Sunflower Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⡉⠀⣀
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢠⣿⡦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⣷⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠘⠟⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⠻⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠐⠖⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⡦⢄⡀⠀⠹⣇⠀⠀⠀⠀⠹⣇⠸⡇
⠀⠀⠀⠀⠀⠀⠠⣤⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⡓⢦⣉⠳⣦⡀⠀⢀⠘⣷⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠙⢷⣬⡱⢌⢷⣦⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢈⣉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣾⣿⣿⣶⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⡉⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢾⣿⣿⣿⣿⣿⣮⣿⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠚⠻⢿⣿⣿⣿⣿⣟⣳⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠶⠶⢶⣾⣿⣿⣿⣻⣮⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣤⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⣀⡠⠴⠶⠟⢛⣽⣿⣿⣿⣽⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡿⣿⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣶⣶⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣁⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠋⠉⢉⣁⣌⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠋⠉⢘⣿⣿⣿⣴⡛⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠐⠓⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⠟⢉⣿⣿⣿⣿⣾⣻⣾⡏
⠀⠀⠀⠀⠀⠀⠰⠶⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⣰⡿⣟⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⠶⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠤⠀⢠⡼⠋⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⡤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⠀⢀⠠⠐⢁⣠⠞⠁⠀⢀⣴⣽⡿⢛⣼⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠐⠊⠁⠀⠶⠋⠁⠀⠀⢠⣈⣿⡟⢀⡾⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣼⡿⠀⣾⡇⠸⠋⡶
⠀⠀⠀⠀⠀⠀⠘⠛⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⡆⠠⠞⠁⠀⠐⣿⡇⢠⣿⠃⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠘⠛⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠁⠀⠀⠀⠀⠀⢿⠀⣼⡿⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠘⠟⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠰⠦⠀⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠲⡙⠟⢑⡄⠶⠲
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣛⣻⣿⣿⣇⡀⠀⠀⠘⣓⣌⠙⣄⠀⠀⢀⠈⡝⠀⢠⠆⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣷⣿⣿⣿⡯⣠⠾⢏⡁⠈⠉⢽⣿⣦⣾⣾⣿⣧⡼⢂⡠⠴⠋⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡿⣻⣽⡿⠙⠁⠈⠓⠩⣭⡴⠤⠄⢺⣿⣿⣿⣿⣿⣿⣿⣶⡚⠉⠉⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠸⣇⠀⠀⠀⡰⡢⢀⠀⣐⡿⢛⠻⢿⣿⣿⣿⣿⣿⠿⠑⢄⡀⠠⠄⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⠋⠀⢭⠶⣏⡰⢋⢔⡿⢻⢟⠿⣏⡉⠀⠀⠀⠹⡏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡞⢠⠋⠁⡠⠚⢀⠌⠣⡀⠀⢏⠀⠈⠂⣄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀⠀⠀⣷⠀⠀⠀⠀⠀⠘⠆⣾⡄⠰⠛⡀⢀⢻⡄⠏⠁⠺⠅⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⡵⡀⠀⢹⡄⠀⠀⠀⠀⠀⢰⡟⠈⣡⢀⣢⡎⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⢻⡂⡈⢂⠘⣇⠀⠀⠀⠀⢀⣿⣡⠾⠛⠭⠋⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⡇⠁⠆⠙⣿⠀⠀⠀⠀⣰⠟⠁⠀⠁⠀⠀⠀⠀⠀⢀⠈⢁⣤⠅⢒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀⣚⠀⠱⣷⢁⠰⠈⢾⡳⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⠔⠋⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠁⡉⠳⠄⠸⣎⠒⢀⢚⣻⠊⡄⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠋⠂⣀⠀⢀⠹⣷⠇⠈⣌⡄⣣⣾⠃⠀⠀⠀⠀⠀⡠⡊⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠡⢂⡈⠀⠉⠑⢻⣖⣾⢯⡀⣃⣿⠀⠀⠀⠀⢀⠞⠁⠀⠀⣀⡀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡁⠐⠐⠂⢿⣇⣹⣿⣿⡏⠀⠀⠀⣠⠋⠁⠀⠀⠀⡀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⠂⠀⠐⠂⢹⣿⣿⣽⡇⠀⠀⣰⢏⠁⠀⠀⢈⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠻⣿⣿⡇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⢠⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠒⠀⠁⠀⡆⡀⡄⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢔⣤⣴⣶⣶⣶⣿⣧⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⣾⣾⣿⣟⣿⣿⡿⡿⣤⠒
⠀⠀⠀⠀⠂⠀⠁⠁⠀⠀⠀⠤⣄⠀⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣽⣽⡅⠒⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡒⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠠⠘⢻⣷⣝⣟⣾⣯⣿⣿⣿⢿⡁⠁⠢⠍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⠚⠋⡟⠛⢿⠛⠉⠉⠄⠀⠀⠀⠀⠀⠀⠠⡀⠈⠁
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⠦⠄⣩⡐⠤⡀⡜⠀⢱⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠤⢨⣆⠀⠀⠙⡄⢹⠀⠀⡸⠋⠸⢠⣩⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠈⠳⡀⠀⢡⠀⡆⢰⠅⠀⣻⠟⠋⠀⣾⣠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣰⣐⠛⠛⠲⠦⣀⣰⣷⣾⣿⣿⣿⣶⣾⡀⡠⠤⠼⢿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠉⠻⢄⣀⠀⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣤⣶⣅⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠄⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣨⠙⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⡦⠄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣦⡚⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡟⠁⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠈⠑⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠒⡤⠤⠴⠊⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠒⠶⣤⠠⠶⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡞⠐⢻⣿⢿⣿⣿⣿⣿⣿⣿⠻⠀⠙⢦⡀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢙⠠⠘⡩⠃⣠⠟⠁⠀⠁⣿⠉⠁⠙⡈⣦⡀⠀⠀⠙⠉⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠸⢻⡄⠀⠀⠀⢯⢸⠀⠀⣇⠁⠑⠂⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡡⠐⠀⠀⠘⢳⡄⠐⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⠣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡤⠀⠠⠂⢀⡤⠛⠀⠘⠋⠀⢠⡄⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣦⠀⠁⠀⠐⠀⠘⠃⠈⠁⢦⣦⡄⠀⠀⢸⣇⣴⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠂⣀⠹⠆⠈⠀⠀⠀⣀⢄⣴⣤⠂⠀⣼⣿⣷⠀⠰⣿⣙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡶⠊⠁⣀⣀⣠⣤⣤⢶⠟⠋⠉⢀⣠⣾⣿⡉⠀⢸⡆⠈⡿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡄⠻⠿⠛⠛⠋⠉⢁⣤⣠⣴⣾⣿⣿⡿⠼⣷⡄⠘⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠺⣿⣿⣼⣷⣶⣾⣷⣿⣾⡿⠿⠿⠿⣿⣭⣅⠀⣀⣉⣤⣤⡙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣿⡿⠋⢀⣈⣽⣿⡛⠉⢉⣿⣭⣦⡀⣾⡟⠉⠉⠳⣄⠀⠈⠙⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡶⠟⣩⣥⡞⠀⠟⡛⠛⢿⣄⡼⠛⠻⡟⠀⠙⢿⣶⣄⡀⠈⣷⣏⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠞⡟⢀⣀⣼⡇⠀⢾⣻⡇⠀⠀⡇⢄⠀⣸⣶⡈⣿⣶⣎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢿⠃⠈⣅⠀⣤⠠⠟⣼⢿⡛⢿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣉⣀⣀⡁⠈⠃⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠛⠋⠙⠛⢻⡆⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡿⠛⠛⠛⠿⠶⣄⣿⡀⠀⠀⠸⣿⡇⠀⠀⠀⠀⡴⠀⣠⡶⠂⠀⣀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣤⣾⣿⠿⣿⡿⠶⠶⠒⠒⠲⣤⡀⠀⣾⣧⠀⠀⠀⠀⣁⣞⡁⢠⠔⠊⣡⣴⣿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢛⣉⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⣿⠀⠀⣰⣿⣿⣿⡿⠷⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⢀⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡇⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⣰⡿⠟⣁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⢰⣦⣽⣦⣶⣿⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣨⣴⡶⠛⠉⠀⠀⠀⢹⡀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠀⠀⠀⠀⠀⠀⠈⣷⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣤⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣬⣿⣉⣿⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢀⠀⣀⢀⢀⠀⣀⠀⢀⡀⠀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⢀⠐⠉⠀⢀⠠⠀⠀⠀⠀⠰⣿⣿⡇⣼⣿⣋⣿⣧⠀⣿⡥⠘⡿⣿⣿⢺⣿⢸⡏⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠁⢨⡥⣤⡄⣥⡌⣬⡤⢤⡅⣠⣤⣤⣠⣠⣤⡤⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠈⠀⢨⣻⠾⣧⣿⠿⣿⡟⢹⣇⣿⣼⢻⡟⡟⣿⣏⣼⢿⡅
