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠘⢇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠤⠳⠄⠠⠄⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃⠈⠉⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⡀⠔⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠂⠀⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠨⠆⣀⠄⡆⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢦
⠀⠀⠀⢘⡀⡘⠠⡴⡀⡀⡛⠀⡄⠀⠀⠀⠀⡀⣀⣀⣠⢿⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠
⠀⠀⠀⣀⠤⠆⠀⡀⠹⢠⠓⢰⠇⠀⠀⡀⠀⠀⠙⠋⠁⠈⠙⠋⢛⣾⣅⡀⠀⠀⠒⠄⣀⣀⡀⣀⢀⣀⡀⠔⠛⠀⠀⠈⠤⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠅⠐⡳⠀⠉⢡⠖⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢹⣿⡇⠀⢶⣀⠆⢠⠤⢤⠤⣤⠤⣤⠀⣤⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠠⠄⡘⢷⠸⠝⠖⡁⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠙⠷⢾⣤⣴⣄⣤⣄⡼⠶⠛
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠁⠁⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣹⣦⡀⣠⣠⣿⣿⣿⡟⠀⠀⠀⡀⠙⣀⢤⣈⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠄⠐⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣯⣿⣿⠿⠿⠁⠀⠀⠀⠃⠀⠀⠁⢠⡎⠀⠀⡼⠀⠀⡄⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⡰⠊⠉⠿⣦⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠦⠔⠁⠀⣰⠁⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣹
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠰⢾⡇⠀⠀⠀⠈⠲⣶⣤⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⡇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠈⠴⠄⠀⠀⠀⠀⠘⢿⣿⣿⣿⠾⣠⡿⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠴⠚⠋⠀⠀⠀⠀⠇⠀⣼⡿⠁⠀⢀⠀⠀⠀⠉⠁⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢸⡃⠀⠀⢀⠀⠀⠀⠀⠀⢀⢨⡆⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿
⠀⠀⠀⠀⠀⠀⠧⠀⣸⠀⠀⠈⢤⣆⠀⢸⠀⢀⣼⣼⠃⢀⠄⠰⣼⣻⣸⣧⣴⣦⣄⠀⠀⠄⢠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠄⠀⣤⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⡔⠒⠉⠒⢣⠋⠁⠀⠹⢻⣇⠀⠀⠈⢷⠀⠀⠀⠀⠈⠛⠻⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡀⣀⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠂⠀⠀⠀⢐⡿⠀⠀⠀⠉⠲⠦⣤⣴⡾⠿⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣤⡄⣠⡾⢇⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⣶⣶⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣷⣦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣨⡛⠓⠉⠇⢸⠅⡀⠄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⢻⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣢⣾⡿⠃
⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠛⠛⠓⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⠄⠀⣠⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣖⢤⡀⠀⠀⠄⡀⠀⠀⢀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⢀⣼⣛⣾⢧⡀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⡁⢄⣉⠇⠠⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣠⠀⠀⠀⠐⠂⠀⠀⠀⡀⠶⡸⠿⠂⠘⢦⣝⣛⣷⠀⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠸⠏⠋⠁⠘⠠⡄⠀⠀⠀⢠⡴⢶⣦⡈⡅⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠠⠑⡄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠆⠀⠀⠀⠴⠀⠈⠀⠈⠀⣠⡿⠇⣤⣀⡄⠀⠀⠀⠀⠠⢀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⢠⡀
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠰⢋⠏⣌⡄⠀⠀⠀⠀⠀⠀⢀⠐⠆⠀⣴⣆⡀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠑⠛⠊⠁⠀⠔⢀⢀⠀⠀⠀⠀⢠⡶⠚⠛⠃⣀
⠀⠀⠀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠁⠊⠀⠀⠺⠟⠀⢃⠐⠀⠀⠀⠸⣿⣿⣿⠀⡄⣠⣴⣷⠄⠀⠠⠠⠀⠈⠛⠃⠀⠀⠀⢠⠀⠙⠀⡀⠙⠿
⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠀⠀⣤⡄⠸⠆⢦⠘⢁⡀⢻⣿⡏⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣰⡄⠠⡤⠘⡑⠢⠶
⠀⠀⢀⠀⠉⢛⢛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠉⠀⠀⠀⠸⠛⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠀⠀⠁
⣤⣶⣤⠀⠀⠘⠟⠀⣀⣠⣄⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠂⡀⠀⣸⣟⣿⣧
⠘⠛⠉⠀⠀⠀⠀⣿⠉⠉⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠹⠶⠷⠃⣀⣀⡀⠈⠃
⠀⠒⠀⠀⠀⠀⠀⠈⠳⠶⠋⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡁⠀⣤⡀⠀⠀⠀⣸⠀⡀⣰⣷
⠀⠀⠀⢀⣤⡄⢰⣷⡀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⡄⠀⠀⠀⣴⣿⣿⢿⣹⡟⣻⣿⡄⠀⠀⠀⠀⠀⠁⠀⠙⠛⠁
⠄⠀⠀⣿⣿⡏⠀⠈⠁⠀⠈⠀⠂⠀⠠⡍⡷⠖⣘⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣷⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠔⠰⢻⡏⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠈⠀⢁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣛⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠈⡁⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢄⣰⡤⠀⠈⠁⠀⠀⠀⠀⠀⠀⢤⠀⠉⠀⡄
⠀⠉⠰⠗⠂⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⣾⠅⠂⢀⣐⡀⠀⠀⠀⠀⠀⠀⠛⠛⠁
⠈⡷⠨⠟⠂⠈⠙⣿⠟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⢻⡏⠁⠀⠀⣁⠄⠀⣀⣀⠀⠀⠀⠰⠀⠀⠀⣀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠈⠀⠿⠿⠀⠀⣿⣷⢀⡶⠄⠸⣄
⢠⣤⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠈⠀⠀⣀⣄⡀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠈
⠸⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⢠⠠⣶⡙⠓⠀⠀⠸⠔⠿⡕⠀⠀⠀⠀⠈⠛⠛⠀⠀⠠⠀⠈
⠀⢠⣠⠄⠀⠀⡄⠸⣷⡷⠠⠀⠃⠐⠅⠀⡰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠠⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠒⣴⠐⡄⠀⢙⣅⡀⠀⠀⠀⠀⠀⠰⢶
⠀⠠⡂⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⢀⠃⠀⠀⢉⣀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⡀⡤⠀⠰⢀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡀⠀⠀⠀⠀⢀⠤⠒⡠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇
⠀⢀⠠⡈⡁⡎⠁⢊⣴⠀⠀⠀⠘⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⡶⠄⠀⠀⢀⠔⠁⢆⠈⠁⢸⡆⠀⠀⠀⠀⢀⣀⣤⣤⣴⣿⡿⣤⡀
⠀⠸⠚⠃⠛⠓⠛⠉⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠀⢀⡎⠁⠀⠀⠀⠉⠰⣧⡜⠃⠈⠆⢠⠀⠀⠀⠀⠻⡀⠀⠀⠀⢀⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⣬⠆⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠈⠛⢉⡀⠀⠛⡀⠀⠀⠀⢸⠀⠀⠁⠉⠀⠀⢠
