Daycation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⣐⠗⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⣶⡶⣿⣛⠳⠶⣄⠀⠀⠀⠀⠀⠉⣰⠟⠉⠉⠻⣆⠛⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡾⣻⠋⢷⣀⣩⡷⠖⠛⠁⠀⠀⠀⠺⠂⣿⠀⠀⠀⠀⣿⠰⠆⠀⠀⢹⡆
⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠃⣻⡴⠞⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠳⢤⡤⠞⠁⠦⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠞⠋⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠐⠓⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⠻⢧⣤⠖⠛⠛⠳⢦⣤⠶⠛⠛⠳⢦⣼⠷⠛⠛⠓⢦⣤⠶⠛⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣠⣄⣀⠀⠀⢀⣀⣤⣀⠀⠀⢀⣀⣤⣀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣞⠋⠀⠀⠉⠛⠚⠋⠁⠀⠉⠛⠚⠋⠁⠀⠈⣻⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣶⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣷⣶⡄⣀⠀⠀⠀⠀⠈⢟⡛⠇⢧⢷⣄⠀⠀⢀⣤⡴⣦⣶⣷
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣿⣿⣿⣿⣏⠀⠀⠀⠀⢀⡈⠀⠀⣠⣿⡞⣳⡄⢄⣹⣷⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣯⠭⠿⢿⣏⠁⢀⠀⠀⠀⢤⡤⠿⣿⣿⡴⠽⠧⠶⣨⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠡⠂⠂⠀⠀⠀⠀⠂⠀⠀⠀⠰⠒⠀⠀⠀⠒⠀⠀⢰⠀⠈⠉⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⣀⠤⢤⠀⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠔⠀⠘⠢⠆⢘⡖⣷⣢⣤
⠀⠀⠀⠀⢶⠿⣿⣷⣤⣥⡄⠰⡏⠀⠀⠀⠀⢐⠂⠀⠞⠉⠂⡠⠀⠀⠰⠋⠉⠁⠀⠀⢀⡿⢴⣿⣵⣿⡿⣷⠄
⠀⠀⠀⠀⠀⠛⢽⣿⢶⣿⣷⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠾⠷⢿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠳⠿⢿⠀⢀⠀⡄⠀⢀⠀⠀⢀⠀⡀⠐⠀⠀⠘⡀⠀⠀⢠⠀⠘⠉⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣬⣤⣤⣤⣄⠀⠠⠀⠀⠀⠀⢉⣀⣤⣀⣉⣉⣉⠐⠳⠧⡨⠛⣯⠄
⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⡟⠗⠀⠀⠀⠀⠙⠂⠉⣿⡟⣿⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⢧⣿⢣⣿⠿⠿⠇

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠸⡌⠡⠀⠀⠤⣡⡧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠉⠛⠒⠶⠤⣤⣉⡙⠓⠲⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠛⠲⠄⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠦
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡤⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠙⠀⠂
⠠⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠏⠄⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⣋⣻⢀⡾⠉⣀⡀⢀⣀⠀⣀⣀⢀⣤⢀⡆⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠉⢹⡟⠁⢾⣽⣇⢿⣭⢼⣭⣯⢼⡏⢼⡵⣯⡽⢼⢫⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠐⠲⠄⠀⠀⠀⠀⠀⠀⠢⠀⢠⢌⣀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢠⠀⠀⠠⠀⣀
⠀⠀⠀⣀⣈⡐⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠏⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⠹
⠀⠀⣀⠛⠉⠉⠈⠛⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠻⣷⠆⠀⠰⣿⠟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⡿⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠈⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠷⠀⡂⡄⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠘⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠠
⠀⠀⠈⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⠀⠀⢰⠈⠀⡘⠂⠀⠀⠀⢀⣀⠀⠐⠀⠀⠀⠄⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⢿⣿⠐⣿⡷⠀⠀⠀⠀⠓⠀⢀
⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⠀⡀⢀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡹⠘⣿⡟⣾⣯⣸⠀⢹⣹⣼⢉⣿⢸⢰⣿⣿⡇⠀⠀⣀⠰⡀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⠋⠛⠘⠁⠉⠙⠘⠁⠈⠁⢉⠋⠈⢈⠈⠉⠉⠁⠀⠀⠡⡂⠁⠀⠀⠩
⠀⠀⡤⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠆⠐⠡
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠐⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣼⣧⠀⢀⣶⡆⠀⠀⣄⠀⠁⠀⠀⠀⢀⣶⡗⠛⣦⡀⠀⠀⠀⢀⡄
⠀⠀⠀⢹⠐⢆⠀⠀⠺⢱⣿⣿⡄⠈⠛⠁⠀⡖⠛⠀⠀⠀⠀⠀⢸⡟⠀⢰⣿⠇⢠⠖⠊⠛⡙⠀⠀⣀⡀
⠀⠀⡠⠄⠧⢘⡂⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠙⠒⠛⠋⠀⠀⠁⠒⠊⠀⠀⢡⣦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⣀⡄⠀⢸⡶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠖⠀⣤⣀⡀⠠⡇
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠆⠀⢻⡇⠀⠀⠻⠁⠀⠀⠀⠂⣦⠀⠀⠹⠆⠐⠀⠀⠀⣓⡪⢭⣓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⢊⣠⡀⡄⠀⢀⡀⠤⠒⠀⡀⢀⣀
⠀⠀⠀⠻⣿⣷⣤⣀⣴⣿⣽⣿⣟⡴⠋⡼⣻⣡⠜⢁⡴⠁⣴⣱⣄⢪⠁⢬⡂
⠀⠀⣤⡾⣻⣿⣿⣿⣿⣷⣾⣿⠋⢀⣼⡽⠠⢃⣴⡿⠁⣞⢹⡿⢮⠂⢹⡄⠱⡄⡠⣄
⠀⠀⠀⣰⡟⠃⢿⡏⢻⢫⣼⡇⡞⢸⠷⢱⠔⢳⣽⢃⣞⡌⠁⣷⠆⠀⠀⠹⣌⠥⠈⠙⠷⡄
⠀⢀⣀⠛⠀⠀⣾⠁⢸⣛⠙⠋⠀⠈⠀⠀⠀⠀⡟⣸⡌⠀⠀⡟⢀⠀⠀⠀⡬⣉⡆
⠀⢂⢻⠿⠦⢬⢩⠀⢸⡙⠀⠠⢼⢤⣀⡀⠀⠀⣾⠡⡄⠀⢰⡟⠙⠀⠀⠀⠀⣄⠃
⠀⠢⠀⣀⣀⠢⡞⢄⢼⣟⡂⠀⡬⠆⠈⠛⠂⠀⢹⠄⡗⠀⣼⡏⠀⠀⠀⣀⣀⣀
⠀⠀⠲⠰⠌⣀⣀⣈⣀⡟⣧⠀⣩⠵⠴⠒⠐⣶⣦⣄⡈⠓⣾⡇⢨⠟⣛⡛⠛⠛⠋⠉⠁⠂
⠀⠀⢀⠈⠓⣑⠉⠈⠈⠋⠀⢰⠁⠛⠻⠿⠣⡉⠉⠛⠃⠀⣿⣤⠄⠀⠀⢀⢠⠀⠀⠀⠀⠐
⠀⠀⠀⠗⠓⠉⠁⠀⠀⠀⠀⢸⣠⣴⣞⣿⡗⠁⠠⣶⠆⢰⣟⣒⠂⠀⠄⠳⠈⠂⠀⣤⠤⡄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣿⣿⢿⡀⠀⠀⠀⠐⠀⡼⠀⣴⠀⣄⣰⢀⣴⡆⢀⡀
⠀⠀⠀⠀⡄⣹⣶⠞⠁⠀⠀⢀⣀⣬⣷⠈⠀⠀⠈⢛⠀⠁⠠⡖⡤⠀⠙⠋⠋⡐⠊⠤⡤⡀⡀
⠀⠀⠀⠰⠀⣿⣿⠀⢰⡀⠀⢈⡟⡷⡇⠀⠀⡮⣑⠋⠀⠀⠄⢀⡥⠁⡂⠀⠂⠀⠀⠀⠢⡀⠈⠁⠠⢀⣀
⠀⠀⠀⠰⠚⠿⣿⠣⠀⣇⣐⡞⠀⣀⡸⠛⢢⡀⠠⣙⡓⢶⡀⠀⣙⠋⠁⠀⠐⡆⠀⠀⠀⠈⠢⣀⣤⣾⣃
⠀⠘⠁⠙⠦⣻⢿⣤⣃⡟⠘⣤⣄⣉⡇⠀⠉⠈⠳⠇⠈⢠⡹⣄⠈⠻⣌⠀⠒⠁⠀⠀⠀⠀⠀⣚⣉⣈⣩⡀
⠀⠀⠇⠀⢁⠈⠳⣌⡙⣟⠛⠃⢫⣤⣄⡀⠀⠀⠀⠀⠀⠀⣇⠈⣷⠄⠈⠀⠀⠀⠀⠀⠀⠀⡠⠿⡇⣿⣿⡏
⠀⠀⠸⣠⠾⣄⠀⢸⣿⡟⠁⠀⠀⠁⠀⠉⢢⣀⣠⣀⡀⠀⠹⡼⠁⠉⠉⠀⠀⠒⠒⠒⠒⠈⢠⣿⠧⠈⠉⠙⠦
⠀⠀⠀⠑⢄⠀⠑⢌⣿⣧⠀⠀⠀⠀⡀⢠⡿⣏⣽⣻⣿⡄⠀⠈⣢⢀⣀⣀⡀⠠⠔⠒⠒⡠⠖⠁
⠀⠀⠀⠀⠀⠑⢄⠀⠙⢿⣧⠀⠀⠀⢹⠸⣿⣿⣿⡿⠿⣀⢤⣺⡝⠣⠄⡀⠀⠀⠀⠤⠊⠀⠀⠀⠀⢀⡴⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠙⢷⣄⠀⠀⢳⡚⠉⠁⠀⠀⠈⢢⣁⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⢀⣴⡿⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠉⠃⠀⠀⠑⣄⠀⠀⠀⠀⣜⣽⣿⣻⡟⣯⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣀⡤
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠠⡄⠀⢀⣼⡀⢀⣀
⠀⠀⠀⠀⠀⠀⣷⠀⢸⣿⣷⣼⣿⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠠⣷⣾⣇⣾⣿⣿⣿⣿⣿⣿⣿⢷⣽⣝⣶⣤⣀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⠙⢿⣿⣿⣦⣿⣲⡤⣀
⠀⠀⢠⣾⣿⣿⣿⣿⣹⣿⢻⣿⣿⣷⣿⠸⡿⣷⣤⡙⡟⠿⣿⣿⣿⣦⠙⣦⣀⠀⠀⢠⡤⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠦⢤⠤⠤⠴⠖⠒⠛
⠀⡴⢫⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⠸⣧⣿⠛⣿⠻⣮⡀⠈⢿⣿⣿⣧⠘⢿⣷⣄⠀⠀⠀⠒⠚⠉⠉⠀⠀⠀⢀⣀⠀⠀⠒
⠊⢠⢟⣿⡟⢸⢻⡿⡇⠀⣿⣿⣿⣿⡆⠹⣿⣤⠹⣷⣮⡻⣆⠀⢻⣻⣿⣇⠈⢿⣿⣷⣄⠀⠀⠀⠀⢠
⠀⢋⣾⡿⠁⡟⢸⠃⠀⠀⠿⢹⣿⣿⣇⠀⢻⣿⡆⡏⠻⣟⠦⡑⠲⣿⠛⠹⠲⣾⢿⣿⣿⣷⡄⠀⠐⠂
⠀⢸⡿⠁⢠⠃⡿⠀⠀⠀⠀⠸⢹⣿⣿⠀⡈⣿⡟⣿⣷⡘⣷⣌⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⣿⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠂
⢀⡞⠀⠀⠀⠀⠁⠀⠀⠐⠂⣤⢼⣿⣿⠀⠁⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣉⡁⠈⢿⣆⠀⠀⠀⢤⣤⡀
⠈⠀⠀⠀⠀⠀⠀⣠⣶⠾⢟⣠⡯⣿⣿⠃⠀⠈⣿⡟⣿⣿⣯⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠃⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠰⠒⠯⠉⣠⣄⣬⣬⣄⣇⣬⣤⡴⢤⣦⣷⣷⣿⣿⣷⣿⣿⣿⣶⣤⣶⣶⣶⣶⣦⣠⣼⣧⣤⣦⣜⣦⣄⢐⣤⣠⣤⣀⣀⣀⡀
⠀⠀⠀⠒⠟⣻⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠿⠓
⠀⠀⠀⠀⠰⠶⠟⠛⠉⢹⡏⠙⠿⠻⣿⢿⡿⠿⡿⠛⣿⠛⠛⢿⠏⢹⣿⠋⠉⠉⠛⢻⣿⣏⠻⣿⠻⠿⠟⠙⢹⣟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠸⡇⠀⠀⠀⡇⠀⠀⠘⣿⢸⣿⠀⠀⠀⠀⢈⣿⠉⠀⠀⠀⠀⠀⠀⢸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⢠⣶⣶⠘⣿⠀⠀⠀⠀⢀⡇⠀⢰⣶⡶⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠀⡇⠀⠀⢠⡄⠀⣈⣿⠉⠀⣿⠀⠀⠀⠀⢸⡇⠀⠘⠯⡉⠂⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠰⠂⢸⡇⠀⠀⠴⠃⠰⡇⠀⠀⣸⡷⢻⡿⢾⠓⡂⣿⠀⠀⠀⠀⣠⡇⠀⢠⣿⣥⣶⡆⠀⢸⠇⠀⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⢰⣿⣿⣟⠺⡛⠒⣞⣻⣿⣿⡶⠖⡲⢻⡓⢂⣼⠟⣿⣿⣷⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⡇⠀⠀⠀⠀⠺⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣛⠁⡰⢋⣹⣿⣿⣧⣀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠁⠉⡍⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⣿⠿⠿⣿⣿⣿⡏⣼⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠉⠁⠚⠛⠃
⠀⠀⠀⠀⠀⠀⢠⣄⢳⢸⣿⡆⣷⣵⡄⢨⡇⠀⣸⡟⣿⣿⡇⠀⣿⣿⣿⣾⠿⢿⡟⣻⣿⣶⡿⠟⢿⣿⣿⠏⢸⡄
⠀⠀⠀⠤⢶⣶⣜⠿⣗⠈⢩⠅⠻⠛⠛⢺⣷⣶⣹⣶⣿⣿⣷⣴⣿⣿⣿⣷⣶⣿⣾⣿⣿⣿⣶⣶⣦⣼⣿⡆⢼⣧⣤⣀⡀⠁
⠀⠀⠀⠀⠙⠛⠛⢂⣼⣶⣤⡖⣽⣉⡈⠙⠷⢶⣾⠿⢿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⣩⠉⣙⠀⠛⠛⠛⠛⠋⠉⠀⠃
⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣇⣙⡻⠻⣿⣿⣧⠙⠂
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠘⢹⣿⣿⡷⠀⠡⠿⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⣴⠃⣾⡆⢳⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⣪⠭⢭⣒⢄
⠀⠀⠀⢰⣶⠄⠀⠀⠀⣴⣶⠀⠀⠀⣿⠀⣿⡇⢸⡇⠀⠀⠀⠀⠘⣛⡃⠀⠀⠀⠀⡎⡞⠁⢦⠀⠈⣎⠇
⠀⠀⠀⠘⠛⠁⠀⢀⠀⠛⠛⠀⠀⠀⠘⢦⣿⡧⠞⠀⠀⠀⠀⠀⢈⣋⡁⠀⠀⠀⠀⢇⢧⡀⠘⠇⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⢀⣬⣭⣥⣀⠀⠀⠀⠈⠫⢝⣒⣒⠭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⢻⣆⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⢀⣶⣶⣶⣶⣄⠀⠀⠀⠀⢿⣧⣤⣾⡏⠀⠀⢀⣇⣀⠀⠀⠀⢀⣸⡆⠀⢤⣤⣴⣿⣷⣾⠟⠁
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⢿⣿⡟⠀⠀⠀⠈⢇⡀⣈⠛⢅⣀⡠⠃⠀⠀⠀⢹⣿⠿⣿⡄
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⣀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠴⣻⡿⡿⣿⡻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢹⣿⡏⣵⡿⣷⡍⣿⠀⠀⠀⠀⡿⠀⠠⠘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠿⠷⠮⠛⢫⠶⢿⠀⠀⠀⠀⠁⠀⣸⠀⠀⠀⠀⠀⠀⢠⣤⠃⠀⠀⠀⠀⠀⠀⢀⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠂⠀⠀⠀⠀⠐⠛⠚⠒⠒⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠤
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣴⣿⠿⠟⠂⣿⡂⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠠⠁⣷⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⣿⣷⡄⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⠛⢲⢷⣄
⠀⠀⠀⠀⠠⠁⣤⢹⣧⠀⠀⠀⠈⠃⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣆⠻⣷⡄
⠀⠀⠈⠀⠛⠛⠛⠛⠛⠃⠈⠀⠀⠀⠀⠐⠚⠛⠋⠀⠀⠀⠀⠀⠙⠋⠙⠃⠀⠀⠀⠀⠀⠀⠐⠛⠿⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠑⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠠⠄⠀⠀⢀⣀⡃⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁
⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠴⠒⠒⠒⠲⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠾⢧⣄⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡭⠷⣦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠙⠷⣄⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡜⣩⡿⠋⠉⠁⠀⠀⠀⠈⠳⣄⠀⠀⣠⡟⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠔⠚⢂⠀⠀⠀⢠⠶⢦⣀⠈⢑⡌⠒⠤⠖⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠋⠀⠀⠈⠉⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠀⠀⠠⣄⣀⡀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣛⣥⠖⠂⠀⣀⠀⠀⠈⠉⠛⠛⠻⠶⠶⠿⠿⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠛⣉⣥⠶⠛⠉⢀⣠⠴⠛⠉⠀⢀⣠⠄⠀⠀⣠⣾⣿⠯⠤⢄⡀⠀⠀⢸⡆
⠀⠀⠀⢀⣀⣀⣀⣤⠤⠴⠶⠒⠛⣋⣉⣥⡤⠶⠚⠋⠁⣀⣠⠴⠚⠉⠀⢀⣠⡴⠞⠋⠀⢀⣤⠾⠋⠁⠀⠀⠀⣀⣽⠆⠀⠀⣿
⠀⠀⣙⣯⡁⠀⠀⠀⠐⠖⠚⠛⠋⠉⠁⠀⣀⣠⡴⠖⠛⠉⠀⣀⣠⠴⠞⠋⠁⠀⣀⡤⠞⢋⡡⠖⠊⠉⠉⠉⠉⠉⠀⠀⠀⠀⢻⡆
⣠⠞⠁⠀⣙⠲⣄⡀⠀⠀⠀⠀⠰⠖⠛⠋⠉⢀⣀⣤⠴⠖⠛⠉⠀⢀⣠⠤⠖⠋⠁⠀⠠⣎⡤⠴⠒⠁⠀⠀⠀⠀⠀⣀⡀⠤⣼⡇⠠
⠛⠂⠂⠉⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠘⠛⠉⢁⣀⠠⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⣤⣿⠀⠤⠤⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⠷⣶⡤⠈⢉⣠⣤⡤⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠿⣿⣿⣶⡶⠀⠈⣷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣪⣤⣤⣤⣴⣞⣭⣤⣶⣶⣶⣟⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣳⣦⣤⣤⣤⣤⣤⣤⣾⣥⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⢒⣿⡀⠤⠤⡇⠀⠀⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣳⣤⣤⣷⣴⣶⣾⣿⣿⣿⠁
⠀⠀⠈⠀⢀⣀⣀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⣯⣟⣿⣆⠀⠀⠀⠀⠐⠦⠄⠐
⠀⠀⠠⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣏⣽⣿⠟⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠉⢉⡉⠁
⠐⠚⠛⠿⠷⠶⠾⣟⠛⠛⠹⠛⠿⣷⣿⠟⢻⣿⣿⡿⠿⠽⠛⠛⢛⣖⣿⢿⣿⡟⠉⠉
⠀⠀⠉⠛⠛⠀⠰⠦⢭⣍⣉⣁⠀⠈⠛⠋⠬⠽⣿⠅⠀⠒⠒⠒⠒⣂⣉⡭⠉⠉⠀⠒⠒⠒⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠁⠀⠈⠉⠑⠒⠀⠀⠀⠉⠉⠓⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠒⠒⠒⣿⡂⠤⠤⣯⠀⠀⠀⠀⣀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣦⣤⣼⣴⣶⣾⣿⣿⣿⠏
