Unemotional Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢀⣤⣤⡀⠀⠀⠀⣀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⠉⠉⠁⠀⠀⠾⠿⠷⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠗⠂⠀⠒⢄⠀⢀⡠⠤⠄⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠉⠉⠉⠉⠉⠉⠉⠉⢙⠃⠀⠀⠀⠀⠀⢻⠋⠀⠀⠀⠘⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⠐⠶⠀⣿⡇⠲⠂⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⠞⠁⠈⠓⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣴⠒⠒⢶⠒⠶⠲⡶⠒⠒⢶⠖⠒⠲⡖⠒⠒⢲⠖⠖⢲⡄⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠻⠶⠶⠾⠶⠶⠶⠷⠶⠶⠾⠶⠶⠶⠷⠶⠶⠾⠶⠶⠼⠃⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠁⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠹⣤⣄⡀
⠀⠀⠀⠀⢀⡴⠏⢁⣤⣷⡀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⣰⣧⣄⠉⠷⣄
⠀⠀⠀⢠⡞⢀⡴⠋⠀⠀⠙⡇⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⡟⠁⠀⠈⠳⡄⠚⣦
⠀⠀⠀⡞⠁⡾⠁⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠹⡆⠙⣆
⠀⠀⢸⠁⢸⠁⠀⠀⠀⠀⠀⠳⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⢶⠶⠇⠀⠀⠀⠀⠀⢹⠀⢹
⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇
⢠⠴⠷⠶⠷⢤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢹⠉⢽⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠍⢽⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠴⠷⠶⠷⢤
⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠄⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠄
⠳⠤⠤⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠉⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠴
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣧⣤⣤⣤⣤⣤⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣤⣤⣤⣤⣤⣤⣤⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠆⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⢦⣤⣀⠀⣀⠀⣀⠀⠀⠀⠉⠉⠉⠀⢀⣠⡤⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⠒⠂⡄⡹⠁⠀⠀⠀⠑⢄⠔⠈⠉⠁⢺⠋⠁⡄⠒⢲⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘⣨⠵⠖⡧⠤⠤⠤⣤⠤⣼⠤⣤⠤⠤⢤⠟⠓⠶⣭⣚⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠁⠀⠀⠱⣄⠀⠀⢀⣠⠋⠳⢤⣠⡤⠊⠀⠀⠀⠀⠉⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢺⠇⠀⠀⢠⡤⠤⢤⡤⠤⠤⡤⠤⠤⢤⠤⠤⢤⡤⠤⠤⣤⠤⠤⣤⠀⠀⠀⢿⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⣾⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠤⠤⠤⠦⠤⠤⠧⠤⠤⠼⠤⠤⠤⠧⠤⠤⠤⠤⠤⠼⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⢒⡚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣀⡱⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣁⣸⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⠋⢀⣀⣤⣤⣀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡖⢦⡀
⠀⠀⠀⠀⠀⢀⡤⠶⠚⡇⢀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡞⠀⣰⠋⠀⠀⠀⠈⢳⡀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⡟⠲⠦⣄
⠀⠀⠀⠀⣴⠋⣠⠴⠛⠳⣼⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡴⠛⠳⢤⠉⢳⡄
⠀⠀⠀⡼⠁⡼⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢧⠀⠹⣄⠀⠀⠀⢀⡼⠁⢠⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⡄⠹⡄
⠀⠀⢸⠇⢴⠃⠀⠀⠀⠀⢸⡇⠀⢀⠤⡀⡇⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠛⠋⠉⢀⡴⠋⠀⠀⠀⠀⠀⠀⡇⡠⢄⠀⠀⣿⠀⠀⠀⠀⠀⢳⠄⢿
⠀⠀⡾⠂⡿⠀⠀⠀⠀⠀⢸⡇⠀⠱⠄⠜⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠤⠼⠁⠀⣿⠀⠀⠀⠀⠀⠸⡇⠺⡇
⢀⣠⣯⣰⣇⣀⠀⠀⠀⠀⢸⡇⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⣿⠀⠀⠀⠀⢀⣀⣷⣨⣧
⡞⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠛⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⡟⠋⠀⠀⠀⠀⡾
⡇⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠷⠤⠤⠤⠤⠤⢤⡤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⣤⠤⠤⠤⠤⠤⠴⠇⠀⠀⠀⠀⠀⢧⡀
⠳⣄⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠼⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠿⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠠⠀⠀⠠⠄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠄⠄⠀⠀⠈⢷⡀

⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠤⠤⠤⢀⣤⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠐⢿⣷⣦⡀
⠀⠀⠀⠀⠄⠀⠀⠀⢀⣤⣤⡾⠟⠛⠛⠁⠀⠀⠉⠉⠛⠹⠖⣀⣄⠀⠙⢿⣿⣦⡄⡀⠀⠙⢶⣆
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣀⡀⠈⠉⠘⠻⢦⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣤⠀⡄⢀⠀⠀⠀⠀⠙⠻⡶⠀⣀⣠⣬⡟⠰⣟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⢿⠃⢿⣿⣦⡟⣄⢹⡌⢌⢣⡙⣄⠢⣀⠨⠒⠙⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢀⣠⠄⣿⡇⢸⣿⣿⣇⢹⣶⠙⣈⢷⡁⡌⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢃⡴⠿⡇⠀⢿⣿⢙⣾⣍⢳⣸⢷⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⢆⠠⡀⠀⠀⢹⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢁⠒⠋⢀⠴⣯⠀⠸⣿⣾⣿⡟⢷⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⠓⢔⡅⠀⠀⠀⠉⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡴⠓⢡⣌⠀⠘⣿⣿⣯⢻⣾⣷⡟⠀⠀⣄⡖⣯⣑⢦⠀⢰⣏⡿⣩⠾⡑⡅⠀⠀⠀⢡⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢈⣡⣿⠀⠀⢸⣿⣻⢿⣿⡿⡁⠀⣰⡾⣽⡗⣢⣿⠀⢢⡟⣱⡟⢢⡞⠃⠀⠀⠀⢰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡿⢋⣵⡄⠀⢨⣿⣿⣿⣿⠣⡀⣶⣿⣿⣟⣾⢯⡖⣰⢏⣾⠛⣴⡿⢱⡖⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠌⠱⠀⠀⠀⣿⣿⣿⣯⠓⣼⣿⣿⣿⣾⣿⠟⣼⣿⣿⢟⡴⠛⠈⠋⠈⠻⠀⠀⠘⣤
⢀⡤⠀⠀⠒⡒⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠿⠟⠋⠉⠁⠉⠉⠉⠀⠈⢉⠘⠛⠛⠁⠀⠀⠀⠀⠐⠶⣦⠀⠀⠀⠁
⠉⠁⠀⠀⠁⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠰⠂⣀⠀⢠⡀⡀⠀⠑⣾⠇⠀⠀⠀⣤⣠⣼⣇⣶⠶⢸⡗⠀⠘⣶⡶
⠀⠀⢀⠀⠀⠀⢸⠿⢿⣳⠄⠀⠀⠀⠀⠀⠐⢻⣥⢶⠛⠻⠷⠿⠞⠃⠀⠀⠈⣷⠀⠀⢀⠀⠀⠉⠀⠀⠀⢸⡇⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⡟⠳⠂⢈⠓⠀⠀⢀⠀⠀⠀⠈⣷⡘⣷⢶⣴⣦⠀⢀⡄⣤⠀⢃⡀⠐⠁⠀⠀⢠⡆⢄⠀⠀⠇⠀⢠⡿
⣟⠀⠀⠀⠀⠀⠻⢤⡀⠢⣁⠀⠀⠈⠱⣄⠀⠀⠸⣧⢿⡾⠋⠁⣀⠘⣧⠀⡄⡞⠁⠀⠀⠀⠀⣼⣷⡄⣇⠀⠀⠀⢠⠁
⠙⠀⠀⠀⠀⠀⠀⠠⠈⠑⣌⠁⢠⣆⠀⠙⠀⠀⠰⡼⠟⣿⠃⠀⣿⠀⡿⡎⢀⠀⣾⠀⠀⠀⠀⣿⣞⢻⣇⠀⠀⠀⢠
⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠈⠔⣿⣷⡻⠀⠀⢀⡄⢳⡟⣻⣇⠀⣿⠀⢻⣿⡟⡀⣿⢤⠀⠀⠀⢿⣿⣿⡙⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⠟⠁⠀⠀⠠⢣⢸⣿⢋⣿⣶⣽⢀⣼⣿⣯⠛⠀⠀⠀⠀⠀⠈⣿⣧⠓⠀⠀⠀⠁
⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡄⠙⣇⢻⣏⣼⣿⡏⠈⢉⣀⡍⠠⠤⢮⣀⠀⡀⠀⠙⡏⠃⠀⠀⡘
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠃⣶⢹⡰⣿⡜⡯⠀⣠⢿⣿⣿⣄⠀⣼⣻⢆⠙⣄⠀⠉⠀⠀⢠
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡄⠀⢹⠀⢸⣿⠁⢟⣳⠣⠀⠿⠋⠉⠉⠋⠃⠙⠋⠛⠷⠈⢦⠀⠀⠀⡜
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠰⡆⠐⢿⡇⠘⣥⣆⠀⣀⠐⠒⠶⠶⠖⠒⠒⣦⣠⣄⠈⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠺⣿⡅⢡⠹⣿⠝⢳⠳⡄⠀⠀⠀⠴⠈⢏⠛⠛⠀⢰⠃
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠈⡿⣿⠀⠄⢻⠞⡐⠃⠐⠚⠛⠓⢾⣥⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠢⣄⠀⢻⡟⣇⠀⢈⠇⠰⡴⢶⣾⡧⠀⠀⠉⢢⡀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠦⡈⠁⠘⣷⣻⡄⠀⠎⡀⠁⢢⡹⡇⠀⠀⠀⠸⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠑⠦⡀⠙⠣⠀⠈⡰⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣉⡀⠀⠀⠘⣧⣄⡀⠀⠁⠀⠀⣀⣀⡀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⣧⠀⠀⠀⢻⣿⡿⣿⠀⠉⠁⠀⠀⠀⠀⠌⢤⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⢵⣄⠈⠀⠀⠀⢺⢿⡇⢹⠆⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⡿⠉⠀⠀⠀⠐⠟⠳⠀⠀⠀⠐⠊⠿⠘⠀⠀⠀⠘⠓⠦⠄
⠀⠀⠄⠁⠀⠀⠈⠃⠀⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠒⣼⣧⠔⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⣀⣀⣀⣸⣇⣀⣀⣀⣸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⢆⠀⠀⠈⢁⡜⠳⣌⣁⣀⠜⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢠⠤⠤⢤⠤⠤⢤⠼⠥⢤⡤⠬⠧⡤⠤⠤⡤⠤⠤⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠸⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠷⠶⠶⠷⠶⠶⠇⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠦⡀
⠀⠀⠀⠀⠀⣠⠴⠒⣿⠀⢻⠀⡰⠒⠢⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠔⠒⢄⠀⡟⠀⣿⠒⠦⣄
⠀⠀⠀⢀⡞⢁⡴⠚⠙⠦⣼⡇⠘⠢⠚⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠓⠔⠃⢸⣧⠴⠋⠓⢦⡈⢳⡀
⠀⠀⠀⠟⢠⠏⠀⠀⠀⠀⠀⠙⢿⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⢀⡀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠻⡄⢻⡀
⠀⠀⣼⠀⡾⠀⠀⠀⠀⠀⠀⠀⢈⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡁⠀⠀⠀⠀⠀⠀⠀⢷⠀⣧
⠀⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹
⣠⠼⠷⠾⠦⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠴⠷⠾⠧
⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠲⡶⣶⣶⣶⣶⣶⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⣶⣶⣶⣶⣶⢶⠖⠋⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠐⡞⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂
⠉⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡜⠛⠋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠙⠛⢃⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⠛⠛⠀⠀⠶⢶⡄⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠒⠒⠠⡀⢀⠤⠠⢄⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣎⣀⣀⣀⣀⣸⣃⣀⣀⣀⡳⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢡⡀⠀⠈⢁⡜⠣⣉⣀⡠⠃⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡶⠒⠒⡖⠒⠲⠖⠒⠲⠖⠒⢲⠒⠒⢲⠒⠒⢦⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⡆⠀⢀⠀⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠰⣁⠵⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⢸⢪⣈⠎⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡖⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢁⡤⠤⠦⢄⡈⠳⡄⠀⠀⠀⠀⢸⠀⠀⠀⠸⡟⢢⡀
⠀⠀⠀⠀⣠⠖⢉⣹⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠏⠀⠀⠀⠀⢹⡀⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢠⣏⡙⠲⣄
⠀⠀⠀⡜⢃⡜⠉⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⡄⠀⠀⠀⠀⣰⠃⢸⠃⠀⠀⠀⢸⠀⠀⠀⠀⣿⠉⠀⠙⢦⠘⢦
⠀⠀⣸⢁⡞⠀⠀⠀⠀⣿⠀⠀⢀⠀⡅⠀⠀⠀⠀⠹⣄⠈⠲⠤⠤⠞⠁⣠⠋⠀⠀⠀⠀⢸⠀⡀⠀⠀⣿⠀⠀⠀⠀⢣⠈⣇
⠀⢀⡇⢸⠁⠀⠀⠀⠀⡿⠀⠸⠀⠕⡀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⢸⠪⠈⠃⠀⣿⠀⠀⠀⠀⠘⡆⢼
⢀⣸⣇⣾⣀⠀⠀⠀⠀⣿⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⣿⠀⠀⠀⠀⣀⣷⣸⣇
⡏⠀⠀⠀⠈⡇⠀⠀⠀⠉⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡟⠉⠀⠀⠀⢸⠁
⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⣶⢲⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡒⣶⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⢸⡄
⠙⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣯⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠉⢳⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣀⡄⠀⠀⣀⢸⡅⣀⠀⢨⢤⣀⡀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠖⠋⠁⠑⢄⣀⡠⠎⠑⠢⠔⠊⠀⠀⠉⠳⢤⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⠤⠤⡤⠤⠤⠤⢤⠤⠤⠤⠤⢤⠤⠤⡄⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠒⣒⡏⣠⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⢤⢹⣒⠒⠦⣄
⠀⠀⠀⠀⣠⠚⡤⠚⠉⠉⠑⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣉⣉⠙⠢⣄⠀⠀⠀⠀⠀⠀⠅⠅⢸⠊⠉⠉⠓⢤⠓⣄
⠀⠀⠀⡴⢡⠞⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠋⠀⠀⠙⢦⠘⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠳⡌⢦
⢀⡔⠚⠣⢏⡀⠀⠀⠀⠀⡠⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⢣⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⠀⠀⠀⡹⠜⠓⢢
⡜⠀⠀⠀⢠⠃⠀⡠⠖⣋⡇⢸⡀⠀⣀⠀⠀⠀⠀⠀⠳⣄⠑⠢⠴⠚⢁⠜⠁⠀⠀⠀⠀⣀⠀⠀⡟⢸⣙⠲⢄⠀⠘⡄
⠑⠢⢤⡰⠋⠀⡞⢠⠊⠁⠈⠛⢳⡈⠀⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⡼⠛⠁⠈⠑⡄⢣⠀⠙⢇⠤⠔
⠀⠀⠀⠀⠀⡸⢠⠇⠀⠀⠀⠀⠀⠉⢹⣯⣭⣭⣍⣍⣍⣍⣍⣭⣍⣩⣭⣭⣭⣭⣭⣩⣭⡟⠉⠀⠀⠀⠀⠀⠸⡄⢇
⠀⠀⠀⠀⠀⡏⣸⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⢐⢐⠀⠀⠀⠀⡆⠢⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣇⢹
⠀⠀⠀⢠⠊⠉⠉⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⡖⠦⠤⠤⣤⣤⠤⠤⠴⢲⡏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠑⡄
⠀⠀⠀⢸⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⣀⣹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⣀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⡇
⠀⠀⠀⠈⠒⠒⠒⠊⠀⠀⠀⠀⠀⣠⠊⠉⠁⠉⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠈⠉⠑⣄⠀⠀⠀⠀⠀⠑⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⠀⠀⠶⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠼⠤⠤⠤⠤⣤⣤⣤⣠⣄⣠⣠⠤⠤⠤⠤⠤⠧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣏⠉⠛⣹⢏⣋⣩⠇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⠀⠀⠀⢠⡤⢤⡤⢤⡤⢤⡤⢤⡤⢤⡤⢤⡄⠀⠀⠀⣿⣦⣤⣄⡀
⠀⠀⠀⢀⣴⡿⠛⠉⠙⢿⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⡿⠋⠉⠛⢿⣦⡀
⠀⠀⢠⣿⠟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⣿⡄
⢠⠋⠛⠻⡄⠀⠀⣀⣰⣿⣶⣾⣿⣿⣷⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣆⣀⠀⠀⢠⠟⠛⠙
⢿⣄⣠⡶⠃⣠⣾⠟⠻⣿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠛⠛⠛⠛⠛⠛⣿⣿⠟⠿⣷⣆⠘⢷⣿⣿
⠀⠈⠉⠀⢰⣿⠃⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣚⣞⣒⣛⣻⣷⣶⣿⣿⡿⠀⠀⠹⣿⡆⠈⠉⠁
⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣷
⠀⠀⠀⡖⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⢲
⠀⠀⠀⣇⣀⣰⡟⠀⠀⠀⠀⠀⣀⣤⣼⢿⠀⠀⠀⠀⠀⠀⠀⠀⡿⣧⣤⣀⠀⠀⠀⠀⠀⢻⣆⣀⣸
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠾⠶⠶⠶⠾⠂⠀⠀⠀⠀⠀⠀⠐⠷⠶⠶⠶⠷⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠐⣀⡐⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢸⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠸⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠿⡄⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡎⠀⠀⠀⠈⢻⠋⠀⠀⠑⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⣇⠀⠀⠰⠂⡾⡆⠒⠀⢀⠇⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⠲⠤⠤⠚⠁⠈⠙⠊⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣠⠤⢤⡤⠤⢤⡤⠤⢤⠤⠤⣤⠤⠤⣤⠤⢤⡀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠓⠒⠒⠓⠒⠚⠒⠒⠚⠒⠒⠚⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢆⡀
⠀⠀⠀⠀⡠⠖⢉⣹⡀⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡇⣸⣉⠑⢦⡀
⠀⠀⠀⡜⢁⡜⠉⠀⠙⡇⠘⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠜⠀⡟⠁⠈⠙⣄⠙⡄
⠀⠀⣼⢁⡟⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠘⣇⢹⡄
⠀⠀⡇⢸⠁⠀⠀⠀⠀⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠁⠀⠀⠀⠀⢹⠀⣇
⢀⣸⣇⣾⣀⠀⠀⠀⠀⠀⠙⠚⠚⠒⠒⠒⣖⢳⡞⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⣶⢛⡖⠓⠒⠓⠒⠚⠁⠀⠀⠀⠀⢀⣸⣆⣿⣀
⡏⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈
⡇⠀⠀⠀⢲⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⠂
⠙⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦
⠀⣔⣂⢶⠀⠀⢸⠓⠋⢃⠇⠀⢀⣀⣀⠀⠀⠤⠤⠤⠀⠐⠒⠒⠒⠒⠒⣒⣒⣛⣉⠷⠀⠀⠣⢤⠼
⠘⡇⠀⢇⢆⣀⡸⠀⠀⢸⢆⡴⠥⠄⠐⡒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢹⠀⡄⠠⠤⢼
⠀⢳⡀⠈⠑⠋⠁⠀⢀⡿⢸⡇⠀⠀⡠⠟⠓⠒⠒⠒⠂⠉⠉⠉⢉⠉⠉⡷⠀⠀⢸⣼⠈⠀⠀⢹⠇
⠀⠀⠙⠦⠤⣤⠤⡶⠋⠀⠈⡇⠀⣞⣀⣀⣁⣀⣀⣀⣀⣀⣠⣤⣤⠴⠞⠁⠀⠀⢸⡾⣄⠤⠔⠋
⠀⠀⠀⠀⠀⢻⠀⠸⡀⠀⠀⡇⠀⠀⣟⠒⢢⠤⠤⡤⠔⡖⠒⠊⡽⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⡀⠤⠒⡆
⠀⠀⠀⠀⠀⠘⡇⠀⢧⠀⠀⠳⠤⠤⠬⠵⣾⣴⣶⣷⣦⣷⣖⣋⣀⣤⣤⡤⠤⠤⠤⠗⠁⠀⢠⠎⠀⡔⡩⠘⠁
⠀⠀⠀⠀⠀⠀⢻⠖⠉⠓⢄⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⣿⠀⠀⠤⠄⡄⠀⠀⢀⡠⢤⠤⠒⠺⡀⠈⠺⠤⠤⣄
⠀⠀⠀⠀⠀⠀⢸⣄⠢⢀⡼⠒⢄⣠⠾⠥⠀⠀⠻⠛⠛⢓⠒⡒⠒⡎⡼⠒⠊⢯⠀⢀⡧⠴⠖⠛⠦⣤⣤⣔⠳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠛⠒⠢⢼⢠⣦⣄⢀⠀⠀⠀⠀⠀⡅⠁⣇⢳⠒⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠛⠛⣋⣂⣀⣀⣠⣤⣤⢤⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠋⢻⠉⠀⠀⠀⠀⡇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⢸⡀⠀⠀⠀⠀⡇⠀⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣁⣠⡤⢦⡬⠇⠀⠀⠀⠀⠓⠊⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⣤⣤⡀⠀⠀⢀⣀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⠉⠉⠁⠀⠀⠾⠿⠷⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠗⠒⠐⠒⢄⡀⢀⡠⠤⢄⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠃⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠘⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⡤⠤⠤⠤⠤⠤⢼⡟⠛⠛⠛⠶⠛⣻⡟⠳⠚⠛⢻⡧⠤⠤⠤⠤⠤⠤⠤⢤⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣠⠞⠁⠈⠓⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣴⠒⠒⢲⠖⠒⠒⡶⠒⠒⢲⠒⠒⠲⡖⠒⠒⢶⠒⠒⢲⡄⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠻⠶⠶⠾⠶⠶⠶⠷⠶⠶⠾⠶⠶⠶⠷⠶⠶⠾⠶⠶⠾⠃⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠁⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠹⡦⣄⡀
⠀⠀⠀⠀⢀⡴⠋⢁⣡⢷⡀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢰⣷⣸⣧⣇⣹⠷⣄
⠀⠀⠀⢠⠞⢂⡴⠋⠀⠀⠙⡇⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣄⣀⢀⣠⣄⣤⣼⡿⠀⢸⣿⠉⠀⠈⠻⣴⠛⣧
⠀⠀⢀⡞⠁⡾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠹⡞⠙⣧
⠀⠀⢸⡁⢸⠁⠀⠀⠀⠀⠀⠳⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠃⠀⠀⠀⠀⠀⢹⠀⣹
⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇
⢠⠴⠷⠶⠷⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢹⠭⢽⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠭⢽⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠶⠷⠶⠷⢤
⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠤⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠄
⠻⠤⠤⠤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠾⠇⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣀⣀⣀⣀⡠⠐⠒⠠⣀⡀⠤⢄⣀⣀⣀⣀⣀⣀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠈⠉⠉⠉⠉⡇⠀⢀⡄⢼⢀⡄⠀⡍⠉⠉⠉⠉⠉⠈⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠴⠋⠑⠦⠒⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⡠⠴⠒⢶⢹⠀⠀⠀⠀⢠⠤⠤⠴⠴⠤⠤⠤⠤⠤⠤⠄⡤⠤⢦⠀⠀⠀⠀⣿⢱⠖⠲⠤⣀
⠀⠀⠀⠀⡰⢋⡴⠊⠉⠙⢾⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣸⠀⠀⠀⠀⣿⠞⠉⠉⠲⣌⠳⡀
⠀⠀⠀⡜⢠⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢣⠘⡄
⢀⠖⠚⠲⢇⠀⠀⠀⠀⢠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⢀⠷⠚⠒⢆
⡎⠀⠀⠀⡸⠀⢠⠔⣉⢽⣸⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣿⣸⣍⡱⢄⠀⠸⡀⠀⠀⠘
⠉⠒⠦⠜⠁⢰⢋⡞⠁⠀⢹⣀⣓⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣁⣿⠀⠀⠑⣎⢧⠀⠙⠤⠒⠊
⠀⠀⠀⠀⠀⡏⡺⠀⠀⠀⠘⢦⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠟⠀⠀⠀⢸⡈⡇
⠀⠀⠀⠀⣸⣄⣇⠀⠀⠀⠀⠘⠧⠤⠤⠤⢤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⢤⠤⠤⠤⠤⠟⠀⠀⠀⠀⢀⣇⣷⡀
⠀⠀⠀⣸⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢹
⠀⠀⠀⢿⠀⠀⢀⡎⠀⠀⠀⠀⠀⢀⡤⠤⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠸⠤⠤⣄⠀⠀⠀⠀⠀⠈⣆⠀⠀⢸
⣀⣀⣀⣀⣉⣉⣉⣀⣀⣀⣀⣀⣰⣧⣤⣤⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣯⣤⣤⣤⣤⣷⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠁⠀⠀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣦⣤⣤⣤⣤⣤⡔⣨⣤⣬⡑⣤⡄⣒⣐⠢⣤⣤⣤⣤⣤⣤⣤⣾⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⣿⡿⣿⡿⣿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢀⣠⠏⠳⢤⣤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡏⣾⡇⠀⠀⠀⠀⢸⡟⠛⢻⠛⠛⢻⠛⠛⢻⠛⠛⢻⠛⠛⢻⠛⠛⣿⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠙⢿⡇⠀⠀⠀⠀⢸⣇⣀⣸⣀⣀⣸⣀⣀⣸⣀⣀⣸⣀⣀⣸⣀⣀⣿⠀⠀⠀⠀⠀⣿⠟⠉⠀⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⢀⣤⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⡇⣀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⣄
⢠⡏⠀⠀⠉⢻⡆⠀⠀⠀⣀⣤⡾⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣤⣤⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣤⣿⣿⣦⣄⡀⠀⠀⠀⣾⠋⠉⠀⠈⣧
⣿⡀⠀⠀⣴⣼⠁⠀⣴⣿⣿⠿⢷⣿⣟⣿⢿⣟⣻⣿⣿⣿⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣽⢿⡭⣿⣷⠿⢿⣿⣷⡄⠀⢹⣴⡆⠀⢀⣸
⠈⠛⠻⠿⠟⠁⠀⣼⣿⡟⠁⠀⠀⢹⣏⣻⣶⣟⣛⣻⣛⣻⣄⣀⣸⣟⣛⣛⣛⣛⣛⣟⣋⣐⣛⣛⣛⣛⣛⣫⣳⣾⣛⣿⠁⠀⠀⠙⣿⣿⡄⠀⠙⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⢸⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢀⣤⠿⠿⣤⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⠼⠿⢧⣄
⠀⠀⠀⠀⣿⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⣀⣀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣀⣸⡇
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣼⣯⣤⣤⣤⣤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣤⣤⣬⣿⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣟⣟⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣯⣭⣽⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣦⣤⣤⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣷⡀
⢰⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷
⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠈⠛⠻⠿⠿⠟⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⠛⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣿⣿⣿⣿⣿⣿⣛⣉⣀⣀⣀⣈⣙⣻⣿⣿⣿⣿⣿⣿⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡙⠒⠦⠐⠒⠂⡀⢀⠄⠠⣠⠴⠒⣋⡉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢐⣰⠵⣄⣀⣀⣀⣸⡇⣀⣀⣨⠶⠮⣆⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠋⠀⠀⠣⣀⣀⣠⠎⠑⠤⠤⠊⠀⠀⠀⠙⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣼⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣧⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢗⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠣⠌⡃⠀⠀⠀⠀⠀⣠⠄⠒⠒⠠⢄⠀⠀⠀⠀⠀⢘⠠⠜⠸⣄
⠀⠀⠀⠀⢀⣠⢤⠋⣿⠀⠀⠀⡅⠀⠀⠀⢀⠎⢠⠔⠊⠑⠢⡄⠱⡀⠀⠀⠀⢰⠀⠀⠀⣯⠙⣤⣀⡀
⠀⠀⠀⡴⢋⡤⠚⢦⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⡴⠓⢤⡙⢦
⠀⠀⡼⢠⠏⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠘⣄⠙⢤⣀⣀⡤⠋⣠⠃⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠹⡄⢧
⠀⢀⠁⡞⠀⠀⠀⠀⡇⠀⡄⠐⡆⠀⠀⠀⠀⠈⠳⠤⣄⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢳⢸⡀
⢀⣸⣠⣇⡀⠀⠀⠀⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⢀⣸⣄⣇
⡏⠀⠀⠀⢱⠀⠀⠀⠙⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⠋⠀⠀⠀⡎
⡇⠀⠀⠐⡞⠀⠀⠀⠀⠙⠛⠛⠛⠛⡿⢳⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡞⢿⠛⠛⠛⠛⠋⠀⠀⠀⠀⢳⠂
⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⠶⠤⢄⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣮⣤⣤⣤⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣤⣤⣤⣤⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⠋⠁⠀⠀⠿⠷⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠉⠉⠐⣄⡀⠒⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⢺⠤⠤⢤⠤⢼⠤⡤⠤⢼⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠢⣄⣀⠴⠃⠑⠦⠖⠃⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣤⣤⣤⣤⡀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠓⠒⠛⠒⠒⠓⠒⠚⠒⠒⠓⠒⠚⠒⠒⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠸⠀⢻⠀⠀⠀⠀⠀⢀⡠⠤⠖⠦⠤⡀⠀⠀⠀⠀⠀⠘⠇⠸⠸⡆
⠀⠀⠀⠀⠀⢀⣠⡞⢹⠇⠀⠀⢸⠀⠀⠀⠀⣠⠋⣠⠔⠒⠒⢤⠈⢢⠀⠀⠀⠀⢨⠀⠀⠀⢿⠙⣆⣀
⠀⠀⠀⣠⠞⣁⠴⢧⣸⠀⠀⠀⢸⠀⠀⠀⠀⡇⢰⠃⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⣠⠷⢄⡙⢦
⠀⠀⢰⠇⡜⠁⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⢧⠈⢧⡀⠀⠀⣠⠃⢠⠃⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠹⡄⢷
⠀⢀⡗⢸⠁⠀⠀⠀⣿⠀⢠⠀⣼⠀⠀⠀⠀⠀⠳⢄⣈⣉⣉⣠⠔⠃⠀⠀⠀⠀⢨⡄⢠⠀⢸⡇⠀⠀⠀⢱⠘⡇
⠀⢸⠁⡏⠀⠀⠀⠀⣿⠀⠈⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢸⡇⠀⠀⠀⠈⡇⢽
⡖⠉⠉⠉⢳⠀⠀⠀⠻⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠾⠃⠀⠀⢰⠋⠉⠉⠑
⡇⠀⠀⠀⣸⠀⠀⠀⠀⠸⠤⠤⠤⠤⢤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⣤⠤⠤⠤⠤⠼⠀⠀⠀⠀⢸⡀
⠑⠶⠶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣽⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠉⢦

