Cute crying Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠒⠒⠒⠲⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⣼⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⠋⡠⠂⠀⠀⠀⠀⠀⢠⣿⠀⠀⢹⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠜⠁⠀⠀⠀⠀⠀⢠⡿⠈⡆⡴⢼⠀⠀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢰⢃⠎⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⢃⡇⠀⠀⠀⠀⣦⡀⠈⠙⠳⣤⣀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠈⠀⠀⠀⢀⠔⣀⡾⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠉⠓⠦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣠⠞⠋⢀⣀⣀⣀⣀⣀⡀⠀⢀⣤⣤⣤⣤⣤⣌⣛⣦⣄⡀⠀⠀⠁⢳
⠀⠀⠀⠀⠀⣀⣸⡃⠀⣀⣴⠿⣷⣿⣿⣿⡿⢿⡝⢍⠉⠀⠀⠀⠀⡜⣿⠏⢙⣿⣿⣿⣿⠙⢳⠢⠀⡸⠲⡄
⠀⠀⠀⠀⢰⠋⠉⡿⡄⢹⠁⠀⣿⣿⣿⣾⣧⣤⣿⠘⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⠀⢈⠀⠀⣿⠆⡇
⠀⠀⠀⠀⢹⣄⠺⣇⠁⠘⡄⠀⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠿⠃⠀⡸⠀⢠⠗⠊
⠀⠀⠀⠀⠀⠙⠓⠺⡄⠀⠘⢦⡀⠈⠉⠉⠉⠀⠀⠀⠀⠰⣤⡼⠃⠀⠠⢀⡀⠀⠀⣀⡠⠚⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⡑⠒⢒⡈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣈⠉⠩⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⠀⠀⠀⠀⢠⠞⣉⡩⢍⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⢿⠈⠁⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣀⡠⠜⠋⠉⠛⠒⠒⠋⠉⠉⠳⠤⣀⣀⡱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⣤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⢻⣄⣀⡼⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡞⠁⠉⣷⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠃⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢲⡀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⢶⣄⠀⠀⠈⠁⠀⠀⠀⣴⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠀⠀⣠⣶⠟⠉⠰⡆⠀⢰⡞⢳⡄⠀⣴⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠙⠲⠼⠷⠾⠥⠶⠋⠀⢀⡖⠀⠀⠈⣿⣤⣶⣤⡀
⠀⠀⠀⠀⢠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠄⠀⠘⠁⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠂⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⣀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠘⣳⡶⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠳⣦⠀⠀⠀⢸⡿⠛⠉
⠀⠀⠀⠀⠀⣾⠉⢻⠄⠀⠀⠀⠀⣾⠟⠛⠛⠀⠀⠀⠁⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣠⣿⠃⠀⠀⠀⠀⢰⠟⠉⢳
⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⣿⡄⠀⠀⣀⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⢀⣀⣤⡶⠛⢁⣤⡾⠟⡵⢶⡶⣦⠀⠀⠈⠳⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⠻⣦⣄⣀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠐⠞⢿⣏⣀⣼⠇⠀⠀⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠟⠛⢛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣉⠀⠀⣠⡾⠟⢿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⢷⣀⣀⣠⡾⣳⣦⡀⢘⣛⣠⣚⡛⠁⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⠟⠀⠀⠀⠀⠀⢸⣿⣾⣤⣤⣦⣭⣍⠉⠀⠀⠼⣿⠟⣽⡿⣿⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠁⣼⡟⠁⠀⠈⠙⣷⣄⢀⣴⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠉⠉⢿⣄⣿⠀⠀⠀⠀⠀⠘⣿⠛⠁⠀⠀⣻⣦⣼⣷⣄⠀⢀⣼⠟⠛⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠈⠻⢿⡆⠀⠀⠀⠀⠀⣿⣧⣴⡶⠟⠋⠀⠀⠉⠙⠛⠛⠁⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢤⣤⣀⣀⣀⠀⠀⠙⠻⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠔⠓⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠤⠤⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⣽⠻⣌⠱⣞⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠀⠀⠑⣄⣷⡏⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠉⠉⢀⣿⡿⠯⣍⣉⡳⣄⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢳⡘⢧⡇⢹⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⡙⢦⣀⠀⠀⠀⠀⠘⢧⡀⠀⢻⡀⣧⠏⠀⠀⢀⣠⡀⠀⠀⢠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⠈⠳⠦⣄⠉⢦⡈⠓⣦⣄⡀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠉⠒⠋⠀⠀⠀⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠳⣄⠀⢸⡇⠀⠙⠛⠁⠀⠉⠓⠦⣄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⠺⠧⣤⣀⣀⣀⣀⣀⡀⠀⠈⢳⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠦⡀⢳⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⠒⢢⡴⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⡖⢡⠄⡠⠤⣴⠋⠀⠀⠀⢀⣀⣀⣀⣀⡤⠤⢤⣀⠀⠀⠠⣄⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⢠⡏⢸⠁⢰⠃⠀⠀⠠⣎⢥⡴⠖⠂⡀⠀⠀⠀⠀⠉⠀⠀⠉⠳⣦⢤⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠚⠀⡏⠀⠀⠀⠀⢠⣏⣠⢞⠟⣡⠚⠉⠉⠓⠂⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠐⡇⠀⠀⠀⢀⣤⡉⠀⠘⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠠⣞⠛⠲⢬⣦⡈⢦⠀⠀⠀⠀⣷⠀⠀⠀⠘⢆⠙⣆⣶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⡭⠽⣦⣌⠳⡌⢷⠚⠛⠉⠙⠀⠀⢯⡉⠲⣷⠈⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠘⠲⠶⠶⠬⣁⠀⠀⠀⠀⢀⣀⣀⣰⣄⠈⠳⣌⠃⠸⠂⠻⠚⠋⠉⠉⠉⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠉⠉⠉⠉⠁⠀⠙⠒⠼⢦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠂⠀⠀⠀⠀⠀⣀⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢋⠀⠀⢠⠔⠂⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠀⠀⠀⠀⠀⢸⣧⡞⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢥⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠘⡀
⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠠⠤⣤⠘⣿⣆⠀⢀⠀⠀⡆
⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠙⢛⠁⠚⠃⠀⣠⠀⠀⠀⠀⠐⠒⠦⠀⠘⢿⣷⣦⣿⡄⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⠷⠚⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠐⢦⣱⠏⠉⠙⣖⣶⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠠⢀⡆⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠸⡅⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠀⣰⣡⣾⣷⡸⣄⠀⠀⢀⡤⠶⠶⠗⠀⡜⠀⠀⠀⢀⣩⣤⣾⣿⣿⡟⣆⠘⢮⡆⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣭⣉⠉⠉⠀⠤⠐⢈⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢯⢿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠀⣹⠋⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠟⡛⠀⠧⠴⠋⣀⠴⠁⠀⠿⠿⣿⣿⣿⣿⣿⡿⠋
⣔⡡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠤⠆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡴⠀⢠⠆⠀⠀⠀⡄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢼⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡴⠳⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⣫⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⢗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠄⠸⡀⠀⡠⠖⠒⠦⣤⠤⠜⠓⠓⠐⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⣠⠤⠚⠁⠀⠙⣆⠠⠏
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠛⠋⠛⠛⠛⠒⠶⠾⢳⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢍⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢳⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠀⢀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠸⡀⠀⠀⠀⢀⠗⣄⠀⠀⢀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣴⠋⠀⠄⠀⠀⠑⠒⠐⠒⠀⠀⠈⠑⠂⠁⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠘⢄⠀⠀⠙⢦
⠀⠀⠀⠀⡼⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⢳⡄
⠀⠀⢀⡾⠁⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢹⡄
⠀⢀⡞⠀⠀⠀⠂⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢶⠀⠀⠀⠠⠀⠀⠀⠀⢻
⢀⡾⠀⠀⠀⠀⠆⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣸⠃⠀⠀⣀⣀⠀⠀⠘⣇⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣼⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⡗⠦⢤⣤⠞⠁⠀⠀⠪⣁⡠⠗⠀⠀⢈⡗⠒⠚⠙⡆⠀⠀⠀⠀⢠⣄⡀⠀⣰
⣏⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⣱⠀⠀⢸⠀⠀⠀⠀⢀⡼⢄⡀⠀⠀⠀⠳⡄⠀⠀⢽⡀⠀⠀⢀⡟⠀⠉⠛⠉
⠹⣦⣀⣀⣠⡶⠋⠘⢦⡀⠀⠰⡁⠀⠰⡇⠀⠀⢀⠤⢅⢀⠴⠧⡀⠀⠀⠘⣄⠀⠀⠀⡽⠀⣠⡞
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⢦⣴⠃⠀⢰⠁⠀⠀⡏⠀⠀⡟⠀⠀⢳⠀⠀⠀⣼⠀⠀⠀⣹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣇⡀⠀⡇⠀⠀⣿⠀⠀⢸⠀⠀⠀⣘⣧⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⢛⡇⠀⠀⣿⡀⠀⢸⡖⠚⢿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠜⠁⠀⡸⠀⣇⠀⠀⠳⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢀⡴⠁⠀⠘⢦⡀⠀⠀⢀⡟
⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠉⠉⠀⠀⠀⠀⠀⠉⠙⣟⠉