⠀⠀⠈⠁⢀⣀⣀⡀⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣋⣯⣽⣻⣇⠀⠀⠀⠀⠀⠲⠄⠐⠒
⠀⠈⠡⠴⠶⠶⣾⣟⣛⣛⣿⣿⣿⣿⣟⣽⣿⠟⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠈⠍⣉⠁
⠒⠚⠛⠿⠷⠶⠾⣟⡛⠛⠫⠛⠻⣷⣾⠿⢛⣿⣿⣿⠿⠯⠟⠛⢛⣷⣛⡿⣿⣿⠉⠉⠁
⠀⠀⠉⠛⠛⠀⠐⠦⠭⣍⣉⣁⠀⠈⠛⠋⠥⠽⣿⡧⠀⠐⠒⠒⠒⣒⣀⡭⠉⠉⠀⠐⠒⠒⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠛⠃⠀⠀⠉⠑⠒⠒⠀⠀⠈⠉⠙⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣆⣼⣏⣝⣻⣶⣄⣶⣤⣴⣦⠀⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣿⣯⣿⣿⣿⣿⣿⣽⣿⣧⠿⠃
⠀⠀⠀⢀⠊⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⠃
⣢⡬⠞⠉⠀⠀⠀⠀⠸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣥⡴⠃⠀⠀⠀⠀⠀⢠⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⡇
⠁⠀⠀⠀⠀⠀⠀⠂⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠹⣷⣀⡀⡒⣴⣿⣻⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠃⠀⢀⢄
⠀⠔⢸⣖⣷⣻⣍⢻⣿⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣀⠃⠀⠀⠀⠈⠱⠀⠄⠂⠀⠂⠨⠒
⣤⣤⣼⣿⣽⣧⣿⣟⣿⣾⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⡄⣀⣸⣿⣿⢻⣿⣿⣶⣴⣶⣶⣤⡆⢶⡆
⣿⣾⣿⣽⣿⠽⠗⠛⠛⠛⠉⠛⠛⠛⠿⣿⣿⣿⠟⠁⠀⠀⠀⠄⠀⢀⢀⡹⣿⣿⣿⣿⣿⣻⣿⣿⣟⡿⠟⠉⠁⠈⠀⠁⠀⠀⠈
⣿⡯⠝⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⢉⠀⠀⠀⢤⡀⢦⣀⢀⣄⢳⣻⣿⣿⣿⣿⢿⣷⣷⡟⠁
⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⡘⢤⣰⣀⡀⠴⠄⢀⡀⠰⣦⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⡷⣿⡇
⠀⠀⠀⡀⠀⠒⢑⣆⣾⡟⣿⣿⣿⣿⣿⣿⣷⣀⣨⣽⣷⣿⣿⣿⣿⢿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡦⡀
⢀⣀⢀⡁⠀⠀⠒⣌⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣷⠦⠄⠀⠀⠀⣠⣤
⢷⣿⣿⣿⣷⠎⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠙⠙⠛⠛⠛⠛⠻⠟⣋⡉⢉⣀⣀⣉⣩⣅⣀⡀⢶⣦⣐⠷⣶⣮⣽
⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⣀⣤⣴⣦⣄⡀⣷⣶⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣦⣭⣻⣿⣿⣿⣿⣿⣿⣮⣝⡛⢶⣭⡙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢸⠂⢐⢧⡀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⢸⡌⢀⣤⡞⠐⠃⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⡂⢀⠔⣸⣿⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⡉⣰⡿⣿⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣤⠾⢂⣾⣿⠀⡟⣧⠀⠀⠀⠈⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⢈⠘⠁⠀⣾⣏⡏⠀⡇⢿⡀⠀⠀⠐⠒⠀⠀⠀⠸⠆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡤⠁⠀⠀⣾⣿⣿⡇⠀⡇⢸⡇⠀⠀⠀⠀⠑⡀⠀⢠⠅⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⢎⡀⠀⢀⡿⣿⣿⣿⠄⠠⡇⠀⣿⡂⠀⠀⠀⠀⠈⠆⢀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣤⣉⣀⠀⡀⠀⡇⠀⢻⣏⠀⠀⠀⠀⠀⠀⠸⡷⡶⢦⣤⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⣤⣼⣶⣤⣤⣤⣃⣀⣀⣀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⢠⣴⠶⠾⠿⡭⣤⣒⡚⠛⣛⠛⠛⠻⠿⠟⠛⠻⠿⠿⠿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⠁⠤⠤
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠃⠀⠤⠖⠊⠉⠩⠵⠖⠛⢳⡖⢀⣤⡴⠶⠶⢟⣩⠴⠤⣤⣴⣶⡆⠨⢤⡤⠉⠀⢀⢀⡤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠴⠤⠈⠭⢉⣉⡥⠴⠶⠒⠒⠒⠲⠄⠈⠉⠉⠀⠀⠀⠉⠛⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣳⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣩⣾⣿⣫⣽⣭⡽⠁⢻⣿⣿⢷⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⣿⣿⠓⠋⢥⣁⢠⣲⣮⣭⣟⡋⠙⠾⣯⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣿⡿⢡⣬⣻⣿⣿⣿⣿⠋⠁⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣠⣾⣟⡵⢈⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣯⣿⠏⠀⠾⢽⣿⣿⣿⣿⠀⣠⣴⣶⡲⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣠⣿⣿⣗⠀⠉⣤⣿⣿⣿⣿⡻⡿⠛⠋⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠔⠉⠤⣲⡞⠿⠛⠉⠀⣄⢀⢶⣿⣿⡿⢇⣁⠤⠤⠴⣿⣿⣿⣷⡀⠠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢀⠀⢶⣎⣷⣿⣿⣿⣿⡏⡓⠀⠀⠀⠀⠀⢨⣭⣻⣿⣿⣷⣶⣶⠟⢛⡿⢟⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⡧⢋⠠⠀⠀⢼⣿⣧⣶⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠈⠝⢋⣤
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣯⣭⣽⣿⣷⣶⣟⣃⡉⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⡿⠷⠉⠉⠀⠀⠀⠤⠶⣺⣿⠟
⠀⠀⠀⠀⠀⠈⢻⡿⠿⢿⣛⣿⡿⣿⠿⣥⡐⠀⠀⠀⠈⢻⣿⣿⣾⢿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⣴⣶⣦⣀⠀⠀⠨⠈⠃⠀⠀⢀⢠⡄⢀⢰⣶⣿⣿⣿⣟⠷⠉⠻⠿⣖⠀⠀⠀⠀⠀⢀⣤⣴⣿⠇
⠀⠀⠀⢸⣿⣿⣿⣿⣯⠄⡤⣸⣖⣶⣦⣼⣿⣿⣼⣷⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠠⠖⣛⡛⠉
⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠻⠍⠛⠛⠛⠓⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠿⠿⠿⠿⠿⠟⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡠⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠱⠄⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⢦⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠂⢾⡷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠙⠆⢆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠸⢻⡏⠀⡇⠸⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠁⡌⡇⠀⢧⠀⢩⣄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢸⠇⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢘⡀⠀⡈⢿⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣇⠀⠦⠈⠟
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡑⢀
⠀⠀⠀⠀⣸⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠷⢀⠀⠀⠀⠀⢀⡹⢦⣶⡀
⠀⠀⠀⢀⣿⣿⣦⠂⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠲⠶⣽⣾⣿⣿⣦⡀
⠀⠀⠀⠈⠛⠛⠷⠾⠷⣤⣤⣤⣀⣀⣸⣻⣰⣀⣀⣠⠀⡀⠀⠀⠈⢂⠀⠀⠀⠀⠈⠉⠙⠛⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣄⣼⣭⣭⣿⣿⣡⣶⠰⣧⣧⣤⠧⣀⣸⣦⣤⣴⠶⠒⠒⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣴⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠙⠹⠟⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢢⡄⢠⡀⠀⢀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢚⣂⣄⣠⠧⣤⣒⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠔⠃⠀⡉⠁⠃⣀⢈⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠲⡀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⠱⠞⣠⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠁⣈⢁⡐⠸⣦⡶⠓⡖⣒⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣤⡶⠈⠁⡀⡤⡈⠀⢃⡄⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢠⡄⣀⢠⡄⣻⠃⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⢠⡇⢸⣣⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠻⣰⢃⡾⢀⡿⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⢀⡵⢃⡞⢁⡾⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⣠⡶⢋⡴⢋⣠⡾⣴⠛⠁⠀⠀⠗
⠀⠀⠀⠐⢄⠀⠀⠀⠀⢀⣀⣀⣤⡷⠶⢞⣋⣥⠞⣛⡿⢟⡁⠼⠋⣰⠆⠲⡄⠄⠀⢄⡀
⠀⠀⠀⠀⠈⠻⣭⠭⠭⠭⠭⠵⠶⢒⣛⣩⡥⡞⠛⣉⡴⢾⠶⠀⠀⠉⠀⠀⠉⠀⠀⠶⡇
⠀⠀⠀⠀⠀⠀⠐⢖⣒⣚⣛⣋⣩⣭⡥⠴⠶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣀⣰⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠀⠀⠀⠸⠿⠄⠀⠀⠀⠀⠀⠀⠠⠿⠇
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⡏⣿⣿⡟⣽⠟⣿⡿⢡⣾⣿⢟⣽⢙⣿⡟⣽⣿⢹⣿⣿⣿⠀⠀⠀⠀⡆⠀⠀⡴⢒⡦⠀⣰⠋⠀⢀⠖⢲⡄⠀⡴⢀⢰⡆
⣿⣿⣿⣇⣿⣿⣧⣿⣇⣿⣷⣸⣿⣿⣮⣿⣸⣿⣦⣿⣿⢸⣿⣿⣿⡀⠀⠀⠀⢇⠀⠀⠓⠀⣇⠔⠻⠄⠐⠈⠂⠸⡁⠈⠃⠀⣸⣇
⣿⣿⣿⣿⠋⣿⡟⢻⢻⣿⢫⡻⣿⢩⡻⣿⠛⣽⣿⣿⡟⣼⣿⣿⣿⠀⠀⠀⠀⢤⣆⠀⣦⢠⡄⢠⠶⡄⢰⠶⡄⢠⡖⠀⠔⠁⡼
⣿⣿⣿⣿⢻⣿⡇⣦⡎⡇⢸⡇⣿⢸⡿⣹⢰⣾⣿⣟⣽⣿⣿⣿⣿⠀⠀⠀⠀⢡⠀⠀⡏⠛⡇⣿⠀⡇⢸⠀⣹⢸⡏⠁⠄⠔⠁
⣿⣿⣿⣿⣷⣿⣧⣿⣧⣿⣜⣵⣿⣸⣵⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠀⠇⠀⠃⠙⠖⠁⠻⠖⠁⠘⠷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⣠⡤⠼⠗⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠉⠁⠀⠀⠀⠀⠀⢠⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⡤⠤⠶⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠖⠛⠋⠉⠁⢸⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣻⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⡏⣄⣀⡠⠤⢲⠚⠀⠈⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣤⡤⠶⠒⢺⠏⠁⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡆⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⢀⣴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⢀⡠⣆⣴⡟⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⣠⠴⡶⠛⠭⠠⢠⣏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⡾⡔⠚⠋⡀⠟⢀⣠⣴⣶⣖⣾⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠉⠀⢀⡧⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣗⣊⣥⣴⣾⣿⣿⣿⠿⠛⡿⣿⣿⣿⣋⢀⡀⣀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠈⣛⠛⡛⠋⣋⣯⣍⢓⣻⣷⡎⢿⣻⣯⠙⣿⣿⣿⡟⠛⠶⣶⣿⣷⣞⣉⣀
⠀⠀⠀⠀⠙⠉⠀⠀⡠⠙⣉⣠⣿⣭⣽⣿⣿⡞⢛⣯⣥⣶⣿⣟⡛⠟⢛⣩⣶⡈⠀⣍⣛⣛⠛⠻⣿⣿⡿⢶⣿⣯⣟⡛⠁⡤
⠀⠀⠀⠀⠀⠒⠒⠂⠉⠉⢭⣥⠄⢘⣿⣛⡉⠉⠥⠼⠛⠋⠉⠩⠔⠂⣸⡿⣟⠁⠀⢶⣭⣹⡧⣠⠤⢴⣶⣶⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣦⠄⠀⠉⠁⠀⠀⠀⠉⠙⠉⠀⠀⠒⠬⠭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢉⡁⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠉⠉⠉⠁
⠀⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠀⠠⠤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠔⠊⡛⢻⣷⣦⣰⣄⡀⢠⣀⠀⠀⠀⠀⢀⣀⡀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠡⠠⠼⠂⠀⠐⣂⡐⢀⠴⠄⠀⢠⣄⣤⣤⠧⢙⣵⢿⡿⣻⣿⣿⣿⣶⠈⠳⠀⠀⠀⠀⠉⠁⠤⣤⣶⣶⣤⣴⣿⣦⣄⣴⣦⡈⣩⣥⣆⡀⣀
⢤⣴⣶⣶⣷⡴⠈⣤⣤⣶⣴⣦⣤⣠⣼⡽⠁⡡⢖⣫⣾⣿⠟⣫⣿⣷⠀⠈⠲⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣛⡏⡠⣊⣝⠙
⠀⠈⠁⢀⣠⣤⣄⣀⠙⢁⠉⠙⠉⣁⠤⢚⡩⠔⣪⡷⣛⣵⣾⣿⣿⣿⣿⡄⠀⠀⢮⣧⣀⣦⣳⣰⣤⣀⣠⡀⠈⢉⣙⡛⠛⠛⠛⠛⠛⠛⠋
⠤⠤⢒⣛⠩⠥⢚⣛⣭⡅⠤⣒⣩⠔⢊⣭⠶⣛⣵⣾⣿⣿⡿⣿⣿⣿⣿⢃⠄⠀⠀⠒⠯⠹⠧⣦⡂⢥⣠⡬⠍⡉⠈⠍⠋⣠⢾⣤⡦⡤⡚
⣂⣉⠡⠴⢒⣛⣭⣴⠴⠞⣋⣥⠴⣚⡭⢖⣫⢗⣫⠟⣛⣥⢞⣫⣟⡿⣻⣷⣙⠏⠢⡀⠀⠈⠁⠪⠉⠉⠉⠚⡉⠍⠓⠈⠙⠁⠀⠀⢛⡯⠭
⠵⢖⣚⣛⠯⣉⣠⠤⢒⣫⣽⣶⣿⠵⣚⡿⢞⡋⣀⢜⣫⣕⡿⣛⣵⣿⢟⣻⣿⣿⣿⣈⣀⠈⠷⠀⢀⣀⢒⣀⠒⣓⠒⠢⠠⠤⠤⣠⣤⣤⡴
⡭⠿⣒⣛⣭⠷⠖⣛⡭⢖⣛⠭⠖⡫⠁⠾⠋⢝⣒⡽⠚⢁⣮⠟⣫⣵⠿⣫⣿⡿⢋⣽⣿⠟⣿⢿⣿⡿⢟⣿⣿⣿⣷⣾⣷⣷⣿⣿⣡⡟⣰
⠘⠋⢉⠡⢐⣂⡥⠔⣚⡭⢗⣢⡴⣖⣡⣴⠾⢋⣡⣴⠞⠋⣰⠞⣩⣵⡻⠛⣡⣶⠿⢋⡠⢊⡥⠞⣩⠞⣡⣿⣿⣯⣞⣿⣿⠟⢩⡾⠉⣡⣯
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠳⣆⠀⠀⠀⠀⣴⠛⠉⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢹⡀⠀⠀⣼⠃⠀⠀⠀⠡⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⠶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠘⣇⠀⢸⡇⠀⢰⡇⠀⠐⠀⢀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠉⠀⢀⠀⠀⡀⠀⠀⡀⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡟⠀⢸⠇⠀⡿⠀⠀⢀⡾⠋⢻⣾⠁⠀⣰⠟⠙⣧⠀⢀⡼⠋⢻⣾⠃⠀⣼⠃⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠃⠀⣼⠀⣸⠃⠀⢀⡾⠁⠀⣼⡇⠀⢰⡏⠀⢰⡏⠀⣾⠃⠀⣸⡏⠀⢠⡏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣠⡼⠃⠀⢠⡟⢠⡏⠀⠀⢸⠇⠀⢰⣿⠀⠀⣿⠀⠀⠛⠀⣰⡇⠀⢠⣿⠁⠀⣼⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⠀⠀⣿⠀⢀⣿⡇⠀⣸⣿⠀⠀⠀⣰⣿⠁⢀⣾⡟⠀⣰⣿⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣰⣧⠟⠀⠀⠀⠀⠹⠶⠟⠉⠷⠾⠃⠙⠶⠶⠟⠁⠸⢧⠞⠁⠿⡴⠋⠻⠴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣁⣀⣀⣈⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⠀⠈⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣧⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠙⠛⠋⠁⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⠉⠉⢉⣀⣀⣀⠀⠀⢀⣉⢍⣉⠉⠁⠀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⣴⣿⠁⠀⢹⣿⡄⠀⢸⣿⡇⠀⢹⣿⡄⠀⣿⣿⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⡆⠀⢸⢿⣿⡇⢰⣿⣟⠀⠀⠀⣿⣿⠀⢸⣿⡇⠀⠸⣿⣷⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡆⠀⢸⠈⣿⣷⠀⡇⣼⣿⡇⠈⣿⣿⠀⠀⢠⣿⡟⠀⢸⣿⡇⠀⠀⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⣿⣿⠁⣾⣿⡇⠀⠈⠛⠧⠤⠾⠋⠀⠀⢸⣿⡇⠀⢀⣿⣿⠀⣿⣿⡧⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⢿⡏⠀⢽⣿⡇⠀⢀⡖⠉⠉⠳⡄⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣸⠀⠀⠈⠁⠠⠿⠿⠧⠀⠸⣤⡄⠀⠀⣷⠀⠀⠼⠿⠧⠠⠾⠛⠀⠠⠿⠿⠧⠤⠼
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⢩⠟⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠭⢉⡁⠀⠀⠀⡀
⠀⠠⣂⠁⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣢⣄⣰⣤⢻⣿⣴⣶⡴⡀⠴⠀⠀⠠⠐
⠀⣲⠿⣗⠁⠀⠀⠄⠀⡠⠀⠀⡀⢯⡻⣽⡿⢏⣵⣬⠏⠙⠁⠐⠈⠄⠀⠀⠈
