Riding Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡟⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⠡⠒⣶⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠂⠀⠀⡿⠀⢀⣤⣶⠆⠀⠀⠀⠘⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡾⠁⢀⠔⠋⢀⣴⢸⢛⣧⠀⠀⠀⠀⠀⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⡶⣿⠁⠰⣯⣴⣀⠙⠟⡾⠀⢻⣷⡄⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠿⠋⢩⣡⣄⢀⢸⡇⠠⣯⣿⣛⡤⢞⢁⣠⣾⣿⣧⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⣰⣹⣿⣿⠇⢸⡇⠈⢉⣏⠉⡀⠘⣷⣿⠟⣿⣿⣿⠟⡝
⠀⠀⠀⠀⠀⠀⣰⡿⠛⠁⢀⣠⣾⣿⣿⣿⡏⢠⠈⢃⣄⣼⣿⣿⣿⠀⠟⠁⠀⠻⣇⠈⢸⣿⣤⡄
⠀⠀⠀⠀⠀⣼⢟⡤⣴⣾⣿⣿⡿⣿⠿⠿⣧⠀⠈⠉⢡⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠱⡄⢈⡟⠁
⠀⠀⠀⠐⠛⣾⣿⠖⠚⣿⡏⠀⠀⠀⠀⠀⢹⠇⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡷⠋
⠀⠀⠀⠀⠀⠘⢯⣷⣾⣿⣿⠀⠀⠀⠀⠀⣼⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⢫⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⡷⠀⠈⠀⢠⠋⣰⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⢿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⣼⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⠖⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⡦
⠀⠀⠀⢠⡀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⡆
⠀⠀⠘⢿⡟⡥⢿⣶⣤⡈⠉⠙⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣲⣾⣰⠃
⠀⠀⠀⢿⡇⣐⠈⣿⣿⡿⣷⡄⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠃⠁⠲⣿⣿⣧⡏⢿⡆⠀⠀⠀⠈⠙⢧⣤⡀⠐⣶⣾⣿⣿⣿⡷⣠⣤⡀
⠀⠀⠀⠀⠀⠠⣠⡟⠈⢻⣿⣈⠇⠀⢀⣤⠀⠈⠛⠛⠁⢠⣾⣽⠹⢟⣿⠾⢃⣶⡇⡀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠛⠾⠃⠀⠸⣿⣿⡀⠠⣿⠟⠀⠀⠀⠀⠀⣾⠟⠁⠠⢉⣴⣿⣿⣿⣇⣩⢆⠀⢈⠙⠋⢷⣶⠶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡇⠀⠀⠀⠀⠀⡼⠋⢀⣤⣵⣿⣿⣿⣿⡿⣿⡏⢶⡄⠀⢭⣒⡾⣿⠇⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⡞⣶⡇⠀⣿⣿⣿⣿⣿⣿⢟⣁⣿⣷⣦⠉⡆⠀⠉⢳⣿⠆⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⣘⣻⡧⠄⣿⣾⡏⢸⣿⣿⣿⣿⣿⣿⣿⢃⢻⡀⣀⣖⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⣹⣿⠇⢀⣿⣿⣧⠈⢿⣿⠿⠟⠛⠛⢻⣿⣦⠉⣴⣼⣯⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣾⣍⣉⢠⡍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠹⣿⡄⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣿⡄⠀⠸⣿⣆⠘⢿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠆⠀⠉⡼⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠀⡀⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠚⠛⠋⠀⠵⠤⠽⠶⠶⠶⠖⠶⠂⠀⠀⠐⠓⠒⠀⠠⠦⠐⠾⠛⠉⣋⡄⢴⣶⣶⣶⠦⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⣟⡛⣻⡛⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠂⠀⠄⠀⠠⠀⠀⠀⢀⣠⡤⣾⠄⠬⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠽⢧⡄⠀⠀⠀⠀⠀⡠⢞⠁⢰⡇⢙⠡⠳⠤⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⢼⣿⣿⠟⢁⠀⠀⠀⠠⠆⠀⢀⡼⠓⠀⠀⢘⡰⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠂⠈⠿⠙⢯⠀⠀⡀⠀⠀⢠⢠⣾⠌⠀⠀⠠⢸⣇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠠⢈⣉⠀⢠⠀⣀⠂⢸⡁⠀⠀⠀⠀⢸⠘⣆⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⢡⠀⠀⡈⠁⠂⠲⠮⡀⣏⡆⠀⠀⠀⠀⠈⢧⢻⣆⡴⠛⠉⢙
⠀⠀⠀⠀⠀⠀⡇⠠⠙⠄⠀⠇⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠇⠀⠀⢻⡏⠀⠒⠀⠤⢠⡀⠈⢿⣥⡄
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢤⠔⠃⢠⡀⠀⢸⣧⠀⠀⠀⠀⠀⠁⠉⠙⠒⢀⠚⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⢀⠀⠂⠈⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠨⠡⡀
⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⢀⠀⢀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⢀⠀⠁⠐⠄⡀
⠀⠀⠀⠀⠃⢀⠁⠀⠀⠄⢠⡑⠈⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠐⠢⣄⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⠃⠀⠀⠑⢦⡠⠜⠃⠉⣿⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠍⠀⢀⣷⣶⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠐⠀⠀⠓⢄⣐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡅⠀⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠒⠀⠀⠂⠀⠀⠀⡀⠠⠀⠠⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠆⠀⠀⠀⠀⠃⠀⠀⠛⠿⠛⠄⡀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⣾⣿⡀⠀⠀⠀⠏⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⢘⠟⠷⠄⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠔⠦⢄⡀⠀⠀⠀⠀⠀⠁⠀⠑⠄⠀⠈⠉⡠⠀⠀⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡀⠀⠀⡀⠓⠄⠀⠀⠄⠛⠐⠀⠀⠤⠀⠀⠀⠴⠀⠈⠁
⠀⠀⠀⠀⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡙⣋⣄⣤⣤⣴⣶⣶⣷⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⡍⠹⡶⠊⠛⠻⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡞⠀⠰⠆⢁⡘⠃⠀⠈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⣻⠃⢴⡀⠀⠀⡀⠀⠜⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡝⣆⠀⠀⠀⠀⠐⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢳⢉⣼⣶⣤⡄⠀⣶⣿⡶⠀⠀⠀⢀⠀⡀⣀⣆⠔⢰⡷⣐⣄⢀⣴⣾⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠗⡃⣸⣿⣿⡿⠛⢺⡟⠻⣷⡀⣀⣰⣮⣿⣮⣿⡿⡄⣾⣟⣻⣿⣦⣻⣿⡿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⣵⣿⣿⣿⣷⣶⣼⣷⣶⣾⣿⣿⣿⣿⣿⣿⢿⡇⡨⢟⠦⣉⣿⣿⣭⣋⠙⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣕⡻⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⣸⡈⡀⢀⣅⢨⣼⣌⡓⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣩⠃⠀⠀⢰⣿⡿⠋⠀⣘⣿⣿⣿⣿⠟⠁⠀⠀⡿⢻⠃⠘⢃⠎⡜⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡐⠀⠀⣰⣿⠋⠀⠰⠾⣿⣿⣿⠟⠻⣄⠀⠀⠀⡇⢸⠆⢠⡾⠀⠉⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣟⡟⣃⣠⣶⣿⠇⠀⢀⣴⣿⣿⠟⠁⠀⠀⠈⠳⢤⡀⢳⡀⢟⣧⡶⠤⠤⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠈⠉⠉⡍⢉⣿⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠙⠲⣿⣿⣯⢴⣶⠆⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡙⠁⠀⠀⡌⢀⣿⣇⣠⣿⡟⠇⠠⡀⠘⢄⠀⠀⠀⢀⠃⠀⡠⠨⣝⢃⠘⠛⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠸⠁⠀⠀⢰⠀⣸⣿⣿⡿⣿⢰⠀⠀⠈⢂⠈⡄⠀⠀⡄⠀⠠⢇⠀⠉⠟⠛⢄⣂⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠃⠀⠀⠀⡄⠀⣿⣿⣿⣇⣿⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢢⠺⠀⠀⠀⡐⢄⠹⣿⣿⣹⡿⢨⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣁⣵⡀⠀⠐⡀⠈⣿⡿⣻⣶⡆⠀⠠⠄⠈⠑⢲⣶⣤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⣃⣸⠈⠢⡀⠈⠶⢌⡉⠙⢄⣡⡀⠀⠀⠀⣀⢼⣿⡿⠿⢦⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠙⡅⡸⢠⣴⠙⣄⣼⣎⠀⠀⠈⠁⠈⠀⠉⠓⠂⢠⠀⠉⢢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢈⠞⠉⠇⠘⣿⣦⡻⢿⣁⣈⡉⠉⢆⠀⠀⠀⠀⠀⡆⠀⢀⠎⠐⢄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⠄⠎⠀⠀⠛⠛⠇⠀⠀⠀⠑⠆⠈⢢⡀⠀⠀⢠⣤⣤⡎⠀⠀⠢⠠⠤⠺⡀
⠀⠀⣠⣄⣇⢂⡄⠀⠀⠀⢀⢛⡅⡔⠁⠀⠀⡄⠀⠇⠀⠀⠀⠀⠳⡀⠁⣹⠀⠀⣾⣿⣿⠀⠀⠀⠰⢀⣀⣀⠔
⠀⣻⣿⣿⣿⣿⣇⠀⠀⣠⣾⣧⠔⠁⠀⠀⠀⢈⠀⣉⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⢙⠃
⠀⠻⠿⢿⠿⠿⠿⠿⠤⠛⠉⠁⠀⠀⠀⠀⠀⠈⠥⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠐⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣾⡁⠀⠀⠀⠐⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⣥⡴⠾⣥⡤⠀⠁⠀⢀⠀⠀⠀⢀⢟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⢀⠀⣦⡈⠐⠓⠈⠉⠛⢒⡞⠿⠿⣶⣄⡴⠃⠀⠀⠠⣠⠈⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠛⢿⣿⣿
⠀⠀⠈⢡⣯⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠁⠀⢨⢴⡏⠀⠀⠐⠒⠋⠉⠉⠛⠻⢅⠀⠀⠀⢸⣿⠟⣆
⠀⠀⢀⣾⠁⠀⠀⣠⠀⢢⣾⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠰⣴⣦⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣼⣿⠀⠈
⠀⠀⡜⠻⢶⡶⢟⣡⠖⠉⠀⠙⢦⠀⠀⠀⠀⠀⠀⠘⢯⡓⠬⠻⣧⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⢸⠀⠀⠀⢻
⠀⠸⢷⣶⠏⠊⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠈⠀⢀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣀⣠⠴⠊⠀⠀⠀⠀⠠⠃⠀⠐⠛⢋⣀⡴⠞⠋⠙⠀⠀⠀⠀⢀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⣾⡿⠿⠦⠤⠤⠴⠖⠁⠀⠀⠤⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠿⢿⣿⣿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⢀⣤⣶⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠆⠀⠀⠈⠋⠀⠀⣤⠀⠀⢀⡀⠀⠋⠑⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠍⠈⠐⠄⠀⠀⢀⠀⠀⠀⠀⠀⠃⣼⣿⣦⣄⠀⠀⠸⠿⠿⠿⢿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠈⠂⡀⠘⢷⠶⠁⡠⠂⠀⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠘⠀⠀⠲⢀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⣤⣤⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢠⣽⣿⣿⠏⠀⠀⠀⠂⠀⠀⢀⣴⣿⠟⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂⠐⠒⠀⠀⠀⠀⠀⣀⣌⡿⣿⣧⣀⡀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠂⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠙⣿⡇⠈⠉⠛⠿⠿⠿⠿⠿⠟⠃⡀⠢⠀⠀⢀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣠⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠠⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣧⠀⠀⠀⣠⠀⠀⠀⠀⠀⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠘⠛⠃⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡇
⢄⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣆
⠈⢿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⣈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⢶⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠔⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡔⠚⠛⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣴⢋⠠⠎⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⡀⠀⢀⣤⣤⡔⠋⣁⠠⢴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣿⡿⠗⠚⣩⣿⣿⡷⠋⠁⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡿⠛⠁⠀⡠⠞⠀⣠⢀⠀⣠⡤⠾⠃⠀⢀⣠⠀⠐⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⠋⠀⠀⠀⣼⡡⠀⣾⠃⠀⣼⠿⠶⠶⠶⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠁⠉
⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⢠⣤⣾⠁⣰⣶⡟⠰⣼⠇⠀⠀⠀⢀⠀⢀⣀⣤⡿⠀⠀⠀⣆⡀⣸⣿⡟
⠀⠀⠀⠀⠀⣹⣿⠃⠀⣤⣾⣿⣿⢿⢺⣯⡙⠀⠸⣿⣶⣶⣶⣾⣿⣼⣿⣿⣯⠅⠀⠀⢀⡿⠛⠛⠋
⠀⠀⠀⠀⢸⣿⠇⢀⣼⣿⠏⠁⠀⢸⣿⡇⠀⢙⠂⠈⠉⠛⠛⠛⠛⠛⣿⣷⣿⠀⢀⣀⣾⠃
⠀⠀⠀⠠⣬⣿⡠⠤⢴⣽⡄⠀⢀⣿⡿⡇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⡀⣿⣿⠁
⠀⠀⠀⠈⠉⠻⣤⣤⢾⣿⣯⡤⣿⣿⢸⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣅⠈⠛⢢⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠘⣧⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠂⣰⠇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡌⠀⠀⣿⡆⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠊⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⣿⠇⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⠁⢊⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⡄⣀⣀⣀⣠⣤⣾⣾⡤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠒⠀⠁⠀⠈⠉⠉⠉⠁⠈⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠐⣶⣄⠀⠀⠀⡜⠁⠀⠘⣆
⠀⠀⠀⠀⡄⠀⡄⣰⠀⣤⣴⣶⣶⣿⣯⣾⣿⣿⡇⠀⠀⡄⠀⠀⠀⢸⡆
⠀⠀⣴⣀⡙⢂⡑⠋⠀⠀⠘⠲⢮⣝⡻⣿⣿⣿⡟⢠⡆⠃⠀⠀⠀⣼⣧
⠀⠀⠈⠉⣱⣿⡿⠀⠀⠀⠀⠀⠀⠈⠙⢮⡙⢿⣿⡿⠁⠀⠀⡜⠘⠿⣿⡀
⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⠢⠉⠀⣠⣦⠼⠁⠀⠀⡘⠷⡄
⠀⠀⠀⠀⣿⣿⠀⠀⣠⠃⢻⠀⠀⠀⠀⠀⠀⠀⢾⠿⠋⠁⣀⣀⣀⣴⡷⠀⣽
⠀⠀⠀⢠⡇⠙⡿⠋⠁⢀⣸⣤⠤⠔⠒⠉⢀⠔⠁⠀⠀⣀⡤⠖⠀⠀⢶⡛⠿⠃⠀⠀⠤⠤⣤⣀⡀
⠀⠀⠀⠸⣷⡿⠃⠀⠉⠀⠸⣇⠀⠀⠀⢰⠫⣠⣤⠀⠀⠀⢠⠟⠛⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠸⣧⣹⣿⡆⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠛⢻⡇⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣠⣴⣆⣀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣼⣿⡟⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⡠⣶⣶⡦⠤⠤⠤⠀⠘⣇⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⢀⡆⠀⠐⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢁⣤⡆⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢠⠞⠋⡅⠀⠀⢀⡞⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠛⠉⣧⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢹⠀⠀⢹⡄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⣿⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣸⣇⠀⠀⠹⣆⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣀⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⢹⣧⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠉⠀⠀⠀⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣦⡀⠀⠀⣰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡿⢿⡽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⣽⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣐⣤⠀⠀⠀⢀⣰⣿⣦⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢏⣁⢠⠤⣴⡟⣻⣿⡿⠋⠉⠛⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡿⢻⣧⣤⡀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⢥⣸⣿⣌⠀⠀⣸⣦⣀⣀⣀⣀⠠⢴⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣼⣿⣿⣿⣿⡿⠁⠈⠛⣿⣿⡷⣶⡉⡈⠡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⢹⣍⢻⣿⣷⢾⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⠾⠟⠛⣿⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⡈⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢺⣿⠇⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣽⣧⣸⡙⠠⣀⠀⠀⠀⠤⡖⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣿⡿⣿⣆⢿⣀⠘⠀⠐⢁⣄⣰⣤⣀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢸⣿⣶⣭⠓⣰⣆⣾⣿⡿⢋⡅⣼⣿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣴⠀⠉⠟⠁⠀⠁⣼⣧⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠾⠟⠛⢻⣷⣀⠀⠀⠀⣠⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣷⠀⠀⠀⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢰⣟⣇⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣻⣿⡟⠀⢀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⣿⠏⢀⡼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠛⢿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣷⠁⠀⠀⠀⢀⣠⣶⠚⡿⡚⠆⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠀⢀⡤⠖⢻⣦⠤⠖⠻⣄⡴⠚⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⢿⠟⢻⣿⣧⡼⢉⡤⠟⠉⠀⠀⠀⢰⢿⡄⢤⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣈⠓⢌⣫⣿⠖⠋⠀⠀⠀⠀⠀⢀⣿⠘⣟⣄⠀⢀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⢿⣿⣿⣿⣿⣿⠋⠛⠿⠿⠦⠤⠤⠤⠤⠤⣤⣾⣙⣆⣨⡿⢯⣉⠜⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⢻⣏⣛⣛⣾⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠻⢯⡐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⣿⣿⠼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡿⡷⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢠⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢟⡞⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⢀⠀⠀⠀⢀⣠⠋⢸⣧⠀⠀⠀⠀⠀⠹⡄⠀⠀⠐⣿⢿⡿⠇⠀⠀⢻⡆⠀⢀⡀⠀⠀⠀⢀⣀⢰⡏
⣸⡗⠒⠒⠉⠀⠀⣴⣿⡀⠀⠀⠀⠀⢠⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠻⣄⣸⣇⠀⠀⠀⠀⠙⠷⣽⣦
⠘⠧⣤⡄⣠⡶⠊⠀⠈⢧⠀⠀⠀⢀⡾⠛⠿⣍⠙⢻⣿⠒⠒⠠⠤⠒⠒⠋⠉⠉⠛⠚⠓⠦⣤⣀⡀⠉⠑⢦
⠀⠀⠉⠙⠁⠀⠀⠀⠀⢸⠂⠀⣠⠞⠀⠀⠀⠘⣇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⢀⡨⠓⣄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠋⠀⠀⠀⠀⠀⢹⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢾⣄⣀⣀⠞⠙⣇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡏⠀⠀⠀⠀⠀⠀⠘⠳⣄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡚⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⡟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⣴⣿⣿⣿⠗⠁⠀⠀⢀⣀⠠⣦⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⣀⣳⣦⣿⠿⠛⠉⠉⠉⠉⢛⢷⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡉⠉⠉⠛⢿⣿⣿⡛⢹⣇⠁⠀⠀⠀⠤⣠⢄⣶⢾⣿⡄
⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣦⣄⣠⠤⠔⠒⠦⠤⣼⣿⣿⣶⡄⢀⣍⢻⠿⠛⢃⡉⠒⢤⣠⡔⢳⡞⠸⠐⠨
⠀⠀⠀⣰⣿⣿⠟⣿⣿⠟⢩⠟⠉⠀⠀⠀⠀⢀⡄⠈⣩⣿⣿⣿⣿⡿⠀⡄⠀⠈⠇⢰⣿⡯⢐⣽⣣⣬⣦⠼⠄
⠀⠀⠚⢻⣿⣿⠀⠉⠀⠀⡏⡎⠀⠀⠀⠀⠀⠎⠀⠸⢿⣧⡋⠹⣿⡀⠠⡁⠀⢠⢄⠨⡉⣀⢀⢿⡏⠙⣧⠰⠆
⠀⠀⠠⣿⡿⠃⠀⠀⠀⢸⢃⢣⠀⠀⣠⠞⣁⣀⡘⢦⡀⠉⠁⠀⠹⣷⣀⣷⣄⠀⠀⢈⡼⡿⣉⣸⡇⠀⠉⠁
⠀⠀⠚⠋⠀⠀⢠⠊⠉⠁⠉⠀⣀⣀⡴⠚⠙⠛⠛⠷⠶⠦⠤⠴⠶⠾⠟⠛⠉⠙⢚⣿⣃⡩⠾⠋
⠀⠀⠀⠀⠀⠀⠸⢠⠚⢹⣿⠉
⠀⠀⠀⢀⠀⣴⢛⠃⠀⣼⡟
⠀⠀⢰⣿⡁⠌⢫⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡶⠂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢀⣤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣠⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠿⠿⠷⠶⣶⣤⣀⠀⠀⠀⠀⠀⣀⠀⣀⠤⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡭⠶⠶⠒⠒⠒⠒⠲⠶⠤⢭⣙⠆⢠⣤⣾⣿⣋⣁⣀⣨⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⢃⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣨⢾⠟⠀⠀⠈⣉⠿⣛⣀⣵⣧⣀⣀⣀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⢀⣀⣀⣿⣿⡁⠀⢀⣨⣝⣿⣷⣦⣄⠸⣧⠀⡠⠞⢡⣁⡄⠀⠀⠉⡴⠋⠉⢻⠈⣽⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣀
⠀⠀⠀⠀⠉⠛⣿⣿⣿⡛⢍⠻⣿⠻⢿⣿⣿⣷⣿⠋⠀⠀⠸⣝⣿⠀⠀⠼⠁⠀⠀⠘⠀⠈⢻⣿⠁⢠⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠛⡿⢿⡟⠀⠱⡈⡀⠀⣹⠿⣿⠇⢀⠀⢀⠀⠉⢻⠄⠘⠒⠒⠂⠀⠀⠀⠀⠀⢹⣦⣾⡄⠀⠀⠀⠀⠀⠀⠀⣽⡇⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢦⣔⣸⣿⡎⠀⠀⢩⠀⢾⣴⠃⠀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠁⠀⠀⢸⡄⠈⠁⠀⢰⣿⠿⢷⡖⠂⠀⠀⢀⣠⣴⣿⣿⣿⠿⠟⠻⣦⠀⠀⠀⠀⠀⢿⡇⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣷⣼⡧⠴⠶⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠸⡇⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣠⠞⠋⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠘⣄⡀⢻⣄⠀⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⡼⠁⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢇⠀⠘⢿⡌⠿⠦⡀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠞⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠘⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢦⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⠀⠀⠀⠀⠀⣴⡥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⣼⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣆⠛⢛⣿⢾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠉⢍⡴⠋⠀⢰⡌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠹⠛⠿⢿⣿⠀⠀⠀⠀⠀⣀⣠⡾⠉⠀⢀⠆⣼⡇⠲⢠⣄⣀⠨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢼⡅⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⢈⠗⠉⠹⣄⠈⣀⠈⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣤⣴⡾⠿⠷⠆⠀⡀⣤⣿⡇⠀⠀⠀⣄⣀⢠⡀⠻⣤⣄⠉⣴⠾⢓
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠚⢆⠀⠀⠀⠘⣓⠈⢿⡄⠀⠀⠀⠏⣙⠂⠹⣶⣿⣅⡾⠛⢀⣈⣓⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣶⣮⠙⢦⡀⠀⠀⠁⢄⠈⠁⣄⠙⣷⠲⣎⠙⢁
⠀⠀⠀⠀⠀⢀⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣿⣿⣿⠀⠀⠙⠶⣄⡀⠈⠄⢀⣨⣿⢁⡱⠌⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣀⠀⠀⠀⠀⠀⠀⠀⣸⣟⡿⣿⠄⠀⠀⠀⠈⠙⠓⠚⠛⠛⠀⠙⣅
⠀⠀⠀⠀⠀⠀⡀⡈⠁⢻⣍⠛⠀⠀⠀⠀⠠⢦⣻⠿⠠⣿⠀⡃⠄⠀⠶⠤⠞⠃⢶⡄⠀⠠⠋⠛⠠⢄
⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠙⣧⡠⠀⠀⠀⡠⠞⠁⠀⠀⢸⣧⠀⠉⠳⣄⠀⠰⠆⠔⠎⠀⠀⠰⠁⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢹⠛⠄⢠⠋⠀⣦⠠⠄⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠠⠀⠲⡄⣀⢁⠀⠀⠀⠀⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣿⡉⣴⠇⠀⢀⣡⣤⣄⣀⣿⡟⠀⠀⣄⠀⠠⡄⠀⠀⢀⠀⠀⣀⠠⠀⠉⠠⠀⠶⠀⠀⠀⢠⡄⠈⢘
⠀⠀⠀⠀⠀⣶⠈⡷⠀⠀⠟⠀⠁⠉⠀⠀⢸⡇⣿⣿⡿⣏⢠⠀⠀⠈⠁⠀⡀⠐⠚⣋⠃⣴⠀⠉⠀⠀⣤⠀⠀⠒⠀⢰⠞⠁⠀⡎
⠀⠀⠀⠀⠀⠈⠀⠀⢠⣀⣼⡀⢰⡄⠀⠀⣽⣧⣿⣿⡇⢸⡄⠁⢠⡄⠀⠠⠃⠀⠀⠉⠀⠀⠁⢀⠀⣰⠃⠚⠀⠀⡠⠊⠀⠠
