Attention deficit hyperactivity disorder Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⣤⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⣄⡻⠟⣣⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⠻⣏⣡⣾⣦⡀⣼⠃⠀⣀⡀
⠀⠀⠀⠀⠀⣿⠰⣿⣿⠀⣿⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠓⠋⠛⠃⠛⠀⣷⠀⠀⠀⠀⠀⠀⢿⣿⠛⠷⣆⢿⡄⢸⠇⣼⢏⣤⡶⢾⡿⠂
⠀⠀⠀⠀⠀⠙⢷⣾⣷⡞⠁⠀⢸⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣶⣄⢀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⢳⠀⠈
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣤⣶⠾⠇⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣼⠏⢹⣧⣀⡀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣇⣀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⣯⣄
⠀⠀⠀⠀⠀⠀⠈⢙⢰⣿⡇⣼⣿⣣⣊⠁⠀⠀⠀⠀⠀⢸⡇⣾⣿⡆⣻⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⡀⢿⣿⡿⣿⣸⣶⡿⡿⢀⣀⡀⠀⠀⠀⠈⠳⣮⣭⡶⠋⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⣿⠛
⠀⠀⠀⠀⠈⠉⠁⣿⣟⣥⣍⣿⡿⢶⣾⠈⠉⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⣉⣼⣿⡀⠀⠀⣀⣁⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⣀⡬⠵⣿⡟⠻⣾⡷⢥⣀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣧⠀⠒⠒⣬⣤⣼⡇⠐⠒⢢⣭⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢰⡆⠀⠀⠈⠉⠀⠀⠀⠀⠐⠟⠛⠁⣰⡿⠁⠀⠀⣿⠉⠉⠀⠀⠀⢸⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡤⢠⢠⠈⡆
⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡀⢂⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢠⡄⢀⣤⡀⢠⡄⢀⣠⣄
⠀⠀⠀⢠⡞⢻⣶⣯⡁⠀⡀⣠⡄⣴⠶⡤⣄⣤⢰⠶⡄⠀⠀⢰⠒⠒⡒⠒⠲⡌⢃⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠸⣇⠻⣿⠟⣸⠇⠸⣿⡿⠂
⠀⠀⠀⠈⢡⣿⣿⠏⠛⠛⠑⠋⠓⠻⠖⠃⠃⠙⠸⠖⠃⠀⠀⢨⠀⠀⠁⠀⠀⡇⡏⠠⠄⠄⠤⠈⡆⠀⠀⠀⠀⢰⣿⣿⣦⠀⠙⣿⣿⣿⠋⠀⣴⣿⣿⡆
⠀⠘⠻⠶⠟⠈⢻⣄⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⣿⡷⠀⠀⠀⠈⠉⠉⠉⠉⠹⠇⣦⠤⠤⠤⠤⠔⠁⠀⠀⠀⠠⢬⣯⣭⡯⠤⠤⣿⣽⣹⠤⠤⢝⣯⣟⡥⠄
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⠀⠀⣿⠛⣿⠀⠀⣿⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠘⠟⠀⠀⠟⠀⠻⠀⠀⠻⠃⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⠟⠛⠫⡁⠀⠉⢙⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠃⠀⠀⢏⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣀⣀⡴⠀⢠⠴⠒⠶⣄⠈⢁⠤⠤⣄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣭⣠⠞⠋⣶⡠⡖⣄⣆⡧⡖⣆⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⣬⣭⡉⠉⠉⠁⠁⢉⣵⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣤⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢰⢆⢤⣄
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣁⣀⣈⡀
⠀⠀⠀⠀⠀⣿⢿⣵⣂⣀⣀⣩⢿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣾⢿⡟⣿⢿⡆⠀⠀⠀⠀⠀⢠⣶⣶⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠋⡟⠁⠀⠙⣧⠀⠀⠀⠀⠀⠾⢡⣿⣿⣿⡌⠷⠀⠀⠀⠀⠀⣿⢸⣷⣿⢸⡇⠀⠀⠀⠀⠀⣿⣿⣴⢇⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣠⠏⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⢸⡏⣿⠈⠀⠀⠀⠀⠀⠘⣿⣿⣿⣸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⢴⢰⣦⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢸⢸⣿⠻⡄
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⣀⡀⠀⠀⠀⠀⠹⣿⣿⠃⣦⣀⣰⠆⠀⠀⠀⠈⢸⢸⡟⠃
⠀⠀⠀⠀⠀⣀⣠⣼⣿⣷⣄⠄⢠⠛⠀⠀⣠⣤⣴⣿⣿⣦⣜⢄⡼⠀⠀⣠⣤⣴⣿⣿⣦⣜⢄⠔⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠓⠊⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠘⠁⠀⠀⠛⠛⠛⠛⠛⠛⠛⠘⠀⠀⠀⠀⠀⠀⠈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⡟⢻⣆⠀⠀⠀⠀⢠⣾⣿⣫⣭⢻⣦⠀⠀⠀⠀⠀⣾⡉⠻⠿⢏⣳⠀⠀⠀⠀⢠⡶⢿⣿⣿⡿⢦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⡱⣿⢾⣿⡿⠀⠀⠀⠀⣼⣿⣿⡬⢫⣾⣿⠀⠀⠀⠀⣠⣿⣷⠾⡿⣸⣿⠇⠀⠀⢠⣿⣶⡅⣭⣍⢱⣾⣿⡀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣾⡿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣸⣿⠋⠀⠀⠀⠘⣿⣿⣧⡻⢟⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠙⢿⣿⣅⣩⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⡆⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⣶⣾⣶⡆⣶⡆⠠⠀⠀⢀⣾⣾⣶⡀⠀⠀⠀⠀⣸⣿⡇⣿⣿⠀⠀⠀⠀⣼⠋⠁⠉⢷⠀⠀⠀⠀⠀⠀⢶⣶⡄
⠀⠀⠀⠀⠀⠸⣿⣿⡿⡇⣿⡇⢰⠈⠀⠏⣾⣿⣷⠹⠀⠀⠀⢀⣿⣿⡇⣿⠟⠀⠀⠀⠀⠻⣄⣀⣠⡾⠀⠀⣴⠖⠲⢶⡟⠙⠃
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠂⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⢛⣫⡇⣿⣤⣀⡀⠀⠀⠀⣈⣿⣁⠀⠀⢸⡇⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠸⠗⠇⠀⠀⠇⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⠀⠿⠿⠿⠇⠿⠿⠿⠿⠀⠀⠀⠉⠿⠉⠀⠀⠀⠙⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠠⠶⣀⣀⠶⡄⠀⠀⠀⠠⠶⣤⡄⠶⡄⠀⠀⠀⠠⠖⣠⣠⠶⡄⠀⠀⠀⠠⠶⣤⡄⠶⠄⠀⠀⠀⠰⢆⣀⡰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⣠⡀⠀⣤⡀⠀⠀⠀⢀⣠⠀⠀⣤⡀⠀⠀⠀⠀⢠⡶⢶⠿⡖⢠⠀⠀⠀⣠⡀⠀⢠⡀⠀⠀⠀⢀⣄⠀⢀⣄
⠀⠀⠈⠀⠘⠙⠀⠀⠀⠀⠀⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠁⠉⠙⠀⠁⠀⠀⠀⠉⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⠄⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⡴⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠉⠉⠉⠉⠹⠁
⠀⠀⠀⠋⠤⠶⠛⠆⠀⠀⠀⠐⠋⠶⠆⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠱⠶⠘⠓⠀⠀⠀⠘⠣⠶⠞⠛


⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠠⠖⢠⣤⠚⠆⠀⠀⠀⠰⠶⢤⣤⠳⠄⠀⠀⠀⠠⠖⢢⢤⠚⠆⠀⠀⠀⠀⠰⠶⣤⡄⠳⠀⠀⠀⠴⠒⡤⡴⠳