⣶⣶⣒⣶⣶⣺⣻⣫⣫⣿⣿⣿⣟⣟⣽⣟⣞⣖⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⢶⣶⣶⣲⣶⡶⣲⣶⣲⣖⡖⣲⣲⣲⣲⣒⣒⣒⣖⣖⣐⣖⣶⣷⣟⣶⣟⡿⣳
⡯⣚⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿
⡯⢔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢽
⣓⠕⡂⠀⠀⣿⢿⡽⣟⣿⡆⢸⣿⣿⣽⣿⡇⠀⠀⢸⣿⡇⢸⣿⣟⣽⣿⡇⢠⡿⣫⢾⣿⣦⢸⣿⣿⣿⣿⣿⢸⣻⣿⣽⣿⠇⣿⣿⣿⣟⢗⡄⠀⠀⠀⣿⣿
⢸⠬⡇⠀⠀⣿⣿⣧⣼⣟⡇⢸⣷⣿⣤⣤⡄⠀⠀⢸⣫⡇⢸⣿⣿⣤⣤⡄⢸⣽⡇⠀⠛⠛⠀⠀⣿⣿⡇⠀⢸⣫⣷⣤⣤⠀⣿⣪⡇⢸⣿⣷⠀⠀⠀⣗⢽
⢸⡪⡇⠀⠀⣿⣻⡷⢯⣿⡆⢸⣿⣿⠛⠛⢃⣀⣀⢸⣯⡧⢸⣿⣿⠛⠛⠃⢸⣿⡇⠀⣤⣤⠀⠀⣯⣾⡇⠀⢸⡫⡟⠛⠛⠀⣿⣶⡇⢸⣿⡿⠀⠀⠀⡯⢽
⠸⣪⡇⠀⠀⣿⣿⡇⢸⣿⣇⢸⣿⣿⣶⣶⡞⣿⠿⣾⣿⡏⢸⣿⣿⣶⣶⡆⠸⣿⣳⣶⣿⡿⠀⠀⣿⣾⡇⠀⢸⢿⣿⣶⣶⡄⡿⡺⣳⣿⣿⠇⠀⠀⠀⡯⣼
⢸⢕⡇⠀⠀⠉⠉⠁⠈⠉⠉⠈⠉⠉⠉⠉⠁⠈⠉⠋⠉⠀⠈⠉⠉⠉⠉⠁⠀⠈⠉⠋⠉⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⡯⢻
⢸⡭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢺
⢼⣊⣋⣉⣙⣉⣟⣙⣙⣙⣩⡫⡫⡫⡫⢋⣋⢫⢏⣝⣏⣏⣋⣯⣿⣻⣫⡫⣫⢫⢉⢝⣝⣝⣽⣩⣩⣫⣿⣻⣟⣽⣟⣽⣿⣯⣟⣝⣭⣭⣫⣫⣯⣫⣫⣪⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣴⣤⣴⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⣛⣉⣭⣭⣭⣍⣙⡻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣫⠴⠋⠉⠀⠀⠀⠀⠀⠈⠉⠳⢬⡛⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⢫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠋⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⠀⢠⠀⠄⢠⠀⣤⠠⠀⡠⠠⠀⠄⡄⠄⢠⠀⠀⣤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⡀⢸⠀⠀⢸⠀⣛⠀⠈⣄⠀⠀⠀⡇⠀⢸⠀⡀⣿⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⢀⠈⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⡄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣴⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣌⡳⢦⣄⣀⠀⠀⠀⠀⣀⣤⠖⣋⣴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⣦⣭⣭⣍⣩⣭⣥⣶⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠛⠋⠙⠉⠈



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⢿⣿⠛⠛⠉⠉⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⡿⠿⠟⢻⡏⠉⠁⣀⣨⣿⡀⠀⣿⡆⠀⢹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⠟⠛⠛⠻⣿⣀⡀⠀⢠⣶⣷⠀⠘⠛⠋⢻⣧⠀⠸⣿⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣶⣿⣿⡿⣿⡿⠛⠋⠉⢉⣿⡇⠀⢴⣦⣀⣸⣿⣿⠀⠈⣿⣿⡆⠀⢰⣶⣿⣿⡄⠀⠛⠁⢀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⡿⡿⠿⠛⢻⣿⣿⣧⠀⠸⣿⡀⠀⠿⠟⢻⣇⠀⠸⣿⡿⠿⢿⣿⡇⠀⢸⣿⣿⠀⠈⠁⢀⣸⣧⣤⣶⣶⣿⣿⠿⠿⠟⠃
⠀⣶⣿⣿⣿⠿⠟⠛⠛⠻⣿⡆⠀⢠⣶⣾⣿⣿⣿⡄⠀⢿⣇⠀⢠⣤⣴⣿⠀⠀⠻⠇⠀⢸⣯⣽⣀⣀⣿⣿⣷⣾⣿⣿⠿⠿⠛⠛⠉⠁
⠀⢹⣿⣿⣿⡄⠀⢲⡆⠀⢸⣷⠀⠈⠉⢀⣻⣿⠿⣧⠀⠸⣿⡀⠀⠛⠉⠉⣷⣤⣤⣤⣴⣿⣿⣿⡿⠿⠟⠛⠋⠉
⠀⠈⣿⣿⣿⣷⠀⠈⢁⠀⠙⣿⡆⠀⠻⠿⠿⣧⠀⠙⠀⣠⣿⣧⣤⣶⣾⣸⣿⠿⠿⠛⠛⠉⠉
⠀⠀⢸⣿⣿⣿⡆⠀⢹⣇⠀⠸⣿⣀⣀⣠⣤⣾⣿⣾⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⣿⣿⣿⣷⣀⣬⣿⣶⣶⣿⣿⡿⠿⠛⠛⠉⠉
⠀⠀⠀⢸⣿⡿⣿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡖⠉⠑⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢸⡇⠀⠀⡂⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⢤⢀⠎⠀⠀⠀⠈⠣⠀⠤⠃⡄⠀⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⣠⢃⣴⠶⠶⠶⠶⠶⣆⠹⣄⠀⠀⠂⠀⠀⠀⠀⠀⠑⠊⠀⣠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿⠀⣀⠀⠀⠀⠀⡀⢸⣿⣿⢇⠀⡰⢁⣾⠃⠀⠀⠀⠀⠀⠹⣧⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢻⡿⢸⣿⠀⠀⠀⢸⣿⢸⡟⠀⠀⢳⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢙⣷⢘⡟⢉⣍⠁⠀⠈⢉⣍⢹⡿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⠀⠉⠀⠀⠂⠈⠉⠀⠀⣄⡠⠎⢢⠙⣧⠀⠀⠀⠀⠀⠀⢀⡾⢁⠾⠃⢸⣿⠀⠀⠀⢸⡿⠘⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡄⠀⠀⣠⠤⠤⠦⣅⠀⠀⢀⠎⠀⠀⠀⠣⡘⢷⣄⣤⣤⣤⣠⡾⢡⢮⣤⠀⠀⠀⠀⠀⠐⡄⠀⠀⢠⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠢⠤⠴⠂⢀⠴⠋⠀⠀⠀⠀⠀⠱⠄⠬⡥⢠⠄⠈⠰⠃⠀⠻⣆⠀⢰⠶⠶⠞⠶⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡗⠂⠚⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠈⠲⢄⠑⠶⠚⣁⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠀⢻⠈⢹⡇⠀⠀⣿⠈⠉⠉⠘⠢⡄⠀⠀⠀⠞⠉⠉⠈⢦⠀⠀⠀⠀⣀⣤⣤⢴⡇⠉⠁⠿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢾⠀⠈⠉⠒⠊⢹⠀⠀⠀⠀⠀⠘⢆⠀⠈⢆⡀⡠⠤⡿⠀⠀⡰⠋⠀⢸⣿⠀⢇⡀⣠⠂⣿⡟⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⢸⣀⠶⡀⠀⠀⠀⠀⠣⡀⢠⠉⡏⢸⠁⢠⠎⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢀⡄⣫⠀⢠⣀⣀⡠⠊⠀⠀⠈⢢⠀⠀⠀⣠⢇⢸⠀⡇⢸⡴⡁⠀⠀⠀⠀⢼⣿⣀⡀⠀⢀⣀⣿⣷⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⢳⣄⠔⠉⡃⠈⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠙⢤⡔⠁⠀⢻⠀⠣⢼⠀⠈⢢⠔⠊⢙⣼⣿⣿⡇⠀⢸⣿⣿⣧⡜⠒⢄⡴⠃⠈⢢
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣔⠁⠀⠀⠀⡃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠈⢢⠀⠀⡆⠀⠸⣀⠔⠁⠀⠀⢘⠉⠉⠉⣹⠀⢸⠉⠉⠉⢡⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠘⡄⠀⢀⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⠀⠀⠀⠈⠀⠀⢸⠢⠔⠁⠀⠀⠀⠀⣽⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠘⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⣀⣇⣇⠀⠀⠀⡆⠀⠘⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣄⠰⡄⠀⠀⠀⠀⠀⠀⣠⣎⣉⣩⣿⣿⣿⣿⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢈⡆⠉⠑⢦⠀⢀⢴⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⢀⡅⠰⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠁⠀⠀⠀⡰
⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠘⣄⢀⢄⢠⡿⠃⠀⠉⡉⣉⠉⠀⠈⠻⣿⣿⠀⠀⡎⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡸⢀
⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢈⡯⠶⠋⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⣧⢻⠰⣇⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⠀⠀⠀⢣⡟⢼
⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⠼⠻⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⡀⠀⠀⠈⢸⠾
⠀⢠⡀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠑⢄⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣄⣠⣤⠃⠀⠀⢠⣄⣀⣤⣴⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠉⠉⠉⠙⠄⠀⠀⠉⠉⠉⠉⠉⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠿⠋⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠻⢿⣿⣿⣿⣷⠀⠀⠀⠀⠰⠋⠀⠀⠀⠰⠿⠤⠊⠀⠀⠀⠘⠤⠼⠂⠀⠀⠀⠈⡆
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡾⠟⠛⠛⠛⣉⣉⡙⠛⢛⠛⠻⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⣩⠀⢰⣾⢛⡁⢰⣿⠈⠛⠀⠉⣿⠗⠃⢠⣬⣙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢋⡅⠀⠀⢻⣧⠀⣿⡟⣁⠸⣿⣀⣶⠀⢠⣿⠀⢠⣿⣯⡉⠁⣠⣍⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⢶⣯⣡⡦⠀⣤⣿⡇⣙⣛⣭⣤⣼⣿⣷⣤⣬⣥⣀⠿⣧⡌⢀⣾⠟⣹⡷⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢋⣴⣶⡄⠙⢿⣴⠞⣨⣷⡿⠟⠋⠉⠉⠉⠀⠈⠉⠉⠙⠛⠿⣶⣤⡻⢦⣾⠟⠁⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠻⣷⣼⡛⢷⢎⣵⡿⠟⠁⠀⢀⠀⠀⣠⣷⡦⠀⣤⣆⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠹⣿⣄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠈⠿⣢⣾⠟⠁⠀⠀⠀⠺⠿⠀⠘⠛⠓⠀⠉⠋⠀⠀⣀⣀⣀⣀⣽⣿⣦⣤⣶⣶⣶⣾⠿⠿⠿⠟⠛⠛
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣰⣿⠃⠀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⢿⠿⠿⠿⠟⠛⠛⠛⠉⠉⣉⣉⣁⣤⡀⢠⣤⣶⣶⣦⡄
⠀⠀⣀⣀⣀⣿⣯⣤⣤⣴⣶⣶⣶⡿⠿⠿⠿⠛⠛⠛⠛⠉⢉⣉⣉⡀⠀⣠⣴⣶⣤⡀⢰⣾⣿⣿⠿⠇⣿⣿⡛⠛⠃⠘⣿⣏⠉⣿⣿
⠀⠘⠛⠛⠛⠋⠉⠉⠉⠁⣀⣤⣤⣤⡄⠀⠀⠀⣾⣧⠀⣿⣿⠟⠛⠃⢐⣿⡏⠉⠿⠷⠀⠀⣿⣿⠀⠀⢸⣿⣷⣾⡧⠀⣿⣿⠀⢻⣿⡄
⠀⠀⠀⠀⣿⣿⠿⣿⣷⡄⢸⣿⡏⠉⠁⠀⠀⠀⣿⣿⠀⢻⣿⣶⣶⡆⠘⡟⣧⠀⢀⣀⡀⠀⢸⣿⡇⠀⠸⣿⣇⢀⣀⡀⢻⣿⣤⣼⣿⠁
⠀⠀⠀⠀⢹⣿⣤⣼⣿⠃⠸⣿⣿⠿⠿⠀⠀⠀⢻⣿⡆⢸⣿⡏⠀⠀⠀⢻⣿⣀⣸⣿⠇⠀⢸⣿⡇⠀⠀⠿⠿⠿⠿⠃⠘⠛⠛⠉⣁⣀⣀⡄
⠀⠀⠀⠀⢸⣿⡟⠻⣿⣆⠀⣿⣿⣀⣠⡄⢿⣗⣼⣿⠇⠈⣿⣿⠿⠿⠀⠈⠛⠛⠛⠋⢀⣀⣀⣉⣤⣤⣤⣤⣶⣶⣶⣶⠿⠿⢿⣿⡟⠛⠛⠋
⠀⠀⠀⠀⠈⣿⣧⠀⢿⠿⠄⠻⠟⠛⠛⠃⠈⣉⣉⣉⣀⣤⣤⣤⣴⣴⣶⣶⡾⠻⠿⠿⠟⠛⠛⠛⠉⠉⣹⣿⠃⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣶⣶⡿⠿⣿⣿⠟⠛⠛⠛⠋⠉⠉⡉⠀⢀⣀⣠⠀⢠⣤⡀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠘⠛⠛⠙⢿⣯⠉⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠒⠿⠄⢠⣿⡿⠆⠈⠉⠀⠀⢀⣴⣿⠟⣰⣟⠻⣶⣄⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⣠⣦⣌⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣤⣶⠿⢋⣥⠶⠈⠻⢷⣬⡿⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⢀⣼⢿⣥⣿⢃⣤⣍⡛⠻⠿⠾⣿⣶⣿⠾⠿⠿⠛⢉⣥⡶⠊⢿⣶⡋⣀⡀⢉⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣮⡉⣼⡟⠀⣼⣿⣌⠁⠀⢰⡖⢰⡶⠶⠆⣾⡟⠿⠎⠈⢻⣆⠀⠙⠿⣫⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣘⠿⣤⠀⣠⡄⣿⠇⢸⡿⠶⠀⢻⣇⢠⣶⠀⠈⢟⣠⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣬⣛⣋⣀⣸⠿⠶⣂⣈⣛⣻⣥⡶⣺⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢁⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⢠⣟⠁⠈⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠺⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣌⡙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠻⠛⠋⠁

⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⡀⠤⠤⢤⣤⣤⡤⠤⢤⣤⣠⡤⠤⢤⣤⡤⠤⣤⣤⠤⡄
⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠈⠈⣉⣉⡉⢉⣉⡉⠉⢉⡉⢉⣉⡀⠀⣉⣉⡉⢉⣉⣉⢉⣉⡉⣉⣉⡉⠉⠉⠉⠉⠉⠉⡃⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣏⣹⡷⢸⣯⡅⠀⢸⡇⢸⣯⡅⣸⠉⠉⠙⠈⣿⠁⢸⣯⡅⢻⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠿⠹⠆⠸⠷⠆⠲⠾⠃⠸⠶⠆⠙⠶⠴⠖⠀⠻⠀⠸⠶⠆⠸⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠂⠀⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣶⣶⣶⣶⣎⡁









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

⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣄⡀⠀⠀⠀⠀⣀⡀⣠⣀⡀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⢀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠓⠃⠁⠋⠰⠀⠀⠀⠰⠘⠈⠐⠁⡃⠀⠀⠀⠆⠃⠁⠚⢨⠀⠀⠀⢀⠙⠉⠁⠃⠀⠀⠀⠀⠀⠋⠈⠘⠀⠂⠀⠀⠀⠐⠃⠁⠋⢸
⠀⠀⠀⠀⣀⠀⡄⠠⡄⢀⡀⠀⢀⣀⠀⠀⢈⠀⣃⠀⠀⢀⡄⣀⠀⡀⢸⡀⠀⠀⣸⢀⡀⢀⡀⣄⠀⠀⢀⡁⠀⠀⠀⢀⣀⠀⠀⣀⠀⡀⠀⡀⢈⡀
⠀⠀⠀⠀⠒⡆⠀⠀⠀⡖⠂⠀⠐⠚⠀⠀⠂⢀⠒⠁⠀⠑⠃⠀⠀⠀⡘⠊⠀⠈⠚⡀⠀⠂⠀⠓⠁⠀⠐⢂⠀⠀⠀⠘⠚⠀⠀⠒⠃⠀⠀⠀⡖⠂
⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠀⠀⠀⠀⠑⠀⠐⠁⠀⠀⠀⠀⠈⠒⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠑⠀⠐⠁⠀⠀⠀⠀⠈⠂⠀⠊

