Detergent Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠤⠤⠤⠤⠤⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠽⠟⠻⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⢞⠀⠀⠀⠀⠀⡠⠐⠒⠒⢲⠓⠂⠤⠤⠄⠒⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⢀⠤⣀⡜⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣼⠀⡇⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⡠⠄⠒⠒⠒⢢⠀⠀⡴⠲⡄⠀⢽⠀⣃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢰⠀⢸⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢨⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⡇⢸⡋⠁⠒⠒⠒⠰⠦⠤⠴⠖⠐⠒⠒⠂⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠣⠤⠜⠀⢸⠂⣀⣀⣀⡠⠔⠒⠒⠒⠒⠢⠤⠄⠠⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⡀⠀⢸⣿⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⠤⠤⠤⠐⠚⠀⠀⢸⡀⣙⣒⣢⣤⣤⡤⠤⠤⠤⠤⠐⠒⠊⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⢶⣶⣶⠿⠿⠿⠟⠛⠛⠛⠻⣿⣿⣏⣛⠶⢶⠒⠒⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠒⠻⢶⠶⠶⠶⠛⢛⣛⣋⣉⣡⣭⣤⣤⣤⣼⣄⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⡇⠀⠀⠀⠀⠀⢸⢀⠚⠻⠭⢿⣿⣛⣉⣭⣭⣥⠭⠿⠿⠓⠚⢹⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣄⣸⣨⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣠⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠼⠷⠖⠚⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⠲⣄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡧⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡤⣤⣤⣤⣤⣤⣤⡤⡤⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠤⣄⠀⠀⠀⠀⡼⠋⠈⢹⡆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⠃⠀⠀⢸⡇⠀⢸⣧⣤⣤⣤⣤⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⣠⠟⠈⢳⡄⠀⠀⢿⠀⠀⢻⠀⠀⠀⢸⡇⠀⢸⡷⠶⠶⠖⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣰⠋⠀⠀⠀⠹⡄⠀⠘⣆⠀⠘⣇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⣏⠀⠀⠀⠀⠀⡷⠀⠀⠘⣦⠀⠈⢧⣀⢸⡇⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠘⠦⣄⣀⣤⠞⠁⠀⠀⠀⢸⠀⠀⠀⠉⠛⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠤⠤⠤⠤⠤⠤⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠒⠒⠒⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠉⠉⠉⠉⠉⠉⠉⠉⢧⡀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⢸⠋⠭⠭⠭⠭⠙⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠈⠳⡾⠠⠤⠤⠤⠤⠤⠔⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⡀⠀⡜⠀⠀⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡠⠖⠊⠉⠀⠀⠀⠀⠙⣄⠃⠀⡎⠀⢙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢸⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠤⠄⠤⠔⠊⠉⠀⠀⠀⠀⠉⠙⠒⠒⠒⢢⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢹⠈⠦⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠸⠇⠿⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⡿⠿⠿⠿⢿⣷⣄⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣡⣶⣿⣿⣿⣶⣍⠻⣷⡄⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣾⣿⣿⣿⠩⣿⣿⣿⣷⡹⣿⡄⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣾⣿⣿⡻⣿⣿⣿⣿⣿⡏⢷⢹⣿⣤⣤⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⢡⣿⣿⣿⣷⣿⡿⣫⡛⣿⣿⢻⡜⣛⡻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡸⣿⡿⢛⡛⠿⠿⣮⣴⣿⣿⢸⢃⣿⣿⣷⣮⣭⣵⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢿⣇⠿⣿⣾⠇⣽⣿⣷⠝⡿⣸⣿⣿⣿⣿⣿⣿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡜⢿⣇⠻⠿⣸⣿⣿⣷⡾⢣⣿⣿⣿⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡻⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣮⣭⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠒⠒⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣉⣉⡉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠶⠶⠶⠤⠤⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠙⠛⠛⠒⠒⠶⠶⠶⠤⣤⣤⣤⣀⣤⠶⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⢀⠀⡀⢀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠷⠻⠾⢻⣽⡅⣻⣄⡿⣄⣨⢠⣤⢀⣀⠀⠀⡇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⣄⣠⣀⠀⡀⢉⡌⠁⠉⠉⠋⠘⠘⣿⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠏⠁⠙⠉⠛⠛⠿⠻⡇⡷⠆⠀⢠⣴⡿⠁⠀⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠦⢤⣤⣀⣀⡀⠀⠀⠀⠚⠡⠚⡴⢂⠀⠀⣿⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠦⠤⣤⣄⣀⡀⣸⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣤⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⡠⠤⠤⠤⠧⠄⠀⠀⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⠀⡠⠀⡜⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⢰⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠤⠒⠉⠉⠉⠑⡀⢰⠉⢣⠀⠀⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠃⠀⠀⠀⠀⠀⢀⠁⢸⠀⠀⡇⢸⠒⠒⠀⠠⠤⠤⠤⠤⠤⠀⠐⠒⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠤⠔⠁⢸⢀⢀⣀⠤⠐⠂⠀⠐⠂⠤⠄⠠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⣀⣀⣀⣀⣀⣀⣀⠠⠆⠀⢸⠘⠤⢀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣤⣴⣶⣾⠶⠿⠿⠿⢿⣿⣶⠒⣦⣤⠠⠐⠒⠣
⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⢺⠀⠈⠐⠛⢳⠶⠖⠒⢚⣛⣛⣩⣭⣥⣥⣤⣼⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠣⠀⠀⠀⠀⢸⠀⠋⠋⠝⠿⣭⡭⠭⠴⠶⠛⠛⠃⠉⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠒⠤⢄⡀⣇⣀⡤⠤⠴⠒⠒⠋⠉


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

⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣴⠶⠶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣸⠦⠤⢾⠀⠀⠀⠀⢰⠁⠀⢱⡀⠀⠀⠀⡠⠊⠁⠧⡀⠑⠢⣤⠐⠊⠁⡸⠈⠑⢄
⠀⠀⠀⠀⠊⣤⡏⠈⠉⠈⢆⠀⠀⠀⣠⠀⠀⠠⡇⠀⠀⡰⠁⠀⠀⠀⠀⠁⠚⡄⡃⠉⠁⠀⠀⠀⠈⢢
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠈⠆⠠⠊⠀⠀⣀⠀⠈⠲⡭⠅⠀⢐⣒⣒⣒⡤⡄⠇⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⢠⠊⠁⠀⡇⣿⡇⢠⠀⠀⠀⠀⠀⡇⠀⢿⣤⠧⠤⠤⠤⠤⠤⠤⠄⠀⡃
⠀⠀⠀⠀⡗⠐⢒⠒⢒⣒⣒⢺⠁⠘⠀⠀⠀⡇⣿⠀⢸⠀⠀⠀⠀⠀⡇⠀⣿⣛⣗⣒⣒⣒⣒⣒⣂⣂⡐⡇
⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠣⢙⡃⢸⠀⠀⠀⠀⠀⡇⠀⣿⣿⡧⠤⠤⠤⠤⣤⣤⣤⣤⡆
⠀⠀⠀⠀⣟⠤⠀⠀⠀⠠⠤⣻⡀⢠⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⣿⡤⡥⠤⠤⠤⠤⠤⠤⠤⢤⡇
⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠁⢸⡇⠈⠉⠀⠀⠀⠉⠀⢸⣁⡒⠒⠀⠠⠧⠐⣯⣿⣏⣉⣉⣉⣉⣉⣉⣉⣀⠇
⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⠈⠑⠒⠀⠠⠤⠄⠐⠒⠁⠀⠉⠉⠉⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⢤⣄⣈⣛⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣤
⠀⠀⠀⠘⠋⣤⡶⠚⠋⢉⣠⡤⠶⠒⠚⠓⠛⠒⢖⣶⣦⣤⣌⠉⠛⢷⠀⠀⠀⠀⠀⢠⣾⡿⠯⠉⣉⠩⣥⠴⠶⠶⠀⠶⣤⣀⡀⠀⢐⢶⣈⡀
⠀⠀⠀⠀⡜⠉⢂⣴⣾⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠈⠀⠀⠀⠀⡰⢫⣿⠃⠀⠾⢋⠠⢴⣚⣩⣽⣶⣶⣶⣭⡋⠀⠀⠻⣿⡇
⠀⠀⠀⠈⠁⣠⣿⠟⠋⠀⣀⣤⣶⣾⠿⠿⠿⣿⣷⣶⣄⡀⠈⠙⣿⣷⠀⠀⠀⠀⣇⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠊⢾⡝⣆⡀⠀⠘⡇
⠀⠀⠀⠀⢠⠇⠁⢀⣴⡾⣟⣉⣥⣤⣶⣾⣿⡟⣀⠉⠻⣿⣄⠀⠈⠿⠀⠀⠀⠀⣿⡟⡙⢠⢻⣿⠿⢻⣿⣿⣿⡷⣦⣄⠀⢰⣿⡿⣿⠀⠀⡇
⠀⠀⠀⢠⡏⠀⣠⣿⣿⣿⣿⣿⣿⣿⢛⣋⡉⠈⠛⣷⣴⡞⣿⡆⠀⠀⠀⠀⠀⠀⣿⠟⣿⡻⠍⠀⠀⣾⣿⣿⣀⣀⠈⢹⣇⣼⣿⠋⠐⣁⠀⡅
⠀⠀⠀⠸⠃⢠⣿⠃⠛⣭⢵⣿⣿⡏⠛⠙⠻⣶⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⣿⣇⡃⠀⢰⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣾⢙⣿⡷⡇
⠀⠀⠀⢸⠀⢸⡇⠀⢸⡇⣼⣿⣿⢡⣾⣷⡆⢹⣷⣿⢿⣷⣾⣿⡄⠀⠀⠀⠀⠀⣻⠀⣿⡇⡂⠀⣾⣿⣿⣷⣾⣿⣿⡿⣿⣿⠹⣿⣬⣷⠂⠁
⠀⠀⠀⢰⠀⢸⣧⠀⢸⣷⣿⣿⢇⣈⣿⣿⣿⢿⣿⡟⣿⣿⣻⡿⠁⠀⠀⠀⠀⠀⣿⠀⣿⠘⣗⢰⣿⣿⠧⣿⣿⠹⣿⣿⡿⢿⡄⢬⠋⠁⠀⣦
⠀⠀⠀⠈⡆⠸⣿⡄⠀⣿⣿⡿⢸⣿⢿⣿⣷⣾⡿⠓⠛⣻⡏⠀⣠⡇⠀⠀⠀⠀⢻⡀⣿⠀⠈⣾⣿⣿⢰⣿⡟⠀⣈⣁⣠⣄⡤⠃⠀⠀⠀⣿
⠀⠀⠀⠘⢳⠀⠙⢿⣾⣿⣿⠳⡿⠟⠼⠿⠽⠃⢀⣴⡾⠋⢀⣴⡿⠇⠀⠀⠀⠀⢸⠃⣿⡇⢰⣿⣿⠣⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⢀⡈⡡⢛
⠀⠀⠀⢀⡈⣦⡄⢀⣿⣿⡏⣶⣤⣤⣤⣤⣶⠾⠟⠉⣀⣶⡿⠋⢀⠀⠀⠀⠀⠀⢸⡆⢸⡛⣾⣿⡿⡆⠀⠀⠀⠀⠀⠀⢀⣀⠀⣚⡷⠋⣀⠘
⠀⠀⠀⠀⡇⠸⣷⣾⣿⡿⢁⠀⠉⠩⠍⠉⡀⣀⣤⣶⠿⠋⠀⣤⣾⠀⠀⠀⠀⠀⢸⡏⢸⢇⣌⡙⠲⢤⣿⣿⣛⣺⣲⣜⢭⠖⠒⠉⠠⠊⠁⢸
⠀⠀⠀⢰⠱⠀⠉⠋⠱⠶⣿⣿⣿⣷⣿⣿⡿⠟⠋⠁⣀⣴⣾⠿⢋⠀⠀⠀⠀⠀⢸⡧⣼⣧⣉⠛⠲⠦⣤⣨⣍⣅⠀⣤⡤⠶⠘⠋⠀⠀⠀⣸
⠀⠀⠀⠘⠆⢲⣧⣆⣀⣀⡀⡀⠀⠀⢀⣀⣀⣤⣶⣾⠿⢋⣁⣠⣼⠀⠀⠀⠀⠀⢸⡗⡿⠻⢾⡿⣶⣶⣶⣶⣶⣶⣶⠤⠶⠶⠛⠟⠛⣫⠟⠉
⠀⠀⠀⠀⠀⢈⠛⠻⠿⠿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠖⠓⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠙⣆⡀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⠆⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⢠⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠋⠉⠛⠉⠙⠛⡇⠀⠀⠀⠀⠈⠁⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠄⠀⠀⠀⠀⢀⡞⠀⢀⡼⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠢⠀⠀⠀⠀⢀⡾⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠋⠉⣉⡇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⡼⠁⠀⢸⠀⠀⠀⠀⠀⣠⠞⠋⢀⣠⠴⠖⠛⠋⠉⢹⡀⠀⢀⣀⡾⠁⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡸⠁⠀⠀⢸⠀⠀⠀⢠⠞⠁⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⢳⣀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣼⠃⠀⠀⠀⢸⠀⠀⢀⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠃⠀⠀⠀⠀⡏⠀⠀⡿⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠚⠁⠀⠀⠀⠀⣼⠃⠀⢰⠋⠀⠀⠀⠀⣰⠁⠀⠘⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⢧⡀⠀⠀⠀⣰⠁⠀⢠⠏⠀⠀⠀⠀⢰⠇⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢠⠇⠀⢀⡞⠀⠀⠀⠀⢠⡟⠀⠀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⠀⠀⠀⢀⡞⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣈⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⣆⠀⢀⡞⠀⠀⠀⠀⢸⡆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⢷⠟⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣄⣤⣤⣠⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣠⣄⣠⣤⣀⣠⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠛⢻⣿⡟⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⢀⣠⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣀
⢀⣿⣿⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠙⢿⣷⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣷⣦
⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣦⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠈⢿⣷⡄⠀⠀⣀⣤⣴⣿⡿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠈⢿⣿⡀⠀⠛⠿⢿⣿⣦⣼⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠹⣿⣆⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠘⣿⣷⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⠀⠀⠀⢀⣴⣿⣿⣧⣀⠀⠀⠀⠹⣿⣧⡀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⢹⣿⡆⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⣿⣿⠀⠸⣿⣿⣿⣏⢈⣿⣿⣿⡷⠀⠀⠈⢿⣿⣦⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠀⠀⠀⠉⠻⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠉⠛⠿⣿⣶⣶⣾⡿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⢠⣤⣶⣿⡟⠻⣿⣶⣦⣄⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣾⣿⠟⠛⠉⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡄
⣿⡟⠀⠀⠀⠀⠀⠸⢿⣿⣿⣇⣨⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡟⢙⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣧
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣠⣾⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⢿⣿⣿⣅⣼⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⢸⣿
⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠈⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠻⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠃
⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⣿⣿⡟⠛⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠐⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⣤⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠉⠉⢳
⠀⠀⠀⠀⣠⠤⠤⢤⠧⢤⣤⣤⡤⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠒⠒⠒⠒⠛⡆
⠀⠀⠀⡎⠀⣀⣀⡼⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⡇⢸⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣀⣀⡀
⠀⠀⠀⡇⢸⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡤⠄⢀⣈⣉⣉⣉⠉⠁⠐⠒⠒⠒⣒⡶⡄
⠀⠀⠀⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠀⠀⣠⠤⠒⠒⠐⢦⠀⢠⡖⢆⠀⢡⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠉⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⡎⠀⠀⠀⠀⠀⠈⡆⢸⡇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢣⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⡎⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⡇⢸⡇⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⢀⡠⠤⠤⠤⢄⣀⣀⢀⠀⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⡎⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠸⣇⡰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⣸⣈⣉⠒⠒⠒⠒⠒⠒⠒⠒⠊⣉⣀⣇⡇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇⠀⠀⠈⠉⠙⠛⠀⠐⠛⠋⠉⠉⠀⠀⢸⠓⠒⠒⠂⠤⠤⠤⢄⣀⣀⣸⣀⡤⠤⡇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠤⢤⣤⣀⣀⣀⡀⠀⢸⠀⣀⣠⠇
⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠀⠈⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣉⣉⣉⣙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣿⣛⣛⣿⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠋⣿⡏⣿⡟⢻⣿
⠀⠀⠀⣤⣤⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣿⣇⣼⣇⣸⣿
⠀⠀⠀⣿⣧⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠛⠛⠛⠛⠻⣿⡄
⠀⠀⠀⠈⠉⠙⠛⣿⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⣿⣷⣴⣦⣶⣾⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⢀⣿⣼⡟⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣥⣿⣷⣶⣶⣶⣶⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠻⠟⠋⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⠀⠀⢀⠀⡀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⣼⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡁⠀⠀⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠈⡝⠉⠉⠉⠉⢫⡞⠻⣬⡟⢻⣽⣟⣛⣛⣛⣛⣻⡏⠉⡇
⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠮⠷⠾⠩⠷⠾⠹⠷⠷⠷⠾⠷⠷⠧⠤⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠠⠄⠤⠤⣤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠉⠉⠓⠢⣄⠀⠀⠀⡔⠉⠁⢀⣀⡴⠊⠨⠰⠍⢶⠂⣱⣈⣓⣤
⠀⠀⠀⠀⢸⠀⠀⠀⣠⠊⠀⡠⠒⣉⣁⣀⣁⠒⢄⠀⠙⣄⠐⠁⠀⠀⠀⣴⣭⣥⣤⣤⣬⣥⣴⡀⠀⠀⠈⡇
⠀⠀⠀⠀⢸⠀⠀⣰⠃⢠⠊⡴⠋⠁⠀⠀⠈⠙⢦⠑⡄⠘⣆⡇⠀⠀⢰⠦⠤⠤⠤⠤⠶⠤⠴⡇⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⡏⠀⡄⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢹⠆⠀⢀⠷⠶⠶⠶⠶⠶⠶⠶⠶⢶⠀⠀⢠⠁
⠀⠀⠀⠀⢸⠀⠀⣇⠀⢁⢸⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣸⢰⠄⠼⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⢄⣈
⠀⠀⠀⠀⢸⠀⠀⠹⡄⠈⢄⠙⢤⣀⠀⠀⣀⡤⠋⡰⠁⢠⠏⠘⠐⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⠒⠒⢠
⠀⠀⠀⠀⢸⠀⠀⠀⠙⢦⡀⠑⠢⠌⣉⣉⠡⠔⠊⢀⡴⠋⠀⠀⡀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠲⠤⣤⣀⣀⣤⠤⠖⠋⠀⠀⠀⠀⡇⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡁⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠃⠈⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⢁
⠀⠀⠀⠀⠈⠢⡄⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⢠⠶⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣸



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠉⠁⣤⠔⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠈⠁⠢⢀
⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⡤⠔⠈⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠒⠀⣈⡉⠍⠁⠀⢢⠀⠀⢀⠄⠐⠀⠀⢖⠒⠢⡴⠁⠀⠀⣀⠄⠐⠉⠀⠀⠀⠀⠀⠀⠁⠢⢽⡀
⠀⠀⠀⠀⠀⠋⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⢃⠔⢁⣠⠄⠀⠀⠀⠉⢹⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠃⠀⠀⠀⠒⠂⠀⠀⠠⢄⡀⠀⢸⣷⠟⠉⠀⠀⠀⠀⠠⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠒⠂⠠⠝⣂⣸⣧⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠈⠒⠒⡒⠢⣄⡉⠐⠢⢔⣋⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⣇⠀⠙⢦⣉⠀⠀⡸⡏⠉⠙⡏⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡏⠀⠉⢻⣏⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠸⣷⣤⡀⠈⢉⠿⢀⠈⠀⠀⢳⣶⣽⣷⣦⣄⣀⣑⡒⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠛⠉⠀⠀⣠⡟⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠁⠸⠢⢄⣀⠀⠀⠇⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠲⣤⠀⠀⠀⠀⣇⣀⡤⠤⠒⢛⣿⠁⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠉⠁⠀⣀⣀⠀⠠⣄⡀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠈⣇⠀⠀⠀⡟⠀⡐⠀⡆⠈⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢃⠸⠀⠀⠀⠀⠀⢇⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⢹⠀⠀⠀⡇⢀⠁⢠⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⠀⢗⠒⠂⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⢰⠃⡌⠀⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠂⠀⡧⢀⢀⠴⡃