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢀⡀⠀⢰⣶⣴⣶⣆⣶⣶⣠⣰⣶⣶⣰⣠⢶⢤⡶⠄
⠀⠀⢀⣀⡀⠈⡈⠀⠀⠀⠀⣱⠞⠉⣅⠀⠘⠠⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⣸⠿⠻⠿⡷⠻⠿⠟⠇⠿⠏⠻⠻⠽⠧⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⣀⣶⢿⡏⣼⣯⡞⢂⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢠⡒⠁⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢀⣿⣿⣷⠍⣿⡟⠵⣠⠪⡂⠀⢻⣂⠄⠀⠀⠀⠀⠀⢈⠳⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠐⠃⠀⠀⠀⠀⠀⠀⠐⡆⠀⢸⡿⣾⣿⣷⣤⣃⣰⢾⢯⣷⠀⢈⡏⠀⠀⠀⠀⠀⠊⠀⡐⣶⣶⣶⣶⢶⣶⡖⣦⣶⣶⣆⢶⣶⣶⢶
⠀⠄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⢿⣿⡿⣟⣿⢿⣽⣿⣿⡟⠀⢰⡇⠁⠀⠀⠀⠀⠠⢀⢻⣦⣤⣤⣰⣟⣻⢸⣿⡷⠀⣷⣿⡗⡟⢾⡀
⠀⡐⠀⠀⠀⠀⠀⠀⠀⠰⢃⡀⠈⡹⠿⣿⣿⣿⣿⠟⠋⠀⣠⠯⠀⠀⠀⠀⠠⡄⠤⠤⠾⠁⠉⠉⠁⠉⠉⢉⣉⠁⠀⠈⠉⠉⠁⠉
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⣀⠀⠀⠉⠉⠀⠀⣠⠞⠁⠀⠀⠄⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢠⣤⡤⣭⣤⣤⡄⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⣥⣭⣭⡍⠁⠉⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠂⠀⠀⠀⠀⢠⣄⡀⣠⣀⡀⣻⣛⣇⣻⣣⢀⣀⢀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠻⠷⠸⠿⠿⠿⠿⠿⠛⠾⠛⠿⠞⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡤⡀⠀⠀⢀⠎⠙⢦⠤⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡶⣤⡀⢐⠀⠀⠁⢜⡄⢀⡞⠀⠀⠘⡇⢀⠔⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡇⠉⠓⢎⡀⠀⠙⢾⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⡷⠁⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠙⢄⠀⢸⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⠀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠈⢆⠀⢇⠀⠀⠀⢸⠀⠀⠀⠀⣠⠃⠀⠀⡰⠀⠀⠀⣀⠬⠤⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠛⠋⠳⡕⢄⠀⠀⠀⠘⡄⠘⡄⠀⠀⢸⡀⠀⢀⡔⠁⠀⢀⡜⠁⢀⣤⠾⠒⠈⠉⠉⠑⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⢎⠳⣄⠀⠀⢳⣄⢹⣆⡠⠘⢧⡤⣾⠁⢀⡴⠋⢀⠔⠊⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠉⠲⢄⡀⠀⠈⠓⢮⣢⠠⡖⠁⠈⠨⠃⠂⠖⢂⠆⠑⢋⠀⡴⠁⠀⣀⣀⣀⣀⣠⠄⠤⡀
⠀⠀⠀⠀⠀⣠⠔⠛⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡸⡇⠀⠊⠀⠀⠀⡀⠄⠀⠀⠀⠄⠈⠹⣃⡴⠟⠋⠉⠉⠀⠀⢀⣌
⠀⠀⠀⠀⣀⣉⡑⠂⡤⠤⠤⠤⣀⠀⠈⢛⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠁⠀⠀⣐⣏⣀⠠⢤⣀⠀⠀⣴⠋⠈⠢⡀
⠀⠀⠀⠀⢱⡀⠈⠁⠀⠀⠀⠀⠀⠉⠛⠒⢺⡧⠀⠀⠀⠀⡠⠐⠒⠘⠁⠈⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⣩⠟⠢⡉⠑⠢⠤
⠀⠀⠀⠀⠀⠙⠒⢤⣀⠀⢀⣀⣀⠀⠀⣀⣈⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣁⣀⣠⠔⠚⠣⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣋⠭⠤⠤⠤⠐⠒⠛⢛⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡴⠚⠻⡍⠉⠀⠀⠀⠀⠈⠦
⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⣀⡤⠔⠛⣩⡯⠾⢦⣀⣀⣀⠀⢀⡀⣀⣰⠋⠀⠀⠀⠈⢶⡤⣤⠄⣀⡀⣈⣂
⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢀⡤⠞⢉⡤⡾⠋⠁⠀⢠⠖⠋⠉⢩⠟⠉⢻⠉⠉⣧⣄⣀⣀⠤⠤⠛⠈⢆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡉⢀⡴⢺⠃⢀⠴⢉⠎⠀⠀⢀⣴⠁⠀⠀⡴⡏⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⣾⡴⠁⠀⡞⠀⠀⡰⠋⡇⠀⠀⡼⠁⡇⠀⠀⢸⠀⠀⢸⠦⣀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢸⠀⢀⡞⠀⠀⢳⠀⢰⠁⠀⢣⠀⠀⢸⠀⠀⠀⡇⠈⠉⠓⠒⠒⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⢀⠎⢰⠀⢠⠞⣆⣌⠀⠀⠀⡷⡄⠀⣧⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠀⠈⣦⠊⠀⠈⢻⡀⠀⢰⠁⠈⠢⡼⠈⠢⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠃⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⡠⠀⠀⠀⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢠⣿⠞⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢱⠀⠀⡇⢀⡧⡀⢐⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠤⣴⠶⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢦⡀⣿⣎⣀⣀⡿⣼⡟⣵⣿⣃⠔⠀⡠⠞⠁⠀⠀⠀⠀⣠⣠⣤⣾⣿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡈⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣡⠊⡀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠄⠚⠁
⠀⠀⠀⠀⠀⠶⠶⠦⠄⠀⠀⠀⠀⠈⠑⠲⢤⣁⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣥⣾⠆⢁⡔⠀⠀⠀⠀⠀⠀⠀⢠⢔⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣤⣬⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡭⠭⠥⠤⠀⠐⠚⠁⠀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣻⣫⣥⠦⠔⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⡄⠀⠀⠀⠀⢨⣶⣦⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠂⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣍⡀⠀⠀⠀⠀⠶⢾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣈⠉⠁
⠀⠀⠀⠀⠐⠀⠶⠶⠒⠂⠀⠈⠓⠀⠀⠀⠀⠤⢀⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣬⣁⡀⠀⠀⠰⢒⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢀⣠⠶⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠉⠻⠛⠳⢤⡀⠀⠉⠢⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⢀⣀⢀⡀⠀⠉⠁⠀⠋⠁⠴⠋⠁⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⢿⣇⠀⠀⠀⠢⣄⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡛⠀⠀⣿⡟⡏⠹⣿⣿⡙⢿⡀⠹⣿⡔⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⢉⠀⠀⠀⠀⢀⠔⠀⢠⠀⣸⡇⠀⠀⠛⠁⢇⠈⢣⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠂⠈⠠⠀⠀⢠⠟⠀⠀⠀⣠⡁⠀⠀⠀⠀⣱⠁⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⢀⡴⠛⠠⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⡟⡈⠀⠀⠀⠀⠀⠀⢠⡇⢀⠂⠀⠐⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⠄⠀⢰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣧⣦⣶⣤⣆⡄⠀⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⣄⡀⢸⣶⣼⣿⣿⣿⣿⣤⣤⡄⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣂⠀⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡠⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠞⠉⣩⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⣀⣤⠞⠁⢈⣿⠿⢻⡟⠙⢿⡗⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠠⣾⡇⠀⢸⣧⠀⢠⡑⢄⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣹⠀⠀⢀⠀⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣿⣦⠀⠀⠀⠠⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠤⠡⣈⠋⡙⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣄⡀⠑⢶⣿⡧⢹⣆⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠊⠀⠉⠒⢄⡀⠀⢸⣿⠀⠀⢐⣿⣏⣉⠙⠻⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⠀⠀⠸⢿⣿⠛⠷⣢⡀⢩⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠛⠷⠛⠒⠀⠀⣿⡇⠀⠀⠀⠀⠈⠙⢷⣮⡻⢷⣽⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆⣿⡼⠿⠞⠷⠻⢶⣼⡗⠀⣀⣀⡀⠀⠀⠀⠈⠛⠶⣿⣿⣿⣦⣠⠤⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠟⠋⠀⠀⠀⠀⠀⠀⣈⣿⠇⠠⣄⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣯⣕⡀⠀⠘⠂⠠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣧⣤⡀⠠⣔⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠯⡄⢍⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡷⣆⢀⡴⢶⣴⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⣤⣰⣦⣄⢀⡞⠀⣸⠋⠀⢸⡇⢸⡧⢶⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⢹⡄⠀⢹⡇⠈⠻⣇⣾⠇⠀⠀⢸⣷⠏⠀⣸⡶⠛⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣉⠩⣹⡍⠻⣧⡘⣼⡇⠀⡀⠹⣿⠀⠀⢀⣿⠋⢀⡴⠋⠀⢸⡟⠛⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠒⠛⠳⠾⢿⡀⠈⠙⢿⣿⡀⢷⠀⣿⢀⡇⣾⣏⣆⡞⠁⠀⠀⢸⣧⡤⠾⠗⠒⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦⠽⠷⣤⣀⠀⠀⠙⢮⣦⡈⠻⣷⢸⣿⣿⣼⣷⣿⣾⣿⠁⢀⡄⢀⡾⠁⠀⠀⣠⠾⠷⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠉⠙⢶⣴⡌⣳⣽⣷⡿⡿⣿⣻⣟⣿⣿⣿⣿⣷⢏⣠⡾⠶⠶⠶⠿⠷⣶⡆⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠠⣶⠶⠛⠉⠙⠳⢤⣤⣽⣿⣿⣿⣿⡯⣯⣟⣿⠼⡝⣷⣣⣟⣿⡷⣋⡥⠖⠀⠀⢀⣠⠞⠳⠶⢯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣄⣀⣀⣤⣬⣿⣿⣟⢻⣯⣷⢻⣸⣟⣯⣯⣿⣻⣺⣿⣥⣴⣶⣶⣞⡋⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠉⠁⢀⣉⣩⣽⣿⣿⣿⠯⡿⣗⣯⢿⢺⣿⡷⣷⣿⠼⣭⣻⣿⡿⠛⠛⠻⣿⣋⡉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢨⣽⡿⠛⣛⠉⣡⡴⠿⢻⣿⣿⣿⣹⡍⣽⢚⣟⡷⣿⣻⣭⢟⣣⣿⠿⣭⣍⣉⣀⣤⣽⠿⠳⣤⣶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⣩⠟⠁⣀⣀⣀⣴⣾⣿⣷⣾⣽⣛⠾⣛⣏⣷⣾⣾⣟⠀⠀⣹⣶⣏⣁⠀⣀⣠⡴⣿⡷⠾⠗
⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⡿⠛⠛⣋⣩⣵⠟⠉⠁⣀⣿⡉⠙⢿⣿⢿⣿⣟⠋⠉⠙⣿⡿⠿⠧⣤⣉⠛⢿⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣳⠟⠋⢉⡟⠁⠀⠈⠉⠀⠈⣻⣾⡶⣿⠋⢻⢻⡿⡷⠦⡼⣿⠒⠲⢤⡉⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⣹⣿⠟⠛⠛⠛⣛⣻⣿⠋⠻⠀⡏⠀⢸⠈⡇⠹⣄⠀⢸⣯⣄⣀⣀⣀⣸⡗⠛⠋
⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣻⣟⣚⠛⠛⠉⠉⠁⢹⡄⠀⠠⡇⠀⡎⢠⡷⣤⣈⠁⠀⣧⠀⠉⠉⠀⠈⠛
⠈⠻⣥⡀⠀⠐⠶⠦⢤⣤⣄⣀⠈⠉⠙⡛⠳⢦⣄⠀⠀⠙⢦⣄⣧⠀⠀⣼⠁⠀⠉⠛⠶⣼⣆
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠚⠛⠛⠳⢶⣿⣀⠀⠉⠳⣄⠀⠀⠈⢻⡄⠀⣿
⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠠⠤⠴⠶⠚⠛⠿⣦⡀⢹⣆⠀⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣿⣦⡀⠀⣿⠈⢹⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⣠⠖⠊⠀⢀⡀⠈⠉⠛⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⣤⣤⡴⠶⠻⣯⡈⠻⣆⢸⠀⢸⡆⠀⠀⣼⠋⠀⠀⢀⣠⣿⣷⣾⣛⣉⠉⠉⠁⠀⠀⠀⠀⠉⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠙⣿⠀⢸⡇⠀⢸⡇⢀⣤⠾⢿⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠀⢸⣧⡶⢿⣿⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠋⣠⡾⠛⠛⠶⣤⣤⣀⣀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣶⣶⣶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣥⣬⣥⣼⣤⣼⣬⣼⣯⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⠊⡆
⢰⠀⢠⠇⡄⡇⠀⠀⢀⢆
⡎⠄⡎⢰⡇⢧⡀⠀⡞⡈⢧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⢸⠁⣼⡇⣾⠀⢰⠁⠗⠀⠳⡄⠀⠀⢀⡼⡇⠀⣠⢾⠁
⠀⠀⠣⣿⣿⠃⠀⢸⠀⠀⠀⡀⠹⡄⣠⠏⠀⣇⡼⠁⠘
⠀⠀⠀⢻⡏⠀⠀⠀⠆⠀⣇⣁⣄⡿⠃⠀⠀⡟⢰⠁⢰⠀⣼⠀⠀⠀⢀⡔
⠁⠀⠀⡼⠀⠀⠀⠀⢸⡀⣿⣿⡟⠀⠀⠀⠀⣿⣿⠀⠸⣰⠃⣇⡠⠀⡸
⠀⢰⣰⡇⠀⠀⠀⠐⠈⣇⣿⠏⠀⠀⠀⠀⠀⣿⣿⣠⠞⢁⡤⠋⠀⢠⠇⡠⠔⠊
⢠⠀⡟⢠⠀⠀⠀⠀⡀⢸⡏⠀⠀⠀⠀⠀⠀⣿⡿⠁⡴⠋⠀⠀⠀⣸⣭⠂⣜⡠⠐⡇⠀⢀⣴⠁
⢸⣴⠇⡘⠀⠀⠀⠀⠇⢸⡇⠀⠀⠀⠀⡀⠀⣿⣴⠟⠁⠀⠀⠀⠀⣿⠿⠚⠉⠀⠀⣧⠴⢡⡇
⠠⣿⠀⡇⠀⠀⠀⠀⢠⢰⡇⠀⠀⠀⠂⠁⢠⡿⠁⠀⠀⠀⢀⠀⡼⠁⠀⠀⠀⠀⠀⣷⡞⡼
⡆⣿⣀⣧⢀⢰⡄⠀⣼⣿⡇⠀⠀⡘⠰⠀⣼⠀⠀⠔⠀⢠⠂⣰⠇⣀⢀⠀⠀⠀⣠⡏⠼⠁⢀⣠⣒⣁
⣾⣿⣿⣼⣿⣿⣤⣶⣿⣿⣧⣴⣶⣷⠁⣼⣿⢃⠎⠀⢠⠃⣴⣿⣿⣥⡤⠤⠒⠉⠁⠀⢀⡴⢛⠔⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡕⣅⡔⡰⢁⣾⠿⠛⠉⠁⠤⠂⠀⠈⠀⣴⣟⡵⣥⠆⠀⠀⣀
⢻⣻⣯⢤⣻⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⢾⣴⣋⣡⠖⣊⡥⠖⠁⠀⠀⣠⣞⡡⠀⣰⡃⠔⡐⠋⢀
⣗⣲⣙⣎⠷⣿⡟⣾⣻⣉⣦⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠗⢋⠡⠀⠀⠀⣠⠾⠛⠛⠛⠉⠉⢉⡭⠊⠉
⢾⣿⣿⣿⣿⣽⣿⣧⣿⡤⣛⠾⣼⠥⣿⣿⣿⣿⣿⣿⡷⠾⠛⣉⣤⣶⣿⡁⠀⠀⠀⢀⣤⣖⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⢻⡗⡶⣧⣽⣿⣿⣿⣷⡦⠶⠿⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠚⣒⣠⡤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⠧⣟⢛⣿⣿⣯⣴⣶⣯⣥⣔⣢⡤⠤⠀⠶⠖⠓⡀⠀⢀⡠⠐⠚⠛⠋⡀⠐⠢
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⡴⣛⣋⣿⣿⣿⣿⣿⣿⡥⠴⠖⠒⣀⠠⠐⠊⣁⣤⣶⡿⠛⢉⡩⠙⠉⠀⠀⢀⣀⡴⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⢭⣚⣝⣻⣿⣿⡟⠛⠛⠒⠊⢉⣉⣤⣤⣶⣿⣥⡤⣤⣈⡉⠙⠒⠒⠒⠊⠉⡡⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢺⢥⡜⣹⣿⣿⣿⣶⣿⣿⣿⣻⣖⠤⠤⣉⠙⠛⠲⢶⣒⠒⢒⣀⣈⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣴⡀⢀⢠⡀⠘⠀⣸⣰⠞⣠⢃⠄⡠⢂⡴⠃⢀⡾
⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⡄⠀⠳⡜⡄⣇⢠⣠⣿⡏⣰⣣⠈⢀⡴⠛⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣜⢦⣀⣼⣷⣿⣿⣿⣿⣿⣿⣷⣾⣿⠤⢀⡀⠄⠐⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠞⢥⡀⠀⠀⠒⠒⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⣉⠀⠀⠀⠀⠀⢲⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣀⣤⣤⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠦⣄⡉⠉⠉⠋⡀
⠀⠀⠀⠀⠀⠉⠀⠐⠶⠛⣻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⣿⣧⠀⠉⠁⠒⠶⠟⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠈⠻⣷⣄⠀⣤
⠀⠀⠀⠀⠀⡀⠋⠀⢀⠔⠁⢠⠟⣿⣿⣿⢻⣿⣿⢹⣧⡉⠀⠂⣄⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⢨⡏⣼⠘⡏⡃⢸⣿⠘⣆⣿⣿⣷⣤⢼⣿⣿⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠃⡇⢀⠀⠇⢸⣿⠄⢹⣿⢻⡟⢹⡆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠸⠀⠀⣤⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠠⠀⠀⠈⡀⢀⡄⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣢⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⠻⡿⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠶⠗⢡⡄⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠙⠋⠿⠉⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣶⣶⣤⣧⠀⠀⠁⠀⠀⠀⠀⠀⢤⠀⡀⡀⢀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣾⡟⢹⣿⡖⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣾⣿⣿⣿⣿⣷⠆⠉⠒⠀⠀⠀⠀⠀⠈⠉⠉⠺
⠀⠀⠀⠀⠀⠀⠐⠀⠻⣁⠻⣦⠉⡼⠻⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠂⠸⠽⢤⣤⠉⠀⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⡀⠿⠟⣩⠉⠘⠘⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠦⠈⠀⠀⠀⠀⣀⣶⣾⣿⣿⡟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣟⢿⣿⣿⣟⡟⠃⠀⠀⠀⠀⠀⣀⣄⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣠⣄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⣦⠦⣦⠄⠀⠠⡿⠟⠿⠚⢳⠉⠁⠀⠀⠐⡀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⣠⣤⣼⣯⣿⣿⣿⣿⣿⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣶⣿⣿⣆⢰⠇⠀⠀⠀⠴⠛⠀⠀⠀⠀⠀⣄⠸⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠩⠷⣿⣿⣿⣿⣿⣟⠹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⢹⣿⣿⣿⣿⡏⠿⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠓⠀⠙⢾⠞⠻⠋⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣿⣦⣻⣟⠛⣭⠛⠀⡐⠀⠀⠀⠀⣰⡆⣀⢠⡶⣀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠔⠘⠋⠛⠁⠀⠀⠄⠀⠀⠀⠀⣜⢇⣴⡿⠒⠆⠈⣉⣿⣬⣳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠃⠀⠀⠀⠀⠀⢿⡿⠿⠉⠀⢀⣴⣿⣿⣿⠍⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⡴⢶⡶⠦⡄⠐⠚⠛⢛⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⣷⣤⡀⠀⠀⠀⢀⠀⠀⠘⢄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡉⠙⠀⠁⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⡀⠀⠀⢳⣿⣿⣿⣿⣿⣤⠔⠀⠈⠀⠀⠀⠈⠙⠾⡦⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⡤⣙⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣼⠿⠋⠁
⠀⠀⠀⠀⠀⢘⡀⠀⣾⣿⣿⣿⣿⣿⣿⡋⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⠍⠙⠒⠧⢄⡀⠀⠀⠀⠀⠈⠈⠟⣧⠀⠀⠀⠀⠀⠀⢠⠟⠋⠁⠈
⠀⠀⠀⠀⠀⠈⠁⠒⢿⠻⠿⣿⡿⠿⡋⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠱⠊⠶⠂⠋⢆⡚⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⠿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠂⢇⠀⠀⡩⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡔⢤⠘⣤⠐⢀⢠