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⢄⠐⣀⠄⠀⠀⠰⠿⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢄⡠⠄
⠀⠀⠀⠀⠂⠉⢢⠀⠀⠀⠀⠀⠀⢸⡉⡀⠀⣙⠆⠀⠀⠀⠀⠀⠀⠀⠠⢠⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠯⠐⢻⣁⣰⠴⠂⠀⠀⠀⠸⡈⢣⡄⠰⠀⠀⠄⠀⠂⠠⡀⢀⠁⠀⠀⠀⢀⠃⢸
⠀⠀⠐⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢏⡦⣙⠆⡀⠀⠀⠈⠢⠀⠀⠮⠀⠐⠀⠁⠄⠀⠈⠀⠀⡠⠀⠌⠀⠀⣤
⠀⠀⠠⡀⠀⣀⡀⠀⠀⠇⠀⠀⠀⠀⠈⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠼⠒⡀⠀⠀⠀⠀⠀⠁⠐⠒⠉⠠⠐⠊⠀⠀⠀⠀⠣⠀⠄⠀⠘⢀
⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⢀⠴⠂⠀⠁⣀⡀⠀⠘⠁⠀⠀⠀⠘⢶⣷⡁⠈⣷⢫⡴⠂⠀⠀⠀⠀⠀⠀⢐⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠂
⠈⡀⣠⠐⠋⣩⣿⡛⠒⠤⠐⠀⠀⠀⢩⠉⠉⢀⡛⠳⡆⠀⠀⠀⠀⠀⡄⠒⠋⠄⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠡⠈⣴⠅⠂⠀⢀
⠀⠀⠀⠀⠐⢣⡔⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⠄⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠛⠤⠾⣷⠞⠊
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠃⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠈⣉⡃⢱⡀⠀⠀⠀⠀⢀⡴⡛⠕⠚⠉⠳⣤⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠐⢄⡀
⠀⠀⠉⠐⠂⢀⣀⣀⣀⠐⢣⠀⠀⠀⠀⢠⠢⢀⡔⡀⠁⡀⠀⠀⠀⠀⣾⠂⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠠⠊⢀⠀⠀⠀⠒⠤⠀⠁⠀⠀⢰⠉⠁⡀⠀⢰⠀⠁⡀
⠀⠤⠀⠈⠉⠉⠉⢉⠉⠉⡟⠁⠀⠀⢠⠀⠀⢊⠜⢀⠄⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠄⢀⠀⠀⠀⡀⠐⠀⣤⠀⠠⢀⠶⠘⠁⠀⠉⠲⢆⣀
⠀⠀⠈⠂⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠣⠤⠆⠠⠊⠀⠀⠀⠀⠀⠀⠸⠦⠄⠐⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠉⠃⢰⣦⣶⡆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⣄⣀⡀
⠈⠀⠀⠸⢟⡿⠈⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⢀⣿⣿⣿⠃
⠀⠀⢰⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⢹⡿⠿⠃⠀⠀⠀⠀⡤⠠
⠀⠀⢸⠀⠀⣷⠀⠀⡷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢰⣏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠛⣦
⠀⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⢘⣀⣀⠀⢀⠛⠋⠁
⠀⠀⠀⣄⠀⠻⠀⠀⠠⠄⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠘⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣈⠊⠀⠀⠀⠪⢂⠀⠀⠀⠀⠃⠂⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠄

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⡲⣄⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⣀⢀⡀⠐⠂⠀⠀⠔⢁⡄⢀⠀⠀⠿
⠀⠀⠂⠀⡤⢈⠀⡀⠀⠤⠀⠀⠀⠠⠀⠈⠐⠀⣠⣄⠄⠀⠀⠀⢈⠀⠀⠀⠀⠰⣇⡠⠙⠛⠨⠚⠁⠆⠀⠈⠄⠀⠈⠂
⠀⠃⠐⠀⡀⠘⢀⠁⠀⠀⠉⠀⠀⠠⠀⠀⠀⠈⢀⡀⠱⠤⡅⠀⢀⠀⠀⠀⠀⢸⠛⠿⣷⣦⣱⠈⠀⠀⠁⠀⡀⠑⠀⠞
⠀⠰⡆⠀⠀⠣⠀⠀⢂⠀⢀⠤⠍⠐⣀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠁⠀⠀⠀⠀⠻⣷⡢⢄⠉⠛⠈⠀⠀⠀⠈⠋⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠁⢀⡁⢤⠀⠀⠀⠄⠀⠀⠈⠀⠘⠻⠿⠀⠀⠀⠀⠀⠀⣀⠈⠛⢷⡽⢀⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠂⢀⠃⠀⠒⠀⠂⠀⠀⠂⠀⠀⠀⠀⢠⠀⠄⠖⡀⠈⠐⠂⢁⠐⣄⠘⠛⠀⠀⠈⠀⠀⠀⠀⠄⠀⠠⠀⠀⠠
⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⠁⠁⠒⠂⠀⠠⠀⠀⠀⠀⠀⢡⠀⠀⠀⠂⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠
⠀⠀⠁⠀⠴⠆⠠⢠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠀⢰⢹⡿⡏
⠀⠀⠄⠀⠀⠀⠀⠀⠙⢖⡂⢁⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⣸⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡠⠀⠀⠀⣰⠻⢿⣿⣿⣷⣭⣭⣏⣨⣿⣿⣿⣿⠛⡆⠀⠀⠆⠀⠀⠀⠀⡔⠀⢿⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠙⠀⠀⠀⢿⢘⣻⠻⠛⣿⢸⣿⡇⠾⢛⠛⡍⠿⡃⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣀⠀⠘⢼⣧⣄⣷⣾⣬⠿⠧⠿⠶⠿⠾⠷⢖⣁⠀⠀⠠⣀⠀⠀⡀⠴⠀⠀⠠⠢⡀
⠀⡐⠁⠄⠂⠀⢄⠀⠁⠀⠠⠀⢠⡾⠻⠎⠁⠠⠀⠀⠀⠤⢄⠀⢤⠀⠀⠀⠀⠊⠀⠌⠐⠀⠀⠤⠀⠘⠂⣀⣠⣤⣤⣤⠁
⢰⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠁⢳⡤⢈⢤⠀⠂⡀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⢀⠀⠂⠔⠀⠀⠀⠀⠀⢰⡷⠲⠴⠞⣩⡷
⠈⡀⠀⠂⠤⠀⠁⠀⢠⠃⠀⠀⠐⢀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠑⠀⠉⣠⠂⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠰⠀⠀⡔⠡⠘⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⢠⠓⠄⠔⠲⠒⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠁⠀⠀⢪⠒⢹⠂⡄⠀⠑⠲⠷⢦⣤⡤⠠⠜
⠀⠀⡀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢨⠉⠁⠀⠀⡀⠘⢐⠀⠀⠅⠀⠀⠰
⠀⠀⠙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠙⠃⡀⠀⠀⠒⠀⠈⠀⠒⠀⠀⡀⠀⠀⢂⠀⠀⠒⠀⢀⠈⠀⠢⠤⠂⠀⠂
⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⠀⠀⠁⠀⠰⠀⠀⠀⠀⢂⠀⠀⠀⠈
⠀⠀⠀⠀⣠⣄⡈⠘⠲⣄⣄⠞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠿⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⢀⣼⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⠀⠒⠂⠀⠀⠀⠀⠒⠂⠈⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢺⠤⣄⣀⣀⣀⣀⣀⠀⠀⠠⠐⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⠚⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣀⡠⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠒⠋⠍⢀⡠⠚⣳⢦⡀
⢀⣀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀⠀⠀⠁⠀⠉⠀⠉⠙⠳⢄⡀
⠀⢆⣿⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠤⢀⣀
⠀⢌⠛⡙⢷⣦⣤⣠⡤⠄⠀⠀⠀⠀⢀⣀⣀⣬⢴⣯⢠⣼⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⡷⠤⠒⣟
⠀⢀⣷⡊⠐⠶⠒⠿⣏⣹⣛⣻⠋⢭⣍⣡⣤⣀⣉⢩⣾⠁⠀⠈⠐⢄⠀⣠⠶⣾⡿⠋⣹⣏⣉⣉⡤⣤⡴⣞⣋
⠀⢸⠩⡓⠶⣄⣀⠀⠀⠀⠈⣑⠀⢀⡰⠀⠈⠭⠤⠎⣿⡀⡀⡄⠀⠀⣼⠉⠲⡌⠀⢮⡌⢿⠑⢺⢥⡂⠌⣓⡽
⠀⠈⠳⠄⠀⣄⡈⠛⠀⠤⡄⠀⣄⠉⣀⠀⠀⡀⢠⠞⢱⠙⢤⢣⠆⢸⣿⡇⢸⣌⣵⠪⠷⣘⡆⢘⠶⠼⠷⣧⡂
⠀⠐⡀⠀⠈⠉⠉⠉⠁⠒⠚⠃⠈⠛⠁⠀⠁⠈⠁⡀⠎⠀⠀⠙⢄⣋⠹⣧⠀⢿⠮⣉⡛⢒⠯⡴⣷⠒⠒⠓⠁
⠀⠀⠈⠁⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠙⡄⠹⡦⡞⢡⣈⢙⠆⠑⢌⣻⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⡐⡴⢳⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⢄⠀⠀⠠⠀⠀⠀⡀⠔⠃
⠀⠀⠀⠀⠀⠈⠊⠀⡄⠄⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢇⠀⠀⠠⠀⠢
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠘⠒⠂⠀⠐⠂⠈⠀⠀⠀⠀⠈⠊⠠⠀⣀⣀⠁⠎⠀⠄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠘⣇⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⣷⣀⠤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠰
⠀⠀⠀⠀⠳⠄⠔⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠂⠀⠀⡠⠄⠒⠂⠐⠀⠄⠀⠀⠀⠁⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⢀⡧⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⢈⢘⡀⠀⠀⠆⢀⠀⡄⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠱⡀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⠰
⠀⠀⠀⠿⢤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⢰⡀⢀⠄⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⣉⠉⠉⠉⠉⠉⠀⠀⢠⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡂⡒⠠⡀⠀⠄
⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⢦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠄⠠⠀⠈⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡉⠀⠀⠀⠈⣆⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠂⠀⠃⠀⠀⠀⠆⠀⠀⡀⣀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣝⠠⠐⠓⠀⠒⠒⠊⠁
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⡈
⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠉⠑⠚⠒⠋
⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠤⠤⠀⠀⠉⠀⠀⠐⠦⡀⠀⠀⢎⠀⣈⡀⠠⢀⣠⠀⠀⠀⠀⠤
⠀⠀⠀⡡⣈⢹⡒⠒⡢⡄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⠙⠃⠀⠠⢠⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠒⠚⠀⠈⠉⠉
⠀⠀⠀⠣⠈⠀⠂⠀⠤⠢⠌⡀⠁⠀⠀⢰⣀⠀⠀⡄⠀⠀⠀⠠⠀⠰⠀⠀⢉⢀⡘⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠳⢄⣇⡀⠐⠂⠂⢀⣆⠀⠄⠐⠁⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠑⠶⠕⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠁⠓⠁⠐⠁⠀⠀⠀⠰⠈⠀⠄⠀⠀⠀⢠⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚

⣰⣖⠀⣺⡂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠰⢀⡁⠀⠀⠀⠀⠀⢀⠄
⢨⠇⠀⢹⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⢡⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡤⣀⠀⡄⠀⠀⠀⠄⢘⠀⠢⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠉⠉⠃⠀⠀⠀⠀⠦⢀⡁⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠈⠀⠀⠀⠆⠀⠀⠀⠘⠙⢐⠂⡀⠀⠀⠀⠀⡬⢁⡃⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⢀⣤⣦⢄⡀⠀⠀⠀⢈⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⢵⡅⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠋⠃⠃⠀⠀⠀⠀⠀⢐⡀
⣿⣿⠿⠿⠻⠿⡿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠰⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠠⢒⠀⠀⠀⠀⠀⠀⢀⣞⠁
⠀⠖⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡜⠁⠀⠐⢤⡹⠀⠈⡀⠀⠀⠼⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⠀⠀⢠⡄⠀⡠⠀⠀⠀⠀⠀⠉⠡⠀⢁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⡀⢤⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣭⡢⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀
⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⠠⠀⠤⢠⠀⠀⠀⣀⡀⢠⣠⠄⠀⠀⠀⠀⠀⡀
⠈⢀⠰⢒⣶⠀⠀⠀⠀⢘⠓⢀⠿⡅⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠐⠻⠋
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⣠⡄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⢀⣀⣀⠀⡀⠀⠀⠀⢀⠁⠈⠀⠀⠀⣼⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠂⠀⢀⠁⡀
⠀⠢⠀⠀⠀⠀⠘⠁⠀⠰⡄⡀⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠔⠈⠀⠈⠐⠠

⠀⠀⢀⣀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠆
⠀⢰⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠉⠀⠀⠀⠂⠀⠀⢠⣄
⠀⠸⠀⢸⠀⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠰⠀⠀⠀⠀⠀⠀⢑⣄⠉⢠⠁⠔⠀⠈⢢⠀⠀⢀⠇⠠⠔⠀⠠⠝⠀⠁⠀⠀⠀⠈⠀⠄⠀⠐⠀⠐⢈⠀⠩⣎⡀⢀⠄⠒⣢⢠
⠀⠀⠀⠀⠠⠄⠒⠀⠒⣆⠀⠈⢆⠀⠰⠠⡀⢣⠀⠢⣀⣤⠠⠄⠀⠀⠀⠄⠀⠀⡀⢀⠀⠀⠁⠀⡀⢁⠎⠀⠤⡌⠀⠙⠒⠒⠊⠉
⠀⠀⠀⡦⠄⠀⠀⠀⠨⠐⠀⠀⠀⠑⠠⡐⢈⠐⠀⣀⢸⢞⠵⠀⠀⠀⠠⡡⠤⠀⠇⡀⠀⠁⠀⠀⡰⠁⢎⡀⠀⠀⠀⢀⠀⠀⣀
⠀⢸⡀⠈⢈⠀⠀⣀⠴⠲⢙⠌⠜⡐⠢⡀⠀⠀⣾⠆⠀⣧⣟⠀⢀⣢⡌⠀⠀⠘⠈⠀⠇⠐⡠⢊⠀⠀⢘⠈⠉⠉⠀⠀⠀⠀⠀⢤
⠀⠀⣀⡀⠈⠀⡘⢑⣠⡀⣄⡄⠰⣔⡢⠽⠀⣀⣁⡀⡀⠘⡇⠀⠀⠈⠒⠠⠤⠻⠑⠀⠀⠁⠀⠈⠜⢀⠈⠁⠉⠀⠰⠀⠁⠆
⠀⠀⡇⠘⣆⠈⠐⠂⠀⠊⠐⢒⣉⡠⠔⠁⠸⠇⠀⠈⣡⠂⢀⠀⠀⠀⢀⢈⠁⠀⠀⣀⣠⣤⣤⣌⠀⠙⠀⠀⠑⠀⠀⠀⠀⠄⣀
⠀⠀⡇⡔⠈⡆⠀⠉⠈⢉⠉⠁⠀⠀⠀⠀⢺⡀⠀⠀⠟⠀⠘⢐⡀⠐⠁⠈⠀⠀⠺⠿⣯⠿⠷⠽⢧⠀⠆⠀⠀⠆⠀⢰⣅⡠⠂
⠀⠀⠣⡈⣠⠇⢀⠀⠈⠧⣈⠁⠐⠈⡩⠃⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠤⠔⠁⢀⣀⠀⠤⠂⠁⠠⠒⠁⠀⢀⣀⠀⡀
⠀⢀⠀⡀⠀⡐⠑⠄⠈⠆⠀⠀⠈⠀⡀⢀⡄⢴⣯⠒⡄⢀⢔⡀⠄⠀⠠⢏⠝⠀⠀⣀⠀⠀⣀⢀⠀⠀⠔⠈⠄⠀⡴⠁⠈⣆⣄⡅
⠀⠓⠒⠀⡐⠀⠀⠀⠀⠀⣀⠀⠨⠌⠰⠖⠘⢁⡠⠊⠔⠗⠐⠠⢤⡶⠂⠀⠀⢄⠀⢠⡄⠀⢀⠀⠀⢁⠀⠀⠀⠐⠠⢀⠔⠁⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠚⠀⠐⠂⠀⠒⠈⠀⣀⣩⣄⠦⠔⠛⣡⡀⠀⠀⠀⢀⠇⠀⢀⠀⠮⠩⠠⠍⢡⠘⠂⡈⢒⣈⠦⠀⡀
⠀⢀⠀⠆⠊⠣⡀⠀⠀⠀⡰⠀⠤⠀⠀⠘⠃⠀⠉⢠⡄⠀⠀⣚⠭⠁⣄⡀⠐⢁⡀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠁
⠀⠘⠦⠀⠀⠀⡤⠀⠀⠀⠚⡟⠠⠈⢀⡴⠖⠋⠃⠚⣳⣠⡄⠈⡀⠄⠈⠀⠀⠈⠁⠀⣰⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠖⡄⡠⡄
⠀⠠⢄⡈⠡⠊⠀⠃⠀⠀⠀⠈⠂⠀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠈⠐⠄⠂⡄⠀⠂⡬⠂⠀⠁⠐⠒⠒⠒⠒⠊⠉⠃⡀⠀⠀⠀⠀⠃
⠀⠐⠀⡀⠀⢁⠀⢊⠔⡠⢄⠐⠀⠠⠄⠀⠀⡠⡴⠄⡈⠀⠀⢠⠀⠀⠀⢀⠋⡀⢄⠀⢠⠆⠀⠀⠀⠀⢀⢀⠀⠸⣰⠀⢨⠙⠈
⠀⠀⠂⠒⠈⠀⠀⠘⡌⠃⠈⠀⢑⠀⡄⠄⠠⡀⠀⠀⠀⠀⡀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠪⠩⠉⢬⡇⠈⠀⠠⡀⠀⠀⠂
⠀⢀⠀⡒⠒⡋⢆⠀⠣⠠⠊⠀⠁⡐⠁⣀⠄⠀⠀⠀⡐⠀⠀⠻⠀⠈⠐⠂⠀⠀⢀⠤⠊⠁⠀⢀⠤⠀⠘⢲⠔⠁⠀⠰⣶⢂⠡⠄
⠀⠈⠀⠀⡄⠀⢈⠀⠀⠊⣉⠢⠀⠈⠁⠃⠃⠀⠢⠀⠀⢀⣀⠄⠀⠀⠀⠃⢀⠄⢃⠀⠀⠠⢀⠀⠀⢀⡠⠃⡆⠀⠀⠄⠋⠉
⠀⠀⠈⠀⠉⢀⠀⠀⠀⡈⠀⢠⠀⢀⠀⠀⠀⠀⢀⣀⣀⠉⢀⠀⠀⠀⠕⠀⢘⠠⠂⠉⠁⠉⠡⠊⠛⠩⠐⠊⠀⣐⠀⠀⠀⠀⢠
⠀⠀⠀⠄⠀⠀⠀⠀⢀⠰⠀⣀⠉⠂⢠⠔⢠⠸⡁⠀⡩⠆⠀⡜⠀⠈⠀⠀⠀⠀⠀⠀⡴⣲⠀⠔⠢⢠⠐⡆⠀⠀⠀⢀⣀⡀⠀⠁
⠀⠠⠴⠀⢁⠈⠀⠀⠀⠑⡃⠀⢀⣀⡀⠙⠉⠀⠥⠤⠧⠀⠠⠀⣀⠈⠂⠒⠃⠀⢀⠀⠈⠁⠀⠂⠁⠀⠘⠀⠀⡚⠃⠀⠀⠀⠑⢲
⠀⠀⡴⡺⠀⡼⠃⢀⣄⡀⢀⠄⠁⠀⢘⠀⠀⡠⠐⠀⣂⣄⠀⠀⠈⠀⢠⠄⠀⠀⠈⠠⠄⠂⣤⣴⣴⠀⠀⠀⠀⠱⡀⠀⠀⠀⡠⠋
⠀⠐⣇⠤⠑⠁⢠⠀⠀⠀⡁⠀⠀⡠⢊⡀⠈⢠⠊⠁⡀⠀⠂⠤⠤⠄⠊⠀⠠⠀⠁⢀⣀⡠⠂⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⢴
⠀⠀⠈⠐⠒⠂⠚⠀⠀⠀⠈⠀⠀⠀⠈⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣰⠛⠻⡆
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⢻⡏⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⣏⡸⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠦⠶⠛⢻⠶⣤⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠓⠲⢤⣤⠶⠛⠉⠀⢹⡆
⠀⢀⡾⣧⣀⣈⣇⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡿⢀⣴⣋⣙⣦⣭⣹⡟⢷⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠘⣇
⣴⣯⣤⡟⠁⠈⠙⢷⣄⠀⠀⠀⠈⠉⠛⠲⢶⢺⠀⠀⠀⠀⣾⣼⣶⣫⡟⠉⠉⢳⣤⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⡏⠀⠀⠀⠙⣧⠀⠈⠛⢦⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠉⠻⢶⣤⣤⣤⣤⠤⠚⠾⠅⠀⠀⠀⢹⡀⠈⠉⣉⠛⠋⡿⠃⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⢸⡆⠀⠀⠀⠀⡿⠀⠀⠀⠈⣷
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠙⢲⡴⣷⠀⠀⠀⠀⠀⢳⡀⠀⠉⢀⡼⠁⠈⠁⠀⠀⠀⢷⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⠶⠤⠶⠚⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣤⣤⣤⠴⠿⣄⡇⠀⠀⠀⠀⠀⠀⠳⣄⢀⡞⠁⠀⠀⠘⠃⠀⠄⠘⡆⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠈⠉⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠘⠃⠀⠐⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠁⠀⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⡛⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄⠀⠈⠛⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣧⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⢳⣤⡏⢻⣆⣠⣯⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠘⢧⣄⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⣀⡈⢳⡏⠉⣻⣾⠙⣧⠈⢿⣹⠆
