Breast cancer awareness Emojis & Symbols

⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠉⡇⠀⠘⣭⡁⠃⠀⠀⠆⣀⡨⠊⠂⠀⠞⢰⠈⢇⠀⠾⡶⠉⢳⡜⣋⠄⠠⡄⢹⠀⡇⡴⠉⠣⢎⠙⣤⡎⠄⠀⠀⠠⢁⡄
⠀⠀⠀⢀⡟⠅⠀⠘⠶⠃⠈⠀⠀⠀⠇⠁⠦⠀⠋⠀⠈⠀⠈⠾⠀⠹⠤⠈⠀⠉⠦⠀⠀⠈⠀⠃⠙⠀⠁⠀⠀⠈⠓⠀⠀⠄⠰⠛⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣿
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠐⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄
⠀⠀⠀⠱⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⢿⡀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒
⠀⠀⠀⠐⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠘⣄⠩⠐⠲⠆⠸⠘⠦⠀⠀⠀⠀⡀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠠⢖⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠙⣆⠀⠘⠆⡁⠄⣀⡶⠶⠾⣶⣶⣤⣌⡀⠐⠁⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣀
⠀⠀⠀⣀⣠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠗⡠⢊⡴⠋⢁⣀⣀⠀⠀⠀⠉⠛⢿⣦⠀⠁⠠⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠋⠃⠈⢀⡞⠁⡴⠋⠀⠀⠱⣆⡀⠤⠴⠦⡙⢏⢆⠒⢡⠏
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⢰⡔⠁⠀⠀⣼⠃⢸⠁⠀⠀⠀⢀⣾⡇⠀⠀⠀⠘⠈⡄⢆⠾⠂⠉⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢦⠄⠀⠀⣿⠀⢸⠀⠀⠀⠀⢼⣼⠃⠀⠀⠀⢀⠀⡇⠸⡀⠈⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⢈⠴⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢻⡀⠘⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡸⢰⡇⠀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉
⠀⠀⠀⢑⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⡁⠀⠀⠘⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢾⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠛
⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⠆⠀⠀⠹⡀⠀⢇⠀⠀⠀⠀⠀⠀⡰⠁⠀⣿⠀⢸⠀⢹⠒⠲⠀⠀⠀⠀⠀⠀⠀⣉⠴
⠀⠀⢠⠌⡠⢬⠀⠀⠀⠀⠀⠀⠈⠉⢱⡠⠼⡀⠀⠀⢳⡀⠈⢧⠀⠀⠀⢀⡞⠁⠀⣸⠆⠀⠷⠤⣀⡒⠃⠀⠀⠀⠀⠀⠀⠘⠒⠠
⠀⠀⠀⠉⣌⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠥⠀⠀⠀⠡⡀⠀⢣⣀⣴⠋⠀⠀⣰⠏⠀⡈⠐⢂⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃
⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠣⠀⠀⠀⠐⢄⠈⠿⢁⠄⠀⣴⠏⠀⣔⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⣀⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠁⠀⠀⠀⠀⠳⠖⠁⢠⡾⠃⠀⠀⠀⠙⠆⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢰⣏⠀⠠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡀
⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠀⠀⠈⠛⢿⣄⡀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈
⠀⠀⠀⢂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⣠⠟⠣⡀⠀⠀⠀⠉⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠈⣓⣐⡃⠀⠀⠀⠀⠀⠀⠀⣀⢲⣤⡞⠁⠀⣠⡞⠁⠀⡠⠋⠢⣀⠀⠀⠀⠀⢉⣿⠏⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄
⠀⠀⠀⠀⣠⠊⡁⠀⠀⠀⠀⠀⠀⠀⠙⣉⠘⣷⣴⠞⠁⠀⣠⠎⠀⠀⠀⠈⠳⣄⡀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣿⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢛⡤⠃
⠀⠀⠀⢈⠐⠚⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠃
⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⡠
⠀⠀⠀⠠⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢁⡤
⠀⠀⠀⡠⢀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃
⠀⠀⠀⠀⠟⠓⠀⠂⡄⠀⢀⠴⢆⣤⠀⢰⡀⠂⠀⢀⠀⡠⠘⢀⡴⠀⣤⡄⠀⠀⡄⡎⣠⠀⡰⡀⢀⡄⠀⠀⢀⠄⠀⠀⠈⢠⠟⡳
⠀⠀⠀⠀⡸⠣⠀⠀⣠⣀⢿⣀⡐⠁⢳⠁⠻⣉⡥⠈⠈⠧⣀⠘⠇⠠⠉⠻⢄⠀⠀⠋⠁⣬⡅⠑⡼⣀⢀⡒⠻⣀⡁⠀⠀⠀⡿⢄
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠈⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣟⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⡟⠋⠉⠉⠉⠉⠙⠳⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢹⡀⠀⠀⠀⠀⠀⠀⣰⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠳⡀⠀⠀⠀⢀⡼⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⣄⠀⣠⠞⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢨⡿⠃⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⣠⡟⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣴⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⢾⡇⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡴⠃⠀⢷⡀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣀⣀⡀⠙⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠛⢹⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⡀⠀⣿⠀⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣶⣿⣿⣿⣷⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣿⠟⠋⠉⠉⠛⢿⣏⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠁⠀⠀⠀⠀⠀⠀⠉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⢀⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣵⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢏⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢏⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃⠀⠀⢻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣟⣿⣿⣿⣿⠀⠀⠀⡄⠀⣤⠀⢠⠀⢀⠀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡟⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢀⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⡀⣀⣀⡀⡀⠀⢀⣀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠀⠁⠀⠈⠁⠈
⡟⠛⠉⠻⠿⠛⢿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⢀⣤⣀⣤⣶⣤
⠀⠲⠂⠀⠀⠀⠀⠀⢠⡀⠺⢘⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢾⣽⡿⢻⣿⣿⣿⣿⣿⣯⣹
⠀⠛⠃⡔⠀⠢⠀⣀⠈⠁⡄⡠⡐⠊⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣽⡻⡿⣷⣿⠿⣿⣫⣿⣝⣿⣬
⠀⠴⠖⠈⠀⢠⠄⠉⣤⠈⠁⠓⠦⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣛⣯⣷⣿⠻⣿⣟⢿⣿⣾⣭⣛
⣦⠀⠶⣄⡀⠛⢁⡤⡀⢀⠀⣀⠀⢀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⣿⣿⣿⡟⢿⣤⡿⠟⣫⣿
⢬⠀⠀⣈⠁⠀⠀⠀⡀⠙⠛⠉⠉⠙⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣴⣶⣶⣬⣾⣿⣿⣿⣿⣷⠿⣿⣿
⢀⠀⠸⠉⠀⢇⠀⠀⠚⠀⠀⠶⠀⢧⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⢃⣿⣙⣿⣿⣽⣿⣿⢇⣿⣶⣹⣿
⠀⢘⣷⣴⡆⠀⠐⢦⠀⠐⠃⣀⠀⠀⣙⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⠿⣯⣽⣿⣫⣽⣿⡏⠛⠁⣾
⠴⠄⢹⣿⡇⠀⠀⠙⡆⢁⠀⢁⣩⣄⣉⣠⣿⣿⣿⣿⣿⣿⣿⡿⢙⣿⣿⣳⡀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠿⠷⢷⣿⢿⡏⣴⣿⣿⡇⠀⢸⣿
⠴⢂⡸⣿⠁⠘⠃⠀⠁⢸⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢹⣿⣿⣧⣼⣷⠀⡼⢯
⡀⢣⠁⠙⠀⠀⢠⡄⠀⠚⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⢻⣿⠀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣿⡿⣿⣿⣿⣴⣿⢳
⠁⡀⠐⣢⠀⠙⠀⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠻⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣴⣿⣻⣿⡿
⡠⡍⡘⢚⣁⠀⣠⠀⠙⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣯⣶⣿⠻⣿⠷⣿⣼⡷
⠃⡥⠀⢀⣄⠀⠀⠀⠲⠔⠂⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣯⣿⣹⣿⣿⣿⠿⢿⣿⡓
⣤⠀⣠⠀⠀⠀⠘⠆⠈⠁⣀⠈⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠿⣷⣾⣯⣼⣿⣿⣿⠻⣿
⠀⢠⠈⠠⢄⠀⠈⠀⠦⠀⠆⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⣿⣋⣿⣿⣿⢿⣻⣾⢻
⠸⠏⠀⢠⣀⠀⠀⣠⠀⣤⠀⣦⠀⠸⡇⠈⣿⣿⣿⣿⣿⡀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡧⣸⣿⠛⣿⠻⣿⠻⣿⣿⣿⢿⣿⣦
⠶⣄⠀⣱⠀⠸⠇⠈⠀⠉⠀⠀⠐⠐⠂⢀⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣽⣽⣿⣿⣷⣿⣿⣏⣽⣿⢹⣿⠿
⢀⣈⣀⠈⠀⠀⠀⠄⠐⠇⠠⠀⠈⣢⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⣾⣿⣻⣏⣽⣟⣿⣿⣿⣾⠿⢿
⡂⠉⠀⠀⢀⠚⠈⠃⢀⠀⠲⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣩⣿⢿⣧⣾⣭⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠛⠛⠉⠉⠉⠉⠛⠻⢿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢡⣿⣿⠇⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠸⣿⣿⡌⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⢸⣿⣿⣀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠉⠙⠿⣿⣿⣦⣀⣿⣿⡇⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠂⢿⣿⣿⣀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣨⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⠚⠛⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆
⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄
⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⢀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷
⠺⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠖⠉⠉⠈⣉⣁⣐⣄⠀⠀⠀⠀⠀⣯⡗⣭⡕⢸⠁⡯⡇⢫⡁⣽⠀⠀⠀⠀⢀⣤⢻⣿⡗⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠌⠂⢠⠊⠀⣮⡀⢈⠄⣄⠀⠀⢀⡓⢃⠂⠘⢘⢂⢃⢃⠑⢃⠚⣀⠀⠀⠀⢸⣿⣇⢀⣜⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠁⢨⠋⠀⢀⣨⠠⠔⠒⠉⠁⠆⠸⡄⠀⠹⡟⡿⢻⣟⡟⣿⣿⣻⣿⣿⣻⡟⠁⠀⠀⠈⢿⢯⢾⣹⠋⢸⠇⠇⠇⠸⢈⠈
⠀⠀⠀⠀⠀⠀⠀⢗⠀⢀⠆⠉⠁⠀⠀⣠⠄⠒⠉⠀⠀⠆⠀⣰⣷⣿⣾⣯⣧⣿⣿⣿⣿⣽⣿⣷⠀⠀⠀⠀⣰⣿⣿⣣⡄⢐⠀⠆⢠⣐⢠⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢀⡌⠤⠔⠊⡏⠀⢸⠀⠀⠢⠁⢬⠂⠀⠀⡤⠄⡤⡄⡤⡄⡤⠄⡤⢠⢦⡀⠀⠀⠀⣴⣿⣿⠃⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⡇⣠⠆⠠⠁⠀⡤⠂⠀⠀⠀⢇⡄⡏⡇⡇⡇⢇⡄⣏⠸⠻⠀⠀⠀⠀⢸⡿⠁⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⠐⢊⣁⡀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠠⢄⡤⢠⠠⠄⣤⢠⠀⣤⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠓⠘⠐⠂⠻⠘⠀⠉⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⣏⡷⢸⣹⠆⣏⠀⣏⡇⢺⡙⢸⡇⠀⠀⠀⠀⠀⢀⣾⣿⣟⢞⣿⡄⠀⠀⠀⠀⠀⠀⢺⣹⢸⣏⡇⣿⡁⣞⣱⠰⣍⠊⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⢸⠸⠆⣧⠀⠇⡇⠲⡽⢸⠇⠀⠀⠀⠀⠀⣾⣿⣿⣧⣎⣿⣿⡄⠀⠀⠀⠀⠀⢺⡼⠸⠏⠇⢯⡀⠯⢸⠰⣬⠆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡭⡍⡭⢍⢩⢭⢉⢭⣩⡿⡍⡭⣍⠀⠀⠀⠀⣼⢏⣿⣿⣿⣿⣿⡞⣷⡀⠀⠀⠀⠀⣰⠲⢠⠶⡄⡖⣦⢰⠲⢰⠂⢰⢲
