Cry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣠⢤⡀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⡔⠊⠛⠁⠀⠋⠁⠀⠈⢱⠴⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⡞⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢸⡄⣴⠋⠉⠓⠀⢀⡞⢡⡟⠉⡷⢤⠀⠀⠀⠀⠀⠀⠀⣠⢤⡤⢤⣀⡀⣏⢀⡴⠒⣤⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⡠⠟⣠⠞⠀⡼⠀⣸⠛⠃⠀⠀⠀⠐⠻⡇⠀⡇⠀⡇⠹⡍⠉⠀⠀⣸⠀⡟
⠀⠀⠀⠀⠀⠀⢠⠇⠈⣷⢹⠏⠀⠊⠀⡠⠚⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢳⡀⠱⡀⠡⡀⠹⣴⠒⢲⣏⠀⡗
⠀⠀⠀⠀⠀⠀⢿⠀⡞⠙⡟⠀⠀⠀⠀⠀⢠⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⠀⠀⠙⣴⢃⡸⢀⡷⣄
⠀⠀⢀⡠⠶⠒⠻⡄⢳⠄⡧⠀⠀⠀⠀⢠⡞⢁⠤⠀⢠⠀⠀⠀⢐⠀⠀⣀⠉⡆⠀⠀⠀⠀⠀⣿⠈⣷⠋⠀⠈⠳⣄
⠀⢠⠟⠀⠀⠀⠀⠹⣧⣾⠁⠀⠀⠀⠀⣸⠁⠠⠂⠀⠈⠲⠤⠔⠊⠀⠀⠇⢱⡏⠀⠀⠀⠀⠀⣞⠀⣿⣀⠀⠀⠀⢹⡆
⠀⢸⠀⠀⠀⠀⠈⣹⠁⡏⠀⠀⠀⣀⣴⡏⠀⡀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡿⠙⠻⣄⠀⠀⠀⢸⡇
⠀⢸⠀⠀⠀⠐⠚⠃⠀⣇⠀⢀⠞⠁⢸⠃⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠲⣄⠀⠀⣰⠃⠀⠀⠈⠂⠀⠀⣼⠃
⠀⠀⢧⡀⠀⠀⠀⠀⠀⢸⡴⠋⠀⢀⡿⠤⣀⡴⢤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠞⠙⣆⠈⠳⡴⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠳⣄⢀⡾⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⣨⠷⣾⡁⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠘⢦⣄⣀⣀⣀⣠⡤⠞⠛⣇⠀⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠛⠶⠦⢤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠁⠈⣇⠸⡏⠙⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠖⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⡟⠀⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⠓⠲⠶⠶⠶⠒⠛⠋⠉⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡟⠒⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣄⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡑⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠀⠀⠀⠀⠀⠀⢰⡟⣴⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⣀⣀⣀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⡇⢀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣼⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⡇
⢴⣂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⢟⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠘⣿⣧⡀⠠⡀⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⡤⠀⠀⠀⠈⡨⠄⣉⠀⠀⢠⡶⠂⠀⠀⠀⠀⠉⠙⠂⠀⠘⠿⣿⣷⣷⠧⠼⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢳⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⠀⠀⠙⠦⡽⢂⡀⠈⣿⣹⡗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⠀⠀⠀⠀⠀⡠⢀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠙⡄⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⠀⠀⡴⣡⣿⣿⣌⢦⠀⠀⠀⢀⡤⠶⢖⠗⠀⣠⠃⠀⠀⠀⢀⣉⣤⣾⣿⣿⣿⠳⡀⠱⢌⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣽⣒⠋⠉⠑⠢⠤⠠⠘⠁⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⢒⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠎⠀⠀⠀⠀⠀⠀⠈⠘⠿⠻⠿⢿⣿⢿⡟⠰⡀⣈⠖⠋⢀⡞⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣠⠄⣀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⠁⡄⠐⠋⠀⠀⠀⡄⠉⠉⠛⠛⠋⠉⠋
⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡐⠀⠀⠉⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡰⠃⠀⠚⠃⠀⠀⠀⣶⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣀⠀⣸⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠞⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⢈⡽⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡄⠀⢇⠀⢀⡤⠖⠒⠦⢄⡤⠄⠛⠚⠒⠘⠁⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⣀⡤⠖⠀⠀⢲⡀⣀⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣭⣥⣤⣤⣤⣤⣼⣷⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⢤⣠⠴⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢳⡀⠀⠀⠂⠀⠀⠀⠑⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠞⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠖⠲⠴⠴⠖⠋⠁⢀⠀⠀⠀⠀⢀⡀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣀⣤⡾⠋⠀⠀⠀⠀⠈⢿⣶⣤⣀⠈⠳⣄⠀⠁⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣀⠔⢁⣠⣴⠾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣮⣝⡲⢄⡀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠖⡻⡏⠡⠚⠋⠉⠀⠀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠉⠛⠛⠛⠓⠎⢰⣄⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠁⡇⠀⠀⠀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠀⠀⠀⢸⠀⠐⠄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⣠⠊⠙⡇⠀⠀⢀⣤⣶⣿⡿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣾⣿⣷⠶⠖⠂⢸⠖⠒⠢⡀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠃⠀⠙⡏⠀⠈⢩⣿⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣹⣿⠟⢰⠇⠀⠸⠀⠀⠀⠱⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢇⠀⠀⢰⠀⠀⠙⢦⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠞⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢆⠀⠸⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⡇⠠⠀⢀⠆⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠑⡈⠓⠒⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⢅⣀⠴⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠀⠀⢸⡄⠀⠀⠀⠇⠀⠈⠀⠀⠐⠤⠄⠀⠂⠤⠀⠀⠀⠀⠀⠸⠂⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢹⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡘⠀⠀⠀⠀⢠⠹⣄⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⡄⠈⢳⡀⠀⠀⠀⠐⠛⠛⠛⠒⠛⠛⠛⠃⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⠄⠀⠀⢠⠀⠀⠀⠉⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣦⠊⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠳⠦⣤⣤⠴⠚⠁⠀⢸⡇⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣢⠞⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡷⢤⣀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡋⠁⠀⠀⣀⣀⠤⠒⢸⠃⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹⠒⠤⣄⣘⠄⠈⠉⠉⠉⠉⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡩⠟⠋⠉⡏⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⢉⠙⠳⢦⣄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠓⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠒⠒⠒⠦⣴⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠐⢀⣀⣀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢳⡀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢴⣶⣦⣄⠀⠀⣠⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠁⠀⠀⠀⢠⠞⠀⠀⡞
⠀⠀⠀⠀⠀⠸⠟⠋⠀⢀⡏⠀⠀⠀⠀⠘⡖⠋⠉⠉⠉⠒⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⢶⡁⠀⢀⡜⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⣶⠋⠀⠺⠷⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⠀⠀⠀⠈⡅⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢧⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢡⠀⠀⠒⠶⠿⠾⣷⡄⠀⠀⠀⣀⣀⡀⠀⠀⠾⡿⢭⣤⣄⠀⠈⣧⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠤⣄⡀⠀⠀⢸⠀⠀⠀⢦⠀⢰⡀⠀⠀⣴⠋⠁⠈⠙⢦⠀⠀⢱⠀⠀⡇⠀⠀⠸⠚⠉⠉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢤⡙⢦⣀⠎⠀⠀⠀⢀⠅⠀⡇⠀⢰⠃⠀⠀⠀⠀⢸⡆⠀⢼⠀⠀⢸⠀⠀⠘⢴⠷⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⡁⠀⠀⠀⠀⠀⠀⡏⠀⣴⠁⠀⣾⠀⠀⢀⠀⠀⢸⠀⠀⠈⡆⠀⢣⡀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣃⠀⠀⠀⠀⠀⠀⣱⠀⠈⢦⠀⣿⡴⠋⢉⠟⠀⣾⠀⠀⢼⠁⠀⢸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠀⠀⠀⡖⠁⠀⡴⠋⠀⡟⠀⠰⡇⠀⠀⡇⠀⠀⠈⢢⠀⠈⢦⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣷⠀⢀⡷⠀⠀⣧⠤⠶⠛⠛⠛⢛⡇⠀⢠⡏⠀⠀⡎⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣇⡀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢳⣀⣤⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⠤⢤⣤⣤⠤⠴⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠛⠛⠛⠛⠛⠛⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠶⣦⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⢰⣟⠻⠿⠇⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀
⠀⠀⠀⠀⣹⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⢀⠀⠀⢻⡄
⢠⡿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡾⠀⠀⢀⡇⠀⠀⢸⠀⠀⠀⣷⠀⢸⡄⠀⠈⣿
⣼⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⠁⠀⠀⣸⠀⠀⠀⣼⠀⠀⠀⡇⠀⠸⡟⡄⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢠⡞⠛⠦⡀⠀⠀⣸⠇⠀⠀⠀⣸⠃⠀⠀⢠⡏⠀⠀⠀⡇⠀⠀⢰⡇⠀⢰⠇⠸⡀⢸⣇⣀⡀
⣿⠀⠀⠀⠀⠀⠀⢹⢿⠉⠉⠀⣰⣿⠀⠀⠀⣰⡇⠀⠀⠀⡾⠀⠀⠀⡼⠀⠀⠀⣸⣇⣠⠞⠀⠀⠇⢼⡯⠤⠿
⢻⡄⠀⠀⠀⠀⠀⢈⠸⣄⣠⠾⠁⣿⣀⣀⡴⠙⣇⣀⣠⣾⠁⠀⢀⣴⡇⠀⠀⣰⠇⣀⣀⠀⠀⠀⣴⢾⡇⢀⣄⣄⡀
⠸⣧⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⠀⣨⣽⣷⠶⢦⡈⠉⠁⠈⠓⠚⠋⠀⠙⠒⢚⠵⢋⡽⣍⠙⡆⠀⢠⣼⠇⠈⠓⠶⠃
⠀⢻⡄⣾⠛⢛⠢⣄⡧⠀⠐⢂⣜⣡⠾⠟⠳⣤⡇⠀⠀⢀⣤⠤⣤⡀⠀⠀⠘⠲⣏⠉⠙⡞⠁⠀⠀⣿⡀
⠀⠈⣷⠘⠲⢬⣗⠀⠀⠀⠀⠀⠀⢙⠀⠀⢞⠀⠀⠀⣰⠋⣀⣀⡀⠙⣆⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⣾⠁
⠀⠀⣿⠀⠀⠀⠈⠳⢚⠇⠀⠀⠀⢿⠀⠀⡼⠀⠀⠀⡟⠉⢁⣤⠿⠀⢸⡄⠀⠀⡧⠀⠈⡇⠀⢀⣴⠏
⠀⢠⡿⠀⠀⠀⠀⠘⠛⠳⢤⣀⠀⢰⡀⠀⢸⠂⠀⢀⡀⠀⣀⢈⣦⣠⣤⠇⠀⢰⡁⠀⠘⣧⣴⣟⠁
⠀⢼⡇⢀⣾⠁⠀⢰⠀⠀⠀⡉⠛⠶⢦⣀⣸⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⢀⣥⡤⠞⡋⠀⢻⡄⣀⣴⠾⠷⠤⣤
⠀⠈⠛⠛⠛⠷⠶⠛⠻⠶⠞⠷⠶⢦⢶⣬⣭⣛⡷⠶⣄⠀⠐⠶⠶⣶⢶⡖⠛⣫⣡⠶⡼⠟⣶⡾⠟⠋⣠⡴⠾⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⠉⣳⢄⠈⠙⣦⣴⠚⠁⣀⡽⠛⠻⠶⠖⠚⠋⣁⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⣠⣤⡏⠈⠳⠞⠁⠈⠳⠚⠉⣇⣀⣀⣤⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡾⠋⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠛⠦⣄⠀⣼⠃⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠟⢰⡏⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣀⣀⣀⣀⣀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣹⠉⠉⠉⠉⠁⢹⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⡿⠀⠀⠀⠀⠀⠸⣇⣿⡄