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠱⠐⠁⢀⡁⠐⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⠀⠀⠀⠣⠀⠆⠀⠀⠀⠄⠀⠄⠀⠀⠀⠇⠄⠂⠀⠀⠀⢀⡀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡅⠑⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢀⠊⢉⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢡⠀⢁⠀⠀⠁⠀⢸⠀⠀⠀⠉⠉⠁⠀⠀⢠⠀⠀⠀⠀⠘⠀⡌⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⡀⠈⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠂⢀⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠒⠁⠀⠘⡄⢀⠆⠀⠀⠀⠀⠀⠀⠀⢆⣀⠜⠀⠀⠑⢁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠑⠒⠃⠀⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⢩⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⠁⠀⣀⣠⡤⢼⣦⣄⡀⠈⠉⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠛⠉⠉⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⣼⠀⠀⠉⠓⠶⣤⣀⠀⠈⠉⠛⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠚⠋⠉⠁⠀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣠⣤⣤⣀⣀⡈⠉⠓⠦⣤⣀⠀⠉⠛⠳⣤⣀
⠀⢀⣠⡤⠖⠛⠉⠀⠀⣀⣠⣤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠦⣬⣷⠟⠁⠀⠀⠈⠉⠻⣄⡀⠀⠀⠈⠙⠲⢤⡀⠀⠉⠙⣳⢦
⠀⣿⠣⢤⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠶⠤⣤⣤⠽⠿⠚⠋⢁⣼
⠀⢹⣦⣀⡈⠙⠲⢦⣄⡴⠒⠛⠷⠶⠛⠉⠉⠳⣄⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠒⣶⠊⠁⠀⢀⣠⡴⠞⠉⣿
⠀⠈⣧⠈⠉⠑⠦⣄⡈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠈⠢⣄⣤⡤⠤⠶⠦⣤⣤⣤⣀⡀⠙⠳⣦⡤⠔⠚⠉⠉⢧⠀⠀⠀⢸⡦⠖⠛⠉⠁⠀⠀⠀⡏
⠀⠀⢹⡄⠀⠀⠀⢠⡍⡗⠦⣄⡉⠛⠶⣤⡀⠀⠀⠀⠈⠓⠲⠶⠒⠀⠀⠀⢀⡩⠿⠚⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣧⠀⠀⠀⠘⣿⡅⠀⠈⠙⠲⢄⡈⠙⠛⠶⣦⣄⡀⠀⠀⠀⣀⡤⠶⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢻⡀⠀⠀⠀⠻⣕⢤⡀⠀⠀⠀⠙⠲⢦⣄⣀⠉⠛⢳⡖⠋⢁⣠⠴⠖⢻⡇⠀⠀⠀⠀⡄⠀⠀⠀⢸⡇⠀⣸⠀⢿⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠛⠾⢷⣶⣤⣀⣠⠟⠀⠈⠙⠲⢼⡗⠚⠉⠀⠀⠀⢸⠁⠀⠀⠀⡼⠀⡀⠀⠀⢸⡇⠀⠏⠀⢸⡆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⢠⠃⠀⠀⢸⡇⠀⠀⣀⣸⡇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡟⠀⠀⠀⠸⠀⡌⠀⠀⠀⠸⡷⠞⠋⠉⠁⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⣀⣴⠇⠀⠀⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⣠⠶⠶⠖⠚⠋⠁⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧⠶⠋⠁⠀⠀⢀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⢸⡏⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣼⣧⣤⠶⠚⠋⠁



⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁
⠀⠀⠀⢰⣰⠀⠀⢸⢾⡇⠀⠐⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠐⠀⠐⠀⠂⡰⠂
⠀⠀⠀⢸⢼⡀⠀⢸⢻⡄⠀⢸⣿⡿⣿⣿⣿⠇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⣳⣄⣀⣠⣜
⠀⠀⠀⡼⠘⡇⠀⠸⠻⠇⠀⢸⣿⣷⢾⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠟⠘⠇⠀⠀⠀⠀⠀⢸⣿⣿⣾⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢿⣋⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⠾⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠘⠓⠒⣄⣀⡀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠘⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠂⠒⠛⠓⠀⢰⣿⣿⢸⡀⠀⠀⠀⠀⢀⣶⠆⠀⣀⠁⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄⠀⠘⣿⣿⣿⠁⢾⣦⠀⣀⠀⠁⠀⠸⠿⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⡀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⠀⠀⠁⠀⠻⠷⠀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣤⣴⡄⠀⠀⠀⢈⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣠⠖⢉⣉⣉⠑⢦⡀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⢀⣼⣿⣡⣤⣤⣿⣷⠀⠀⢠⠎⠈⠛⠁⠱⡄
⠀⠀⠀⠀⣼⢁⣾⡿⣿⣿⣿⠂⢱⡀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠉⠁⠐⠃⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⡇⠐⣯⠀⠀⠀⢹⠀⢸⡇⠀⠀⠀⢀⣿⡟⠶⣄
⠀⠀⠀⠀⠘⣄⠙⠷⣶⡶⠟⢀⡞⠀⠀⠀⠀⢸⣿⣿⣦⣬⣷⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠈⠑⠀⠤⠀⠒⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠆⠀⠸⢿⣿⣿⣿⠟⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣾⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡈⠉⠉⢳
⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡖⢲⢰⠊⡇⢰⠉⡇⠀⠀⢰⠧⠈⠁⠘⠦⠀⢰⡍⠉⠨⢷⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⠇⠙⠁⠈⠉⠁⠈⠈⠁⠀⠀⠘⢤⣆⣐⡶⠃⠀⠳⣤⡀⣠⡞⠀⢸⡆
⠀⠀⠀⠀⠀⠀⣿⠤⠤⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠿⠷⠶⠶⠾⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⣀⣠⣤⠤⢤⠤⢤⣀⡀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠴⡾⠉⡜⠁⣰⠃⢠⠎⠀⡜⠓⣦⡀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡴⢣⠞⣠⠎⢀⡴⠁⣰⠃⢀⡞⠀⣰⠃⢸⣆⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣼⡵⠃⡴⠃⢀⠞⠀⡴⠁⢀⠎⠀⡰⠃⣰⠋⢸⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⠟⢀⡞⠁⣠⠋⢀⡞⠀⢠⠎⠀⡴⠁⣰⠃⣰⠋⣼⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⢠⠞⠀⡰⠃⢠⠎⠀⣠⠋⢀⡞⠁⡰⠃⡰⡥⠚⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠋⠀⡜⠁⡠⠃⠀⡴⠁⢠⠎⢀⡼⠁⡼⠑⣇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠀⢹⣀⠞⠀⡴⠁⢀⡞⠀⣠⠋⢠⡞⢀⡜⠀⠼⠉⡿⠲⡆⠀⢠⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⣏⢀⡜⠁⢠⠎⠀⡰⠁⢠⠏⢀⡞⠀⡼⢀⠖⠀⡶⠀⠀⠸⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⢿⡀⣰⠃⠀⡼⠁⣰⠋⢀⡎⠀⠜⢁⡟⢠⡿⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⠧⣄⡞⠀⡴⠁⢀⠎⠀⠌⢀⣏⠴⠋⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠉⠚⠓⠒⠛⠒⠚⠋⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠃

⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠱⠤⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢈⠤⠂⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠚⠀⠀⠀⠁⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠒
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⡇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⠀⠀⢠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠄⠃⠀⠀⠀⠀⠐⡀⠀⠁
⠀⠀⢀⠆⠀⠀⠀⠀⠀⠣⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢡
⠁⠀⠉⠒⠒⠶⠤⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠈⠁⡀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠠⠐⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠁⠀⠈⢆
⢘⠃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⠀⢀⣂⣰⠀⠄⠀⡂⠀⢠⠀⠀⠒⠊⠀⠀⡀⠀⠀⡀⠀⡆⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⢂⠈⡁⠀⠠⢀⣤⠤⠤⠃⠉⠀⠀⠀⠠⠀⠴⠀⠅⢤⡄⠴⠶⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⠀⢀⠴⣠⣤
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⠔⢊⠉⠑⣧⠞⢁⡸
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠴⠒⠋⠹⢓⠎⠁⠀⠉⠂⠀⠀⠀⠙⠀⠋⠘⠉⠿⣧⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠂⠉⢀⡀⠀⠀⠠⠄⢀⠀⠐⠐⠀⠠⠀⠀⠀⠀⠐⠂⠠
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⣀⠀⠀⠀⠉⠀⠂⠀⠀⡄⠀⠀⠀⠀⡁⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢀⡼⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⠀⠀⠀⠁⠈⠄⠀⠀⠀⡀⠀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠻⠄⠀⠀⠃⠀⠀⠀⢀⠀⠃⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⡀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠
⠀⠉⠭⠩⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠠⠇⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠉⠀⠀⠀⢀⣈⡙⠛⢄⡀⠀⠉⠑⠒⠲⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⣀⣈⡉⠒⠈⢉⡢⠖⠊⢩⢳⠀⢹⠙⠤⢄
⠀⠀⠀⠀⠀⠀⠀⡼⠶⠶⠶⠒⠒⠒⠒⢚⣧⣲⣤⣀⣀⣀⣀⣉⣉⣡⣖⣉⡉⠉⠛⠒⠚⠒⠒⠶⢇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣏⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣸⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠯⠭⠭⠭⠭⠭⠭⠭⠭⠽⠿⠭⠭⠭⠭⢽⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡆⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡸⠓⠒⠛⠓⠒⠒⠒⠒⠚⠛⠛⠒⠒⠒⠒⠒⠒⠳⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⠧⠤⠤⠤⠤⡤⠤⠤⠤⡤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠵⣄⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢙⠶⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠶⠒⠒⠒⠒⠒⠶⠒⠒⠲⠖⠶⠶⢶⠖⠒⠒⠒⠒⠒⠒⠒⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⠀⠘⠃⠂⠘⠛⠀⠛⠁⠀⠛⠀⠀⠀⠀⠘⢣⡤⠿⡼⠉⠿⣂⠉⠉⠉⣑⠳⠋⢢⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⢄⣠⠤⠤⠤⠤⠤⠤⠤⣄⠤⠤⠤⠤⠤⡴⠋⠀⠀⠑⠢⣄⡀⣩⠶⣍⢁⣀⠤⠜⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠹⡀⡏⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⣐⣂⣴⣐⣀⣐⣰⣖⣀⣀⣐⣦⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠺⠭⠭⠭⠭⠭⠭⠭⠭⠽⠯⠭⠭⣷⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣟⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡞⠒⠒⠒⠂⠀⠶⠶⠶⠶⠶⢾⣦⡷⠶⠶⠶⠶⠶⠆⠐⠒⠒⠒⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⢺⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⢺⡭⣷⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠀⠀⠐⠒⠒⠒⠒⢺⣷⡟⠒⠒⠒⠒⠒⠀⠀⠈⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢠⡐⠂⢰⠐⠄⢠⠀⡆⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣐⠀⡀⠀⢱⣎⣈⠐⠡⣀⡨⡅⠀⠉⠠⡀⢀⠴⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃⠠⡆⠀⡂⠙⣏⡥⢀⠛⢿⢏⠀⠃⣤⡀⣿⡏⡄⠧⢀⢀⠁⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢠⠀⣜⣠⢾⠛⡏⢫⠿⣦⣼⠒⡿⣠⡁⠀⠷⣷⠂⠜⡠⠁⠖⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣠⢉⣽⡈⢛⣶⣬⣏⠘⢁⣍⠿⢻⣿⡴⠛⢻⣿⡅⡲⢎⣽⣇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢘⡟⢃⣞⣱⣧⣿⣵⣾⣷⣞⣿⣿⣽⡤⣿⣬⣤⣤⠜⢃⡈⡛⠂⠊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠚⢆⠈⣋⣀⡍⢫⣯⣽⡍⠥⣿⣿⣿⣿⣿⣷⣿⣞⣷⣾⣿⢂⣻⣶⣎⡹⡇⢀⢦⡆⠁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠹⠀⢠⣿⠈⡙⠘⣬⣿⣷⣶⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⢻⣏⣻⡓⢻⠮⣨⣁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡾⢗⣁⣈⢓⣻⣿⣿⣿⣯⠿⣾⣷⣾⣯⣈⣿⣿⡶⣟⣻⡿⣿⠛⢫⣶⡄⢞⠣⢙⠁⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡈⢠⡏⠉⣴⣡⣽⣯⣷⣮⣿⣴⣯⣿⣿⣿⣿⣿⣟⣛⣿⣿⠟⡿⣋⣿⣵⣦⢎⠟⣈⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⡴⢣⡍⢟⣲⠼⣿⠿⣿⣯⣾⣿⣿⣿⣟⣺⣿⣿⣇⡟⠸⣧⡟⢬⠉⢁⡀⠤⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⢊⠋⠉⠷⣬⣿⢶⣸⣻⡿⣿⣿⠻⣿⣿⢛⣽⣿⣛⣿⡅⠿⣞⢃⠁⣸⣻⠃⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢂⢃⡀⢽⣯⣀⢾⣽⢮⣤⡤⣿⣿⡟⣿⢹⣿⡷⣼⣿⣟⠻⠟⢟⡰⠅⠱⠒⠊⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠌⡙⠳⠆⡸⠚⠫⠙⢻⣾⢗⣾⠟⣟⠱⢦⡽⢻⢷⣬⡸⢋⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠠⠓⠃⠒⠉⣼⣠⣥⡴⢦⠐⣀⣼⢿⡐⢻⣯⡴⣤⠐⠴⠻⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⠠⠒⡀⠉⢻⠳⠛⠊⢁⡱⠥⠚⠙⠂⡁⠀⠀⢀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠋⠁⡀⠁⡀⠈⠴⢆⢉⡆⠹⠄⠋⠒⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠤⠄⠂⠐⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⢰⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢰⡀
⠀⠈⣤⣤⣤⣤⣤⣬⣭⡍⠀⠀⠀⢸⣿⡆⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠁⠠
⠀⠀⣤⣉⡉⡉⢉⣩⣍⣀⠀⠀⠀⣼⣿⡟
