Thirteen colonies Emojis & Symbols

⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⣿⠉⠉⠉⠉⢉⣉⠉⣉⡉⠉⠉⠉⠉⣉⣉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⣿⠀⠀⠀⠀⢸⣿⠈⢩⣿⠀⠀⠀⣾⠉⠉⢀⣴⢦⡄⢹⡇⣤⢶⣄⢠⣤⣤⡀⣭⢀⣴⢶⣄⢠⡶⠦⠀⠀⠀⣿⣧⢀⣾⣇⢀⣴⢶⣶⢰⣶⢶⡄⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⢸⣿⢤⣀⣹⠆⠀⠀⢷⣀⣀⠸⣧⣠⡟⣼⡟⣧⣠⡿⢸⡇⢸⡇⣿⠸⣟⣛⡟⢈⣙⣷⠀⠀⢰⡯⢹⣿⠃⣿⠸⣇⣠⣿⢸⣇⣠⡟⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠈⠀⠈⠉⠀⠈⠁⠀⠁⠉⠀⠈⠉⠁⠈⠉⠉⠀⠀⠈⠁⠀⠁⠀⠉⠀⠈⠉⠉⢸⣏⡉⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⢻⡀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠃⠀⠀⣤⢄⣤⣀⡀⠀⠀⠘⠳⣄⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿⠤⠠⠄⠀⠠⠀⠤⠤⠤⠀⡀⣠⠟⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⡞⠙⡆⠀⠀⠀⠀⠀⠀⣠⡼⠛⠉⠁⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠲⣄⠀⠀⣸⠁⡼⠃⠀⢳⠀⠀⢀⡠⠞⠚⠁⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠁⠀⠀⠻⠶⠛⠋⡼⠁⠀⠀⢸⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠃⣀⣀⡀⣀⠀⠀⢀⠀⣿⡀⠈⠋⣠⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⣰⠇⠀⠀⣀⢉⣁⣉⠀⢠⣏⣉⢉⡉⢉⣉⡁⠰⣧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⢹⡖⠒⠒⠲⠲⡆⠠⡀⢘⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠉⠉⠉⠉⠙⢢⣄⡀⠀⢸⡇⠀⣀⡠⣶⠛⠳⢛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣀⣀⢀⡀⢀⡀⢀⣀⡀⢠⡞⠀⠉⣳⣾⠷⢍⠐⠺⠟⠛⠂⠀⠈⠐⠀⠖⠀⠐⠆⠠⠀⠰⠰⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠞⠁⠀⢠⡾⠄⠀⢠⣤⢀⡀⢀⣤⢠⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠙⢤⡀⠀⠀⣴⢾⡙⣧⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠐⣿⢠⡇⢈⡉⠏⠀⠀⠦⠶⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣽⢲⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠘⠙⠋⠸⠛⠙⠛⠀⢀⠀⣙⣠⣷⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣉⡁⠀⠀⠀⣠⣀⠀⢀⣠⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠛⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠲⠆⠖⠘⠒⠀⠀⠀⢦⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣴⠿⠤⠤⠤⣄⠀⠀⠀⠀⠀⠴⠖⠰⠴⠖⠴⠆⠀⢀⣉⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⣠⣶⣟⠁⠀⠀⠀⠀⡀⠀⠈⣛⡈⠊⠲⣄⠀⠀⠀⠀⠀⠀⢀⣀⣬⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⢰⡿⠀⠈⢷⡀⠀⠀⠀⠃⠉⠋⣉⠉⠀⠀⠈⢷⡀⠀⢀⡴⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⣴⠋⠀⠀⠀⠀⠈⢦⡐⠀⠛⠁⠙⠛⠉⠓⠀⠀⢀⣹⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣨⡇⣀⡶⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠻⡄⢀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠠⠂⠠⣴⣶⢴⣾⣿⢻⣯⣤⣤⣤⡄⠰⠠⠄⠄⠀⣿
⠀⣿⠀⠀⢻⡓⠚⠋⠛⠉⠻⠋⠋⠳⡄⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⢻⡟⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢼⡇⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⢰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⡇⣠⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⢣
⠀⠀⣥⡤⠥⢍⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠈⢴⠂⠤⠲⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠙⡂
⠀⠀⠈⠀⡠⠆⠉⠒⠂⠀⢐⠠⡀⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠒⡏⠀⠀⠀⢀⠠⠚⠁
⠀⠈⠁⠔⠀⠀⠀⠀⡀⠀⠀⠈⠈⠒⠚⠀⠀⠀⠀⠀⠤⣤⠊⡀⠀⡀⠀⠀⠰⠀⠀⢀⡴
⠀⠀⠂⠀⠀⠀⠀⠀⠁⠡⠀⠠⠀⠀⠀⢀⠄⠀⢈⢈⣠⠟⠀⠀⠀⠀⠀⠀⡁⠀⠐⠆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢡⠁⠀⠀⠀⡈⣱⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠂⠉⢈⡙⢧⣀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡠⠔⠀⡠⠚⠇⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⡁⣀⠼⠞⠐⡉
⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⠈⢁⢀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠁⡄⢙⠉⠓
⠀⠺⠇⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡟⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣠⠖⢺⠒⣄⠀⠀⠀⠀⠘⠂⢆⣴⢶⣖⠀⠄⣠⠙⣄⡠⠁⠀⠀⠀⠀⠀⠒⠀⠐⠒⠖⠒⠒⠀⠒⠒⠒⠒⢸
⠀⠀⠀⠤⠤⡷⠄⢾⠌⢸⠇⠆⠀⠀⠀⠒⢊⡔⠃⠀⠑⡀⣼⠠⣵⠀⣐⢢⠀⠀⠀⠀⠀⠀⠄⠀⠂⠔⠄
⠀⠀⠀⠀⠀⠑⠦⣴⡤⠟⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡀⢱⣑⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠈⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠔⠢⠔⠒⠁⠀⠀⠀⠀⠀⠀⠘⣏⠀⡤⠠⠤⠴⠀⠀⠀⠀⠀⠈⡁⣁⠀⠁⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢂⡶⠀⠒⠐⠐⠒⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠃
⠀⠀⠀⠀⠀⠔⠒⠒⠃⠠⡔⠀⠈⠈⠓⠤⠤⢄⠀⠀⠀⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡀⢑⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⢠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠁⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠸⡷⠒⠒⠀⠓⠤⠤⠀⠀⠀⡀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁⠀⠁
⠀⠀⠈⠉⠙⠢⣀⠤⠤⣀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢠⠦⢤⢠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢣
⠀⠀⠀⠈⠇⠘⠁⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠹⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⢀⡤⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡊⠵⠲⠤⠴⢤⠀⠀⠀⠀⠀⠀⠀⡠⠚⠻⣨⠊⢦⠋
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⠋⢒⠄⠀⠀⠀⢀⡸⠄⠀⠀⢽⣒⣻⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠙⡆⠀⢘⣅⡠⠤⠔⢦⣸⡼⠋
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠀⠀⠀⠗⠊⢫⠀⠀⠀⣀⣸⣨⠁
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠒⠞⠛⢢⣿⡹⡀
⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠀⠀⠀⠀⠀⠉⣏⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣠⠤⠐⠂⠉⠻⣳⠄
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣁⡠⢄⣀⣀⡜⠁⠀⢀⣀⣀⣀
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠙⠤⡀⠀⢀⠎⠀⡠⢊⡡⢴⡦⢄⡙⢢
⠀⠀⠀⠀⠀⠈⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠙⠶⠃⠀⢰⢁⡎⣷⡾⢹⣾⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣀⣀⣀⣇⠀⠀⢸⠙⡛⣳⣤⢠⣾⠋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠲⠤⠒⠬⠒⠢⠀⠈⢆⠀⠀⠣⡘⠣⢽⣏⠤⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠲⣄⠀⠀⠀⠀⢀⡠⠊⠉⠉⠲⡀⣘⣦⡄⠀⠀⠀⠀⠀⠣⡀⠈⡆⠀⠀⠈⠓⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡴⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣶⣶⣶⣦⣀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠁
⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠈⣿⣿⣿⠀⠀⠀⠀⠀⠰⠿⠿⠛⠛⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣀⣤⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠂⣠⣶⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠘⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⣧⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂

⢰⠒⠒⠒⠒⢒⣶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠒⠀⠀⠀⠀⠀⠀⠀⠒⢶⡆⠐⠒⠒⠒⠒⠒⠒⠒⠂⠰⡦⠐⠐⠀⠒⢂⡶⠀⠒⠀⠒⡖⠀⠀⠀⠂⠰
⢸⡄⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡀⠀⠀⠀⠀⠀⠀⣦
⢘⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠌⡀⠐⠁⠀⢀⣀⠀⢀⣀⠄⠊
⢠⠀⠀⠰⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡃⠂⠀⠀⠂⠀⠀⠈⠁⠤⠐⢶⠇
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠎⢀⠔⠁⠀⠂⠀⠘⡀⠀⠀⠠⠤⠀⢤
⢸⡤⠊⠁⠈⢧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠁⡔⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢢⡸⠶⠢
⢀⡠⠤⠔⠂⣤⣨⣷⡆⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠔⠁⠠⡄⢀⠎⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⢀⡀⠀⢀⡀⠻⢜
⠈⠀⠀⡀⠼⠉⠡⢄⡀⠉⠙⠃⢟⠁⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢀⡹⠀⠀⠀⠀⢠⡎⠠⠦⠤⠀⠆⠆⠀⠐⣄⠀⢀⣼⠁⡶⣓⠤⣤⠶
⠘⡛⠛⠟⠀⠀⠀⠀⢹⠀⠀⠀⠈⢃⡀⠀⢈⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠀⣡⡄⠀⠀⠀⢰⡇⠀⠀⠀⢈⢟⡉⠁⣹⡟⠉⠰⣤⣀
⢸⠃⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢀⠌⠉⠀⠋⠁⠀⠁⠀⠀⠀⠀⠀⢀⣀⡴⠁⢀⠀⡀⠀⠀⡔⠀⡀⢛⡿⠀⠀⠀⠘⢳⢦⡶⠒⠉⠀⠀⠺⠁⠀⠀⢀⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠥⠊⠑⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠷⠈⠀⠌⠀⢀⠻⠋⠈⠂⠀⠇⠀⣿⣾⠋⠀⠀⣤⡿⠛⠁⠀⠀⠀⠀⠀⠀⠒⢤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠀⠀⠀⠀⠀⠂⢀⠠⠠⠠⢀⠀⡠⡜⢀⢴⡀⣀⢀⡀⠐⠈⠀⡆⠛⡽⠀⢣⠄⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡁⠀⠄⠀⠀⠀⠀⠂⠲⠀⠀⢤⡀⠀⢘⠟⠁⠀⠀⡉⠀⠀⠀⠠⠀⠆⠰⠧⢤⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡰⠖⠐⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢦⠈⠐⠈⠀⢣⡘⠁⠋⠘⠃⠀⣏⠳⠶⠾⣟⣉⠱⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠑⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠈⠉⠉⡉⠋⠉⠉⢢⠀⠀⠀⠀⠳⠲⠶⠒⢠⣴⠗⣬⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⣬⣥⣤⣤⣤⣄⠊⠁⢄⡸⠄⣀⣸⣦⠀⠈⠳⣦⢘⡃
⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠄⣠⣟⣥⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠶⠀⠀⢀⣀⠀⠀⠀⠀⠀⡤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠁⢀⣆⠀⠀⠀⠀⢀⡀⡄⠐⢡⢠⡿⣴⢦⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠶⣈⠁⠛⡈⣡⠄⣠⢬⠁⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠧⠀⠌⠀⠀⠀⢈⡆⠉⣾⠀⡷⢷⣿⣶⣶⣶⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠀⠀⠀⠀⠀⠀⠀⠙⠶⡟⠻⣀⡿⠀⠉⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢹⠧⠀⠤⠠⣤⣤⠤⣤⢠⡄⠙⡇⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⣿
⠀⠀⠀⠀⠀⣀⢈⡷⠋⠰⠶⠶⠶⠖⠦⠀⠤⠤⠴⠴⡤⣤⣤⣤⠟⠣⣤⡇
⠰⠶⠀⢶⠀⡹⠛⠀⠀⠐⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣀⣭⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻
⠐⠀⠀⣠⠎⠑⠆⠀⠀⢠⣤⣤⣤⣤⡄⠈⠂⠀⠀⠀⠀⢀⠠⠿⠿⠋⠀⠀⠈
⠀⠀⡴⢁⡄⠀⠈⠲⡀⣤⣤⣤⣤⣀⣀⣄⣄⠀⢀⠀⠰⠃
⠀⠀⡃⠈⢷⡀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⣿⠀⠈⢷⠄⠀⠀⠈⠆⠀⠀⠀⢠⠔⠋
⢀⠀⢹⡄⠀⠀⠛⠀⠀⠀⠘⣤⠗⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢴⡦⡦
⡼⠀⠀⠳⣄⠀⠀⠐⠋⠀⡖⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣦⣤⣴⡆⢶⢰⣶⣶⣤⠀⢠⣀⣤⣤⣠⣦⣴⡄⣴⣄⣶
⣿⣄⡀⠀⠈⠢⡄⠀⠀⢰⠁
⣎⡙⠛⠟⢠⡄⠘⠶⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠛⠳⣄⠀⠛⢷⣄⠀⠘⠆⠀⠀⢰⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠈⠓⠂⠐⠒⠒⠒⠀⠒⠀⠒⠂⠀⠒⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈
⣯⣄⢀⡈⣦⣀⠈⣻⠃⢀⣇⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠
⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⣀⠀⢀⣀⡀⡀⢀⣀⢀⣀⡀⠀⣀
⠀⠈⠉⠉⠉⠉⠉⠉⡞⢫⣉⣉⡀⠀⠀⠈⠀⡀⠀⠀⠀⠀⢠⡤⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⠃⠸⠗⠷⠼⠜⠻⠃⠛⠀⠀⠀⠸⠤⠛⠎⠑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⠉⠉⠉⠉⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢻⠉⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠏⠀⣿⠘⠛⠟⠛⠀⠀⣸⡏⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀⠀⣰⠞⢡⡏⠀⠀⢸⠄⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠐⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠙⠶⠇⠀⡼⠃⠀⠀⢸⠀⠀⡴⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⢸⡇⢤⣶⠆⠸⠷⣾⠁
⠀⠀⠀⠀⠀⠀⠒⠒⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⣀⣀⣸⣇⡀⠀⢀⣠⠤⣿
⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠓⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣀⡠⡄⠀⠀⢰⠏⠉⠉⣉⣙⣛⠋⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠓⠒⠃⠈⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠶⠋⠁⠀⠀⠈⠉⠁⠃⠀⠀⣼⡀⠀⢀⣉⣉⣉⣀⣤⠀⠻⣄⣸⡿⣄
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠈⠉⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠒⠒⠛⠉⠉⠳⣆⠀⠀⠀⠀⠀⣿⢉⡉⡍⠉⠉⣿⠟⢯⣷⠶⢮⡽⠗⠋
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⣀⠀⠀⣿⣠⡤⣶⠶⠶⢿⠞⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⢰⣒⢤⣶⡄⠀⠀⠀⠀⣸⠃⠉⢳⡄⢿⠥⠖⠋⣹⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⢉⠈⠈⡁⢉⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠁⠈⠁⠁⠀⠀⠀⢰⡏⠶⠛⣰⣧⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠉⠉⠉⠀⠉⠉⡉⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠉⣉⡀⠈⠉⠁⠈⠁⠀⠀⢈⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣦⣀⡤⠞⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡾⢋⣡⣤⡴⠦⣄⢠⡤⢦⠀⣉⣡⣽⣿⣅⡀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⢸⡏⣹⠸⡟⣯⡙⢷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⣿⠀⣿⢤⠝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠶⣼⡿⣦⠙⢛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⢄⡄⣴⣆⠀⠀⠀⠀⠀⢸⣿⣿⣦⢸⣧⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠗⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠻⢞⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣯⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠾⠷⣦⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⡌⠇⣀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⠏
⠀⠀⠀⢀⣀⣀⣠⡼⢯⠶⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣍⠁
⠀⠀⣾⠛⣟⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠟
⠀⠀⣿⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠛⣦⠀⠀⠀⠀⠀⣴⠋⠁