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠿⠟⠛⠛⠛⠻⠿⠶⢶⣦⣤⣄⡀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⣿⡏⠹⣧⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⣿⡿⠛⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⢀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠁⢿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢀⡾⠋⣿⠀⠀⠀⠀⠀⢀⡼⠋⣿⡀⠀⠀⠀⠀⣼⠃⢻⡄⠀⠀⠀⠀⣰⠿⢦⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⣠⡤⣤⣄⠀⠀⠘⢿⣄⣀⣀⣠⡶⠋⠀⠀⠘⣧⡀⠀⢀⣠⠞⠁⠀⠘⢷⣄⣀⣠⡾⠃⠀⠀⠻⣦⣀⣤⡾⠃⠀⠀⣰⡏⠀⣾⣟⣻⡆⠀⢀⠀⠀⠀⠀⣼
⠀⠀⠻⠦⠴⠿⠃⠀⠀⢰⡟⠉⠉⠁⠀⠀⢤⣀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⠀⠀⣀⡉⠉⠀⠀⡟⠀⠀⠀⣸⡟
⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⡇⠀⠀⠀⢤⣤⣀⣉⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣀⠀⠀⠀⣿⠀⠘⢿⣹⡧⠀⢰⡷⠛⠉⠉⢻⣇
⠀⠀⠀⣾⣻⡿⠋⠀⠀⣼⠇⠀⠀⠀⠀⠈⢉⣉⣛⣻⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣛⡛⠛⠋⠁⠀⠀⠀⣿⡀⠀⠀⠉⠀⢠⡟⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠉⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⣺⠟⠉⠉⠉⢻⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠸⣏⠉⠛⠛⠳⡶⠄⠀⠀⠘⢷⣄⣀⣠⡴⠛⠛⠛⠀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣴⠋⠀⠀⠀⠸⠛⠁⢀⠈⠻⠄⠀⠀⠀⢸⠋⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠉⠉⢡⣴⣶⡶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠹⡄⠀⠀⠀⠀⠚⠘⠊⠓⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠈⢿⡀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢰⡟⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢹⡄⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⣤⣈⣷⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢻⠀⠀⣀⣠⣤⡶⠟⠁
⣾⣿⠛⠿⠿⠿⠿⠶⠿⣿⡟⠛⠛⠛⠛⠿⠿⠶⢾⣷⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⣴⠾⠿⠟⠛⠿⣷⣤⡀
⠈⠛⠿⢶⣦⣤⣤⡤⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠶⠶⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⢻⣇⣿⣄⣠⣤⣿⣦⣤⣀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣤⡀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢻⡆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡴⣾⡃⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠁⠘⣷⣀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⡶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⣙⣿⠄
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⠈⢉⣈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠻⠿⣷⣄⡀⠀⠀⣀⣀⣤⣶⣿⠀⡀⠰⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣵⡾⢛⡽⢚⣭⡽⠿⠿⠿⠾⠿⠿⠿⠿⣿⣷⣿⣿⡿⢟⣫⡽⠟⠁⢸⡇⠈⢦⡹⣎⢿⣿⣿⣿⣿⣿⣿⣿
⠟⢠⠏⡴⠋⣡⣶⣾⠿⠛⠛⠛⠛⠛⠛⢛⣉⣩⣵⡶⠛⠉⠀⠀⢠⣿⣧⠀⠀⢻⡽⡌⣿⣿⣿⣿⣿⣿⣿
⢀⠏⡾⢡⣾⠟⣩⣴⠶⠾⠿⠿⠿⠛⠛⠛⠉⠉⠀⢳⠀⠀⠀⢀⠉⣁⣿⡆⠀⠈⣿⣷⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠁⠀⠀⠀⢀⡿⣿⢻⡽⡇⠀⠀⢻⡿⡆⣿⣿⣿⣿⣿⣿
⣿⣿⣷⢹⠃⠀⠀⠀⢀⣠⣤⣶⡶⠿⠿⠟⠋⠀⠀⠀⠀⠀⠘⡟⠴⠋⠀⣧⠀⠀⢸⣇⢳⠹⣿⣿⣿⣿⣿
⣹⣿⣿⢸⠀⠀⠀⠖⠋⠉⠀⢀⣠⣤⣶⡶⠶⢦⠀⠀⠀⠀⠀⠹⣄⠀⠀⠸⡆⠀⢸⡿⣾⣧⠸⣿⣿⣿⣿
⣿⣧⣇⡏⠀⠀⠀⠀⠐⠺⣟⡛⠏⣻⣣⠧⠚⠂⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⣿⣤⣿⠃⢹⡟⡆⢻⣿⣿⣿
⠸⡞⣼⢳⡄⠀⠀⠀⣀⣀⣨⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿⠻⣆⠀⣿⣿⢸⣿⣿⣿
⡆⢿⢿⡀⣷⠴⠚⠉⠁⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡔⠀⣿⠀⠀⠹⡆⣿⣿⢸⣿⣿⣿
⣷⢸⡸⠷⠃⣀⡴⠒⠚⠛⢧⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⡟⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿
⣿⢸⢋⡿⢩⠓⠒⢦⣴⠟⠛⠛⠶⠦⠬⢷⣄⡀⠀⠀⠀⠀⠀⢀⡤⠶⡞⢸⡇⠀⠀⠀⣿⣿⡿⣸⣿⣿⣿
⡇⣸⠻⣧⡈⠳⣤⠞⠁⠀⢀⣀⣀⣀⣀⣀⠀⠙⡆⠀⣀⣤⣒⡥⠾⠋⣿⢸⠀⢀⣠⣼⡟⣼⢇⣿⣿⣿⣿
⢡⣇⠀⠙⢿⡾⠃⠀⢀⡔⠉⠉⠉⠉⠉⠉⠁⠀⣿⠙⠛⠯⣤⣤⣤⡾⠃⢸⣾⣿⣿⣿⢁⣿⢸⠟⠋⠙⠛
⡿⢿⣧⣀⢠⠇⠀⢰⡿⠀⠀⣀⣤⠴⠞⠋⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⢸⡏⢠⡶⠶⢶⡄
⠀⠀⠙⢿⣿⠀⢠⣿⠁⠀⣰⠁⠀⠀⣀⣠⠔⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⡟⠀⠈⣿⠀⢸⣇⠘⠀⠀⢸⡇
⣤⡀⠀⠀⣧⢴⣏⡇⠀⢰⡏⠀⢠⡟⢿⠀⠀⠀⠀⠀⣿⢶⠶⠶⢶⣾⠉⠀⠀⠀⢿⡄⠈⢿⣦⣀⣀⣉⡴
⡛⠿⣷⣦⡀⠀⠙⣷⠀⣸⡇⠀⢺⠀⠀⢰⠀⠀⠀⠀⣿⣿⣷⣤⡀⠙⠷⣤⣀⡀⠈⠻⢶⣤⣭⣭⠽⣳⣖
⠻⢶⣌⠻⣷⡀⢀⣨⡴⢧⣿⡀⢸⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣚⠵⣫
⠀⠀⠈⢳⡌⣷⡸⣿⣦⠈⢻⠹⠏⠀⠀⡾⠀⠀⠀⠀⠈⣿⡿⠿⠙⠀⠉⠙⠛⠻⠿⢯⣭⣟⣺⠭⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⢠⡁⠀⢌⣷⠠⠀⠰⠥⠀⠀⢤⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠖⠀⠀⢠⠖⢋⡤⠂⠉⠀⠉⣢⣦⡀⠀⠀⠈⠒⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔⡚⠃⡰⠋⢠⣎⡀⢠⣊⣿⣤⣷⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠹⠀⠀⠀⠉⠀⡰⠁⢰⣣⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠁⠀⣿⣿⣿⣿⣿⣿⢋⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠄⠘⣿⣿⣿⠿⠿⠿⢿⠿⠟⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡀⠀⠿⠉⠀⠀⠀⡀⣀⠀⣀⠤⠼⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠒⠀⠀⠥⠐⠛⠈⣉⠉⠛⢛⣋⡨⠇⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡠⠤⠔⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⣀⠠⠄⠒⠈⣠⠀⢷⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠴⠒⣀⠈⠅⠒⠹⠓⠀⢉⣀⡤⠤⠐⠒⠚⠘⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⠯⠦⠞⠀⠀⠀⠀⢷⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠀⠀⢠⡤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⠐⠊⠉⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠠⠔⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣄⠀⢀⣀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣀⢹⡆⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁⡉⢦⢀⡀⠀⢡⠀⣳⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠈⠀⠜⣸⠏⠓⢮⣤⠷⡋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⠀⠀⡀⠀⠈⠿⠀⢠⠃⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡃⠀⣡⠄⡕⢢⠀⠀⠀⠘⢄⠀⠀⠀⢸⠸⣀⣴⢲⠋⠛⢌⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠥⠀⠀⠸⠥⠴⠆⢄⠈⠐⢦⠱⠓⠊⢹⠾⢉⠸⠀⠆⠀⠈⡆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠠⢃⡄⠀⠠⢶⠃⢸⠀⠀⠀⠱⣷⣊⣁⠀⠀⠀⠤⠄⠶⢶⡗⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⠔⠁⠀⣠⠣⣄⣀⠴⠃⠛⠛⠩⣉⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣄⠤⠚⠉⠀⠀⠒⠒⠂⢄⠀⢄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢸⠃⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣫⠟⢫⠞⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⢀⣄⠀⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⡀⣠⣯⣿⣵⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣯⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣽⣿⣿⣻⣍⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣵⣿⣿⣻⠏⢰⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⣫⣿⣿⠿⠋⠁⢀⣸⣿⣿⣿⡏⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣥⣴⣾⣿⡿⠋⠁⠀⢘⣦⠂⢙⣿⣿⣿⢀⢨⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣿⣿⣿⡾⣾⡿⣻⣿⢧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⢰⣿⣵⣿⠻⠂⡄⠅
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⣼⣿⣿⣠⣿⣿⡿⠁⠀⣶⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣶⡶⠦⠾⠛⣶⣤⣿⣿⡿⣿⡿⠋⠨⡬⢻⠋⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⣀⡼⠋⠋⢀⣼⣿⣿⣿⣫⣿⣿⠋⠁⠀⠀⠀⢀⡘⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣤⢞⣿⠁⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡸⡟⠷⣅⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠉⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣤⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠀⠈⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⣶⣿⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣽⣿⣿⡿⠣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡟⢠⣾⣶
⠀⠉⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢻⣿⣿⣿⣿⣿⠁⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣰⣿⣿⣿⣿⢿⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⣿⣿⣿⡏⢡⡾⠁⠀⠉⢻⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠿⡿⣿⡿⠦⣿⠃⠀⠀⢀⣿⣇⡀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⣄⠀⠀⠸⣿⣿⠃⠀⠀⠉⠺⢿⣿⣿⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠀⠀⢸⡿⠀⠀⠀⢻⣷⡀⠀⢰⣦⡇⠈⣿⣿⣶⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⢸⠆⠀⠀⠀⢸⣿⣿⣧⠀⢘⠁⠀⣿⣿⣿⡇⠀⠈⢿⡿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⣀⠀⠀⠀⠨⡟⢹⣿⡇⠈⠀⠀⣿⣿⣿⣿⡷⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⢀⡿⠀⠀⠀⢸⣿⣸⣿⠃⠀⠀⠀⣿⣿⣿⡿⢿⠀⣠⡈⠀⣿⣿⣿⣿⣿⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⡁⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⢀⡟⠋⠹⡇⠀⣶⣿⣏⣤⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⠀⠀⠑⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⢈⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⢴⡗⠘⣧⠀⠀⣿⣿⣿⣿⣦⠄⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠃⠀⠀⠀⢀⠤⣄⣠⣤⣄⡀⣀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣠⠏⠀⠀⠈⠉⠁⠙⠿⠙⠦⡀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠤⣀⡎⠛⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⣤⣦⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡏⠀⣿⠀⠀⠀⡰⠋⠀⣼⡆⠀⠀⢠⠤⡄⢹⢻⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢀⡈⠁⠀⠀⠧⢤⣀⣻⠃⠀⢀⡇⢞⣿⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⠉⠉⠉⠳⣽⠀⠀⠀⠀⣀⠸⠇⠁⠀⠀⠘⢦⠤⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢫⠏⠀⠀⠀⢀⡴⠒⠲⣄⢧⠀⠀⠀⠛⣀⠀⣀⣄⣀⠀⠛⢱⣆⡏
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣸⠀⠀⠀⠀⡎⠀⠀⠀⠈⡆⣷⢤⣄⠀⠛⠋⠉⠙⠛⠳⣿⣠⠞
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢻⠀⠀⠀⢸⠇⠀⠀⠀⠀⡇⠘⢎⡻⣗⡦⢤⡤⠤⣤⡖⠊⠡⡷
⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⠛⢦⡀⠀⢞⡀⠀⠀⠀⠀⣳⠀⠘⠟⠢⠔⠋⠀⡰⠁⣧⢰⡆
⠀⠀⠀⠀⠀⠀⠀⢧⠀⡏⠀⠀⠙⢦⡀⢹⠉⠉⠉⢹⠁⠀⠀⠀⠀⢀⡠⠞⠉⣿⠁