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⡟⢻⢸⢸⢸⣀⣈⣿⣅⡟⣇⠀⠀⠀⠀⠉⣼⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⢻⣠⢸⠛⡇⡇⣿⢸⣠⢸⡁⢸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣚⢓⠒⡒⠒⢚⡒⡛⢊⠑⣉⠐⡂⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⡀⠀⠀⣠⢠⡀⡀⠠⢠⠡⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠹⠢⡆⢤⠳⠂⠀⠀⠀⢄⠇⠀⠀⠀⠀⠀⠈⠉⠉⣿⡋⣿⠋⠉⠉⠀⠀⠀⠀⠀⠈⡁⢒⠂⠋⠉⠁⠁⠀⠘⠐⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡏⡇⢈⠋⠂⡏⣷⢸⠁⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠇⡇⠀⠺⡦⠇⠿⠸⠀⢿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣷⣄⣸⢦⡀⠀⠀⠀⠀⠀⠀⣖⡦⢐⣢⢰⠂⡖⡆⢔⠆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⢸⡴⠃⠈⡷⠀⠀⠀⠀⠀⠀⢯⠗⠨⠱⢸⡀⠏⠇⢬⠇⠿⠀⠀⠀⠀⢠⣶⣿⣷⣶⣤⡀⠀⢀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠸⢤⡾⠁⠀⡔⢡⣠⠀⠀⠀⠀⠀⡠⠄⡠⡄⡠⡄⡡⠄⡴⢠⢦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢊⠞⠀⢀⣾⣷⡈⠘⠀⠀⠀⠀⠀⢇⡄⡏⡇⡇⡇⢇⡄⣏⠸⢻⠀⠀⠀⠀⠸⣿⠹⢷⢻⡾⣷⢧⡿⣞⡿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⠞⣝⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⢧⣽⣾⣿⣿⣿⣿⣾⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠋⠀⠈⢢⣹⠀⠀⠀⠀⠀⠀⣠⣠⡀⠀⠀⡄⢀⢠⢀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁⠉⠓⠀⠊⠃⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢶⡀⠀⣿⡆⢲⡄⠀⢰⣶⠂⠀⠀⠀⣼⣿⡆⠀⠀⣰⣾⢿⣦⠸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⣿⠃⠀⠀⠀⣿⣿⣷⠀⠀⣿⡏⠐⠟⠂⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢺⣧⠀⣿⡧⣴⡟⠀⢸⣿⠀⠀⠀⢸⣿⠋⣿⡄⠀⠙⠻⢦⣤⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡀⣿⡇⠸⣷⠀⢸⣿⠀⠀⠀⣾⡿⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠇⣿⡇⠀⣿⡆⢸⣿⠀⠀⢀⣿⡇⠀⢸⣷⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠴⠿⠀⣿⠇⠀⢸⡇⠸⡿⠀⠀⠸⡿⠁⠀⠘⣿⠎⠿⠄⢠⠿⠃⠀⠀⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⠿⠇⣰⡟⠉⣿⡇⠈⣿⡟⠈⣿⡄⣼⣿⠉⠿⠧⠀⣾⡏⢈⣿⡀⣿⡿⠦⠼⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡀⣿⡇⠀⣿⡇⠀⣿⡇⠀⣿⡇⣿⡏⠀⢠⣤⠸⣿⡃⢉⣉⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠿⠃⠸⠷⠴⠿⠧⠠⠿⠇⠀⠿⠇⠻⠷⠤⠼⠛⠀⠻⠷⠤⠿⠁⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠇⣶⠀⠀⠘⣦⠀⣰⢻⡇⢸⡇⢱⡄⣼⢟⡆⠀⣷⠀⡴⢀⣴⢶⡀⢰⡟⠛⢠⡞⠂
⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⠀⡇⢀⣀⠀⣸⢀⣿⢸⡇⢸⣇⠼⢱⣿⠚⠁⢠⣿⣶⡇⢸⣧⠞⠁⠘⠧⡀⠘⢇
⠀⠀⠀⠀⠀⠈⢹⡟⠁⣿⡀⣷⠘⣿⢀⡟⢸⡏⢸⡇⢸⡿⡆⠀⠛⠆⠐⣼⠋⢿⡇⠸⣿⡀⢀⡀⠀⠘⣆⠀⠈⡆
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠙⠃⠈⠃⠉⠉⠀⠉⠀⠈⠁⠘⠁⠙⠂⠁⠀⠀⠀⠀⠈⠓⠀⠈⠉⠀⠀⠠⠼⠋⠀⠉⠁

⠀⠀⠀⣴⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⣆⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁
⠀⠀⠀⢈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣾⠟⢻⣷⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⠹⣿⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⣠⡶⣦⡀⠀⠀⠠⠄⠀⠠⠀⠀⠀⢠⠾⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⢿⣄⣼⠇⠀⠀⠀⠈⠄⠁⠀⠀⠀⠸⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⢈⣿⣏⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⢀⣿⣿⡀
⠀⠀⠀⠀⠿⠋⠻⠇⠀⠀⠀⡀⠃⢀⠀⠀⠀⢾⠏⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⢰⠞⢲⠀⠀⢀⣤⣄⠀⠀⠀⢀⣴⣦⡀⠀⢠⣤⣤⣤⣄⠀⠀⡰⠒⢦⠀⠀⠀⠀⠤⠀⠀⠠⠄⠀⢠⠶⠶⣄
⠀⠀⠀⠀⢹⣄⣾⠃⠀⠸⣦⡿⠀⠀⠀⢸⡆⢸⡇⠀⢻⣿⣍⣿⡿⠀⠀⢿⣄⣾⠇⠀⠀⠐⠀⠑⡐⢁⠌⠀⣧⡀⠀⣼⠂
⠀⠀⠀⠀⢀⣿⣇⠀⠀⣠⣿⣧⡀⠀⠀⠈⣿⣟⠁⠀⠀⢻⣿⣿⠁⠀⠀⣼⣿⣧⡀⠀⠀⠀⠈⠆⠈⠏⠀⠀⠘⢷⣾⠏
⠀⠀⠀⠠⡿⠃⠻⡧⠐⡿⠁⠹⡷⠀⠀⣾⠟⠻⣧⠀⠀⢻⡿⡿⠀⠀⣾⠟⠀⠙⣿⡆⠀⠠⠀⡀⠃⡀⢀⠀⣠⡿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠂⠀⠛⠁⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡮⠙⠁⠉⠀⠃⠘⢉⣙⣒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣻⢋⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠉⢁⡰⢈⠄⠀⣠⠖⠉⢩⠏⠈⠙⢎⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢡⡛⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⠓⢀⠢⣜⠃⠈⠀⢰⠃⠀⠀⡞⠦⣄⣠⣾⠀⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⣿⣿⣷⣿⣷⣾⣏⢿⣧⠀⠀⠀⠀⠀⢠⡉⠁⣬⡫⠀⠀⠀⠀⣞⣀⡠⠴⠓⠊⠉⠀⢸⠀⠐⢷
⠀⠀⠀⠀⠀⠀⠀⣰⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣇⠀⠀⠀⠀⡨⡄⠀⠈⢁⡤⠴⠒⠋⠉⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠙⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠋⠀⠀⠀⠀⢱⠆⠀⢠⠏⠀⠀⠀⠀⣀⡤⠔⢺⠉⠁⠀⠀⢋⠁⢂⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⡖⢀⣞⣤⠤⠖⠚⠉⡇⠀⠀⣿⠀⠀⢀⠈⢈⠁⢠⡽
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠱⣍⡁⠀⠀⠀⠀⢀⡇⠀⠀⡏⠀⡐⢄⠰⠀⠰⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣿⡟⢻⣿⡟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠢⡆⢀⠀⠀⢸⠁⡠⠊⠁⠈⠓⠀⢠⣨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠤⣆⡘⢋⣤⢠⣄⣰⡬⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⣖⡄⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢿⠛⣻⠋⢰⢿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⣠⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣪⡿⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠠⡜⢦⢼⠟⠀⠀⠀⡼⠁⠤⣄⠆⠀⠀⠀⠀⢹⣿⡟⣛⢿⡰⢿⡎⣿⣿⡇⣺⡿⣸⢫⡟⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠇⢠⡿⣨⠏⠀⠀⢀⣾⣧⠀⠏⠀⡇⠀⠀⠀⠀⠀⢻⣷⡉⡜⣧⣛⣧⣹⣯⣧⣻⣇⣫⡞⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⣾⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢠⠞⢣⡙⢽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣠⠋⠀⠀⠙⢦⢋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⠁⠀⠀⠀⠀⠈⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠹⡌⢷⡘⣆⢳⡘⣆⢻⡘⣇⢳⡘⠆⠃⢸⡇
⢧⠙⣄⢳⡘⡆⢳⡘⠄⢣⠘⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⡶⠾⠛⠛⠿⠶⣦⣀
⣌⢳⡘⢆⠱⡈⠆⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⡀⣀⣠⣈⣹⣧⡀⠀⠀⢀⣴⠾⠛⠛⠛⠷⢦⣄⡀
⡘⢆⠱⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣿⡶⣶⣾⣿⣿⣿⠟⠋⠉⢹⡇⠀⢀⣿⠃⣠⣶⠀⣀⠀⠀⠉⠻⣦
⡱⡈⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡏⠀⠘⠿⠁⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠿⠋⠘⣷⣝⢿⣶⣄⠀⠹⣧
⠱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣿⡆⣠⣤⣌⠙⢳⡝⣿⣷⡀⢿⡄
⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡷⠶⠞⢻⡏⠀⠉⠀⠀⠀⠀⠀⢬⣹⣦⡴⠏⠀⠀⢸⠟⠀⠙⠻⠦⠀⠘⠟⢿⣿⣇⢸⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠁⠀⠀⠀⠀⢸⡇⠀⢸⣄⠀⠀⠀⠀⣠⣁⡟⠀⠀⠀⠀⢿⣶⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠘⢷⡀⢠⠀⠈⣿⡀⠀⣿⣷⣤⣠⡼⢯⡉⠀⠀⠀⠀⠀⠸⣟⠛⠀⠀⣀⡀⣠⣾⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠹⣧⢸⡇⠀⠘⢷⣴⡿⠃⠀⠉⠀⠈⢷⡀⠀⠀⠀⠀⢀⣉⣿⣿⠟⠉⠀⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢈⣿⢨⣷⣀⣀⠀⠉⠁⠀⠀⠀⠀⣆⠈⣷⡶⠶⠟⠛⣿⠋⢿⡇⠀⠀⣼⠋⢸⣷⣄⡀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⢸⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⣿⠀⣯⠀⠀⠀⣸⠇⠀⢸⡇⢀⣾⠃⠀⢸⡇⠈⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⢸⣿⠉⠀⠀⠀⢠⠇⠀⠀⢠⣿⡄⠸⣇⠀⠀⣿⣤⡄⢸⣇⣾⠃⠠⣤⣸⡇⠀⢀⠀⠀⠉⢻⣆
⠀⠀⠀⠀⠀⠀⢸⡟⣿⡇⠀⠀⠀⠀⡨⣿⣿⢸⣿⠀⠀⠀⢠⡏⡴⠀⠀⢸⣿⣿⡄⢹⡄⠀⠀⢿⣅⠀⣿⠃⢀⣸⡇⠈⣡⠞⠁⠀⠀⠸⣆⢻
⠀⠀⠀⠀⠀⠀⢸⡇⢻⣧⡶⠶⠶⠞⠻⣿⣿⣾⣿⠀⠀⣰⡟⣼⢣⠆⠀⣼⠟⠿⣿⡀⣷⠀⠀⠀⠙⣶⣿⠶⠛⠉⠀⣰⠏⠀⠀⠀⠀⢠⣿⢸
⠀⠀⠀⠀⠀⠀⣸⡇⢸⣿⠀⠀⠀⠐⠭⣿⡇⣿⡇⠀⣴⢏⣼⢣⡏⡄⢠⡟⠀⠈⣿⡇⢻⡆⠀⠀⢠⡿⠁⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⣼⡏⣼
⠀⠀⠀⠀⠀⠀⣿⡇⠘⣿⠀⠀⠀⠀⢬⣿⢹⣿⣇⣾⢏⣾⣣⡟⡼⢡⣼⠃⢀⣼⣿⣿⡟⠀⠀⠀⣼⠇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣠⣿⢡⡿
⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡄⠀⠀⠀⣸⡿⢸⣿⣿⣻⡿⣱⠟⣼⢣⣿⡟⠉⠙⢿⡋⢹⡇⠀⠀⢠⡿⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⣲⣿⣏⣾⠃
⠀⠀⠀⠀⠀⠸⣯⠀⠀⣿⡇⠀⠀⢠⣿⡇⣿⣿⣿⣟⣽⢏⣾⢣⣟⡿⠀⠀⠀⠈⠻⠾⢧⣤⣤⣼⣧⣄⣀⣀⣼⡏⠙⢷⣄⢠⣼⣿⡟⣼⠇
⠀⠀⠀⠀⠀⢸⣯⠀⠀⢸⣇⠀⢠⣿⣿⡇⣿⠇⣿⣿⣫⡾⣱⡏⢸⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠀⠀⠈⠛⣾⣯⣴⠏
⢠⠀⠆⡄⠐⢠⢛⣿⣶⣼⣿⠀⠈⠻⣿⡇⢿⡄⢻⣿⡟⣵⠏⢀⡾⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠈
⣼⢸⢠⡇⡇⣼⡾⠻⢿⣿⣿⡀⠀⠀⢻⣷⢸⡇⢸⡛⠻⢿⡶⠛⢁⣿⣿⣿⣿⣿⡿⠀⠉⠛⢻⣶⣦⣤⣄⣀⣀⣀⡀⣀⣼⣿⡇
⣇⣿⣼⢸⣿⠏⠀⠀⠀⠀⢿⡇⠀⠀⠘⣿⢸⣷⠘⣷⣶⣿⣷⣤⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⠁⠛⠫⠿⣻⣿⣿⣿⣿⣿⣿⣧
⠿⠿⠿⢿⡏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡼⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠩⢟⡿⢿⣿⣿⡄
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⢸⡇⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⢻⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢸⡇⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⣿⠀⢠⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠰⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡟⠁
⠀⠀⠀⣿⣠⠇⡴⢀⠀⠀⠀⢸⣿⣿⡀⠀⠐⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⠛⠛⠶⠶⢦⣤⣤⣿⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣧
⠀⢀⣾⣿⢃⡾⢡⠎⠀⠀⠀⠀⣿⢹⣷⠀⠀⠈⠹⡇⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢧⢻⠹⡙⠿⣿⡆
⠀⢸⡿⢣⡞⣠⠏⠀⠀⠀⠀⢀⣿⣬⣿⠀⠀⠀⢰⣷⠀⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⣷