⠀⡼⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⣴⢄⣀⡀⠀⠀⠀⠀⠈⢳⣦⣤⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠁
⠀⠀⠀⢰⠡⣀⣾⣤⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠃
⠀⣧⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣴⠟⠉
⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣤⠶⠞⠃
⠀⠀⠘⣧⣤⣤⣀⡀⢀⣀⣠⣤⣄⣼⠟⠁
⠀⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣤⡀

⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⢐⡇⠀⠀⠀⣴⠠⢶⡄⠀⠀⡴⠶⠀⣀⡀⢰⠀⣀⡀⢀⢀⠀⠤⠀⣀⡀⢀⣀⠀⠀⢰⡆⢀⣶⠀⢀⣀⡀⣀⡀⠀⠀⠀⢸
⠠⡇⠀⠀⠀⣿⣀⠙⡧⠀⠸⣇⢀⢸⣉⣿⢸⢼⣉⣿⢼⠉⣷⣿⣾⠿⡗⢙⣯⡀⠀⣼⢻⣾⢻⡰⣏⣹⣿⣏⣹⠆⠀⠀⢸
⢈⡇⠀⠀⠀⠈⠈⠉⠁⠀⠀⠈⠉⠀⠉⠁⠈⠀⠉⠁⠈⠀⠁⠁⠈⠉⠁⠈⠉⠀⠀⠉⠀⠁⠈⠁⠉⠉⣹⣯⡉⠀⠀⠀⢸
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⢳⠀⠀⠀⢸
⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⠀⠀⠀⢸
⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠘⢆⡀⠀⢸
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡞⠀⠀⠖⠠⠀⠆⠀⠈⠑⣆⢸
⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⢧⠉⠁⠀⠀⠈⢈⣩⠴⠞⠁⢸
⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⠀⠀⡞⢡⠃⠘⡄⠀⢀⡴⠲⠋⠀⠀⠀⠀⢸
⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠁⠀⠈⠓⠛⠱⡃⠀⢀⢧⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸
⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡴⠋⠐⠶⠂⠄⠀⡤⠴⠧⠤⠤⠞⡷⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠋⠁⠀⠈⠑⠂⠃⠰⡥⠤⠤⠤⡌⠀⠙⣾⣧⠀⠀⠀⠀⠀⠀⢸
⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠉⠉⠉⢳⣄⡀⠘⡇⣀⢤⣶⡛⠾⢉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠠⠄⠠⠀⠀⣞⠀⠨⣿⠟⠂⠉⠋⠉⠑⠀⢈⢈⠁⠈⠁⠀⠈⠁⢸
⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⢠⣇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠉⠙⢧⡉⠉⣥⢭⢳⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢧⣀⢻⡸⣤⣤⠓⠀⠐⠒⠐⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠄⠄⠤⠤⠤⠀⠈⠻⢱⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠑⢾⣉⠁⠈⠀⡀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢐⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠛⠓⠒⠒⢒⠒⠒⠒⠒⠒⠒⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠨⡇⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⠀⠀⠀⠀⢉⡁⣀⣀⣀⠀⠑⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢐⡇⠀⠀⣠⣶⠊⠉⠉⠈⡀⠉⢒⠀⠠⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⠀⢸
⠐⡇⠀⣸⠏⠈⠳⣄⠀⠀⣉⠈⣉⢀⠀⠈⢳⡀⢀⡔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡇⠀⢀⠀⠀⠀⠀⠀⢸
⠨⡇⢸⠁⠀⠀⠀⠘⢢⡀⠁⠀⠀⠀⠁⣀⡤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⡈⢻⣴⣧⡜⠃⠀⠀⠀⠀⠀⢸
⢐⡇⠈⢷⠐⠆⠐⠀⠆⠟⢆⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡹⢿⡾⣏⠙⠉⠀⠁⠁⠀⢸
⠠⡇⠀⠈⠣⣄⠀⠀⠀⠀⢸⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠈⠃⠀⠀⠀⠀⠀⢸
⢈⡇⠀⠀⠀⠈⠙⢦⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢡⠀⠀⠀⠀⠀⠀⠀⢸
⠐⣇⣀⣀⣀⣀⣀⣘⣾⣛⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⠟⠉⠉⠉⠉⠉⠉
⡇⠀⠀⣠⠴⠒⠤⠄⣄⡀⠀⣀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⡞⠉⡄⠀⠀⠀⠀⠀⣠
⡇⠀⠀⠑⠤⠄⣀⠀⠀⠈⠉⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠈⡇⠀⠀⠀⡇⠀⢡⠀⠀⢀⡠⠎⠁
⡇⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢰⠤⣀⡀⡁⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⠞⠁⠀⠀⠀⠀⠀⣧⠀⠀⢀⠃⠀⠀⢀⡴⠉
⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠉⠀⠀⠀⠀⢀⡤⠖⠋⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡟
⡇⠀⠀⠀⠀⠀⠀⣥⠖⠓⢄⠀⠀⠇⠀⠀⠀⠀⡴⣋⣁⡤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠚⠒⠀⠉⢡⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠞⠀⠀⢀⣀⡠⠴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⢤⠤⡀⠈⡉⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⣀⡤⠚⢉⣠⣔⣋⣀⣀⣀⣀⣀⣀⡀⠀⠠⠤⠤⠤⢤⡀⠀⠀⢸⠀⣀⠠⠜⠒⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠈⣁⡤⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠓⢦⢞⣥⣶⡶⠗
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⡸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⡆⠂⠀⣉⣉⢉⠉⠉⠉⣿⠉⠙⡢⣤⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠒⠋⠱⡀⢸⡏⡀⣇⣰⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠁⠀⠀⠀⠙⢍⡁⠰⡄⢴⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠣⡜
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⠖⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠵⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠤⠄⠀⡶⠒⠒⠒⠈⠉⠉⠉⠈⠉⠀⠀⠀⠀⡤⢛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠃
⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃
⡇⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣠⠤⠤⠤⠤⠐⢤⠤⠤⠤⠤⣄⠀⠀⠀⠀⢠⡞⠉
⡇⠀⠀⠀⡤⠤⠐⠓⠒⠂⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡤⠏
⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⡇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡄⠀⠀⠀⠀⠀⢀⠞⠁
⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣠⠔⠁
⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡞⠁
⡇⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⡇⠀⠀⠀⠀⠀⠀⠧⠤⠤⠶⠖⠒⠒⠒⠦⠚⠓⢻⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠎⡉⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠉⠒⠠⣍⡒⠤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣠⣤⣄⡀⠀⠈⠑⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣄⠀⣤⢄⣀⡜⠁⢀⡴⠋⠁⠀⠈⠙⢦⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢥⡇⠀⠀⠀⠀⡔⠉⢆⠀⠀⠀⠀⠀⡠⡫⠊⠁⠀⢀⡠⢘⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⣠⠔⣉⠉⠭⣉⣿⡲⡀⠀⠀⠹⠛⡟⠀⠀⠀⠀⠀⣿⠁⠀⢀⠔⠁⢀⠎⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡾⠁⠀⡌
⠀⠀⠀⠀⢰⠁⡜⠁⠀⠀⠈⡇⢸⠄⠀⡠⠃⡰⠁⠀⠀⠀⠀⠀⣾⠀⢠⠋⠀⠀⡌⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠋⠀⠀⡰
⠀⠀⠀⠀⣾⠟⢆⠀⠀⠀⡠⠃⡜⢆⠉⣀⠔⠁⠀⠀⠀⠀⠀⠸⡆⢠⠃⠀⠀⡸⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⢠⢻
⠀⠀⠀⠀⠑⠵⢤⣉⣉⣉⣤⠮⠒⡌⢷⠻⠼⢖⢄⠀⠀⠀⣠⡳⢁⠏⠀⠀⢀⣇⡀⠀⠀⠀⡰⠁⠰⠁⠀⠀⠀⠀⢀⠇⠈⡄
⠀⠀⠀⠀⠀⢀⠊⢣⠰⡊⣴⣺⢷⢘⡌⢆⠀⠀⠑⠵⣖⠮⠛⠁⡘⠀⠀⣠⠋⠑⡦⠕⡒⡴⠁⣰⠁⠀⠀⠀⠀⢠⠋⠀⢠⠁
⠀⠀⠀⠀⠀⢸⠀⡇⠱⡑⣌⠥⠒⢉⣠⡼⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⠁⠀⠀⠉⠒⠼⠁⢠⠏⣒⠤⣀⠀⡰⠁⠀⠀⡜
⠀⠀⠀⠀⠀⠘⡄⠸⡄⢱⣠⣴⠾⠛⠉⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⠁⢠⠋⠒⠢⠟⠒⠿⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠘⣶⠛⢹⠻⡀⠀⠀⠷⣄⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠃⠀⠀⠀⠀⢠⠃⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠱⡀⠀⠸⡈⠢⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢃⠀⠘⣦⠜⠓⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠜⢆⠀⠈⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡡⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡠⡔⣒⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡄
⠀⠀⠀⠀⢀⡀⠤⢠⠀⣀⠀⠀⠀⠀⠰⠒⣟⣏⢭⠅⠃⠀⠀⣀⣀⣤⡤⠚⡁⠀⠊⠁⢲⠶⢤⠤⣄⡀⠀⠀⢍⠀⠈⠁
⠀⠀⠀⢸⢼⢶⢺⠻⠉⠉⣀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⡖⠋⠹⣉⡀⠀⠀⠁⢀⢀⣀⣉⠤⠖⠁⣢⣿⠂
⠀⠀⠀⠘⠚⠉⠈⠀⠀⠀⠘⢻⡿⢛⠁⠀⠀⠀⠀⠀⠈⠻⠶⣤⣄⣈⣉⣉⣉⣉⣡⣤⣤⣤⡶⠾⠋⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣤⠆⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠉⠉⡤⠑⠀⠀⢀⡀⡔⢢⠀⠻⠇⠀⠀⠀⠀⠀⠠⠀⠀⡤⡤⣦⢤⢤⡀⠺⠿⣀⡖⡗⢟⢻⢹
⠀⠀⢀⡠⡤⠴⠀⠀⠀⡈⠀⠀⠀⠁⠀⠀⠀⠀⠛⠀⠈⠐⠃⣠⠀⣇⢀⢹⣸⡼⠋⠀⠀⠏⠳⠶⠼⠼⠼⠄
⠀⠀⠀⠀⠀⠀⣀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠼⠀⠠⡻⠀⠈⠉⠉⠀⠀⠀⢐⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠄⠖⠈⠀⠀⠀⢀⢀⢀⠀⠀⣈⠋⠀⠀⠀⠸⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠈⠑⢦⣀⣷⣦⡀⠀⠀⢠⣶⣶⣄⣴⠀⢰⣷⠿⣿⡟⠃⣿⣯⣩⢹⣿⣹⠗⠀⠀⠀⠈⡗⠒⠂⢰⠂⠐
⠀⠀⠀⠠⢤⣀⣀⠀⠀⠀⠉⠃⠀⠀⣿⣁⣿⡏⢿⣧⣼⠏⠀⣿⡇⠸⣯⣤⣤⠸⡿⠙⠷⠀⠀⠠⠀⢹⠋⠓⣾
⠀⠀⠀⠀⠀⠈⠃⠀⠀⡤⠶⣄⠀⠀⠘⠛⢉⣤⣄⢩⡤⢤⡀⣴⢶⡀⢀⣴⢶⢠⡶⠖⡂⠈⠀⠀⠀⠾⠲⠶⠻⣤⠐⠐⠂
⠀⠀⠰⠖⠶⢶⡀⠀⠀⢧⣀⠞⠀⠀⠀⠀⠘⠳⢦⣼⣷⠾⠛⣿⠾⣧⢼⣇⣠⠜⣟⢋⣁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠻⠷⠖⠀⠀⠀⠀⠀⢈⠠⠂⠈⠛⠛⠁⠛⠀⠀⠉⠀⠀⠀⠉⠁⠀⠛⠉⠉⠀⠀⠀⠀⠉⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡰⠀⣔⢈⠀⢀⡀
⠀⠀⠀⠀⠉⠰⠶⠀⠀⠀⠀⢀⠖⠉⢠⠄⡀⠀⢁⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢦⣀⡀⠉⠀⠄⠈⢁⣸⠔⠋⠀⠀⠇⠀⠀⠄⠀⠈⡷⠀⠀⢀⠀⠄
⠀⠀⠀⠃⣄⡀⢀⡀⠤⢾⡁⠀⠀⠀⠉⠋⠍⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠁⠀⠀⣌⠀⠄⠀⢀⡀⠀⢠⠐⢀