⠀⠀⠉⠉⠉⠙⠉⠉⠉⠽⠆⠰⣿⠿⠿⠃⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠐⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⢸⡟⠀⢠⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠈⠉⠛⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⢰⠛⣿⣿⣷⡀
⠀⠘⠁⠀⠟⠀⣀⢀⡄⠀⠀⠀⠸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣾⣿⣿⠁
⠀⠀⠀⢀⠀⠀⠻⣤⣧⠀⠀⣀⡀⠙⠻⠿⢟⠁⠀⠀⠀⠀⠀⠀⠰⠐⠐⠇⠈⠀⠀⠉⠀⠀⠀⠔⠂⠈⢻⣿⡯
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀
⠀⠀⣠⣤⣠⣬⣌⢁⠀⠀⢴⠀⠀⠆⠀⣠⣴⣦⣤⣄⣠⣀⣀⣄⣀⣤⣴⣶⣿⣿⣷⡄⠀⠀⢸⣿⣿⣧⡀⠀⣀⣠⣤
⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⠇⢶⣿⣿⠿
⠀⠀⠀⠉⠉⠁⠀⠀⠀⣤⣤⡄⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢀⠀⠈⠉⠁⠀⢈⣉⠉
⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠂⠈⠙⠿⠦
⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣦⣤⠀⠁⠀⣀⣀⣀⣀⣀⠀⠀⢰⣿⣿⣽⡟⢀⣠⣦
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠀⠀⠀⠉⠙⠉⠉⠉⠀⠀⠸⠟⠟⠋⠁⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⠘⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠃⢰⣷⣤⣤⣠⣿⠃⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢍⠁⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠃⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡶⠦⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⢠⡤⠠⣄⡜⠋⠹⡀⠀⠀⢠⡆⢀⠦⣄⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢇⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⢸⠷⡄⠀⠀⢀⡇⠀⢳⡀⠀⣰⠃⢸⡀⠀⠀⠀⣀⠀⠀⠀⢀⡖⠲⡆
⢀⡠⠊⠁⠀⠀⠀⠀⠁⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⢦⡀⡼⠀⠀⠀⠻⡴⠃⠀⠈⡇⠀⣠⠞⡻⠰⡖⠂⠋⠀⠀⠻⢠⣤
⠉⠒⠠⣤⠀⠀⢀⢀⣀⡀⠠⠖⠋⠀⠀⠀⠀⠀⣟⠒⠦⣄⡀⢸⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⡇⠀⢈⠆⠀⠀⠀⠂⣾
⠀⠀⠀⢸⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⣄⣀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣸⣤⣴⡷⠤⡤⠟
⠀⠀⠀⠀⣧⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠃⠀⢈⠻⡀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⣹⠛⢦⡀⠀⠀⠀⠘⠛⠉⠀⢠⠏
⠀⠀⠀⠀⠀⠀⡴⠤⣄⠀⠀⠀⢰⡖⠒⠛⠳⡆⢠⡤⠐⠋⠀⠀⡠⢶⣉⠁⠀⠀⠀⢀⠔⠁⠀⠀⠈⠲⢄⠀⠀⠀⠀⣴⣃
⠀⠀⠀⠀⠀⡜⠀⠀⠽⠦⢤⣤⡀⠙⠢⣄⠀⠛⠚⠁⠀⠀⠀⡜⠁⠀⠈⠉⠒⠤⣤⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠉⠒⠒⢤⣤
⠀⠀⢶⡐⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣈⣳⡄⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⡀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⡦⠀⠀⢀⡀⠀⠀⠸⣞⠉⠉⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⡸⠁⠰⣎⠁⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⠓⣻
⠀⠀⠀⠀⣇⣀⡠⠞⠉⠉⠘⠚⠉⠑⢤⡀⠀⠀⠀⢀⠇⠒⠀⠀⠤⠤⠀⣀⠀⠀⠀⣃⠀⠠⠔⠊⠁⠀⠀⠀⠀⠰⠁⠀⠀⠈⠉⠲⢄⠀⠀⠀⠀⠛⠢⡄⢀⣀⣨
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⠶⠒⠒⠋⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣀⣉⡶⠀⠀⠀⠀⣧⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⢛⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⡴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠎⠋⠀⣠⠔⠉⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⡰⢻⣄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡞⠉⠳⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠙⠉⠓⢄⠑⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⡶⠦⠿⢦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⣀⣀⠀⠉⠂⢵⣼⡆⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⣄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠙⡄⠀⣸⣠⡟⠲⠛⠁⠀⠀⠀⠀⡴⠋⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠁⢈⠉⠉⠉⠁⠀⢠⣦⠀⠀⠀⠀⠀⠀⠑⡄⠀⣷⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⢍⡁⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⠉⣇⠀⠀⢀⡴⠋⠸⡆⠀⠀⢀⣶⡀⠀⠈⢦⣿⣮⣀⠀⠀⠀⢸⡟⠒⠦⢤⣀⠹⡄⢀⢀⠀⠀⠀⠀⠀⠀⢸⣀⡶⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣰⠏⠀⠀⠀⢳⡀⢀⡞⠀⢳⡀⠀⣼⠋⠀⠈⠛⠲⢤⣘⡆⠀⠀⠀⠈⠙⢋⠏⠈⢳⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠳⠟⠀⠀⠀⢳⡀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠠⠤⠄⠚⠀⠀⠀⠛⠒⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⢠⣀⠀⢁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠊⠀⠀⠀⠀⠀⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⣀⡔⠁⠉⠳⠾⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠟⠒⠤⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠒⠋⢉⣉⡀⠀⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠒⠛⠉⠉⠀⠀⠠⣴⣶⣾⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠒⠋⠉⠉⠉⠁⠀⠒⣂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⡤⠔⠒⠒⠒⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⢀⡞⠀⠀⢀⣤⣶⣶⣤⣀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⣿⣿⣿⡿⠛⣁⠥⠤⠤⠴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡼⠀⠀⣴⡿⢋⣴⣾⣿⣿⣧⡀⠀⠀⢿⣷⠀⠀⠀⠀⣿⣿⡏⣰⠋⠀⢀⣀⠤⠴⠒⠒⠒⠚⠛⠛⠒⠒⠲⢶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢢⡇⠀⣰⡟⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⡇⠀⠀⠀⣿⣿⢀⠇⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⣀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢸⠀⠀⣿⠃⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⢈⡞⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⢸⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⢸⠀⣀⣤⣴⣶⣿⣿⡿⠿⠿⠿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢸⢸⠀⠀⣿⡄⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⡿⠀⠀⠀⣿⣷⡌⢻⣿⣟⣯⣥⣶⡶⡶⠷⠿⠿⣆⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠜⡆⠀⢹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