Good Morning Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣀⠀⠀⢀⠀⢱⠀⢀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣚⠙⠒⠤⣄⣀⣰⡩⠇⠀⠈⠑⢤⡈⠃⠈⠀⠊⠠⠋⡠⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣼⣁⣨⠆⠀⠀⢁⣀⠀⠀⠀⢠⠃⠀⠀⠀⠐⠦⠄⢀⠔⠚⠉⠒⢦⠈⠤⠖⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⠚⢸⠁⠀⠀⠀⡼⢷⡞⢙⢇⠖⢉⣿⠀⠉⠉⠉⢓⣒⠀⡎⠀⠀⠀⠀⠀⡇⠐⠒⠚⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⠼⡅⠑⠋⠙⠋⠈⠓⠉⠻⠽⠀⠀⢠⣬⠀⠀⠙⢀⠀⠀⠀⠀⡤⣄⠀⢀⢤⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢳⠀⢀⡀⠀⠀⢀⡖⣆⡀⢠⣤⡠⠋⡵⢀⣰⠃⡇⣠⡔⣾⢀⡏⢀⣇⢾⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣷⠤⣼⠀⠫⡹⠀⠀⢹⡇⠏⡝⢸⡠⠃⡼⠀⡏⠸⢸⢡⠃⠇⠋⢸⣀⠞⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣁⠴⠋⠉⠉⠀⠀⠀⠀⠀⠀⣇⠞⠀⠀⢧⡼⠁⠀⢈⣋⣀⣀⠀⢀⠤⡀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⢤⡀⠈⠑⣷⠴⠋⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡤⠃⠀⠀⠈⠑⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠞⠉⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣏⣀⣀⡠⠀⠀⠠⠠⣄⠀⠀⠐⠒⣄⠀⡠⠴⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣴⠋⢢⡴⠒⢘⠀⢣⡞⠁⡨⢼⠁⠀⣼⠁⠀⠀⠀⠀⣴
⠀⠀⠀⠀⣀⠀⠈⠉⢳⠀⠀⠈⠛⠒⢸⡇⠀⢸⣏⡁⠋⠀⠸⣯⠍⠁⠘⠦⠜⠹⣧⡀⠀⢀⠰⠁
⠀⠀⠈⠀⠇⠈⠙⠲⢼⡃⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⡄⠀⠀⠐⡆⠀⠀⢀⠌⠉⠓⠂⠀⣰⠃⢀⠀⠒⢲⡄⠀⠀⢲⠆⠀⢲⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢣⡀⠀⠀⠱⣄⠔⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣼⠁⠀⢀⡾⠀⠀⣼⠁⠀⡀⠻⠦⣤⣤⠀⢀⣄⠀⢰⡄⢀⠀⠀⡠⣄⠀⠐⡆⢀⡴⠒⢶⡔
⠀⠈⠉⠉⠁⠈⠑⠲⠤⠐⠂⠁⠀⠎⠀⠀⠀⢰⡏⠀⠀⣸⠇⠀⢠⡏⢠⣀⠬⢣⠀⡰⠁⢠⠃⣿⠀⣼⠁⡿⠀⡔⢀⡏⠀⣼⠃⣼⠁⠀⣼⠀⠀⠀⠀⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠀⠀⣿⠁⠀⠀⡟⠀⠀⣼⠁⢸⣗⢀⠋⠀⣧⡠⠃⢰⠇⠀⡏⠸⣧⠜⠀⢸⠇⠰⣇⠔⠛⠖⢊⡏⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠛⠀⠀⣿⢀⠀⠉⠥⠤⣀⠀⠀⠀⠀⠀⠀⠻⢤⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⢸⠃⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣀⠠⠐⠻⣇⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⢀⠓⠒⡟⠒⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢸⣆⠐⠁⣀⠜
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣷⠀⠀⢸⡇⠀⠀⣿⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⢻⣇⠀⢻⡄⠀⠈⠁⠀⠀⠁⠀⠀⠛⠀⠀⢀⣴⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠙⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⣄⠀⠀⢠⠿⠋⠀⠀⠀⢸⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠈⠋⠀⣠⣾⡿⠛⠋⠉⠉⠉⠉⠙⠻⢿⣿⣦⡀⠀⠀⠞⠀⠀⣿⣿⣿⢰⡇
⠀⠀⠀⠀⠀⠀⣠⠞⢀⣴⣿⣿⣿⠿⢿⣷⡄⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠙⢿⣿⡀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⣰⠏⢠⣿⣿⣿⡿⠁⠀⠀⣿⣷⠀⠀⠈⠁⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠈⠋⠀⠈⠛⠁⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⢀⡿⢀⣿⣿⣿⣿⠁⠀⠀⢀⣿⡏⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⣴⣾⡿⠟⢶⣄⠀⠀⠀⠀⣴⣾⣿⣾⣿⣿⡇⡄
⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡏⠀⠀⠀⠘⠋⠀⠀⢰⣿⣿⠋⠉⢻⡄⠀⢸⣿⣿⠀⠀⠀⢹⡆⠀⢀⣾⣿⡟⠁⣸⣿⣿⡏⡇
⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡇⠀⠀⠀⣀⡀⠀⢀⣿⣿⣿⡀⠀⢸⡇⣀⣾⣿⣿⣆⡀⠀⢸⣧⣴⣿⣿⡟⠀⢀⡏⣿⣿⡇
⠀⠀⠀⠀⠘⣷⠘⣿⣿⣿⣿⠀⠀⢸⣿⣿⠀⢸⣿⡿⢿⣷⣶⣾⠟⢻⣿⣿⠛⠿⠿⠿⣿⡟⠁⣿⣿⠃⠀⣼⠁⢸⣿⣷
⠀⠀⠀⠀⠀⠻⠀⠹⣿⣿⣿⣧⠀⠀⣹⣿⡄⠸⣿⣷⡀⢀⣼⠏⠀⢸⣿⣿⡇⠀⠀⣰⡿⠀⠀⠻⣿⣤⡾⠃⠀⠀⢿⣿⣆⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⠏⠙⣿⡇⠈⢛⠿⠟⠁⠀⠀⠈⠻⣿⣿⣶⣾⠟⠀⣠⠀⠀⠈⠉⠀⠀⠀⢀⠀⠻⣿⣷⣶⠟
⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠉⠁⠀⠀⠀⡼⣷⠰⣟⢹⠀⠀⠀⠀⠀⠀⠈⢉⡉⠀⢀⠀⠈⢀⣤⠀⠀⢀⣴⡿⠛⢻⡆⠀⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡄⣴⣦⢀⣶⣦⠀⠀⢧⡼⠀⠙⣾⣄⠀⠀⠀⠀⠀⠀⠿⠇⢀⣿⡇⢀⠞⣿⠀⢠⣿⡟⠀⠠⣿⡇⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⢠⡜⣿⣷⡿⣿⣼⠁⣿⠀⢀⣤⣄⢀⡼⢁⣿⢠⣷⠀⡴⣿⠀⣰⡄⢸⢻⣇⡼⠸⣿⠀⣸⣿⣠⠞⢠⣿⠇⢀⣴⠞⠁⠉
⠀⠀⠀⠀⠀⠀⠁⢿⣿⠀⢿⡟⠀⣿⠀⣸⡷⢿⡏⠀⣼⢇⡞⣿⣼⢰⡟⢀⣿⡇⡟⠘⠿⠃⠀⠻⠾⠋⠉⠁⢀⣸⣿⡿⠟⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⠁⠀⢻⣧⣿⡇⢸⡇⢸⣏⡼⠀⢿⠇⢸⣧⠎⣿⣾⠁⠀⠴⣤⣤⣴⣶⣶⠿⣿⠛⢻⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣧⢸⡇⠸⠟⠁⠀⠀⢀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠿⡾⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢧⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⠿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣻⣿⣿⣿⣿⣻⡿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠀⠈⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠆⠀⠀⠀⠂⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⢀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠄⠐⠀⠀⠀⠐⠤
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⡆⠠
⠀⠀⠀⠀⠐⢄⠆⠘⠀⠁⠄⠈⠴⠀⠀⠀⠀⠀⠀⠀⠀⣸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢛⡇⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⣀⣤⡀⠀⠈⠁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣤⣮⣁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡴⠊⠀⠛⠉⠳⢤⣀⣠⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⡀⢀⢈⠂⠘⢿⣣⢀⣍⠈⣵⢦⣀⠄⢸⡇⣤⠈
⠀⠀⠀⠀⡀⠠⠀⠀⡀⠀⠀⠀⠐⠀⢠⢼⣧⠀⣤⡄⢰⡆⡏⠁⠀⣿⢄⢀⠀⠀⠀⡀⠠⠐⢸⠚⠓⠉⠑⣒⠗⠒⣻⣿⣿⣾⣿⣾⣾⣷⣷⣾⣟⢿⣶⡂
⠀⠀⠄⡀⠀⢤⣀⡞⠈⠀⡀⡄⠂⢰⣼⢠⣤⠀⣤⣤⠀⠀⡇⠀⢠⣯⣀⠀⠀⠀⠀⠆⠈⠑⣼⡂⡀⠛⡻⣀⡚⢛⣛⠟⠛⠛⠋⢽⣿⣿⣿⣿⣿⣾⣿⠇
⠀⠀⡀⠉⠀⠀⠉⠀⠀⠀⠉⠁⠀⠠⢤⣄⠀⠀⠈⠉⠉⠁⣷⣾⡿⢏⠉⠁⠀⠀⠀⠂⠉⠀⠈⠭⠙⠋⡉⠙⠋⠉⠻⠿⠽⢭⡟⣛⣻⠟⢋⡁⠀⠚⡉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠈⠉⠉⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠲⠂⠐⠂⠀⠀⠀⠠⠅⠀⠀⠀⠒⠒⠒⠀⠤⢀⣀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⢈⠙

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⡀⠀⠌⠀⠀⠈⠂⠐⢤⠠⠄⡀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠤⠃⠀⠀⠀⠀⠀⢀⠠⠄⡤⠂⠐⠁⠀⠈⠠⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⣀⠀⠀⠀⡀⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠠⣀⠀⠀⠀⡀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠊
⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠂⠁⠀⠀⠀⠀⠈⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡄⠀⠀⠀⠄⠀⡔⠁⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢄⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠌⠀⠔⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠒⠂⠈⡄
⠀⠀⡠⠐⠒⠠⡀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠔⠀⠀⠃⠀⠒⠀⠀⠀⠀⠀⠠⡀⠀⢁⠔
⠀⠈⠀⡄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠈⠢⢈⣉⠠⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⡄
⠀⠀⣀⠀⠀⠀⠀⢀⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⡀⣉⠀⠀⢀⡀
⠀⠀⠡⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⡔⠁⡠⢄⡨⠢⠀⢀⠀⡀⠑⠖⠁⡀⢀⠀⠙⡀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⢅⠀⢱⠀⢀⠀⡈⠀⡘⠨⡀⢀⠃⠀⠀⡇⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠤⠊⠢⢀⣀⠀⠐⠁⠤⣀⡀⠠⢚⣀⢉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠧⠠⠄⠠⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠄⠀⠠⠀⠀⠀⠄⠄⠠⡄⠀⠀⠀⠠⠠⠄⠀⠠⢠⠆⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠛⠀⠀⣤⠀⠀⠀⠀⠀⡆⠀⠀⢈⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠠⡆⠀⠀⠀⠀⢀⡀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠃
⠀⠀⡡⠀⠀⠀⠀⠀⠀⠒⡄⠀⢎⠀⡱⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠊⠀⢀⡄⠀⠀⠀⠰⡁⠀⡢⠀⠀⡉⡡⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⢀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠀⠀⠀⠀⠘⡜⠀⠀⠀⢐⠀⠈⠆⠀⢌⠀⢱⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⠈⠲⠘⡀⢀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡄⠀⠀⠐⠉⢙⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠄⠠⠌⠱⠂⢹
⠀⠀⡡⠀⡔⠀⠂⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢀⠀⠈⢲⠈⢂⣀⣀⡠⠚⢰⠀⠀⠀⢀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠄⠐⠀⠀⢈⡰