⠀⠀⠀⠀⠀⠀⠐⠀⣀⠸⣤⣿⣿⣿⣶⣾⣿⣇⣿⣿⣇⠀⠻⡄⠘⣧⡀⡀⢀⠀⠛⢦⡘⠀⣠⡌⣠⣀⣤⢀⡴⠋⠀⠀⣰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣍⣡⡿⣿⣿⡟⣩⡟⠁⠘⠦⣘⠇⠀⠈⠦⣄⠀⠱⣘⣣⣨⡎⠁⠀⠀⠀⣠⠶⠔⠃⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⢋⡍⠈⣿⣿⠗⠟⠀⠰⠦⢄⡈⠛⠶⢇⡠⠀⠁⠀⠙⢫⡝⠀⠀⠀⠀⠘⢠⣀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢘⡃⠀⠀⠀⣿⣿⡃⠙⠛⠙⠁⠀⠙⢲⣤⣈⣙⣠⣤⣄⡀⠈⠓⠀⡀⠀⠀⠘⠆⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⢡⠆⠀⠀⠹⠄⠉⠁⠀⠀⠀⢀⣴⠟⣿⣿⣿⣿⣿⠏⠁⠀⠐⣄⠈⠄
⠀⠀⠀⠀⣠⣤⣄⣀⣰⣿⠀⠀⠀⡀⢘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⠿⢿⡿⠛⠁⠀⠀⠀⠑⢤⣀⠸
⠀⠀⢠⡾⠉⣩⢿⣿⣿⣧⠀⠀⠀⠀⠨⡉⢿⢛⣦⠶⢾⣛⣠⣄⣴⣦⣷⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢡
⠀⠀⢻⣷⣾⣿⣦⣌⡛⢿⡀⠀⠀⠀⠠⢀⣌⣻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢡
⠀⠀⣴⣿⣿⣿⣏⣉⣿⣾⡷⠀⠀⠀⠀⠈⣸⡿⠟⢿⣿⣿⣿⣯⡟⠋⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢳
⠀⠈⠉⠻⠿⠛⠿⣦⡍⣍⣷⢀⠀⠀⠀⠀⣼⠃⠀⠈⠻⣿⣿⣿⠄⠀⠀⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠁⠀⠀⠀⣿⠀⠀⠀⠀⣿⠽⠟⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠆
⠀⠀⠀⠀⠀⢠⣴⡿⢿⣟⣹⣿⠀⠁⢀⠞⠁⠀⠀⠀⢀⠿⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠲⢺⡀
⠀⠀⠀⠀⠀⣼⣿⣴⣤⣿⡿⠇⠀⠀⡸⠀⠀⠀⠀⠀⠀⡄⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠊
⠀⠀⠀⠀⢠⣿⡟⠛⠋⠀⢉⠀⠀⢾⠁⠀⠀⠀⠀⠀⠢⣁⠄⠘⡀
⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠈⡀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠁⠚⢄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠒⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⠔⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⣷
⣶⣶⣶⣶⣴⣶⣶⣴⣶⣶⣤⣤⣶⣦⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶
⣿⣿⣿⠻⠙⠛⣿⠋⢹⠛⢛⡟⠟⢛⣿⢟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣷⣿⣷⣿⣾⣿⣿⣷⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣄
⠀⠀⣦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠋⠙⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡶⠃⣠⣴⡖⣀⡀
⠀⠀⢿⣿⣶⣾⣿⡄⠀⠀⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠂⠈⣿⢹⠏⢀⣶⣄⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣴⣾⣿⣿⣿⡯⢂
⠀⠀⠀⢹⣿⣿⣇⠀⠀⢀⣿⠡⡀⣤⣬⣿⣧⡀⣠⣴⡖⠀⢀⣶⣄⣀⣤⠐⠂⣠⠟⢃⠻⠿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣥⣦
⠀⠀⠀⣿⣿⡟⢿⡆⠀⠀⢻⣆⠜⠛⠛⠛⠋⣡⣿⣿⣷⣀⣈⣿⡟⠛⠁⠀⠜⠥⠊⠉⠈⢠⠀⠛⠻⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠄⠐⠋⠛⠻⣿⣿⣿⣿⣧⠄⢀⠀⡀⠂⠀⢠⠀⡄⢣⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡾⠅⠀⠀⣼⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⡼⣢⢰⠂⣄⠉⠊⠡⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠴⢧⣄⠀⠀⠀⢀⠄⣠⡞⠐⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢿⢣⠳⡆⠈⣟⠁⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠄
⠀⠀⠀⠀⡠⠊⣁⣀⠀⠈⢳⡄⢒⣣⠞⠩⠁⢠⡄⢆⠀⠀⠀⠀⠘⢿⣿⣿⣛⠃⠳⡟⠛⠌⢻⣿⣷⣴⣒⠐⠒⠚⠛⠿⠿⣅⡀
⠀⠀⠀⢀⠂⠀⠙⠋⢈⡀⠀⢻⣏⠁⠀⣃⣠⠎⠀⠀⠑⠄⠀⠀⠀⠈⢻⣿⣿⣤⣤⣇⠀⠰⢶⣿⣿⠏⠉⠛⢦⡀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠛⢛⡂⢴⠏⢀⣠⠼⠟⠛⠻⣉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⠀⠀⣿⣷⣦⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠘⠬⣖⡠⠃⠈⠳⣄⡀⠀⠀⠉⢻⠦⠤⣀⣂⣀⣀⣀⣀⣀⡤⠖⠋⠀⢹⣿⡇⠀⠻⣿⣿⣷⠀⠀⢸⡇⠀⠈⡆⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠖⢺⡇⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢷⣄⡀⠈⢿⣟⠀⠀⣼⠃⠀⠈⢴⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⢻⡎⠻⣿⣾⣿⣿⣦⡾⠃⠀⠀⠀⢠⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠰⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⢸⠻⣦⣼⣿⣿⡿⣿⣧⡀⠀⠀⠀⣼⠀⠄⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠸⡆⠀⢹⣿⡏⢓⣿⣿⡟⠀⠀⢠⠏⠜⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⡀⠈⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠀⠀⠀⠀⢹⠀⢸⣿⠐⠿⠿⠿⠀⠀⣰⡏⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣖⠛⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⡟⠀⠀⠀⢀⣠⠞⠁⠙⢦⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠻⣿⡛⠀⠠⣀⡀⠀⠀⠀⠀⠀⠈⢠⠖⠒⠀⠀⠀⣠⠈⣰⡿⢁⣠⡴⠞⡻⠁⠀⠀⠀⠘⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠈⢳⡀⠘⠆⠀⢀⡀⠀⢦⡀⠀⡟⠀⠀⢠⠀⢰⣧⣼⣿⣿⣍⣁⣶⣄⣳⡀⠀⠀⠀⠀⡏⢸⣿⣿⠖⠊⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠈⠳⢤⡈⢀⡴⠛⠙⠋⠙⠲⡇⢀⠔⠁⠀⣸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣿⣼⣿⣿⣤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡇⠀⠠⢂⣼⣿⣿⣄⠀⠀⠈⠉⠙⠛⠛⠛⠋⠀⠀⠀⠙⠿⠟⠁⠀⢹⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⢻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣤⣶⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣰⣿⠃⠸⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣤⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢠⣴⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠄⠀⠐⠲⠿⢿⡶
⠀⠀⠀⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠁⠾⠋⠉⠀⠀⣴⠲⢤⠚⠁
⠀⠀⢈⡟⣣⡿⣿⡟⠀⠀⠈⠉⣿⠛⢿⡄⠀⠀⠀⠀⢠⡇⠀⡎⡇
⠀⠀⠀⢀⡟⠀⠙⢧⠀⠀⠀⣠⠇⠀⠀⠹⡄⠀⠀⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠞⠀⠀⠀⠈⠳⠀⠰⠁⠀⠀⠀⠀⠹⠆⠀⠀⢸⡷⠖⢤⣤⡀⠀⢀⡤⠖⣛⣛⣛⣛⣛⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣸⣀⠠⣀⠀⠈⠙⠷⡀⠈⠉⠀⠀⠀⠀⢀⣉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠋⠀⠀⠀⠉⢻⣿⡿⢹⠋⠙⡇⠀⢀⣤⡎⠲⣤⣟⣠⣶⣿⣭⣥⣀⣹⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⣤⣸⡟⠀⠀⠀⢀⣨⠄⣸⡿⠃⠀⠈⣿⣿⠟⠉⠟⠕⢹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣿⡀⠀⠀⠀⢀⣿⣿⣧⡀⠀⠀⠀⡸⠀⣿⣦⠀⢢⣷⢸⠁⠉⣶⣇⣤⠚⠁⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢸⠇⠀⠀⢠⡞⠉⠛⠻⠿⣷⣤⣠⣇⣀⣏⣿⣄⠀⠁⠾⠀⠀⠛⠟⠁
⠀⠀⠀⠀⠀⢀⣿⣿⡟⢀⡞⢀⠄⣶⣿⠃⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⣿⠛⠶⡄⠐
⠀⠀⠀⠀⢀⣼⠿⠋⠐⠛⣱⠋⢀⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠘⢆⣧⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⡜⠁⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀⠞⠜⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢤⣧⠀⠀⠀⠀⠀⠀⠀⠀⢱⣧⡀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⡶⣶⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⠟⢽⠯⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⢀⣘⣧⣰⣤⣶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⢾⣥⣿⣿⣷⣾⣯⡈⠉⠛⠻⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠜⣱⣾⣿⣿⣿⣿⠟⠛⣿⣿⣦⣤⡀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣌⠲⡦⣸⣾⡏⠀⠀⠀⠀⠀⠀⢀⡿⣽⣿⣿⣷⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠄⢀⡀⠀⠀⠀⠀⠉⠻⡿⢃⡔⢿⣿⣷⡾⠧⠀⠀⠀⠀⣸⣷⣿⣿⣿⠟⡁⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡐⢊⡤⠖⣛⣛⣛⠻⢷⣦⣀⠠⡤⣎⣴⢻⣿⣸⣿⡇⠐⠒⣶⠶⠂⠈⠉⠉⠉⡉⠋⠉⠠⡤
⠀⠀⠀⠀⠀⠀⠎⢠⠏⡐⠀⠀⢀⠀⢙⠒⣌⡻⠃⢠⣿⣿⣇⢿⣧⢣⡿⡀⣦⡈⠀⠀⠀⢐⡀⠀⠈⠀⣠⠄
⠀⠀⠀⠀⠀⢐⠀⡟⠀⠀⠐⢄⡴⠂⠒⣂⠈⠀⡴⢿⣽⣿⣿⣼⣿⡆⢰⣣⣿⣿⠶⣄⠢⣀⠿⣀⡀⠔⠁
⠀⠀⠀⠀⠀⢸⣾⡇⠁⠀⠄⣾⠀⣾⣟⡧⣀⡈⡄⠘⣿⠫⠿⢧⣤⢻⣮⢾⣿⣿⣞⢧⠀⠀⠀⡿⢶⣤⣀
⠀⠀⠀⠀⠀⠸⣿⣿⡀⡀⢀⠼⢧⡈⠛⠋⡉⠀⠀⠀⣿⡆⠴⣿⣿⠈⣧⢰⢾⣭⣬⣆⠂⠀⠈⠀⠀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡐⠀⠀⠌⠉⠹⠁⠀⠁⡂⢀⣿⢟⣸⣽⠾⠴⠧⢖⡛⣿⣾⣿⡆⠀⠒⠀⠀⠀⠀⢀⣤⣴⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠤⠀⠀⠀⡀⠔⣡⣾⠏⠀⢸⢀⣤⣄⠶⣘⣇⣾⣟⣻⣥⠀⠀⠀⢰⣒⣾⡀⠈⠉⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣦⣴⣶⣾⡿⠋⠀⠀⠀⠈⡅⠠⠈⠻⢿⡮⣿⣯⢶⣆⣴⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⣾⣿⣟⡿⣭⡟⠏⠙⠄⠉⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡷⣿⡀⠀⢴⠤⠦⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣿⣿⣶⣄⠘⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠙⢻⣿⡎⡑⠖⠈⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠁⠘⠳⡄⠡⠆⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠄⠀⠀⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣦⣥⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣿⣿⣿⡤⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⣿⠆⠀⢸⡿⠛⠉⠀⠀⠀⠀⠀⣼⠧⡄
⠉⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡏⠀⠄⠈⠟⠿⠀⢈⡛⠆⠀⠀⡀⠀⠀⣀⣿⡀⠨
⠞⠛⠉⠳⣄⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠂⢆⠐⠂⠀⠀⠀⢀⣴⣿⣧⣴⡞⠀⠀⠈⠀⠀⠾⠿⣦⡀⢠⡧⠀⠠⣼⣿⣦⡈
⠀⠀⠀⠀⠙⣿⠀⠀⢀⠸⣂⡀⠁⠀⠀⡠⠃⠀⠱⡀⠀⠀⠀⠛⢿⣿⣿⣿⠶⠂⠀⠀⢀⠀⠀⠀⠀⣽⣃⠂⠘⣿⣇⡜⣛
⣶⣾⣦⢀⡀⠹⠷⣶⡮⠴⠙⠛⡂⠀⠠⡿⢦⣴⣶⣧⡀⠠⠄⠀⠀⠉⠙⠟⠓⠀⠀⠀⠀⠂⠀⠀⣐⣯⠀⠐⣿⠿⡛⠗⠹
⣹⡝⠈⠁⠀⠠⡤⠀⠀⢠⣮⠀⠋⡀⠀⠃⠀⠉⣸⠁⠄⠀⠀⠀⣀⠀⢺⣧⣄⠀⠀⠀⠤⠀⠀⣠⣾⠟⠡⠥⢘⣾⣃⣼⣳
⢿⣿⠢⠤⠐⠀⡀⢀⠀⠈⠉⢠⠆⠀⢀⡠⠤⠜⠁⠀⠀⠀⠀⣄⠀⠀⠀⡀⠉⠉⢉⡀⠀⠀⠉⢽⣷⣽⣀⠈⠻⠟⠛⠛⠛
⠀⠉⠁⠀⠘⠁⠀⠠⢠⣀⠄⠉⠀⠀⠈⠐⠂⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠉⠀⠠⢿⣿⣷⠀⠀⠀⠉⢹⣤⠀⠀⠀⠠⡴⠆
⠘⠋⠉⠀⠀⠉⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⢤⡆⡀⠀⠀⠠⠀⠀⠀⠀⠀⠲⠒⠂⠀⠀⠉⠁⠐⠶⠦⠈⠃⠂⠀⠠⢶⣿⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣤⣶⣠⣠⣤⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⢾⣿⣿⣿⣿⣿⣿⢿⡿⣿⣽⣿⡿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣾⣿⣇⡡⡷⢪⣏⣿⣧⣴⣯⣿⠷⠷⡾⣿⢿⣾⣬⣿⣯⡍⣰⣦⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡻⠿⠉⣵⣿⣿⣿⣿⣯⣴⣏⣴⣾⣿⣷⣿⣾⣽⣿⡿⣭⣼⣿⣿⣛⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠳⣌⣿⠛⢛⠟⢿⣿⡿⢿⣿⠻⠿⠿⠻⣹⣿⠿⣿⣿⣾⣿⡯⠿⢿⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣇⣘⣟⡟⢻⠾⣦⣌⢈⣷⠀⠙⣷⣄⠈⢧⣙⡞⢀⣹⣦⣽⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡟⠁⠀⠀⣾⣧⣤⠄⠙⣧⡼⠃⢿⡿⣿⣿⡼⣭⣿⣾⡿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⡈⢋⡹⣻⣿⣿⡍⠰⢧⣀⡏⢾⣯⣷⠀⢹⣦⣦⣴⣊⣵⡿⠮⣵⣾⠏⠀⢀⣼⣧⡴⠾⣜⢿⣿⣿⠛⠳⠄
⠀⠀⠀⠀⠀⠀⠀⢛⣟⣟⣼⠋⠛⠑⢦⣼⠟⠉⠀⠈⣿⣶⣿⡟⣿⠿⠟⠋⠀⠀⣸⡿⠷⠾⠟⠛⠁⠀⠀⡒⠛⠋⣹⢿⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⢺⣻⠛⢿⣿⡛⠓⢀⣽⣷⣦⣤⡤⣿⣿⠃⢰⣇⠀⢐⣰⣦⣴⣟⣃⣤⣀⠀⠀⢀⡠⠔⠋⠁⣈⣝⣻⣿⣿⠷
⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⣿⡗⢠⣿⠏⠉⡟⠿⣷⣿⣿⣤⠢⡙⢶⣟⠁⠀⠉⠉⠉⠉⠙⠻⠿⣿⣀⣠⡤⠾⣄⣙⣻⠛⢿⡷
