Marmoset Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⠛⠿⠙⡿⠱⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢶⡟⣷⣶⣯⣿⣷⡬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣈⣿⠉⠧⠅⢻⡽⠷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣷⣾⣳⢤⣴⠿⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⢿⣿⡿⢦⣿⣿⣿⣿⣇⣀⣀⣀⣀⡠⢴⣖⠀⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠌⣉⣣⣻⠼⡟⠻⡿⢡⡃⡌⠉⠉⠀⠀⣀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀⠏⣮⡴⢢⣛⡚⠛⣺⡥⣿⣸⣶⢠⠼⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣿⣿⣿⣛⣛⣋⠙⠋⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣿⠿⠋⢉⠉⠀⠀⣠⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣷⣿⠋⠀⢀⣾⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠉⠋⠙⢳⠆⢸⣿⣿⢫⣽⠀⡀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡏⠀⠀⠀⠈⢦⡰⢿⡿⢘⡽⣑⡇⠀⠀⠀⠀⠘⣁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⡇⠀⠀⠀⠀⠀⢡⣤⠀⠠⠏⠁⠁⠀⠀⠀⢀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠘⣿⣶⣼⠀⠀⠀⠀⠀⠀⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠁⠀⠀⠀⠀⠀⠈⢿⡓⠀⠀⠠⠄⢀⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣶⣆⣀⣠⠄⠀⠀⡄⠁⣠⣶⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠛⢻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇


⣶⣶⣶⢶⣿⠷⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⢶⣶⣶⢶⡶⣶⣷⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣴⡿⠛⠛⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣧⠛⣠⡜⢣⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠦⢦⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⢸⣿⣿⡿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠻⣿⣿⣷⠈⠉⠛⢿⣿⡆
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠹⣿⣿⣧⣀⡀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠆⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠐⠂⠐⠒
⠀⠀⠀⡀⠀⣰⡿⠃
⣀⣀⣈⣛⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣫⡽⢋⣴⣾⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⢡⣾⣿⣇⣾⣷⣤⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⣿⣧⣿⡿⣿⣷⣿⣿⣋⣍⠙⢻⣿⣯⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⠷⠖⠋⢻⣿⣿⠃⠀⢤⣿⣿⠩⣦⣿⣻⣿⣿⣿⡁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠨⢫⣎⣽⠀⢀⠀⢸⡟⢿⣶⠀⠀⠿⠿⣾⣿⣿⣿⣿⣿⣦⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠚⠇⠀⠀⠀⢉⣄⣸⣷⣾⣿⡄⠀⠀⠀⠹⢻⣿⣽⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⣦⡞⠀⠀⠰⣏⢸⠛⣙⣿⣿⣿⣦⣴⣷⣿⣿⣿⣿⣿⠟⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠁⠀⠀⠀⣋⣾⣾⡿⠁⠀⠈⣹⣿⣿⣿⣿⣿⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⠀⠀⠀⣰⣾⡿⠋⠙⠻⣿⣶⣾⣿⣿⣿⣿⢟⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡇⢠⠠⣿⠛⠀⠀⠐⠀⢹⣿⣿⡆⠀⢿⡻⢾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣧⣿⠂⠀⢠⠟⠀⣸⣿⣿⠁⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠂⠀⣿⡧⠶⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡇⣀⣸⣿⣷⣾⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠉⠉⠉⠛⠩⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⣤⣀⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣶⣾⠛⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⢿⠟⠿⣿⡏⢿⣿⣿⣿⣿⣿⣤⣿⣟⣤⣝⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣼⣷⢸⣖⣆⣿⣧⣼⣿⣸⣿⣿⣿⣿⣿⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣻⣟⣿⣯⢻⣾⣿⣿⣟⡛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣛⢿⣿⠿⠛⠋⠛⠿⠿⣿⣿⣿⣿⣿⣿⣲
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣙⢿⣿⣿⣿⣿⣷⣶⡍⠉⠻⣿⣿⣿⣿⣷⣧⡀
⠀⢀⣠⣴⡞⣿⣍⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⢧⣾⠛⣏⠿⣿⣿⣿⣿⣙⣦⡀
⣠⡿⣷⡬⠟⡛⠛⡿⢻⡿⣿⡿⢿⠿⠻⡿⠿⠿⣿⣯⣯⣭⠿⢛⣛⠻⠛⡟⠉⠁⠈⠻⠟⣹⣷⣿⣿⣏⣾⣿⣿⠇
⣿⣿⣻⠀⠀⠀⠀⠁⠀⠀⠉⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣤⣶⣾⡏⣻⢿⣿⣿⣿⣿⣿
⠸⠟⣩⠇⣄⣀⣀⣀⣀⣀⣀⣠⢀⡤⣠⢀⣤⠄⣄⣀⠀⣀⣀⡀⠀⣠⣤⣆⣼⣿⠇⡿⣿⣷⣽⡺⣿⣿⣿⣿⠇
⠀⠈⠻⢶⣧⣿⣷⣿⣿⠿⡿⠿⠿⠿⠿⢿⣿⣷⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣷⣷⡰⣿⣿⣷⠽⣿⣿⣧⣴⣄⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣿⣦⣽⣭⣥⣦⣿⣿⣿⣿⣿⣥
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⠟⡻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡃⠃⣷⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠙⢿⣿⣾⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⢠⢿⣤⡀⠙⣆⠀⣠⣎⠰⡦
⠀⠀⠀⠀⠀⠀⠀⣯⠈⢿⣿⣶⣬⣾⣻⠟⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠉⢻⣿⣿⠏⣀⡤⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠇⣰⡆⠸⣿⡿⠋⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣇⣿⡷⠚⢺⠆⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢘⡿⠋⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡲⠿⠻⢿⣿⡄
⠀⠀⠀⠀⠤⠐⠊⠁⠀⠀⠀⡀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣤⣼⣿⣿⠇
⠀⠀⠀⠀⠄⠀⠀⡠⠴⠂⢻⣧⠀⠀⠀⣴⠚⠓⢦⡀⠀⠀⠀⠀⢀⡞⠈⠙⠟⣿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢿⣄⣀⢸⡇⠀⠀⠀⠀⣾⡇⠀⢀⠀⠀⠀⡈⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⣌⣩⠞⠁⠀⠀⠀⠀⡈⢻⣤⡈⣶⣤⣿⣷⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⣼⣿⡞⢿⢋⣴⡾⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠃⠀⠑⣿⠏⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠒⠒⠉⠉⠁⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣶⣦⣴⡲⣤⣤⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⣽⠯⠚⠛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠞⢙⠟⠒⠾⣏⡇⠀⠀⠀⠀⢀⣤⣶⣶⣿⠀⣠⣴⣿⣧⠺⣦⡸⣾⠂⡄⠁
⠀⠀⠀⠀⠀⢀⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣽⣿⣶⣿⣿⠇⠿⡄⠉⠡⡿⠀⠁
⠀⠀⠀⠀⠀⢌⡾⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣷⣿⣏⠴⠳⣿⣿⣿⢉⠈⠀⠀⢁⣼⠃
⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠷⣿⣿⡇⠺⣿⣿⣯⣿⡿⣭⣝⣠⣼⠏
⠀⠀⠀⠀⠀⢾⢟⠀⠀⠀⠀⠀⠀⠀⢸⣁⣴⣿⣿⣿⡴⠛⢯⣍⣁⣀⣀⣽⣿⠟
⠀⠀⠀⠀⠀⠘⠆⣷⠤⣀⠀⠀⢀⣠⢾⡿⠿⠿⠟⢿⣿⣤⠈⢻⣋⣩⣅⢣⣰⣗⠀⠀⢠⣀⢀
⠀⠀⠀⠀⠀⠀⠈⣓⣦⣿⣿⣥⣽⣿⣶⠶⠶⢿⣿⣾⢿⣷⢠⠀⢙⣿⣿⣿⣿⡿⣿⣦⠾⢤⣈⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠂⠈⠉⠀⠀⠤⠼⠛⠼⡨⠟⠛⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠊⠉⠉⠉⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠄⠀⢀⣠⡄⠤⠀⢤⢀⣠⠏⣠⠂⠀⠀⢀⠀⠀⠀⠀⠀⣀⣸⡿⣿
⠀⠀⠀⠀⠀⢀⠄⠋⠀⠀⠀⠀⠀⠀⢹⠏⢡⠔⣦⠀⠀⠀⠉⠰⠃⢀⣴⠞⡉⠀⠀⠀⠀⢀⣹⠟
⠀⠀⠀⠀⢠⣋⣤⠄⠀⠠⠤⣀⣆⡴⢋⠄⠾⠀⠛⢚⡛⠶⢦⡀⠀⣾⠟⠁⠀⠀⠀⠀⠀⢶⠟
⠀⠀⠀⠀⣿⣟⣡⠀⠀⠀⠀⠈⣿⡙⢣⣶⡄⠀⠠⡿⢟⠇⢘⡇⢠⠀⠀⠀⠀⠀⠀⠀⣘⡞
⠀⠀⠀⠀⠸⢻⡏⣀⠀⠀⠀⣠⣧⠰⣄⡉⢁⡀⢠⠀⠀⢠⡎⠀⣾⡦⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠹⣿⣏⠀⠀⠀⠈⢿⡇⢸⡏⠀⣀⣠⣤⡄⠀⡇⠀⠙⠃⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣇⡀⠀⢠⡿⠀⠀⢵⡀⠉⠀⠀⠀⣰⠇⠀⠐⢶⣄⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠖⠉⠀⠀⠀⠀⠙⠲⠶⠦⠚⠁⠀⠀⠀⠈⠟⠀⢰⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠇⠀⠀⠀⠀⠀⢀⠤⡞⢻⡿⠁
⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠁⠙⡀⠀⠀⠀⠀⠐⠉⢆⣷⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⣠⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⣠⡞⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⢘⠋⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠞⠛⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⢰⡿⠁⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⣄⡀⠀⠀⠜⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⢀⣾⠇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣿⠁⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⢈⡏⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣴⣋⣤⣤⣤⣤⣤⣀⠀⠀⠀⣠⡿⠃
⠘⠁⠀⠀⠀⠙⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣀⣴⠋
⣸⡇⠀⠀⠀⠀⠀⢉⣷⣤⣤⣀⠀⢀⣄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠰⣌⣷⡟⠁
⢸⠀⠀⠀⠀⣠⣶⠟⠉⠉⠉⠉⠛⢏⡉⠉⠀⠛⠛⠛⠛⠂⣴⠶⠓⠒⠛⠉⠁⠒⠛⠛⢆⠘⣆⢻⡼
⢸⣦⠀⠀⢈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡿⠾⠁
⠸⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠈⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡙⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠦⣈⡋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⡴⠊⠻⣦⡀
⠀⠀⠀⠸⡀⠀⠀⠀⡄⠀⠀⠀⢀⠜⠓⠣⢦⡹⠁⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⡁⢠⠛⢉⠿⣦
⠀⠀⠀⠀⢻⡇⠀⠀⠱⠿⠒⠶⢃⡴⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢱⣦⡴⠁⠀⠈⢷
⠀⠀⠀⠀⠀⠘⣶⡀⠀⠂⢶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⡀⢺⡆
⠀⠀⠀⠀⠀⠀⠈⠙⢶⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠲⠤⠚⢻⡇
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠤⢄⢴⣿
⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣅⠀⠀⠀⠀⢠⠇
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢠⡾⠛⠢⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠈⠓⠶⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣰⠋⠀⠀⠠⠋⠉⢹⡶⠒⢲⠟⠉⠀⢡⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⢷⡟⠀⠀⢀⠃⠀⠀⣿⠀⠀⠈⡀⠀⠀⠀⠳⠄⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠙⠶⣤⣼⡁⠀⠀⣿⠀⠀⠀⠹⣄⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢿⣦⣤⣤⣠⠼⠷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣤⣀⡀⠀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣿⣿⣿⣶⣶⣾⣷⣾⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⣻⡟⡻⢋⣹⣿⣿⣽⣿⣿⣿⣿⣧⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠿⣿⣿⣿⣿⡿⠿⢻⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢧⣽⣿⣿⣿⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠲⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣇⠀⠀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣀⣸⣿⣿⣿⠿⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣦⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣽⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣀⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣿⣿⣿⡿⢥⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣾⣿⡟
⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠟
⠀⠈⠉⠛⢹⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣶⣄⣀⣤⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⡀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡁⠀⠀⣾⣿⣿⢁⣼⣿⠟⢻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⢨⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠘⣿⣿⣿⣽⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣰⣿⣿⣿⣿⡏⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠃⠀⠀⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣾⣿⣿⣿⠁⠀⢘⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣴⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⣏⣠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⣀⣠⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⢀⠽⠛⠻⢿⣿⣷⣿⣿⣿⣿⣶⣿⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⡁⠌⠛⠋⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⣿⣿⡾⠀⣤⣄⢀⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⣠⠀⠀⠀⢘⣿⣿⢿⡦⠈⠅⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⡏⠀⠀⣠⣾⣿⣿⣿⣷⣴⣶⠒⠓
⠀⠀⠀⠀⢀⣴⠻⣿⣿⣿⣤⣿⠿⠿⠿⠖⠘⠛⠿⠿⢿⣿⣿⣿⣿⣿⡿⠁⢻⣿⣿⣿⣿⣧⣶⣿⣽⣿⣿⡿⢻⣿⣄⡀
⠀⠀⠀⣰⠿⢿⣧⡸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣯⡉⠛⠛⠻⢿⣿⣯⣤⡀
⠀⠀⢠⣿⣶⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣘⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⢻⣿⣷⡀
⠀⠀⢸⣯⣈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣷⣶⠄⠻⣿⣿
⠀⠀⠘⣿⠿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡆⠀⠘⠛
⠀⠀⠀⠻⣷⣿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⢺⡿⢹⣿⣿⡃⠀⠀⠐⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠙⢧⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣤⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⣸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠋⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⠸