⠀⠐⠄⢠⠈⡀⠁⡤⠐⠀⠀⢀⡔⠉⢢⠀⠀⠠⡀⠀⡠⠀⠀⠈⠢⠴⡀⢀⠱⠠⠊⠀⠀⠀⠠⡀⠀⠘⠀⠀⢀⠄⠑⢄⠀⠀⠀⠁⠂⠈⡀⢁⠀⢡
⠀⠀⠀⠀⠂⠑⠠⠁⠀⠀⠀⠀⠈⠤⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠒⠈⠑⠂
⠀⠠⠄⠀⠀⠀⡀⠀⢀⠀⠀⢀⣀⣀⡀⠀⢀⠀⠀⢀⠀⢀⠀⠤⠄⠀⢀⣁⣀⠀⠀⢀⠀⠀⡀⢀⣀⡀⠀⠀⢀⠠⢄⠀⢀⠠⠄⣀
⠀⠐⠀⠁⠀⠀⡇⠀⠀⢀⠀⡀⠀⠀⠰⠊⠀⢀⡀⠀⠈⠣⠀⢀⢄⠀⠉⡄⠀⠁⡀⠀⠀⠀⠉⠉⠀⠈⠢⡀⠀⠀⠀⠊⠀⢀⢀⠀⡱⠀⠀⠐⠈⢡
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢦⠀⢠⠀⢸⠀⠀⠁⠀⢡⠀⠀⠃⠰⠠⠃⠀⡀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠀⠈⢀⠂⠠⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡆⠀⠻⠀⠀⠀⢾⠀⠘⠀⠘⠠⠤⠊⠀⢀⠃⢀⠀⠀⣶⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠐⠌⠱⠂⠀⡀
⠀⢰⠉⠰⠀⠀⡅⢀⠄⢀⣀⡀⠸⣀⣀⠖⠄⣀⣀⡀⠔⢃⡀⡸⠢⡀⠀⢁⣀⡀⠈⠢⣀⣀⠄⠀⣄⣀⠀⠈⢀⣀⣨⠓⠄⣀⣀⠠⠐⠀⠀⠀⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣸⢆⡂⠀⠂⢸⡄⠀⢃⠀⣠⠄⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⣼⠇⠀⡏⣿⠇⠀⡴⢸⡏⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⢺⡇⠸⡀⠞⠀⠻⠀⠔⠀⠘⢇⠰⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣾⢳⡄⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠻⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⡇⠈⣧⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⢶⡀⢰⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⣼⠁⢸⠇⠀⡾⠀⣴⠀⡄⠛⣴⠆⠀⠀⣿⠀⣿⠀⢠⠀⢀⢚⡖⠀⡾⢠⡟⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠀⣸⠃⢰⡇⠀⠀⠀⡟⠀⠀⠀⠃⢰⡇⠀⡟⢀⠆⣸⠃⢰⡇⢼⡇⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠈⠃⠁⠀⠀⠑⠀⠀⠀⠀⢸⠃⡘⠳⠊⠀⠠⢀⡈⠁⠀⠈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠠⠊⠀⠀⠈⣿⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡟⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠠⠐⠋⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠈⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⡴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣀⣠⣀⠀⠀⠀⠀⢰⣶⠀⠈⠀⠀⠀⠐⠁⠔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⣼⡿⠛⢿⣷⡄⢠⣾⣟⣻⣿⡏⠀⣴⣿⣻⣿⡟⢰⣿⣷⣾⢿⣦⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣤⣤⡄⢸⣿⠉⠉⣿⡇⠀⣿⠛⠋⣿⡇⢸⣿⡟⠁⢸⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⣷⡀⠀⢻⣷⣈⣽⣿⠃⠘⢿⣦⣴⣿⠃⠀⢿⣧⣴⣿⠃⢸⣿⣁⣠⣾⠏⠀⡸⢟⣠⣄
⠀⠀⠀⠀⠀⠀⠙⠷⠬⠁⠀⠀⠙⠛⠛⠁⠀⢠⠤⡍⠉⠀⠀⠀⠀⠉⠉⡀⠀⠈⠉⠉⠉⠁⠀⠀⠐⣻⣿⣅
⠀⠀⠀⠀⠀⠀⠾⠛⠃⠀⢀⣀⠀⠀⠀⠀⡀⢻⣄⡇⢀⡀⢀⣀⠀⠀⣤⠁⡀⢀⡤⢤⠀⣠⠶⣤⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⢹⣧⢶⠄⣾⣽⣧⠟⣻⠆⣷⡟⣹⠁⣸⣃⡴⣷⠏⠀⡟⣰⣇⣀⣼
⠀⠀⠀⠀⠀⠀⠀⣶⠀⠹⠃⠸⠇⢸⡴⠷⡴⠃⢾⣁⡼⠙⠀⠻⠞⠁⠉⠀⠉⠀⠘⠷⢃⡤⠷⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢴⡄⢀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⢧⣠⡖⠀⠀⠀⠀⠈⡴⠀⡄⠀⡄⠠⡄⠰⡌⠀⠀⠀⠳⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠇⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⠴⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣀⣠⠤⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡼⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣾⠀⠀⠀⠈⠀⠀⣀⣤⣄⡀⠀⠀⢀⣀⣒⡒⠒⠒⢲⣶⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⡏⠛⠛⠛⣷⢠⡿⠉⠀⠈⠹⣆⢠⡟⠉⠉⠙⢦⡀⠈⣿⠀⠈⢧⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠸⣧⠀⠀⢀⣿⠸⣧⠀⠀⠀⣰⡟⢸⣇⠀⠀⠀⣸⠇⠀⣿⠀⠀⢸⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠙⠷⠶⠞⠃⠀⠙⠻⠶⠿⠋⠀⠀⠙⠳⠶⠛⠋⢤⠤⠿⠤⠴⢫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣤⡀⠀⠀⠀⢀⣠⣦⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣿⠻⣷⣤⣴⡿⠋⣿⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠙⢆⠀⢀⣴⠞⠛⠛⠛⢶⡄⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣿⠀⠈⠙⠋⠀⠀⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⣾⡇⢠⣤⣤⣤⣤⣤⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠹⣷⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⣴⠞⠛⠛⠳⣄⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠛⠻⠿⠷⠾⠟⠁⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢸⣯⠀⠀⠀⠀⣽⠇⠀⠀⠙⠲⠤⢤⠤⠔⠋⢠⡄⠀⣦⣠⠶⠳⣦⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠷⣦⣴⠾⣫⣴⣶⣄⠀⢠⡤⠶⠶⣦⠀⢠⠄⢠⡿⠁⠀⠀⣿⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣀⣴⠞⠉⠀⠀⣿⠀⢸⠃⠀⠀⣿⠇⣼⠀⢸⡇⠀⠀⠀⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⣁⣀⣠⣤⣶⠟⠀⣿⠀⠀⠀⣿⠀⣿⠀⢸⡇⠀⠀⠀⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣿⠉⠉⠉⠙⣧⠀⠀⠿⠀⠀⢀⣿⠀⣿⠀⢸⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⠲⠶⠶⠦⠀⠘⠏⠀⣿⠀⢸⡇⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣠⠴⠒⠒⠒⠒⠦⢤⣁⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠸⣇⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠃⠀⠈⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⢩⡛⢫⡆⠀⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⢻⠟⠀⣼⣿⣿⣿⣿⡿⠋⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⢀⣾⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⢠⣄⠀⠈⠛⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠉⠀⠈⢳⡀⠀⠀⠙⠿⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣿⣿⠂⠀⠀⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⣼⣿⡇⢀⣾⣶⠀⡞⠁⡀⢠⣾⣷⢀⡟⢳⡄⢀⣾⣿⠟⢳⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⡼⣿⣿⡷⢻⣿⡟⠸⡁⢀⡥⢾⣿⡿⠈⠧⣼⣇⣸⣿⡟⠀⠈⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⢀⡾⢸⣿⣿⠁⢸⣿⡇⠀⢨⠏⠀⠸⣿⣇⠀⢀⡿⠉⠹⣿⡇⠀⢠⣿⣿⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣠⣿⣿⡿⠀⠀⠙⠿⠖⠋⠀⠀⠀⠙⠻⠶⠋⠀⠀⠀⠙⠻⠖⠋⠈⠛⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢫⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢸⣿⡿⠀⢠⢲⡦⢲⡖⣶⠀⣴⠲⡄⢿⣰⡦⠀⣶⢶⡆⢰⣶⢰⡆⣶⠀⡴⢢⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣾⣿⠃⠀⠀⠸⣧⠸⢧⣿⠀⡧⠴⠀⠀⠸⠇⠘⠿⢸⡇⡸⠧⠾⠇⠿⠸⠧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣰⣿⠏⠀⠀⢀⣴⣤⠀⠈⢿⠜⣀⣤⡄⠀⣤⣶⣤⡀⠹⡧⠃⢀⣀⡀⠀⢀⡔⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠿⡿⠋⠀⠀⠀⠀⠻⠿⠋⠀⠘⠻⠿⠏⠀⠀⠀⢾⣿⠇⠀⢸⣰⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢠⣴⣦⡀⣰⠛⢦⠀⢀⡀⣾⠇⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⢻⢻⡆⣟⣴⢸⡇⣿⡆⢸⣰⠟⣿⡿⠀⡀⠈⠵⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢁⠔⢁⣸⡧⢼⡯⣸⢱⡿⢳⠷⣟⡸⠹⡇⢸⠇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠉⠁⣰⠃⢸⠇⠸⡥⠃⠈⠳⠋⠀⢩⠀⠀⢙⠋⢠⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢃⣶⣦⠀⠘⠤⢯⣄⠸⡆⢀⣶⢀⣤⠀⡆⣼⡠⣾⠃⣿⡠⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⣼⣏⠞⣿⢰⡿⣸⠀⡟⢸⡧⠱⣏⠸⡇⠛⠁⠛⢊⣉⣀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣿⠇⠀⣿⢿⢀⠆⠈⠗⠉⠁⠀⠀⠀⠀⠀⠀⢰⡟⠁⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠟⠁

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠂⠀⣀⠀⠀⠀⢠⣢⡘⠋⢈⠷⣣⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸
⠀⠀⠀⠀⠀⢤⣈⠂⠀⠀⠎⠁⣏⠹⢗⣋⢁⠙⠧⢔⡄⠀⠀⠠⠺⠇⢀⠀⠀⠀⠀⠈⠁⣠⣞⠱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠙⠁⠛⢣⣄⣓⢬⠄⣬⡒⠇⠀⠠⠀⠀⡀⠀⢉⠖⠀⠀⠾⢿⡟⠉⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢶⢄⣤⣼⢀⠁⠾⠧⠕⡀⡄⠀⠀⡀⣠⢴⠛⢋⠠⢂⠀⠤⣀⡄⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠐⠂⢌⠉⠰⠆⠁⠀⠈⠉⢿⡁⠊⠁⠀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠈⠑⠂⠤⡀⠀⠀⠁⠈⠼⠀⠀⠀⠈⠙⠷⠤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠢⣄⠉⠒⠄⣐⠂⠀⣆⡀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠄⡠⠀⠀⠤⠀⠀⠀⠠⢠⠐
⠀⠀⠀⠀⠉⠀⣠⣿⡟⠓⠚⢷⣾⡚⠛⠋⠙⠲⠀⠀⠀⠠⡀⣠⡆⠀⠈⢹⣦⡇⣀⠀⠂⠠⠠
⠀⠀⠠⠊⢀⠾⠛⣿⠷⠒⠂⠀⠀⠘⠯⠶⠲⢾⠆⠀⠐⣎⠂⠀⠀⠀⠀⠈⠨⠛⡧⢶⣠⣇⣰
⠀⠀⠀⠈⠁⠜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⢀