⠀⠀⠀⠀⠀⠀⠡⡌⠃⠾⠀⠴⠖⢈⡀⣜⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠁⡘⠧⠀⠄⡅⢶
⠀⠀⠀⠀⢠⣕⠒⣃⣊⠐⣦⣄⣌⢛⡉⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣀⡀⢄⣠⣵⣾⣻⡆⡠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠂⠀⢈⣾⣿⣿⣏⢘⣃⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠐⡤⢢⢴⠀⠄⠀⠀⠀⠀⠜⢊⡁⢈⣿⣿⣏⠋⡈⠿⢺⠞⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠒⠀⢀⠎⢻⠁⠀⠀⡞⠉⢠⠄⠀⠘⠧⢰⢆⠉⠫⢢⣶⢦⡲⣾⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠔⠂⠄⠀⠀⠀⠀⠒⠈⠓⠤⣄⣼⣶⣾⣶⣷⣤⡠⠀⠈⠶⡀⠰⠤⡃⡞⠀⠚⠀⠅⠐⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⢓⠀⠀⠀⠘⠆⡀⠈⢋⡁⢤⣤⣾⢣⣷⣿⣷⣶⣹⣧⣄⡊⠐⡱⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠠⠄⠂⠠⡀
⠀⠀⠀⠀⠠⠒⠈⠑⡄⠀⠀⣷⡏⠀⠀⠉⠒⠒⠊⠉⠀⠐⠛⠀⢀⣼⣏⣿⣿⣿⣿⣿⣟⣿⡏⠉⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⢀⡔⠚⠈⠉⠁⠘⠂⣄
⠀⠀⣤⠚⠁⠀⠀⣀⠋⠐⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣁⡠⠚⢷⣜⣿⢿⡿⢟⣼⣿⡣⠠⠤⠰⠀⠀⠀⠀⡠⠐⠀⠲⡀⠀⠀⢻⡎⠀⠀⠉⠓⠒⠛⠉
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡊⠀⣀⠬⡿⠛⡷⠻⠟⠉⢠⠈⢦⠀⠂⠀⠀⡠⠚⠀⠈⠉⣉⠃⠢⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡠⠐⡁⠀⠐⠀⠀⢠⣀⡁⠈⠀⠀⠀⠀⠀⠉⠓⠛⠉⠀⠀⠀⢹⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⠀⣿⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢶⣷⠂⠂⠀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⣀⡀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡼⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠄⣸⡇⠄⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⢤⠀⠀⠀⣯⡼⠁⠐⠦⢤⣤⠤⠄⠃⠀⠀⠀⠀⠀⠀⠙⠦⢀⡈⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠀⠀⠀⣈⠒⢄⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁⠀⠈⢷⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⢀⣿⠀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡀⠉⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠀⠀⠀⣾⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⣠⣤⣿⣤⣏⡀⠀⠀⠠⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠦⣤⣾⣿⣿⣿⣿⣿⣿⣶⡀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⣏⠀⠘⢁⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⠋⣰⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡷⢩⣃⢀⡄⠉⠙⣿⣿⣿⣿⣿⣿⣿⡿⠿⠣⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠰⠿⣶⡾⠁⢸⡥⢰⢀⡤⠟⠉⠙⠟⠋⠙⠁⠀⠰⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⢰⣿⣷⣴⡟⠤⡜⠋⠁⠀⣀⠀⠀⣰⢆⠀⠗⠀⠰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣼⣿⡏⠀⢹⣰⣷⡀⠀⠖⠛⢣⣴⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⣿⠃⢀⣠⡾⣿⡏⠁⠀⠀⡀⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⡴⠛⠉⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢸⡗⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⡴⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⣠⣖⠉⠀⢢⡀⠀⠀⠀⠀⢠⣰⠁⢀⢶⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢙⣷⣦⣾⡿⠀⠀⠀⠻⣿⠈⠀⢀⣠⣿⢿⣷⣿⣼⡅⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠸⢿⣿⣯⡁⠀⠀⢦⣿⠃⠀⠠⣽⡷⣿⣿⣿⣿⡟⠀⡴⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠸⢿⣿⣧⡀⠀⢰⡿⢃⠐⣤⠛⣧⣹⣿⣿⣿⡟⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣖⠀⠀⣿⣿⡇⢠⣼⡇⢀⣼⠅⠁⠼⣷⣾⣿⠛⠁⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⢀⣈⣷⣆⡐⢺⡇⠈⠻⣦⡀⢨⣿⠀⢰⠏⢀⣾⠃⠀⠀⠀⠉⠉⠙⢀⣀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⣠⣽⣿⣿⣷⠞⠇⠀⠀⠙⡇⣸⠃⡴⠋⠀⢸⠇⠀⠘⠀⠄⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⢸⣿⣿⣿⠋⠀⠀⣀⠄⠀⠀⠸⠗⠀⠀⠀⠀⡿⠀⠀⠒⠒⣄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⢿⣿⣿⠃⢀⣸⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣶⣶⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⢸⣿⠏⠀⣸⠇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⣿⣿⣷⣆⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⣸⠟⢀⣶⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠏⠈⢻⣿⣄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠶⠛⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⣄⠀⠘⠙⢷⡌⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠿⠶⣦⣦⣤⣍⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⠀⠀⠀⠘⢃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⢀⠀⠘⠀⢂⢀⠀⠃⠠⠀⠀⠰⠊⠀⠀⢀⠄⡚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠇⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠠⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⢀⠀⠊⠀⠀⠀⠀⡀⠁⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⢰⣀⣤⣤⡴⣇⣀⠀⢀⠎⠀⠀⠀⢀⠤⠚⠁⠉⠀⠐⠁
⠀⠀⠀⠀⠠⡶⠤⠄⠀⠒⠒⠓⡀⠀⠀⠀⢀⡴⠚⡏⠉⠓⡬⠀⠈⢛⢓⢪⡀⠀⠀⠀⠁⠀⡀⠀⠠⠮⢀⡀
⠀⠀⠀⠀⠀⠘⢄⠐⠀⠀⠀⠀⠈⠒⢄⢈⡿⠑⠠⠠⢜⠊⠠⡆⣁⠍⠰⠰⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠒⠒⠂⣼⢁⢀⢂⠴⡬⣙⡀⠚⡠⠆⣁⠘⢉⠄⢧⢀⠀⠤⠀⢀⣀⡄⠊
⠀⠀⠀⠀⠒⢉⠉⠁⠀⠀⠀⠀⠀⠀⠉⡟⣁⠁⣛⠖⠢⠡⠬⡿⣭⠓⡍⠡⠬⠦⢼⡀⠀⠀⠀⠀⠀⠀⠈⣩⠶
⠀⠀⠀⠀⠀⢀⣈⠔⠂⠀⠄⠀⠋⠀⠐⣿⢉⠐⠍⡴⠇⢲⣊⠵⡈⠥⡴⠐⡒⠒⣺⢁⠀⠀⠀⠀⠀⠠⢆
⠀⠀⠀⠀⠠⣁⠀⠀⠀⠀⠀⠐⠂⣀⠥⠻⣎⡐⢒⣁⠘⠀⢶⠙⢤⠀⠈⠮⡁⣰⣿⣄⡀⣀⠀⠀⠀⠀⠀⠈⢑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠒⠉⠀⡠⠊⡹⠷⢮⣰⣆⡃⠠⠆⢦⣈⣃⣤⠖⠋⠑⡍⠐⠄⠈⠑⠒⢖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠊⠠⠊⠀⠀⠀⠘⠉⢛⠋⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⣠⡁⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠘⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠀⠀⠀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⡌⠁⠢⡀⢀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠈⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠃⡠⠚⠀⠀⠠⡀⠀⡇⠀⠑⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠈⠀⠀⣀⡗⠁⠈⢄⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣾⣿⣿⣾⣇⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠐⠛⠛⠛⠛⠓⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠶⢶⣶⡶⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⢻⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⣿⢿⣾⣿⠻⡟⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠀⠆⠀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣤⣿⢷⡞⣇⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢐⠀⠀⠈⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠴⣯⢻⣜⣿⣽⣧⡟⣽⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠤⢀⣬⣾⣿⣿⣶⡠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣽⣷⣿⣿⣿⣿⣾⣭⡿⣻⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠘⢿⣿⣿⣿⣿⠟⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠚⣯⣾⣷⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡋⠉⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣻⡟⣿⡿⣿⣿⣹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⡀⠃⠀⠄⠐⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣿⢽⣟⣿⣧⢿⣟⡞⠏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠞⠀⠁

⠀⠁

⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⡆⠀⠊⠁⠠⡆⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠈⠀⢀⡇⡌⠀⢠⠤⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠑⢦⣿⣿⣿⣷⣤⡂⠀⢀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢲⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢈⣵⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡠⠀⠀⢉⣿⣿⣿⣿⣿⣿⡿⠓⠠⡀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⡢⠒⠛⡻⢿⣿⢿⠛⠣⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡜⠀⠀⡀⠀⢰⠇⠘⠀⠀⠘⠂⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢊⡅⢀⠼⠀⠀⠷⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠉⠁⠈⠁⠀⣠⣀⡆⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠈⠁⠁⠀⠀⠀⠀⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠄⡀⠀⠀⢀⡴⠊⠈⠉⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠂⠶⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⠀⡇⠀⠀⣠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⡿⠀⠀⠘⣿⡀⠀⠀⠘⠃⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢶⠀⠀⢿⠆⠀⠈⢻⡀⠀⠀⡟⠀⣀⡀⠀⠂⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣷⣤⠀⠀⠀⠀⠀⢳⡀⢀⠁⣸⠏⠀⠀⠀⠰⡿⢃⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⠈⠁⠀⠀⢳⣄⣾⣿⣿⣴⣿⣞⣵⣶⡦⠾⠛⠛⠙⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠛⠂⠵⣦⣄⢬⣿⣛⣻⣿⣽⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣶⢤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⣠⣴⣶⡶⠶⠂
⠀⠀⠀⠀⠀⠀⢀⣤⠮⠾⠛⠙⠃⠀⠸⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣭⣥⣴⣮⣭⣀
⠀⠀⠀⠀⠀⠐⠋⠉⠀⠂⢠⣤⣤⠴⠾⠟⢋⡿⣿⣿⣿⣿⣿⣟⣿⣿⡒⠈⠑⠀⠙⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⣠⣴⠋⢠⡟⣿⣿⠉⣿⠹⣷⣄⠉⠓⠶⣶⣶⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢡⣤⣶⢋⠘⠁⠀⠈⢀⠁⠉⠀⠉⠀⠈⠹⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠛⠋⠀⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⣷⡀⠠⠆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠀⢠⠀⠀⠀⠀⠸⣆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠁⢸⣷⡆⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠡⠼⠲⠀⢲⣦⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⡠⣖⣡⣼⠟⢂⣽⣶⣷⣿⡷⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣠⡶⣿⣿⣿⣖
⠀⠀⠀⠀⢘⡶⢾⣿⣭⣾⠿⠛⠋⠉⠙⠻⢦⡀⠀⢸⡟⠃⣀⠴⠊⠀⠀⠀⣿⣷⡟⢿⣶⣅
⠀⠀⠀⣌⣽⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⡄⢸⡇⢰⠃⠀⠀⠀⠀⠀⠌⣝⣿⡆⣻⡟
⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡇⡿⠀⠀⠀⠀⠀⠀⠹⢜⣿⡯⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡃⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣀⠀⡴⠘⡄⢀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡀⢸⠁⢧⢰⠁⠹⡀⠀⣷⠃⢰⣣⠖⠁⡤⠖⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠈⠺⡄⠈⢿⠀⠀⠹⡄⢹⠀⡼⠁⠀⢰⠀⢀⣾⠤⠖⣲⠶
⠀⠀⠀⠀⠀⢠⡀⠀⢃⠀⠉⠒⢤⣙⢦⣸⡄⠠⠀⢻⣼⡾⠁⠀⠀⡼⢀⡞⠁⣠⣞⣁⡀
⠀⠀⠀⠀⠀⠈⢏⠓⠮⣷⡀⠑⢄⠈⠻⣿⣧⣠⣧⣼⣿⣧⣴⣇⣰⣷⣯⠴⠚⠉⠀⢀⣆⣀
⠀⠀⠀⠀⠀⡤⢬⣷⣄⣀⡙⢦⡀⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⠔⠈⣀⠔⠁⠀⣀⠵
⠀⠀⠀⠀⠀⠱⣄⡠⠤⠬⠭⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣞⣁⠤⠖⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠊⢄⡀⠀⠀⠤⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠓⠒⠶⢶⣒⠒⠋
⠀⠀⠀⠀⣤⠤⠤⠭⠟⠒⠶⢦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⣀⡈⠕
⠀⠀⠀⠀⠈⠓⢦⣤⠴⢚⡽⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣭⣉⡉⠉⠀⠙⢆
⠀⠀⠀⠀⠀⢖⡉⢀⠔⠉⠠⠔⠊⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠧⡀⠙⣎⡉⠙⢿⡓⠚
⠀⠀⠀⠀⠀⠀⠉⠁⠀⡠⢤⡶⠋⣡⣾⠃⢸⠛⢻⣿⠟⢿⠋⢻⢿⠦⣄⠈⠂⠈⢻⡲⢤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡼⢁⡇⠀⠂⢠⠏⡟⡆⠈⡀⢸⡌⠳⣌⠑⠢⢄⣀⢳⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠶⠯⠖⠚⡿⠁⢸⠀⠀⡰⡟⠀⣇⠹⡀⠀⢸⠷⡀⠘⡶⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠴⠚⠠⠊⢠⠇⢠⢿⠀⠑⡀⡸⠀⢳⢀⡇⠈⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠁⠸⡆⠞⠀⠁⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⢻⣷⠇⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⢾⡀⠀⠀⣄⠀⠟⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣾⣧⢾⣠⣿⣠⡁⠀⣴⠃⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⣼⣿⣿⣿⣿⣿⣧⣾⡿⠛⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠑⢮⣶⣿⣿⣷⣿⣿⣿⣯⣿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢤⣤⣤⠴⠞⠛⢿⣿⣿⣿⣿⣿⣿⢿⣝⠷⠮⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣤⠂⠀⣹⡿⠿⣻⡟⡉⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⡔⠚⠛⠁⠀⡏⠃⠣⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⢡⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⠄⡀⠀⠀⢸⡇⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠛⠉⠀⣠⠞⠁⠀⠈⠳⣄⢸⡇⠀⠀⠁⠀⢠⣶⡄⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠘⢸⠃⣀⠴⠒⠒⠒⠽⣿⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡖⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠒⠉⠀⠀⠀⠀⣀⠀⠒⠒⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣰⡔⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡤⠀⠀⢐⣴⠾⠞⣋⢺⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⢀⣰⠟⣡⠼⠇⠁⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⣸⢣⡾⠃⠀⠠⠀⠀⠀⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢀⡁⡾⠁⠀⠄⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣁⢠⠀⢠⣄⡠⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡾⠟⠛⠒⠋⠉⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣾⣿⢿⣿⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢿⣿⣾⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠈⢻⠀⠈⠁⠹⠁⢸⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠟⠁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⢀⣸⠤⠤⢥⣄⣀⠀⠀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⣄⣠⠞⠁⠀⠀⠀⠀⠀⠙⠦⡠⠒⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡠⠀⠀⠤⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠆⠀⠠⠄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⡶⠂⠀⠀⠀⡨⠧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠦⠀⠀⠀⠀⠙⣿⣿⣦⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣶⣶⠖⠀⠀⠀⠀⡸⠒⠦⣤⢤⠤⠖⠊⠣⡀⠀⠀⢤⣀⣻⣿⣿⣿⣿⣿⣆
⠀⢀⣾⣿⣿⣿⣿⡿⣻⡾⣶⠃⢀⡀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⢀⠀⢀⡀⢫⣹⣿⣿⣿⣿⣿⣿⣆
⠀⢸⣿⣿⠿⣿⣷⣾⣿⣿⣿⣶⣿⣇⡄⠀⢠⠀⢠⠀⠀⡄⠀⡄⠈⣿⣾⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡄
⠀⢾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷
⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠟⠛⠋⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠑⡄⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠙⡆⠀⣀⣼⡀⣁⠂⣠⣊⡰⠁⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⣾⣆⣴⠿⢛⡻⣭⢭⣉⣻⠿⣿⣯⡄⢂⢀⡀⠈⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢵⣷⡟⢠⡔⠉⢠⣤⣶⣾⡋⢳⡼⣿⣿⠄⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠈⣿⠁⢸⡇⠸⣿⣿⣿⣿⣿⠅⢹⡾⣿⣒⠈⠉⠁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣽⣧⠸⣧⡀⠛⠻⠿⠾⠋⠀⢸⣿⣿⣏⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣊⣾⣿⣦⣜⢷⢶⣤⣤⣤⣤⠞⣛⣽⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠉⢉⠿⣶⣶⣶⣷⣴⡾⣾⠟⠛⠏⡀⠀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠸⠉⡟⡿⠁⠈⢆⠀⠀⠑⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠈⠀⠘⡇⠀⠀⠀⢂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠐⡄⠀⠀⢸⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⠠





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣶⣄⡀⠀⠀⠀⣀⠰⢯⠉⠘⠙⠉⢇⠘⠑⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⣟⣳⢧⣶⣿⡷⠀⣠⠄⠥⠴⢌⣦⡀⣀⢠⣞⠀⡐⠁⢀⡵⣄