⣿⣿⡿⠿⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣾⣿⣷⡄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⠉⣿⡇⣸⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⢦⣤⣶⡿⢾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⠶⢿⡟⢻⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢿⣿⣿⣿⣿⣿⡿⣁⣀⢀⣀⡀⠀⠀⡀⠠⢥⣤⡤⢤⣽⣦⣻⣿⣿⣿⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⣠⣼⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⣛⣀⣁⣀⡀⠀⠈⠉⢛⣟⣛⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣰⣿⣾⠿⣿⣿⠛⠉⠉⠀⠠⡶⢂⣖⣴⣾⡿⠿⠿⠿⠿⣿⣶⣤⣤⣈⣉⣈⣩⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⢻⠷⣿⣥⣴⡟⣿⣿⢧⣤⣄⠀⢠⣶⣿⠏⣿⣧⡀⠛⠉⠰⠚⣱⡏⠙⠛⠿⠿⠿⠿⠛⢿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢉⣴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠿⠷⠾⣿⢿⣷⣶⣶⣶⣿⣥⣴⡶⠿⠶⠄⠰⠦⠐⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⠉⠉⠉⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣤⣤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⣀⣠⣤⣤⣤⡄⠀⠚⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⣰⣿⡿⡿⢿⣿⢧⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠞⠯⣼⣧⣤⣾⣿⠾⠫⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣁⣤⣾⣇⡈⠉⠡⠀⠀⠇⠀⠀⣿⣦⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣰⣿⢄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣽⣻⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣼⣯⣿⡷
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡿⠉
⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿
⠀⠀⠀⠀⢠⣿⣿⣿⣭⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠋⠁
⠀⠀⠀⠀⣿⡽⡻⡿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣳⡿⣿⡏⠁
⠀⠀⠀⣸⣟⣿⢿⣿⣿⣿⣿⣽⣟⣿⡛⠿⣿⣿⣿⣿⡿⣿⣟⣉⣼⣛⣵⣧⣿⣧⣀⣀⠀⡀
⠀⠀⠀⡿⣿⣷⣴⣿⣏⣟⢹⣟⡿⠻⣿⠷⣎⡹⣿⣿⣿⣼⢿⡿⣽⣿⣿⡿⣿⡟⢿⡿⢿⡿⠷
⠀⠀⠀⣿⣦⣿⣩⢿⣯⣿⣷⣼⣿⣿⣿⢿⣿⣷⢻⣿⣿⣿⣎⣿⡿⡿⢷⣦⣤⣈⠲⠌⠀⠁
⠀⠀⠀⢹⣿⣿⣿⣾⣾⣶⣹⣽⣯⣦⣵⣷⣿⣿⣿⠟⠛⠉⠉⠙⠷⢿⣿⣿⣿⣿⣷⣶⡴⣠⢄⣠⣄⣤⡀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡤⣴⣔⣶⣶⣄⡀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡿⣿⣿⣿⡿⠷⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⠏
⠀⠀⠀⠀⠀⠈⢻⣽⣿⣿⣦⡀⠀⠿⠟⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣮⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⣿⣿⠇⠀⠀⠀⠀⢀⣤⣾⣿⡟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⢼⠟⡘⠉⠀⠙⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠚⠆⠃⠀⠀⠀⠀⣻⠿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣥⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣵⣿⣿⣦⣄⡀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣏⡿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠙⠿⢿⣿⣿⣿⣿⣶⣻⣿⡿⠿⠋

⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀
⠀⠀⢠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠛⠛⠙⢻⡧⠀⢰⡟⠉⠛
⠀⠀⢿⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⣰⢿⣷⣄⠘⣧
⠀⠀⠈⠓⠶⠶⣿⣿⣿⣿⣿⣶⣤⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣰⠋⠀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠻⣿⣿⣿⣷⠹⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⡀⠀⢈⣻⠇⠀⠀⠀⠀⢻⡀⠀⠉⠉⠀⠀⢀⣴⣾⢾⣿⢦⣄⠀⣀⢀⡀⠀⠀⠀⣼⡇⢠⣾⣿⣿⡿⣿⣇⢹⣇
⠀⠀⠀⠀⠀⠀⢿⣿⠻⣿⣏⢹⣿⣾⣿⠤⠿⠃⠀⠀⠀⠀⠀⠈⢷⣀⢀⣀⣀⡀⣾⣿⣏⣾⣿⣿⠻⡟⢻⣿⣿⡆⠀⠀⢻⣷⠘⢿⣿⣿⣿⣿⣿⢸⡟
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠈⣿⡿⣿⣆⡀⠀⠀⠀⣀⡀⠀⠀⠀⢉⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠈⠁⢺⣿⣿⠇⠀⠀⠈⢿⣧⡘⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣰⣿⠃⠀⢸⣿⠀⠙⢿⣮⡛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣼⠟⠋⠀⠀⠀⠀⢴⠿⢣⣽⡟⠛⠉
⠀⠀⠀⠀⠀⣿⡅⠀⠀⢸⣧⣤⣤⡀⠈⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠻⠷⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⡄⠀⠈⠉⠙⢻⣿⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⢻⣿⠁⠀⠀⠀⠀⠈⠻⣷⣝⢷⣀⣀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⣠⣴⠿⠿⠿⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⢸⣟⣀⡀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠃⠀⠀⠀⢿⣏⠀⠀⠐⣨⡿⠃
⠀⠀⠀⠀⠀⠻⣧⣈⠀⢀⣴⠏⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣤⣴⣿⣧
⠀⠀⠀⠀⠀⠀⣈⣻⣶⣾⣿⣶⣄⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣽⢿⣿⣷⡄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠛⠛⠛⢷⣶⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⢷⣆⠀⢠⣼⠋⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣬⣿⣷
⠀⠀⠀⠀⠀⠈⠻⣯⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠸⠿⠟⢻⣦⡀⠀⠀⣠⣮⣿⠿⣿⣿⣶⣤⡄⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠻⣿⣦⣾⡿⢿⠃⠀⠀⢹⡟⠻⡷⠶⠶⠂⠀⠀⠀⠀⠀⣠⣼⡿⠁⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠈⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠱⠿⡷⠶⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⣀⣤⣴⣤⣀⡀⠀⠀⠀⠀⠴⣤⡀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣄⣀⡆⠀⠀⢸⠇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠸⣿⡁⠀⢀⣹⣇⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢿⣿⡿⢿⣿⣷⣤⣠⣾⣀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠻⠦⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⣿⠛⠿⣿⣿⣿⣶⡄⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⡿⠀⠀⠀⣠⣤⣌⣿⡇⠀⢸⡇⠀⠀⠀⠈⣿⣿⡇⠀⢀⣾⠁⠀⠀⠀⠀⠀⠙⠲⠦⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠙⠻⣿⣿⣿⣶⠟⠁⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⢻⣄⡀⠀⠀⣿⣿⣇⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣧⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠻⠿⠄⠰⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣶⣶⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠝⠛⠛⠋⡉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠘⠛⠃⠘⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠐⠂⠈⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠾⢿⣦⡐⠀⢠⣤⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡦⠀⠀⡟⠋⠁⣠⠀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣿⠇⠀⠀⣧⣆⣰⣿⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣥⠀⣿⠟⠀⣠⣤⣿⣿⣿⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⣸⡇⢠⣿⣿⡿⠛⢉⣼⣧⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⣿⠀⠀⠟⠋⣀⣴⣿⡟⢻⡆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⣠⣤⣾⣿⣿⡿⠁⣸⣇⢰⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢉⣿⣿⠃⣸⣿⡇⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠰⣿⣿⡟⢠⣿⣿⠟⢂⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠩⣿⡟⢼⣿⣿⠃⠈⣻⡟⠀⠀⠃⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠏⢀⣿⣧⢘⡟⣿⣷⣾⣿⠃⠀⠀⠀⢤⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣶⣿⣧⠀⠸⣿⢇⣾⣇⣿⣿⡿⠃⠀⠀⠀⠀⠬⢅⠌
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣺⣿⣿⣽⣿⣿⣧⣠⣤⣄⡀⠈⠉⠁
⠀⠀⠀⠀⠀⢿⣛⣛⡉⢁⣀⣀⣀⣉⣹⡏⠛⠛⠛⠛⠻⠿⣿⣿⣿⠷⠿⠿⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠚⠛⠙⠟⠛⠋

⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣦⣤⠀⠀⡀⣀⣀⣠⣤⣤⣄⣠⣶⣶⣤⣤⣄⣶⣶⣶⠒⡦⠠⣤
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⡛⣿⣏⣿⣽⣿⣿⠿⠿⢿⣿⣿⢶⣿⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡏⠀⠙⣿⠛⠀⢿⠀⢨⣿⠿⠛⠉⢹⣿⡿⠛⠋⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⡀⠀⢀⣸⣿⣧⡈⠀⠸⣇⢀⣤⣾⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣧⣤⣾⣟⣿⡙⠇⠀⠀⠈⠀⠘⠡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠛⠽⡿⣿⠇⣴⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠂⠀⠀⠀⢀⣿⡟⡇⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⢠⣶⡏⢠⣿⣷⡀⠠⠒⠀⠤⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠁⠀⠀⠀⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⣴⣶⣶⣾⡿⣿⠁⡘⢋⠀⠛⢦⣄⡀⢀⠀⣠⣆⣀⡀⠀⠀⣀⠀⡀⢀⣴⣿⣿⣶⣤⣄⣀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣀⢀⣠⣿⣿⣿⣿⣿⠁⢰⣾⠃⠀⣀⣘⣷⠁⠈⠛⠛⠋⠉⠑⠀⠁⢋⣽⣿⣿⣿⣿⡿⢿⣷⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠐⠛⢿⣿⣿⣿⣿⣿⠋⠀⣿⣿⡀⠀⣟⠻⣸⠗⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣁⣿⣿⡿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣿⣿⣿⣧⣤⣿⣿⣿⣿⣧⣿⠿⢋⣁⣀⣀⠀⠀⠀⠀⠀⢸⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⢸⣿⣿⠙⢿⣿⣿⣿⣿⠟⢉⣾⠟⠛⠙⠻⢿⣦⠀⠀⠀⠈⠷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣷⡄⠀⠘⣿⣿⡿⠀⣸⢿⣿⣿⣧⡀⣼⣿⠀⠀⠀⠀⢘⣿⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠘⣆⡀⠀⠈⠟⣁⣤⣾⣿⣿⠷⠀⢸⣷⣿⣯⠙⣷⢿⣿⡄⠀⠘⠿⠿⠋⠀⢰⣾⣿⣿⣿⢻⣿⣿⣿⣿⣶⣾⣟⡛⠿⠧⢤⡤⠄
⠀⠀⠀⠀⠀⠐⢌⡻⠄⠠⢾⣿⣿⣿⣿⡋⠀⣴⣿⣿⣿⠟⠀⠿⠀⠻⣿⣶⣤⣀⣀⣀⣤⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠥⠀⠐⣿⣿⣿⣿⡟⣷⣆⣿⣿⡟⠋⠀⠀⢀⣤⣤⣤⣍⣛⡛⠻⠟⠛⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⣿⣿⡋⠀⢹⣥⡦⠀⠂⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠃⣠⣿⠻⡅⣼⠀⣾⣿⣿⠿⠿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡋⣾⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⢹⡿⠁⠀⠀⠀⠈⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠘⡏⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡂⢦⣤⠤⠄⢠⣤⣤⣄⣀⢀⣀⠈⠁⣀⢀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣯⣭⣥⣬⣉⣥⣀⣄⣙⣂⣰⣶⣶⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣿⠟⠻⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠘⠿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡜⢇⢰⡤⠂⠒⡆⡦⡂⡆⢆⢰⠀⢒⠀⡖⠒⢢⡐⢠⡄⠂⢠⡀⡄⠔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣚⠁⠀⢠⣶⣿⣿⣿⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⠄⢀⣾⠯⠍⠉⡿⣿⡄⠀⢐⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⣌⣤⣿⣧⠀⣺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡍
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⡿⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠋
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠃
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⣼⣿⠛⠿⢿⣿⣏⠀⠘⣿⣿⠇⠀⠹⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⢠⣿⡟⠀⠀⠀⠙⡿⠃⠀⢿⣿⡀⠀⠀⠀⠙⢿⣶⣤⣀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇
⠀⠀⢸⣿⡇
⠀⠀⠀⣿⣷
⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⣤⣤⣤⣀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⣶⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⣿⣿⣦⣄⣠⣴⣶⣤⣀⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣀⣘⣋⣩⣿⣿⠿⠟⠃⠀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣽⠳⣄⣻⣿⡵⠏⠉⢻⣿⡿⠏⣿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢇⠈⠻⢄⣹⣿⡏⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣇⡈⠳⢄⡈⣿⣿⠄⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢷⡈⠓⡄⠈⠻⣾⠉⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠻⡆⠻⢄⠙⠳⣞⣿⣧⣠⡀⠀⠘⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣦⡙⠶⣈⠳⣶⣿⣿⣿⣿⠿⣦⣴⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠻⣧⡌⣱⣿⣿⣿⣿⣿⣦⡈⠉⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣍⡛⢦⡌⢉⣹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣟⠷⢦⣤⣌⣽⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣙⡿⣆⠭⡸⠣⠤⠿⣿⢿⣿⠿⡿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠒⠒⠶⢒⣿⣿⣿⣿⠒⠀⠀⠀⠀⠈⠁⠁⠤⠶⣦⣀⡀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢿⣿⣿⣿⣿⣿⣛⣛⣛⣽⠟⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠟⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢿⣧⣤⣻⡿⠁⠀⠙⣿⣭⣥⡴⢂⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠸⣦⣤⣽⠟⠉⠀⠀⠀⠀⢹⠶⠶⠶⣛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣼⠛⠁⠀⠀⠀⠀⠀⠀⣼⠳⠶⢚⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⣒⣚⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢞⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠷⠾⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢃⣄⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⢠⣾⣿⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⠁⢀⣼⣿⠀⢰⣶⠀⢰⡆⠀⢶⡆⢸⡆⠀⣿⠀⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠾⣿⣇⣀⣾⣿⡀⣸⣿⣄⣾⣷⣼⣿⣶⠿⣾⣿⣴⣗⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠰⠈⡿⠛⠀⠀⠀⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠴⣶⣶⡶⢶⣶⣶⣼⣿⠿⢻⡿⠃
⠀⠀⠀⠀⠀⢹⠃⠀⠀⢀⣾⣿⡿⠛⡌⣿⣿⠷⡄⠀⠁⠶⢶⠄
⠀⠀⠀⠀⠀⢸⠁⠀⠀⣾⣷⣤⠒⠲⠷⠀⠿⣤⠃⠀⡀⣤⡄
⠀⠀⠀⠀⠀⠈⡇⠀⡀⣿⣿⣿⡷⠒⡆⠂⣠⠟⠀⠑⢼⣟⡀
⠀⠀⠀⠀⠀⢠⡟⢰⢳⣿⣿⣿⣿⣷⣶⣿⣿⡎⠀⠀⣈⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠈⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣴⡎⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢿⣿⢀⣿⣿⣧⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⢨⣿⣿⡏⣹⡗⣿⣿⣿⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣛⣿⣿⡿⣴⣿⣿⣿⣿⣟⣈⣿⡿⣿⣿⣿⡄⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠉⣿⢉⣯⣠⣍⡛⣃⣴⣿⣿⣿⣿⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣳⠉⢺⣯⣿⣿⣿⣿⣫⣿⣿⢩⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⣿⣟⣀⠀⣄⣨⣾⣿⣿⡟⣽⣿⣿⡟⣃⣸⣿⡿⣿⣿⣿⣿⠶⣤⡀⠉⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠒⠀⠀⠀⠀⠀⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⡹⣶⣿⣿⣦⣅⠤⡈⡠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡠⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣈⣻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⠛⠿⣽⣿⣿⣏⣡⣿⣦⡙⢀⡌⡀