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠁⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠊⠀⠔⠁⠐⠛⠀⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢀⠰⡌⠢⠀⠀⠀⣀⠀⠑⠤⠄⠤⠂⠀⢀⠙⢦⡁⢠⠂⠀⡼⠷⠀⣤⣤⣦⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠚⠁⢀⠀⠙⠢⠀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠻⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠈⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡐⠆⡀⠈⠢⡠⠄⠀⠀⠀⠀⠘⠦⠄⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⡟⠁⠀⠀⠀⠀⠀⠀⠂⠉⠂⠀⠐⠄⠀⠐⢁⠀⠀⠀⠀⠠⠔⠀⠀⠀⡠⠀⠘⡟⣩⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣽⠁⠀⠀⢀⡀⠀⠀⠀⠐⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢠⡿⢉⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣇⠀⠀⠰⠶⠦⠀⠀⠀⠀⠈⠁⠀⠀⠐⠠⠀⠁⠄⢈⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⠗⠫⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠉⠂⡠⠀⠀⠀⠀⢀⠀⠐⢀⠑⠒⠀⠀⠀⠈⢀⡴⢶⡶⠾⠋⠀⠐⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢷⡀⠀⠀⡀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠤⠠⠁⠀⠀⢀⣴⡿⢞⡩⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠳⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⡶⠛⣻⠟⣫⠔⢋⠄⠀⣀⠔⢀⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣼⣧⡈⠃⠀⠀⠀⠁⣀⡤⢴⠟⢋⠀⣫⣎⠀⡠⠊⡁⠐⣁⠤⢊⣵⠞⠁⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡽⠛⢛⠛⢛⡿⠋⠐⣀⣴⣾⠋⠉⠠⣠⠐⣨⠔⠋⣡⠞⠛⠁⠔⡉⠑⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣔⠋⠀⣠⢾⣯⢟⠍⠀⠰⠊⠀⠀⢀⡴⠊⠁⠀⠀⠐⠪⠔⠁⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⢞⡵⣫⠕⡡⠂⠀⠀⠀⡠⣚⠕⠈⠐⠪⠒⡡⠀⠀⢐⡴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡾⠋⠚⠑⠄⠀⠀⠀⠀⠈⢈⠠⠂⠀⣀⡴⡪⠔⠀⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠅⠀⠠⠀⠀⠀⠀⠀⠀⡠⠚⢁⣀⡠⠚⠁⢀⠄⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠔⠁⠀⠀⢀⠀⢀⠄⠊⠀⢀⣿⠉⠉⠛⠒⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠘⣡⠖⠀⠀⠈⠕⠂⠀⠈⡠⢞⠡⢛⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡴⠚⠁⢀⡀⠀⠀⠁⠀⠠⢊⠀⣠⠖⡩⠂⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠶⠋⠀⠀⠀⠂⠀⠀⠠⠀⠡⣔⠕⠊⠄⠠⢠⠞⠁⢈⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⡈⠁
⠀⠀⠀⠀⠀⢸⣿⣟⡤⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠈⠱⢻⡷⠛⠛⢻⡏⠈⠁⠀⠀⠀⢠⡟⣹⣿⣿⣧⠹⣆⠀⠀⠀⠀⠀⢸⣯⣿⣼⡇⣿⠀⠀⠀⠀⠀⠀⣾⣿⣏⣥⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠀⠿⣿⢿⡿⠆⠉⠀⠀⠀⠀⠀⠘⢻⣿⢻⡇⠛⠀⠀⠀⠀⠀⢠⣿⣿⣿⡧⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠻⡁⣿⣦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠐⡅⣿⡎⢷
⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⢀⡠⡀⠀⠀⠀⠀⠘⢿⣿⠟⠰⣦⢄⡰⠆⠀⠀⠀⠀⢀⡅⣿⠃
⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣦⣄⠔⢲⠛⠀⠀⢀⣤⣤⣾⣿⣷⣦⣜⢤⠜⠀⠀⣠⣤⣴⣿⣿⣷⣤⡣⣤⠇⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⠒⠊⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠓⠘⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠋⠀⠀⠀⠀⠀⠀⠈⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⢷⡄⠀⠀⠀⠀⠀⣴⣿⡿⣛⡻⣷⡄⠀⠀⠀⠀⠀⣰⠞⠿⣿⣿⠓⣄⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣿⡟⣵⣮⢱⣾⣿⠀⠀⠀⠀⢀⣿⣿⣧⡻⣋⣿⣿⠀⠀⠀⠀⢀⣿⣷⢠⣶⡆⣿⣿⠀⠀⠀⢀⣾⣧⠈⢙⣛⠟⣤⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣭⣾⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣥⣽⣿⠏⠀⠀⠀⠀⠘⣿⣿⣷⠍⣾⣿⠏⠀⠀⠀⢸⣿⣿⣇⢿⣿⢇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⡷⠐⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢀⣛⣟⣁⠀⣘⡃⠁⠀⠀⠀⢀⣻⣋⠀⠀⠀⠀⠀⠀⢠⣾⣟⣿⣦⠀⠀⠀⠀⠀⣠⡶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣰⣿⡇⠘⢀⠀⢠⢿⣿⣿⢧⡀⠀⠀⠀⠀⣾⣿⣯⣿⣿⠇⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⢘⡿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⢿⡿⠘⢻⡇⡼⠀⠁⠋⠾⣿⣿⠆⠃⠀⠀⠀⣰⣿⣿⣧⣿⠟⠀⠀⠀⠀⠈⠳⣤⣤⡴⠏⠀⢀⡾⠋⠉⠻⣏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⢸⡇⡅⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣉⣩⣵⣿⣿⣦⣤⣄⡀⠀⠀⢀⣤⣯⣤⠀⠀⠸⣇⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠸⠃⠀⠘⠃⠁⠀⠀⠀⠀⠋⠛⠀⠀⠀⠀⠘⠿⠿⠿⠗⠻⠿⠿⠿⠃⠀⠀⠀⠀⠟⠀⠀⠀⠀⠉⠓⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣶⡀
⠀⠀⠀⣠⢀⣄⢀⡘⢮⣿⡵⠃⠀⠀⠀⠀⠀⣴⢋⣉⣀⣉⢳⡄⠀⠀⠀⢀⣄⣀⠛⡯⢾⠦⣼⠁⣠⡄
⠀⠀⠀⠹⢼⣿⡼⠁⢸⣿⡇⠀⠀⠀⠀⠀⢀⣿⣧⣤⡀⢀⣼⡇⠀⠀⠀⠈⠛⠈⡻⠛⠚⠚⠓⡏⠙⠁
⠀⠀⠀⠀⢸⣿⡇⠶⠛⣠⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢿⡌⠓⠶⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⡀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣀⠀⠀⠖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣇
⠀⠀⠀⠀⢈⣴⣿⡰⣿⣬⠁⠀⠀⠀⢸⡰⣿⣸⠆⣠⣀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠒⢢⣿⣻⢾⣿⣽⠐⠒⠀⠀⠀⢹⣿⠃⠀⢙⣻⡄⠀⢘⣛⣧⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣠⠹⠿⠛⠿⠫⡄⠀⠀⠀⣀⣾⢻⡄⠀⢸⣥⡿⠀⢈⣯⣼⠂⠀⠀⠀⠀⠀⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠉⠀⠞⠁⠀⠸⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⣀⠀⡀⠀⡀
⠀⠀⢰⢲⣾⣍⣀⢠⡄⡶⣤⣠⣴⢦⠀⢠⠂⢠⠀⠊⠃⠤⠤⠤⡀⠀⠀⠀⢻⡟⠸⣟⣿⣣⠇⢺⣿
⠀⢤⣤⠟⣯⠈⠁⣠⣭⣭⣬⣬⣬⡅⠀⠈⠠⠤⠠⠄⢀⡀⠀⢀⠇⠀⠀⢀⣿⣿⣀⣸⣿⣟⣀⣿⣿⡇
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢶⠈⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⢸⡟⣷⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁⠁⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣶⣤⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠘⣿⢿
⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⢷⣜⣛⣋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡁⣀⠀⠈⣙⢷⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⢿⡩⣾⣷⡄⣰⠏⠀⢠⡀
⠀⠀⠀⠀⠸⣇⠸⣿⡿⢸⡇⠀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡘⠓⠂⠉⠉⠛⢰⣧⠀⠀⠀⠀⠀⠘⢿⡟⠛⢷⣜⣧⢸⡇⣰⡏⣤⠶⢻⡿⠂
⠀⠀⠀⠀⠀⠙⢷⣶⣾⠋⠀⠀⣿⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣶⣦⢠⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠶⠿⠛⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢠⣿⠁⢻⣧⣄⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⠌⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡠⠤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠶⡀⢀⣄⡘⣀⣄⢀⡶⠆⠀⠀⠀⠀⠀⡀⢀⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣻⣿⡅⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⣧⠻⣿⠟⣼⠀⢀⣤⣄⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢴⠦⢄⣭⣿⢩⡇⣿⣛⣛⡃⠤⡶⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠘⠿⢿⣄⠀⠀⠈⠻⠿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠘⢿⢷⣿⡆⣿⣛⡻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣀⡐⠶⠞⢿⡄⢀⣀⠶⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⣶⠋⠙⠛⢁⠛⠛⠉⢶⠄⠀⠀⠀⠀⣠⣤⡿⠈⣿⡄⠀⠀⣾⠶⠿⠃⠀⠀⣶⠷⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠾⠋⠀⠀⠀⠿⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⠈⠘⠁⡇
⠀⠀⠀⢀⣤⣤⣜⡿⠃⠀⠀⣀⠀⣀⡀⢀⢀⡀⣀⡀⠀⠀⠀⡈⠁⠀⠀⢀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⣿⢰⣿⣿⠀⣷⢠⣾⣿⡆
⠀⠀⠀⠸⢃⣿⣿⠿⣦⠶⢰⠿⡌⣇⡽⢿⢺⡿⣇⡽⠀⠀⢸⠀⠀⠗⠀⠀⡇⡔⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⣨⣿⣭⡀⠙⣶⣭⣭⡾⠃⢠⣽⣯⡄
⠀⠰⣦⣤⡿⠻⣯⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣴⣦⡀⠀⠀⠘⠒⠀⠒⠀⢤⡇⡇⣈⣈⣁⡁⣸⠀⠀⠀⠀⢀⣿⡿⡿⣃⣀⣸⡿⡿⣇⣀⡸⣿⡿⢇⡀
⠀⠀⠀⠉⠀⠀⣸⠇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⡆⠀⢸⡿⢿⡇⠀⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⠇⠀⢸⠇⢸⡇⠀⢸⡇⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠰⠋⠀⠎⠀⠶⠦⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡀⣈⠳⠄⠀⠀⠀⠀⡀⠢⣄⡀⣀⠀⠀⠀⠓⢤⡊⠀⡠⠀⢀⣾⡄⢀⣀⣠⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢠⠞⠁⠀⠐⠮⣀⡘⢀⠤⠒⠉⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠉⠈⠀⠀⡉⠀⠀⣨⣿⡿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠃⢀⠠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠄⠀⡁⠀⠀⠀⠀⠀⢤⡀⠉⠁⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠄⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡆⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁⠂⣠⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣲⡞⠂⠀⠀⠂⠀⠀⠠⠀⠄⠐⠂⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢶⡲⢒⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠤⠄⠁⠀⠀⠀⠙⠁⠀⢸⡶⠟⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣺⠁⠀⠀⣀⣛⡀⠀⠀⠀⠀⠠⠉⠠⠀⢀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⠞⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠉⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢄⡁⡰⠀⠀⠀⠀⠀⣐⣀⣀⣤⠾⠋⡀⢁⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⡀⠀⠐⠀⠂⠐⠀⡀⠀⠀⠀⠀⣠⢞⡽⠟⠉⠁⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⢷⡀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣁⣄⣀⣀⣤⣤⡾⠟⣩⠖⠁⠀⠀⢀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠹⣦⠄⣠⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠛⡩⢟⠁⠶⢋⠴⠊⡀⠊⢀⡠⢚⡡⠖⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠷⣄⣀⣀⣀⣀⣠⡴⠞⠛⠋⣠⣬⣔⠗⠀⠔⢁⠄⣀⡠⠖⣡⡾⠏⢀⡠⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡋⢉⠩⢉⡭⠋⠄⢠⡴⣾⣿⠁⠀⢐⠴⠂⠠⠊⢉⡤⠚⠉⠀⠊⡡⢂⢡⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣏⠀⣠⡴⣫⢞⡩⠂⠀⠘⠁⠀⢀⣠⠖⠉⢀⡄⢀⠐⠉⠂⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢞⣵⢞⡵⠫⠔⠁⠀⠀⢀⢴⡫⠂⠁⠀⠑⢊⡡⠂⠀⣀⣱⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠋⢁⠁⠈⠂⠀⠀⠀⠀⠀⡡⠔⠈⠐⣠⠴⠫⠂⠁⢸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⡀⠐⠀⠀⠀⠀⠀⢀⡴⠋⢠⣄⣴⣊⡀⢀⡄⣠⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⡧⠊⠀⠀⠀⡀⠀⡠⠐⠁⠀⣀⣾⠀⠈⠉⠙⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢊⡴⠋⠀⠀⠈⠐⠀⠀⠀⡠⢚⠵⢊⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣠⠞⠋⠀⢀⠀⠀⠂⠀⢀⠔⢉⠔⡡⠖⡩⠊⢈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡴⠛⡁⠐⠀⠐⠁⠀⠀⠄⠀⠡⡺⠔⠋⠄⠠⢈⠞⠁⠀⣹⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠿⠿⣸⠇⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠓⢦⡄⠀⠀⠀⠀⠀⣀⠀⠰⢿⢂⣴⣄⢠⡟⠉⡀
⠀⠀⠀⠰⣇⢾⡿⢸⡇⢈⣿⣿⠁⠀⠀⠀⠀⠀⠀⢐⣷⡘⠚⠘⠚⠃⣿⠀⠀⠀⠀⠰⢿⠚⠲⣼⣇⣹⣉⣟⣠⠶⣿⠆
⠀⠀⠀⠀⠉⣿⣾⡏⠀⣸⡟⢿⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣦⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⢹
⠀⠀⠀⠀⢀⣿⢻⡇⠛⠉⢠⡾⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠘⢷⡌⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⣀⣀⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠛⢠⣶⢤⣶⣂⡚⠁⠀⠀⠀⢠⡆⣶⣦⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢠⣄⢘⣻⢿⣯⣿⠿⠇⣠⡄⠀⠀⠈⢳⣯⣷⠋⠀⢿⣿⡀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠛⡟⡟⠃
⠀⠀⠀⠀⠀⠸⢿⣶⣼⣟⣿⠇⠀⠀⠀⠀⠀⢸⣿⣟⠀⣀⢶⠞⣿⠀⣀⡲⡞⣿⠀⠀⠀⠀⠀⠀⠀⡷⡇
⠀⠀⠀⠀⠀⠎⠈⠉⣀⠉⠉⠱⠂⠀⠀⠀⡴⠾⢃⣽⠂⠀⣾⠛⠛⠀⠀⢸⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄⠤⡀
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡶⣶⣿⡋⠀⢀⡄⣠⢄⣄⣠⡤⢄⠀⠀⡄⠈⡀⠀⠍⢃⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⠇⢿⡸⣿⢇⡿⠸⣿⡇
⠀⣀⡈⣱⢿⡏⠙⠋⠘⠙⠛⠊⠋⠙⣑⠊⠀⠀⢇⣀⣁⣀⡀⠈⠠⠠⠠⢸⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⣿⠀⢸⣿⣷
⠀⠈⠙⠃⠈⣷⠀⠀⠙⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣁⠰⠂⠀⠀⠈⠀⠀⠀⠀⣿⣿⡏⠀⣽⣿⣯⠀⢹⣿⣿⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠸⠇⠀⠿⠀⠿⠀⠸⠃⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠿⠿⣸⠃⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠓⢦⡄⠀⠀⠀⠀⠀⣀⠀⠰⢿⢂⣴⣄⢠⡟⠉⡀
⠀⠀⠀⠰⣇⢾⡿⢰⡇⢈⣿⣿⠁⠀⠀⠀⠀⠀⠀⢐⣷⡘⠈⠘⠛⠃⣿⠀⠀⠀⠀⠰⢿⠖⠲⣜⣇⣹⣉⣟⣠⠶⣿⠆
⠀⠀⠀⠀⠉⣿⣿⡏⠀⣸⡟⢿⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣦⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⢹
⠀⠀⠀⠀⢀⣿⢻⡇⠛⠉⢠⡾⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠘⢷⡌⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⣀⣀⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠓⢠⣶⢤⣶⣂⡚⠁⠀⠀⠀⢠⡆⣶⣦⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢠⣄⢘⣻⢟⣧⣷⠿⠇⣠⡄⠀⠀⠈⢳⣯⣷⠋⠀⢿⣿⡀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠛⡟⡟⠃
⠀⠀⠀⠀⠀⠸⢿⣶⣼⣟⣿⠇⠀⠀⠀⠀⠀⢸⣿⣟⠀⣀⣶⠞⣿⠀⣀⣲⡞⣿⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠐⠎⠈⠉⣀⠉⠁⠱⠂⠀⠀⠀⡴⠾⢃⣽⠂⠀⣾⠛⠛⠀⠀⢸⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠉⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠤⡀
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠃⡇
⠀⠀⢀⡶⣶⣽⡋⠀⢀⡄⣠⢄⣄⣠⡤⢄⠀⠀⡄⠀⡀⠀⠍⢃⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⠇⢿⡸⣿⢇⡿⠰⣿⡇
⠀⣀⡈⣱⢿⡏⠙⠋⠈⠙⠛⠊⠉⠙⣓⠊⠀⠀⢇⣀⣁⣀⡀⠈⠠⠠⠠⢸⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⣿⠀⢸⣿⣷
⠀⠈⠙⠃⠈⣷⠀⠀⠙⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣁⠰⠂⠀⠀⠈⠀⠀⠀⠈⣿⣿⡏⠉⣿⣿⣯⠉⢹⣿⣿⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠇⠀⠿⠀⠿⠀⠸⠂⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⠟⠛⠛⠿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠛⠉⠀⠀⠈⣇⠀⠀⢠⠞⠉⠉⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡦⣤⡤⠊⢀⣴⠊⠉⠙⠳⠄⠀⡴⠒⠒⢦⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣤⣴⠉⢁⣾⡄⡏⢳⣾⢴⢸⠙⡆⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⣬⣤⡉⠉⠁⠉⠈⠈⢩⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣀⣤⣴⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠻⢾⣷⠃⠀⠀⠀⠀⠀⠐⠦⡀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡐⠂⠀⠁⠀⠀⢀⡀⠘⠧⠀⠀⠀⠠⠠⠔⠃⠀⠈⠀⠀⢦⡀
⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⣠⠀⠉⠀⠀⠈⠓⠈⢻⣦⡀⠀⠀⠀⡀⢦⣑⠢⣄⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⣷⣯⣗⣒⠣⣖⣀⡀⠀⠀⠀⠀⣿⢿⣿⠀⠀⠀⠙⢶⣝⢷⢒⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣶⣶⣶⠶⠒⠉⢸⡟⢘⣟⣇⠀⣀⠀⠀⠈⢹⣮⣥⣶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢸⠇⣸⣿⣿⣿⣿⣿⡅⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡄⠠⠴⠋⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡳⢄⠀⠀⠀⠙⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣯⡄⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⢿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣴⡄
⠀⠀⠀⢀⠀⣀⠀⡀⢧⣻⣫⠞⠀⠀⠀⠀⠀⠀⡴⢋⠉⣉⣙⢦⠀⠀⠀⠀⢀⣄⣀⠛⣏⢴⡦⢠⠏⢁⣄
⠀⠀⠀⠸⣜⣿⣣⠇⢠⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣬⣁⠀⠉⣼⡇⠀⠀⠀⠈⠛⠉⠳⠿⠼⠧⠯⢾⠛⠟
⠀⠀⠀⠀⢸⣿⡇⢤⠾⠇⣽⠆⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⣿⠟⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡜
⠀⠀⠀⠀⢾⡁⠿⣤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⢨
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦
⠀⠀⠀⠀⠘⠆⣴⡌⣴⣄⠞⠀⠀⠀⠀⡄⣴⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⣤⠀⣻⡿⣇⣿⠿⡇⢠⡀⠀⠀⠙⣾⣷⠋⠐⢿⢇⠀⠀⠸⡿⡀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⡦⣿⣿⠃⠀⠀⠀⠀⠀⡿⣿⠀⠀⢲⢛⡇⠀⠐⡖⣻⠀⠀⠀⠀⠀⠀⠿⠿
⠀⠀⠀⠀⠘⠁⠉⣠⠉⠁⠛⠀⠀⠀⠰⠞⢃⡼⠂⠀⣿⠉⠁⠀⢸⡏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⡀⠐⡄
⠀⠀⢀⣀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⢠⡄⣴⣄⢤⢠⣤⡄
⠀⠀⠘⣹⣿⠷⠴⠲⠷⠯⠵⠗⠿⠯⠇⠀⠀⠀⠂⠀⡁⡆⡀⡀⠐⡄⠀⠀⠀⣽⣯⡀⢳⣿⣷⠋⢨⣿⡅
⠀⠛⠶⠋⢻⡄⠀⠰⠶⠶⠶⠶⠾⠷⠀⠀⠈⠀⠁⠐⠃⡧⠀⠀⠐⠁⠀⠀⠀⣿⣿⡅⢸⣿⣿⠀⢸⣿⡧
⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⠇⢸⡏⢿⠀⢸⠉⡧

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⢻⣘⣿⣣⠇⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⢦⡀⠀⠀⠀⠀⣀⠀⠰⢿⣃⣴⣄⣰⠏⢁⡀
⠀⠀⠀⠸⣇⢿⢇⡽⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⣉⡁⠉⠉⣸⡇⠀⠀⠀⠀⠻⠟⠛⣮⣇⣽⣰⣯⡶⠻⠟
⠀⠀⠀⠀⠘⣿⣿⢀⣠⡿⢙⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⣶⡿⠃⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣰⡟⢿⣌⡁⠀⠞⠁⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠀⠀⡞
⠀⠀⠀⠀⠈⠳⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢠⡄⢀⡈⢃⡀⢠⡄⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⡀
⠀⠀⠀⠀⠀⣤⣿⣯⢿⣿⣦⠀⠀⠀⠀⠘⣇⣿⣇⡿⢀⣤⡄⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠘⠂⣶⣿⣛⣿⣯⣭⠐⠛⠀⠀⠀⢨⣿⡏⠀⠀⣙⣱⡄⠀⢈⣛⣷⡄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢀⡌⠿⠟⠻⠿⢫⡄⠀⠀⠀⢀⣸⡟⣷⠀⠀⣽⣤⡇⠀⠀⣭⣼⠇⠀⠀⠀⠀⠀⠀⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠉⠁⠰⠏⠀⠀⠿⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠖⠈⡆
⠀⠀⢀⣤⣤⣿⠃⠀⢀⢀⣀⢀⢀⢀⣀⠀⠀⡀⠁⠀⠀⡲⠇⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⢶⢰⣿⡆⡆⢰⣶⡄
⠀⠀⠘⣱⣿⠟⠳⠃⠛⠺⠴⠛⠙⠻⠜⠀⠀⡂⠀⠃⠀⠅⡎⠄⠄⠌⡇⠀⠀⠀⢰⣿⣦⠈⣷⣿⡞⠁⣴⣿⡆
⠀⠉⠛⠃⠙⡦⠀⠀⠛⠛⠛⠛⠛⠻⠓⠀⠀⠀⠀⠀⠈⣃⠗⠒⠂⠐⠁⠀⠀⠀⢺⣭⣷⠒⣺⣯⡗⠒⣿⣭⡗
⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⢿⠀⡇⠀⢿⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢴⣿⡆⣲⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⣀⠀⠈⣽⠻
⠀⠀⠀⠀⣰⢀⣴⣤⢠⡄⠙⣶⣭⡶⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣠⢠⠄⣤⢻⡄⠀⠀⠀⠀⢀⣾⣤⣤⡁⢿⡘⣿⠛⣸⠇⣀⣰⣦
⠀⠀⠀⠀⠹⢦⣛⣫⡼⠃⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣄⡀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠙⠃⠀⢹⠾⠧⠿⠴⠿⢾⡉⠙⠋
⠀⠀⠀⠀⠀⠸⣿⣿⡆⣤⣴⠿⢈⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⣰⡟⢹⣇⣀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠙⢷⠄⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣀⣀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠘⠧⢠⣤⡈⣤⡄⠠⠓⠀⠀⠀⠀⠀⡄⣠⣤⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣾⣾⣿⡆⣻⣻⣷⠀⠀⠀⠀⠀⠀⢷⣝⣛⣵⠇⠀⣶⣶⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡿⠇
⠀⠀⠀⠀⠛⠁⣾⣟⣘⡃⣿⣧⣵⠌⠙⠃⠀⠀⠀⠀⣿⣿⡇⠀⠀⣉⣩⣶⠀⠀⢀⣉⣹⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⢀⡨⢽⣿⠇⢷⡶⢭⣀⠀⠀⠀⠀⠀⢀⣿⢻⣇⠐⠒⣩⣥⣼⡇⠐⠒⣭⣥⣿⠀⠀⠀⠀⠀⠀⠀⠘⠃⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⣴⠀⠀⠀⠉⠀⠀⠀⠀⠛⠛⠁⣴⠏⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠁⠃⡇
⠀⠀⠀⣠⢤⣤⣟⠋⠀⠀⣀⢀⣄⣀⡀⡀⣠⣀⠀⠀⢀⠬⠥⠤⠤⡑⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠐⣇⢾⣿⡇⣿⠀⣿⣿⠄
⠀⠀⠀⠛⣼⣿⠟⠳⠞⠸⠻⠼⠤⠛⠏⠇⠧⠜⠀⠀⢰⠀⠈⠁⠀⡇⢸⢀⢀⡀⡀⠇⠀⠀⠀⠀⣰⣿⣷⠀⠙⣷⣿⣾⠃⢠⣾⣷⡄
⠀⠘⠳⠾⠋⠻⣆⠀⠀⠰⠶⠶⠶⠶⠶⠶⣷⠆⠀⠀⠈⠉⠉⠉⠑⠇⢸⠤⠤⠤⠤⠂⠀⠀⠀⠠⢼⣛⣛⠤⠤⣟⣿⣯⠤⢬⣻⣟⡧
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⣿⠀⠀⣿⠙⣿⠀⢸⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠙⠀⠀⠋⠀⠋⠀⠈⠃⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄

⠀⠀⠘⠁⠶⠞⠓⠀⠀⠀⠀⠋⠶⠎⠻⠀⠀⠀⠀⠋⠰⠶⠛⠂⠀⠀⠀⠘⠱⠶⠘⠓⠀⠀⠀⠘⠱⠶⠚⠓


⠀⠀⠀⢠⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠘⠉⠒⠎⠉⠀⠀⠀⠐⠋⠒⠆⠙⠀⠀⠀⠀⠘⠋⠘⠀⠁⠈⠀⠀⠘⠙⠒⠎⠉⠀⠀⠀⠘⠁⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠠⠶⢶
⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠙⠀⠈⠉⠉⠙⠁⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠈⠁⠒⠊⠙⠀⠀⠀⠈⠉⠚⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠂⠉⠀⠀⠀⠈⠑⠒⠊⠁


⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠓
⠀⠀⢀⣤⠀⢠⣄⠀⠀⠀⢀⣤⠀⠀⣄⠀⠀⠀⠀⣠⡄⠀⣠⡀⠀⠀⠀⠀⣠⡄⠀⣠⡀⠀⠀⢠⣄⠀⢠⡄
⠀⠀⠈⠀⠉⠃⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠈⠙⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣄⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠣⡤⠃⠀⠀⠀⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠘⣏⣙⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⡅⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⣰⢻⡇⠀⠸⡇⣧⠀⠀⠀⠀⠀⠀⠐⠛⣿⠀⠀⠀⣿⢹⠰⡸⠀⠀⠀⠀⠀⠉⠟⠀⠀⣿⡏⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⢀⠠⠄⠂⡀⠀⣀⣀⣀⣀⣠⣀⣄⡈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⣠⠖⣋⠁⢋⣹⠶⠶⡋⠉⢉⣁⣐⣲⣄⣉⣈⢳⣄⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢠⠞⠡⢊⢄⢶⡋⠄⠂⠄⢚⡻⢭⠋⠉⠉⠀⠙⣬⠋⠝⠷⢄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡏⡰⢋⡴⢋⡽⢒⠭⠐⠈⠀⠀⠀⠑⢄⠀⠀⠀⠸⠆⠀⠀⢳⡀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣟⣰⡊⠔⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠸⢈⠃⠀⠘⡇⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⣿⠞⠛⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⢡⡏⠀⠀⢰⡏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠜⠛⢷⡈⠺⣦⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢋⠈⠀⠀⣸⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⢦⡀⠙⢶⣬⣙⠶⣄⡑⡀⠀⠀⠀⠀⣀⡴⠃⡠⠹⣂⡬⢴⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠢⢄⣑⢮⣉⠛⠻⠿⠿⣦⣥⣤⣨⡴⣮⠴⠃⡏⣠⠃⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠉⠉⠩⠿⣟⡂⠀⠀⠀⠀⠐⠚⠃⣀⡼⠟⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⡀⠀⣠⣤⣄⠀⡄⠀⣠⠀⡤⣤⡀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢀⣞⣳⡀⣿⠀⢸⠆⡷⠶⣿⢠⡇⠀⡷⠀⠀⠀⠀⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠚⠀⠈⠃⠙⠒⠋⠀⠃⠀⠛⠈⠓⠚⠁⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣶⣤⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⢷⣌⣛⣋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡁⣀⠀⠈⣙⢷⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⢿⡩⣾⣷⡄⣰⠏⠀⢠⡀
⠀⠀⠀⠀⠸⣇⠸⣿⡿⢸⡇⠀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡘⠃⠂⠉⠁⠊⢸⣧⠀⠀⠀⠀⠀⠘⢿⡟⠛⢷⣜⣧⢸⡇⣰⡏⣤⠶⢻⡿⠂
⠀⠀⠀⠀⠀⠙⢷⣶⣾⠋⠀⠀⣿⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣦⢠⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠶⠿⠛⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⢠⣿⠁⢻⣧⣄⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡿⠌⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡤⠤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠶⡀⢀⣄⠈⣠⣄⢀⡶⠆⠀⠀⠀⠀⠀⡀⢀⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣻⣿⡅⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⣧⠻⣿⠟⣼⠀⢀⣤⣄⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢴⠦⢄⣭⣿⢩⡇⣿⣛⣛⡃⠤⡶⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠘⠿⢿⣄⠀⠀⠀⠻⠿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠘⢿⢷⣿⡆⣿⣛⡻⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣀⣐⣶⠞⢿⡄⢀⣀⣶⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⣶⠋⠙⠛⢁⠛⠛⠉⢶⠄⠀⠀⠀⠀⣠⣤⡿⠈⣿⡄⠀⠠⣿⠶⠿⠃⠀⠀⣾⠷⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠾⠋⠀⠀⠀⠿⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠈⠘⠀⡇
⠀⠀⠀⢀⣤⣤⣜⡿⠃⠀⠀⣀⠀⣀⡀⢀⢀⡀⣀⡀⠀⠀⠀⡈⠁⠀⠀⢀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⣿⢰⣿⣷⠀⣷⢠⣾⣿⡆
⠀⠀⠀⠸⢃⣿⣿⠿⣦⠶⢰⠿⡄⣇⡽⢿⢺⡟⣇⡽⠀⠀⢸⠀⠀⠗⠀⠀⡇⠔⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⣨⣿⣯⡀⠙⣶⣭⣭⡾⠃⢠⣽⣯⡄
⠀⠰⣦⣤⡿⠻⣯⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣴⣦⡀⠀⠀⠘⠒⠀⠒⠐⢤⡇⡇⢈⠈⡁⠁⣸⠀⠀⠀⠀⢀⣿⣿⣿⣃⣀⣻⣿⣿⣇⣀⣸⣿⣿⣇⡀
⠀⠀⠀⠉⠀⠀⣸⠇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⡆⠀⣼⡿⢿⡇⠀⢸⡿⢿⡇
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⠇⠀⢿⠇⢸⡇⠀⢸⡇⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⣿⣿⡏⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⠸⣿⡆⢠⣶⣶⡄⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⣤⣹⣿⡜⠿⠿⢃⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣴⣿⣿⣿⣧⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠿⣷⣾⣿⢻⣿⣿⡟⣿⣿⣿⣿⠁⣰⣦⣴⢲⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⢻⣿⣿⣿⡏⠀⢩⣍⣬⢭⣬⣩⣤⢤⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⣿⣿⣙⣿⣷⡀⠛⠛⠙⠛⠙⠙⠙⠚⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣸⣿⡇⢿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿⡿⠀⠈⢋⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⠃⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠗⠈⠀⢨⣶⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠠⠀⢹⣭⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣿⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣾⣿⡿⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣇⠯⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⢿⣿⡄⢠⣾⣿⣦⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣟⣡⣌⣿⣿⡜⠿⢿⠟⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡼⣿⣿⣿⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡏⠀⣠⡄⣤⣤⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠈⣿⣿⣿⣸⣿⣿⣿⣿⠁⠰⠟⠷⠻⠾⠻⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣯⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⣿⣿⣿⣿⣧⠀⢀⣿⣇⣿⣹⢾⠶⣿⣟⣻⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣛⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⣸⣿⡟⣮⢿⣿⣧⠀⠀⠁⠈⠁⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢠⣿⣿⠁⢿⡇⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣼⣿⠇⠀⠈⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣿⡟⠀⠀⠀⠐⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡤⠃⠉⠘⣋⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣬⣤⠀⠀⢸⠿⠭⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠂⣄⢈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡿⠟⠛⠻⠿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠋⠀⠀⠘⣆⠀⠀⢀⡜⠛⠙⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢦⠀⠀⠀⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄⣀⣠⠖⠀⣠⠞⠛⠓⢦⡄⠀⣠⠶⠶⢤⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣀⡴⠛⢉⣶⡀⡖⢦⣰⣠⢳⠖⣦⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⣘⣉⠃⠓⠋⠙⠈⠘⠓⣩⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣠⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⣈⡤⣀⣠⣀⣀⣠⠴⠶⠶⢶⠲⠶⡦⣌⠁⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡴⢋⠕⢀⡤⠚⠉⢁⣦⣤⠤⠴⠾⠿⠶⡲⣼⢷⣄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⡎⣠⠗⡨⠾⡃⠁⡀⠁⠐⠈⠁⠄⠀⠀⠀⢹⡆⠑⠉⣅⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⢘⠕⡫⢐⠨⠂⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⠇⠆⠀⢸⡆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢺⣮⢿⠏⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⡸⠁⠀⢸⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠼⢿⣄⠪⣦⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣸⢎⠁⠀⠀⣸⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠪⣄⠉⠲⣬⡙⠦⣄⠡⡀⠀⠀⠀⢀⣠⠞⢁⢚⣆⣔⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⠤⣈⢪⣍⠛⠻⠿⠶⣤⣬⣔⣥⢦⡵⠒⠫⣠⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠉⠋⠿⢿⣂⠀⠀⠀⠀⠚⠉⢀⡼⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⢠⡄⠀⣴⠶⣄⢰⠀⢰⠄⡶⠶⡄⠀⠀⠀⠀⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠯⠽⡄⣿⣀⡿⢸⠋⢹⡄⣇⣀⡟⠀⠀⠀⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠀⠁⠈⠉⠀⠈⠀⠈⠀⠉⠉⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠉⢹⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⢀⡠⠳⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⠀⡿⠻⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠤⠄⠀⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⢀⡼⢿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣬⣇⠀⠃⠀⢸⢻⡇⠀⣀⠀⠀⠀⠀⠀⠤⣶⡄⠀⠀⣴⣶⡇⢀⣤
⠀⠀⠀⠀⠀⠀⠞⢹⡇⠀⠀⠷⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠀⠀⠀⢹⠸⠇⠳⠟⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⣿⠇⢀⠸⡟




⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⢄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠻⠶⣾⡷⠂⠀⠀⠀⠀⠀⠀⠀⠲⣄⠐⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠢⠄⡀⠁⠀⠀⠀⠀⠠⠀⢻⡏⠀⠀⠀⠀⢀⢀⣠⠖⠀⠀⠃⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠄⠀⠀⠤⣄⡀⣷⣄⠀⠀⠀⠀⠀⠀⢨⠉⢤⣀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⢸⣤⡲⢤⣀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣷⣄⠀⠀⠀⢠⣄⡻⠦⣬⣘⠒⢆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣮⣭⣐⡾⠭⠤⣄⠀⠀⠀⣀⢀⣿⠸⡏⣿⠀⠀⠀⠀⠉⠿⣮⣙⡏⣩⠀⠀⠀⢀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠒⠉⠀⢸⣿⠀⢳⣛⡆⠀⢀⡄⠀⠀⠀⠉⣿⣦⣭⣷⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠐⡧⠀⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠙⠟⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣠⡾⠃⠘⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠙⠻⣿⣷⣌⢩⡁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣷⣝⠲⣄⣀⠄⠀⠀⠌⠉⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣖⡂⠀⠀⠠⠀⢠⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣷⣾⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠋⠉⠙⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠿⠿⣸⠃⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠓⢦⡄⠀⠀⠀⠀⠀⣀⠀⠰⢿⢂⣴⣄⢠⡟⠉⡀
⠀⠀⠀⠰⣇⢾⡿⢸⡇⢈⣿⣿⠁⠀⠀⠀⠀⠀⠀⢐⣷⡘⠚⠘⠘⠃⣿⠀⠀⠀⠀⠰⢿⠖⠲⣜⣇⣹⣉⣟⣠⠶⣿⠆
⠀⠀⠀⠀⠉⣿⣿⡏⠀⣸⡟⢿⡀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣦⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⢹
⠀⠀⠀⠀⢀⣿⢻⡇⠛⠉⢠⡾⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠘⢷⡌⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⣀⣀⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠛⢠⣶⢤⣶⣂⡚⠁⠀⠀⠀⢠⡄⣶⣦⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢠⣄⢘⣻⢟⣧⣷⠿⠇⣠⡄⠀⠀⠈⢳⣯⣷⠋⠀⢿⣿⡀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠛⡟⡟⠃
⠀⠀⠀⠀⠀⠸⢿⣶⣼⣟⣿⠇⠀⠀⠀⠀⠀⢸⣿⣏⠀⣀⠶⠞⣿⠀⣀⠲⠞⣿⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠎⠈⠉⣀⠉⠁⠱⠂⠀⠀⠀⡴⠾⢃⣽⠂⠀⣾⠛⠛⠀⠀⣺⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠋⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡶⣶⣽⡋⠀⢀⡄⣠⢄⣄⣠⡤⢄⠀⠀⡄⠀⡀⠀⠌⢃⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⠇⢿⡸⣿⢇⡿⠸⣿⡇
⠀⣀⡈⣱⢿⡏⠙⠋⠘⠙⠛⠊⠋⠙⣑⠊⠀⠀⢇⣀⣁⣀⡀⠈⠠⠠⠠⢸⠀⠀⠀⠀⣾⣿⡇⠀⣿⣿⣿⠀⢸⣿⣷
⠀⠈⠙⠃⠈⣷⠀⠀⠙⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣁⠸⠀⠀⠀⠈⠀⠀⠀⠀⣷⣶⡆⠀⣴⣾⣧⠀⢰⣿⣶
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠇⠀⠿⠀⠿⠀⠸⠃⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠘⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠉⠉⠉⠙⢻⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⣷⣄⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⣁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠆⠀⠀⣠⣤⣤⣤⣤⡄⠀⠀⠸⣿⠄⠀⠀⢀⣿⡇⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠉⠉⠉⠁⠀⠀⠀⠉⠀⢀⣠⣾⡿⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⠿⢋⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠁⠀⢀⣤⣶⣶⣶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⢸⡿⣡⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣰⣿⢋⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⠀⠀⠀⠁⢿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡿⠋⣰⣿⢃⣾⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⣿⡀⠀⠀⠀⠈⠙⠛⠛⠛⣹⣿⠟⠙⠛⣋⣉⣉⣉⠀⠀⣰⣿⣧⣬⣯⣹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣤⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⣰⣿⢛⣿⡟⠀⠀⠈⠉⢉⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣰⣿⢃⣾⣿⣀⣀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣬⣟⢻⣿⡟⠁⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢙⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⣧⠀⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



