Echinoderm Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣦⡴⠶⠶⠶⠾⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣷⠛⠀⠀⠀⠀⠀⠀⠀⢁⡤⠒⡁⠂⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢁⡵⢛⡟⠯⠩⣟⣿⣁⠠⠀⠀⠀⠀⠀⢀⡞⡱⠃⠀⠀⢺⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡿⣴⠁⡀⠶⣼⣿⣿⣿⣷⣎⡦⠀⠀⡁⢸⣇⡇⠀⠀⢀⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢷⣼⣄⣠⡾⠋⠊⢉⠗⢙⣿⠴⠀⠀⡤⠘⣿⠳⣄⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣴⣶⣄⣄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣼⠧⠆⠀⠀⠀⢠⠌⢷⣌⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠀⠀⠀⠢⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠘⠀⠀⠀⠀⠘⢁⣼⠇⠀⠀⠀⠀⠀⠀⠠⢠⣿⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⡆
⠀⢀⣀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⣤⣶⠛⡞⢻⣆⡀⠀⠀⢀⣸⣤⢀⠀⠙⠘⠁⢸⡇⡂
⠀⠀⠀⠙⣇⠀⠀⠀⠀⢿⣿⡁⠀⠀⢠⣿⢤⡄⢔⣀⡶⠀⠉⢻⣆⢠⣾⡿⢿⣆⣤⣿⣟⣋⣉⠛⢾⠷⠿⠞
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⠘⣿⡗⡠⠘⢿⣧⣤⠾⠛⣥⣀⣠⣤⣟⣛⣇⣀⣸⣷⠟⠣⠿⠉⠉⠈⠀⠂
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢽⣇⠀⠀⠁⠀⠀⠀⠀⠙⣿⣋⠅⢰⡏⠈⣙⣿⠏
⠀⠀⠀⢀⣿⡆⠀⠀⠀⢠⢤⣿⠓⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣶⣿⣷⡾⢯⣿⣔⡊⠀⠀⠀⠀⠀⣠⡼⠾⢶⣴⣲
⠀⠀⠀⠀⠹⢷⣤⣦⣌⣷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣧⢦⠀⠀⠀⠀⠘⢛⢷⡄⠀⠀⠀⣿⠏⡶⠚⢂⡘⣷⡁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⣺⣿⣅⡀⠀⠀⠀⠠⢤⣿⠁⠀⠀⠀⣿⡖⡁⠀⢸⡜⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⡏⠿⠍⣟⣿⣯⠈⣟⣽⣿⣈⠀⠀⠀⠂⢸⡿⢠⠀⠀⠈⣿⣏⡇⠀⢀⣈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢧⡄⠀⠀⠀⠘⠿⣿⠀⢱⣹⣿⡇⠁⠀⠀⠆⣿⣇⣿⣄⡔⢴⣿⡗⠃⠀⣾⣽⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⡀⠀⠀⠀⣴⢲⣿⣤⠴⣼⣿⢡⠀⠀⠀⢂⠉⠿⣿⣷⣶⡿⠯⠀⠀⣰⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⣠⣀⠐⣁⣿⣿⣥⣼⡟⠉⠂⠀⠀⠀⠀⠀⠐⠀⠛⠙⠀⠀⢀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡿⠿⡟⡛⠡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡿⠋⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣶⠆
⠀⠀⠀⠀⠀⠰⠶⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠿⠟⠉
⠀⠀⠀⣰⠟⠀⠀⠀⠀⠘⢿⣷⣦⠀⣠⡀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠶⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠸⠋⠀⠀⢰⣾⣿⠃⠀⣩⣾⣿⠟⠀⣤⣤⡀⣾⣷⣶⣾⣿⣧⠀⠀⠀⣰⣶⣤⣀⡀⠀⠀⠀⠻⣷⡄⠀⠀⠳⣄
⠀⠀⣦⣤⣄⢰⣿⠏⠀⣴⣿⠋⠈⢹⣿⡿⢛⣿⣿⡿⠿⣿⣿⣿⣿⣦⣀⡐⠉⠉⢻⣿⣧⣀⠀⠀⠀⠹⣿⡀⠀⠀⢿⣷⡀
⠀⢴⣇⠉⠻⣿⣁⣴⣄⣿⡿⠀⠰⣾⠟⢁⣼⠛⢉⣶⣄⣸⣿⡏⠙⣿⣿⣷⣄⠀⠀⢹⣿⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⢸⠟⢳⣤⠈⠉⢰⣿⡇⠀⠀⣼⡃⣠⠀⠉⣾⠿⠄⠈⢹⡏⠁⠀⠸⣿⣿⡿⠃⠀⠀⣿⣿⠀⠀⠀⡀⠘⠛⠀⠀⠀⢸⣿
⠀⠀⢿⡆⠈⠢⣀⣼⡿⠃⠀⢀⡹⠿⠁⠀⠾⠋⠀⣠⡿⣿⡷⠂⠀⠀⠈⣿⠟⠀⠀⠀⣿⡿⠂⠀⠀⠉⢰⣿⠀⠀⠀⠺⣿
⠀⠀⢀⡀⠀⣴⡉⣉⣷⡆⠀⠘⣿⣶⠀⠀⠴⣦⡀⠛⣤⣾⣷⣴⡶⠀⠀⣿⣿⡶⠀⢀⣿⣿⡆⠀⢀⣀⠾⠏⠀⠀⠀⢠⣿
⠀⠀⠸⡿⠀⢹⣿⡟⢿⡏⠀⠀⣽⡅⠀⠀⠀⢰⡗⠀⠛⣷⣿⣿⡄⠀⠀⣹⣿⣆⢀⣿⣿⡤⣿⠂⠈⢿⣦⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⣴⠏⠉⣿⣿⣿⠖⠘⠻⠁⠀⠐⠂⢸⣿⠀⣴⣿⣿⣧⣤⣴⣾⣿⣇⠀⣿⣿⣿⣀⠀⢠⣤⣬⠟⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⣠⣤⣾⠛⢿⣶⣶⣾⠟⠁⢀⡀⣿⣇⠀⢙⠿⢋⣿⣿⠛⣿⣿⠁⢀⣾⣙⣿⠉⠀⢈⣻⠟⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠙⠉⠙⠀⠀⠙⣿⣿⣄⡀⠛⠁⠘⢿⠁⠈⠀⠻⣿⣿⣿⣿⠇⠸⣿⣿⡿⠋⢳⣆⠻⠃⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠙⣿⣿⣧⡾⠛⠳⣤⠛⠃⠀⠀⠛⣿⣿⣅⣀⣀⣽⡿⠁⠀⣀⡘⠁⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠻⣿⣿⣷⣾⣧⣤⣿⡇⠀⣠⣾⣿⠏⠉⢁⠿⢿⣤⠶⡾⠉⢀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠟⠛⣿⡋⠉⠁⠀⢴⣀⠀⠀⢼⣿⣶⡀⣀⣼⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠸⠇⠀⠀⠀⠙⠓⠘⠂⢠⣾⠟⠛⠀⠀⠋⠈⢻⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠐⠆⠀⣀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠉⢠⡀⠀⠀⠟⠁⠀⠀⠀⢠⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⣀⠀⠀⢀⡜⠁⠀⣤⣤⠀⣠⣾⡿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠉⠁⠴⠟⠉⠀⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⢀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⣀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠐⢀
⠀⠀⠀⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠁⣦⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣃⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢰⡆⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠆⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠉⠁⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⣿⣦⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠙⠷⣴⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠿⠇⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⠸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣽⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠟⠂⠐⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡀⠾⠇⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠁⠀⠀⢰⣷⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠿⠃⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣾⡇⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠋⠁⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠤⠀⠉⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⣀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠒⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⠁⠲⠆⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠂⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠀⠀⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢂⣀⠀⠀⢰⡎⠁⠀⠀⠀⠀⠈⠉⠆
⠀⠀⣀⡀⠀⢤⣶⡆⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠻⢷⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣴⣶⣶⡤⠤⠶⣶⣿⡿⠋
⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⠛⠋⠠⡿⠛⠉⠉⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠀⠀⠘⠿⠿⠛⠛⠃
⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠃⠀⠀⠀⠘⠻⠿⠿⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣶⣶⣶⣶⣦⣤⣶⣾⣿⣿⣶⣶⣶⣶⣾⣷⣶⣷⣾⣿⣷⣶⣶⣶⣤⣤⣤⣤⣴⣶⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣶⣶⣴⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣃⢀⣀⣀⠀⣀⣀⣀⣀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠧⠐⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⠀⡙⠀⠠⠆⠈⠆
⠀⠀⢠⣤⣄⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠒⠠⣐⠃⠀⠺⠺⠄⠣
⠀⠀⠸⠿⢿⠛⠯⠶⢩⣯⣷⡠⡀⣠⡐⠀⠀⠀⡀⠘⠛⡃⣭⣟⢫⢸⠁⠀⡄⠸⠈⢀
⠀⠀⠈⢁⠀⠀⠀⠠⠀⠈⠁⠋⠙⠋⠿⠧⣴⠠⣾⢋⣛⣙⠽⠯⠁⠀⠘⠀⠷⠀⣐⣅⡐⢢
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠠⠆⠄⠀⠀⠀⠀⢑⣸⢛⡟⣳⢽⡟⠛⢥⢀⡦⡞⠚⢻⣷⣶⣷⡞⣷⣝⣀⠔⠀⣆⣠⡠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠖⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⣓⢚⣞⠧⣘⣂⢤⠐⠃⠚⢃⣀⠈⠀⠀⠉⠀⠀⠈⠙⡿⠋⠭⠁⠻⢶⠷⠖⢶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⠀⡐⡠⢷⢛⣙⡟⠓⢘⣣⡄⢯⡀⢀⠀⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢄⠀⢨⠘⣷⠏⠉⠁⢠⠄⠸⣥⣋⡧⠐⠈⠀⠘⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⢀⡠⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢀⢰⣿⡇⠆⠀⠀⠀⠀⠀⠰⠉⢣⣺⠗⠄⠀⠀⠀⠈⠀⠀⠀⡠⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⡿⠁⠘⠁⠀⠀⠀⠀⠀⠀⢌⠨⣿⠄⠀⠀⠀⠀⠐⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠀⣂⣴⢆⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡐⠟⠐⠆⠀⠀⠀⠀⠀⠀⠀⠵⠂⠀⠐⠸⡋⢿⡀⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣃⣶⢠⡐⠀⡄⠀⠀⠀⠀⡀⢠⠄⠂⠀⠀⢂⣐⡙⢾⡷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠘⣶⡔⡉⠐⠬⠁⠀⠀⠀⠀⠄⢀⣠⠠⣠⢀⠀⠀⠈⠀⠐⠌⢹⣷⡀⠀⠈
⠀⠀⠀⠀⠀⡠⠂⣼⠃⡠⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠰⣠⣷⠂⠀⠀⠄
⠀⠀⠀⠀⠴⢞⡹⡟⢢⠘⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠠⠀⠀⢈⣩
⠀⠀⢠⣾⣆⣴⠨⣀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠘
⠀⠀⠰⡯⠋⢟⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠁
⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠐⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣭⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣴⡄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡶⡄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⣭⡅⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⣀⡀⠀⠀⠀⢀⣾⠇⠀⠘⠶⠋⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⢀⡀⢈⠉⠉⠙⠛⠛⠛⠛⠉⠀⠀⣴⠛⣦⠀⠀⠙⠻⠿⠶⠶⠶⠶⠶⠖⠒⠛⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡈⠁⠻⠃⣞⡧⣠⠶⡄⠀⣀⡀⠀⠈⠛⠁⠀⢀⣠⣀⠀⡤⣄⢠⣶⡄⢶⠆⠗⠘⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠘⠚⠁⢾⣉⡿⠀⣴⠟⢶⡄⠸⣥⡿⠈⠳⠚⠀⠉⢀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠉⠀⠀⠻⠶⠾⠁⠀⠀⠀⠀⠀⣠⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⢠⡞⢻⡄⠀⠀⣶⠛⡆⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣤⢤⠙⠋⠀⠀⠀⠙⠛⣡⣄⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣀⡓⠞⠁⠀⠀⠀⠀⠀⠀⠳⠾⣁⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢀⣌⠳⠃⠀⣠⣶⠿⠛⠻⢷⣄⠀⠘⠯⣃⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣬⠛⠁⢀⡾⠋⠀⠀⠀⠀⠀⠙⢷⡄⠀⠓⣣⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠲⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠶⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣉⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠆⠶⢶⣶⠚⠛⠛⠛⠛⠛⠿⠿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢉⡒⠋⠀⠈⠁⣬⢠⣴⠦⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣌⠛⠠⠶⢖⣂⣀⣺⡧⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⢠⣿⣿⢿⣿⡟⠈⠃⠀⠈⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠛⢁⣠⣿⣿⡿⠻⣿⣧⠀⠀⠀⠀⠀⠈⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛⠁⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⣤⣷⣿⣾⣦⣄⠀⠀⠀⢠⣴⣿⣿⣿⣦⡄⠀⠀⠀⠀⡠⢴⣶⣦⢄⠀⠀⠀⠀⣠⡔⡆⣲⢠⡄