⠀⠀⠀⠀⠘⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠖⠦⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢡⣶⡀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⣦⠀⠉⠀⣐⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⣄⠀⠀⠀⡠⢤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣤⠀⣀⠈⢧⠀⠐⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣞⠀⠀⠀⠀⠀⠱⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠍⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⡍⠠⠇⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠤⠀⠀⠐⠉⠀⠀⢀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠀⠀⢘⠂⡢⠀⠀⠀⣇⣸⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄⠀⠀⠔⠀⠀⠀⠀⠀⠈⠱⠀⠀⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⠀⠀⢠⣀⠀⠁⠀⡀⠀⠀⠀⢀⣀⠀⠀⠄⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠀⠚⠋⠀⠀⠄⠁⠀⠀⠀⡀⠀⠀⠠⠀⢠⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠈⠀⠀⠎⢀⡀⢀⠀⠆⠀⣀⣀⠇⠀⠀⠄⠂⠀⠒⠐⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⢀⠔⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠀⠒⠒⠶⠒⠒⠚⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠒⠒⠒⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⡄⠁⡄⢀⠤⠐⠒⠠⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠠⠒⠉⠉⠒⠁⠀⠀⠀⠀⠀⠱⠄⠒⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠤⠧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⣠⠴⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠀⢀⠀⡶⠶⣄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⡰⢀⠀⠀⣸⠃⢀⠀⠀⡠⠋⠒⠂⠁⠀⠈⠉⢜⣇⠀⠀⢧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠬⢀⠆⠀⢾⡀⢀⠎⡈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢱⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠸⠀⠀⠀⠀⠀⢀⠀⠈⠎⠀⢸⣺⠀⠀⠀⢣⡀⣀⡄⠀⠰⢄⠈⠤⡤⠼⠀⠸⠇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⢀⠈⡆⠀⠀⠀⠈⠁⠀⢠⡀⣡⠀⠀⠀⠀⠀⠜⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠣⡘⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⢏⠔⠁⠀⡨⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⡀⠀⠈⠐⠓⠢⠤⢀⣀⣀⣀⠠⠤⠐⠚⠒⠁⠀⠀⡔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⡁
⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⢀⠀⠁⠀⠠⠀⠐⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠄⠀⠀⠁⠀⠀⠐⠋⠀⠀⠀⡆⠀⠀⠠⣷⠄
⠀⠀⠘⠀⠀⠸⢥⡾⠿⠀⡀⠀⠀⠈⡀⠀⠀⢘⠀⠀⠀⠤⠀⠀⢀⡇⠀⠀⢀⡀
⠀⠀⢀⢀⠀⠀⢮⣀⡀⠀⠱⠀⠀⠀⠁⠀⠀⠸⡠⡀⠀⠀⠀⢀⠎
⠀⠀⠀⢫⢢⠀⠀⠙⠀⠀⠀⢆⠢⢀⡀⢀⡴⠁⠑⢌⣒⣀⠶⠋⠠⠴⠶⢢⣤⣤⠴⠊
⠀⠀⠀⠀⠳⣑⠠⢀⡀⢠⠎⢀⠁⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠈⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠐⠂⠠⡴⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠂⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡠⡀⠀⠀⢀⡔⠣⡐⢄⡀⣀⣠⠴⠇⠀⠀⡸⠀⠀⠀⠀⠀⠒⠼⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠃⠄⠤⠄⠚⠀⠀⠈⠑⠒⠈⠁⠘⠒⠯⠒⠁⣀⠤⣀⡀⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠠⠕⠓⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠡⣑⡦⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢦⠀⠀⠀⠀⡇⠀⠀⣰⠆⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠂
⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠘⣇⠀⠀⠀⡇⠀⢀⡟⠀⠀⢀⡜⠁⠀⠀⡀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠙⢦⡀⠈⢦⠀⢄⠈⡆⢰⠀⡇⡞⢸⢡⠃⣠⠏⠀⠀⣠⠞⠁⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⠢⡀⠑⡀⠣⠘⠘⠀⡇⠃⢃⠃⡴⢁⠖⡡⠚⠁⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠓⢬⡑⢌⠂⠈⠂⠠⠀⠀⠃⠀⠀⠎⠐⠁⠊⣠⠔⠋⡀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠙⠓⠦⢌⡐⠬⠐⢄⡔⢁⠔⠈⠉⠉⠀⠢⡈⠢⠔⠈⠄⠒⡁⠤⠒⠋⠉⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠶⠤⠤⠄⢀⣁⠀⠄⢠⠁⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢈⡁⢠⠤⠤⢖⣶⣦⠖⠒⠚⠋⠀⠉⠉⠉⠉⠉⠉⠉
⠀⣀⣀⣤⣤⣤⠤⠖⠒⠒⠒⠒⠦⣄⡀⠀⠒⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣀⣀⣀⢂⣀⠴⠃
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⡀⠀⠈⣈⡦⠤⠤⠤⠤⠤⠖⠋⠉⠀⠀⠀⢀⡞⠁⣠⠴⠀⠀⠐⠒⠀⢀⣀⡀⠀⠠⠄⠰
⠀⠀⠀⠀⠀⠠⠀⠐⠀⣤⡀⠀⠀⠀⠀⠀⡀⠀⠈⠉⡳⣄⡠⠄⢀⣀⣀⣀⣀⡀⣠⠴⠒⠚⠁⢔⡛⠁⢀⡄⠀⣤⠒⠚⠁
⠀⠀⢀⡀⢀⣀⠀⡀⠀⢀⡁⢉⣁⣔⢒⠤⠬⣤⣤⣤⣩⣭⡵⠶⠄⠀⠀⠀⣀⣴⠃⠀⠀⢀⣀⠀⠀⡀⢀⡩⠄⣲⡉⠑⣒⡓⢂⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⡴⣃⣠⠯⢦⡷⠾⠮⣍⣀⣀⣀⡐⣀⣁⣂⣀⢀⠉⣃⣀⡹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠖⠒⠦⢤⠴⠶⢚⡒⣋⣀⣀⣠⠤⠤⠄⠤⠭⠭⠭⠍⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣠⡴⠒⠒⠒⠛⠚⠛⠛⠒⣞⣉⡈⠀⠀⠀⢩⣤⠤⣝⣒⣒⣂⢁⡀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠄⠀⠠⠤⠤⠤⠄

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣴⠋⠀⠀⠀⢀⡴⠦⣄⠀⡤⠶⣄⠀⣠⠴⢼⡇⠀⠀⣤⠤⢤⡠⢦⡄⢀⡤⠦⣄⠀⣤⠤⢠⡤⠦⣄⠀⡄⢠⣤⠴⣄⠀⣠⠴⢤⡄⢸⡇
⠀⠀⠀⢻⡄⠀⢙⡇⢾⡀⠀⣿⢸⡇⠀⣸⠂⣇⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⡇⢸⡅⠀⣸⠂⣿⠀⢸⡇⠀⣿⠀⡏⢸⡇⠀⢸⠀⣇⠀⢸⡇⠀⠃
⠀⠀⠀⠀⠉⠛⠋⠁⠈⠙⠋⠁⠀⠉⠛⠁⠀⠈⠛⠉⠁⠀⠀⠉⠀⠈⠁⠀⠁⠀⠙⠛⠁⠀⠉⠀⠈⠁⠀⠉⠀⠁⠈⠁⠀⠘⠀⢈⣙⣹⠇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⣠⣶⣾⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠈⠙⢿⣿⣿⣷
⠀⢀⣴⣶⣦⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣠⣶
⢀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣴⣾⣿⣿⣦⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⣤⣀⣤⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣽⡟⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡌⠿⢡⣿⢛⣭⣙⢿⣿⢹⣿⡟⢻⣟⠛⣩⣿⣿⡿⢛⣭⣹⡿⢋⣭⡛⢿⡇⢨⣯⠁⣹⡿⣋⣍⡻⣿⢟⣩⡙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⢸⣿⣿⢈⣿⢸⣿⡇⢸⣿⢸⣿⣿⣿⡇⢿⣿⣿⡇⢿⣿⡗⢸⡇⢸⣿⠁⣿⡇⣭⣭⣥⣿⢨⣭⣥⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣦⣭⣥⣾⣿⣦⣭⣦⣼⣿⣼⣿⣿⣿⣷⣮⣭⣽⣷⣮⣭⣴⣿⣧⣼⣿⣧⣿⣷⣬⣭⣽⣿⣦⣭⣭⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⢤⣀⠈⠐⠤⣀⣼⠁
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠠⠃⢀⣀⠀⠀⡞⠀⠀⠹⡆⠀⠀⠀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠢⠤⠀⠀⠀⢰⡁⠈⣧⠀⢷⡄⠀⠀⡇⢀⡔⠛⣿⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣠⡄⠀⠀⠀⢸⣷⢠⡟⠀⣾⡛⠶⣴⠗⠺⣧⡼⠻⣆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢘⣿⣀⣀⠔⠁⣉⣉⡀⠀⠘⠳⠒⠁⠀⠀⠀⣠⠀⠉⠓⠦⠄⠊
⠀⠀⡠⠒⠉⠉⠉⠉⠉⠉⢹⡏⠁⠀⢠⠏⠀⠀⢹⠀⠀⠀⠀⣠⠤⡀⢰⡇⠰⣦
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢄⣿⣀⢀⠀⠊⠀⣄⠀⣼⠃⠀⠀⣸⣇⡴⠃⠀⠀⡠⠔⠒⢦⡀
⠀⠸⣆⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⣏⠀⠀⢸⠇⢰⣏⠀⣿⣆⣀⠔⠹⠏⠉⠓⡶⣮⣀⣀⣀⡼⠁
⠀⠀⠙⠳⠦⠤⠤⠖⠋⠀⠀⠀⠀⠀⢿⣄⣀⠾⠧⠜⠛⠊⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⡀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠱⢃⡴⠖⠶⢤⣀⠀⠀⠀⠀⠀⢠⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⢌⠳⢄⡀⠀⢀⣼⣜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠏⠉⠉⣩⠍⣓⠳⢤⣵⡒⣮⠻⠟⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣆⣀⣈⡴⠲⢤⣵⢤⠤⠃⣼⡷⠖⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣴⡙⠷⣤⡗⣿⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⡄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣛⡷⡟⢸⠀⠀⠀⠀⠀⠀⣴⣋⠭⠖⠒⠂⠈⠁⠀⠉⠀⡨⢿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠟⠀⠛⠀⠀⠀⠀⠀⠀⢸⡷⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⢦⡀⠀⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣤⣄⣁⣀⣀⣀⣀⣀⣀⣸⣇⠀⠠⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡉⠙⠯⠍⠉⠙⠛⠛⠛⠉⠉⠩⠽⣶⣬⢹⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡓⠆⠀⠀⠀⠀⣀⠤⠤⠶⠤⣄⣀⡀⠀⠸⣧⠿⢽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣤⣀⣀⣠⠞⠁⢀⣠⣤⡀⠀⠙⣦⠀⠀⢰⢾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⣴⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⢭⣿⣧⠀⢿⣿⣿⣿⣷⣿⠁⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⡢⠔⠛⣦⣬⠉⠛⠿⠋⠡⣪⠟⢩⠤⢌⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣗⡀⠀⠀⠙⠳⠶