⠀⠀⠀⠈⢷⡀⠉⠛⠶⣄⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⠙⠲⢤⣄⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠹⠧⣤⣤⣤⣤⣤⣭⣅⠀⣠⣤⣤⡤⡤⡤⣤⣤⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡾⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠃⠀⠀⠀⠀⠀⠀⠘⣦⣴⠃
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠁⠈⠀⠉⠙⠻⣦⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⢀⣴⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠛⠛⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠒⢂⣾⣷⣆⡾⢀⣆⡷⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⣾⡿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣋⣠⡴⢾⣿⣿⣿⣿⣿⢿⣿⣿⣵⣢⠆⠀⠀⠀⣿
⠀⣿⠀⣸⠋⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣽⠋⠀⣿⠁⠊⣹⣿⢿⡇⠀⢹⣿⠗⠀⠀⠀⠀⣿
⠀⣿⠀⠁⠀⠀⠀⠀⢠⣀⢶⣋⣹⣍⣍⣉⣉⠙⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠇⣀⣀⣤⠄⠀⠀⣿⡛⠁⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠰⣄⢤⣘⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣯⡡⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣃⠀⠀⠀⠀⣀⣄⣀⣀⡄⠚⠉⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠙⢛⣻⣿⠋⠀⢸⡁⠈⠼⣿⠿⠇⠈⢷⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠚⠋⠁⠈⡉⠈⠉⠀⠀⠠⠂⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠈⠲⢻⣿⡀⠀⠀⠁⠦⠤⠴⠂⠀⡄⠈⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⢿⣶⠮⢴⣬⠤⠐⠋⠐⠂⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠦⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣲⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⡴⠋⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡑⠀⠀⠀⠀⠀⢀⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣀⠀⠀⠀⠀⠀⣾⢁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡌⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠐⠒⠓⠂⠀⠀⠀⠀⠀⠀⢄⣀⣀⡈⣏⣆⠀⠀⠀⠀⢳
⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⠀⠠⠖⠂⠀⢀⡀⠀⠀⠀⠀⠤⢄⡀⠘⣜⢦⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠋⠀⠀⠀⢴⡭⠖⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⡄⠈⠀⠄⢮⣬⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠉⠱⡂⠀⢸⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠵⠋⠀⠀⠀⠀⠀⡴⠁⠀⠆⢃⠀⠀⠀⠀⡀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠐⢋⡠⠋⠀⠘⢦⠀⢦⣢⠀⠀⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡄⠀⠀⠂⢐⡂⠐⠚⠃⢀⡀⣀⠐⠁⠀⠀⠄⠀⠈⠉⠀⠀⠀⠀⡈⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢆⠈⠀⠀⢀⠀⠀⢢⠀⠀⢠⢣⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡖⠀⠀⠀⠀⠀⠀⠁⠳⠄⠀⠱⣧⠀⠀⠀⡄⢀⠖⠋⢀⠏⠀⠀⠀⠀⢀⣜⡼⠀⢀⡎⠞
⣠⠄⣀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠁⡄⠐⠁⠀⠀⢠⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠀⢀⡉⠁⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣠⠃⠀⠘⠁⠀⠀⠀⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣈⡄⠠⠗⠚⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠋⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣇⣀⢀⡀⠡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠘⢤⡤⠚⠁⠈⠉⠒⠊⠁⠀⠈⠁⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣢⣤⣖⣚⣉⣀⣀⣀⣷⣐⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⠉⠉⠉⠛⠓⠒⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⠙⠦⣀⡤⠞⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣀⣀⠀⠙⣆⠀⠀⠀⢀⣠⠖⠛⠉⠁⠀⠀⠉⠳⣄⠀⠀⠀⣀⡤⠤⠬⠷⢦⣀⠀⠀⠀⠀⣾⣁⣤⣤⣤⣤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠓⢾⡄⠀⡴⠋⣠⠤⠶⠖⠒⠒⠒⠶⠦⣼⡆⢀⣞⣡⣤⠤⠤⢤⣄⣈⡙⢦⡀⠘⠉⠀⠀⠀⠀⠠⢤⡶⠶⠤⣄⡀
⢀⡤⠶⠒⢒⡶⠶⠀⢠⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠠⠖⠋⣩⠟⡇⣼⢯⡙⠒⠦⡀⠀⠀⠈⠉⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢙
⣏⠀⠀⡰⠋⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⢰⠇⢹⡀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚
⠈⠓⠋⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠐⠚⠋⠉⠀⠀⠀⢀⡴⠋⠀⠀⢷⡀⠀⠀⠀⠀⠉⠉⠛⠂⢀⣇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡞⢹⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠖⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣾⣝⣳⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⣞⣯⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠾⢷⣿⣭⣽⣿⣛⣛⣛⣛⣛⣿⣿⣭⣿⣾⣿⣿⡿⠿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠉⠉⠙⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣀⠎⠀⠉⠉⠋⠑⢿⠲⢄⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡤⣄⡜⠛⠀⠀⢀⣀⠀⠀⠀⠀⠈⢣⣴⡀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠁⢸⡇⠀⠀⡜⠁⢠⡇⠀⠀⡠⢢⡀⡏⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢿⢦⡄⠀⠀⠈⠓⣦⠬⠇⠀⢠⠃⢿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠞⠉⠁⠀⢀⣀⡑⢇⠀⠀⠀⣦⠛⠀⠀⠀⠈⣿⣛⢠⠇
⠀⠀⠀⠀⠀⠀⢠⠞⠁⡎⠀⠀⠀⡴⠁⠀⠙⢎⣦⡀⠀⠠⡦⠶⠿⠶⣤⣤⢛⡞
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠠⡇⠀⠀⠀⢸⠘⡝⢷⣤⣄⣀⣀⣀⡤⠝⢫⡄
⠀⠀⠀⠀⠀⠘⡄⠀⡰⠳⡀⠀⢸⠀⠀⠀⠀⢸⡄⠘⠷⠬⠔⠃⢠⠏⣇⢰⡀
⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠈⠢⣄⢹⠉⠉⠉⡇⠀⠀⠀⠀⣀⠔⠋⢹⠁
⠀⠀⠀⠀⠀⡔⠉⠳⡇⠀⠀⠀⠈⠻⡀⠀⠀⢇⠀⠀⠀⣰⢇⠀⠀⠸⡀
⠀⠀⠀⠀⠀⡇⠀⠀⢱⠀⠀⠀⠀⠀⢱⡀⠀⠈⢶⣉⠉⠈⡟⢆⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠸⣤⣤⣄⠀⠀⠀⠀⢀⠜⠻⢄⡀⠀⠀⠉⢲⡃⠈⠢⡀⢀⡈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠉⠉⠓⠚⠁⠀⠀⠀⠈⠛⠙⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⠿⠿⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⢀⣤⠖⠛⠉⠉⠙⠛⠿⠿⣿⣿⣿⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⣶⣦⠀⠀⠀⠈⣷⠀⣔⠚⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣺⣿⣿⠀⠀⠀⠀⣿⠀⢿⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢀⡀⠀⢳⡄⠀⠀⠠⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⣠⠊⠁⢠⠏⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠈⠙⢶⣤⣀⡀⠀⠀⢀⣀⡄⠀⠉⠀⠀⠀⠰⡄⠄⣀
⠀⠙⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠰⢦⣤⣀⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠠⠀⠀⠀⠀⢳⡀⣸⠆
⠀⠀⠀⠀⢀⡀⢰⠀⠀⢣⠀⠀⡰⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠤⠎⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣙⣷⣦⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⣋⣵⣾⣿⠟⠛⢉⣿⣿⣿⠿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣷⣤⣈⣿⡿⠛⣩⣴⠾⠛⠋⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠋⠻⣿⡿⠛⢡⣿⡀⠀⠀⠉⠁⣀⡀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠉⠛⢿⣷⣾⠟⠁⠀⠴⣾⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⣼⠏⠀⢠⣿⣿⡄⠀⠀⣠⡾⠋⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⢿⣿⠛⣿⣦
⠀⠀⠀⠀⠀⠀⣰⢃⣿⡏⠀⠀⠀⢰⣿⠀⠀⢼⠿⠛⠀⢀⣾⠋⠀⠀⠀⠀⠻⠛⠁⠾⠛⠁⠚⠁⠀⠀⣠⣤⣤⡿⠇⠀⢀⡛⠛⠂⢬⡋⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢿⡞⢿⣇⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠘⠻⢷⡄⢀⠛⢠⣿⠟
⠀⠀⠀⠀⢀⣴⣿⣿⣄⠻⢷⡄⠀⠀⠀⣶⣴⣶⣄⠀⢸⡏⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠿⠛⠉⠀⠴⠶⠶⠻⢶⡄⠀⣻⣿⡇⠞⠋
⠀⠀⠀⠀⣿⣿⣿⡇⠈⣳⡄⠻⣄⠀⡀⠸⢿⣿⣿⠀⢺⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠞⠉⣿⣇
⠀⠀⠀⠀⣿⣿⣿⣥⣾⡿⠁⠀⠈⠁⠀⠀⠈⢿⣿⠄⠘⠁⢿⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⠉⠙⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠸⣷⡄⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠈⠀⣿⠇
⠀⠀⠀⠀⢸⣿⣿⠠⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⢰⣿
⠀⠀⠀⠀⠘⣿⠿⠀⣀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣋⣸⣿
⠀⢀⡀⠀⠀⠉⠰⣿⣿⡟⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠈⣿⡇
⢠⡿⠁⠘⢦⠀⠀⣠⡏⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⢸⣁⣷⣄⠈⣧⣼⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⢸⡟⠉⢹⣆⢻⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣥⣤⣄⡀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣤⠶⣤⣶⠿⢻⣶⣄⠀⢰⠟⠁⢙⡆
⢸⡇⠀⣾⣿⠆⢀⡀⠀⠀⠀⠀⠐⠋⠙⣿⠙⠛⣫⡿⢿⣦⠄⢹⣧⠀⠀⠀⠀⡴⠂⠀⢠⣴⣶⢶⣶⡿⢃⡴⠛⣡⡴⠛⠁⠙⠧⠀⣠⣿⣿⡇
⠈⣧⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⡀⠀⢸⣿⠇⠀⠀⠈⠁⠀⠘⠋⢰⣿⣜⣿⣷⣿⠁⡾⠁⢀⣠⣴⠞⠻⣦⠛⠁⣿⠁
⠀⢻⡄⠹⣧⡀⢸⣧⠀⠀⠀⠀⢀⡄⢀⡀⠀⠐⠂⠀⡼⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⣿⠀⡇⢰⡟⠁⣠⣴⡆⠙⢷⡀⠻
⠀⠘⣷⡀⠘⢷⠀⣿⡀⠀⠀⠀⠘⠶⠟⠁⠙⠀⠀⠊⠀⠀⠀⢀⣤⠦⠦⢤⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠛⢀⡇⣸⡇⣸⣿⣿⣿⠂⠀⢹⣆
⠀⠀⢹⣧⡀⠈⠁⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣄⠀⠀⠀⠰⠶⣄⠀⠀⣿⠁⠀⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣯⠀⢠⣾⠏