⠀⠠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠶⣟⠇⠀⠑⠀⠀⢜⢧⣳⢣⡏⣞⠜⡣
⠀⠘⠛⢻⡿⠻⠻⣿⠛⠃⠀⠀⠈⣿⡛⠉⢙⣿⠁⠀⠀⠀⠀⠀⠐⣯⠃⠀⠀⠀⠀⠀⠑⠷⡉⣀⠝⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⢀⣀⣀⠀⢀⣿⣧⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣿⡇
⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠟⠋⠁⠘⠻⢿⣶⣶⣿⣿⣶⣶⣶⡶⠆⠀⠙⠻⢿⣷⢻⣭⡟⣶⣶⠶⠖
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⣿⣯⣿⣹⡏
⠀⠀⠀⠀⢰⡿⠋⠀⠙⢿⣧⠀⠀⠀⠀⠠⡾⠟⠉⠀⠙⢿⣆⠀⠀⠀⠀⠀⢀⣾⠟⠉⠉⠻⣿⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⠀⠘⣿⣿⣿⠋⣼⣷⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠐⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢻⣏⣸⣿⠏⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠁⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢠⡀⢸⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢛⠤⠀⡆⠈⣫⡻⣦⣄⣀⠤⢄⡠⠤⠤⠶⡶⢶⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⡚⢉⠛⠋⠻⠿⠿⠿⠾⣯⢵⠟⡄⠀⠴⠀⣹⡿⠀⡉⠆⠋⠈⢡⡀⠢⢀⣱⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣤⣅⣀⠉⠁⠄⠀⠤⢁⡀⠑⠈⢃⡀⠔⠀⠁⠀⠀⣁⠰⠘⢃⣠⣤⣀⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠯⣷⠤⣄⢀⠈⠀⠒⠠⠀⠀⢀⠀⠒⠰⡁⢀⣠⣴⣽⡳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢌⣲⣦⠀⠄⢀⠘⠢⠺⠀⠂⠐⠘⢳⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠈⠁⣰⠂⠔⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡞⢀⠘⠀⣤⣿⡦⠠⠘⢁⡀⠒⢈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠜⢀⠁⣀⣬⣿⠿⠿⣴⡦⢀⠁⠆⠀⠘⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠄⢡⠼⣳⠞⠁⠀⠀⠀⠙⠻⢷⡆⡑⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠣⠀⣠⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⣄⠀⣤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⣾⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⢀⠄⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠐⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠎⠀⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢀⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⣿⡇⠀⢀⠉⠛⠿⢶⣦⣤⣀⣀⣀⣀⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀
⠀⠀⢻⣇⠀⠊⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠉⠛⠛⠿⠿⠶⠶⢶⣶⣤⣤⣄⣀
⠀⠀⠈⢿⣦⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢄⡸⣺⣭⠍⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡦⠉⠛⣤⠂⠀⠀⠀⠀⠀⠀⢀⡈⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠙⢷⣄⠀⠂⠘⠀⠀⠀⠀⠀⢸⢸⣿⣿⣦⣶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣧⣴⠂⢸⠀⠀⠀⠁⠀⠀⠀⠄⠠⠀⠀⢀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠂⠀⠀⠀⠸⡌⠛⠿⠟⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠛⠛⠉⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣄⣀⠀⠈⠓⠦⠴⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠓⠒⠚⠉⠀⣠⠶⠒⠛⢛⣲⣶⣶⣤⣤⣤⣤⣤⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⠙⢦⡀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⢰⠇⠀⢠⣾⠟⠋⠉⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⠀⠈⠉⠳⢤⡀⠑⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠘⢀⡨⠀⠀⠀⠀⡴⠋⣠⣤⣶⣶⣶⣦⣤⣄⡀⠳⣄⠀⠣⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢀⠀⠀⠀⠀⠀⢀⣼⣵⡿⠋⠁⠀⠀⠀⠀⠈⠉⠛⠷⣾⣷⡀⠀⢀⡀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠁⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠈⠁⢀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡀⠂⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠈⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠁⢠⠀⠀⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠲⠦⠤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⡏⠀⠀⠀⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⣀⠀⠀⠀⠉⠁⠂⠄⡀⠀⠀⣰⢿⠁⠀⠀⠀⣰⠻⠀⠀⠀⢠⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡄⠀⠈⠛⢶⡦⢤⣀⡀⠀⠀⠁⠲⣿⠃⠀⠀⠀⢠⠇⡆⠀⠀⠀⣎⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⡄⠀⠀⠀⠈⠑⠢⢌⠙⠲⢄⡀⠀⠀⠀⠀⠀⡜⢰⠂⠀⠀⠀⡏⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡸⢦⡀⠀⠀⠀⠀⠀⠉⠢⣄⠙⢦⡀⠀⠀⠰⢡⠋⠀⠀⠀⠀⠈⠺⢧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡘⢙⣦⠀⠀⠀⠀⠀⠀⠈⠑⠤⡙⢦⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣸⢀⣷⠀⠀⠀⠀⠀⠀⢀⣀⢨⢹⣿⠶⡶⢶⡒⠒⠒⠒⠒⠲⠶⠤⠤⣄⣀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠛⠉⠁⠀⢀⡠⠔⠒⠉⢀⡠⠔⠉⡟⡄⠀⠀⠀⠉⠉⠑⠒⠒⠒⠒⠒⠒⠚⠛⠛⠂⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⣀⠤⠒⣉⣠⡤⠔⠒⠉⠁⠀⠀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⡴⠾⠓⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠴⣾⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠀⠀⠀⣠⠶⡶⢲⡖⠺⡛⡏⢹⣁⣧⠼⠋⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢣⠀⠂⠀⠀⠀⠀⣿⣄⣇⣸⣇⣰⠥⠟⠚⠉
⠀⠀⠀⠀⢠⣶⢥⣤⣤⣤⣤⣤⣤⠤⢤⠴⠶⠖⢲⡋⢻⠀⢇⢸⣨⠷⡄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢸⣿⠉⠁
⠀⠀⠀⠀⠀⠉⠛⠳⠿⠦⠾⠤⠼⣆⣨⣆⣰⣆⣴⣧⡼⠤⠛⠻⡇⡰⠉⣦⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⢰⠉⣇⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⢠⡟⣦⠀⠀⠀⠈⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣇⡏⢳⢄⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣷⢀⡷⡄⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣹⡄⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢠⢤⣴⡆
⠀⠀⠀⢀⢰⣿⣡⣀⡀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⡩⠀⠈⢺⣿⡷⠼⠦⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⣶⣼⢿⣿⣿⣆⠋⠀⠉⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣁⣀⠀⣸⣿⡗⠒⠐⡶⢧⡴⢀⡀⠀⢸
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⣤⣠⡾⡉⢀⣾⡿⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣍⠉⢻⣻⡧⡀⢰⣇⣠⡷⠀⠙⠖⠋
⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⠟⣠⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣀⠑⢸⣹⡷⢻⡾⣟⡿⢷
⠀⠀⠀⠀⠀⢸⣿⣿⠃⣾⣿⣿⣿⣿⢟⣶⣿⣴⠃⣺⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢸⣿⣇⣸⡡⣿⡁⡨⠁
⠀⠀⠀⠀⠀⢸⣿⣿⡾⣿⣿⣿⣿⣷⣿⣿⣋⣭⠾⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⣟⣥⡀
⠀⠀⠀⠀⠀⢢⣿⣿⣷⣿⣾⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠓⠀⠀⠀⢸⣿⣇⣠⣽⣿⣿⣿⡃⢀
⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⠠⠴⠒⢻⣿⡇⢀⡟⢙⡃⠘⣃⡼
⠀⠀⠀⠀⠈⣷⡯⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣷⠿⣦⠾⠛⠚⣟⢱⠖⢦
⠀⠀⠀⠀⢰⡿⠴⠂⠀⠀⠠⣴⡄⠀⣶⣦⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣼⣿⡇⠘⠙⠑⠀⠀⠹⣤⣠⡾
⠀⠀⠀⢀⣼⣣⠎⠀⠀⠺⢷⡿⡏⠉⠹⢿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠁⠈⠒⠁
⠀⠀⠀⢀⣏⡀⠀⠀⢰⣤⣎⡀⣐⣶⣶⡀⢻⣤⣀
⠀⠀⠀⠨⣿⠀⠀⠀⠈⣸⣿⣯⣀⣏⣈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠻⣦⠀⠀⠀⠈⠡⢼⡿⢿⣿⠉⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣶⣶⣦⣤⣼⣿⣿⣷⣤⣶⣶⣶⣶⣾⡿⠆
⠀⠀⠀⣤⠀⠀⠐⡆⠀⡀⢠⠀⠀⢠⡄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⣾⣶⡞⢽⣿⡟⣹⣾⠆⢰⣾⠉⠀⠀⠚⠛⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢹⡿⣿⡃⠉⢳⣿⣿⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⡟⠉⠙⢿⣿⣿⣄
⠀⠀⠀⠀⠳⡹⡧⢸⡿⣿⠃⠀⢸⠿⠀⣀⡄⠀⠐⠆⠀⠀⢦⠄⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠘⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠐⠤⠚⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠂⠀⠈⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣾⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡃
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⢳⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⣄⣀⣀⠀⢀⡠⣤⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣄⣰⣿⣿⣿⢿⣬⣭⠻⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣯⣿⡇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⢿⢿⣿⣿⣿⣅⢻⣿⣿⠗⢼⣿⣿⠇
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠈⢿⣿⣿⣧⣭⣽⣾⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠛⠉⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⠛⠛⠻⠿⢿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⡈⣁⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⡀⠀⠀⠀⠁⠀⠔⣠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⣀
⠀⠀⠀⣀⣃⢂⣀⣤⣀⣤⣐⣠⠀⠀⠀⠀⠀⠢⠁⣦⠀⠂⠈⣁⡈⠈⠁⠚⡩⠐⢀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠁⠙⡔
⠀⠀⣀⣸⣿⣿⣿⣴⣿⣿⣿⣷⡠⡀⠀⠀⠐⠻⠞⢀⠀⠀⠈⠙⠉⡅⠀⠀⠀⢥⣳⠀⠀⡔⢄⠁⠀⢀⠉⠀⠀⠉⠀⢀⠀⠀⠃⠀⢐⠄
⠀⣀⣸⣯⣿⡿⠿⠟⠛⠛⢫⣿⣿⣗⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠈⣶⡆⠀⠐⡦⠂⠀⠀⠢⠤⡠⣤⢤⡬⣷⢶⣤
⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⡤⠀⠴⠃⠉⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠈⠁
⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠊⠂⠱⢄⡀⠀⠀⡀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠋⠈⠙⠊⠀⠙⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠌⢀⡀⠈⠠⠀⢒⣴⠄⠀⠀⠀⠀⠁⢈⠀⠀⢀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠁⠡
⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢀⠗⠂⠈⢀⣀⣀⠈⠀⠙⣡⣊⢀⠀⠀⠼⢠⠈⠀⠠⠀⠀⠀⠀⠁⠀⡀⠀⠈⠀⠈⠔
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠘⠻⠏⠀⠄⠀⠀⠘⠈⠆⠀⠀⠀⢰⠯⠀⠀⠀⣶⠂⠀⠈⠒⠢⠤⠤⡤⠤⠽⠿⢦⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣶⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠌⠀⠀⠀⠠⠐⡀⠀⠀⠴⠀⠖⠉⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠂⠱⠠⣀⠀⢀⡀⢀⡀⠀⠔⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠶⠛⠉⠉⠉⠉⠙⠓⠢⣄
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⠀⠀⠈⠉⠓⠒⠒⠒⠒⠒⠲⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⣀⡀⠐⠀⡭⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢁⠀⡤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⣠⠖⠂⠂⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠐⠒⠒⢺⠕⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠧⠀⠠⢄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢹⡏
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⣴⣶⣶⡶⠬
⠀⠴⣾⣿⣿⣿⣛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿
⡶⢾⡿⠿⣿⣿⣿⣷⣶⣤⡀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢸⣟⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⢻⣦⣟⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⢾⢍⡙⣿⣷⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣙⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⠘⢳⣾⣿⣿⣶⡀⠀⠀⠀⣿⣿⣿⣿⣿⢝⣈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⡀⡈⢽⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⣿⣿⡇⠏⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠅⠀⢻⣿⣿⣿⣿⣷⡀⢿⣿⣿⢿⣿⠇⠱⠾⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⠐⢀⠻⣿⣟⢻⣿⣷⣼⣿⣿⣞⣅⣄⠀⠰⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⡆⠙⣿⣧⣿⡿⣿⡿⣿⣏⣻⣹⠆⠀⢯⣿⡄⠀⠀⣀⣤⣶⣶⣾⣿⡟⢶⡛⠾⠻⠶⠿⠛⠛⠉⠉⢁⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡷⢧⡘⢿⣿⣷⣿⣿⣿⡿⣿⣿⡆⠀⢘⣿⣧⣶⠿⠷⡟⠿⠸⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⣄⣀⣄⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⣧⡐⣛⣻⣿⣿⣿⡿⠿⣿⣿⣧⣴⣿⠯⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣆⣀⣦⣴⣴⣾⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣭⠅⢛⣿⣿⣿⡟⠈⠻⠿⠟⠟⠉⠀⠀⣀⣠⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⣀⡀⢠⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠁⠛⢿⣿⣟⢻⠷⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠁⠀⠀⣴⣾⣿⣿⣾⠀⠈⠛⠛⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠉⠀⣀⣴⣿⣿⢿⣿⣿⣿⣿⡀⠀⠈⢱⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⣤⣾⣿⣿⡏⢸⣿⣿⣿⢿⣶⠀⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠃⠀⠀⣪⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⣠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⡦⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⣠⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠐⢿⣧
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⢺⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠆⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣋⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠆⠀⢺⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠐⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⣿⡇
⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⢻⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⢉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⣤⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠸⢩⣠⣴⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠸⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠊⢁⣀⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠩⢿⣧⠀⢀⠤⠂⠉⠀⠀⠀⠄⢨⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠘⣿⣷⠉⠠⢂⠀⠐⣈⣰⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⠐⠒⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠹⠛⠀⠀⢀⡰⣿⣿⠟⠁
⣀⡤⣄⠒⣂⣐⢈⠡⣑⠀⠐⡐⡀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⢚⣷⡿⠟⠁
⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⢷⣶⣶⣾⣤⣤⠀⢀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠂⠤⠤⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣵⣤⣽⣶⣶⠗⠀⠀⠀⠀⠐⢨⡄⢀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠈⡜⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⣴⡿⠻⢶⣧⣯⣷⣤⢢⣅⠀⣠⣤⣅⡤⡆⠀⠂⠺⣱⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡁⠠⠀⠀⢔⢿⡿⠁⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⢿⣶⣢⡀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢐⣮⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⢀⢲⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⢀⣰⢶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⢀⡂⣠⣺⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣥⣤⠾⠿⠿⠿⠛⠋⠁
⣿⣿⡷⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠤⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠖⠦⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢡⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣶⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡌⠀⠀⢀⠀⣁⡀⣀⡄⠀⠂⢂⡀⠀⢀⠀⠀⢀⣀⠀⠀⠀⣀⣀⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⢀⠀⠁⠀⣰⠦⢀⠙⠛⡛⠃⠂⠠⢯⣠⣤⣾⠁⠀⠀⢨⠀⠂⣸⣿⠟⠁
⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠰⢒⣋⠉⠀⠖⠉⣤⠀⠖⠀⠀⣹⡏⢁⠀⠀⡀⢀⣦⡦⢨⢇⣤⣤⡾⠂⣴⣾⡿⠁
⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠂⠀⠲⠒⡒⠶⠟⢁⡀⠤⠀⠀⠸⢫⡄⠚⡟⠛⠠⢄⡄⣿⡟
⠳⣄⡀⠀⢀⣀⠀⠀⠠⠶⠀⠰⠆⠀⠐⠎⠀⠠⡞⢁⡤⠉⠓⣠⣉⡭⠀⠋⠁⠀⠿⢖⣤⡀⠁⠀⠀⡑⠂⠀⠀⢻⡇
⠀⠀⠉⠛⠺⠷⣦⣷⣀⣢⣀⠌⢁⠀⠀⠀⠀⠀⠑⠈⣳⡶⣶⡟⠩⠁⠐⣿⠀⠀⢀⣬⡑⢿⣾⢿⣿⡿⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣤⣤⣔⠀⠀⠀⠒⠀⠲⡴⠶⠆⢰⣤⣴⡿⣅⠛⢣⣉⠸⢠⣍⢐⠚⠀⢀⡎⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣶⠁⠀⠀⠀⡉⢀⠾⣀⢨⣿⠑⣿⢂⡈⠙⠷⣿⢡⣼⣿⣤⣼⠋⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢢⠀⠡⠔⠀⠀⠿⢦⠛⡛⠛⠁⠲⠄⠀⠐⠂⠛⠏⣍⢤⡄⠀⠠⣈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠺⡇⢰⣥⣤⣤⣼⡟⠀⠁⠀⢐⣴⣈⣀⣻⠃⠀⠀⡈⠀⠈⠀⠄⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠏⠀⠉⠙⢁⠧⠔⠉⣰⣿⠛⠉⠉⠉⠙⠓⠳⠶⣦⣀⡶⠂⠀⠀⠄⠀⠀⠀⠀⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠃⠀⠀⠀⠋⣠⠈⣥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣈⣁⠀⠄⠄⠐⠒⢆⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠈⠀⠙⠙⠃⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠦⢤⣤⣤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣀⣶⠆⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠁⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠲⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠆⡀⠶⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣈⢀⡾⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠞⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡶⢻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⣿⣹⣯⣽⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⢿⣿⣿⠟⢻⣅⣽⣶⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⣿⡋⣿⠛⢿⠿⢿⡿⠿⣦⣾⣇⣈⣷⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣿⣷⣾⣧⣴⠿⢿⡏⠙⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⠿⣤⣾⣷⣾⡁⣹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⣤⣾⣿⣿⣿⣿⣧⣼⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⣶⣿⣿⡿⠛⠿⣿⣿⣷⣼⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣻⣾⣿⠿⠋⠀⠀⠀⠈⠙⢿⣿⡾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣭⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⡏⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣯⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⡗⢎⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⢧⢭⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠄⢈⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⣼⠆⡺⠜⣅
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡾⠦⠑⠼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⣠
⠹⢜⡓⠲⡴⢧⣭⣡⡆⣰⠄⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠄⢈⠒⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠴⠒⣈⠣⠀⠀⠀⣀⣽
⠀⠀⠉⠓⢮⣽⠛⣿⠿⣿⣷⡿⢦⣾⣍⢸⡖⠒⡤⠤⣀⣤⢶⣤⡇⠀⢀⡷⠚⢷⡤⠀⢠⠀⠒⠈⠸⢄⠜⠒⠉⠬⠀⢰⣠⡴⠖⠉
⠀⠀⠀⠀⠀⠀⠉⠑⠾⣇⣙⠇⢰⣪⢩⡿⡿⠾⠇⠂⣿⢉⢀⣹⡇⠀⣿⠀⠀⢸⠷⠴⠞⠁⠂⠉⠀⠀⢠⠀⢺⣤⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠚⢧⣰⡂⢸⡐⢁⠀⠈⠛⠻⠙⢁⠀⢹⠷⠛⠃⠀⠀⠀⡢⢠⡄⢀⡤⠼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⢼⠶⠗⢖⡄⠐⠀⠀⠀⡠⣶⠤⣴⠀⢈⣧⣼⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠏⣠⣤⣄⠰⣿⠀⢀⢘⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃⠀⣴⡟⠙⢽⡇⡀⠛⠚⠛⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠐⣤⣴⡿⠓⣤⠚⠷⠾⠛⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠐⠀⠀⠀⢰⡖⠃⠀⠐⠶⠛⠳⡠⠂⢰⠛⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠆⢄⡀⠐⣀⣼⠋⠀⠀⠀⠀⠀⠁⢏⠉⣂⠀⠒⠊⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⠄⠈⠂⢡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣁⣑⠀⠩⠁⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⢃⢺⣀⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠀⠐⠠⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡗⢅⠈⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢚⢱⣀⠰⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢀⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠾⢳⡀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢼⣿⡏