⣾⠁⣶⡹⣦⣀⠂⠀⠈⠀⠀⠸⡏⣮⡇⡷⠃⢈⢱⡇⠌⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⣐⢀⠠⠈⠠
⠙⠞⢿⣿⡿⠟⠋⣠⠤⢤⣿⡁⢿⡟⢧⣇⢰⣾⡀⠸⡦⠀⠠⠀⠂⣤⠐⣄⠀⡀⠀⢠⣶⠆⢛⠣⠀⠀⠐
⠀⠀⠀⠈⠰⣖⠊⠁⠀⢩⠧⠍⠰⠂⠉⣅⢨⡀⢄⣲⣽⢷⡴⣷⣤⣿⣻⠿⠋⠀⠀⡟⢁⠘⢿⡷⣇⣮⣁⣀⢀⠀⠠⠑⢄⠈⠀⠠⡀
⠀⡀⢀⣻⡦⢌⣙⣒⠒⠛⠒⠁⠄⠠⣦⢽⣞⠓⠈⣮⣿⡶⠀⠈⡫⠅⢠⣖⣤⣤⠜⠀⠹⢿⣶⣯⣦⣭⣭⡅⢠⡗⣠⣦⣅⣩⣷⣴⡿⠿⠄
⠀⠈⠀⠉⢉⠉⣉⠉⠆⡀⣮⠹⣀⣶⣿⢺⣍⣙⣒⣪⢞⠁⣶⣄⠻⢷⡬⣭⣥⡄⠠⡤⠴⠶⢶⠓⠷⠶⠶⠦⠫⠶⣜⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢠⠸⡦⣹⠳⣔⣦⢮⠙⠛⠛⣋⣉⣉⠫⢅⡐⣯⣳⣬⡿⡏⣲⡉⡓⠈⡓⣤⡤⠶⣞⢿⠻⣿⠗⠊⢰⢶⣻⡛⣻⡛⢏⠛⠛⠁
⠀⠀⠀⠀⠀⠉⠓⠦⣄⠸⣷⣦⣌⣛⠓⠲⠮⣽⡲⠿⠲⡿⣮⣻⣤⠽⡿⣿⣒⠛⠾⠿⠖⠚⠛⠉⠠⡖⢄⣈⠲⢶⡐⢄⠝⠾⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠖⠉⠉⠁⠀⠀⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠁⡉⠙⠷⠖⠒⠒⠲⢶⢻⣯⣹⠯⠭⠓⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡜⢐⠂⡖⢠⠂⢀⡴⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠑⣊⡀⠁⠄⠀⡾⠂⠀⠀⢼⠃⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠂⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⡙⠒⠒⠘⢄⠀⠀⠀⡏⠀⠀⠀⠊⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠈⠂⠀⠄⢀⣁⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠰⡒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠓⠚⣶⣆⣁⡀⠀⠀⠀⠀⠀⠊⠠⠢⠁⡀⢰⠀⠀⠠⢂⠐⡀⠠
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢡⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⢸⠀⡄⡀⠀⠀⠈⢀⠐⡀
⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠉⠀⢂⢀⠀⠈⠀⠀⠀⠀⠀⢠⢒⡄⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠎⠿⠳⡀⠀⠀⠀⠀⠀⠺⠁
⠀⠀⠀⠀⠀⢹⡄⠂⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠑⢌⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⢷⠴⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⣂⣨⣬⣥⣥⣤⣀⡀⠆⠀⢀⠈⠁⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⢸⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠒⠒⠋⠉⠀⠠⠠⠤⠣⣀⠀⢀⠐⡁⠀⢄⠀⣀⣀⣀⠞⡞⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠘⠟⠫⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠉⠁⠉⠉⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠉⠢⠀⠀⠀⠀⠀⢀⡤⠤⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠑⠀⠀⠉⠀⢀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠠⣀⠄⠞⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⡡⠀⠀⠁⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠁⡠⠴⠊⠁⠀⠀⠄⢀⢠⡅⡀⠀⡆⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⡐⠊⣷⡄⠨⠄⠑⠄⡀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠋⠠⠀⠀⠀⠀⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠢⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠐⠒⠒⠒⠒⠒⠒⠒⠶⠖⠒⢒⠒⠒⠠⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠤⡤⣄⣀⣀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢲⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠂⡇⠀⠀⠀⠉⠉⢻⠛⠛⠛⢛⠟⠛⠛⠯⠒⠒⠢⠤⠶⡶⠶⠶⠶⠶⠶⠶⠶⠆⢠⠀⠀⠀⠘⠀⠤⠤⠄⠈⠑⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⢚⠩⢹⣷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗
⠀⠀⠀⠀⠀⢀⡤⠇⠋⣉⢡⡀⡀⣨⠀⠀⠄⠆⠙⠥⠾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁
⠀⠀⠀⠀⢰⠉⠀⠀⠈⠉⠉⠁⠑⢲⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⠀⠠⠼⠽⠹⠦⠀⢀⠸⠀⠀⠀⠀⢰⡀⢠⠇⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠔⠁
⠀⠀⠀⠀⢸⠀⢁⣋⣘⢀⣁⠀⢨⡻⠰⠄⡀⠨⢤⣤⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢸⠀⣀⣘⣚⣒⣁⡀⢸⡟⠱⠊⠈⠁⠰⠏⠙⠃⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡠⠤⠤⠠⠤⠠⠊
⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠁⢸⣧⢤⠰⠤⠤⠤⠤⠴⠦⡆⢐⠂⠀⢀⣀⣀⠀⢘⢒⣀⣐⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⡀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⣤⠀⢠⣸⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⣠⡀⡀⢹⡀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣠⣿⣧⠀⣁⢀⣿⡇⣷⢸⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣴⡄⠀⠀⠀⣰⢋⣿⠀⢸⣿⡇⠀⡿⠸⣿⣰⠇⠘⠋⢸⠃
⠀⠀⠀⠀⣀⣀⣀⡀⠀⣾⣿⣂⣠⠄⠀⠹⣦⣼⣿⡇⣰⠆⢠⣧⣿⡟⣀⢸⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⣼⡟⠁⠀⠙⢠⣿⡿⠋⢁⣤⡄⠀⠀⣽⣿⠁⢿⡶⠸⠿⠁⠿⠋⠀⣉⣠⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠹⣇⠀⠀⠘⢻⣿⡇⢰⣿⢾⣧⠏⣴⣿⡟⠀⠀⠀⠀⢀⣠⡴⠞⠛⢉⣁⣤⠴⠒
⠀⠀⠀⠀⠈⠙⢦⡀⠸⣿⡇⠀⠀⠈⠁⠀⠛⠁⠀⠀⡠⠴⠚⠉⣁⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⣀⣤⡿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠈⠁

⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣭⣭⣭⣍⣉⡉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣫⠥⣶⣶⣶⣾⡯⢭⣙⠓⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣶⣟⡛⠉⠉⢙⣛⣻⢯⣗⠦⣙⠷⢄⡈⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢢⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣟⡉⠉⢹⡄⢴⣟⣿⣟⢷⣮⠙⠪⣻⢦⣙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⢰⢲⠇⠈⠀⠁⠈⠀⠀⢀⣴⣶⣶⣦⣄⡀⠀⠀⠈⠛⠋⠀⢠⡇⡸⣿⣾⢡⡆⠹⣵⣄⠈⠳⣮⠑⢦⣉
⠀⠀⠀⠀⠀⠄⠀⡱⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣭⣄⡀⠉⠛⠻⣷⣦⡀⠀⠀⢀⡼⠀⢉⡩⢪⡞⣀⣉⣉⣿⣷⣤⣌⣳⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠿⡤⠈⠹⡄⠀⠀⠀⠈⠛⠶⣦⠞⣡⣔⣩⣾⠿⣻⣿⣿⣥⠤⣄⠉⠛⡝⠻⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡒⠝⢧⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⣾⣷⠾⣛⠿⣫⡵⣻⠟⣫⠽⣿⣿⡌⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣞⠀⢀⡀⠙⢷⣤⣤⠏⠀⣀⣤⡾⠿⠛⣉⠤⢊⠵⢋⠔⡽⠁⢸⠁⣻⣿⣾⠷⢁⡴⢁⠜⡠
⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⡻⣝⠛⠛⠿⢿⣶⣿⡿⠷⠿⠛⢛⣛⣩⠥⠔⢒⣩⠴⢚⢁⡴⢋⡜⠁⣰⡞⢦⣙⢿⣍⣛⣛⣊⣡⣖⣥
⠀⠀⣠⣴⡿⡻⠝⣚⣉⡙⠊⣿⠢⢭⣑⣲⣶⣬⣿⣿⣿⣿⣯⣭⣴⣶⣒⣩⣩⣤⣴⣴⣯⠶⠿⢶⣿⣿⣧⣤⣭⣳⣿⣷⣶⣾⣟⡛⠫
⠰⠟⣱⢋⠊⠔⠉⣁⣍⣉⣴⣿⠴⠚⠉⠉⠥⢖⣛⣩⣙⣛⣿⣿⣯⣭⣭⣭⣄⣤⣤⠤⠶⠶⠖⠲⠤⠤⢄⣀⠀⠉⠉⠙⠛⠛⠿⠿⠷
⢀⢰⠃⠔⠈⠀⠀⣯⣿⠿⠟⡁⠄⣢⠴⠚⢋⣉⣡⣤⣤⣶⣶⠖⠛⠛⠟⠿⠟⣛⣛⣛⡛⠿⠟⠻⠿⢶⣶⣤⡭⢽⣶⣶⣶⣤⣤⣤⣤
⠈⢸⠀⠐⡐⢄⡁⠒⣂⣈⣤⠶⣚⣁⣤⡴⢞⣿⣭⣽⣿⣿⣿⢿⣷⣶⣦⣤⣄⣀⣈⣉⣉⣉⣉⣉⣭⣭⣤⣤⣭⣐⣒⠦⢄⣀⣀⣀⣀
⢈⠸⣇⠀⠉⠦⢍⡉⣉⣥⡴⠿⢛⣩⡵⠾⠛⠉⡉⠁⢀⣀⣠⣴⣶⣶⣿⣿⣿⣷⣤⣤⣤⣴⣞⠫⣅⣶⣶⠦⣌⠙⢧⡈⠍⠐⠛⠟⠟
⠐⠀⢙⣷⣤⣤⠶⠛⠉⢀⣠⡶⠛⠉⠀⢐⣨⣴⣒⠋⠩⠁⢈⠔⠑⠡⣟⡿⡯⠛⢦⣙⠻⢯⣈⠥⠚⢹⡀⣾⣼⡁⠀⢳⡀⠁
⠘⠛⠛⠉⠁⠀⢀⣠⠶⢟⠉⢐⣠⣴⣊⣉⣀⣬⣍⣁⣒⣮⣀⣤⣀⡬⠜⠋⠁⠀⠀⠙⠻⣔⡛⠶⣄⠀⠙⢮⣳⢶⣮⡤⠛⢦⡀
⠈⢀⣀⣀⣤⢖⣋⣁⡤⠴⠚⠋⡉⠩⠄⠀⠒⠐⠒⠒⠒⠬⣭⣍⣉⡛⠛⠶⠦⣤⣀⡀⠀⠀⠉⠙⠛⠻⢦⡀⢌⡙⠛⠻⠷⢶⢿⣷⣶
⠸⠿⠟⠛⠛⠛⠋⢉⣭⣭⣉⣙⠛⠒⠲⠶⠤⠤⠤⠴⠖⠒⠒⠒⠛⠛⢛⣛⠋⠭⠽⠿⠷⠶⣶⣤⣀⡀⠀⠉⠳⣽⣧⣅⡠⠄
⠠⡤⡤⠴⠶⠚⣋⣉⣉⣉⣉⣉⣉⣛⣒⡒⠶⢤⣤⣤⠴⣖⣒⣂⣉⣡⣤⣤⡤⢤⠤⠄⣒⣒⡈⢛⠿⣯⣿⡛⢲⣶⣿⣿⣿⣮⡄⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠤⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣆⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⢠
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢀⡇⠀⠀⣆⠉⠁⠀⠀⠀⣶⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋
⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⠀⠀⠀⠀⠀⠆⣷⡄⣤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⣿⣷⣤⣄⠀⠀⠀⠀⠀⠼⠿⠿⠿⠆⠀⠀⠀⠀⠀⠛⠁⠛⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣷⡆
⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⢀⢂⠀⠀⠀⠀⠀⠀⢰⡆⣠⣴⣶⡆⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⢰⣿⣏⣿⣧⠀⠀⠀⠀⠀⢡⡾⡆⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡇⠀⠀⠀⠀⡀⣾⠟⠁
⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠛⠱⠙⠓⠀⠀⠀⠀⠸⠇⠿⠿⠇⠇⠀⠀⠀⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⡆
⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠉⠁⠉⠉⠈⠁⠀⠀⠀⠀⠀⡇⢩⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣶⣶⣶⣶⠶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⢶⣶⡶⡶⣶⠶⡶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⡎⡰⠠⣀⠈⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⣀⣄⠀⣐⣟⣦⡽⠧⠶⢤⡉⠢⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠤⢄⡠⢔⣏⡛⢷⣷⣞⢯⠀⠲⡀⠀⠀⠹⠓⢄⠑⢄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⠎⠀⠀⠀⠀⠀⠉⠉⣉⣿⢠⡃⣡⠀⡇⠀⣀⡾⠀⠀⠑⡌⢢⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠔⠚⡄⠀⠀⠀⠀⠀⠪⡀⢸⠁⠯⡄⠀⠱⠜⠀⠀⠀⠀⠀⢈⡄⢡⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠃⠠⡄⢼⡄⠀⠀⠀⠀⠀⠀⢶⣘⣾⡀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⢣⠤⡇⠸⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠊⡠⠤⠤⠤⢄⠉⠆⠀⠀⠑⣦⡀⢀⠔⠒⢲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠃⢰⠀⢸
⠀⠀⠀⠀⢀⡄⠘⠀⠃⠀⠀⠀⠘⠂⠒⠀⣄⠀⠀⠑⠼⠦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⡆⢰⠀⠄
⠀⠀⠀⠀⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠈⢻⠊⠉⠁⠀⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠁⠆⠀⠄⠀⠀⠀⢀
⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢠⢭⣶⣤⣤⣤⣤⣤⣠⣧⡼⠤⠾⠖⢺⠿⢛⡛⠮⡛⠛⠛⠛⠛⠛⢋⡇
⠀⠀⠀⡈⠀⠸⢄⣿⡀⠀⣀⣀⡀⣿⡀⠜⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠰⠡⡿⢋⠿⡗⡘⡄⠀⠀⠀⠀⢸⢠
⠀⠀⠀⡇⠀⠀⠀⠻⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢨⠀⡠⠔⠉⡐⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢠⠐⢵⢆⣠⡳⠁⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠤⣀⡀⠀⠀⢸⢀⠁⠀⢀⡇⡗⠢⠄⠀⠀⢀⡀⢨⡄⠤⠐⠈⢣⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇⡆
⠀⠒⢲⠀⠀⡔⠉⠉⠉⠉⠉⠉⠉⠉⠉⠱⠀⠀⠹⠛⠲⠠⠄⣉⡁⣈⣉⣈⡉⠠⢼⢡⠔⠂⠀⠛⠀⠐⠲⠇⠀⠀⠀⠀⠱⡀⠀⠀⡌⠀⠀⠀⠀⢀⡀⠴⢁
⡆⠀⠘⠀⠀⠃⠴⠲⠀⠤⠤⠤⠤⠄⠴⠀⡇⠀⢸⠀⡠⠆⠤⠤⣀⢀⡀⠀⣤⠤⠸⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡵⡄⢠⡏⠀⠈⠉⠁⠀⠀⠐⠸
⡏⠁⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡄⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⢸⠀⣄⠀⡠⠫⢦⣼⣆⣄⠀⠀⠀⠀⠀⠀⠀⡅
⢇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⢀⠃⠠⠤⠤⠤⠤⠤⠤⠤⠄⢠⠆⠀⠀⠀⠀⠀⠀⠀⡆⢀⠔⠑⠂⠀⣾⠁⠙⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠙⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠏⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠜⠈⢸⡄⣀⣀⣀⠀⠤⠐⢋⠀⢀⣀⣀⣀⣠⣤⠤⠦⠤⠤⠤⠤⠤⠤⠼
⣤⣤⣬⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣼⠟⠛⠃⠀⣰⡟⣿⠀⠘⣿⣟⠀⠀⣻⣿⠂⠰⣶⠆⢻⣿⠂⠻⣿⡇⠀⠀⢲⡶⠆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⠀⣿⡆⠀⣿⣿⡀⢠⣿⣿⠀⠀⣿⠀⢸⡟⠀⠀⠘⣷⡀⣰⡿⠁
⠀⠀⠀⠰⢦⡀⣿⠀⠀⠀⣸⡇⠀⢻⡇⠀⣿⢻⣇⣼⠏⣿⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⣿⡟⠀⡀
⠀⠀⠀⠐⢒⡃⣿⠀⠀⠀⣿⣧⣤⣼⡇⠀⣿⠈⣿⡿⠀⣿⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣸⡗⣋⣁
⠀⠀⠀⠐⠋⠀⣿⡟⠛⠀⣿⠁⠀⢸⡇⠀⣿⡄⠙⠃⠀⣿⡄⠀⣿⠀⢸⡇⠀⢀⠀⠀⣿⡗⠶⡄
⠀⠀⠀⠀⠀⠀⣿⣇⠀⢀⣿⡄⠀⣸⡇⢀⣿⡇⠀⠀⢀⣿⣇⢴⣿⡄⠸⣷⣤⣾⡇⢠⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⠉⠁⠀⠛⠛⢨⣭⠁⠀⢀⣠⣉⠀⠀⠀⠀⢠⣾⠀⢰⡆⠀⠀⣰⣶
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢰⣷⡀⢠⡴⠲⣼⣿⠀⢰⣿⠁⠹⠇⣠⡶⠛⣾⣿⠀⢸⣿⠀⢀⣿⣿⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣾⡟⠳⣿⡇⢠⣿⣿⠀⢸⣿⠀⠀⢀⣿⡇⢠⣿⣿⠀⢸⣿⡄⣼⠏⣿⣷⠞⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⢿⣧⠟⢹⣿⠀⣾⣿⣆⢀⡾⠻⡷⠟⠘⣿⡄⣾⠉⠛⢉⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡖⢄⠠⡰⠈⢿⣾⠇⠈⠛⠋⢀⢶⡀⠀⡀⠻⠿⠃⠀⢀⣾⢣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡔⡁⠀⠘⢄⠀⠠⠀⠤⠒⠤⠔⠁⠀⠉⠉⠑⠤⠤⠦⠤⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠉⠉⢀⡀⠐⠂⢰⣴⢰⣰⣐⠐⠀⠲⠆⠐⠄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠒⠈⠉⠮⠁⠡⠺⠀⠢⠐⠐⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣾⣷⠀⣠⠆⢄⣀⣠⣾⠻⣷⠀⠀⠀⠀⠀⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢹⣶⣼⣿⡛⣾⣿⣄⠈⢿⣿⣿⡇⣿⣶⣦⣀⠀⠀⢀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣀⡄⣀⣀⣾⣿⡛⠉⠳⡌⠿⠃⢀⣻⣿⣿⣿⣼⣿⣇⣿⣧⡔⠫⠀⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠻⠆⠀⠀⠠⡘⡄⠀⠈⡏⢹⡗⠛⡿⢿⣿⣿⣿⣧⣤⣰⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠘⠛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃⠈⠁⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡘⣸⠀⣿⢠⣿⣿⣦⣄⠄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⢀⣴⣒⣠⣶⡿⠟⠻⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⣸⣧⣿⣿⣿⣿⣿⡀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠛⠋⠋⠛⠛⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡟⠠⢱⣿⣿⣿⣿⣿⣿⣿⣦⡞⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠈⢀⠀⠀⣴⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠈⠀⠀⢿⡟⢏⣿⣿⣿⣍⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠠⠿⠖⠚⠛⠛⠛⠛⠻⣿⡶⠶⢿⣥⣤⠀⠀⣀⣠⣤⠀⠀⠀⢚⣿⡿⠃⠀⠀⠀⠀⢀⡀⠀⣠⠔⠀⣰⡿⠻⣿⣿⠟