⠀⠀⠀⠀⠀⠀⡴⠚⠣⣧⠀⠀⠀⠀⠙⢾⡀⠀⠀⠸⡀⠀⠀⠀⢠⢿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢸⡁⠀⠀⢹⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢳⡤⠖⠒⠉⢯⢧⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠙⠒⠢⣄⡸⠈⢣⡀⠀⠀⠓⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠤⣀⣀⣀⣠⠴⠋⠈⠙⠲⠤⢤⣀⣀⡴⠃⠀⠀⠙⢦⣰⢦⣀⣀⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⢀⣤⠾⠟⠛⠋⠉⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠉⠙⠛⠻⠶⣄⡀
⠀⠀⠉⠀⠀⠀⠀⢀⣀⣤⣤⣤⣦⣤⣤⣀⡀⠀⠈⠉⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠉⠁⠀⢀⣀⣤⣤⣴⣤⣤⣤⣀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⣹⣿⣿⣿⠿⣷⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⣼⢿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⢻⣿⣿⣻⣿⡿⠀⠀⠙⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢿⣿⣟⣿⣿⡏⠀⠈⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠛⠻⣦⡀⠀⠙⠻⠟⠋⢀⣠⡤⠞⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠲⢤⣄⡀⠙⠻⠟⠋⠀⢀⣴⠟⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠻⠶⢶⡶⠞⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠋⠀⠀⠀⠀⢠⠔⠢⣄⣲⣶⣤⣀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠉⠉⠈⠑⢿⡌⠳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢰⠻⣼⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢠⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡤⠦⣼⠀⠉⠀⠀⢠⠞⠁⠈⢳⠀⠀⠀⠀⢠⠤⢤⠱⠏⣽⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣼⢠⠶⡌⠀⠀⠀⠀⡏⠀⢰⣯⣿⠀⠀⠀⢰⠃⢀⣀⡇⢸⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡈⢦⡇⠀⠀⠀⠀⠉⡉⠛⠛⠃⠀⠀⠀⠸⠤⣼⣾⠃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⢦⠁⠀⠀⠀⠀⢰⢻⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡀⠀⢀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⢸⡸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡞⡇⠀⠀⠀⣤⠶⠶⣖⣲⣄⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣇⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠔⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠺⡅⠀⠸⡌⠉⠙⠒⠒⠒⠒⠒⢲⠻⣅⠀⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠒⠦⣀⠱⡄⠀⠱⡄⠀⠀⠀⠀⠀⠀⢸⠀⢸⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠳⡝⢆⠀⠘⠦⣀⠀⠀⠀⢀⠞⠀⢸⠃⢧⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠑⢦⣀⠈⠙⠒⠚⠁⢀⡠⠋⠀⠘⡆⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣈⣉⣓⣒⣒⣋⣉⣀⣀⣀⣀⣇⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⠻⣆⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠋⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⣀⢰⠀⢀⡀⠀⠀⠀⢸
⠀⡇⠀⣴⣿⠿⠋⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⢉⣤⣶⣾⣿⣷⣿⣾⣿⡅⡀⠀⠀⢸
⠀⡇⢰⠟⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⠋⢰⡋⠙⣻⡿⡇⠈⣻⡿⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠰⣤⣾⣭⣧⣤⣤⣍⣀⣠⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠤⠤⠖⠀⢀⡿⠉⠀⠀⠀⢸
⠀⡇⠀⠀⠘⢾⣶⣿⠟⠋⡟⠛⢻⣿⡟⠳⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠂⠀⣤⠄⠲⠖⠲⠖⠀⢀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠢⠿⣿⠀⠀⠓⢄⣉⠥⠁⡀⠙⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠐⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠈⠉⢷⠦⠶⡤⠄⠂⠀⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠑⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⡇⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⢶⡄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣀⠀⠈⢢⡀⠉⠐⢇⠀⠈⠳⡄⠀⠀⠆⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡄⢸⣦⠀⠀⠀⠀⠈⠣⡀⠀⢹⠀⠀⠀⠑⠀⠀⠘⣆⠤⣦⠀⠢⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠀⠀⠀⢸⣦⠄⠘⢮⡹⠀⠸⣀⢀⡄⣦⣀⣼⠿⠋⠀⠀⠈⠂⠢⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⠀⠁⠈⠙⣦⢻⠀⠈⠿⠷⠾⢿⠟⠁⠘⠀⠀⠀⠀⠀⠑⣌⠓⢄⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠹⣄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢆⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢤⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡶⠚⠛⠛⠓⢠⡀⠀⠀⢀⡌⡽⢿⣿⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠂⡇⠀⠰⡾⢿⣷⠂⠐⠈⠀⠀⠈⠀⠈⠉⠛⠁⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠔⠉⠀⡠⠈⠢⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⡇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠐⠀⠀⣠⠋⠀⠀⠀⠀⠰⡷⠄⠀⡀
⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢀⢀⠒⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠀⠀⣸⠃⠀⠀⠀⠀⠈⠐⠈⠢⣀⡧
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠹⠘⡄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⢠⡟⠀⠀⣀⠄⠀⠀⠠⡀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠑⠙⣄⠀⠀⠀⣠⣶⣶⣯⡿⢿⣷⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠀⠀⠈⠁⠀⠀⠄⠊⢁⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⡘⣆⠀⠀⠈⢻⣖⣚⣫⡿⠋⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠈⠢⣀⣴⡦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢳⡄⠀⠈⠋⠈⠳⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⠎⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠰⠻⣇⠀⠀⠀⠀⠀⢹⡷⢄⡀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⠛⡄⠀⠑⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠁⠀⢀⣄⠀⢀⠟⠀⠀⠈⠉⢻⡟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⣿⠀⢐⡀⠀⠀⠀⠉⠡⠖⠉⠀⣠⠀⠀⠀⢈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢁⣴⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢭⡀⠀⠠⢄⣀⣐⣯⣵⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⠟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣦⠀⣠⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠌⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣠⣤⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢀⣤⣿⣦
⠀⠀⠀⢀⣾⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⣴⣻⣿⣿⣿⣷⣄⡀
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣠⣴⢟⣵⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣀⣠⣴⠞⡽⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠈⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⣋⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣱⣦⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⠿⠗⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⣠⠤⢂⡥⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠐⠬⡑⠢⢄⡈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⢀⠔⠉⠀⠀⠀⠀⠀⠀⠐⠤⠖⠋⠛⠶⠖⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣





⣿⠿⠿⠿⡿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣿⣿⣟⣿⣛⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⣿⠟⠉⠉⠉⠻⣿⣿⠿⣶⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⡄⠀⣠⣴⣶⣶⣦⡀⠀⣄⠈⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⢠⣿⡇⠀⣴⣾⣀⠀⠘⣿⡆⠈⠛⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⣾⣿⠁⢰⣿⡟⠉⠽⢿⣷⠀⢸⣿⣦⡄⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⡈⣿⣇⠀⠙⠛⠋⠀⣸⣿⢃⣠⣶⡿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠻⢿⡄⠘⣿⣷⣤⣤⣿⡿⠀⣸⠿⠋⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣰⣧⠀⠈⠛⠿⣿⣿⣷⣤⣤⣤⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠈⢿⣿⣦⣄⡀⠀⠈⠙⠛⠛⠉⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⡀⠀⠀⢻⣿⣿⣿⣷⣶⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⣇⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡐⣇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣤⣶⣶⣾⣷⣷⣾⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣤⣤⣌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡝⠙⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⡿⣄⣷⣄⠀⠀⠀⡠⣄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣷⢺⡉⠻⠀⣴⣻⡆⠀⢀⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⣀⣤⣊⣀⣀⢷⣽⣿⡿⠁⠀⠀⠫⠟⠀⡀⠭⢥⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠶⠖⣋⠉⠁⣀⠀⠀⠈⠑⢦⡁⠀⠀⠀⠀⠈⠁⠀⠴⠆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠶⡺⣷⠀⠀⠀⡜⢯⡷⡄⠀⢀⣾⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⡠⠂⠀⢠⠂⠀⠀⢠⣏⠉⠀⠀⢰⡝⠉⣀⠁⠠⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠸⠀⠀⣿⠨⠇⠀⣴⠀⢈⠡⠰⠇⠓⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠀⠀⠠⣽⠀⢣⠀⢻⣦⠈⠳⠀⣶⣠⣀⡀