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠖⠛⢉⣹⠿⠀⠀⠀⠀⠘⠶⢿⣿⣄⠀⠀⠀⠀⣧⣟
⡇⠀⠀⠀⠀⠀⣴⠀⠀⣀⣼⣶⣾⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⢿
⡇⠀⠀⠀⠰⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⢢⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟
⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣇⠹⣆⠀⠀⠀⠀⠀⠀⠹⠟⠀⢸⢣⡄
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⡖⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣯⠞
⡇⠀⡁⢰⣿⣿⡿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢈⡇⠀⠀⠀⠀⠀⠀⠀⢸⠇
⡀⠀⡗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠟⢩⡇⠀⠀⠀⠀⠀⠀⣶⣾
⠇⠀⠸⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡸⠁⠀⠀⠀⠀⠀⠀⠉⠁
⡄⠀⠀⠙⣆⠘⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⡙⠁
⠇⠀⠀⠀⠀⠙⢦⣀⠉⠻⣿⠟⡛⣋⣉⡿⠤⠴⠶⠒⠛⠓⠛⠃
⡆⠀⠀⠀⠀⠀⠠⠼⠛⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠛⠛⠻⣿⡶⠤⠥⠤⠭⠭⠿⠛⠛⠳⢦⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠈⣧⠀⠀⠀⢀⡆⠀⠀⠀⢀⣈⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⢻⡀⠀⠀⢸⣇⣀⣀⣰⠏
⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠸⢦⡀⠀⠀⠀⠀⠀⠀⣼⠛⠓⠒⠻⠁⣿⠇⢸⠋⠀⠈⣿
⡇⠀⠀⠀⠀⠀⠠⠿⠦⣤⣤⠀⠀⠙⠦⣄⡀⠀⠀⢀⡯⠴⠶⠶⢶⡀⢻⠀⢸⠆⠶⠤⣏⠀⠀⢀⡠⠂⠁
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣠⡏⠉⠑⠒⢾⠀⠀⠀⠀⠀⡇⣾⡷⣾⠀⠀⠀⢸⠖⠋⠁⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠳⠀⠀⣸⠀⠀⠀⠀⢀⠃⠻⠃⣷⠀⠀⠀⢸⣀⣀⣀⣀⠘⠉
⠆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠣⢤⣀⡀⠀⠀⠀⠀⠀⢸⠶⠚⠛⠉⢹⣤⣿⡆⣿⡤⠤⠴⣏⠀⠀⠀⠀⢱⡄
⡆⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠉⠉⠀⠁⢀⡰⠏⠀⠀⣀⣤⠏⠙⠿⠃⠸⡄⠀⠀⠈⢳⡀⠀⠀⣸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣠⠟⠓⠀⣶⢚⣽⣿⣿⣿⣿⣿⣷⣿⣣⣤⠖⠋⢳⡄⠈
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⣿⠤⠀⢴⢳⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡄⠀⢠⡇
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢷⣀⠤⠸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⡛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡋⠉⠳⣶⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠹⣄⡀⠈⠀⠈⠙⠻⠛⠛⠛⡏⠁⠀⠻⣤⠖⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⡇⠀⠀⠀⣷⣀⠴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠷⠖⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣴⡴⠞⠁⢀⣠⢖⣠⠔
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⣤⠀⠉⠙⢿⡄⠄⠀⠠⡤⠤⢞⣩⣞⢩⢙⣾⣋⠤⣶⠞⠛⠉⣉⣠⣔⣠⠤⠂
⠀⠀⠀⠈⠑⠲⠄⠀⠒⠦⠄⠀⣁⠐⠒⠀⠀⠀⠈⠁⠀⠈⠀⠙⠀⠈⠈⡱⢶⠟⣣⠾⣯⣅⣀⣤⣤⠤⠴⠒⠂
⠀⣈⡉⠉⠉⢉⠠⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⠀⡨⢺⣺⡗⢯⢿⣿⣯⣉⡉⣙⣒⠖⠂
⠲⢦⡤⠭⠟⠥⠠⢄⣠⠀⢀⣀⠀⠀⡁⢀⠠⡰⣎⣀⠀⠀⢀⠀⢀⢐⡁⡴⣘⣏⣼⣿⣗⣾⣿⣿⣿⣿⣿⣒⣒⠋
⠈⠉⠉⠛⠿⢵⡶⡿⠗⠚⠫⠔⢉⣻⡽⢶⡗⠛⢾⠓⣾⠿⠿⣿⠿⢿⡿⣟⡻⠻⣿⠿⠿⢽⣟⠻⠳⠤⣍⡛⠿⢿⣧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣉⣉⣀⣀⣈⣀⣀⣀⣀⣉⣀⣀⣁⣀⣀⣀⣀⣽⣀⣀⣀⣀⣀⣈⣙⣂⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠸⣇
⠀⢰⡟⠙⠛⠶⣤⣀⣀⡀⠀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀
⠀⠸⣇⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣌⡙⠛⠓⠶⠶⠶⠦⢤⣄⡀
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣶⣿⣇⣈⠣⠀⠀⠀⠀⠀⠀⢰⣿⣏⣀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⢇⠻⠿⠋⡠⠁⠀⠀⠀⠀⠀⠢⡛⠛⠋⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⠤⣀⠉⠀⠊⠀⠠⣀⠀⠀⢀⣀⠄⠈⠀⠉⠀⡴⠊⢉⣭⠿⠶⠶⠶⠶⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢠⣋⡴⠶⠛⠒⠶⢦⣬⣣⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡧⠁⠀⠀⠀⢀⣀⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⠉⣂⣤⢶⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣀⣔⣫⣴⣿⣯⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡥⠶⠾⢿⢿⣏⠿⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣟⡿⠿⣾⢹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⠟⠓⠀⠀⠀⠛⠀⠁⠉⠀⠀⣤⠀⠀⠀⠀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⢿⣿⠉
⠀⠀⠀⠀⠀⠲⣶⣼⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿
⠀⠐⢾⢿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⢀⠤⠄⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⡀
⠀⠀⠈⠙⠙⠿⠿⣿⣿⣷⣤⣄⣠⣤⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣴⡶⡅⠀⠉⣠⣃⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠛⠉⠙⠻⠿⠉⠛⠟⠟⠛⠛⠛⠙⠛⠏⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢈⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⢒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠂⢐⡞⠄⢀⠀⠀⣀
⠀⠀⠀⠀⠈⢦⠈⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⠔⠋⠈⠀⠀⠉⠀⠓⠘
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡰⠃⠀⢀⡴⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⡇⠀⠀⡀⢀⠜⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳⣄⠀⠀⠉⠢⣀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠂⡰⠋⠀⠀⣠⠃⠄
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠳⣄⠀⠀⠈⠳⠶⢴⡏⠀⠀⠀⠈⠷⠖⠊⠀⠀⣠⠞⢁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢱⠁⢀⠀⠀⠀⢖⠣⠀⢠⠞⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⠀⠀⠀⠈⠀⣰⠋⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣿

⣶⣴⣤⣦⣴⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣴⣭⣽⣥⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠰⣴⣤⣄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢎⠉⠀⠉⠛⢷⣅⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠜⠀⠀⠀⠀⠀⠹⣷⢮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠑⢊⣽⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⣈⣴⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠁⢀⣰⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⣀⣴⣻⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⠔⢫⣷⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠻⣿⣤⣄⠣⠀⠈⡀⢀⠀⣠⣞⣤⣴⣾⣿⣿⡿⠟⠁
⠀⢶⣶⣿⣿⣾⣟⣿⣁⣘⠀⠀⣀⣀⡀⢄⡀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⢩⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣯⣫⣉⣽⣙⣙⢹⣟⢟⢺⣶⣶⢄⣴⠄⠀⠀⠀⠀⣞⣹⡿⠛⠛⠋⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⡿⠂⠀⠀⠀⠂⣈⡏⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠛⠛⠋⠋⠀⠀⠀⠀⠀⣼⣿⠿⠿⠒⠻⠾⠒⠚⠾⠶⢟⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠⣾⣿⢴⠶⠶⢶⠶⠷⠶⠤⠖⠲⠿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⢊⣀⢈⣶⣿⡿⠉⠻⢷⣿⣿⣿⣾⣷⣶⣴⠶⡖⣻⠻⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢀⡠⠾⣅⢚⣷⣿⡿⠋⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣧⣌⠁⠃⢀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⣾⣋⠤⣨⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣆⠞⡀⠆⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣴⣾⣚⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣔⢐⠄⡿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⠷⣫⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢶⣾⠿⠏⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣀⣀⠀⡀
⠀⠀⢸⡆⠀⠀⣿⡇⢾⣾⠗⠋⠂⠁⠀⠒⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⢿⣧⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾
⠀⠀⣸⣇⠀⢀⣼⣷⠀⠀⠀⠀⣴⢿⣾⡶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⣀⣭⣿
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣽⣾⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠸⣿⣿⣿⠰⣾⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣆⡆⠀⠀⠙⢻⣷⣤⣀⠀⠀⡀⠀⠀⢀⡄⠀⠀⠃⣀⡖⢸⡿⣿⣽⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡳⣿⣿⣿⣿⣿⣿⢷⣤⣠⣄⣀⠀⠀⣾⣿⣿⣧⣿⣾⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡤⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡆⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣸⡇⣀⡇
⠀⠀⠀⠀⠀⠀⢠⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⢹⠐⢸⠇
⠀⠀⠀⠀⠀⠀⠈⢻⡄⠁⢉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡄⡇⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡉⠲⢄⡈⠛⢢⣄⡀⠀⠀⠀⠀⣸⠃⠀⢹⡇⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣶⢉⠳⢤⡀⠝⠳⠦⣄⡴⡃⡄⠀⡼⠡⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠤⠐⠶⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⢉⠳⢤⡐⠀⠍⡑⠀⣠⡇⣀⢦⠻⡤⠤⠤⠤⡒⡒⠊⢉⣀⠀⣀⠠⠀⠀⣰⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣎⡠⠉⠳⣶⣶⢖⣿⠄⠂⠀⣂⣀⣤⠴⠞⡛⠛⠉⣉⣬⣄⣤⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠨⠀⣠⢙⡍⣘⡶⣛⠋⡉⢀⡀⠁⣀⣠⠤⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠄⡡⢊⡵⠟⢛⠛⢷⡀⡂⠐⡿⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠂⡠⣪⠖⠫⣠⣔⣦⡀⠈⢷⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠕⢀⡴⠛⢃⣨⠞⠋⠁⠹⣧⡀⠊⢷⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠅⣡⠶⠉⢀⠴⠋⠀⠀⠀⠀⠀⠘⣆⠂⠈⣧⠁⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⡡⠺⢡⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⣇⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠐⣨⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠘⡆⠚⣧