⠀⢀⡶⠒⠒⠒⠒⠚⠛⠛⠛⢛⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⣟⣉⣉⣉⣉⣹⠂⠀⠀⢿⠘⡇⣠⡤⣤⣴⣿⠟⠁⠀⠀⢸⣏⣉⡙⠳⢴⡃⣿⢰⡿⣧⠀⠻⡄
⠀⠘⠹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⡴⠟⠉⠉⠉⠉⠉⠲⣄⠀⠸⠀⠀⣿⡀⠁⢹⡇⠀⠀⠀⠀⠀⢀⣀⡿⢦⠀⠙⢧⣸⠃⣼⣆⣀⣽⡦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⣰⠛⠛⠻⣿⢦⡼⠃⠀⠀⠀⠀⠀⠈⢿⠙⠛⠓⠒⠚⠛⠚⠛⠉⠁⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣄⣹⣦⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡏⠀⠉⢻⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⠶⠛⠶⣿⣶⣦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⢁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣿⣿⠷⠮⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⢀⣾⡭⠽⠧⠬⣍⡉⣿⣋⣽⣇⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡴⠶⠶⢶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⡀⠀⠀⣤⠀⠈⠙⠳⢦⡀
⠀⠀⣠⠞⠁⡀⠘⠀⡀⠈⠙⢦⡀⣽⡛⢯⡉⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠰⢦⠀⣤⠈⠁⣠⠌⠛⢦⡀⠀⠀⠀⠀⠀⠀⢸⣧⣌⠉⠛⠻⢧⣄⣀⡄⠀⠀⠙⢦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠉⠀⢠⠀⠙⣦⠙⣿⢛⣷⠘⡆⠀⠀⠀⠀⢾⠀⠞⠀⠀⠀⠈⣠⠄⠀⠴⠖⠈⢷⠀⠀⠀⠀⠀⠀⢸⣇⠊⣷⠀⠀⠦⠈⠙⠳⣄⣠⠆⠀⠹
⠀⠀⠹⣄⠉⠀⠠⠄⠀⠀⠀⠀⢠⠌⣧⠉⢻⣽⡆⡇⠀⠀⠀⠀⠈⡿⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⣾⠇⠀⠀⠀⠀⠀⢸⣏⡴⠏⢠⠖⣛⣉⣽⡳⣬⣻⣦⡤⠶
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠰⠆⠀⠀⠀⠘⡇⢸⢉⣷⠇⠀⠀⠀⠀⢰⡟⠖⠛⠛⠳⢶⠶⠛⠉⠳⠶⠞⣩⡷⠀⠀⠀⠀⠀⢸⡁⠀⠀⣟⢾⣙⣧⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠐⠀⠀⢻⠟⢫⠏⠀⠀⠀⠀⠀⠀⢻⡗⠛⠛⠛⠛⠻⢿⣝⡛⠛⠋⣹⠃⠀⠀⠀⠀⠀⣾⠛⢳⣀⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣀⣨⡿⢦⠾⠃⠀⠀⠀⠀⠀⠀⠿⠖⠋⠁
⣶⣶⣶⠶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⡐⠓⠒⠓⠒⠓⠒⠒⠒⠢⢤⣶⡄⠀⠀⠀⢀⣤⡴⢲⠖⢢⣄
⠀⠀⠀⢀⣴⠞⠋⢉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠒⠚⠒⠚⠛⠓⠉⠁⠀⠀⠀⠀⠀⢀⡾⣠⣤⣼⣄⣤⣼⢳⠀⠀⠀⠀⠀⢰⠨⠤⠤⢼⡀
⠀⠀⠀⣾⠁⠀⠀⣀⡀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡞⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠟⠀⠒⡒⠚⣣⡀
⠀⠀⠀⣟⠁⠀⢰⠋⠙⠂⠂⣸⠃⠀⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⢀⢄⡀⣸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠘⢦⣀⡉⡄⣀⣠⡴⠋⠀⠀⢠⣀⡆⠀⣿⡅⠀⣾⠙⡶⠻⠼⠋⢹⣿⡃⣠⡏⢰⡟⡇⣾⣹⡀⠀⠀⠀⠰⠄⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣤⠞⣿⡀⠀⠘⠳⠔⠛⠚⠁⠀⠀⠀⠈⠁⠉⠉⠛⠉⠀⠉⢉⢽⠇⠀⠀⣠⠶⣦⡀⠀⠀⠘⠛⠋⢥⢈⡭⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠀⠄⠊⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠒⠀⢀⠀⠈⠋⠀⢀⡾⢥⣬⣏⣝⣷⡄⠀⣀⣴⠟⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣐⡡⢀⠁⡆⣿⡄⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⢐⠒⠤⣀⠀⠀⠄⠀⠀⣿⠄⣺⢲⠓⡇⢁⡟⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣠⠶⠛⠛⠛⠛⠓⢦⠀⠘⠿⢻⣄⢀⠢⢀⡇⠀⢀⡤⠚⠉⠀⠀⠴⠀⠀⠀⠉⣢⡈⠡⠀⠐⠢⡀⠙⠶⣍⣹⢙⣳⠟
⠀⠀⡯⢏⠉⠉⣢⠀⠀⢸⠀⠀⠀⠀⠙⠳⠾⠛⠀⡴⠉⠀⠀⠀⠀⠀⠀⡐⣈⠀⠂⠀⢌⠀⠀⠀⠀⠈⠢⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠈⠓⠚⠛⢶⠖⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡦⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣲⣶⣾⣷⣰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣼⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠀⠻⠀⠀⠀⠀⠀⠹⡛⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠨⡇⠆
⠀⠀⠀⠀⠀⠀⠳⠛⠾⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⠤⡤⢤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⢈⡶⠤⢴⡄⢰⠋⠁⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠼⠂
⠀⠀⠀⠀⢀⠎⠁⢰⢏⠤⠂⠑⠀⢸⠆⠀⠀⡆⠀⠀⠀⠉⠢⠤⠄⢀⣀⡜⠙⠀⠸⡁⢙⠀⠀⢀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠘⣄⠐⠬⢀⡀⠠⠊⣠⠞⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⡼⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⢠⣤⢴⠶⣀⣲⠶⣤⣼⣄⠀⠀⠀⡧⠀⠀⡠⠇⠀⠀⠀⡴⠁⠀⠀⠀⠀⢿⠀⠀⠆⠀⢀⡿⢶⡆
⠀⠀⠀⠀⠀⣤⠤⢤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠈⠓⢧⠤⠭⠥⢴⣎⡓⢋⠁⠀⠀⣤⠤⠚⠀⠀⠀⢀⠜⠁⠀⠀⢲⠀⠀⠸⡄⠀⠂⠀⢠⣧⠟⠁
⠀⠀⠀⠀⠀⢷⠋⠉⠉⠙⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢩⠀⡀⠀⠀⠤⠀⠀⢀⡀⠞⠁⠀⠀⠀⣴⠀⠀⠀⠀⢇⠀⠥⠀⢸
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⡇⠀⠀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠒⠒⠒⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣤⣤⣤
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⢰⠃⠀⢺⣯⣭⣭⣝⣳⠀⠀⠀⠀⠰⣽⣿⣿⣯⡿⠀⠀⠀⢠⢻⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⠉⠉
⠀⠀⠀⠀⠀⠈⠲⠶⠦⠤⠞⠁⠀⠀⠀⠈⠈⠉⠉⠀⠀⢠⠇⠀⠀⠀⣇⣠⣤⣄⠀⠀⠘⢼⣿⡿⠀⠀⠀⠀⠘⠾⠟⠀⠀⠀⠀⠀⠀⢠⠴⠚⡚⠒⢄
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⣀⡀⣹⣇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣫⠄⠠⢑⡊⡇
⠀⠀⠀⣔⣒⣒⣚⣛⣒⣒⣒⣆⣀⣀⣀⣠⡤⣤⡄⠀⢸⣇⠀⠀⠀⠀⢨⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡔⣊⣉⣀⣀⣀⣉⣑⣦⡀⠀⠘⠰⠷⠶⠶⠶⠥⠗
⠀⠀⠀⣇⣭⣄⣬⣡⣤⣄⣤⡟⠉⠁⠓⠛⠉⠉⠁⠀⠀⠛⢷⣦⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣭⣭⣥⣭⣭⣭⣭⣭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠲⡄⠀⠀⢰⡷⠂⠁⠀⠀⠀⠀⠀⠀⠚⠈⡀⠀⠀⠀⠀⠀⢰⠒⢦⣤⣤⡴⠖⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢠⠀⠀⠀⢀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠲⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡒⠀⢠⠀⠀⠀⡠⠘⢩⢃⠀⠀⠀⠀⠀⠄⠀⠈⠉⠂⠀⠀⠀⠀⠀⠔⠇⢘⢁⠀⠀⠘⠢⠰⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠘⠠⠸⠁⠀⠀⠱⠀⢐⠄⠀⠀⠀⠀⠀⢄⠀⠀⣁⠎⠀⠀⠀⠀⠠⢆⢨⡉⠡⠀⠀⠀⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠰⢦⣤⣤⡶⠂⠂⠀⠀⠀⠀⠉⡙⠃⠀⢠⠊⠀⡰⠀⠀⠀⠀⣠⣤⣄⠀⠀⠘⠣⣄⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠶⠛⠀⠀⠀⠀⠀⠀⢀⠀⢠⠇⠰⠋⠀⠀⠀⠀⢼⠁⡠⢸⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⡄⠀⠀⠀⠁⠈⠀⠀⢠⡀⢈⣶⠀⠈⠃⠒⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⢀⠇⠀⠐⠂⠀⠀⠀⠀⠀⢡⡸⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⢀⣠⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠀⡟⠀⠀⠰⣵⣷⢿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠁⡀⠀⠀⠀⡂⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠆⠀⠀⠁⠴⠊⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣂⠀⠀⣠⠃⠀⠀⠀⢃⡀⢺⠀⠀⠈⠻⠷⠴⠞⠋⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⢡⠆⠩⠄⠀⠀⠀⠀⠀⠀⠀⠓⠂⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡠⠤⣀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⡆⢀⣲⢺⡿⣦⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⢶⡁⠀⠀⠀⡙⠆⠀⢀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣵⣿⣿⣿⠋⠀⠀⠠⣶⣶⡶⠀⠀⠙⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⢀⡠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⡤⠠⠤⠠⡀⠐⠴⣔⡶⠤⠴