⠀⠀⠀⠠⠔⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⣀⣀⣒⣀⡀⠀⠐⢶⣬⠁⠀⠀⠉⢹⣤⣶⠉⠉⠉⢴⣦⠖⠁⢀⠔⠛⠻⠟⢛⠶⡟⠋⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠤⢤⣀⡀⠉⠉⠉⠉⠀⠀⠀⠀⢀⣉⡿⠛⠀⠀⠉⠥⢀⣀⣠⡶⠤⢀⣾⠗⣀⡤⢀⠀⠠⣾⣿⣴⣶⡟⠁
⠀⠀⠀⠀⠀⢠⣤⡾⠋⠁⠀⠠⣄⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠀⠀⠈⠁⢀⣬⣭⠤⣤⣤⣤⣭⣤⣤⣶⣯⣵⣿⣿⣿⣿⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⣅⡀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣴⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣤⠀⠀⠀⠀⠀⢪⠍⠃⠳⣻⢢⡀⠀⠴⣶⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠄⠀⣬⣴⣿⢇⣿⠐⠤⢻⣟⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠚⠛⠳⠀⠰⠀⠀⠀⠙⠒⠛⠻⠛⠃⠛⠛⠑⠺⠿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠀⠀⠈⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⣀⣀
⠀⠀⠀⠀⣠⣤⣧⣁⠣⠀⠀⣠⠄⠀⠀⠀⠀⡀⠀⢠⠤⡀⠀⠀⠀⢀⠤⠤⠀⠀⠉⢠⡟⣽⣗⣿⣦⣄
⠀⠀⠀⠀⠻⠽⣿⣟⣻⣿⡀⠉⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠚⣉⣿⣻⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠩⠾⣻⣿⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⡭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⢈⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠦⠂⠀⠀⠀⠔⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⡟⡿⣦⠈⠀⠀⠀⠴⠜⠻⣿⣿⣿⣻⣷⣶⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠾⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⣇⡿⣟⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠠⠀⠈⠉⠀⠀⠀⠀⠒⠂⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠄⠀⠀⠀⢀⠀⠀⠉⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠘⣧
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠹⡆
⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠲⠚⠛⠛⠛⠛⠛⠛⠶⠖⠀⠀⠂⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠛⠛⠛⠛⠛⠛⠛⠁⢠⠿⣄⢀⠞⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⣠⠏⠀⢸⢿⡀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣄⣀⣀⣀⠀⣀⠀⠀⠚⠛⠛⣉⣉⣉⣙⠛⠛⢻⡀⢀⡼⠶⣷⠄⠠⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣉⣉⣉⣉⣉⣉⣛⡋⠁⠀⠰⠦⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠋⡀⠀⠼⠂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠑⢄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⡀⠀⣿⠽⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢂⡀⠀⠀⠀⡜⠀⠀⠠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣭⣿⠉⣷⣦⣅⣀⣀⣀⢀⠀⢘⡇⠀⠀⠈⣀⠀⠠⣀⣑⣤⡶⠂
⠀⠀⠀⠀⣀⣒⡒⢶⣶⣦⣤⣤⣦⣄⣸⣿⣿⣿⣿⡶⠶⠿⠤⠿⠤⠬⠥⠼⠷⣶⣾⣟⣛⠉⣛⠽⣁⡀
⠀⠠⠄⠀⢻⡛⠛⣿⣯⣽⠟⢛⣻⣏⣙⠛⠃⣿⣿⣿⣍⣻⣶⠿⠀⣲⣿⢗⠓⠿⠯⠀⠿⢿⡋⠤⠟⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠈⠀⠰⠴⠂⠨⠤⢈⣭⠉⠷⠾⢤⣀⠈⠑⡊⠁⢤⠘⠻⠿⠓⠂⠈⠁⠐⠂⠀⠠⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠄⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠁

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⣰⠁⠈⢷⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡄
⠀⠀⠀⠀⡇⠀⠀⠘⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠿⣷⣾⣼⣾⡿⠿⠷⠆
⠀⠀⠀⠀⡇⠀⡜⠀⣿⡄⠀⢀⡇⢀⣀⠀⠀⢀⣀⠀⠀⣀⡀⠀⣀⠀⢀⡀⢠⣾⠟⠻⡟⠛⢭⣳⣄
⠀⠀⠀⠀⠙⠊⠀⠀⢸⡇⠀⣸⢡⡟⢹⡇⢠⡟⢹⠇⣼⠋⣿⠀⣿⠀⢸⡇⣿⡁⠀⠀⣷⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠇⢸⡇⣿⡇⣸⡇⠀⢀⣿⢰⣿⢀⣿⠀⣼⡇⡜⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠘⠛⠉⠛⠉⠳⠶⠋⠛⠋⠙⠋⠙⠚⣹⡏⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢹⡇⠀⠀⢰⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⢀⠀⢀⣀⠀⣀⣀⢀⣀⠀⠀⢸⠁⠀⣼⢣⣄⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢩⣽⣽⠆⣿⣉⠸⡝⠃⠀⠈⢂⣚⡁⢛⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⠙⣦⣿⠀⠀⠹⣆⠀⣴⣿⣿⣿⡆⢼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢸⢿⣤⠟⣿⣀⣶⣤⡟⠀⠈⠿⣿⠛⠃⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⢦⣀⣤⠖⠲⣤⣀⣀⣤⠶⠲⢦⣀⣠⠶⠲⢦⣀⣀⡴⠶
⠀⠀⠀⠀⠀⠀⠲⠶⣄⣀⣠⠴⠶⢤⣀⣈⣩⠽⢦⣄⡀⢀⣨⡵⠦⣄⡀⣉⣥⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⢃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢠⡟⣀⡾⠋⠁⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⡟⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡜⡿⠁⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡼⠁⠈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⡼⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⡼⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡾⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋⣠⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠉⠉⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⢀⣴⢟⣁⣤⠀⠀⠀⠀⢀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠸⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠂⠀⢀⣴⣿⣿⣿⣭⣤⠴⠶⠖⢻⣿⣯⣤⣤⣤⣀⣀⣀⣀⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠲⠿⠻⠭⠉⣡⣀⣀⣀⣀⣴⣁⣀⣀⣠⠤⠤⢤⠤⠤⡌⣿⡓⠒⠂⠀⠤⠠⠤⠀⢀⣠⣤⣤⣤⣤⣤⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣛⡛⠻⠿⣯⣭⣄⣀⡈⠃⠸⠧⣬⣍⣀⣀⣀⣀⣀⣀⣀⣀⣐⠆⠀⢉⡿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⡿⠛⠛⠛⠻⢿⣿⣟⠶⠶⠶⠶⣬⣭⣭⣭⣤⣤⣤⡶⠶⠚⠋⣁⣠⡾⠀⠠⠔⢒⣋⣥⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣾⠁⠀⠀⠀⠙⢿⣷⣤⡀⠀⠚⠁⠀⠉⢻⣿⣿⣿⣿⠿⠛⠛⠉⣀⣤⡶⠾⠛⠉⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠀⠀⠀⠀⠉⠻⢿⣟⣓⠛⠀⢀⣠⡟⠈⠙⠛⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⠀⠀⢠⡄⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⢻⡆⠀⠀⠈⣿⠀⠀⣿⠃⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡀⠀⠻⠀⠀⠀⠛⠀⠀⠁⠀⠀⣰⠟⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠈⠻⠄⣀⣤⠴⠶⠒⠲⠶⢦⣄⡈⠁⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄⠀⣠⠞⠉⠒⠉⠉⠉⠉⠉⠀⠈⠙⢦⡀⠀⠀⠀⣀⣤⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣶⣦⣤⣀⠀⡼⣣⣶⣶⣶⣶⣦⡄⣤⣶⣶⣶⣶⣦⡙⠄⠐⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠉⠉⠉⢰⠃⢻⣿⣿⣿⣿⠟⠀⠘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠤⢶⣶⠄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣶⡈⡄⠀⡠⢀⣤⣤⣾⡀⠀⢍⠉⠉⠀⠀⠀⢐⠒⠬⣍⠉⠁⡠⢀⣤⣤⣤⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠃⠙⠛⠉⢻⣿⠄⠀⠀⠀⢀⣴⣿⠿⠿⣷⠆⠱⠀⠃⠙⠛⠉⢻⣿⡄⢀⢀⣿⡇⠀⠀⣠⣤⠈⡄
⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢀⣿⡇⠀⠀⢀⣤⣶⣶⣾⣿⡷⠈⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣷⠈⠘⣿⡇⠀⠀⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣼⡿⠁⠀⠀⣿⣟⠁⢠⣿⡇⠀⠀⠀⠀⢹⣿⣤⣀⣀⣤⣦⠀⠀⣿⣟⠁⢠⣿⡇⠀⠀⠀⠻⣿⣦⣠⣿⡇⠸
⠀⠀⠀⠀⠀⠸⡈⣿⣧⣾⡿⠁⠀⠀⠢⡙⠿⠿⠿⠿⣿⣾⠆⠸⠰⣿⠟⠛⠛⠛⠋⠉⠀⠠⡙⠿⠿⠿⠿⣿⣾⠆⠀⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠁⠘⠿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⠀⠀⠀⠀⠀⠀⠀⠀⡤⢂⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣶⣀⣀⢀⣠⣤⡈⠢⠀⠀⣠⣤⣤⣌⠂⠀⢀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢀⣤⣴⣤⣁⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⠛⠛⣿⡟⠙⣿⡄⠀⣾⡟⠁⠉⢿⡇⠐⢡⣶⠿⢿⣿⠏⢀⠄⣴⣴⣿⣋⣠⣽⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⠃⠀⣿⡇⠀⢿⣇⠀⢀⣼⡏⠀⣿⡇⠀⠸⣿⡀⠀⠑⠈⢻⣿⠛⠋⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠿⢏⡀⠀⠻⠃⠠⡈⠻⠿⠿⠋⠀⠀⠘⠻⠿⠿⠿⠿⠾⢆⠕⠈⠛⠿⠿⠿⠟⢋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⣿⢿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣟⣛⣛⣿⣿⣿⣿⣿⡻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠛⠒⠪⢥⣂⢄⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⠀⣿⠿⠶⢮⣑⠮⣒⢄⡀⠀⠀⠀⠀⠀⢀⣤⠶⠒⣒⣒⡒⠤⢄⣀
⢉⣉⣉⣉⡓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⢸⡆⢿⡀⣴⣶⣬⣙⠮⣓⢭⡲⠤⣤⣤⡴⠟⢁⣴⡿⠋⢉⣉⣉⣓⠲⢭⣓⡲⠤⣤⣀⣀⣀⣀⣀
⠛⠋⠉⠉⠙⠛⢦⣑⢄⠀⠀⠀⠀⠀⣼⠃⣠⣾⠇⢸⡇⢹⣿⠟⠛⠷⣮⡓⢬⣓⠶⢤⣤⣶⠿⠟⠀⣰⡿⠋⣩⣭⣙⡓⠦⣍⡓⠶⢤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠷⢦⣌⠳⣕⢤⡀⠀⣰⠇⣸⠏⢁⣠⣾⡇⢸⣿⠀⢠⣶⣤⣙⠳⣬⣛⠶⣤⣤⣤⣤⣾⡿⠃⣸⣿⠛⠛⠛⠷⣦⣍⡓⠶⣤⣤⣤⣤
⣶⣶⣶⣶⣴⣶⣦⣬⡓⢮⡳⢬⣙⣉⣰⡟⢠⡿⠋⣁⣤⣾⡿⠀⣼⣿⡟⠛⠿⣦⣝⠻⢶⣤⣬⣥⣤⣤⣾⣿⠃⣠⣾⣶⣶⣤⣉⠻⢷⣦⣬⣭⣭
⣤⣤⣀⣉⣉⣉⣉⣉⡙⠳⣭⡳⢬⣉⡋⢀⣾⠃⣾⡿⠋⢉⣀⣴⣿⡟⢀⣴⣶⣦⣙⠻⢶⣤⣍⣉⣉⣉⣉⣀⣴⣿⠟⠋⠉⠛⠿⢷⣦⣤⣉⣉⣉
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⣭⡓⢮⣝⣛⣃⣼⡿⠀⣾⣿⠿⠛⠋⣠⣾⣿⡿⠿⠿⢿⣦⣍⣙⣛⣛⣛⠛⠛⠛⢉⣠⣶⣿⣷⣶⣤⣌⣙⠛⠛⠛
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣦⣭⡓⢮⣝⣛⠛⢁⣼⡿⢁⣴⣾⣿⠿⠟⠋⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠛⠛⠻⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣙⠳⢮⣭⣛⡛⠛⣁⣾⡟⠉⣀⣤⣤⣴⣶⣾⣿⣿⣿⣷⣦⣤⣴⣶⣶⣶⣶⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠶⣦⣍⣙⠛⠛⢋⣠⣾⠟⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⣆⠀⠀⠈⠁⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⢻⣶⠟⠁⠀⠀⠀⠀⢀⣰⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠆⠀⠈⠻⣿⣦⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣦⠀⠀⠘⠋⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣴⡟⢙⣷⣶⡄⠀⠀⠀⢀⡀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠷⠶⣿⣧⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⡄⠀⠀⠀⠁⠀⠀⠀⠘⣧⣸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⣿⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⡿⣧⣀⣤⠟⢀⣾⣅
⠀⠀⠀⠀⠀⠀⠿⣤⣤⣭⣴⠾⠋⠁⠉⠻⢦⣄⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠈⠛⢶⣴⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⣀⣴⠿⠛⢿⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⢸⡇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠷⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠀⠀⢀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡟⠀⡀⠀⠠⠴⠀⠀⠀⢀⡀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⣀⣠⡄⠀⠠⢄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⣀⣤⢾⡟⣿⠛⢛⡀⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣩⠿⠼⠓⠋⠻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠁⠀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢀⡀⢴⡶⠚⡿⠇⠀⠀⠸⣗⠒⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡨⠀⢀⣤⣾⡯⣶⠚⣿⡾⣤⣼⡦⠴⠶⠾⣶⡿⠦⠴⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣷⠾⢛⣉⡥⠷⠞⠒⠛⢟⠉⠉⠀⠀⠀⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠠⣄⠸⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣶⣿⣿⣿⣿⣛⠿⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣤⠶⢺⡿⢸⣶⣞⢫⣾⢿⣿⣿⣿⣙⡻⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠛⡉⠀⢸⣷⢞⣵⣞⣷⣾⣿⣿⣿⣿⣿⣿⡦⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣟⣷⡿⠺⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⠇⠀⠁⠀⠀⠈⠹⡿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠦⣤⡶⠶⠖⠒⠲⢶⣶⣤⡽⠿⠿⠉⣤⣦⡀⢀⣀⣰⣶⣇⠀⢠⡀⠃⠐⠶⠖⠀⠀⠀⠀⠒⠶⠖⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⡗⣰⡿⣶⣶⣶⣤⠀⠐⠒⣯⣷⡷⠈⣽⣾⣿⡏⣀⡘⠻⣿⣿⣃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠡⣶⣾⣍⠙⣃⣠⡔⢛⡿⠃⠀⠚⠿⣻⣥⠙⢿⣷⣄⠀⠀⠀⠀⠈⠁⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠙⠛⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⢟⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣫⣍⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣦⣀
⠀⠀⠀⠴⠷⠶⠾⠿⠿⠷⠟⠟⠿⠾⠷⠶⠦⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⠆
⠀⠀⠀⠀⠀⠀⢀⣤⣦⣴⣿⣿⣶⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⢛⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠛⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣾⣷⡏⠀⠘⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⢶⣶⣾⣦⡀⠀⠀⣴⣿⣿⣿⣿⠿⢿⡿⠶⠤⠤⠄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⡀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣻⡃⠉⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢟⠛⢷⠀⠀⠀⠀⢠⣶⣄⡼⠛⠿⠀⠀⡿⠋
⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣷⡤⣤⣄⣰⣦⣀⡀⠀⠀⢀⣠⣾⣿⣿⣿⣻⣿⣿⣄⣀⡀⡀⡀⠀⠀⠻⠇⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠋⣿⣿⣶⣬⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣿⣭⣭⣭⣽⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠲⠶⢾⣿⣟⠻⠿⢿⣿⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣠⣾⠿⠿⠛⠿⠿⣿⣀⠁⠀⠀⠀⢠⣶⣶⡆⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⠟⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⣀⣤⣿⣿⣿⣧⠘⢆⠀⠀⠀⡄⠀⠀⠀⠀⢀⡴⠟⢛⣻⣷⣄⣀⣠⣴⣞⣀⣀⣀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠁⠀⠀⠈⠉⠁⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠔⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣤⣶⣷⡆⠀⠀⠀⠀⠀⠈⢀⣾⣿⠇⠀⢀⣴⡟⣛⠁⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⢀⣤⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠘⢿⠁⣠⣶⣶⣿⣟⣿⡶⠂
⠀⠀⠀⠀⣠⣾⣿⣽⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣵⣾⣿⣿⣿⣿⣼⣿⢦⣴⣾⣿⡛⠀⠀⠀⠀⠐⢿⣿⣿⣮⠟⠋
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⠐⠓⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠈⠉
⡾⣶⣷⢶⢶⡷⣶⠶⢶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣿⣶⣶⣶⣿⣿⣷⣶⣶⣾⣿⣾⣷⣶⣷⣾⣷⣾⣶⣶⣶⢾⣷⢶⣶⣶⣶⠶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠂⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠢⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠠⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⢦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠒⠛⠛⠛⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠰⠿⣦⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢆⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⡿⠛⠋⠉⠀⠀⠀⠀⠙⢷⡀⠀⠀⢀⣴⠋⠀⠀⠐⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⠤⠦⠀⠀⠀⠀⢀⣤⣄⡀⠀⠛⢍⠲⢄⣀⡴⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⣀⠞⠀⠈⠙⠒⠖⠋⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⣋⠁⠀⠀⠉⠓⠶⢤⣤⣄⣀⣀⣀⣀⣾⣿⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⢋⣩⠴⠛⠉⠀⣀⡤⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣛⠛⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠛⢋⣉⣤⠶⠚⠉⠀⣀⣤⠶⠛⠉⠀⠀⣀⡴⠖⠀⠀⣀⣴⡿⠿⠓⠒⠢⢄⡀⠀⠀⢻⡄
⠀⠀⢀⣀⣀⣠⣤⡤⠤⠶⠶⠚⠛⢉⣉⣡⣤⠴⠶⠛⠋⠉⠀⣀⣤⠶⠛⠉⠀⠀⣀⣤⠶⠛⠁⠀⢀⣤⡾⠛⠁⠀⠀⠀⢀⣀⡤⠗⠀⠀⠘⣷
⠀⠀⢈⣿⣄⠀⠀⠀⠀⠐⠒⠛⠛⠉⠉⠀⠀⢀⣀⣤⠴⠞⠋⠉⠀⢀⣀⡤⠶⠛⠉⠀⠀⣀⡤⠞⠋⣁⠴⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿
⣠⠞⠉⠀⢈⡳⢦⣀⠀⠀⠀⠀⠀⠠⠶⠖⠛⠉⠁⠀⣀⣠⡤⠶⠚⠋⠁⠀⢀⣀⠤⠖⠛⠁⠀⠀⣼⣁⡤⠔⠂⠁⠀⠀⠀⠀⠀⠀⣀⡀⠄⣿⠀⠠
⠻⠦⠀⠂⠉⠀⠀⠉⠛⠦⣤⣀⠀⠀⠀⠀⠀⠒⠛⠋⠉⠀⣀⣀⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⣀⣰⡿⠠⠄⣀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣄⡂⠒⠈⢉⣉⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⠀⢺⣿⣿⣧⣤⣤⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠈⠉⣠⡴⠚⢋⣉⣭⣭⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠈⠉⠉⠉⠁⢀⣠⠟⢀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠷⠾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢦⣄⠀⠀⠠⡇⠀⠀⢹⣦⣀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣯⠑⢦⣀⣇⠀⠀⠸⣿⡷⡑⢢⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡃⠸⠀⠀⣹⣿⠄⠀⢸⠇⡇⠀⠀⠻⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢼⣿⠀⠀⠸⠁⠀⠀⠀⠀⡼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⣿⢇⠀⡚⠀⠀⠀⠀⠀⠀⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣷⢸⠀⠇⠀⠀⠀⠀⠀⠀⢹⣜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣻⡋⡞⠀⠀⠀⠀⠀⠀⠀⢸⣻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡄⠀⠀⠀⢀⠀⣸⢾⣶⠃⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⢂⠀⠀⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣅⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡅⢣⠀⠀⠀⠀⠀⠈⣀⠚⠉⠃⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⢀⣠⣤⣽⣿⡧⠖⣂⣉⣀⠀⠀⠀⠀⠸⣿⣧⢸⠀⠀⣀⡀⠀⢈⣵⡖
⠀⠀⠀⠀⠀⠀⣰⣿⠁⣀⠔⠀⠀⠀⢀⡈⢻⣷⣶⣭⣿⠭⠍⣡⠄⠀⢀⣈⣿⣿⣬⠁⠀⣁⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠨⠷⠩⠿⣁⣈⠉⠉⠉⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣠⣶⣃⣤⣶⣿⣿⣿⣿⡟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⡏⠉⣿⣷⠂⢀⣠⣤⣾⣿⣿⣿⣿⠿⠋⠉⠙⠿⢀⠴⠃⠀⠄
⣠⣄⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣴⡿⢓⢀⣷⠀⢸⣿⡇⢀⣆
⣿⣿⣿⠿⢿⠂⠉⠚⠦⡀⣶⣬⣀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣇⠉⢈⣉⣶⣾⣿⣿⣿⡀⣿⡿⠛⢸⣿⣦⣤⣀⣀⣠⠤⢢
⠉⠉⠉⠛⠢⠀⠀⠀⠻⣦⣤⣈⠉⠛⢿⣷⣾⣶⣷⣿⣿⣷⣾⣿⡿⠿⠿⠿⣾⣟⠿⠿⣿⡿⠿⠁⠹⠆⠀⢿⣿⣿⣏⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⡤⠌⠉⠉⠉⠛⠶⡿⠍⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⣿⡯⠀⠘⢷⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠤⠒⠒⣒⠤⠀⠀⠀⡠⢴⢒⡦⡄⠀⠀⣀⠤⢶⣤⡀⠀⠀⠀⡠⢤⡤⠄⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⡄⠀⠀⠀⠰⡁⠀⠀⣠⣎⠀⢸⡋⠀⠀⣠⠞⢁⢠⠋⠀⠀⢀⠠⠊⠀⡏⠀⠀⠀⠀⡤⠊⣿⣟⠁
⠀⠀⠀⠀⠀⡀⠄⣀⡉⢙⠉⣼⡇⣜⢘⡗⢲⠊⣱⣮⣿⠨⣷⠖⡆⡹⢀⠀⡀⢉⠒⡒⠒⠉⠨⢠⡁⣏⡲⠶⣖⠃
⠀⠀⢐⡇⠀⠀⡀⠀⠄⠀⠐⢸⠏⠁⡎⡧⠃⢐⢸⡿⠋⡄⢸⡦⠃⢠⢩⠀⠇⠀⡀⢟⠄⠁⢰⠋⡡⠋⢠⢺⣇⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⠀⠀⠄⣠⠁⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠄⠠⠐⠰⠀⠁⠁⠢⠘⠁⠀⠪⣼⠀⠀⠀⠀⠔⠃⠘⠰⠀⠁⠊⠅⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠁⠀⠀⣿⡆⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⣾⣿⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⢠⡿⠃⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⢩⡶⢲⣿⣿⢧⣤⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠈⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣿⣆⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⣠⣤⠤⡀⣤⣤⠄⠀⢠⣤⡄⠀⠀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢿⣿⡄⠀⠀⢸⣿⠃⠀⠀⢀⣴⣿⠁⠀⢸⣿⡿⠀⠀⣾⣿⠃⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢀⣿⠟⠀⠀⠀⢸⣿⠀⠀⡠⠚⣿⡏⠀⢀⢾⣿⠃⢀⠴⣿⡟⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠙⠒⠈⠀⠀⠈⠓⠂⠁⠈⠛⠂⠁⠀⠙⠓⠋⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⣄⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠿⠟⠛⠛⠛⠓⠶⠦⠤⢤⣄⣀⣀⣀⣸⣿⣟⡤⠋⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣇⠀⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢤⡄⠀⢀⣤⠀⠀⠤⣤⠤⠄⠤⣤⠤⠀⣠⡤⠤⣄⠀⠀⣤⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⡼⠙⣇⠀⠀⢸⠀⠀⠀⣿⠀⢰⠇⠀⠀⠈⣧⠀⡏⢧⡀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢺⠓⠒⢻⡆⠀⢸⠀⠀⠀⣿⠀⠸⣆⠀⠀⢠⡏⠀⡇⠈⢳⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠛⠀⠀⠀⠃⠀⠘⠀⠀⠒⠛⠒⠀⠈⠓⠚⠋⠀⠀⠃⠀⠀⠛


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣇⠠⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠀⠀⠀⠀⠀⡀⢀⣀⣧⠜⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠦⠶⠒⠚⡟⠉⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢬⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⡢⠐⠀⠀⠈⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠚⠋⠉⠁⢸⠇⠀⠀⠀⠀⠰⡆⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢻⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡃⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠷⣾⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⢤⠖⠻⠟⠁⠂⡂⡾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⣀⠦⡜⡾⠉⠉⡠⠘⢁⣤⣴⣾⣿⣯⣷⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⡀⠿⠐⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣬⣥⣶⣿⣿⣿⣿⣿⣋⠻⢿⣿⣿⣿⣁⣀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⢀⡖⢮⣙⣛⡛⠉⢩⣽⣭⣙⣋⣿⣶⠳⣿⢿⣯⢙⣿⣿⣿⠝⣛⠷⣴⣶⣶⣾⣍⣀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠠⠌⠋⣁⣬⣿⣭⣿⣿⣿⡞⢛⣯⣥⣶⣿⣿⣛⠛⠛⣉⣵⣆⠁⢨⣉⣛⣛⠙⠻⣿⣿⠿⠶⣿⣯⣟⡛⠁⠠⠄
⠀⠀⠀⠀⠀⠐⠒⠂⠉⠉⠉⣭⣥⠀⢼⡿⠛⠋⠁⠤⠼⠛⠋⠉⠩⠕⠂⢀⣿⠿⡋⠀⠰⣮⣍⣻⠥⠤⠤⢴⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠁⠀⠀⠀⠘⠻⢿⣷⣶⡄⠀⠒⠉⠀⠀⠀⠈⠙⠛⠉⠁⠀⠢⠭⣭⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⣿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢠⣤⠀⠀⣠⠀⢠⣤⠀⠀⢀⣤⡀⢀⣤⡀⠀⠀⣤⡄⠀⣠⣤⣤⣄⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⠛⠀⢸⣿⠀⠀⣿⠀⢸⣿⣇⠀⣾⣿⡇⢸⣿⣷⠀⣸⣿⡇⠀⣿⣿⠉⠁⠀⣿⣿⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⠀⢸⣿⠀⠀⣿⠀⢸⣿⣿⣼⢿⣿⡇⢸⡿⣿⣦⡟⣿⡇⠀⣿⣿⣶⡦⠀⣿⣿⣠⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣿⡇⢸⣿⡀⠀⣿⠀⢸⡇⢿⡿⢸⣿⡇⢸⡇⢹⣿⠁⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡾⠟⠀⠈⠿⢷⡾⠏⠀⠸⠇⠸⠃⠸⠿⠇⠸⠇⠀⠏⠀⠿⠇⠀⠿⠿⠶⠶⠀⠿⠿⠀⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠂⠀⣀⠀⠀⠀⢲⣶⣶⣶⣶⣦⣴⡤⠠⠤⠀⠀⣶⡆⠀⠀⣠⡀⠰⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠐⠈⠋⣉⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⢀⣤⡤⠀⠘⠃⠀⠀⠠⠄⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⡀⠂⠀⠀⠀⠉⠛⠀⠀⠀⠀⢻⣿⣿⣿⣿⠐⠉⠀⢀⣤⠀⠄⠀⠃⠰⣤⡈⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣶⡔⠓⠀⢸⣀⠀⣄⠀⠀⠠⣄⡀⠸⣿⣿⣿⡇⠀⠀⣴⡟⠁⢠⠄⠀⠀⢠⡄⠉⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣶⡸⣿⣿⣶⠀⡀⠀⠉⠲⣿⣿⣿⡇⢀⣾⠏⠀⢀⡏⠀⣀⠀⠀⠙⠀⠀⠐⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⠀⢺⣿⣷⣿⣿⣿⣶⣄⠀⠀⢰⣿⣿⣿⣷⣿⣿⠀⠀⠘⠀⢠⠇⠀⠀⡀⠀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠈⠀⠻⣿⣿⣻⣿⣿⣿⣈⣿⣾⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠹⡄⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡴⠃⠀⠀⢠⡌⠙⠌⠉⠹⣿⠋⠉⠉⠙⠻⣿⣿⣿⣧⣼⠀⠀⠀⠀⡀⢄⡀⣧⢇⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠆⠀⠀⠃⠀⠀⠀⣼⣿⣴⠃⠀⠀⣀⠀⠙⢿⣿⣿⣷⣄⣧⣾⣿⣷⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣧⡀⡌⢀⡀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠐⠀⠀⢻⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣾⣧⣼⣯⡅⠀⢰⡿⠛⢉⣉⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⢠⠀⠀⠀⣨⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⡅⠀⠚⣠⣾⣿⠟⣫⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣻⡇⠀⠀⢸⣿⣿⣵⣿⠟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠉⠛⡝⠹⠇⠈⠀⠀⠘⠛⣽⣿⣟⣵⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠑⠆⠀⠀⠂⠀⠀⠰⠶⠒⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣠⡀⠈⠠⣤⣤⣤⣤⣽⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠉⠻⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣄⠀⠉⠉⠉⠉⣉⣵⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠃⠀⠘⠁⠀⠀⠒⠀⠈⠛⠿⠿⠿⠿⠿⠄⠠⠀⠙⠛⠂⠠⠴⠾⠋⠛⠋⠙⠿⠿⠿⠿⠇

⠀⠀⢠⣶⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⡀⢀⢀⡀
⠀⠀⠘⣶⣦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡠⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈
⠀⠀⠀⠀⢸⡆⠀⢠⠀⣸⡇⠀⣴⠖⡆⠀⢸⡇⢠⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⡅⠀⠘⠢⢀⠀⠀⠀⠀⠊⠀⠈⠃
⠀⠀⠀⠀⠀⣿⠀⡟⢀⡿⣇⢸⡟⠀⠀⠀⡿⣷⠀⢧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⢡⡏⣿⢰⡏⠃⡞⣹⠇⡖⣸⡇
⠀⠀⠀⠀⠀⢹⣧⠇⢸⠛⣿⠸⣧⠀⡴⢸⠛⣿⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠉⠙⠊⠳⠊⠉⠘⠞⢋⢸⡏
⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠛⠀⠉⠚⠁⠀⠀⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⡂⠉⠠⠀⠄⠉⠀⣷⡿
⠀⠀⠀⠀⢰⣶⠀⠀⣴⡆⣰⣤⣆⠀⣶⠶⢤⡀⢰⡖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠁
⠀⠀⠀⠀⢸⣿⣇⣸⢿⡇⠸⢿⡟⠀⣿⠀⠈⣿⣼⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⢢⡄⠀⠀⠀⣤⠐⠲⠾⠂
⠀⠀⠀⠀⢸⡇⢻⡟⢸⡇⢸⣳⢮⣆⣿⠀⣠⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠂⢿⡀⣿⣧⡏⢠⣆⡏⢰⠟⠀⠱⡟⠂