⠀⠀⠀⠀⠀⢔⡖⠆⡶⢂⠀⠀⠀⠀⢲⢲⢒⠖⡄⠀⠀⠀⡐⡖⠖⣲⠠⠀⠀⠀⠀⢴⠶⠖⡖⠀⠀⠀⠀⠀⡶⠲⢲⠒⡀⠀⠀⠀⣐⡖⠆⡶⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠄⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣒⡀⠓⠀⠂⣐⡂⠀⠰⣲⠀⠀⠐⠀⣒⠄⠀⢔⡇⠀⠀⠀⢸⡢⠀⠠⣲⠀⠂⠐⠂⣗⠄⠀⢔⡂⠀⣀⠀⢰⡲⠀⠀⣒⡄⠂⠀⡂⣐⡂
⠀⠀⠀⠀⠀⠣⣀⡈⡠⠀⠀⠀⠀⠀⢄⣀⢀⠄⠀⠀⠀⠀⠠⣀⣀⡠⠂⠀⠀⠀⠀⠃⣀⠁⡠⠀⠀⠀⠀⠐⢄⣀⢀⠄⠀⠀⠀⠀⠠⡚⡈⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣖⣲⣶⣶⣶⣶⡄⢀⣶⣶⣾⣯⣴⣶⣶⣶⣶⣶⣶⣶⣶⠆⡼⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⡿⢿⣏⣭⣭⣿⠟⢻⡿⠿⠛⠛⠀⠈⠁⠚⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡝⢻⣿⢿⣿⡇⠰⣿⣿⣿⣿⠋⠁⢀⣠⠄⢀⣀⠀⠀⠀⣠⣶⣶⣄⣠⣄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢣⣴⢶⢶⣄⢷⣄⠙⠿⠃⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠸⣿⣿⣿⠟⠀⣻⡷⠀⣸⣷⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢹⠏⠁⠀⠀⣛⣥⡶⢰⠂⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⢠⣶⣤⣾⣿⡿⠙⠘⢀⣼⣿⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣯⠈⠻⣯⣿⣿⠿⠛⠛⠻⣶⠳⠶⢾⣿⣧⣀⠀⠀⠀⠀⠘⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡼⠋⣠⠀⣹⡟⠁⢂⣀⡀⠈⠉⠀⠀⠠⠉⠛⠿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡀⢻⣾⠟⠁⢆⠀⠈⠁⠁⠀⠀⠀⠀⠁⠸⠗⡄⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣙⣡⡮⠨⠀⠈⢀⠀⠀⠀⠁⠀⠀⠀⠐⠀⣀⡐⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⣦⣤⠀⠀⠑⠂⢀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠠⢸⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣼⡇⠀⢿⣿⠓⢄⠀⠀⠊⠻⠷⣤⣤⡤⠠⣾⣷⣆⠀⠀⠙⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡇⠀⢸⣿⡔⣆⢀⢀⣀⠀⠀⠀⠀⠀⣤⣼⣿⡘⠂⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣠⣼⣿⣥⣬⣿⣿⡛⠱⣤⣤⣠⣶⣿⢩⣿⣧⠄⠁⣬⠸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡟⣿⣽⢻⣿⣿⣿⣿⣿⣥⣌⣉⣁⡿⠿⣿⣿⣿⢻⡄⣢⠽⠺⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠙⠛⠿⠒⠛⠁⣿⡟⣿⣟⡉⠀⢈⣿⣿⣿⣿⣿⢻⡇⠀⠂⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⣖⣲⡆⢀⣇⢀⡳⠄⠀⢀⣀⠈⠉⠉⠉⠋⠸⠇⡰⣤⣨⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⠉⢡⠊⠉⠁⠉⠀⠀⠉⠉⣻⠀⠀⠈⠀⠀⢈⡟⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠀⢠⡀⢽⣷⣶⣶⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠉⠙⠛⠏⠉⠏⠱⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⠉⠀⠀⢀⡈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣠⣎⣀⣀⡀⠀⠀⠉⠲⡄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣤⣤⣬⣉⣉⠓⠲⢤⣢⡈⠀⠠⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⣌⠙⢦⡀⠸⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⣧⡀⣷⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⠃⢀⣀⡀⠈⠉⠛⠿⣟⣫⡍⣼⣿⡿⢩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⡏⢉⣠⣉⡙⠒⠀⠀⣿⡟⣰⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢿⡩⠤⠤⠄⠀⠀⠀⣿⠁⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⢳⣖⣂⣀⣀⣤⣴⠇⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣈⠨⠿⠿⠿⢛⣸⣿⣿⠟⢙⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⡟⢻⣿⣿⣿⣿⣿⣿⠟⠁⣠⠏⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⡼⠀⢸⣿⣿⠿⢟⣯⣶⣶⡟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⢰⠇⠀⠀⠀⢠⠖⠉⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣾⡄⠀⠀⣴⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣼⣃⠀⠀⣠⠞⠁⠀⢀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉




⡶⡶⢶⠶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⢶⣶⣶⡶⠶⣶⢶⣶⣶⢶⣶⡶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣿⣆⣸⣿⣤⣾⣇⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⣿⣷⣿⡟⣿⣿⣿⣿⣿⢿⣷⣴⡿⠁⠀⠀⠀⢀⠀⢠⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣹⣿⣿⣿⠟⢣⢻⣉⣩⣽⣧⣿⣿⣿⣿⣾⡟⠰⣦⣼⣷⣾⣷⣿⣶⣿⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣛⠿⣅⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣉⠉⢻⡟⠁⠈⢻⣿⣧⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣾⣿⡿⠟⠛⠉⠹⡍⠉⠉⠛⠻⣿⣿⣿⣯⣷⣾⣿⣦⣤⣾⠿⣿⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣰⣄⣶⣲⢽⣿⣫⣿⣿⠟⠉⢦⣀⣠⠤⢶⣷⠶⠦⣤⣞⠀⠈⠛⢿⣿⣾⣿⣿⡿⠀⠀⠈⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠃⠀⣠⠞⠻⣀⠀⠠⡿⠄⠠⣯⠟⠓⣤⢀⣨⢿⣿⣿⣻⡾⢿⡟⢻⣜⠛⠂
⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠲⣴⣇⢀⡀⠋⠀⣀⣅⣄⠴⠉⠢⡀⠘⢻⡀⠀⢻⣿⣿⣷⣾⢷⡞⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⡇⠀⢰⡏⠈⠛⠀⢠⣿⣿⡿⣇⣾⣦⠀⠀⠀⠈⣧⠀⠀⣿⣿⣿⣿⣿⣙⣿⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⢼⣗⣲⡆⠀⣿⣿⣿⣅⣿⣿⣿⠆⠀⠓⠂⣿⠉⠉⣿⣿⣿⡿⡜⡟⠛⠒⡾⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⡇⠀⣠⡀⠘⢿⣿⣾⣿⣿⠟⠀⣰⢦⣀⡟⠀⢀⠿⣿⡋⡠⢟⣙⣤⣘⡳⣇⠑⢄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⡔⠋⠻⢭⣻⣿⣿⣿⡄⠀⣹⣾⠟⠓⢀⡀⠈⠉⠉⠀⣠⡄⠀⢉⡟⠓⠦⣼⣿⠒⠽⣱⡟⠉⠉⠉⢻⣎⢶⡩⡵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣧⡀⢀⣸⣿⣿⣽⣿⣿⣎⠁⠈⠳⣤⣼⠋⠀⠘⠇⠀⠈⣭⡶⠋⠀⠀⣜⢫⣏⣀⡇⢿⡀⠀⠿⠀⢠⡿⢘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⠛⠉⢻⣿⣿⣿⣿⣿⣿⢿⣿⣷⣄⠀⡰⠉⠛⠒⠒⡗⠚⠉⠁⠘⢠⣬⡷⠿⢿⣭⣵⠛⢌⠻⣦⣤⣴⠟⡡⠯⣝⡳⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣄⣀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣦⣤⣄⣀⣧⣤⣤⣶⠔⣶⣿⣇⣀⣸⣧⣈⣣⣴⢫⠖⠒⢶⢻⣠⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣹⣿⣿⠏⠀⠉⣿⣿⣾⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⢛⣿⡿⢧⢿⣿⠟⠻⣎⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⠿⣷⣤⣴⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⢸⣿⣿⣿⣷⡒⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣛⣛⣿⣾⠂⠉⠉⠙⣿⣿⣿⠉⢹⣿⣿⡇⠈⠉⠒⢦⣄⡀⠀⠀⣰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣄⠀⢀⣰⣿⣿⣿⣷⣿⣿⣿⣿⣦⣤⣴⣿⣿⣿⣷⣦⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⢿⣿⣿⣿⡟⠋⠉⠻⣿⣿⠏⠁⠈⠙⣿⣿⣿⣿⣌⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⡀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣿⣿⣿⠉⠙⠁⠙⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⡿⠿⣿⣦⣴⣾⣿⣿⣿⣷⣾⣿⣿⡉⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡿⠉⣿⡿⠻⣿⡟⢻⣿⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠻⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠖⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⢰⣟⠋⠁
⠀⠀⠀⠀⠀⠀⡔⠁⡠⠔⠣⡀⠀⠀⠀⠀⠀⠀⠀⡈⠂⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⣆⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⠈⢻⣂⠈⠑⠒⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡵⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⡠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⣀⣁⡀⠀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⢎⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⣄⣀⠀⣁⠐⠂⠐⠒⠀⠩⠶⠶⠀⢸⡟⣕⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⣯⣼⠃⣿⣭⠃⢀⣿⢰⣷⠲⢠⡖⢠⡤⣤⢀⢠⡍⡉⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠘⠃⠿⠀⠿⢠⠰⢾⡏⢰⡇⠁⢿⠁⠀⠀⣿⠀⣸⡇⠀⣾⣇⣷⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⡀⢀⣀⠀⠀⠀⠁⠈⠀⠁⠐⠛⠀⠿⠣⠆⠿⠹⠏⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠁⢂⠜⡹⠀⠉⢉⣀⡖⣖⣂⠠⣤⡤⠤⠤⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠍⠉⠁⠀⠏⠁⠉⠉⠨⠩⣷⢹⡄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠂⠐⠀⠀⠀⠀⠴⠷⠓⠈⣪⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠛⠓⠒⠒⠂⠒⠂⠀⠉⠉⠛⠃⠉