⠀⠀⠀⠀⠀⢆⠀⠁⠀⠀⠀⠀⠀⢀⠂⠀⠀⡀⠀⠀⢲⡄⡇⠆⠈⡀⠹⠈⠁⠀⢀⣀⠀⠉⠁⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢡⢠⠀⣆⢧⢻⡀⠸⣇⠀⠙⣄⠀⠀⠀⠀⠈⠉⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢆⠱⣸⡈⢧⠳⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠣⠘⠹⡼⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⣤⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠸⣿⡩⠵⠶⠂⠀⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⣦⣶⣷⠶⠆⠰⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⣀⣀⡀⠀⠀⠀⠈⠑⠒⠺⣿⣥⣠⣴⡀⠀⡦⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⢄⡀⠀⡀⠸⡄⠀⠈⢠⡀⢷⣤⠏⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⡿⠲⠴⠛⠉⢢⠙⠢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠐⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⠃⠠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⠀⠙⢦⡀⠀⢀⣠⡴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠙⠓⠦⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⠈⣻⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠘⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠆⠀⠈⢣⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣸⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣷⠀⡈⠳⡀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡟⠀⠘⠋⢀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⠏⠀⡇⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢠⣿⣿⣇⣠⠈⢆⠀⠀⠀⠀⠀⠀⠈⠳⠬⠁⠤⠚⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⡜⢿⣿⠿⠀⡸⠀⠀⢀⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⠢⠤⠤⠚⠁⠀⠀⠛⠿⠿⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⡀⠀⠀⡸⠢⠤⠔⠁⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⠈⢀⠀⠀⠀⠀⠀⣀⠴⢾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣀⣀⣀⣀⡀⣀⣀⣀⣀⡠⠤⠶⠚⠉⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢹⡆⠀⠀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡀⠀⠀⣸⠇⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡇⣠⡾⠋⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⣇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠷⠒⢒⣿⣄⠀⠀⢀⡇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢀⣇⣀⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⣀⡀⣠⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠶⠶⠶⠶⠶⣧⣄⣀⣀⣠⣀⣼⠦⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⢀⡶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣼⡇⠀⣈⣿⡆⠀⠀⢠⣤⣤⣴⡾⠋⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣶
⠀⠀⠀⣿⣧⣾⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣷⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⣿⣿⢿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⡟
⠀⠀⢸⣿⢁⣴⣜⡟⠀⠀⠀⣿⢃⣤⡌⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠿⠿⠈⠻⠃⡀⠀⠀⠀⠹⡘⢿⠟⠸⠿⣿⣿⣿⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⡄⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⡿⠛⢿⣿⡏
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⢡⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣀⣀⠀⣿⡿⣲⠀⠀⢀⣀⠀⠀⠀⢀⢴⣥⣃⠁⢀⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⣿⡿⠶⡞⢻⣟⠩⢰⣿⠸⢿⣠⣷⡂⣼⢿⣯⣄⣀⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣍⣅⡄⠔⡶⠙⢄⡘⠋⣞⠺⣿⣿⡉⢻⠚⡏⠰⢾⣿⡩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠙⠆⠁⠀⠺⠀⡄⢠⢸⣿⣿⢦⡏⡁⢠⣯⠛⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⢌⡒⠾⠘⣷⣿⡟⢾⠳⡇⢸⢋⡐⢛⠛⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠛⣫⣀⣷⣘⠙⣷⠀⠀⢸⢣⡞⣉⡥⡶⢲⡶⣶⣿⣌⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠁⠀⠀⠀⠛⠿⣿⣏⣹⡆⠀⢈⣾⣧⣿⢶⣴⣯⣶⠷⠎⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠑⠀⠀⠀⠙⢻⣿⢿⡇⠀⠀⣾⣿⣿⡿⢿⣿⣿⡗⠾⢿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠶⠦⠀⠀⠀⠋⠁⠉⠋⠴⣶⡿⠿⠿⣿⣆⡙⠹⠶⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢓⡀⠀⠀⠀⠀⠀⣈⡋⠀⠀⠀⠛⠋⣹⣷⣿⣿⣟⣶⣟⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠢⣄⣀⠀⠀⠀⠉⠉⠓⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣟⠻⣶⣤⣤⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢷⣾⣿⣿⣿⣿⣾⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣱⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢠⠎⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣸⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⠿⣿⢟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⠁⢈⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣸⣿⡏⣿⣿⡿⢿⣿⣿⣭⣿⣿⢿⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠹⠛⠻⢻⣥⡾⣿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣀⣤⡴⠂⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠄⣤⣤⣴⣶⣴⣶⣿⣶⣿⣿⣿⣾⣿⣿⣥⣾⣿⣿⣐⣭⣴⣶⣮⣤
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣵⣿⣿⠿⠿⠟⣫⣥⣤⣤⣀⣨⣭⣤⣤⠀⠀⠀⠀⠉⠉⠉⢩⣭⣿⣿⡶
⠀⠀⠀⠀⠀⠀⣴⣟⣂⢠⣤⣴⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⣀⡀⠀⠀⠛⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠐⢉⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣂⣤⣌⣻⡇
⠀⠀⠀⠀⠀⠀⣄⣸⡇⣀⣿⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢿⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠚⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋


⣿⣿⠟⠿⠛⠿⡿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡇⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢁⣾⠆⠀⠀⠒⠀⠐⡁⢍⢀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠂⠀⠀⠀⠲⠿⠄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣀⣀⣀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡲⢀⠀⠀⣌⠡⠂⠴⣇⡁⠀⠀⠀⠀⠐⠀⠀⠦⠀⠀⠀⠂⠀⢈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠄⠀⢈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠐⣦⠄⠀⠉⠀⣆⡀⠀⡨⠜⡁⠀⠀⠀⠀⠀⢈⢧⡀⠀⠀⠯⠀⠀⣠⠌⠁⠀⠀⡸⢿⠀⠀⢻⡄⠀⠀⠦⠀⠀⣰⠆⠄
⠀⠀⠀⠀⠀⠟⠢⠀⠠⠋⠂⠶⠺⠳⠚⠣⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠝⠲⣒⠖⠪⠉⠀⠀⠀⠀⣅⡘⠀⠀⠀⡘⠀⠀⠀⠀⠈⠫⠐
⠀⠀⠀⠀⠀⠈⠶⠆⠀⠀⢸⠁⠀⠀⠀⠀⢣⡀⠀⠀⠀⢋⡄⠀⠀⠀⡌⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠉⠁⠀⠀⡐⠧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⡶⠆⠀⠀⡆⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠈⢍⡄⠀⢘⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠓⠀⠀⢰⡆⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠑⠗⡎⠁⠀⠀⠀⡀⢠⠀⠸⡀⠀⠀⠲⠆⢠⡁⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠈⠈⠢⢀⠆⠀⠀⠀⢀⠀⡀⠀⡘⠀⠀⠀⠀⠀⠀⠰⡆⢸⠀⠀⠀⢸⠀⡰⠀⠀⠀⠘⠼⡇⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⣀⠁⢙⣀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⠃⢀⣸⠉⠀⠀⠀⠀⠀⠈⠂⠦⣤⠀⠀⠠⣤⣤⠊


⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣀⣀⣀⡠⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢄⣀⠀⢀⣀⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡌⢠⠀⠨⠉⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⢠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠓⠀⠐⠒⠚⢃
⠀⠀⠀⠀⠀⠀⠀⠁⠣⡈⠀⠠⠐⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⡄⠀⢠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠉⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢀⡓⠀⠈⠀⢒⡀⠁⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⢰⣅⠀⠘⠛⢦⣄⠀⠀⠀⠀⠴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠘⢿⣿⡿⠾⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠰⠖⠀⡟⠲⠤⠀⠀⠀⠀⠀⠠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⡄⠀⢠⡄⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠸⣻⣄⡷⢤⡀⠀⠀⠀⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⣼⡧⠀⡀⠀⠌⡄⠀⠁⠀⡀⠁⠀⠀⠀⠀⠀⠻⢇⣰⠀⣀⠀⢠⠀⡦⠐⠫⠑⠄⠀⠀⠛⠄⣡⡤⠀⠀⠀⠀⠀⠀⠀⣤⠃
⠀⠀⠀⠀⠀⠀⢿⣷⣄⣹⠴⠁⠣⠼⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣲⢃⣀⣈⣒⡃⠠⠐⣀⠂⠀⠀⠀⠀⠀⠐⢃⡰⠒⠀⠘⠦⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⣀⣀⣀⡛⠛⠁⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣤⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⡀⠄⠀⠀⠀⢠⣇⣄⣸⣿⣿⣿⣿⣿⣿⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠿⠟⠛⠛⠛⠛⠻⠿⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⣴⣿⡇⠀⠀⠀⠀⢰⣿⣦⠀⠉⠛⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣴⣾⣿⠟⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⡀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣴⡿⠛⢉⡿⠋⠉⠛⠛⠀⠀⠀⠀⠛⠛⠉⠙⢿⡉⠛⢿⣦⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣴⠋⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⣦⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠃⠀⠀⣾⠁⠀⢀⣠⡤⠶⠚⠛⠛⠓⠶⢤⣄⡀⠀⠈⣷⠀⠀⠘⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠇⠀⠀⢸⠇⢀⡴⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢦⡀⠸⡇⠀⠀⠸⡆⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⡿⠀⠀⠀⣿⣰⠟⠀⠈⣉⣉⣉⠉⠉⠉⠉⣉⣉⣉⠁⠀⠻⣆⣿⠀⠀⠀⢿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡇⠀⠀⠀⣿⡏⢀⡴⠛⠉⠉⠉⠛⢦⡴⠛⠉⠉⠉⠛⢦⡀⢹⣿⠀⠀⠀⢸⣧⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣿⢀⡿⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢿⡀⣿⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⣠⡴⠛⠉⠀⠀⠉⠛⢦⣄⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠈⠙⠛⠋⠁⠀⠀⠛⠉⠉⠛⠀⠀⠈⠙⠛⠋⠁⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣠⣴⡶⠾⢿⡇⠀⠀⠀⠀⢿⠛⠶⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⠶⠛⡿⠁⠀⠀⠀⢸⡿⠷⢶⣦⣄
⠀⠀⠀⠀⠀⢿⣥⣀⣀⠀⠛⠶⠶⠖⠚⠋⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠙⠓⠲⠶⠶⠛⠀⣀⣀⣬⡿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠷⠶⢶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠾⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠞⠛⠛⠛⠛⠛⠶⠶⣤⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣼⠋⣷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠋⣉⣽⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢰⡏⠀⠀⡇⠀⢸⠀⠀⠀⢀⠀⠀⢰⡀⠀⠀⢳⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣿⠀⠀⣰⡇⠀⢸⡆⠀⠀⢸⠀⠀⠀⢧⠀⠀⠈⢷⡀⠀⠀⠀⢳⡀⠀⠀⠀⢀⣧⣀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⣿⠀⢰⠁⣧⠀⠈⡇⠀⠀⠸⡇⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⢷⡀⠀⣴⣭⣤⡜
⠀⢾⣉⣙⣿⠀⡏⠀⠹⣄⠀⣷⠀⠀⠀⢻⡀⠀⠀⠹⡄⠀⠀⠈⣷⡀⠀⠀⢸⡷⣄⠀⠀⣿⢡
⠀⡀⠀⠀⣿⣄⡃⠀⠀⢈⣉⠁⢧⡀⠀⠀⡷⣄⠀⠀⢸⠦⣄⣠⠇⠙⠦⣤⡼⠃⠈⠓⠶⠋⢸⠀⠀⠀⠀⠀⢀