⠀⠀⠀⠻⣿⣦⣀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠙⠓⠛⠛⠃⠀⠰⠶⣦⠾⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⣿⡿⠋⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠈⠙⢿⣧⠘⣿⡄⠀⠀⠀⠀⠀⣟⢛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠘⣿⡄⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠘⢷⡀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠶⡶⠾⠛⠉⠉⠉⠉⠉⠛⠳⣤⣄⠀⠈⣿⡄⠀⠈⢿⣆⠀⠀⠀⠀⠐⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠸⣿⣦⠀⠈⢻⣦⠀⠀⠀⠀⠙⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⣿⡿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠙⣇⠀⠀⠀⠀⠀⠘⣯⣬⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢹⣷⡈⠛⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡴⠀⣿⢿⣷⣀⠀⠀⠄⠀⠀⠀⠀⠀⠘⣿⣿⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢻⡇⠀⠀⠙⠻⣷⣄⡀⠀⠀⠀⣀⣀⠀⠀⢀⣠⡴⠞⠁⠀⠀⣿⠀⠉⠛⢿⣶⣤⣀⣀⠀⣀⣠⣾⣿⣿⣿⠈⣷
⠀⠀⣀⣀⣀⣤⣾⠏⠀⠀⠀⠀⠀⢀⣉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⢠⡞⠀⠘⢧⣄⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠟⠃⠀⣿
⠀⠸⠿⠛⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣶⣤⠀⠀⠀⠀⠀⠈⢻⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⢿⣿⣷⣦⡙⠷⡄⠀⠀⠀⠀⠀⢠⠞⠁⣴⠟⢻⣿⣷⣄⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠
⠀⠰⢦⣤⣀⣀⣀⣀⣠⣤⣶⣾⡿⠿⡿⣷⣦⣬⣛⣿⣿⣧⠈⠁⠀⠀⠀⠐⠁⣠⣞⣡⣴⣾⠟⢿⣿⣷⣄⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄⣀⣠⣤⣖⣩
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣷⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⣠⡄⠙⠿⠿⢷⣦⣤⣄⡀⠘⢿⣿⣿⣿⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⡿⠋⠁⠀⠀⠀⠀⠙⠫⠤⠀⠀⠈⢿⣿⣿⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠟⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⡤⣤⣀⠀⠀⠀⣀⠤⠖⠚⠋⠉⠉⠉⠉⠙⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠳⡔⠋⠁⠀⠀⠀⣀⡤⠤⠦⠤⣄⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠈⠓⢲⠶⠤⣼⡆⠀⣠⠔⢉⣀⣀⣤⣤⣀⣈⣣⠀⢠⠔⠋⣉⡉⠙⠒⢤⡀⠀⠾⠒⠛⠛⠛⣋⣁⣀⡀
⢀⣠⠤⠤⣤⠄⠀⡰⠃⠀⠀⠀⠁⡰⠁⠀⠁⠀⠀⠀⠠⠖⢒⠿⣆⣿⡛⠯⣍⠉⠉⠙⠂⠙⡄⠀⠀⠀⠀⠀⠉⠳⣄⠉⠑
⣎⠀⣠⠞⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡠⠴⠚⠁⣸⠉⡇⠉⠓⠦⢤⣀⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠲⠚
⠈⠉⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢣⡀⠀⠉⠉⠀⠀⠀⣠⠜⠁⠀⠘⣆⠀⠀⠀⠀⠉⠉⠁⣾
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠴⠒⠋⠁⠀⠀⠀⠀⠈⠓⢤⣀⠀⢀⣀⠜⠁⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣀⠀⠈⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠈⠻⠿⣿⣿⣿⡿⠿⠟⠛⠋⠁⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣾⣽⣳⣶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡴⣶⣻⣽⣾⣿⣿⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣼⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣶⣿⣿⣿⣿⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠘⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣾⣿⣷⡄⠀⠀⠷⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣷⣦⣠⡄⣀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣺⣿⣿⣿⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⣽⢿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⡿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⣻⣯⠽⢀⠦⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢹⡄⠸⣘⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⣿⣿⣿⣶⡶⠀⠀⠀⢠⠀⢀⣸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣏⣠⡀⠀⢻⣿⠿⠋⠀⠀⠀⠀⠘⠀⣠⣿⣿⣿⠀⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⣶⣶⣴⣶⣿⣿⣿⣿⡗⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠻⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋⠉⢹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⢿⣿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣧⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠙⣿⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠻⣿⣿⠺⡟⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⣿⣿⣿⣿⣷⣋⡉⠙⢻⣿⣦⢻⣿⣾⣷⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠻⣿⣿⡿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⠉⠀⠈⠧⠀⠈⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠉⠉⠁⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠄⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡠⠤⠔⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠉⠉⠀⠉⠀⠀⠂⠀⢀⠈⠐⠀⢀⠀⠈⠐⠀⣆⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠙⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡈⠀⠄⠀⠀⠑⠠⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠘⢆⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢐⠀⠀⠀⠐
⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⠈⠳⣄⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢤⠤
⠀⠀⠀⠠⠁⠀⠀⠠⠂⠀⠀⡠⠁⠀⠙⠢⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⣀⣀⡀⠠⢴⣢⠄⠴⠀⠡⡀
⠀⢀⠔⠁⠀⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠤⠀⠒⠀⠉⠀⠀⠒⠠⠀⠈
⠐⠡⣤⠐⡈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢃⠀⠀⠀⠀⡀
⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡁⠐⠀⠈
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠉⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠛⠻⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠁⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠀⠙⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢁⡀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠐⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠓⢦⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣾⠀⠀⢇⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠆⠀⠁⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣤⠀⠀⠀⠰⡀⢸⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠢⠞⠀⠀⠀⠀⣾⣿⠟⠋⠉⠉⠉⠛⢿⣿⣷⡀⠀⠀⠙⠋⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠖⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣄⡀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠛⠛⣋⣁⣀⠀⠀⠀⠀⠀⠀⣀⣈⣙⠛⠛⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⢠⣾⣿⡿⢿⡷⠀⠀⠀⠀⢾⠿⠿⣿⣷⡄⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⡇⠀⠀⠀⠘⢻⡇⠀⢘⡇⢀⣀⣀⡀⢸⡇⠀⢸⡟⠃⠀⠀⠀⢸⣎⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡞⡼⠃⢻⡀⠀⠀⠀⢸⡇⠀⢈⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠀⢀⡟⠘⢧⢳⡀
⠀⠀⠀⣠⠖⠛⠛⢾⡁⠀⠈⢷⡀⠀⠀⢸⡇⠀⢀⡿⠿⠛⠛⠿⢿⡀⠀⢸⡇⠀⠀⢀⡾⠁⠀⢈⡷⠛⠛⠲⣄
⠀⠀⣼⠃⠀⠀⠀⠀⣷⠀⠀⠀⠳⣄⠀⢸⡇⠀⢨⡇⠀⠀⠀⠀⢸⡅⠀⢸⡇⠀⣠⠞⠀⠀⠀⣾⠀⠀⠀⠀⠈⣧
⠀⠀⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠳⢼⣇⠀⢸⡇⠀⠀⠀⠀⢸⡇⢀⣸⡧⠞⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸
⠀⠀⠳⣄⣀⣀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠉⣿⢾⠷⠤⠤⠤⠤⠾⠟⡟⣿⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⣀⣠⠞
⠀⠀⠀⠈⠉⠉⠓⠋⠀⠀⠀⠀⣠⠴⠖⠒⠒⠻⢾⡀⠀⠀⠀⠀⠀⢀⡷⠟⠒⠒⠲⠦⣄⠀⠀⠀⠙⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠸⢤⣀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⡠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠔⠈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠀⠀⠀⠀⠙⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣀⠀⠒⠢⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠒⠢⠈⠁⠀⠉⢆⢀⡀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀⣀⠀⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠂⠀⠒⠀⠀⠐⠀⢀⡴⠁⠀⠀⠀⠀⠁⠐⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠂⠀⠧⠤⣀⣤⣤⣤⣤⡀⠀⠀⠀⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢸⣿⠿⠟⠉⢉⡽⠀⢀⡴⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠄⣈⡙⡒⠊⠉⠡⠐⠚⠛⠉⠉⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠒⠂⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠤⠀⣀⣀⣀⣀⣀⣀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠾⠔⠒⢋⡉⣉⡀⡀⠠⢌⡉⠙⡇⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡈⠈⢀⣻⠁⠈⠠⠀⢄⢤⢈⡳⠄⠑⡀⠀⠀⣀⠠⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠳⣄⠘⠄⠈⠀⠀⡘⠒⡌⢢⠔⠂⠤⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠔⠒⠉⠙⠛⡇⠀⠀⢀⡧⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠒⠒⠋⠉⠉⠉⠉⠉⠉⠙⠒⠒⠲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣠⣾⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣿⣷⡄⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠸⠏⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠹⠇⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠹⠿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣄⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠉⠉⠒⠒⠤⢤⣤⣀⣀⣀⣀⣀⣀⣤⡤⠤⠒⠒⠉⠉⠀⠙⠛⠛⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠿⠿⠿⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠿⠿⠿⠶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⢠⣿⠃⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢻⣧⠀⠀⠀⣼⡟⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠘⣿⡄