⠶⠖⠛⠁⠀⠠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠐⠩⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⣄⣀⣀⣤⣤⣄⣀⣀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⣤⣌⡒⠦⣄⡀⠀⠀⠀⠀⠀⠸⣯⣀⣉⣛⠙⠛⠛⠛⠉⢙⣻⣿⠇⠐⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⠬⠙⠓⠶⣭⣓⠦⢄⡀⠀⠀⠀⠈⠉⠙⢛⣛⠛⢛⣛⣋⣉⣁⠀⠀⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢙⡻⢶⣮⣀⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠢⡈⠙⠽⠳⢶⣄⡀⠀⠀⠈⠑⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⢦⣄⣐⣐⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣄⣭⣤⡁⢂⣡⡼⣁⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⠛⠋⠥⠤⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠟⢯⣽⣭⣷⡌⠉⠙⠛⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⠁⠉⠀⢈⣉⣭⣍⣁⣀⠀⠀⣶⣦⡙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣿⡿⢃⣤⣾⠿⠛⠋⠙⠛⠛⠿⢶⣤⡙⣿⠆⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣾⠿⠿⣾⣿⣥⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⢹⣿⣶⣻⡿⢝⡗⣠⠶⢦⡀⣉⣙⠛⠲⠦⢄⣀⠀⠀⠀⠀⢻⣿⣆⣠⡀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡀⣸⣿⣿⣿⣿⠞⠃⠻⣤⠼⢹⡃⢨⡇⡾⠲⡄⠈⠙⠓⠦⣤⣸⣿⣖⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣷⡿⠁⢹⣿⣛⣿⡟⣳⡶⠶⢦⣭⣉⡘⠧⠴⠃⢀⡾⠀⢀⡄⠉⠛⠶⣿⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠳⢦⡄⣨⠏⠀⣿⣟⠊⠙⠁⣿⡇⠀⠀⠀⠈⠉⠓⠶⠦⣬⣓⠆⢾⣁⡾⣡⠶⣌⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⢠⣿⡷⠄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣍⡀⢧⣤⢈⣴⣂⡌⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⠯⣷⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣷⣤⣘⠹⡇⠀⠀⣸⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣙⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡳⠉⠛⢠⣿⠛⢦⣀⡞⠁⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣓⠀⠀⣠⣿⠃⠀⢠⡏⢀⣀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⣀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣵⣿⠇⣴⡿⠃⠀⠀⣿⢿⠻⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣠⣼⣿⡛⠹⣿⢋⣼⡿⠃⠀⠀⠀⢻⡾⠛⠲⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣓⠀⠀⢴⣿⣏⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣆⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠁⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠄⠄⢀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠠⠂⢀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠆⠀⠁⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡄⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⠄⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠘⠀⠀⠀⠏⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠠⡤⠀⠀⠀⠚⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠰⠈⠀⠁⠂⠄⠀⡀⠄⠀⠤⠀⠂⠠⢀⠄⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠤⠐⠀⠄
⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠁⠂⠀⠀⠀⠀⠈⠡⠐
⢠⡴⠂⠔⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠅⢈⣳⣴⠧⢠⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⡌⢑⡋⠐⣤⠀⠀⠀⢀⡀⠀⢀⠈⡗⠆⡀⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⡀⠀⠀⣀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠘⠓
⢸⠀⠈⠁⠠⠤⡔⠀⠀⠘⠸⠠⢤⣚⣉⠻⠉⠓⠂⠈⠀⠰⠶⡄⠀⠀⠀⠀⠀⠀⡐⠇⠐⡋⡀⡙⣆⣴⡢⠨⡑⠀⠀⠀⡄⠁⠍⠁⠀⢀⠀⠄⣀⠤⢠
⠘⠀⠀⠀⠀⣠⠃⠨⡀⣄⠀⠃⢀⡡⠗⠈⠁⠘⠄⠉⠠⡔⢒⡆⠀⠀⠀⢀⠀⠀⠀⢰⣆⢀⠐⠊⠀⠇⠑⠀⠀⡀⠀⠀⠊⢀⠀⢀⠀⠠⡀⠤⠲⠆⠒⠂⠃
⠀⠀⠀⠀⠀⢳⣄⠀⠈⠉⠀⢸⡉⠀⠂⠀⡀⠀⠤⠀⠤⢤⡄⠀⠈⠂⡀⠀⡀⡀⠀⠼⢤⠀⠑⠀⠐⠛⠒⠀⣰⠀⠀⢂⠀⡀⣀⠈⡀⠘⣧⠐⠀⠚⠒⢾⡗
⠀⠀⠀⠀⠀⠀⠋⠈⠂⠆⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠉⠈⢁⠀⣀⠀⠀⢴⠏⠀⠀⠀⠀⠀⠀⠐⠋⠀⡁⠀⡄⠀⠐⠀⠀⠈⠋⠀⠀⠀⠀⠘⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣾⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠄⢣⣶⢶⡄⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⠻⠆⢣⣾⠻⣆⠀⠀⣰⡿⣷⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣎
⠀⠈⠻⡾⠃⠀⠀⠙⣻⠟⠀⠀⠀⠀⠀⠀⣾⣿⣧⣛⣚⠃⠀⠀⠈⣛⠛⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠟⠉⠀⣀⣀⢾⡁⢰⠄⠀⠀⠀⠀⠀⠙⠛⠃⠛⠁⠂⣤⣄⢺⣁⢰⠆⣀⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠺⣉⣹⠆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠃⠉⠁⢺⣏⢹⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡄⣄⣼⣗⠶⠖⠒⠒⠒⠒⠒⢦⠒⠒⠚⠓⠖
⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣤⣇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⢀⡆⠈⠁⠀⠀⠈⠉⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢷⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⡠⢄⡀⣤⣶
⠀⠀⠀⠀⠀⢿⠶⡄⠀⢘⡃⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⠉⠀⠈⠛⣀⡄⠀⠀⠀⠀⠲⣿⡵⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠰⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠾⡇⠀⢀⠀⠀⠠⠐⠊⠁
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠈⣄⠀⠀⠸⣿⡂⠀⣀⠀⠀⠀⢰⣾⠚⢗⠀⠀⠀⠀⠀⠀⠀⣴⣂⣽⠒⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣷⣰
⠀⠀⠀⠀⡅⠀⠀⠀⠘⠻⠃⢻⠀⠀⠈⠉⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠰⣤⢧⠆⠀⠀⠀⡉⢟⣿⣻⢏⠛
⠀⠀⠀⠀⠛⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠛⠞⠀⠀⠀⠀⠀⣼⠈⢑⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠢⠉⠅⠀⠀⠀⠀⢠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⡜⠀⠀⠀⢣⡘⢂⡕⠀⠀⠀⠼⡀⢀⠷⠀⠀⣀⣀⣀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠒⠋⠀⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⡠⠖⠋⢩⣿⣿⢧⡀⠀⠹⠿⠟⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡼⠁⠀⣰⣿⣿⣿⠀⢹⣦⠄⡀⠀⠀⠀⠀⡜⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣼⣡⣤⣾⣿⣿⣿⡏⠀⠇⣸⡧⢒⡀⠀⠀⠘⠓⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡹⢧⡀⠈⠻⣿⣿⡇⢀⣿⠧⣒⠥⣊⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢀⡴⠆⠀⠀⠀⠀⠀⠀⠀⢀⡩⢔⡡⢛⠶⣄⣈⣻⣧⣾⠅⡊⠔⡪⠔⠀⠀⠀⠀⠀⠀⢰⡏⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣶⣿⣔⡢⠄⡀⢀⠀⢀⡠⢒⠥⢒⠥⣂⠥⣊⠅⡋⠕⡫⠔⡪⠔⡩⢐⡡⠀⠀⠀⠀⠀⠀⠘⡇⢰⣄⣳⡔⠊
⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣌⢒⢡⡶⠥⠶⠥⣊⠵⠾⠵⣎⠔⣨⠴⠯⢶⣩⡶⠦⠶⠥⢆⠀⠀⠀⠀⠀⠀⢀⡹⡄⠻⠇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢿⣿⣿⣧⣿⣿⣿⣷⠎⣴⠛⠛⠲⢀⡶⠛⠳⡌⠛⣡⠞⠛⢦⡉⢰⡟⠛⠳⣆⢳⡀⠀⠀⠀⠒⠁⠀⠘⢆⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⡿⢰⡇⠀⠀⠀⣸⠁⠀⠀⢻⠀⡟⠰⠷⠀⣧⢸⡇⠀⠀⢹⡆⣷⢀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠃
⠀⠀⠀⠀⠀⢀⡴⠇⠀⢿⣿⣿⣿⠟⠿⣿⣿⠛⣿⡇⢸⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⡇⠐⠒⠀⣿⢸⡇⠀⠀⢸⡇⣿⠔⣊⠔⡢⠄⡀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠸⣿⣿⣷⣀⣰⣿⣿⣿⣿⣧⠸⣇⠀⠶⣶⢿⡀⠀⠀⣸⠀⣧⠘⠛⢀⡟⢸⡇⠀⠀⢸⡇⣟⡨⢔⡩⢖⡡⢂⠡⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠲⠶⢋⣄⡓⠶⠞⣡⣶⣌⠳⠶⠛⣡⡘⠷⠶⠶⢋⣴⡯⢂⠡⢒⠥⢊⠅⡊⠔⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢙⡿⢿⣿⣿⠿⣿⣿⡿⠿⣿⣿⣿⠿⠿⢿⣿⣿⠿⣿⣽⡿⢿⣿⢿⣿⢿⣿⣿⠿⣆⠥⣊⡥⠎⢴⣊⢔⡨⢔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣆⠹⢁⣶⠈⢡⡶⠲⣦⠙⢠⡖⠓⠲⣮⠁⣶⠸⣿⢰⡆⠀⡆⢠⣆⢹⡇⢰⠈⡿⢡⡖⡒⠢⠙⡯⢒⠥⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⣿⢸⡿⣦⡞⣿⠀⡟⠀⠀⠘⡇⢸⡇⠀⠀⢸⡆⣿⢧⠉⢸⡇⠀⡇⠰⡿⣆⠁⢸⠀⢁⡟⢰⠭⢳⠶⢋⠅⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢈⡀⣿⢠⡇⠀⡂⠀⣿⢸⣧⣤⣤⠟⠀⣿⠈⢧⣸⡇⠀⡇⠀⡇⠘⣆⣺⠀⢸⡇⣿⣊⣕⣊⠔⡨⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⢿⡇⣿⠀⣇⠀⠅⠀⡟⢸⡇⠈⢷⡀⠀⣿⢠⡌⢻⡇⠀⡇⠀⡇⢠⡘⣿⠀⠸⣇⠉⠤⣤⡌⡏⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠐⡦⠤⣄⡼⢦⣠⡄⢸⠸⠇⣸⡅⠿⢠⡙⠦⡤⠞⣁⠸⠇⣿⡈⠷⠀⠿⢀⣿⠸⠇⠀⠇⠀⠇⢸⡇⠿⢈⣧⡙⠦⡤⠞⣰⠃⠀⠀⣴⠞⠁
⠀⠀⠀⠀⠀⣱⡤⢶⠇⠀⠙⢧⠈⠑⠚⠉⢻⣶⣿⣿⣷⣶⣾⣿⣷⣾⣿⣿⣶⣿⣶⣾⣿⠷⠚⠓⠲⢛⠶⣿⣿⣶⣾⣿⣿⠓⠒⠊⠁⢀⣰⠟⠁