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⢀⡀⢸⡇⠀⣀⣴⠆⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇
⠀⠀⠀⣸⣟⠚⣿⣿⢷⠀⠀⠀⣤⠿⣤⠀⠀⠀⢀⣬⣯⣄⠀⠠⠁⢸⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠟⣦
⠀⠀⢸⣿⣿⣷⣿⡇⠘⠀⠀⢠⠇⠶⠻⡆⠀⢠⠞⢻⣿⠉⠋⠃⠀⢸⣿⠀⠑⡄⣤⣀⡀⠀⠀⠀⠋⡇⠀⢻⠑
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⢠⢓⡿⣿⡿⠟⠀⠀⠀⣳⣾⡏⠁
⠀⠀⠈⠙⠉⠹⠹⠀⠀⠀⠀⠀⢱⢲⡆⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠸⠟⠀⠈⠉⠀⠈⠙⣾⡆⠀⠀⢿⢸⠃⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⣠⣤⠀⠀⣠⠶⠋⠀⠰⣶⠀⣼⣿⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣻⣃
⠀⠀⢀⣼⣯⣬⢿⡙⠂⠀⠀⣿⣿⣷⣿⣿⡇⠀⢺⣿⣿⣿⣿⡀⠀⠰⠆⠀⣨⣯⣤⣀⣶⠀⠀⢠⡾⢻⣿⡿⣦⣸⠁
⠀⠐⠏⢿⣿⠻⠏⠀⠀⠀⠀⢿⣿⡿⠟⠛⠃⠀⠀⢻⣿⣿⣿⡇⠀⠀⠐⠚⠙⣿⡇⠀⠀⠀⠀⠋⢲⣾⣿⡧⠈⠿
⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⡶⠛⠻⣷⡀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⠿⡇⠀⠀⠀⠀⠀⠀⣿⢻⠇⠀⠀⠀⢀⣾⡇⠀⠈⣿⣧⡄⠀⠀⠀⢹⢻⡇
⠀⠀⠀⠃⠀⠃⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⡀⠀⠀⠀⠀⠀⠀⢐⠈⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢇⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠒⠒⠃⠐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣦⡀⠀⠀⣉⠐⠄⠀⠀⡀⠀⠌⣠⠀⠀⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠠⠉⠀⠂⠀⠀⢄⠙⠋⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣄⣠
⠀⠀⠀⣀⡴⠶⣤⡀⣀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠵⠋⣠⠇
⠀⠀⠀⠈⢮⠂⠀⠈⠙⠻⢶⣠⣀⢀⠀⠀⠉⢁⣀⣲⣶⢶⣖⣒⣐⣒⠊⠀⠀⢀⣀⠔⠉⠀⠀⡘
⠀⠀⠀⠀⠀⠑⢕⠄⠀⠀⠀⠈⢹⠋⢤⡄⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⢺⡋⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠸⠀⣖⠄⢸⠀⠀⠀⠀⠠⠀⠀⢨⣍⣩⡅⠀⠁⢀⡠⡢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⢐⡀⢸⠀⠠⠤⠦⡠⠅⡀⠐⢒⡔⠂⠀⡏⢣⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢻⠀⢔⡀⠀⢉⣉⣉⣈⡀⠈⠁⠨⡵⠮⡅⠀⡇⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡸⠀⠀⠀⠀⠈⠁⠛⢸⠁⠀⠀⠐⠪⠭⠂⠀⣌⠛⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢡⡀⠀⠀⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⠛⠛⠯⠭⠭⠭⠿⣩⡟⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠸⢄⡀⠀⠀⠀⠀⠀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠄⡄⢹⠄⠀⠀⢀⡈⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠈⠒⠲⠶⠖⠒⠉⠀⠀⠀⠀⠁⠲⠆⠤⡤⡤⠪⠀⠀⠀⠀⠂⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠅⠍⡠⡾⠏⠀⠀⠀⢈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠋⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢻⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣿⣿⠋⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣤⣀⣲⣾⡿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡼⣿⣹⣿⡏⢀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣉⡛⠻⠇⢸⣿⠛⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⣡⣶⠞⣿⡿⢃⢽⣿⡿⣿⡟⠋⠉⠉⠙⠛⠿⣿⣿⣿⣿⣶⣮⣽⣤⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⢀⡉⡏⣾⣿⢡⣿⠞⣥⣜⡿⠃⣀⣄⣀⣀⣤⣤⢀⠉⠙⢿⣿⣟⣿⠟⠀⠀⠀⠀⠀⠘⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠻⢦⣽⠋⢩⣽⣿⣿⣄⠻⣯⠀⠐⡭⠝⢿⣿⠿⠛⢾⣿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⣷⣿⣇⣤⣿⣿⣛⠟⢻⣿⡏⠀⠀⠀⠀⠘⠋⠀⠀⠘⣇⠸⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣃⣀⣙⢿⣿⣷⣿⣿⣿⣿⡀⠻⠄⠋⠷⠆⠀⠀⠀⠀⠴⢶⣴⣿⣄⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣉⣩⣽⣿⣿⣿⡆⣙⣿⢻⠛⣦⣤⡆⠀⠀⠀⠀⢀⣀⣠⣜⣘⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⡟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣩⣿⣿⣿⡠⡍⠴⣹⣿⣻⣷⣿⡇⢱⡀⠀⠀⡀⣎⠀⣰⠶⣶⣿⣿⣿⣀⣀⣀⣴⡎⠛⢛⡏⡍⢉⢹⢿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢆⣿⣻⣿⣟⡏⠈⠹⣏⣿⣷⠀⠻⣷⣶⣷⡈⠉⠀⣠⣠⣽⣿⣿⣿⣿⣿⣿⣷⡄⢸⡇⢨⣽⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣙⣧⣈⡍⠉⣽⣿⣧⣤⣴⣿⣿⣿⡆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⠿⣿⣷⣸⡇⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣶⣾⣿⡿⠟⣿⣿⣿⡿⢳⠀⠈⠂⠀⣸⣿⣿⣿⡿⣿⣿⡟⣳⡿⠛⠉⠀⠈⣉⣳⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢰⣿⣿⣿⣿⣧⣼⣿⣿⡟⠀⢻⡇⠀⠀⠘⣿⠋⡠⢋⡔⠉⡿⢰⡟⠀⠀⢠⡶⠋⠉⢄⡙⠻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠐⣿⡀⢠⠞⣡⣴⣦⣈⠀⠀⢠⣿⠀⠀⣴⠋⠉⢢⠀⠀⠉⠢⠌⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠏⢰⣿⡆⣿⠃⣀⠴⣿⣿⢿⣿⣦⣀⣾⡇⢀⡾⠁⠀⠀⠄⢀⡤⠔⠚⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠀⠀⣾⠇⠸⣯⠀⢻⣿⠟⣵⠟⢋⡽⠉⠙⢠⡞⡐⢠⠋⣠⠖⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣇⠀⣰⣯⠁⠀⠹⣦⣿⢡⡞⣡⡶⡛⠁⠠⣤⣿⡿⢠⠇⠔⢹⣿⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢰⣿⣏⠂⢀⠀⣿⢃⠏⣰⠟⢘⠅⠀⢀⣿⣿⢣⣿⢸⡄⡸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣿⣿⣾⣷⣷⡟⠀⣠⣾⣿⣯⡿⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠃⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠘⠉⠉⠂⠀⠀⠀⠀⠀⡄⠀⢀⡄⠀⠀⠀⠀⠸⠿⠟⠃⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠠⠶⠶⠄
⠀⠀⠀⢀⡀⢤⣴⢄⠀⠀⠀⠀⢀⠠⣶⣾⢃⠀⠀⢀⢘⡮⣶⣴⢄⠀⠀⠀⠀⠀⢐⣶⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⣿⠇⢰⡏⢹⡅⠀⠀⠀⣼⣆⡿⠁⣾⠀⠀⠀⠀⢘⠻⡟⢻⠀⠀⠀⠀⠐⢋⣿⡙⠂⠀⠀⠀⠀⡀⠘⡇
⠀⠀⠀⠀⠘⠐⠃⠺⠃⠀⠀⠀⠀⠚⠀⠀⠿⠀⠀⠀⠀⠈⠒⠓⠚⠀⠀⠀⠀⠸⣟⣛⣻⠏⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⢉⠀⠀⠀⠀⠀⠸⠛⠛⠂⠀⠀⠀⠀⠐⠟⠛⠉⠀⠀⠀⠀⠀⠀⠛⠉⠓
⠀⠀⠀⠁⠄⠐⡞⠀⠀⠀⠀⠀⣠⡾⢶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣶⣷⡄⠀⠀⠀⠀⠀⠄⠀⡠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠿⣿⡾⠟⠛⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠠⠝⠀⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢀⡀⣉⡇⠀⠀⠀⠀⠀⣆⠈⣩⠀⠀⠀⠀⢀⢧⣀⣨⡃⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⢳⡇⠀⠀⠀⠀⢀⣯⠉⠉⡧⡀⠀⠀⠀⠀⠞⠔⢑⠂⠀⠀⠀⠈⠁⢈⠀⠉⠀⠀⠀⠀⠀⠐⡖
⠀⠀⠀⣆⣀⣀⣾⠁⠀⠀⠀⠀⣸⠈⣄⡔⢻⡁⠀⠀⠀⠰⢈⠧⠈⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠈⠉⠁⠉⠁⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⡀⢠⡿⠁⠀⢸⣧⣤⣴⣶⣶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠻⠿⠃⠀⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢠⡄⠀⠀⠀⢻⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⣷⣄⠀⠀⠀⣸⠏⠳⣦⣄⣀⣀⣀⣴⠟⠳⣦⣀⣀⣀⣰⠟⠻⢦⣄⣀⡼⠛⠶⢶⣶⠟⠃
⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⣤⣼⠏⠛⠛⠋⠁⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣽⡿⣀⣀⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢸⣿
⠀⠀⠀⠀⠀⣰⡟⠁⣾⠉⢉⣙⣧⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣄
⠀⠀⠀⢀⣼⠏⠀⠀⠙⠷⣤⣍⣩⣷⣀⠀⠀⢀⡏⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⣠⡾⠁⠀⠀⠈⢿⣧
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠋⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠈⢻⣦
⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠈⠙⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⠀⢻
⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠛⠶⢤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠾⠛⠉⠀⠀⢸⣷⣄⣀⣀⣾
⢻⣇⠀⠀⠀⢀⣴⡾⠻⣯⠀⠀⠀⠀⠀⢀⣴⣟⠀⠀⢠⣾⣤⣶⡟⠁⠀⠉⠉⠉⣩⣿⣟⠛⠋⠉⠙⠛⣿⣉⣉⣴⣄⠀⠀⠀⠀⣀⣴⡿⠁⠙⠛⠋⠁
⠈⠻⢷⣶⣶⠟⠋⠀⠀⠻⣦⡀⠀⠀⣠⡾⠋⠛⢻⣿⠟⠉⠁⠀⠙⢷⣤⣠⣴⠟⠋⢸⠉⢷⣤⡀⣠⡾⠛⠻⣿⡍⠙⠻⠷⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠿⠋⠀⠀⣠⡟⠁⠀⢀⣀⠀⣀⣀⣈⣉⠀⢀⣀⣤⣤⣤⣈⠛⠋⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣹⡟⣉⠉⣉⣹⡿⠿⠿⢦⣤⡈⣹⣷⣤⠶⠞⠃⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠙⢿⣯⡽⠋⠀⠀⠀⠀⠀⢈⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣠⣴⠾⠛⠙⠛⠻⠶⠶⠶⠶⠶⠶⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣀⣀⣀⡀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⢀⣀⣀⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⢻⡿⠛⠛⠛⠛⠉⠛⠻⠟⠛⢿⡟⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠿⠶⠶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⢦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣉⣀⣈⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡶⠀⠀⠀⢲⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⣄⡀⠀⠀⣀⣮⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠳⠀⠀⠀⠙⢻⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣆⠀⠀⠈⡓⠛⠀⠀⠀⣼⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣦⡀⠘⠿⠿⠃⣠⣾⣿⣿⠿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣿⣿⣿⣿⡹⣶⣤⣤⣾⢿⣿⠋⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⢎⣿⣿⠏⠈⠅⣀⢸⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⣠⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣤⣴⠷⢯⡿⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⣆⢈⠙⢁⣠⣜⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡹⣿⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣾⣿⠿⢿⠿⠁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠿⠟⠛⠥⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣠⠀⣠⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⣠⣻⠂⠀⢈⠁⠰⠦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠺⠐⠩⠙⠀⠈⢦⣤⣅⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡀⠀⠀⣀⡀⠀⠉⡿⠡⣤⡒⡆⠀⢀⠀⠄⠐
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠩⡐⠐⠲⣋⡦⠴⡤⡒⠐⠀⠙⣦⠀⠀⠠⠐⠈
⠀⠀⠐⢋⣠⣀⠀⠁⠀⠀⢐⣶⠦⠄⠠⡄⠀⠠⠀⡀⡿⠀⠀⠈⠉⡔⠸⡁⠦⠔⠆⢱⡖⠀⠄⠀⠐
⠀⠀⠀⠉⠩⠙⠛⢡⡾⠋⣡⠦⢄⠀⠀⠈⠁⠀⠀⠈⢷⠄⠀⠠⠦⣤⠓⠉⣀⡙⠉⠉⠂⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⢀⣬⣾⣝⡛⠛⠦⠄⠀⠀⡀⠀⠀⠀⢈⣀⠏⠙⠋⠃⠀⠀⠀⣀⠀⡀⣌⡉⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣼⣿⠋⢻⣿⣿⣶⣤⡨⢒⡠⠑⠶⡶⠦⠴⠮⣿⡾⢍⡿⠋⢷⢿⣦⡀⠉
⠀⠀⠀⠀⢠⡾⢈⠁⡤⣋⡽⣿⣿⣿⣿⣿⣟⡿⣤⣥⢈⡵⢀⠀⠈⠳⣦⡀⠨⠑⢭⣟⠛⠂⡀
⠀⠀⠀⠀⣸⠀⡈⢼⡁⠯⠀⣼⣟⠛⢿⣿⣿⣿⣿⣿⣿⡙⢧⡑⢄⠀⠈⠻⣷⣦⠀⢿⠳⢄⠈
⠀⠀⠀⢀⣿⣧⠈⣆⢱⡀⠘⣿⢻⡄⠀⠹⣿⡏⠃⣿⡻⠿⣶⠁⢄⠀⠢⠄⠀⢻⣷⣀⢀⠀⣽⣆⣦
⠀⠀⠀⠀⠡⢾⡇⣘⣷⣟⡷⣬⣍⣷⣤⣀⢿⣿⠈⣼⣷⡆⢸⣧⡀⢀⠀⠈⢶⠀⠜⢏⠘⡇⠈⠋⢧
⠀⠀⠀⠀⢸⠔⢳⣼⠣⣽⡭⢚⠙⠛⠻⠿⣿⣬⠜⣽⠙⠃⠀⠀⠉⢦⠐⠨⡎⢶⢀⣿⣤⢹⣦⠀⢸⡆
⠀⠀⠀⠀⠈⣤⡀⣿⣷⣿⣝⡾⢿⣭⣿⣽⣿⣷⣾⡝⣡⡄⠀⠀⠀⠈⣁⠀⣽⡌⢠⡝⣾⣬⣽⣧⡿⠃
⠀⠀⠀⠀⡀⢽⣦⢻⣿⣧⢿⣷⣿⣿⢴⣷⣶⣾⣿⡟⠉⠀⠀⠀⠀⢠⠉⠁⣈⣿⣶⣙⢿⣿⣿⠟
⠀⠀⠀⠒⢀⡿⣿⠾⠿⣿⡏⠀⠀⠉⠙⠿⢽⣿⣿⣿⣤⣄⠀⠀⣠⣾⡷⢤⣛⣻⣿⣿⠻⣿⠏
⠀⠀⢠⣾⣿⣾⠟⣿⣦⣝⣷⡀⠀⠀⠀⠀⠀⠙⢻⣷⣬⣙⠷⣸⣿⠏⠀⠀⢸⣿⣷⣿⣷⠇
⠀⠀⠾⠿⠿⣧⣄⠹⠿⣯⠻⠷⡄⠀⠀⠀⢀⡴⠞⣹⢿⠟⣵⡟⣾⠀⠀⠆⢺⣹⣿⡿⠋
⠀⠀⠀⢀⡤⠀⠈⠙⠳⠈⢮⠀⠀⠀⠀⠈⠜⠡⠚⢉⣳⣿⠫⡼⡃⠁⠀⠈⣩⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⢈⠟⠧⣾⢽⠃⡄⢀⣣⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠘⣶⢻⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⢹⡄⠀⠀⢀⣀⡤⠤⠶⠶⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡒⠊⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡜⠀⠀⠈⠉⠙⠒⠒⠒⠤⠤⠤⠤⠄⠒⠒⠒⠙⡏⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠀⠀⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⡄⠐⢄⣀⡠⠂⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠇⠀⠀⠘⠦⡤⠟⠀⠀⢀⣀⡀⠀⠀⢧⡀⠀⣠⠇⠀⠀⠸⣀⡤⠪⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠂⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡴⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⡴⠴⠃⠋⠾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⢾⡉⠁⠀⠀⠀⠀⣹⣆⠐⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣠⠤⠞⠉⠈⠛⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⠞⠉⠀⠀⠀⠀⠀⠓⠖⠒⠒⠒⠒⡶⠶⠶⠶⠶⡞⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢉⡟⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡇⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢸⣃⠀⣰⢿⠃⠀⠀⢸⠓⢦⡀⠀⠀⠀⢿⠀⠀⠀⠀⡗⢰⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⣏⡉⡉⣧⢿⣀⣀⢀⡏⠀⢠⡇⠀⠀⠀⡼⣶⢤⢤⣴⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠒⠮⣿⣟⣁⡀⠀⠈⢹⠛⠦⣼⠁⠀⠀⠀⠙⠋⠉⠉⠙⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡟⠀⡏⠉⠉⠑⡿⠲⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠲⠴⣧⣰⣇⣀⠀⢐⠇⠀⣸⠛⠒⠒⠲⠶⠶⠶⠶⠶⠒⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡟⠁⢠⠤⠤⠤⠤⠤⠤⠴⠶⣦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣛⣛⣒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣉⣉⣉⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⠇⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠒⣛⠒⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠀⠀⢀⡀⠀⠘⠀⢀⡄⠀⠀⠱⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠐⠀⠀⠈⠁⠀⠜⠀⠈⠁⠀⢀⠆⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠲⠂⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠑⢼⡀⠀⢹⠀⠀⢸⠀⠀⢸⠅⠀⡤⠀⠁⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠠⠼⠄⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡯⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⢹⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢣⠀⣀⡄⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⠀⡇⠀⠀⠀⠀⢀⡇⢸⣀⠀⡝⠒⢄
⠀⠀⠀⠀⠀⠀⢀⠚⢄⣠⠞⠉⠀⠘⠺⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠀⡇⠀⠀⠀⠀⢸⠗⠃⠀⠉⠢⣄⡠⠓⡀
⠀⠀⠀⠀⠀⢠⣁⠀⡜⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⢧⠀⣀⡄
⠀⠀⠀⠀⢀⠃⠀⡝⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢏⠁⠐⡀
⠀⠀⢰⠊⡉⢉⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⣉⠉⠑⡄
⠀⠠⠊⠈⠁⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣤⠀⢠⠄⠀⠀⠀⠀⠀⢠⡄⠀⠤⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠁⠀⠈⠉⠓⢄
⠀⠀⠀⠂⠁⠉⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⡇⠀⠀⠀⠀⠀⢸⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠉⠈
⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠚⡇⠀⠀⠀⠀⠀⢸⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠲⠲⡇⠀⠀⠀⠀⠀⢸⠖⠒⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣗⢒⠲⡇⠀⠀⠀⠀⠀⢸⠖⢒⣺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⠀⠀⠈⠙⢆⠀⠀⠀⡰⠋⠉⠀⠀⠀⠉⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠈⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠐⠂⠉⠁⠉⠙⠛⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠠⣄⠀⠀⠀⠀⣀⠄⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣾⣿⡗⠀⣾⣿⠆⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠤⠐⠃⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠉⠁⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠂⠤⡤⠤⠐⠒⢸⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⢀⠗⠀⢀⡁⠐⠲⢄⠀⠀⠀⠀⠀⣰⣄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⠄⣀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠠⠊⢻⡟⠀⢲⡄⠠⠟⠈⠁⠐⠢⡀⢧⡄⠀⣀⠖⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠑⠮⡑⢠⡀⠀⠀⠙⠢⣄⠐⠁⠀⣾⣇⠀⠀⣧⠓⠀⠀⠀⠀⠀⢰⡀⠐⢘⣥⠔⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡠⠤⡀⠀⠈⠑⠮⣐⠄⡀⠀⠀⠱⢦⣘⣿⣿⠀⡀⠊⠁⠀⠀⠀⢀⡀⣏⠁⠘⠉⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠠⢀⡞⢀⠌⠠⢄⠈⢢⠀⡀⠀⠈⠑⠤⣣⢄⡀⠀⠉⠛⢯⣈⠑⠀⠀⠀⢀⠰⠯⠵⠄⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠠⢡⠏⢠⠊⠀⠓⠐⠀⡘⠂⠀⠑⠢⡀⠀⠀⠙⠪⡕⡠⠀⠀⠈⠙⠢⣄⢰⡇⠘⢦⡀⠀⠀⠀⡘
⠀⠀⠀⣀⡄⢠⠃⡐⠃⠔⠃⠀⠒⠉⠀⠰⣉⠒⠐⠀⠀⡤⡀⠀⠈⠑⠪⣐⠤⣀⠀⠀⠙⢣⢀⠈⠻⣄⠀⡐
⠀⡀⠁⠈⣶⠃⠀⠙⠊⢠⠀⢰⡀⠀⠔⢆⡠⠂⠀⢀⠊⠠⠙⠓⠤⡀⠀⠈⠑⠦⡑⠆⡀⠈⠀⠑⠦⣌⠋
⡀⠻⡤⠐⠉⠑⠢⣀⠀⠀⠁⠛⠄⠈⠒⣀⠔⢤⠠⠃⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⡕⠢⣀⠀⠀⠉⠂⢄
⠙⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠑⠂⢻⠀⠚⠀⠪⠁⡠⣀⠀⣀⠔⢀⠤⡀⠁⣀⢀⠀⠈⠑⠤⣑⠠⢀⠀⠀⠑⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠉⢠⠁⠐⢂⡀⠉⠎⡰⠁⠀⠇⠘⢃⠀⠉⠢⡀⠀⠀⠑⠦⣉⠢⣄⠀⠀⠈⠲⢄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠲⢄⡀⠀⠈⠒⠤⠄⠁⠰⡀⠠⢀⠀⢀⠊⡐⠁⠾⢁⠉⠂⢄⠀⠈⠑⠢⣍⠢⢄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡀⠀⠀⠑⠄⠀⠔⠁⡰⠁⠜⢀⠜⠀⢎⠑⠠⡾⠘⠢⠀⠀⠈⠑⢤⠑⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢠⡀⠀⠀⠀⠰⡠⠂⢀⠊⡀⠲⢄⠀⠐⠠⠐⠀⢸⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠠⣀⠀⠀⠀⠢⣀⠙⠂⣀⠂⡠⠁⠐⢀⠆⢀⡴⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠙⠢⣄⠀⠀⠁⠘⢃⠈⠃⠊⡠⠂⢀⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠉⠀⠉⠀⣠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡉⠢⢄⡀⢀⡼⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣭⣭⣭⣗⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣞⣛⠻⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⣯⣶⣶⣶⣶⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢁⣽⣿⣿⣿⣷⣿⣷⣶⣶⣦⣬⣿⣷⣶⣶⣿⣿⣧⣼⣯⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡱⡿⠛⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠘⠛⣛⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠳⠍⠢⣽⣟⣶⠖⠖⡾⠛⣻⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⡄⠐⠐⠗⣃⣈⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢿⣿⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠁⠀⣸⣿⡇⠀⢀⣂⣾⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠀⠀⠀⠀⠀⣿⣿⠃⠄⠤⢗⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⢒⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣧⡀⠀⢠⣿⡟⠀⠀⠀⢀⢀⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡻⣿⣿⣏⠀⠰⣾⠏⠀⠁⠀⠘⠋⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠨⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣐⣪⣯⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠹⣿⣿⣿⣇⠀⠰⠀⠠⣶⢪⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢀⢁⡀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⢄⢛⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⣽⣥⣶⣶⣖⣒⡖⠀⠀⣿⣿⣿⣿⣷⢨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡷⢸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⠻⡅⢈⣋⡻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⡷⡖⢋⢿⠿⣦⢸⣾⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⣸⡿⠋⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣷⣶⣦⣺⡈⣿⣿⣧⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠟⣃⣧⠤⠂⠠⠀⠄⠀⠀⠀⠈⠉⠛⠿⠿⣿⡇⢈⢿⣿⡄⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠈⠛⠛⠂⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣰⠋⢻⣀⣀⣀⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠉⠻⠃⠀⠘⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⠘⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣆⡀⠀⠀⢀⣇⡀⠀⠀⣼⡀⠀⢠⣇⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢻⢦⡼⠓⠒⠊⠀⠉⠓⠒⠋⠀⠙⠒⠚⠁⠈⠉⠉⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠤⣄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠳⠬⠽⢦⣀⣠⠇⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢦⡀⢀⡼⠁⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠂⠤⠐⠋⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⠀⠀⠀⢀⡼⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠴⠋⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡴⣿⠀⠀⠀⢀⡄⠀⠀⠈⣉⣰⡖⠒⠶⠶⠤⢤⣴⠶⠒⠚⠋⠉⡀⠀⣸⣷⣶⣏⣤⠤⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠋⠀⠘⢦⣀⣠⠾⠛⠛⠛⢻⡏⠀⢉⣹⠶⢶⣋⠉⠈⣳⠶⠶⠒⠚⠛⠋⠉⠉⢹⠀⣈⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⡀⠀⠀⠀⠀⣀⣀⣠⡼⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠲⢤⣤⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡟⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣸⣇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⢩⡟⠛⠛⠛⠛⠻⡍⠉⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠦⢤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⣉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡒⣄⠀⣸⣹⡆⠀⠀⢠⠊⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢷⡜⣧⢻⡄⣷⢺⡇⠀⠀⠠⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠙⣇⠀⠀⠀⠀⠀⢀⣤⣤⣝⣦⡹⠞⠊⠉⠉⠉⣽⢳⠀⣂⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⠠⢈⢽⡀⠀⠀⠀⣾⠞⢁⡽⠉⢀⠀⡄⣸⠤⡷⣿⢸⠇⠨⠂⠐⠂⠔⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠲⢶⡀⠀⠀⠀⠙⠲⣄⣀⣈⣳⡞⠀⠀⣄⢷⣼⡶⣛⣿⠿⠿⠶⡄⢧⣀⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⣌⡂⠄⠉⠈⣩⠋⠹⡀⢤⣝⣿⡋⠘⠻⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢉⡦⠍⠢⠀⠀⠀⠈⡉⠐⢻⣔⠗⠁⠀⠀⢠⣤⡥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠉⠀⠀⣎⡠⣀⣄⣀⣦⠐⢾⣎⣉⡟⠀⠀⠀⠀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡞⢁⠴⠐⠦⡉⢳⡟⣫⡅⠠⠞⠀⡀⡤⣼⠙⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⠀⣼⠀⠡⠁⠀⠁⢸⠀⣽⣿⡷⢀⠀⠀⠭⠁⠛⠀⠐⣿⣲⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⢀⠼⣆⠢⢅⣀⡠⠎⣰⣾⢛⡀⠨⣿⠛⠓⠲⣦⠠⢤⠋⠉⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣢⠏⠀⢌⢷⣦⢤⣴⣶⡿⠃⢄⠐⠀⠈⠣⡀⡐⠉⢛⠨⡆⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢫⣷⠃⢀⣡⣴⠎⠉⡛⠉⠁⠀⠀⣠⣷⣄⠂⢰⠌⠿⠷⢊⣼⠉⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣏⡟⠀⠠⢬⡿⠖⠦⢤⣤⠶⠓⠊⠉⠉⠀⢱⣬⠾⣚⣿⠉⠀⠒⡖⢌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⣇⣀⣀⡸⠂⢀⡋⠒⠠⠷⣶⡴⣤⠆⢚⣛⣦⠰⣿⡿⠃⢀⢠⣉⢦⢚⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣻⠉⠉⠉⣗⣠⣁⣰⣼⣷⣦⡀⢿⡤⡆⠄⣼⢀⣠⠇⠐⡠⢄⠓⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⣷⠇⠀⢀⡔⠉⠉⠉⠁⡉⠱⣏⣀⣙⠛⢛⣁⣈⡇⠀⠠⢀⡟⠑⡄⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⣴⠛⢦⣇⠈⠟⠀⠀⠀⠀⡰⠀⠁⠘⠒⠚⠈⠉⠳⡀⠒⣄⠑⣄⡧⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡼⠛⢄⠀⠂⢝⡴⠱⠆⠀⠀⠀⠀⠀⢀⠛⡘⡞⠥⡇⢸⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣝⢦⣴⠋⠓⠦⣆⡈⠃⠀⠀⠉⠁⠀⠀⠠⠄⡡⠛⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡼⠓⠃⠀⠀⠀⠀⠙⠳⠦⢴⣤⣤⣤⡤⠶⠛⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⣿⠟
⠀⠀⠀⠀⠀⠀⣠⡶⠋⣠⣿⣥⣶⠶⠆
⠀⠀⠀⠀⢀⡼⠋⠀⠞⣫⡵⠋⠁
⠀⠀⠀⣰⠏⠀⠀⠀⠘⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡀
⠀⢀⡾⠃⠀⠀⣠⠶⠛⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢥⣄
⢀⡾⠁⠀⠀⣰⠋⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⢧
⡾⠁⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⡃
⠛⠒⠒⣻⠇⢠⠀⠀⠉⢳⡀⠀⠀⠘⣆⠀⠀⣀⣤⠴⠶⠶⠶⠶⠦⢼⣆⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⡟⠀⣸⡇⠀⣴⢦⣙⣦⡀⠀⠈⠳⣏⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⡿⢀⡀⣠⣞⣀⣀⣀⣀⣤⣤⡤⠶⠶⠚⠛⠉⠉⠁⠀⠀⠀⠹⣆
⠀⠀⢸⣇⠀⣿⢷⣼⠃⠈⢙⣶⡟⣦⠀⠀⠙⠳⠦⣤⣄⣀⣠⣤⢴⣿⠟⠙⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠛⠛⠀⠉⠀⠀⠀⢀⣻⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⣩⣬⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⣞⠉⠁⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣤⣄⣀⠀⠐⠀⠤⠀⠠⠤⠀⠚⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⠀⠀⣠⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠉⠙⠓⠒⠒⠒⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠟⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⣛⡛⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣙⠳⠶⠿⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣸⡓⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣀⡐⠀⠤⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣿⢿⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠓⠲⠲⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⡆⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⠶⠧⣤⣤⣤⣀⣀⣀⡀⠈⠛⠛⠲⠶⢤⣄⡀⠀⡜⠀⠀⢷⡟⣧⠳⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠠⣤⣤⢀⣀⡀⠀⣀⢀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠒⠒⠚⠿⠿⠤⠤⢤⣼⣿⣈⣦⣹⣄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⣿⠀⣿⣿⠀⢹⣿⡇⠙⣿⠀⠀⢲⣶⡶⠀⣤⣤⡀⣤⡄⠀⢀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⠒⠶⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⣿⣿⢰⣿⡃⠀⣿⣿⣣⡖⠁⠀⠀⢸⣿⡇⠀⣿⣿⠀⡸⠃⣰⣿⠋⠈⣿⢳⡟⣺⣷⡖⣶⠰⣶⣦⢠⣤⠀⣄⣀⡀⡀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣸⣿⡇⢸⣿⣇⠀⣿⣿⠀⢃⢀⣤⡄⣿⣿⠃⢰⣿⣿⢸⡇⢀⣿⣿⠀⠀⠉⠉⠀⣿⣿⠃⠛⢰⣿⡟⢀⠹⠀⣿⣿⡇⣿⣧⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠙⠋⠈⠛⠛⠸⠿⠿⠰⠾⠙⣿⢣⣿⡿⠀⣸⣿⡏⢀⣴⠈⣿⡿⠀⠀⡀⠀⢀⣿⣿⠀⠀⢸⣿⡇⣿⠀⠀⣿⣿⠀⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠁⠛⠋⠀⠙⠿⠤⠞⠁⠀⢸⣿⣿⠀⢀⣿⣿⠇⣠⡆⢰⣿⣿⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⣶⠒⠶⢤⣤⣤⡤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠘⠛⠓⠚⠋⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣧⠸⡀⠀⣸⠋⠙⡏⠉⠉⠛⠛⠛⠒⠒⣶⠶⣶⠤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⢀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣀⣀⣘⡄⠳⡴⢃⣠⠶⠃⢀⣀⣀⣠⣤⣤⢤⣿⠰⣿⡦⠴⠶⠖⠒⢾⡿⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠋⠉⠉⠉⠉⠀⠀⢰⡟⠙⠛⠉⠉⠉⠁⠀⢸⠁⣸⣿⣦⠀⣱⡄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠙⠋⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⠟⢠⡟⠻⣿⠀⣿⠇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣭⣥⠤⠚⠁⠀⠀⠀⢀⣀⣀⣤⣤⣾⣤⡾⠦⣤⠈⠛⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣤⣤⣠⣤⣤⣿⠿⢦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠦⣅⠀⠀⠀⠀⠀⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦
⠀⠀⠀⠀⣀⡀⠀⢀⢀⣇⡈⢙⢣⢂⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⢣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⣹⣷⡀⠼⢾⣯⠟⠛⢛⣛⡭⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡃⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⢰⣿⣿⣧⢠⣠⠿⠠⢽⣿⡁⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢶⡖⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠈
⠀⠀⠀⢸⣿⡏⣧⢺⣷⣿⡀⢿⣦⣾⣟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠐⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠰
⠀⠀⠀⠈⢿⡁⠻⠿⢿⠟⢿⣤⣿⡦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡐⠂⡀⠀⠀⠀⠊⡄⢧⡀⠀⠂⣐⠉
⠀⠀⠀⠀⢈⣷⣀⠀⠻⡟⠃⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢂⠀⠂⠀⠀⠀⣁⡄⠸⣆⠈⡅⣘
⠀⠀⠀⣰⣿⡷⣿⠳⡶⣶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠆⣀⣠⣾⣿⣷⠎⠋⣸⠷⢋⡀
⠀⠀⢸⣿⣿⣷⡀⠉⣶⣿⡄⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣄⣀⣀⡀⡀⠈⠻⠟⠛⠃⠎⡉⠈⠉
⠀⠀⢸⣿⣿⣿⣿⡆⢹⣿⡄⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡉⢁⡤⣤⣤⣤⣤⣶⠛⠄⠀⠐
⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣷⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠈⢻⣿⣿⣶⣄⣌⠛⠋⠋⠠⠠⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠈⠉⠛⠉⠉⠉⠁⠀⠁⠀⠉
⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠉⠑⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠼⠟⠓⠒⠒⠿⠤⠤⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣼⡐⠀⠀⠊⡉⢳⣶⠪⡉⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠀⠈⡞⠀⠳⠽⠊⠍⠳⠿⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣶⣿⠀⠀⢠⣤⣄⣄⣔⣲⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡏⡞⠀⡀⠸⠝⠉⠋⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⠤⠬⠸⣿⣿⣿⣿⣟⣭⢓⣂⠀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡉⠁⠉⠂⠈⡃⠁⢀⢢⠀⠀⠀⠀⠀⠀⢄⠆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠠⡘⠀⣀⣠⠀⠇⠀⢈⣀⣤⡤⣴⣤⡤⠶⢖⠆⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠘⢦⣤⣾⣿⡇⡿⠀⠀⢽⠀⠴⠊⡉⠁⠙⢲⢘⠅⠠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣌⠀⠀⣰⣿⣿⣿⢳⡇⡆⠀⣻⠀⠓⠀⠁⠀⠀⡡⢸⡇⢠⡀⢘⡀
⠀⠀⠀⠀⠀⠀⠰⠡⢌⢱⣴⣿⣿⣿⣿⣾⡇⠀⠀⣎⠎⠰⠀⠀⠒⢀⢊⢸⡇⢸⣷⠆⠘⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡉⣹⣿⣿⣿⣿⠁⡆⠀⣜⠐⣀⣃⣡⣤⣤⠴⠶⠃⢸⣿⣴⠤⠄⢀⠖⠻⡉⠁⠈⡰
⠀⠀⠀⠀⠀⠀⠀⠷⠶⠿⠀⢸⣿⣿⣿⡏⡾⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠑⠂⠠⢠⡀⢀⣽⢿⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣣⡀⠀⠀⣿⣿⣿⢳⡇⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⢅⣀⣀⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢉⢣⣀⠀⠻⠿⢿⣾⣃⡵⡀⠀⣀⣈⣤⣤⣴⣷⣶⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢄⡈⠟⡉⠠⠀⣿⣿⡿⠟⠛⠋⢹⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢠⠘⣇⠀⢀⠀⠿⣿⠇⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠿⠒⠋⠀⢀⣿⠀⠀⠀⠀⠀⠆⣤⡠⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡉⢲⡤⠄⠂⠳⢘⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢈⠄⣡⣤⠶⢦⡌⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣠⡇⠀⠀⢸⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢈⢠⡏⡏⠀⠀⠀⢸⠀⠀⢰
⢠⣴⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣸⢹⠁⠀⠀⠀⢀⣠⡤⠾⠂⠂⠀⢀
⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡍⣀⣀⠀⠀⣀⣼⣿⣶⣄⣠⠴⣒⠻⠆
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣙⣉⠁⠀⢀⣀⣭⣏⠥⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣟⣻⠿⣿⣷⡎⠉⢀⡨⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣶⣿⣶⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣀⠠⡶⠀⣦⠠⡆⠀⠠⠆⠀⠠⣦⣴⠀⣰⣤⣶⠀⣦⠀⠀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⠠⠽⠘⠿⠄⠿⠀⠠⠆⠀⠸⠋⢿⠀⢹⠿⣿⡇⠿⠒⠤⠄⠉⠉⠈⠁
⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡏⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠻⣷⠘⢿⢿⣿⠙⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠻⠆⠸⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢸⣿⣿⣿⣿⣿⡟
⠀⠀⢸⣿⣿⣿⣿⣿⠁
⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⠇
⠀⠀⢸⣿⣿⣿
⠀⠀⢸⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⢿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⠔⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠥⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠠⢧⣀⠀⠀⠈⢷⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠃⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠧⠤⢴⠄⠀⠈⠳⡄⠀⠀⢧⠀⠀⢀⣋⣀⣀⣤⣄⣼⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣧⢀⡤⣍⡦⡀⠀⠳⣞⠉⠀⠀⠀⠀⠀⡀⣹⢀⣀⣰⣃⣀⣀⣠⡤⠤⠶⠖⠚⠋⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡟⡾⠀⠈⠳⣿⢆⠀⠈⠓⠒⠦⠤⠴⠚⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠴⠚⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠙⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⣀⠀⠀⠀⠀⠤⠀⢀⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣠⠜⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠉⠉⠙⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⡴⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢌⡓⠠⠧⢤⣀⣀⣀⣀⣀⡀⠀⠊⢀⢀⣀⣀⣀⣸⣓⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢬⣀⣀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣼⡙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣇⣀⡉⠉⠐⠒⠠⠤⢤⣀⡀⠀⠀⡜⠉⢧⣿⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⣥⣄⣀⡀⠀⣀⡉⠉⠉⠉⠉⠓⠐⠒⠒⠘⠳⠶⠤⠤⢸⣇⣣⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⡿⢸⣿⠀⣿⡿⠙⠇⠀⢰⣶⠆⢰⣶⠠⣤⠀⣠⠄⣀⢀⡀⣀⠈⠉⠉⠉⠐⠒⠒⠒⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⡏⣿⣦⢀⣿⡗⠟⠀⠀⢸⣿⠀⣾⣿⣰⠁⣼⣿⠀⠹⠺⢹⣿⠋⠇⣿⡿⠸⡆⢲⣶⢠⣄⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⠛⠃⠻⠟⠸⠿⠇⣼⠺⡟⣿⡿⢀⣿⡇⢈⡄⣿⡇⠀⠀⠀⢸⣿⠀⠀⣿⡇⡎⠀⣿⡿⢸⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠘⠓⠒⠁⠀⠿⠿⠀⢸⣿⣇⣴⢀⣿⡇⣾⡟⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⠉⠁⢛⢲⠒⠒⡶⢤⠤⠤⠤⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⡌⢧⡼⢁⡼⠃⠀⣀⣀⣀⣀⡍⢸⣍⣩⡭⠭⢶⡶⠒⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⡉⠉⠉⠁⠀⡼⠛⠃⠉⠉⠉⠁⡏⢰⣷⡌⢱⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣀⡀⠀⣀⠔⠁⠀⠀⠀⠀⠀⡼⢁⣏⠙⢇⡼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡟⠉⠉⠁⠀⠀⠀⠀⠒⠛⠛⣛⢋⣉⣑⣂⣾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠧⠽⠿⠿⠷⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠓⠛⠛⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣤⣤⣤⣶⣿⠿⢛⣿⣿⣿⡟⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣿⣿⠿⠀⣰⣬⣭⠁⠀⠀⠙⠛⠻⣿⣿⣷⡄⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠟⠀⠈⠉⠀⠀⠀⢿⣿⡿⠀⠀⠀⣶⣄⠀⠀⠉⠉⠀⠀⠀⠈⠳⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⢠⣄⠀⢠⣤⣶⣶⣆⠠⣶⡄⠀⠀⠀⣿⣿⢰⣷⣄⠀⠀⠀⠀⠀⢶⣦⣍⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⡇⠘⣿⣷⡌⠿⣿⣿⣿⣄⠙⢿⠆⠀⠀⢿⣿⠘⣿⣿⣆⠀⣠⡀⠀⢸⣿⣿⣦⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣘⡿⠃⠀⠈⠉⠛⠓⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠟⠀⢻⣿⣿⡆⠹⠿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠁⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣤⡀⠀⠀⠀⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⡄⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⠀⠀⠀⣰⡄⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡁⠀⣰⣿⣷⠇⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠃⠘⢻⣿⡿⠂⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣀⣀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠁⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⣿⣦⡌⠻⣦
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣀⡀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⣇⠀⠈⢻⣿⣟⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⠋⠉⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠀⣿⣤⣦⡀⠉⠛⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⡆⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠀⣸⣿⣿⣿⣧⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣴⣿⣿⣿⣿⣿⢃⡀⠀⣸⡏
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⡿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⣿⣿⣿⡿⢟⣩⣴⠾⠋⠉
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⣹⣿⣿⡾⠟⠉
⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢿⡁⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠸⣿⣏⡼⠁⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠈⠶⣤⣤⣤⣤⡴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⡞⠻⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⢻⡄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⣶⠟⠀⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡼⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣄⢠⠄⠀⠀⠀⢀⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠘⣧⠴⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢈⡟⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣏⡛⢷⣄⡀
⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⣇⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⠋⠙⡏⠙⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡌⠙⢦
⠀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠉⠈⡟⠁⢸⣆⡀⢀⣀⣠⣤⣀⣠⡶⠦⣤⡟⠀⢀⡿⠦⠀⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⣿⣿⣿⠏⠴
⠀⣰⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⠂⠙⣏⠀⠀⢿⡇⠀⢸⣧⠀⣠⠌⠑⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠜⠉⠛⠛⠋⠰⠹⠉⠁
⠀⠈⠻⠛⣿⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠒⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠁⠀⣾⢿⡱⠛⠿⠷⢦⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠣⠄⠀⠀⠉⠳⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⠀⠂⢀⠀⠁⠀⠀⣀
⠀⠀⠀⠈⠀⠀⡀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠉
⠀⠠⠈⠀⢀⡀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠦⠁
⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠰⠁⢉⠄⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠒⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠈⠱⣫⠆⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⡄⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠂⠀⠀⢀⡀
⡔⠐⠂⠀⠀⠀⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⢀⠁⠀⢀⠀⠀⡀
⣑⣐⣁⣀⣠⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣘⣰⣄⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣿⠀⠀⠀⠀⠄⠄⢺⣿
⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠠⡗⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠖⠁⠀⠀⠀⠠⢌⣳⢺⣿
⣿⣟⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠋⠉⠙⢛
⣿⣿⣟⠀⢴⣷⢤⡤⠔⠂⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣰⡆⠀⢀⢀⠀⠀⠹⣿⠇⠀⣀⢀⣿
⣿⣿⣿⠀⠨⣏⢪⡀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⢀⣼⣷⡀⠀⠙⠀⡀⠀⣼⣿
⠟⢻⣧⠀⠈⡟⠁⠛⢄⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡴⢦⣬⣍⣻⡷⠀⣠⣼⡇⢰⣿⣿
⠀⠀⢈⠆⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⡟⠻⡟⠁⠀⢛⠇⠀⢤⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠂⢀⠾⢿⠅⠐⠘⢦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠉⠀⠁⠀⠀⠀⠁⡜⣇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢠⣴⣴⡇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⡀⠀⠿⢿⠁⠈⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤

⠐⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠋
⡄⠀⠀⠀⠀⠀⠀⠐⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠂⠄⠀⠀⠀⠀⠰⣍⡀⢀⠠⣈⠩⠍
⡗⠀⠀⠀⠀⠀⠀⠀⠢⠀⠑⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉
⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣦⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠿⢯⣼⠏⢹⣮⣤⣤⡄
⣷⣤⣤⣦⡄⠀⠀⠒⠀⠀⠀⡀⢀⡀⠀⠀⠻⣝⢶⣤⣦⡴⠞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠋⠉⠛⠧
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣷⣿⣿⣷⣾⣧⠀⠀⢀⡀⣈⣈⡈⠐⣽⠉⣀⣋⣁⣹
⣿⣿⡿⠟⠒⠒⠂⠀⠃⠐⠃⠀⠊⠋⠀⠠⠌⠁⠀⠉⠀⠐⠀⠃⠀⠀⠤⠄⠆⠤⠀⠤⠥⠰⠦⢠⠤⠈
⣿⣿⠇⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠩⠠⠭⠅⠄⠭⠭⠽
⣿⣿⠃⠄⠀⠀⠀⠨⠉⠋⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⢀⣥⠀⠀⠀⢀⣸⣄⠀⠀⠀⠀⠀⠉⠀⠀⠃
⣿⡿⠀⠀⠀⠀⠀⣀⡄⣺⣶⠿⢛⣻⣿⣿⣿⣿⣿⣯⣽⣿⣿⣶⣶⣶⣿⣿⣿⡇
⠋⠁⠀⠀⠀⠀⠼⣽⡿⠛⠓⣶⣾⣿⣿⣿⣿⠟⢻⣿⣿⡿⠿⠿⢻⣿⣿⣯⠟⠁
⣿⠂⠀⠀⠀⠐⢤⡯⠤⡤⠤⣤⣬⣥⣤⣤⣤⣭⣬⣥⣤⣤⣴⣶⣼⠿⢿⢸⡆
⣟⣀⠀⠀⠀⠀⠋⠀⠀⢀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉
⡏⠁⠀⠀⠀⠀⠀⠀⠓⠉⠙⠁⠘⠐⠃⠊⠀⠀⠂⠂⠀⠒⠒⠀⠁
⣯⣤⣤⣤⣤⣤⣽⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⢀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠉⠉⠉⣙⣢⣀⠀⠀⠈⠿⠋⠀⠀⠙⠿⠋⠀⠀⢀⣴⣚⣋⡉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠙⢶⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⢻⠀⣾⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⡴⠋⡀⠀⠀⡘⠷⣄⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣭⣥⠴⠚⠁⠀⠀⠈⠳⢮⣭⣍⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠠⢄⣀⣠⠞⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⠲⢤⣀⣀⠄⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠳⠶⢤⣷⣤⣀⣀⣀⣀⣀⣀⣼⣤⡴⠶⠚⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠉⠉⠉⠛⢶⣤⡀⠀⢀⣠⠞⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁


⡶⡶⢶⢶⡶⠶⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⢶⣶⠶⠶⠶⠶

⣿⣿⣿⣿⡿⣿⣿⡀⠘⣿⣿⣿⡀
⣿⣿⣿⣿⣤⣻⣿⡟⣸⡛⡟⣿⣷⣤⠴⠦⣀⠀⠀⠀⡀⠀⠀⠀⢀
⣿⣿⣿⣿⡟⢿⣿⣿⣿⢿⣿⣶⡟⣿⡶⢼⢃⡤⢠⡾⠀⠀⠆⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⡈⠀⣹⣿⣄⣠⣘⣽⣿⣿⡇⠘⠿⠷⠞⠉⠀⠀⢰⠀⢄⠀⡀⠀⠀⠀⠀⠀⠄⣀⣠⠄⠋⠀⠀⡀⠀⠀⠘
⣿⣿⣿⣿⣷⣤⣼⣿⣭⠈⢹⣯⣷⣮⣌⣤⣤⢠⣤⠀⠠⠒⠁⠙⢦⡑⢤⠃⠀⠈⠀⡤⠋⣁⣀⡤⠂⠀⠀⠀⠀⢀⠀⠁
⣿⣿⣿⣿⣯⡽⢿⣿⣿⡀⠀⠋⠫⠙⠉⠉⠉⢹⡋⠀⠀⠀⠀⠀⠀⠉⠪⣧⣤⠥⠤⡒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠎⠀⡤⠳⠀⠠
⣿⣿⣿⣿⣿⠁⡏⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⢋⠀⠀⣡⡇⠀⢤
⣿⣿⣿⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⠀⡼⠁⠈⠋
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡎⠀⠀⠾⠪⠁⠀⠀⢠⠂
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢊⠞⠛⠏⢠⠀⠀⠀⠀⠀⢶⠀⡀⢀⡐
⣿⣿⣿⣿⠿⠿⠏⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⣀⠴⡣⠂⠀⠀⠀⠀⢠⢃⠔⠀⡀
⣆⣀⣾⣶⣶⣦⡄⠀⢀⣀⡀⣤⣄⣠⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢲⡄⠀⣀⠀⠀⠐⠊⡠⠊⠁⠒⠀⠀⠀⡴⠋⡠⠔⠉
⣿⣿⣿⣿⣿⣟⣛⣫⣍⣈⡩⢽⣿⣿⣬⠃⠀⠺⠉⠉⠁⣀⡀⠀⠀⠀⠀⡠⢡⣾⣶⣾⠋⠀⠀⢀⡞⠁⠀⠀⠀⠀⠄⠀⡠⠎
⣿⣿⡿⠟⠋⣡⠤⠛⠓⠚⠋⣻⠿⣷⣼⣟⣦⣆⠰⠒⠈⠀⠀⠀⠀⢀⠀⠀⣠⣟⠟⠘⠃⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠺⣷⣿⡁⠙⢷⣆⡀⠀⠀⠀⣰⠂⠀⢐⣽⡃⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡘
⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠘⢄⡘⢇⠈⢻⣿⣆⣠⡴⡟⣠⣾⠟⠉⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠤⠉⠉⠀⠠⡇
⣿⣟⣷⠒⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢀⣷⡐⠆⠀⢻⣿⡯⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⢀⠸⠁⢀⠀⠀⠀⢀
⠿⡿⡿⠿⠉⣉⠙⠒⣒⠂⠐⣶⠃⡤⣎⣾⢿⡅⢰⢃⡞⢹⠇⣀⣿⣿⢠⣀⠀⠀⠀⡢⠀⠀⡠⠆⠀⠀⠄⠀⠀⡀⠉⠀⠒⠊⠁⠀⠀⠊⠈
⣀⡠⠤⣤⣤⣀⣀⠀⠀⠈⣹⠃⡜⢰⣾⣿⡞⢁⡾⣼⡇⠘⠸⣽⣿⡿⢄⠚⠛⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂
⢰⣾⣔⣻⣥⣴⠞⠟⠲⢤⣏⡼⢏⣿⣿⠏⠃⣾⣧⡟⢀⡄⠀⢹⢦⡅⠨⢦⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤
⣨⣝⡻⢽⣳⡆⡠⠀⣠⣿⣿⡇⣾⢟⡽⠡⢸⣿⣿⡇⠀⠀⠀⣿⡘⡄⠀⠀⠑⠤⠚⠉⠣⡑⠀⠀⠔⣀⣩⠌⠁
⣿⣿⣿⡝⢿⠏⠠⠞⢩⣿⡟⢸⣿⣾⢀⡆⣿⣿⡿⠀⠀⠂⠀⢻⡅⢁⠀⠀⠀⠀⠣⡀⠀⠈⠁⠀⠈⠁
⣿⣿⣿⣿⣦⣿⡒⠄⣸⡿⠁⣸⡟⡏⢸⣴⣿⣿⢇⡆⠀⡀⠀⠸⣿⢼⡆⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃⣸⡿⠁⠁⢸⣿⣿⡿⣸⠆⠀⠃⠀⠀⢿⠀⠉
⣿⣿⢿⣿⣿⣿⡿⠋⠀⣰⡿⢁⠀⠀⣿⣟⣿⠇⠹⠀⠀⠀⠀⠀⠘⡄
⠉⠉⠉⠐⠋⠁⠀⠀⠀⠁⠱⠁⠀⠀⠿⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡉⠉⣉⡉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠅⠀⠽⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠒⢂⠀⠀⠀⠠⡁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣶⣵⡄⠀⠀⠀⠀⢉⠂⢠⢦⡤⣠⣴⡀⣀⣀⣆⣬⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⢿⠃⠀⠀⠎⢸⠶⠀⠁⣀⣴⠆⠲⣾⠩⡀⠡⠀⠀⠀⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠂⢘⣂⡴⠖⣀⡈⣶⢀⡆⠚⣯⠷⠶⣿⠀⣧⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣠⣯⣉⡙⠾⣏⣼⣧⠎⠱⠊⢿⣤⣼⡿⠀⠘⣧⣷⡄⢶⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡍⡷⠤⡙⢲⣿⠿⠋⠀⠀⠀⠈⠻⢿⠃⠀⠀⠈⢻⡏⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠉⡇⢻⠀⢬⣽⣿⡄⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣠⣅⠈⠁⣾⢿⣿⣧⡀⣨⣧⣤⣤⣤⣁⣀⠀⢀⣾⡝⢿
⠀⠀⠀⠀⠀⠀⠀⢉⢁⣿⡿⠉⠹⠀⠋⠀⣈⣿⡙⠛⠩⠉⠭⠬⣽⣿⣿⣿⡿⢅
⠀⠀⠀⠀⠀⠀⠐⣯⢽⠈⡏⠀⠀⠀⢰⣞⣱⠉⡙⠁⠀⠀⠂⠛⠛⢟⠻⣧⡈⠢⣅⢠
⠀⠀⠀⠀⠀⠀⠀⣥⠞⠀⠈⠀⠈⠀⢸⠀⠉⠙⠀⢰⠀⠀⠀⢌⣀⡙⠉⣿⡅⠢⠈⢹⣖⣷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠁⠀⠀⢸⠀⠀⠀⢂⣸⣷⠀⢠⣾⣧⠁⠀⠘⣧⠀⠀⡼⣻⢋⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⣴⣶⣾⠀⠀⠀⢸⣿⠟⠐⢾⣿⣧⠄⠀⠀⢿⣷⣾⣿⠹⢹⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣰⢏⣴⣿⣿⡿⣏⠀⠆⠀⢸⡟⠀⠀⠈⢿⣷⡀⠀⠀⠈⢻⡿⢧⠜⠟
⠀⠀⠀⠀⠀⠀⠈⠱⣯⣾⠛⣿⠛⠀⣿⠀⠀⠀⢺⣇⠀⠀⠀⢀⣇⣿⡈⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢀⣿⠀⠀⢸⠛⠲⣶⣿⣿⠀⠀⣠⢿⠟⡛⣿⠙⠛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⢸⡏⣱⣿⣿⡟⠀⣶⣿⣊⡔⠁⣮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣠⣴⣇⠙⢹⣾⣿⣶⣯⣝⣽⣅⣴⣶⡒⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣴⣾⣿⣿⣿⡿⣤⡯⠼⣿⣿⣿⡆⠀⠈⠁⠹⣿⣿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⢤⣖⣹⣿⣿⣿⣿⣿⣿⡿⠁⠋⠀⠀⠸⡟⣿⣧⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡷⠄
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⣄⣀⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣠⣴⣾⣿⣿⣿⡿⠧⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣿⣿⣿⣿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⣶⣴⣤⣶⣶⣶⣶⣶⣦⣾⣿⠀⣴⣶⣦⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⠛⠛⣿⡿⠟⠛⠛⠻⢿⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⡇⢸⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢉⣉⣉⡉⢻⡇⢸⣿⣿⡇⢸⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡇⢸⡇⢸⣿⣿⡇⢸⣿⠀⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣈⣉⣉⣁⣈⣁⣈⣉⣉⣁⣈⣉⣀⣉⣹⣿⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣡⣴⣾⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠆⢀⣠⣴⣾⣿⣿⡟⢉⣉⠙⠿⠿⠿⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠟⠷⠀⠉⠛⠿⣿⣿⣿⣧⡘⠛⣠⣶⣶⣶⡶⠞⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢸⣷⠀⠀⠀⢰⣤⣉⠛⠿⣿⣿⡿⠟⢋⣡⣴⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣶⣤⣡⣴⣾⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣠⡴⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣸⣇⠀⣀⣠⡤⠖⠚⠋⠉⠉⠉⠉⠉⠙⠲⢦⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⢚⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠉⠙⢦⡀
⠀⠀⠀⠀⠀⢿⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠧⣄
⠀⠀⠀⠀⠀⠀⢀⡿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⣼⢁⡞⠀⠙⠒⠦⠤⣄⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⡤⢤⡴⠛⠁⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰⡀⢀⡀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣤⣼⠀⠀⠸⡇⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⢤⠀⠙⢤⣀⣠⠞⠁⠀⣰⠇
⠀⠀⠀⠀⢸⡀⣭⠀⠀⠀⠻⣦⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣸⠀⠀⠀⠸⣅⣀⡴⢫⢙⡇
⠀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣭⣽⡦⠀⠀⠈⠛⠶⠚⠁⠀⠀⠀⠀⠈⠉⠀⣶⠞⠁
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⣿⠀⠀⠀⠀⠀⠰⠖⣶⠖⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠿⣌⠓⠦⢤⣤⣤⣤⠖⢋⣷⣀⠀⠀⠀⠀⠀⢀⣤⣄⢀⣀⣠⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠁⠀⠈⠳⠶⠛⠉⣿⠉⠳⠞⢻⠉⠛⢶⣄⠀⣴⣯⠧⢼⣏⠉⠛⠻⣇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⣤⡴⣶⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣦⣄⡀⢨⡿⡽⠁⢠⣄⡉⠻⢦⣤⣾⣄
⠀⠀⠀⠀⠀⢀⡾⠃⠀⣠⠾⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠈⣻⢟⡞⠀⠐⢤⣈⠻⢦⡄⠀⡹⢈
⠀⠀⠀⠀⢠⡟⠀⢠⡾⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣀⡼⣫⠋⣀⠐⠦⣄⡉⠓⠆⢀⡞⣡⠟
⢠⣤⣀⣀⣟⠀⢰⠟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠟⡴⠁⢠⡈⠓⢦⠀⠉⣠⣴⣏⣼⡇
⠻⢦⣭⡟⠉⠻⠿⢦⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠏⢾⠀⠀⢦⡉⠳⠄⠀⣰⠿⢦⡈⠻⣷
⠀⠀⠈⠷⣷⣒⣯⣙⠳⢦⣄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣦⡈⠛⠶⣄⠉⠲⠀⢰⡟⠳⠄⠀⣰⠏
⠀⠀⠀⠀⠀⠉⠀⠉⠛⠿⠿⠷⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⢦⣄⠈⠙⠶⣤⢏⡿⢶⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⠀⠉⠳⣦⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠒⢶⣶⢤⣤⠾⢦⡴⠞⢻⡇⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⠀⠀⠀⠀⢹⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⢸⡇⠀⠀⠀⠀⠀⢸⣇⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣭⣍⡿⠁⠀⠀⠀⠀⠀⠸⣏⣉⣉⣻⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⢔⣴⣤⡶⣶⣆⢤⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣿⢲⠟⢉⠛⣿⠉⣈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣚⣻⣎⣽⣰⣿⣯⣿⠇⠀⣟⣼⠽⠀⠀⠀⠀⠀⠀⠀⠶⠂⢚⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⢻⣿⣅⢀⣹⣿⣿⢰⣿⡿⣷⠆⠀⡄⠀⠀⢀⣴⠶⣮⣤⠈⡉⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣵⣧⣦⣶⣾⣿⡅⠉⢱⣿⣿⡾⡤⣿⣿⣿⣿⠷⣧⣾⣿⣇⢹⡇⠀⣰⣿⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣈⣽⡾⠿⣿⣿⣿⣿⣿⣾⣿⣿⣀⣼⣿⣿⣯⣿⣿⣿⡿⣿⣿⣿⣿⣶⣶⣼⣿⣿⣏⡵
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣞⣯⣽⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣟⠛⢯⠑
⠀⠀⠀⠀⠀⠀⠉⠿⣿⣧⣙⠛⣿⣿⣿⣿⣦⠤⢿⣿⡿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣷⣦⡛⠂
⠀⠀⠀⠀⠀⠀⠘⠀⣿⢿⣟⠀⢹⣿⣿⣿⡙⣶⣾⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥
⠀⠀⠀⠀⠀⠀⠐⣾⣿⡿⢿⣀⠀⠘⢿⣿⣿⣿⡿⣿⣫⣍⠉⠙⠛⢛⡛⠻⠿⠿⠿⣿⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣻⡿⠼⠿⣿⣦⠀⣹⣿⣿⣾⣿⣿⣏⠻⠂⠀⠀⠀⠀⠉⠁⠀⠐⠓⠒⠛⠿⠁
⠀⠀⠀⠀⠀⠀⢀⣈⡉⠰⠀⠿⣧⣨⣿⣿⡟⣼⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⣰⠀⠀⠀⢾⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⡀⠀⠀⠀⢀⡿⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠋⠉⠉⠉⠻⠉⠉⠉⢉⣩⠽⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠭⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⡴⠞⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡖⢺⡇⣴⣶⣦⢤⠀⠀⢀⣤⣴⣶⣄⢸⡇⠀⢀⡞⠉⡟⡱⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢸⠇⠸⣿⡿⢿⠀⠀⢸⢿⣿⣶⡏⢸⡇⠀⠸⡄⠘⡇⢇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⠀⠐⢲⠄⠀⠀⠀⠀⠠⣤⡈⠁⠀⡇⠀⠀⠑⠒⢛⡏⠁
⠀⠯⢭⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⣈⣙⣒⠲⠶⠶⠶⠾⠆⠀⠀⡇⠀⣀⡤⢾⡉
⡜⠳⠴⢧⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠉⠛⠛⠛⠒⠲⠶⠶⠷⠺⡅⠀⠀⠙⢦⡀
⠈⠒⠒⠙⠲⡏⣸⠣⣄⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣤⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠙⠳⣄⠈⠙⠛⠛⠛⠉⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⡏⠀⢀⠀⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠛⢻⡇⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠛⠋⠉⢻⠻⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠄⢠⣄⣀⣀⣀⣐⡂⠁⠤⠀⠠⠄⠠⡄⠇⢿⠀⣀⡤⢒⣹⡄⢹⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠤⠤⠤⠄⣀⣀⣉⣉⣉⣉⣉⠛⠓⠒⠒⢻⣋⠤⠚⠁⢸⣷⡞⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢻⠀⠀⠀⠀⢸⣧⡟⣲⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣠⡞⡵⠛⢫⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⢲⡶⠶⢶⡤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣿⣠⡴⠛⠁⣇⣧⠀⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣸⡁⠀⠀⠀⠀⠀⣼⠉⠉⣿⠉⠉⠁⠀⠀⠀⠈⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠶⢾⣷⡀⠀⠀⠀⠀⣹⣀⠠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡛⠁⠀⢀⡴⠋⠀⣇⠀⣀⠴⠚⠁⠉⠛⡿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠭⣭⣭⣽⠴⠖⠋⢱⡻⠷⠤⢤⣄⣀⡞⢁⡼⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣒⣶⣶⣷⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢳⡄⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠳⣴⠏⠀⠸⠟⠛⠋⠉⠉⠉⠉⠙⠛⠛⠛⠷⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣘⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣄⡀
⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣤⠀⠀⠀⣆⠀⠀⠸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⣿
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡀⠀⠀⠀⠀⣾⡀⠀⠀⠀⣼⡀⠀⠀⣼⠀⠀⣀⡿
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠘⣦⣀⢹⡦⠤⠤⠋⠉⠓⠦⠤⠾⠋⠙⠲⠤⠖⠋⠙⠒⠒⠋⠉⣿⠋
⠀⠀⠀⠀⢈⣽⢆⣀⠀⠀⠀⠀⢹⡌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿
⠀⠀⠀⣠⠟⠱⣏⠨⠽⣄⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣿⠀⠸⣧⡀
⠀⠀⣴⠏⠀⠀⠈⠙⠛⠛⢳⠶⠞⠁⠀⠀⢹⡀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⠚⠁⠀⠀⠈⣷
⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠉⠐⠒⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟
⢰⡏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠃⠀⠀⠀⠀⠀⠀⢀⡾⢷⣄
⣿⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⢀⡀⢹
⣿⠀⠀⠀⠀⣠⣾⢀⣀⣀⠀⢀⡀⠀⠀⣽⠛⠒⠦⠤⠤⠤⣤⣤⣤⣤⣤⣤⠴⠶⠒⢋⡵⢛⡷⠞⣫⡿⣾
⠙⢦⣤⣴⠞⢱⣟⠛⢧⡉⠉⠚⢷⡦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠛⢳⣿⣁⣀⣤⣤⠶⠛⠉
⠀⠀⠀⠀⠀⢾⣍⣙⣤⣤⠤⠴⠾⢧⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡿⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡇⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠉⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⡟⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠛⠛⢻⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠉⠉⠉⠉⡏⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣧⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣷⣀⣀⣿⣀⣀⣸⣇⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠲⠏⠀⠟⠚⠋⠉⠉⠙⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⢠⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢲⢄⡷⠀⠚⠉⠒⠶⠚⠉⠒⠒⠊⠙⠒⠋⢙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡗⢢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠙⠒⠛⡤⠔⠀⠀⠘⢄⠀⠀⠆⠀⠀⠀⢀⡈⠂⠐⠁⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡴⠂⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⡰⣟⠀⠀⠀⣤⠀⣸⠛⠒⣦⠀⠀⠤⢤⣤⣴⣒⡚⠉⢀⣸⠓⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠘⠦⡤⠞⠉⠉⠁⣀⡾⠉⢆⢀⡴⠋⠀⢙⢧⡉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢉⡇⠀⠈⠉⠀⠀⠀⣏⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⣁⣠⣴⠊⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣟⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⢤⠴⠶⣶⠶⠶⠶⣤⠤⢤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠚⢻⡀⠀⢠⡏⠓⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣧⠀⢸⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⡆⡏⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣾⣭⣛⡋⠂⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠉⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠿⣿⣿⠀⣴⡾⣶⣄⣸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣠⣿⣿⠈⣿⣤⣼⡿⣿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠆⠈⠉⠉⢠⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣻⢿⠿⣀⡀⠠⠤⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣾⡧⠠⣤⣖⣲⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢰⣾⣿⣷⣿⣿⣿⣷⣦⣿⣿⣿⣾⡟⠑⠆⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠊⠀⢰⣠⣤⣿⡎⠇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠉⠉⠙⠛⠏⠉⠀⠀⠀⠀⢠⣼⣿⣿⣿⣷⢸⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⣖⣶⣶⣶⣲⣖⢦⠀⠀⠀⠙⣿⣿⣿⣿⢸⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⡘⢰⣲⠀⠀⣿⣿⣿⡟⢸⡇⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠉⠀⢡⣿⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⣿⠏⣰⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠐⠁⠀⠀⢂⣾⣿⣄⠹⣿⣿⢏⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠂⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢷⡀⢀⣾⣿⣿⣏⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠉⠻⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⢾⠦⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠉⢾⣳⣿⣷⡖⠈⠁⠀⢰⠓⡄⢰⢠⢴⣶⣴⢂⣿⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠙⢷⣍⠀⠜⡰⠀⣼⣶⣥⡾⠿⠼⢿⣟⢯⣽⡂⠙⢦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡤⣄⠘⣛⡙⢆⠉⣦⣿⣿⡟⣿⣟⣿⣿⣯⣿⢟⣷⣴⣶⣿⢾⡗⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣦⢹⡿⣮⢻⣧⣿⢫⣉⣭⠑⢙⢿⣿⣿⣿⣿⣿⣿⣏⣈⡄⢀⣀⠤⠒⠺⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡈⠻⠇⢀⣜⣿⣿⣿⣿⣯⡳⠌⣡⣭⡉⢻⡿⢻⣿⣮⣼⣦⣻⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣼⡛⠏⣨⡿⣿⠿⣿⣻⣿⣏⡁⢸⢱⣿⣿⣾⡗⣿⣿⣃⡝⣧⣽⢯⣜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⡇⠘⢿⡻⣶⣝⣿⢿⣧⣙⠃⠘⡎⢿⣿⡿⢡⣿⣿⣿⣿⣻⠟⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡒⠒⣚⣻⡄⠺⣿⣿⣿⠻⡷⣽⠇⣠⣛⣿⣦⡿⣶⣿⣿⣿⣿⣾⢻⠃⠀⠑⢲⠫⢭⣓⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣹⣷⠶⣾⢯⣭⣄⢹⣿⢟⣷⠅⣉⣉⡙⢿⣿⣿⢂⣼⣿⣷⣍⣡⠄⠉⠀⣀⠈⢦⣻⣥⣍⣁⠢⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⡟⠚⣾⡷⠜⣫⣿⣁⣼⣟⠙⢿⠀⣛⢁⣾⣿⣿⣿⣩⡇⠸⣄⠰⠐⠠⠚⠉⢠⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡐⢉⣰⢎⣼⣿⣿⣿⣿⣤⠟⠠⠿⢸⣿⣿⣿⣿⣻⠃⠀⠛⣷⡌⠄⠠⣤⡐⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡸⠟⠋⢜⣿⣿⢟⣿⣿⣻⡟⢽⣷⣾⣷⣷⢾⣿⣿⣽⠁⢂⢰⡀⠈⠙⢦⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡤⠠⣯⠟⢃⡈⢉⣃⠘⣄⡈⢙⢷⡟⠻⣦⠙⠻⠈⣳⣧⡀⠑⠀⠀⠀⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠄⠠⠔⠉⠁⢻⡉⠂⠿⡞⣻⢶⣟⢰⣻⣦⠀⠀⠙⢾⡓⠒⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⢂⡀⠀⠈⠇⠄⢸⡿⠏⠻⠇⠀⠀⠸⠖⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠃⠐⠃⠀⠀⠴⣫⠄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠐⠁⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣄⠀⠀⠀⠈⠋⠁⠀⠀⢠⣤⡀⠀⠀⢸⣿⡦⠀⠀⠀⣀⡀⠀⠀⠀⢰⣷⣄
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠈⠉⠀⠀⠀⠀⢘⡛⠀⠀⠀⢾⣿⣿⣿⣶⡆
⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣷⣤⣄⣻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠛⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡛⠛⠀⠀⠀⠀⠙⣿⣶⡄⠀⠀⠀⠀⠹⡿⠆⠀⠸⣿⣿⣿⣿⣿⡟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠻⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⣠⣾⠿⠿⣻⣟⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⢀⡀⠀⢀⣿⣿⣿⣿⣴⣾⣿⡿⢿⣯⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⡀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⣾⡿⠃⠀⠸⣿⣿⣶⣿⣹⣿⡿⢻⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⣶⣄⠀⠀⠘⠿⣿⠆⠀⠀⢹⣧⣄⠀⠀⠀⠀⢀⡀⢀⡀⢰⣷⣶⡤⠀⠀⠀⠘⠃⢀⣀⣰⡿⠻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢲⣦⡀⣀⣉⣽⣥⣾⣿⣾⠟⣻⣿⣿⣾⡋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⣿⣿⣿⣧⡈⠉⢀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣤⣴⣦⣴⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣋⣁⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠘⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣧⣶⣤⣤⣾⡆⠀⠀⠀⣦⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣛⡛⠿⢿⡇⠀⠀⣴⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⠉⠁⠰⢿⣷⡄⢀⡀⠙⡿⠋⣤⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣾⣿⣿⣰⣿⣷⠸⡇⢠⣤⡶⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣇⣈⣥⣤⣤⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠘⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣟⠿⢿⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠻⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣏⠻⠿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣭⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣭⣃⢹⣿⠀⠈⠙⠻⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣏⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⠿⠛⠻⠏⢿⣿⡟⠿⠏