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

⠏⠀⢈⡈⠀⠈⡙⠀⠘⠋⠀⡄⣀⢀⣀⠀⠘⢀⠈⠠⠇⠀⠔⠈⡐⠀⣈⠉⡀⠀⢰⡄⠀⢺⣦⠾⠛⠊⠓⠘⣢⠀⢦⠀⠈
⢄⠀⠚⠙⣢⣀⡀⠀⠀⠀⠀⡀⠀⠈⠙⡈⠀⠀⠀⠀⢀⠄⢚⠘⠃⣀⠀⠈⢳⢄⡉⢦⣴⠀⠀⠀⠀⠀⠀⠰⢤⣬⡤⢄
⠀⠀⠀⠀⢠⠿⡦⢀⠈⢐⡁⢁⣻⡆⠀⠁⠀⠈⠀⢶⣶⠀⢨⣍⠀⠀⠀⡀⠀⠠⠐⣊⡋⠃⢀⠐⠂⠀⠈⡉⡄⡸⢻⣶⣴
⠀⢐⠈⠁⠀⠀⠀⠀⠀⠙⠉⣂⠁⠐⣃⣄⠲⠀⠀⠀⠊⢠⣾⡶⣤⣠⣶⣁⡌⢁⠈⠉⠀⠛⠀⠀⠀⢀⣦⣡⣈⠑⠈⠉⠘
⠦⢤⣶⣄⠀⠀⠀⠐⢒⢰⡇⠀⠚⠃⠉⠹⣇⠀⢆⡸⢿⠞⠢⣧⠀⠻⠿⠟⠃⠀⠀⠀⢀⡠⠀⠰⠋⢸⣿⠏⠋⢀⣦⠀⠘
⠈⠻⣿⠾⠀⢀⡀⠠⠿⠋⠡⠤⠌⡸⠯⢤⡞⢁⠤⠀⠠⢶⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢾⣛⣿⡟⠀⠀⠙⣩⡀
⣴⡊⣡⣶⣦⡍⣿⠀⢤⠀⢠⢦⣀⠀⠀⠈⠁⠋⠈⠓⡤⠈⠱⠄⣀⠀⡀⠠⠀⠉⣘⠀⢰⡧⡀⣫⢟⠉⠀⠤⣅⠀⠿⠃⠈
⢠⡴⢀⣤⢸⠇⢙⣀⣠⠀⠀⡀⠙⠷⠂⠀⣀⣀⡀⠈⠀⢄⠀⣀⠄⣀⡄⢀⣀⡠⠃⣠⡿⣗⣻⣶⡿⠇⠐⢷⠞⢈⣤⠀⢀
⠀⠑⠙⠁⠀⠀⢄⠀⢆⠀⢀⣄⡰⠆⢀⣀⠒⠒⠺⡆⠁⢈⠀⢷⡒⠁⠀⠙⠋⢠⣴⣿⡇⣿⡏⢻⠀⠀⢀⠸⠁⠈⠉⠀⡹
⠀⠀⠀⠀⠀⠀⢈⣄⢸⡧⢄⠘⡏⡡⠌⣁⡂⠠⡀⠉⠀⠀⠰⢻⡟⢀⠒⣀⣠⡍⣭⡀⠁⠻⠉⠛⡄⠀⠠⣼⣷⡔⣠⠠⠁
⠂⠘⠈⠂⢀⠀⠀⡈⡎⠉⢀⡷⠀⠀⠀⠉⢁⠔⠁⠒⠖⢀⠄⡀⠀⠀⠀⠁⠈⠀⢀⡉⠰⢀⡀⠀⠀⠀⠀⠀⠘⠈⣁⠀⠈
⡄⠀⠈⢿⡟⠛⠉⡽⡆⠐⢬⡀⠀⠀⣠⣴⡆⡈⠄⠠⠖⢊⣭⣴⠦⢀⡀⠀⠀⠀⠘⡟⢀⣀⡄⠀⠲⠂⠀⠀⠀⠔⠀⠑⣦
⡅⠀⠒⠁⠀⣀⡀⢀⡀⠠⣎⣯⣴⣮⡒⢬⣠⣇⡀⢴⠆⠀⣏⣀⣠⣴⣙⣍⠄⢡⣉⡻⠉⠥⢶⠃⠈⠀⠀⠀⠁⠀⢀⡤⠈
⠀⣟⠤⠘⢃⠈⢁⠀⢀⣤⠹⢅⣤⣿⣿⡦⠹⡟⠋⠀⠀⢀⢿⠿⢹⣏⠉⡖⠟⢻⣿⡆⠀⠀⠻⢀⡼⢡⣦⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⡀⣀⢀⢀⣈⠄⡆⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⡗⠋⢁⡴⣊⣽⣥⠴⢧⡅⠂⣀⣤⠶⠖⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⣘⣰⣷⣶⣿⣻⣧⣯⣼⣿⣱⣷⣾⢯⣰⠶⣿⣶⠾⠒⡀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢥⣯⡴⣻⡟⣹⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣵⢧⠬⢾⣡⠗⡃
⠀⠀⠀⠀⠀⠀⠀⠂⠠⢈⣮⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣶⢻⣞⡴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠠⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠟⡯⠬
⠀⠀⠀⠀⠀⠀⡰⢀⡜⢁⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡼⠖⡷⢊⠂
⠀⠀⠀⠀⠀⠀⠀⢘⡰⢊⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣥⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠴⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣷⣿⣷⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣽⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣯⣽⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⡯⢝⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣸⠟⠋⠉⠉⠸⠖⣿⣿⠯⠶⢿⣿⣿⣟⠓⡋⠠⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠊⠁⢀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⠉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢶⣄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣽⠆⠀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⣳⠆⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣿⣿⡿⠁⢠⡴⠖⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠠⠶⣄⠙⢿⣿⠟⠀⠀⠀⠀⠀⠀⢰⣿⣁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⢠⣿⣿⠃⠀⠈⠙⠛⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⠀⣸⣿⠏⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣬⠋⠀⠿⣯⡀⠀⠘⣧⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠙⠛⠁⠀⠀⠒⢸⣷⠀⠀⠈⠻⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠛⠻⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠷⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣠⡴⠟⠋⠁⠀⠀⠀⠀⣰⡟⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠈⣱⠟⠛⢷⡄
⠀⠀⠀⠀⣠⡶⠟⠉⠉⠉⠉⠀⠀⠀⢀⣠⣶⣦⣴⣟⡀⠀⠀⠙⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠋⣿⠀⠘⢳⣾⠋⠀⣠⡞⠻⣦
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠠⣾⠛⠉⠀⠀⠈⣹⡿⠛⠂⠀⠀⠙⠻⢶⣭⣙⣛⣻⣿⡿⠛⠛⠛⢿⡍⠀⠀⢀⣿⠆⠀⠀⠙⠳⢾⡋⠀⣰⡟
⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⡆⠀⠀⣻⣦⣴⠟⠁⠀⠀⢀⣤⣀⣈⣿⠿⠋
⠀⠀⠀⠀⠈⠻⣦⡖⠀⠀⣴⠂⣴⠟⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡾⠃⠉⠁⠀⠀⠀⣠⡾⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡴⠟⠛⠉⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢶⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣴⠾⢶⣄⠀⠀⠀⠀⣿⡷⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⣠⡾⢃⡴⠋⠹⣧⡀⠀⠀⢹⣇⠀⠀⠈⠉⠙⠛⠳⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣠⡾⠋⡠⠋⠀⠀⣰⡟⠻⢦⣄⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⣶⣦⣤⣾⠃
⠀⢀⣴⠏⣠⠞⣡⣜⠳⣾⠋⠀⠀⠀⠙⠷⣿⣍⡛⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⠻⣧
⣰⠟⣡⠞⠉⡞⣡⢘⡶⠻⣦⡀⠀⠀⠀⠀⠀⠈⠛⢦⣬⡿⠛⠻⠶⢶⣤⣤⣤⣿⠁⠀⠀⠀⢹⡇
⠛⢶⣧⣤⣴⠿⠋⠉⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠈⣽⠏⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣦⣀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⡀⠀⠀⠉⡿⠛⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠓⢦⣀⠉⠿⣤⡾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣌⡑⠲⣎⡁⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡙⠢⣼⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣷⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢰⠲⢄⡖⢦⣰⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠒⠊⠓⠋⠘⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⡇⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠘⠇⠀⠸⠇⠀⠀⠀⠀⠰⠆⠸⡇⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠛⠒⠶⢦⣤⡀⢠⡴⠶⠶⠶⠶⠶⠶⠶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⢰⡄⠀⠀⠀⠀⠀⢸⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣿⣹⡇⠀⠀⠀⠀⣤⠀⠀⢸⣇⣈⣀⣀⣀⣀⣀⣀⣸⡷⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣈⣉⣀⣀⣀⣤⡴⠿⣦⣀⡀⢹⡏⢉⡉⢉⡉⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⠉⢉⣉⠉⠉⠀⣀⣀⠀⢹⣧⣼⡇⠘⠁⠘⠇⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⠀⠺⠻⠀⠀⠀⠻⠟⠀⢸⡇⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣿⠀⠀⠀⣀⣄⣀⠀⠀⠀⣸⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠿⣧⡀⠐⠋⠉⠙⠃⢀⣴⠿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⢸⡟⠷⣶⣶⣶⠶⢻⡿⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⢸⣧⡾⣏⠀⣹⡷⣾⡇⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠛⢿⡄⠈⢁⣀⣀⣀⣀⣀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⢸⣏⣉⣉⣉⣽⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣈⣷⣀⣈⣉⣉⣉⣉⣉⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⣶⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⢻⠿
⠀⠀⠀⠀⢀⡀⢀⣄⡀⢀⠈⠧⣌⣉⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣀⢄⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡈⠉⡇⠴⣿⠦⢠⠏⠀⢠⣄
⠀⠀⠀⠀⠘⣇⡹⠿⢃⡼⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⠙⠦⠹⠀⠿⠀⠎⠰⠚⠹⠟⠁
⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⣠⡏⠙⣆
⠀⠀⠀⠀⠀⠀⣽⠿⣷⠀⠋⠉⠀⡴⠋
⠀⠀⠀⠀⠀⠸⣯⡀⠛⠶⠦
⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⡟⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠙⠂⠔⠆⠀⡆⢀⠚⠉⠀⠀⠀⠀⠀⣶⢰⣾⣦⢸⠄⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢀⣤⡄
⠀⠀⠀⠀⣠⣀⠀⠃⠀⠀⠀⠠⠀⠇⢀⣠⡀⠀⠀⠀⠘⢦⣭⣵⠞⠀⢸⣿⣷⠀⠀⠀⠰⣿⣿⠀⠀⠀⠈⣋⣤⡤⢤⠘⢻⣿⡟⠃⡴⢶⣬⣟⠁
⠀⠀⠀⠀⠈⠁⠀⡎⠁⠀⠀⠀⠀⠢⠀⠈⠁⠀⠀⠀⠀⢸⣿⡿⠀⠀⢠⣄⡼⣷⠀⠀⠀⣄⡼⣿⡀⠑⠚⠉⢿⣷⡈⠀⢸⣿⡇⠀⢁⣾⣿⠋⠳⠛
⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠢⠀⢤⣀⠀⠀⠀⠀⠀⣀⣾⠉⢷⡀⠀⠀⣾⣤⣿⠀⠀⠀⣾⣤⣼⠇⠀⠀⢀⡞⠁⠱⠴⠚⠉⠛⠶⠟⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⣧⠀⠀⠈⠁⠀⠀⠀⠀⠙⠋⠉⢠⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠂⡆⣼
⠀⠀⠀⢀⣤⣤⣹⠟⠀⠀⠀⡀⢀⣀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆⢸⡀⣶⣿⡆⣶⠀⣾⣷⡆
⠀⠀⠀⠸⢡⣿⣿⠳⡤⠆⡼⢷⣸⣨⢿⡗⡿⣯⣸⠂⠀⠀⠄⠀⠀⠀⠈⠀⢰⠶⡶⢶⢶⡆⠀⠀⠀⠀⢀⣽⣿⣅⠈⢳⣬⣭⣴⠋⢀⣽⣿⣅
⠀⠰⢦⣤⠟⠻⣇⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣶⣄⠀⠀⠀⠁⠀⠀⠀⠐⠀⢸⣶⣷⣶⣶⠇⠀⠀⠀⠀⣘⣿⣿⣟⣀⣘⣿⣻⣗⣀⣘⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣷⠀⢰⡷⠲⡆⠀⢰⣿⢿⣷
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿⠀⠀⠇⠀⠇⠀⠸⠟⠸⠟

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣧⣲⣯⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢶⣶⣄⠀⠀⠀⠀⣴⡄⢀⠀⣤⡀⡀
⠀⠀⠫⠻⣶⣦⡀⠒⢟⣿⣤⣆⣼⣿⣿⣆⡑⢀⣰⣤⡴⣤⣁⡐⣤⣴⡖⠰⣤
⠀⠀⠘⣷⠞⣿⢗⡛⡌⣹⣿⣿⠿⣯⠈⢹⠞⠿⢻⣴⣟⣿⣿⠐⢿⡿⣻⠃⠘⣣⣰⡆⠶
⠀⢤⡠⢄⡀⢺⠾⣷⣿⢿⣿⣏⢀⡩⡙⢷⠄⠀⠀⠈⠙⠉⠛⠀⢸⡇⢷⣤⡼⢫⡽⢃⠀⣴⠀⣄
⠀⠀⢙⢻⣯⡾⢷⣿⣾⣿⣿⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢿⡀⠱
⠀⠀⣄⠱⣾⠃⢺⣿⣿⠋⠁⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢢
⠀⠀⣼⣄⠀⠉⣾⣿⡇⢼⡦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃
⠀⠀⠘⣿⣶⣷⣿⡟⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⢰⣾⡿⣿⣿⣿⡟⡟⢡⣄⣤⣀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠘⣿⣿⣿⣿⢋⡤⠸⣧⠄⠀⠀⠉⠙⠛⣷⣶⠶⠚⠂⠐⠂⠤⢀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣼⣄
⠀⠀⡈⢛⣿⢿⡇⣾⠗⠀⡿⠂⠀⠀⠀⠀⠀⠈⢷⠶⢦⡂⠀⠀⠀⠀⠠⢠⣄⣤⠾⠋⠀⠀⣠⡾⠈⣠
⠀⠀⠀⢈⣱⣾⡇⢿⢀⣾⠓⠀⠀⠀⠀⠀⠘⣀⣈⢠⣿⣦⣈⣿⠟⢣⡰⠿⢟⢻⣶⣦⣀⠈⢤⠛⠀⡿
⠀⠀⢀⠺⡟⢿⣇⡀⢸⣿⡆⢠⣴⠀⠀⠈⠛⢻⣮⠻⢯⠚⣿⢹⣴⣯⠿⠀⣾⢈⡿⠷⠹⣿⢣⡄⡘
⠀⠀⢺⠒⢿⣾⣿⢡⠈⠻⣇⠀⠀⠀⠀⠀⠠⠜⢻⠀⠀⢹⡏⠙⠁⡇⠀⠀⢩⡆⠰⠑⡆⠚⢇
⠀⠀⠙⠀⢨⣽⣿⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠁⠀⠀⣸⡏⢼⡂⠙⢦⠈⢥⠀⠆
⠀⠀⣤⠀⣾⣿⠳⣷⣄⣀⣼⣏⠀⡤⠀⠀⠀⢀⠢⡄⢰⠃⡐⠀⠀⢀⠀⢠⡟⠙⠾⠹⡆⠀⢣⢈⣆
⠀⠀⠈⣻⡉⢿⠀⢹⣿⡏⢙⡿⠀⢼⠀⠀⠀⡻⡄⠀⢸⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⡆⠘⠀⢀⡤⠡⡄
⠀⠀⠸⠿⣷⣿⠐⢈⣿⣿⣀⠀⠀⣼⡀⠀⡸⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠘⣧⠀⢠⠘⢃⡀
⠀⠀⠶⢀⣿⣟⢠⣼⣿⣿⡏⠀⠀⠸⣀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠐⡏⠀⠂⣸⡇⠀⠑⡀⠘⡇⠀⠇
⠀⠠⢰⡇⣿⣧⠋⢹⣿⣿⡇⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⡄⠀⠳
⠀⢀⣾⣿⣿⣿⠆⠈⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠟⠀⠀⢈⡤⠀⠀⠰
⠀⠸⣿⣿⣿⣿⠀⢐⢾⡟⢿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠈
⠀⠀⣿⣿⣿⡿⠀⠠⠛⡁⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢀⣶⡏⠀⠀⠀⠀⠀⢀
⠀⠀⡿⢻⣿⠗⠰⢷⡄⠐⣀⣤⡅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄⣸⠇⠀⠀⠀⢠⣶⠟⠇
⠀⠀⠛⣼⣏⣤⣤⣤⣼⣶⣿⣿⣟⠦⣀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⣻⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠈⠀⢨⡄
⠀⠀⠚⠛⣿⡿⢻⡿⣷⠶⠿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡤⠄⠀⠀⠀⠀⠀⠀⠂⠻⣤⣄⡀
⠀⠀⠀⠠⠘⣷⢿⣿⡗⠀⠈⠚⢀⠐⣧⢴⣄⣄⠀⠈⠉⠁⠀⠁⡈⢠⣡⣗⠌⠀⠀⠀⠀⠀⠀⠀⣹⣿⠆
⠀⠀⠀⠀⠂⢸⡾⠟⣏⣀⠠⠀⣈⡀⠀⠀⠈⢿⡻⣎⠊⣡⣅⡘⢰⠈⡳⣿⣄⠀⠀⠀⢀⠀⢀⣾⡟⢳⡶⣤
⠀⠀⠀⠀⠀⠋⠀⠀⠸⢿⣿⠲⠁⠙⠚⣿⠻⢦⡗⠸⡇⠀⣿⡇⢠⣤⢠⡿⢏⠂⣤⣄⠎⠈⡳⡈⠢⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣠⣸⢷⣬⣄⢸⡇⠀⠀⢠⠈⠃⢈⢹⠈⠀⠘⠿⣿⠏⢀⡀⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⢀⠍⠞⠘⢃⣀⣄⣀⣀⡶⢀⣈⣠⢰⣤⢰⡄⠚⠿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⢠⡖⠳⠃⠀⣿⠋⠠⠁⠘⠏⠈⠙⢻⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⣠⣄⣤⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤
⢨⠀⣯⡄⣦⡤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⢓⠂
⢘⣠⣶⡉⢱⡶⡀⠀⡄⠲⣆⠀⠀⡠⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠿⠗⠀⠀⠀⠀⠀⢀⡀⢈⠄⠀⠐⢎⠟⡙⢿⡧
⢘⠚⠃⠽⢈⡉⠍⠒⢆⠒⡌⢉⠿⣿⣿⢿⣿⡾⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣀⡀⢀⣀⡈⣿⣶⣶⡠
⠈⠉⠀⠀⡘⠁⠂⠀⡀⠂⠉⠀⣉⡹⣹⢬⣿⡃⠀⠀⣠⣰⣶⣔⣷⣄⣀⣀⢤⣤⢴⣶⠖⢲⣲⣋⣛⣏⣽⣋⣙⠳⠿⠾⠿⠽⠷
⠈⠀⠁⠈⡒⠚⠃⠀⠃⣬⡄⣐⡟⠐⣄⣀⣡⣿⡀⣸⣿⣿⡟⡛⣛⣛⠛⠛⠻⡿⠩⠭⠉⣥⠀⠀⢀⠠⣄⣀⢀⣤⠰⢦⡤⠀⣤
⠸⣷⣄⣸⢷⣤⡆⠀⣠⣿⡧⣴⡾⢿⣶⣞⣿⣿⣿⣿⣿⣷⣆⣷⡶⠻⢶⢶⣶⣿⣷⠲⡆⢹⣷⠄⠿⠀⠹⠟⠸⠗⠀⠘⠟⠀⠟
⢸⣿⢿⣿⣯⣾⡁⠀⣷⣤⣤⣽⣥⣤⣾⣿⣿⣿⣻⢿⣿⣿⣬⣿⣯⣄⣬⢠⣭⡟⣤⢠⣤⠤⣶⣤⣶⠶⢷⣶⣶⣶⠶⢶⣦⢄⣰
⢸⣿⣧⣛⢋⣟⡃⠀⡟⣟⣿⡿⠛⣟⢻⢭⡎⠉⢿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⠀⣯⣇⡳⠀⢿⣿⣯⡀⢨⣽⣋⠿⠀⣴⠛⢨⣟
⢸⢯⣾⣽⣿⣉⡇⢀⣿⣉⢸⣧⣿⣿⣤⢂⢳⡆⣼⡿⢿⣂⡱⣇⢁⠤⣍⣽⣭⣄⣽⣟⡙⠻⠉⣫⠙⣶⠒⠁⣹⣿⣿⣿⣿⡏⡁
⢸⣷⣧⣼⣏⣹⡏⢈⣿⣼⣿⣿⣿⣿⣿⢾⣧⣲⡿⣿⣾⠽⣷⣻⣯⣢⡿⣿⣿⣹⣯⣿⣯⡼⠛⣟⢋⡛⠛⠛⣛⠛⣛⣋⡿⠷⠶
⠈⠟⠛⠛⠚⠛⡃⢘⠛⠛⠿⠛⠻⠿⠛⠻⠛⠛⠳⠟⢿⡿⣿⢿⡿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣿⣿⣷⣧⣤
⠘⠛⠒⠒⠀⠀⠙⠉⠉⠉⠀⠠⠠⠌⠿⠙⠂⣤⣤⣶⠒⠓⠋⠛⠉⠉⠩⠉⠀⠀⣀⣈⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣾⣷⣶⣶⣶⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⠿⠿⠿⠿⠿⠻⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠟⠛⠟⠟⠻⠿⠟⠛⠟⠟⠟⠟⠻⠿⠟⠻⠛⠻⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣾⣿⡿⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣇⠯⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⢿⣿⡄⢠⣾⣿⣦⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣟⣡⣌⣿⣿⡜⠿⠿⠟⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡼⣿⣿⣿⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡏⠀⣠⡀⣤⢤⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠈⣿⣿⣿⣸⣿⣿⣿⣿⠁⠰⠟⠷⠻⠾⠻⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⣿⣿⣿⣿⣧⠀⢀⣾⣇⣿⣹⢾⠶⡗⣟⣻⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣿⣛⣟⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⣸⣿⡟⣮⢻⣿⣧⠀⠀⠀⠈⠁⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢠⣿⣿⠁⢿⡇⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣼⣿⠇⠀⠈⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⣿⡟⠀⠀⠀⠐⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠉⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡤⠃⠩⠘⣫⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣬⣤⠀⠀⢸⠭⠭⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠂⣄⢈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⡀⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⢰⢂⢄⠀⠤⣤⣄⣀⣴⣉⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠣⢙⡆⠻⢦⡀⠘⡴⠊⠉⢳⡄⠀⠀⠈⠺⢺⡗⡀⠀⢨⠻⠋⠙⡟⢢⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠁⢀⣀⣅⣸⡀⠀⠰⣅⡴⠄⠀⠀⠀⠀⠀⠀⢠⠃⡷⠀⠢⠀⠸⡇⣜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣦⡀⠀⢀⣸⣿⡧⠝⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⢧⠤⡤⣤⣼⣤⣤⢤⣤⠀⠀⠀⣠⠤⠴⠶⢾⠀⠉⢀⡰⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠉⠉⠉⠉⠉⠉⢉⡏⠉⠉⠁⠀⠀⢀⣎⣡⡤⢲⣶⠋⠀⣠⣏⠀⠀⠀⠀⠈⠉⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⣀⣤⣶⣿⡿⠋⢴⣿⣿⣾⡿⢋⣩⣷⡄⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⠋⠀⣠⣔⣊⣀⡿⠿⡏⠀⠀⠀⠈⠙⠁⣰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠤⡾⠓⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠅⣼⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⠁⠀⠀⠀⢠⣾⣿⣿⡿⠋⢹⠉⠙⡄⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣾⣿⣟⣫⠤⠤⠔⠒⠚⠉⠉⠀⠀⠀⠀⠀⢀⡠⠾⠟⠛⠛⠒⠈⠉⢇⠀⢩⠑⡄⡜
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢸⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣠⣤⣄⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡾⠋⢛⠿⣿⣿⣿⣿⣿⡉⣉⣙⡛⠻⠿⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎⠀⠂⠉⠻⣿⣿⡇⠀⠀⣀⣉⡉⡚⠈⠑⡄⠀⠀⠀⠀⠀⠀⠸⠠⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡴⠁⠀⠀⠦⠤⡔⠁⢹⣗⣒⣂⣁⣭⣉⡇⠀⢀⠯⠽⠀⣒⣒⣒⣐⠁⢰⠤⠄⠬⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢃⠎⠀⠀⠀⠀⢢⠎⠀⣠⠎⠑⠒⠩⠭⣉⡉⡓⠈⠁⠀⢀⣀⡠⠤⠀⠘⠒⠊⠹⢹⢹⠉⠉⠐
⠀⠀⠀⠘⠮⠶⢌⣁⠎⣤⡀⠀⣀⠔⢁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⡏⠒⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⣳⣤⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠗⠒⠨⣙⢂⢄⡀⠠⡐⣰⣆⡀⠐⠚⠲⠤⢄⡀⠐⠂⠀⠀⢠⠄⠀⠄⠰⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⢐⠳⡴⣿⣤⣽⣛⢿⣶⣽⣿⣿⣿⣤⡔⣒⣻⣄⠵⠒⡀⠐⠲⣉⠀⠈⠂⠈⠀⣀
⠀⠀⠀⠀⠀⠀⢄⢀⡀⠀⣮⣶⣴⡯⣿⣷⣽⡾⣏⣻⣾⣿⣿⣿⣿⣧⠍⢈⣿⢶⣷⣉⣷⢦⡾⣴⣅⠀⢀⡆⠈⠠
⠀⠀⠀⠀⠀⢀⡘⣾⣄⡀⣹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣯⣠⠎⣈⠆⠠⠂
⠀⠀⠀⠀⠀⠀⠸⡟⡁⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢦⣻⣿⣿⣆⢨⢺⡄⠁
⠀⠀⠀⠀⠀⠰⠆⡠⢻⣿⣞⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢁⢾⡀⠒
⠀⠀⠀⠀⠀⠀⠘⡳⣼⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢹⠼⠁
⠀⠀⠀⠀⠀⠀⠈⣧⣾⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠾⣏⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡧⢻⢗⠠⠄
⠀⠀⠀⠀⠀⠀⢀⠄⢧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣯⣿⣨⢨⣄⠃
⠀⠀⠀⠀⠀⠀⠀⢣⢼⣾⣻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⡟⣅⠌⢈
⠀⠀⠀⠀⠀⠀⠀⢲⠰⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣋⠗⡸⡇⠁
⠀⠀⠀⠀⠀⡄⠐⠘⠀⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣿⣯⡞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠔⢉⣷⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣽⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢠⠘⣻⠋⢹⣿⡿⠾⣿⣻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡿⠳⣻⣍⣣⣿⢞⣿⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢟⣉⠛⣉⣟⣦⣟⠟⢙⣾⣩⣿⣿⡿⢫⣿⣟⣿⣮⣿⣿⣾⣧⢷⣿⠙⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠙⠖⠻⢩⣡⡬⠟⠛⠿⢟⠹⠏⠙⢺⠃⠘⠘⢹⠏⠣⣭⡟⣻⡻⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠉⠻⠧⠉⠁⠐⢫⠞⠀⡐⠁⠈⠉⠁⠂⠙⠯⠁⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡠⠞⠓⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠋⠁⢀⣠⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠈⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣦⠀⠀⠀⢻⣿⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⠀⢠⣾⡿⣛⡻⢷⣦⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣸⣿⣿⣿⡆⠀⠀⣿⣿⣿⡟⠀⢸⣿⠘⣇⠿⣸⣿⡀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⣤⠀⠀⢻⣶⣿⡗⣿⡿⢁⣴⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⣷⠀⠀⢸⣿⣿⣿⠈⠁⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣶⣶⣾⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⡿⠿⠇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠉⠙⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠻⠿⠃⢠⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠘⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀
⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⣤⣤⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾
⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠀⠀⠸⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠠⠐⠉⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠡⢀⣀⠴⡵⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢐⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢄⣶⠠⡄⣀⣀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣅⣀⠀⡌⠩⢕⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠦⣌⣉⣩⡀⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢱⡀⠀⠀⠀⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⠀⢃⠀⢠⠟⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠈⣄⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠙⢓⡒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠈⠁⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣽⣧⠀⢢⠀⠀⠀⠀⠈⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢂⢀⡾⠘⡷⢤⠗⠀⠀⡄⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠈⠀⠁⣑⠿⠴⠚⠤⣀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢺⠋⠈⢠⣤⠐⠒⠀⠙⠃⡁⠀⠀⠀⠀⢀⠄⠒⠉⠁⠁⠀⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠉⠀⠂⠇⠀⠀⠀⠀⠀⠈⣦⠀⣠⡶⣥⣦⢄⣸⠇⠐⢾⠻⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⢾⣖⠉⡛⡀⠀⠀⠢⢄⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⢄⠙⣧⠀⠀⠀⠀⠀⠣⣙⠢⣀⡀⠙⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠑⢌⠺⡄⠀⠀⠀⠀⠈⠓⢌⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠁⠀⠀⠀⠀⠀⠀⠀⢀⣨⠤⠇⠀⠀⠀⠶⣀⠳⡈⢢⡀⠀⠀⠀⠀⠈⠂⣸⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢞⠉⠉⠉⠉⠉⠉⠉⠐⣷⠛⠉⢛⡻⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠛⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠰⠂⠀⠐⠀⠐⠐⠀⠀⠐⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠈

⠀⠀⠀⠂⠀⠔⠀⢉⠀⠈⠀⠀⠀⠡⠀⠁⠈⡁⠲⣠⠀⠄⠤⠀⠀⢀⡌⠈⡥⠀⠠⠀⠈⠀⠆⠁⢠⡀⠁⠀⠸⠀⣀⣀⠠⠳⡁⠀⠀⠀⠀⠐⠈⠁
⠀⠲⠁⣀⣤⡤⡢⠞⠂⠀⠄⠀⠀⠀⠀⠀⢀⡤⠖⠢⣀⣠⡄⣤⠊⠠⠀⠀⠀⠀⠀⡀⠈⠀⢳⠄⠫⢤⣁⡤⣤⣀⣔⡋⠑⢪⣠⠐⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠸⠃⠀⠑⣀⠀⣀⣆⡈⢳⠀⢂⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣃⢰⡇⠀⢦⠃⠎⠀⡀⠀⢀⣠⠋⠄⠐
⠀⠱⡀⠀⠀⠠⠀⠈⠀⠀⠡⠀⠘⡦⡀⠀⢹⠢⣀⠞⠀⠀⠈⠀⠀⢸⠀⠀⠀⠐⠀⠈⠀⠉⢹⡏⣠⡏⠀⠄⠀⡁⠀⠸⠁⡠⠀⠙⠎⠉⠁⠀⠰⠄
⠀⠑⠠⢄⡀⣀⣀⠀⠒⠁⠀⠐⠀⡄⠁⡴⢀⡒⠀⡁⠀⢤⣀⣐⣀⠀⠒⣏⠀⠀⠪⠀⠀⠁⠐⠣⢾⡳⢤⣀⣀⡰⣄⢀⠴⠌⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢠⠈⠁⠀⠀⠠⢨⠅⠉⠄⠀⠁⠉⠁⠆⠀⠠⠁⣤⠀⡩⠂⠀⠀⠀⠀⠡⡐⠉⠉⠁⠙⠂⠐⠀⠐⠄⢀⡤
⠀⠀⠀⠀⠀⣆⠂⠀⠀⠀⠰⠦⢄⡈⡀⠀⠀⠈⠒⠀⠀⢀⠀⠀⠀⣀⢆⠀⠩⠖⢫⣋⡈⠀⠀⠤⡆⣄⣁⣠⠀⠀⠀⠀⠀⠀⢠⡖⠈⠀⣀⢀⢀⠆
⠀⠀⠀⠀⠀⡆⠘⠷⣀⢄⡀⣷⠔⢿⣹⠉⠁⠀⠀⠀⠀⣀⢀⣀⠜⠉⢚⠊⡠⣃⢀⡜⣿⣤⡀⠀⢰⡡⣴⠁⠂⠀⠀⠂⠤⣵⠏⡐⢀⠀⠐⡦⣀
⠀⠀⠀⢀⠬⠀⠀⣀⠂⠀⡘⠀⠊⠙⣟⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⣰⡟⢈⠁⡁⠈⠙⡏⠀⠉⠁⠐⠀⠉⠠⠚⠃⠀⠂⣠⠟⢂⠁⠀⠀⠘⠁
⠈⠀⡀⠀⠀⠠⠈⠛⢠⠌⠀⠰⢢⡟⡍⠐⠁⡒⠠⢤⠀⠀⢀⠶⠊⡅⠱⠄⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠣⡀⠀⠐
⣀⡞⠀⣀⣤⢖⡲⠚⠅⢰⣦⠀⠐⠂⠿⠇⠘⣄⠀⠀⠀⠤⠤⠐⠋⠀⠢⣀⠒⡀⠀⠄⠀⠀⠐⣀⠀⠀⠀⡀⠀⠂⠘⠁⠀⠀⢐⡰⠁⢠⠄⢀
⢌⡁⠀⠀⠀⠀⠀⢀⡴⠋⠙⢊⣀⠀⠀⡐⠄⠱⣄⢲⡌⠀⠀⠀⠀⠀⠀⠙⠈⠲⠀⠀⠀⠀⠀⠛⣄⢿⠋⠀⠀⠀⠀⠄⢀⠔⠈⠗⢀⢈⠀⠀⠉⢀
⠂⠠⡰⠀⠀⠀⠀⠋⠀⢀⠡⠐⢉⠓⠀⠗⠰⢿⡄⠚⠀⠤⢄⠀⠀⠃⠀⠀⠀⠖⠀⠉⠉⠓⣸⢯⡡⠞⠐⠷⢴⡧⠄⠈⡄⠀⣠⠿⠀⠈⠉⠒⠎⠉
⠀⠲⢄⡀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠈⠂⠧⠀⠀⡷⠀⠠⠄⠂⢈⡁⠁⠤⠀⠀⠀⠀⠈⠰⠁⠀⠙⠀⠀⠀⠀⠡⡠⠂⣠⠞⠁⠀⣀⣄⡀
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠐⡀⠰⠀⠀⡀⠚⠁⢴⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣵⠨⠰⣇⡒⠱⢀⠉⢄⠰⠀⠀⡀⠈⠀⠀⠙
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠂⡀⠁⠀⠸⣄⠀⢀⡀⠓⡇⠀⠐⠀⠈⠑⠀⠠⢠⡤⠙⠲⠄⣀⠈⢱⣇⠈⠀⠀⢂⠠⠔
⠀⠀⡀⠀⠠⣅⠀⡄⢠⠀⠀⢧⠀⠴⠀⠀⠄⠀⠀⠀⣄⠠⠧⡤⠀⠀⢼⠀⠒⠄⢀⡁⠢⣀⡀⠀⠀⠀⢀⢸⢷⠀⢘⡙⢠⣆⡎⡀⠀⠀⠀⠄
⠀⢀⠀⢀⠊⠀⠀⣀⡏⠀⠀⠀⠀⠀⢀⡐⠀⢀⠀⠀⢨⠐⣇⢁⠀⣀⡬⠂⢀⠴⠀⠁⢀⠀⠀⠀⠀⠀⡬⠰⠾⣗⠙⢀⣠⠃⠹⠧
⠀⠃⠀⠀⠀⡠⠖⠏⠁⠀⠀⠀⡀⠉⠌⠀⠀⠀⠉⠁⠀⠀⠠⡬⠟⠿⣅⠠⠙⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢡⠀⠛⡻⢭⠀⠀⠑⣆⠚⠂⠀⠀⠐
⠀⠘⢀⠀⠘⠂⠀⠒⠀⠀⢠⣄⡀⣤⣬⣖⠀⣀⠀⠀⠀⣶⠖⠓⠉⠁⠺⠙⣲⣄⣤⣀⣤⡀⠣⡀⠹⡀⠈⡠⠘⣿⠟⠉⠒⠶⣢⣴⣍⣥⣤⣈
⣀⡄⠋⠀⠀⠀⠀⠀⠠⡔⠁⠢⠀⠀⠀⢸⡛⣿⣉⣶⡃⢨⣠⠴⠀⠀⠀⠓⠋⠑⠀⠀⠀⠁⠀⢏⡐⢗⠺⠀⢠⡏⠐⠈⢀⠶⠊⣷⠀⢀⠀⠉⠀⢀
⠉⡟⠐⠀⠤⠤⠲⣤⠀⠀⡶⠂⢀⠁⠁⠞⢻⡿⠩⡷⠠⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⠃⠀⠘⢤⣀⣸⡹⠄⠘⢈⠀⡠⢀⠙⡍⠉⠈⠛
⠀⠠⠠⠀⠀⢀⠀⢀⢣⠌⠉⣅⢉⣀⣴⣃⣎⢃⠀⢟⠠⠀⠀⢀⠀⢐⠀⠀⠀⠀⢈⠀⢠⣄⠈⠂⠀⣠⠂⠈⡀⢇⡀⠃⢤⡴⠐⠓⢻⣂⣀⢈
⣦⡈⠂⠐⢀⠤⠆⠊⡨⠂⡠⡗⣠⠨⠁⠁⠜⣹⣆⠙⠄⠀⠀⡀⠰⠃⡀⠀⢀⠀⠀⠈⠁⠁⠉⠲⢫⠁⠀⠀⠀⠁⠠⡢⡀⢠⣲⣤⠚⡩⠿⡀⠙⠆
⠀⢬⣓⠀⣀⣀⠒⣤⡜⠒⠀⠀⠀⠐⠀⢀⡞⠉⠠⢍⡛⢦⡀⣀⠂⣠⡅⠀⠁⡀⠀⠈⠀⠀⠛⠘⠠⢭⡐⢆⣈⣠⠂⢐⣵⠀⢹⠀⠳⠀⠀⠂⠀⠘
⠀⠀⠻⠀⠀⡇⠀⡀⢣⠄⠀⢱⠀⠐⠀⠀⡀⠀⠀⠀⠙⠀⠙⢀⠰⠁⢠⠀⠊⠄⠀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠛⠁⠀⠁⢸⠓⠂⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢛⡛⠀⠿⣿⣽⣷⠀⠀⠀⠄⠄⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠼⣿⣷⡞⠛⠋⠙⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⣀⣀⠠⠾⡏⢸⠎⠹⠛⢁⣠⠄⠖⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠊
⢀⠴⠒⢯⠁⡄⠀⠀⢠⠘⣄⠁⠀⠀⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠛⣿⣄⠀⠀⠀⠠
⠋⠀⡀⠀⢇⣧⡉⠂⢸⠀⢈⣦⢠⡀⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⢰⡶⠀⠀⢻⣼⡇
⠀⠀⠘⢄⠸⡏⡇⠀⢸⠳⡎⣿⠀⡂⢱⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡴⣠⠀⠈⠈⠀⣺⠏⢁⡇
⠀⠀⠀⠈⢳⠃⢻⠀⠈⣼⣱⡇⢠⠃⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠡⠆⠋
⠀⠀⠀⠀⢸⠀⠨⣇⢀⣷⠟⠀⠈⡠⠄⠘⠀⠉⠁⣀⢦⠖⠒⣶⠾⡷⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠐⠀⠰⠀⠀⠠
⠀⠀⠄⢂⣸⡀⠀⡽⢈⡀⣨⠔⠉⡠⠴⡂⢽⡽⠋⠠⣮⠣⣰⢯⡄⣷⠀⠀⢑⡖⠀⢸⣿⣶⢦⡄⠀⠀⠀⠀⡀⠂
⠀⠔⠸⠁⠂⠙⠚⠓⠋⠴⠧⠀⠊⢄⣌⢴⡟⠀⠀⢀⣺⣶⣿⣟⠐⢹⡣⡀⢸⡏⠀⢸⣯⣿⡇⣿⡄⠀⠀⠀⠀⠀⢀
⡀⠀⠀⠀⠀⠀⠀⡰⢡⣀⠀⠀⠈⠴⠈⡾⠁⠀⠀⠀⢹⣿⠃⣿⠀⢘⣇⠈⢻⠃⠀⢸⣿⣿⣿⣿⣷⡀
⠈⠑⠢⠤⢄⣁⢰⡇⣤⠉⣆⢣⠀⠀⠸⡁⠲⢴⡄⣆⢸⡇⢠⢿⣧⡨⣿⠀⢠⠀⠀⢸⣹⣿⣿⣿⡟⣷⠀⠘⠀⠀⠐
⠀⠀⠀⠀⡸⠀⢈⡵⡇⢠⠇⠐⡄⠀⠀⠻⢿⣶⣌⣻⣿⠀⠀⢸⣿⣏⣿⠐⢆⠀⠀⡏⣺⢏⣿⡿⢞⣿⡲⡄⠄
⠀⠀⠀⡴⢡⢖⠏⠀⡇⢸⡆⠀⣸⡄⣠⣶⣿⣷⣿⣿⣉⣀⢀⣊⣝⢟⡿⠀⠀⢳⡜⣘⡁⢺⣿⡟⢉⡑⠒⠽⣆⠀⠁
⠀⡠⠊⠀⠀⡎⠀⠀⢇⠈⡇⠀⣿⣿⠟⣫⡿⠗⠻⠋⢛⠛⢟⠟⢹⠟⠁⠀⠀⠀⠀⠀⠌⠋⡃⢋⣠⠀⡀⠀⢹⢿⡉
⠊⣧⠀⠀⢸⠃⠀⠀⠸⡄⢻⡀⠻⣟⡾⠉⠠⠂⠀⠈⠜⠇⠀⢰⡏⠀⡀⠀⠀⡀⠀⣀⡠⡎⠁⠡⠠⠞⣠⠆⢈⠏⠁
⣘⠈⢧⠀⡼⠁⠀⠀⠀⢳⢄⡉⠂⠹⣷⣶⣦⣤⣄⣄⣀⣨⣂⣸⡇⡠⠛⠉⠉⠉⠁⠁⠀⠈⠀⠀⠀⠚⠑⠋⠁
⠃⠁⠈⠳⡇⠀⠀⠀⠀⠘⣆⣯⣱⠦⠤⠛⠛⠋⠉⠁⢀⣤⣼⡇
⡰⠀⠀⠀⢱⠀⢠⣖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠤⢄⡀
⠀⠀⠀⠀⡇⠀⠘⢦⣙⠲⠤⣀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠀⠠⡄⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⣷⠀⠀⠀⢻⡑⠢⢄⡉⠒⠤⣀⠀⠀⠀⠀⠀⠓⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀⡀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡈⠁⢨⣉⣅⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠤⠩⠥⠉⠰⡆⠠⠠⠆⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⣁⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣷⣘⣋⣙⣝⣛⠛⠁⡀⢀⢀⡖⠶⠲⡲⠒⠒⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡉⣭⢩⣍⣩⣤⣻⡛⢛⠛⣛⠛⠛⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠄⠠⡤⠤⠤⠶⠢⠿⠼⠿⠿⠿⠼⠟⠨⠭⠍⠁
⠀⠀⠀⠠⠬⠭⠭⠬⡭⠭⠸⢿⠾⠾⠰⠷⠷⢷⠿⠿⠿⢿⠏⠿⠿⠷⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣾⣿⣲⢾⣾⢺⡶⡗⡷⡶⣾⢠⣴⣴⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣠⣤⣰⣀⣀⣤⣒⣆⣄⣰⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣚⣛⡛⡋⡛⣛⣛⣛⣐⢒⢲⠆⡄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠭⢭⠘⢛⠛⠛⠿⠛⠟⠘⠛⠁⢟⢛⢛⠛⠛⣈⠉⠉⠭⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠿⢛⠿⣛⣋⣛⢛⣻⣛⣛⣛⣘⣛⣛⡛⡛⡛⣛⢛⣈⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣼⣼⠭⡦⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠒⠂⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠅⠾⠶⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣛⣛⣙⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⠀⢒⡒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠛⠟⣋⣭⣧⣤⣦⣶⣶⣷⣾⣭⣽⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢛⣯⣴⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠻⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠀⠀⠀⠀⠀⢀⡀⢄⡀
⠀⠀⠀⠀⠀⢪⣀⣀⣈⣲⡀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣔⣉⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⢠⠋⠉⣩⠷⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣋⣡⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣷⠀⠸⡇⠀⠀⠀⠺⣍⡉⠙
⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢠⡞⠉⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⣿⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⣘⡧⠀⠀⠀⠀⠀⠀⣾⣁⣀⡈⣷⠀⢸⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠘⣷⠶⠶⠚⠛⠻⠏⢹⠇⠀⠀⠀⠀⠀⠀⠸⣄⣉⣩⠟⠀⢸⣧⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠙⢦⣀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉⠁⠀⠀⢸⣷⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠻⢿⡿⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠞⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠞⠋⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣬⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⣃⠹⢿⣿⣿⡏⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⢀⡟⠉⣻⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠙⠙⠿⡿⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡶⠛⠓⢲⡇⠀⡸⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣛⡿⠿⢿⣶⣤⢤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣇⠀⠤⣾⢧⣴⠁⢰⠏
⠀⠀⠀⣀⡴⠶⠛⠛⠛⠉⣠⡶⠋⠁⠀⠀⠀⠈⣧⣄⣀⣙⣷⣀⠀⠀⠀⠀⠀⠀⣠⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⢁⣀⠨⠛⠁
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⠀⠙⢛⠿⠶⠶⠾⠟⢹⣄⣽⣧⡄⠀⠀⠠⠄⣠⡴⢋⣤⡾⠃⠠
⠀⠀⠙⣶⠃⠀⡀⠀⢀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠻⣷⣶⣶⣶⣿⣯⠾⠛⠁
⠀⠀⠀⠘⠷⣾⠁⢘⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠖⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣦⠀⠀⠀⠀⠀⠀⢰⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⡾⢋⡔⠙⣧⠀⠀⠀⠀⠀⣿⡯⠛⠛⠻⠶⠶⣤⣤⣀⣀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⢀⣴⠟⣱⠋⢀⣴⢻⣆⠀⠀⢀⣠⡿⣶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢻⡟
⠀⠀⠀⣠⡾⢃⠜⠁⣼⣿⢷⡎⢻⡄⢀⣿⣏⠀⠙⢷⣄⣀⠀⠀⠀⠀⠐⠶⢦⣴⣟
⠀⢀⣼⠏⡰⣏⠀⢀⡿⠃⠈⢷⡀⠙⢋⣿⠟⢦⡴⠛⠉⠙⠻⢶⣤⣀⣀⣠⣴⣿⣷⣤⣀⡀
⣠⡿⢡⠞⠁⣸⣷⠟⠁⠀⠀⠈⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠙⠻⢦⡌⠙⣷
⠛⠷⠿⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⢲⣾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⠛⢿⠿⠟⠉⠛⢛⣷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣉⣓⡒⠶⠒⠦⠤⣤⣤⣏⣀⣀⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠶⢶⣶⣦⣬⣭⣍⣹⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣀⣀⣀⠀⣀⣤⠴⣤⣤⣠⣄⡐⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡁⠐⢨⢁⠀⢈⡽⠟⡩⠶⢧⣀⡘⡂⠬⠶⠈⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡳⠺⠒⢒⢶⠯⢷⣥⣄⣀⢰⣆⡘⢛⣶⣄⣤⣔⣣⠀⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠡⣤⢖⣁⠴⢿⣾⣿⡫⠭⠿⣧⡶⣋⣉⣉⣟⣙⣽⣷⠿⠺⡍
⠀⠀⠀⠀⠀⡀⠀⣘⣵⣰⢯⠏⠉⠙⡳⢺⣟⠽⠟⢟⣻⣟⡏⠓⢻⠷⢤⣉⣿⠟⠉⠀⣒⠲⠂
⠀⠀⠀⠀⠈⠀⠠⣃⠞⠀⠎⠀⠀⠁⢇⡫⠩⣋⡉⢘⣉⣘⣥⠴⠒⢒⣣⣾⣷⡒⠒⠃⠒⠠
⠀⠀⠀⠀⠀⠀⠊⠵⠀⣄⠀⢒⠎⢤⣌⣹⣶⣿⠿⣫⣝⣁⣾⣶⡚⠛⠉⠐⠁⠀⠈⠐⠦⢀⢠⠂
⠀⠀⠀⠂⠀⠀⠈⢆⠀⠐⣤⣯⣴⢥⠴⣤⠾⣿⣞⠝⠋⠉⠀⢹⣖⣾⣳⣧⣶⣭⠤⠶⢋⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠞⠗⠢⣎⣬⣅⣊⣵⠷⠶⠖⡶⢟⣿⢛⣹⣏⣍⣻⣾⡾⠖⠛⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠉⠨⢠⣠⢈⡀⣑⠤⡐⢳⣎⣿⠯⢴⣾⡭⢻⣤⠂⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡧⠀⠀⠈⢩⠙⢯⣼⣋⣿⢞⠿⠾⠛⠛⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃⠠⠤⢐⠟⠛⠉⠁⠀⠀⠁⠐⠂⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⣀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣶⡾⣿⣿⣿⣿⣷⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣯⡿⣶⠋⠋⠈⠁⠻⠣⡟⣿⣿⣿⣿⣿⣿⣿⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠐⣿⠼⣿⣿⣿⣿⡟⠋⡟⠁⠟⠀⠀⠀⠀⣊⣸⡇⡟⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢰⣿⡀⠀⢁⡇⠉⠘⢾⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣁⢀⣨⣸⣟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡟⠙⠀⠈⠀⠀⠀⠀⠙⠘⣿⡇⠀⠀⠀⠀⠎⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢠⡄⠠⠐⠉⢁⡤⠤⠀⠈⠙⠻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⠀⢠⡀⢀⣠⣄⣀⣤⣄⠀⠀⠄⠀⢠⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢫⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠸⠈⣿⣿⣿⣿⡿⠇⠀⢠⡤⡤⡸⠃⠀⠀⠀⠀⢀⣄⣤⣤⣦⣿⣅⣿⢠⠀⢻⣿⣷
⠀⠀⠀⠀⠀⢸⣿⠦⠰⢠⣿⣿⣿⡋⠀⠀⠀⠘⢻⣷⠇⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⢻⣿⣿⡄⠈⣿⣟
⠀⠀⠀⠀⠀⢸⣿⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⣸⣿⣄⠀⠀⣠⣶⠿⣷⣄⣠⡤⠄⠀⣸⣿⣿⣿⡀⢿⣿
⠀⠀⠀⠀⠀⢸⢇⣴⣿⣿⣿⣿⣿⠉⠀⡀⠀⠀⢻⠃⣁⡀⠀⠾⠋⠈⣽⡿⠟⠀⠀⠀⣿⣿⣿⣿⣷⣿⡿
⠀⠀⠀⢴⣤⣼⣿⣛⣿⣿⣿⣿⣿⣶⣶⡷⠶⠶⠞⠛⢓⣦⣤⣤⣴⣦⣤⣧⣄⣀⣀⠀⠾⣿⣿⣿⣿⢱⡇
⠀⠀⠀⠙⠛⠋⠭⣭⣿⣿⣷⣤⣤⣤⣼⣿⣶⣴⣿⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣷⣽⣶⣾⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠘⣿⢫⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣼⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠁⠹⠛⢻⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠿⠻⠿⠛⠉⠹⠋⠉⠉⠋⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⣿⣿⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠉⠁

⠁⢀⠠⠀⢡⣠⢀⢀⠀⠤⠦⣀⣁⠀⠀⠀⠀⠀⠉⢀⢠⣄⠀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⢂⠀⠂⠀⠄
⠀⠂⠛⠃⡔⠀⠈⣸⠀⠠⠀⠀⠀⠀⠀⠀⡌⠓⠶⢬⠂⠋⠀⠀⠂⠀⠠⠀⠀⠀⢀⠂⢼⢇⣄⣾⠀⡀⢊⡠⣾⣀⢀⡀
⠀⠀⠀⣀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠘⠃⠀⠀⠀⠣⠀⠺⠃⠀⠀⠶⠬⡀⢂⠉⠁⠀⠠⡿⠀⠁⢸⣿⠃
⠘⠰⢢⠈⠀⠀⠘⠃⠀⣀⣀⣴⠇⠀⠀⠀⢀⠀⠀⡄⠀⣴⢓⣂⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠔⠒⢀⠀⠟⠢⠄⠈⠟
⠀⠀⠀⠒⡀⠂⠀⠐⡀⠉⠋⠁⠀⣸⣧⡤⠄⠁⠀⠀⣸⢫⣦⣏⠩⠀⢀⠀⠀⠁⠀⠐⠂⠀⢀⠀⢄⠀⠀⠀⠉⠀⠀⠠
⠒⡀⠀⢀⣀⣠⡀⠀⠐⠀⠀⠀⠊⠉⢛⠁⠙⡔⠲⡄⠋⠀⠉⠛⠃⠀⠠⠀⠀⠀⢐⠀⠀⠀⠈⠂⠈⠐⠩⠰⠃⠓⠂⢠
⡞⣟⣿⠁⠈⠛⠃⠀⢀⠦⢐⠀⡀⠰⣈⣀⣠⠇⠘⢤⡤⢲⠄⠀⣀⠀⠄⢠⡉⣆⢸⡆⠀⠀⠀⠗⠰⣰⣶⣦⠀⢀⣄⣀⠁
⠛⠛⠃⢰⣷⣆⠀⠀⢀⠀⠈⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢸⠀⢀⡈⢷⠀⠀⢷⡟⡌⢻⠀⠅⢀⠀⢠⣿⠻⣟⠠⣾⣿⣿
⣠⣄⡠⠛⠉⠉⠀⠐⢿⠃⠀⠀⡀⢠⣶⣿⣤⣤⣠⣀⣔⠊⠀⠀⠀⠘⣇⠐⠀⢡⣠⣤⡄⠀⠀⠀⢸⣿⣿⠟⢸⣿⣭⣿
⢿⣿⠀⠀⠀⢀⡀⢀⣤⠀⠀⠀⠀⣿⠋⡛⣛⡻⠿⠿⣿⡇⠀⠀⠀⠄⠋⠀⠄⠀⢿⠟⠃⠀⠀⠁⠀⠉⠉⠀⠀⣿⣿⠃
⣤⠁⠀⠀⠀⠿⢿⠓⠤⣀⠁⠀⠘⠿⠤⣄⣈⣁⠀⠀⣼⢈⠐⠴⠀⢀⣀⠀⠀⠀⠀⠓⠀⡔⡒⢍⡉⠐⠂
⠁⠀⠀⠀⢀⣀⠁⢀⠰⠔⠄⢠⡀⠀⠀⢀⢀⡈⠙⠛⠑⣭⣦⣾⣦⣶⣤⣤⠀⡂⢤⡐⢀⠁⣀⠋⢈⡂⡸⠃⠒⠀⠤
⠀⢀⡄⠀⠀⠉⠀⠀⠀⠀⠀⠔⠀⠐⡂⠈⠻⠓⠄⣀⡑⠄⠙⠛⠿⣧⣭⣿⣿⣷⣴⡛⠀⡬⡛⠒⠐⠂⠒⠐⠙⠚⠢⠐⠁
⠀⠀⠀⡈⠀⠄⠐⢐⡐⠂⣀⠤⠤⠴⠥⠤⣄⠀⠀⠻⠗⠐⠀⠀⠀⠀⠈⠉⠉⣩⡉⠁⢀⠀⠈⠀⠀⠀⠀⠀⠀⠔⡢⠀⠛
⠀⠀⠀⠉⡀⢆⠀⢋⠁⠘⢀⣀⠀⢀⣤⡄⠈⣷⡐⠈⠐⠁⠀⠀⠀⠀⠀⠀⢨⣀⠞⢀⠀⠙⢀⠀⣀⣁⠀⡘⢃⣀⡡⠼⣳
⠀⠀⠐⡆⠘⠀⠲⠂⠀⢸⠘⠟⠀⠈⠛⠁⢠⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠛⠣⡏⠠⡈⢀⡅⠸⠍⡀⠈⢺⠃⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⡆⡠⠠⠠⠠⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠁⠀⢀⠀⠰⠀⠉⠀⠠⠄⡀⠄⣶⣿⡷⢿

⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⢤
⠀⢠⣿⡟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⣀⠈⣇
⠀⠸⢿⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣇⠀⢸⠃⠠⡃
⢠⡀⡸⠂⠾⡁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠹⠀⠀⠐⠒⠒⠒⠶⠶⠶⣿⠆⠀⠐⢷⠒⠒⠒⠒⠚⠓⠀⠙⣤⣘⣄⠜
⠈⢻⣅⠀⠀⠈⢢⣼⠋⠀⢀⣀⠤⠤⣤⣤⠋⠑⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡘⠁⠀⠈⡄
⠀⢸⠙⣦⠈⢳⣞⠉⠒⢊⡥⠒⠒⠚⠀⣿⡄⠀⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡄⠀⢠⢠
⠀⢸⠀⠈⣷⡏⡇⠉⠉⠁⠀⠀⠀⠀⠀⡏⡇⢰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢸⢸
⠀⠀⣀⡾⠁⠹⣇⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⢸⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠀⠈⣼
⠀⣰⣿⠀⣀⣀⡟⢧⡀⠀⠀⠀⠀⠀⢸⠀⢳⢸⠆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡄⡃
⠸⠋⡇⠀⠀⠀⢰⠈⠳⠀⠀⠀⠀⠀⢸⠓⣞⢉⡦⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠒⠏⢱
⠀⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⠏⢸
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡌
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄
⠀⠀⠸⠤⣤⣤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠯⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠤⠤⢤⡇
⠀⠀⠀⠘⠧⠤⠤⠬⠃⠀⠀⠀⠀⠀⠀⠰⣉⣉⣉⣀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣤⣄⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣤⣼⡿⠿⠾⠿⠛⠛⠿⠷⠿⢿⣧⣤⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡾⠟⠋⠉⠀⣤⡤⢶⣄⠀⣶⡆⣶⡦⠀⣄⡉⠙⠻⢷⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠉⠀⣴⣦⣄⠀⣹⣧⡼⠟⠰⠿⠍⣿⡇⣰⡿⠉⣷⡄⠀⠉⠻⣿⣇
⠀⠀⠀⠀⠀⢰⣶⣾⠋⠀⠀⠀⠀⣿⠛⠛⣉⣤⡴⠶⢖⠒⠒⡲⠶⢦⣬⣙⠛⠋⠀⠀⢀⡀⠀⠙⣷⣶⡆
⠀⠀⠀⠀⠀⣼⠟⠁⠀⣲⣦⠀⠀⣡⡶⣛⠍⠐⠈⠁⠀⠀⠀⠀⠈⠁⠂⠩⣛⢶⣄⠀⠻⠓⠀⠀⠈⢻⣧
⠀⠀⠀⣶⣾⠏⠀⣀⠀⠀⠁⣠⠞⡡⠊⠀⠀⠀⠀⠀⡷⠀⠀⡀⠀⠀⠀⠀⠀⠑⢌⠳⣄⠀⣄⣀⣤⡀⠹⣷⣷
⠀⠀⠀⣼⡏⢀⡞⠛⣷⠀⣼⢋⠊⠀⠀⠀⢀⠀⠀⢰⠁⠃⡐⠀⡀⠤⠒⡚⠀⠀⠀⠑⡝⣧⠁⣵⡿⠁⠀⢹⣧
⠀⢠⣶⡿⠀⠘⠻⢷⠋⣼⢣⠁⠀⠀⠀⢄⠈⠢⠀⡌⠀⣀⡤⠢⡀⢀⠀⠀⢀⡀⠀⠀⠈⡜⣧⠘⣁⣠⣤⠀⢿⣶⡄
⠀⠈⣻⡇⢰⣷⣶⣶⢰⡏⠆⠀⠠⢀⣀⡈⠑⠀⠡⠔⠊⠁⠀⠀⠈⢄⠀⠄⠊⠀⠀⠀⠀⠰⢹⡆⢿⣉⣹⡄⢸⣟⠁
⠀⣤⣿⠃⢰⣶⣧⡆⢸⠑⠀⠀⠀⠀⠀⠉⠀⠘⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠑⢂⡤⠀⠀⠀⠊⡇⢈⡛⠋⠀⠘⣿⣄
⠀⠙⣿⡆⠀⣠⣬⡁⢸⡰⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⡠⢂⠀⠀⢀⠀⣇⠀⠉⢁⡀⠀⠀⠀⢄⡇⠸⢻⠿⠇⢠⣿⠋
⠀⢀⣽⡇⠘⣏⣉⣿⠸⣇⠆⠀⠀⠀⠀⢀⠀⢸⠀⠀⣐⡀⠑⠐⡁⠀⡇⠀⠀⠀⠘⠀⠀⠐⣸⠇⠿⠿⢿⠃⢸⣿⡀
⠀⠘⠿⣷⠀⠛⠋⢙⡄⢻⡜⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠊⠀⠀⡏⠐⠀⠀⠀⠀⢀⢣⡟⣰⢷⣦⡄⠀⣾⠿⠃
⠀⠀⠀⢻⣇⠀⢀⣾⢟⢀⢻⣌⢄⠀⠀⠀⠀⠀⠤⢤⣀⣀⣀⡀⠀⠀⠃⠀⠀⠀⠀⡠⣡⡟⠀⢿⣤⡼⠁⣸⡏
⠀⠀⠀⠿⢿⣆⠈⠋⠉⠙⠀⠙⢦⡑⢄⠀⠀⠀⠀⠀⠀⡈⠈⠉⠉⠉⠀⠀⠀⡠⢀⡴⠋⢀⠀⠀⠉⠀⣰⡿⠿
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⢠⣦⠀⠙⠷⣬⣂⠄⢀⡀⠀⠁⠀⠀⢀⠀⠄⣀⣥⠾⠋⠀⠀⠻⠯⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠘⠿⢿⣄⠀⠈⠉⠀⠀⣠⡤⣍⡛⠳⠶⠶⠤⠤⠶⠶⠞⠛⣩⣤⡨⡏⠀⠀⠀⠀⣰⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⠘⢿⣀⣾⠏⢸⣿⣐⣶⠂⣴⡏⢻⣏⠈⠙⠻⠟⠀⣀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢷⣦⣄⣈⠉⠀⠚⠿⠸⠿⠀⠙⠳⠚⠛⠀⣀⣠⣴⡾⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠙⢻⣿⡶⢶⣶⣶⣶⣶⡶⢶⣿⡟⠋⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠋⠀⠀⠈⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠉⠛⠓⣀⣛⡛⠿⢿⣿⣿⡿⠿⢛⣃⣤⣚⣋⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⣤⣶⣿⣿⡿⠿⣒⣤⣤⣐⠻⢿⣿⣿⣿⣿⣿⣿⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠃⢠⣿⣿⠟⣋⡥⢶⣿⣿⣿⣿⣿⣿⣶⣮⣝⡻⢿⣿⡁⠘⠉⣠⣤⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢘⣩⣶⣿⣿⣿⣮⠙⠿⣿⣿⣿⣿⣿⣿⡿⠟⣲⣬⡃⠀⠀⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡴⠋⠸⣿⣿⣿⣿⡿⢋⣾⣿⣶⣬⣭⣭⡉⢴⣶⣿⣿⣿⠇⠈⠳⣄⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣨⣭⡍⣴⡞⡻⠿⢿⣿⣿⡿⣛⡛⢷⣦⢉⣭⣥⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠆⠸⣿⣿⡇⣿⡔⢧⣻⢆⣿⣿⠸⣥⢝⣆⣿⢸⣿⣿⡇⠐⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣿⣿⣶⣶⣿⣿⣿⣷⣶⣿⣿⣿⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣧⣤⡄⠀⠘⢿⣷⣿⣶⣵⣾⣷⣤⣾⣿⠃⠀⠀⠀⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠃⠀⠀⠀⠀⠀⣰⣷⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣐⢾⣿⣿⣿⣿⣿⣿⡷⢂⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⢿⡿⠿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⡿⣿⣿⣿⣶⣶⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⠟⡛⢋⣥⣬⣵⣷⣦⣴⣦⡙⣋⣛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣍⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢈⠀⠈⠲⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠉⠉⠈⠻⣿⣿⣿⣿⣿⡄⠀⠀⢀⡔⠉⠀⢈⡆
⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣴⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⢰⠋⠀⣰⠖⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⢠⡀⠀⠈⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣶⠀⢿⣿⣿⡇⠀⠀⠀⠐⠳⣈⠉⢳
⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⢀⣀⣉⡶⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⢈⡏⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⣼⣋⡀⠙⣯⡄⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠸⣧⠴⠶⠒⠛⠿⠉⡿⠀⠀⠀⠀⠀⠀⢫⡉⠙⣛⠃⠀⢿⡁⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣧⠀⠀⠀⠀⠹⣄⡀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣦⣾⣃⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠛⠛⠋⠹⡆⠀⠀⠀⠀⠀⠀⣠⣼⡶⠾⣇⡑⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣰⢿⣿⣿⣷⣾⠃⠀⠀⠀⠀⢠⡾⠃⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠧⠤⣝⣿⣿⡏⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣼⡁⣸⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡄⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⢀⣴⠟⠀⠀⠀⠀⢸⠁⡀⢈⣿⠀⡸⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣹⠿⢷⡟⠙⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠘⣇⠀⠙⠋⠛⣧⠔⠃
⠀⠀⠀⠀⢀⡄⠀⢤⣀⣀⣀⣰⠃⢰⠃⠀⢠⡟⠛⣾⡟⣿⠶⢦⣤⣀⣠⡤⡶⣿⢷⣄⠀⠀⠀⠀⠀⠀⣰⠋⢀⡤⠀⠊⠁
⠀⠀⠀⠀⡌⠀⡽⠋⡀⠀⠈⠁⠀⠘⠒⠦⣼⡗⢀⣿⠇⡗⠀⠲⣟⣨⡷⠂⠀⢻⣾⣿⣦⣄⣀⣠⣴⣋⡥⠞⠉
⠀⠀⠀⢰⠁⠀⡿⠃⢁⡀⢀⡴⠞⠳⣤⣀⣼⣧⣼⡟⣸⠃⠀⣼⠋⢉⡗⠀⠀⢸⣿⡇⠈⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⢳⡔⠉⣰⠏⠀⠀⠁⠘⠭⣝⣿⠿⠛⠁⠀⣸⠃⠀⠀⣳⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣞⠀⢠⡏⠀⠀⠀⠀⠀⢰⣩⡿⡀⠀⠀⠀⢻⡄⠀⠀⡼⠀⠀⢸⡿⠁
⠀⢠⡄⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⣮⣼⣏⠛⠳⠶⢦⣤⣼⣟⣋⡀⠀⠀⢸⡇
⠀⠐⠀⠈⢡⣦⣀⡀⠀⠀⠀⠀⠀⠀⢰⣵⣿⣤⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢳⡿
⠀⠈⠀⣴⠟⡡⠋⢱⣶⣄⡀⠀⠀⠐⡞⣾⠇⠙⢷⣄⣄⠀⠀⠀⠀⠒⠦⢤⣿⠁
⠀⣰⡾⢋⠼⠅⠀⣸⠟⠀⠹⣇⠂⣶⡿⠟⠶⠖⠋⠈⠙⠻⠶⣤⣄⣠⣴⣾⣿⠦⣤⣀
⣴⡟⡴⠋⢀⣼⠞⠁⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⢳⡆⠉⣿
⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⡾⠃
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣡⣿⣥⣤⣤⣤⣀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣀⣀⣉⠙⠛⠃⠀⠈⡽⠛⠳⣤⡀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣾⣥⣭⣍⣍⣛⣓⣚⠳⠶⠤⠬⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⢸⡟⠀⠀⠀⠀⢀⢀⣤⣴⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⠀⣢⠀⢸⠀⢸⣷⡄⠀⠀⠀⣿⣿⠁⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠠⣿⢿⠿⠃⢘⣻⡷⢸⠀⢸⣿⣧⣄⠀⠀⠉⠛⠄⠐⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡸⣾⣦⠄⠌⡿⠁⢸⠀⢸⣿⣿⣿⡀⠀⣀⣠⠒⣀⡐⡤
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢁⣀⣆⣀⠀⠀⠘⠀⣿⣿⣿⣿⣧⣰⡿⠆⠈⠙⠉⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣶⣶⣶⣶⡶⢱⣾⣿⣿⣿⣿⡟⠉⠿⠆⢤⠀⢀⣀⠯⠉⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⡇⢸⡿⠋⠩⠉⠩⠤⠀⠀⠄⠩⠤⠬⠍⠃⠸⠿⠷⠶⠶⠾⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠐⠘⢛⢛⣛⣛⣛⣋⢸⠀⢰⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠀⢠⣦⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠙⡟⢻⣯⣞⠀⢸⡇⠀⠀⠀⠀⢠⢶⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⢸⠀⢸⣿⡟⣠⣠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠇⢸⣿⣟⠀⠘⠇⠀⠀⠀⠀⠸⣿⡟⠀⠇⠀⠀⠀⠀⣷⣿⣷⣀⣿⢸⠀⢸⠏⢸⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣛⣛⠃⠀⠀⠀⠀⠀⠀⣽⣷⣤⠀⠀⠀⠀⠀⠙⠻⣿⠟⠁⠈⠀⠘⠀⠀⣙⣷⣎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⣛⣋⣙⣙⣛⠆⠀⠀⡰⣶⣛⣛⠓⠻⠀⠐⠀⢀⣤⠴⡿⣿⡚⠀⢄⠀⠀⢴⠿⠯⠋⠁⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠉⠈⠀⠀⠀⠀⠀⠿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠻⠿⠛⠛⠋⠈⠀⠀⠈⠚⠿⠟⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠔⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⢠⡄⠀⠀⢠⠀⢠⠀⠀⠠⠀⠠⠀⠀⠤⠤⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠠⠠⠠⠀⠀⠀⠄⠠⠀⠄⠀⠀⠠⠄⠤⠠⠀⠤⠠⠀⠀⠀⠠⠀⠀⠄⠀⠠⠄⠀⠶⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠆⠤⠄⠀⠶⠠⠄⠤⠤⠤⠀⠄⠀⠠⠤⠀⠀⠤⠤⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠘⠀⠀⡀⠤⣀⠠⠤⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣀⡈⠳⣤⣄⡀⠀⠦⡄⠈⠀⠹⠒⠢⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠁⣠⣨⠆⠀⢠⠋⠀⠀⠰⣤⡇⡀⠐⢄⠀⠤⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠑⠂⡤⢀⠊⠀⠀⢛⠀⠀⠀⣸⢣⠀⠉⠀⠈⡡⢔⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⣉⡀⠀⠪⠀⠒⢀⠁⠈⢉⡀⠶⠊⡀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠂⠀⠀⠀⠀⠀⠁⠀⠈⢉⠒⠀⢤⡀⠀⠈⣱⡔⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⠀⢰⡆⠀⠀⠀⠘⡧⠀⠀⠰⠁⠀⣤⡟⠐⡄⢒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠃⠀⢀⠀⠀⠈⠲⢄⣄⠟⠙⢂⠙⢙⡣⣤⠯⠇⢀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠗⡙⠀⠀⠀⡠⠀⢈⢨⠱⠚⢉⣝⣯⣄⣉⡹⠽⠁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⠈⠀⠀⠈⠀⠀⠀⡀⠀⢀⡎⠚⠉⠀⢹⡷⣅⣱⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⢄⡀⠀⠠⢟⠶⠛⡁⢀⣠⡴⠉⣠⡌⣫⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠉⠢⢭⣠⡀⠀⠓⠤⠄⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷⣤⣀⣀⠤⠤⠒⠉⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⢲⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠙⡆⠀⠐⠂⢚⣀⣀⣀⣀⣑⣊⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠘⣢⠴⠥⣄⣴⠊⠉⠀⠀⠀⠀⡀⢤⡈⠉⠒⢢⣴⣁⠀⠀⢠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢊⠴⠚⠉⠁⠀⠀⡜⠀⠉⠓⢦⡀⢠⠀⠓⠤⠃⠀⡰⠋⢀⠈⠑⠢⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡖⣀⣰⣃⠀⠀⠮⠆⠀⠀⢡⢀⠄⠀⠤⠽⡞⠀⠀⡀⣠⠞⠀⢰⠁⠈⡂⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⡏⠀⠈⠉⠓⠲⠤⣘⠒⠋⡠⠖⠂⠀⠂⢄⠀⠳⠧⠄⠀⣀⣑⣈⣀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠑⡄⠀⠀⠀⡇⠀⠀⢀⣀⣙⣢⡄⢁⠊⠀⡔⠢⡀⠀⠀⠑⡀⠴⠒⠉⠀⠀⠀⠀⠀⠉⠓⠦⣀⠠⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠁⠀⣀⡤⢷⠚⠉⠉⠀⠠⡊⠁⢸⠛⠉⠄⠀⠈⠱⠐⠒⡇⠀⣶⢟⡀⠀⠀⢠⠒⠒⠄⠀⠬⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠴⠊⠁⠀⠘⡄⠲⠁⠀⢀⡩⢷⠈⢆⠀⠀⠄⠄⠀⠀⡰⢡⣄⡙⠀⠉⠢⣄⠘⠤⠤⠂⠀⠀⠀⠀⡖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡔⠁⡠⢄⠀⠀⠀⢱⣀⠤⡴⠯⡀⠈⠀⢀⠱⣦⠤⠤⡴⠮⡀⢎⠱⢌⣀⠀⠀⠈⠳⣄⠀⠀⡠⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠑⠊⠀⢀⡴⠊⢧⠀⠓⠚⠀⢀⠴⠁⠀⠈⢂⡐⠁⠀⠈⠦⡀⠀⠈⠉⠑⢆⠀⠈⢆⠀⠑⠤⠊⠀⠀⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⠯⢤⠀⠈⠇⠀⢐⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⡔⢂⣼⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠅⢠⠞⠉⠂⠐⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠀⠀⠀⠃⠀⠀⢰⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠊⠀⠀⠀⠀⢄⣀⠇⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠈⠁⠀⠈⠑⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠑⠤⠃⠀⠀⠀⢠⠄⠠⡀⠘⣄⠀⠀⠀⠀⠀⠀⡠⠁⠀⣰⠁⠀⠑⠀⠀⠀⠀⡎⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⡄⠀⠐⢄⡠⠂⠀⠀⠉⠁⣉⠉⠉⢉⣠⡀⠀⠘⠦⠤⠊⠀⠀⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠀⠀⠀⠀⠀⣀⠄⡀⠀⠸⢅⠅⠀⣇⠀⢨⠀⠀⠀⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠣⠠⠃⠀⠀⠀⢀⡀⡈⠉⠁⠀⡠⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠠⢤⠀⠀⠨⣀⡸⠀⠀⠐⢇⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⣀⡀⣀⠀⢀⠀⠀⢀⡀⢀⠀⣀⡀⢀⠀⡀⠀⢀⢀⠀⣀⡀⢀⡀⢀⠀⣀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⡀⡇⠀⢸⠀⣗⠂⠘⢡⡅⢸⠀⢸⢸⡀⡸⢸⠱⡇⠀⣃⢀⡇⣗⠂⢸⠀⢸⢸⡀⠀⡇⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⡆⣠⠰⣀⠀⡖⡆⢰⠂⢰⣒⠄⠰⠆⢠⠒⠀⢲⠂⢠⢰⠀⠆⡄⢲⠂⠠⣠⠀⢠⡖⢢⢠⠀⣖⠀⡔⠒⡄⡖⡢⢰⠒⠄⢰⠂⢰⢒⠄
⠀⠀⠀⠀⠀⠘⠃⠙⠀⠋⠀⠃⠀⠸⠄⠘⠙⠂⠋⠙⠘⠢⠀⠘⠀⠘⠀⠟⠀⠃⠐⠀⠀⠃⠀⠘⠇⠚⠐⠀⠨⠃⠣⠐⠃⠋⠑⠸⠀⠃⠸⠀⠘⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣄⠀⢦⠀⠀⠀⠀⠀⡀⣰⠋⠁⠈⠹⣆⢀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⢁⣼⠃⠈⢁⠀⠀⠀⠈⠉⢻⣀⠈⠁⣠⠏⠉⠀⠀⠀⣀⠁⠀⠀⣼⠛⠋⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠉⢻⡟⠁⠀⠀⠀⠀⢰⠏⠀⠀⠀⠘⠷⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣄⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⣤⣤⣈⣀⡀⠀⠀⠀⢠⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠵⠚⠉⠹⣆⠀⠀⠀⠀⠀⠈⣡⠞⠁⠀⠀⠀⠉⠉⠉⠋⣿⠉⠀⠀⣿⠀⠀⣀⣀⣀⣀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⢰⡏⢀⡀⢀⠀⠀⠀⠀⣀⣀⡟⠀⠀⠀⣿⣀⣸⡏⣀⣉⣀⣉⣈⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣀⡤⢿⡆⠀⠀⠀⠸⣇⡟⢻⠋⠓⠶⠤⠾⣿⠛⣇⠀⠀⠀⠈⠉⢹⡇⠰⠶⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡵⠞⠋⠀⠀⠀⣀⡀⢻⡇⢸⡇⠀⠀⠀⠀⣿⠀⣿⠀⣀⡀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡤⠤⠀⠶⠒⠂⠘⠋⢉⣀⣭⡤⠼⣇⣸⠇⠀⠀⠀⠀⢿⣀⡿⠤⣬⣁⣀⠉⠙⠀⠘⠒⠂⠀⠶⠦⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠉⠁⠀⢀⣠⣿⣿⣄⠀⠀⠀⢀⡿⣿⣧⣀⠀⠀⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣠⡴⠛⠁⠹⣆⠉⠳⠦⠴⠛⢠⡟⠀⠙⠳⣤⡀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⣤⠴⠖⠋⠁⠀⠀⠀⠀⠘⢧⡀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠉⠓⠶⢤⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠈⠇⠹⠘⠋⠘⠙⠙⠛⠙⠋⠘⠁⠈⠑⠚⠋⠓⠛⠁⠛⠛⠘⠁⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠒⢶⡀⠀⠀⠀⠀⠀⢰⡖⠒⣶⠀⠀⠀⣶⠒⠒⠒⠒⠒⠲⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣀⠀⠈⣧⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣤⠤⠤⣤⣀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⡿⡆⠀⠸⡆⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠈⠻⡄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡾⠀⢻⡀⠀⢻⡀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠸⢧⠤⣬⠧⠀⠈⢧⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⡿⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣀⣀⣀⣀⣠⡀⠀⠘⣇⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⢀⣠⡾⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣼⠁⠀⠀⠀⠀⢿⠀⠀⢹⡄⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⠙⠙⠋⠉⠁⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠃⠀⠀⠀⠀⠀⠘⠓⠒⠒⠓⠀⢸⡇⠀⣿⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣾⠛⠛⠓⠶⣄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣄⣀⣀⣀⣀⣼⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠘⣧⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⣹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠋⠉⠉⠉⠉⢻⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢠⡟⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⢿⣤⣤⣤⠴⠋⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣸⠀⠀⠀⠀⠀⢸⣀⣀⣸⠀⠀⠀⢸⣇⣀⣿⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣛⣩⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠋⣰⡾⢋⣥⣶⣾⣿⣿⣿⣦⣼⡟⠁⠉⢹⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⡟⢰⠋⣰⣿⣿⠟⠋⣉⣹⣿⣥⣶⣦⣤⣶⣿⠛⠁⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡀⠻⠀⠠⢏⡘⠁⠴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣴⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣿⣷⡀⢸⣆⢸⣷⡄⠀⠀⠀⠀⠉⠹⣿⣿⣛⣻⣿⣿⣿⣯⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣿⣇⠸⣿⣿⡄⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⡿⣛⣋⣤⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⡇⢻⣿⣆⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡈⠻⣿⠄⠛⠀⠀⠐⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠀⣸⣿⣿⣿⠛⠳⣦⠈⠀⠀⠀⣀⣠⣀⣀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⣧
⠀⠀⠀⠀⠀⢀⣾⠇⣾⠟⣡⠀⠀⣿⡟⣿⣿⡀⢀⠴⠀⠀⠀⠀⠉⠋⣽⢿⡿⢷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣵⣿⠇
⠀⠀⠀⠀⣴⣿⣿⠸⣿⣼⡇⢸⡇⣿⡄⢻⣿⣇⠀⠀⣠⡄⠀⠀⠀⠀⠈⠂⠀⠺⢀⡿⠀⠀⡀⢈⠛⠛⠛⠑⢢⣿⣿⠿⠋
⠀⠀⠀⢼⣿⣇⣻⣿⠳⣽⣇⠸⣝⢆⠳⡄⢿⡟⠂⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡞⠹⣿⣶⠶⣦⣀⣾⡟⠁
⠀⠀⠀⣾⣿⣿⣿⡅⣀⠀⠙⣷⣜⢾⣧⣿⣿⣷⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠁⠘⣻⣿⣿⣸⣷⣦⡀
⠀⠀⠀⣹⣿⣿⣿⣼⣏⣀⣦⢸⣿⣷⣿⣿⣿⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠲⠀⣄⠀⢸⠄⠀⠀⠀⢰⣿⣿⡝⡇⣿⣿⡷
⠀⠀⣼⡟⢻⣿⡋⢷⣌⣉⣡⡿⣿⣿⠟⢿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠐⠛⠀⠀⠀⣰⣿⣿⣿⢫⣿⣿⣿⣿
⠀⢠⣿⠃⢿⣿⣷⣼⣿⣿⡿⢟⣼⢟⠉⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⢰⣬⡙⠷⣦⣄⡀⠀⠀⢀⣴⣿⣿⣿⡧⠞⣋⣡⣤⡜⣇
⠀⠘⣿⣷⣬⣽⣿⠿⠯⠿⢲⣿⠁⣯⣀⣴⣿⣿⡏⠹⣄⠀⠀⠀⠀⠘⣿⣿⣶⣤⡍⠉⣀⣴⣿⣿⣿⣿⣯⢞⣭⢥⣤⣤⡹⣾⡀
⠀⠀⣾⠟⡏⢹⣿⣶⣶⣶⡿⠻⣌⠻⠿⣿⣿⡿⠁⠀⠘⢦⡀⠀⠀⠀⠈⠙⠙⠉⢀⣤⡽⠿⠛⠋⢁⣠⣯⢞⡵⠛⢉⠉⠻⣾⣷
⠀⠀⢻⣦⡻⠶⣿⣿⣿⣿⣷⣾⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠉⣳⣤⡀⠀⠀⢀⣴⡏⢡⣤⣾⢟⣿⣿⢿⣿⡏⢠⣴⣿⣷⡤⠀⠙⢦⡀
⠀⠀⠀⠙⠻⠿⠟⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⣾⡿⣡⣿⣿⣿⣾⣿⢿⠟⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⢸⣿⢡⣿⣿⣿⠿⣛⡵⠋⠀⠀⢦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣤⡙⢾⣿⣸⠿⣿⠶⠚⠁⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⣶⠄⢰⡿⣄⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡛⠛⠛⠁⠀⠈⢷⣝⠳⣄⣀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⣷⠀⠈⠙⢿⡖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠻⠆

⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣿⣶⣤⣀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⡿⠿⠀⣠⣾⡿⠛⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡸⠿⢿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⣾⠟⠁⠀⠀⣠⣴⣾⡿⠿⠿⠛⠻⠿⠿⣿⣶⣤⡀⠀⠀⠈⠻⣿⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⣠⣾⠿⠋⠁⠀⣀⣀⣀⣀⣀⡀⠀⠈⠛⢿⣷⣄⠀⣴⣿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠈⢁⣾⡿⠁⠀⣠⣶⣿⠿⠛⠛⠛⠻⢿⣷⣦⡀⠀⠙⣿⣦⠈⠁⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⢀⣿⡟⠀⢀⣼⡿⠋⠀⢀⣀⣤⣄⣀⠀⠈⠻⣿⣆⠀⠘⣿⣧⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⣸⣿⠀⠀⣼⣿⠁⠀⣰⣿⠟⠛⠛⢿⣷⡄⠀⠸⣿⡆⠀⢸⣿⡆⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⣿⣷⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢻⣿⠀⠀⢿⣷⠀⠀⢻⣷⣄⣀⣀⣴⣿⠇⠀⢠⣿⡇⠀⢸⣿⠇⠀⠀⠀⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠘⣿⣇⠀⠘⢿⣧⡀⠀⠉⠛⠛⠛⠋⠁⠀⣠⣿⡟⠀⢀⣾⡿⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠙⣿⣦⠀⠈⠻⢿⣶⣤⣄⣀⣀⣠⣴⣾⠿⠋⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠈⠻⣷⣦⡀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⣀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣤⣤⣤⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠉⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢈⣨⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣴⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢶⢾⡁⣤⣶⣶⣦⣄⣠⠄⡀
⠀⠀⠀⠀⠀⡀⠀⣤⢼⣿⣿⣿⣿⣿⣿⣯⣾⡄⠀⠀⠀⠀⠀⠀⠀⠐⠙⣻⢾⣼⣿⣿⣿⣿⣟⣿⣥⣾⠟⡆
⠀⠀⠀⠀⠀⠈⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⠊⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣳⠟⠁
⠀⠀⠀⠀⠀⢼⣼⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢢⡀⠀⠀⠀⠀⠀⠋⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠
⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈
⠀⠀⠀⠀⠀⠀⢸⣎⣿⡷⣿⣿⣿⣿⣿⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡧
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠇⢏⠏⠓⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⢟⣿⣿⣿⣿⣿⡟⠋⠀⣠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⠘⠷⠃⡹⠓⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣿⣿⣿⣷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡴⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣯⣿⣿⣿⣿⣿⣿⣿⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣿⣶⣶⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣬⡭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠛⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⡠⠊⢀⠔⠀⢤⣦⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⡄⠀⠈⠢⣀⠆⠀⠀⠀⠀⣴⡆⠀⠀⢁⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠟⠀⠈⠦⣉⠀⠃⠀⡠⠐⠊⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠒⠐⠀⠀⠉⠉⠁⠘⣿⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⡈⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠘⠋⠁⣨⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⠇⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⢀⠀⠑⠀⠀⠀⠠⠀⠀⠀⡀⠐⠀⠀⠀⠀⢢⠂⠀⢸⣏⡾⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣥⡟⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡇⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠄⢠⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⠿⠊⡐⢴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠑⠠⠆⠀⠀⠀⠀⢀⠁⠊⠀⠉⡂⠀⠀⠀⠀⢀⡴⢶⣶⠞⠋⠁⠀⠀⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣰⣿⠗⣉⠔⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⡶⠛⣛⠟⢋⠴⠊⠀⠀⠀⣠⠄⣀⢼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣽⣧⡐⠂⠀⠀⠀⠀⠀⣀⣤⣴⠟⠋⠰⡫⣆⠀⢀⠔⢁⠀⠊⣠⠔⣫⠴⠋⠁⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⣽⠶⠶⠶⠶⢶⠟⠋⠀⢀⣤⣾⠛⠃⡀⢀⠁⢂⡡⠔⠋⣠⠞⠋⠡⠄⠈⠄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⣠⠞⠁⠀⣠⠟⣻⠟⠃⠀⣠⠖⠁⠀⠉⣀⠔⠋⠀⠀⢀⠀⢊⠔⢰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣦⣠⢞⣵⢟⠕⣋⠄⠀⠀⠀⢀⠴⠊⠅⠀⠔⡠⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣫⡴⠋⠜⢁⡨⠁⠀⠀⠀⠐⠡⢊⡠⠀⠀⢀⡤⢂⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⢀⡠⠖⠁⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⢁⠄⠀⠀⠐⠀⠀⠀⢀⠔⠋⠀⣶⠶⠿⣤⣆⣤⣯⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⠕⢋⠀⠀⠀⠠⢂⡀⠀⠁⠀⣠⠔⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣡⡴⠁⠀⠀⠀⠈⠀⠀⠀⡠⢊⠑⢈⡴⢋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢉⡤⠚⠁⠀⠀⠐⠀⠀⠀⠀⠐⢁⠄⡡⠒⠡⠊⢁⡴⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⠔⠋⡄⠂⠀⠀⠀⠀⠀⠀⠈⠀⠊⠑⠉⠀⠊⠂⢑⠋⠀⣠⡸⢷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⢠⢀
⠀⠀⠀⠀⠀⢶⣾⣇⣴⣶⠛⠛⠀⠀⠀⢀⡼⠍⢥⢠⣶⣶⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢾⣷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠅⠐⠀⠀⣀
⠀⠀⣠⢀⠆⠿⣿⡿⠿⠿⣁⢀⣄⠀⠀⠀⢗⣈⡀⣾⣿⣿⣿⣿⠂⠀⠀⠀⠐⠂⢰⣶⣿⣿⣷⡆⠀⠀⠀⠀⠀⠠⣿⡿⠃⣤⡌⠛⠁
⠀⠀⠀⠉⠁⠀⠈⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣤⠀⠀⢠⡄⠀⣤⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⢸⣷⣰⣿⣛⠀⣀⠀⠀⢆⣿⣶⣀⣾⣷⣰⣿⣦⣰⢶⣷⡄⠀⠀⢀⣿⣿⣋⣶⡆⠀⠀⠸⣿⣿⣄⣀⣀⡀⠀⠀⠘⣻⣆⣀⣶⣆
⠀⠀⠀⠹⢻⠟⡿⢰⢹⠀⠀⠀⠋⢹⠿⡿⢿⠿⠿⠿⢿⠏⠋⠀⠀⠀⠸⠻⢿⠟⠛⠇⠀⠀⠀⠹⠿⡿⠿⠿⠇⠀⠀⠀⠿⠿⠿⡿⠿

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿
⠀⠀⠀⣀⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢰⣟⡒⠋⣤⠀⠀⣠⡀
⠀⠀⠀⡿⣿⣿⣿⡁⠀⠠⣶⣶⣀⣤⡄⠀⠀⢰⣵⡶⠀⣼⣤⣿⣷⣞⣤⠀⠉⣾⡧⠀⠀⠀⢴⣴⡆⣠⣤⠀⠀⠀⠀⠀⢠⣴⣆⢠⣤
⠀⠀⠀⠀⣿⣿⣿⡇⠀⢾⣿⣿⣿⣿⠇⠀⠀⣸⢷⡀⢀⠐⣿⣿⣿⣿⣿⠀⠀⡟⡇⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠀⠈⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