⠀⠀⠀⠀⠐⠁⠀⠠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⣰⣾⡿⠯⣿⣿⣿⠛⠉⣽⣿⣿⡻⠋⠁⠀⠀⠐⣿⣿⡱⢆⣈⠙⠿⣋⣿⣿⣿⣿⡄⢀⠀⣀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠤⠀⠀⠀⠀⢠⣾⣿⣿⣿⡼⣿⣿⣿⡃⣑⣾⣿⣿⠿⣷⡀⠀⡠⣺⣿⣿⣿⣿⣿⣿⣶⠊⣿⡟⣻⡫⢻⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠉⠉⠉⠙⠋⠉⠉⠉⢸⣿⣿⠀⣷⢻⣿⣯⣿⣿⡿⢿⠷⣯⢘⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠀⠀⠀⠀⢸⡏⡉⢙⡿⠁⡠⠆⡁⠀⠤⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠁⠀⣿⣿⡿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⣀⣤⠄⠀⠀⢠⣿⣿⣿⣾⡇⠤⢠⡆⠉⠄⠰⠤⠒⠈⣠⠄⠠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣿⡡⢶⣧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡦⠾⠟⠛⠋⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣻⣿⢋⣸⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣏⠉⡉⠻⢿⠟
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠠⣾⣿⣿⣿⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢚⡹⣿⣿⣷⣍⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡟⠁⢀⣲⣿⣿⣿⣶⠶⢶⣶⣤⠶⠖⠶⣿⣿⣿⣇⢀⡍⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣸⣍⣝⣿⣿⡿⠀⠘⣿⣿⣿⡆⠈⠙⣿⣿⣿⣝⣵⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠊⠤⠤⠤⠤⠿⠽⠦⠤⠀⠀⠓⠈⠁
⣿⣿⣿⠿⠿⠷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣾⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣶⣷⣶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠋⠀⠀⠉⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠴⠒⠾⠷⠶⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠶⠶⠶⠒⠒⠛⢉⣧⠀⠐⠾⠆⠀⢶⡦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠷⠖⠓⠐⠛⠒⠀⠀⠀⣼⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡵⠁⠀⠀⠀⠀⠈⠒⠛⠷⠒⣦⣶⢾⠟⠂⠚⢧⣀⣀⣀⡀⠀⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠈⢤⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢀⣠⠈⣠⣢⣭⣤⣤⣄⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⡠⢶⣞⣿⠟⢁⣠⡽⠟⠉⠈⢹⣷⡀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⡟⢠⠿⠋⢀⡴⠛⠁⣀⣀⣀⡀⢨⣿⣧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⠳⠃⢠⡴⠋⠀⠀⠀⠉⠀⠈⣤⡿⣿⡇⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠀⠀⣰⡟⠁⢸⡇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⡾⡛⢤⡀⠈⠓⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⡤⠁⠀⠀⢀⣴⡟⢃⡼⠛⠻⢦⢿⡀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡶⣿⡀⠀⠀⠀⡼⠀⠀⠀⢠⣿⠯⠤⢿⣧⣀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠟⣾⡿⣷⠋⠁⠑⠲⠶⢧⡀⠀⢀⣀⣀⣤⠄⡀⠈⠹⣍⡑⣦⣄⠀⠉⠛⠤⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⣮⣛⠛⠻⠿⠶⢲⣶⠤⠤⣤⣤⢤⠤⢤⡤⠀⠀⠀⢈⣁⡀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠖⢀⠁⠨⡛⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠤⠤⠴⠶⠶⠶⠶⠶⠶⠦⠤⠤⣀⠀⠀⠙⠲⢦⣄⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠆⠤⠤⠄⠁⠂




⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⠤⡴⠊⠰⠋⠰⢄⡀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⣄⠀⠀⠀⠀⠀⠈⠀⢀⡀⠡⢀⠤⠐⠂⠤⡀
⠀⠀⠠⠒⠀⣈⠁⠀⠼⠁⠀⠎⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠙⡄⡧⠊⠉⠉⠑⠔⡀
⠀⠊⡴⠉⠀⠀⠀⠉⢂⠀⢸⠀⠀⠀⠀⣀⡆⠀⠀⠀⡀⣀⠀⡇⢇⠀⠀⠀⠀⠰
⢸⠀⡁⠀⠀⠀⠀⠀⢸⠀⠀⢆⠀⠀⢹⣿⠥⠒⠒⠒⠻⢟⢀⠇⠋⠀⠈⢢⢤⣡⠁
⠈⢆⠣⡀⠀⠀⠀⠀⢘⠀⠀⠠⠓⠉⠁⠈⠀⠙⠀⠀⠀⠈⠈⠉⠣⣀⠀⠘⠢⢄⡉⠑⢄
⠀⠈⠢⢌⣑⣒⣐⣀⡤⢲⠋⠀⠀⣀⣀⣀⣤⣄⣀⣁⠠⠤⠤⣄⣀⠸⠝⢄⡔⢉⠭⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠚⠋⠉⠀⠀⠀⠠⢤⡀⠄⠀⠀⢀⡠⠂⠈⠈⣗⢁⠄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠒⠤⠤⠤⣤⣤⠤⠤⠔⠒⢎⠁⠀⠀⠘⠄⠈⠁⠀⢀⣠⠆
⠀⠀⠀⠀⠀⣀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢣⠀⢀⡰⠀⠀⢀⠄⠛
⠀⠀⠀⠀⡜⠁⠀⠀⠈⠺⠀⠀⠀⠀⡤⠤⠀⠀⠀⠐⠚⡁⠀⠀⢛⡝⠁⠀⠀⡌
⠀⠀⠀⠀⡄⠀⠀⠀⠠⣀⠆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢃⠀⠀⠎⠀⠀⠀⣰
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠸⠆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡦⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠛⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⢈⡷⣆⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⡏⠁⢀⠝⠁
⠀⠀⢀⢀⡀⠀⠀⠀⢵⠀⡰⠁⠀⠀⠀⠀⠉⠒⡄⠀⢀⡼⠁⠀⠉⡀⠒⢄⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢄
⣠⠐⠁⠀⠔⢁⡀⣀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⢹⠒⢯⣠⣀⣀⣀⣈⣃⣀⡶⠚⠀⠀⠀⠀⢰⠀⠀⠤⠠
⠑⠪⣉⡠⠔⠡⠄⠁⣀⡰⡆⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠃⠂⠤⠄
⠀⠀⠀⠀⠑⠒⠋⠉⠀⠀⠹⠴⢄⡤⣄⡴⢤⠞⠀⠀⡄⠀⠀⠈⠀⠂⠈⡆⠀⠀⠀⢀⠀⠐⢄⠀⢈⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠀⠓⠆⠉⠀⠀⠉⠀⠒⠊⠐⠢
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⣶⣀⣀⣶⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠂⠀⠈⢻⣿⣿⡟⠁⠀⠐⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⣤⡶⢦⣄⣰⣿⣏⣤⣽⣿⣿⣦⡱⣄⠀⠀⣠⢎⣴⣿⣿⣯⣄⣹⣿⣆⣠⡴⢶⣤
⠀⠀⠀⠀⠀⣸⠏⣰⣿⣿⣿⣿⠟⠉⠀⢀⡀⠉⠙⢿⣶⣷⡿⠋⠉⠀⠀⠀⠉⠻⣿⣿⣿⣻⣆⠹⣇
⠀⠀⠀⠀⠀⢻⡀⠀⣽⣿⣿⡏⠀⣠⡾⡛⣟⡛⢦⠀⢻⡟⠀⡴⠟⢻⣛⢷⣄⠀⢹⣿⣿⣯⠀⢀⡏
⠀⠀⠀⠀⠀⠘⣧⢸⠁⢎⣿⣇⠀⣿⢸⣧⣾⣿⡎⡇⢸⡇⢸⢱⣧⣼⣿⡇⣿⠀⣸⣿⡳⠈⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡈⢻⣿⣦⡙⢌⡛⠚⣋⠔⣡⣪⣔⣄⠣⣙⠚⢛⡡⠋⣴⣿⡟⢁⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣯⠉⠀⠈⢉⡵⠊⠁⠀⠀⠈⠙⢮⡉⠁⠀⠈⣹⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⠋⠀⠀⠻⠆⠰⠟⠀⠀⠙⣶⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠓⠢⠤⠤⠤⠤⠔⠚⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢦⣄⣀⣀⣠⡴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⢳⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠚⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠂⠁⠀⠀⠈⠐⠈⠀⠀⠀⠁⠢⡀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠤⣠⠁⡜⠀⠀⠀⠀⠢⢄⣀⣀⠠⠄⠀⠀⠀⠀⠀⢡⡠⠔⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠤⡀⠀⢸⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⡇⢸⠀⠀⡠⠄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠔⡺⠊⠁⠀⡄⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⡁⠀⠉⢺⡒⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠲⡽⠁⡠⠊⠁⠀⠈⠁⠀⢰⠁⠢⠒⠑⠄⠀⠉⠀⠀⠉⠢⡀⠫⡵⠃⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⢹⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⢸⠡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣧⡀⠀⠀⠊⠙⢔⠐⠂⠐⠂⠒⢒⠜⠉⠂⠀⠀⣠⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠦⣀⠀⠀⠀⠉⠐⠒⠒⠈⠁⠀⠀⢀⡠⢞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠉⠁⠒⠢⢀⡀⣀⠤⠒⠂⠉⠁⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣂⠀⠀⠀⡠⠄⠀⠀⠄⡀⠀⠀⢠⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣠⠊⢸⠀⢀⠎⠀⠀⠀⠀⠀⠙⠄⠀⠇⠑⢄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⡀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⠀⡔⠁⠀⢸⠀⡎⠀⠀⠀⠀⠀⠀⠀⢰⠀⡆⠀⠀⠱⡀⠀⠀⠑⢤⠀⢀⠔⠉⢀⣀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠃⠀⠀⠀⢬⡖⠁⢠⠊⠁⠀⠈⢆⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⠜⡄⢃⠀⠀⠀⠀⠀⠀⠀⠘⢀⠗⠤⣀⠀⡇⠀⠀⠀⢨⠀⡰⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢛⠁⠀⠀⠈⣺⣄⢀⣀⣀⣀⣀⣀⣶⠁⠀⠀⠀⢹⠀⠀⠀⠀⢘⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄⠀⡰⠊⠀⠀⠀⠘⡄⠀⠙⠤⣀⠉⢢⠀⠀⠆⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢈⡲⢌⠢⢄⡀⠀⠀⠈⠢⢄⡀⡠⠔⢋⠔⣊⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠸⠀⠈⢄⡠⠸⡂⠀⠀⠀⠀⠏⠤⣠⠃⠀⢸⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⣀⠠⠂⠀⠀⠈⢆⡠⠃⠀⠀⠀⠀⠦⣠⠊⠀⠀⠀⠦⣀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡈⢀⠁⠀⠀⡀⠀⡣⡀⡨⠆⠀⠀⠀⠀⠀⠀⢆⢀⣴⡁⠀⡀⢀⠀⢀⠉⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣻⢦⡴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠓⢦⡀⠀⠀⣀⡤⠤⠴⠆⠉⠀⠛⢈⣀⠀⠀⢀⡴⠒⠲⣤⡀⠀⠀⠏⠈⡇⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⡟⠀⣠⠆⠲⠄⣱⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣌⠰⠤⡀⠈⢷⡀⠀⡇⠀⠧⡤⠖⠋⣀⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⡦⠀⠀⠀⢸⡇⠀⣟⠀⠀⡼⠃⠀⠀⠀⠀⣠⡀⠀⢀⣠⡀⠀⠀⠀⠀⠹⣄⠀⠸⠀⢸⡇⠀⣿⠀⠀⡇⠀⠀⠙⠒⠂⠤⣄
⠀⠀⣠⠄⠀⠠⠤⠤⠤⠾⠀⠃⠀⠀⠀⠈⢷⡀⠻⡀⢸⠁⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠁⠀⡀⠀⠀⠀⢻⠀⡘⠀⣼⠃⠀⢿⠀⡰⠀⢀⠀⠻⣐⠠⠄⠼
⠀⠀⠈⠉⢉⣹⠇⠀⠀⡀⠀⢸⡆⠀⠀⠀⠀⠻⢦⡌⢹⣤⣤⣴⠒⢶⣄⣀⠀⠀⣀⣠⡴⠏⠙⡧⠈⠙⠿⣅⢀⡼⠃⠀⠀⣼⠀⣤⡤⠊⠑⢦⡌⣳
⠀⠀⡠⠚⢉⡠⣤⠀⠀⠐⠄⠈⣇⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⠀⠀⢹⡇⠀⠀⠀⣰⠃⣸⠁⠀⠀⠀⠀⠈⠁
⠀⠈⠳⠚⢁⡔⢁⠖⠑⠦⣀⣠⡘⣆⠀⠀⠀⠀⠀⡇⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⠇⠀⢀⡾⠁⢠⡏
⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠈⢧⠈⢷⣄⠀⠀⠀⢷⡀⠀⠀⠈⠓⠢⠤⠄⠀⠀⠤⠤⠔⠊⠁⠀⠀⠀⢠⡟⢀⣴⠟⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠉⠳⢦⣄⣀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡶⠋⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠙⢦⡀⠀⠈⠙⠛⠻⣿⠓⣦⢤⣤⣀⣀⣀⣀⣀⣀⣤⡴⣾⠛⠋⠁⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠉⠉⠉⠙⢦⡙⢶⣄⡀⠀⢰⠏⢰⠁⠀⠀⠀⠉⠉⠉⠁⠀⢸⠀⠹⣦⡴⠶⠛⠋
⠀⠀⠀⠀⠀⣰⠏⢀⡴⠖⠒⠶⣄⠀⠀⠈⣇⠀⠈⠛⢳⡏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⡀
⠀⠀⠀⠀⢰⠇⢠⠋⠀⠀⠀⠀⠙⣆⠀⢠⡇⠀⠀⠀⣸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢳
⠀⠀⠀⠀⣿⠀⢾⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡷⢤⣀
⠀⠀⠀⠀⠸⡇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣿⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠹⣆⠘⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣰⢧⡀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠉⠙⠲⠶⠤⣤⡤⠶⢺⠏⠀⠻⣄⠀⠙⢦⣄⣀⡀⠀⣀⣠⡴⠟⠀⢀⡴⠃⠀⠙⢦⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⢤⣀⣀⣀⣴⠏⠀⠀⢠⡟⠳⣤⣀⠀⠉⠉⠉⠉⠁⣀⣠⠴⠋⠀⠀⠀⢀⡼⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⠏⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⢀⣤⠞⠋⣠⡤⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠟⠋⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠓⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠉⠛⢛⡛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⣤⠶⠖⠒⢾⡏⠋⠀⠙⡆⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠐⢢⡹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠁⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⣉⣁⣤⡄⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢿⣀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠿⠶⠾⠇⠾⠻⠲⠷⠶⠿⠰⠶⠾⠷⠞⠳⠾⠒⠶⠿⠐⠖⠲⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣧⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⣿⣧⡀⠀⠈⠄⠀⠀⠀⠀⣹⣿⢀⣤⣶⣾⣿⣿⣷⣶⣤⣀⢸⣿
⠀⠀⠀⠀⠘⠀⠀⠀⡌⠀⠀⠀⠀⠀⣠⣾⣧⢠⣶⣶⣶⣷⣄⠀⠐⡀⠀⠀⠀⢿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⢰⣄⡀⠂⢠⣾⡛⠙⠻⣿⣿⣶⡄⠈⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡔⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⠏⠠⠠⣿⠋⣡⡀⠀⠙⢿⣿⡄⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢼⣩⡅⣩⣭⣭⣭⣭⢈⣭⣭⣭⣭⣭⡈⠀⢀⠀⠀⠀⠄⠀⠀⢆⢠⠋⠀⠀⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠸⢀⣠⢠⠤⣬⣿⣇⡿⠿⠟⠛⠛⠚⢛⡟⠛⢿⡿⣁⣀⠄⠀⠐⠀⢀⠀⢀⠀⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⠀⠀⠀⠐⢀⠈⢰⡏⠁⠐⡄⠀⠀⢀⠔⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡡⠄⠀⠀⠀⠙⠄⠀⠀⢉⡀⠈⡷⢖⣶⣞⣻⣄⣁⠔⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⠉⠭⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠀⠀⠀⠀⠀⢀⠓⢒⡄⠀⠒⠦⡤⠤⠤⠴⠒⠋⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠒⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⢃⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⠀⠤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠴⠀⠀⠀⠀⠀⠀⣿⣿⢿⠇

⠀⠀⠀⠀⠀⠀⣀⢠⣤⣴⣶⣶⣶⣦⣄⣀⣀⣀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠊⣇⠑⢄
⠀⠀⢀⠤⠒⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢆⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠀⠀⠀⢣⢂⣀⣁
⠀⠎⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⡄⣀⢈⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⠀⠀⠀⠠⠤⠤⠀⠀⢀
⢰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡆⠀⠩⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠖⡀⠀⠠
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⢀⠔⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢈⡴⢨
⠀⡄⠀⠀⢹⣿⣿⣿⣿⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⣶⠟⠃⠂
⠀⠘⡄⠀⠀⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢊⣴⣾⠟⠁
⠀⠀⠈⠢⡄⠀⠀⠹⣿⣿⣿⣆⠀⠀⠈⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣾⡿⠊
⠀⠀⠀⠀⠸⠒⠠⠀⠀⠉⢩⠍⠋⠖⡀⣶⡒⠒⡘⠁⠐⠀⠶⣓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⡄⠀⠀⠀⡜⠀⠀⠩⠄⠀⢀⠀⠀⠀⠀⠉⠉⢀⠒⠄⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢰⠀⢸⣴⡾⡄⠀⠀⠹⣶⣦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠆⢁⡠⡆⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠻⡀⠀⠔⠛⢿⣿⣿⣿⣿⣿⣿⣿⡖⠒⢶⣻⣿⠿⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣈⠩⠀⠉⠉⠛⠛⠿⠿⡇⠀⡟⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠢⠠⡁⠀⠀⠀⡠⠀⠒⠲⠶⢦⡄⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡈⠀⠀⠀⠀⠀⠈⠙⠱⡄⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠁⢈⠀⠄⣄⠠⠀⡐⠀⠀⡀⠈⡀⠃⠐⠠⡀⠀⢐⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠁⠴⢡⡄⣀⢠⡄⠲⠀⠀⠀⠀⠀⠄⡀⣀⣴⠇⢀⠀⠀⠉⠁⠐⠓⠄⡀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠃⠀⠘⢺⠟⠋⠙⠙⠿⡗⠃⠀⠀⠀⠀⠀⠀⠉⠁⢆⡭⠌⠀⠂⠀⠀⠀⠀⠀⠒⠀⠈⠀⠀⠀⠂