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣟⢿⠅⢺⡩⠑⠀⣀⠘⣻⣿⣿⣿⣿⣿⣴⣊⠥⠤⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⠋⣿⠀⠀⠀⡤⠙⠉⠉⣴⠾⢿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠰⠊⠀⡤⠞⣡⠎⢰⡿⣿⡻⣏⠙⠀⠀⠘⣖⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣰⠀⡜⠁⡠⠊⡀⠱⢄⠀⢽⢀⠐⢠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢿⠀⠀⠀⠀⠀⠃⣸⣆⠀⠑⢀⡜⣆⠃⠈⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⢺⣟⠁⠀⠸⡇⠀⠀⠀⠀⢰⡏⣀⣄⣼⠮⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠂⢻⠁⢐⠤⣧⠀⠀⠀⠀⣾⠞⠋⠁⠈⠀⠀⠀⠀⡠⠀⠀⣐⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠐⡤⠑⣴⡤⠈⡀⣿⣄⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢔⡠⠔⠏
⠀⠀⠀⠀⠀⠀⠂⠲⢄⠈⣧⠸⠀⠝⢦⢂⠀⣿⠀⠀⠀⠀⠀⠀⢠⡾⠉
⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠘⣧⡎⠈⣈⢐⣠⡏⠀⠀⠀⠀⢀⡔⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡁⠈⠁⠹⣧⡾⣏⡘⣹⡇⠀⠀⠀⣠⠊⠀⠀⠀⠄⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠢⠀⠀⠑⠹⣧⣹⣿⣿⠀⠀⠀⣰⡉⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⣀⣁⣼⣿⣿⣿⠀⠀⣼⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠂⢀⠀⠔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀⠀⠈⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠐⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢠⡀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠀⢰⠁⠀⢀⡀⣸⡄⢠⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠠⣀⠘⢮⣧⢾⡿⣿⣿⣿⢿⣿⣾⣤⣿⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠰⡆⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⢈⣶⣿⣿⣿⣿⣿⣽⢟⣯⣿⣿⡿⣿⣦⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣀⠠⠖⠀⠐⠂⠉⠀⠀⠀⠠⣀⡀⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣻⣟⣟⣠⠔⠀⠀⡀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢽⡿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⢽⣿⡆⢤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡾⡭⣍⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣻⠧⠬⠄⠀⠀⠀⠤⠤⢀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡿⣿⣻⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⣾⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠈⣠⠞⢻⣿⣟⢿⣻⣻⣋⣿⣿⣾⣿⣿⡃⠙⠒⠤⣑⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰
⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠈⠀⠀⠛⡵⡟⢻⡿⡿⣿⡿⠟⠛⠻⡀⠉⠀⠀⡀⠀⠀⠐⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠄⠀⠀⠀⡜⠃⠀⠈⠃⠀⠀⠀⢡⠀⠀⠀⠘⠀⠀⠀⠀⠈⢂⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡤⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠀⠀⠰⠁⠀⠀⠀⡄⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣄⠸⠙⢦⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣀⠣⡲⢄⡀⢐⠁⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣘⡄⠀⠈⠳⡄⠹⠁⠀⢀⠿⢠⠆⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢦⠀⠀⢣⠀⠇⠀⡆⠀⢸⣶⠟⠁⢀⡂⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣀⠀⠿⠶⢤⣄⠀⢡⣤⣸⣷⣾⣾⣧⣤⠊⠀⢀⣀⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣙⠻⢷⡀⠀⠀⢄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⣉⡌⠁⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠚⠳⢄⠀⠉⠓⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠉⠉⠉⠉⠑⠦⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⠀⠚⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣥⣄⣀⠴⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠓⠒⢤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣀⡀⠀⠀⢀⡤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠁⠀⡼⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠓⣄⠈⠙⠦⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⣶⢿⠄⠀⣼⠟⠙⠿⢿⢻⢟⠿⠻⣄⠁⠀⠈⠳⡤⠤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢠⠊⢠⣾⠁⠀⠀⠀⣸⠀⡀⠀⢠⢸⢦⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⠀⠊⢹⠀⠀⠀⠀⢹⣸⠀⠀⣸⠘⠀⠈⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⡙⠃⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡞⣧⠀⠀⡤⢄⡼⠁⠈⡇⣠⠞⢩⠇⠀⡀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢦⡀⢸⡇⠘⣆⢸⠀⠈⢣⡀⠀⢻⠃⠀⣾⣠⠊⠀⢠⠔⠋⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⡇⠀⠙⢾⡇⠀⠹⣿⠀⠀⠀⢳⡀⢸⡄⢀⡿⠁⠀⠀⡆⠀⠀⣼⣡⡤⠴⢖⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠙⠲⢤⣀⠙⢦⡀⢹⠀⠀⡀⠈⣧⢸⣧⡟⠀⢀⠀⢠⡇⢀⡼⠋⠀⣠⡴⠋
⠀⠀⠀⠀⠈⡗⢦⣄⠘⣆⠀⠢⡀⠈⠳⢦⣹⣼⡇⠀⢡⠀⢸⣿⣿⠀⢀⡆⠀⡼⢀⡞⢁⣠⠾⠗⠒⠂⢰
⠀⠀⠀⠀⠀⠙⣆⠈⠙⠾⣷⡀⠈⠳⣄⡀⠙⣿⣷⣶⣿⣿⣿⣿⣿⣶⣿⣤⣾⣷⡿⠚⠉⠀⡠⠀⠀⡴⠷⠤⢤⡀
⠀⠀⠀⠀⡦⠤⠬⣷⣄⣀⣀⡙⢦⣀⠈⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡴⠒⠁⢀⣤⠊⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠱⣄⢀⣀⣠⣤⣭⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡶⢋⣀⣤⠶⠛⠷⠤⣄
⠀⠀⠀⠀⠔⠋⠉⠀⠀⠀⣀⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢥⣤⣀⣤⣤⠤⠬⠷
⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⣀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠤⠤⠀⢀⠀⠉⠓⠢⡀
⠀⠀⠀⢶⡒⠒⠛⠋⠉⠉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⠤⢤⡒⠁
⠀⠀⠀⠀⠉⠓⣶⡤⠖⢛⣩⠟⠋⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣮⣅⣀⡀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⡴⠛⠁⢀⡴⠋⠀⣀⠴⠚⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣄⠀⠙⢦⡉⠉⠙⢿⡒⠒⠚
⠀⠀⠀⠀⠈⠙⠲⠋⠀⠀⠁⣀⣠⠴⠚⣩⣿⠋⢹⡿⠿⣿⣿⣿⣿⣿⠻⣿⣿⣦⡀⠈⠑⠄⠈⠻⣶⣤⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⣉⠽⠋⢀⡼⢱⠇⠀⡼⠁⢠⡟⣿⡀⠈⡏⠀⢹⡘⣦⠙⠲⣄⡀⠀⠀⠙⡆⠉⠳⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⡞⠀⡾⠀⠠⠁⢠⡟⢰⡏⣇⠀⢰⠀⢸⣇⠈⠳⣄⠀⠉⠒⣤⢤⣸
⠀⠀⠀⠀⠀⠀⠰⠾⠷⠖⠚⢉⡟⠀⠀⡇⠀⠀⣰⢿⠁⠘⡇⠘⡆⠀⠀⢸⠟⣆⠀⢸⡷⣄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⣠⠶⡃⡠⠞⠁⡿⠀⢠⣧⠀⠘⢄⠀⣸⠀⠸⡄⢸⡇⠈⠳⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⣃⠴⠃⢸⡀⢀⠞⠐⠃⠀⠀⢹⡜⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠓⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⢀⠄⠢⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠢⣀⠆⠀⠈⠇⠀⠀⣧⠊⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠠⠤⣸⠀⠀⠀⠈⡀⠀⢸⠀⠀⢠⠃⠀⠀⣠⠞⠏⣉⣿⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠈⢣⡀⠀⠀⢣⠀⢸⠀⠀⡌⠀⠀⠀⢡⡴⡶⠏⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠉⠉⠉⠒⠦⣄⡑⢄⠀⠈⢆⠘⣆⠀⡇⠀⠀⣰⠉⠀⡠⠔⠊⠉⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠙⠢⣕⣤⣼⣿⣿⣶⣿⣦⣶⠃⡠⠊⠀⢀⡀⠤⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠚⠛⠒⠤⠤⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠒⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⠔⠒⠒⠒⠒⠒⠶⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠠⠤⠒⠒⠒⠒⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡤⢚⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⣀⠀⠉⠐⠒⠠⢤⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⣀⣀⡠⠤⠖⠊⠁⡠⠊⢉⠟⠛⢿⣿⠿⠛⢣⠀⠀⠀⠉⠢⢄⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⠎⠀⢠⠃⠀⠀⢸⠂⠀⠀⠀⠳⡀⠀⠀⠀⠀⠑⠖⠠⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡴⠁⠀⢠⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⢦⡀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠹⠁⠀⠀⡎⠀⠀⠀⠀⡎⠀⡄⠀⠀⠀⠸⠀⠈⠒⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠤⠐⠈⠃⠀⠀⠀⡼⣿⠀⠀⡀
⠀⠀⠀⠀⠒⠒⠒⠀⠤⠀⣀⡀⠀⠀⠀⠀⠀⠡⣠⠤⠊⠀⡏⣆⠀⠘⠦⡀⢠
⠀⠀⠀⠀⠀⠀⢦⠐⠂⠀⠀⠀⠉⠐⠢⣄⠀⣀⣀⠀⠀⠀⡇⢘⠳⡮⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠓⠂⡐⠀⠠⠀⡀⠀⠀⠑⠄⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠬⣀⡀⢰⠀⠀⠃⠸⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⡄⠀⠀⠆⡠⠂⠁⠀⠀⠀⢀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⣿⡀⠀⡀⣠⠄⠀⠀⠀⣀⠤⠒⠒⠂⠀⠉⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢱⡾⠋⠀⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠣⢀⡖