⡇⠀⠀⠀⣿⣿⡇⢸⣿⢛⣭⡤⣶⡖⣶⡇⢾⣿⠰⠀⠀⢠⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢳⠀⠀⠻⣷⣈⠻⣿⣿⣿⡿⠁⠀⠀⣾⣿⠀⠀⠀⠀⣿⣿⣿⠈⣿⡟⣛⡁⣭⡄⣶⡆⣶⣖⢳⣶⣶⣾⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢧⠀⠀⠈⠻⠿⠾⠿⠋⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⣿⣿⣿⡄⢿⡟⣻⣅⣭⣤⢴⣆⢰⡆⢰⡦⣼⣿⣽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⢻⣋⢨⣥⢨⣦⢰⡦⢰⡆⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⣀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠈⣿⣿⣿⢈⣭⢰⣧⢰⣦⣼⡧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⣿⣿⣿⣉⣿⢨⣯⣸⣯⣼⡇⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⡇⢸⣿⣿⣏⣿⣭⣯⣼⣯⣽⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡄⡇⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋

⠀⠀⠀⠀⠀⠀⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠚⠓⣶⡼⢿⣾⣷⣾⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⠏⠀⠀⠀⡰⣿⠃⢋⣴⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⣠⠋⠀⠀⢺⡂⠁⠀⠐⠛⠛⠛⠿⠛⠶⠇⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢽⠀⠀⡁⠀⠠⢔⣾⡅⠀⢀⣻⣛⣻⡟⡟⢛⡟⠉⠉⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⡾⠏⠀⡇⠀⢀⡼⣻⢸⣷⣦⣽⣏⢙⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⣇⠐⠡⣰⡇⠻⠛⣧⡈⣻⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢀⠀⠀⠀⢀⣠⣤⣆⣀⣨⣿⣿⣧⠶⢻⣿⣿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠲⢶⡿⠟⠛⢉⣽⠟⠉⠁⢈⣿⡿⠛⣧⣠⣼⡿⠿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠋⠌⣿⠂⢤⣾⡟⠊⠁⢉⣿⢻⡗⢂⡾⣻⡟⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⢀⣁⣈⣆⠔⠋⠀⠀⢠⣿⣿⣿⣴⠪⣭⣬⡙⢦⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢚⣿⣿⣏⣀⠀⣠⣟⣯⡿⠋⠁⢚⣃⣨⣤⣤⣤⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣥⣽⣿⣿⣿⡿⠿⠿⠿⠿⠿⠻⠛⠛⠋⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⡉⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣀⣀⣀⡀⡀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣿⣿⡳⡑⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⠀⢿⣿⣿⣷⠹⡜⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⣇⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠇⠛⠀⠂⠁⠀⡀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⢿⣿⣿⣿⣿⡿⢻⡗⠋⠀⢀⢀⡀⠀⠀⠀⡀⠠⠀⠀⠀⢀⡰⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠛⠛⢿⡈⠙⠓⠈⠀⠀⠀⠭⠤⠤⠿⠶⠶⠒⢡⢖⣞⡋⠁
⠀⢤⣤⣄⣠⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠁⠀⠀⠀⠀⠐⠒⠂⠐⠒⠒⠂⡀⠉⠀⠈
⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠐⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡉⢩⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣥⣄⣀⣀⣀⣁⣀⣠⣤⣤⣶⣾⣿⣿⣿⣍⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡅⡎⠉⠉⠉⠉⠉⠉⠉⠉⡆⣴⠞⠻⣦⡀⣴⠞⠻⣦⡀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣀⣀⣼⠃⣷⣀⣀⣼⠃⣿⠛⣿⢛⡟⢻⡛⣻⡛⣻⢛⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡧⠻⠳⠟⠛⠛⠛⠺⠒⠛⠣⠬⠛⠛⠡⠠⠬⠟⠛⠥⠠⠿⠛⠛⠛⠛⠛⠛⠻⠛⠿⠛⠛⠰⠀⢾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠴⠶⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣀⡤⠤⠒⠒⠒⠒⠤⢤⣀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⡴⠋⠁⣀⣤⣤⣤⢤⣤⣤⣀⠈⠙⢦⡀⠀⠀⠹⣦⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠃⠀⠀⡰⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠙⢆⠀⠀⠘⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡏⠀⠀⣰⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣆⠀⠀⢹⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠐⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⠂⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⠀⠀⣇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣸⠀⠀⢀⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣧⠀⠀⠘⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣠⠃⠀⠀⣼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣆⠀⠀⠈⢦⡀⠈⠳⢦⣄⣀⣀⣀⣀⣠⡴⠞⠁⢀⡴⠁⠀⠀⣰⠏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠙⠢⣄⣀⠈⠉⠉⠉⠉⠁⣀⣠⠔⠋⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠉⠙⠒⠒⠋⠉⠁⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⣤⣤⣠⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠣⢤⡤⠤⠤⠤⠤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⢤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⢀⣼⣷⡀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠘⠛⠻⣿⣿⠿⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠠⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⣿⣿⡿⠿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠉⠁⠈⠉⠁⠈⠉⣄⡤⣀⡄⠈⣠⢌⡉⠉⣉⠋⡋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⡀⢸⠀⠀⠀⢊⡧⣷⠇⠈⠷⠾⠟⠀⠳⠶⠿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠉⠉⠉⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠂⠒⢒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣆⢐⡀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⣴⠶⠟⠛⠛⠷⣦⣑⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠄⡀⠹⣀⡀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠄⢏⠈⢰⡇⠀⠀⠀⠀⠀⠀⠁⡈⣆⢸⢢⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠘⠓⠀⠀⠀⡤⣾⠿⠭⣡⠀⠎⠤⠵⠾⢇⣀⠀⠀⣀⣀⡴⠊⠀⢸⠄⠀⠀⢼⠆
⠀⠀⠀⠀⠀⡠⠀⠴⠴⠵⣤⣤⣦⡺⠿⠓⠶⠾⠿⠼⠃⣤⣀⡙⠊⣩⠍⢱⠒⠨⠆⠰⠇⠰⠠⡄⣀⣸⢠⠄⢀⢸⡀