⠀⠀⠀⠀⠀⠀⢀⣬⡓⢾⣀⣿⣷⡿⠃⠀⠀⡇⠀⡏⠻⣿⣿⣿⡻⣦⣙⠳⠤⣀⡀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠉⠁⠀⠀⠀⢸⠁⢀⠃⠀⠉⠻⣿⣿⣦⣝⠳⢶⣌⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠶⠶⠀⠀⣀⣤⣿⣯⡿⢣⠔⣠⣙⢿⣾⣷⣔⡲⣦⢀⣀⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⣠⣤⣀⣦⣴⣾⣿⣿⠿⣛⡔⢠⣾⣿⡿⢿⡛⡛⢦⡍⢿⢻⣿⣿⣿⣿⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⡿⢿⡛⡿⢉⣯⠗⠚⠺⢟⠡⢾⢯⣹⣿⠼⢃⡿⣌⢻⢨⣁⠛⠻⠽⠍⢿⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⣿⡿⠍⠠⡾⢶⣿⣿⠃⣼⢟⡹⢏⣰⣿⣇⢱⣶⠇⣎⢳⡜⠗⣼⣑⠝⢶⣿⢖⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣛⣿⢵⣷⣶⡤⣶⣿⣮⡿⡐⣷⣷⣶⠟⣎⢵⣷⣙⠧⡖⡇⠶⣙⣏⣾⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⢽⣿⣿⣿⣏⣭⣜⣿⡜⢷⣿⣷⣽⣽⢫⣿⢧⡹⣷⣽⣣⡼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣿⣿⣯⣷⣻⣿⡾⢿⣿⣿⣏⣿⣾⣷⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠛⠛⠋⠉


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

⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠁⠀⠈⠉⠻⡿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠹⡇⠀⠀⠀⠀⠀⠀⢱⠹⣿⣿⣿⢴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠀⠀⠺⠇⠀⠀⠀⣿⣿⣿⣿⣿⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠘⠙⡿⣿⣿⣯⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠖⣈⣴⣿⣿⣾⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⠦⣀⣬⠋⢀⣄⠀⣀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢃⣴⣶⠾⠿⢷⣿⡏⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡏⣠⣴⡶⣮⠙⠃⠀⠒⠰⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⣀⡉⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠶⠦⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠂⠒⠀⠆⠀⠀⠒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⢀⡀⣈⢀⡁⢈⡉⣙⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⡁⣨⢀⡇⢨⡀⣩⢸
⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠠⠠⠦⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⢀⣤⣤⣶⠿⠛⠛⠘⠛⠻⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠘⡛⡛⠛⠛⠻⢿⣿⣦⣄
⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⣷⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⢠⠀⠀⠴⠀⠀⢹⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠹⣿⣧
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢀⣶⣶⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣿⣿
⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⠏⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣶⣾⣿⡿⠟⠋⠀⠀⠀⠂⠄⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣶⣶⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⡟⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⢷⡎⠀⠀⠀⠀⣀⣠⡶⢲⣶⠶⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠇⠀⣀⡤⠚⢧⣤⡴⠾⢧⣁⡤⠽⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡾⢿⣿⣿⣠⠎⣉⡸⠖⠉⠀⠀⠀⣼⣿⢀⣀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡈⠣⣀⢯⣿⡵⠞⠉⠀⠀⠀⠀⠀⢠⡇⢸⣣⡀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⠗⠾⣯⣿⣄⣀⣀⣀⣀⣀⣀⣠⡞⢷⡀⣳⣷⣖⢋⡹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠄⠠⣶⡿⠿⢶⣼⣿⣿⣿⣿⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠉⠙⠳⢼⡏⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⠛⠛⠻⢻⣿⣿⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡰⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡷⠋⢻⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡰⠁⣿⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⢰⣿⣯⣽⡅⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⢰⣤⣀⡀⠶⠚⠁⢀⣿⡄⠀⠀⠀⠀⠀⢸⣄⡀⠀⠈⠉⠙⠋⠁⠀⠀⠘⢷⠀⠀⡆⠀⠀⠀⠈⠲⣦⡹⣄
⢺⡇⠀⠀⠀⢀⣠⠺⠛⢧⠀⠀⠀⠀⠀⣾⣿⣿⠷⣶⣦⣤⣀⣀⠀⢀⣀⣈⡷⠶⠷⢤⣄⣤⡀⠀⠈⠙⠻⠷⣄
⠀⠉⠿⢧⠔⠛⠁⠀⠀⠘⡆⠀⠀⢀⡾⠁⠀⠙⢧⠀⠙⣇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⢤⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣠⠏⠀⠀⠀⠀⠈⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⡿⠁⠲⠋⡼⢦⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⢰⠏⠀⠀⠀⠀⠀⠀⣿⡀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠎⠀⠘⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣈⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣍⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥⠬⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣿⡄
⣟⠁⢹⣋⣛⣛⣛⣛⣏⣛⣛⣛⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣟⣻⣿⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢲⣊⣯⠭⠭⠭⠭⣹⣃⡖⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡭⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢭⡒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢊⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⡑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢬⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣤⣤⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⡉⢉⣿⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡅⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⣾⡟⠛⠛⢻⣷⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢨⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢼⡀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡁⠀⠀⢈⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⢀⡯⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⢣⠀⠀⠀⠀⠀⠀⣰⣿⣱⠁⠈⠉⠉⠁⠈⣏⢿⣆⠀⠀⠀⠀⠀⠀⡜⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠳⡀⠀⠀⠀⣼⣿⣳⠃⠀⠀⠀⠀⠀⠀⠘⣞⣿⣧⠀⠀⠀⢀⠞⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⠦⣀⣾⣿⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣿⣷⣀⠴⠩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢫⡟⠊⠭⣑⣒⡲⠲⠖⣖⢒⣊⠏⠑⢻⡝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢇⡞⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢳⡸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣛⣻⣯⣾⣀⣀⣀⣀⣀⣤⣶⣾⣷⣶⣤⣀⣀⣀⣀⣀⣷⣽⣟⣛⣓⣀⣀
⠀⠀⠀⠀⠀⣀⣤⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣀⣀⣤⣀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠻⠿⠿⠟⠉⠉⠉⠙⠻⢿⣿⣿⡿⠟⠉⠉⠉⠉⠻⠿⠿⠟⠋⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⣠⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣠⣜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⡀⠀⠉⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⡀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⡄
⠀⠀⡼⢫⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠶⠾⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⢽⣿⣻⠛⣄⣀⣸⣇⠀⠀⠀⠀⠀⠀⣠⣤⠀⣾⣿⣤⣼⡶⣖⣦⡦
⠀⠀⠀⣿⣧⠀⠈⠳⢤⣼⡋⠀⠀⠀⠀⠀⠀⠾⢹⣿⡇⠀⠀⠀⣯⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠥⢿⡿⣿⣼⣷⣾⠷⠟
⠀⠀⣸⠏⠹⣇⠀⣀⡾⣏⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⣤⣦⣭⣁⡉⠉⠀⠀⠀⠀⠀⠐⠛⠋⢀⣀⣹⣯⣀⣀
⠀⠐⠋⠀⠀⠻⠄⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇

⠀⠀⢀⡔⠺⠁⢙⢈⠓⢢⡀⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⢠⠏⢀⠂⠁⠀⠈⠐⢈⠩⡆⠀⠀⠀⠀⠀⢄⠀⠀⠀⣀⡀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠟⠉⠉⠹⡄⢀⣀⡀
⠀⣬⠀⠄⠀⢸⣿⡧⠀⠠⠄⣽⠀⠀⠀⠀⣤⠀⠷⠐⢾⣿⣿⣤⣀⡄⠁⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⡿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢠⠜⠏⠀⠙⣆⣠⠏⠉⢳
⠀⢸⡄⠀⢄⡞⠉⢳⡠⠈⢠⡆⠀⠀⠀⠀⠀⠈⠁⠚⢺⣿⣿⠤⠌⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣀⠀⠀⠀⠀⠀⠀⠁⠒⠊⠀⠀⠸⢆⠀⠀⠀⠀⢀⡼
⠀⠀⠸⢦⣞⠁⢀⠈⣳⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠃⢻⣿⡇⠙⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠒⠉
⠀⠀⢠⡎⠉⠈⠛⠁⠉⢹⡄⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⠷⠆⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⢠⡄⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡒⣤⣶⡞⠁
⠀⠀⢸⣾⣆⣀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣍⢾⡿⣉⣯⣥⣤⣄
⠀⠀⢸⡟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠸⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣴⣾⠕⡩⠭⢗⡁
⠀⠀⢸⣀⣀⣘⣀⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⢀⣾⠷⣤⡀⠀⠀⠀⢸⣺⠀⠀⠀⠀⠀⠀⢸⣇⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣫⠖⣩⠔⠊⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡾⢯⡀⠀⠉⠐⠀⣴⢸⢼⠀⠀⠀⠀⠀⠀⠿⡿⣾⠛⠃⠀⠛⡟⠂⠀⠀⠀⠀⠀⠘⡿⢋⡤⠋
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢴⠛⠁⢸⡇⠀⠀⢠⣤⣿⣾⣿⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠈⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⡶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢴⡀⢺⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡻⠗⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢠⣶⣄⣤⣤⢴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠙⣹⣿⣉⣉⣀⣀⣀⣀⣈⣁⠀⠀⠀⠉⢠⣿⢿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠘⣿⣿⢡⢐⠑⢻⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⣠⣄⣠⣤
⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡀⠙⠋⠀⣀⣀⣠⣠⣾⣿⣿⡇⠀⠀⠀⠀⠈⠛⠷⢶⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢴⠏⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡠⢄⡠⢼⡧⢄⡠⡄⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣶⣿⣿⠿⢿⡟⠉⢻⣿⣿⣟⠉⣓⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠀⠘⣿⠛⢮⣥⢹⣿⠴⠍⠛⠛⠋⠉⠙⠓⠦⢤⡀
⠀⠀⠀⠀⣠⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠶⠈⢀⠀⠻⣇⠈⠿⠂⣚⡂⣰⡆⣠⣀⣡⡀⠀⠀⠀⠉⠓⢦⣀
⠀⡠⣶⣿⣿⣿⠻⣿⣷⣭⣽⣿⣿⡿⢿⡿⣿⣿⣿⠋⣀⠀⠀⠈⠙⠳⠂⢉⣩⣧⣼⣿⣿⣀⣀⣈⣈⠁⠈⠁⠀⠠⠄⠀⠀⠙⠳⣆⡀
⣿⣧⣾⣿⣏⠙⢄⡀⠹⣿⣿⣿⣿⣿⣿⣼⣿⣿⡟⣇⠹⣷⡙⣷⠴⣤⣴⣾⣿⣽⣿⣿⣿⠞⠠⣤⠤⢍⣀⣄⠀⠀⠐⢼⠂⠀⠀⠀⠛⣦⡀