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⡀⠀⠺⢀⠀⠠
⠀⠀⠀⠐⠀⠀⣼⠟⣉⣭⣝⢿⡦⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡘⣲⡼⢟⡲⢧⡀⠁
⠀⠀⠀⠀⠀⢸⣿⢰⣿⣿⣿⠀⣟⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢿⠿⢸⡏⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠻⢧⣌⣉⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣀⡀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠁⠘⠛⠷⠟⠻⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠈⢃⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠋⠀⠁⠀⠈⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡶⠶⠦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣽⣷⣦⣶⣶⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠉⠉⠙⠲⣤
⠀⠀⠀⠐⠀⠀⢼⠏⠀⠀⠀⠈⡷⠀⠀⠐⠀⠀⠀⠀⢈⠀⠀⣶⣿⣿⣿⣿⣿⣟⠁⠀⠁⣀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⡀⠉⢇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢼⣿⣿⣿⣿⣿⡟⠉⠈⠀⠄⠀⠀⠀⠀⢈⠘⡇⠀⠀⠀⠀⠀⠀⢸⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠾⠛⠒⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠉⡿⠛⣿⠛⠀⠀⡀⡄⠀⠀⠀⠀⠀⠈⠀⠚⢦⣀⡀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⢀⠀⠀⠙⢄⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠉⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣧⢸⡆⢰⢁⢁⠀⠀⡴⢋⡔⠁⡠⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢄⡐⡼⣾⣿⣿⣷⣰⡸⢸⣠⡞⣴⠏⢀⡾⠁⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢄⢢⡀⠀⡀⠹⣦⣻⣾⣿⣿⣿⣿⣿⣧⠘⣹⣿⣫⣶⣫⣶⠟⢁⡠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠶⣝⢶⣬⣳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣥⣶⡫⠐⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡐⢬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣤⠴⢚⣡⢚⣀⠀⠀⡲
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠲⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣛⡉⠉⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢒⣀⣉⡙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⢚⣙⣻⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⠍⡛⠲⢌⡑⠲⠤⣀⣀⣀
⠀⠀⢀⣀⡀⠀⣀⣠⠴⢖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣝⣲⡤⢄⡻⠆⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣀⠴⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣷⣦⡄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⡤⠚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⣀⠀⠉⠻⣟⠦⣀
⠀⠀⠀⠀⠀⡐⠀⠀⠈⣁⡴⠞⠉⢉⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣟⡲⢭⣓⠦⣄⡀⠱⡦⠭⠧
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢠⠞⠀⠀⢀⠼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⡿⣟⠛⠷⢬⡓⠈⠉⢛⣷⣄
⠀⠀⠀⠀⠀⠀⣤⡤⠴⠊⣠⠔⡁⠀⢊⣴⠡⠀⡴⠁⣿⢻⡿⢿⡟⠉⠧⠙⢮⡉⠳⣄⠘⢦⡁⠂⠄⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢈⢈⣔⣡⠾⠃⠀⠜⠀⣼⡇⠈⠃⢸⡇⠀⠀⠀⢈⡿⡄⠈⢷⡀⠙⠢⠤⣀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⣄⢎⣤⣾⢿⡇⠀⢀⡏⢻⣷⣄⢄⢸⠃⡀⠀⢰⢽⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣌⠛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣆⣠⣤⣯⣀⡀⢀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣴⣾⣿⠿⠿⠿⣿⣿⣿⣾⡿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣳⣾⣿⣿⠁⡀⠀⢀⣼⣿⣿⣿⣇⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⣻⣿⡁⢿⣶⣿⣿⣿⣿⣻⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣷⣶⣿⣿⣿⢩⣼⠉⣠⣄⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠀⠠⠴⠟⠉⠟⠁⡀⣼⣿⣧⠀⠙⠆⣴⣿⣿⣿⡇⠀⠀⣠⣶⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣏⣠⣶⠄⠀⠀⠀⠁⠀⠀⠀⠀⢿⡿⢿⠁⠀⠈⠁⢹⡿⠟⠁⣰⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢻⠿⠛⣿⣿⣿⠏
⠀⠀⠀⠐⢶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠁⠈⠉
⠀⠀⠀⠀⠀⠻⣿⣿⣿⡾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⣤⠀⣀⡠⢦⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠈⣉⣿⣿⡿⠙⠻⢤⠀⠀⠈⠀⠀⡀⢘⣦⣿⣿⣿⣿⣿⣿⣿⣄⣤⠊
⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⠃⠀⠀⠀⠐⠦⡀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⣀⠤⠀⢴⠦
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⢀⣀⡀⢁⣀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠝⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠂⠀⠀⠀⠀⠀⠸⣛⠿⣿⡟⠛⠻⡶⡗⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⡾⠀⠀⠀⠀⠀⠉⠀⠘⢃⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⠃⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢋⣿⠟⠛⢁⠀⠉⣡⡄⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠈⠁⠀⠀⠁⠀⠀⣿⠇⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⣶⣶⣶⣶⣶⣴⣦⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣦⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣴⣦⣴⣤⣴⣦⣤⣶⣤⣤
⣿⣭⣭⣹⣭⣽⣥⣭⣽⣯⣭⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣭⣭⣽⣿⣯⣭⣭⣭⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀
⠁⠁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠂⠀⢋
⠀⠀⠚⠉⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠀⡀⣁⠀⠒⠀⠀⡽⠷⡦⠔⣒⣂⣊⠉⠅
⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠢⠀⠀⠈⠓⠤⣦⠀⠫⡓⠤⣀⠩⣄⠐⢠⠁
⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣦⣌⠁⣈⡵⠃
⠀⠀⠀⠀⠙⢄⠠⣄⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠂⢄⡀⠀⠀⠱⣄⠐⢦⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⣀⠰⠄⠄⠀⠃⠀⡀⠀⠈⠂⠀⡀⠀⠀⠐⢒⣚⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣍⡲⠲⠒⣜⠁⠀⠀⠀⠉⠙⠂⠀⠀⠈⢰⡠⡒⠈⣑⡺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠼⠄⣀⣀⡀⢀⠀⠀⠀⡀⠀⠤⠥⠘⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⣷⡄⠀⠀⢰⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⣿⡄⠀⠘⠻⡇⠀⠀⠀⡿⠀⠀⠀⠀⢠⠄⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣄⠀⠘⠀⠀⠀⠀⠱⠀⠀⠀⠁⢠⡶⠃⠀⠀⠀⣠⣟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠛⠿⠄⠀⠀⢄⡀⠀⣦⠀⣴⢀⣾⣁⠄⣀⡀⠀⣘⣥⣴⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣆⡀⡀⠀⠀⠀⢿⣤⣿⣿⣿⣾⣿⣯⣾⡿⠓⠋⠁⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠉⠁⠀⠷⣦⣄⣾⣯⣤⣾⣷⣿⣾⣿⣏⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠭⠿⠷⠶⠤⢤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⣤⡤⠶⢾⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠥⠉⠑⠉⠁⠀⠐⢚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⢶⣄⠶⣶⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⣤⠤⠾⠟⠛⣹⠿⣿⣿⣿⣿⣿⣟⡻⣯⡓⠀⠀⠀⠀⠛⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⢀⣠⡞⠁⣸⢿⡿⣿⠙⡏⠹⣷⣄⠈⠑⢶⣦⣤⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⢉⣀⣤⡶⣡⠟⠀⠀⠁⣸⠁⠛⠀⠉⠀⠈⠻⣷⡀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠻⡞⠁⠀⠀⠀⣠⠁⠀⠀⠀⣶⠀⠈⣷⡌⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡁⠀⢐⠀⠐⡁⠀⠀⠀⠀⣿⡀⠀⠙⠛⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠠⠀⢰⣀⠀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣐⠂⣀⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠠⢤⠀⢁⡀⢌⢿⣦⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢒⣰⣶⠖⢀⣤⣾⣽⣿⣿⣿⡀⠀⠀⠀⢸⣿⠀⠀⠀⡀⠀⠲⠣⢹⣿⢻⣿⡆⢀
⠀⠀⠀⠀⣈⣽⣿⣿⣧⣾⡿⠛⠉⠀⠀⠀⠉⠛⢦⠀⠀⢸⠉⠀⣠⠊⠀⠀⠀⠀⠸⢿⣿⣍⢿⣷⡤
⠀⠀⠀⣄⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⢸⠀⣺⠁⠀⠀⠀⠀⠀⠀⠰⢌⣿⡌⣿⡟
⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠡⢻⣿⡇⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⣀⠀⠀⠀⡐⠀⠁⠀⡈⠀⠀⠑⠂⠐⠂⠅⠀⠀⠀⢀⠠⠤
⠀⠀⠀⠀⠰⣄⢠⠀⠀⠀⠀⠈⠵⣂⠀⠀⠉⠉⠀⢄⣴⢀⡆⠀⢀⠐⠀⡉⠀⠀⣐⠮⠁⠀⠀⠀⠀⡄⣠⠄
⠀⠀⠀⠀⠀⠠⠜⠂⡸⠀⡔⠀⢤⠁⡞⠘⠀⠀⠑⣾⣿⣾⣷⣶⣯⠄⠀⠀⢠⠋⠈⣥⠀⢠⡄⢆⠀⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⡰⠃⢀⠞⠁⠘⠂⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠛⠀⠳⡀⠘⢆⡈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠺⠁⠀⠀⢠⠊⠀⡽⢿⣿⣿⣿⣿⣿⣿⡷⣄⢀⡀⡴⠀⠀⠈⠗⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠈⠟⠿⣿⡿⠿⢥⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠜⠒⢲⢀⠈⠀⠁⠀⡀⢀⠁⣠⡿⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠰⠀⠀⣀⠀⡈⠓⠀⠃⠀⠀⠈

⠀⠀⠀⠀⠆
⡀⠀⢠⠂⡇⠀⠀⢀
⡝⢀⢇⣇⢣⠀⢀⠎⢦
⠀⢺⢸⣿⣸⠀⡼⠸⠂⠳⡀⠀⠀⡴⡇⠀⡠⡎
⠀⠈⢺⣿⠃⠀⢡⠀⡀⠀⠹⣀⠞⠀⣧⠞⠀⠁⢀
⡀⠀⠈⡏⠀⠀⠀⡄⢻⣤⣶⠋⠀⠀⣯⣼⠀⡇⡸⠄⠀⠀⡔
⠀⢀⣸⠁⠀⠀⠆⢣⢸⡿⠁⠀⠀⠀⣿⣯⢀⡽⠁⡱⠊⢰⠁⢀⡤
⢀⢸⠏⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⣼⡷⢋⡴⠋⠀⠀⣿⡊⢠⢀⠰⠂⠀⣠⠂
⢸⡼⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⣿⡴⠋⠀⠀⠀⢠⡿⠗⠋⠀⠀⡥⠎⡅
⠸⣷⢸⠀⠀⠀⠀⣄⣷⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⡷⡹⠁⠀⢀
⣟⣿⣼⣦⣸⢂⣰⣿⣧⠀⢀⡃⠀⣼⡄⡠⠀⠀⠀⣼⣤⠄⠄⣀⡠⠞⠛⠁⣠⢖⠥⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⡕⡡⡠⢡⣾⡿⠟⢛⡉⠀⠀⠀⣠⢞⣑⡁
⢿⣿⣫⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣕⡴⣋⡥⢔⣠⠔⠀⠀⢀⡞⡉⢉⡌⠀⠰⠊
⣟⣎⣳⡗⣿⣿⣟⣏⣥⣿⢿⣿⣿⣿⣿⣿⣿⡿⢚⠉⠀⠀⣀⡴⠛⠛⠂⠉⢉⠬⠋⠁
⣾⣿⣿⣿⣿⣿⣶⡷⣯⣞⣿⢺⢿⣿⣿⣿⠿⠟⣋⣡⣴⣾⣧⣀⣀⣀⣤⣾⣁⣀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣭⣾⣿⣿⣿⡟⣛⣩⠍⠉⠉⠉⠉⢁⣀⡈⠉⠉⠉⣉⣩⣭⠖⢊⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡷⣿⣿⣿⣿⣿⣛⣃⡩⠍⢀⡈⠄⠀⣀⣴⡾⠖⠂⠔⠂⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣿⣻⢿⣿⣿⠿⠿⠧⠒⢒⣈⣡⣤⣶⣉⣉⣉⠒⠚⠤⠆⠒⠒⡨⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣯⡼⣹⣿⣿⣷⣶⣾⣿⣿⡢⠬⠍⣙⠓⠶⣔⣒⣂⣀⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠤⣀⠄⢀⢀⠈⢀⡠⠀⠈⢢⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠣⡀⠰⠌⠀⢠⠃⠀⠈⠄⠀⢀⠔⠁⠀⢸⢀⠰⠤⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠈⠙⠈⠀⠠⡀⡛⠄⢠⠃⠀⠀⠀⠘⡔⠁⢀⠀⠀⠈⣁⠀⠀⢈⠁⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠑⠺⠤⢥⠀⠀⠀⠀⠀⠰⠇⠀⡌⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡸⠁⠀⠀⢘⠉⠀⠀⢰
⠀⠀⠀⠀⡖⠲⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠇⠀⢡⠀⡀⠀⠀⠀⡆⠀⠀⡀⢠⠃⠀⠀⡠⠁⡠⠀⠀⣼⠠⠒
⠀⠀⠀⠄⠤⠀⠷⠀⢀⣀⡁⠀⠰⠀⠄⠄⠘⡄⢀⢂⣡⣀⡔⡰⡀⢠⠞⡴⠁⠀⢀⣴⡡⠞⠒⠀⠁⠀⢀⠆
⠀⢀⢀⣥⡀⡀⠀⠀⠀⠀⠙⠂⡀⠀⠀⢈⣷⡼⣯⣿⣟⣯⣽⣿⣿⣷⣪⣄⡀⢐⠟⠁⣀⠤⠒⠀⠀⠚⠛
⠀⠑⣄⠀⡑⣌⠀⠀⠀⠀⠀⠀⠈⢀⣼⣿⣞⣿⣻⣏⢿⣿⣟⣿⣿⣻⡿⣿⡧⣏⠄⡈⠐⠀⠀⠀⠀⠀⠀⠀⢀⠄⠓
⠸⡉⠉⠁⠀⠀⠓⠠⠀⠐⠒⠂⠠⣾⣿⣾⡿⣷⣿⣿⣿⣿⣿⣟⡝⢿⣯⢻⣾⣿⡧⠠⠄⠀⠀⠀⠀⢀⡠⠖⠙⠂⢄
⠀⢘⡦⠐⠂⠀⠁⠀⠀⠀⠨⢄⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⠂⢀⡤⠤⠶⠾⢉⡀
⠐⠀⡤⢀⠀⠄⠀⠀⠀⠀⣐⠶⣿⡿⣯⣫⣿⣿⣿⢿⠟⠙⠻⢿⣿⢿⣏⣿⣿⣿⢟⣡⣀⡀⠀⠀⠀⠀⠉⠻⢦⡴⠃
⣠⠊⠐⠉⠉⠒⠤⠄⠠⠤⠄⢒⣿⢿⢟⣽⣽⡿⣿⣾⣶⢶⣶⣴⣟⢽⣿⣷⣵⣿⣟⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡢
⠀⠠⠋⠐⠤⠀⢠⠄⠂⠐⠚⡐⢺⣿⣪⣿⡿⢿⣋⣿⣷⣿⣿⣧⣟⢿⣿⢿⣿⠿⡛⠢⠑⠢⠤⠤⠤⠄⠀⠶⠘⢧
⠀⠀⠀⠀⠄⡴⠁⠀⢀⠤⠊⠰⠁⢳⢾⣿⣶⣹⣿⣼⣾⡹⣿⣽⣿⣿⡿⢯⣿⡟⠀⠉⡒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠉⡝⠁⠀⠀⠀⠀⢀⡤⠊⢀⡼⡋⠗⣿⣮⣟⣽⣷⣿⣿⣿⣿⣻⠖⡁⠈⠄⠀⠀⠀⠈⠲⡒⠒⠖⠒⢏⠉⠉
⠀⠀⠀⣀⢀⡤⠤⢤⠒⠀⡼⠁⠀⠊⠀⠀⠀⡸⠨⡉⡋⠋⠉⠹⢃⠘⢾⡀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣄⡀⠀⠀⠂
⠀⠀⠀⠀⠘⠀⠀⠆⡐⠐⠁⠀⢀⠃⠀⠀⠀⠀⡰⠁⠀⠀⡆⠀⠀⠀⠈⣧⠀⠑⢤⣀⡀⠀⠀⠀⠀⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠈⡙⢀⣀⡌⠀⢀⠈⠀⠀⠀⢀⠔⠀⠀⢀⡀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⣯⠉⠙⠸⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⡞⠀⠀⢀⠴⡎⠆⠀⠀⢈⡧⠀⠀⠀⠀⠘⡤⡀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢤⠊⠀⠘⡇⠀⠀⡠⠎⠀⠱⡠⠀⠀⢠⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⠀⠚⠃⡠⠺⡀⠀⠀⡰⠁⠀⠀⠓⢄⡐⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢀⠔⠀⠀⠀⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠃⠀⡆⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣇⢄⢀⣡⣤⣤⣤⣷⣀⡅⣴⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠢⠀⠀⠀⠈⠲⣬⣿⣿⣯⣿⣿⡯⣿⣿⣿⣿⡀⡀⠄
⠀⠀⠀⠈⡤⠀⠤⠀⠀⠀⠀⣀⠀⠀⠢⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⡹⣿⣷⡄⡀
⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣯⢠⠔⠚⠁⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢯⣽⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡟⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣙⠂⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠀⠀⠀⠊⢀⠿⣿⣾⣿⣿⣾⣿⡿⢿⠛⠀⠀⠉⠑⠀⠀⠀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠈⠈⢸⠏⠉⠛⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡰⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡀⠀⠀⠂⠀⢸⠇⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢱⡀⠘⣇⠀⠈⠀⣀⢨⠀⢀⣴⢁⠔⠀⠀⢀⠔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣀⢵⣄⣸⣶⣶⣾⣿⠾⠦⣾⣿⡗⣀⡤⠒⠁⠴⠚⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⠞⣻⣭⣍⠓⠊⣿⣿⣟⣴⠖⠂⠀⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⢐⣂⣐⣻⣿⣿⣿⠃⢶⣿⣿⣿⣿⡆⢹⡿⣿⠅⠒⠂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⢙⣿⣿⣿⡇⠼⣿⣿⣿⠿⠃⢸⡇⣿⠗⠢⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⢀⡀⠴⣋⣽⢿⣿⣿⣶⣄⣈⣤⣤⣴⢛⣽⣿⠗⠁⠀⠀⠀⠈⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢁⠐⠉⠙⢿⣿⣿⣿⣿⣾⣿⡿⠿⣧⡀⠀⠀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣾⢿⣻⠏⠙⢮⠀⠀⠡⠁⠐⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⡜⠰⠀⢣⠀⠀⠈⢧⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠠⠀⠀⣦⠀⠀⢸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠃⠀⠀⠀⠀⠄

⠀⡀⢀⠀⠀⠀⠀⠐⡠⠤⠤⣄⠈⠀⣠⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡀⠀⡀⢀⠀⠀⠀⠀⢆⠤⠤⢤
⣤⣷⣮⣁⠀⠀⠀⢰⡙⠶⣄⠀⢀⣤⣿⣮⣅⠀⠀⠀⢀⣳⣬⣍⡉⠀⣀⣤⣷⣮⡀⠀⠀⠀⣌⠳⢆
⣿⣿⣿⣿⡦⡆⠀⡀⠀⡅⠀⣀⣿⣿⣿⣿⣿⡦⡦⠀⣀⠁⡩⠣⢐⣨⣿⣿⣿⣿⣿⠴⡄⠂⡈⢨⠀⢠⣹
⣿⣿⣿⡿⠃⢤⣀⣿⣷⡧⢀⠐⠻⣿⣿⣿⡿⠗⢠⣀⣿⣿⣷⢀⠸⠚⠻⣿⣿⣿⠿⠂⢄⣘⣿⣿⡄⡀⠚
⢁⡈⠠⢀⢀⣍⢿⣽⣿⡗⢐⠆⠒⠁⡈⠠⢀⠄⣅⠿⣿⣿⡟⢐⡞⠱⠊⢀⠈⠠⡠⢨⡩⢿⣿⣿⠃⣓⠐
⠁⠙⠀⡄⢺⠏⡀⠙⠙⠠⠀⠀⠂⠁⠉⠃⡀⣾⢃⠃⠉⠙⠀⠄⠀⠀⠀⠁⠙⢤⢰⡾⢁⠈⠉⠃⠰
⠀⠀⠀⢹⠾⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠵⠃

⠉⠙⡻⣿⣿⡖⠒⠈⣉⣭⣷⣦⡀⠀⠙⣆⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣇⣾⡇⣶⣶⣶⣤⣤⣤⣤
⠁⠌⢁⣽⣿⡇⠠⠘⣿⣿⣿⡟⠀⣿⣿⠻⣿⣻⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣾⣿⡿⠁⠀⠈⢙⢿⡿⢀⣀⣿⣿⢿⣜⢻⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠉⢁⠀⠈⠉⢉⠉
⢛⣛⣛⡟⢆⠀⠀⠀⣼⡾⠻⡀⠈⠿⢿⠿⢿⠿⠿⠿⠷⣶⠿⠿⠀⠀⠀⠀⠀⠸⡀⠀⠸⠐⠐⠄⠀⠑⠸⠸
⠋⢉⣸⠙⢷⣣⣤⡞⠁⡇⠀⠙⠖⠀⠀⠇⠸⠀⠀⠀⠀⠀⠀⠀⢃⠐⣶⣤⡀⠀⠀⠉⠒⠂⣶⣦⣤⣴⣶⣶⣶
⠀⠿⣿⣿⣿⣿⡿⠇⠀⠛⠀⠀⠀⠀⠜⠀⡼⣀⣐⠁⠂⠂⠀⠀⠀⠀⠙⠻⠛⠶⠆⠀⠖⢲⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣾⣆⠉⠀⣀⣀⡠⠤⠤⡖⠒⠛⠖⠞⠛⠒⠖⠒⠒⠒⠒⠖⠖⠒⣦⢤⣂⣤⣀⣀⣻⣷⠏⠉⢩⣿⣯
⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠈⡇⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠚⢻⣿⣿⠛⣿⣿⣷⣀⠙⣿⣿
⣿⢿⣿⡟⠉⠉⠩⠉⠍⠉⠉⠍⠩⡇⠀⠈⠈⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⣿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⣿⣽⣿⡃⠀⠀⠀⠀⠀⠁⠀⠀⠈⡇⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡧⠸⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿
⣿⡿⠿⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣿⣛⣿⣿⡏⠉⠉⠉⠉⣹⠉⠉⠉⠁⠀⠀⠀⡀⠀⠀⠀⠈⣿⡿⠻⠻
⣶⣶⣶⡆⣿⣿⣯⣨⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇⠀⠀⣈⡠⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠅⡆⠶
⣿⣿⣿⡇⢿⡿⠛⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠚⢹⢙⣤⣼⣿⣶⣻⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣼
⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠵⡤⣯⣄⣹⢿⣿⠇⣴⣼⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣶
⣿⣯⣿⣿⢸⣷⣤⣀⣤⢾⣿⣿⣿⣿⡿⠟⠻⠿⠿⠷⠠⠤⠾⣟⣿⣿⣿⣼⠟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⣿⡿⠿⠿⠎⣿⣿⣿⣿⣦⠹⣿⡟⠁⠤⣀⠤⠰⠶⠤⠀⢄⠰⠌⠻⠁⠈⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