⢯⡤⠟⠀⢺⣄⡁⢀⡞⢩⠭⣍⠲⣝⠲⠖⠃⠈⠙⠚⠋⠀⠀⢀⡞⢉⣽⣟⠢⣄⠀⡀⠀⢀⡏⢀⡴⠴⢦⡀⣼
⠀⠀⠀⠀⠈⣿⠀⠀⠑⡞⠉⢉⠖⠋⠀⠀⢀⡤⠖⠢⢤⡀⠀⠘⠲⣏⠉⠙⡶⠞⠀⠀⠀⠈⠛⠋⡖⢀⡼⢁⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣗⠀⠈⣆⠀⠀⢠⠏⢀⣤⠤⣀⣱⡀⠀⠀⣸⠀⠀⢣⡀⠀⠀⢠⡤⣀⡴⠛⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠹⣆⠀⠀⡏⠀⠠⡇⠀⠀⣾⠀⠙⢲⠦⠀⠈⢷⠀⠀⣸⠂⠀⣞⣡⢤⡀⢀⣧⠼⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠙⢷⣤⡟⠀⠀⣹⠀⠀⠻⠶⠴⠯⣤⠶⠦⡼⠀⠀⢹⠀⢠⠏⠀⠀⡷⠋⠀⠀⡀⠀⠐⣆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠙⠳⢦⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡴⠛⢦⣤⣨⣱⣦⣤⣴⠷⣤⣤⠟⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡼⢷⣤⣦⣩⡙⣛⡷⠲⣖⠒⠂⢀⡤⠞⢙⡟⠁⠀⠀⢰⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⠛⢦⣀⠈⣹⠶⣏⣀⡴⠛⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⡀⠀⠈⠙⠁⠀⠈⠉⠁⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣧⠀⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡤⠾⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⢹⡟⠛⠛⠛⠛⠛⠻⣏⠉⠁⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠸⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣧⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣤⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠑⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣦⡀⠸⠂⡀⠀⢸⡄⠀⠀⡀⠺⠀⣠⣾⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠉⢻⣿⣧⠤⣶⣿⣿⠬⣿⣷⠀⠘⢇⠀⣸⣧⠀⢀⠜⠀⢰⣿⡯⢽⣿⣿⡤⢀⣽⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠀⢿⣿⡟⠉⠁⣻⡄⠀⠀⠠⠉⠇⠀⠀⠀⠀⣼⣃⠉⠙⣿⣿⠇⠘⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠉⠠⠔⠛⢻⣇⢀⡐⠀⠀⠀⠀⠀⠀⢠⣿⠛⠓⠤⢬⠡⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⢶⢟⣷⡁⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣒⠓⠒⢓⣛⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣠⣧⣺⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠚⠛⠉⠁⠟⠻⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠄⠂




⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡊⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⡶⠶⡏⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠧⠤⠦⠤⠧⠼⠤⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⡀⠉⠉
⢈⠉⠆⠀⠀⡴⠂⠉⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠒⠢⡄⠀⠀⢀⠔
⠀⠈⠘⠀⢠⡀⠀⠀⠠⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⡀⢐⠀⠀⠦⠔
⡠⠀⢠⠄⡰⢆⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⣼⠀⠀⣀⣀
⠑⠊⠁⢀⠇⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠒⠀⠁⠈⡆⠀⠑⠤
⠀⢠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠑⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢆
⠀⠈⠦⣠⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⡠⠋
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠙⠋⠁⠉⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⠿⠿⠛⠛⠛⠛⠛⠒⠛⠂⠉⠉⠉⠉⠛⠛⠛⠻⠿⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋
⠀⠀⠀⠀⠀⢐⠑⠃⠀⠳⢝⣲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡫⠞⠁⠵⠤⡀
⠀⠀⠀⠀⠰⡋⠀⠊⠀⠀⠀⠀⠀⡈⠉⠓⠲⠦⠤⣤⣤⣤⣤⠤⠴⠖⢚⡉⠀⠀⠀⠀⠀⠂⠐⢧
⠀⠀⠀⠀⠀⠹⣅⡠⠆⠒⠒⠊⢩⡃⣠⠤⢄⠀⠀⠀⠀⠀⠀⡠⠤⢄⢸⠉⠉⠒⠒⠤⢄⠀⡲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠉⠁⠀⢀⡧⠤⠤⠬⠥⠤⡇⠀⢀⠁⠙⢲⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠉⠀⠀⢈⡆⠀⠄⠁⠀⠀⡇⠀⠀⠈⠁⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡎⣩⣀⣀⡀⢀⣠⡛⡄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⡠⠃
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠋⠉⠉⠉⠉⠉⠉⠙⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣦
⠀⣾⠃⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠟⠀⢠⡶⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣄⡀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⠀⠀⠀⠀⠀⠀⠀⠶⠶⢶⣤⡀⠀⠀⣸⠇
⠀⠀⠀⣿⡀⠀⠀⣿⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⣴⠋
⠀⠀⠀⠹⣧⠀⠀⠈⠁⠀⠀⠀⠀⢀⣐⠛⠛⠛⠛⠛⢿⣦⠀⠀⠘⠷⠄⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣸⡏⠁
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⢀⣿⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠰⠋
⡴⠀⠈⡷⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠙⠻⠖⠒⠒⠚⠁⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⡠⠚⠛⠛⠋⠉
⠷⠄⠐⠁⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢈⡽⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠲⣿⡀
⠀⠀⠀⢧⠜⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠙⣿⣄⡀⠀⠀⠀⢀⡠⠟⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠻⢷⣦⣄⡠⣴⣦⡄⠀⠀⣤⠶⠶⣦⣀⡰⠋⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠈⢻⡇⠠⢾⣿⣤⡀⣿⡶⠆⢹⣿⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣆⡀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢻⣷⡟⠀⠀⠀⣿⡇⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣶⣤⣀⣼⠃⠀⠀⠀⢀⡾⢿⣧⣀⠀⠀⢸⣷⠄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠉⠙⠛⠛⠛⠓⠛⠉⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⡀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢴⠂⠂⢏⠁⢸⠀⣿⠀⠈⠀⠁⠰⠂⣠⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡄⠈⢧⡀⢧⣰⣼⣤⣼⣤⣿⣤⣧⣾⣤⣢⣾⣁⣨⠟⠀⡰⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢄⠢⣘⢦⣌⠲⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣟⣁⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢦⣀⠠⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣔⡪
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠲⣭⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠻⠿⣿⣿⠻⣿⣧⣤⠔⣀
⠀⠀⠀⠀⢀⣀⠀⠉⠲⢦⣤⣬⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⣿⣿⠀⠈⠛⢿⣿⣅⡀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⣿⣿⡿⠃⠀⠀⠀⠀⢿⣿⡆⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⢌⠋⡉⢀⣿⡏⠀⠀⠀⠈⣿⣿⣿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣦⡙⢿⣿⣇⠀⠀⠀⠀⠀⠈⢿⣷⣤⣴⣿⣿⣿⣿⣿⣿⠟⢧⠠⡀⣠⣾⡟⠀⠀⠀⠀⣠⣿⣿⡿⢁⠉⢉⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⣛⣿⣦⡙⠻⢦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣹⣿⢠⢨⠘⢠⣼⣿⣿⡿⠋⠀⠀⣀⡤⢾⣿⠿⠛⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠩⢛⣷⣤⣉⠓⠦⣤⣀⡀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣾⠿⢟⣋⡤⠔⣒⣿⢵⡚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢀⠔⠛⣻⣶⣦⣌⣉⣙⠒⠒⠒⠀⠀⠀⢀⣐⣂⣬⣵⠶⡞⠻⡏⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⠉⠀⡼⠋⢹⠋⠹⠏⠙⠋⢻⠟⠉⢻⠁⠈⠏⠇⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠀⠀⠀⠀⠀⣀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⢺⡐⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⡇
⢶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⣀⡀⠀⠀⠀⠀⠀⠀⢉⣑⠒⠘⡟⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠔⠀⠀⠀⣠⣢⠄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠁⢀⠨⡊⠑⠀⠠⣇⣐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⠂⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠉⠡⡂⠀⡅⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠮⠔⠃⠀⠀⠀⠀⡰⠁⠈⠌⠀⠀⠀⠀⡀⢠⠀⠀⠀⠁⠀⠀⠀⠐⣋⡴⠃⠀⠱⡀⠢⣀⠀⠀⠀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡄⠀⠈⠀⢐⠐⠊⠁⠠⠀⠄⠈⠀⡀⠔⠀⠀⠀⠀⠀⠀⢠⠹⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠇⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠈⡄⠀⠀⠀⠀⢠⢰⠀⠀⣎⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠇⠀⠀⠣⠤⠋⣀⠜⠀⠀⠀⠀⡴⡫⠃⠀⡼⠈
⣎⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠤⠂⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡰⠀⠠⠆⠀⠀⢀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⣐⠧⠞⠁⠀⠀⠀⠀⠀⢸⡀⠀⢀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠩⠞⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⢸⣄⣀⣀⠨⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠑⠤⠚⠁⠀⠉⠓⠉⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡤⠀⠀⢄⠀⣸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣭⣥⣤⣤⣤⣼⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢠⣟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢠⡞⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡿⠀⠀⢰⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⣿⣿⣿⣿⠁⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢠⣞⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣀⣤⣤⣤⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠶⣤⣴⠖⠀⣷⠀⠀⠳⠶⠶⠃⠀⢹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠚⠉⠉⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢰⠀⢸⠀⢸⡆⠀⡆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢱⣀⣬⡶⢾⠶⢾⡧⣼⣁⣠⠃⢀⠇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣄⡠⢷⠋⣻⣀⣧⣼⣤⣬⣤⣼⣈⡏⠛⡿⣄⡴⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡔⢉⠶⠚⠉⠁⣿⣿⡟⠁⠉⣿⣿⣿⠍⠛⠦⣞⢳⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡜⠁⠀⠀⠀⢀⠹⣿⣷⣦⣶⣿⣿⡟⡔⠀⠀⠀⠙⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠂⢄⡀⠀⠈⢦⡈⠛⠻⠟⠛⣁⠐⠀⠀⣀⠤⢚⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢱⠃⠈⡵⣒⡦⢤⠄⢰⡒⢉⠁⢴⢈⣧⠤⠷⡉⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡰⠁⠀⡜⢁⡾⠉⠹⠒⢺⡖⠚⡒⠉⣧⠈⢆⠀⠙⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⢀⣾⡇⠀⡄⠀⣾⣧⠀⣇⠀⢸⣷⡀⢃⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⢸⠁⢠⣿⣿⡀⢸⠀⠀⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