⣿⣡⣿⣿⣄⡈⠀⡔⢊⢸⣿⢻⣿⣿⣿⣿⣿⣿⣧⠙⢿⠜⢷⠈⣷⣿⣿⡟⣱⣿⣿⡷⢮⣧⡿⣿⣴⣶⣤⣿⠛⠀⠀⠀⠀⠀⠀⢀⡄⠻⠛⠦
⣿⡟⢻⣿⣿⣧⣄⠺⣀⣿⣿⣿⣟⣻⣿⠷⣿⣏⣤⢠⣄⣤⣤⣄⣼⣿⢿⣿⣿⣿⣿⡿⠟⠻⡑⠀⠞⠉⣿⠀⠀⠀⠀⠀⢳⣄⡠⡦⠴⡂⠀⠀⠐⢆
⣿⣿⣾⠟⢿⣿⣿⣿⣿⣛⣿⣿⣿⣿⢀⣼⣿⡟⠛⠠⢃⣼⣩⣋⣿⣿⣿⣿⣿⡿⠿⡱⠞⢁⠀⠈⡀⠘⠛⡸⣧⠆⠚⠁⠀⢀⡄⠀⠀⠁⡶⠆⠀⣼⣷⡀
⣈⠻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣯⣤⣶⣶⣾⡿⣿⣿⣿⣿⡟⠉⢑⡂⣰⠆⠀⢠⣾⠷⠀⢄⡷⠈⠀⠈⠀⠠⣄⡸⠩⠶⣆⢀⠀⠘⠻⢿⣿⡄
⣋⡘⣪⣹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⣿⣿⣿⣍⡁⠞⠉⣁⣿⡟⢻⡏⢣⣁⠈⠛⣟⣳⠒⠈⠛⠀⣷⡎⢀⠀⢀⡠⠀⠛⠛⠁⠀⠈⠀⠹⠿⠀⠾⢟⠀⣹
⡟⢢⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡆⠑⠮⢹⣿⠛⣿⣇⣰⣿⣷⣃⢹⡍⢻⣿⣶⣿⣼⡒⢂⡰⠆⠠⠀⡀⢀⠿⠄⠀⠀⠀⠀⠀⠀⠈⠀⠛
⣿⣾⣿⡿⢿⣽⣿⣿⢿⣷⣿⢿⣿⣿⡿⠿⠟⣿⣿⣿⣯⣶⣾⣿⡀⠛⣿⣿⣿⡿⢿⣴⣿⡟⠟⢋⡿⡿⡿⠛⠛⣳⣶⡆⣄⠈⠀⠀⠀⣠⡴⠾⠶⣶⣀
⣯⠉⢉⣀⣠⣿⣿⣿⣯⣹⣼⣧⣿⢾⣥⣴⣶⣿⣿⣿⡟⢻⣿⣿⣧⠀⢸⣿⣿⣷⣫⣿⣟⠛⢞⣻⣴⣛⣷⣿⣷⣿⣿⣧⡀⠀⠀⠀⢰⡏⠀⠐⠂⠈⢻⡆
⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣸⣿⣽⡉⠀⢸⣿⣿⣿⢿⣻⠏⣁⣼⣿⣿⣿⣿⣿⣾⠿⣿⣿⠀⠲⡖⠀⠬⣷⣆⡄⠺⣿⢠⣿⡀
⣿⣿⣿⣛⣾⣿⡟⣿⠋⢿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⠸⢿⡆⢀⡄⣸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣫⣼⣿⣿⣽⣿⣿⣿⡀⠷⢀⡿⠲⣌⠛⣷⡆⠁⣼⡇⠙
⣬⠀⠈⢻⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⢿⣟⣿⣿⣿⣿⣷⣤⣿⣤⣤⣿⣿⡿⢿⣿⠻⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠁⠟⣠⡎⣴⣮⡥⠱⠆⠀⠀⢈⡁
⣿⣷⡾⠻⠿⣿⣮⣿⣿⣿⣿⣿⠙⢛⣿⡿⣻⣿⣿⣿⣿⣟⣾⣿⣿⣿⡿⣿⣷⠀⣼⣿⣿⠙⣡⡄⣀⣴⣿⣿⣿⣿⣯⠀⠴⠟⠁⠋⠁⠀⠀⢴⡆⠀⣌⢛
⣿⣧⡀⠀⠀⣸⣿⣾⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠋⢻⣭⢹⢻⣿⠀⢸⣿⠀⣿⣀⣿⠀⢹⣿⡟⢸⣿⡧⣿⣿⠻⡄⠀⠀⠀⢀⠀⠸⣷⡘⣻⡾⠏⠘⠐
⣿⣿⣿⣤⣤⣿⣿⣿⣾⣿⡿⠄⢠⣿⣿⣿⣿⣿⣿⡁⡀⢤⣥⣴⢶⣿⣿⣿⣿⣶⣿⠉⣿⣤⣹⣫⣿⣾⣿⣷⣿⣧⣤⠰⡶⠲⡶⢢⡁⠀⠈⢳⣿⡄⠀⠘⠃
⠉⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣴⣿⣭⣿⣿⣿⣿⣻⢦⣴⣦⣿⢇⡼⢡⣏⣭⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠆⠁⠀⣤⡌⠹⣆⠀⢸⡿⠁
⣰⣿⣿⣿⣿⣿⣏⣼⣿⣿⠙⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣛⣿⣿⣉⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠄⠡⠄⠳⠃⠀⠛⡀⠘⠃⠀⢀
⣿⣿⣿⣿⣿⣿⡿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⣿⣿⡿⢿⡿⣿⣿⣿⡿⠿⠛⣿⣿⡏⣿⣿⣉⡿⣿⡏⢀⡈⣀⠀⠐⠚⠀⠚⠃⠃⠀⠀⢀⣀⢤
⣿⣿⣿⣿⣟⢿⣷⣾⣿⣿⣿⣿⣽⣿⣿⣿⡳⠝⢃⡿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣷⣴⣿⣿⡿⠶⢿⣿⣿⣷⣿⠁⣬⢃⠁⢄⡁⠀⠁⠐⠀⠀⢠⣤⠈⠀⠶
⣿⣿⣛⡻⣿⣿⣿⡿⢿⣿⣉⢿⣿⣿⣟⣛⡳⠶⣛⣶⡹⣿⣿⣿⣷⣮⣿⡟⢻⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⠄⢠⡎⠁⢀⠙⠁⠀⠠⠀⢀⠘⠛⠀⢾⣶
⣿⣿⣿⣷⠋⣿⣿⣷⣿⣟⣿⣿⣿⣏⣬⣹⠿⣛⠻⢾⠻⣾⣿⣿⣿⣯⠟⣻⣿⣿⣿⣿⣿⡇⠀⡤⠸⣿⣿⣿⣇⠀⠀⠉⡀⠠⡌⠑⠘⢛⣀⡟⠀⠀⠀⠀⢸
⢿⣿⡏⠉⠁⢿⣿⠿⠿⠿⢿⣿⣿⠷⣶⠾⣶⣿⣦⣿⣃⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣇⢀⡴⢰⣿⣿⣿⣏⠰⡄⠀⠃⠀⠈⠁⠀⢉⣌⠳⠀⠈⣰⡄⠈
⡾⣿⠇⠈⡉⠐⢶⣄⣡⡀⢸⣿⣿⣿⡛⠗⠮⣽⣛⣛⣋⣉⣴⣶⣿⣿⣿⣿⡧⡼⠏⢻⣿⣿⢃⡁⠘⣿⣿⡟⣿⣅⠰⠆⠀⠀⠀⠀⠀⢠⠽⠀⠀⢀⠉
⣯⣴⣶⣿⣦⠀⣾⢳⣿⣿⣿⣿⣿⣿⡟⢦⣤⠀⣍⡈⣩⣿⣿⣿⣿⣯⣽⣿⣧⣤⠀⢆⡻⣿⣉⣤⡴⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠁⠀⣀⠂⡀
⣿⣿⣿⣷⣾⣿⣯⣷⣏⣼⡟⠋⠉⠉⠻⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢾⢛⣿⣯⣴⣿⣷⣿⣿⡉⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠠⠀⠀⠀⠀⠀⣀⡞⠁
⣿⣿⣿⣿⣿⣿⣿⡋⣽⣟⠀⢀⣠⣶⡻⣮⠻⢿⣿⣿⢿⣿⣷⣍⡉⣄⠈⠻⠋⣿⣯⣿⡟⢹⣿⣷⠀⠾⠀⠀⣭⠍⠉⠉⠉⡶⠀⠈⠙⠛⠀⠐⢆⣉⠋
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠿⠛⢷⣿⣿⣷⣾⡿⠻⣿⠛⠯⡁⠘⠷⣻⣿⣿⣟⣶⣛⣿⣞⠷⠀⠀⠀⠀⠰⠆⠀⠀⢀⠀⠀⣠⡄⠀⠈⠁
⣿⣿⣿⡟⣛⡋⠛⠿⢶⣤⣶⡿⢯⡜⢆⣘⣳⡟⣩⣀⠈⡟⢒⡠⠎⠳⣤⣸⣦⣿⡟⣿⣿⣣⣿⣿⣿⣷⠀⠉⠀⠀⣀⣤⣖⠀⠈
⠛⢿⣿⣷⣉⣷⣿⣷⣤⣤⣽⣿⣧⣤⣿⣎⣉⣈⣿⣿⣧⣼⡏⠁⡘⣷⣿⣭⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠋⠀⠈⠈⢳⡄⠀⠘⠃
⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣿⣿⡿⠿⠟⠛⠟⠛⠻⠛⠟⠟⠿⢿⠛⠉⢠⠀⠀⢴⣾⣦⠤⠋
⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣵⣿⣿⣏⣿⣽⣿⣿⣿⣿⠿⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢣⡄⢸⣄⠴⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣭⣭⣿⣷⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⢀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⠲⠤⠄⠠⠤⠀⠠⠤⠶⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠿⢿⣿⣿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⢀⣤⣶⣶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠆⠀⠀⠈⠋⠀⠀⢤⠀⠀⢀⡀⠀⠉⠑⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡉⠈⠀⠄⠀⠀⢀⠀⠀⠀⠁⠀⠁⣼⣿⣦⣄⠀⠀⠸⠿⠿⠿⢿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⡀⠘⢷⠶⠁⡀⠂⠀⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠘⠀⠀⠲⢀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⢂⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢢⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⣀⣠⣤⣤⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠉⠉⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⣀⣨⡿⣿⣦⣀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠙⣿⡇⠈⠉⠛⠿⠿⠿⠿⠿⠟⠃⡀⠢⠀⠀⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⣀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⠛⠃⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃
⢄⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣆
⠈⢻⣶⣶⣴⣶⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠙⠻⠿
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡶⠂⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠞⡀⠰⠀⡉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢋⣄⣀⣀⣬⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣿⣽⣯⣿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣷⣷⡾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣶⣷⣿⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣟⣣⠀⠀⠀⠐⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⠒⢤⣀⠀⠀⠀⢹⣾⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⣾⣦⡀⠑⡄⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⠓⢀⠇⠀⣰⣿⣿⡿⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠿⠿⣿⣿⣿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠛⠃⠀⠚⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠈⠉⠉⠉⠁⠀⠂⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣀⠀⠀⢀⠤⠂⠐⠠⠀⢀⠀⠀⠀⣠⠀⠀⠀⠁⠀⠡⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣷⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⢯⣣⠙⠁⢀⡇⠀⠀⣀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⡈⠀⠀⠀⢉⠉⡇⠀⠀⠉⠀⠀⠀⢠⠄⠀⠀⠀⡀⠀⠀⠀⢀⣿⠇⠠⠁
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠃⠀⠀⢀⣤⣾⣿⣿⡄⢡⠀⠘⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠏⡠⠁
⠀⠀⠀⠻⢿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⠀⢂⠀⠈⠪⣄⠀⠰⣤⡤⠒⠀⠀⠀⠀⠀⣠⣴⣿⡿⠃⡔⠁
⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠑⢀⠀⣰⣷⣤⡀⠀⠀⠀⠀⣀⢤⣾⣿⣿⠟⠀⠈
⠀⠀⠀⢀⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠱⣿⣿⣿⣤⣤⣾⣿⣿⣷⠀⢻⣿⡇
⠀⠀⠠⠃⠘⠁⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣿⣿⣿⠟⢿⣿⣿⠏⠀⠀⠉⠓⠀⠀⠘
⠀⠀⣾⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⣿⣿⣿⣷⣀⠀⠀⠄⠼⠟⠋⠁⠀⣠⣿⣯
⠀⢀⡀⠀⠀⠀⠉⠙⠻⢿⣿⣦⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⣿⡿⠛⠄⢀⣀⣠⣤⣶⣿⣿⣿⣿
⠀⠈⠋⠀⠀⠈⠒⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣅⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠿⠿⢷⣶⣶⣶⡾⠿⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠲⣶⣿⣶⣶⣄
⠀⠀⠘⠠⡀⠉⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠒⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏
⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁
⠀⢀⠀⠀⠎⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇
⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡐⠉⠂⠄⠀⣴⣿⡟⢀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢸⣿⣿⣿⣿⣿⣿
⠀⢘⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⠂⡀⠘⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣴
⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⣀
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠉⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⣀⣐⡐⣖⠒⢄⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠋⠑⠀⠌⠔⡠⢌⡐⠠⢄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⢧⡂⠄⢀⡀⠀⠀⠀⠈⠉⠛⣲⣾⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠌⢠⠉⠓⠶⠤⣭⢤⣴⠶⠾⢿⣋⣡⠗⠈⢀⠁
⠀⠀⠀⠀⠀⠀⢠⣌⣄⡊⠔⠁⠀⠀⠀⡂⢠⠀⠀⠀⠀⠀⠀⠘⣗⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢤⡀⠀⠒⠒⠤⡒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡡⠀⠤⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⢁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⡖⠒⠂⢪⠀⠆⠀⠀⢠⣄⣀⣀⣀⣀⣀⡀⠤⠄⢒⣈⡥⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⣀⠀⠀⠁⠁⠐⠒⠻⣿⠶⠖⣚⣩⣽⣶⢺⣏⢿⣈⣧⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣠⡤⠐⠂⠉⠉⠉⠀⠀⠒⠿⣟⣋⠭⠔⣚⣇⢻⣓⣋⡭⣵⠲⡞⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡏⡏⠉⣀⡲⠦⠀⠀⠀⠸⠖⠚⣩⠞⣹⡞⢿⡌⣷⣹⣇⠿⢜⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⣟⣉⠥⠔⡾⠀⠀⠀⢠⣠⠞⣡⠞⠁⢹⡛⡯⠭⠑⠒⠉⠁
⠀⠀⢀⡤⠒⠋⠉⠉⠉⠙⠲⢤⡠⢊⡴⡇⡇⠀⢀⠌⡁⠀⠀⠀⠘⣡⠞⠁⠀⣀⠴⢧⢻⠉⠉⠉⠒⠦⣀
⠀⡴⠁⣠⠖⢫⠉⣏⠉⡵⡲⢊⡴⢏⠀⡇⡇⢠⡂⢠⣀⠠⠤⠀⠚⡅⠀⢀⠞⠁⡠⣞⡌⣯⠏⢉⠖⢄⠈⠳⡀
⡼⠀⡰⢥⡀⠈⡆⢇⡼⢋⡴⢋⣆⠈⣧⣇⣧⠨⡷⢾⢛⣷⢦⠤⠴⠃⢀⡏⢀⣎⣀⠈⢿⡸⣧⠏⠀⣀⡵⡀⠹
⡇⠀⡧⠤⠬⠵⣞⠛⡴⠟⠛⠋⠉⠉⠁⠀⠀⠀⢇⠮⢊⠗⠃⠀⠀⠀⢸⠀⢸⣀⣈⡭⢶⡟⢳⣎⠭⠤⠤⡇
⢇⠀⢇⢀⡤⠚⡽⡟⣝⠫⢍⡉⡶⠓⡶⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠸⡄⠸⣀⡤⠚⣱⢻⢻⠈⠓⠦⣀⠇⢀
⠘⢆⠈⠣⡀⡰⠁⢳⠘⢆⣀⠝⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⢄⡰⠁⢸⠀⢧⠀⣠⠎⢀⠞
⠀⠈⠳⢄⡈⠙⠒⠚⠒⠋⢁⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠉⠒⠚⠒⠚⠉⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠏⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠃⠀⠐⠢⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢎⣡⠵
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠐⠀⠀⠐⠒⣘⣀⠀⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠬⠤⠤⠤⠥⠬⠬⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⠉⠉⠉⠉⠉⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⣲⢷⠀⠀⢀⡀⠀⠰⠖⠚⠉⠁⡼⣆⣀⣀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⠶⢶⣤⣄⢀⡔⠁⠈⡗⠛⠋⠸⣀⠀⠀⠀⣠⢊⣠⣽⡶⠶⢶⣾⣄