⠀⠀⠀⠀⠈⠙⢦⡼⢀⣠⣴⠚⠁⠀⠀⠀⢘⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠣⠤⠄⣊⠴⣋⠜⠀⠉⠛⠛⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠰⢻⡉⡗⠞⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⠟⠃⠤⢭⠩⠭⠤⠚⠁⣠⡶⠀⠀⣠⠄⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠞⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠒⠒⠂⠀⠐⠒⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⠆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⢤⡀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠰⡄⠆⠀⠀⠀⠰⡆⠀⠀⢀⣀⢉⢲⣄⣄⢀⣀⣠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢀⠇⠨⠧⠦⠆⠦⠽⠶⠤⠤⠰⠒⢳⣳⣋⡭⠶⠷⢿⠛⠿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡜
⠀⠀⠀⠀⢰⣅⡰⢀⢠⣀⠴⢬⣀⢀⣠⢀⡴⠖⠉⠈⣃⠀⡀⡄⠈⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠱⠚⠓⠊⠉⠓⢳⢹⣔⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠛⠶⢦⣀⡋
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡴⠛⠂⠉⠒⠀⠤⡀⠈⠑⢆
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡅⠤⣠⣤⡀⠀⠀⠀⠐⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⣼⣁⡀⠀⠀⠀⠀⠉⠙⠢⣀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠑⠒⠂⢤⡀⠀⠀⠹⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠶⠴⠶⠒⠐⠋⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣀⠀⠀⠀⠈⠒⢴⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠉⠒⠤⡂⠄⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠠⠄⣀⣤⣈⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠳⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢤⠂⠁⠠⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢑⠆⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢦⠀⠀⡀⠀⠈⢀⠀⠰⡆⠁⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠤⠚⠃⠀⠀⠁⠀⡃⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣴⢯⣉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠛⣦⡼⠟⠛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠳⠶⢿⠁⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠳⠦⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣴⠎⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣱⣾⡄⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢿⣯⡼⠛⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠘⣃⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡿⣶⡛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣶⡾⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠈⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢉⣿⣾⠟⠣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠷⠟⠈⢇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⠴⠖⠛⣛⣛⣛⣋⣉⣉⣉⣉⣍⠩⠭⠭⠽⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠴⠶⠶⠶⠶⠶⢶⣟⣛⡳⢶⣤⡀
⢠⡞⢻⡷⠖⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠉⠙⡆
⢻⡄⠈⠳⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣤⡤⠴⠶⠞⠋⠁⠀⠀⠀⢹
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠲⣄⠀⠀⢀⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⢠⡇⠀⠀⠀⠀⣠⠛⢳⡀⠀⣸⠀⠀⢧⣀⣠⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⡄⠀⠀⠀⢰⠋⠉⢻
⢸⡇⠀⠀⠀⠀⣿⠆⠈⠳⠞⠃⠀⠀⠈⠉⠁⠀⠀⠀⢨⡇⠀⠀⠀⣠⠞⠋⠛⠳⣄⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⢀⡄⢀⡼
⣾⠀⠀⠀⠀⢸⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢠⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣹⣦⣤⡴⠾⠛⢻
⡿⠀⠀⠀⠀⣿⠿⠦⠤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠖⠂⣾⠀⠀⠀⠘⡷⠒⠒⠲⠖⠛⠷⢶⡄⠀⠀⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆
⠱⣄⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢹⠀⠀⠀⠀⠀⣀⣀⣤⠴⡇
⠀⢹⠶⣮⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⠤⠤⠤⠤⢾⡀⠀⠀⠀⣸⠓⠚⠛⠛⠉⠉⠁⠀⠀⢸
⢀⡟⣁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⣈⡉⠉⠉⡁⠀⢠⡀⢀⣀⡀⢀⡀⠛⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣿⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⡆⠀⡟⠉⢹⠀⠘⡛⠳⣼⣇⢸⡦⠀⠀⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⠁
⠀⠈⢳⣾⣥⣀⣀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠛⠀⠙⠶⠞⠀⠀⠁⠀⠈⠋⠈⢉⣉⣀⡀⣥⣤⣤⣤⣤⠤⠄⠶⠶⠒⠉⠉⠀⠀⡇
⠀⠀⡿⠂⠀⠈⠉⠉⠉⠛⠋⠙⠛⠛⠒⠋⠘⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⣟⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠈⠙⣿⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠛⠋⠉⠹⡆
⠀⠀⠀⠸⣧⠀⠈⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠸⣧⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠃
⠀⠀⠀⠀⠀⠈⢹⡷⢦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠊⠉⠉⠸⠁
⠀⠀⠀⠀⠀⠀⠘⣶⡠⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣋⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠚⠛⠛⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡟⣩⣉⣐⣀⡜⣁⠀⣠⣀⡜⣠⠆⣠⠆⣤⣤⣼⣷⠷⠏

⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⡀⠀⠈⠀⠀⠀⠂⠐⢠⠠⠄⡀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠤⢄⠐⠀⠂⠀⠀⠈⠂⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡀⠀⠀⢀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⢡
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢊⡠⠂
⠀⠈⠀⡎⢑⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠢⠀⢁⠠⠀⠀⠀⠀⠐⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠂⠀⠀⠀⡄⢰
⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢀⠀⠀⣀⠀⠀⣀⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⢀⣀⣀
⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠄⣠⠘⠒⠁⡀⠠⡀⠑⠎⢀⠄⠄⠀⠃⠀⡤⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡤⠉⡁⠘⠄⠀⠆⠀⡃⠠⠀⠠⠀⠠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠔⠉⠢⠀⠀⠠⠊⠑⠄⢀⠀⠐⠃⠀⠀⠠
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠲⢰⠒⠐⠖⠀⠒⠂⠂⠐⡖⠒⠂⠀⠂⠒⠒⠒⠒⠂⠐⠂⠒⠒⠂⠂⠐⠒⠒⠒⠒⠒⠲⠒⠂⡆⠴⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠅⡀⠀⠀⠀⠀⡇⠀⠀⠭⠂⠀⠀⠰⠂⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠀⠀⠀⡨⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠀⠀⠀⠀⠀⠐⠐⠀⠐⠅⢀⠔⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⡠⠐⠂⡀⠀⠀⠀⠒⠀⠀⣠⡀⠀⠀⠀⠊⠀⠈⠂⠀⠨⠈⠆⠀⠀⠀⠀⠠⠒
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠐⡆⠀⠀⠀⣆⠀⠨⠒⠒⢄⠀⡁⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠘
⠀⠀⣀⣀⠀⠑⠩⠄⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⡆⠀⠀⠈⠀⢉⠀⠀⠀⠀⡃⠀⡂⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠂⠲⠁⠂⠀⡇
⠀⠀⠱⠀⠄⠈⡂⠠⡀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠠⠇⢄⠀⠀⡖⠉⢢⠀⢀⠔⠁⠂⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⢐⠀⠀⠀⠀⢀⠒⠀⡊⢑⠀⣁⠂
⠀⠘⠀⠤⠀⡉⠀⠖⠂⠀⠀⠠⡊⠀⠠⠀⠀⠁⠀⢀⠜⠀⠀⠀⠂⠒⠀⠠⠓⠐⠀⠀⠀⠀⠢⡀⡠⠂⠀⠀⡔⠈⠑⡄⠀⠀⠀⠙⠀⢈⠁⡄⠀⠆
⠀⠀⠀⠈⠁⠈⠒⠀⠀⠀⠀⠀⠈⠆⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠈⠈⠀⠁
⠀⠀⠠⠀⠀⠀⠄⠤⠤⠀⠀⠀⠠⠤⠀⢀⠠⠄⠠⠄⡀⡠⠀⠀⠠⢀⡠⠄⢀⠀⠀⠠⠀⢠⣀⣤⠀⡀⠀⠀⡤⠐⢄⢀⠠⠀⠠⢀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠘⠁⠀⡀⢀⠀⠈⠣⠀⠀⢀⠀⠀⠄⠀⠡⡀⠀⠀⢸⠀⠀⠀⠈⠢⡀⠇⠀⢘⠀⢀⠀⢄⡠⠓⠀⠀⢃⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠞⠀⣠⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⢸⠀⠀⠀⠀⠀⠈⠃⠀⢸⠀⠁⡐⠀⠂⠠
⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠋⠀⢀⠀⠈⠂⠐⠁⠀⡠⠀⢀⠀⠐⢇⠀⢈⠓⠄⠀⠀⢸⠀⠀⠀⢸⠢⡀⠀⠀⢘⠀⠑⠀⠘
⠀⠲⣀⡐⠀⠀⠤⠤⠇⠠⠤⠄⠠⠤⠬⠁⠀⠤⠤⠄⠈⠥⠤⠌⠢⢀⠀⡤⠤⠀⠈⠢⠤⣤⠀⢠⠤⠜⠀⠈⠢⠤⠜⠐⠠⠤⠤⠐⠁⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⢿⠿⡿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣿⣿⣿⣻⣿⣟⣻⣟⣿⣿

⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⡠⠀⠀⠀⠀⠀⡄⣐⣰⣂⡀
⠀⠀⠀⣤⣿⣿⣿⣿⣤⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⠬⣿⣿⣿⡎⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⣽⣿⣿⣿⡧⠀⠀⠀⠐⣾⣿⣿⣿⡒
⠀⠀⠀⢠⠿⢿⡿⢯⠀⠀⠀⠀⠀⠹⠿⠟⠃⠀⠀⠀⠀⠈⠽⠿⠿⠓⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠐⢚⠿⡿⢟⠓⠀⠀⠀⠈⠝⢿⠿⠛⠌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣄⣂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⡄⣂⡐⢀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⢀⢹⣿⣿⣿⡧⠄⠀⠀⠀⠠⣿⣿⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⢒⢾⣿⣿⢀⡒
⠀⠀⠀⠻⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠚⡻⢿⠿⡓⠂⠀⠀⠀⠀⠋⠛⠑⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠁⠆⡉⢁⠲⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢤⣰⣦⡆⡀⠀⠀⠀⡀⢦⣴⣤⠆⡀⠀⠀⠀⡀⢆⣶⣠⢄⠀⠀⠀⢀⡄⣴⣇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣅⡂⠄
⠀⠀⠀⣽⣿⣿⣿⣿⡥⠀⠀⠠⣽⣿⣿⣿⣿⠥⠀⠀⢠⢽⣿⣿⣿⡯⡄⠀⠀⣀⣻⠁⠀⠙⡟⠆⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠅⣾⣿⣿⣿⡎⠄
⠀⠀⠀⠚⣻⢿⣿⡟⠂⠀⠀⠀⠊⣻⢿⢿⡛⠂⠀⠀⠀⠊⡻⠿⢿⡓⠂⠀⠀⠈⣙⣷⢤⡞⠻⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠂⠝⠿⠿⠟⡔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠠⡰⠘⠰⢢⠀⠀⠀⠀⢀⣠⣤⣆⡀⠀⠀⠀⠀⣠⣢⣖⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣷⣶⣄⠀⠀⠀⢀⠰⣀⣆⡐⢀
⠀⠀⠠⠅⢰⣿⣷⡄⠩⠀⠀⠀⢺⡏⠀⠈⣿⡂⠀⠀⢸⣹⠁⠀⠈⣳⡅⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠌⣿⣿⣿⣿⡅
⠀⠀⠀⢫⢌⠙⢋⠠⠑⠀⠀⠀⠙⠷⡦⣶⠟⠀⠀⠀⠘⢭⡷⢤⡴⡿⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠀⠀⠀⠐⢙⠿⠿⢟⠐
⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣾⣽⣾⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⢀⣤⣶⡿⠟⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⢀⣠⣴⣶⣾⣿⣿⢷⣄⢀⣾⣿⡿⠋⢸⣿⠀⢠⣾⣿⡿⣃⡀⠀⢠⣿⣿⡟⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢠⣾⣿⣿⡿⣿⣿⡿⠀⠀⠀⣼⣿⡟⠀⠀⣼⡟⢠⣿⣿⠟⠀⣿⡇⢠⣿⣿⠏⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠘⠻⠿⠋⣰⣿⣿⠃⠀⠀⢰⣿⣿⠁⠀⢰⣿⢃⣿⣿⡏⠀⢰⣿⠇⣸⣿⡿⠀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⢸⣿⡏⠀⣰⡿⠃⢸⣿⣿⠀⢀⣿⡟⠀⢻⣿⣇⣴⡿⠁⢿⣿⡇⠀⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⢀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠻⠷⠶⠋⠀⠀⢸⣿⣿⢀⣾⠟⠀⠀⠀⠉⠉⢉⣴⣦⡀⠛⠿⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠋⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⡀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⣰⣿⣿⣿⠃⢀⣾⣿⡇⠀⣠⣾⣿⡿⢿⣿⣿⠇⠀⣼⣿⣋⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⢠⣿⣿⣿⠃⢠⣾⣿⡿⠀⢰⣿⣿⠏⠀⢿⣿⠏⠠⣾⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁⠀⠀⣾⣿⣿⠇⣴⣿⣿⣿⠃⢀⣿⣿⠏⠀⠀⠀⠁⠀⢠⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⢻⣿⣧⡾⠟⣿⣿⡏⠀⢸⣿⣿⠀⠀⢀⡄⠀⠀⣾⡿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⢀⣶⠉⠉⠀⠀⢿⣿⡇⠀⢀⠻⢿⣤⣶⠟⠃⠀⢠⣿⠃⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠙⠛⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠈⢿⣿⣷⡄⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠐⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⡁⣄⠀⠀⢀⠾⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠂⡄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣷⠈⠑⢤⡀⠀⠀⠱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡤⠀⠐⠶⠀⢈⣷⠖⠊⠉⠠⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠄⠀⠀⠀⢀⠘⢃⠀⠈⠛⠂⠀⠀⣧⡀⢀⠀⡀⡀⠀⠀⠀⠀⢀⢦⡉⠀⠀⠀⠀⠀⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠑⠄⠀⠀⠀⠘⢦⣌⡶⠒⠉⢋⢠⡐⠛⢷⡄⢾⡄⣿⢎⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⣴⣤⡖⠁⠀⠻⠆⠀⠀⠘⢧⣄⠀⠄⣼⡻⣧⠋⠀⢀⠀⡀⠀⠀⢰⡄⢀⡄⠀⠀⠀⣀⡤⠶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣂⢘⡦⣀⡈⠋⠀⠀⠀⠀⢒⡀⣠⡀⠠⠈⠀⠀⠀⠀⠀⠢⠀⠄⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠉⠀⠀⠀⢠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠤⠼⣷⠲⢤⣤⣄⠀⢀⠀⢀⠛⠀⠘⠆⠀⠀⠀⠀⠀⠰⠃⠀⠀⠳⠀⠀⠀⠐⣿⣿⣿⣅⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠉⠉⡿⡇⠁⠀⠀⡀
⠀⣠⠞⠁⠀⣀⠀⠀⠀⠀⠠⠄⠒⠒⠀⠐⠒⡒⢏⣉⠂⠀⠀⠐⠀⢀⢂⠀⣾⣎⣠⡀⠀⠀⠀⠒⠉⠋⠀⠀⢀⡄⠀⠁⠀⠀⠀⠈⣢⠁
⠈⠁⠀⠀⢀⠛⡄⢠⠰⠶⡴⣂⡠⠔⠂⢀⡠⠿⠻⠁⠄⠀⠀⠀⠀⠈⠛⢷⣿⣿⠟⣈⣤⡀⠀⠀⠀⠰⠀⠀⠈⠀⠀⢸⡀⠀⡀⠄⠑⠂⠄⡀
⠀⠀⠀⠀⠈⡶⢷⡞⢣⠀⠀⠀⢀⣦⣀⣀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠰⠈⠙⠉⠉⠀⠀⠀⠀⢀⠀⠀⠈⠁⠁⠀⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠠⣤⠀⠀⠀⠀⢸⠃⠉⠲⣍⠀⠀⠀⠀⠚⠧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣼⢟⣒⡖⠀⢀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⢠⠀⠀⠀⠩⠇⢤⣤⣄⡀⠄⠂⡄⡀⠀⠀⠀⠀⢀⣀⠀⠀⠚⠁⡡⠈⠀⡀⢀⣾⣴⣤⡄⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣈⠱⢆⡨⠶⠃⠀⠀⠰⣿⣿⡇⠀⠀⢀⠁⠀⠀⡙⠿⡿⠁⠀⠀⠀⠾⠀⢀⣤⣽⣿⣯⠉⠁⠀⢀⣀⠀⠠⠄
⠀⠀⡠⢀⣿⣃⠈⡱⠊⠉⠀⢀⣬⡄⠀⠀⠀⠐⠁⠀⠙⢓⣠⠄⠡⠀⠀⢠⠄⠀⠀⠀⠀⠀⠄⠀⠰⠺⡿⣿⢯⡀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠉⠁⠀⠛⠂⠀⠀⠀⢀⣾⠋⣠⢳⠄⠀⠀⠀⡀⠀⠉⢻⡀⡄⠀⢠⡏⠀⢸⠀⠀⠀⢰⠀⡠⠀⠀⠏⠁⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣃⠜⠁⠀⠠⡄⣠⠞⠁⠀⠀⡸⣿⠃⡠⠀⠇⣱⡄⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⣤⠈⠏⢀⠀⠀⠀⠊⠣⠀⡀⢀⠀⠀⣘⡇⠀⠀⡐⠋⠛⣽⠅⠆⠀⠆⠀⠄⠀⠀⠀⠀⢀⣣⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢰⡗⠁⠿⠷⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠉⠀⠀⠢⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⣸⡁⠈⠑⠂⠤⠤⠤⠔⢠⣏⠀⠀⣤⡄
⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠀⠀⠀⠀⠀⠀⠁⠀⢳⠙⢄⠀⠀⠀⠀⠀⠀⠀⢻⠅⠀⠊
⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡦⠄⠿⠉⠀⠐⠚⠹⣆⠈⢣
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠙⠀⠀⡧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡄
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⢀⠀⠀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠔⠈⠛⠉⠢⣄⣠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⢲⣏⣹⡉⣵⢤⡠⠀⣆⡄
⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⠀⢐⠻⠄⠰⠆⠶⢨⠀⢀⡇⠀⠀⠀⠀⠀⠈⣽⠉⣉⣡⠝⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯
⠀⠀⠠⠀⠑⠞⠀⠀⠲⠀⠘⠚⠘⠃⠸⠶⠤⢘⣠⣾⠷⠆⠀⠀⠈⠠⠀⠻⠰⠤⠤⠶⠤⢶⣭⡬⣥⠼⣿⡿⠿⠟⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠚⠛⠁⠰⠀⠀⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠩⠥⠍⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⢠⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⢁⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢂⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣤⣤⣤⠋⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣹⡷⠴⣠⣄⠱⣿⣶⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣚⠋⠶⣦⣝⣿⣷⠘⣿⠇⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠞⠉⠐⢿⣦⣈⣿⣷⣻⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠏⡀⠀⠐⠄⠙⡿⣮⣿⠛⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠦⡀⣊⣢⠟⡫⠃⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⠭⠁⠜⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠤⠄⠠⡇⠀⣤⠀⠤⠤⠤⠤⠤⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣂⣉⣀⣲⡤⢶⠤⠃⢀⠰⣶⠦⠴⠄⠀⣀⣀⡀⠀⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠴⢏⣙⣇⣸⡠⡧⠼⣦⠀⠈⠐⢦⣤⠤⠤⠤⢤⣄⠀⠙⠢⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣶⢮⣉⣉⠭⠄⣀⠀⠠⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢑⣤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣽⣂⠈⣉⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⡄⠐⣁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣝⡻⣟⠀⣴⡂⠀⠀⠀⢠⣶⡄⢰⡯⢦⡀⢂⡀⣇⢈⣀⡥⡞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢈⢀⡇⠁⠈⠋⢮⡇⠀⠀⠂⢨⠟⡻⢿⠺⠾⠟⠛⠋⠙⠁⠃⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠜⠻⠀⠀⠀⠀⢀⠀⠀⢀⠓⢸⡃⢌⢂⢃⠀⡀⠠⠠⠀⠀⡘⢰⠀⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠃⠀⠀⠀⠀⣠⣆⠀⠤⠅⣼⡷⠶⠶⢄⠀⠀⠁⠆⡀⠀⠃⡈⠀⠁⢈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⣠⡾⠃⠈⠳⠶⠞⣦⣀⠀⡀⢋⣆⠀⠀⠠⠀⡘⢀⠃⠃⠠⢸⢠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⠀⣔⠝⢁⡀⠠⠠⠤⠤⣴⣿⣤⡟⢀⠄⠘⣧⡀⠀⠈⠁⠸⢰⡖⠓⠮⡈⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉⠠⢄⠀⣠⣶⣯⢁⣿⠃⠀⠀⣀⠘⢟⡄⠀⠀⠃⣼⠀⠀⠀⠡⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠆⠀⠨⡥⣀⡠⢶⣦⣙⡿⣿⠀⢀⡄⠀⠀⡜⡌⠀⠀⢀⠻⠀⣄⠀⠀⠀⠠⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣁⠀⠔⢸⠷⣶⣝⣿⢷⠻⡃⠈⣠⠂⡘⡘⠀⠀⢨⡘⢀⠶⣈⡁⠾⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠴⠐⠀⠀⠀⠀⠰⠘⢆⠶⠻⠷⠼⢋⢾⡈⠤⠁⠐⠁⣲⠌⠀⠀⠀⠀⠃⡈⡀⢁⠁⠆⠀⢠⡸⠃