⠀⠀⠀⣴⠇⠀⠈⠇⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠋⠀⠐⢦⣤⠄⠒⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢲⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠰⠀⠇⠀⠤⠄⠀⠀⠀⠀⠀⠤⠄⠇⠰⠇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠆⠤⠀⣼⠁⠀⠀⢹⣄⠀⠤⠶⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠉⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⡠⢴⣶⢶⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠴⠀⠘⡄⣠⠟⠋⠛⢆⡁⡜⠀⠰⠤⠤⠤⠤⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⣠⠀⠀⠀⠘⠈⠂⠀⢀⡀⡤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠈⠀⠀⠙⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠐⠒⠂⠲⠀⣶⡇⠀⠀⠀⠀⠀⠀⣷⡆⠰⠂⠂⠒⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣾⣿⡷⠒⠒⠒⠒⠒⠲⣿⣿⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢨⠿⠁⡇⠀⠀⠀⠀⠀⠀⡏⠹⢯⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠲⡞⢣⣤⣧⠤⠤⠤⠤⠤⢤⡧⣤⢛⡶⠒⠒⠒⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠾⠉⡈⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡘⡹⢦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⢞⡥⠊⠀⠇⢠⣇⣀⣀⣀⣀⣀⣀⣇⠀⢇⠈⠢⣙⢦⡀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠴⠋⢀⠔⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠈⠑⢄⡈⠓⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⠔⠉⣠⠜⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⢤⡀⠓⢌⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠔⠁⠀⢸⠀⠀⠀⠀⠀⠀⢈⡯⠉⠉⣩⡉⠉⠨⣏⠀⠀⠀⠀⠀⠀⢨⠀⠀⠑⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⡎⠀⠀⠀⣿⡇⠀⠀⠈⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⡇⠀⠀⠀⣿⡇⠀⠀⠀⡟⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠲⡞⠀⠤⠄⠀⣀⠀⡇⠀⠀⠀⣿⡇⠀⠀⠀⡇⢀⣀⠀⠤⠄⠐⠶⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠤⠤⠤⠬⡇⢹⡶⠶⢾⣿⡗⡶⠶⢺⠃⡻⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢁⠀⣿⣿⣿⡿⢿⣿⣿⣿⠀⠃⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣰⣄⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣴⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠉⠉⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠉⠉⠉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⠀⠀⠀⠀⠀⠄⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠄⠤⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⣀⣼⣷⠶⣄⡀
⠀⠀⠀⠀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠛⣡⠞⠁⠈⠢⡀
⠀⠀⠘⠤⡐⢂⣉⡵⠦⡀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⣀⣠⣴⣾⡿⠛⠉⡠⠞⠁⠀⠀⠀⣠⣾⣆
⠀⠀⠀⠀⠈⠢⢔⢛⣮⣍⠶⣄⠀⠀⣜⣀⣠⣤⣶⣾⣿⠿⠛⠋⠁⠀⠔⠉⠀⠀⠀⠀⣠⣾⡿⢋⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠑⢶⣊⣻⣭⠵⠴⡿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⢋⣴⠟⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠄⠒⠒⠻⣦⣀⡛⣮⠡⠤⣐⢖⠐⡤⢄⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⣁⠴⠋⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠈⠟⡆⠘⢸⡟⣿⠃⡇⢸⠚⣀⣤⣴⣾⣿⠿⠛⣁⠤⠊⠁⠀⠀⠀⣠⡾⢋⡅
⠀⠀⠀⠀⢀⡇⠤⣐⣒⠆⠀⢰⣿⢀⣧⣥⣬⠷⢷⡛⣿⡿⠛⠋⣁⠤⠐⠈⠀⠀⠀⠀⢀⡠⠞⢁⣴⣿⠃
⠀⠐⠽⠋⠉⠹⡀⠀⠀⠀⠀⡼⠉⠀⢛⣉⣁⣲⣉⠽⠦⣚⣺⡉⠀⠀⠀⠀⠀⢀⡠⠒⠉⢀⣴⠟⠋⠎
⠀⠀⠀⠀⠀⠀⠈⠢⠄⠤⠚⠁⠀⠀⠀⠻⡉⠁⠈⠒⢍⡩⠷⣜⣓⣄⡠⠔⠊⠁⣀⣤⠾⠋⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⣤⠴⠷⠮⡩⠕⠐⠛⢢⠶⠛⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣤⣶⠾⠒⠋⠉⠀⠀⢀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⢿⣍⣹⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠟⠛⠉⣉⡠⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠏⠛⠁⠀⣄⣠⢦⣿⣿⣿⣿⣿⣿⡿⠿⢛⡛⢿⣿⣿⣿⣿⠋⠄⠠⠀⠀⢽⣦
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠊⢴⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡆⡛⢿⢣⣻⣿⡏⠃⠀⠀⣤⠀⠁⢸⣿⡇
⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠿⢿⣿⣷⡤⡺⣿⣿⣿⣿⠟⠋⠉⠈⠀⢀⠀⠀⠃⢧⠈⡆⢿⣿⣇⣄⠀⠃⢬⢀⣸⣾⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣥⣠⣼⣿⣿⣿⡿⠿⠛⠉⡏⢰⠻⣦⠀⠀⢸⡀⠀⠰⡘⣤⣇⢸⣾⣿⣮⣻⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣏⣽⣿⡟⢻⠟⠋⣹⣀⢀⣀⣬⣧⣺⡟⢿⣴⣴⣾⣷⣤⣤⣵⣌⣛⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⢻⣿⣿⣷⣾⣷⣿⣿⣿⣤⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢭⡏⠈⠢⠤⠌⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⢿⡿⠫⢉⡉⠉⠉⠛⣿⣿⢿⣿⣿⣿⣿⡏⣾⣛⡄⢉⣿⣿⣦⢹⣟⢇⣠⣿⣯⠂⠀⠀⠀⠀⠀⠄⢻⠿⣿⣿
⠀⠀⠀⠘⠟⣽⢛⠀⠉⠉⠀⠂⠀⠀⠀⠻⣷⡽⣿⣯⣿⣿⣿⣿⣇⡸⣿⣿⣿⣷⣬⡠⣉⡛⠿⢦⣥⣀⣀⠀⠀⠀⠘⠓⠈⠙
⠀⠀⠀⠀⣼⣛⣊⠈⠁⠀⠀⠀⠀⢠⡾⠟⣉⢹⣽⣿⡟⢯⠍⠛⠾⠦⠉⣽⠛⣿⣿⣿⣿⣿⡗⠲⣤⣍⣙⠛⠻⠿⠁⠀⠘⠀⣱⡄
⠀⠀⠀⠀⣿⣅⣈⣀⣤⣤⣤⢶⣦⠟⠁⠀⠁⣼⣿⣿⣿⢋⣶⣶⣶⣶⣶⣶⠐⣿⣿⣤⣿⣿⣿⣤⣀⣠⣍⣝⣿⣿⣶⣤⣶⠛⠓⠚
⠀⠀⠀⠀⣿⡆⠛⠮⠙⠷⠟⠋⠁⠀⠀⠈⣠⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⡅⢿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣉⣿⣿⠏