⠀⠀⠀⠀⠀⣠⡾⠋⠁⢡⠀⠀⠀⡹⠿⣆⠀⠀⠸⡆⣦⠂⠀⠀⣠⠞⣱⠟⠉⠈⣇⠀⡸⠁⠙⢷⣄
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠈⣆⣠⣎⡀⠠⢽⡦⠤⢴⢷⡿⣄⣀⡔⠁⢸⡏⠀⠀⠀⢸⣤⠃⠀⠀⠀⢻⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣗⣒⡒⠒⣺⣿⠒⣻⣧⢈⡝⠁⠀⠀⢿⡇⠀⠀⠀⠺⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⢸⣉⣽⣧⠄⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠈⠷⣤⣀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⡀⠀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⢀⣬⡉⠀⠀⠀⠀⠀⠀⠀⠀⣸⡙⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠒⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⡀
⠀⠀⠺⠛⣿⠻⠓⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⠄⠀⠀⠀⠀⠘⣀⡾⢧⣈⠃⠀⠀⠀⠀⡼⣧⣼⣷⣤⣿
⠀⠀⣛⣃⣿⣛⣁⠀⠀⠀⠀⠀⣿⡿⠋⢿⣿⡀⠀⠀⠀⠀⠀⣸⣙⣙⣄⠀⠀⠀⠀⠀⢿⡿⠟⠹⠿⣿


⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⣷⣄⡀⣄⠀⠀⠀⠀⠀⠀⠀⢆⡇⢹⢢⠀⠀⠀⠀⠀⠶⣄
⠀⠀⢶⣛⣓⡶⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢃⡄⠀⠀⠀⠀⠀⠫⣇⣸⠎⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣀
⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣴⣯⣶⣿⣧⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣭⣶⣮⣥


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣧⣸⡄
⠀⠀⡗⡖⡖⡖⡇⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣼⢻⡟⣧
⠀⠀⠃⠃⠃⠃⠃⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⢼⡇⢿


⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣦⠀⣴⣦⡀⠀⠀⠀⠀⣤⡄⣀⡀⢤⣴
⠀⠀⢰⣿⡂⢠⠿⠀⠀⠀⠀⢀⣤⣤⡀⣿⢿⡇⠀⠀⠀⠀⣿⣿⠀⢻⡿⠁⠀⠀⠀⠀⣜⣁⣈⠁⢀⣁
⠀⠀⡈⠋⠂⠉⠀⠀⠀⠀⠀⠸⣿⣿⠇⢶⣶⡆⠀⠀⠀⠀⠈⠇⠀⠈⠃⠀⠀⠀⠀⠀⠘⠁⠘⠏⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡋⠉⠉⠉⠉⠙⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠀⣿⣿⣶⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣃⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠢⠀⠀⢀⢄⣀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠉⢙⣇⣰⠬⣈⡴⣿⣧⢤⠁⣔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡤⢠⠟⠇⠀⠸⣿⣾⢑⣲⡿⣛⠀⣮⡀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠧⠐⢃⠶⠰⠋⠀⠁⢀⠈⠈⡂⠄⠒⠛⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣈⢭⠇⠙⠢⡀⠐⠇⡤⢋⢠⣎⠀⣳⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⡀⢈⢴⣦⠀⠠⠠⡇⠀⠟⡴⣏⠆⢠⠞⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠮⠜⣉⡴⠓⣠⢶⠆⡠⠼⢀⡔⢰⠀⠀⠠⢛⠤⠀⠈⣀⠀⠐⠄
⠀⠀⠀⠀⠀⢀⡴⡁⠀⠀⠀⣠⠈⠉⠁⢆⠘⢄⡠⠃⠑⢁⡔⣈⠒⠁⡠⢒⠝⠁
⠀⠀⠀⠀⠀⣾⠎⠤⠠⢆⡜⠘⠔⣟⣰⠀⠰⡴⡢⠒⠲⣣⠊⢀⠄⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠫⡔⡅⣌⡢⢀⡴⢙⠀⡼⡘⡼⡸⠑⠲⢸⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢸⡅⠈⠁⠘⠴⣇⣠⠼⠚⠀⡇⢿⡇⠀⠠⡠⠋⠀⡀⠀⠈
⠀⠀⠀⢀⠜⣧⠁⠀⠂⠀⠈⠀⠀⠀⣠⣷⣪⠋⠠⠊⠀⠀⡄⢀
⠀⢀⠔⡡⠚⠮⠑⢦⣀⣀⣄⣠⠼⠚⢳⠞⢁⠔⠀⠀⠀⠀⠀⡄
⡠⢃⢜⣓⣢⠤⢄⣀⠈⠙⠂⠤⣀⡴⠃⡴⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⣠⠋⠀⠀⠈⠁⠀⠉⠑⠒⣤⠊⣠⠊
⣿⡿⠿⠿⠻⢿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣄⠀⠦⢾⣿⠘⣿⣿⡿⠟⠿⡿⣿⣴⣦⣄
⠀⠀⢀⣤⠶⠂⡻⠉⡿⢿⠟⡳⢶⡴⢻⡷⠀⢹⣛⣧⣀⠀⣴⠋⣹⣟⡛⠻⣄
⠀⠀⠉⠹⣿⢿⣦⣤⣄⠁⠀⡈⠐⠂⢉⡱⢀⠀⢹⣏⣿⡶⠀⠘⠻⣏⠑⢺⣾⡄
⠀⣿⡾⠂⢬⣀⠑⡄⡻⠂⢀⣅⣀⠐⢬⠟⠜⢻⣿⡟⠁⠀⠄⠀⠀⢀⠐⣠⡟⠙⢦
⠀⠘⣷⣖⠋⢡⠴⠘⣷⣤⠀⡈⢳⠀⣈⣆⣃⢀⣿⣤⣄⠻⣄⠄⣴⠃⢘⠿⣧⠀⠾⡇
⠀⠀⢃⡀⢶⠶⠐⢛⣯⠁⣄⣼⣾⣿⣿⣿⣿⠛⢿⡻⢟⣷⣟⣿⡟⣥⡄⣶⣷⣜⠀⡋
⠀⠀⠀⠻⢆⣸⣶⣾⣉⣤⣿⡟⢛⠛⣻⠛⣿⣭⢩⣥⣼⣿⠯⣭⣟⣁⣶⣬⣏⣻⣿⣦⣀
⠀⠀⠀⠀⠀⢽⡿⣿⣯⣷⡟⠃⠘⢋⣿⠀⢣⣾⡟⣹⠿⠻⠖⡘⠁⠜⠛⢿⡻⣿⠟⠻⢽⣷⣶⣦⠤⣀⡀
⠀⠀⠀⠀⠀⢰⣾⢿⠛⣯⢁⣴⠂⣬⣈⣁⡸⠏⡷⠽⠿⢦⡒⣡⣤⡴⠬⡿⣏⣰⠴⢞⣥⡑⠛⣿⣿⣧⣷⣄
⠀⠀⠀⠀⠀⠠⣧⡴⢋⣼⠿⡏⠀⠀⠀⠁⠘⠋⢁⡔⠿⡺⠿⠻⢶⣦⣀⣀⣤⣤⣶⣭⣴⣿⣿⣷⠿⣿⣾⣿⣧⠄
⠀⠀⠀⠀⠀⠀⠙⣶⠎⡴⢳⠴⠶⠛⣶⣶⣒⣋⡶⠦⠌⠀⣴⢓⠟⣡⠄⠛⠛⣩⠟⠛⣿⣿⣧⣄⡀⠈⠉⠃⠌⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣾⠿⠀⠉⠀⠀⠀⠉⣩⠛⠻⠁⠀⣠⠖⣵⡏⠀⠁⠀⣀⠀⡀⢀⠂⣦⠿⠻⠛⠃⠈⠉⠀⢈⠻⠿⣦
⠀⠀⠀⠀⠀⢠⣿⠂⠠⠀⠀⠀⢴⠶⠎⠉⠀⠠⠀⠀⠁⣼⠿⠃⠠⣤⢞⠁⢈⣿⣿⡅⠛⠐⠀⠰⠈⣥⠆⢀⡀⢠⠘⠽⡆
⠀⠀⠀⠀⠀⣾⣿⡄⠆⠠⠴⠂⠀⠀⠀⠀⠠⠤⠶⢶⡾⠁⠀⡠⠞⠳⢆⡰⣫⡞⡁⠴⠃⠀⠀⠀⠀⠀⠀⠈⠛⠃⢼⣤⣿
⠀⠀⠀⠀⠀⣿⣆⠙⣆⣀⠀⠀⠀⠀⠀⠘⣅⠀⡠⢋⠃⣤⠛⠠⢄⣀⠈⢰⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⣶⣿⠿⠻⢆
⠀⠀⠀⠀⠀⢿⣎⠛⣿⠥⠐⠒⠀⠈⢛⡄⣻⠞⢠⡄⠈⠀⠀⢀⡾⠟⠛⠀⡃⠘⢧⣀⠁⣠⡄⢸⣇⡴⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠘⣿⣇⠇⠀⠀⡀⡀⠀⠈⢿⡅⢀⣴⡄⠀⢀⣰⡏⡖⢠⡀⠀⠀⠂⠘⠋⣢⣴⠟⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⢹⣿⣦⡤⠚⠁⠀⣀⣤⠊⠀⠙⠄⠀⣴⡏⠀⠙⠀⠄⠠⠖⢀⠀⠘⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣷⡔⠋⠽⣣⠀⡔⠀⣐⢨⡾⠃⠀⠀⠄⣠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠄⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡏⠋⢀⣖⠂⠙⠟⣶⡖⢁⠞⠀⢸⡇⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣤⢻⣯⠀⢈⡤⣿⢛⡉⢀⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣠⠅⠈⠀⠋⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠃⣼⣿⠖⠁⡝⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠶⣤⣤⡼⠀⢀⣄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡋⢀⣧⣽⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠈⠁⢀⠶⣾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣈⣿⠟⠳⢮⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⢀⡤⠞⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡜⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⢠⡦⣄⣀⡀⠼⠃⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⡇⢸⠰⠀⠀⡎⠍⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⣀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠠⠛⠁⠄
⠀⠀⠈⠁⠀⠈⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣼⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡘⡛⡀⣀
⠀⠀⠀⠀⣀⣤⠶⠚⣩⠞⢡⠇⠹⡌⠳⣍⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣫⣾⣹⣿⣹⣮⡻⣶⣤⣀
⠀⠀⢰⣛⣉⣀⣠⣞⣁⣀⣟⣀⣀⣳⣀⣈⣳⣄⣀⣉⣛⡆⠀⠀⠀⠴⠾⢿⠟⠩⡾⠿⠣⠿⠿⠧⠻⠿⡮⠝⢿⠿⠶⠄
⠀⠀⠀⠉⢠⡏⠈⢹⡏⢹⠉⢹⡏⢩⡏⢹⡍⠀⢹⡀⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⢸⣿⢸⣿⠀⠀⡆⠀⠈⡄
⠀⠀⠀⠀⣼⠀⠀⢸⠃⢸⠀⢸⡇⢸⡇⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⢸⣿⢸⣿⠀⠀⠇⠀⠀⢰
⠀⠀⢀⣠⣇⠀⢀⣸⡀⢸⠀⣸⣇⢸⡇⢀⣇⡀⠀⣸⣄⡀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠀⢸⣿⢸⣿⠀⠀⢠⠀⠀⠈⣄
⠀⠀⠸⢤⡽⠁⢿⣭⡿⢸⠸⣯⣽⢟⡇⢿⣭⡿⠘⢯⡴⠇⠀⠀⠀⠙⠛⠀⠀⠻⠃⠀⢸⣧⣤⣿⠀⠀⠻⠃⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀
⠀⠀⢀⣤⣴⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣦⣤⡀⠀⠀⠀⠤⠤⠯⠭⠭⠭⠭⠭⠭⠭⠬⠭⠭⠭⠭⠭⠧⠤⣄
⠀⠀⠘⠓⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣊⣉⣉⣉⡉⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠐⠂⠒⠢⠉⠉⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠴⢢⡤⠲⢤⠖⠑⠢⠒⠊⠑⢤⡤⠤⣕⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡵⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⣶⣀⠤⠌⠛⠓⢊⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⣉⠭⠍⡉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡘⠁⠀⠀⠘⡆⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡇⠀⠀⠀⠀⢱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⠒⠒⠒⠒⢻⠀⠸⠶⠶⠖⠒⠲⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠨⡆⠀⠀⠀⠈⠑⠲⠧⠤⣤⣤⣞⣹⣟⣉⣉⣉⡭⠿⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢙⣲⣤⣤⣄⣀⣀⣀⣀⣀⠀⣠⢿⣟⢉⣉⡤⠴⠖⣿⡽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢞⣉⣉⡤⠴⠒⢋⣙⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠛⡟⠓⠒⠒⠤⣤⣄⠀⠀⠀⠀⠀⢏⣠⠤⠖⠛⣩⠟⢻⡤⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣯⣠⡤⠶⠚⠉⣩⡃⠀⠀⠀⠀⠩⠀⠀⣠⠞⢁⣴⠚⢧⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠀⣿⣠⡤⠶⠚⢋⣿⠀⠀⠀⠀⠀⡇⣠⠞⠁⣠⠞⠁⠀⠈⣇⠸⡄
⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠙⠓⠲⢤⣀⠀⣠⠞⢀⣿⠀⣿⠀⠀⠀⣠⠋⡆⠀⠀⠀⠀⠀⡟⠁⣠⠞⠁⠀⠀⠀⣠⡼⡄⢿⠛⠉⠙⠛⠒⠶⣤⡀
⠀⠀⢀⡴⠋⠀⢀⣠⠤⠶⢶⠶⠦⢤⣀⠀⣨⠟⢁⡴⠋⢸⠀⣿⠀⠀⡴⠁⢰⠁⠀⠀⠀⠀⢀⣧⠞⠁⠀⠀⢀⡴⠋⠁⠀⣳⠘⣧⢶⠶⠤⣄⣀⠀⠉⠳⣄
⠀⣰⠋⠀⢠⠖⠉⠘⣆⠀⢸⠀⢀⡞⣩⠟⢁⡴⠋⢧⡀⢸⠀⣿⠀⣾⣤⣀⣾⢦⡐⠒⠒⠊⠉⠈⡇⠀⠀⢠⠏⠀⢀⡴⠻⣍⣧⢹⣼⠀⠀⡼⠉⠳⣄⠀⠈⢧⡀
⢰⠃⠀⣰⢯⣀⠀⠀⢹⡄⢸⢀⣾⠞⢁⡴⠋⣳⠀⠀⢧⢸⠀⣿⣀⣹⣿⠤⣿⢻⣾⣷⣶⣤⣤⣴⠇⠀⢠⠏⠀⢠⣏⠀⠀⠘⢿⡄⢿⢀⡞⠁⠀⠀⢈⣷⠀⠀⢷
⡟⠀⢀⡇⠀⠉⠓⠦⣄⣳⡼⣟⢁⣴⣿⣶⡯⠽⠷⠒⠛⠋⠉⠉⠁⢸⡃⢠⢇⡞⣿⣡⠎⠀⠀⠀⠀⠀⣾⠀⠀⡏⠈⠙⠓⠦⣄⣻⡼⣿⣠⠴⠖⠋⠉⠈⣇⠀⠸
⡇⠀⢸⡟⠛⠛⠛⠒⣛⣧⣀⣼⣏⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⣋⡴⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠸⡧⠴⠶⠒⢒⣺⢿⣀⣸⢷⣖⠒⠒⠒⠒⣿
⢻⠀⠀⢧⠀⢀⡴⠞⢁⡞⣿⢳⡉⠳⢤⣉⠉⢹⠏⠉⢻⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢧⢀⡤⠖⠋⣠⠏⣿⢹⡀⠈⠙⠲⢤⣠⠇⠀⢸
⠘⣧⠀⠈⢿⡉⠀⠀⡾⠁⢸⠀⠻⡄⠀⠈⣳⠏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢯⡀⠀⣰⠃⠀⡇⠀⢷⠀⠀⠀⣠⠟⠀⢠⡟
⠀⠈⢧⡀⠀⠙⠦⣼⡁⠀⢸⡆⢀⣹⡤⠞⠁⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠙⢶⣇⡀⢀⡇⠀⠈⣧⣠⠞⠁⠀⣠⠏
⠀⠀⠀⠙⠲⣄⡀⠀⠉⠉⠉⠉⠉⠁⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠉⠙⠛⠛⠉⠉⠀⣀⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⢹⣿⠋⠈⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⠀⠀⠀⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠁⠐⠀⠈⡹⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⣂⠀⠀⠊⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣂⣴⣶⣷⣷⣶⣄⡀⠀⠀⠀⢠⡾⠀⠀⠀⣼⣷⡂⠀⠀⠀⢸⣮⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⡿⠿⡿⠿⡿⣿⣧⣤⣾⣇⡀⠀⠉⢻⣿⠁⠀⠀⢀⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣧⣴⢶⡞⢆⣙⣯⡉⣿⣿⣷⣶⣵⣇⢼⣿⠀⠀⢠⣾⡽⠁⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⡄⠀⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣼⣻⡿⣻⣤⡿⠶⢟⢷⣿⣻⣏⣭⣧⣷⡾⣿⣿⣿⣿⣿⣿⣦⣶⣿⣷⣤⣤⣴⣷⣴⣶⣾⣷⣶⣶⣾⣿⣷⣶⣶⣶⣶⣦⣾⠁
⠀⠀⠀⣶⣿⣿⡇⢾⣾⠶⣿⣿⣟⣻⣿⣯⣭⣧⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠋⠛⣟⣟⣿⡿⢻⣿⣟⣿⣿⣿⣿⣿⣿⡄⢀