⠀⠀⠀⠀⠀⠀⢠⣞⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡥⠘⠌⢸⡆
⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡤⣤⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣤⣿⢤⣜⡂⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣤⡄⠐⠂⠀⣼⣧⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⡶⠛⠛⠓⠚⠊⠉⠙⢦⢠⡄⠀⠀⠀⠀⠀⠀⡾⠃⢸⡇⠀⠀⠀⡟⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⢠⡌⢉⡷⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢰⠇⠀⢾⡇⠀⠀⠀⣏⣘⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⣆⠀⠀⠈⠁⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⣴⠟⠀⠀⣾⠀⠀⠀⠀⡿⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢈⡓⢤⣄⡀⠤⠚⢫⠀⠀⠀⠀⠀⣠⣟⠁⠀⡠⠞⠃⠀⠀⠀⠀⣷⡈⠻⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠛⠁⠈⠁⠀⠀⠀⠀⠀⣠⡏⠀⢀⠟⠀⣤⠖⠶⠢⣤⡀⠈⢻⡄⠸⢷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⢰⠀⢠⠞⠃⠀⠀⢡⠈⠙⢦⡀⠹⣄⠈⣇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⠛⠀⢰⠇⢠⠛⠀⠀⠄⠀⠠⠀⠀⠋⣧⡀⢳⡄⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠒⡀⣻⠀⠀⠀⠀⠀⣯⠀⢀⠎⢠⠋⠀⠀⢒⣶⠿⣶⠓⠶⣄⠀⠙⣄⡷⠠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣈⠀⠈⡁⣿⠀⠀⠀⠀⡾⠀⠀⡎⢀⠃⡄⠀⣰⠿⣀⢀⡿⠀⠀⠈⠻⣄⢛⣼⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣀⡀⠀⢹⠀⠀⠀⢰⠗⠀⡜⠀⣞⠀⠀⣰⠃⢀⠈⠉⠢⡀⠀⡀⠀⢿⡈⢿⣛
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠤⠄⠄⠀⢸⠀⠀⢀⡏⠀⢰⠃⢰⠋⠀⣸⢃⡞⠉⢀⠀⠀⠀⠟⢳⡀⠈⣇⢹⡘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣒⣀⡀⠻⠀⠀⡼⠁⠀⠛⠀⡏⠀⣰⠃⡞⠀⠀⠈⠷⠒⠻⠀⠀⣧⣠⣿⠘⣷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠤⢤⠠⡄⠀⠀⡇⠀⠠⠂⢠⠀⢰⡟⢰⡇⠀⠀⡀⠀⠀⠀⠷⠐⠋⠀⢻⢀⣇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠒⠒⠒⢠⠀⢸⠃⠀⠾⠀⣾⠀⣾⠀⢸⡀⠀⠈⠁⠀⣠⠂⠀⠀⡴⠆⢸⡆⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣀⣀⣈⠙⡃⠸⠁⠐⡇⢀⡏⢰⡟⠀⢸⡇⠀⠈⢰⡆⠈⣄⣠⠚⠁⣦⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠤⠶⠀⠃⣞⠀⠀⡇⢸⠃⣼⡗⢓⣨⡗⠒⠀⠀⠃⠀⡇⠀⣄⣠⡇⣟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⢿⡇⠀⠛⡇⢸⠀⢸⣇⡞⢻⡇⠀⠠⡄⠘⠓⢷⠀⠈⠈⣿⣇⠀⢠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣒⣂⣐⣃⣼⡇⡀⠸⡇⡿⠀⠸⣿⠀⠘⢆⠀⠀⡀⠀⢠⡰⠶⡆⢰⣿⠋⠑⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠄⠰⠖⠚⣧⡀⠀⣦⡟⠀⠀⢹⡇⠁⠀⠳⡀⠀⡀⢀⠀⠀⠙⣿⡟⠉⢸⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠒⠒⠒⠂⠈⡁⠀⢹⣧⠀⠀⠀⢿⡄⠠⡄⠘⠦⠏⠈⡄⠒⣠⣿⠤⠀⣼⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⣒⣂⠐⡂⢹⡀⠀⢿⡀⠀⠀⠀⠙⠶⣄⣻⣀⢘⣦⣴⣶⠟⠁⠀⣼⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⢠⡤⠀⠤⠄⢷⠄⠘⠁⠀⠀⠐⠀⢀⠁⠉⠉⠉⠋⢀⠀⠀⠁⣼⡁⠰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠶⠒⠒⠀⠀⠈⢳⣀⠀⢀⢠⠈⠀⠀⠀⠀⠈⠀⠈⠀⠀⣠⢾⠁⠈⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣉⣀⠁⠀⠀⠤⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠛⠁⠀⠐
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠤⠄⠐⠒⠒⠂⠀⠙⠓⡶⠖⠖⠒⠛⠋⠉⠠⠄⠀⠤⠀⠐⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣋⣉⣉⣉⣉⣀⠀⢠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠁
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢢⡄⠀⠸⠀⠀⢰⠃⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⣠⠀⠈⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⢃⣴⢪⠊⣀⣿⡆⠀⣶⡌⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡇⠀⠙⡀⣸⣄⠈⠁⢠⡈⠧⠘⡝⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣧⠰⠉⠹⡋⠋⢸⡷⠸⣿⠀⢀⣧⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⣏⡆⢱⣧⠀⢀⢾⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⣀⢬⢲⣬⣥⡤⠣⣤⣥⣃⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠛⠉⠐⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠀⠈⢀⣴⠃⣴⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⣴⣿⠷⠀⠟⠁⠀⠹⠷⠄⣴⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⢀⠂⣠⣶⡿⢃⣴⡷⢀⢀⡤⢶⡗⠰⣶⡝⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠃⡁⠁⢠⡔
⠀⠀⠀⠀⠀⠈⠀⢉⡥⣴⣿⡿⢣⣿⠋⣟⡏⢠⣦⠙⣿⣶⢤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⡊⢠⢀
⠀⠀⠀⠀⠀⢀⠀⣟⣿⢋⣥⣶⣿⠏⠰⣿⢧⡿⣞⡤⣬⢛⣋⡀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠂⠠⠁⠀⠹⠁⠀⢀⠂⠀⢌⠊⠀⡊⠙⡓⠚
⠀⠀⠀⠀⠀⢠⠀⠛⠃⣸⣿⡟⢡⣶⡷⣠⣸⡟⣧⠉⣁⢸⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡰⠀⠁⢁⠢⠆⢠⡄⠁⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⢢⠀⠸⣿⠏⢁⣼⣿⠀⣿⡇⢙⣋⣼⣽⠀⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠈⠀⠈⣠⠀⢠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠛⠞⠋⠐⠿⠃⠸⠿⠛⢋⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠲⠀⠀⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢗⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡻⣿⣷⣄⠀⠀⠀⢀⣠⣶⣿⡿⡟⣾⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣶⣾⣼⣿⣿⣷⣶⣾⡿⢯⣽⢫⣩⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣎⣋⣱⢏⣿⣁⡦⡔⠯⢿⠪⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠶⢺⣿⣾⣦⣿⢳⢺⣧⣷⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣿⠿⠿⠙⣀⠺⡛⣟⣾⣿⣿⣯⣿⣳⣿⣷⣿⡏
⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⡿⢿⣿⡽⠁⣂⠠⠀⡆⠷⣽⢿⣿⣿⣿⣿⠫⣿⣿⣿⣷⣄
⢠⣶⣿⣿⣿⣿⣻⣿⣿⣾⣿⣿⣷⣗⣣⣭⣶⡃⣤⡤⢿⣼⢿⠟⣦⣯⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣒⣿⣦⣿⣜⢿⣻⣿⣲⡖⣛⣟⣿⣿⣻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣷⣼⣿⣓⣿⡿⠿⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣮⣖⣿⡿⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢯⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠘⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠐⡁⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⠰⠀⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⠂⠐⠊⠀⠠⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠁⠠⠅⠠⠄⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⠀⠠⡤⠀⠀⢨⡽⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡁⠀⠄⠀⠀⠠⡴⠀⠂⠀⠐⠻⡤⣀⣀⣀⣀⡤⠤⠦⠴⢞⡷⠋⠋⠙⢭⣷⡄
⠀⠀⠀⠀⢀⡄⡶⢤⣀⣤⠄⠢⡤⠠⠤⣀⣠⠐⡤⠰⠤⠞⠁⠀⠀⠂⣁⠀⡀⠀⡄⠀⠤⠂⠈⠀⠉⠀⠁⠠⠀⠀⠀⠀⠀⣀⡠⠀⠶⢂⣱⠏
⠀⠀⠀⠀⢸⡉⠁⣀⢠⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠑⢀⡀⠀⠉⠛⠁⣀⠀⠠⠶⡀⡁⠀⣀⢠⣤⠔⠲⠛⠀⠀⠀⢠⡥⠞⠁
⠀⠀⠀⠀⠀⠹⣠⡌⠁⠈⠚⠀⠀⣀⣀⢀⡠⠀⠁⠈⠁⠂⠀⢠⡀⠀⣸⠉⢀⣀⠄⠀⢠⣀⣠⡟⠑⠚⠁⠁⠀⠀⠀⠀⢰⡴⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⢧⣆⣠⠀⠀⠄⢀⠀⠺⠔⠃⠴⠂⠠⠟⠛⢉⡀⠀⠀⠀⠐⠀⠈⠉⠐⠐⠀⠁⠄⠀⢠⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⣤⡤⠀⠉⠐⠀⠠⠄⠐⠂⠀⠀⠀⠠⡄⠉⠉⠀⠀⠰⠀⠈⠁⠀⢀⠄⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⠆⠀⠀⠀⠐⠂⡀⠚⠘⢤⣴⠏⠀⠀⢄⣀⡴⠃⠀⠀⠀⠀⠐⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣁⠀⠀⠀⠀⠀⠐⠂⢀⡀⠃⠄⠀⠀⡁⠠⣠⠆⠀⠁⠀⠀⠀⠟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⠀⠢⠔⠀⠀⠀⠀⠀⠀⠀⢀⠂⡀⠐⠖⠁⠀⠐⠀⠈⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠀⠀⠀⠲⠂⢀⠀⠁⢀⠠⣀⡠⢤⡀⠀⠀⠀⣀⠙⠁⡠⠀⠀⠀⠚⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡬⠀⠀⣀⡐⠊⠄⢀⣩⡷⠾⠛⠋⠛⠾⣵⣢⠀⡀⠀⠡⠤⠀⠤⠀⠀⠀⠡⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠭⠀⠀⣠⠀⠀⢰⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠳⠶⢯⣼⠖⡄⠀⡀⠠⠼⠀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡳⠀⠀⡉⠁⠀⣽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢿⣀⠀⠈⣡⢀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⡸⠃⣀⣾⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠞⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡐⣺⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠊⠀⣠⢀⡠
⠀⠀⠀⠀⠀⠀⠠⠠⠄⠤⣄⠈⠑⠳⣆⠀⠀⢠⠄⠴⣫⣕⣒⢣⣟⣁⣴⠖⠛⢃⣉⣴⣀⠤⠂
⠀⠀⠀⡀⠀⡑⠢⠀⢐⡒⡄⠠⠄⠐⠀⠀⠀⠈⠀⠀⠀⠉⠀⠁⠩⢶⠛⣵⣿⣧⣠⣤⣤⣔⠒⠂
⠀⠀⠠⠬⢁⣀⠀⠂⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠨⡹⢿⣿⣞⣿⣿⣤⣬⣭⣝⣉
⠀⠀⠭⠿⢭⣭⣁⣦⣶⢠⠴⠂⠤⡤⣀⣦⢾⣳⣂⣤⣴⣤⣴⣶⣾⢵⣷⣿⣿⣾⣿⢿⣟⡻⠷⣶⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠬⠔⠒⠉⠙⠃⠀⠉⠘⠁⠀⠋⠀⠉⠉⢳⠀⠉⠈⠉⠑⠢⠄⠉⠑⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠱⡀
⠀⠀⠀⠀⠰⡀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⢄