⠀⠀⠂⠀⠀⠀⣎⠀⠀⠴⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⡀⣀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣄⣀⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠲⣤⣀⣤⠴⠂⠐⠦⣤⣠⣤⠖⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣧⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⣼⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣩⡄⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠛⠛⢻⠀⠉⠀⠀⠉⠀⡟⠛⠛⠛⠛⠛⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀⠀⠀⠀⠀⠀⠍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠃⠀⣠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣰⣿⣫⣶⠿⠛⠂⠀⠀⠀⠀⠐⠂⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⠟⠛⠀⠀⠒⠂⠀⠶⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⠟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡶⠀⠀⣠⡤⡀⠀⠀⠀⠀⠀⠒⠫⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠐⢿⡿⢋⣵⠄⣦⣄⠀⠈⣧⠀⠀⠀⠀⠀⠀⣀⣀⡠⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠈⣇⠀⡀⠀⠀⠳⣈⢀⡴⠛⠉⠱⡄⠘⡑⠒⣒⣛⣋⡩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣽⠋⢀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡆⢹⣿⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠁⠘⠃⠁⢐⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⠓⡿⠀⠁⠀⠀⠀⠀⠀⢠⠊⠉⠳⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠄⠀⠀⡉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠁⠀⡄⠀⠀⠀⠀⠀⣸⠄⠲⠖⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠑⢄⡠⠒⠀⠀⠀⡀⠀⡇⠀⢀⠔⠊⣀⠀⠀⠠⠂⢀⠴⠒⢀⡠⠆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠁⠢⣀⣰⠉⡒⠀⣜⣡⣀⠈⠀⢃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⠎⠀⠀⠉⠙⠀⣡⣬⣌⢣⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣗⢷⡙⠲⠦⠀⠀⠀⠖⢹⣻⠇⠀⠁⣴⠅⢀⡅⠀⠀⠀⣀⠤⠒⣶⠀⠀⠀⠀⠀⡠⠚⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣻⣆⣹⣟⠳⣤⠤⢤⡔⣊⢟⡀⠀⠀⠀⠑⠦⣄⣀⡠⠊⠁⠀⠀⣿⠀⠀⠀⡠⠊⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠹⣉⡙⡿⠿⠛⠉⠛⠃⠀⣀⡤⠖⠚⠛⠁⢀⣠⡄⠀⠀⠘⡦⢚⠾⠁⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡭⠍⢉⡀⠀⠀⣀⠠⠐⠚⠁⠀⠀⠀⠀⠔⠁⠘⠀⢀⡴⣊⠔⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⠞⠁⠀⠀⠁⢀⡥⠚⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠀⠀⠤⠀⠘⠈⠀⠀⠀⠀⠒⢦⡁⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠎⢸⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⢸⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⠇⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⢀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⣀⡀⠀⠀⣀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠉⠓⠶⠿⠟⠾⠿⠛⠲⠮⠛⠛⠻⠛⠛⠳⠂⠈⠛⠒⠲⠦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣆⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⣴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⢷⣄⡀⢀⣴⠟⠁⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠳⣄⠀⢀⣠⠞⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡈⢷⡀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣠⠟⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⢦⣝⣶⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣩⠞⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⠉⠁⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠉⠁⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠛⣦⡀⠀⠀⣠⠞⣩⠭⣍⡿⠿⣷⣄⣀⣴⣾⠿⢏⡭⠭⣙⢷⡀⠀⠀⢀⡴⠛⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣩⣭⡅⠀⠈⢙⣶⡶⢋⠎⢀⣽⣶⣶⣄⠈⢯⠛⡞⠁⣤⣶⣶⣥⠈⢳⡛⢶⣾⠋⠀⠀⣨⣵⣽⣦
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⢻⣿⣀⠰⣦⡛⣇⢾⠀⣎⣨⣿⣿⣿⡇⢸⢸⠀⢸⣿⣿⣿⣀⡇⢈⡃⣾⢋⣴⠂⣀⣿⡏⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣷⡞⢹⡏⢷⣄⣻⠻⡿⠘⢆⠘⠿⢿⡿⠟⢀⣞⣤⣧⡈⠻⢿⡿⠟⢁⡼⠁⡿⢻⣗⣠⠿⣹⡏⣳⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡹⢾⣷⣀⡙⠻⢧⣄⣀⣈⣑⣦⣤⡄⠒⢩⡏⠀⢿⠙⠒⢤⣤⣖⣋⣀⣀⣠⡾⠟⢁⣠⣿⡾⢫⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡀⠈⠉⠁⠀⠀⠈⠉⠉⠉⠁⠉⠙⠳⢦⣧⣀⣿⡴⠞⠋⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁⣠⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣹⣦⣄⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢀⣠⢾⣋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣡⣴⣛⣛⡛⠛⠓⠲⣶⣦⣤⣀⠀⠀⠀⠀⠎⠀⠀⠀⠀⣀⣤⣴⡶⠒⠛⠛⣛⣛⣻⣦⡉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣟⠉⡀⢀⡔⢶⣿⣷⣾⣭⠷⣤⡀⠠⢀⠀⢀⣴⢾⣽⣶⣿⣡⡶⢠⡀⡄⢙⡿⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⡿⠋⡤⠁⠀⣤⠸⣿⢻⣿⣿⢸⣿⡿⣦⣤⡶⣿⣿⠦⣿⣿⡟⣿⢳⡄⢀⠀⡎⠙⣿⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡎⠁⠚⢠⡿⣧⣽⣎⠛⣿⠰⣿⠷⣏⣿⣇⢻⣷⢶⡟⡛⣻⣧⣾⣷⠘⠃⠘⠠⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⢀⣵⣟⣛⣾⣿⡏⢻⣿⢧⣮⣴⡟⡛⣹⣦⣢⢾⣿⠛⢹⣿⣷⣛⣳⣌⡀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣿⠟⠃⠀⢈⡻⠿⣭⣇⢻⡿⣸⢧⣿⡟⣏⢻⣯⢸⡌⢿⠇⣼⣭⠿⣛⠁⠀⠙⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢩⢟⡤⢀⠀⠈⢻⣿⠏⣼⠷⣶⣿⢦⡟⣴⣿⣬⢏⡼⣿⣶⢾⣇⢻⣾⡏⠀⠀⠀⣾⢻⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⢧⠀⠀⠀⣸⣧⢾⣿⣆⢛⢃⣿⡉⣿⢿⡿⢹⣧⠙⡋⣼⣿⣦⣾⡇⠀⢀⢀⡟⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⣏⣿⢠⣿⡟⣿⢻⣿⠷⣥⣬⣥⢿⣿⠛⡏⢿⣧⢸⣏⣷⣐⡥⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣧⣛⣰⣧⠻⡟⣸⢿⣿⡿⣎⠿⠃⣿⣌⣋⣼⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣻⡏⢾⡿⢻⢿⡁⣾⣿⣷⢹⠿⡟⣿⡎⣹⣟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢏⠙⢦⡶⢟⡀⢳⠴⠤⢴⡏⢀⡳⣤⡴⢁⡹⣏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡏⠀⢿⣿⠋⣴⢟⡀⠀⣐⠿⣆⠻⣿⠇⠀⡷⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣜⣡⡿⢿⡟⠁⠠⠉⢿⡿⢷⣍⡆⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢉⠿⣷⣏⣴⢀⠀⠘⣦⣓⣼⢯⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢻⡁⣼⠈⠀⠀⡧⢙⠏⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⣎⠐⣼⠳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⣰⠁⢳⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠓⠈⠉⠀⠀⠈⠁⠀⠀⠀⠈⠉⠐⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡴⠁⢀⠔⠈⠁⠀⠀⠈⠙⢦⡀⣠⠖⠋⠁⠀⠀⠉⠙⢦⠀⠀⠀⠹⣆⠀⢀⣠⣤⣀⡀
⠀⠀⢀⡔⠉⠁⠈⠉⠳⣾⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢹⡖⠉⢀⣀⡈⠻⣆
⠀⠀⢸⠀⠀⡠⠲⠦⣄⣿⠀⣎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡧⠚⠉⠉⠹⠀⡟
⠀⠀⠘⣇⠀⠀⠀⠀⠈⢹⡀⢹⡀⠀⠀⠀⠀⠰⡾⠃⠀⠀⠀⠀⠿⠇⠀⠀⠀⢀⡼⠁⠀⠀⠀⢸⣅⣀⠀⠀⢀⡼⠁
⠀⠀⠀⠈⠓⠦⣤⣴⡍⠉⠀⣀⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠑⠲⣄⠀⠠⢬⡗⠀⠁⠀⠤⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣹⠀⢐⡄⠣⠀⢊⣁⠆
⠀⠐⢎⠂⣜⠣⠀⠉⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣉⠩⠭⠐⠈⠹⣦⢀⠀⠀⠘
⠐⠯⢉⡓⢸⠀⣶⠤⢄⣀⣀⠀⠉⡓⣶⣤⣄⣀⣈⠒⠠⠄⠀⠀⠀⢀⣀⣀⡤⠴⠚⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠦⠀⡍⢀⣈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠈⠂⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⠊⡡⠤⠤⢌⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡇⢸⠁⠀⠀⠀⠱⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⠀⢇⠸⢄⣀⡠⠒⣦⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠻⡄⠀⠈⠓⠤⠤⠤⠚⡝⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠓⢒⠤⠤⢤⠤⣤⠐⠒⠶⣄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡠⠊⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠜⠁⠀⠀⠈⠣⣈⠓⠤⣀⡈⣧⠀⠀⠀⢸⣀⣀⠤⠖⢉⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣍⡹⠀⠀⢀⣎⣩⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠨⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⢙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠼⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⢀⡠⠀⠀⠀⠠⡀⢆⣬⡱⣧⣴⢧⣂⡀⠀⣀⡟⣐⠀⡀⠐⣤⠆⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣄⠘⠀⠐⡥⣻⣯⡉⢙⢻⣻⠞⠙⠚⠐⣷⣾⣿⢰⢤⣂⡄⢀⡰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣼⣷⣾⣷⡾⠟⠛⠉⠉⠉⠻⠤⣧⡀⠶⠐⠚⠛⠻⢿⣿⣷⣡⡿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣿⣿⣿⢁⠄⠀⣄⣀⣀⣀⣀⠀⠀⠀⣄⣄⠀⠀⠀⠙⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⡿⣿⣿⣿⣦⣴⣶⣿⣿⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⠻⠏⠀⠍⢽⣿⠯⣿⢿⣟⣟⠋⠉⠙⠙⠿⢻⣿⣿⣿⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡿⢿⣿⣿⣗⣂⣠⡾⠋⢀⠀⠈⠋⠀⢀⠀⠠⠀⠀⠤⣸⣿⣿⣧⠙⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣿⣿⠟⠻⣏⠁⠀⠈⢳⣄⣠⡴⠫⠠⠐⠀⠀⠢⣨⣿⣿⣿⠔⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣿⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⣷⡜⢻⢷⣶⠒⠀⠄⠀⠤⠤⠤⠤⢤⣶⣶⠟⢺⣿⣛⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣇⠈⢫⣿⠠⢀⣀⣀⡀⠀⡀⣴⠹⣿⠏⠸⢫⣿⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⠀⢹⠀⢹⠋⠉⠑⠀⠉⡇⢰⠏⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢃⢸⠀⠀⠀⠀⠀⠁⣸⠀⠀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡄⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢛⣫⣭⣭⣿⣿⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠃⢐⣛⣛⣛⣛⣭⣭⠵⢚⣴⣯⡻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠛⠉⠉⠉⠉⣀⣠⣴⣿⠟⠘⡿⣎⢿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⣀⣤⣤⣴⣶⣶⣿⣿⣿⠿⠛⠁⠀⠀⢻⢻⣆⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⡟⢀⣴⣿⣿⠿⣿⣟⣛⠋⠉⠁⠀⢠⡴⠒⠒⠆⠘⡏⣿⣎⠃⠀⠀⠀⠀⠀⢀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⡇⣼⣿⠏⣴⡎⢉⣈⣉⠃⠀⠀⠀⠉⢠⣶⡶⣦⠆⢳⡘⣿⣆⠀⠀⠀⠀⠀⢸⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢻⣿⡏⢸⣿⡟⢏⡹⡿⠃⠀⠀⠀⠀⠁⠉⠝⠃⠀⠈⢷⡈⠻⢷⣤⣀⣀⠴⠃⣠⢞⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣷⢸⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠛⢶⣤⣄⣀⣤⡴⠞⣡⠟
⠀⠀⠀⠀⢀⠄⠀⠀⢿⠘⣿⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢿⣶⣤⣤⣤⣤⡶⠟⠁⠀⣀
⠀⡄⠀⠀⢢⠀⠀⢀⡟⠀⣿⣿⡇⣷⣄⠀⠻⣍⣩⡽⠃⠀⣀⣾⡇⢻⣇⠀⠀⠀⠉⠀⠀⠀⣰⣾⣿⠃
⠀⢱⡀⠀⠀⠙⠛⠉⠀⢠⣟⣾⡇⢸⣿⣷⣦⣄⣀⣠⡤⠚⠹⣿⣧⠈⢿⡄⠀⠀⠀⢳⡄⠀⠉⠉
⠀⠀⠙⢦⣀⡀⠀⢀⣤⣯⠞⢹⠃⢸⡇⣿⣿⣧⠀⠀⠀⠀⠀⠙⢿⣷⡈⠻⣆⠀⠀⠈⡇⠀⠀⡀⠀⢀⡄
⠀⢀⠀⠀⠈⠉⠉⠉⠉⠀⣠⠏⠀⣾⠃⣿⣿⡟⠀⠀⣀⡤⠶⠛⠉⠉⠛⢦⡈⢧⡀⢰⠁⢠⠞⣠⣶⣿⠁
⠀⢸⡀⠀⢀⡀⠀⢀⣠⡾⠃⠀⣼⠏⣸⣿⡿⠁⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠻⡄⠳⣘⢠⡏⣸⣿⡿⠃⡴
⠀⠀⢳⣄⠀⠙⠛⠋⠁⢀⣠⣾⠏⣰⣿⠟⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢻⠘⣇⣛⣁⡤⠞⠁
⢦⣄⡀⠙⠷⣶⣶⣶⣾⣟⣫⣵⡾⠟⠁⠀⣀⣠⠤⠤⠀⠉⠛⢶⣄⣇⠀⠀⠀⠀⠀⢀⡔⣡⡭⠤⠤⡀
⠈⠻⣷⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢠⡶⠋⠁⠀⣀⣀⡀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⣸⠋⠀⢧⠻⣿⣦⡀
⠀⠀⠀⠁⢄⠰⡠⠚⠙⢲⡀⠀⣰⠏⠀⣤⠾⠋⠉⠉⠉⠛⢦⡄⠈⣿⠀⠀⠀⠀⡰⠃⠀⠀⠀⠑⠪⠝⠛
⠀⠰⠶⠶⠦⠑⢷⠀⠀⠀⠇⠀⣿⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠹⡄⡟⠀⣀⣴⣋⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠻⣄⠻⣦⣀⣀⡄⠀⠀⠀⠀⠀⢇⡤⠞⠋⠉⣀⣀⣀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠉⠛⠻⠛⠋⠀⠀⠀⠀⢀⠔⠉⠀⠀⣠⣾⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀⣀⣀⣤⠔⠚⠁⠀⠒⠊⠉
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣧⣶⣶⣶⡶⠏⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢏⣿⠋⠂⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡾⠛⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠁⠀⠲⣦⡄
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿
⠀⠀⢰⣿⠛⢻⣿⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠿
⠀⢀⣿⡇⠀⢸⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⢠
⠀⠸⣿⡅⠀⢸⣿⠁⠀⣸⣿⡿⠟⠿⠻⣯⣡⠆⠀⢀⣴⣿⡇
⠀⠀⣿⣧⠀⣾⣿⠀⢰⣿⣏⣴⣠⠀⡇⣯⢤⡼⡄⠺⣿⠿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠠⠖⠂
⠀⠀⠹⣿⣶⣿⠇⠀⢹⣿⣿⣿⡏⢠⠁⠘⢶⣶⣞⣀⠐⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠀⠀⠀⢀⠄
⠀⠀⠀⠙⣿⣿⡀⠀⣿⣿⣿⡟⠀⡼⢀⣶⣾⠻⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠶⠤⠴⠃
⠀⠀⠀⠀⢸⣿⣿⣦⣽⣿⡿⠀⢰⣿⣿⣿⡿⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⢀⣴⡛⠉⣠⣔⡀⢀
⠀⠀⠀⠀⠸⣿⡌⠛⠿⠿⠦⢀⢈⠠⡨⣇⢻⣾⣟⣧⣌⣿⣶⣤⣶⡟⢻⣿⡟⠙⠛⠻⣦⣤⡶⣿⣫⣖⣉⡀
⠀⠀⠀⠀⠀⢿⣷⣤⠶⠒⠛⠛⠛⠗⠟⠚⠈⠈⠀⠀⠉⠛⠛⠓⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⢀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⣾⠋⠀⠙⠿⣦⣄⣀⣀⣀⣠⣤⣴⠶⠛⠋⠉⠀⠀⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣓⡦⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡴⠖⠚⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠻⠁⣠⡶⠉⠀⠙⠳⣝⡆⠀⠀⣠⡴⠋⠉⠙⠋
⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢰⡟⠀⠀⣦⠀⠀⠀⠉⠲⣴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⠁⠀⠚⠁⠀⠀⠀⠀⠀⠘⣾⡄⠀⢸⠁⠀⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣟⠛⠃⢀⣴⠀⠲⠦⣀⠀⠀⠀⠀⣸⠀⠀⢹⣷⡀⠘⣇⠀⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⠃⣀⡼⠀⠈⠓⠀⠀⣠⠏⠞⠀⢀⡇⠱⡄⠈⠳⢦⡙⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡀⢀⣀⣀⡀⠔⠁⠀⠀⢀⡼⣧⠀⠙⣆⠀⠀⠙⠲⣝⣦⡙⠦⣄⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣝⣒⣾⠋⠉⠛⠲⢾⣉⡁⠈⠳⢄⡈⠳⢤⡄⠀⢀⣹⣿⣷⣄⣙⣦⣤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣒⣒⣒⣒⣀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠷⠶⠶⢄⠁⠉⢙⡛⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⠀⢀⣀⣀⣀⠹⣎⢻⡄⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠉⠉⠙⠇⠹⠆

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⢾⣿⣷⠀⠀⠀⣠⣤⣄⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢠⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠙⣿⣷⡀⣼⣿⣿⣿⣷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣯⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢸⣿⣿⣿⣿⣿⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⢸⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣇⢀⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣤⣶⣾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⠀⠙⠀⠙⠻⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡀⠀⠀⠀⠀⠈⠦⠐⠊⠉⠉⠐⢄⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠞⠉⢙⣄⠁⠀⡇⠀⠀⡀⢤⡀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⡸⠋⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁⠈⣗⠀⠁⠀⢼⣧⢰⠇⠀⠀⠸⠏⣸⠀⠀⠀⡘⠀⢀⠃⣠⠒⠲⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠠⢚⠡⠐⠂⠀⠘⢋⣀⠀⠀⠀⠀⠀⠙⠀⠀⢰⠁⠀⢸⠎⠉⠃⠀⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠘⢷⣄⣰⠃⠁⠀⠀⣀⠀⠀⠀⠉⠁⠀⠀⠚⠩⠆⠀⠀⠀⠉⢒⢌⠣⡀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢿⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⣩⡏⠀⠀⠀⠀⠀⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠛⠓⠚⠛⠒⢤⠽⠯⠭⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⠀⠀⠀⠀⠀⣰⣾⠿⠋⠀⠀⠀⠀⠀⠀⠈⠣⣤⡴⠖⠛⣆⡀⢀⡀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣰⡏⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠈⠉⠙⢻⡆⢀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢀⣴⠏⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠀⠀⣼⠛⠘⠀⡂⠀⣾⡇
⠀⠀⠀⠀⠀⢀⣠⠞⠋⣀⣴⠟⠁⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢸⠟⢙⣶⣄⠀⠀⠀⠀⠀⠀⠈⢿⣄⣴⠏⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⢀⡴⠛⢁⣤⠾⠋⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣼⠁⠙⢧⡀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⢀⣠⠟⠁
⠀⠀⣰⠟⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⣇⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇
⠀⢠⡟⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣿⡀⠀⠀⠀⠙⣷⡦⢄⡀⠀⠀⠀⢀⡼⠁⠈⠻⣦
⠀⢸⡇⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⣏⠁⠀⣀⣤⠞⠉⠀⠈⠿⣦⡀⠴⠋⠀⠀⠀⠀⣼⡧
⠀⠸⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣤⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⢻⡄⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠃
⠀⠀⠀⠻⣄⠀⠙⢷⣤⣀⣀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁
⠀⠀⠀⠀⠈⠳⣦⣀⠈⠉⠛⠛⠛⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠟⠛⠻⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠛⢿⡶⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠶⠦⣤⣤⣶⣤⣤⣄⣀⣀⣀⣀⡀⣈⡀⠛⠩⣉⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠷⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⠋⢹⣿⣿⡏⠙⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣘⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⣿⣿⣿⣿⣿⣿⠛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⡟⠀⠀⠘⡇⠀⠙⢿⣿⣿⡿⠋⠀⢸⠃⠀⠀⢻⣿⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⣸⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎⠀⠀⠀⠉⠉⠉⠉⠙⠒⠲⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⣠⣶⣿⣿⣷⣈⣿⣝⢿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⣀⠀⠀⣠⣾⣿⣿⣟⠷⠞⠉⠉⠉⠀⠟⠿⢿⣿⣷⡄⠒⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢸⣿⣯⣹⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠐⢶⣷⣦⣿⣿⠀⠀⠉⠉⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⡜⠁⢀⢀⣿⣿⣿⣿⣿⣏⣻⠀⠀⠀⣀⠈⠑⡄⠀⠀⠀⠀⢙⣿⣻⣧⡤⠖⠚⠉⠁
⠀⠀⠀⣠⠴⠚⠛⢛⣷⣶⣾⣅⡀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⢿⠛⠉⠀⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⣠⠟⠋⠁
⠀⠀⠀⢀⣐⠔⣀⠄⠉⠛⣿⣟⡿⣶⣄⠀⠀⠀⢸⠙⢿⡿⠻⠷⢋⠀⠀⠀⠀⠀⠀⠀⢀⠞⡀⠉⠣⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠉⢻⣷⣶⣤⣠⠄⠘⠿⣾⣿⣷⣄⢀⡼⡆⠠⢐⠀⠀⠸⡄⠀⠀⢸⣶⣄⠀⠆⠀⠙⢢⠖⡠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣁⠄⠈⠿⣭⡻⣿⣼⠃⠄⠨⠀⠀⠀⠙⣆⠀⠀⠙⠛⣀⠤⣢⠖⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢶⣤⡤⢀⡀⠙⠿⣿⣦⡀⢀⠈⠹⣯⣿⣶⣂⠎⠀⠀⣀⣤⣾⡷⠒⠒⠉⠁⣘⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣔⢀⡀⠀⠘⠿⣷⡴⠂⠀⠈⠉⠛⠦⣀⠹⠿⠛⠁⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⡤⠀⢀⠀⠀⠉⠑⠲⢶⣄⣀⠄⠈⠙⠲⢤⣤⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠥⣖⠁⠀⠀⠀⠀⠉⢻⣿⣦⣴⠄⣀⠈⢙⣦⣀⠈⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣭⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⣁⠤⠀⠀⠹⢿⣿⣯⡁⠀⣀⠘⢿⣷⣄⠀⠀⠉⠓⢦⡀⠀⠀⢴⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠁⠀⠀⠙⠻⠿⣌⠄⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣀⣀⣶⡆⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⣈⢹⣿⣿⣿⣿⣿⣷⣾⢿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⡿⠿⠿⠿⠛⣋⣭⠹⢯⣷⣾⣿⡿⠛⡿⠿⣍⢳⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣤⣤⡤⣤⣶⣬⣭⣤⣉⣉⠉⠁⢠⣾⣿⣖⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣄⠉⣹⢿⣿⣿⣿⡦⢘⣿⣿⠛⠋⠈⣹⠟⣿⠿⢿⠟⠛⢋⣽⣭⣷⣦⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⡀⣀⣠⡄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣏⣀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢠⡿⠻⢿⡿⢻⣿⣿⣿⣷⣾⠟⢿⢿⣽⠛⠿⠿⢛⣩⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⣼⣤⡀⢀⣿⣸⣿⣿⣿⣿⣿⡀⠈⠛⠐⠃⠀⠀⠘⠋⠋⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⡟⠛⣿⣯⣙⣿⣿⣿⣿⣿⠖⠐⡲⢷⠞⠒⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⣨⣭⣽⣿⣶⢿⣾⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⢿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠟⣴⣋⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠙⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢠⣤⠛⠋⠛⢼⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠒⠂⠀⠀⠄⠙⠛⢹⣿⡿⠟⠛⠿⣿⣿⣭⣾⣷⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⣾⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢠⠈⠀⠀⠁⠀⠀⠀⢸⣿⣷⠀⠀⢀⠈⣿⢟⡭⠇⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⣿⣿⠂⢹⣿⡿⠋⢹⣿⣿⣿⣿⠟⠀⠐⠀⠀⠃⠀⠀⢀⠀⡀⠀⣼⣿⣿⣷⣄⣿⡗⣡⣿⠅⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢾⣿⣦⢀⣿⣿⣀⣿⣿⣿⣿⠃⣤⠀⡁⠀⠀⠁⢀⠀⠌⣀⠐⣼⣿⣿⠿⠿⠛⠋⣴⠿⠻⢛⡃⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠿⠿⢿⣿⣿⠿⣿⠙⢿⣿⠯⠆⠀⢣⠀⣡⠒⠯⡴⠶⠈⠙⠉⠉⠀⠀⢀⣀⣀⣤⣠⣤⡞⠉⠁⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⢠⣤⣿⣏⣀⣾⣿⣷⣄⣿⣆⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⢀⣴⣶⣿⡿⢿⣿⣿⡟⠿⢿⣿⣿⣿⣿⢿⣄⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠘⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⣠⡴⢾⠿⣿⣿⣿⡏⣠⣿⣿⣿⣷⣀⡀⠉⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⢿⣿⡟⢿⣿⠈⠉⠀⠙⠦⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⠋⠀⠘⣿⣧⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⢿⣿⣿⣿⣿⣿⣿⣯⠅⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣤⣀⣀⣤⣤⣾⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣖⣤⣶⢿⡿⣫⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⢋⣷⢟⣽⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡿⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡦⡽⠛⠁⠀⠀⢀⣴⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢼⣿⡠⡀⠙⠋⣿⣿⣥⣤⣀⠀⠀⠀⠀⣠⣶⣶⣿⡿⢋⡟⢀⡄⠀⠀⠀⢨⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣧⡀⠀⠀⠹⣿⡅⠀⠃⠀⠀⠀⣞⢩⣿⣿⢗⣰⣿⣿⡏⣀⣀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠁⣾⣀⣴⣿⣿⣿⣷⣦⡀⠘⠃⠾⣋⣴⣿⣿⣿⣿⣟⣽⣇⣺⡵⠖⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠘⠛⢿⣿⣿⣿⣿⣿⣞⡁⢀⠀⠀⠀⣀⠀⠀⣰⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠉⠉⠛⢿⣿⣿⣷⡾⣿⣿⣿⣿⣿⣿⣿⣊⣅⣀⠄⠘⠉⢴⡿⠋
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⣿⣿⠁⠀⣠⣴⣿⡿⠟⠁⠀⠈⢈⠽⣿⣿⣿⣿⣿⣯⡷⠀⢀⣈⣍
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⢈⣿⣿⣿⣿⠉⠀⠀⠛⠋⠁⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⠀⠴⠖⠀⠀⠀⠠⠒
⠀⠀⠀⠀⠈⠳⢤⣀⣙⣷⣤⣀⠀⠀⠉⢸⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠐⠿⢻⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢌⣹⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣿⡿⢋⣤⣤⠄⠀⠀⢀⠄⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠽⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣤⣴⣦⠀⠀⠀⠀⠀⠀⢛⣿⣾⠋⠁⣠⣤⡴⠊⠁⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠛⠁⠀⠀⠀⠀⠀⣴⣿⡿⣷⠞⢉⡡⠈⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⠛⠋⠁⠏⠈⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⣾⣟⣽⠁⠀⠀⠀⠀⠀⢠⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢼⣿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣤⠞⠀⡶⠋⣝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠉⠓⠀⠀⠀⠀⠈⠹⠋⠉⠉⠓⣄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡼⠁⠀⣠⠔⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣄⠘⣤⠖⣉⡡⠬⣉⠢⡀
⠀⠀⠀⠀⠀⡠⠒⢉⣀⣀⣀⣈⠉⠚⠃⠀⢰⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡈⠀⠀⠈⡆⢻⠊⠁⠀⠀⠀⠱⡘⡀
⠀⠀⠀⠀⠜⢀⡖⠉⠀⠀⠀⠀⠉⢳⠀⠀⢼⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⠀⢀⡀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⢰⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⣳⣿⣇⣤⠤⠤⠤⢿⣾⠇⢀⡇⡜⠉⠉⠑⢄⣀⡴⣡⠁
⠀⠀⠀⠘⡄⢳⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠙⣤⡤⠴⠛⠛⠁⠤⣄⠀⠀⠠⠈⠒⠺⠤⣇⠀⠀⠀⢸⡉⠙⠓⠤⢄
⠀⠀⠀⠀⠱⡄⠳⢄⣀⠀⠀⠀⠀⡠⠃⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠳⣤⡄⠀⠉⢉⣦⢄⡀⠑⢄
⠀⠀⠀⠀⠀⠈⠒⠤⢌⣉⣉⣉⣠⠴⠚⡟⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠴⠦⠤⢤⣤⡀⡿⡍⢢⡔⢉⡤⠦⢄⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠞⠋⠉⠀⠀⠀⠀⠀⢀⣀⣀⡠⠀⠀⠀⠀⣀⠔⠁⢸⠀⢳⠋⢠⡄⠀⠁⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⢤⡖⠋⠁⠀⠀⢸⡀⠈⠛⠁⠈⠁⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢀⠀⠹⣄⠀⠀⠀⢠⠁⠀⠀⠀⠀⣶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠢⠤⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠸⣄⣠⢤⠏⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⢰⠤⠔⠂⠀⠀⠀⠀⠋⢁⠀⠀⠀⢹⡤⠋⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠠⡀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠸⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢹⣤⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠳⣄⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠈⢹⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⣤⠞⣹⢷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢸⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠤⢀⣹⡀⠀⡼⠀⠀⠀⠀⠀⠀⠉⠓⢦⠀⠀⠀⢠⠟⠀⠀⠘⠑⠂⠢⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣄
⠀⠀⠀⠀⣀⠔⠉⠊⣡⡔⠀⠀⠀⠀⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣤⡞⠋⠀⠀⠀⠀⠉⠲⠄⠀⢭⣉⡇⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⢈⠂
⠀⠀⠀⣟⣂⠭⠴⠊⢀⡰⠒⢲⠞⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡽⠀⠉⠛⠛⠓⠒⠶⠒⠒⠒⠒⠋⠀⠀⠀⠀⠄⠒⠠⡜⠀⠀⢈⣁⡈⢑
⠀⠀⠀⠈⠙⠲⠴⠒⣩⠐⠒⣁⣠⡤⠔⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢠⠔⠒⠀⢤⡄⠤⢀⣤⠀⠀⠀⠀⠀⠘⢄⠀⠀⠣⣀⣠⡎⠀⠈⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠀⠀⠀⠳⠶⢦⣤⠶⣤⠶⠦⠾⠁⠀⠀⢇⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⡖⠐⢂⠀⠉⠘⢄⠀⢀⡰⠤⠤⣄⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠐⠂⠒⠤⡆⠁⠀⡄⠈⠁⠁⠰⠦⠊⠒⢫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠶⢲⡆⠀⠘⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣤⣀⣤⠴⠦⣄⡀⠀⠀⠀⠀⠀⢁⣴⠋⡀⠀⣴⣏⣤⡄⠀⣴⣋⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠙⠏⠁⠚⠉⠀⠀⠀⢸⡇⣀⡀⠀⠀⠀⠛⠛⠋⠁⠀⠉⠉⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠙⢳⡄⠀⠀⣠⡤⠴⠶⠶⢦
⠀⠀⠀⠀⠀⣽⠆⠀⠀⠈⢮⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡶⢿⣤⣤⣤⡄⠀⠀⠀⠘⢿⣦⣼⠃⠀⠀⠀⠀⢘⡷⠶⠤⣤⣀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⢸⡷⠶⠶⠞⠋⠁⢀⠀⠤⣄⡀⠈⠙⢦⡤⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠈⢷⣶⠒⠒⠦⢤⣀
⠀⢀⣠⣾⣅⠀⠀⠀⠀⠀⠀⠀⢀⣙⣷⣄⣾⠁⢠⠶⢦⣄⠀⢀⣀⣠⡾⠁⠀⠀⠀⢻⡄⢀⣴⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠸⡏⠳⡄⠀⠀⠈⠉⠓⠦⣄
⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡇⠀⣿⠀⠀⣹⡦⠈⠉⠁⠀⠀⢢⡶⠃⠘⣷⡾⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠛⠶⠚⢿⠃⠀⠀⣰⠀⠀⢸⡇⠀⢰⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷
⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠘⠦⠤⠟⠁⠀⠀⣸⠇⢀⡾⠁⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣷⠀⠀⠀⢀⣀⡠⠋⠀⣾⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡉⠂⠛⠋⠉⠀⠀⣸⠏⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⡳⣶⣶⣤⣤⣴⡿⠀⠀⠀⠀⠀⢀⡍
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⣴⠾⠛⣃⠀⠉⠙⠛⣿⠃⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣠⡶⠟⣉⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠛⢷⣿⣋⣴⠿⣫⣾⡿⠛⢾⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⣤⣄⣀⣀⣀⣈⣿⣿⡿⠿⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⣠⣤⣄⡀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠪⠤⢍⡉⣻⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠈⢉⠉⠉⠐⠒⠥⢄⣀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠃⠀⠀⠀⡠⠀⠈⠙⠢⣄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⣿⣦⠸⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠃⠀⠈⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠫⠌⡿⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⡼⠣⠀⠀⠀⠈⢋⠉⠉⠉⠉⠉⢳⠀⠀⣰⣻⠿⠴⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠕⠭⡁⢸⣦⣄⣀⠀⠀⠑⠤⢀⡠⢔⣁⠔⠺⣅⠀⠀⠀⣀⣀⠀⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣒⣁⡀⠉⠉⠉⠉⠙⠋⢷⡉⠉⢁⠄⠀⠀⠈⠓⣤⠚⠉⠩⣇⡀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣼⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠉⠹⡁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣴⣿⣶⣄⡠⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⣿⣿⣦⡤⠤⠔⠾⣿⣿⣿⣿⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠘⡏
⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢹⠿⠛⠛⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⡩⠉⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠹⡍⠁⠀⠀⠀⢀⡊⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠙⢦⡀⢰⣾⣿⣿⡤⠤⠀⢒⡿⠃⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠀⠈⢷⣅⣀⠀⠀⠀⠀⠀⣠⠊⠉⣛⠻⡉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠤⠶⠚⠉⠀⣘⠲⠦⠀⠀⡴⠉⠑⣷⣄⠱⢤⣀⡜⠁⠀⢉⡶⢦⣀⠔⠛⠓⣾⣉⣹⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⢳⣂⡉⠤⢿⣦⣀⢩⡙⠢⡴⠋⠀⠀⠀⠀⠀⠀⢾⣀⠤⣬⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⣉⠵⣽⡁⠈⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢉⡝⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣊⣩⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠁⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⡤⣄⠀⠀⠹⣿⡿⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣴⡾⠻⢿⣶⣤⣿⠁⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣸⡟⠀⢀⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣶⣄
⠀⠀⠀⠀⠀⣿⠃⠀⠀⢻⡀⣿⡇⠀⢠⣾⡟⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠸⠇⣿⡇⠀⢸⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣁⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠟⠀⢀⣾⡛⠉⠛⠃⠀⢸⣿
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢀⣿⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣏⠀⠀⠛⠉⠉⠓⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⣆⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⢿⣶⣦⣤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠙⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠃⠀⠀⠘⣿⣿⣿⣿⡟⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⡟⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⠙⠻⠷⣦⣤⣄⣀⣀⣀⣀⣤⣤⡶⠻⠏⠀⢠⡿⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⡴⠒⠢⡈⠛⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠀⠀⣸⠇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⡴⠛⠳⢶⣇⠀⠀⠘⣾⣿⠿⠛⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠙⢻⣿⣦⡀
⠀⠀⣀⣘⣄⠀⠀⠈⠀⠀⠀⠘⠃⠀⠀⣰⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⡿⠛⠻⢿⣿⡿⠁⠀⠀⢸⡿⠟⠛⢢⡀
⠀⢾⠉⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠿⠁⠀⠀⠀⠋⠀⠀⢀⣼⣧⡀
⠀⠈⣳⣤⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠛⠉⠉⢳
⠀⢺⡅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠈⠻⡦⠄⣀⣠⡴⠛⠻⣿⡿⠋⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠁
⠀⠀⠀⠀⢀⣤⣾⠀⠀⠈⠛⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠁
⠀⠀⠀⣰⠟⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⢻⠟⠋⠉⠻⣿⣿⣶⣶⣾⣿⣿⣿⠟⠋
⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⡼⢋⡡⠄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠓⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣦⡀⠀⠀⠚⠁⠉⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⣀⠀⣠⡟⠀⠀⠀⠐⠦⢌⢳⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣴⠾⠛⠁⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣴⠶⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣀⡀⢠⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠉⠁⠀⠀⠁⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇⢳⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡐⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡜⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠼⢦⡼⠃⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⡐⠁⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠎⠀⠀⠀⢧⣀⣀⣀⣀⣀⣤⣤⣀⢼⠠⠤⠴⠶⠶⠶⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠮⠍⠤⠛⠀⠀⡂⢽⠩⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⠀⠀⣠⡆⠀⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣧⠇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣶⡞⠀⠀⣿⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⢣⣀⠀⣀⣀⣠⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢀⡄⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⡸⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠌⠁⡅⠀⠀⠀⠀⡠⠂⢰⠀⢠⣷⠃⠀⠑⠌⣢⡀⠀⠀⠀⠀⢠⡾⠛⠉⢦⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⢠⠊⡠⠊⠀⠀⡇⠀⠀⣠⠊⠀⠀⠀⡇⠀⣿⣶⣄⡀⠀⠈⠳⢄⠀⠀⠀⣼⠃⢠⠔⠊⠛⢾⣤⡀⠀⠀⡼⣧⠀⠀⠀⣼
⠀⠀⠀⠀⡐⠁⠊⠀⠀⠀⠀⢻⠀⢸⠃⠀⠀⠀⠀⡇⠀⠉⢻⠁⠉⠂⢀⠤⠊⠀⠀⣸⡇⠀⡇⠀⠀⠀⢈⡉⠁⠀⣿⠁⣿⡶⠶⢶⠋
⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠒⠒⠊⠁⠀⠀⢀⢜⡜⡇⢰⠃⠀⠀⠀⣈⡁⠀⠀⣯⠀⢉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣤⡤⠖⠊⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠀⠼⣦⣀⣀⣴⠋⢧⠀⠀⠘⡇⢨⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣄⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠹⣄⠄⠀⠀⠉⢉⡰⠀⠸⡆⠀⢠⠃⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⢻⡄⠈⡁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠉⠱⠖⠊⠉⠁⠀⠀⠀⢻⡀⣼⠀⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹⡀⣧⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡇⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣇⡟⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡺⣿⠧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⡴⠚⣇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡛⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⣷⣤⣾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⠟⠁⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⣤⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠡⠁⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⡄⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠀⠀⠀⠀⠐⠀⣄⣀⣀⣤⠊⠀⠀⡇⠀⠀⠀⣴⠃⠁⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡿⠿⡿⢿⠀⠀⢰⡇⠀⠀⠀⢈⡆⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠲⣄⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣞⣀⣀⠀⠀⡼⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠁⢾⠀⠀⠀⠀⠘⠢⠄⣀⠀⠀⢀⣀⡠⠔⠛⢆⠀⢸⣉⣉⣁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡈⠑⢄⣀⠤⠎⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠤⠐⠊⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠶⠦⠴⠶⠶⠒⠚⠛⠉⠉⡗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⣀⣠⣞⠁⢠⡟⠐⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠦⣀⣠⠏⠙⠋⠉⠉⠀⠉⠑⣯⠝⢃⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣰⠋⠉⠀⠀⠀⠀⠀⢀⣴⣯⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢤⣉⠓⠶⢤⣀⠀⠀⠀⠈⠉⠛⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠷⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⡿⠿⠛⠛⠿⢿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⢸⡏⠉⡉⠉⠻⣿⣿⣿⣿⡟⡉⡙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣽⠁⠾⠂⠀⣿⣿⡇⢻⣿⡿⢻⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆
⠀⠀⠀⠀⣞⢉⠀⢀⣀⣴⣿⣿⡇⢸⣧⣤⣵⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠰⣇⠀⠀⠈⣿⣿⣿⠟⢠⣿⣿⣿⡏⢸⣿⣿⣿⣿⣟⢷⣦⣄⠀⠀⠀⠻⣿⣿⣿⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠳⠤⠤⠾⠿⢯⣥⣾⣿⣿⣿⣟⠓⠈⢿⣿⣿⣿⣷⡅⠙⢿⣿⣦⣄⠀⠙⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠈⠛⠙⠀⠀⠈⢻⣿⣿⣿⣿⣦⡈⠻⣿⣿⣷⣤⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣄⢄⣀⠀⢜⣶⣮⡻⢿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣤⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡎⣿⣇⠀⠈⠙⠛⠿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣼⡏⠙⢦⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠉⠳⣤⡀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⢀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⣿⢿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣇⠀⢸⣿⣧⡻⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠈⣿⣿⣿⣶⣺⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇⠀⠈⠙⠛⠛⣷⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠁⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠙⠛⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠀⣀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⣿⡆⠀⠀⠀⠀⠐⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⡿⠋⠀⣠⣴⣆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⣿⣿⣿⣿⡉⠉⠀⠀⠀⠉⠛⠛⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⣿⣷⣄⠈⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀
⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣾⣿⣯⡀⠀⠙⢿⣿⣿⡆⠀⠈⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦
⣾⡿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣦⡀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢀⣴⣿⣿⣿⣧
⠙⣿⣦⠀⠐⢶⣾⠂⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣦⣤⣴⡾⠟⠀⠀⠘⠛⠉⣀⣼⣿⡆
⠀⠈⠻⣷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣧⣤⣤⣀⡀
⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠻⣿⣶⣤⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠘⡷⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⣿⣿⠿⣿⣦
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣶⣤⣤⣶⠟⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠋⠀⠀⠸⠟⠁⢀⣾⣿⣷⡀
⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠠⡿⠿⠛⣿⣷
⠀⠀⠀⠀⠀⠹⣿⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠋⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡀⠀⠈⠻⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣏⠀⠈⠙⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠁⠀⠀⠀⠀⠉⠉⠁⡀⠀⣿⣿⠃⠀⣠⡀⠀⠀⣠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⣿⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣷⣤⣶⣿⣤⣾⣷⣴⣿⣿⣷⣾⣿⣿⣶⣾⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⠿⠿⠿⢿⣿⣿⡟⠋⠀⢈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠙⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠙⠛⠛⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⢠⡀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣤⣠⠀⢀⣤⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⣠⢤⢠⣄⠀⢀⣀
⠀⠀⠀⠜⠁⠀⠀⠛⠃⠀⠘⠁⠀⠀⠀⠀⠂⠁⠈⣇⠀⣴⠃⠀⠐⠀⠀⢠⣆⡄⠈⣡⡀⢆⠷⠂⡠⠘⡇⢫⢶⡄⠀⠀⣴⠮⠃⡟⢘⡄⣱⠉⡸
⠀⠐⠀⠂⠀⠀⠀⠐⠁⠁⣠⡦⠤⠦⠀⠀⠀⢀⣤⡌⠀⠈⠂⠀⣀⣀⣠⠾⠊⠀⡞⠁⠀⠀⠓⠂⠀⠀⢧⡀⢨⠃⢹⠀⣧⢀⣠⠇⡈⠒⠉⠒⠃
⠀⠀⠀⠀⢰⣶⡂⠀⠀⢰⢿⣾⠃⢀⠀⢠⣄⣀⠀⠉⠀⣀⢠⣤⠀⡉⠀⠀⠀⡰⠂⠀⢀⡀⠀⠠⠀⣤⠀⣿⣈⡀⠈⢀⣁⣼⡇⢘⠑⢦⡉
⠀⠀⠀⠂⢀⠟⡀⢐⠀⠈⠦⠽⠀⢘⡀⢉⢱⠟⢷⣖⡶⠿⠧⠉⢀⡩⢀⣄⠘⡇⠀⠠⡟⠁⠀⠀⡰⠃⠀⡟⠙⠃⠀⠀⠉⠉⡄⢈⣀⡐⠓⢷⡀
⠀⠀⠐⠀⠁⢠⠈⠀⠃⣀⣴⣾⡇⠀⠘⠠⠀⢀⣠⣿⣄⡀⠀⠠⠂⢀⠎⠸⠃⠀⠀⠀⢀⡀⣼⠋⡀⠀⠄⢶⣿⠶⠀⠀⢀⠀⠀⠈⠛⠤⠄⠚⠁