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣥⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⡿⠿⠏⣰⣤⡀⠀⠀⠀⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣽⣄⣠⣶⣿⣿⣿⣿⣦⠛⠑⡊⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⠿⣿⡿⢿⠛⠀⣳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠋⠉⠙⠀⠄⢀⣀⠈⠉⢺⡏⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣐⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡧⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠿⠿⠿⠿⠿⠹⠿⠿⠿⠶⣶⡿⣷⠆⢀⡆⡄⡀⠀⢄⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣋⠔⠒⠈⠉⠁⠈⠉⠐⢄⠀⠀⠉⠁⠁⠀⡠⠀⠀⠀⠀⢸⢀⣠⠖⠓⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⢀⠔⠁⠀⠠⣄⢀⣶⡿⠁⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢠⣦⣌⣈⡟⠉⠉⠉⠉⠉⠉⠉⠉⢉⠇⣑⠀⠋⠣⣀⢀⣐⡦⢾⣿⣿⠁⠀⣰⡾⠛⠛⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣶⠒⢶⣶⣶⣶⣶⣶⣶⣶⣿⣴⣤⣀⣀⣀⢀⣠⡄⠴⠛⠁⠉⠀⣾⣿⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠙⠻⢿⣿⡿⠿⠿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⡀⠀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣻⣿⡿⢿⣿⣶⣶⣶⣄⣠⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠿⠟⠛⠋⠀⢤⣤⣬⢯⠍⠍⠇⣀⣤⠏⢉⠉⠉⠹⢴⠊⢛⡛⣻⣷⣤⣤⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠈⣀⣐⣙⣛⡛⢛⡛⣓⣤⡶⠟⢋⡇⠀⠈⠁⠀⠀⢸⣶⣶⣶⠈⠙⡉⠉⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡘⡿⡿⢿⠿⡇⠀⠀⣘⣡⠴⠚⠉⠁⠀⠘⠃⠀⠀⠈⠭⠭⠙⠿⠿⠿⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠉⠣⣶⠶⠶⠿⠿⠿⠿⢀⣀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠁⠙⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⡀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⠀⠘⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣇⣀⣀⠈⠀⠀⠀⢀⢸⠤⠀⠀⠀⣀⠀⢠⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠶⠶⠾⠾⣿⣿⣿⣷⣶⣿⣿⣯⣾⣟⣿⣿⣿⣷⣦⣿⣿⣿⡿⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠉⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⠶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣀⣤⣀⠀⠀⠀⢰⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢈⣸⠟⣱⠿⢿⣷⢤⣤⠎⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⠈⠁⠀⣰⣯⠉⢿⣶⣡⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣴⣆⠀⠐⠚⠉⠙⣷⣤⠈⠙⣷⣞⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠚⠡⠾⢿⡲⢦⡀⠀⠚⠛⠛⠛⢳⡆⠙⠻⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣋⠀⠀⢠⣷⢞⡛⢤⣉⠓⣦⡀⠀⠐⠋⠙⢦⡀⠈⠿⣄⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡉⠟⠉⠉⠹⣿⣿⡟⠛⠻⠛⠓⠛⠶⠤⣤⣀⣈⣹⢦⣄⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣷⣶⣤⣀⠋⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⣿⣿⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⢿⣿⣶⣤⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠛⢿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣾⣿⡿⢿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠈⠩⡄
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣭⣿⣿⣿⣿⣿⣶⣍⣻⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠚⡄
⠀⠀⠀⠀⠀⠀⣬⣧⣄⣀⣀⢀⣀⡀⠀⠀⡀⠿⠿⠟⠋⡙⠻⣿⣿⣿⣿⣿⣭⡛⢿⣿⣿⣿⣿⣿⣿⣶⣤⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠉⠉⠉⠈⠉⠙⠉⠛⠛⠛⠛⠁

⣿⡿⠟⠛⠛⢻⣿⣿⣿⣶⠀⠀⠀⠈⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣹⡿⠟⠋⠀⠈⠉⢹⣿⣿⣿⣷⣶⣿⣿⣿⡟⠀⠙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣟⠋⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠰⣶⠟⠛⠋⠛⠁⢼⣿⣿⣿⡇⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠿⡟⠿⠋⠁⠀⠈⠀⢰⣦⠀⠀⠀⠀⠀⣿⣶⣶⣦⠀⠠⣾⣿⣿⠟⠁⠈⠁⠀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⢀⣴⣆⠀⠉⠛⠉⠀⣴⣶⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿
⠷⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠉⠙⠉⣽⡅⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⠿⠓⠰⠶⠶⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠿⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⡷⠄
⠁
⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡀
⠁⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣯⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠆
⣿⣿⣿⣷⡌⠁⠀⠀⠀⠀⠀⠐⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⡀⠐⠂⠀⣠⣤⣾⣿⡃⠀⢀⣤⣆⠀⠀⣴⣦⣀⣀⣀
⠿⠿⠟⠀⠀⠀⠀⠀⡀⠀⠠⠶⣾⣿⣯⣀⣀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣶⣦⣤⣼⣽⣿⣿⣩⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠷⣶⣿⣿⣿⡿⠿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⠷⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠋⠋⠹⠙⠛⠿⠿⠿⠿⠟⠋⠛⠿⠿⠷⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠿⡿
⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣀⣤⠤⠤⠀⠠⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷
⣩⣯⣨⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠉⢉⡉⢻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣘⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⠛⠛⠉⠉⣻⣿⣯⣍⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣴⠾⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠷⠦⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠯⡄⠉⢹⣿⡿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣋⣀⣤⣆⣠⣤⣤⣤⣴⣿⠀⠀⠘⠁⣶⣿⣦⣤⣼⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⣤⣴⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣀⣠⣀⠀⠀⣦⣴⣿⣶⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣄⠀⠀⣠⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⣡⡾⠋⣹⠛⠛⣯⠙⢷⣌⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⣠⠞⠋⠀⢰⡏⠀⠀⢹⡄⠀⠙⠳⣄⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠁⠀⠀⢀⣤⠞⠁⠀⠀⢀⡿⠀⠀⠀⠀⢿⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⢠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⡄
⠀⠀⠀⠀⠀⢾⣄⡀⠀⣀⣤⣄⡀⢀⣠⣴⣏⠁⢀⣠⣤⣀⠀⢀⣠⣿⣀⠀⣀⣠⣤⣀⠀⣀⣿⣄⡀⠀⣀⣤⣄⡀⢈⣹⣦⣄⡀⢀⣠⣤⣀⠀⢀⣠⡗
⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠈⣿⠋⠁⠀⠉⠙⠋⢹⡇⠉⠛⠉⣿⠀⠉⠛⠉⢸⡇⠉⠛⠉⠀⣿⠉⠛⠉⢸⡏⠙⠋⠁⠀⠈⠙⣿⠁⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⡶⠶⢴⣯⣀⣀⠀⠀⠀⢀⣀⣀⣾⣀⣀⠀⠀⠀⣿⠀⠀⣀⣀⣸⣇⣀⣀⠀⠀⣿⠀⠀⠀⢀⣀⣷⣀⣀⡀⠀⠀⠀⣀⣀⣽⡦⠶⢶⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡿⠀⠀⠀⣸⠁⠉⠉⠉⢹⡇⠀⠀⣿⠀⠀⡏⠉⠉⠉⠉⢹⠀⠀⣿⠀⠀⢸⡏⠉⠉⠉⠈⣧⠀⠀⠀⢿⠁⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠈⠳⠦⣤⣤⡾⠃⠀⠀⠀⠹⣦⣀⣀⣀⣼⠃⠀⠀⣿⠀⠀⢷⣄⣀⣀⣠⡾⠀⠀⣿⠀⠀⠘⣧⣀⣀⣀⣴⠏⠀⠀⠀⠘⢷⣤⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢰⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⡆
⠀⠀⠀⠀⠀⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣀⠀⠘⠃⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣇⠂⠀⠀⢀⣤⡾⠷⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟⣷⠈⢀⣶⣶⡄⠀⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣌⣿⣿⣿⠆⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⢷⠶⡴⠶⠶⠶⠾⠿⠃⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢀⠀⣌⠖⠒⢶⣒⣀⣀⣁⣤⣤⣤⡔⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⠋⠈⢻⣿⣿⣿⠏⠉⠉⠉⠁⢀⣀⣿⠖⠒⠂⠀⠐⠀⠀⠈⠿⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣾⠋⠀⠁⣀⣤⠶⠞⠛⠫⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣸⠇⠀⢀⡾⠋⠠⠀⠀⢀⣀⣠⣄⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟⠀⠀⢸⡇⠀⢀⠀⠘⣏⣹⠿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠁⠀⠀⠸⣇⠀⠈⠄⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢻⡄⣀⣡⠀⣈⣿⣄⠀⠀⠀⠀⡠⠄⠀⠉⠉⠁⠀⠄⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡉⠉⠉⠀⠐⠄⡀⠸⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⢀⡀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⣸⣿⠃⢀⣾⡿⢉⣶⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⢻⣿⡀⠘⣿⣷⣾⡿⠃⢨⣶⡶⠾⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠛⠛⣿⣿⡀⠘⢿⣿⣿⡿⠋⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠉⠉⢀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠁⢀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⣄
⠀⢸⣷⣤⣶⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡟⣿⢀⣤⡀⠀⠀⠀⢀⣠⣴⣿⣯⣶⣿⣷⣿
⠀⠀⢸⣿⣿⡀⠀⢸⡗⢄⣤⣿⣷⠀⣤⡶⠀⣼⣦⣤⡄⠀⡰⣟⡙⠻⢿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠄
⠀⠀⠸⠿⠉⠇⠀⠈⠳⠈⠉⠉⠁⣾⣿⣿⣶⣾⣏⠁⠀⠈⡀⠀⠀⠐⡀⠉⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⠈⠀⡐⠀⠉⠻⣿⣿⣷⣶⣐⢤⢤⢁⠓⠔⠀⠀⠀⠈⢻⣿⣿⣿⠁⠈⠉
⠀⠀⠀⠀⢀⠠⠦⣄⠀⠀⡀⢀⡜⢁⠀⠀⠀⠈⢿⣿⣿⡿⡃⢲⡈⣿⢀⡀⠀⠀⠀⠀⣿⣿⣿⠄
⠀⠀⠀⡀⠡⣦⠀⠈⢧⡨⠞⢡⠁⡸⠀⠄⠀⠀⠀⠻⣿⣿⠉⢹⠉⢀⣹⣿⡷⢥⣍⠉⠉⠙⠓⢤⡀
⠀⠀⠀⠦⠤⢠⡔⢂⣈⡷⠦⡖⠺⡄⠀⠀⠁⠀⠀⠀⠙⢿⣿⣿⣦⠀⢹⣿⣅⠀⠈⠳⡄⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠻⢶⡠⠉⠑⢄⡀⠀⠁⢳⠤⢄⣄⣀⣀⣀⡠⠴⠋⠉⢿⣇⠀⢿⣿⣷⠀⢀⡇⠈⣢⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⣀⣹⣯⠀⣼⠃⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⠃⠀⠀⠀⡠⠃⠀⠈⣷⣌⣿⣿⣿⣿⡁⠀⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⠉⣿⡏⣳⣿⡿⠀⠀⡜⠐⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢸⠀⣿⠇⠛⠛⠃⢀⢾⣁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠌⠀⠀⠀⠀⠀⠀⠃⢀⠤⠀⠀⠀⡐⢰⡿⠀⣀⣤⡞⠁⠀⠘⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠱⡀⠐⠉⠀⡀⠠⡀⠀⡇⠀⢠⠀⣼⣴⣿⣗⣋⣥⣘⣄⠀⠀⠀⣽⣴⣾⡔⠒⠢⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠙⠦⣄⡴⠋⠉⠉⠛⡇⠐⠁⢀⣿⠿⠿⠿⣿⣿⣿⣿⡧⠀⠀⢻⣾⣿⠶⣄⠀⠇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣴⣿⣿⣷⡀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⣘⣀⣐⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣇⣴⡞⠸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⡀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡿⠋

⠀⠀⠀⣀⡤⣤⡴⢺⣟⢶⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⡋⠑⠢⡀
⠀⠚⠛⠁⠚⠛⠀⠚⡟⠀⠙⠛⠊⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠣⢄⡀⡇⠀⣠⠃⠀⠀⢀⣀⡠⠤⠒⠊⠉⠢