⠀⣿⣵⠏⣴⠏⠀⠀⠀⠀⠀⠈⢻⡏⢿⣄⣄⣠⣄⣽⠀⣿⣿⣿⣿⡿⠟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⣿⣫⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠹⣿⣿⣿⣿⡆⢹⣿⣿⣯⠖⣃⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠘⢿⣿⣿⡇⢸⣿⣿⡷⣫⠔⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣶⡶⢎⣉⣠⣤⠀⣿⣿⣿⡵⣋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⡿⠁⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⢻⡇⠀⠀⢸⣿⣿⣿⡀⢿⣿⣿⣞⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣃⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣇⣸⣷⣀⣀⣸⣿⣿⣿⣇⣸⣿⣿⣯⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣇⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠉⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢄⡀
⠀⠀⠀⠀⢠⣿⠟⠛⠛⠛⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠟⠛⠛⠛⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡤⠤⠤⠤⢤⡷⡄
⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢆⠀⠀⠀⡼⠁⢳
⠀⠀⠀⠀⢿⣿⣿⡄⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⢦⠀⡴⠁⠀⡼
⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⢿⡁⠀⡴⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠳⡞
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⢣⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠱⡄⠀⠘⢆
⠀⠀⠀⢀⣴⣿⣿⡿⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡰⠛⣆⠀⠈⢣⡀
⠀⠀⠀⢺⣿⣿⠟⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠟⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⡼⠁⠀⠈⢦⠀⢀⠟
⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠳⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣤⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢉⡄⠐⠐⠲⣌⠉⠉⠉⠀⠀⠀⣀⣀⣀⣤⣀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠸⠂⠀⣀⢰⣶⣿⠟⣛⣭⣻⡿⢣⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣤⡀⠀⠀⠀⡀⠌⢀⣼⣷⠎⢿⠟⠚⠛⠛⠛⠀⢙⣿⠬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠈⠻⣿⠂⠀⠙⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣥⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠰⣟⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣆⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠾⣡⣄⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⠔⠁⠀⣀⡀⠙⠃⠀⠀⠀⠀⢨⠟⢹⣿⡋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣠⡿⠛⣿⡷⠀⢠⡄⠀⢆⠀⠀⠒⠊⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡎⠹⣿⣧⡀⠀⠀⠉⠶⠶⠜⠃⠀⠘⠃⠀⠘⢦⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢸⣼⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡤⠖⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢱⡀⠛⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠙⣦⣼⡀⣰⠯⠤⠶⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⢹⣦⡀⠀⠀⡀⠀⠰⠉⠁⠀⠀⠀⠀⠀⣴⣦⠐⠇⠀⠀⢸⠇⠀⠀⠀⠀⠺⠟⡏⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠸⢿⣿⣿⠐⠁⡸⠃⣰⠂⠀⠀⠀⠀⢺⣭⣥⣶⡇⠀⠀⡾⠀⠀⠀⠀⠀⠀⢐⡇⠀⣇⡴⠒⢦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⣀⣀⣠⣽⣶⢰⠀⢰⣇⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⢰⠇⠀⠀⠀⠀⢸⡝⢎⣧⠞⠁⢀⡴⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠈⢳⡤⠤⡤⢄⡀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⡰⠋⠀⢀⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠟⠁⡿⠀⢸⣠⠏⢠⠞⠀⣠⠟⢲⡖⠖⠚⠁⠀⠀⠀⠀⠀⠀⢸⠇⣸⣇⣸⠁⢀⡴⠋⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢰⡇⢠⠞⠁⠰⠋⢀⡼⠃⠀⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠉⢸⡀⠾⠀⠰⠋⠄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠀⠀⢾⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠸⠁⡄⡤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠘⠁⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷
⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⢸⣿⣿⣿⣿⠏⣡⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠻⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡈⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⢁⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣷⡈⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⡇
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣠⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠈⠻⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠙⢿⣷⣤⣶⣶⣦⣤⣄⡀⢀⣠⣤⣶⣶⣶⣤⣾⡿⠋⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⣻⣿⡿⠟⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀
⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⢀⣴⣿⠟⠉⠻⠿⣷⣶⣦⣤⣤⣴⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠈⢻⣷⣤⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣄⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠈⢻⣿⣄⠀⢾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠙⠉⡃⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠹⣿⣦⡀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠙⣋⣡⡀⠀⠀⠀⠙⣛⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠈⣿⣿⣄⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠈⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⣠⣾⡿⠙⢿⣷⡄⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠈⢿⣷⣄⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠋⠀⠀⠀⢹⣿⣦⡀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⢠⣿⠟⠻⣿⣆⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⣀⣠⣤⠸⣿⣆⠀⠘⣿⣷⣦⣴⣿⠟⠉⢿⣷⣄⠀⠀⣠⣿⠿⣷⣄⣀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠋⠀⠙⠿⢿⡿⠿⠋⠉⠉⠀⠀⠀⠀⠙⠿⢿⠿⠿⠋⠀⠙⠛⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⣤⣤⣤⣤⣤⡄⢸⣿⣿⡟⠛⠛⢿⡟⠛⠛⣻⠛⠛⣿⠛⠻⡟⠛⡟⠛⣿⠛⡟⠛⠛⠻⣿⠛⠛⢻⡟⠛⠛⢿⣿⣿⡇⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠈⢿⣿⣿⣿⡗⢸⣿⣿⡇⠘⠃⢸⡇⠈⡛⣿⠀⡄⠋⠀⢸⡇⠀⡇⠀⠘⠀⡇⠀⣷⠀⣿⠀⡛⣻⠇⠘⠃⢼⣿⣿⡇⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⢿⣿⣿⣿⢸⣿⣿⣇⣸⣇⢸⣇⢈⠋⣻⣀⣧⣀⣇⢘⣇⣀⣇⢰⣆⢀⣗⣀⣋⣠⣟⣀⣙⢻⡇⣸⣇⣸⣿⣿⡇⣹⣿⣿⡿⠁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣤⣭⣭⣭⠌⠉⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠉⠉⠉⠉⠉⠉⠁⠉⠁⠉⠉⠉⠉⠉⠉⣥⣤⣭⣭⣴⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠛⠛⠛⠋⠙⠋⠛⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠋⠛⠛⠛⠙⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⣰⣿⠃
⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠘⣿⡆⠀⠀⠀⠀⠘⠿⣿⣷⣤⡀⠀⢀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁
⠀⢸⣿⠏⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⠟⠛⠉⢹⣷⡀
⠀⠀⠻⣶⣤⣤⣤⣿⣿⣷⣶⣶⣶⣾⣷⡄⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠻⢿⣿⣶⣄⣀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠛⠛⠛⠻⣿⣿⡟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠿⠿⣿⣿⣿⣿⣿⣶⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢀⣴⣿⠟⠁⠈⠉⠙⠛⠛⠁
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣄⠀⠀⠀⠀⠀⣶⣤⣀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠟⠋⠁
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢉⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⣾⣿⣿
⢻⣿⡇⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣶⣄
⣼⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡇
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣀⣄⠀⠀⠀⠀⠀⣠⣴
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣾⣿⣿⡏⠀⠀⠀⠀⣰⡿⠛
⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⢹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠋
⣶⣤⠀⠀⠀⠀⠀⢿⡏⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶
⠘⣿⠇⠀⠀⠀⠀⠈⠻⣷⣶⣤⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣄⣀⣠⣾⣿⠋
⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠀⣾⣿⡇⠀⠙⠻⣿⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠉⠉⠙⠛⠀⠀⠀⠀⠀⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣠⣾⠃⠀⠀⠀⠀⠀⠠⠾⣿⠟⠁
⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⠿⠃
⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⠋⠁
⣿⣿⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⠿⠛⠋⢹⣿⣿⠀⠀⠀⠀⠀⠀⠰⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠉⠉⠉⠙⢿⣿⡿⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⣀⣤⣤⣤⣼⣿⣿⣦⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠿⢶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⢿⣿⣿⠛⠛⠛⠻⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣤⡀⡂⢢⢤⠤⠌⡭⡭⠩⢬⢥⡄⣐⣂⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡲⠽⡚⡙⠉⠠⢁⠂⠀⠂⠈⠀⠰⢁⠀⠎⠄⡐⠠⢁⢋⠗⡦⡈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣎⠁⠀⠠⠁⠁⠂⠀⠀⠀⠀⠐⠠⠃⠀⠌⡐⠐⠀⢀⠃⠌⡐⢰⠇⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠘⣇⢠⠁⠀⠄⡌⡈⠀⠐⠀⠠⢁⠀⠀⡈⠀⠀⠠⠀⠀⠌⠐⠠⢡⠀⠀⠀⠸⡗⡄