⠀⠀⠀⠀⠈⠋⠀⠀⠈⠟⠈⠾⠑⠏⠻⠋⠁⠀⠘⠗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠿⠸⠏⠓⠀⠉⠓⠉⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠉⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢂⡞⠁⠌⠀⢀⠀⣀⡀⡀⣤⢠⡆⡴
⠀⠀⠘⣧⢀⠇⡤⣴⢀⡶⡆⣠⢤⡆⣠⢠⡆⠀⠋⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣾⣇⡜⣴⣡⣏⢾⡤⠾⠶⠗⣻⣺⣃⡀⣀
⠀⠀⠀⢻⣼⠘⠧⢻⡸⣇⣠⠿⠜⣇⠧⢺⡧⣒⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⣠⠜⢀⠀⠀⠀⠀⢠⡞⠛⠃⠈⠉⠉
⠀⠀⠀⣈⠃⠀⣦⢠⣄⠶⣴⢠⣴⠀⢐⡽⠋⠿⡿⣿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢁⡴⣇⣰⠋⡠⢠⣠⢰⡏⣴⣛⡄
⠀⠀⠀⠹⡇⠀⠟⠋⠿⠴⠻⠜⠻⠀⠀⠀⠀⣸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡟⠸⠇⠿⢀⣛⣃⣛⣉⠅⣩⣵⢶⣤⡀
⠀⠀⠀⠀⢷⠀⡄⠋⠑⢤⣚⡉⠢⣴⣋⠓⢤⣂⠀⠀⠀⠏⠘⠉⠉⠉⠈⠉⠈⢀⣸⡵⠶⠒⠛⠉⠉⠉⠀⠀⠀⢸⣿⣍⣈⣿⣷
⠀⠀⠈⠑⠛⠋⠀⠀⠑⠉⠀⠉⠉⠁⠈⡟⡩⡠⠁⠀⢠⠄⣄⣠⡀⠀⢀⢤⢠⢨⠁⠀⢠⢠⡄⡄⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠈⠈⠁⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⣈⣹⣤⣾⠦⠆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⠁⠀⢀⣀⣤⣴⠦⠆
⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⣬⠉⣠⡞⠁⢀⣤⣤⠀⣠⠀⢀⣄⢀⡾⠁⠈⢀⣠⣤⡍⢡⣾⠁⣠⡍⠀⣀⣤⣄⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠋⠁⠧⢰⡯⠚⠿⠚⠿⠚⢩⣇⡸⣇⣠⠴⣯⠔⠻⠞⠁⢿⠈⢸⠷⠊⢟⡠⠟⠹⠟⠉⣧⠖
⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⢀⣀⣀⣀⣤⠤⠤⠤⢤⢴⡟⠶⠒⠒⠒⠂⠒⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⣣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢳⠀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡜⣧⠀⢻⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣽⡄⠈⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡀⢨⣿⡄⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠠⠐⠒⠁⠈⠉⠀⠀⠀⢸⣧⣼⠟⢻⡄⠀⠰⡀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⣿⣄⠀⠀⢀⡄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⢿⢸⡆⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⢀⣠⣀⣶⡾⠿⠯⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⠛⠃⠒⠶⠶⠦⢤⣤⣴⡇⠀⣠⣾⣦⣴⣯⣀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠉⠙⠻⠿⢯⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⠸⢿⢰⣶⡤⣬⣤⣤⣀⣄⡄⠀⠀⢀⣀⣀⣤⠤⡶⠃
⠀⠀⠀⠀⠀⠰⣬⣵⣾⣿⣿⡏⠉⠉⠀⠀⠀⣀⡀⣀⣒⣒⣴⠺⣥⡿⣿⠶⠞⠛⠫⠉⠑⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠿⣿⣦⣦⣤⣤⡤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠬⠽⠷⠶⣿⣿⠠⠔⠒⠤⠄⣀⣀⣤⠤⠀⠀⠤⣤⣤⣤⡼⠛⠛⠁⢠⣤⡤⠤⠄
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⣉⡉⠀⢀⣀⣀⣀⣉⣉⣉⣀⠀⠄⠀⠀⠀⣉⡥⣤⣄⣓⡙⠉
⠀⠀⠀⠀⠀⠀⠠⠔⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡆
⠀⠀⠀⠀⠀⣠⣤⣤⠀⠠⠀⠤⠂⠐⠤⠿⠿⠄⠤⠤⠤⠤⠤⠤⠄⠼⠿⠇⣄⠀⣤⠠⠄⠄⢤⣤⣤⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⡄⠒⢠⠑⠀⣀⣼⣿⣿⣿
⠀⠀⠀⠀⠘⠉⢿⣏⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠉⢂⠀⠀⠀⠀⠣⢀⠼⢀⠀⣿⣉⣿⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡸⠀⠀⠀⠈⠂⠀⠐⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣤⠀⠈⠁⠈⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣸⠀⠀⠰⠈⣉⣀⣉⠀⠀⡅⠀⢨⠀⠀⢀⡁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢶⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠤⠤⠀⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢶⠧⣼⡤⣷⠞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠁⠀⣿⡿⢋⢞⣼⣷⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢾⠤⢾⠦⢼⠦⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠃⠁⠀⠀⠛⡁⠁⠙⢙⠉⠂⠀⢈⣀⡀⣀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠾⣖⠃⠀⠻⢦⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡡⢐⣂⣐⡀⠌⠐⢄⠘⠓⠚⠛⠀⠀⠀⠀⢰⠀⠀⢰⠆⠀⠀⠈⠳⠿⣤⢤⡬⠏⠀⠀⠀⡇
⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠐⠠⢢⡞⠉⢉⣩⣿⣶⡀⠄⢂⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠷⠀⢰⠶⢶⠶⠞⠁⢾⣶⣶⣶⣶⠀⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⣴⣉⠹⣿⣿⣿⠰⠈⠀⠀⠀⠀⢀⡀⠀⢐⠀⠈⣻⠇⠔⠒⠋⣀⠖⠷⠲⠶⠶⠶⠂⠀⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡄⢀⢻⣿⣿⣿⣿⣿⣿⡟⡈⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠐⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⢄⠀⢝⠻⠿⠿⠟⠩⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠁⠀⢄⣁⣈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠇
⠀⣀⣀⣠⣤⣤⣤⡀⢀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⠀⠀⠀⠸⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣽⣿⣶⣶⣶⣶⣦⣴
⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣠⣤⣶⣿⣿⡇⠀⠀⠘⡇⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿
⠀⣄⡀⠀⡀⠀⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠈⠤⠖⠲⠾⡇⠛⠋⠉⠉⠙⠋⠉⠉⠀⠀⠀⠉⣭⣿⣿⡿⠿⣿⣿⣿⡇⠀⠀⠈⠉⡉⢭⡉⣿
⠀⣿⣶⣾⣿⣿⣿⣶⣾⡇⡼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣿⣿⣷⣶⣶⣶⣶⠆⢤⠆⠰⣿
⠀⣿⠛⣿⣿⣿⣿⣿⣿⠟⢀⣀⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣤⠀⠀⠤⢶⣿
⠀⣿⣶⣿⣿⣿⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⠿⢿⡿⠿⢿⠿⠿⠿⠿⣿⠿⠿⣿⠿⣿⣿⣿⡿⠆⠀⠀⠀⢾
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠉⠙⠁⠀⠠⠭⠄⠈⣽⡋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠀⠀⠀⠀⡄⠀⠠⠄⠀⢀⡀⢸
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂⣆⣠⣤⣼⣅⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠈⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣷⣶⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⢂⣾⣧⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠂⠀⠰⡶⠾⣿⣦⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠓⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡿⣭⣁⡄⠀⢶⣿⣶⣼⣧⣤⣤⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⢿⣶⢦⣤⣤⣤⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣟⠻⢿⠷⣶⣦⣤⣤⣤⣤⣄⠁⠈⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠭⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠦⠤⠤⠾⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⡀⠀⢰⠃⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⡟⣾⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⡇⢀⡏⣼⣹⡖⣸⠇⢁⣴⣫⡷⢰⡆⡎⣷⡠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢸⣿⢱⠋⠖⢹⡏⣼⣿⠋⢔⢉⡟⣹⢳⠸⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⡼⠀⠉⢸⡷⠙⠛⠁⠈⠸⡧⠙⠛⡰⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡌⢃⣿⣷⣇⢚⣷⣬⣾⣷⣯⢘⣷⣤⢟⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢶⣶⠶⢶⣦⣤⣤⡶⡶⢶⡶⢾⣵⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⣉⣉⠛⢛⠛⢋⣉⡉⢉⡃⠞⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠮⠇⠘⢷⣾⡗⠛⠀⠛⢷⣷⡾⠃⠀⣶⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠁⣩⣴⣿⣦⡌⡈⢁⣾⣿⡏⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⡄⢠⣦⠀⠀⡀⠀⠀⣶⠒⠲⣆⠀⣶⠒⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⢻⡿⠙⣿⣿⣿⣿⣿⠉⣭⣍⠻⣿⠋⣭⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢻⡼⣿⠀⢾⣿⡇⠰⣿⠀⠀⣿⢸⣿⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠠⡎⢃⡆⣿⡅⠀⢸⣿⠀⣿⣿⠀⣿⠐⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠀⠁⠿⠀⠀⠁⠀⠀⠿⠤⠼⠋⠘⠿⠤⠄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣠⣿⣿⣇⣿⣿⣿⣿⣿⣀⣛⣋⣴⣿⣀⣛⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⢠⢲⣄⠔⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⣨⣿⣡⣦⣴⡮⣉⣈⡀
⠀⠀⠀⠀⠀⠀⢀⣰⢶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣅⠈⠁⠂
⠀⠀⠀⢀⡤⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣋⡤⠤⠄
⠀⠀⠰⠞⠛⠻⣷⡍⠱⣤⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣖⣀⣀⠁
⢐⣁⣀⣀⢦⡀⣝⢦⣄⢪⣭⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠁⡽⠿⣿⣽⠷⠄
⠾⠛⠛⠿⢿⣿⣾⣿⣿⣿⣿⣭⣷⣴⡀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣹⢿⡃⠠
⠀⠲⢤⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡹⣿⣿⣿⣿⢆⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀
⠀⢠⡀⣌⣻⢟⠚⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡄
⠀⠈⢿⣿⣿⣷⣷⣦⣦⣵⣴⣦⣄⡹⠿⣿⣿⣿⣿⡿⣿⣿⣿⣦⡑⠲⢶⣾⣷⣴⣾⣷⣦⣴⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣄⢔⢮⣉⡉⠻⣿⣮⣝⡿⣿⣿⣷⣦⣬⣭⣭⣿⣿⣿⣯⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣉⣉⡭⠭⠭⠉⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠊⠉⠀⠀⠡⡀⠈⠀⠲⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠄⠐⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡀⠀⢀⠀⠀⠄⠀⠂⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⠠⠄⠒⠈⠠⡀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣀⠠⠀⠘⠀⠀⠀⠀⢸⣇⢀⠀⠤⠃
⠀⠀⠀⠀⠀⢀⣐⡁⠀⠀⠀⠀⠀⣀⡀⠀⠉⠢⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⣄⣀⣀⡀⠀⠀⠀⢸⣿⣿⣦⣀⠐⠦⠀⠁⢀⠑⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣶⣤⣿⡟⠛⠛⠛⠆⠀⠂⡐⠷⢦⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠈⢂⠀⠀⠀⢠⣿⣿⣿⣿⠟⠋⠁⠀⠈⠙⣷⣦⡀⠀⠀⢑⠠⣤⠉⠀⠉⡠⣦⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠈⠀⠘⢦⢀⡀⠠⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢘⢃⠀⡴⠉⠀⢠⡀⠠
⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⡀⠀⠀⠀⢏⠀⢳⠌⠁⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠂⠈⢁⠀⠀⣤⣀⠉
⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠲⣶⣦⣤⣀⠈⠉⠓⠒⠲⠖⠒⠛⠒⠵⠖⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠋⠀⠄⠚⠤⠀⠃⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠉⠙⠛⠛⠓⠶⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠠⢂⣠⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉



⡿⠿⠿⠿⡿⠻⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⣨⠞⠛⢵⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣛⡓⣨⠐⠿⣾⠦⡀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⡿⠛⢃⡘⠟⠀⢩⣦⡀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⣿⣿⣿⣿⣷⣄⣼⣿⣶⡀⠀⠉⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠗⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠁⢀⣀⡀⡘⣿⣿⣿⡿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢀⣤⣾⣿⣿⠦⡀
⠀⠀⠀⠀⠀⢠⣖⣟⣟⣗⣦⠀⢸⠀⠀⠀⠙⢢⣴⣶⣦⣄⠀⢠⡞⠁⠆⠀⠈⠛⠉⡟⠀⠉⠦⡀
⠀⠀⠀⠀⠀⡧⢼⠤⡧⢸⠤⡇⢸⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠳⡼⡄⡧⡼⡤⠃⢸⠇⣠⡀⠀⠀⠈⢻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣬⣭⣭⣭⣀⣄⢸⣍⠀⠀⠀⠀⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢸⣿⡄⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠞⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠈⠉⠶⠲⠴⡴⠴⠒⠏⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⡀⠤⠈⢣⠀⠀⣄⡀⠀⠀⡰⠃⠈⠁⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠉⠉⡏⠀⠀⠀⢱⡀⡄⠀⠈⠀⢃⠀⢃⠈⠓⠶⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠀⠸⡤⠴⠃⠀⠀⠀⠈⢇⠀⠀⠀⠀⠛⠀⠸⠀⠄⠀⠀⠀⢠⠀⠂⢸
⠀⠀⠰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⣄⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⢀⠀⠈⠲⢄⣀⠐⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠄⠀⠢⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠚⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣤⠤⣄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠄⠀⠀⠀⢴⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⣅⠈⠀⠀⠀⣮⠰
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⢡⠀⡠⠐⢀⢸⠀⠈
⠀⠀⡠⠒⠒⠒⠆⠀⠀⠀⠀⠀⡄⠠⣔⣦⡴⠾⠂⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡄⠂⠀⣸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡎⠁⠀⠀⢊⣧