⠀⠀⠀⠀⠀⣠⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠉⠁⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⣈⡿⠛⢉⣩⣭⢭⣁⡀⠀⠀⠀⠀⠀⣸
⢴⣤⣀⣀⡀⢛⣿⣿⣷⣿⡷⠶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⡠⠔⠒⠒⠁⠀⠀⠒⠒⠬⡉⠘⠓⠋⠉⠀⡇⣞⠁⠀⠀⠀⠀⢉⠄⠀⠀⢀⠔⠁
⠰⡟⠛⠿⠉⠘⠿⠉⡏⠻⠇⠀⠸⠿⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⣶⣶⣲⣒⣒⣒⣒⣁⣠⣴⣤⣶⣆⣅⣈⣓⣦⢤⠤⠶⠭⠤⠔⠊⠁
⠐⠒⠓⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠃⠈⠀⠉⠀⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀
⠀⠀⠀⠀⢀⠰⠇⠀⠀⠙⠀⠀⠸⠦⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⠞⣿⢹⡟⣟⢶⡦⣄⡀
⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠸⣿⡿⠃⠓⠢⢤⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⣴⠏⣴⠏⢼⠇⢸⡇⢹⡇⠹⣦⠹⣦
⠀⠀⠀⠉⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡻⠿⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⠂⠀⠀⠀⠀⢺⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡎⠀⠱⡀⠀⠀⠀⠀⠀⣻⣿⣋⣀⣻⣿⣾⣷⣿⣟⣀⣻⣿⣋
⠀⠀⠀⢀⠀⠀⠀⢠⠋⠀⠈⢦⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⡜⠈⡄⠀⠱⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠻⠂⠀⡰⠃⠀⠀⠀⠈⢢⡀⠄⠻⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡐⠀⠀⠘⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠸⡗⠀⠀⣤⠀⠐⠸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣂⣀⣴⣀⣀⣀⣀⣘⣄⣀⣣⡀⠀⠀⠀⠀⢀⡀⠈⠉⠁⠹⣿⡯⠈⠉⠁⢀⡀
⠀⡀⢸⣯⣤⢀⣴⣶⣦⣾⣶⣶⣦⣄⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⡇⠀⣡⡈⢰⣿⣧⠁⣬⠁⢸⡧⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣸⣿⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠠⢦⠀⠀⠀⠀⠀⣸⣿⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣷⣤⠀⠀⢀⡇⠀⣦⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢉⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣤⡀⢸⠀⠀⢸⡄⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠚⠀⠈⠁⠀⠃⠀⣤
⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣤⣀⣏⡇⠀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⠿⣿⣿⣿⠟⠉⢫⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒
⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡎⠉⠈⡇⠀⠘⡄⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⠁⠀⠀⠛⠐⠀⠃⠀⠀⠀⠠⠄⠀⠠⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠸⠉⢇⠀⠀⣀⠤⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠏⠹⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⢸⠁⠀⠈⣧⡎⠀⠀⢳⣠⠔⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⢀⣴⠁⠀⠀⠈⢤⠀⠀⠁⠀⢀
⢠⠒⣉⣉⣉⣉⣉⡑⠢⢄⡀⢸⠁⠀⠸⡄⠈⠓⢤⡴⣁⠣⢄⡴⠋⡇⠀⠀⡸⢀⡠⠔⠒⢢⠀⠀⠀⠀⠀⣠⠀⠀⠺⠃⠀⠀⠀⠀⠘⡇⠀⠀⣄
⢸⡛⠦⠤⢤⢤⣤⠴⠃⠀⢉⠦⢄⡀⠀⠈⢒⣒⡩⠤⠤⢄⣀⣈⣉⣉⡷⢭⣛⣉⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⡀⢷⠆⢀⠀⢀⡀⠀⡀⠰⡞
⣀⣉⣓⣒⡺⣿⢿⡿⡂⣚⣁⣀⣀⣈⢉⣉⣉⣀⡀⡀⣀⢀⠀⡀⣀⣀⢀⡀⣀⢀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣼⣤⣤⣤⣤⣁⣀⢀⣀⢀⡀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠛⣻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣖⣒⣲⣒⡶⠶⣶⣒⠓⠲⠶⠒⠲⢶⠒⢒⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⠀⠘⠀⢸⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣀⣉⣿⢟⡏⠉⠻⣕⠀⢀⣠⡄⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡧⢼⣤⣊⠷⠿⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠃⠉⢽⣿⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢀⣀⣀⣀⣠⣽⣿⣿⣿⣿⠀⠀⠀⠠⠤⠤⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇
⠀⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢷⣾⣿⣿⣿⣿⣾⣿⡶
⠉⠙⠛⠛⠛⠛⠻⢿⣿⣿⣿⡿⠿⠟⠛⠻⠛⠛⠋⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠙⠻⠿⠟

⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⡀⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⣾⣿⣷⣆
⠀⠀⢀⣤⣤⡀⠀⠀⢀⣾⣦⡀⠀⠀⢠⣦⠉⠁⠀⠀⠉⠄⣦⠀⠀⣤⡄⣀⡀⢤⡄⠀⠹⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢹⢹⣿⡄⠀⣤⠀⠀⠀⠴⠀⠀⠀⠠⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠿⠾⠟⠇⠧⠀⢠⡄⠀⣠⠃⢣⠀⠀⣤⠀⠀⠀⠀⢀⠔⠀⠀⠐⢄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣠⣸⣴⠀⠀⠀⠀⠀⠀⠁⠈⢠⡤⠀⠀⠁⠀⣀⡁
⠀⠀⠀⠀⠀⠀⠘⡉⠉⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠀⠠⠄⠀⣀⠀⢦⡀⠈⡏⠠⣠⠆⠀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⠀⣠⣴⠛⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠀⠀⠙⢺⣷⠚⠁⠀⣠⡀
⠀⠀⠀⠒⠒⠀⠀⠀⠀⠚⠛⢻⣿⣶⣿⠛⠛⠓⠀⡄⠀⠀⠀⠉⠀⠀⣤⠀⠀⠈⠉⠀⠶⠿⠿⠿⠷⠆
⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠶⢿⣿⢛⢿⢠⠾⠅⠀⠀⣀⣀⢀⣀⣀⢀⣀⣠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢉⣉⣬⡉⠀⠀⠆⠆⠞⠟⠿⠻⠲⠰⠰⠀⠀⡷⢴⠀⡦⢾⠐⠺⣭⠍⠀⠀⠀⠀⠐⠚⠒
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⢀⡀⡀⣀⣀
⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠇⠀⠸⠹⠧⠯⠼⠤⠧⠽⠼⠯⠧
⠀⠀⠀⠈⠀⡀⠈⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⢄⣀⠀⠀⢀⣠
⠀⠀⠚⠋⠁⠀⠁⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠈⠀⠀⠀⠘⠛⠀⠉⠘⠛⠊⠉

⠀⠀⠀⠶⠏⠁⠙⠁⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⠆
⣀⣤⠿⠶⣷⣤⣄⡈⠂⠉⠀⠀⠀⠀⡀⠀⠀⣤⠀⠰⠆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡄⠤⣤
⢹⣿⠀⢲⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⣠⠄⠠⠶⠦⠄⠈⠹⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣰⠄
⢹⡏⠀⠀⠁⠀⠐⠀⢀⠈⠙⢷⡚⠛⠉⠙⠳⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⠟⠒⣿⠋⠉⠁
⢸⡟⠁⢢⡀⠒⢠⠀⠀⠘⠷⠈⢧⠀⠀⠀⠀⠈⠓⠀⠉⠙⠓⠤⡤⡤⣤⠀⠢⢤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⣴⡏
⠈⣧⠀⠀⠙⠾⠁⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠙⠀⢶⡇⠀⠘⠃⠀⠀⠀⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠙⠷
⠀⡇⠀⠀⠀⠀⠉⡖⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡏⠚⠦⣐⠃⠐
⠀⡇⠀⠀⠐⢠⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢀⡀⠀⣤⠾⣇⠀⠐⠈⠓⠀⠀⠀⠙⠤
⠀⡀⠀⠀⠀⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⠟⠀⠀⠀⠀⠀⠄⢀⣄⠀⣀
⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠛⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⡶
⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠐⠦⠀⠘⣥⡴⠶⠤⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠹⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠁⢀⣶⠟⠁⢠⣀⣀⣤⠀⢘⡤⢄⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡠⢤⡀⠀⠀⣇⢐⡄⠀⠐⠀⠀⠌
⠀⠀⠀⠀⠀⠐⢢⣼⣦⣶⠛⠋⠙⢛⣛⠛⡿⠷⠿⢾⣦⣤⠜⠋⠃⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⢀⡀⠀⡌⠀⠀⠉⠒⠦⣘⣿⠃⠀⢳
⣠⣤⠶⠶⠿⠟⢉⠁⠀⠈⠛⢶⣦⡤⠷⠄⠀⠁⠀⢀⡈⠉⢢⣄⡀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⢊⢿⣇⡀⢀⠒⠀⠀⠀⠘⣿⠀⢀⡼
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⢠⠏⢺⣿⣿⠿⠾⠂⠀⠀⠀⠀⠀⠠⠄⠰⡵⢂⡐⢛⣯⣽⠿⠛⢳⡀⠀⣀⡴⣿⣶⣏⣀
⠙⣿⣿⣿⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣦⡔⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠾⠛⠿⠯⠈⠀⠀⢰⡇⠀⢹⣧⠿⢠⣈⢻⣆⠐⠶⡄
⠀⣸⣿⣿⣷⡄⢁⣤⣀⠀⠀⠀⣀⠀⠀⠀⠻⢷⣦⡤⠴⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢀⠀⡦⢀⢄⣈⡔⢀⣶⣤⣘⣳⣤⡞⠃⠀⠛⡀⢠⡅
⠀⣈⣍⡙⠉⠻⣤⠀⠈⠀⠀⢺⡿⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⡀⠀⢰⡅⢠⢸⣿⣷⣬⣷⣿⣿⣿⣾⣿⣷⣷⣸⣷⣾⣷
⠀⠻⠿⢿⣧⡖⠀⠀⠀⣰⣄⠀⡁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⣿⡋⣽⣇⠸⣇⢠⣾⡟⣏⣿⣿⡿⠟⠛⡍⢋⣉⣙⣽⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⡄⠀⢻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢋⠙⠻⢁⡿⠏⠈⣿⠈⠏⠀⢸⣿⣿⢠⡾⠛⠏⠙⠏⣹⠟⠁⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⠈⠉⠉⢉⣡⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠀⠘⢋⡀⠀⠀⣹⣷⡄⠰⣼⣿⣿⠁⠀⠀⠀⣀⡴⠧⢤⣤⠜⠁
⠀⠀⢀⡀⠀⠀⠠⠤⠤⣀⠀⠀⢈⣻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡁⣼⡿⠉⠁⡄⠀⢸⡿⣿⡄⣿⡇⣿⠷⠞⠋⠙⠋⠀⠁⠀⠀⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠉⠁⠀⠀⠀⠀⠀⣰⢻⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢻⣿⣿⠃
⠀⠀⠀⠀⠀⢀⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⡄⢀⢠⣟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠙⣼⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⣠⣾⣿⣿⣿⣶⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣴⡻⢋⣲⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⣿⣿⣿⣿⣧⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠁⠀⠀⠀⠀⠐⠦⡀⢰⠀⠀⠐⢦⣽⠧⡄⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣷⣶⣿⡿⠿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⢀⡀⣸⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠤⣤⡙⢿⠀⠉⠀⢀⣯⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⣿⣿⣿⠟⠋⠁⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡀
⠀⠀⠀⣀⣤⣤⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠻⠛⣢⣤⣜⢁⠙⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣁⣀⣤⣤⣾⡿⠋⠽⠛⠁⣀⣤⣴⣿⠀⠈⠿⣛⣷
⠀⡜⢻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠐⣀⢫⠀⠟⠈⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠫⠛⠛⠛⠉⠀⠀⠀⠀⣈⣡⡼⣻⣥⣾⣿⣿⣿⣿
⣤⣤⣄⣼⣿⣍⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡤⠻⠶⢿⡦⢈⡦⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⣹⣿⣿
⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠰⢺⡷⣶⠶⠿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠟⣩
⠻⠿⠛⠻⢿⣿⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⣷⣻⣦⣿⠀⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠰⠿⠿⣿⣶⣿⣿⣿⡧⢋⣭
⠠⠀⢠⣾⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⠻⣇⣹⠂⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣉⣁⣈⣋⣠⡉⠿⣟⣿⣿⣶⣿⣿