⠀⠀⠀⠀⠈⣀⠴⠒⠒⠀⠀⠉⠛⠛⠓⠒⠉⢉⣿⣿⡡⠤⠤⠭⠥⠥⣶⡌⠫⣥⠒⠒⠺⣯⣐⣧⠚⠁⠊⠒⢺⡞⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠠⠁⡤⣤⢤⣤⣠⣀⣂⣀⡂⠀⢂⣾⠛⣛⣋⠀⢛⠛⡃⠀⡻⡇⠈⠈⢡⡶⢾⡇⢾⠶⠞⠋⢂⢴⠟⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠠⡀⣹⠈⢛⠛⠚⠛⠘⠋⠛⠛⠋⠘⠛⠛⠀⠛⠒⠃⠀⠛⢓⣦⡔⣸⣁⣀⡐⠽⣤⣤⡶⠗⠁⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠶⠆⠳⠶⠖⠘⠿⠾⠘⠟⠒⠂⠚⠛⠟⠀⠛⠛⠛⢀⡇⢈⠉⠉⠓⠋⠁⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠻⠶⠆⠿⠿⠂⠷⠶⠆⠷⠽⠷⠸⠿⠟⠘⠿⠗⣡⣾⣶⣶⣶⣶⣶⢶⠷⠷⠶⠖⢶⢶⣶⣶⣇⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠓⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⠈⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠛⠛⠛⠛⠿⠶⠶⠶⣦⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⣉⣠⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣉⣉⡉⠛⠛⠛⠷⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣤⡶⠟⠛⣩⣴⠟⠿⣿⡟⠛⠩⣉⠉⠉⠛⠛⠻⠟⠛⢻⣧⣭⣭⣿⡿⣿⣿⡿⣷⣶⣶⣤⣤⣄⣩⣭⣟⢿⡄
⠀⠀⠀⠀⣼⠏⠀⢴⣿⣏⣀⣙⣂⡈⠻⣶⣶⣧⡶⠶⠾⠛⠛⠷⢶⣌⣿⡄⢰⠈⢢⣀⠹⡻⣿⣍⣽⣿⡛⠋⠉⢤⡙⢿⣇
⠀⠀⠀⠀⠹⣧⣀⣀⡀⠉⠉⠉⠛⠛⠻⠶⠿⣿⣶⣶⣔⣀⣒⣒⣈⣉⣻⣿⣼⠶⣦⣄⣤⡶⠿⠿⢭⡉⠙⢦⡀⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠈⠹⣿⠛⠛⠻⠶⠶⢶⣤⣤⣤⣀⣀⣀⠈⠉⠙⠛⠛⠿⠿⢿⣶⣦⣤⣽⡿⢿⡷⣦⡀⠉⠀⠀⠀⢀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⠶⠶⣦⣤⣤⣄⣀⣀⣀⣠⣼⣷⠘⣷⠀⠹⠄⠀⢸⡇⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⢻⡆⠀⢰⠦⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⣿⠀⢿⡄⠀⠀⡆⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣧⣨⡇⠀⢸⡀⡇⠀⢸⠉⣿⠀⢸⠛⡶⠀⣠⣤⡄⠀⠀⠀⢰⣿⡇⢸⡇⠀⠀⠃⠀⠀⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢰⡶⣦⠀⢨⣭⡁⠀⠘⠶⠿⠀⢸⣤⣇⠀⣿⠀⡇⠀⠀⠀⠸⢾⡇⣿⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣇⣹⠀⢸⡇⣿⠀⢸⡏⢻⠀⢰⠶⣤⠀⢙⡛⠃⠀⠀⠀⢀⣸⣧⢻⣿⠀⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣬⢭⡄⠈⣛⡛⠀⠸⠧⣾⠀⢸⡀⣿⠀⣿⠉⡇⠀⠀⠀⢸⣯⣿⢸⡏⠀⣧⠀⠀⠀⠸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡀⡇⠀⡏⢹⠀⢰⡶⣦⠀⢀⣉⣉⠀⠻⠶⠇⠀⠀⠀⠘⢻⡇⣸⡇⠀⢸⡆⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⠓⠇⠀⢿⣼⠀⢸⣇⣻⠀⢸⡇⢹⠀⢰⠶⣦⠀⠀⠀⢰⡟⣿⣿⣄⣤⣬⣇⣠⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠷⠼⠂⢸⣀⡏⠀⠀⠀⠸⠷⢋⣼⠟⠋⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⢶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠶⣦⣤⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⡠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣃⡀⠆⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠦⠀⠀⠀⠶⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀⠀⠀⠛⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣛⣢⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠛⢣⣄⠁⠀⠀⡀⣀⠻⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀
⠀⠀⠀⠀⠀⠀⡶⠊⠀⣤⣀⡀⠁⠉⠴⠆⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠤⡈
⠀⠀⠀⠀⠀⢰⣷⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠲⣶⡆⠀⠀⠦⠄⠀⠤
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠁⠀⣄⠀⠀⠉⠀⠀⠀⠀⠃⠀⡀⠈
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣤⣤⣶⣦⣄⡀⠀⠀⠀⣿⠀⠀⠀⢀⣤⣶⣶⣦⣤⡀⠀⠀⠀⡇⠐⠀⠸⠀⠀⠀⠀⠀⠀⢀⡀⣀⣅⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣇⠀⠀⠠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣿⠀⠀⢰⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢿⣮⣿⣿⣿⡿⠅⠀⡀⠀⣿⠀⠀⠀⠻⣄⣾⣿⣿⣿⡿⠁⡀⠀⡃⠐⢂⠀⠀⠘⠁⣀⡦⠀⠀⠀⠀⣀⣀⣼⡖
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⠀⠉⠉⠉⣀⡠⠞⠁⠀⣿⠀⠀⠀⠀⠈⠙⠛⠛⠉⣠⠔⠁⠀⣧⠀⣀⣤⣀⠀⠀⠀⡀⢀⣀⣤⠄⠀⠀⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠿⠟⠛⠀⠀⠤⠤⠄⠀⠤⠤⠤⠤⠤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⠄⠀⠀⠀⠀⡤⠀⠀⠀⠄⠀⢠⠀⠀⡄⠀⠀⠄⣄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⢤⣼⠀⢴⠋⠌⠠⠀⠀⢠⣤⢠⠄⠸⠁⠀⠈⠀⠀⠅⠀⠀⠀⠈⡄⠀⠠⠀⠹⠆⠀⠈⠂⠢⠉⠿⠆



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣽⣯⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣷⣷⣶⣿⣿⣷⣶⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢠⣤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⣾⢷⡀⠹⡀⢸⡘⡆⠀⠀⡟⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⢹⡈⣧⠀⠀⠀⢷⡇⠀⠀⢀⣀⠀⠸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⣤⠀⠱⡀⠈⢧⢸⡄⠀⠀⢸⡇⠀⢰⠃⣿⠀⠀⢰⢻⠀⠀⢀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠙⣷⡄⠀⠀⠈⣆⣇⠀⠀⠘⠁⢀⡏⢠⡏⠀⠀⣞⡞⠀⣰⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡓⢦⣄⠀⠀⢻⡀⠀⠀⠈⢿⣄⠀⠀⠘⣿⠀⠀⠀⠀⣸⠁⣾⠁⠀⢸⡟⠁⠀⠁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⣷⣄⠀⠻⣄⠀⠀⠀⢻⣆⠀⠀⠘⣧⠀⠀⠀⣿⣼⠇⠀⢠⠟⠀⠀⣠⡾⢛⡇⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢷⣄⠀⠀⠻⣦⠀⠀⠈⠀⠀⢀⣿⡏⠀⠠⠋⠀⣠⡾⠋⢀⡞⠁⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠉⠳⣦⡀⠹⣧⠀⠀⠀⠀⢸⡟⠀⠀⠀⣠⣾⠟⢁⡴⠋⠀⢠⠞⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⠭⠷⠶⠤⠀⠀⠀⠉⠳⢼⣷⡀⠀⠀⠟⠀⠀⣠⡾⢋⣡⡴⠋⠀⠀⠀⠀⢀⡤⢞⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠖⠂⠈⠑⠀⠀⠀⠴⠿⠟⠛⠉⠁⠀⠀⠀⣀⣴⣞⣭⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠀⠀⣀⣀⣤⣤⡶⠚⠁⠀⠀⣰⠂⠀⢠⠀⠢⣀⠀⠀⠀⠐⠒⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢛⣋⣩⠅⠂⠁⠀⠀⠀⣠⣾⠁⠀⠀⠀⣧⠀⠈⠳⣦⣄⡀⠀⠀⠀⠠⣤⣤⣤⣴⣚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⡀⠀⠀⣀⠜⡱⠃⠀⡄⠀⠀⠸⣷⡀⠀⠈⠻⢍⡓⠶⣤⣀⠀⠤⣄⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⣠⠞⢁⡼⠁⠀⢀⣧⠀⠀⠀⢳⠙⣄⠀⠀⠀⠉⠓⠦⢌⣹⣶⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⣴⡟⢁⣴⠏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠣⡈⢧⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⢠⡆⠀⠀⢼⢸⡇⠀⠐⣄⠀⠀⠾⠆⠀⠈⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠸⣿⠁⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