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢧⠀⠀⡀⠐⠠⠀⢀⢀⠀⠀⠀⡀⠰⠠⢀⠀⠀⠂⠈⠀⠀⢠⡏⠀⠀⠀⠐⢌⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰⠠⢀⠃⠀⠀⠀⡀⠀⠀⠀⢃⠁⠀⠀⠀⠀⢂⠢⣁
⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣆⡀⠀⡀⡀⠈⠀⠐⢡⢁⠂⠀⠄⠐⠀⠀⠠⢀⠂⢢⡟⠀⠀⠀⠀⠠⡀⠕⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠈⢷⡀⢠⡠⠠⠦⠧⠒⣚⣚⣚⡚⠲⠷⠦⢧⣄⣆⣠⠁⠀⠀⠀⠀⠢⠀⠌⡴⣿⠀⠠⠄
⠀⠀⠀⠀⠈⡀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣏⡙⠛⠒⠒⠶⠤⢤⣉⣉⣛⡒⠛⠧⢭⣩⠇⠀⠀⠀⠀⠀⠠⠑⡈⡄⣽⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡇⠀⠘⢰⠀⠀⠀⠀⠀⠀⠈⢦⣈⡙⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠀⠀⠀⠀⠀⠈⢄⠱⠈⡠⢹
⠀⠀⠀⠀⠀⠺⡀⠘⠀⠀⡄⠀⠀⠀⠀⠀⠀⠙⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡈⠌⠆⢡⢣⡟⢐⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠠⠀⠈⡘⡘⢰⣓⣂⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⠀⠁⢀⢁⠁⡞⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⡼⠡⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠆⠀⠀⠠⠀⡼⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⢀⠀⣠⡞⠀⡂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡼⠉⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠁⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠈⠠⠈⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠈⣠⠞⠁⢈⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡴⠏⠠⠐⠀⠀⠀⢉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣡⠔⠋⢀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢀⡴⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠄
⢇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠁
⠈⢂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢻⠇
⠀⠀⠑⣄⠀⢀⠀⢀⠠⠈⠀⠀⢀⡾⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⡐⠁⠀⠀⠀⠀⠀⠁⠂⠜⢊⡴⠯⠉
⠀⠀⠀⠀⠑⢤⡀⠘⠀⠀⡄⠀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠀⠀⠀⠀⢀⠀⠀⢈⣤⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠄⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⢄⠀⠐⢀⣀⣤⠴⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡄⠀⠀⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠘⠓⠀⠈⠁⣿⣧⡶⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠛⢻⡿⢷⣤⣀⣴⠞⢿⣯⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣿⣥⣶⢿⡿⢧⣄⣸⣿⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠉⠀⣸⣷⠀⠉⢻⣿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣿⠻⣦⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣧⡶⠟⠁⠀⠈⠛⢿⣿⣶⣤⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣼⠏⠁⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠛⠳⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⢿⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⠃⠀⠀⠈⣿⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠘⣿⡀⠀⠀⠀⢸⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠠⣿⠃⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣤⣴⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⡶⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡯⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡕⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣥⣤⣤⣤⣴⣶⣶⣶⣶⣦⣴⣦⣤⣤⣤⣤⣤⣤⣤⣀⣄⣨⣯⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣡⡿⣣⣿⣉⡿⠏⣉⡿⠛⣽⡟⣹⡿⢉⣽⠿⢉⣿⢻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣶⣏⡿⠏⣴⡟⠑⣴⡟⣡⡾⢃⣼⠛⣠⣾⠉⣶⢿⣽⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣵⡟⣡⡾⠇⣨⡿⢣⣴⢋⣴⠟⣡⡾⠏⣠⡿⣳⡾⣡⡾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢃⣼⡟⣠⣾⠋⣰⡿⣡⡿⠃⢶⠟⠡⣾⢏⡿⢯⣴⣯⡶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠣⠈⠛⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⠛⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⡰⠲⢆⠀⠀⠀⠀⠀⣰⠶⣦⠀⠀⠀⠀⠀⠀⠶⠲⡄⠀⠀⠀⠀⠀⣴⠶⣦⠀⠀⠀⠀⣴⠶⢦⠶⠶⣦⠀⠀⠀⢠⡶⠶⣆
⠀⠀⠀⠀⣷⣠⡿⠀⠀⠀⠀⠀⠹⣦⡿⠀⠀⠀⠀⠀⠰⣆⢠⡆⠀⠀⠀⠀⠀⣷⠀⣾⠀⠀⠀⠀⢿⣄⠀⢀⣴⠟⠀⠀⠀⠘⣷⣴⡏
⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⣰⡿⣷⡀⠀⠀⠀⠀⢀⣽⣿⡀⠀⠀⠀⠀⠀⢹⣿⡋⠀⠀⠀⠀⠀⢙⣷⣿⡁⠀⠀⠀⠀⢀⣾⢿⣄
⠀⠀⠀⠴⡟⠉⢿⠆⠀⠀⠀⠰⡿⠁⢹⡷⠀⠀⠀⢰⠟⠋⠈⠻⣶⠀⠀⠀⢴⡿⠋⢿⡦⠀⠀⣤⡾⠛⠁⠈⠻⣶⡄⠀⠰⡿⠃⠀⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⡀⡄⢠⢀⣤⠀⣴⢦⣠⡤⠦⣤⡀⣤⣤⠦⢠⡬⣄⡤⡄
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⡌⣿⢿⡟⣼⠿⣆⣿⢿⣹⣟⣃⣿⠳⣿⣿⣛⢈⣳⡆⣙⣦⢀⣤⣤⡀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⢰⣏⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡶⣤⠰⡴⢠⠶⣄⣴⢯⡅⣤⠶⡄⣬⡉⣤⠉⠀⠈⢡⣯⠀⠀⣿⠀⠀⠀⢿⣆⣼⡇
⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣍⢀⣇⢸⣛⡧⣿⣻⡇⣧⣀⡟⣿⠹⣿⠀⠀⠀⠀⢻⣧⣼⡟⠀⠀⠀⣨⣿⣿⡀
⠀⠀⠀⢠⣾⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⢴⠀⡴⢤⣴⡢⣶⠐⡆⡴⡃⣤⣠⣴⡆⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⣼⡿⠋⠹⣿⡆
⠀⠀⠀⠙⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠚⠀⠓⢊⠛⠂⠚⠒⠓⠑⠛⠃⠙⡓⠛⠀⠀⠀⠀⠙⠁⠙⠋⠀⠀⠛⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠃⠋⣂⣈⠉⠉⠀⠘⠈⠘⠀⢈⡁⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢰⡉⢙⡆⠀⠀⠀⠀⣸⠛⠛⣧⠀⠀⠀⣰⠀⠠⣏⣽⠀⢰⡆⠀⠀⠀⢰⡏⢹⣦⠀⠀⠀⠀⠀⣾⡉⣹⡆⠀⠀⠀⢠⣆⠛⣰⡆
⠀⠀⠀⠀⠘⣻⣿⠃⠀⠀⠀⠀⠻⣷⣼⠟⠀⠀⠀⣿⡀⢠⡾⢷⡄⢸⡏⠀⠀⠀⠘⣿⣾⠃⠀⠀⠀⠀⠀⠘⣷⡟⠀⠀⠀⠀⠈⠿⣶⡿⠁
⠀⠀⠀⢀⣾⠟⠻⣷⡄⠀⠀⠀⣰⣿⣿⣦⡀⠀⠀⢿⣷⣄⠀⢈⣴⣿⡏⠀⠀⢀⣴⠟⠻⣧⡀⠀⠀⠀⢀⣾⠟⢿⣆⠀⠀⠀⠀⣼⣿⣧
⠀⠀⠀⠻⠋⠀⠀⠙⠟⠀⠀⠈⠿⠁⠈⠿⠁⠀⠀⠀⠹⠿⠆⠸⠿⠋⠀⠀⠰⠟⠁⠀⠀⠈⠻⠆⠀⠐⠟⠁⠀⠀⠻⠗⠀⠀⠘⠟⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠉⠉⠉⠉⠉⠓⠦⠄⠀⢀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠖⠒⠒⠒⠋⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡤⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢳⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠳⡄⢀⠴⠋⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠑⢄⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠙⡇⠀⠀⢀⡴⠓⠲⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠢⡀⠀⠀⠀⠑⣴⠋
⠀⠀⠀⠀⠀⠀⠙⠒⢶⠋⠀⠀⠀⣸⣤⣀⠀⠀⢦⡀⠀⠀⠈⠳⣄⠀⠀⠀⠈⢷⣄⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣤⠚⠁⠀⠈⣇⠀⠀⠙⠂⠀⠀⠀⠀⠐⢆⡀⠀⢀⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⠖⠋⠉⢳⡀⠀⠘⠢⡀⠀⠀⠀⢹⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠁⠀⠀⢀⡼⢇⠀⠀⠀⠈⢢⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠖⠋⠀⠀⠑⢄⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⢸⣿⣷⣄⡀⣀⣤⣤⣼⣿⠀⠂⢠⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣤⠄⢈⣹⣿⣿⣿⣿⣿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣶⡄⢀⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣼⣿⠇⠀⠈⠈⣿⡟⣿⣿⣿⣿⣿⡇⠀⠙⣩⣈⠙⠛⠻⣿⣾⣿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⠿⠿⢷⡄⠀⠉⠀⠘⢿⣿⣿⣿⣿⡀⢌⡛⣋⠸⣿⠆⡃⢻⡿⢻⣌⣡⡉
⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣷⣋⣤⡀⢴⡶⢿⣾⣿⣿⠓⠈⠀⠀⠉⠉⠃⠸⢿⣯⣷⣶⣾⣿⣿⣷⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢿⣋⣠⣤⣾⣿⠉⢉⡴⢦⣠⠜⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠟⣀⠉⡛⢿⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠈⠿⢟⣿⡍⢸⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠀⠀⢂⣴⣶⣿⣷⣾⣿⣷⠀⠀⠀⢹⣿⡏⠁⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣻⡭⣵⣿⡿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⠙⣿⡿⠙⢀⡀⠀⣿⡏⠑⠂⠀⠒⠁
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣍⠀⠀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠠⠄⣹⣷⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠘⠟⠉⠙⢿⣿⡟⠀⢀⣀⣼⣿⣧⠀⠀⣾⣿⠿⢷⣀⡀⠉⠀⠀⠀⠈⡟⣀⠈⢉⢸⡿⣦⣀⣀⡤
⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠻⠀⢰⣿⣿⣿⠋⠉⡲⠼⡏⠀⠀⠀⢹⣿⣶⣿⣿⣿⣷⣧⣠⢦⣈⡼⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠐⢾⣿⣿⡟⠐⠀⣙⣛⣉⣁⣀⠉⣈⣿⠀⠀⢹⣿⣿⣿⠟⠿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⡏⠀⢠⣭⣭⣽⣿⣿⣿⣻⣿⣧⡀⠀⢻⡟⠉⠀⠀⠈⠁⠀⠀⠀⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⣴⡶⠆⠒⠂⣤⠄⠛⠛⠿⣿⣇⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⣽⡀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠐⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣀⣀⣀⣀⣸⠁⠀⢀⠀⠀⠀⡀⡀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢸⣀⣀⣀⣀⣀
⠀⠀⠘⢇⠀⠀⢨⣿⠀⠀⢹⣏⡿⢸⣯⣍⢸⣿⣤⣿⡇⣿⠀⣿⣾⡇⢹⡏⣿⢸⣯⣉⢸⣏⣿⠂⠀⢸⣿⠀⠀⢀⠟
⠀⠀⠀⠈⢧⠀⢸⣿⠀⠀⠼⠏⠿⠸⠧⠤⠸⠇⠿⠹⠇⠿⠀⠯⠻⠇⠸⠧⠟⠸⠧⠤⠸⠇⠿⠆⠀⢸⡟⠀⢠⠏
⠀⠀⠀⢠⠏⠀⠸⡿⣄⣀⣠⣀⣀⣀⣀⣠⣀⣠⡀⣀⣀⣀⣄⣄⣀⣤⣄⣠⣀⣀⣀⣤⣠⣠⣀⣀⣀⣼⡿⠀⠈⢧
⠀⠀⢰⣏⣀⣀⣀⣈⣉⣉⣉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣉⣉⣉⣁⣀⣀⣀⣧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠉⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣾⣿⣿⠟⠀⠀⠀⠙⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠴⢿⣿⠟⠁⠀⠀⠙⢿⣿⡷⠄
⠀⠀⠀⠀⠀⠹⡿⠃⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⠻

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⡠⠤⠤⣄⣾⣿⡷⠚⠉⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠢⣿⣿⣆⡤⠤⠤⡀
⠀⠀⠀⢧⣀⣀⣠⣿⣿⡷⠤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⣿⣿⢧⣀⠀⣀⠇