⠀⠧⠀⠀⠀⡠⠒⠉⠀⠀⠁⠐⢀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡈⢡⠀⠰⠁⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧
⠀⠀⠀⠀⢈⠀⠀⠀⠈⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠓⠦⣤⣤⠴⠋⠀⠀⠄⠀⢀
⠀⢀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⢃⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢈⠦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⢀⠀⠀⠀⢸
⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢀⡀⠀⢀⠠
⠀⠀⠀⠀⢀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢂⡶⠛⠲⡄⣴⠚⠳⣆⢰⡗⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢧⣀⣰⠇⢷⣄⣠⠟⢸⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢠⡀⢀⡤⣄⢀⣀⠀⣠⢤⠀⣤⣄⢀⡤⡀⢠⢀⠀⣄⢠⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠞⠳⠸⢤⡤⠸⠣⠀⠧⡶⠆⠿⠇⠻⣤⠟⠸⡼⠀⠏⠾⠸⡦⠇

⠀⢀⣀⣀
⠀⠘⡔⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠄⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠠
⠀⡡⠂⠀⠑⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠑⠂⠤⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⠀⠀⠀⡠⠀⡀⠀⠀⣀⠀⠀⠀⠲⢁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠔⠁⠀⠀⠀⠀⠉⠐⡄
⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⢀⣠⠴⠶⠦⣄⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣄⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⢳⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠀⠀⠀⠀⠁⠀⠀⠀⡘⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢐⡀⠑⠄⢀⠀⠀⢀⠠⠞⠀⠀⠀⠘

⠀⠀⠀⠀⠠⠀⠀⠠⢄⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠻⣷⡶⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⢆⣂⡠⠧⠄⢀⡀⠀⠀⠀⠀⠈⠐⠨⠻⣭⣑⢲⣤⡀⠀⠀⠀⢰⣿⡒⢂⡀⠀⢀⣴⡿⡀⠀⠀⠀⠀⡄⠐⠀⡀
⠀⠀⢹⡀⢙⢴⣤⣾⣾⣿⣽⡁⠀⠀⠀⠫⡇⣰⠶⡧⢢⣜⣰⠂⠀⠀⠐⣭⣛⡻⢟⠶⠗⠚⣡⠀⠀⠀⢀⡀⡀⠁⠠⠁⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠍⠋⠀⠠⠀⠀⠀⠀⠀⠚⢦⣄⡔⢌⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠒⠆⠀⠐⠂⡀⠀⠀⠀⠀⢠⣶⣦⣄⡔⠦⢤
⠀⠀⢀⣄⡟⠛⠂⣸⢻⣵⠦⡀⠀⠀⡀⢂⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⢻⢿⢿⣷⣞⠨⣧⡄⠀⠀⠈
⠀⠀⠿⣀⠀⠀⠰⣿⢲⢵⣡⡶⠀⠀⠀⠀⡈⠐⠀⠀⠚⠈⢠⠀⠀⠀⠀⠀⠀⠐⠯⠷⠏⠉⠛⢳
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠲⠤⠠⠠⠤⠶⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡐⠀⢄⠀⠂⠈⠁⣀⠀⠀⠀⠠⡚⠢⠈⠙⠴⠿⠆⠀⠀⠀⠀⢀⠀⢔⠂⠀⠂⠀⠀⠀⢰⡎⣻⣷⢿⣯⣗⣦⣄⡀
⠀⠀⠀⠣⠩⠄⢄⢠⣤⠔⠀⠛⠀⠀⠀⢷⡖⢂⣂⠀⠀⡀⠢⠂⠀⠀⠆⡀⢀⠀⠐⠀⡀⠀⠀⡀⠀⠉⠉⠦⢤⠿⠒⠣⣴⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠁⠀⠀⠀⠈⠑⠦⢄⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⢠⡌⠀⠀⠀⠀⠀⣾⠶⡀⠴⢄⠠⠐⡆
⠀⢀⡈⣿⠀⠀⠀⢨⡙⡐⢈⠰⠚⣶⠖⢲⠁
⠀⠀⠐⠘⡾⢱⢄⠃⠅⢐⠨⠀⢁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢋⢉⠤⢝⢤⡛⠀⠈⡀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠑⠄
⠀⠀⠀⠈⣻⡣⣋⠓⢠⣈⣲⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠂⠀⢀
⠀⠀⠀⠘⠂⢈⠖⠨⠌⠀⠾⢀⠄⠓⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠐⠒⠂⠒⠀⠇⠘⡀⠀⡐⠃⠤⢀
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⡀⠁⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⢀⣁⠀⠀⡐⠀⡜⠀⠀⡷⠎⡀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⡀⠀⢠⣾⡟⢨⢤⣴⠎⠀⠀⠀⢠⠆⠀⠀⡔⠔⡀⢀⠊⡄⢀⡜⠀⠈⠀⠀⠀⠁⠀⠈⢃⠠⠊⠀⠀⡀
⠀⠀⣘⣖⠒⠦⠙⡒⢿⡟⣑⠭⣄⣀⡀⠀⠒⠁⠈⠄⠀⠢⠐⠀⢀⠎⠀⠊⠀⣀⡠⠄⠀⠀⠀⠀⢠⠂⠀⠀⠀⠔⠑
⠀⠌⠀⠈⠀⠈⠀⠬⠰⠎⠄⠀⠀⠀⠈⠢⡠⠄⠀⠘⡞⠀⠀⠀⣀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠄
⠈⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠖⠁⣤⠶⠛⠉⠀⠐⠒⠂⠉⠀⠒⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠠
⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⡀⠀⢀⠙⢉⠉⠥⠀⠀⠀⠀⠔⠂⠄⠀⠀⡤⠆⠐⠄⢀⠔⠀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⠉⠉⣚⡁⠀⠃⠀⠀⠁⠐⠀⣀⠀⠀⢀⠀⣀⠄⠀⠀⠀⠁
⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⢈⡄⠀⠠⠐⠀⠀⠑⠀⠂
⣶⣶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

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

⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⢀⡍⠑⢖⠓⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠜⠁
⠐⠄⡈⠒⠀⠐⠂⡁⠀⠀⠀⠀⠀⠀⠁⠉⢀⡙⢌⡁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠆
⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠄⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⡖
⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢠⡾⣞⣷⢠⠃⠀⠀⠀⠀⠁⡉⢀⠀⠐⠀⡎⠉⢲⠀⠈⡓
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⡽⠐⠑⠡⠋⢈⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠓⠒⠚⠁⢀⠁
⠀⡀⠐⢠⠀⠀⢀⡂⣀⠤⠂⠀⠀⠈⡀⠀⠀⠀⡘⢸⠀⠀⠀⠠⡴⠀⠀⠀⢀⣤⣄⠀⣀⡤⠖⠁⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠆⠀⢀⢠⠟⠁⠂⠀⣁⡀⠀⠀⠀⠀⠀⠀⢀⠑⠂⠀⠁⠀⠑
⠀⠀⡄⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠔⢬⡀⠤⠂⠉⠀⢀⣀⣀⡀⠀⠀⠀⠙⠀⠻⡄⠀⢀⡄
⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⢣⡐⠉
⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡀⠢⠀⢀⠀⠀⠠⠄⠀⡀⠁⡀⠌⠀⠀⠀⠀⠀⠈⠂⡀⠐⠀⠀⠪⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠈⠑⠀⠀⠄⠀⠀⠀⠀⠘⢀⠀⠀⠐⠀⡈⠐⠀⠀⠄⠀⠈⡄⠰⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠐⣤⠀⠀⠆⠀⠀⠈⢢⠈⡇⠀⠀⠀⡅⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⡅⠀⠀⠀⠨⠃
⠀⠀⠀⠐⠋⠀⠀⠀⠂⠈⠁⠄⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⡓⠂⠀⠀⠀⠀⠁⠀⠀⠐⠀⢰⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠓⢄⢀⡇⠀⠀⠁⠨⢆⠐⢀⠀⠐⠀⠠⠀⠀⠀⠄⠀⠤⠁⠀⠀⠠
⠀⠀⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄⠀⠀⠱⠤⡈⠀⠀⠀⠂⢀⣀⠴⠊
⠁⣀⡀⣠⣶⣿⣧⣴⣾⡟⠀⠀⠀⠀⢀⡀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠠
⣈⣿⣿⣍⣟⣿⣿⣿⣯⣷⣤⠤⠄⠒⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡲
⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣛⠆⠀⠀⠀⠄⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠟⠛⢻⢿⣿⣿⠂⠃⠀⠙⠋⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠘