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⣿⡆⠀⢰⣿⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠈⠻⠛⠀⠀⠀⠀⠀⢹⣷
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⣿⡆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣼⡇⠀⢸⣧⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⣶⣤⣀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⢹⣧⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⢠⣿⠃⠀⠘⣿⡄⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⣼⡏
⠀⠀⠀⢻⣧⡀⠀⠀⠈⠛⠷⢶⣤⣤⣴⠶⠟⠋⠀⠀⠀⣠⣿⠃⠀⠀⠀⠘⣿⡄⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⢀⣼⡟
⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣭⣭⣽⣯⣬⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣀⣀⡼⠁⠀⠀⣠⠋⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⠃⠀⠀⣠⢞⣡⡤⠶⠞⠛⠉⠉⠉⢙⡇⠀⠀⡰⠃⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⠇⠀⢀⣼⠟⠋⠁⠀⠀⠀⠀⠀⠤⠶⢯⠀⠀⠘⢁⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⡤⢤⡀
⠀⠀⠀⠀⠀⠸⠧⠴⠛⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠧⣤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠘⢻⠶⠶⠤⢶⠟⠁⠀⠀⠀⠀⠀⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣀⡀⠀⠀⠀⠀⣛⣓⠀⠀⠺⡉⠉⠉⠙⣆⠀⠀⠀⠠⣖⣲⠄⠀⠀⠘⣆⠀⠀⣞⠀⠀⠀⣋⡁⠀⢰⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⠀⠀⢨⠤⠀⠀⠀⣽⠀⢀⡜⠃⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣽⠀⠀⢸⡆⠀⠰⠤⠀⢠⡟⠀⢴⡟⠒⣦
⠀⠀⠀⠀⠀⠀⣴⠋⡽⠂⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⢾⠁⠀⠈⢣⡀⠀⠀⠀⠀⠋⠙⠀⠀⠀⢰⡇⠀⠀⣾⠀⠀⠀⠀⣠⠟⠀⠀⠀⠙⠲⠛
⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠈⡧⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⢳⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢾⣄⣀⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠒⢺⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠁⠙⠒⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠈⠁⠀⣺
⠀⠀⠀⠀⠀⢰⠀⠈⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠑⠀⠀⠊⠘⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⣽⣿⣿⣻⣿⣏⣉⠑⣦⡀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣻⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠛⣾⡿⠿⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠏⢀⣀⣈⠀⠀⠈⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡤⠼⠉⢿⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣪⠖⢢⣀
⠀⠀⠀⠀⠀⠀⣔⠃⠐⠀⠀⠉⠉⠉⠑⠲⠤⢤⣀⣀⣀⣀⣀⡤⠤⢖⠊⠉⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠃⠠⠄⠐⠒⠀⣨⢀⠀⢤⡀⠀⠀⠀⠀⠀⠠⢄⣠⠀⠐⠂⠀⢤⡀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠃⠉⠀⠀⠁⠤⠄⠈⠄⠀⠀⠀⠁⠀⠢⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣇⠀⠂⠀⠀⢰⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣮⠜⠢⠤⠤⠤⠯⡇⠀⠀⢀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠛⠿⣶⣿⣿⡿⠁⠀⠀⠀⢠⣶⣿⣷⣦⡀⠀⠀⠀⢀⣾⣿⠿⢿⣷⡄⠀⠀⠀⠹⣿⣿⣤⣴⣶⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⡀⢀⣀⣈⣿⣿⣇⠀⠀⠀⢠⣿⠟⠁⠘⣿⣧⠀⠀⢀⣾⡿⠁⠀⠀⢻⣿⠀⠀⠀⠀⣿⣿⠛⠁⠀⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠻⣿⣿⣿⠛⠷⣄⠀⠈⠋⠀⠀⠀⠙⠋⠀⠀⠘⠛⠁⠀⠀⠀⠀⣿⠀⠀⣰⡾⢿⣿⣿⣿⣶⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠈⠀⠈⠁⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠛⣿⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⣠⣿⣿⣿⣇⣀⣀⣿⣀⣀⣸⣿⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠘⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣤⣤⣶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠉⠉⠉⠉⠉⠐⠒⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣾⠟⠉⠁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠉⠻⣷⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠘⠋⣠⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣄⠙⠃⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⡆⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⣠⠒⠉⠉⠒⡄⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⢠⣅⣀⣀⣀⣀⣨⡆⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢺⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡗⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠓⠒⠤⠄⣀⣀⣀⣀⣀⣀⠠⠤⠒⠚⠻⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠛⠛⠉⠉⠉⠉⠁⠈⠈⠁⠉⠙⠽⠻⠯⢁⣠⣰⣤⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠤⣄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⢸⢏⡾⡿⠟⠋⠑⠋
⠀⠀⠠⠇⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⢀⣀⣀⠀⡤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡾⣿⣛⣿⣉⣿⣯⣟⣿⣷⢟⡰⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣧⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿⣲⣤⣀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⣠⡾⢏⣾⡿⠟⠋⠉⠀⠀⠰⠟⠻⢿⣿⣿⣿⣿⣿⣷⣏⣷⡄⡀
⠀⠀⠀⠀⠀⠉⣪⣀⣠⣤⣴⡾⢋⣴⣿⠏⠀⠀⠀⠀⠀⠀⢰⣶⣦⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠋⡴⡶⠿⠿⠏⠛⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣾⢿⣵⣷⣦⣍⠣⠹⣿⣿⣶⣟⣠
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⡐⠂⠀⠀⠀⠖⣲⠦⢤⣀⣀⠀⠀⠈⠻⣿⣿⣿⡿⠿⠿⢃⣀⣥⣾⣿⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠀⠀⡠⠗⠒⠁⠁⠀⠛⠋⢶⡖⣶⣶⣶⡖⣾⠿⡿⠟⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣼⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣹⠇⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣽⠇⠀⢀⣾⣿⣿⣿⡿⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣾⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⣠⣤⣶⣦⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠙⠲⠞⠋⠀⢿⠀⠈⠛⠛⠛⠁⠀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣠⡤⠦⣤⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠄⠀⠀⠀⠀⠀⢀⠤⢄⡀⠐⠄⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⣀⠤⢄⠀⠀⠀⢰⠃⠀⠀⢹⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⡠⠚⠁⠀⠀⣧⠀⠀⣮⠀⠀⠀⠘⢆⡠⣄⢀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⠎⠀⠀⠀⠀⠀⠈⣹⠀⢻⠀⠀⠀⠀⠀⠀⢸⠈⢇⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡰⠃⠀⠀⣀⣴⡿⠂⠀⢧⣀⠼⠀⠀⠀⠀⠘⢷⣼⠀⠈⡆⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣰⠁⠰⠖⢛⣛⡛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢛⣙⣤⣴⠃⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢀⠇⣠⡴⠛⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢻⣿⣿⣷⣤⡀⠀⠓⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣘⡴⣿⣷⣄⣀⣿⣷⣾⣿⣿⡄⠀⠀⠀⠀⣰⣿⣦⣀⣤⣿⣶⣿⣷⡏⢦⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀⠀⡿⡇⢹⣯⣿⣿⣿⣿⣿⣿⠏⣧⠀⠀⠀⠀⡏⢿⣽⣿⣿⣿⣿⣿⣿⠃⢨⣇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⡇⡜⠀⣇⠀⠙⠿⣿⣿⡿⠿⠋⢀⡇⠀⠀⠀⠀⢳⠈⠛⠿⣿⣿⡿⠟⠁⠀⣼⠘⠦⣄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡼⠀⡇⠀⠹⣦⡀⠀⠀⠀⠀⢀⣠⠞⠰⡂⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⢸⢠⡦⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⢀⡇⠀⠀⠈⠛⠛⠶⠶⠾⠛⠁⠀⠀⣀⣀⣀⡀⠀⠀⠙⠻⠷⠶⠾⠻⠛⠁⠀⠀⠀⡞⠀⢱⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠉⠀⠀⣰⠀⢰⠀⠀⠀⠀⠀⢀⠴⠋⣁⣀⡀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡀⠘⢧⣀⡼⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣰⠃⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠥⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⠀⠀⡸⢧⣀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠈⠉⠛⠛⠲⠶⠶⠦⠤⠤⠤⠤⠴⠶⠶⠶⠛⠛⠋⠉⠀⠉⠉⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠷⠂⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⣀⠀⠱⣀⣀⠀⠀⣠⠔⠒⠂⠐⠢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠆⡁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠤⠒⠲⠞⢀⡠⠔⠒⠒⠒⠒⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠤⠤⠶⠃⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠲⠤⣄⠀⠰⠒⠒⠶⢤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠖⠄⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⣾⠉⠢⣄⡠⠔⠒⠈⠉⠁⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠸⣄⠀⢀⡀⠀⠀⠠⠤⠒⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢣⡀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠐⠖⠊⠉⠢⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠤⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠁⠀⠀⠐⠀⠂⠈⠀⠀⠀⠈⠈⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠛⠛⠛⠛⠛⠛⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿
⣿
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠘⢷⡀⠀⠀⠀⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⣤⡶⠶⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣴⣶⣶⣶⣶⣶⣶⣶⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣼⣶⣿⣿⣿⣿⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠛⠋⠉⠉⠉⠉⠙⠛⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡿⠟⠋⠁⠀⠉⠉⠉⠻⣿⣿⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢
⠀⠀⠀⠀⠀⢀⣴⠾⠟⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠑⠪⢻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠍⠲⠉⢀⡠⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣾⣯⣷⢷⢠⠀⠀⠀⠀⠀⠀⠔⡀⡀⢨⣴⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⡟⠙⢿⣿⣿⡿⠋⢉⢻⣿⣿⣿⠈⣯⡄⠀⠀⠀⠀⠀⣼⣰⢀⣿⠿⠯⢝⣿⣿⣿⣿⠟⠁⢀⣈⡻⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢻⠿⣟⠒⠉⠛⠓⠈⠁⠀⠉⠟⠉⠀⠁⠁⠀⠀⠀⠀⠀⠉⡇⠈⠋⠀⠀⢤⠈⠉⠉⠁⣀⣉⠭⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠐⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢀⣐⡭⠔⠂⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⡠⢒⣷⣦⢀⡠⣢⠄⢂⠄⣊⣤⡶⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⢺⣿⣷⣿⣿⡿⢾⠤⣊⣥⣾⢿⡿⠛⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⠈⠙⠋⠛⠋⠉⠉⠉⠁⠈⠛⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣅⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⣤⣤⣤⣀⣀⣠⣴⣶⢶⣿⣶⠾⣿⣷⣶⣦⣤⣤⣀⣀⠀⢼⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⢿⣿⡿⠿⠿⠿⠿⠿⣿⣷⣿⡿⠟⠛⠛⠛⣻⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣹⣦⣀⡀⠀⠀⡀⠀⠀⢀⣀⣀⣴⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢲⣾⣾⣷⣿⣿⣿⡟⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣍⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⢠⣤⣀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠉⠉⠉⠉⠉⠛⠷⠂⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠾⢷⣄⠀⠀⠀⠀⠀⣠⣴⠾⠛⠁⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢋⣁⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡴⠞⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠒⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⣈⣉⣉⣑⣶⣶⣦⣤⠀⠀⣿⣯⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠦⠀⠠⠶⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⣀⣤⣤⡤⠴⠶⠶⠶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⣸⡇⠀⠘⠻⠦⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⣤⣄
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡾⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⢫⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠰⠞⠿⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠰⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇⠘⠻⢦⣀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⡀⠀⢈⡁⢰⡄⠀⠴⠦⢀⡴⠟⠁⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⠟⠀⠈⠛⠀⣿⢀⣴⠟⠃⠀⠀⠀⠀⠉⠛⠳⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡾⠋⠀⠀⠀⠀⠀⠀⣴⠈⢹⡟⢛⣻⠂⠀⣀⣤⣤⣄⡀⠀⢿⡁⢼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠉⠉⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠉⠙⠁⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣿⢸⡷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣧⣄⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⡿⠃⠀⠀⠀⠀⣠⡾⠃⢸⡇⠀⠈⠉⠛⠲⠶⠶⢆⣠⣴⠟⠁
⠀⠀⠀⠀⠀⣀⡤⢖⡿⠛⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⠇⣼⡿⢿⣶⣄⣀⠀⠀⠿⣀⡵⠟⠁⢀⣠⣤⠶⠿⠋⠀⠀⠘⠗⠀⠀⠀⣀⣠⣴⡾⠿⠛⠁
⠀⠀⠀⠀⠈⣯⡴⠋⠀⠀⠀⣿⠀⠀⠰⠂⠀⠀⠀⣴⠏⢠⣿⠇⠀⠈⠉⠛⠛⠶⠶⠤⠒⠒⠋⠉⠀⢀⣤⣀⣀⣀⣀⣤⣤⣶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣠⡾⠃⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⠷⢶⣿⣧⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⡄⠛⢙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⣤⢸⣏⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠙⠿⠙⠛⠻⠷⢶⡶⠀⢀⣀⣤⣤⣤⣤⣤⣴⡶⠾⠛⠉⠀⠀⠁⢸⡟⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠈⣻⡄
⠀⠀⠀⠀⣴⡾⠟⢶⡴⠌⢿⡄⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠉⠛⠳⠦⣤⣀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣠⡾⢏
⠀⠀⠀⢸⡟⠀⠀⠀⣠⣴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠉⠛⠶⣤⠀⢰⣿⣥⡴⠟⠁⠀⠈⢷⡀
⠀⠀⠀⠈⣷⡀⠀⣾⡏⠀⠀⠰⣞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⣄⡀⠀⠀⠀⣠⡿⠉⠁⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠘⢷⡄⢿⣧⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠰⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠈⠻⣦⡙⠳⣶⣄⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣮⠻⢷⣦⡀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⠈⠙⠀⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠉⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⣿⠋⠉⠙⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠶⠶⠾⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠛⠲⢦⡀⠀⠀⠀⠀⣀⡤⠼⠿⢿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢈⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡴⠛⠁⠀⠀⠀⠀⠀⠈⠉⠻⣍⠉
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⣦⡀⠀⠀⢸⡇⢠⡒⣶⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣿⡿⠃⠀⠀⢸⡇⠘⢯⡿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠸⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⢀⡠⠀⢠⠄⠀⠙⣦⠀⠀⠐⠒⠒⠀⠀⠒⠐⠂⠀⢒⡾⠉⠳⣄⠀⠀⠀⠀⠒⠀⠀⠀⢰⠏⠀⠀⣀
⠀⢏⠀⣠⠃⠀⠀⠀⠈⠀⠀⣄⡀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⠚⠀⠀⠀⠀⠀⠸⡀⠐⡄
⠀⠀⠉⠀⢀⢠⠄⠀⡇⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁
⠀⠀⠀⠀⠧⠜⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠋⠉⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⣠⠴⠶⠶⢄⠀⠀⠀⠀⠀⠀⠉⠳⢦⣰⡇
⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠉⠉⠀⠉⠙⠛⠻⠿⠿⠿⠟⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡴⡋⣈⡙⠛⠉⠀⠀⠀⠀⢰⣶⣶⢯⡀⠀⠀⠀⠀⣒⣦⣤⣤⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⣏⣛⡿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠊⠀⠀⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣭⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠚⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⡀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄⠀⠀⠖⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠢⠀⣀⠔⢀⠠⠞⢄⡀⠃⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣨⡄⢀⠞⢁⠞⠁⡠⢤⢀⣞⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⠀⠀⠘⠂⢠⠋⢠⢋⣠⣤⣿⣿⣿⣿⣿⣿⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⠛⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠸⣿⣿⡿⠿⠿⢿⠿⠛⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡐⡀⠀⠟⠁⠀⣀⠄⢤⢀⣤⣒⣟⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢄⠀⠁⠀⠐⠂⠉⠠⠄⠈⢉⡥⠐⠃⠀⠀⠀⠀⢀⠄⠠⡀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠁⢀⣀⠀⠠⢔⡫⣄⠀⠤⠐⠂⠈⣀⣠⢲⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⢽⣀⡶⠀⠀⠀⢧⡤⠐⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⢀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠘⠠⠊⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠰⠔⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠳⡀⠐⡒⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠢⡄⠠⠀⠘⠀⢧⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠅⠀⠕⣸⡜⢠⣦⡵⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡄⠀⣀⠀⠙⠇⠀⡌⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠠⠆⡴⠢⠀⠀⠀⠃⡀⡀⢀⣤⢀⣴⠚⡍⠙⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢂⠀⠀⠓⢚⡀⡎⠀⠑⢜⡍⣀⠼⠋⠄⠀⠀⠀⢘⡀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠬⠖⠀⢈⠝⠀⢱⡀⠀⠈⡟⣔⣦⠤⠤⠀⠁⠭⠝⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡁⢀⡤⠃⠙⠲⠯⠄⡀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢄⠀⠀⡀⢱⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠋
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣾⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣄⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣀⣤⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⢉⣤⣤⣄⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⣠⡞⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⢳⣄⠘⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡿⠛⠉⠉⠀⠀⠉⠉⠛⢿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⢀⣠⣤⣤⣤⣤⣄⡀⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠘⠳⠦⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠶⠤⠤⠤⠤⠤⠴⠞⠋⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠐⠲⠶⠶⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠶⠖⠂⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣾⡿⣿⠀⠀⣾⠉⠻⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⣷⠀⠀⣿⢿⣷⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠉⢡⡟⠀⢠⡿⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢿⡄⠀⢻⡎⠉⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⣾⠃⠀⣸⡇⠀⠀⠀⣠⠚⠉⠁⠈⠉⠓⣄⠀⠀⠀⢸⣇⠀⠈⣷⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢀⣧⣤⣤⣤⣤⣤⣤⣼⡀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⢰⡟⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⢻⡆⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⢸⡇⠀⠀⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⠀⠀⢸⡇⠀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⡇⠀⠀⣿⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿⠀⠀⢸⣧⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⣿⡋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠾⠛⠁⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⡶⠶⠶⠶⣤⣤⣤⣤⣴⠟⠁⠀⠀⠀⠈⠛⠷⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣤⣤⡶⠶⠶⣤⡀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣤⣤⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡶⠾⠛⠉⠉⠉⠉⠻⢦⣄⣀⣀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠔⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣓⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠦⠀⠀⠀⠀⣀⣠⠤⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠢⠤⣀⡀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⢰⠊⠲⡀⠀⠀⠀⢠⠤⠒⠂⠘⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠓⠒⠲⠤⣀⡀⠀⠀⠀⠀⣀⢤
⠈⠳⢤⣱⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⡰⠁⣠
⠀⠀⠀⠀⠀⠀⢿⠤⠤⠐⠒⠒⠈⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠂⠤⠤⠄⣀⣠⡇⠀⠀⠓⠈
⡠⠔⠒⢲⠄⢀⡞⢄⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⣀⡀
⠳⠤⠚⠁⠀⣸⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠤⠤⠒⠋⠀⣧⠀⠈⠣⣀⠈
⠀⠀⠀⣠⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡀⠀⠉
⠀⠀⣜⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⢈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢳
⠀⠀⠘⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣀⡤⠋
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢿⡏⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠙⣟⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡴⠢⡄
⠀⠀⠀⠀⠀⠀⠀⣞⠀⠈⡣⠀⠈⠳⢬⣙⣶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⣡⠔⠋⠀⡠⠛⠛⣦
⠀⠀⠀⠀⠀⠀⣼⠉⠉⢐⠑⠄⠀⠀⠀⠈⡆⠀⠈⠉⠛⠲⠶⢤⣤⣤⣀⣀⣀⣀⣠⣤⣤⠴⠶⠚⣋⡱⠀⠀⠀⠀⠀⠀⠠⠄⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠈⢳⠂⠁⢀⣀⣠⠤⢤⠤⣾⢺⠃⠀⠀⠀⠀⠀⠀⠀⢠⠭⠫⢬⠀⠀⠀⠀⠀⠀⣿⡛⢦⠤⣤⣄⠀⠀⠐⠢⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠉⠈⠀⢀⡟⢀⣷⡷⢤⡞⠉⠉⠳⡄⠀⠀⠤⠤⠤⠤⠀⡟⠉⠉⠓⡤⠧⣧⡈⡆⠀⠈⠉⠙⠦⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢞⠉⠇⠀⡤⠤⠀⢠⠗⠒⠲⠶⠶⠖⠒⡚⣧⠀⠤⠤⡀⠀⠉⢹⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢧⡀⠂⠈⠹⠀⠀⠀⢸⡆⠀⢀⠄⠁⠀⠀⠀⡞⠀⠀⠀⠘⠉⠐⠃⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⣧⠀⠀⠀⠁⠀⢀⡼⢧⠂⠁⠀⠀⡐⠀⠀⡿⡄⠀⠀⠁⠀⠀⢠⣇⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢸⣠⠜⠳⠤⠤⠦⠤⠤⠺⢥⣹⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠀⠀⢀⡜⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠲⢦⣤⣤⣤⣤⡤⣤⣤⠴⠚⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠁⠀⠀⠈⡽⠉⠉⠹⡍⠀⠀⠀⠹⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢹⡆⠀⠀⢀⣹⣄⣠⣼⣇⠀⠀⠀⢼⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠛⠶⠖⠚⠉⠀⠀⠀⠀⠈⠙⠒⠶⠞⠃⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢯⡀⣈⣓⣄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⣔⣋⡀⢨⠇
⢀⣤⣄⣀⠀⠀⠉⠀⠀⠈⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠀⠀⠈⠁⠀⢀⣀⣤⣄
⢯⣀⣠⠽⠷⠄⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⣤⠴⠶⠦⠄⠀⠀⠀⠀⠀⠀⠠⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠴⠿⢥⣀⣨
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⣼⠀⠀⠀⠀⠀⠀⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠶⠀⠀⠀⠀⠀⠀⠀⣧⠴⠶⠶⣄
⠀⠀⣀⣤⣤⣀⣸⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⡇⣀⣤⣤⣄⡀
⠀⢾⡁⣠⠞⠉⠉⢧⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡼⠀⠉⠙⢦⡀⣹⠆
⠀⠀⠉⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⣹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠁⠈⠳⣄⠀⠀⠀⠀⠀⠳⠶⠒⠛⠛⠛⠒⠶⠞⠀⠀⠀⠀⠀⣀⠜⠁⠈⠙⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣄⣀⣀⣀⣀⣀⣠⡤⠖⠛⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣒⢢⡀⠐⢆⣢⠀⠀⠀⠀⠀⠈⠃⢀⣠⣾⣿⣿⠇⠀⠀⠀⣔⡲⠀⢀⡔⣒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢀⠀⠈⠃⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠀⡀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⣀⡤⣖⣯⣭⣵⠆⠀⠀⠀⠰⣶⣬⣭⣝⡲⢦⣀⠛⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⢀⡴⠞⠁⠾⡭⠤⢤⣷⣀⣇⠀⣀⣀⣴⣊⣀⣈⠙⠀⠈⠛⢦⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⣀⣈⠙⣶⠏⠀⠀⠀⠀⠒⠚⠋⢻⣥⣄⣀⣠⡽⠙⠲⠤⠄⠀⠀⠀⠀⠀⠹⣦⡶⠋⣉⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣭⣭⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣿⣻⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⣼⠃⠀⠀⠀⠀⠀⢀⣤⣶⣿⣏⠀⠀⡇⠀⢨⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⠃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡞⠓⢦⠀⢀⣤⣤⡀⠀⢻⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⡿⠀⢠⡴⢦⣄⢀⡞⠉⣹
⢠⡶⠲⣝⢦⠈⢳⣿⠀⣰⠟⠀⠈⢷⡀⢠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣾⠃⠀⠹⣦⠀⣿⡋⠀⣞⡱⠚⢳
⠈⠓⠦⣄⠉⢠⡞⠁⠀⣏⠀⠀⠀⠈⢷⣌⢷⣌⠛⠿⠿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⠟⢁⣿⠀⣠⡾⠃⠀⠀⠀⣸⠀⠀⢹⡆⠀⣴⣒⣋
⠰⣏⣉⣉⠀⠘⠂⠀⠀⠛⠷⣦⣄⣀⡀⠙⢷⣍⡓⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣡⣴⢞⣡⣾⣋⣀⣤⡴⠶⠛⠉⡀⠀⠈⠁⣀⠤⢤⡼
⠀⠀⠀⠀⠙⠲⠶⠖⠻⣦⣄⡀⠈⠉⠙⠛⠛⠻⠿⢷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣭⣶⠿⠋⠉⠉⠉⠀⢀⣠⣶⠾⠋⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⢈⡝⠛⠻⠿⠿⠿⣿⡿⠿⠿⠛⣏⠉⠀⠀⠀⣀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣰⡟⢀⡀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡈⣷⣤⣶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡴⠚⠁⠀⠀⠀⠀⠀⠀⠘⠺⣥⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣰⡟⠉⠻⣦⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⣀⣠⣤⣼⣿⣥⣀⣀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⣠⠞⠛⠻⣆⡀
⠀⠀⠀⠀⠀⣴⣯⠙⣧⣤⠾⠘⣧⠀⠘⢯⣉⣳⣾⡷⠖⠋⠉⠠⠀⠀⠀⠀⠀⠈⠩⠙⡳⢦⣻⣶⡩⢉⠇⠀⣰⠏⣴⣄⣴⠟⣹⣦⡀
⠀⠀⠀⠀⢾⣷⡌⠟⠁⠀⠀⠀⠘⣧⠀⣾⣩⣿⣿⣮⣓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⣩⣭⣷⣏⣹⠄⢰⡏⠀⠀⠀⠈⠳⢇⣼⣷
⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⢀⣴⢹⣆⡾⠋⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠈⠳⣄⡿⣶⡀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠘⣷⣴⠶⠖⠋⠛⠰⣿⡄⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⡧⠸⠙⠶⠤⢴⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⢹⡇⣠⣴⡶⠾⠛⠛⠷⣧⣤⣀⣀⣀⣠⣼⡾⠟⠛⠷⠶⣦⣄⡀⣿⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⣸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⣤⣄
⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠉⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠈⠁⢀⣤⣤⣤⣤⣤⣄⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣤⣤⣤⣤⣤⣀⠀⠉
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠉⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⢿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⢿⣿⠋⠙⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠲⢶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⢠⣿⣆⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢠⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠘⢿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠁⠀⣀⣤⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⠋⠀⣠⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠿⢿⣦⣄⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠁⢠⣾⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣤⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣰⠁⣰⠟⠁⠀⢀⣠⣐⣂⣸⡇⢠⠄⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⢶⡞⢉⣉⣉⣁⣂⣀⠀⠀⠀⠉⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠇⠘⠁⠀⣠⠞⠋⠉⠁⠀⠉⠉⠛⠶⣞⠀⠀⠀⠀⠀⠀⠀⠜⢣⡴⠛⠉⣉⣀⣀⣉⣉⠛⢦⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡇⡜⠀⠀⣠⠎⢀⡤⠖⠚⠉⠉⡉⠙⠒⢦⣌⢣⡀⠀⠀⠀⠀⠀⣴⠋⣠⠞⠉⠁⠀⠀⠀⠈⠙⠳⣝⣦⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢰⢃⡴⠋⠀⠀⠀⠀⢁⣤⣴⠀⠀⠈⢳⣷⠀⠀⠀⠀⢰⢇⡞⠁⠀⠀⠀⢀⣾⣿⣁⣠⠀⠊⢻⡆⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⣯⡞⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⣷⠀⠀⢻⡄⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⡀⠀⣷⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠠⡈⠻⠿⠟⢁⠄⠀⢸⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠂⢌⡉⢉⡠⠊⠀⠀⡟⠀⠀⠀⡧⣄
⠀⠀⠀⠀⠀⣠⠖⠛⠂⠀⠀⠸⣆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⡇⢀⡤⠄⠀⠀⠀⠘⢦⡈⠢⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠀⢀⣀⡼⠃
⠀⠀⠀⠀⠀⠳⣌⣷⡄⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠤⠴⠖⠚⠁⠀⠀⠀⠀⠀⠁⠀⢢⠀⠀⠀⠀⠉⠛⠓⠒⠛⠋⠁⠀⠀⠀⢀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠈⠁⢻⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⠄⠒⠈⠀⠀⠀⠀⠀⠲⠤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠃⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⣩⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⣁⠠⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣌⡑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣉⡒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⠬⠭⠤⠼⠷⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠒⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠈⢆⠀⠄
⠀⠀⠀⠀⠀⢰⠁⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡆
⠀⠀⠀⠀⠀⡇⠀⠋⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⠀⠄⠀⠀⢻
⠀⠀⠀⠀⢰⠃⠀⣠⣴⠾⢻⡟⠉⢻⣿⣿⠓⠆⠀⠀⠀⠀⠴⠛⢹⠟⠙⢿⣿⣿⠳⣦⣄⠘⡀
⠀⠀⠀⠀⢸⠄⠚⠟⠁⠀⢸⣷⣤⣾⣿⣽⡇⠁⠀⠀⠀⠀⠀⠀⣿⣷⣴⣿⣿⣽⠀⠀⠙⠳⠇
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠠⢰
⠀⠀⠀⠀⠀⢣⠀⠀⠢⡀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡀⠔⠁⡜
⠀⠀⠀⠀⠀⠘⡆⠀⠠⠀⢁⠒⡒⠂⠈⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⢰⠁
⠀⠀⠀⠀⠀⠀⠘⢄⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣒⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⡰⠃
⠀⠀⠀⠀⠀⠀⠀⢈⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠞⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣀⣀⣀⣀⣀⣀⣀⠤⠔⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⡿⠿⠋⠉⠉⠛⠲⢦⡀⠀⠀⠀⠀⣀⡤⠼⠿⢿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢨⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡴⠛⠁⠀⠀⠀⠀⠀⠈⠉⠻⣍⠉
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⣦⡀⠀⠀⢸⡇⢠⡒⣶⣄⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣿⡿⠃⠀⠀⢸⡇⠘⢯⡿⠏⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠘⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⢀⠠⠀⢠⠄⠀⠙⣦⠀⠀⠐⠒⠒⠀⠐⠒⠐⠂⠀⢒⡾⠉⠳⣄⠀⠀⠀⠒⠒⠀⠀⠀⠰⠏⠀⠀⣀
⠀⢏⡀⣠⠃⠀⠀⠀⠈⠀⠀⣄⡀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⠞⠀⠀⠀⠀⠀⠸⡈⠑⡄
⠀⠀⠉⠀⢀⢠⠄⠀⡆⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁
⠀⠀⠀⠀⠧⠼⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠉⠉⠉⠉⠉⠙⠛⠲⠦⣤⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⣠⠶⠶⠶⢄⠀⠀⠀⠀⠀⠀⠉⠳⣦⣰⡇
⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣠⠞⠲⢤⣿⣶⠤⣰⣤⣀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢠⣰⠃⠀⠀⠀⠀⠀⠀⠈⠿⠈⠳⣄⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡤⢤⢰⠏⠛⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⢣⣰⡄⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠁⢸⣿⠀⠀⠀⢠⠞⠉⢈⣷⠀⠀⠀⢀⡤⣄⠈⡿⢻⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠙⠀⠀⠀⣏⣀⡀⠘⣿⠀⠀⠀⡞⢠⢺⡆⡇⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠚⢣⡓⣞⠀⠀⠀⠀⠀⢨⣯⠙⠃⠀⠀⢰⣇⣈⣻⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⠟⠁⠀⠀⠀⠀⣀⣀⡉⢻⡀⠀⠀⠀⣾⡎⠉⠀⠀⠀⠀⠀⢼⡏⡁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡏⠀⠀⠀⠀⣰⠋⠀⠀⠙⢦⢳⡄⠀⠀⠀⣴⣦⣴⣖⣒⣦⣄⣀⠘⢟⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⡌⢏⢲⣦⡀⠈⠁⠀⠀⠀⠈⠉⢻⡥⢋
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠁⠈⢦⣝⠮⠽⠒⡶⠒⢒⣶⡋⠁⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⠎⠹⣄⠀⠀⢏⣀⣀⠀⠀⣀⣀⡧⠀⠘⠛⠓⠒⠋⠀⢀⡞⠀⡷⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠈⠓⢄⠀⢹⠉⠉⠉⠉⡏⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⡏⠁
⠀⠀⠀⠀⠀⠀⠀⡤⠞⢧⣸⠀⠀⠀⠀⠀⠙⢾⡄⠀⠀⠀⢿⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠘⣆⣀⣤⠤⠞⢧⢳⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠘⢦⣄⣀⠀⢘⡎⢣⡀⠀⠀⠘⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢣⣴⣴⣤⡀⠀⠀⠀⠀⠀⢀⡴⠛⠿⣄⡀⠀⠀⠀⠈⠙⣾⠀⠀⠱⣄⠀⢀⡀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠴⠒⠉⠀⠀⠀⠀⠉⠓⠒⠶⠶⠚⠁⠀⠀⠀⠈⠑⠾⠛⠶⠶⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠀⠀⠀⡂⠉⠁⠈⠁⠀⠸⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⡠⠞⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢴⠀⠀⠐⠏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠸⡀⡠⠒⠆⠀⡠⢒⠖⢦⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⢀⡠⢄⠀⢠⠇
⠀⠀⠀⠀⠀⡇⢇⠀⢀⠔⡡⠊⢠⠃⡘⠓⠀⠀⠀⠺⡁⠱⠈⠉⢎⠉⠀⢸⠠⡇
⠀⠀⠀⠀⢠⠃⡸⣧⠃⠀⠀⠀⢁⠜⠁⠀⠀⠀⠀⠀⠱⡈⠂⠀⠈⢿⣩⠳⢀⡃
⠀⠀⣀⠤⠼⡄⣦⢨⠀⠀⠀⢀⠞⢀⠀⡀⠀⠀⠄⠀⡘⢇⠀⠀⠀⠈⡇⢫⠞⠉⠳⡀
⠀⡼⠁⠀⠀⣸⡶⠏⠀⠀⠀⡸⠀⠂⠀⠐⠒⠐⠁⠀⠁⣾⠀⠀⠀⠀⣇⣸⠄⠀⠀⢹
⠀⡇⠀⠀⠀⠜⢸⠀⠀⡤⢚⡇⠐⠀⠀⠀⠐⠀⠂⠀⠀⢿⣄⠀⠀⢸⠃⠉⠢⠀⠀⢸
⠀⠱⡀⠀⠀⠀⠀⣦⠊⠀⡸⢄⣈⢄⡀⠀⠀⠀⠀⢀⡤⠚⣄⠱⣤⠎⠀⠀⠀⠀⢠⡇
⠀⠀⢣⠀⠀⠀⠀⠘⢆⣰⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠼⠳⢥⣀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠑⠒⠶⠒⠂⠁⢘⡦⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢒⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠉⢱⠙⡖⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⢄⡀⠀⠀⠀⣀⣀⠤⠴⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣰⡇⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠒⢤⣄⣠⡇⠀⠀⠀⠀⠀⠀⠀⠋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⣀⡠⠤⠚⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⠿⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣤⣀⣾⣿⣿⣿⣴⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠛⠿⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄⠀⠀⠀⠀⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠘⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠂⠀⠀⠀⠀⠀⣀⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠀⠀⠀⠀⠀⢸⢇⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠠⠴⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠘⡀
⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠠⠤⣤⠘⡞⡄⠀⠀⠀⠀⡆
⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠙⢀⠀⠚⠃⠀⣠⠀⠀⠀⠀⠐⠒⠦⠀⠘⢜⠦⡀⠀⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠐⠷⠚⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠐⢦⣰⠄⠀⠐⡄⢶⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠠⠀⡆⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠘⡀⢀⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠀⣰⠁⠀⠱⡘⣄⠀⠀⢀⡤⠶⠶⠗⠀⡜⠀⠀⠀⠀⢩⠤⠊⠀⠀⠘⣆⠘⢮⡆⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠈⠛⠭⣉⠉⠉⠂⠤⠐⢈⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⢠⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢣⢺⠀⠀⢀⣄⠀⠀⠀⠀⢀⠀⣹⠉⡧⠀⠀⠀⡄⠀⡠⡒⠀⠀⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⠂⡀⠀⠧⠴⠊⣀⡴⠁⠀⠀⠊⢀⢴⡵⠃⠀⡼⠈
⣔⡡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠤⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡰⠀⢠⠄⠀⠀⠀⡄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢼⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡴⠳⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠐⣫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⢗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠄⠸⡀⠀⡠⠖⠒⠦⣤⠤⠜⠓⠓⠒⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⣠⠤⠚⠁⠀⠙⣆⡠⠏
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠠⠄⠀⠀⠀⠄⢀⡀⣠⣤⣤⣤⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣀⡀⠀⠀⠠⠄⠀⠈⣻⣿⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠤⠀⠀⠁⠒⠠⠄⡀⠈⠉⠛⠿⣿⣧⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠁⠢⢄⠀⠀⠙⠢⢀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠈⢣⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⡈⠂⢄⠀⠀⠁⠠⠀⠈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠆⠀⠳⡀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠨⠐⣠⣀⠀⠑⠌⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⡘⠀⠀⠀⡘⠲⣄⡀⠀⠈⠐⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠿⠒⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⢀⠜⠀⠀⢀⠔⠀⠀⠀⠙⠣⠂⠠⠀⠀⠀⠀⠁⠂⠀⠀⠤⠤⢀⠤⠤⠀⢒⣫⠖⠆⠚⡀⠘⢿⣿⣿⣿
⣿⣿⠟⠁⠀⢀⠔⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠌⠁⠄⠀⠀⠌⠀⠠⠔⡒⠚⠀⠀⠐⠂⠈⡰⠀⠀⠈
⣿⣥⣤⡐⣈⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡉⢃⠀⠀⠀⠀⢀⣴
⣿⣿⡿⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣷⣶⣶⣾⣿⣿
⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠖⠲⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⡼⠁⠀⠀⠀⠉⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠘⣆
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠓⢦⡀⠀⠀⠀⠀⠘⡆
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣤⣹⣷⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⣟⣤⠀⡇⠀⠀⠀⠀⠀⢻
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⣈⡙⣉⡴⠃⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⣛⣁⣴⣇⠀⠀⠀⠀⠀⢸⡆
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⡏⠓⢦⡀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⢠⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢦⡀⢸⠇
⠀⠀⣇⠀⠀⠀⠀⡏⠀⠀⠀⠀⢻⠀⠀⠀⣀⡤⠴⠖⠒⠒⠒⠲⠦⢤⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⣼
⠀⠀⠸⡄⠀⠀⠀⠳⣄⠀⢀⣠⠏⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠳⣄⠀⢀⣠⢿⠇
⠀⠀⠀⢳⣀⡴⡇⠀⠈⠉⠉⠁⠀⠘⣇⠀⠀⣀⡤⠖⠒⠛⠒⠲⢦⣀⠀⠀⣸⠃⠀⠀⠈⠉⠉⢠⣿⢦⡀
⠀⠀⠀⡴⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⣠⠏⣼⠀⠙⢦⡀
⠀⠀⠸⡅⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢿⠀⠀⢨⠇
⠀⠀⠀⠉⠛⠋⠁⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠶⠦⠴⠶⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠲⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⣰⠏⠀⠀⠀⠀⣤⣤⣴⣶⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣶⣤⣤⠄⠀⠀⠀⠈⢷⡀
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢠⡾⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡆⠀⠀⠀⠀⣠⡟⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⣷⠀⠀⠀⠀⣟⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠘⣇⠀⠀⠀⠻⣦⣀⣀⣤⠟⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠙⣧⠀⠀⠀⠀⠉⠉⠁⠀⢀⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣳⣶⣶⣶⣶⣶⣶⣶⣖⣛⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⢶⡄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⣀⣿⣀⣠⣞⣁⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⠙⢻⡟⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠰⣦⣤⣀⣀⠀⠀⠀⠀⠀⠸⡇⠀⠋⠀⠀⠀⢀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣻⣿⣷⠶⠂⢀⣀⠀⠴⢶⣿⣯⣍⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⢉⣀⠚⠁⠀⠉⠀⠰⢦⣍⠙⠛⠷⢶⣤⡄⠀⠀⠙⣯⡛⣦⠀⠈⣿⠀⠀⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣽⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⠃⠀⢻⡆⠀⠹⣦⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣥⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣤⣬⣙⡛⠁
⠀⠀⢀⣴⠶⠶⠶⣮⡉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠒⢿⠛⠛⠳⡶⢦⣤⡀⢿⣄⠉⢳⡄⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⠻⣦
⢀⡴⠋⠀⠀⠀⠀⠈⢿⡄⠀⣿⠀⠀⠀⢀⡴⣾⠀⠀⠀⠀⣠⣶⡟⠉⠀⣿⠀⠀⢸⡆⠀⠀⣇⠀⠀⣿⢷⡝⠳⠾⠃⠀⠈⢻⡝⢦⡀⢸⠃⠀⠀⠀⠀⠀⠘
⣼⠃⠀⠀⠀⠀⠀⠀⠈⣿⡀⢹⣇⠀⠀⣾⠁⣿⠀⠀⢠⣾⣧⣼⣧⣤⣤⣿⣤⣤⣼⣧⣤⣤⣷⣤⢤⣾⣦⣿⡄⠀⠀⠀⠀⠀⢿⣼⣧⣿⠀⠀⠀⠀⠀⠀⢠
⢿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢻⣆⠀⠻⠶⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⠶⣷⡾⠀⠀⠀⠀⠀⠈⠛⣿⢿⣄⠀⠀⢰⡿⣦⣾
⠘⢷⣄⣀⠀⣀⣠⣴⡏⣿⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠉⠀⠈⠁⣀⣀⣸⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⣾⠋⠀⠉⠛⣿⠻⣇⠘⣷
⠀⠀⠉⠛⠻⣿⠉⢹⣇⡿⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⠀⠙⠶⠋
⠀⠀⠀⠀⠀⢻⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠈⠻⣿⣄⡀⢸⡇⠀⠀⢸⡇⠀⠀⣿⠀⢀⣠⡿⠋⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣈⣙⠛⠿⢷⣤⣤⣼⣧⣤⣶⠿⠿⠛⠉⣀⣠⡴⠟⠋⠀⠀⠀⢰⡶⣄⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡆⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣴⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠸⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣤⠶⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⢦⣄⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⠀⠘⡇⠀⠀⠀⠀⣿⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⣿⡇⢰⡇⠀⠀⠀⠀⢿⠀⣼⣿⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣘⣛⣵⠟⠀⠀⠀⠀⠀⠈⢷⣜⣛⣃⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⣈⣉⣭⢆⣤⠶⠛⠛⠛⠲⢦⡠⣌⣉⣉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⣇⡀⠀⠀⠀⠀⣠⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠲⠶⠖⠒⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⣄⠀⠀⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣜⣋⠉⡠⠤⡦⠒⠀⠄⠀⠀⣀⣀⣰⠆⠀⣠⠀⠦⢀⠠
⠀⠀⠀⠀⠀⣠⠉⠀⣠⠾⡛⢛⣿⣿⣿⣿⡿⣻⠟⣿⣿⣿⣿⣭⣭⣷⣏⣉⣑⣲⠾⣟
⠀⠀⠀⠀⠀⠀⠀⠄⠐⢋⣵⣿⣷⣿⣿⣷⣶⣶⣶⣿⣶⣾⣿⠿⠋⠻⢿⣿⣿⣿⣷⠟⠀⠐
⠀⠀⠀⠀⠀⠀⠘⡠⢶⣾⣿⣿⣿⠋⢡⣿⣿⡏⠘⠋⠉⠁⠀⠰⠀⠀⠈⠉⠹⢿⣿⣗⢆⣺⡁
⠀⠀⠀⠠⡉⢠⠲⣼⣿⣿⢻⣿⡿⠀⠀⠀⠀⠆⠀⠰⢀⣀⡤⠂⣀⣠⣄⡛⠂⠛⠹⣿⣿⣭⢤⡄
⠀⠀⠀⠀⠛⣽⣟⣹⡿⣿⢿⣿⠄⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢾⣟⣿⣿⣿⡆⠀⠀⠹⣿⣿⣿⡻⢴⠿
⠀⠀⠠⠂⠀⢸⣷⣿⣿⠷⡀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣼⣿⣿⣿⣿⣷⡶⠀⠈⢻⣿⡟⢷⣾⢤⣦
⠀⠀⠀⣄⠀⡼⢿⣾⡇⠆⠀⢦⣆⣤⣤⣤⣀⠀⠀⠀⠹⠿⢟⣿⡿⠿⡟⠙⣟⠄⠀⠈⢁⣿⣿⣾⣿⣾⡆
⠀⠀⠑⣻⢾⠛⣼⣿⡁⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠻⡄⠀⢸⣷⣿⣿⣿⣿⣇⠀⠀⡀
⠀⠀⡖⠸⢏⡇⠟⢿⡇⢹⣿⣿⣟⣁⣨⣭⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡈⢿⠻⣿⣿⣿⣿⡯⠀⣧
⠀⠀⠘⣧⠠⠀⣿⠄⠀⢸⣿⣿⣿⣿⣿⣷⡟⠀⢷⣿⣿⣾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠠⣷⠆⣀⠍⣽⠿⡏⠲⢠⠏
⠀⠀⠀⠓⠀⠀⠙⠁⣀⠘⣿⣿⣿⣿⣿⡏⠁⠀⢸⣿⣿⠟⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠋⠀⡧⠄⠸⠎⡟⠀⢁
⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠈⣽⣿⣿⡀⠀⠀⠀⣿⣿⠋⢀⣴⣾⡿⠛⢉⡭⠀⠀⠀⠀⠐⠘⣅⠀⠀⠀⠻⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠘⢾⡄⠀⠰⡏⢃⣰⣿⠟⢉⣠⣴⣿⠟⠀⠀⠀⠀⠀⣠⢈⣥⣄⡷⠀⢈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⣿⣷⣿⣿⣷⣤⡇⢸⣿⣧⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⣾⢿⠈⣿⣿⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⢿⣿⣷⣿⣿⣿⣿⠏⠁⠀⠀⠀⢀⣠⣴⡾⡿⠋⠜⠉⢋⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠻⣦⠿⢿⡛⣿⣿⣏⣀⣠⣤⣴⣿⣿⣿⡿⢣⠅⠀⠘⠀⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠃⠿⢿⣿⣟⣟⣟⠻⣿⡽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠋⠉⠉⠀⠀⠀⠈