⠀⠀⠀⠀⠈⠉⠀⢻⣿⣿⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⠀⢸⣿⣿⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣀⣾⣿⢏⣴⣿⡄⠀⠀⠀⠀⣼⣷⣌⢿⣿⣆⣀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣽⡛⣺⡿⣫⣶⡄⠀⠀⣴⣮⡻⣿⡒⣻⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⣛⣏⣴⣿⠟⠀⠀⠀⠘⢿⣷⣌⣝⣻⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣟⣿⣿⡏⠀⠀⠀⠀⠀⠈⣿⣿⣟⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣫⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⢻⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣠⣿⠛⠙⢻⣷⣀⣤⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠈⠙⠻⣿⣤⣤⣼⡿⠟⠉⠁⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡏⠈⢻⡧⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⣿⣧⣤⣾⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⣤⣴⣾⣿⠉⠉⢹⣿⣷⣦⣄⣀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⢸⣿⠀⠀⢸⣿⠀⢉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⣿⣿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⣿⠿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⢿⣶⡀⠀⢸⣿⠀⠀⠸⣿⠀⠀⠀⣿⠇⠀⠀⣿⡇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠘⢿⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠙⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢴⣾⣿⣿⡄⠈⠂⠙⠛⠀⠀⠐⠀⠀⠀⠀⠎⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠋⡿⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣼
⠀⡠⠒⠃⠀⠒⢀⠀⠀⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⢀⣾⣟
⠞⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠉⠉⠤⠤⠤⠄⢀⡴⠒⠒⠒⠠⡀⠀⠀⠈⠃⡀⠀⠀⠀⠄⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣀⣶⣿⡟⢉
⠂⠒⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⣄⡀⢈⢢⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣷⣿⣿⣷⣾⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠐⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢯⣿⣿⢿⣿⣿⣯
⠷⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⡠⠒⠀⠀⠐⢉⣿⡿⠄⠉⠏⠛
⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢵⣤⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⠀⠀⠈⡟⠒⠠⠀⠀⠀⠣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠙⠧⠀⢀⠀⠀⠀⠒⠤⢤⣿⣿⣿⡇⠀⣿⣇⣠⣴⢅⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠠⣤⡼⣿⣿⣿⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⢈⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠠⠀⠀⠀⠑⠀⢀⡎⠀⠄⠺⠃
⠀⠚⠀⢤⡀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢔⣾⠿⠛⢿⡇⠐⠦⠀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠈⠐⠛⢧⡀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠄⣀⣀⣀⡀⠤⢰⠞⠋⡠⠀⡀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠁⠀⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠒⠻⣷⢶⣷⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠔⠋⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣀⡄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⢆⠀⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠁⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⢸⣇⣸⣀⣠⣾⠿
⠀⠀⠀⢀⡇⠉⠉⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢱⣄⣆⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣽⣧⣾⣿⣿⡿⠿⠃
⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡀⠀⡜⠁⠀⠀⢀⣴⣞⡥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡏⡁⠀⠀⠀⠐
⠀⠀⠀⡀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢤⣀⠀⠀⠀⠀⢻⣿⣷⣀⣠⡄⠀⣤⣿⣿⠟⢀⡀⠀⠀⠀⠀⠢⡄⢀⠍⠀⠂⠉⠷⣁⠂⠤
⠒⠀⡉⠁⠀⠈⠀⠀⠐⠄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠈⠙⢿⣿⡛⠃⢰⣿⣿⣩⠆⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠓⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣶⣶⣉⡄⠓⢦⣹⣿⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠈⠞⠛⠙⠋⢻⡿⢿⠅⣠⣆⠋⣼⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⢢⠴⢦⣄
⠀⠀⠀⣲⢢⢶⡶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⡻⢽⢚⣺⣿⠏
⠀⠀⢶⣁⣳⠺⣨⠬⣝⣫⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⣠⡶⢶⣆⠀⠈⠛⡄⠀⠀⠀⠀⠀⢀⢀⢄⣦⣟⣷⣷⢺⡝⢏⠋⡧⢏⠟⠁
⠀⠀⠀⠙⢾⡑⢳⣾⢳⢣⢿⣖⡿⣽⡟⣶⡴⡄⣠⢠⠀⡀⡀⠘⣆⠀⢾⣗⣼⣧⣙⡗⠀⢠⡇⣀⣠⢀⣢⣽⢓⣟⣿⣟⣏⢡⡌⠦⢡⢚⡸⠟⠁
⠀⠀⠀⠀⠀⠈⠛⠌⣍⢏⢟⣛⡞⡳⠯⣮⣔⡫⣹⣫⢞⣖⡇⡧⢏⣳⣨⢿⠿⠾⣿⣧⣶⣿⢷⡛⣫⢇⢞⢾⢺⣛⢛⢛⣘⠐⣼⣬⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢾⣟⣯⢇⠧⡳⠿⣿⡽⠜⡬⣀⡸⢚⣲⢿⣿⣷⣶⣿⡟⢮⡤⡁⡥⣰⢪⣻⡓⣣⢹⡞⢻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠦⣟⣁⢢⣈⡣⢜⡺⢖⡃⣏⢸⣿⣅⣠⣽⣇⣀⡟⠍⣏⠦⣉⣆⣩⠬⠞⠉
⠀⠀⠀⢠⢤⣠⣒⡆⡆⡆⢄⠠⡀⠀⢄⢆⠰⡙⡏⢷⢲⣾⢼⣾⠴⡿⣻⢿⡃⢹⣿⣟⠽⢛⠼⠼⢓⣻⠫⣀⣤⣀⣤⣀⠀⢠⣤⣀⣀⣀⣀⣀⢀⣀
⠀⢠⢓⣂⡸⠜⣌⢲⠃⡷⠛⡾⡴⠴⡈⡀⢗⡗⡎⢇⢫⢤⡽⢰⡉⢧⢹⠸⣧⣸⣿⣼⣓⡀⡦⢈⣙⣚⢃⠃⡧⠷⣵⢻⣼⣬⣿⣶⣷⣺⢻⢿⣩⣩⣟⣦⡀
⠀⠀⠙⠲⠶⣭⣔⢆⠹⡴⢷⡒⣏⢥⢹⢘⢣⢓⣩⡽⣋⢖⡥⢡⢍⣓⡸⠂⣿⢼⡿⣃⢷⠱⡚⡄⠢⠛⢾⢾⡯⣙⡹⣞⠻⠳⢺⢼⠹⢻⠫⣕⣮⢩⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠘⠒⠒⠚⠑⠚⠓⠚⠒⠚⠛⠋⠉⠈⠁⠀⠀⣿⣼⡇⠈⠉⠑⠳⠨⠵⠌⠦⠻⠿⣽⣟⣭⣯⠍⠾⠶⠌⠚⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣛⣻⣻⣩⣙⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣭⣿⣯⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⣀⣀⣀⣀⣀⣿⠀⢀⣀⣀⠀⣀⣀⢀⣀⠀⣀⡀⣀⢀⡀⢀⠀⣀⣀⠀⣀⣀⠀⣀⣀⠀⠀⢾⣀⣀⣀⣤⣀
⠀⠀⠈⢦⠀⠀⢸⣏⠀⢸⣧⣿⠀⣿⠤⢸⡿⣶⢿⡇⣿⢸⣿⣾⠀⣿⢹⡇⣿⠤⠀⣷⣼⡃⠀⣺⡇⠀⠀⡴⠁
⠀⠀⠀⠈⡧⠀⢸⣿⠀⠘⠃⠘⠂⠛⠒⠀⠃⠛⠘⠃⠛⠘⠃⠛⠀⠛⠚⠁⠛⠒⠀⠃⠘⠃⠀⣿⡇⠀⢼⠁
⠀⠀⠀⡼⠁⠀⠸⣟⣶⣶⣶⠶⠶⠒⠒⠒⠒⠂⠲⠖⠲⠖⠖⠶⠶⠖⠖⠒⠶⠶⠶⠲⣖⣶⣶⣿⠇⠀⠈⢣
⠀⠀⠚⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠒⠒⠒⠒⠒⠒⠓
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿

⠀⠀⠀⣴⣿⠿⢿⣶⣾⡿⠿⣷⣆
⠀⠀⠀⣿⣇⠀⠀⠈⠁⠀⠀⣿⣿
⠀⠀⠀⠹⣿⣦⡀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠈⠻⣿⣦⣴⣿⠟⠁⠀⠀⠀⠀⠀⣰⣿⠟⠉⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠙⠛⠿⠛⠉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⢀⣴⣶⣿⣷⣿⣿⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⣠⣶⣾⣷⣶⣤⡀⠀⠀⠀⠙⢿⣶⣀⢀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣆⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⢿⣦⡀⠀⢰⣿⡏⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠙⢿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠙⠿⣷⣄⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠉⠁⠀⢸⣿⡇⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⣉⣁⣀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⣿⣷⣴⣿⠟⠛⠻⣿⣤⣾⡿⠛⠙⢻⣷⣤⣤⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢀⣠⣾⡿⠋⠀⠀⠀⣠⣿⡿⠋⠀⠀⣠⣿⡿⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⣠⣾⡿⠋⠀⢀⣴⣾⡿⠋⠀⢀⣾⣿⣿⣶⡄⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠉⠉⠀⢀⣴⣿⠟⠁⠀⣀⣄⠙⠋⠁⢀⣿⡿⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣠⣾⡿⠋⠀⠀⣠⣾⡿⠁⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠛⠛⠛⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣠⣾⡿⠃
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⣿⣿⣶⣤⣤⣤⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⠀⠀⠀⠀⠘⠿⠟⠋⠁⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣧⠀⠀⠀⢀⣠⡤⠤⠤⠤⠤⣤⣀⠀⠀⠀⢰⡇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢹⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⣸⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⢀⣀⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀
⠛⠛⠳⠶⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⡤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⣀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣴⣯⠤⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢬⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⠀⠀⠀⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣉⣹⣏⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣦⡀⠀⠩⣭⣭⣿⠁⢀⣴⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡟⠙⣦⣄⣀⣀⣠⣴⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⡞⠋⠁⠀⠉⠛⣆⠀⠀⢠⠞⠉⠀⠀⠉⠳⣄⠀⠀⣠⠞⠉⠀⠀⠉⠳⣄⠀⠀⣠⠞⠉⠀⠀⠉⠳⡄⠀⠀⣰⠋⠉⠀⠈⠉⢳⡀
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡆⠀⡏⠀⠀⠀⠀⠀⠀⢹⠀⠀⡏⠀⠀⠀⠀⠀⠀⢹⠀⠀⡏⠀⠀⠀⠀⠀⠀⢻⠀⢰⡇⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡼⠁⠀⢳⡀⠀⠀⠀⠀⢀⡾⠀⠀⢳⡀⠀⠀⠀⠀⢀⡞⠀⠀⢷⡀⠀⠀⠀⠀⢀⡞⠀⠈⢧⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⢀⡽⠷⠤⠤⠴⠿⣥⡀⠀⣀⡽⠶⠤⠤⠶⠯⣄⡀⢀⣠⠽⠶⠦⠴⠶⠯⣄⡀⠀⣠⠽⠶⠤⠤⠶⢯⣀⠀⢀⣨⠿⠦⠤⠤⠶⣯⡀
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠹⡾⢁⡤⠤⢤⣤⣀⣀⡤⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢤⣀⣀⣤⡤⠤⢤⡈⢷⠏⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⡆⠀⠀⣧⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⠀⠀⢰⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⢦⣙⡗⠒⠶⠦⣤⠴⠞⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟⠳⠦⣤⠴⠶⠒⢺⣋⡴⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠟⢦⡀⠀⠀⠙⢧⡀⠀⠀⠙⢦⡀⠀⠈⠙⢦⡀⢀⡴⠋⠀⠀⢀⡴⠋⠀⠀⢀⡼⠋⠀⠀⢀⡴⠻⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⢧⡀⢀⡽⣶⣄⠀⣠⡇⠀⠀⠀⠀⢹⣦⣀⠀⣸⠇⠸⣇⠀⣀⣴⡏⠀⠀⠀⠀⢸⣄⠀⣠⣶⢯⡀⢀⡼⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠀⡇⠈⠉⠁⠀⠀⠀⠀⠀⢸⡇⠈⠉⠁⠀⠀⠈⠉⠁⢸⡇⠀⠀⠀⠀⠀⠈⠉⠁⢸⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⠉⠈⠟⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠅⠀⠀⠀⢶⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠹⣿⣿⣩⣭⣭⣤⣭⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⢠⢤⠶⠶⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⡶⠲⢦