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣻⣿⣿⣿⣿⣋⡁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢞⠘⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠿⣿⡿⠿⠿⠟⠛⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣽⡷⣾⣟⣻⣻⣿⣿⡽⣿⢶⣄⠀⣀⠔⠋⠀⠀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⡿⣶⠗⢿⣿⡏⠡⠎⢳⡀⠈⢦⠹⣿⡀⢀⣀⠀⠚⠁⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣻⠅⠀⢿⣀⣼⣿⣿⠰⡖⡈⢿⡑⡈⣧⢻⣿⠉⢻⣷⠀⢘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠤⢸⣹⣇⣾⣿⣿⣷⣆⣘⣿⣷⣷⠿⢺⠻⣦⣿⠿⡚⡟⣧⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⣿⣖⣸⣆⣿⣿⡿⢿⣿⣏⣿⣭⣿⣴⡾⣿⣿⣿⠛⡄⣃⢡⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢷⣻⣏⣿⣧⣼⣿⣷⣾⣿⣿⢿⡟⣾⣿⣿⢿⡛⣿⡇⢡⠸⠈⡜⡗⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢺⠻⣿⡧⣈⠛⣿⢹⣿⣿⣿⣶⣿⣿⣿⠛⠀⣇⢻⣷⠈⡆⠆⢡⢻⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⡇⠉⢿⣿⣷⣿⡿⢿⣿⣾⡟⠉⠁⢸⣆⣀⣸⣨⣿⣿⣿⣼⡬⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⠀⠸⡄⠉⠀⣷⣀⣽⣷⣳⣶⣿⡿⠿⣻⢿⣿⣮⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣏⣦⣤⣷⣾⠿⢿⡟⠛⣿⣏⣽⣿⣶⣾⣿⠟⠁⢸⣿⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣽⣿⣷⣿⣷⠾⢿⠛⣉⣉⣥⡇⠀⠀⠀⠀⠀⢸⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣆⠀⠉⠉⠀⠀⠈⣻⣿⣿⣿⣷⣦⣤⣀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣟⠛⠟⠀⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠘⠛⠻⢯⣽⣷⡾⠁⠀⠀⠀⢀⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⣿⡇⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⢀⡀⠀⣀⣀⣴⣿⣿⣿⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⡿⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⡠⠃⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⠛⠛⠛⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⠒⢒⡘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣷⣶⣯⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡔⠋⠉⠒⣌⠆⠀⠀⠀⠀⠀⠀⡴⠁⠀⢠⠊⠀⠈⠱⡌⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡻⣿⣿⣿⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⣄⠀⠀⢀⠆⢠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣄⡀⠀⣸⠁⢃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡏⠁⠒⠉⡆⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⠀⠉⠉⢩⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡿⢿⣿⣿⡿⣘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡄⣰⡀⠀⠀⢀⣷⠃⠀⠀⠀⠀⠀⠀⠘⠦⠄⢼⠀⠀⠀⡰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⣿⡿⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢣⣀⣠⡎⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡧⣀⠴⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣿⣛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⡻⠿⠿⡗⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⢩⠓⠤⠺⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⣀⣠⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣇⠤⡼⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣣⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⠟⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡸⠚⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⠀⡅⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⢀⡇⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠖⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠙⠊⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⠤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠚⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠄⠠⠀⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⠇

⣿⣟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⡀⠀⠀⠀⠀⠀⠤⣒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⡩⠄⠀⠀⣀⣬⣤⣁⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⡄⡄⠀⣠⣿⣿⣿⣿⣿⣿⣦⠀⢱⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⡀⢀⡀⠀⢿⣿⣿⣛⣭⣭⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣄⠀⠀⠀⠈⠻⣿⣿⣷⣝⠻⣿⣷⣝⠿⢿⣿⠿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠀⣠⣶⣎⠿⣿⣿⣿⣮⣝⣛⣛⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣿⣿⡿⢻⣮⡻⢿⣿⣿⣿⣿⣿⣿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠀⣼⣿⣿⣷⣮⣭⣿⣭⣽⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢨⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠐⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠻⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⣄⣀⡀⠀⣀⡀⣒⣂⣂⠒⣐⣂⡀⣐⣒⣊⣑⣒⣒⣒⣒⣒⣒⣒⣂⣀⣀⣀⣠⣤⣀⣀
⣷⠚⠛⠛⠋⠙⠛⠙⠛⠛⠋⠀⠉⠉⠁⠉⠈⠛⠛⠈⠙⠀⠈⠁⠁⠉⠉⠁⠀⠉⠀⠉⠛⠋⠀⠉⠁⠀⠈⠉⠈⠉⠁⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠈⠀⡀⠀⠀⣀⠛⠀⠀⢀⡀⠀⣀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⣽
⢸⠀⠀⣤⣤⣤⣤⣤⣄⠀⢠⣤⣦⣤⣶⠀⠀⠰⣶⣾⡆⠀⣶⣲⣤⣶⠀⠀⣴⣾⣷⣶⣦⡔⢿⣿⣿⣿⣿⣿⠇⠸⣿⣿⡿⠿⠀⢸⣿⣿⢻⣿⣿⡆⠀⠀⢹
⢸⠀⠀⢿⣿⣿⠙⣿⣿⡆⠀⣿⣿⡏⠉⠀⠀⢸⣿⣿⡇⠀⣿⣿⡏⠁⠀⢸⣿⣿⠁⣿⣿⣿⠀⠈⣏⣿⣧⠀⠀⢰⣿⣿⣇⣀⠀⢸⣿⣿⠸⣿⣿⡇⠀⠀⢼
⢸⠀⠀⢰⣾⣿⣾⣿⣟⡃⠈⣿⣾⣷⢶⠀⠀⠘⣿⣻⡅⠀⣿⣿⣿⣿⠀⢸⣿⣿⡇⠙⠉⠉⠀⠀⣿⣿⠿⠀⠀⠘⣿⣿⡿⠟⠀⠸⣿⣿⠀⣿⣿⡇⠀⠀⣿
⢸⡀⠀⠈⣿⠿⡇⣿⡿⡧⠀⣿⣿⡏⠁⠀⠀⢸⣿⣿⠇⠀⣭⣿⣿⠀⠀⢸⣿⣿⡁⣻⣿⣿⠀⠀⣹⣿⣷⠀⠀⠀⣿⣿⣧⣠⡀⢸⣿⣿⣤⣿⣿⡇⠀⠀⢻
⢸⡇⠀⠀⣿⠷⡄⢻⣿⣇⠀⣿⣿⣿⣿⡇⠰⡟⣻⡷⠂⠀⣿⣿⣿⣿⡇⠘⢿⣿⣷⣿⡿⠋⠀⠀⠻⠿⠿⠀⠀⠀⠿⠿⠿⠿⠇⠘⠛⠃⠘⠛⠛⠁⠀⠀⢸
⢸⡇⠀⠀⠉⠈⠁⠉⠉⠁⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢗⣶⡶⠶⠶⠦⠶⠶⠶⠶⠶⠶⠆⢰⡤⠆⡠⠄⠤⣤⣄⣥⡀⠶⠠⠄⠀⠀⠠⠤⠤⠤⠤⠀⠀⠤⠀⠀⠀⠀⠠⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⡉⢡⡉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠁⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣦⡴⠦⠴⠴⠶⢶⢤⣤⣤⣤⠀⠤⠤⠤⡤⢤⣤⣤⢤⣄⠤⠀⡀⠀⢀⣤⡀⠀⣠⣔⣤⣔⣐⣲⣀⣀⣀⣤⣀⣠⣄⣀⢀⣀⣀⣀⣀⣀⢀⡀⡀⠀⣀⣀⡀
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⣿
⣼⠀⠀⢠⣦⣰⣶⣦⠀⠀⣶⣶⣶⣶⣦⠀⣶⣶⣶⣶⣦⠀⣴⣶⣤⣤⣤⡀⠀⠀⣠⢠⣷⣷⡀⢂⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⣀⡀⠀⣠⣤⣤⣄⣀⠀⠀⣿
⣿⠀⠀⣸⣿⣿⣽⣗⠀⠀⣿⣿⡏⣿⣿⡆⣿⣿⡍⣿⣿⡆⣿⣿⣟⢻⣿⣧⠀⣾⣿⡿⢿⣿⣿⠈⣿⣿⣃⢸⣿⡟⠃⢼⣿⣿⣿⠇⢰⣿⣿⠿⣿⣿⡆⠀⣿
⣿⠀⠀⣿⣿⡿⣿⡽⠀⠀⣿⣿⣤⣿⣿⠁⣿⣿⣤⣿⣿⠁⣭⣿⣿⣼⣿⡿⠀⣟⣿⡿⢸⣿⣿⡁⣿⣿⣿⢸⣿⡿⠀⣾⣿⣿⢀⠀⢸⣿⣿⢀⡿⣿⡇⠀⣯
⣿⠀⢸⣿⣿⠀⣿⣿⡆⠀⣿⣿⠿⠟⠋⠀⣿⣿⠿⠟⠋⠀⢻⣿⣿⢻⣿⣷⠀⣾⢏⣷⢸⣿⣿⠇⢹⣿⣿⣿⣿⡇⠀⣿⣿⣿⡿⠇⢸⣿⣿⢨⣿⣿⡇⠀⣿
⣿⠀⢸⣿⣿⠷⣽⣿⡇⠀⣿⣿⡇⠀⠃⠀⣿⣿⡇⠀⠀⠀⢸⣯⡉⢸⣯⣭⠀⣯⣾⣿⢸⣿⣿⠁⢸⣿⣿⣿⣿⠁⠀⣿⣿⣿⠀⠀⢨⣿⣿⢰⣿⣿⡇⠀⣿
⣿⠀⠿⠿⠿⠀⠿⡏⠿⠐⠿⠿⠇⠀⠀⠸⢿⠻⠇⠀⠀⠀⠸⠿⠿⢸⡿⠿⠀⠹⢿⣿⣿⡿⠏⠀⢸⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⡇⢸⣿⠟⣿⣿⣿⠃⠀⣿
⢿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡄⢀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠉⠀⠉⠈⠉⠩⠭⠭⠭⠭⠭⠤⠍⠉⠀⠒⠒⠒⠒⠰⠀⠐⠀⠒⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⠆⠠⠴⠄⠀⠶⠤⣤⡤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠙⢁⡄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠠⠼⠤⠤⠤⠤⠤⠤⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠤⢀⠀⠀⠀⢀⠠⠤⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡂⠀⠄⡂⠁⠀⠀⠁⡊⠄⠀⡆⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠐⠠⠩⠔⠁⠀⠀⠑⠬⠡⠐⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂⠂⠘⠈⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠈⠈⠀⠂⠃⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠐⠆⠀⠀⠖⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣸⡿⠞⢋⡴⠆⠀⠀⠀⠀⢰⣶⣶⣄⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡈⣤⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣤⣨⡿⢯⠄⠀⠀⠀⡇⠸⢻⣿⣴⠇
⠀⠀⠀⠀⠀⠤⠉⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣏⠀⠀⠀⠀⠀⢸⠀⠀⠘⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⠛⡿⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠈⠯⠄⠀⠀⠀⠀⡌⢀⣆⢠⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⢨⣅⣪⠉⣦⠙⠛⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢰⡃⠈⢀⢿⡀
⠀⠀⠀⠈⠀⠂⡆⠀⠀⣠⠐⠋⠀⡈⠉⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⡶⣶⠱⣤⡾⠟⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠙⢦⣘⢿⣯⣭⡇⠀⠀⢀⡴⠂⠀⠀⠀⠄⠋⠀⠀⠀⠀⡀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡶⣶⢶⠒⠊⠀⡀⣀⠐⠋⠀⠀⠀⢀⣠⡖⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⡉⠋⠃⠍⠙⠁⠀⠀⠀⠀⢀⡴⠟⢛⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⡀⠤⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⡿⠆⠀⠀⡀⠀⠀⠀⠀⠀⠲⢻⠝⠁⠑⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢏⡀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⡀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠈⠛⠛⠛⠋⠁⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⢀⣤⡄⠒⠚⠛⠒⢠⣤⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢠⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤⡄⢸⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⠀⣤⣄⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠘⠁⣸⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⣾⣿⡇⢸⠀⠿⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⡏⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⡇⠈⣿⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⠁⠀⠀⠛⠋⠀⠀⠀⠀⣀⡀⠈⠛⠁⠀⠉⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠂⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠗⠚⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⢀⠟⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠻⣄⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠙⢦⡄⠀⠀⠉⠒⠖⠀⠀⠀⢠⡴⠋⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠈⢳⣦⣤⣤⣤⣤⢴⡟⠁⠀⠀⠀⠀⠀⠈⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⢀⣠⣤⠤⢼⡇⠀⠀⠀⠀⢰⣷⠦⠶⣤⣀⣀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢉⡾⠉⣿⠀⠘⠃⠀⠀⠀⠀⢀⠇⠀⢰⡏⠻⣉⠑⢦⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠰⡏⠀⠀⠈⣷⠀⠘⢧⡀⢀⣤⠛⠀⢰⡎⠀⠀⠈⡷⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢸⡄⠀⠀⢠⡄⠀⣠⠟⠛⢧⡀⢠⡞⠁⠀⠀⣤⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢳⡞⠁⠀⠀⠀⢳⣾⠃⠀⠀⣠⠉⠀⠀⠀⠀⠀⠉⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠈⢣⡀⠀⠀⠀⢀⠃⠀⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠈⣇⠀⠘⢃⠀⠀⠀⠟⠀⢰⡇⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠃⢸⡄⠀⠀⠈⠳⣄⡸⠃⠀⢿⣀⡾⠋⠀⠀⠀⣿⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⡰⠞⠉⠀⠀⠀⠸⠁⠀⠀⠀⠀⠈⠙⢿⣿⠾⠉⠀⠀⠀⠀⢀⠉⠀⠀⠈⠉⢶⡄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠶⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢿⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⣠⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⢀⣀⠀⣶⣽⣿⡅⠀⢠⣤⡀⣠⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⣿⡟⣿⠟⣍⠙⢦⣈⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠛⣿⣇⠘⣋⠁⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠉⠁⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠈⠻⠶⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠉⠉⠉⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣤⣤⣤⣤⣤⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠇⢸⠀⣾⠀⣤⡘⠿⢤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⢰⠿⠶⠿⠶⠿⡁⠀⠈⢱⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⡀⠀⣀⣤⡀⣿⣄⣀⣴⣧⡀⣄⣤⣄⠀⣽⣤⠀⣤⡦⢄⣤⣤⣄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋
⣯⡀⣀⣀⣀⣀⣀⣠⠶⠖⠶⠶⠶⠖⠲⣶⠶⠖⢶⣄⢀⣀⣀⣀⣀⣀⣸⠛⠛⠛⠛⠿⡿⠛⠛⠛⠉⠛⠉⠀⠀⠀⠀⣠
⣿⠀⠉⠁⠈⠉⠈⠙⠷⠒⠺⠗⠒⠒⠒⠿⠒⠒⠛⠃⠈⠉⠀⠈⠉⠉⢹⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠛⠉⠉⠉⠙⠋⠉⠉⠙⠋⠉⠛⠉⠉⠋⠙⠋⠙⠋⠉⠙⠛⠉⠉⠙⠉⢻⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⣀⣠⣶⡿⠛⠿⠿⠀⠀⠀⠀⠀⠀⠹⠿⠛⢿⣷⣤⣀⠀⠀⠈⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⠿⠿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡗⠀⠀⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⠛⠛⠛⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠶⠶⢶⣤⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⣿⡄⠀⠀⠀⣼⡇⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠉⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣿⠁⠀⠀⠀⢹⡟⠋⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣴⣿⣿⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠸⣇⠀⠀⣴⣿⣿⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠘⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣦⡶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⣤⡴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣖⡩⠔⠊⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣿⡯⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣒⣒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣤⣤⣤⣤⣤⣐⣀⡠⢄⡀⣓⠘⡧⠼⣆⢢⠈⠿⣿⣿⢿⣷⠧⣭⡉⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠈⠩⢥⣿⣿⣿⣯⣵⣊⣝⠉⠩⡤⢼⣶⡷⣞⢿⣯⡑⠦⠉⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠈⡿⠐⠩⠞⣡⣿⢿⣿⣶⠀⢧⣀⠟⠈⠈⢣⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠁⠁⠈⡘⢿⢿⡳⠂⣠⠁⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠴⠀⠀⣩⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠛⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⢐⡆⢄⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠛⠒⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣤⣤⣤⣀⣸⣿⣦⣠⣶⣿⣷⡄
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡀
⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠘⢿⠿⠿⠛⠙⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⢸⠗⠏⣰⡿⢀⣿⣿⡿⢿⣿⣿⡟⠛⠋
⠀⠀⠀⠲⡀⠀⠀⠀⠀⠉⢁⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣈⣿⣟⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣀⣀
⠀⠀⠀⠀⠀⢈⣴⠶⠟⠛⠛⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⠀⠀⠉⠉⢻
⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⡏⠀⠙⣿⡁⢠⣄⠀⢀⡀⢸
⠰⢠⡾⠋⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡈⠻⣾⢿⣿⣧⠀⢀⣿⠃⠰⠀⣶⠖⠁
⢀⣿⠀⠀⣴⢿⣧⠀⠀⢈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠿⢿⣿⣷⣿⡀⣤⠊⠀⠛⠿⠀⠀⠈⠁⠀⢀⠇
⡈⠀⠉⠾⠃⢸⣿⠀⠀⠨⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣠⠈⠁⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⣀⠔⢺⣿⠀⠀⠀⠛⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⠀⢰⡏⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⡰⢆⠀⢰⡇
⠉⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣾⡇⠀⣰⡿⠋⣄⢀⡶⠖⠲⠞⠁⠀⠐
⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⢠⡿⠀⣸⣿⠇⢠⡄⠈⠁
⠀⠀⠀⢀⣿⠀⣿⢰⡶⣶⢠⡤⠲⡏⢯⢻⡄⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡾⠁⠀⠙⠟⢡⢿⡇
⠀⠀⠀⢸⡏⢰⡇⢸⠇⣿⠈⣿⠀⢻⡈⡆⢿⠀⠀⠀⠀⢰⡿⠀⠀⠀⢠⣿⠃⠀⠐⠶⠶⣨⠘⣧
⠀⠀⠀⢸⡇⢸⡇⣾⠀⣿⡄⢹⡇⢸⡇⡇⢸⠆⠀⠀⠀⣾⠇⠀⠀⠀⢸⣿⠀⠀⣤⣤⣤⢸⠶⣿⡇
⠀⠀⠀⢸⡇⢸⡇⢻⡄⢹⣧⠈⣧⢸⡇⡃⢸⠀⠀⠀⢰⡿⠀⠀⠀⠀⢸⣿⡆⠀⠀⡄⢰⡏⠀⣿⣷⡀
⠀⠀⠀⢸⡇⢸⡇⢸⣇⠘⣿⠀⣿⠘⡇⠃⢾⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⡇⠀⠸⣷⠸⡇⢠⣿⣿⣷
⠀⠀⠀⢸⠇⢸⡇⠸⡟⠀⢻⠀⣿⠀⢷⠘⢸⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⡇⣧⠸⣿⣿⡿
⠀⠀⠀⠿⢠⣿⣥⠶⢇⠀⣧⠀⢿⠀⣼⠀⠼⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⡇⢹⡀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⣿⣇⣀⣼⡿⠿⡼⠇
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠾⣀⣀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣶⠒⠒⠃⠤⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠀⠀⢸⠀⠀⠀⠀⠟⢣⡈⠉⠒⠢⠤⠄⣀⣈⢙⡋⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⢠⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⣀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡆⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠈⠀⠀⠁⢦⡂⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠆⠀⠁⠀⠀⠀⠼⠁⠀⠀⠀⠀⠈⢢⡄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠰⢤⠉⡳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣴⣄⣤⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠈⡶⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠁⡄⢫⡹⠣⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡈⣰⠟⣿⣿⡏⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠶⢁
⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠿⠛⠃⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⡷⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢠⠟⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠃⠀⠈
⠀⠀⠀⠀⠒⡀⠀⡠⠊⠀⠀⠀⠚⠙⠒⣤⣀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⣇
⠀⠐⢀⣠⡶⢦⡼⠀⠀⠀⠀⠀⠄⡠⠊⠀⡉⠉⠒⢄⣈⠃⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠄⡶⠆⠀⠀⡀
⠀⠀⢀⠈⠛⢿⠙⠆⠁⠀⠀⠀⠀⠀⠀⠀⠈⢆⡠⠀⠩⣆⠀⠀⠀⠀⠀⣤⠴⠴⡀⡛⠋⠁⣀⡁⠰⠄⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠈⢄⠀⠀⠀⠀⠐⠂⠀⡣