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣀⠤⠀⠂⠈⠁⠀⠰⢠⣄⠀⠀⠠⣆⠀⠀⠀⠇⠠⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠖⠢⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⣀⠀⠈⠀⠈⠈⠁⠀⠀⢠⠃⠀⠀⠀⠸⡀⠐⣀⢀⣼⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠈⣠⡀⢞⣀⠀⠀⠀⢀⣖⠀⠀⡀⠀⠀⠀⡀⠂⠀⠀⠀⠠⣐⢂⡡⠤⠔⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⠁⠀⠀⠈
⠀⠀⠀⣀⡀⠀⡄⡀⠀⠴⠒⠉⠀⡀⠀⠀⠛⠿⠛⠈⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢒⣢⡄⠀⠀⠀⠀⠀⢠⠊⣀⠀⠀⢀⡐⢆
⠀⠀⠀⣷⣶⢶⠷⡶⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⢃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⣿⣿⣽⣽⣷⣤⡤⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⢀⡀⠀⠀⠀⠐⠇⠀⠀⠀⠀⡇⠀⢐⣀⠀⠀⠀⣀⠀⠘
⠀⣶⣶⣷⣗⣖⣶⣾⣿⠃⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠆⠀⠀⠀⠀⠹⡭⠐⣠⣤⣢⣤⠐⢭⠽⠁
⠀⡿⣿⡯⡯⣯⣭⣿⡟⠀⠀⠀⠀⡆⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⠀⠀⡀⢀⣄⣤⡀⠀⠸⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠃⠿⠶⠾⠷⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡽⠌⠑⠀⠀⠀⢪⣿⣷⡴⣿⣿⠃⠀⠀⠀⠀⠀⣀⣾⣿⡿⠿⠟⠛⠿⠿⣿⣷⣂⡀
⠀⠀⠀⠔⠀⢀⠀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠂⠀⠀⣾⣿⣿⣇⠀⢀⣀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠢⠄⠆⠉⠁⠄⠴⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⠁⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠠⠀⠀⡇
⠀⠀⠀⣠⠀⠁⠁⠀⠀⢱⠁⠀⠀⠀⠀⠀⠀⠠⠤⢀⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠙⢀⣒⣂⠤⠘⠀⠀⠀⠄⢐⣒⣀⠚⠁
⠀⠀⠀⠃⠁⠁⠀⠀⠁⠩⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⢠⣀⡄⢷⣾⠾⡅⠀⠀⠀⠀⠀⠀⠀⢚⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⡇⠀⠀⠀⠄⠀⠀⢀⠎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢠⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢴⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠤
⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⣤⣇⣀⠄⠀⠀⢀⣼⣿⡿⠀⠀⢀⣀⠄⠄⠐⢻⣿⣿⢑⣾⠄⠀⠒
⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠭⣖⣊⡭⠽⢟⣿⣹⣿⣿⣷⣶⣾⣿⣛⣁⠀⡁⠤⠠⢖⠒⢀⣈⣻⠃⠘⡁⠀⠀⠒⠀⠤⠄⠁
⠀⠀⠀⠀⡀⠬⠢⠴⠒⠤⠤⢽⣿⣿⣿⣷⣲⣶⣦⡤⠤⡤⠤⢤⣄⣀⣀⣈⣨⣑⣮⣧⣿⣶⡿⠤⠀⢱⠀⠌⠉⠡⠤⠤
⠀⠉⠁⠭⠿⠶⠶⠶⣤⣤⣬⡍⠉⠙⠛⠻⠿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠑⠢⠄⢸⣄⣀⣀⠀⠤⠀⣀
⠀⠀⠀⠐⠚⠉⠓⠀⠀⠘⠛⠩⠟⠓⠂⠐⠓⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠢⠴⠐⠒⠒⠉⠳⠀⢠⣀⣀⣤⡄⠤⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⠿⠿⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣾⣷⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣇⣰⣦⣿⣷⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣶⣿⣾⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⠹⣿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⢻⣿⢿⡯⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣧⡘⠠⢻⡋⢀⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠺⠟⢀⡼⢻⣃⣴⣆⢀⣤⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⢿⣿⣿⡀⢸⣿⣿⣿⡋⠀⠀⠀⠀⠀⢀⢴⣾⡿⠟⠛⠿⣿⣿⣶⣴⣿⣤⣿⡿⢻⣿⠟⣹⣟⢀⠻
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠙⣿⣇⡟⢹⡟⠛⠻⣾⣿⣷⡄⠀⠀⣠⡄⣘⣁⣹⣄⡈⠹⣷⡦⢭⣭⣽⠥⣤⠁⠏⢁⣨⢈⡁
⠀⠀⠀⠀⣀⡼⣿⡦⠀⠘⣻⢗⣶⣷⣄⢸⣿⣧⣾⣷⣷⣦⡀⠟⢿⡿⠀⠀⠤⠴⠿⠏⠛⠿⠟⠷⣿⣏⣛⣛⣩⣤⣨⣤⡾⠛⡟⣿⣿⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠻⠊⠉⠉⢻⠿⠿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠋⠉⠉⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣠⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠒⢿⣿⣿⡟⠋⠻⠟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣀⣄⣠⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠈⢻⣿⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⢿⣿⢿⣿⢿⣍⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⢀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⣿⠀⠙⣼⣿⣿⣾⡿⠛⠋⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣶⣄⢢⢈⡄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠛⠻⠷⣿⣶⡿⢸⠻⣿⢿⣷⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠣⡹⢫⢿⡿⢠⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣰⣤⣤⣄⣉⠿⣾⣾⡏⣾⡁⣸⡇⣤⣌⠛⠳⠀⠀⠒⢀⣀⡀⠀⠄⠀⠐⠒⠚⠋⠀⠀⠀⠀⡼⡁⠈⠀⢻⡏
⠀⠀⠀⠀⠀⠲⠖⠋⠙⠁⠉⠐⠩⠟⠋⠩⣾⠭⠯⠷⠛⠉⠰⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡾⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡿⠁⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣿⠃⠀⠀⢠⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⡿⠀⠀⠀⡄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣺⡇⠀⠀⠀⠁⠀⡜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⣿⡇⠀⠀⢨⠀⠀⠀⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣹⣷⠀⠀⡄⠀⠀⠄⢼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢹⣿⡆⢀⠁⠀⡀⠠⢼⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⢿⣿⡌⠀⠰⠀⠀⣾⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠘⣿⣷⡀⡀⠀⠀⠈⡇⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⢿⣷⡇⠀⠀⢠⣿⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢄⣦⠈⢿⣧⠀⢐⣾⣿⡄⠀⠀⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠉⠺⠾⣿⣧⠀⠁⣿⣶⡀⠀⢉⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢐⣾⣿⣿⣧⠀⢻⣿⣯⣶⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣠⣴⣾⡿⠟⠋⠁⠀⢙⠁⠉⠉⣩⣭⣍⠉⢉⣴⡿⠁⠐⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⢿⣶⣶⣾⣷⡾⠿⣦⣄⣬⡉⣿⢿⠿⠿⠿⡿⢶⣾⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣴⣮⣤⣤⣬⣤⣴⣦⣌⣙⣏⣉⡛⠻⣛⣛⡹⢟⣋⣟⣉⠉⣉⠛⣿⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⣿⠿⠿⠿⠛⠛⠛⠛⠋⠉


⡶⠶⠶⠷⠖⠲⠶⠶⠶⣶⣷⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡶⣶⣶⣶⣷⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⢶

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢀⡄⠀⠠⠀⠃⠀⠀⠘⠀⠄⠀⠠⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⢀⣤⣽⣿⣿⣶⣿⣿⣶⣄⠀⠀⠀⣘⣀⣠⣬⣦
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣼⠟⠻⣿⣿⣿⣿⢷⡄⠀⠈⠀⠰⣶⣿⡿⢿⡿⣿⡷⠆
⠀⠀⠀⠀⠀⣼⠀⢀⠄⠀⣹⠂⠀⠀⣿⠀⠀⡄⠆⠄⠀⠀⠈⠀⠠⠀⠂⠀⣼⠁⠀⠁⠀⢸⣿⠟⣿⣿⡄⠛⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣽⠈⠀⠐⠈⢸⠀⠀⠀⣿⠀⠀⠱⡀⠀⠀⡀⠐⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠃⠀⢻⠈⠁⠀⠀⠀⢐⠀⣴⣯⠛⠻⠙⣿⡟⢶⣄
⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠄⢋⣼⣿⠋⠀⠀⠄⠘⢧⠀⢹⡆
⠀⠈⠛⠛⠛⠐⠛⠛⠛⠛⠃⠛⠛⠛⠈⠀⠀⠀⠀⠈⠢⣀⣀⣀⣠⠔⠁⠀⠀⠠⠤⠠⠤⠀⠀⠀⠸⡆⠀⠀⠁⢠⣿⣿⣿⠀⠀⠀⠀⠀⠈⢷⣼⣷⡀
⠀⠀⣀⣀⣀⣀⣠⡴⣶⣶⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣄⣴⡿⢹⣿⠇⠀⠀⠀⠀⠀⣦⡀⠙⣿⡇
⠀⢀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠈⠁⠀⠘⠏⠀⠀⠀⠀⠀⠀⣿⣿⠢⠾⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⢈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠚⠀⠘⠃⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠠⣤⣴⣋⣤⣀⣀⠀⠀⠀⣸⠁⠀⣇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠀⠀⠀⠂⣲⣶⣶⣶⣶⣶⣿⣿⠇
⠀⢠⣶⡾⣿⣿⣿⣿⣿⣟⠛⢷⠀⢀⡏⠀⠀⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢁⠖⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣿⣿⠋⣿⣿⣿⣿
⠀⠘⠁⢠⡿⢿⣿⣿⣿⣧⠀⠀⠀⡸⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣹⣿⣿⢀⣿⣿⣿⣿
⠀⠀⠀⠸⡇⢸⣿⡏⠉⠿⠇⠀⢀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⣄⣂⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⡠⠀⢤⠀⠘⣰⣿⣿⣿⢸⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠶⠶⣶⣶⠶⠶⠯⣿⣧⣀⣀⡀⠀⠎⠀⠈⠉⠙⠓⠉⠓⠶⠤⠀⢀⠌⠀⠀⡄⠀⠘⠿⠿⣿⠟⠘⠿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠶⠶⠋⠙⠁⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠤⠆⠽⢤⡤⣤⣼⣣⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠂⣁⣤⣾⡿⠟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⠻⠷⣶⣶⣦⣶⣬⡟⠛⠛⠻⡿⠾⠿⠿⠿⠷⠤⠤⠴⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⢾⣿⣿⣄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠿⣦⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠄⢸⡯⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⠀⠀⠀⢰⣶⣶⣶⡦⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⠀⡄
⠀⠀⠀⢀⠀⣿⠁⠀⢀⣀⡤⠴⠖⠈⠒⢄⠀⠀⠀⠓⡐⠺⣿⣿⣿⠀⣿⠀⠀⠀⣸⣿⡿⠛⠑⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠁⠀⣿
⠀⢠⣤⣤⡆⢿⣀⣀⣈⣿⣷⣦⣤⡤⢴⣶⠃⠀⠀⠀⠀⠀⢸⣿⣿⡀⠞⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣐⢟⣽⠊⠩⠭⠭⠭⠴⠿⢿⡻⢆⡿⠑⠀⠠⠀⠀⠀⣸⣿⣿⣗⡂⡠⠀⠀⣀⣀⣀⣀⣀⣾⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣆⣀⣀⣰⠟
⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠙⠋⠁⠉⠈⠉⠁⠉⠈⠈⠉⠉⠉⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠈⠁⠉⠉⠉⣥⢻⣶⣦⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⣠⡀⠚⢂⠀⠢⡾⠋⠉⠲⢿⣿⣿⣶⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣡⣶⣦⣠⣤⣄⡻⠿⠃⣩⠀⠾⢿⣮⡢⡀⠀⠀⠉⠛⠧⣈⠢⡀⠀⠀⠀⠀⠀⡠⠒⠫⠍⡑⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡞⠀⣼⣿⠌⠪⡢⡀⠀⠀⠀⠀⠉⠘⠢⢀⣀⠔⠁⠀⠀⠀⠀⣥⠏
⠀⠀⠀⠀⠀⠀⢀⢊⡾⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣶⣎⣁⠀⠀⠻⠮⡢⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣿⣿⡄⠀⠀⠀⠈⠪⡢⡀⠀⡰⠃⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠰⠀⢀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠙⠀⠀⠀⠀⠀⠈⡢⠊⠀⠀⠀⠀⠀⢀⠔⠑⡀
⠀⠀⠀⢀⠠⠒⠈⠀⠀⢣⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠐⡀
⡠⠶⠬⠤⠤⠤⠤⠴⠶⠦⠧⠬⠿⣿⣿⣿⠋⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⣠⣮⡠⡀⠀⠀⠀⠀⠱⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡏⠻⠧⣤⣄⠀⠀⠀⠀⠀⢀⠔⠉⠁⢐⠎⣠⡄⠀⢀⣴⣿⣿⣿⣿⡮⡢⡀⠀⠀⠀⠡
⡇⠀⠀⣠⢖⡞⢻⠻⡖⢤⡀⠀⡇⡇⠀⠀⠀⠈⠳⣄⣴⣤⣴⣥⣀⠀⣠⣢⡾⢋⢠⠊⠀⠈⠛⠛⠛⢻⠁⠈⠪⡢⡀⠀⠀⠡
⡇⠀⢰⠋⢹⠉⢹⠉⢹⠉⢳⠀⡇⣧⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣧⣭⠂⠁⠀⡄⠀⠀⠀⠀⠀⠌⠀⠀⠀⠈⠪⡢⡀⠀⢃
⡇⠀⢻⠛⢻⠛⢻⠛⢻⠛⢻⠀⡇⡇⠡⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠔⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠪⡂
⡇⠀⠈⢷⡺⡖⢺⢒⡞⣲⠏⠀⡇⡿⢀⣡⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠋⠒⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⢀⣀⣉⣛⣛⣛⣋⣁⡀⠀⡇⡟⠍⢂⠡⠀⠀⠀⠀⢸⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⡀⠈
⡇⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⡇⣿⡌⡄⢂⠡⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⡀⠄⠊
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠌⣒⠥⠆⠤⠀⠘⠿⠀⠤⠄⠐⠂⠁
⡇⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃⡯⠒⠁
⣬⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⡆⠨⠀⠁⣰⠏⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⡴⠢⡀⣀⢠⠋⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠤⠬⣤⡙⡀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠰⠀⠀⠨
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢘
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⠁⢀⢀⠀⠀⠀⠀⠀⠀⢠⣂⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠃⠋⠣⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠈⢧⣀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠁⠀⠐⠨⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⣒⣒⣒⣒⣒⣂⣁⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤
⠀⠀⠀⠀⠀⠀⠀⠓⠒⠤⠤⠤⠤⠤⠔⠂⠀⠀⢀⠰⡀⠀⠀⠀⡀⢀⠀⠀⠀⢀⡌⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠈⢿⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⢦⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠼⠿⠟⠙⠛⠁⠀⠺⢽⣷⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣠⡴⢤⡀⠀⠀⣉⠛⠶⣤⣀⠈⠳⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣠⣾⣭⣷⣿⣿⣿⣶⣄⠙⢦⡈⠻⣷⡢⡀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⣀⣬⡿⠋⠁⠀⠀⠀⠙⣿⣿⣷⣤⣹⣌⢮⣿⡹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡜⣿⣇⣿⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠇⣿⣯⣿⠇⢸⢇⠄