⠇⠀⠄⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣯⢩⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠘⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢈⣿⠿⠛⠋⠉⠁⠀⠀⠈⠉⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠱⡀⠀⢐⡂⠀⠀⠐⠀⠀⠁⠂⣰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠉⠁⠀⠈⠾⡿⠟⢻⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⣿⠿⠛⠋⠉⢉⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⣿⣿⣶⣾⣿⣿⣿⣶⡄⠀⠀⠀⠹⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠽⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣀⣂⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠽⣿⣿⣿⣿⣿⣿⣿⡇⣀⣼⠏⠛⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡉⣹⠟⠛⣿⣿⣿⣿⣿⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣾⣾⡿⠛⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣿⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠈⠛⠟⠋⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣤⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⠿⠛⠛⣿⢛⡛⡻⠿⣿⣡⠀⣤⠀⠀⠀⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠂⠤⠿⠚⠾⠧⠟⠒⠛⠛⠒⠛⠚⠉⠉⠉⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣁⣤⣶⣶⣤⣬⣐⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣴⣾⠿⠟⠛⡟⣙⣿⠛⣿⡿⠿⢿⣿⠀⠈⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣯⣤⣀⠀⠀⠡⡀⠿⠛⠻⠷⡀⢀⠀⠀⠀⠀⠀⣙⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏⠁⠈⣿⣶⣦⣬⣀⣀⣀⣀⣈⣀⣤⣤⣶⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡇⠛⠀⣿⣿⣿⣿⢉⡏⢿⠁⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡿⠋⢻⠀⠁⢸⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⠀⠀⢸⠀⠀⢸⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢿⠀⠀⠈⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢸⠀⠀⠾⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡠⣦⣤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡃⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⣿⠻⣷⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣔⣤⣀⡀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠐⠋⠙⠿⠿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠔⣻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣶⣶⣦⣤⣶⣷⡆⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣰⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣿⡟⡇⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠀⡠⠁⠀⠉⠀⠈⠀⠈⠁⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠄⠀⠀⠐⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣤⣶⣿⣷⣿⣿⣿⣶⣶⣾⣿⣷⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⡶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⡡⠐⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠊⠍⡛⠶⣤⣀⠀⣀⣀⣤⣤⡴⠶⠶⠶⠶⠟⠁⢀⠊⠀⣠⠄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠠⡄⠀⠈⠑⠄⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢩⣆⠤⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠶⣆⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⠀⠀⠀⠀⠀⠀⣨⣶⠌⡆⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢘⠟⣀⠆⠀⠀⢀⠀⠃⠉⢊⣀⣀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠠⠀⠀⠛⠀⠀⠄⢀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣇⣀⡀⢀⠌⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⣉⡨⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠁⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⣴⡏⠉⠻⡆⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡿⠀⠀⠀⢻⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⢸⡁⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⢸⠃⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠘⢦⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠈⢳⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠊⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠚⠷⣄⠀⠀⠀⠀⠀⠈⠑⢴⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡄⠀⠀⠈⡆⢸⡛⣧⠀⣀⠀⠀⠀⠀⣠⠀⡇⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠥⠴⠥⠴⠖⠋⠀⠈⠻⠧⣤⣴⣥⢤⣿⠊⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⣀⣠⣄⣀⣸⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⢀⠴⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣴⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣶⣤⣀⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⡿⣿⣿⡿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⢿⣿⣿⢿⠛⢿⣧⡀
⠀⠀⠀⠀⠀⠙⢻⣼⡄⠱⢭⣩⠴⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⢮⣉⡩⢎⣠⣷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣽⡟⠁⠶⣶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠶⢆⠙⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠢⡀⣀⡤⠴⠖⠒⠒⠒⠶⠤⣄⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡰⢂⣕⣆⠀⠀⠀⠀⠀⣔⣌⡲⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣧⠀⠀⠀⠀⠀⠣⣻⣷⠏⠀⠀⠀⠀⠀⠿⣷⡷⠃⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣂⣘⠄⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⢨⣀⡀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠈⠠⠀⠀⣀⡤⢖⠉
⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠛⠉⠁⠀⠘⡄
⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⡞⠀⠀⠀⠀⠀⣀⠤⠖⠐⠲⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠖⠒⠒⠒⠒⠦⢤⣀⠀⢸
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢯⡈⢆
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣖⠀⠀⠀⢀⣠⢤⡤⠤⢤⣀⠀⠀⠀⠠⡙⡌⡆
⢧⠀⠀⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠶⠖⠋⠉⠀⢸⣠⡂⣔⣈⣇⠀⣹⢀⡷⢃⡇
⠈⢷⣄⠀⠀⠈⠉⠛⠒⠒⠒⠲⠒⠶⠶⠶⠶⠿⠶⠶⠖⠒⠒⠒⠒⠛⠛⠛⠛⠉⠋⠉⠉⠉⠉⠉⠛⢶⡎
⠀⠀⠈⠓⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠒⠶⣶⣤⣴⡞
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⣻⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⠀⠀⣤⣤⣤⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡅⠀⠀⣴⠟⠋⠀⠀⠀⡀⡉⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⡩⠀⠀⠀⠀⠐⠐⠀⠀⠄⠀⠰⠆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣄⠢⠀⠀⠀⠈⠋⠀⡀⠀⢈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⣻⡿⣇⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⣀⠠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⢸⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢸⣿⣳⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣶⣶⣾⣿⣿⡗⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣟⣽⣿⣾⣽⣛⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢀⣠⡴⠖⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⢠⠿⠋⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠹⣶⠞⠛⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠙⣧⠀⣴⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢙⡿⠖⢀⢎⡤⠤⢼⣀⣶⠀⠀⠀⠀⠀⢸⢶⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠴⠀⠀⠀⢀⡠⠞⠉⠀⠀⢰⠏⠀⠀⢀⣹⡆⠀⠀⠀⠀⣠⠟⠈⠃⠴⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⣿⠀⠀⠀⠘⣻⡟⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠘⠷⠤⠴⢞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞
⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠐⠒⠋⠀⣷⣄⠀⠀⠀⠀⢀⣠⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣧⣿⡀⠀⠀⣠⠴⠲⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⠀⣠⠖⠋⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⣿⢁⣴⡶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣈⣀⣀⡤⢾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣼⠀⢈⠉⠓⠒⡶⠶⠶⠶⠛⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⠀⠀⠀⢳⡀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⣤⣤⣤⡼⠇⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣀⣀⣿⠋⢧⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡿⠶⠦⠉⠁⠘⣦⣤⣤⡤⠴⠖⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠒⠲⣮⣤⠞⠁⡼⣸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠺⢧⣀⠀⠀⠀⠠⠤⠾⡵⠷⠒⢀⣠⢟⣶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣈⣿⡓⠛⣛⣓⣶⠶⣶⣾⠷⣖⣚⣉⣓⣋⣽⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠭⠭⠭⠔⠒⠋⠁⠈⠉⠒⠒⠫⠍⠓⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠱⣄⠀⠀⠀⠀⠀⠀⡴⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠓⠚⠛⠛⠓⠚⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⣦⡄⠀⠀⢠⣤⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠤⢤⣄⣼⡁⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⢀⣸⣆⣤⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⢶⠯⢭⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⢨⠥⢿⡖⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠓⠲⠆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠶⠒⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⠀⠀⠀⠀⠉⠛⠋⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣿⣿⣿⡿⠁⢠⡆⠀⢴⠀⠀⡆⠀⠀⣀⣤⣄⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠉⠉⠀⠀⢸⡇⠀⢸⠀⠀⡇⠀⢰⣿⣿⣿⣷⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢸⡇⠀⣽⠀⠀⡇⠀⠀⠙⠛⠛⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⡞⢱⠂⢿⠀⣦⠳⡄⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠉⢹⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡾⠋⠳⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣟⡀⢈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋
⡿⠿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠈⠻⣦⣄⣠⣤⣤⣴⡿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣻⣿⣿⣿⣿⣿⣇⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠐⠟⠋⠁⠉⠙⠙⠛⣛⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⢾⡿⠆⠀⠀⣾⠿⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣐⣀⡀⠏⣀⣼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⠒⢶⠿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⢿⢿⣟⣿⡿⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡿⠟
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈
⠀⠀⢾⣿⣿⣿⣿⣿⠟⠛⠛⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣰⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⣿⣿⡇⠀⠀⢰⡀
⠀⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠁⠃
⢰⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⣀⣀⣴⣧⣀⡀⣀⣠⡴⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣧⣶⣿⣿⣿⠿⠿⠛⠛⠛⠛⠿⢿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠟⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⣉⣤⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢩⣀⣤⣴⣔⣄⣌⠉⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣯⣶⣿⣿⣿⣿⣯⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⣂⣈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣶⣮⡹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢷⣦⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⡿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣇⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⡿⣿⢷⣦⣀⢀⣀⢀⣰⣾⢿⣿⣿⣿⣿⣿⣷⠆⠐⣀⠀⢀⠀⣠⠎⠰⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⣇⢹⣠⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣥⠞⠁⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠻⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⠻⠟⢁⡀⠈⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡍⠀⠐⢌⠻⣮⡁⠈⠉⠁⠀⠙⠉⠁⠀⣠⢰⡏⠀⠀⠀⠠⠊⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⡄⠀⠼⣙⣻⣿⣦⣀⢠⠀⠀⢀⣴⣾⠻⠁⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠽⠟⣿⢿⣷⢰⣾⣿⣯⠔⠚⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢁⣿⣰⣿⡞⠀⡁⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣀⣼⡟⠙⣿⣇⡆⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣾⣷⣾⣿⣿⣷⡖⢾⣹⣇⡾⠥⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠐⠛⠛⠁⠙⠛⠛⠃⠈⠛⠛⠋⠀⠀⠛⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠛⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⣠⣤⣄⡀⠈⡉⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⣾⡟⠀⣴⣶⡀⠈⣿⡆⠙⠻⣶⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⢠⣾⠃⢰⣿⠟⠙⢿⣷⡀⢹⣶⣄⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⢻⣷⡀⠙⠟⠃⢀⣿⢇⣠⣶⠟⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣀⠘⠿⡆⠘⣿⣦⣤⣼⡿⠁⣸⠟⠋⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣷⡀⠉⠛⠿⣿⣿⣶⣶⣶⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠘⢿⣷⣤⣀⠀⠈⠙⠛⠉⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣽⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⡃⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢲⣶⡶⠦⠐⠒⠂⠶⣶⣤⡂⠀⠀⠀⠀⠐⣶⣶⡶⠄⠐⠒⠠⢴⣶⣴⠂⠀⠀⠀⠀⢐⣶⣶⠤⠄⠀⠀⠤⣶⣶⡖
⠀⠀⠀⠀⢼⠋⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⡿⠉⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠹⡧
⠀⠀⠀⠀⠆⠀⠠⠒⠄⠀⠐⠒⠀⠀⠃⠀⠀⠀⠀⢠⠁⠀⢾⣴⠀⠀⣧⡤⠀⠈⡄⠀⠀⠀⠀⠘⠀⠀⢠⡀⠀⠀⡠⠀⠀⢰
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⡀⠀⠈⠁⠠⠄⠉⠁⠀⢀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠤⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠒⠀⠀⢀⢜⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠚⠓⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠒⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠂⠐⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠂⠀⠐⠐⠁⠁

⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢹⣿⠟⠋⠁⠀⠈⠙⡻⣿⡇⠀⠀⠀⠀⠈⣿⡿⠛⠉⠁⠈⠉⠛⢿⣷⠀⠀⠀⠀⠀⢸⣿⡿⠛⠈⠉⠉⠘⠻⣿⡏
⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠥⠽⡆⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⢰⠋⠀⡀⠀⠀⠀⡄⠀⠈⠗
⠀⠀⠀⠀⡃⠀⠀⠴⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠊⠁⠀⠀⠀⠑⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠘⣷⠇⠀⢘
⠀⠀⠀⠀⠡⠀⠀⠀⢀⣉⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢆⠀⠀⠀⢈⡁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⣹⡀⠀⠀⠀⠌
⠀⠀⠀⠀⠈⠳⠄⡀⠀⠁⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠘⠦⢀⠀⠈⠁⠀⡀⠴⠃⠀⠀⠀⠀⠀⠀⠹⠄⡀⠀⠛⠁⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢠⣠⣠⣀⠠⠤⠀⣀⣀⣤⠄⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠠⣀⣠⣀⡀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⣸⡟⠉⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠙⢿⣇
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠃⠀⣴⣠⠀⠀⣄⣀⠀⠘⠀⠀⠀⠀⠀⠸⠁⠀⣀⡀⠀⠀⣀⡀⠀⢃
⠀⠀⠀⠀⡅⠀⠐⠀⠀⣀⠁⠔⠁⠀⡀⠀⠀⠀⠀⠘⠀⠀⠙⠟⢀⡀⠻⠋⠀⠀⠂⠀⠀⠀⠀⢀⢠⠌⠀⠈⣀⠈⠀⠀⠄⢨
⠀⠀⠀⠀⠰⡄⠀⠀⠠⠶⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣡⡀⠀⠀⠠⠄⠀⠀⢀⣌⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠤⠄⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠘⠐⠤⢀⣀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠈⠛⠢⠄⣀⣀⠠⠔⠛⠁⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⣀⣀⠠⠐⠋


⣶⣶⢶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⢶⣶⡶⣶⣶⠶⣶⢶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠋⠉⠉⠉⠉⠉⠙⠛⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠉⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⢀⣠⣶⣿⣿⠿⠛⣩⣿⣿⡿⠛⠉⠉⠛⠿⣿⣷⣦⡀⠀⠉⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⣿⠏⠀⢰⣿⣿⣿⣧⡀⠀⢀⣄⠀⠘⣿⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢰⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠈⣿⡄⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⣰⡿⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⠉⠉⠉⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣷⣄⡀⠀⠀⠀⠀⠙⠿⣶⣦⣤⣤⣤⣶⡾⠟⠋⠀⠀⠀⣀⣤⣾⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣄⣀⡀⠀⠀⠉⠉⠁⠀⢀⣀⣠⣤⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠹⣿⡀⠀⠀⠀⠀⣠⣿⢿⣦⠀⠀⠀⠀⠀⣾⠏⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢹⣷⠀⠀⠀⣰⣿⠃⠈⢿⣇⠀⠀⠀⣸⡟⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣸⡿⠀⠀⢠⣿⠃⠀⠀⠘⣿⡆⠀⠀⢹⣧⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠟⠁⠀⠀⢸⣿⢠⡀⠀⠀⢹⣧⠀⠀⠈⠻⠷⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣜⠷⠄⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡁⠀⠀⠀⠀⢀⣠⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠰⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠐⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡀⠀⠀⠀⠀⡇
⣤⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⢉⡁⠀⠀⠀⠀⠀⠀⠒⠲⠆⢹⡱⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣠⠄⠀⠀⠈⡠⢀⡉⠀⠀⡔⠀⠀⠀⠀⠈⠙⠂⠀⢑⠝⠢⠀⢀⠧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠉⠲⢃⡄⠀⠂⢹⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠴⠀⠀⠀⠀⠀⡐⠁⢇⢺⠀⠀⠀⠀⠀⢀⣀⡀⠀⡇⠀⠀⠀⠠⠖⢀⠇⠀⢣⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢤⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⢀⠀⠈⠪⣳⢤⡤⠴⠏⡉⠋⢀⠔⠁⠀⣠⠄⠐⠒⠁⠀⠀⢀⠱⡀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⠀⠀⠀⠈⠙⠒⠀⠀⠀⠩⢤⢴⡒⠉⠀⠀⠀⠀⢠⠀⠀⡜⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠈⠚⠆⠀⠸⣷⡀⠀⠀⡀⢐⠔⠋⡸⠁⠀⠠⠞⢀⡜⡜⠀⢠⠧⠃
⡠⠀⡀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠉⢡⠀⠚⠁⠀⠀⡀⠀⠉⠋⠀⠀⠉
⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠀⢀⠉⠀⠀⢀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡰⠃⠀⠈⠀⠀⠀⢸⠀⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⢤⠠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠁⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡀⠰⠀⠀⣠⠤⠤⣄⣀⡀⠜⠶⠄⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⠤⠒⠀⠀⢢⢀⠼