⠀⠀⠀⠛⡙⠉⠀⠀⠀⠀⠀⠀⠠⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣀⡤⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠉⠐⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⣤⡶⠾⠛⠛⠉⠉⠉⠙⠛⠛⠷⢶⣤⣄⡀⠀⠀⠈⠲⣄
⠀⠀⢠⢀⡄⣠⣠⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣠⣾⣟⠥⠒⠈⠉⠁⠒⢤⡀⡰⠉⠉⠓⣄⠀⠉⠻⢷⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢸⣾⣿⣿⢻⡇⠀⠀⠀⢠⠊⠀⠀⢀⣾⢫⠊⠀⠀⠀⠀⠪⠕⠘⠓⢹⣧⠀⠀⠀⢨⠗⠲⣦⡴⠋⠙⣆⠀⠀⠈⠣⡀⠀⠀⠀⠀⢸⠀⠑⡄
⠀⠀⢸⣧⣿⣿⣾⡇⠀⠀⢠⠃⠀⠀⣰⡟⡱⠁⠀⠀⠀⠀⠰⠆⠀⠆⢰⡆⡟⠀⠀⠀⠈⢦⣁⣎⣣⣌⣰⠽⣷⡄⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠸⡀
⠀⠀⠘⣿⢿⠿⣿⠃⠀⢀⠃⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡲⠀⢀⠃⠀⣀⡀⣀⠀⣃⠤⠈⣧⠶⣀⣠⢿⡄⠀⠀⠱⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠈⢲⡖⠁⠀⠀⡎⠀⠀⢀⡿⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡉⢡⣒⡄⢍⠙⠶⡴⣿⡯⠟⠀⠀⢿⡄⠀⠀⠇⠀⠀⢸⠀⠀⡸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠇⠀⠀⢸⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡳⠞⢔⡣⠈⠒⢁⠼⢄⣩⠧⠀⢀⡀⠘⣷⠀⠀⢸⠀⠀⢸⢀⠜
⠀⠀⠀⠀⢸⡇⠀⠀⢰⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠃⢞⡆⣀⡰⠽⠃⠀⠀⠀⠀⠀⠀⠘⡄⣿⡀⠀⠈⠀⠀⢸⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⢿⢀⠎⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢔⡲⠣⠗⠭⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⡇⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢸⢰⠀⠀⠀⡇⠀⠀⡼⠋⠀⠀⠀⠀⢠⠔⠉⠀⠀⡴⠒⠲⢤⡀⠪⢵⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⢸⠀⠀⢈⣿
⠀⠀⠀⠀⢸⢸⠀⠀⠀⢡⠀⠀⠑⣾⣄⣀⡀⢠⠃⢠⣊⠉⢆⠙⢅⠠⠀⠛⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⡟⠀⠀⡆⠀⠀⠸⢨
⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢇⢰⠒⠛⠀⡇⠈⠁⠀⡆⠀⠐⡎⣰⠫⢿⠒⠛⢁⢴⠦⢕⠢⢤⡀⠀⠀⠀⠀⢀⠞⢠⡿⠀⠀⡸⠀⠀⠀⡆⢸
⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠈⢎⠒⠢⣀⣼⡀⠀⠀⣇⠄⢸⠃⡌⠀⠬⡆⠀⢂⢏⠔⣹⡤⡖⠸⡂⠤⠤⠔⠉⣰⡟⠁⠀⡰⠁⠀⠀⠀⡇⢸
⠀⠄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⠣⡀⠀⠈⢿⣦⡀⠈⠋⠁⠀⠹⡀⣴⠀⢀⡤⠹⢏⠐⡤⠬⡷⡝⠀⠀⣠⡾⠋⠀⢀⠔⠁⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠻⣦⣄⡀⠀⠀⠈⠁⠀⢺⡈⢆⣲⠇⠈⠑⢉⣠⣴⠟⠋⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠂⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣑⣶⣥⣴⠶⠞⠛⠉⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠉⠉⠉⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⠀⠀⠾⠂⠀⠀⠀⠛⠆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢀⡀⠀⢀⢄⣀⠀⠀⢧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣻⣿⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣣⡙⠃⠀⠀⢰⠀⠘⠲⠼⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠙⣧⠀⠀⠈⠙⠦⣀⣀⣀⣀⠴⠀⠀⡟⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠚⠃⣤⣀⠉⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣸⣯⢳
⠀⠀⠀⠀⠀⠀⠀⡴⠯⣀⣨⠟⠃⡏⠙⢦⣄⣀⡈⢀⣓⣃⡤⢾⣅⠀⠀⠀⠁⣽⢛⠿⣀⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢉⣀⡂⠇⠀⠀⣼⠋⡏⠉⢫⠀⠱⠸⣏⢦⡀⠀⠘⣌⠷⢂⣩⠟
⠀⠀⠀⠀⠀⠀⠀⣰⠯⢻⢩⢉⡟⣧⢀⣼⠃⠀⠃⠀⠘⡀⣄⢤⡹⣆⡛⣤⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⢰⡇⡇⠘⢸⢸⡇⡎⢹⡃⠀⠀⢞⢢⣠⠁⠟⢌⡇⠙⢟⠁⠀⡸⠀⡇
⠀⠀⠀⠀⠀⢠⡏⡇⣧⠀⢸⢸⡇⠃⣨⡧⠀⢠⠈⡇⠁⠀⢀⣘⡵⠁⠈⡇⢠⠃⠀⢹
⠀⠀⠀⠀⠀⣸⡃⡇⢹⣧⢐⣨⡷⠟⢫⡀⠀⣸⣅⡇⢠⠞⠉⣡⣤⣤⡼⠱⡾⠀⠀⡼
⠀⠀⠀⠀⠀⣿⡇⡇⠀⢹⠻⣿⡄⠀⠀⣿⡛⢫⠟⢠⢻⢳⢻⣽⠀⠳⣄⢀⡠⠄⠰⠳⢤⡄⡀
⠀⠀⠀⠀⠀⣿⠁⠇⠈⢸⢀⠀⢷⡄⠀⠘⠷⠋⠀⣾⢸⢸⣹⡇⠀⠀⢠⠋⠐⠒⠀⣀⣠⠤⠈⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣿⠷⢿⣦⣼⣬⣀⣆⣻⣄⠀⠀⠀⣸⣃⣸⣴⣿⣡⣤⣶⠾⡎⠁⠐⠁⠀⠀⠀⣠⠏⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠉⠉⠙⠛⢧⣀⣴⣯⣿⣿⣿⣿⣿⣿⣿⣄⠈⠒⠤⠤⠤⠔⠚⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠤⠴⠶⢦⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⣆⠉⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⣤⣤⣼⣿⣀⡀⠀⠀⠈⢷⡀⢿⢀⣩⣿⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠛⢦⡀⠀⠀⢳⣾⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⣴⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⡿⢫⣉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠐⠀⢀⠀⠀⠀⠀⡄⡀⠀⠀⢀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠃
⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢓⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠱⡀⠀⢀⣀⠀⣴⠂⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢡⠶⠂⢠⠆⠀⠀⠀⠀⠜⡁⣈⡈⠀⠀⣀⢠⡀⡀⣄⣀⡠⠀⠀⠀⢰⡆⠀⠄⠈⠀⠉⠁⠈⠀⠀⢻⣄⡀⠀⢀
⢀⠀⠀⠀⠀⠂⠀⣄⠀⠀⠀⠡⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠈⠀⠀⢠⡄⡒⠚⠀⠀⠀⠉⠁⠄
⣄⠀⡆⠀⠀⢀⡀⠀⠶⠀⡠⠐⠁⣀⣄⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠸⠛⠓⠲⡀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠀⠀⠛⣠⠄⠠⠆⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢰⡀⢠⣰⡀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡘
⠀⠀⠠⠤⣭⣿⣿⢿⣤⡤⠀⠀⠻⡏⠀⠀⠀⣷⡞⠀⠠⠰⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⡾⢠⣉⠅⣿⡀⠀⠙
⠀⠀⠀⠰⠤⠞⠸⠦⠤⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠐⠀⠠⠁⠰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⠉⠐⠤⠗⠹⠇⠀⠈⠡

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠰⠏⢀⠀⠀⠀⠈⠉⠑⡄⠈⠁⡜⠀⠤⠀⠘⢂⠀⠀⠀⢰⠉⣀⠴⢄⠀⡼⠮⠑⠀⠀⠀⠀⠀⠁⠰⠀⢀⢄⠈⠀⠈⡆⠸⣡⠑⠀⢀⡠⠤⣤⣤⡀
⠀⠀⠀⡀⠀⢀⣀⠠⠄⠊⡍⠀⠀⢱⠀⠈⢠⢄⠀⠡⠀⠠⡁⠀⣁⠀⡈⠀⠀⠀⠀⡄⠁⠀⠐⠀⠀⠀⠐⠅⠀⠁⠂⡜⠀⢀⡈⠙⠀⠷⠦⠄⡸⢺⠁
⠀⠀⠀⢥⣁⡐⠠⠀⠀⠐⢈⠇⠀⠀⠑⢄⠀⠢⡑⢄⠇⠀⠈⠍⡹⢪⠅⠀⠀⡀⡰⠀⠀⠀⠇⠀⠂⠨⠀⠀⠀⢢⠎⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢰
⠀⢠⡄⠸⠄⠤⠀⠈⠑⠈⣀⣤⡀⠄⡤⢀⠉⠁⠐⠀⢠⣞⡃⢸⡞⣵⠀⠀⢀⠀⡕⠉⠈⣄⠣⠂⠰⢀⡈⢈⠔⠁⠀⢱⠶⠤⢤⡄⠀⠐⠀⠀⠒
⠀⠈⠃⠀⠠⡆⠀⢀⠖⠍⡀⠀⠌⡐⠠⠄⣘⢦⡀⠀⠸⠋⠀⠀⢯⡖⠀⠀⠀⡟⠀⠀⠀⣦⠀⠄⠐⠄⠐⠁⡐⠀⠀⠸⣄⣀⠀⠀⡀⠈⡅⠀⠀⠋⠂
⠀⠀⣠⠦⡄⠀⡠⢁⡨⠴⢤⡸⣒⣒⣫⠭⠒⡏⠀⡤⠴⠦⡐⡀⠸⠇⠀⠀⠀⠈⠉⢁⠊⠙⠊⠁⠀⠀⠀⠐⡠⠁⣤⠀⠀⠀⠀⠀⠁⠂⠂⠁
⠀⠀⢷⠀⠸⡄⠈⠣⣉⢈⢉⣉⣍⣍⠤⠴⠚⠀⠀⡇⠀⠀⢀⡜⠀⠠⠈⠐⠀⢀⣀⡀⠀⠀⠀⣀⣴⣶⣶⢾⣄⠀⠈⠀⠈⠀⠁⠀⠀⠀⡠⠆⢤
⠀⠀⡯⢀⢢⠘⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⡀⠻⣀⠀⡀⡠⠗⠀⠘⢜⡥⠀⠃⠀⠈⠀⢀⠚⠿⣶⠽⠿⠿⠿⢧⠀⡂⠀⠀⣐⠀⠀⠶⠤⠠⠂
⠀⠀⠹⣄⣉⡰⠃⢀⠀⠈⠣⢀⡉⠀⠒⢉⡹⠋⠀⠀⠈⠉⠁⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠰⡤⠤⠙⠄⣀⡀⠠⡤⠀⠁⢠⠐⠂⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠄⠑⡤⠀⢆⠀⠀⠈⠉⠀⠀⣀⣠⢴⢮⡫⢆⠀⢀⡔⠠⠀⣀⡈⣩⢋⠕⠀⢀⠀⠀⠀⠀⠁⢰⠀⠀⠤⠘⠠⠀⢀⡜⠀⠘⡄⡅⢰
⠀⠪⡤⠔⠀⡌⠀⠀⠀⠀⡔⠀⠀⢠⠉⡈⣷⡼⠽⠞⠉⡠⢊⠴⣎⠨⢅⡠⣥⡤⠀⢀⢀⡀⠀⠀⣉⠉⠀⠉⠁⠀⠃⠀⠀⠀⠀⠬⡀⢀⡴⠃⠈⠓⠁
⠀⠀⠀⠀⡘⠀⠠⠠⠁⠈⠀⠪⠇⠀⠅⣀⡀⠤⠄⠂⠉⡠⡦⢂⣀⣠⡮⠞⠁⢀⠢⠂⠀⠈⡆⠈⠉⢀⣀⠖⡆⠐⠚⠠⠠⡆⠀⢦⠤⠸⡀
⠀⠀⠀⢀⠠⢤⡐⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡦⠀⠾⠒⠋⠉⠉⠀⢠⡺⡷⠀⠀⠀⢄⠜⠀⠀⢠⠛⠘⠁⠭⠬⠁⠨⠤⠌⠶⠀⠀⠈⢉⠔⠀⢄
⠀⢰⠀⠈⠀⠀⠱⠂⠀⠀⠠⡐⣥⣬⠁⠠⠀⢀⣀⣀⣠⠀⣿⣆⠀⠀⠹⠏⠁⡐⠦⠂⠁⢰⠦⠀⢘⢂⠀⠀⠀⠤⠄⠤⠐⢠⡄⠀⠀⠀⣌⠀⠀⢸
⠀⠀⠉⢀⣀⠀⣰⠚⡀⠀⠀⠀⠼⠁⠡⠀⠠⠟⠋⠁⠀⠈⠱⠿⠿⠃⠀⡄⠊⠀⠀⠀⠀⠀⢠⠀⡸⢄⣂⡈⠀⠀⠀⠀⣀⣠⠦⠀⠀⢠⠁⠀⠔⠺
⠀⠰⠢⠤⠤⠊⡀⠀⢁⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠃⢀⠄⠠⠀⠀⠑⠀⢠⠀⣉⡠⠖⠂⠀⠀⠀⠀⠩⠉⠭⠭⠀⠐⠈⠠⠄⠠⡀⠀⢀⠇
⠀⠘⡆⠠⠀⣀⡠⠈⢁⠊⡥⠀⡁⢱⠀⠢⢄⣀⡀⠤⠶⠗⢠⠃⠀⠀⢀⡀⢠⠀⠀⡘⠀⠀⢠⠀⢠⡟⠩⠀⠀⠀⠀⢀⠠⠀⠀⠳⡟⠀⠈⢸⠁