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠱⠈⠖⢎⢦⡀⠋⠀⠀⠀⠖⢠⡳⠁⠀⠠⢀⠂⠈⠰⢡⠁⠄⡘⠰⠀⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠚⠭⠴⠶⠖⣂⣀⣀⣰⠏⠀⠀⢀⠂⠌⡀⢀⢃⢃⠆⡠⢁⢃⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠐⡐⡀⢀⠎⠎⡰⢁⠎⣀⠎
⠀⠀⠀⠀⠀⠀⠐⠢⠀⠂⠀⠊⠑⣠⣉⠂⠑⢊⠔⡠⠂⠂⠐⠀⠁⡠⢁⠌⠔⠜⠀⠀⠎⠈⠀⣤⠞⣣⠀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢂⠠⠀⠄⢉⡰⠛⡰⠦⣤⢀⣀⣀⢀⢀⡀⣀⡀⢀⡤⠀⠄⣐⢞⠕⢁⠈⡡⢊⠐⢁⠔⡡⢂⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠡⠒⢁⠔⢉⠔⢊⠤⠂⠠⠀⠀⠀⡁⠀⡠⠂⠔⠠⠂⡠⢁⠄⡡⠊⡄⠁⠔⢁⠘⠁⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠊⠐⠀⠐⠀⠊⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠀⠀⠀⠀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠄⠤⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⣤⠑⠊⠀⠀⣠⠄⠀⠁⠀⠀⡀⠀⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠆⠀⢤⠀⠀⠸⢠⣤⡴⠩⠉⠉⠀⠀⠀⠉⠐⠂⠄⠀⠀⠈⠤⠄⠒⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡛⠁⠀⠂⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠢⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠐⠃⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢐⡀⢀⡄⢰⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠀⠀⠀⢺⠀⠀⢀⠁⠀⠀⡀⠀⠐⠂⠀⠀⠀⠀⠀⠈⢀⡁⠀⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢽⣁⡀⡀⠠⠐⠚⠀⠀⠀⢦⠃⠀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⢀⣆⠽⠚⢟⠂⠀⠆⠀⠈⠉⠉⠉⠀⠀⠀⠒⠠⢀⠀⠐⠈⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠚⠭⣄⠀⠀⠀⠀⠸⠄⡀⡀⠀⠀⠀⠀⠂⠐⠀⠄⠤⠉⡀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⡀⠁⠐⠀⠀⠀⠤⠠⠊⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢀⣀⣀⣀⡀⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⢀⠀⠀⠀⣀⠄⠐⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⡀⠉⠁⠈⠉⢨⠙⡡⣌⣆⠆⢀⠈⠳⣎⠡⠐⢁⣠⠴⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠐⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⣀⡀⠙⢇⣀⠋⣀⠈⠁⠐⠄⢷⡀⠙⡤⠖⢋⣡⠖⠃⡇
⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠘⠅⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠈⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⢰⠀⠀⠀⠐⠁⠀⠀⠀⠀⠄⠊
⠀⠀⠁⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠤⣀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡴⠋
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠞⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⠴⠋
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⢀⢀⡀⠀⢀⠠⣴⠁⠀⢀⡎⠀⡀⠀⣀⠀⢀⣀⡀⢠⣞⣀⣀⠁
⠀⠀⠀⠀⠹⣧⣀⣀⡀⣠⠞⢰⣁⡸⠧⢴⣁⠼⠧⠰⡧⠐⠃⠀⢀⡾⠀⢾⠤⠚⣯⠠⣯⡉⠠⠟⠯⡖⠉
⠀⠀⠀⠀⠠⠤⠤⠤⣴⠯⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡾⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⡠⠒⠚⠛⠓⠲⠦⣤⣀⠀⣠⡞⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⠛⠦⣤⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠚⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠻⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢿⡘⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⡝⢿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠀⡇⢲⠚⢓⣲⡶⠤⠤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⣛⣻⡇⢾⢭⣥⠭⠿⣛⣛⣛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡤⣼⣧⣤⣬⣁⣀⣙⣆⣒⣂⣀⣀⣠⣧⣤⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢛⠁⠙⠛⠶⠾⠿⠮⠿⠭⠿⠿⠿⠿⠙⠛⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⠉⡔⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⡾⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⢦⡳⣀⣿⣿⣿⢿⢿⢿⣿⡿⠿⠿⡿⢿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠳⣽⠷⠀⠀⢀⣀⡀⡀⡀⣀⣀⣀⢀⡀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠲⠽⣿⣿⡶⣒⡶⡾⡾⣶⢾⢮⣽⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣮⣝⣂⠀⠀⠹⠌⣊⣡⢩⢉⣈⡱⠃⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠴⣒⠈⠻⢷⣿⣶⣶⣿⣷⣶⣾⠿⠋⣀⣒⢦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⣫⣽⣷⣄⡈⠀⠁⠁⠀⠈⠈⠁⣠⣾⣯⢍⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠤⠤⠬⠭⣭⡭⣭⠭⠤⠤⠴⠞⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣮⣤⣚⣛⣛⣓⣒⣒⣒⣒⣚⣛⣛⣛⣤⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢸⣿⡀⢸⣦⡀⣿⡏⠀⣾⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠹⣶⣦⣿⣷⣤⣿⣿⣿⣷⣼⣿⣧⣾⡟⠀⣤⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣼⣿⡿⠟⠛⠋⠉⠉⠙⠛⠿⣿⣿⣧⣾⣷⣀⣴⣾⠟⠁
⠀⠀⠀⠒⠶⢶⣤⣤⣀⠀⠙⠾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⡿⠀⢀⣀⣀⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣩⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⠤
⠀⠀⠒⠛⠛⠛⠛⠛⠛⢛⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡛⠛⠛⠻⠿⠷⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠓⠂
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⢸⣿⠟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠻⢿⣦⣄
⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠋⢁⣴⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⢦⠀⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢻⡟⠀⣿⡿⣿⣿⠻⣿⡿⣿⣧⠈⢻⣷⡀⠀⠀⠀⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠈⠀⣸⣿⠁⠉⡏⠀⣿⣇⠀⠘⠂⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠘⢃⣀⣉⠀⠰⠇⠀⠀⠀⠀⠀⠀⣄⠹⣇⠹⠀⠀⡜⢀⡀
⠀⠀⠀⠀⠀⡀⣄⣴⠟⢯⡓⣄⠀⠀⠀⠀⠀⠀⠙⠁⡄⠀⡀⠀⡀⠀⠀⠶⠂⠀⠀⠀⠲⠀⠁⢈⣤⣤⣄⠐⣡⡴⡆
⠀⠀⠀⠀⠀⢀⠸⡧⣸⣅⣼⣇⠀⠀⠀⠀⠀⠛⠃⠰⠀⠢⣀⣀⡡⠄⠁⠠⡤⠀⠀⠨⠭⠄⠀⣿⣿⣿⣿⡇⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠛⠏⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠶⠒⣡⠌⠛⠛⠋⠀⢌⡙⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤⠀⠲⠄⠀⠀⠀⠀⠀⠀⠺⠃⠀⡆⢰⠀⠘⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠲⠄⠸⡄⠀⢠⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢃⣀⠃⢠⠆
⠀⠀⠀⠐⠶⣄⠢⠄⠐⠈⡔⢀⣤⡄⠀⠀⠀⠀⠀⢠⠿⣟⣛⡛⠿⣷⡀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣦⡀⠤
⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠠⠄⠀⢤⠄⠀⠀⠀⠀⢿⣜⢾⣜⣟⡶⣿⠁⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡇⠤⠄
⠀⠀⠀⠙⠋⠁⠔⡀⠄⣀⠢⠘⠲⠄⠀⠀⠀⠀⠀⠈⠮⣯⣿⣿⡵⠃⠀⠀⠀⠁⠀⠀⠐⠂⡘⠿⣿⣿⣯⠟⠡⢄
⠀⠀⠀⠀⠚⠁⡸⠁⠀⠘⡄⠐⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⢀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠀⣠⠆
⠀⠀⠀⠀⢠⣀⢻⠢⡸⠣⠞⣏⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣤⣀⣹⠟⠀⠀⠀⠀⠑⠧⢤⣤⣤⠀⠀⠀⠀⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠍⠫⣝⢦
⠀⠀⠀⠀⠈⣲⠄⠀⠀⠀⠀⠀⠺⣍⣀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢆⢞⣻⣾⣿
⠀⠀⠀⠒⠛⣡⣟⣀⠀⠀⠀⠀⣏⠈⠁⠀⠀⠀⠀⠀⠈⠢⣈⣋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠧⣂⠥⣕⣵⠏
⠀⠀⠀⠀⠘⠉⠀⡶⠉⣦⠲⡏⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠂⠀⠀⠀⠰⠷⠁⠀⠀⠀⡀⠀⠀⠀⢰⠲⡀