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⢀⠉⠀⠀⠀⠀⠀⠁⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⢁⡀⠈⠉⠀⠈⠉⠢⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⠄⠠⠅⠀⠐⠒⠲⡆⠀⠘⡦⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢃⠐⠂⠐⣃⠀⠀⡀⠀⢸⠀⠀⠱⠊⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡥⠆⠀⠴⠒⠆⠀⠀⠁⠀⠀⠀⠀⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢀⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠣⡀⠀⡀⠀⠠⠂⠐⠢⠖⠈⠀⠀⣰⠀⠀⢀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠈⠢⣅⣁⢂⠤⠄⠀⠀⠤⠒⠁⠅⢠⣀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠈⠉⠢⠄⣀⠤⠒⠒⢄⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⢀⠠⠤⠤⡀⡀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⡀⠀⠀⠀⢀⡇⢰⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠉⠁⠈⠀⠈⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢤⣤⣤⣤⠤⠚⠦⠤⠤⠔⡩⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡄⠀⠀⠀⡄⠀⠀⠀⢂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⢀⡇⠀⠀⠀⠘⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡨⡉⠉⠗⢒⡖⠒⡰⠇⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠈⠁⠐⠐⠚⡆⠈⠘⠑⠉⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢀⠶⢄⡀⠀⠀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠋⠁⠀⠀⠈⠉⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠻⠿⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠙⢿⣦⣀⣀⣴⣟⠉⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣿⣿⣿⣿⣿⣿⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⢀⣿⣿⢻⡛⡏⠈⡿⣟⠻⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄⠀⠀⠀⠸⣿⣿⣬⣵⡇⠀⢷⣭⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣿⣿⣿⠉⠰⠶⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠛⠿⠟⠀⠀⠐⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⣿⣟⠃⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⢿⣿⣿⣷⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⢿⣿⣿⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⢸⣿⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣗⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣤⠀⠀⢀⣄⠀⢀⢤⠀⠀⢠⢄⠀⢠⢄⠀⠀⡠⢄⠀⣠⣄⠀⠀⣠⡄⠀⢀⢤⡀⠀⢀⢤⠀⠀⠀⠀⡤⡀⠀⠀⣠
⠀⢰⣿⣿⣿⣿⣿⡆⡌⠀⠉⠉⠁⠈⡄⡇⣀⠉⠉⡁⢸⠀⣿⢿⣿⣿⠿⣷⠀⡼⠘⠉⠉⠉⠀⡇⠀⠀⢰⠑⠋⠀⠙⠂⡇
⠀⠘⣿⣿⣿⣿⣿⠃⢣⡈⠁⠤⠉⣠⠃⢇⠚⠣⠌⠓⡹⠀⢷⣿⣿⣿⣷⡿⠀⢳⡈⠁⠀⠘⢠⠇⠀⠀⢸⡀⠛⠠⠘⢃⡇
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠐⠒⠈⠁⠀⠀⠉⠐⠒⠉⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠈⠑⠒⠈⠁⠀⠀⠀⠀⠈⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣠⠤⠖⠚⠋⠉⠉⠉⠉⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⢦⠖⠉⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠈⠒⠶⣤⠤⣌⣧⠀⠀⣠⠖⠋⣁⣀⣀⣀⣀⡈⢧⠀⢀⡤⠒⠛⠉⠛⠲⢤⡀⠀⢰⠷⠒⠒⠒⠒⠚⣁⡀
⠀⢀⣠⡤⣤⣀⠀⢀⡞⠁⠀⠀⠙⠀⡜⠁⠈⠉⠉⠀⠀⣠⠬⠽⣿⡇⣾⠶⢯⣉⠉⠉⠓⠒⠙⢦⠀⠀⠀⠀⠀⠈⠙⢯⡉⠙⠲
⡞⠁⢀⡴⠋⠀⢀⠎⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋⢰⠃⡇⠙⠲⢬⣀⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠑⢤⠴
⠙⠒⠋⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠒⠚⠉⠁⠀⠀⡰⠋⠀⠹⣄⠀⠀⠀⠉⠙⠒⠒⢀⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⢀⡞⢹
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠈⠙⠒⠒⠚⠉⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⣦⣀⡀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⢀⣀⣤⢾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣷⣯⣽⣟⣶⠶⢦⣤⣤⣤⣤⣤⠶⣶⣛⣯⣿⣾⣿⣿⣿⡿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⢛⣿⡴⠛⠉⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠘⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠙⢛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠘⡷⠋⠉⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠘⣻⠷⠂⣠⣂⡤⠤⢼⡀⢰⠄⠀⠀⠀⠀⠀⢹⢶⡟⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠄⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⣵⠏⠀⠀⠀⡘⣆⠀⠀⠀⠀⠀⣠⡟⠀⠃⣠⠞⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠿⣿⢦⣤⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣬⡧⠀⠀⠀⢿⣄⣀⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⣉⠠⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⡆⠀⠀⠀⠀⢀⣀⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⡄⠀⠀⠀⣀⡴⠞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠣⣄⣀⣠⠞⠉⡉⣉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠞⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⠎⠜⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣀⣀⡀⠤⠚⡷⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡀⠉⠛⠒⡒⠶⠶⠚⠛⠋⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⣇⣀⣀⣀⡨⠧⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡿⠛⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢐⣏⣉⡉⠓⠀⠹⡀⠀⠀⢀⣀⣀⣤⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣄⣀⣠⠄⠀⣠⠟⢻⢏⡏⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠁⠀⠀⠙⠛⠛⠁⢠⠏⣼⢁⡀⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⣍⣛⣶⣤⣀⣀⠀⠈⠙⢛⡟⠉⣉⣠⣴⣞⣵⢿⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⠤⢽⣮⣭⣥⣬⠭⠟⣋⡿⠿⣟⡻⠭⣤⣤⣭⡤⠿⣚⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠚⠉⠁⠀⠀⠈⠉⠉⠒⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠘⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠤⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⢀⠄⠀⠀⢀⡔⠀⠁⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⡀⠀⢀⣰⣃⣤⣴⣯⣤⣤⣶⣋⣀⣀⣠⠴⠃⠈⠢⣀⠔⠀⠀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⣠⣀⣴⣷⣿⡿⠛⠛⠋⠉⠙⠻⣯⡙⠛⠛⠿⠷⣶⣶⣶⠛⠙⡄⢀⣠⠖⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⡄⠀⣧⣴⠿⠛⢉⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠉⠛⢿⣿⣿⡋⠁⢀⣀⣴⠞⠁
⠀⠀⠀⠀⠂⣷⡾⠋⠁⠀⠀⣸⠃⠀⠀⢀⣾⣿⣿⣦⠀⠀⠀⢻⡀⠀⠀⠀⠀⠠⠴⠿⣿⠟⠛⠋⠉
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣿⣿⣿⡟⢀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⣸⠟⠛⠒⠢
⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣀⡀⠉⠁⠈⠉⠉⢁⡿⠀⠀⠀⠀⠀⣠⡾⠛⠓⠦
⠀⣸⡃⠀⠀⠀⠀⠀⠀⠄⠈⠉⠙⢯⣉⠁⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⢀⣠⣾⠋⠉⠒
⠀⣏⠱⢄⡀⣐⣀⣉⣀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠞⠋⢁⣀⣠⣴⠾⠻⣍⠉⠃
⠀⢨⢿⡛⠉⠉⠉⠉⠉⠉⠛⠛⠒⠒⠶⣶⠖⢲⡒⠻⡏⠉⠻⠀⠈⠃⠀⠈
⢠⠇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁
⡾⠀⠀⠈⣇
⡇⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢠⣄⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠾⠛⠛⠛⠛⠛⠲⠦⠠⠦⣄
⠀⠀⠀⠀⠈⠙⠒⠷⡄⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠟⠲⣄⠀⠀⠀⠀⣀⣠⣤⣖⣋⣭⠴⠋
⠀⠀⠀⠶⠤⢤⣄⣀⠀⠀⢠⣿⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠈⠳⣄⠀⠀⠉⠉⠀⠁
⠀⠀⠈⠉⠉⠋⠉⠉⠉⠁⢸⡏⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⣾⠁⠀⠛⠦⠭⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤
⢀⣀⣠⣤⠤⠒⠀⠀⠀⠀⣾⠉⣍⡓⠀⠀⠀⠀⣀⡴⠚⠁⠌⠙⠛⠋⠁⠀⠀⡀⠀⣨⡍⠉⠛⠒⣦⡀
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠉⢀⡠⠖⠈⠁⠀⠀⠀⠐⠀⠈⢢⠟⠀⠾⠁⡞⢁⡤⠄⠀⠀⠈⠓⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡶⠋⠀⠀⠀⠀⣠⠜⢳⡖⣒⠂⠀⣠⣤⣄⠀⠱⣏⢰⡂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣰⠃⠀⠀⠉⠁⠀⣾⣿⣿⣿⠏⠀⠈⠉⠁⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⣰⠇⣿⠑⠦⢤⣀⣀⣀⡀⠀⣰⠟
⠀⠀⠀⠀⠀⣠⣤⡶⠀⣾⠁⠀⠀⠀⠀⠀⣰⠏⣿⣦⣄⡀⠀⠀⢾⢙⣻⠟⠀⢀⣀⣤⡾⠋⠀⢿⠀⠀⠀⠀⣈⣭⣵⠞⠋
⠀⠀⠀⠀⣯⠵⠋⠀⠀⣿⠀⠠⠄⠀⠀⢠⡏⢰⡿⠈⠉⠛⠳⠶⠤⠉⠥⠖⠛⠉⢉⣀⢀⣀⣀⣠⣤⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⢀⣀⡴⠋⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠙⠿⠿⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠆⠉⣷⣄
⠀⠀⠀⠀⠀⠀⢸⣟⢿⡷⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠞⠁⠰⠂⣿⠸⣦
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠙⢧⡀⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⡏⠀⠈⢳⣄
⠀⠀⠀⣠⡶⠶⣤⠌⢳⡀⠀⠀⠀⠀⠀⠙⢦⡈⠑⠲⠦⣄⣀⠀⠀⠀⢀⣾⠁⢀⣤⠿⡁
⠀⠀⠀⣿⠀⠀⣠⠶⠂⠁⣀⣀⣀⣀⣀⣀⣀⣙⣲⣄⠀⠀⠉⠛⠶⠀⣼⡧⠶⠋⠀⠀⠻⣄
⠀⠀⠀⠹⣄⢸⣧⠀⠀⠙⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⣤⡀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠙⢦⡛⢧⣄⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠀⣧⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠙⢶⣝⠻⣦⣀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣧⡀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣮⣙⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣉⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠙⠓⠶⢤⣄⣀⣀⣀⣠⣴⡟⠀⠈⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣹⣏⣛⣹⣿⣈⣍⣻⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣿⣿⣭⣭⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠒⠒⠒⠲⠤⣄⡀⣴⣢⠼⠻⣋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⡀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⢀⣾⣧⣰⣦⠀⠀⠀⣾⠋⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡜⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣽⣼⣿⣌⢹⣿⣀⠀⣸⡟⠖⠉⠥⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢸⣿⣦⣶⣦⣧
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣌⠻⣿⣥⣼⢁⡬⢂⣠⣤⣤⠀⠀⠀⢾⣿⣿⣿⣿⡆⠀⣿⣿⡿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣽⣎⠱⡜⣿⣿⣾⣣⣿⣿⡾⣿⣷⡀⠀⠸⢯⡶⠛⠋⠑⠓⠲⣶⣦⣤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣿⣾⣿⣿⠿⣞⡵⣶⣻⣿⣿⣄⣖⠐⢿⡅⠀⠀⠀⠀⠹⡟⢸⠀⠀⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢿⣻⣵⠛⠋⠉⠙⣿⣿⣿⣿⣿⣷⣾⣿⠶⣄⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⢴⣿⣿⣿⠂⠀⠀⢠⣿⣿⣿⣿⣿⣟⣿⡏⠀⠈⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣿⠳⠀⠀⣸⠀⣻⠟⠙⢉⣉⣀⣀⡙⢂⠀⠀⠀⡗⠂⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⣟⠛⣄⠆⢸⣾⠇⣴⣾⣿⡟⣿⣿⣗⣦⡄⢰⢠⠃⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⡿⢿⣿⣧⡹⣦⣿⠟⠛⢛⣁⣒⣺⡿⠃⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠉⠩⣉⣛⣿⣿⣷⡘⢿⠷⠞⠋⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠒⠒⠒⣒⣒⣶⣿⣿⣿⡄⠃⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⣉⣩⡭⠥⠶⣲⣿⣿⣧⣤⣤⣴⣾⣿⡾⣟⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⢀⣀⠴⠖⠋⣩⣶⢟⡿⢋⡿⢹⠛⡇⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⠉⠀⢀⣤⡾⠋⣠⠞⢀⠟⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠘⠁⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⢦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠳⠄⠒⠀⠙⠀⠀⠉