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⣀⣠⡴⠶⠟⠛⠛⠛⠋⠉⠉⠙⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡴⠚⠛⠛⠷⠶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⢳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠺⣯
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠇⠀⠈⠉⠓⠶⢦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡴⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣠⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣤⣼⠀⠀⠀⠘⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢠⡄⠀⠹⣦⣄⣀⣤⠞⠁⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠰⡏⢠⣟⠀⠀⠀⠀⢹⣦⡀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠁⠀⢀⡴⠞⠙⢷
⠀⠀⠀⠀⠀⠀⠳⣤⠛⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⣀⣴⠶⢦⣄⠀⠀⠀⠘⢿⣦⣀⣀⣠⡾⠁⠀⠀⠀⠀⠙⠷⠶⠛⢀⡛⣠⡾
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⠾⠿⠇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡶⠾⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠛⢷⣄⠙⠁⠀⢤⣤⣤⣶⣌⠉⢀⣼⣧⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⣠⣤⣀⡶⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠉⠀⠀⠀⠙⢷⡶⠟⠋⠀⣿⠀⠙⠷⠿⢻⡏⠙⠻⢷⣦⡀⠀⢠⡾⣫⠤⢤⣽⡏⠉⠛⠻⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡀⠀⠀⠉⠻⣷⢟⡿⠉⢀⡀⠙⠻⣶⣄⡀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⣠⣴⠿⠛⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡿⠛⠷⣦⣤⣾⢋⡞⠁⠀⠈⠻⣶⣄⠀⠉⠛⠻⢿⡿⣶
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⣴⡾⠋⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⣠⡿⢣⠟⠀⠀⠉⠲⣤⡀⠙⠷⠶⠀⠀⣼⠃⣴
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣇⢀⣴⠟⣤⠃⠀⠈⠳⣦⣀⠀⠙⠶⠄⠀⢠⡾⢁⣾⠋
⠀⠀⠀⠀⠀⣸⡏⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡾⢣⡞⠁⠀⠛⢶⣄⡀⠙⠛⠦⠀⢀⣰⠟⣰⡟⠁
⣴⡿⢶⣤⣴⣿⣄⣀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣰⡟⣠⠟⠀⠀⠚⢦⣀⠈⠛⠂⠀⢠⣿⠛⠻⣾⣟⣧
⠙⠿⢦⣴⡏⠀⠈⠛⠛⢻⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣴⠏⠐⣏⠀⠀⠐⢦⣄⠉⠻⠆⠀⢀⣿⠛⢶⡄⠈⠙⣿⡆
⠀⠀⠀⠹⣷⣿⡰⢚⣏⠙⠿⢶⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣦⡀⠈⠻⢶⣄⠀⠈⠳⠆⠀⢀⡾⠛⠦⣀⠀⠀⢰⡟
⠀⠀⠀⠀⠈⠉⠙⠿⠉⠛⠷⣦⣾⡻⣷⡀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣦⣄⠀⠈⠛⢶⣀⡀⢀⡼⢿⣦⡀⢀⣠⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠙⢷⣤⡀⠀⠈⠛⠛⢡⡿⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣿⠀⠀⠉⠻⣶⣄⡀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡶⠶⢶⣶⣤⣤⣄⣠⣼⣧⣠⣤⡶⠿⣿⠁⠀⠀⠀⠀⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡏⠉⠉⠉⠀⠈⢻⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠿⢧⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣴⣤⣬⣿⡆
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣄⠀⠀⠀⠀⠀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇⠀⠀⠀⠀⠘⣇⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠦⢶⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢸⠃⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢄⣠⠱⠀⠀⠀⠀⢹⡿⣿⣦⣄⠀⠀⢸⠀⠘⠀⢀⡆⠀⠀⠀⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣾⡇⠈⠻⢿⣷⣦⣬⣄⣥⣴⣿⣷⣄⣀⣀⣠⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠙⠛⠟⠛⠋⣿⣿⠁⠀⣤⠤⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⢻⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣆⣠⠞⠉⠀⠀⠀⠀⠉⢻⡿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⢀⣿⣇⣀⣀⠀⢠⡶⢶⡀⠀⠀⠀⡏⠀⠘⣿⡀⣴⡾⢛⣻⣷⠶⠿⢶⣿⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⡾⠋⠉⠁⠀⠉⠙⢾⣷⡵⠙⢦⠀⢰⡇⠀⠀⠸⣗⣏⠀⢿⠁⠀⠀⠀⢸⣿⣇⣀⣼⡓⠒
⠀⠀⠲⡶⠺⠀⠀⠀⠀⠀⠀⢹⣿⡀⢀⣠⣴⣦⣄⡀⠀⠙⣯⠂⠈⠳⣾⠀⠀⡀⠀⢹⡟⠦⣼⡿⠟⠁⠀⣼⠹⡏⠀⠈⣷⣤⣤⣀⡀
⠀⠀⠸⠃⢤⠂⠀⠀⠀⠀⠀⣾⣿⣎⣾⠋⠀⠀⠉⢷⠀⠀⢸⡷⣄⠀⠈⠀⢠⣷⠀⠀⢿⣀⡀⠀⣀⣤⡾⣣⡾⠷⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣷⡀⠀⠀⠀⣸⠀⠀⣸⣷⣿⣷⣤⡀⣼⠹⣧⣠⣬⣿⢿⠟⠛⠉⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⡤⠶⠿⠿⠿⠿⢿⣿⣿⣾⠻⠦⠤⠞⠃⠀⢀⢝⡉⢛⠊⠻⠿⠛⠀⠙⠋⠉⠐⢆⣱⣤⣤⣤⣿⣦⡀⠀⠀⠰⢯⣉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⡸⢿⣧⣵⣀⠀⢀⣀⣴⣿⡗⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⡌⠷⠄⠀⠀⠁⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣠⠞⠁⠀⢈⠿⠛⠛⠛⠋⠉⢿⣿⣷⡀⠀⠀⢠⣴⡶⣔⣆⠴⣤⣆⠤⠰⣦⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⠋⠀⣠⠴⠶⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠔⢃⡀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢃⡀⢠⠊⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⢀⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠖⠚⠛⠛⠛⠓⠛⠚⠛⠛⠻⠷⠶⠾⠿⠿⠿⠶⠶⠶⠶⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⠟⣩⣤⣌⠻⣆⠀⠀⠀⠀⠀⣴⠟⢩⣭⣍⠙⣦⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⠃⠰⣿⣿⣿⠀⣿⠀⠀⠀⠀⢰⡏⠀⣿⣿⣿⠀⠈⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡀⠀⠘⠛⠁⠀⣿⠀⠀⠀⠀⢸⡇⠀⠈⠛⠋⠀⣠⠏⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⣄⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⢿⣄⣀⣀⣠⡾⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢛⣛⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⣀⡀⠀⢀⣶⠖⢿⡀⠈⠛⠉⠉⠉⠉⠁⠀⠀⠀⣠⡶⠶⣦⣤⣤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠶⠶⠶⠶⠿⠿⠟⢻⣿⠀⢸⣿⣛⣻⣿⣿⣿⣿⣛⣛⠛⠛⣿⡇⠀⣿⠤⠤⠴⠶⠶⠶⠶⠶⣶⡆
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠦⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⡿⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⡏⠉⠁⠀⠀⢀⣠⣿⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣧⣿⣍⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⢀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣀⣀⡀⣹⡆⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢻⡏⢉⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡟⣿⠋⠉⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡇⠀⠀⠀⠀⠀⠀⢿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠈⣛⡿⢿⡿⣷⣶⠶⣦⣼⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⣀⣀⠀⠀⢈
⣠⡾⠋⢰⣿⣅⠈⠙⢶⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢳⣶⠾⣿⠟⠻⣿⡉
⢿⡀⢼⠛⠁⠈⢻⡦⠀⣿⠀⠀⢿⡤⠤⠶⠶⠶⠶⠶⠒⠂⣿⡇⢸⣟⠛⠛⠛⠛⠛⠛⠛⠋⣉⣉⣹⡇⢐⣿⣛⣛⠛⠒⠲⠶⠶⢄⣸⡇⢰⡟⢁⣸⡿⢶⣄⡈⠛
⢸⡇⠸⡇⠀⠀⢸⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠛⢿⣆⣸⡟⠛⠛⢻⣦⠀⠀⠐⣿⠉⠉⢹⣧⡾⠋⠉⠉⠛⢻⡆⠀⠀⠀⠉⠃⠘⣇⠘⣏⠀⠀⢩⡇⢰
⠈⣷⢀⣿⠀⠀⣸⡃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣼⠁⢸
⠀⠸⠟⠉⠀⠀⠘⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣆⡿⠀⠀⢿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⠳⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⠀⠀⢀⣀⣤⣤⣤⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠖⣾⣿⣿⣿⣿⣿⣿⣿⡛⠿⠟⠀⠀⠈⠛⢻⡿⠿⠿⠿⠿⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠉⠉⠉⠉⠉⠉⢷⡀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣀⣠⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⠀⣾⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠘⣿⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⠀⠀⠀⠀⠀⢀⣿⡇⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⢃⣿⣿⣿⣿⣿⡄⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⠀⠀⠀⠀⠀⣾⡟⣾⣿⣿⣿⣿⣿⣿⡼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⡇⠀⠀⠀⠀⠀⣿⠁⣿⣿⣿⣿⣿⣿⣿⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠣⣸⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⡇⠀⠀⠀⠀⢠⣇⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⣿⣿⡏⣿⣿⣿⣿⡆⠉⠀⠀⠀⠀⠀⢿⠛⠀⣿⣿⣿⡏⣿⣿⣿⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠁⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠐⠲⠐⠃⠀⠀⠀⠀⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢙⣃
⠀⡀⣀⣰⣟⣀⣀⣀⣀⣀⠄⣀⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣡⣀⣀⣀⣀⣀⣿⣆⣀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⡀
⠄⠀⠀⠀⢸⠉⣻⠀⠀⣼⠉⠁⠀⠀⠐⠃⠀⠀⠏⠁⠀⠀⠄⠀⠆⠀⠈⢡⠀⠀⠀⣼⠉⠁⠀⢰⠇⢰⠆
⠀⠀⠀⠀⡟⢻⠁⠀⢀⠏⠉⠀⠀⡀⠀⠀⠀⠸⠁⠁⠀⢰⠁⢀⠀⠀⠀⡞⠀⠀⢀⡏⠉⠀⠀⠼⠀⠾
⡄⠀⠀⠀⠁⠈⠀⠀⠈⠁⠁⠀⠈⠛⠁⠀⠀⠀⠈⠁⠀⠈⠛⠉⠀⠀⠀⠁⠀⠀⠈⠉⠋⠀⠀⠈
⠈⠒⠀⠒⠲⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠒⠒⠒⠒⠒⠐⠒⠒⠲⠒⠒⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⣠⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠐⣆⠀⣄⡀⢀⠀⣠⣤⣤⡶⠶⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢉⡤⠍⠛⠒⠤⢄⣀⣀⠤⠤⠐⠒⠒⠠⠤⢄⣉⠉⠛⠭⣕⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⢔⠢⡜⢱⠀⠙⠢⡀⠀⠙⢢⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢠⣚⢎⠈⡧⡭⣃⠀⠈⢦⠀⠀⢱⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡤⠤⠏⠣⠛⣦⣟⣁⠣⢢⠀⢇⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⡠⢊⡥⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢖⢊⠔⠉⠉⠑⡄⠮⡄⣱⠸⡄⢸⠀⢠⠃⢸
⠀⠀⠀⠀⠀⣠⠊⠀⢏⣵⡜⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠎⠀⣎⡸⡀⠀⠀⠀⡼⠰⣛⣁⡏⠁⢸⠋⠁⢀⠎
⠀⠀⠀⢀⡾⠤⢃⡐⠠⠤⠤⠀⠀⠈⠑⠒⠒⠒⠒⠉⠀⠀⠀⠰⠥⡌⢒⠒⣊⣐⡏⠁⠈⠀⠀⡼⠤⠒⠁
⠀⠀⠀⢸⣀⣀⣀⣈⣉⣒⣀⣀⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣑⣃⡀⣀⢀⣀⣀⠜⠁
⠀⠀⠀⠀⠓⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠋⠉⠛⠛⠒⠶⠶⠦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⠖⠒⠒⠒⠲⠦⠤⢤⣀⣀⡀⠀⠉⠉⠙⠓⠲⣤⡀
⠀⣀⣠⢶⡖⢲⠀⣠⡄⠀⠀⠀⠀⠀⠀⡟⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⢤⡀⠈⢻⠶⣄
⢿⡉⢣⠀⣇⣸⠏⣡⡟⠀⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡸⠀⠈⠳⣄
⠀⠙⣆⣳⣯⡧⣴⠋⠀⠀⠀⠀⠀⠀⡞⠀⣸⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⡾⢀⠃⠀⠀⠀⠈⡇
⠀⠀⣹⠥⠶⠒⢻⠇⠀⠀⠀⠀⠀⢰⡇⠀⡏⠀⠀⠀⠀⠛⠛⠒⠲⠦⠤⣤⠀⠀⠀⠀⠀⢐⠇⡌⠀⠀⠀⠀⢠⡇
⠀⠀⣟⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣾⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠁⠀⠀⠀⠀⣸⠁
⠀⠀⣿⠤⠤⠀⠈⣧⠀⠀⠀⠀⢠⡏⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠀⠀⠀⠀⠀⡟
⠀⠀⢸⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇⠀⠷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡇⠀⠀⠀⠀⢸⠃
⠀⠀⠘⣷⠒⠉⠀⠀⠹⡄⠀⠀⠈⠳⣤⣀⡀⠀⠉⠉⠛⠒⠲⠶⢤⣤⣀⡀⠀⠀⠀⢠⠇⢸⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠹⡄⢀⡤⠂⠀⠙⢦⡀⠀⠀⠀⡽⠋⠙⠓⠲⠤⢤⣄⣀⣀⡀⠈⠉⠉⠛⠛⠁⢀⣎⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠹⣏⠀⠀⢀⠀⠀⠙⠳⠶⡟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⠶⠖⠋⠉⠹⡆
⠀⠀⠀⠀⠀⠘⢦⣴⠋⠀⠀⡰⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣀⣤⠿⠶⠶⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣴⣁⣀⡼⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠋⠨⡇⠀⠀⣶⠀⠀⣰⠁⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡀⢀⣀⣀⣀⣀⣀⠀⠁⠀⠀⢠⠞⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⠉⠁⢸⠁⠉⠉⠛⠶⣄⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⠤⠤⠤⠤⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⢷⡀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⣤⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⢦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣸⠧⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠈⠀⠀⠀⡟⠀⠀⢀⣠⡤⠖⢛⡗⢲⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⠧⠶⠛⡟⠙⢻⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣼⣀⣤⣼⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣧⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⢴⠶⣤⡀⢀⣀⣠⠖⠺⡁⠀⠘⡀⠉⠛⠒⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⠶⠶⠶⣶⠒⠋
⠈⢧⠀⠙⢫⡈⠱⡀⠀⠸⠄⠀⠑⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠘⠛⠳⠖⢦⡀
⠀⠈⢧⠀⠀⢣⠀⠳⠀⢀⣀⣀⡴⠓⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡠⠂⠁⠀⢠⠃⠀⣤⠀⡸⠛⡆
⠀⠀⠈⢧⡀⡼⠦⣤⠴⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢠⠃⠀⢀⠃⡜⠀⢀⡇
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠻⠤⠴⠿⢶⡇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛

⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⣷⠀⠀⠀⢀⣠⡴⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠰⠒⠛⠙⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣟⠒⠶⣄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠶⣆
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠱⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢶⡏
⠀⠀⠀⠀⠀⠀⠀⡾⢀⡞⠀⠈⠙⠓⠦⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⢴⡖⠋⠁⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠊⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⢿⣀⠀⠀⣠⠖⠀⠀⢰⡏
⠀⠀⠀⠀⠀⣾⢙⠇⠀⠀⠀⢻⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⣷⠀⠀⠉⠑⡟⠁⠀⣠⠴⢿⡀
⠀⠀⠀⠀⠀⠻⣌⠋⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠻⣦⣀⣀⣴⠇⠀⠀⠀⠀⠳⠴⠞⠁⠒⣸⠇
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠛⠃⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⣶⠄⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢤⣀⠀⠀⠀⠀⠀⣀⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠉⠻⣄⡉⣁⣿⠿⡿⢿⣅⣠⣾⡷⣤⣄⠀⠀⠀⠀⣰⠾⠻⣦⡴⢦⣼⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⣏⠀⠉⠉⢸⡇⠀⠉⠻⢦⣤⡾⡿⠋⠙⢿⣧⡀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣤⡶⠿⣿⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⢸⡿⢶⣄⡀⣰⢟⡜⠁⠀⢶⣄⡈⠛⠷⢶⣿⢧⣄
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⣠⡶⠛⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢈⣿⣣⠞⠀⠈⠲⣄⡈⠻⢦⡄⠀⣸⠃⣽
⠀⠀⠀⠀⠀⣰⡟⠀⢀⡾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣠⡾⣱⠋⡀⠘⠲⣄⡈⠙⠲⠄⢀⡼⢡⡾⠁
⢀⣀⡀⠀⢰⡏⠀⢠⡟⠁⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⢸⣿⢟⡼⠁⣄⠙⠷⣦⡄⠙⠳⣤⣴⡟⣴⣟
⢾⣏⡛⢳⠟⠳⣴⣿⣄⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⢣⡟⠀⢠⣍⠻⢦⣌⠉⢀⣼⣯⡉⠻⢿⣿⡀
⠀⠈⠙⣿⡴⣀⣠⡶⢾⣧⣀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⢙⣁⠈⠃⣀⣀⠙⠳⣤⡉⠁⣼⣿⣌⡙⠆⢀⣿⠃
⠀⠀⠀⠈⠛⠻⠾⠛⠶⣬⣹⠷⣦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠈⠙⢷⣄⠈⠙⠳⣄⡈⠁⣠⢿⣄⠉⠃⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡏⠳⣦⡀⠀⠙⠳⢋⡾⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣼⠇⠀⠈⠙⢷⣤⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠛⠛⣷⠶⢦⠶⠿⢶⡶⠟⠙⣯⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⠀⠀⠀⣿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣇⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢦⣤⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⣯⣭⣤⣍⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠧⣼⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠙⣡⣿⡼⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⢿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠁⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⡞
⠀⠀⠀⠀⠈⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⣸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⢻⣿⣿⣿⣦⣾⢟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣨⣿⣿⣿⣽⣿⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠤⠂⠀⣀⠀⠠
⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⣤⣬⣿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠜⠤
⠈⣿⣿⣿⣿⣿⣿⣿⡾⢿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⢀⡲⠀⠁
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⣻⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⠀⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⢀⣤⠦⣡⣶⣶⣟⣃
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠞⠉⠁
⠀⠀⠀⢹⠿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⠿⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠶⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠓

⠀⠀⠀⢠⣤⣤⣀⠀⢀⣀⠠⣄⢷⠻⠆⢲⣷⠆⠀⠰⣶⣄⠀⠠⣴⣶⠀⢀⡀⢠⣰⡄⠀⢀⣀⣀⠀⠀⠀⢠⣄⠀⢀⡴⢚⡍⠲⡄
⠀⠀⠀⠈⣹⣿⠿⠈⢹⣿⣷⠙⠇⢀⣄⡉⠻⠋⠀⢤⣤⡁⠀⠰⣿⠯⠁⢸⣿⣈⠁⠀⠺⠿⣟⠛⢣⣤⣀⢸⣿⠦⠘⣄⠀⣧⠀⣸
⠀⠀⠀⠀⠘⠛⠂⠀⠈⠈⠉⠀⠀⠀⠙⠛⠓⠀⠀⠰⠟⠙⠒⠀⠙⠛⠁⠈⠉⠉⠀⠀⠀⠀⠈⠃⠀⠀⠁⠈⠋⠀⠀⠈⠓⠒⠚⠁

⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⢀⣠⡤⠤⢤⣀
⠀⠀⠀⢀⡖⠉⣠⠀⢠⠀⠙⢦⠀⠀⠀⢠⠞⠁⢠⡄⢠⡦⠈⠳⡄⠀⠀⠀⣴⠋⠠⣄⠀⣤⠄⠙⣄⠀⠀⠀⣰⠏⢁⡀⠀⣀⠊⢳⡀
⠀⠀⠀⡿⠀⠀⠘⠶⠞⠀⠀⢸⡇⠀⠀⣾⠀⠀⠘⠢⣤⠃⠀⠀⢹⠀⠀⢰⡇⠀⠐⠂⣤⠒⠀⠄⢸⠀⠀⠀⡏⠄⠨⢅⣠⠍⠁⠆⣷
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠉⠓⠒⠶⠶⠖⠛⠉⠀⠀⠀⠀⠈⠓⠶⠤⠤⠴⠶⠛⠁⠀⠀⠀⠀⠉⠓⠶⠤⠤⠶⠞⠁⠀⠀⠀⠈⠓⠦⠤⠤⠴⠶⠋

⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣰⠟⢉⡀⠀⢀⠙⢳⡄⠀⠀⠀⢀⡴⠋⢁⠀⢀⠈⠳⡄⠀⠀⠀⠀⢠⣞⣋⣁⣀⣈⡙⣦⡀⠀⠀⠀⣰⢞⣉⡁⢀⣉⡳⣄
⠀⠀⢰⡯⢤⡤⠥⠤⠬⣤⠤⢿⠀⠀⠀⣼⠁⣀⡬⣤⣴⠀⠀⢿⠀⠀⠀⠀⡟⢹⣿⣿⢽⣿⣿⠍⣇⠀⠀⢰⡇⢸⣯⡷⠻⣯⡗⠸⡆
⠀⠀⠈⣧⠤⣇⣀⣀⣀⡽⠶⣾⠇⠀⠀⢻⡀⠀⠀⠈⠆⠀⠀⣾⠀⠀⠀⠀⢷⠀⠘⠲⠞⠀⠀⢠⡏⠀⠀⠘⣇⠛⠈⠳⠞⠀⠛⣸⡇
⠀⠀⠀⠙⠦⣄⡀⢀⣀⣠⣴⠟⠀⠀⠀⠀⠙⠦⢤⣤⢤⡤⠾⠃⠀⠀⠀⠀⠈⠳⠦⠤⠤⠤⠴⠛⠀⠀⠀⠀⠘⠳⠤⣤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡤⢖⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⣠⠖⣉⠉⣈⡉⠲⣄⠀⠀⠀⢀⡴⠋⣀⠀⠀⡈⠑⣄⠀⠀⠀⢀⡴⠋⣡⡄⢀⡉⠳⡄⠀⠀⠀⠚⢂⡴⠚⠉⠉⠙⠢⡄
⠀⠀⠀⣼⠁⠀⡙⠀⣹⠀⠀⢸⡆⠀⠀⣾⢠⡎⠥⣀⡤⠉⡄⢸⡆⠀⠀⣼⠁⠘⠧⠟⠸⠽⠀⢹⠀⠀⠀⢠⡏⠀⢘⠀⣸⠁⡄⠹⡆
⠀⠀⠀⢷⠀⠀⠀⠉⠇⠀⠀⢸⡇⠀⠀⢻⡈⠁⠀⠈⠀⠀⠋⢰⡇⠀⠀⢹⡀⠀⠠⣏⡇⠀⠀⣼⠀⠀⠀⢸⡅⠀⠀⠙⠁⠀⠀⢰⡇
⠀⠀⠀⠈⠳⠦⢤⣀⣠⣤⠶⠟⠁⠀⠀⠀⠙⠢⢤⣄⣠⣤⡴⠟⠀⠀⠀⠀⠳⢤⣄⣈⣤⣤⠾⠃⠀⠀⠀⠀⠙⠦⢤⣤⣤⣤⡴⠟

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⡴⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⢿⣦
⠀⢸⣿⠀⠀⠀⣠⡄⠀⠀⢀⣤⣤⣀⠀⢀⣤⣄⣀⠀⢀⣄⠀⣀⠀⠀⢀⣠⣤⣄⡀⠀⣄⠀⠀⠀⣀⠀⣠⣤⣄⠀⢀⣤⣤⣄⡀⠀⠈⣿⡆
⠀⢸⣿⠀⠀⢠⡏⢿⡀⠀⢸⡇⠀⢸⡇⢸⡇⠀⠈⠇⢸⡇⠀⢈⡇⢠⡟⠁⠀⠈⢻⡄⢻⡄⠀⢰⡏⠀⡇⠀⠀⠀⢸⡇⠀⠀⠹⣆⠀⣿⡇
⠀⢸⣿⠀⠀⣾⣤⣬⣦⠀⢸⡗⠐⠋⠀⢸⡗⠒⠋⠁⢨⡟⠛⢿⡀⢸⡆⠀⠀⠀⠸⠇⠈⢷⠀⡞⠀⠀⡟⠉⠉⠀⢸⡇⠀⠀⢀⡟⠀⠙⡇
⠀⢸⣿⠀⠸⠃⠀⠀⠹⠆⠸⠇⠀⠀⠀⠐⠁⠀⠀⠀⠸⠇⠀⠐⠦⠀⠛⠦⣤⠴⠛⠀⠀⠸⠗⠁⠀⠀⢧⡤⠄⠀⠰⣦⣤⠄⠊⠁⠀⣿⡇
⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡛⠁
⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠓




⠀⠀⢀⣤⣄⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⣶⣦⣆⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣖⣀⣶⣶⣖⣶⣶⣦⣦⠀⢰⣶⣶⣶⣶⣤⡀
⠀⠀⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄
⠀⢸⣾⠀⠀⠀⢰⡖⠓⢤⡀⠰⡖⠒⠒⠂⠀⠀⣦⠀⣶⠒⠒⠂⠀⣠⠖⠀⠓⠂⠒⠒⣶⠒⠂⢰⠖⠒⠒⠀⣰⠒⠒⠶⣄⠀⠀⠀⠀⣿⠃
⠀⢸⣽⠀⠀⠀⢰⣆⣀⡴⠃⢸⣧⣤⣤⠀⠀⠀⣿⠀⣿⣤⣤⡄⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠆⣤⡄⠀⣤⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⢸⡇⠀⢹⡆⢸⡇⠀⠀⠀⠀⢀⡿⠀⣿⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⡗⠀⠀⢰⡀⠀⠀⠀⣿⠀⠀⢀⡼⠃⠀⠀⠀⠿⠃
⠀⠸⣿⡀⠀⠀⠘⠃⠀⠈⠃⠈⠃⠚⠛⠀⠛⠛⠁⠀⠙⠛⠓⠃⠀⠈⠙⠛⠛⠁⠀⠀⠃⠀⠀⠘⠛⠛⠙⠀⠛⠓⠛⠉⠀⠀⠀⠀⢀⣷⡆
⠀⠀⠻⣵⣤⣤⣤⣤⣤⣤⣄⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣠⣤⣤⣤⣤⣄⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⢄⣄⣺⠛
⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠁



⣿⠿⣿⠿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠰⢨⡀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠙⣐⠀⠀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠤⠀⢀⠁⠀⠱⡩⡇⡴⠃⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⡀⢲⣃⡧⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⢀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⡀⠂⠀⠀⡀⠀⠀⠀⠘⠄⡟⢠⠒⠉⡉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠈⠀⠀⠀⠨⠀⠀⠀⠀⢀⠀⠁⠀⠀⠁⠁⠀⠀⠀⠘⣿⠃⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢠⢉⢺⡅⡆⠈⠈⢉⠉⣁⠀⠀⠀⠀⠀⡄⢈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢨⠀⢺⡟⠛⠀⠀⠀⠀⠐⠀⠀⠀⠐⢀⢠⡞⠲⠀⠀⠀⠀⠀⠀⣀⣀⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣤⠀⡀⠀⠀⠹⠄⠈⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠘⠿⠯⢧⣤⣤⠬⠷⠀⠀⠀⠀⢀⣀⣀⠘⠒⡒⠘⠣⠀⣛⠧⢤⣀⠾⠗⡐⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠭⢀⠀⠀⢉⡳⠤⠴⠚⠶⠻⠽⠄⠉⠒⠚⠓⠂⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⣦⣭⣓⡢⠤⣀⠀⠀⣀⣀⠤⠤⠴⢖⡒⠒⠚⠑⠉⠁⠐⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⣤⠄

⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⢀⣀⣀⣀⠀⣀⡀⡀⣀⡀⢀⣀⣀⣀⣀⢀⢀⣀⣀⢀⢀⣀⣀⣀
⠀⠀⠀⠀⠈⠉⠀⠁⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠈⠉⠉⠁⠉⠉⠈⠉⠉⠘⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣄⣀⣤⡶⠟⠉⢰⠋⠀⠀⠈⠒⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⣷⠸⣿⡟⢠⡶⠁⡟⠃⠀⠚⠙⢫⣃⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠓⠢⡀⢀⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⠁⠀⢿⠀⠉⣀⣀⣵⢀⠀⢀⣀⡀⣹⢛⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣴⡄⣹⠋⠿⢿⣟⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇⡴⠋⣿⠀⡈⠉⢶⣶⢮⡇⢸⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠘⣿⣿⣿⡏⠀⠀⠈⠙⣦⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⡷⠃⠀⠛⢇⢘⠣⣾⣿⠏⡅⠀⢀⣀⢠⡄⠀⠀⠀⠀⠀⡀⠀⠀⠠⡄⠈⠂⠼⠟⠋⢷⡀⠠⢤⡀⢠⠸⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠁⢀⣴⣧⠄⠿⣄⣠⣧⣰⣿⣴⡟⠁⠀⣁⠀⢶⠄⠈⠩⢷⣶⠆⢀⡟⠀⠀⠀⠎⠀⡀⠀⠀⠀⣉⠚⢻⢆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣧⠀⠚⠉⠁⠀⠀⠀⠘⣿⠋⢻⣽⠇⠘⠁⠈⠓⢄⠑⠢⣘⠄⠀⠀⠈⠁⠀⡘⠱⣦⠀⡤⣼⣾⣿⣿⡭⠾⠓⠊⠉⠐⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⡁⠀⠲⡀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣈⠑⣤⠀⠀⠀⠀⠁⠀⢸⣷⣿⠋⠀⠀⠀⡀⠀⣀⣀⣤⣴⠂⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠀⠤⠀⠙⢄⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠛⠋⠉⠉⠨⠄
⠀⢿⣦⣀⠀⠀⠀⠀⢀⡀⠠⠀⠁⠀⠀⠀⠀⠀⠑⢦⡀⠑⣄⠀⠀⠀⠀⠀⠀⢸⡤⠠⢄⠀⠀⠀⠀⠀⠀⢀⠀⡄⢠⠀⣾⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⢀
⠀⠀⢹⣿⣷⣦⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠚⠋⠁⠀⠀⠀⢦⣁⣀⠡⠀⠐⠃⠀⠀⢀⣀⣭⠴⠶⠆⠆⠀⣿⣿⣿⠇⢀⠀⠀⠘⡄⠀⠀⠀⠘
⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣤⠶⠞⠛⠉⠁⠀⠀⢠⠀⠁⠀⣿⣿⣿⠂⠈⠀⠀⠀⢹
⠀⠀⠸⣿⣿⣿⣿⡿⡿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣸⣿⣿⡇⠀⢀⣦⣀⣠⠜⠀⠀⢀⡄
⠀⠀⠘⢿⣿⣿⣿⣧⠀⠈⢙⢿⣿⣦⡀⠀⢀⣀⣤⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡆⢀⢾⢿⣿⣿⣥⠴⢶⣿⡧⠐⠀⠀⠀⢈⡏
⠀⠀⠀⣾⣿⣿⣿⣿⣆⡈⠉⠃⠈⢻⡷⢻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆⢦⣿⣿⣿⣷⠀⢸⣿⡇⠠⠄⠒⠀⠻⠧
⠀⠀⠀⣿⡏⢿⣿⣿⣿⣿⣧⣤⠀⠈⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⣼⣿⠇
⠀⠀⠀⣾⣷⣄⠙⢿⣿⣿⠻⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⣸⣿⣿⣿⡿⠀⣿⣿
⠀⠀⠀⠈⠛⢿⣷⣬⣟⣽⣿⡆⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠿⠛⠋⠉⠀⠈⣀⣈⠁⠷⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡉⣠⡄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠿⠛⠋⠁⠀⠀⠀⠀⢀⣄⣠⣿⣿⣿⣷⠇⢠⣾⡓⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣅⣿⡆⠀⠀⢀⣀⣠⣴⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⢿⣿⣷⣦⣄⣀⠌⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡇⢺⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠇⠲⠷⠆⠰⠲⠲⠖⠟⠓⠗⠶⠶⠄⠰⠶⠖⠰⠲⠆⠐⠖⠶⠒⠐⠶⠖⠒⠐⠶⠲⠒⠶⠖⠺⠖⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠚⠓⠲⠶⠀⠓⠚⠛⠛⠂⠲⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠛⠓⠒⠛⠚⠀⠗⠒⠚⠂⠛⠛⠛⠃⠘⠚⠛⠛⠚⠚⠀⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⢘⣰⠤⡜⣱⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠀⠀⠸⢠⡎⣥⡀⠀⠀⣼⡉⢻⣾⣧⣹⠁⣯⠄⡴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣽⣿⡀⠠⠘⣿⣿⣿⡷⠀⠀⠘⣑⣚⠷⢟⠑⡍⠀⠚⢩⡍⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢻⡿⣷⡀⠹⠝⠮⢿⣷⠀⠀⣰⣿⢯⡦⣤⣈⠛⠂⠀⢴⣚⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠈⠀⠀⠴⣻⣿⠲⣤⣀⠠⠄⠐⠋⠀⠀⠀⠈⠦⠿⡘⢆⢓⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⢶⠖⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠺⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⠀⠄⢠⠀⠀⠀⠀⠀⠀⣀⠀⢸⡆⠀⠀⢄⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠇⠀⠘⠁⠀⠀⢖⠻⠭⠷⡙⠀⠀⠀⠀⠰⡍⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠒⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠰⠂⠀⠈⢀⡄⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⣶⠲⣶⠖
⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠁⠀⠀⡞⢁⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢵⣦⢦⣈⠀⠟⠢⢀⠀⠀⠀⠀⠹⣶⣤⠤⢤⣤⣶⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡝⠈⡁⣟⠯⠄⣤⡀⠈⠻⡆⠠⣦⣤⣨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠞⢧⠙⢿⡤⠞⣡⠀⣀⠁⠀⠉⠉⠙⠻⠦⢄⢀⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠃⠀⢄⠘⠁⠊⡐⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⢀⢎⣰⡀⣑⢈⠃⠀⠘⢀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣈⡘⡏⢉⡁⠻⠅⠉⢀⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡯⣐⠇⢠⡀⠴⢂⠸⣏⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣀⣠⣼⣿⣿⣧⣄⣀⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣠⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣷⣿⣿⡿⢛⣩⣵⣶⣶⣾⣿⣶⣶⣮⣭⣛⠿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⣡⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣮⡙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣿⡿⣡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣮⠻⣿⣿⣦⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣱⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢹⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⣿⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣷⡹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢻⡿⠟⢿⣿⣷⡝⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡙⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡿⣿⣿⣷⣬⣙⡻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠙⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⠏⠉⠙⢻⣿⣿⡟⠋⠉⠙⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⡏⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⠃⢠⣿⣿⠇⠀⠀⣰⣿⡧⠀⠈⠏⢿⣿⣿⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠸⣿⡟⠀⠀⢠⣿⣿⠇⠀⢀⣤⡌⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢫⠀⣠⣾⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⡇⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠈⢿⣿⣦⣀⠀⣀⣤⣾⣿⣿⠏⠀⠀⣹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠻⢿⣿⣿⣿⡿⠟⠋⠁⠀⢀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⡉⠉⠁⠀⠀⣀⣠⣴⣿⣿⡿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠉⠉⠉⠉⡿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠶⣦⣠⡟⠀⠀⣿⡶⠶⠛⠛⠛⠛⠛⠛⠛⠿⠷⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠙⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣴⠀⠀⠀⢰⡆⠀⠀⠘⣧
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⡇⠀⠀⠀⢿
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⡇⠀⠀⠀⣿⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠰⣦⡀⠀⣀⡾⠛⢦⣄⣀⣀⣤⠟⠳⣤⣀⣀⣤⠟⠳⢤⣤⡼⠓⠶⣶⠾⠃
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢻⠓⠶⠏⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣴⢟⡥⠶⢤⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡀
⠀⠀⠀⢠⡾⠁⠘⢧⣀⠒⢻⣄⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⠃⠀⠘⢷⣄
⠀⠀⣠⡟⠀⠀⠀⠀⠈⠉⠉⠉⣷⠒⠚⠀⠀⠀⠀⠻⣄⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⢀⣀⡀⠉⠓⠒⠊⠁⠀⠀⠀⠀⢻⡄
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣄
⣼⠃⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠙
⣿⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠟⠋⠀⣦⣀⠀⢀
⢿⡀⠀⠀⢀⣠⠞⣿⡀⠀⠀⠀⠀⣠⣞⠀⠀⣰⣠⣴⡟⠉⠉⠉⠛⣻⣿⡛⠛⠛⠛⢻⣟⣉⣭⡀⠀⠀⠀⣀⣴⠏⠙⠛⠋
⠈⠻⠶⠶⠟⠁⠀⠘⢷⣄⠀⣀⡼⠋⠙⣻⡟⠋⠁⠀⠙⠶⣤⡴⠛⠁⠏⠙⢦⣀⣴⠟⠙⢿⣍⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⣼⠋⠀⠀⢤⣤⡤⠤⢤⣄⣠⣴⠶⠶⢦⡉⠀⣀⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠸⣷⣦⣴⠖⠋⠉⠉⠛⢶⡴⠟⠋⠉⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠉⠛⠁⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣄⣀⣠⣤⠶⠛⠛⠓⠶⠶⠶⠶⠶⢶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠰⠿⠂⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⢻⡶⠶⠶⠞⠙⠷⠶⠶⢶⠞⠛⠙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⣉⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠶⠻⣦⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⠉⠙⡿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣩⡽⢗⣀⠈
⠀⠀⠀⠀⠀⠐⢷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣒⣙⣏
⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣰⣿⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠄⠀⠀⡧⠄⠄⠀⠀⠀⠀⢀⣀⣀⣀⡰
⠀⠀⠀⠀⢀⣼⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡈⠐⢦⡖⠂⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠛⠋⠛
⠀⠀⠀⢠⡏⣷⣄⢈⣛⣿⣶⣶⠆⠙⠀⠀⠀⢀⡂⢀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⡀⠀⠀⡄⠸⠠⠄
⠀⠀⠀⠘⠳⣉⡹⠿⠙⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⢠⣺⣷⡏⢐⡂⠁⠀⡈⠃⡀⠀⠈⠠
⠀⠀⠀⣀⠀⠀⢁⣼⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢄⠤⣽⣿⣿⡀⠉⠁⠀⠂⠀⠀⠈⠀⣀
⠀⠀⠀⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⡤⣬⠁⠀⡀⠂⠀⢰⡞⠁
⠀⠀⠀⠠⢄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⠗⡃⠀⠀⠀⠀⠀⢸⡣
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐

⠀⠀⠀⢀⡠⠖⠒⠒⠒⠢⣄⠀⠀⠰⠆⠀⠀⢀⡤⠒⠒⠒⠒⠤⡀⡀⢰⣿⠆⠀⠀⣠⠴⠒⠒⠒⠲⢄⡀
⠀⠀⡰⠋⢀⣤⠄⠀⢠⣄⠀⠱⡄⠀⠀⢀⡔⠁⡴⢲⡀⢀⡖⢦⠈⢢⡀⠀⠀⢠⠎⠁⡤⣄⠀⢀⢤⡀⠙⢆
⠀⣼⠁⠀⠘⠿⠃⠀⠻⠿⠀⠀⠸⡄⠀⡞⠀⠀⠁⠈⠁⠈⠁⠈⠀⠀⢳⠀⢠⠇⠀⠈⠳⠏⠀⠘⠷⠃⠀⠈⣧
⠀⢿⠀⠀⢀⣤⣀⣤⣠⣄⠀⠀⢀⡇⠀⡇⠀⠀⠰⣄⠀⠀⣠⠆⠀⠀⢸⠀⢸⡀⠀⠀⠤⣤⠤⢤⠤⠀⠀⠀⡿
⠀⠈⢧⡀⠀⠀⠉⠀⠁⠀⠀⣠⠞⠀⠀⠙⢆⠀⠀⠈⠉⠉⠁⠀⠀⡠⠋⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠉⠓⠶⠤⠤⠤⠖⠚⠁⣀⠀⠀⠀⠀⠙⠲⠦⠤⠤⠴⠖⠋⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠶⠚⠉
⠀⠀⠘⠟⠀⠀⣀⣀⡀⠀⠀⠈⠛⠀⢰⣿⡆⠀⠀⢀⣀⣀⡀⠀⠀⠠⣶⡆⠀⠸⠟⠀⠀⣀⣀⣀⠀⠀⠚⠃
⠀⠀⠀⡠⠚⠉⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠉⠓⢄
⠀⢠⠞⠀⠰⣄⡆⠀⢦⣰⠂⠈⢧⠀⠀⣰⠋⠀⠤⠤⠄⠠⠤⠤⠀⠙⣆⠀⠀⡼⠁⢰⣫⣷⠀⢰⣏⣦⠀⠳⡀
⠀⣾⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠈⠉⠁⣀⡈⠉⠉⠀⠀⣷
⠀⠹⡀⠀⠈⠓⠶⠶⠖⠋⠀⠀⣰⠇⠀⢧⠀⠀⠀⠰⠋⠙⠆⠀⠀⠀⡼⠀⠸⣆⠀⠀⠀⠺⣤⡽⠀⠀⠀⢀⠏
⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠳⢄⣀⠀⠀⠀⠀⣀⡠⠞⠁⢀⣀⠈⠢⣄⡀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⣤⡀⠈⠉⠉⠉⠉⠉⠁⠀⣀⠀⢠⣶⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠘⠋⠀⠀⠀⠉⠉⠉⠉⠉⢡⣦
⠀⠀⠈⠀⣠⠴⠒⠒⠒⠤⣀⠀⠉⠀⠀⠁⠀⢀⡤⠔⠒⠒⠢⢤⡀⠀⠀⣦⠀⠀⠀⣀⠤⠒⠒⠒⠦⣄⠉
⠀⠀⣢⠊⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⡴⠉⣀⠀⠀⠀⠀⣀⠉⢦⡀⠀⠀⢠⠞⠁⢤⡀⠀⢀⣠⠀⠑⣄
⠀⢸⠁⠀⠘⠷⠂⠀⠰⠞⠀⠀⠹⡄⠀⡞⠀⠀⠈⠷⠀⠀⠾⠁⠀⠀⢳⠀⢠⠏⠀⠀⠰⠛⠀⠙⠲⠀⠀⠈⣆
⠀⢿⠀⠀⠀⣄⠀⠀⢀⡄⠀⠀⢀⡇⠀⡇⠀⠀⢀⣴⣠⣄⣦⡀⠀⠀⢸⠀⢸⡀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⡿
⠀⠈⢦⡀⠀⠈⠉⠛⠉⠀⠀⢀⠞⢀⡀⠙⣄⠀⠀⠀⠁⠈⠀⠀⠀⣠⠋⢀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠙⠒⠤⠤⠤⠤⠴⠚⠁⠀⠙⠋⠀⠈⠑⠲⠤⠤⠤⠤⠖⠊⠁⠀⠉⠀⠀⠈⠓⠦⠤⠤⠤⠤⠖⠋