⠀⠀⠑⠐⠀⠁⠀⠀⠘⡄⠃⠐⠁⠀⡃⢀⠄⠄⠠⡀⠀⠀⠁⠂⠀⠀⢨⠇⠀⡁⠀⠀⠀⠠⠀⠁⠀⢀⡄⠭⠈⠡⢬⡇⠀⠀⠐⢄⠀⠀⠐⠂
⠀⠠⠂⡐⡢⢲⠁⠄⠀⠡⣀⠔⠂⠈⠀⡘⠁⢀⠠⠀⠈⠀⢀⠶⠀⠀⢹⠀⠐⡀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠈⢀⠤⠤⠜⠒⡥⠂⠉⠀⢤⡔⠀⡈⠄
⠀⠐⠃⠈⢰⠈⠃⠚⠁⠀⡔⠀⠒⡄⠀⠒⠉⡯⠆⠀⠠⡀⠀⠉⠐⢀⡘⠀⠀⠀⠸⠆⠀⡠⠏⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⢰⠀⠀⢀⠘⠛⠉
⠀⠀⠠⠤⠘⠒⠐⠉⠃⠀⠈⠃⠁⠀⠀⠀⠀⠇⡈⠀⠀⠈⠐⠒⠒⠉⠀⠀⠀⢒⣄⠀⠪⣁⠌⠒⠠⠄⠶⡉⠐⠶⢚⣁⠤⠊⢀⡀⠐⡀⠀⠠⠂⣀
⠀⠀⠀⠀⠀⠉⠑⠀⠀⢀⢀⡀⠀⠣⢄⡊⠀⣀⡀⢀⡖⠒⠚⢳⠀⠀⢠⠀⠀⡄⠀⠀⠑⡄⠀⠉⠁⡠⡀⠀⣠⠄⠀⡠⡀⠀⠈⠀⠀⠀⠀⠀⠘⠐
⠀⠀⠀⡀⠠⠀⠁⠐⠀⠘⢄⣢⠐⠂⠀⠀⠈⠥⡬⠂⠹⠀⠀⡏⠀⠀⡁⠀⠀⢄⣀⣀⡔⠀⠀⠀⠸⠬⠋⠋⠰⠋⢸⢠⡘⠀⢁⣀⠔⠐⠒⠂⠄⠀⡀
⠀⠀⠒⢀⡠⠤⢄⡀⠀⡀⡄⠄⠀⢀⠄⠂⢄⠈⠀⠀⠙⠒⠚⠓⠒⠒⠁⠠⠄⠀⠀⠈⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡉⠈⠉⠉⢩⠃
⠀⠀⡴⢯⣗⢸⠎⢁⠀⡷⠄⡠⠐⠁⠈⠀⢸⠀⠀⡴⠊⣀⡀⠱⠆⠀⠀⠀⠠⠐⡖⠀⠀⠀⡠⠔⠈⠉⠑⡾⠿⠷⣂⠉⠁⠀⠀⢱⠤⠀⠀⠀⡔⠃
⠀⠀⢿⠷⠑⠁⠀⢸⠀⠀⠀⢀⡀⠀⣀⠔⢡⡀⢸⢠⠎⠁⠀⢤⠈⠐⠂⠀⠐⠊⠁⠀⠐⠀⡀⣀⡄⠤⠔⠀⠀⠑⢄⠀⠀⠀⠠⠄⠀⠀⠀⢈⣁⣰⠆
⠀⠀⠀⠁⠀⠀⠂⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢴⡟⠛⣌⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⠞⢫⠝⠀⢸⡇⠀⢹⡄⠀⠹⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡶⠟⠓⠄⠒⠁⠒⠖⠿⣿⣶⣿⠃⠀⠀⣿⡆⠙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠘⠛⠒⠶⠶⠶⠶⠒⣋⣥⠞⠁⠀⠀⣰⡿⠁⢀⣿⣷⣬⡙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣀⣤⣤⢤⣴⣶⡒⠚⠋⠉⠁⣀⣀⣠⡴⠞⠋⠀⣠⠞⠉⣿⡿⣿⣷⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⡶⠶⠟⠛⠉⠉⠀⠀⠀⠀⠈⠙⠻⢿⣿⣯⣍⣩⣤⣤⣤⣶⣮⣥⣴⣾⣿⠇⠈⢻⡇⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⢛⣿⠏⠀⢀⡾⠁⢀⣾⠁⠹⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⣤⣤⣤⣤⣤⠤⠲⠚⠊⠉⠁⠀⠀⢀⣀⣀⣤⣤⡤⠶⠶⠾⠓⠒⠉⣉⣀⣴⡾⠋⠀⣠⣾⡟⠀⠀⣿⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠚⠋⠉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠚⠛⠋⠉⢀⣀⣤⣾⣿⠏⠀⠀⣠⣿⡆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠼⠿⠛⠋⠉⢉⣽⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣠⣤⣠⡤⠶⠶⠶⢶⣿⣿⣿⡟⠋⠀⢀⣠⠞⣹⠟⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣷⠶⠶⠖⠒⠊⠉⠉⠙⣟⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠉⠻⢷⣤⣄⣀⠀⠀⠀⢈⣹⣿⡿⠟⠋⣠⡾⠋⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⣤⣖⣋⡉⠁⠀⠀⠀⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣿⡿⠿⠿⠛⠛⠉⠁⣠⡴⠟⠉⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢈⣩⡟⠛⠛⠛⠛⠋⠁⠉⠀⠀⠀⢀⣠⣤⣚⣋⡉⠉⠁⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⣀⣀⣤⣶⣿⣿⣿⠿⣿⠷⡄
⠀⠀⠀⠀⢠⣶⢻⣿⣦⣤⣤⣄⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣶⣶⣶⣾⣿⣷⣶⣶⣶⡿⡿⢟⣿⠙⣏⠳⡄⢍⠺⠛⡤⣿⡀
⠀⠀⢀⡠⣞⠫⣵⠍⣿⡟⢋⡉⠻⣭⢉⡿⣛⠏⠛⡿⢙⠟⡛⣩⠉⠛⠙⠛⢛⢏⡹⣹⣙⣏⠙⡏⢩⡈⠁⠈⢦⡔⢠⠀⠈⠙⢀⠈⡄⢁⠀⠄⢤⣑⢮⡄⢻⡀
⠀⣰⣟⡄⠹⠀⠇⠘⣡⠷⠈⡯⠆⠉⠌⠃⠉⡰⠀⢤⠃⠛⠸⢀⠋⠀⠋⠛⠈⠈⠁⠱⠉⡭⠀⡐⠃⠁⠀⠀⡘⠀⠂⣰⡄⠰⡆⠀⡿⠀⢱⠆⢠⡏⠐⠀⣼⣷⣦
⢨⡀⢟⠛⣴⡷⠶⠄⣹⠀⠘⠁⡼⠁⠀⠀⠰⠃⠀⢰⠂⡴⠀⢹⠀⢠⠂⠰⣀⠀⡄⠀⠶⠀⣠⡀⠈⢠⠀⠀⢰⡇⣀⣾⣀⣴⢀⣤⡇⣠⡟⡴⠟⠻⠧⣿⣾⠃
⠀⠳⠈⢄⢹⡀⠀⠘⡉⡴⠛⠉⠸⣆⣰⣦⣤⠷⠒⡴⢀⣡⠼⠚⠳⡄⢠⡖⠉⠈⠓⢤⣤⡊⠉⠉⠳⡄⢷⡏⠀⠈⠙⠏⠙⠀⠈⢙⠃⠀⢙⡎⠀⠀⢠⣸⠆⠀⣼
⠀⠀⢣⠘⣿⣡⠀⠀⢡⢀⡀⠀⠀⢫⣽⣮⠁⠀⠀⢻⣼⠁⠀⠀⠀⣿⡎⠁⠀⠀⠀⣶⣿⠁⠀⠀⠀⣷⡌⠀⠀⠀⢸⣼⠃⠀⠀⡟⠀⠀⡾⠀⠀⠀⣾⠋⠀⡰
⠀⠀⠈⠆⠘⣻⡄⠀⠀⣾⣧⠀⠀⠸⠟⢻⡄⠀⠀⢸⣥⡆⠀⠀⠀⢉⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣄⣤⠀⠀⠀⣈⡇⠀⠀⠸⠃⠀⣴⠁⠀⢀⣿⡏⠀⢠⠃
⠀⠀⠀⠐⡀⢡⣹⡆⠀⠸⣿⡄⠀⠀⡟⢸⡇⠀⠀⠀⣄⣿⠀⠀⠀⢸⠗⠄⠀⠀⠀⣿⢿⠀⠀⠀⢸⣿⠁⠀⠀⢰⣟⠇⠀⠀⡆⠀⢠⠏⠀⠀⡜⢣⠁⢀⠎
⠀⠀⠀⠀⠙⡀⣤⣷⠀⠀⢸⣣⠀⠀⢸⠤⣷⠀⠀⠀⢩⣽⠄⠀⠀⢸⣆⡶⠀⠀⠀⣵⣿⠀⠀⠀⠺⣿⠀⠀⠀⣠⡻⠀⠀⢀⠁⠀⡜⠀⠀⢰⣱⡆⢀⠟
⠀⠀⠀⠀⠀⢡⢠⡙⡇⠀⠈⣿⡄⠀⠀⣆⠹⡆⠀⠀⠈⢿⡀⠀⠀⢸⣽⣷⠀⠀⠐⠛⡛⠀⠀⠀⣾⡍⠀⠀⠀⣹⡏⠀⠀⠘⠀⢠⠃⠀⢀⠟⡷⠀⡜
⠀⠀⠀⠀⠀⠈⡄⢀⠸⠀⠀⢸⣧⠀⠀⢹⡾⣇⠀⠀⠀⢾⡇⠀⠀⢸⣀⣿⠀⠀⢸⢀⣿⠀⠀⠀⣷⡇⠀⠀⢠⣿⡅⠀⠀⡇⢀⡙⠀⠀⡞⣰⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢡⠌⡀⠧⠀⠀⣿⠆⠀⠀⣿⢿⠀⠀⠀⠸⣿⠀⠀⢸⣿⣯⠀⠀⠈⢘⡏⠀⠀⠰⠟⠀⠀⠀⢸⣿⠀⠀⢠⠀⣬⠁⠀⡜⠀⠇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢰⢁⠐⡄⠀⢸⣧⠀⠀⢹⢘⡁⠀⠀⠀⣾⠀⠀⠸⣹⣿⠀⠀⠀⢸⡇⠀⠀⢀⣾⠀⠀⠀⣦⡟⠀⠀⠉⢠⠃⠀⢰⠁⣴⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠂⠀⠀⣷⡀⠀⠀⣿⣿⠀⠀⠀⢿⡀⠀⠀⣼⣿⠀⠀⠀⣾⡇⠀⠀⢘⡿⠀⠀⠀⣿⠇⠀⠀⢠⡟⠀⠀⠗⢸⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠸⣇⠀⠀⢻⠍⡀⠀⠀⠘⡇⠀⠀⠃⣸⠀⠀⠀⠟⠁⠀⠀⢉⠁⠀⠀⢸⠈⠀⠀⠀⣿⠁⠀⡾⠀⠆⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⠀⠀⠈⢀⠃⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠘⡆⠀⠀⢀⠉⠀⠀⠁⠸⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⠀⣀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠒⠢⠤⠤⡤⠄⠀⠀⣀⣀⡀⣀⣀⣀⣀⠀⠠⠤⣤⠤⠤⠤⠒⠒⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠚⠉⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠠⠔⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠶⠚⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡄⠠⠔⠀⠀⢀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠄
⠀⠀⠀⠀⠀⠐⠋⢁⣀⡤⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⢀⠀⢂
⠀⠘⠀⠑⠀⠠⠀⢒⠉⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠆⠃⠠⠀⠀⠀⢸⠀⠀⠓⠂⠉⠂⠉⢀
⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠊⠀⢸⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⡀⢀⠀⠀⠀⢈⡤⠤⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⢠⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠐⠈⠘⠒⠘⠻
⠀⠀⠀⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠄
⠀⠀⡰⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⣀
⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⢀⡀⠈⠐⠀⠀⢰⠀⠀⠀⠀⠀⢀⡴⠒⢢⣄⠀⠀⠨⠀⠀⠀⠀⠀⣀⡀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠃⣈⠁⠉⣈⠌⠀⠸⠀⠀⠀⡐⠢⠄⠭⠭⠬⠥⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⢀⠤⠐⠒⠀⡒⠤⢄⡀
⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠐⡠⠰⠄⠒⠐⡠⢀⡇⠀⠀⠀⠀⠘⠢⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡈⢀⠀⣄⠄⢰
⠀⢀⠀⠀⠘⠑⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠄⠀⠀⢀⠞
⠀⠀⡀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠑⠒⠒⠒⠉⠁⣠
⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠉

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠠⡏⠀⠀⠀⠀⠈⠉⠑⢆⠀⠋⢰⠋⡠⠄⠀⠓⣄⠀⠀⠀⢘⠁⣀⠥⠀⠀⣌⢮⠑⠁⢀⠀⠀⠀⠊⢄⡊⠀⠠⠀⠁⠄⢱⠀⢛⣌⠂⠀⢀⡠⠤⣤⣄⡁
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢤⣋⠃⠀⠘⡄⠈⠂⡄⡀⠈⠆⠀⢠⠁⠀⣁⠀⡸⠀⠀⠀⠐⡂⠀⠐⠀⠠⠀⠀⠀⠆⠀⠀⠐⢀⠆⠀⣀⠑⠃⠰⡯⡤⠄⡹⢺⠁
⠀⠀⠀⠌⡄⠡⠀⠀⠔⡠⠌⡳⠀⠀⠘⢆⡀⠠⣈⠢⣘⠀⠀⠙⡝⡣⢬⠁⠀⠀⠀⠠⠅⠀⠀⠸⠀⠀⠠⠁⠀⠀⠑⡠⠋⠀⠀⠉⠓⢄⠀⡄⠀⠀⠀⢸
⠀⢀⡀⠰⣉⣉⡀⠤⠂⠂⠉⣀⣀⢀⣀⡀⠈⠒⠈⠔⠀⢠⢶⠀⢛⠽⣳⠀⠀⠀⠡⡡⠊⠘⢄⢀⠰⢀⠅⡀⠀⢂⠜⠁⠈⠦⢇⣀⣀⡘⠀⠃⠠⠤⠔⠈
⠀⠈⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⠃⠌⠠⠉⢲⡀⠀⠀⣿⠙⠀⠈⣞⡜⠀⠠⠬⡶⠁⠀⠀⣸⡀⢀⠐⢄⡩⠔⢁⠄⡀⠀⣀⠀⣀⠌⠀⠄⢠⡀⠀⠀⢒⠄
⠀⠀⢀⣄⡀⠁⠀⡈⢁⣀⣎⡀⠦⠬⠐⡦⣮⠵⡎⠀⣀⣤⣄⢀⠀⢻⡃⠀⠀⠀⠙⡂⠐⡦⠛⠬⠂⠀⠀⠀⠀⠌⡔⢀⣀⠀⠉⠉⠀⠐⠂⠁⠀⠆
⠀⠀⢿⠀⢹⡄⠘⠰⠒⠠⠐⠚⠒⠒⣉⣀⡤⠞⠀⢘⠇⠀⠀⢉⡗⠀⢠⠄⢠⠀⠀⡀⠼⠀⠀⠀⠀⢀⣤⣄⣤⣎⠀⠈⠋⠀⠊⠑⠀⠀⠈⠀⣀⡀⣀⠂
⠀⠀⢸⢀⠤⠑⡄⠀⠉⠓⠃⠉⠉⠉⠉⠀⠀⠀⠐⡼⠀⠀⠀⢸⡇⠀⢠⠰⠀⠀⠎⠁⠃⠀⠀⠠⣿⣿⣝⣿⣵⣿⣷⠀⢠⠄⠀⠀⡆⠀⠤⣼⡁⢠⠍