⠰⠀⠀⠀⣴⢠⡤⣲⡂⡀⠀⠀⠀⠘⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠃⠁
⠀⠀⠀⠀⠀⠟⠉⠉⠀⠐⡀⠀⠀⠀⠠⠀⠀⠀⢀⡂⠀⠀⠀⠉⠀⠀⠀⡘⠁⠀⠀⠀⠀⠂
⢠⠰⠀⠀⠈⢣⡤⠄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠘⢧⠣⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢣⠱⡀⠀⠀⠉⠁⠀⠀⠘⢎⠀⠄⢀⣀⣠⡴⠃⠈⠳⢌⣒⣐⠰⠛⠁⠰⠬⠝⣒⣒⣒⣲⠶⠊
⠀⠀⠳⣈⠢⢄⠀⢀⣀⢠⠃⠀⠉⠐⠒⠒⡏⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠈⠑⠂⡠⠄⠒⠁⠀⠊⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⡲⢄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⠀⠀⡠
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠆⠴⠀⠀⢠⡷⠃⠀⠀⣠⠖⠀⡖⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠊⠀⠀⠸⢡⠃⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠑⠜⠐⠀⠀⢀⠞⠂⠀⠛⠀⠀⢀⠃⠋⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣀⠀⠀⠀⢀⣠⠊⢆⡑⠄⣀⡀⣀⣀⠔⡏⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠒⢪⠥⢶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠧⢀⣉⣁⡉⠴⠃⠀⠀⠈⠒⠀⠂⠚⠁⠰⠦⠏⡂⠒⠃⠀⣀⡀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⣀⣒⣂⠭⠕⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠢⠄⠉⠁⢧⠑⢄⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡟⠀⢾⡏⢐⠀⡀⢀⣀⠀⠀⢠⡶⢲⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⣿⡇⣿⡇⡴⢸⡏⠰⠂⣿⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠂⣽⡇⠹⠦⠂⠘⠧⠀⠀⢻⡅⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⢀⣴⠢⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢸⡇⠀⠀⠀⢸⡇⠀⠀⢰⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⠇⠀⠀⠀⢿⡇⠰⠆⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠂⣾⠇⠀⠀⠀⡀
⠀⠀⠀⠠⠊⢶⡀⠀⠀⠀⠀⣿⠀⡐⠀⠀⠼⣧⠀⠀⣠⠀⠀⣀⡀⢠⣿⠀⢀⡶⠀⢠⣤⡈⢠⣿⠀⠀⣰⡟⢩⣶⠂
⠀⠀⠀⠆⠀⠸⣧⠈⢻⡀⠀⣿⠀⠣⣾⡃⠔⠉⠓⢰⡿⠀⠀⢹⡇⢸⡇⠀⣼⡇⠀⠄⣿⡁⢸⡏⠀⢰⡿⠀⣸⡟⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣿⡄⠘⠃⠀⣿⠀⠀⢿⡀⠂⠀⠀⢸⡇⠀⠀⣾⡇⣼⡇⠀⠻⣇⠈⠀⣿⠇⣿⡇⠀⢸⣏⡠⢹⣧⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠀⣿⠇⠀⠂⠉⠀⠨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⡈⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁







⣀⣀⣀⣀⣀⣀⣀⡀⢀⡀⠀⣀⢀⣀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⣀⣀⢠⣤⣄⣒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠾⣟⣋⣉⠉⠉⠁⠀⠀⠈⣀⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠨⣗⡲⠦⢭⣍⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣊⢻⣿⣿⣶⡖⠒⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠶⠋⠀⣤⡀⠉⢿⣿⣍⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⠰⠶⠶⣾⡋⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⡉⠁⠀⡄⠀⠀⠝⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⢤⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⣯⡅⠀⠀⢀⡀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⡛⠻⠿⠿⠿⠯⠷⠢⢒⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⠽⠛⠓⠒⠶⠖⠚⠛⠉⠁⠀⠀⠀⡀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⡜⢆⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⢧⢹⣾⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡿⠿⠿⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⠶⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠙⠛⠦⣄⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢱⡀⠀⠀⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⣿
⠀⠀⠀⠻⠿⠛⠛⠀⠀⠀⠀⣇⠀⠀⠀⢺⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡟⠀⠀⠀⠀⢀⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⢦⣉⠓⠒⠶⠶⢒⡿⠋⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠈⠙⠒⠒⠋⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⣿⠀⣾⢃⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠁⢹⡇⠀⠲⠀⠀⠿⠘⠃⠉⠁⠀⠀⠀⣾⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⣀⠘⠁⠀⠀⢀⣠⡀⠀⣠⢤⠀⣰⠞⣿⠇⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠁⠀⠀⠀⣰⣾⢁⣧⣾⣇⣎⣼⠏⣼⡟⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣀⣀⡀⣸⡏⢙⠏⣿⢁⡟⢹⣯⡞⣿⠇⠀⢠⠇⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⠋⣩⠏⠻⡷⢋⣀⣿⣯⣤⡀⠉⠀⣿⠀⣠⠏⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇⠀⠀⠀⢀⡴⠋⠀⣠⠞⠋⠁⣰⠂⢠⠇⠀⠀⠘⠛⣋⠀⠀⠀⣠⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡘⣿⣄⣠⡴⠋⠠⠀⣼⠃⠀⠀⢰⣏⡴⢫⡞⣠⣾⢀⡾⣩⠇⠀⠀⠩⢶⡛⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣌⠉⠀⠉⠁⣀⣤⣤⣤⣇⠀⠀⠀⣿⠙⡆⠸⠟⢹⣇⣾⠋⠁⣰⠁⠂⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣩⡄⠀⠀⣠⣾⠟⠉⠁⠉⠙⠷⠀⢸⡇⣰⠇⢀⣤⣿⠉⣿⣤⡾⠁⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢀⣼⠟⠁⠀⠀⠀⠀⠐⠂⠀⠸⠷⠋⣠⠋⢰⡇⢠⣤⠄⠀⠀⢠⡟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠉⠀⢀⡀⠀⢤⠀⠠⡇⣠⠟⠀⣞⣧⡀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠉⢡⣤⠀⠀⢀⣤⣤⡿⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠰⠶⢿⡆⣴⡟⢠⢃⣴⡏⡸⠀⣴⠟⢡⣿⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢠⡟⣼⠏⢳⠞⢹⡏⣽⠓⢻⣏⡰⠋⣿⠀⢀⡞⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣴⣿⠃⣿⣠⠏⠀⠸⠟⠁⠀⠀⠉⠀⢠⡟⠶⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣸⡟⠀⠈⠁⠀⠀⡀⢀⡀⠀⣴⠿⢆⡿⣠⣴⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠂⠀⢠⣿⠃⠀⠀⠀⠀⣼⢁⣾⠁⣾⠃⣠⣾⡿⠛⠁⠀⠀⣼⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⡏⠀⠀⠀⠀⢸⣧⢻⣏⣼⣧⡔⢱⡟⢷⣄⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⣿⣧⡶⠶⠾⠟⠈⠁⠈⢛⠀⠀⠀⠘⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⢀⡾⢹⡈⠃⠀⠀⢴⡦
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⡂

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣁⠈⠙⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠷⣶⣤⣈⣉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢶⣦⣄⡉⠙⠳⠦⡤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⠀⢀⡞⢉⡼⠛⣫⣷⠆⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣀⡟⢁⡞⢁⡴⠋⣺⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣾⡄⣼⡁⣼⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡴⢆⢀⣀⠀⠀⠀⠀⠀⠀⠉⡛⠿⣿⣷⡿⡿⢃⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠢⣼⡈⣻⡇⣸⠃⣸⠤⠄⣀⡴⠖⣋⣩⣥⡷⢤⡉⠧⠆⡼⠀⣉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠚⠢⣼⣿⣿⣿⣿⣿⡇⢠⠞⣡⣶⣟⣭⠵⠶⣒⣚⣗⣛⣒⡇⠀⠀⠀⠀⠀⣄⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣁⠒⣿⣿⣿⣾⣧⣿⢧⡏⣼⣿⣿⣽⢶⣛⣋⣭⡭⣯⠭⢽⠃⠀⠀⠀⢈⡲⢤⡙⠌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⡬⣝⠛⡿⢿⢿⣻⢸⡇⡜⢿⣿⣿⣻⣭⡷⠶⠖⡟⠲⢺⣷⣶⣤⣄⣲⣽⣶⡝⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⣞⣾⠉⢻⣧⡼⣾⡟⣼⣷⣜⠦⣝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠿⢛⣩⣾⣿⣿⣆
⠀⠀⠀⠀⢠⠖⠦⣄⣇⠀⠘⣇⠀⣸⡏⠀⠸⣼⣿⣿⣿⡷⣤⣉⠀⠀⠀⠉⢉⣉⣉⣩⣭⣥⣴⣶⣾⣿⣿⣿⣿⡿⢿⡆⠀⠀⢀⡀⠀⡀
⠀⠀⠀⣀⣈⣣⣀⠀⢽⣾⣶⣿⣾⣿⣾⣤⢶⣿⣟⠷⣬⡛⠲⢭⣙⠛⠶⠶⠶⠶⠶⠶⠶⠶⢛⣛⣯⣿⣿⣿⣿⡿⣻⣿⠐⢦⡏⠱⡾⢹⣤⢤⡀
⠀⠀⠸⣅⠀⠈⢽⣿⣿⣿⡿⣛⣛⣻⣿⣯⢸⣿⣝⠷⣄⠉⠓⠂⠀⠈⠀⠀⠀⠀⠐⠒⠛⢛⣋⣩⣥⡾⣿⣿⣿⡿⣫⣿⠰⣴⣿⣶⣿⣟⣅⡼⠶⣄
⠀⠀⡴⠚⠛⠓⠺⣿⣿⣯⣾⣿⣿⣿⣿⣿⡞⣿⣟⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣩⣥⣶⡾⣿⣿⣿⣿⣫⡿⢬⣿⣿⣽⣯⣿⣿⠦⠶⣅
⠀⠀⢙⡶⠖⠶⠚⢿⣿⣿⣿⣿⣿⣿⣿⣉⠳⢻⣿⣿⢶⣍⡑⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣥⣤⠶⢾⣿⣿⣿⣿⣿⣃⡤⠾⣿⣿⣿⣿⣿⠣⣴⠚
⠀⠀⠘⠲⣦⠶⠒⠚⢛⡿⠋⢹⡏⠙⡄⠈⣳⣿⣿⣿⣷⣦⣍⣙⠒⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⢶⣿⣿⣿⣿⢿⣿⣿⣯⣤⡞⠁⡾⢻⡟⢱⡦⠼⠃
⠀⠀⠀⠀⠿⠶⠴⣖⣉⠀⣠⣿⣇⣠⣿⣶⣿⣿⣿⣿⣿⣿⣦⣭⣙⡓⠒⠶⠤⠤⠤⢤⡶⠶⠶⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣷⣾⣧⣸⣓⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣯⣝⣛⠳⠶⠶⠶⠶⠶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠯⠭⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠚⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⡤⠤⠤⠤⠤⠤⠤