⠀⠀⠀⠀⠂⢸⡐⠀⠈⢿⡍⠉⢻⠝⠈⠀⠘⠎⠛⠿⠋⠑⠃⢀⠃⠚⢀⡠⠖⠀⣇⠐⠢⠉⠐⠎⠀⠀⠀⢠⣿⠀⠀⠀⠀⠱⠆⠀⠀⣠⡄⠋
⠀⠀⡀⠀⠈⠠⠏⠀⠀⠀⠙⠒⠡⣦⠀⠀⠀⠀⠀⠀⣡⠀⠂⠊⠠⣶⡁⠄⠂⠀⠙⠀⠀⠄⣀⢦⠀⠙⠤⠀⠀⠀⠄⠋⢀⢄⠐⠒⣾⣷⡤⠂
⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⠙⠃⠀⠀⠀⠀⠉⠈⠁⠀⠂⠐⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⣫⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⣡⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⢉⣡⡴⢛⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣠⣾⣿⣿⣿⠿⢛⣋⣩⣥⣤⣶⣶⣶⠶⠿⠛⠛⢉⣴⡟⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⣾⣿⣿⣿⣽⣶⣿⠿⠟⠛⠋⠉⠉⢀⣀⣠⣤⣶⡾⠟⠉⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⡿⠟⠋⠁⢀⣠⣤⣴⣶⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⠟⠉⢀⣠⡄⠈⣩⡥⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠶⢤⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⢀⣴⣿⣿⠀⠀⣀⣀⢀⠀⠉⠙⠃⠀⠀⠀⠀⠘⠋⠉⣀⣀⣀⠀⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⣴⣿⡟⠈⢿⡄⠰⣿⠛⣿⣿⡟⠦⠀⠀⠀⠀⠀⠠⢾⣿⣿⠛⡿⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣾⣿⣿⣷⡀⠀⠁⠀⠈⠓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠁⣸⣧⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⢻⣿⣿⣿⡟⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⣿⣿⣿⣿⣿⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠴⠀⠀⠀⠀⠀⣸⣿⠟⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢷⢸⣿⣿⡹⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣤⣀⡀⠀⠀⣰⡟⠁⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠈⢧⡙⢿⣿⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠹⢯⣍⣉⡴⠋⠀⢀⣾⠋⢀⣴⡿⠟⠁⠀⠀⠀⢠⡞⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠈⢻⣷⣶⣾⣷⣿⣿⣿⣇⠙⢷⣤⣀⠀⠀⠈⠁⠀⣠⣶⣿⠃⢠⣿⠋⠀⡠⢤⣄⠀⢀⣿⢡⣿⡟⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⢻⣷⡹⣿⣿⣿⣿⣿⠀⠀⠉⠻⢷⣶⣶⣶⣾⣿⣿⣿⠀⢸⣯⠀⠀⠀⠀⢹⡇⠸⣿⣼⡟⠀⢀⠀⠀⢸⣿
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⢻⣷⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠉⠸⣿⣿⣿⣧⠀⠻⣷⣤⣀⣤⣿⠃⠀⢿⣿⠁⣠⣏⠀⠀⣿⣿
⠀⠰⣌⠙⠻⣦⡀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⢿⡇⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣌⡉⠛⠉⠀⠀⠀⠀⠻⢠⣟⡿⠀⠀⣿⡿
⠀⠀⠘⣷⡀⢙⢿⡆⠀⢰⡄⢀⠀⠘⣿⣿⣧⢸⣧⠸⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣯⣙⠛⠿⣿⣶⣌⡓⠶⣄⠀⣼⣻⡇⠀⢰⣿⠁
⠀⠀⠀⠙⢿⣌⠪⡻⣆⠸⡷⠋⠀⠀⠘⣿⣿⡌⡏⠀⠀⠀⢀⠶⠋⠉⠉⠛⢶⣄⠀⠀⠀⠙⢦⣙⢿⣿⣿⣦⣄⠉⠻⣿⣆⠀⠀⢿⡿⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠙⠳⠮⠳⢄⠁⠀⠀⠀⠀⢻⣿⢻⡇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⠓⢌⡻⣿⣿⣷⡄⠈⢿⣇⠀⠘⢁⠴⠋⣠⣴⡶⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠁⠀⣠⠂⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠙⠮⡻⣿⣿⡄⠀⣿⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⢠⠖⠈⠀⠀⠀⠀⠀⠀⢀⣿⣿⡸⣿⡀⠀⠀⠀⣼⠃⠀⣠⣴⡟⠀⠀⠀⠻⣆⠀⠀⠀⠠⢄⣀⠙⡌⢿⣿⡀⢹⠆⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠹⣷⡀⠀⢰⡏⠀⣴⣿⡟⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠉⠳⣬⡘⣿⡇⣿⠀⠀⢀⣀⣀⣀⣀⠐⢤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠈⠻⣄⠈⠇⢰⠿⠋⣀⣤⠤⠤⠄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⢷⡜⠃⠃⢀⣦⠭⠭⠭⠉⠻⢷⣦
⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠟⠛⠉⠀⠀⠀⠘⠻⠿⠿⠶⠦⠁⣶⣦⢀⣈⣀⣀⣀⠀⠀⠀⠀⠈⣣⡴⠖⠒⠄⠀⠀⠀⢿⡀⠀⠀⠙⠛⠿⠿⠶⠶⠆⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠓⢀⣤⠉⡅⢲⣬⣙⠛⠛⠛⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢸⣿⡄⠻⣿⣷⣄⠀⠀⠀⠀⢹⣿⣄⡀⠀⣀⣠⣾⠃⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⢸⣿⣧⠀⠈⠻⢿⣷⡀⠀⠀⠀⠙⠿⠿⠿⠟⠋⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠁⠀⠀⠸⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣀
⠀⠀⠀⠀⠀⣠⣴⡾⠟⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⠻⢷⣦⣄
⠀⠀⠀⢠⣾⠟⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠈⠻⣷⡄
⠀⠀⢰⡿⠃⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠘⢿⡆
⠀⢀⣿⠃⠀⢠⣿⣿⠇⠀⠀⠀⠀⢀⣠⣴⠶⠿⠟⠿⠷⢶⣤⣀⠀⠀⣀⣤⡶⠾⠿⠻⠿⠶⣦⣄⡀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠘⣿⡀
⠀⢸⣿⠀⠀⢸⣿⣿⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⣿⣿⡇⠀⠀⣿⡇
⠀⠘⣿⡄⠀⠸⣿⣿⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣿⣿⠇⠀⢠⣿⠃
⠀⠀⠹⣷⡀⠀⢹⣿⠀⠀⣼⡇⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡏⠀⢀⣾⠏
⠀⠀⠀⠙⣷⣄⠸⣿⡀⠀⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠃⣠⣾⠋
⠀⠀⠀⠀⠈⠙⢿⣿⣇⠀⢻⣇⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⣸⡟⠀⣸⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢨⣿⠂⠈⢿⣆⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣰⡿⠁⠐⣿⡅
⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢿⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠘⣷⡄⠀⠀⠀⠀⠀⠈⠻⢿⣋⠉⠉⠉⠉⣙⡿⠟⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣌⡛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⢛⣡⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣭⣽⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣯⣭⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠲⠦⢤⣤⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠋⠁⠉⠑⠿⣶⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⣤⣄⡀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡤⠖⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⢰⠋⠀⣀⡙⠋⠀⠀⠀⡤⠤⠂⠶⠤⢤⠤⠂⠓⠒⠆⢀⠀⠀⠀⠋⣠⣄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⢻⠀⢰⢹⠙⡆⠀⠀⢈⠀⠀⢀⣀⠀⠀⠀⢀⡠⠄⢀⣨⠀⠀⠀⣾⠈⠉⠀⢠⡇
⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⢸⠀⢉⠀⡀⡜⠁⣴⣲⣦⠑⡄⢐⢣⣆⣶⡄⠈⠂⡀⢁⡇⢀⠀⠀⡼
⠀⠀⠀⠀⡼⠁⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⣠⢿⠀⠀⠉⠛⡩⠀⡇⠈⠈⠉⠉⠁⠀⢀⠻⠜⠁⠀⠀⡼
⠀⠀⠀⡼⠁⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⢻⡌⢷⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠞⢀⣤⣀⣤⠞⠁
⠀⠀⣸⠃⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠟⠀⣧⠀⠙⣤⠃⠀⠐⠁⠀⡀⠀⠈⢠⡏⠀⢰⡇
⠀⢰⡇⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠋⠀⠀⠀⠸⢇⠀⣃⠀⠀⠀⠉⠚⠀⠀⠀⢨⠃⣰⢿⣀
⠀⣼⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠈⢗⠿⣆⠀⠒⠚⠙⠂⠉⣠⠿⠞⠃⠀⠙⠿⣄
⠀⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠏⡐⠀⠀⠀⠀⠀⠀⠀⢸⡃⠈⠙⠲⠶⠶⠶⠛⠁⠀⢀⠀⠀⠀⠘⢧⡀
⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠈⡟⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠐⠿⣄
⢻⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀
⠘⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢈⣳⣄⠀⠀⠀⠀⠀⠀⠈⠳
⠀⢧⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣀⣀⠠⣤⣤⣼⢛⣉⡁⢨⡿⠀⠀⠀⠀⠀⠀⣠
⠀⢸⡆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⠚⠉⠉⢉⣩⡤⠶⠒⠒⠓⠒⠠⡀⠙⣌⠁⠀⠠⣀⠀⢀⡼⠁
⠀⠀⢷⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⢦⡀⠀⠀⠙⣿
⠀⠀⠘⣆⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢦⡀⣀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠻⡄⠀⠀⠘⢦⡀
⠀⠀⠀⢼⡄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠳⡄⠀⠀⠈⡇
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⡀⡇⠀⢀⡇⣿
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⠀⣠⠇⣿⢀⣇⣰⠞
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠁⢠⠃⣜⣀⡷⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡴⣫⡏⠑⠒⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠹⣦⣄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢀⡴⠟⠋⣹⠀⠀⠀⣸⠃⣀⣠⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠶⠚⠛⠒⠦⣤⣀⣀⣰⡟⠀⠀⠀⠀⣠⠟⠀⠀⣠⣏⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⡴⠧⠤⠖⠋⠁⠀⠉⠳⢤⣤⡤⢤⡀⠀⢠⠀⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⠐⠦⡈⣇⠀⡷⠀⢈⠆⣰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡛⠁⠀⢀⣠⠤⠶⠶⠤⣄⠀⠘⡆⠀⢳⢸⠀⠳⠤⠞⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⢸⠆⠀⢙⠀⡼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢨⠀⠀⠉⡅⠀⠀⠁⢤⠤⠤⠤⠤⠤⣤⠠⠀⠀⠀⠀⠀⢀⡀⠅⠀⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠐⠀⠀⠀⠰⠸
⠀⠀⠀⠸⠀⠀⢈⠀⠀⠤⡀⠆⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⡂
⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⣀⡀⠀⠀⠀⡀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠆⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠠⠖⢠⠜⠉⠣⠀⠀⠉⠓⢤⠤⠥⢆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡠⠊⢉⣰⠎⡀⠔⠉⠀⠀⠀⡀⠀⠈⠉⠐⢱⡆⡈⠉⠷⠒⠒⠛⠘⠤⠤⠄⠀⠄
⠀⠀⠀⠀⠀⣧⠔⠁⠀⡌⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠑⡼⠁⢉⠁⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡌⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠃⠀⠀⣰⠠⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢄⡀⢀⣀⣀⣀⠀⠀⠠⠊⠀⠀⠀⠀⠸⣇⠘⣖⣲⠆⠁⠈⢂
⠀⢀⠀⠀⠀⠀⣿⠄⠀⠤⠂⢁⡁⡀⢀⢀⡀⠀⢉⠐⠖⡀⠒⠐⣃⣤⡈⠉⠉⠀⠊⠉⠉⣨⣀⣀⣀⣀⣀⣀⡀
⠀⠈⠀⠀⠀⠀⡏⠤⡎⠀⣀⠿⢣⠄⠀⠀⠄⣉⠞⠵⡀⢘⠀⠀⠉⠘⠁⠉⠉⠉⠋⠉⢻⣿⣉⣉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠰⠄⠲⠚⠚⢁⠄⠊⠐⠄⠂⢀⠀⠁⠀⠉⣛⡛⢛⠂⠻⣃⠀⠂⠂⠀⣶⣼⢇⡀⡈⣧⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠃⠀⠄⠀⢀⠥⢠⠀⠈⠁⠉⠂⠁⢤⠤⢄⠁⠈⠡⠃⠀⠩⡉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⡞⠄⠡⠔⠂⠇⢀⠌⠈⠓⠒⠐⠒⠂⠈⢄⢀⠃⠐⠀⠀⠄⠈⠡⠀⠐⠠⢤⠔⠈⠀⠀⠀⢠
⠀⠀⢠⠘⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠃⠀⠀⠈⠉⠀⠉⠉⠉⠁⠀⠀⠓⠀⠃⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠤⠤⠬⠥⠍⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠐⠂⠠⢀
⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠄⠀⠠⠀⠄⡀⠀⠀⠀⢀⡀⠠⠤⠤⠀⢀
⠀⠀⠀⠀⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⣀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠌⠁⠐⢄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠁⠃⠀⢐⠀⠀⠀⠀⠉⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⡌⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠁⠀⠀⠀⠀⠠⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠁⣀⠠⢄⡀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠤⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢐⠀⢰⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣧
⠀⠀⠀⠀⠾⣇⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣿⣹⣍⣿⣭⣅⣽⣿⣿⠏⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⡀⠀⠀⠀⠀⠢
⠀⠴⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠈⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠐⢀⠀⠀⠀⠀⠂
⠠⠒⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠄⠊⠂⠀⢀⠀⠀⡀
⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠔⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢄⠀⠀⠉⠀⠀⠈⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠
⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢴⠀⠁⠉⠈
⢀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠂⠀⠀⠀⢣⣶⡜⠁
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠀⠄⡀⠀⠀⠀⠈⠀⠀⠂⠀⠓
⠀⠀⠀⠀⠐⠊⠀⢀⠀⠀⢀⠀⠀⠀⠀⢀⡀⢈⠀⠀⠀⠀⠀⢀⡂⡀⠓⢀⠄⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠋⠈⠉⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣁⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡀⠀⠀⠓⠀⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⠁⠢⠀⠀⡀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠴⢊⠉⡑⠂⠌⠳⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⠈⡀⢀⠁⠠⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠉⠈⠓⠲⠂⠀⠃⢛⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠤⠀⠈⠂⢀⡞⡠⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡤⠆⠀⠀⢠⠁⠐⢄⣎⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠺⡤⠀⠀⠀⠀⡈⡺⠐⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣤⣀⠔⠁⢀⠐⢁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠉⠈⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢆⠉⠂⠦⢀⠀⠀⠀⠀⠢⠄⣁⠠⠐⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣀⡁⠈⠀⣖⠀⠀⠘⡎⠳⠀⠀⠀⠀⠀⢀⠠⠄⣀⢣⡀⠀⠀⠱⡀⠀⠀⠀⠀⡆⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⢀⢄⣐⠁⠀⢀⣀⠂⢼⠄⠀⠀⢃⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠃⣸⣧⠑⠘⠢⠄⡬⠁⢨⠈⠁⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⡠⠏⡀⠀⢢⡢⠀⠀⠀⠁⠘⣁⡤⡠⠋⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠑⠢⢄⡈⣙⠁⠭⠀⠡⠲⣀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠂⠀⣠⠊⠐⢈⢲⠀⠈⠀⠈⠀⡔⠂⡆⡀⠀⠀⠜⠃⠀⠪⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡨⠗⢒⠀⠈⠉⠀⠀⠀⠀⣔⠀⣀⠌⣂⢬⢀⡚⠠⡐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠤⠖⠋⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⠂⡀⠀⠀⠈⢆⠀⢰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠲⠉⠠⡴⠁⢀⡀⠀⡈⠀⠠⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠐⠂⠀⢀⠜⠈⡴⢏⢁⠸⠍⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡆⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⠞⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣴⣛⠃⢠⢔⣍⡉⠙⢿⠁⡀⠀⠀⠀⣷