⠀⠀⢱⡈⠒⢀⡇⠀⠀⠀⢳⠚⠒⠀⠤⠄⠒⢶⠂⠈⠃⠒⠶⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⡀⠀⡼⡅⠀⠀⠀⠀⢃⠀⢄⣀⡠⠃⠀⠀⠉⠉
⠀⠀⠀⠙⠙⠋⢀⠴⡀⡀⢄⠉⠀⠐⠒⠒⠊⠁⠀⢀⢠⡠⢂⡀⠀⠀⣀⠁⠀⠀⠒⠒⡶⢦⠀⠉⠉⠀⠀⢘⠻⠀⠉⠁⠀⢀⠇⠀⠀⠀⡀⠀⢣⠈⠂⢢
⠀⣰⠂⢐⠀⢠⠃⠀⠉⠁⢈⠀⠀⠀⠠⠄⠤⡄⡖⣆⡿⠿⢉⡕⢀⡔⢱⠊⠉⠌⠉⠉⠐⠁⠀⠈⠒⠀⠤⠀⠀⠐⠀⢠⠌⠁⠀⠁⠀⠞⠁⠀⢀⠗⠲⣎⠄
⠀⠈⠉⠀⢀⠆⠀⠀⠀⠀⠄⢠⢤⠀⢲⠒⠀⠛⠁⣀⠠⠔⢋⡔⠹⠃⠈⣰⣹⠟⠉⠀⠒⠀⠒⡄⠀⠶⠀⠀⣠⣀⡀⣠⡄⠀⣀⠀⢰⠁⠂⣰⠁
⠀⠀⠀⢀⠎⠀⠀⠐⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⢉⡀⠀⣠⣈⡥⠴⠖⠚⠋⣡⣄⢠⠀⠀⠀⢀⠇⠀⠀⣤⢒⠇⠨⠄⠤⠀⠅⠘⠠⡀⠙⢁⠼⠂⡀⣀
⠀⢀⠀⠰⢈⠋⠣⣀⠄⠀⠀⢀⡂⠀⠤⠄⠀⠀⠙⠁⠀⠁⠀⣤⠀⠀⠀⢞⣭⠍⢸⡀⣀⠔⠁⣀⠀⠀⡀⠀⠠⡈⠉⠉⠁⠉⠉⠁⡁⠀⠀⠀⡘⠀⠀⢁
⠀⠘⢤⡀⠀⠈⠁⣁⡀⠀⠀⠰⠺⣾⠪⠀⠁⢠⣶⠶⠒⠒⠠⢟⡦⣄⡀⠘⠁⡠⠀⠉⠀⠀⠈⠊⠀⠀⡆⠁⠀⠀⠀⠉⠀⠁⠀⢹⠁⠀⠀⠀⠇⠀⢀⡘
⠀⠀⡀⠄⠲⢈⠜⠁⢀⠀⠀⠀⠀⠑⠄⠀⠠⠋⠀⠀⠀⠀⠂⡈⠉⠉⠀⠐⠏⠄⢀⠀⠄⠠⠔⢈⣆⠈⠑⠂⠠⠤⠤⠤⠤⠤⠔⢚⠳⠀⠀⠰⠈⠀⠁⡇
⠀⢨⠁⠙⠀⡁⠆⠀⡠⢀⡠⠄⠤⢄⠀⠀⠁⠀⠀⠀⠀⢈⡄⠀⠔⠈⠉⢂⠀⠈⠁⠐⠀⠄⠂⠉⠀⠀⢀⡄⡄⠀⠀⠀⠀⠀⠈⠀⢀⣎⡆⠐⠤⢤⠰
⠀⠀⢅⢐⡂⠠⠔⠁⠠⡃⣰⠉⢱⠀⢧⠀⠛⠀⠀⠐⠚⠛⠁⠜⠀⠀⠐⠸⡄⠐⡄⠠⠜⠀⢂⠉⠆⠀⠏⠐⡀⠄⠀⠀⣀⠐⠠⠀⠀⠓⠇⠀⡇⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢁⢀⡠⠃⣾⠑⠒⠒⠄⠠⠊⠈⠀⠀⠀⣸⠃⢀⠀⠀⠀⠀⠘⠁⠀⠀⣀⠼⠒⠀⠀⠒⠺⡀⠀⠀⣈⡆⠀⠀⠀⠀⡀
⠀⠀⡁⢨⠽⢹⣀⢓⡀⠈⠢⠚⠁⠀⠀⢰⠁⣀⡤⠊⠀⡇⡀⠰⠿⠀⠃⢸⠀⠈⠄⠉⡁⠀⠀⢀⠴⠊⠁⠀⠀⢀⠔⠂⠀⠉⡹⠊⠀⠀⠀⢾⣟⣀⠤⠂
⠀⠈⠁⠀⠠⡀⠸⢘⡀⠀⠰⣉⣈⡳⠀⠀⠁⠘⠘⡄⠀⠡⡐⠀⠀⢈⣠⠎⠀⠀⠀⠈⠁⢀⠄⢃⠀⠀⠀⠤⢀⠀⠀⠀⢀⡼⠡⡮⠀⠀⠒⠊⠉
⠀⠀⠀⠓⠀⠃⣉⠉⠁⠀⠀⠁⠀⢠⠄⠀⡄⠀⠤⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠨⠦⠀⣑⠬⠤⣉⣒⣒⠚⣥⢊⡛⠋⠥⠐⠊⠁⡄⠄⠀⠄⠀⠀⢀⡀
⠀⠀⠀⢀⠀⠁⢈⠀⠀⠀⡉⡕⢀⠈⠒⠬⠀⢀⣤⡀⢰⡋⠉⠉⣷⠀⠉⢱⠀⠀⠃⠀⠀⠀⡀⠀⠀⢀⡠⣤⠀⡠⢦⡀⣀⠤⡀⢀⠉⠀⠀⠀⠀⠀⠈⠖
⠀⢠⠀⡀⠢⠀⠠⠐⠀⠀⠱⢡⠞⠁⠀⠀⠀⠱⡤⠜⠀⠇⠀⢸⠇⠀⠀⡆⠀⠈⠢⠀⣠⡔⠁⠀⠀⠈⠠⠋⠈⠄⠎⠀⠅⠠⠁⠀⣴⣤⢂⡘⠃⠁⢆⣀⡄
⠀⠀⠉⣀⣤⠐⠤⡀⠀⠀⢀⢰⠀⠀⡠⠒⠒⡄⠀⠀⠀⠉⠉⠉⠉⠀⠈⠀⠰⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢇⠠⠤⠀⠀⠀⠀⣠⠃
⠀⠀⣼⢳⣽⣐⡟⠉⠀⠼⠄⢈⠔⠉⠀⠀⠂⡄⠀⢀⠔⢁⡀⠤⠵⠆⠀⠄⠠⠄⠂⡚⠀⠀⠀⡀⠔⠈⠈⠉⡶⠻⡿⠥⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠔⠁
⠀⠂⢻⡶⠒⠉⠀⠀⡄⠀⠀⠸⢀⠀⣀⡠⠊⣤⠀⡇⡰⠋⠀⢠⢤⠀⠑⠒⠒⠒⠊⠀⠀⠐⠀⣀⣀⠤⠤⠔⠁⠀⠈⠢⣀⠀⡀⠀⠠⠄⠁⠀⠀⣀⣀⢺⠃
⠀⠀⠀⠈⠐⠐⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⠀⠐⠚⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠁⢀⡀⠓⠒⠒⠒⠒⠒⠒⢀⡀⠀⠀⠀⣶⡷⣿⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡠⢺⢀⣁⠆⠁⠀⡂⡾⡀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟⣰⠋⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⢠⡌
⠀⠀⠀⠀⠰⣀⠀⠇⢐⠈⠼⠀⠀⢻⡥⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠤⠲⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢨⣉⢿⡇⠄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠰⠒⠀⠀⢸⠀⠆
⠀⠀⠀⡠⠀⠰⢂⠛⢺⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠡⠄⠄
⠀⠀⠀⢉⣀⠀⠀⠌⠀⠨⠌⢻⠍⠀⠀⠀⠠⠄⠐⠀⠀⠁⠀⠀⠀⠈⠀⠀⢣⠀⠀⠀⢀⢀⠀⠠⠄⠤⣀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠰⢤⢀⠀⠈⠓⠂⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠰⡁⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠭⠙⢲⡄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠊⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⢀⣀⣄⣀⣀⡀⡀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠄⠀⠀⠠⠶⠀⠀⢂⠀⠀⠠⠄⠀⠀⠈⢀⠠⢀⣀⠀⠒⣤⡀
⠀⠀⠀⠀⠨⡉⠁⠙⠀⠛⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⠆⠀⢀⡀⠀⠀⠀⢀⠀⡡⠀⣁⢀⡴⠎⠁⡱
⠀⠀⠀⠀⠀⠱⡒⠲⠲⠒⠒⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⢠⠴⠙⠘⠀⠀⠀⡀⠋⢸⠅⠀⡀⡤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⢀⠉⠃⠀⠀⢒⠈⢡⠀⠠⠇⠀⠘⠀⠂⠁⠑⠀⠀⠀⢀⠀⠈⠀⠀⡀⡁⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⢠⠀⢀⣄⠀⠀⠀⠉⠁⠀⢀⠐⢉⡀⠀⠀⠀⠀⢀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⡘⠀⠀⠠⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢀⣠⠰⠃⣀⢶⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡘⡷⠀⢠⣄⠀⠀⠀⠀⢀⠨⠁⠀⠄⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠾⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢂⢀⣔⢴⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠈⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠁⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠒⢀⠀⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⠉⠀⠀⠀⠈⠀⠀⠄⠀⠠⠠⠔⠲⢖⠒⠀⠥⠀⠀⠀⢢⢢⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⣴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢷⠃⡆⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠘⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⡀⠈⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⣸⣿⡿
⠀⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⣿⢀⡀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠰⣶⡆⠀⠀⠀⢹⡟⠁
⠀⢹⡄⠀⠀⢥⣀⠀⠀⢰⠆⠐⠰⣿⡇⠀⣿⣿⠸⡧⠀⠀⠘⠛⢿⠀⠀⠙⠛⡟⠾⠆⣺⠂⠀⠛⠇⠀⠀⢀⣿
⠀⠈⣇⠀⠀⠘⣇⠀⠀⠘⡄⠀⠀⢸⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣆⠀⠀⣼⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⠀⠀⠠⠀⠀⠈⠀⢀⡼⠋⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠂⠀⠀⡟⠀⠀⠁⠀⠀⣀⣀⡾⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⣀⡴⢛⢡⡙⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡞⠉⠙⢿⡋⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠰⣏⠰⣌⢧⡹⣜⣧⠀⢂⠀⠀⠀⡇⠀⠀⣴⠏⠀⠀⢀⡼⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢷⡙⢦⡻⠍⠘⡇⠀⠂⠀⠀⣿⢠⡾⠁⠀⠀⢢⡞⠁⢀⠔⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠄⡀⠀⠙⠶⣤⣤⣾⡃⠀⠀⠀⠀⣿⠏⠀⠀⠀⣵⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⡾⠃⠀⠀⢀⡾⠁⠀⢀⣀⣠⣤⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠦⠶⠶⠶⠶⠖⠛⠛⣛⣉⣷⡄⠀⠀⠹⣦⠟⣀⣀⣠⣴⡿⠶⠞⡛⢉⣭⠤⡄⠀⢹⡀⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⠶⠟⢛⣉⣁⣸⣧⡤⠶⠞⠛⠛⢉⠉⣤⠶⣆⢸⣏⠁⠈⠓⠶⣤⠀⢸⡟⠉⠉⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣼⠷⠞⢛⣛⣉⠉⢠⡴⠂⢠⡞⠙⠃⣸⠀⣿⣴⠏⢸⣯⡤⠀⠓⠞⠋⠀⢸⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿⠀⠀⣿⠁⣹⠇⢸⣧⠀⢸⣇⣠⡆⠻⠀⠋⠀⠀⢄⣐⣠⣤⠴⠶⠖⠒⣾⠇⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣁⣀⣤⣤⣿⠀⠀⣿⠚⢯⡀⠸⡧⠶⠀⠉⠉⣀⣠⣤⣴⡶⠛⠋⢹⡇⣀⣤⡶⠶⠛⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢸⡇⠀⠉⠀⠀⠀⣀⣠⣤⣶⣾⠛⠉⠁⣿⠀⢻⡄⠀⢸⡟⠉⠀⠀⣀⣀⣤⡤⠶⠶⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠈⠷⠴⠶⠖⣿⠛⠉⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⢻⣆⠈⠓⠖⠛⠛⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⢠⡞⠁⠀⠀⣺⠟⠀⠀⠀⠀⠀⣿⠀⠀⡀⢻⣷⡄⠀⠀⠠⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣝⡳⣄⣴⠋⢀⣤⠶⠚⠛⢓⣿⠀⠀⠐⠈⢷⡙⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠷⠟⠁⠀⣿⣤⡴⠶⠟⢋⣿⠀⠀⠀⠡⠀⠻⠾⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⠀⠀⠠⠀⠸⣆⠀⠀⣀⣼⠇⠀⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠾⠋⠀⠀⠠⠁⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