⠀⠀⣀⡤⠶⠶⠿⠷⢿⣿⣷⣦⣄⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣋⣵⣿⣿⣿⣿⣿⠟⢠⡿⣽⠟⢠⢏⠞⣴⣄⡀⢀⠔
⠀⠈⠁⣀⡤⠶⠞⠛⠻⠿⠿⢿⣿⣿⣶⣄⡈⠉⠙⠒⠶⠶⠾⠛⣛⣩⣭⣶⣿⣿⢿⣻⣿⣿⠿⢋⣴⠟⡽⢋⡴⠫⣫⣾⣿⠟⡡⢋⠔
⠀⠀⠈⠀⠠⠴⢒⣛⣛⣛⣓⣶⠦⣬⣙⠛⠿⣶⣄⡀⠠⣭⣍⣉⣉⣉⡉⠩⠵⣶⣛⣛⣭⡴⠾⠋⠁⠀⠀⣀⣤⣾⡿⢛⣥⡮⣖⡵⠋
⠀⠀⠀⠀⠀⠉⠉⠩⠭⠭⠭⢭⣿⣟⣿⠷⣦⣌⡙⠻⢷⣦⣌⣙⠻⢿⣿⣶⣄⡉⠉⠁⠀⠀⠤⠴⠒⡚⣛⣋⣭⠴⢞⣋⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠻⠿⠿⣿⣿⣿⣷⣮⣭⣅⣀⡈⠙⠻⠿⣶⣮⣭⣛⡻⠷⠶⣤⣤⣤⣤⣤⣤⣤⠤⠶⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡨⠄⠤⠤⢀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠔⠒⡀⠐⠀⠄⣠⠀⠰⠆⠚⠓⠃
⠀⠀⠴⣄⡦⠀⠉⠉⣸⣯⣄⣠⣤⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⢀⢠⢠⣆⡠⣽⣗⠒⠛⠣⢖⠴⠢⢀⠘⠂
⠀⠀⣜⠿⠁⠠⡄⠺⠗⢻⡈⢷⡍⠐⠃⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠝⠙⢋⠝⣿⢶⢋⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠋⠁⠀⠉⠂⠀⠀⣸⡏⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢛⠋⠀⣸⠯⢹⡃⠐
⠀⠀⠀⠀⠀⠸⠂⠀⠀⡛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠀⠀⡘⠀⠀⣼⠋⠊⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠦⠶⠒⠞⠀⠀⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣅⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠐⠂⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣏⠈⣉⣉⣉⣐⠉⠉⠒⢶⣛⣗⣳⣀⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠈⠯⢭⣬⢭⠭⠍⠀⠀⠉⡁⠄⣻⢼⣥⠮⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠘⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠉⠀⠀⠀⠀⠑⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢀⡀⡀⢀⡠⡀
⠀⠀⢸⡀⢸⠊⣀⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠓⡄⢀⡀
⠀⡠⠆⠛⣿⣿⠿⠿⠛⠿⣿⣦⣤⣤⣴⣶⣾⡿⢿⡿⠻⣶⣤⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣣⣀⡟⢁⡸
⠀⠙⠒⠚⣿⡗⠀⣴⣶⡆⢸⣿⣿⠿⠿⠿⣿⣷⠾⡇⠀⣿⣿⣿⡿⠛⠛⠻⢿⣿⠟⢿⣿⠟⢿⣯⣉⣉⡢
⠀⠀⠀⠀⣿⣿⠀⠉⠁⣠⣾⣿⠁⣴⣶⠀⢹⣿⠀⡇⠀⣿⣿⡿⠁⣴⡷⠀⣾⣿⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⣷⣄⠈⠻⡏⠀⣿⡟⠀⠘⣿⠀⡇⠀⣿⣿⡇⢰⣿⠇⠀⢻⣿⣇⠈⠁⠀⣿⣿
⠀⠀⠀⠀⠙⢿⣶⣿⣿⣷⣤⣿⣄⣉⣠⣶⣤⣿⣀⣧⡀⠛⠙⣧⡈⠉⣠⣶⣤⣽⣿⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠉⣁⣴⣿⠇
⠀⠀⠀⠀⠀⣼⣿⠟⠛⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣷⣯⣬⣧⣼⣾⣽⣼⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠀⠀⠀⠀⣿⣿⠀⣾⣿⠿⠁⣼⣿⣿⠿⠿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣦
⠀⠀⠀⠀⠀⣿⣿⠀⣿⣤⣤⣤⠉⣿⠁⣴⠆⢸⡟⢠⣶⡄⠘⣿⠏⣠⣄⣙⣿⠀⠿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⢿⣿⡆⠹⠿⠿⠛⢀⣿⠀⢤⣴⠾⡇⠸⣿⠃⠀⢿⠀⣿⣿⣿⡇⢀⣶⡆⠘⣿⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠻⢿⣶⣶⣶⣾⣿⣿⣷⣤⣤⣴⣿⣦⣤⣴⣷⣾⣧⣈⣉⣨⣧⣼⣿⣇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠉⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⡿⠟⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠈⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠗⠀⠀⠀⠠⠀⠀⠄⡄⠈⡅⠀⠀⠠⠀⠀⠀⢠⢀⡃⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠀⠀⣀⠀⠀⠇⢴⡤⠀⢀⠀⠀⠀⠀⡈⠌
⠀⠀⠀⠀⠀⠀⠄⠀⠉⡀⠈⠁⠘⠃⠀⠀⠀⠄⠀⠀⠀⠠⠤⠀⢀⡐⠁⡼⠀⠤⠤⡄⠀⣠⠇⠀⠹⢠⠁⠆⠀⠰⣀⣀⠀⠴⢴
⠀⠀⠀⠀⠀⡐⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⣀⣀⠀⣰⣭⠀⠄⠾⠀⠞⠑⠀⣂⢀⡦⠴⠆⠑⠚⠁⠗⠐⠂⠂⠈⠍⠀⠐⢀⡆⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠹⡃⠀⠀⠤⠀⠀⠐⠂⠀⠀⣘⢁⠍⠁⠀⠀⠀⠀⠀⠌⠀⠉⠉⠀⠀⠤⠴⠀⠀⠀⡰⠄⣀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⣀⠠⠐⠢⢀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠈⠁⠐⠀⠠⠔
⡠⠀⠂⠁⠀⠀⠀⠀⠀⠉⠐⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠉⠀⠂⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠄⢠⠴⢦⡤⠀⢀⡤⢦⡀⢀⡴⢦⡴⠀⢶⠷⠆⡤⠀⢀⡤⠦⡄⠀⢠⡤⠶⡄
⠀⠀⠀⠀⠀⠀⡼⢀⣠⠏⢰⠃⠀⣼⠁⢠⠏⠀⠘⢡⠏⠀⣰⠃⢀⡏⠀⣰⠃⢀⡞⠀⣠⠇⢠⡟⠀⢰⠃⢀
⠀⠀⠀⠀⠀⢰⠃⣸⢯⡤⣏⢀⣰⡇⣠⢿⡀⠀⣠⣿⠀⣰⡏⢀⣾⠀⣰⡏⢀⣾⠀⣠⢯⣤⡞⠀⠀⡏⢀⡞
⠀⠀⠀⠀⠀⠈⢉⣡⣤⣤⣈⣩⣤⣍⡁⠀⠉⠉⠁⢈⡉⠁⢉⣍⠈⠉⡁⠉⠁⠈⠉⢁⣠⣤⣅⣀⣤⣭⣍⡀
⠀⠀⠀⠀⠀⢠⠿⠟⢛⣿⣿⣿⣿⣿⣷⠀⠀⣀⡀⢨⣿⠆⠾⠿⠠⣶⡿⠀⢀⡀⠀⣾⣿⣿⣿⣿⣿⡛⠻⠿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⣿⡻⣿⡍⠀⡀⢹⡟⣨⣶⣾⣿⣿⣷⣶⣄⠻⡿⠃⠀⢩⣿⢟⣿⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠛⠋⢸⠁⣿⡇⠙⠇⠙⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣷⡶⠸⠛⢸⣿⠈⣇⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠸⠇⠀⢠⣶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣶⣄⡀⠀⠸⠇⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣄⠀⠀⠀⠀⢈⣩⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣝⠉⠁⠀⠀⠀⢠⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣤⣀⠀⠀⠛⠛⢃⡹⣿⣿⣿⣿⣿⣿⣿⣿⢟⡘⠿⠶⠀⠀⣀⣤⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠰⠿⠿⠊⠙⠛⠿⠿⠛⠋⠁⢿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢰⣶⣶⡀⠀⠀⢀⣶⣶⡆⠀⢀⣠⣶⣶⣶⣶⣤⡀⠀⢰⣶⣶⣶⣶⣦⣄⡀⠀⢰⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⢀⣾⣿⣿⡇⢀⣾⣿⡟⠋⠙⠻⣿⣷⡄⢸⣿⣿⠉⠉⠻⣿⣷⡄⢸⣿⣿⣉⣉⣉⡁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⠘⣿⣿⠃⣿⣿⡇⠈⢿⣿⣷⣤⣤⣾⣿⡿⠁⢸⣿⣿⣤⣤⣾⣿⡿⠁⢸⣿⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠘⠛⠛⠀⠙⠋⠀⠛⠛⠃⠀⠀⠉⠛⠿⠿⠛⠋⠀⠀⠘⠛⠛⠛⠛⠛⠉⠀⠀⠘⠛⠛⠛⠛⠛⠃

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

⠀⠀⠀⠀⡜⠁⠠⠒⣀⠀⢠⠀⠀⡄
⠀⠀⠀⠀⠁⣀⢀⣚⣼⠃⠀⠁⠀⡆
⡀⠀⠀⠄⡀⠈⠉⠙⠀⣀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿
⠀⣀⠀⠀⠈⠀⠁⢲⠆⠁⢀⡔⠁⠀⠒⠀⡆⠀⣀⣀⠂
⠓⠚⠱⠀⠀⠀⠘⢸⠁⡰⠋⢀⣭⢁⡀⡀⢠⢬⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡞⠀⠀⢀⠀⡼⠠⠀⣀⣨⣽⠏⣉⣴⠿⠛⠓⠛⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠆⢠⢠⠂⠀⠌⣼⣊⡡⠤⢠⣾⣵⠾⠋⠀⣀⡤⢤⡈⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢰
⠀⡴⠁⠀⡜⣰⠟⠟⠘⣠⠏⣼⠃⠀⠀⡸⠁⢀⡀⣳⠀⠀⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⡞
⢸⡇⠀⠀⢰⠏⠀⠀⢠⠏⣴⠃⠀⠀⠀⢣⠀⢰⣛⣁⡠⠐⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠞⠀⠐⠇
⡞⠀⠀⢐⡣⢀⠀⢠⡿⡘⢿⠀⠀⠀⠀⠈⢢⡀⠀⠀⣀⣤⡀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣆⠈⠐⠋⠉⠛⢶⡄
⡇⠀⠀⠁⠰⠁⠀⢸⠁⠃⠸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠁⠋⠛⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⢶⢒⣤⢀⡔⠃⠈⠉⠀⢀⣤⣤⡄⠀⡫
⡅⢀⠰⢰⡇⠀⠀⡄⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠞⠋⠍⡐⠢⣀⠀⡈⠛⠉⠉⠁⠐⢄⡀⠀⠈⢯⡀⠎⠀⡀
⣿⠌⠆⣨⠀⠀⠀⣷⠐⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠊⠁⣠⠾⠡⢄⢐⠤⠀⢹⡎⠀⠀⠀⠀⠀⢀⠀⠈⡆⠀⠀⠀⠀⠙⠢
⡇⠀⢡⠃⠀⠀⠀⢹⡢⣀⠀⠀⠢⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠀⠀⠀⠀⠳⠆⢂⢰⡇⠀⠀⠀⠀⠀⠘⠃⠐⠉⠀⠀⠀⠐⠂
⣏⠀⠀⠀⠀⠐⠀⠀⣷⠈⡀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠂⠠⡤⠖⠚⠉⠉⠀⠀⠀⠀⠄⠂⠀⠀⠀⠹⡆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢿⣀⠎⠀⠀⠀⠀⠘⠈⢷⡀⠀⣀⡀⢀⡀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⣀⡈⠑⡀⠄⠀⠠⠠
⠈⢃⠀⠀⢀⠈⠀⡀⠃⠀⣙⢶⡀⠀⠀⣀⠄⠀⠀⠀⠑⠒⠤⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⠈⠉⢦⠱⣆⠀⠀⠐⢦⡤⠤⠀⠀⠀⡀⠠⠴⠒⠂⠂
⠀⠈⠀⠀⠆⠀⢀⠀⠀⠀⢀⠀⠙⠳⢶⣌⠂⠈⠉⡈⠤⠊⠀⠀⣀⠠⠔⠁⠊⠀⠀⠀⠐⠈⠉⠙⣗⣿⠀⠀⠀⡀⠑⢦⡀⠀⠈⠀⠐⠂⠄⠀⠀⠀⠒
⠆⠠⠰⡀⠀⠀⠀⠀⢠⠀⢆⠑⠄⠁⠀⠉⠛⠛⠛⠶⡲⠒⣸⠛⣁⠐⠃⣀⠀⠀⠀⢀⠠⠐⠀⠀⢌⡜⡄⠀⠂⠀⠀⠀⠀⢀⠀⠒⠒⠖⡒⢀
⠀⠀⠈⢻⡇⠀⡀⠄⠂⠁⠄⠀⠀⠀⠀⢀⠀⠀⣀⠔⠁⢠⠃⠔⠁⠀⠀⠀⢀⡠⠀⠀⠀⡠⠔⠀⠉⠙⠳⠂⠀⠀⢀⡀⠤⠬⠋⠀⠈⠁⠀⠈⠓⠀⣀
⠀⠀⠀⠈⠻⣦⠁⠀⠀⠨⠠⠀⠀⠀⠀⠀⣈⠉⠀⠀⠀⢁⠂⠀⢀⣀⠀⠈⠁⣀⡤⠂⠁⠀⠀⠀⠀⠀⡀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⢱⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⢎⠙⠑⠒⠒⠋⠁⠀⠀⠙⣦
⠉⠁⠁⠢⡀⠀⠀⠉⠳⣄⠀⠳⣕⠀⠁⠀⣀⠠⠤⡤⣐⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢡⠀⠀⠀⠀⠁⣄⠐⠀⣸
⠀⠀⠀⠀⠘⢄⠢⢄⣀⣀⣙⠷⠾⠷⠤⠤⡬⠥⠶⠒⠙⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠻⠯⠀⠐⠁
⠀⢈⢀⠀⠀⢀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⡀⡂⡀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⡀
⣿⢿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣿⣿⣿⢿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⢤⣩⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠸⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⢧⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⢸⡀⢣⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡇⠀⠀⡇⠈⡇⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⠀⠀⡇⠀⢹⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡇⠀⢰⠃⠀⢸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⡇⠀⡼⠀⠀⠈⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢠⡇⢠⠃⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣶⣦⣥⣶⣶⠿⡿⠭⠿⠟⠛⠒⢲⣼⣿⣧⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⣒⣋⣉⣁⣠⣤⣤⣤⣶⣶⣶⡿⠿⠟⠛⠉⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⣉⣁⣠⡤⠤⠤⠖⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⢀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣏⣀⡀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣷⣆⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢩⣿⣿⡿⠙⣿⡍⠉⢩⣤⣶⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠘⣿⡆⠀⠉⠙⠛⣻⡿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠋⠀⠀⠀⠀⠘⣿⡄⠀⣠⡾⠋⠀⣿⣿⡆⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣰⡟⠀⠀⠀⠘⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠿⠟⠿⠋⠉⠉⠉⠉⠉⠛⠒⠒⠠
⠀⠀⠀⠀⠀⠂⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣤⡄⠀⢀⣤⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⣤⡄⠀⢠⡄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠀⠀⣾⢿⣇⠀⠀⠀⢠⡿⠉⠀⠀⠀⠀⢸⡿⣷⠀⠈⢻⣆⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣸⡇⠀⢰⡿⠈⣿⡀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣿⠃⢻⡇⠀⠀⠹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⠁⠀⣾⡇⠀⢹⣇⠀⢸⡏⠀⠀⠀⠀⠀⢰⡟⠀⠘⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡏⠀⢛⣿⠛⠛⠛⣿⡀⠘⣿⢀⠔⡄⠀⠘⣿⡟⠛⠛⢻⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⢸⡟⠀⠀⠀⠸⣧⠀⠙⣿⣄⣇⡀⠀⣿⠀⠀⠀⠈⢿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⢸⡇⢩⠉⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⠇⠆⠀⠀⠀⠀⠀⠀⣸⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠆⠀⠀⣍⠀⣿⡔⠀⠀⠀⠀⢀⡠⡄⢿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠃⠸⠀⠀⣸⡇⠀⣿⠃⣠⣦⠀⢀⣾⠃⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠠⠂⢸⡇⠀⢻⡤⠃⢻⡇⢸⣿⠀⠀⠈⣿⡄⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠁⠀⠀⠈⠧⠈⠀⠁⠀⣿⠁⠀⠙⠓⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢽⠏⠀⠀⠀⠀⠀⢰⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠈⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠸⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡔⠆⠀⠐⡈⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⢄⠘⠕⢌⣂⠣⠀⣀⡶⢂⣀⡀⣀⠀⢰⡟⠿⠞⢻⠉⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣛⠤⢀⠨⠞⠫⡥⠀⠀⣠⣄⠀⠀⡿⠁⠠⣀⣤⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⢀⠖⠂⠀⠊⠡⡄⠀⠀⠀⠐⢸⡄⠸⢃⣰⢿⠔⠊⠀⠐⣲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢘⢡⡴⠚⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠸⠉⠗⠶⠴⠼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⡟⠂
⠀⠀⠀⠀⠙⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠓⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢀⡴⠻⠿⢿⣶⣤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣭⠞⢡⠶⠶⣄⠀⠈⢙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⡸⣟⠀⠀⠀⠑⠀⢠⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⣠⣿⣶⠶⢂⡠⢂⣴⡵⠁
⠀⠀⠀⠀⠀⠐⠲⠦⠀⠀⠤⠤⠴⠶⠖⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡉⠉⠠⡀
⠀⠀⠀⢀⣠⣤⠶⠶⠦⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠁⠉⠀⠀⠁⠀⠀⡐⠀⣐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠴⠦⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⢀⢀⡴⠛⠛⠓⣮⣦⣰⠶⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⢇⡠⠖⠑⢛⢀⠂⠢⡄⣸⠟⣿⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠍⠐⠊⠀⠰⠶⠟⡿⠖⢄⠑⠉⠉⡠⢓⠐⠒⢚⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⣇⠀⠀⠇⠀⠀⡉⠈⠉⠈⠛⠛⠗⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⣄⣀⣀⠀⠀⠐⠂⠒