⠀⠀⠀⠀⠀⠙⠆⠀⠈⠑⠢⢄⡀⠀⠀⠀⢸⡆⠀⠈⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠀⠀⠈⠑⠒⠤⠰⠃⠀⠀⠀⠀⠓⠤⠤⠂⠒⠒⠉⠉⠀⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢬⡀⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠤⢄⣻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢬⡑⠦⠀⠂⡀⠀⡠⣀⠠⢎⣉⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⠀⠁⠀⠛⠧⠡⠀⠙⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠁⢀⡁⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢔⡾⣀⣀⠐⠐⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠠⣂⣴⠟⣟⠳⢦⣆⠡⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⢀⢤⣴⡾⠋⠁⠀⠁⠀⠀⠈⠙⠶⣭⣐⣤⣀⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣎⣁⣤⡤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠸⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢾⢸⣧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢂⣼⣃⠀⡋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢭⠆⢾⡽⠈⣗⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡹⣿⠂⠢⠀⠰⢟⠔⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⣖⢲⢲⡖⣲⢲⡖⣖⣲⢲⠶⣶⠺⠉⠓⠃⢹⡁⠚⠙⠀⡯⠰⣽⢦⣄⣀⣀⡀⠀⣀⣀⣠⣤⣤⢦⡤⡄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡵⢻⠳⣗⡷⢻⡽⢷⣈⣙⣈⡋⠙⠐⠺⠀⢄⡼⢾⣏⣸⣤⢺⣠⡸⠿⠛⣽⢿⡿⣯⣻⡽⣿⢷⡟⠙⣿⣟⡯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⡀⢉⠀⠓⠘⡧⡼⢯⠜⣗⣳⣶⠖⡾⢿⠉⠀⠀⠛⠺⡟⢛⡆⣵⠡⣮⠔⠷⠛⠒⡛⡃⢿⣹⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢡⣆⡹⢑⣤⣣⠈⣤⣙⣹⠷⡏⠀⢎⣀⡅⠈⡿⢏⡉⣈⣡⡤⣠⠰⣆⡖⢅⡹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣤⠖⡇⠃⠁⠜⢻⠷⠲⢊⣿⣶⠷⣿⠂⠜⣥⡍⠀⣄⢻⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡜⣠⠟⢠⣏⠱⠃⠋⣼⠛⡶⠛⡦⠀⠈⠱⡦⢩⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢪⠉⢤⠿⠀⢐⠁⠀⠘⣔⠛⣞⣩⢷⡀⠈⢻⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⠀⣼⡻⠃⣠⡜⠀⡀⠀⠛⣧⠈⠧⣴⠒⣲⣶⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠲⢄⡼⡌⠁⣠⣧⡄⣞⣁⣸⣄⣞⠳⠆⠈⢺⣏⣹⣏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣩⠾⡯⠛⢀⣼⣻⡤⠟⠉⠀⠀⠀⠈⠛⢯⡠⣀⢹⡆⣿⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⣿⡛⢠⣁⡳⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣟⡽⣷⡿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣞⣦⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⣿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⠊⣠⠖⢉⡤⠝⣷⣤⣀⠀⠀⢀⣴⠟⡹⠋⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣱⣱⣃⡞⣡⠞⣁⠔⢋⣡⣬⡿⠃⢀⡾⢃⡞⠀⣰⠋⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠩⠭⢝⣛⡻⢾⣥⣖⣉⢤⣿⠀⢀⣾⢁⡞⠀⣰⠃⣠⠎⡴⣿⠏
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠉⠑⠮⡙⢷⣾⠃⠀⣼⢇⡞⢀⣼⠃⣰⠇⢀⡾⠃
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠣⡙⢷⣤⣿⣟⣤⠟⣡⡾⢃⢠⡿⠁
⠀⠀⠀⣤⣿⠀⠀⠀⠀⢼⣟⣹⡄⠘⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⠭⠖⢁⡿⠁
⠀⠀⠀⣿⡙⠶⠂⠀⠀⠈⠛⠋⠀⠀⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣒⣒⡂⢸⡇
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⣤⡑⠢⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠄⠐⠁⠀⣠⡾⣿⠮⣛⢶⣄⠀⣀⣴⣿⢧⣄⠈⢿⣿⡳⣦⡙⠢⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿⣋⣀⣈⣿⣮⣿⣿⣾⣏⠑⢬⡓⣭⣿⠌⢿⡻⣆⠙⢦⡀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢏⣿⣯⡙⢮⡑⢝⢷⣹⡶⠟⠋⠁⠀⠈⣷⡘⢷⡈⠻⡄⢈⡲⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣷⡙⢦⡙⢮⣻⣿⠀⠀⠀⠀⠀⠀⠘⣷⡈⢳⡀⠙⣆⢹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢮⣿⣦⡙⢦⡙⣿⡄⠀⠀⠀⠀⠀⠀⠘⢷⡄⠳⡄⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⣯⡢⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠄⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣁⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣉⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠤⠬⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⡤⠤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡂⠘⠛⣿⣧⡀⠀⠀⢀⣀⣤⣴⣶⣾⣿⠿⢿⡿⠿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⢀⣾⣿⣟⣙⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠉⣽⣏⣿⣷⣤⣶⣿⣿⣯⣉⣉⣍⣉⣯⣉⡙⢄⠈⣫⣉⣀⣍⣙⣻⣿⣶⣴⣿⣟⣉⣉⣉⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠤⢤⣴⣿⠿⠧⠄⠷⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠡⠤⠤⠄⠼⠿⠿⣿⣦⡼⢯⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⣛⣛⣛⣃⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣒⣒⣒⣚⣛⣃⣀⣛⡛⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠬⠭⠭⠭⠭⠥⣤⣉⣤⣄⠉⢉⣉⣭⣭⣭⣭⣭⣭⣭⣤⠀⢠⣤⣤⣤⣬⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣂⣀⡐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠒⠒⠒⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣭⣭⣭⣭⣭⠉⣭⣭⣭⣭⣭⣭⣭⣤⣭⣭⣭⣭⣭⣭⠠⠉⢩⣭⣭⣭⣭⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢒⢒⣒⡒⣒⣲⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⡭⣭⠍⠭⡭⠭⠭⠉⠭⠤⠤⠄⠀⠀⠀⠨⣥⣤⣭⡭⠭⠭⠭⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣖⣒⣒⣒⣒⣒⣒⣒⣒⡒⢒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣢⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⡍⠉⠉⠉⠉⠉⠑⠮⠍⣉⣉⠉⠉⠉⣩⣽⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣬⡉⠉⠉⠩⠉⠉⣭⣭⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣖⠒⠲⠖⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠾⠷⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢐⣅⣀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠉⠉⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠁⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡐⠀⠀⡀⠀⣠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠈⠀⠀⣬⠁⠻⠶⠿⠇⠆⢠⣞⣀⣠⡷⠀⠀⠉⠁⠀⢰⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠋⠡⠖⢋⡀⢠⠈⠀⢸⡟⠋⠀⠀⠀⢠⣬⣍⡻⢃⣄⣰⠇⢡⣶⣿⠋
⠀⠀⠀⡜⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠈⠀⠶⢦⢶⡿⠃⠈⠤⠀⠐⠾⣩⠀⢿⡟⠛⡅⣀⣹⣿⠃
⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠴⠀⠠⠦⠀⠀⡎⠀⠰⠙⢁⠔⠙⢂⣈⣹⠇⠟⠛⠀⠷⢶⣠⠈⠀⠀⣉⠆⠀⠁⢹⣏
⠀⠀⠀⠀⠈⠉⠛⠻⠿⣼⣦⣲⣤⣄⠁⣀⠀⠀⠀⠀⠃⠘⣷⢶⠾⠃⠉⠂⢻⠃⠀⢀⣬⢹⣿⡿⢿⣿⡥⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣯⣤⣶⣖⡀⠀⠀⠂⠐⣷⠞⢳⠰⣦⣴⡿⣥⠛⢩⣁⠛⣼⡅⣈⠃⠀⣎⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣖⠁⠀⠀⢈⠁⠾⢧⣼⢿⣉⣿⢠⡄⠙⠻⠯⢤⠽⣧⣴⠏⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⣆⠀⣺⠁⠈⢚⣳⠉⡍⠉⣈⢛⡁⢀⣀⡈⠉⠲⠰⢆⠀⠀⠤⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣻⠀⢷⢶⣶⡾⠇⣠⣀⣄⣴⣷⣦⣬⣯⣄⣀⣤⡄⠀⠀⠀⠀⠀⠂⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣉⠀⠀⠀⣰⠓⠫⡄⣾⠟⠁⠀⠀⠀⠀⠉⠙⠻⠿⣾⣁⠀⠠⠀⠀⠀⠀⢀⡁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢠⣤⡴⣢⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⢃⠀⠈⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠰⠀⠀⢀⡀⠈⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢠⠈⠓⡟⠁⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⢠⡤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠⠁⢠⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⡂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡉⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣠⣿⣿⣿⣦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣿⣿⣿⣿⡟⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠎⠙⣿⣿⣿⣷⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡜⠀⠀⠻⣿⠿⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠞⠀⢀⣀⣀⣸⠄⠔⠂⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡜⠀⢠⡎⢇⣉⢻⠀⡀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡹⠁⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠇⠀⢸⡴⢿⣿⣿⠁⠁⣼⠁⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡙⣺⠃⠈⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡼⠀⢀⡜⠳⠾⠿⠃⠀⠀⠸⡄⣠⠖⣫⣤⣀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⡇⢀⠞⣠⣤⡖⢲⡄⠀⠀⠀⣿⠁⣸⣿⣿⣽⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢾⢀⡞⢰⣮⣿⡿⣿⡇⠀⠀⠀⡇⠀⣏⠿⡿⢞⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡇⢸⠃⢞⣿⡷⠛⠛⡠⠃⠀⠀⡇⠀⢿⡶⡷⢊⡝⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡜⣠⢮⣀⠈⠘⠟⢲⠞⣋⣁⡀⢀⡇⠂⠀⠉⠉⠉⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢰⢡⡷⣚⣿⡇⠀⠀⠀⠀⣯⡇⡇⣸⠁⣠⣤⣠⠞⢲⡀⠀⠀⢃
⠀⠀⠀⠀⠀⣀⡌⢁⣀⡀⢠⠏⠀⠀⠀⠀⠀⠀⢠⠁⢀⠃⢾⣷⣸⡿⠃⠀⠘⠀⠀⢿⠩⠇⡏⣼⣿⢳⣯⣧⠀⢳⣤⢶⣻⣦⡀
⠀⠀⠀⠀⠀⡿⠰⣏⣠⠃⣞⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠀⡘⣉⠿⢤⣀⣤⣄⢲⣤⣄⠀⢸⡃⢻⣿⡧⠞⣽⠀⢀⡟⠫⠿⣿⣿⡄
⠀⠀⠀⢄⡸⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⡇⢈⡿⢗⠚⢷⡰⢖⣾⠾⠁⠈⢳⣈⣤⠀⠉⠛⠋⢹⡀⠈⢷⣔⡾⣫⡟⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠁⣸⡇⠠⡴⣋⠉⣩⣤⣤⣀⠀⠀⡯⣻⠶⠒⠒⠂⠚⠳⣄⠀⠻⡉⠁⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⣿⡆⣽⠃⢡⢾⠁⠀⠈⠙⢧⠀⢸⠃⢀⣤⠦⢴⣤⡀⠈⠳⡀⠹⣄⠀⠀⡤⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸⠀⣿⡦⠋⠀⠸⣖⢀⠙⡀⠀⢺⠀⠸⣠⣿⠛⠠⢠⢻⣿⠀⠀⠘⡄⠘⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠄⢻⣷⠋⠉⠀⣿⠀⠁⠃⠢⣼⠁⠘⣶⣟⢠⣀⡺⠈⣿⠀⠀⠀⠸⠀⠘⡇⠀⢠⠃
⠀⠀⠀⣠⠖⣲⢢⡖⠙⠂⠀⠀⠀⠀⠀⠀⡸⠀⢀⠇⠀⠘⣿⣦⠀⠀⢷⡂⠈⠳⠀⢸⡗⢠⠁⢻⡀⠈⠤⣶⡇⠀⠀⠀⢰⠄⢠⡇⠀⠈⢇
⠀⠀⠀⠛⢰⠇⠘⠒⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡞⠀⠀⠀⠘⢿⣷⢄⡈⠿⣧⣴⡶⠛⢁⣎⠀⣺⡌⣄⢠⣿⠀⠀⠀⠀⢸⠀⣾⢏⡟⢦⠈⢢⡀
⠀⠀⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⠞⠀⠀⠀⠀⠀⠀⠉⠳⣌⣙⢳⣤⣠⢾⣿⢭⣷⡟⢿⣷⣼⠟⠀⠀⠀⠀⡎⠀⣿⣿⢬⣞⡇⠀⠈⠉⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⣿⣿⢹⣧⢸⡟⡄⠀⠀⠀⠀⠀⠀⡼⠀⠀⠹⣍⡓⠊⠀⣠⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠭⠬⠶⠿⠤⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠁⠘⢦⡀
⠀⣀⠀⢀⣀⣀⠀⡿⠀⠀⠀⠀⠀⠐⠦⣄⠀⠙⠦⣤
⡘⢯⠁⣼⠁⡽⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⣀
⠉⠉⢰⠏⠉⠀⠈⠁⠁
⣶⣶⡿⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣄⡀⠀⠀⡇
⠀⠀⠀⠀⠀⡤⠖⠒⠒⠲⠤⢤⣀⣀⠀⠀⠀⠀⢀⡼⠁⠀⣀⡉⠁⠀⠀⡇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣀⠀⠀⠈⠉⠙⠲⠖⠋⠀⠀⠘⠧⠭⠇⠀⢰⡇