⢠⠾⣦⣶⣠⠳⠘⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠚⠿⠱⢇⣰⣦⡼⢮
⢘⠃⠈⠈⠁⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠀⠘
⢘⢠⣒⢳⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢾⢒⣀⢠
⢘⣿⡏⢿⣎⣿⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⢿⣏⣾⠏⣿⣟
⠹⡟⠿⠯⣬⣟⣯⣭⠉⣱⣤⡦⠒⠦⢦⣄⣠⣄⠄⢰⣶⣆⢀⠀⡄⢀⠀⠀⠀⣠⠀⡄⠀⠀⣀⠀⠂⠀⣀⣀⡀⣀⣀⣠⣤⣄⣴⢠⣤⣴⡻⣉⣩⣛⣯⣬⠷⠟⣿
⣤⣤⣷⡾⣴⣽⠻⣿⠈⣿⡿⣿⣷⣶⣟⣿⣿⣴⣾⢡⣍⢴⡟⠇⣾⣮⣟⠷⠆⣚⠐⠇⣜⣣⣿⠟⠋⠑⢯⣿⣯⣽⡏⢙⠛⠏⣉⡀⢿⠟⣶⣬⡟⠛⠋⠿⢷⣾⡟
⠿⢿⣿⣶⣿⡁⠾⢢⣀⣻⠅⠙⠉⠀⠈⠉⣹⡥⢻⣾⣯⣡⣴⠸⠋⠛⠛⢳⣶⢿⣿⣿⣿⠁⠈⣷⠒⣦⣶⣾⠿⡿⠁⠈⢡⡖⠉⣵⣆⣴⣿⣿⢇⣤⠜⣠⣼⣿⡟
⠀⣰⣏⡿⠁⣿⣷⠜⣿⢻⣷⣿⣗⡀⢀⣾⣿⣽⡄⠙⠟⢁⠉⠀⠀⠀⠠⠆⠈⣿⠻⡿⠏⠀⠀⢿⠀⠙⣹⣯⠀⠀⠀⠀⢙⣿⣿⡟⠋⢰⠟⠀⠈⣽⣦⣁⣿⡿⣁
⢸⡿⠛⢡⡜⠻⣿⣀⣹⣿⣿⡿⠎⠥⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡚⠿⠀⢀⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⣤⣀⣰⣇⣸⡿⠿⣡⡔⣯⣶⡶⠀⠿⣟⣿⣿⡅⠁
⣸⠟⠁⡈⠀⠀⠀⠸⡿⢿⡻⠷⠶⠴⣦⡈⠋⠁⣥⣀⠐⠒⠀⠈⣿⡇⠀⠀⠈⢀⡀⠀⠀⠀⢰⣿⣿⣦⡁⠀⢀⣿⡿⢫⠁⣠⣦⣿⣇⠘⠁⠀⠀⢈⣿⣿⣿⣷⠾
⢸⣀⡞⡇⠀⣀⠀⠀⠀⢠⣧⣶⣦⣤⣼⣇⠀⣴⣿⣏⠀⠀⠀⠀⠏⠁⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⡇⠀⣈⣭⡤⠀⣼⣿⣿⣿⣷⠃⠀⠀⢀⢻⣿⣍⢈⠾
⠈⠣⠙⢿⡾⢿⣷⢾⣷⣌⣿⣿⣿⣿⣿⠿⠗⠙⢿⣿⣿⢦⣄⣘⡗⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣀⠉⠋⠀⠀⠛⠉⠁⠀⢿⣿⡟⠉⠁⠀⠀⠞⣹⣿⣌⠁⠳⢀⡾
⠺⠆⠳⡄⠹⣮⡻⣯⣿⣿⠟⠛⣋⣍⠻⣦⣀⠀⢳⣿⣿⣆⡛⠻⠃⠀⠀⠀⠀⠀⠀⣄⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠄⣀⣠⡀⢀⣠⠟⠈⠾⠋
⣙⣠⣀⣶⣀⣈⣛⣚⣉⣠⣖⣀⣙⣻⣷⣜⣯⣗⣆⣠⣠⣎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣁⣀⣀⣀⣰⣇⣀⣀⣀⣀⣀⣚⣿⣷⣿⣿⣟⣽⣿⣋⣀⣀⣀⣀⣀
⣿⢻⠿⠿⢿⣟⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣛⣿⣟⣛⣛⣟⣟⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠉⠁⠀⠀⠈⠉⠛⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣳⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣵⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠉⠉⠀⠀⠀⠀⠈⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⠈⣿⣿⣆⠀⡘⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣇⠹⡿⢿⣦⡁⠈⠻⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣆⠐⡤⠙⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣄⠁⠸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢹⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣀⣀⡀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⢦⣙⡻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣽⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢿⡸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠛⠛⠿⠿⠟⠋⠀⢈⣶⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣾⡿⢿⣿⡿⠟⠛⠁⣴⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⡇⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣰⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠿⠀⠀⠀⠐⣼⣿⣿⢻⠇⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣀⡀⠀⠑⣽⠇⠀⠀⣸⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣉⠁⠀⣼⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠰⡆⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠀⢠⣾⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣶⣼⣿⣿⣿⠀⠀⡄⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠛⠋⠛⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾
⠀⠀⠀⠀⠀⢸⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠼⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣤⣀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⢿⣦⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⡏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣼⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠛⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣴⣿⣿⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢠⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠹⣿⣿⣿⣷⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡾⠿⡿⢿⠋⠀⠀⠘⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⠃
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣂⠐⢁⣰⠐⡐⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡮⠿⣧⠟⡈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠲⠊⠁⠘⠠⠢⠄⡖⠒⠆⢹⠊⠁⠈
⠀⠀⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣄⠘⠓⢂⠀⠀⢀⡀⣾⣗⠦⢀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡴⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⠀⠀⠀⠘⣏⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣰⡦⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠉
⠀⠀⠀⠀⠀⣀⠩⠉⠀⣀⡿⡄⠀⠠⣤⡄⠀⠀⢀⣄⠀⠀⣀⠀⠀⠀⠀⢠⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠤⠛⣿⡆⠀⣤⣾⣷⠟⡴⢾⣿⢀⣠⠾⠋⣠⠁⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢈⣀⠀⠀⢀⡀⠂⠺⢃⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠊⠁⠀⠘⡂⠈⠡⠄

⠀⠀⠀⠀⣀⣀⡀⢠⣾⠛⢷⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣴⠟⠻⣦⠀⣀⣀⡀
⠀⠀⠀⣾⠉⠉⠙⢻⣯⣠⣼⡟⠋⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠛⣿⣄⣠⣿⠛⠉⠉⢹⡆
⠀⠀⠀⠙⠶⣤⣤⢼⡿⠛⢿⡯⣤⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⡬⣿⠟⠻⣿⢦⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠠⢿⣿⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⠧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡟⠉⣿⡶⠶⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡶⠶⣾⡏⠉⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣠⣤⣼⣿⠀⢸⡇⠀⢿⠇⠀⣿⠛⢻⣧⠀⠀⠀⠀⠀⢠⡿⠋⢻⡇⠀⢸⠇⠀⢿⠀⠀⣿⣤⣤⡀
⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⡇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⣸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢀⣠⣴⡿⢋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠻⢦⣄⣀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⣈⣉⣥⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣈⣉⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣄
⠀⠀⠀⢾⣯⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⠀⠀⠀⠗
⠀⠀⠀⠈⢿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⣷⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠹⠟⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠀⠈⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣀⠀⠀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⢠⡾⠿⢷⡄⠀⠀⠀⠔⡀⠀⡰⠀⠀⠀⠀⣾⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠸⣷⣀⣾⠏⠀⠀⠀⠀⠁⡄⢀⠀⠀⠀⠀⣿⣦⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⠀⣙⣿⣏⠀⠀⠀⠀⢀⠄⠀⠆⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢰⡿⠋⢿⡆⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⢠⣿⠋⢻⣧
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠘⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⣏⠀⣹⡀⠀⢠⡟⢛⡆⠀⠀⠀⢰⡟⠛⣷⠀⢀⣾⣿⠿⣿⣿⡆⠀⢠⣏⠀⢩⡄⠀⠀⠀⠀⠁⣀⢀⡀⠑⡀⢠⠛⠉⠉⢣⡀
⠀⠀⠀⠀⠀⢻⣶⡿⠀⠀⠀⢻⣾⠃⠀⠀⠀⠸⣷⣠⡿⠀⠀⠹⣿⣦⣾⡿⠁⠀⠈⢿⣶⡿⠃⠀⠀⠀⠈⢄⠀⢆⣠⠈⠀⠸⣧⡀⢠⣾⠁
⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⢠⣿⢿⣧⠀⠀⠀⠀⣹⣿⡁⠀⠀⠀⣹⣿⣿⡁⠀⠀⣠⣾⠿⣿⣄⠀⠀⠀⠀⠠⠢⡀⠡⠀⠀⠀⠙⣷⡿⠁
⠀⠀⠀⠀⢺⠟⠀⠹⡷⠀⠿⠃⠈⢿⠇⠀⠀⢾⠟⠉⢿⠆⠀⠀⢻⠟⢿⠃⠀⢸⡿⠃⠀⠈⢿⡇⠀⠀⠔⠀⠔⠁⠀⠐⠄⢀⣾⡟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠊⠀⠀⠀⠂⠀⠘⠏⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⡆⣤⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡛⢀⠔⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢄⠀⠐⠁⠀⠀⠘⠁⡀⠀⠒⠲⢄⢀⠠⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠣⣀⠂⠠⠆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⠈⣿⣵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠳⢄⠤⣤⣀⣁⠐⠤⠀⠐⢞⣻⠎⡁⠀⢭⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠠⠅⠀⣼⣿⡿⠀⠒⢄⠀⠀⠉⡆⠈⠀⠀⠉⠸
⠀⠀⠀⠀⢀⠄⠀⠀⠼⠀⠀⠀⠐⢇⠀⠋⠹⠁⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⡜⠒⢀⣤⡂⠀⠀⠀⢰⡀