⠀⠀⠀⠀⠘⢧⣤⡀⣀⠀⠀⠀⠐⢀⣤⢾⣵⣿⣿⣿⢃⣷⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⡿⡃⠀⠁⣉⣾⣿⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠳⠶⢆⣀⣂⣈⡿⢞⣿⣿⣿⣿⡏⡸⣻⣿⣻⣿⣿⣿⣿⣿⡆⣿⣿⣟⣫⣅⣤⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣶⣶⣿⡿⣾⣿⣿⡿⢃⣷⣿⣿⣿⡟⣿⣿⣿⣿⣧⡸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡷⣻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣷⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⢹⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠉⠉⠉⠉⢧⡙⠉⠉⠉⠉⠈⢿

⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠈⠉⠉⠉⠉⠁⠂⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣀⡀⠠⠤⢀⣀⣀⡀⠤⠄⢀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠉⠙⢿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡟⣿⣿⣧⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣄⠙⢿⣿⣯⣝⣛⠛⠻⠿⠿⠟⠛⣛⣫⣽⣿⡿⠋⢠⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣉⠀⣿⣷⣄⠉⠛⠿⠿⣿⢿⣿⣿⡿⢿⠿⠻⠛⢉⣠⣶⣷⠀⣈⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⣿⣿⣿⣿⣿⣸⠑⠒⠂⠤⠄⠄⠀⠤⠤⠐⠒⠋⣿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⢷⠸⠘⡀⠈⠙⠻⢧⣖⣀⣀⣀⣀⣀⣀⣀⣀⣲⡬⠟⠋⠁⢀⠃⠆⡾⠉⠒⠢⢄⡀
⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⢸⠀⡆⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⢠⠀⡇⠀⠀⠀⠀⠙⢢⡀
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⡄⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢠⡇⠀⠀⠀⠀⠀⠀⠹⡄
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡔⠉⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠉⢢⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⣿⣿⠿⠿⠿⠿⠀⠺⠿⠿⠿⢿⣿⡆⠀⢀⣿⣿⡆⠀⠀⢸⣿⡿⠿⠿⠿⠇⠀⠿⠿⠿⠿⠿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣧⠀⠀⢸⣿⡇
⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡟⢸⣿⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⢸⣿⡿⠿⠿⠿⠃⢰⣿⡇⠘⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⣼⣿⢠⡆⣿⣿⠀⢸⣿⡇
⠀⠀⠀⣶⣶⣶⣶⣿⡿⠀⢸⣿⠀⠀⠀⠀⠀⣿⡿⢸⡇⢸⣿⡄⢸⣿⣷⣶⣶⣶⡆⠀⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛
⠀⠀⠀⠀⠀⢀⣤⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⠀⢰⣶⣾⣿⣿⣷⣤⣄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⣤⣀⣠⣄⠀⢀⣤⣀⣸⣷⠀⢀⣀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⣶⠶⠆⢲⣄⡶⢰⡶⢶⡆⣶⠀⠀⡶⠶⣦⢰⡶⢶⡄⢰⣶⠀⠶⣶⠖⢰⠀⣶⠶⣶⢰⣆⢰⡆
⠀⠀⠀⣿⣦⠄⠈⣿⡃⢸⣇⣸⡇⣿⠀⠀⡇⠀⣿⢸⣧⡼⠇⣼⢻⡄⠀⣿⠀⣼⠀⣿⠀⣿⢸⣿⣼⡇
⠀⠀⠀⣿⣀⡀⣸⠟⣧⢸⡏⠀⠀⣿⣀⡘⣧⣀⣿⢸⡏⢷⢀⡿⠺⣇⠀⣿⠀⣿⠀⣿⣀⣿⢸⡇⢿⡇
⠀⠀⠀⠈⠉⠁⠉⠀⠈⠈⠁⠀⠀⠉⠉⠀⠉⠉⠁⠈⠀⠈⠀⠁⠀⠁⠀⠁⠀⠈⠀⠉⠉⠁⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠠⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⣀⡀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠠⡴⢦⡚⠟⠛⠛⠋⠁⠉⠙⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⢉⢄⠠⠄⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠦⣼⢇⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠁⢘⡆⢀⠀⠀⡬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠈⠉⠉⠋⠙⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠆⠦⠼⢀⠀⢠⠃⠐⠃⠀⠀⠰⠃⠀⡠⠈⢠⠰⢿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡜⠂⡌⡿⠃⠀⠀⠀⠀⡀⠀⠐⠈⠃⠀⠘⢸⡄⢣⢹⡀⠀⡤⠂⡄
⠀⠀⠀⠙⠀⠀⠀⠀⢠⡄⠉⠙⠛⠋⠁⢀⣀⡠⠄⡎⡠⣶⡄⠀⠀⡇⠀⠀⡎⢧⣸⠀⡇⠀⠉⠈⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⠉⠀⠀⣰⣆⢷⠶⣧⣣⣪⣼⣄⢀⣘⣌⠻⡦⠇⠀⢀⠀⠀⡀⠆⡀⣀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡶⠿⠷⣿⠿⠿⠿⠾⣇⢽⠟⠛⣿⠋⠛⠟⠟⠛⠈⠀⢠⢿⠉⠁⠀⠈⠁⠘⡁⠈⠀⣸⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⣄⠀⠀⠈⠓⠓⡟⠃⠀⠀⠀⠀⢀⣠⣴⣿⣭⡀⠀⢀⣠⡴⢟⣣⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢹⢿⠁⠀⢀⣄⣰⡗⠆⠀⠀⠀⣴⣿⣿⡁⠹⠿⢗⣛⡩⡵⠞⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠈⠛⢹⡇⣁⠀⠀⠀⠈⠀⠉⠉⠁⠈⠛⠳⠦⠒⠊
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠠⠆⠀⠀⠀⠁⠛⣷⡄⠀⠀⢀⣀⠶⢿⣛⡈⠓⣄⡀⠀⠀⢀⣤⠐⠀⠄
⠀⠀⠀⠀⠀⠀⢰⣏⠤⠀⠀⠀⠀⠀⣾⠋⠤⢻⠀⠀⠘⢭⣕⢠⣬⡍⢘⡏⠀⠀⢀⣿⠃⠀⡀
⠀⠀⠀⠀⠀⠀⣿⡏⠒⢀⣀⣤⣶⡶⠃⠀⠀⣺⡇⠀⠀⣸⡏⢸⣿⠇⠈⣿⠀⠀⠀⢿⣧⣠⡁⢀