⠀⠀⠀⠀⢀⣀⣸⣴⠉⠁⠀⠑⠃⠀⢀⡀⠀⣸⠊⠀⠀⢀⣠⠏
⠀⠀⠀⡜⠉⠀⠀⠹⡀⠀⠰⡦⠀⣀⣈⠁⠀⢉⣉⠓⢾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⢦
⠀⠀⠸⡇⠀⠀⠀⠉⠓⠀⠀⣔⠋⠉⠩⠇⠀⠁⡿⣄⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣀⣤⠞
⠀⠀⠀⠙⠶⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢹⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢰⠟⠉
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣾⠇⠀⢀⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠓⠲⣾⣯⣁⣠⣴⡿⠋⣠⢆⡼⠁⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠙⠲⢤⣉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠉⠛⠉⠉⠤⢞⡯⠞⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⣤⣤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⡏⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⢸⠀⠀⢠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⣾⠀⠀⡏⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣄⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⢦⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⣿⡄⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢳⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡟⠀⠀⠀⡟⢳⠀⠀⠹⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣸⠃⠀⠀⢠⡇⠈⣧⠀⠀⠹⣄⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡏
⠀⣠⢐⣒⣀⠈⠉⠀⠐⠒⠲⣎⠀⣰⠃⠀⠀⠀⣼⠀⠀⠘⣆⠀⠀⠈⢦⡀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢰⠇⠀⠀⢠⠞⠀⡼
⣮⠥⠤⠐⠒⠒⢠⡖⠺⠥⠤⠌⠿⢥⣀⡀⠀⣴⡏⠩⣈⡉⠙⠳⣄⣀⣀⣙⣦⡀⠀⠀⠙⢦⡀⢀⣴⣏⣀⡤⠖⠁⣠⠞⠁
⠉⠛⠒⠋⠉⢉⡥⠽⢓⣒⣂⠀⠀⠀⠈⢹⠾⠧⣞⣉⡡⠐⣂⠭⠄⠀⠀⠀⠀⠉⠑⠒⠤⣄⣹⡿⣤⣄⣀⣤⠴⠚⠁
⠀⠀⠀⠀⡴⢁⡤⠊⣡⠤⠔⢂⣠⠀⢠⠏⠀⠀⠀⡾⣊⠭⠒⠚⣉⣁⣀⣀⣀⠤⠤⠤⠤⠞⠁
⠀⠀⠀⠀⠉⢯⡤⡴⢁⡴⠋⡡⠁⡴⠃⠀⠀⠀⠀⠙⠳⠒⠒⠉⠁⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣼⣯⣤⣤⣷⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⢂⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡀⠠⣀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡄
⠀⠀⠀⠀⣠⠆⡀⠀⢰⣣⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢐⠏⠦⠃⠀⣏⣿⣾⠙⠁⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠀⠀⢠⢿⡵⠀⠐⠈⠉⠩⠕⠒⠐⠒⠀⠂⠀⠀⠀⠀⠀⠠⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⢀⠄⠄⠒⡉⢍⠁⠈⠉⠛⠢⢄⠃⠀⠙⠁⠉⠁⠀⣀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠰⠀⠀⠀⠀⡇⠀⠄⠀⢀⡠⢀⠔⠁⠀⠀⠔⢀⣴⠶⢉⣭⣥⣭⣹⣿⣆⡴⢠⣄⠀⡩⠤⠶⠊⠙⠃⠀⠤⡔⣖⠲⠦⣉⡱⠦⣤⠛⠉⠁⠈⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡰⠋⠀⠀⠀⣠⠂⡟⠃⡀⠈⢢⡴⠀⠲⢷⣍⣝⣵⠋⡄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⣷⠀⠈⠸⠇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⡜⠀⡀⢙⣦⠅⠀⠀⠄⠀⡀⠀⠉⠀⠁⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠲⢼⡆⠀⠀⢀⢠⡀
⢀⠀⢸⠀⠀⠀⢸⡄⠀⠀⠀⢸⡆⠀⠀⣴⠁⠀⣃⠈⢤⡀⠀⠘⡀⠠⠃⠀⠀⠀⠀⠀⣧⠀⠀⢠⡀⠀⠀⡀⠀⠀⠀⠀⢿⠀⡀⢸⢧⣿
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡌⣇⠁⠂⠻⢰⣬⣿⣷⡟⠁⠀⠀⠀⠀⢀⡀⢠⡄⠀⠀⢸⠒⢨⠤⠙⣦⢚⡛⠁⠀⠀⠀⠀⢲⡟⣨⣎⣟⠀⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠙⣄⠀⢳⠌⣻⠿⡧⠁⠀⡄⠈⡀⠀⠚⠀⡿⠘⠀⠀⣾⠘⠀⠀⡸⠟⠉⠉⠂⠀⠀⠀⠀⢸⡇⡟⣿⣿⣿⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠃⣬⡟⠻⣶⠿⠦⣌⡀⠶⠀⠀⠀⠀⢀⡄⠠⠾⠿⠥⠞⠉⠀⠀⠀⠀⠀⠀⢲⡄⢀⣼⡿⠣⣿⢸⠃⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠀⠐⣀⠴⠀⠀⠀⠀⠉⠓⠒⠲⠴⢶⣥⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⢃⡌⠀⠋⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠀⠒⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣀⣠⣤⡤⠤⠤⣲⣾⢻⠏⠀⠁⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠈⠉⠛⣼⠟⢡⣾⠇⠎⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢨⠎⠉⠀⠙⠒⠦⢤⣤⡤⠴⠛⠁⠀⠀⠀⡼⠋⠀⠸⠏⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠄⡲⠀⠀⢄⣟⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⣼⡃⠀⢀⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠉⠁⠀⠀⠀⠃⠀⠀⡾⠊

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣶⣦⣤⣤⣴⣿⣿⢿⡷⣤⣩⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠁⠀⠿⢿⣜⢂⡜⣿⣟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢠⣇⣠⣿⣿⡄⢹⣮⣗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⣿⣿⣿⣿⠿⠻⠛⣿⡿⠃⠀⠀⠀⢠⡾⢉⣿⡇⠈⠙⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣋⣉⣁⣤⣤⣶⣾⣿⠁⠀⢀⣠⡴⠟⢁⣾⡿⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣯⣭⣝⡛⢿⣍⡉⠉⠀⠀⠈⢿⣿⣿⣿⣧⡰⡻⠟⠀⠐
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⠛⢿⣿⣿⡇⠀⠀⠀⢁
⠀⠀⠀⢠⣿⢿⡿⠋⢿⣝⠛⢽⢻⡟⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢯⠛⡷⠶⠤⠴⠂
⠀⠀⠀⣿⣿⡞⠀⠀⠀⠙⢷⣄⠀⢹⡀⠀⣿⡅⣿⠀⠀⠀⠀⠀⠀⠈⢆⢿
⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⢠⣿⣠⣼⠁⠀⠹⣷⢼⡀⠀⠀⠀⠀⠀⠀⠈⣘⡷⠾⢋⠉⠒
⠀⠀⢸⣿⡇⠀⠀⠀⠀⢠⣟⣿⡿⠃⠀⠀⠀⢿⣹⡇⠀⠀⠀⠀⠀⠐⠊⠁⠀⣀⠬
⠀⠀⢿⣿⡇⠀⠀⠀⢰⣯⣿⠏⠁⠀⠀⠀⠀⠘⠛⢧⣴⣶⣦⠄⠀⠔⠂⠀⠀⠀⡀⠀⢀
⠀⠀⢹⣿⡇⠀⠀⠀⠈⢿⣷⣀⣀⡀⠀⢀⡀⠐⠊⠩⠀⣠⠤⠈⠉⠀⠀⠀⠀⠀⠁⠐⠀⠄
⠀⠀⢸⣿⣇⠀⠀⠤⠴⣶⣟⠛⠛⠛⠓⠈⡀⠀⠐⠂⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠘⣿⣿⣤⣠⣄⣀⠀⠀⠀⡠⠚⠛⠉
⠀⠀⠀⢻⣿⣧⡁⠀⠀⠱⣄⢎⣠⣄
⠀⠀⠀⠀⠹⢿⣿⣖⡤⣤⣬⣷⣭⡭⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉

⠀⠀⢠⡤⠖⠲⢶⡶⠶⠖⠲⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠖⠶⠶⣶⡶⠖⠶⢤⡀
⠀⠀⠸⣇⠚⡋⠛⢛⣶⣮⠁⠻⢛⣻⣿⣿⣷⣦⣄⡀⠀⠀⠈⠀⠀⠀⠤⣀⣠⣤⣀⡤⠐⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣻⡛⠟⣈⣷⣶⡛⠟⢙⠖⣸⠃
⠀⠀⠀⠙⣇⢞⣙⠛⠛⠃⢘⠋⢩⣿⣿⣿⣿⣿⠻⣼⣷⣦⣄⡀⠀⠀⢠⣿⣹⣿⣽⡆⠀⠀⢀⣠⣴⣾⣥⢛⣿⣿⣿⣿⣿⡍⠹⡁⠚⠛⠛⣋⠳⣼⠃
⠀⠀⠀⠀⠘⣇⠘⠛⠳⠏⢩⡍⣭⣭⣝⣛⡻⠮⠙⠿⠿⢿⣿⣿⣷⣦⣾⣿⠿⠿⣿⣧⣴⣾⣿⣿⠿⠿⠿⠉⠾⢛⣋⣩⣭⣍⢹⠉⠱⠞⠛⢂⡼⠁
⠀⠀⠀⠀⠀⠈⢳⡜⠷⠶⢲⣶⠂⣈⣙⣉⣙⠀⢩⣝⠒⢲⣿⣿⠽⣿⣿⣇⠆⠰⣸⣿⣿⠹⣿⣷⡶⠒⣏⡉⠀⣉⣙⣋⣁⠑⣶⠖⠶⠾⣣⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢷⣤⣽⣦⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣾⣿⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣭⣭⣾⣧⣤⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣦⠶⣂⡽⢿⡟⣛⣻⣿⣯⣀⣿⣿⣿⠿⢿⣿⣽⣧⣀⣿⣿⣟⡛⣳⡿⢧⡐⠶⣴⣯⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡶⣛⣿⣭⠖⢋⣿⣿⣭⣿⡿⣿⣿⣻⣿⡀⢈⣿⢻⣿⣿⢿⣿⣭⡿⣿⡛⠶⣭⣿⣛⢶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡾⠻⣿⣠⡾⢙⣿⣶⠟⣭⣹⣿⣟⣛⣿⢛⡏⠻⣶⣿⡙⢷⣬⣿⠟⢧⣬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢽⣷⡿⠟⠁⠀⢻⣼⣿⣯⣽⣿⣽⠁⠀⠈⠻⢿⣾⡯⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣭⣽⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡷⢲⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠛⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣠⣤⣤⣤⡀⠒⠂⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⢨⣾⣿⣿⣿⣿⣿⣿⣦⡠⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⢸⡏⠛⠫⠙⠻⠟⣻⣿⣿⣄⡠⠄⠀⠈⠢⡀
⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠂⠀⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠑⡄
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⣅⣒⣠⣤⣹⣿⡏⠀⠀⠀⠙⠢⡀⣀⣈⣂⣀⠀⡀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⢠⣄⣤⠀⠀⠂⢻⣿⣿⣿⠹⣿⠀⠀⠀⢀⠗⠈⠁⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠡⡀⠀⠀⠸⣿⠋⠉⠑⡄⡀⠀⠙⠻⣯⠆⢨⢀⠠⠒⠁⠀⠀⠀⢀⡀⠀⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠐⠢⡊⠀⠀⠈⠁⠂⣼⠷⠊⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢈⡢⠄⠀⠈⠁⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⠊⠁⠀⠀⠀⠀⣀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡿⠿⠛⠛⠛⠛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣷⣶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠙⣿⣆⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⢠⣦⡄⠸⣿⡄⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣃⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⢰⣶⡄⠀⠘⢿⠇⠀⢻⣿⡀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠉⠛⠿⣶⡄⠀⠈⠻⣦⡀⠀⠀⠘⠿⠟⠀⠀⠀⣀⣀⡈⠛⠷⣦⣼⣿
⠀⠀⠀⠀⢠⣿⠃⠀⣠⡶⠶⢶⣄⠈⠁⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠾⣿⣿⣿⡇⠀⠀⠈⠻⣿⡀
⠀⠀⠀⠀⢸⣿⠀⢰⣿⠀⠀⣠⣽⡇⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢸⣿⡄⠈⣿⡄⠀⢿⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠈⣿⣷⡀⠈⠻⣦⡈⠳⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠈⠉⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢰⡆⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⣀⣀⣸⣿⣇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⡄⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⠟⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣄⣀⣠⣤⣿⡿⠋⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⡷⣠⣆⠠⠔⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣒⠀⠀⠘⠻⣿⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡭⠶⣷⢀⡘⠓⣀⠘⠁⠈⢠⠰⠘⠀⢠⡀
⠀⠀⠀⠀⠀⢙⠀⣿⠀⠀⠀⣸⣿⡆⠡⠅⣎⠀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠚⢀⡈⠡⡄⠉⠶⡀⠴⠦⠰⢆⢁⡀⠖⣈⠠⠌⣁⠈
⠀⠀⠀⠀⠒⡰⣴⣿⣧⣤⣴⣿⣿⡞⠈⠁⠀⠀⠀⠉⠒⠀⠀⠠⠄⢤⡤⠶⢀⡐⢃⡀⠛⠄⡤⠘⠀⠀⠀⠙⠳⠴⠮⠰⠦⠁
⠀⠈⠁⠀⡰⠉⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠘⠓⢠⠐⢢⠀⠅⢀⠐⡦⡀
⠀⠀⠐⠈⠀⠀⠀⠀⠹⣿⠿⢿⣻⠅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠠⣌⣀⢚⡀⠈⣀⠘⠠⡆
⠀⠀⠀⠀⠀⠀⠠⠅⠀⡜⠀⡀⣶⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣾⣶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠅⣁⠀⠠⠀⠀⠘⠀⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⢀⠒⠠⠟⠀⠁⠒⠩⢀⡀⠀⠒⠉⢈⡁⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣶⠉⡀⢤⣄⡓⢠⡅⠨⠒⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠂

⠀⠀⢀⣀⣤⠴⠶⠖⢶⣶⣤⣀
⠀⠈⠉⠘⠋⠷⡄⠀⠂⠀⠙⠛⠟⠢⣄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠶⠟⡡⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠐⠁⢘⣧⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⣰⣧⠀⠘⣹⣧⡀⠀⢀⠘⠀⢀⠄⠢⠀⠀⢀⣴⡖⢒⣲⣶⣖⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠔⠒⠀⠤⡜⣫⣿⣻⡽⢷⠏⡰⢀⣀⡴⣻⢾⣧⡕⢌⠛⠀⠀⠈⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢧⣶⣬⣻⣿⠿⢛⡅⢻⢺⡏⠁⠃⠱⡆⠀⡀⠀⠀⠌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣽⠿⠾⠤⠤⢈⠙⠈⢸⠇⢀⠀⠀⠡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠾⠃⠏⠀⠀⠀⠀⠀⠉⢂⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠐⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣽⣿⣧⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⣤⣤⣤⣄⣀⣿⡇
⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⠶⠿⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⣴⣾⣿⣿⣿⣿⣿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⣆⠀⠀⠹⣿⣦⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣷⣤⣴⣶⣶⣄⢹⠀⣠⣀⠀⠉⠉⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠙⢿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣶⡀⠀⠼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠶⣾⣿⠀⢹⣿⣿⣿⣿⣧⠀⠀⣻⣿⣿⣿⠃⣶⣿⣿⣿⣯⠉⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣼⣿⣿⠘⣿⣿⠀⠀⣿⣿⣿⣿⠰⠉⣿⣿⣿⡌⠳⡄⢸⣿⠋⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠀⠻⠿⢣⣾⣿⣿⣿⣿⣆⢠⣿⣿⢿⡇⠀⠀⣿⡟⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣍⣿⡿⣿⣟⠉⠀⣿⠋⣾⡀⠀⠀⣿⣿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠻⢇⣿⡟⠀⠀⢿⡀⣿⠀⠄⠀⣽⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⡟⠁⠀⠀⢸⡇⠀⠀⠀⠺⠟⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠐⠁⠀⠀⠀⠀⠀⠀⠹⠇⡘⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠃⠐⠀⠀⠀⡀⡀⠀⠀⠀⠉⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠆⠰⡀⢀⣔⢠⠚⣽⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢏⡠⠀⠀⠀⠀⠀⠀⢠⢆⠴⣡⣿⣵⣿⣼⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣍⣥⣂⡀⠀⠀⠀⡄⢂⢶⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢉⣁⠀⠉⢙⣿⠅⠈⠀⠰⠃⡅⣿⣿⣿⡿⠋⠁⠀⢀⠈⢿⢇⠀⣠⣤⣴⣦⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⡴⣾⣿⡿⣿⣿⣶⣿⠀⠀⠂⠐⣷⢷⣿⣿⠟⠁⢐⣐⣾⣿⣦⣜⣤⡾⡿⢛⢿⣿⣆⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣾⣿⣷⣹⣿⣿⡿⣿⠀⠀⠁⣴⣼⣾⣿⣯⣼⣢⣼⠟⡚⢦⡹⣿⣿⣷⣧⣬⡼⣿⡏⣿⣿⡇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢤⣿⣿⣿⣿⣿⢻⣿⣿⣦⣥⣿⣣⣿⣿⣇⢸⡿⣿⡂⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠹⠟⡛⢻⣛⠻⣿⡀⠀⠀⢼⣿⣿⣿⣜⢈⡇⡙⠖⣪⣿⡟⠃⠁⠀⠀⠙⠿⣗⣿⣿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠅⣚⠉⠚⢻⡇⠀⡘⢿⣿⣿⣿⣿⣆⡁⠀⠩⣻⣿⠀⠀⣤⣀⠀⣶⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⢁⣿⣿⣿⣿⣿⣿⣿⣷⣄⢘⠿⠀⠀⠘⠛⠂⠋⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢛⣿⣿⣿⣿⣿⣿⡿⠊⠁⠀⣀⠀⠀⠀⠠⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⣿⣿⣿⣿⣿⣿⣷⡀⠙⢰⣾⡇⠀⠀⠀⠀⣀⣌⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⡞⢿⣿⣿⣿⣿⣿⣿⠞⢈⠁⠀⢀⣠⣾⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⣿⣿⣿⣿⣿⠀⠾⢕⡚⠻⠿⣿⠟⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡹⣿⣿⡂⠀⠀⠻⣿⣶⣤⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣷⣄⣀⣀⡺⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁


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