⠀⠀⠀⠁⠀⠀⠁⢁⣤⣴⠊⢨⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠁⡾⠆⢀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠲⠀⠈⠀⠰⠀⠀⠀⠀⢰⠄⡃⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠈⠂⠤⣤⣷⣠⠀⠀⠀⢐⠂⡀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢠⠰⠆⠀⠀⢀⢿⣾⡯⠓⠒⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡐⠀⡀⢈⠠⠁⠀⡏⡐⠒⠠⢀⣰⠿⡐⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⠆⢘⠀⠳⡀⠀⣰⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢢⠀⠀⠀⠴⠐⠀⢠⠃⠀⡬⣿⣹⠶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠁⠢⣤⡷⠛⣮⣀⠤⠚⡁⢀⡄⠀⠀⠻⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⠄⠱⠤⢴⣀⡀⠠⢽⣷⣤⡿⣇⠀⠀⠀⢨⠃⢶⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡄⠒⠁⣘⢹⡀⢀⠀⠀⡘⠙⠀⠘⢆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣀⠠⢶⠻⠠⠂⣡⠀⡛⠰⠀⠈⢃⡀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⢢⢤⡄⠒⠀⠀⣓⠺⠀⡴⠦⠤⠀⠀⠠⠄⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠠⠄⠙⠒⠒⠒⠉⠿⠂⠰⠆⣠⣤⠀⠀⠀⠀⠀⢤⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢁⡀⠀⠀⠀⠀⠐⠶⠆⠀⠀⠀⠀⡀⠶⠶⠀⠀⠙⠠⣤⡀⠀⢀⠀⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠈⢦⡀⠀⠈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⣄⡀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢤⣤⣤⣀⣀⣠⣀⣀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠒⣤⠶⠶⠈⠉⠙⠻⠿⠆⠀⠈⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠃⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠈⠛⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠘⠋⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠀⠀⠀⢠⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠠⠆⠐⠒⠂⠀⠀⠀⠀⠒⠲⠶⠶⢦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠀⣾⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠑⠀⠀⠘⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⡀⠀⠀⠈⠀⠀⠉⣶⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠢⣄⣀⣀⡀⠀⠀⠠⠴⠆⠈⠋⠁⠈⠉⠀⠀⠀⠀⢹⡄⠀⠀⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠁⠀⠀⠀⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠁⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣆
⠀⠀⢉⣉⣉⣉⣉⣉⣉⣉⣉⡉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠿⢿⡿⠿⠿⠿⣿⣿⠿⠿⣿⢿⡿⢿⣿⠿⢿⡿⢿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⠀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠙⣈⡉⢻⡁⢀⡏⠉⢩⣏⠛⢨⣯⠟⢩⡅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠛⠐⠀⠄⠄⢀⠀⠀⡀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠌⠀⠀⠀⢀⡄⠀⠀⠀⠓⠄⠩⠄⣴⡏⢙⣦⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⣢⣿⣿⣿⣷⣤⠤⠄⠲⡆⠀⠙⠿⠚⠧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⡧⠤⠀⢰⣿⣿⣟⣿⣿⡿⠀⠀⠀⣈⠀⠂
⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⡀⠀⢁⡄⣼⢧⡀⠀⠈⣻⢿⣿⣿⠿⠛⠢⣄⢰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠠⢦⠈⠁⠀⠀⠸⡀⠀⠠⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢆⢀⢀⡰⠐⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⢛⡛⢛⡛⢿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣭⣶⣜⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡛⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⡿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣹⣧⣿⡜⢿⣿⣿⣍⢻⣿⣿⣿⣿⣿⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⣽⡿⣏⣽⣿⠟⣻⣿⣿⣿⣧⣿⣯⣤⣉⣿⠇⡼⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡸⢗⣩⣼⠿⠾⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⣿⣿⣿⣿⣹⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⡟⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢷⣿⡷⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢸⣧⣼⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢷⣤⣿⣮⡽⢢⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢚⡇⠹⣻⣎⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⡺⢟⣿⠿⣻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣉⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠚⣿⡿⣯⡍⣶⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⢉⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣋⣙⣿⣿⣿⣷⣼⣧⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⡿⠋⣤⣽⠿⣿⡟⣛⣶⡿⢏⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⡿⣿⣉⣷⡻⣦⡀⣠⡾⠋⢀⡀⠛⢎⡰⠟⣡⣾⣻⣗⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣏⣿⣿⣿⢟⣥⡾⢋⠛⣰⠾⠓⣾⣽⠿⢉⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣾⣍⣛⣉⣴⢋⡞⠩⣷⣦⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢿⣥⠿⠁⠉⠉⠉⠫⢟⡻⠿⠶⣦⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢙⣾⡿⣦⣴⣯⠆⣠⣄⡾⢿⢷⢂⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣅⣶⣿⣧⣼⣧⣭⣷⣊⣽⣛⣋⣴⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢁⣼⣿⣿⡿⣿⣙⣿⣷⣿⠽⣿⡿⢋⣼⡟⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢋⣜⣿⠟⣿⣿⣿⣿⣾⣿⣿⣿⣷⡶⢟⣵⣿⡻⡦⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⣡⣤⣾⣿⣯⣿⣮⣿⣿⣿⣾⣿⣯⣿⡟⣷⡿⠋⣾⣯⡇⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣿⡿⠛⣷⣼⡿⢿⣿⡿⣿⣿⣻⡷⣼⣿⡿⠻⣷⣴⣿⣾⣏⣻⣿⢸⣟⢿⢽⣿⣷⣄
⠀⣤⡀⠀⠀⢀⣴⡿⣿⣹⣾⣿⠿⣽⣿⣿⡯⣥⣾⣿⣿⣿⣿⣙⣶⡿⠋⠀⠀⠘⢿⣿⣿⣿⣿⣿⣹⣿⣾⣠⣦⠿⢿⣷⣄
⠀⢸⣇⣠⣶⣿⠋⣴⣹⡿⠛⢠⣽⣿⣏⣰⣶⣯⣻⣿⡟⠋⣹⣿⠟⠀⠀⠀⠀⠀⠀⠹⣿⣟⣿⣿⢸⣿⣿⣿⡟⢿⣿⠛⢿⣷⣄
⠀⢼⣿⢻⣿⠇⢰⣼⡟⠣⣼⣿⣯⡟⢋⣽⣿⣿⣿⠿⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣼⣿⣹⣿⣿⣾⣿⡼⣿⣿⣿⣷⣦⡀
⠀⠈⣿⣇⠟⡀⢻⠿⣉⣶⣿⡻⢿⣤⣾⣿⣯⣛⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣛⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⣿⣿⠦⣠⡄
⠀⠀⣿⠆⡇⢱⣏⣴⢿⣿⣿⣹⣿⣿⢿⣿⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⣾⣿⣯⣿⣿⣿⣻⣿⣿⡷⢸⡇
⠀⠀⣿⠆⢱⣿⣯⣻⣾⡿⣿⣿⣿⣭⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇
⠀⠀⣿⠆⣠⠟⣿⣿⡟⣁⢾⣽⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣏⣿⣿⣛⣿⣿⣿⣿⣿⡏⣿
⠀⢀⣿⣰⣟⣤⡿⠟⣡⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣙⣿⣿⣿⣿⣿⣷⣿⡀
⠀⢸⡗⢁⡌⠛⣡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⡇⢈⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⢿⣿⣧
⢠⣿⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡲⢿⣿
⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⢶⣶⣶⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣦⡄⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⢲⡾⣽⣿⣿⣿⡿⢵⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠴⣦⣀⠀⠀⠄⠀⠀⠈⠊⠉⠁⠀⠀⠈⠉⠀⠀⢺⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⡌⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣌⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠈⠀⠀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀⠠⠊⠀⣀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠘⡋⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢠⡾⠋⣿⡖⠀⢠⠀⠀⠀⠀⠀⠈⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠹⠿⢯⡀⠀⠀⠐⠒⠊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡞⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠡⡞⠂⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢄⠀⢰⠃⣅⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡛⢆⠈⠲⠀⠀⠀⠀⠴⠛⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⣠⣵⡾⠴⠿⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⠃⢸⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠞⣋⡁⠀⠀⠀⠀⠀⠀⠐⠀⠁⠁
⠀⠀⠀⠀⠀⠀⢰⣝⡿⢏⠀⠀⠀⠉⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣶⣾⣿⣀⠀⢠⠁⢠⣀⢀⣀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡄⢀⡀⠀⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠛⢸⠀⢸⢀⠞⢠⠞⠀⡹⠦⡤⠤⠖⠋⠀⠀⠀⠀⠀⠀⡇⢸⡇⣸⠁⢀⠴⠋⠙⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣿⢀⠼⠃⠰⠋⢠⠞⠁⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠋⢹⠀⠃⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⡋⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢠⡄⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⢙⣷⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣄⣸⣿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⢰⣏⣹⠇⠀⠀⠈⠉⠙⠛⠳⠶⠶⠶⠶⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣻⡀⠘⠋⠁⣹⣿⠷⣤⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠉⠁⢀⣶⡆⠀⣴⡖⠀⢰⣶⣤⠶⣶⡄⠀⢰⣦⡴⢶⣦⠀⣠⡶⠒⢦⡈⣹⠟⣿⡗⠀⢠⣿⠇⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⣸⡿⠀⢰⣿⠁⠀⣼⡿⠁⣀⣿⡷⠚⣿⡏⠀⢸⣿⣤⣿⣿⣤⣼⡷⠋⣼⡿⠁⠀⣼⡿⠀⢠⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠗⠀⠀⢹⣿⠀⣿⣇⣰⢿⣇⣀⣼⣿⣣⡞⣹⡟⠀⢰⣿⣴⢛⣿⠏⠀⣿⡀⢀⡿⠀⢰⣿⠁⢀⣼⣿⡇⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢀⣼⡟⠀⠙⠋⠁⠈⠛⠉⢸⣿⠈⠛⠉⠀⠀⣸⡏⠙⠋⠁⠀⠀⠉⠛⠉⠀⠀⠈⠻⠛⡋⠈⢿⣷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⣠⣤⣄⣀⠀⠸⠿⢀⣴⠏⣹⠆⣿⡇⠀⠀⠀⣤⡤⣤⣄⣸⣿⠀⢠⡾⠋⢉⡷⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠉⠛⠒⠶⣾⡿⠖⠋⠀⠘⠃⠀⠀⠀⠉⠀⠀⢈⣿⡟⢶⣿⠷⠖⠋⠁⠀⠀⠘⠷⣼⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣉⡗⣰⡟⠙⣿⡏⢠⡾⠋⡷⢠⣿⣥⠞⣿⠆⠀⠀⠀⢸⣯⡍⢷⣀⣼⡿⠀⣼⣧⠞⢻⣷⢀⣴⠟⣹⠇⡼⢠⡿⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡋⠉⣰⣿⠁⣠⣿⠀⣿⡇⠀⢀⣾⣿⠃⢰⡿⠀⣿⠆⠀⣸⡟⢛⡿⢉⣿⡇⣰⣿⠏⢀⣿⠇⣼⣟⠉⢁⡼⢡⣿⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠛⠉⠻⠶⠋⠛⠛⠉⠘⠛⠀⢿⣇⡴⠏⠀⠀⠈⠛⠋⠁⠀⠛⠛⠉⠛⠀⢸⣏⣰⠋⠛⠛⠋⠀⠸⣧⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠀⠀⠀⠀⠀⠈⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⢀⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⢀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣄⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢟⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢯⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣱⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⣵⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠁⠹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠰⠦⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⣉⣄⣠⡀⠁⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⡏⠉⠉⠛⣷⡄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⢻⣦⣤⠄⠀⠘⣧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⢀⡿⢀⣴⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣟⠐⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⡿⠋⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⣄⠀⣿⠁⠀⠘⠦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡁⢙⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢠⣶⠿⠿⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢻⣏⠀⠀⢀⠹⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣈⠙⠛⠁⡰⠂⣿⠀⠀⠀⣠⡤⠞⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⢰⡇⠓⠀⢀⡿⠀⣠⠟⣩⠖⠛⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠁⠂⠀⣾⠃⣼⣣⠞⡕⢺⠇⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠖⠁⠀⠈⠛⠀⠀⠈⣸⣾⣏
⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠦⠶⣤⣄⡀⠀⠀⠀⠙⣶⣦⣴⡿⠀⠀⠀⠀⠘⢃⣼⠟⠉⠀⠈⠳⢄
⠀⠀⠀⠀⠙⢿⣄⠰⣖⢛⡿⣶⢶⣬⣇⠀⠀⢀⣀⣽⣿⣿⡷⢦⣤⠶⠖⠋⠛⢿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠛⣷⡈⠫⡻⣄⡈⠉⢛⡷⠀⠉⠁⠉⢻⡏⠁⣾⠁⠀⠀⠐⠀⢼⣿⣆⣤⣤⣶⠷⠚⠓⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣌⠊⠗⣦⣌⠀⠀⠀⠀⠀⣈⡳⠂⠉⠀⠂⣤⣤⣴⣾⣿⣏⣹⣿⡿⠂⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆⠉⠘⢦⡀⠀⡀⣤⡿⠁⠀⠀⠀⠀⠁⠈⠙⠛⣻⣿⣿⣿⣷⣄⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⢿⣿⣂⠠⠤⠤⢤⡁⢀⠊⠉⠁⠀⠙⢯⡀⠙⢣⣤⣜⣓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢚⣿⠶⣿⣏⡿⠀⠀⠀⠀⠙⢬⡄⠀⠀⠀⠀⠀⠉⠀⠀⠛⢉⠻⢿⠦⡙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢻⣌⡇⠀⠀⠀⠈⠀⣸⣷⠀⠀⠀⣀⡀⠂⠠⣶⣁⠦⠤⠴⠴⠙⣣⡘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣿⠗⣀⡀⣤⣤⣤⣼⣿⡷⢿⣾⠉⠀⠀⠀⠀⢩⣤⣥⣉⣉⣉⣉⣥⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⢻⡄⠀⠀⠀⣠⣳⠞⠉⠁⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢡⠉⠈⠉⠁⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⡼⣻⠟⠁⡋⢃⡤⡆⠀⠀⠀⠀⠀⠀⢸⡿⠁⢻⠿⣦⡀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡿⢱⣯⣴⠶⠟⡫⠜⣣⡀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠀⠈⠟⡹⢿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠧⠖⠒⠒⣉⣡⣴⠞⠛⠁⠉⠒⠀⠂⠹⠀⠀⠀⠀⠀⠀⠈⡅⠉⢋⢷⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⣤⣴⡶⠾⠿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⢀⣤⣾⡓⢦⣈⡌⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠙⢷⣝⠦⣍⡃⣿⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣙⠛⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣿⣿⣿⣿⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣿⣿⣿⣿⣀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣿⣿⣿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣬⡍⠛⠁⠾⣿⣿⣿⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣤⣀⣴⢏⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⡿⠿⣛⣵⣿⣿⣿⣿⣿⣿⢏⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⣠⣄⣻⣿⣿⣿⣷⣿⣿⣿⢋⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⢿⣿⡿⢣⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣤⡀⠻⠿⠟⢋⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣷⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣩⣥⣤⣴⣶⣶⣶⣤⣤⣭⣍⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠁⠀⢤⣧⣤⣀⡀⠀⠤⡃⠀⠿⣿⡷
⠀⠀⠀⠀⠀⠉⠿⢿⡿⠏⠀⠀⠐⠚⠁⠀⢸⡇
⠀⠠⡄⠰⡂⣠⠀⠀⠀⠀⠀⠈⠙
⠀⠈⠹⠀⠀⠨⠀⢰⡀⠆⠀⠉
⠀⢀⣰⣀⡀⠀⠀⢀⡡
⠐⢲⣿⣿⣿⠉⠀⠀⠸
⠀⠀⠀⠉⠀⠀⠀⠒⠆⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣤⣾⣇
⠀⡇⠀⡄⢠⡀⠐⠒⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠛⡆⠀⠀⣀⠄⠉⢻⡏
⠀⠀⠀⠉⠈⠠⢦⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠎⠀⢀⡀⠸⠃
⠸⣿⣶⠯⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠈⠛
⢀⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣠⣀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⡃⠀⠈⢐⣆⠘⡀⢴⡀⠠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠉⢻⡇⠀⠀⠀⠸⠀⠀⠈⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠀⠸⠃⠈⠀⠠⣼⣤⣀⠀⠀⠠⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⡀⢄⠀⠀⠀⠈⢹⡿⣿⠿⠉⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⢀⠜⠉⠀⡈⠑⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠒⠂⣀⣉⣠⣤⣤⣤⣤⣤⣉⣉⠒⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠢⣄
⠀⠀⠀⠀⡰⠁⢠⠀⠀⠉⠢⡈⠳⡀⠀⠀⢀⡤⠞⢉⣡⣴⣶⣿⡿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⣿⣶⣤⡉⠒⢄⠀⠀⠀⠀⠀⠀⠊⠀⠠⠲⢄⠈⠱⡀
⠀⠀⠀⠀⠁⢰⠃⢀⠊⠁⢆⠐⢄⠑⣀⠔⠉⣠⣶⣿⠟⠋⣉⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠙⠛⢿⣷⣤⡑⢦⡀⠀⠔⠀⠀⠀⡀⢀⡈⢃⠀⠐
⠀⠀⠀⡄⠀⠋⠀⠈⠀⠀⠀⠀⠈⡶⠋⣠⣾⡿⢋⣠⣶⣿⡿⠟⠛⠛⣉⣉⣉⣉⣉⣉⣉⠛⠻⢿⣿⣶⣄⠈⠻⣿⣦⡙⢦⡀⠀⠀⠀⠀⠀⢘⡀⠂⠀⢁
⠀⠀⠀⠃⢠⠀⠀⠀⡄⠀⠀⠀⡰⢁⣼⣿⠏⣠⣿⡿⠋⣁⡴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣌⡻⢿⣿⣆⠈⠻⣷⣄⠑⡄⠀⠀⠀⠀⠘⠁⢐⠀⢸
⠀⠀⢰⡀⢸⠀⡀⠀⠃⠀⠀⡸⢁⣾⡟⢁⣾⣿⠏⣠⠞⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⣿⣷⡄⠹⣿⣆⠘⠀⠉⠉⣦⠀⠀⡘⠀⢸
⠀⠀⠘⡇⢸⡾⠁⠀⠀⠀⢰⠁⣾⡟⠀⣾⣿⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡈⢿⣿⡄⢹⣿⡇⢀⠀⠀⠄⠀⠀⡄⠀⠸
⠀⠀⠀⢇⠘⠃⢦⣄⡀⠀⡉⢸⣿⡇⢸⣿⡿⢠⠧⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢸⣿⡇⠈⣿⣿⠘⠀⠀⠠⠀⣸⠀⠀⠃
⠀⠀⠀⠘⡄⢡⠀⠀⡀⠀⡇⢸⣿⠁⢸⣿⡇⠸⠀⠑⠈⢢⡀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠊⠀⠀⢸⣿⡇⠀⣿⡿⠀⠀⠀⠀⠰⠁⢀⠎
⠀⠀⠀⠀⠱⡄⢳⡀⡄⠀⡇⢸⣿⡇⠸⣿⡇⢸⡀⠀⠀⠂⡙⢦⠀⠀⠘⡄⠀⠀⢀⠎⠀⠀⠠⠀⠀⠀⢢⡀⢀⣿⣿⠁⢰⣿⡇⠸⠀⠀⡰⠃⢠⣎
⠀⠀⠀⠀⡀⠻⡄⠹⣌⠀⢹⠈⢿⣷⠀⢿⣿⡀⢻⡄⢀⡀⠀⠀⡀⠀⠀⠈⠀⠀⠈⠢⡄⠈⡀⠂⠀⠀⠁⠀⣾⣿⠇⢠⣿⣿⢁⠃⠀⠐⠀⠰⠂⠘⠄
⠀⠀⠀⡴⠀⠖⠁⢢⡈⠢⠈⢧⠘⣿⣧⠈⢿⣷⡄⠳⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⡠⢀⣾⣿⠟⢀⣿⣿⠃⠆⠀⠀⠀⠜⠀⠀⠀⢀
⠀⠀⢰⠁⠸⠁⠀⠀⠙⠢⠀⠈⢂⠘⢿⣧⠈⢿⣿⣄⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢁⣾⣿⠟⢠⣾⣿⠃⠎⠀⠀⠀⠀⠀⠐
⠀⠀⠸⡇⢠⠐⡀⠀⠀⠀⠀⠀⠈⢦⡈⢻⣷⡈⢻⣿⣦⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢠⣾⣿⠋⣠⣿⡿⢁⠎⠀⠀⠀⠀⣱⠄⠀⠆⠀⢠
⠀⠀⠀⠣⠈⢇⠀⠀⠑⠀⠀⠯⠀⠀⠱⡄⠹⣿⣄⠙⣿⣷⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⣴⣿⡿⠃⣴⣿⡟⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠱⡈⠳⣄⠀⠀⡀⠀⠀⠀⠳⡼⣆⠙⣿⣦⡈⢿⣿⣦⠈⠲⡀⠀⠀⠀⠀⢀⠜⢠⣾⣿⠟⢀⣾⣿⠋⡰⠃⠀⠀⠀⠀⠀⣀⠀⠠⠊⢀⠄
⠀⠀⠀⠀⠀⣨⠒⠄⡉⠚⠛⠂⠀⠀⢣⣀⡸⢧⠈⢿⣷⣄⠙⣿⣷⣄⠈⢂⠀⠀⡰⢃⣴⣿⡿⠋⣠⣿⡿⢁⣼⠓⠀⠃⠀⠀⠀⠉⠉⣁⠠⠐⠀⢰
⠀⠀⠀⠀⢰⠃⣖⢀⠈⠁⡀⠀⠀⠀⢢⠁⠀⠠⠑⢄⠙⢿⣦⡈⠻⣿⣧⡄⠑⢄⣠⣾⣿⠟⢀⣾⣿⠏⣠⠟⡀⠓⠈⠀⠀⠀⢀⠀⠀⠀⠄⠈⠀⡌
⠀⠀⠀⠀⢰⠀⢹⣿⠀⠐⢧⣤⠄⠀⢨⠀⠀⠀⣆⠈⢣⡈⠻⣿⣄⠘⠻⣿⣦⡀⠻⡿⢁⣴⣿⠟⢁⣴⠋⢠⠁⠀⠀⠆⠀⠒⠋⠀⠀⠔⠃⠀⠀⠁
⠀⠀⠀⠀⠈⢧⠈⠋⠉⠁⢤⣀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠁⢤⡈⢿⣷⣄⠘⢻⣿⣦⡈⠻⣿⠋⣠⠋⠘⠀⣼⠀⠀⢠⠀⡃⠀⠀⠆⢀⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⣱⢄⠙⢿⣷⣄⠈⠻⣿⣦⡈⠲⡁⠀⡇⠀⢿⠀⠀⠌⠀⡇⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⢱⠀⠱⡀⠰⠁⠀⠸⡂⠜⢁⣼⣷⡄⠙⢿⣷⣄⠈⠻⣿⣦⡈⠲⡇⠀⠘⠀⠌⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⠁⠀⠀⡼⠃⣠⣿⡿⠃⣠⣷⣄⠙⢿⣷⣄⠈⠿⣿⣦⡈⢦⡀⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⡠⠊⢀⣼⣿⠟⢠⣾⣿⠟⢁⠷⢄⠙⢿⣷⣄⠘⠿⣿⣦⡙⢆⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠞⢁⣴⣿⡟⠁⣰⣿⡿⠁⡰⠋⠀⠈⠑⢆⠙⢿⣷⣄⠙⠿⣷⣄⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⣾⣿⠋⣠⣾⣿⠋⢀⠊⠀⠀⠀⠀⠀⠀⠑⢄⠙⢿⣷⣄⠈⠻⣷⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣼⣿⠟⢁⣼⣿⠟⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⢿⣷⣄⠈⢿⣷⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠴⠿⢿⠯⢤⣿⣿⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠽⠿⠶⢤⠟⠛⠓⠒⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠆
⠀⠈⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠶⠤⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⡤⠔⠊⠁
⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠘⠀⠀⠆⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠖⠂⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢀⣠⠖⠚⠋⠉⠉⠛⠲⠄⣠⠶⠛⠉⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣄⡀⠀⣠⣴⣶⣾⣿⣶⣦⣄
⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠙⣦⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⡟⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣀⣀⣠⡴⠟⠀⠀⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⡿⠿⠿⠟⣡⣿⣿⣿⣿⣿⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠻⣤⣤⠞⠁⠀⠀⠘⢦⡀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⣿⣿⣿⣿⣧⣛⢟⣫⣾⣿⣿⣷⣝⢻⣿⣿⣿⣿⣿
⠀⠀⠘⢧⢀⣠⠶⣤⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠙⢦⡀⠀⢀⡞⠀⠀⠀⠘⣿⠿⣛⡛⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⣝⢿⣿⣿⠃
⠀⠀⠀⠈⢿⣁⣠⠾⠳⡄⠀⢀⡀⠘⢦⣄⠈⠻⣦⡀⠙⣶⠋⠀⠀⠀⠀⠀⠀⢾⡿⣫⣬⣻⣿⣿⣿⣷⣝⠻⣿⣦⡙⢿⣷⡍⠁
⠀⠀⠀⠀⠀⠙⣧⣀⡴⠛⢳⡌⠻⠆⠀⠙⠳⣄⠈⣻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢟⣴⣯⢻⣦⣽⣿⣷⣌⡻⣿⡦⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣤⣴⠛⠉⣷⠀⠙⢦⡀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⣵⣶⡎⣿⣧⣙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠉⠳⣄⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠈⠻⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