⠀⠀⠀⠀⠀⠀⢸⣏⡾⠯⠛⠟⠋⠀⡀⢐⣴⡿⠀⠀⠄⡿⠁⢸⣿⠀⠀⢹⡄⠀⠀⢠⡙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⡀⢴⣮⠟⠀⠀⠀⣸⠇⠀⢸⣿⣀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠘⠚⠉⠀⠀⠀⠀⢀⢃⣠⠞⠁⣿⠈⠳⣄⢸⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣮⠿⠁⠀⠀⠀⠀⠀⠈⠹⣷⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠀⠀⠀⠀⣼⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣝⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢔⡣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠑⠤⣉⡁⠒⠚⠟⠭⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠒⢉⣁⡴⠋⠒⢤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠲⠤⠐⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠸⢍⡤⠤⠒⠒⢉⣢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⠃
⠀⠀⠀⠀⠀⠀⠑⢶⡊⢉⣳⣤⡬⠗⢭⡭⢑⣒⠂⠴⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠴⣒⣒⡊⠭⠭⠒⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⠤⠛⢶⣈⣙⣦⡀⠀⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉⠉⠁⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⡉⣉⣷⣤⠜⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠲⢽⣦⡠⠬⠷⣶⣎⣉⣫⡲⢶⡒⠒⣤⣤⡤⠤⠤⠤⠤⠄⠖⠒⠚⠉⠉⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⢟⢾⡉⠙⡍⣤⣖⣶⣽⠝⡄⠘⡀⣱⣀⣀⣀⣠⣀⠠⠤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⡎⣷⠀⢸⢹⡏⠻⣆⠀⡇⢀⠋
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⢒⣊⣩⠇⠀⠀⢰⣿⠀⣸⠤⠄⢒⣚⠿⢿⡓⢒⣄
⠀⠀⠀⢸⣹⠞⠓⠊⢫⠉⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⠀⠀⠈⠲⣖⠊⣙⣧⣤⠝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡤⠼⠳⣎⡉⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡂⢉⣙⢦⡤⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⠤⠛⠒⠉⠉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠉

⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢰⣿⣷⣷⡄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀⠀⠀⠀⣀⣤⣤⣤⡀⠀⣀⣤⣤⣤
⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⡟⣽⣿⡏⣧⠀⠀⢠⣤⣤⣿⡟⣿⣿⣿⡿⠃⠀⠀⠻⠿⠾⣿⣿⣤⣟⡿⠶⠿
⠠⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠⡿⢸⣧⠀⠀⠀⠘⠛⠋⠹⠇⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃
⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⣲⣶⣶⣄⠀⠀⠀⠀⠰⣿⣷⢀⣀⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣷⣦⡴⣶⡦
⠀⠀⠈⣿⣏⣹⣿⠁⠀⠀⠀⠀⠈⢱⣿⡿⢃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡶⢿⣿⣷⡩⢿⠃
⢀⠄⠀⠿⢿⠿⠿⠂⠠⡀⠀⠀⠀⠪⠉⠰⣿⣷⠆⠀⠀⠘⢿⣿⣿⣿⡿⠏⠀⠀⠀⠸⡟⣧⣜⣻⣿
⠈⠁⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠄
⠀⠀⠀⡀
⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⢠⣾⡂⢀⡀⠉⠉⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣿⡆⠀⠠⣄⡀⢀⣠⣤⣀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⢠⣇⢻⣿⢾⣃⡤⣶⠀⠀⠀⠀⣸⣿⣿⡿⠿⠻⠛⠁⠀⠀⠀⠑⣾⣿⣿⣿⡆
⢀⡾⢿⡿⢷⡆⠀⠀⠀⣿⣿⡿⠉⠀⠉⣾⣿⡷⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠻⠷
⠘⠁⠘⠇⠈⠇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⡀
⢀⣴⣿⡾⣶⣄⠀⠀⠀⠀⢠⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣷⣦⣀
⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⣼⣿⣟⣟⣧⣄⡀⠀⠀⠀⠀⠀⠈⠿⠈⠉⠑
⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⡟⠿⠿⠗⠀⠀⠀⠙⢻⠿⠿⡿⠿⠿⣟⠋⠀⠀⠀⠀⢀⠂⠂⢂

⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⣀⣁⢨⡭⣄⣁⣂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⢈⣤⣊⠽⠓⠛⠉⠉⠙⠛⢚⠿⣷⣪⡐⠄
⠀⠀⠀⠀⠊⣴⡵⠋⣡⡤⣴⣒⢲⠢⢤⢄⡀⠀⠈⠙⢿⡌⠄
⠀⠀⠀⠀⣼⣟⣴⣯⠶⡋⣁⡼⣿⡿⡿⢳⠿⣶⣄⠀⠀⠙⢀
⠀⠀⠀⢰⣿⡍⠇⠀⠀⠣⡙⠾⠿⠛⣡⠎⠀⠀⢙⡧⠀⠀⡘
⠀⠀⠀⢸⣷⠉⠓⠶⣶⣦⡬⣝⣲⣯⣥⡔⠾⠛⠉⠀⠀⠀⡄⢀
⠀⠀⠀⢌⠻⣆⠀⠤⢄⣀⡀⠈⠀⠀⠀⠀⢀⡀⠔⠃⠀⡜⠀⢸
⠀⠀⠀⠈⠳⡈⠑⠦⢄⡀⠉⠉⠉⠉⠉⠉⠀⠀⢀⠄⠃⠰⠃⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠭⢍⣛⢒⠩⠍⠖⠋⣠⠂⠠⠋⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⡐⠐⠁⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⠀⠈⢀⠜⠁⠀⡔⠡⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠀⣀⣴⠓⢃⠀⠀⠀⠀⠠⠐⠀⠂⠒⢂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠠⢄⡀⠀⠀⠀⠒⠀⠁⠢⠰⠤⠦⠾⠖⠛⠉⠀⠀⣼⠀⠀⠀⠈⠀⠀⠉⠈⠉⠀⠀⠀⠀⢀⢠⠤⠐⡀
⠀⠀⠀⠰⠀⠐⠀⠈⠀⡀⠂⡁⠐⠢⡀⠐⢄⠀⠀⠀⠀⠁⠀⠈⣼⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠓⠒⠚⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⣀⣀⣐⣤⣾⢻⡄⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠋⠀⠁⢰⠇⠶⠌⣁⠠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠁⠀⠀⠀⠀⠀⣤⢠⡤⡈⠢⡶⠶⠛⣦⣴⣀⣶⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡥⢼⠔⣵⣄⣴⡿⠋⠁⠱⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠘⠛⠾⠁⠀⠘⠀⠠⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠤⠤⠤⠤⠴⠶⠟⠁⠊