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⠛⠁⣠⢖⡆⠀⠀⠀⠀⠀⢠⡖⠲⢤⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠙⠋⠀⡠⠖⣲⠀⠀⠀⠉⠓⠚⠁⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠸⠥⠞⠁⠀⣠⠴⠶⢤⠀⠀⣠⢤⡀⢀⣤⡀⠀⠀⠀⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⢈⡇⠀⡏⢀⡇⢸⢀⡇⠐⡿⠂⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣴⠲⣄⠀⠀⠈⠓⠒⠋⠀⠀⠳⠞⠀⠘⠋⠀⠀⠀⣀⣀⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⡀⠹⣄⠘⡆⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⣠⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡀⢻⣙⡆⠈⠓⠋⠀⠀⠻⠤⠤⠴⠛⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠙⠟⠀⠀⠀⢀⣠⠤⠤⢤⡀⠀⠀⣤⠶⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣀⡤⠔⠚⠉⠀⠀⠀⠀⠙⢦⡀⠉⠉⣀⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠘⠒⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⠛⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⠼⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠖⠀⠀⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⠦⠠⢧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⢸⠀⣨⠅⠀⠀⠀⠀⠀⣿⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⣀⣾⡀⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⢠⠁⢠⠋⠀⠀⠀⣀⡴⠚⠁⠀⠉⠐⠠⡟⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢤⠂⠀⢀⡤⠛⠉⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡜⠁⢀⣴⡟⠀⠀⢀⡾⠃⠀⣠⠖⠀⠀⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⡞⠀⣰⠛⠱⠁⠀⠀⣾⠁⠀⠔⠁⠀⣀⣾⣁⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠹⠀⢸⣷⣶⣦⡄⠀⣸⡏⢀⠎⠀⡠⢞⡥⠤⠒⠾⢿⣆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣾⡏⠉⢿⡇⢀⣿⢧⣂⣀⡀⣐⡿⠁⠀⠀⠀⠀⠈⠑⣏⢤⡤⢈⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢡⠀⠀⢱⠀⣿⠁⠀⠘⣿⢠⡏⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⣠⣶⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⢧⠀⠈⠀⢻⡆⠀⠀⢻⣸⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣠⣼⡯⠼⣫⠀⠀⡀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠃⡀⠈⡈⣧⡀⠀⠘⣟⣇⠀⠀⠈⣧⠀⠀⠀⢀⡠⠞⠉⠉⠀⡰⠁⠀⣠⠴⠄
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡀⠀⠉⢄⠐⢸⣧⠀⠀⢹⡜⣄⠀⠀⠙⣧⡀⠀⠁⡀⠀⠀⣀⣾⠁⠀⢀⡶⠆
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠑⢄⡸⣧⢀⣿⣿⡌⢦⡀⠀⠈⠇⠀⠀⠀⠛⠂⣀⣠⣤⣶⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡟⠁⢀⣁⣤⠶⠚⠒⠂⠀⣛⡿⠟⣋⣵⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠯⣉⣉⣑⡒⠲⠞⢛⣩⠄⠂⣟⡉⠑⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠆⠘⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⠀⣐⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠁⢠⠀⢀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠊⠀⠐⠊⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠄⠁⠀⡄⠀⠙⣢⢹⡄
⠀⠀⠀⠀⢠⡞⠛⠛⠛⠲⠶⠦⠤⣤⣤⣤⣤⣤⣤⡤⠴⠞⡁⠀⠀⠀⠀⠄⠀⠀⠈⠀⢳⡀
⠀⠀⠀⠀⠘⢧⣀⠀⠂⡀⡀⣀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠧⠐⡉⠂⡹⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠳⣮⡂⢈⠉⠀⠠⢀⡀⠀⠀⠀⠀⠰⠘⠀⠀⠀⠀⢂⠀⡒⠠⠁⠐⠘⣁⠐⢨⢭⠍⢉⢙⢛⢛⠛⢉⠉⠉⠩⠩⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣂⠐⡄⠐⠀⡁⠰⢖⡦⠈⠘⠆⠄⠔⠀⠀⠀⠀⠀⠂⠂⠀⠁⠐⠀⠁⣀⠀⡀⠀⠤⠤⡀⡀⠤⣊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡁⢀⠀⣑⠀⠀⡀⠘⠫⠥⡆⡥⡀⢄⡀⠤⠀⠀⠪⠝⠀⠀⢀⡈⢍⠤⠤⢄⣀⡭⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢉⠀⠀⠀⠀⠓⢠⢊⠁⣉⠀⠆⠀⠀⠀⢀⠔⠈⠠⣠⡄⢓⣠⡴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠐⠁⠈⣉⠀⠐⠆⠀⠀⠀⣀⡀⠄⡹⡮⣋⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡈⠀⠀⠌⠀⢃⠄⠀⠀⠀⠀⣠⡀⠀⠀⠠⣔⡆⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣐⠀⠀⢂⠌⢁⠠⠆⠆⢀⠀⠀⠐⠧⠀⢀⣐⣻⠥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠠⢂⠇⣀⡀⡑⠐⠁⠸⢠⠀⠀⠈⢡⡀⠂⣾⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⠐⠉⠀⢤⡄⢄⣡⠴⠖⠓⠶⣅⠣⡀⠀⠻⠀⠾⡤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡶⠀⢈⠇⣋⡴⠞⠉⠀⠀⠀⠀⠀⠈⠳⣧⡀⠀⠀⢂⠩⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡀⠄⢌⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣖⡷⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣈⡵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢄⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣿⣵⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢦⡟⠈⢻⣿⣿⣿⡀⢚⡠⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢿⣿⣷⣾⡿⣶⡜⣿⣿⣿⣃⢛⣷⣿⣯⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⣿⣿⣿⣿⣿⣿⣿⣾⢻⣿⣿⣿⣫⣿⣯⣥⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠿⣿⣻⣿⣾⣻⣿⣿⣆⣾⠉⣧
⠀⠀⠀⠀⢠⣦⣀⠀⠀⣀⡉⣿⣷⢻⣿⣿⣿⣿⣿⣫⢻⢫⣾⣿⣿⣿⣿⣷⣯⣾⣽⣿⣿⣧⣿⡆⢀⣠⣦
⠀⠀⠀⣰⣿⣿⣿⣿⣶⣽⣇⣘⣿⡇⠻⣿⣿⣬⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⡇⢿⣷⣟⣟⣿⣷⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣷⢶⣿⣯⣿⣵⣭⣭⣭⣭⣽⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⠯⣻⣹⣹⢿⢹⣟⣿⣯⣿⡯⣿⣋⣷⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠉⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⣶⠆⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⣄⠀⢠⣾⣷⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠆⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠸⣿⠿⠀⠀⠉⠁⠀⠀⠳⢄⣀⡀⢀⣀⠤⠴⠒⠚⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣠⣄⠀⠀⠀⠀⠈⠋⠀⠀⢶⡆⠠⣀⣵⠟
⠀⠀⣀⡀⠀⠀⠤⠤⠤⠤⠄⠐⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠟⠀⢀⣤⠀⠀⡀⣄⣲⣥⣶⠿⠋⠁
⡠⠋⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠈⢉⣴⡿⠟⠛⠉⠁
⡇⠀⠀⠀⢠⣤⠀⠀⠈⠉⠀⠀⠀⣀⠈⠙⠉⠀⠀⠀⠐⠀⢀⢀⣣⠀⠀⠸⠷⠇⢀⠌⠀⠀⠀⠀⠀⠀⣼⠛⠁
⠻⣶⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠺⡿⠃⠀⠀⠀⠀⠀⠰⡀⠙⢻⢟⠀⠀⠀⠈⠠⠥⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣖⡲⠶⣦⣄⠀⠀⠀⠀⠨⠒⠁⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢷⣌⢻⡆⠀⠀⠀⠰⣦⣤⣤⣤⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⡇⠀⠀⠀⠀⠈⠻⠿⠿⠿⣛⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⣀⡀⠀⠀⢀⣶⣶⡀⠀⢀⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣩⣭⣬⣭⣑⠢⡀⠻⠟⠁⠀⠈⠉⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠀⠀⠈⠙⠷⣬⡢⠀⠀⠾⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⠿⠃⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣴⣶⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠛⠃⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡀⠀⠀⠈⠉⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡢⠤⣤⣤⠴⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⠟⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⠃⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡵⢤⣀⠠⣀⣴⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣷⣶⣟⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣌⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣀⣀⠀⣴⡵⠛⠁⣀⣤⣔⡡⠔⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠂⠘⠂⠐⠲⠖⠄⡀⡈⠻⠆⠀⠀⢐⣖⠒⠛⡴⢯⡤⠖⡽⣯⠔⢚⣿⠉⣁⣠⡤⠶⠯⠴⠒⠉
⠀⠀⠀⢀⣀⡀⢀⣙⡂⠉⣉⣙⣒⠀⠤⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⡛⢩⢼⡿⣷⣤⣤⣴⣶⣖⣚⠉⠁
⠀⠀⠀⠤⣍⣉⠀⡀⠴⠂⠈⠍⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⢠⡀⠈⡕⣥⢿⣯⡷⢻⣿⣯⣄⣈⣉⡭⠝⠋
⠀⠀⢒⣲⣖⡒⡛⡓⠂⠄⣄⡆⢀⣠⠤⣐⣁⣀⠠⠤⢴⢧⡤⢠⠀⢠⣄⣀⣀⣥⣠⣂⡸⣤⣾⣿⣽⣻⣿⣿⣿⣿⣯⣭⣉⣉⣀
⠀⠀⠀⠀⠀⠙⠓⠾⣿⠿⠗⠸⠍⠥⢈⣉⡿⠵⣾⠟⠉⠳⠛⣿⠟⠛⣿⠻⠻⡿⠿⢍⡛⠻⡿⠛⠿⠽⣋⡙⠛⠲⠬⣉⡛⠿⢷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠉⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⣳⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⠃⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡤⣄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢧⣸⠀⠀⠀⠀⠀⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠦⣤⣀
⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠤⠤⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⢹⡆
⠀⠀⢀⡾⠋⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠿⠖⠋⠀⠀⣠⠟
⠀⠀⠈⢧⡀⠀⠐⠯⠽⠇⠀⠀⠀⢠⡖⠒⠒⣦⠀⠀⠀⠀⣀⣀⡀⠈⠁⠀⠀⠀⡠⠶⣦⠀⠀⠿⠶⠚⠁⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠘⠳⠴⠛⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⢠⠞⣳⠀⠀⠀⠀⠀⢿⠙⡆⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣿⣠⠏⠀⠀⠀⠀⠀⠈⠧⠟⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⠏⣸⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢧⡷⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠘⠛⠁⠀⠀⠀⣠⠞⠋⠉⠛⢶⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣠⢶⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢻⣙⡆⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠷⠞⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠉⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠠⡀⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢉⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣾⣷⣿⣿⣿⣿⣿⣷⣦⣄⣠⣴⣛⣉⢀⡴⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡼⠃
⠀⠀⠀⣀⣤⣶⣿⣟⣛⡟⠙⢻⣾⡿⠽⠟⠒⠛⠺⠿⣿⠹⠟⠹⡟⢰⡟⢠⡟⢣⣾⠋⡾⢋⡿⢻⣿⠛⣿⡿⢿⣿⣾⣿⣶⣶⣠⣄⣀⠀⠀⠀⣰⣏⣀⣰⠇
⠠⢶⡿⠋⠉⢰⣴⣿⡧⠇⠀⠀⠈⣻⣶⣶⣶⣞⣿⣿⢻⠿⢿⡟⠛⠳⢶⡾⣶⣦⠀⠀⠀⠈⠀⠚⠃⠀⠉⠁⠘⠋⠘⠛⠟⠛⠛⠻⠟⢿⣿⣾⣿⣿⣻⡏
⣤⣠⠹⢦⠠⣌⠛⠛⠁⠁⠀⠰⠀⣸⡗⢹⠉⠀⠀⠀⣀⣀⣠⡤⠤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⢾⠟⠛⠛⠛⢿⣿⣿⣼⣧
⠈⠙⠻⠶⣾⣭⣀⣀⠀⠀⠀⣾⣆⣾⣧⠭⣷⣶⣞⣁⣀⣀⣒⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠀⠁⠀⠀⠀⠀⠀⠀⠹⣮⠉⠹⡆
⠀⠀⠀⠀⠀⠉⠙⠛⠾⢯⣭⣿⣿⣟⣛⣛⣭⡽⠿⢿⣷⣶⣶⣶⣶⣶⣶⣿⡿⣯⣭⣭⣵⣶⣿⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢳⣾⣿⣯⣭⡭⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠙⠻⣿⡛⠛⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣽⣦⣄

⠀⠠
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄
⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⠶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠃⠀⠑⠢⠂⣠⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠄⠀⠀⠈⠔⠁⠀⠣⣄⠀⠀⠀⠀⢀⠤⠒⣩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⣖⡩⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠑⠂⠠⠀⡀⠊⠀⠀⠀⠀⠀⠁⠈⠆⠀⠀⠀⠁⠀⠀⠈⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢃⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠐⡀⠀⠀⠈⠀⢀⠀⢠⠁⠀⠁⢀⡀⡀⠘⠀⡤⠀⠀⠈⠩⠍⠑⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⡀⠈⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃⠀⠀⡕⠀⠀⠘⠢⠈⠁⠀⠀⠂⠂⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠤⠀⠀⡶⣶⣶⣶⡀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠀⢋⠀⠐⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⢀⣠⠒⠁⠄⠒⠀⠒⠒⠀⠈⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠁⠂⠀⢀⡀
⠀⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠉⢀⡠⠒⠉⠀⡀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⢀⡀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⣀⡸⠒⠂⠈⡁⢀⣤⡀⣀⣀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠘⠦⢤⣀⠤⠤⠀⣩⡴⠐
⠀⠀⠀⣀⠱⠤⠀⠁⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢂⡜⠉⠀⠁⠀⢀⣀⣁⡠⠀⠀⠀⠙⠶⠶⣒⠐⠒⠂⠤⠤⠴⠚⠉
⠀⠀⠘⠁⢀⡠⠄⠀⠛⠀⡱⡀⠧⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡁⢙⣒⢒⣉⠁⠂⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠤⢶⡤⣀⣀⣀⠠⠴⠒⣧⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠘⣧⠀⠉⠙⠈⠶⠀⠄⠛⢪⣀⣠⠤⢶⣛⡋⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⠁⠀⠸⡄⠈⢋⠀⣤⣇⠀⠀⠀⠉⠂⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣹⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⢈⠃⠘⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⠤⠤⣤⣶⡶⠶⠾⠛⠋⠀⠀⠀⠴⠶⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠒⠤⠔⠷⢂⡀⠐⠸⠱⣎⡀⢤⠤⢤⣤⠀⣀⠀⠀⠤⢤⡴⠟⠀⠀⢠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠖⣄⡐⠂⣡⠤⡏⠂⠞⠓⣛⠛⣟⣩⣭⣤⣤⡶⠖⠊⠁
⠀⠀⢠⣄⡠⠔⠒⠋⠉⠀⠀⠀⠉⠀⠈⠑⠳⢤⡭⢄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⣀⠠⠄⣀⠀⢀⣐⢁⠽⠛⠳⠰⠶⠤⠖⣞⣳⠻⣛⢉⡉⣉⠁⠉⠂
⢠⠔⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡎⢀⡀⠀⠀⠈⠑⠂⠠⠤⠤⠀⠀⠊⠉⠈⠉⠙⢧⠦⣊⢀⠴⠶⠘⠛⠉⠀⠀⠉⠙⠛⠛⠀⠀⠢⣄
⡘⠈⣡⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠖⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢅⣤⣼⣙⢦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠳⠽⠧⠼⠐⠶⠆⣠
⠘⡏⠁⠀⠀⠈⠛⢎⡙⡛⠓⠀⠛⠛⣒⢀⡉⠉⠀⠀⢈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠇
⠀⠈⠂⢀⡀⠀⢀⣸⠟⠉⣀⠀⠀⠬⠵⢶⣭⣆⡉⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠁⠀⣴⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡄⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣴⣶⣿⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⡿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠉⠀⠀⠻⠟⠛⠛⠃⠀⠀⠀⠀⠀⣿⡏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣦⡀
⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣦⣶⣦⣤⣴⣤
⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢸⡿⠛⠛⣿⣿⠛⠛⢻⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢿⣿⣿⣿⡿⢫⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⠟⠻⣷⣤⣾⡟⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠸⣿⣿⡿⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠙⣿⡟⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⢀⣤⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠛⢿⣄⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦
⠀⠀⠀⣠⣄⠀⠉⠁⣠⡀⠀⠀⠀⠀⢠⡖⠒⠲⢦⣀⣠⡞⠛⠛⢓⣦⣀⡰⠒⢋⣿⠀⠀⠀⠀⠀⠀⠀⡘⢿⠉⠛⢿⣿⣿
⠀⠀⣤⣿⣿⣷⣤⣾⣿⣿⡀⠀⠀⠀⠘⢷⣦⣤⣤⠽⣿⣿⣆⢠⣿⣿⠏⢴⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠝⠫⠂⠀⢈⣿⣿
⠀⠀⣿⡟⢿⣿⣿⣿⡿⠛⣷⠀⠀⠀⠀⠀⠁⠉⠁⠀⠘⢿⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣴⣿⣿
⠀⠀⢻⣄⣴⢿⣿⡿⣧⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡛⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠹⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣼⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠈⡛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡄⢸⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⢺⣀⣿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡭⠼⠘⣿⣟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⡅⢼⢠⡿⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠀⠪⢸⡏⠾⢿
⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣉⠧⢸⣇⡿⣼⡆
⠀⠀⠀⠀⠉⠈⢙⡙⠻⢿⢿⣾⣷⣶⣶⣤⣤⣄⡀⣀⠀⠀⠀⠀⠀⠀⢸⣤⠰⡖⢨⡟⣻⣻⡁
⠀⠀⠀⠀⠀⠀⠈⠉⠡⣔⡀⣍⡉⠛⠻⢿⣛⣿⣿⣿⣿⣶⣄⣀⠀⠀⣽⠄⢡⠇⡘⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⠒⢰⡆⢠⣉⡛⠛⠿⢿⣿⣿⣷⣶⣜⣡⣈⠠⣘⣣⣽⣯⡰⣴⣖⣌⣱⣁⢛⣟⣿⣙⣿⣮⣉⣽⣴⣶⣶⠲⣢⣰⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣾⣅⢻⠙⣦⢠⡍⠻⠛⣿⣿⣟⣸⠏⠉⠏⠛⠥⠁⢻⠛⠺⠋⠙⠛⠯⠙⢛⣣⣋⣥⣩⣿⣶⡿⣼⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣷⡨⢧⢘⣆⡸⢗⠛⠓⠂⠛⠀⢻⡟⠻⡏⣷⣖⣶⣾⢿⡿⣻⣿⣿⣿⣿⡿⠟⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⡐⣇⡉⠀⠀⠀⠀⠤⠬⠍⣿⣿⠟⠯⠛⠙⠉⠁⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⠚⠃⣠⢁⡀⠉⣖⠛⡀⠞⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢥⢠⡼⠃⢰⡟⣿⣃⡀⠀⡀⠉⣄⡘⠿⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠄⢸⠆⢰⣻⣿⣿⠟⠁⠀⠹⠤⠙⢷⡘⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠀⠀⠒⣠⢿⣿⣾⠏⠀⠀⠠⠀⠙⠦⠈⢿⣬⢱⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠑⡸⠅⢠⢷⣿⣿⠟⠀⠀⠀⠀⠐⣌⡠⠂⡈⠹⡿⠽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⡀⠘⠣⣼⡗⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠱⡂⢟⡦⠙⣷⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⠇⣼⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠣⠄⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠱⠂⣼⣣⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢄⠆⠙⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣴⢃⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢘⠎⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣳⢄⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠰⡶⡄⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣪⠲⣴⣿⠖⠾⢦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⣦⡑⢦⡀⢆⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⢷⣾⣿⡾⠷⠊⠲⠤⣤⣀⣼⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠻⡴⣴⣿⡗⢯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢾⣧⡙⣿⣿⣤⣀⡀⠀⢀⣿⠋⠀⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⣀⢻⣦⡀⠀⣀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⣿⣿⣿⣷⣿⠏⠀⠀⢀⡠⣾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⣾⣶⣿⣀⠶⠀⠠⣤⣄⣠⣠⣄⡀⠀⠀⠀⢰⡟⠻⣌⢮⡻⣿⣻⢿⣿⣷⣤⣴⢿⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠳⣮⡟⢾⣿⣟⡷⠤⣀⢀⡹⣿⠁⠀⠉⠁⡄⠠⠟⠀⠀⠈⠙⠿⣶⣬⣭⣽⣿⣿⠷⠋⠀⢄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢻⢎⢻⣿⣿⣧⣼⣿⣿⡿⠀⠀⠀⢠⣟⣦⠀⠀⢀⣤⣴⣌⡉⢙⠢⣽⣿⣿⣶⣷⣦⣖⠣⢼
⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣷⡄⠀⠀⠀⣙⠷⣝⢿⣿⣿⢿⣿⣇⠀⢀⣶⡔⠁⠀⠀⠑⢖⠒⢾⡯⣙⢶⡑⣿⣷⣦⣶⣤⠀⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡹⣆⢠⡞⠁⠑⢀⡈⠻⣧⣬⣟⢿⣿⣿⡞⠀⠀⠀⠀⢀⠸⣧⣀⣹⣌⣧⣿⡿⣿⣿⣿⡴⣆⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⡜⣾⠃⠀⠀⠀⠉⠂⣌⡈⠙⢦⣿⢿⣶⣤⣀⡤⢄⣤⣼⠿⣿⣿⣿⢿⣿⠀⠁⠙⢿⡌⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡝⢷⣼⡄⢀⣀⣀⣠⣤⣌⡙⠤⢭⡝⣿⣭⣭⣽⡾⠛⠛⠉⠙⢿⣿⣧⠀⣿⣄⡀⠀⣠⣷⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⡗⠦⣄⡀⠉⠙⠉⡉⢕⣒⣶⣿⡤⠉⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⣿⣿⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢻⡄⠀⠙⠿⣷⣷⣌⣦⡼⡏⠻⢿⣧⡖⠀⣤⣦⣾⡿⠈⠙⠻⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣀⣠⣿⠁⠀⠹⣿⡅⠀⠀⠙⠯⣛⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠘⣧⡄⠀⠀⠀⠈⢧⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⢄⣠⣿⣿⣶⣦⢴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠭⢽⡭⠿⠻⠭⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢿⡟⢿⡿⣿⣿⠿⠿⣿⢿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣧⣿⣿⣼⣿⣿⣹⣾⣾⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣯⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢃⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢹⣶⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠸⣾⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠁⣿⡆⠀⠸⡄
⠀⠀⠀⠀⠠⡺⢷⣔⡒⠤⠤⠤⠤⠄⠒⠖⠈⠉⢮⣢⡄⢀⣸⣷⠀⠀⡼⡳⠲⠠⠤⠤⠤⠤⢤⠤⡤⣤⢤⢄
⠀⠀⠀⠀⠀⠈⠒⠍⣛⠯⣖⣦⠤⣀⣀⣀⢀⠀⠀⠘⢻⡳⢾⡟⢀⡜⡵⠀⠠⠀⢀⣀⠥⠶⢒⡋⠭⢝⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢌⡉⠙⠒⠒⠶⠭⠭⣗⣶⡵⠷⣷⣿⣺⡤⠬⠒⣊⠥⠴⠒⣩⠥⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⡀⣀⣤⡞⠗⣿⣷⣤⣾⢶⣒⣚⠉⠉⠀⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠭⠖⠁⣠⢪⠮⡸⢧⢣⠙⠒⠿⠩⢗⣦⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡔⣱⢋⠁⡇⡏⢯⢦⠀⠂⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠎⡰⠁⠂⠁⣅⠁⠈⠫⡳⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠏⡔⠁⠄⠠⠀⣞⣼⠀⠀⠑⣌⠢⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⢃⡔⠀⢀⡤⠒⠉⠀⠀⠈⠑⢄⡀⠓⣙⢦⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⢡⢞⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⠂⡙⢜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣎⣴⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⢢⢫⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣑⣿⠆