Chargrill Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠐⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⣴⡶⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡦⠀⠈⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠀⠀⠐⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣄⣠⣬⡬⠇⠐⠂⠀⠀⠀⠀⡼⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡁⠀⠀⠀⠀⠘⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣦⡄⢀⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⢀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣳⣄⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⢽⣍⡿⣻⠆⠀⠀⠀⠀⠀⠘⢷⣦⣴⠆⠀⠀⢀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣾⣿⡿⠋⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣥⣀⣄⣀⣀⣦⣤⡄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠟⠀⢀⣴⣾⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢿⣿⣿⣻⣿⣿⣿⢿⣿⠿⣿⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠀⣀⡠⣄⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⣿⣿⣿⣿⣿⣏⠉⣭⠍⠩⣿⡿⠁
⠀⠀⢀⣴⢺⣫⠐⡝⠆⠀⠀⠀⠀⠀⣼⠃⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⢠⣤⡀⠀⢀⠀⠀⠘⢧⡀⢹⣿⣿⣿⣿⣦⣼⠃⠀⣰⡿⠃
⠀⠀⠀⢃⠣⠳⡠⠘⡄⡄⠀⠀⠀⣼⡏⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠖⡙⠛⠋⣁⠂⠀⠀⠀⠀⢱⠆⠼⢿⣿⣿⣯⣭⡴⠛⣿
⠀⠀⠀⠀⢣⣱⣴⣷⣿⣶⠀⠀⠀⠋⠑⠛⠋⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠙⠿⠿⠿⡁⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣠⣤⣤⣶⣦⣤⣴⣿⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠰⣟⠉⠙⠛⢿⣿⣿⣿⣿⣿⡿⠶⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⡿⠟⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢠⣶⡀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠐⠚⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡖⠀⠈⢿⣿⡄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣠⠛⢿⣿⣶⡄⠀⠀⠀⠀⠀⠰⠦⠀⠤⠀⠠⠀⠆⠀⠀⠠⠀⠄⢸⠆⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠹⣿⡟⠀⠀⠀⠀⠶⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡜⠀⠗
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠈⡇⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠖⣶⡦⠈⠉⠚⣒⣋⣳⣴⣆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣛⣋⣁⣬⣵⡿⠿⠛⠛⠛⠛⢛⢙⣹⡿⠋⢉⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠩⠈⠉⡠⢂⣰⠿⠁⢉⢉⣋⣉⣀⣽⣾⣿⣿⠶⠶⠤⠬⢿⡿⣿⠷⠰⢤⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣏⣤⣤⣥⣭⣵⣿⣧⣴⣾⠿⠛⢛⣿⣿⠿⠁⠀⠀⠤⣄⣀⣴⠟⠉⠁⠀⠀⠈⠛⣿⣶⠤⠄
⠀⠀⠀⠀⠀⠀⢐⣿⡆⠀⠀⢁⣿⠋⠡⣀⠀⠀⣂⡼⠛⡁⠀⠀⠐⠂⠂⢀⣼⣟⡁⣔⣁⣚⣀⣂⣤⣾⣏⣁⡀⠀⣄⣸⡄
⠀⠀⠀⠀⠀⠀⢨⣿⠷⢦⣤⣿⡇⠒⠓⠳⣀⣼⣟⣁⣠⣄⣤⣴⣤⣤⣴⡿⠋⠀⠛⠉⠉⠉⣩⣟⣽⡋⠉⠉⠉⠲⣾⠟⠧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣶⣰⣮⣿⣗⡶⢶⣾⣿⣟⠉⠉⠉⡉⠉⢉⠄⠹⠋⠀⠀⠀⠀⠀⣠⣾⣿⠟⢁⠀⠀⣄⣴⡾⠧⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⣍⠰⣿⣿⣔⣖⠢⡄⢀⣴⡟⠚⠐⠂⠀⢀⢀⣠⣾⣿⣿⣤⣤⣤⣦⣶⣿⡿⠿⠟⢻⡿⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⢾⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⣾⣿⠟⠛⠉⠉⠉⢉⣽⠟⠋⡀⢀⠀⣠⡾⢁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⣿⣿⣿⣷⣿⣾⣿⣿⣿⣧⣄⣠⣤⣤⣤⣾⣇⣀⣀⣀⣀⣀⡴⣿⣏⣄⡚⣅⣀⣶⣿⣴⣥⣿⠏
⠀⠀⠠⡀⣀⣴⣶⣹⣿⣶⣄⠀⠈⠙⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⢟⡿⢛⡛⠉⠉⠁⣩⣿⣏⣭⣿⡿⣿
⢄⡀⠚⠛⠻⠉⢽⡿⣿⢻⣿⣿⣲⣤⠈⠻⠿⣿⣿⣿⣿⣤⣻⣿⡟⣿⣀⣀⠀⢒⣤⣾⠛⠀⠨⡍⠀⣠⣾⣿⣿⣿⣿⡿⢣⡿
⠀⠈⠛⠲⠦⢤⣈⠰⣥⣿⣿⣿⣿⠃⠄⠀⠄⣈⢿⣿⣿⣷⣿⣿⡌⢿⣿⣽⣦⣘⡋⠉⠁⢀⣠⣴⣾⡿⣿⠋⢻⣿⡿⠁⣻
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣿⢿⠏⢀⠀⠐⠂⠀⢙⠻⡝⢻⣿⣿⣿⣿⡟⡻⡿⢸⣿⣿⣿⣭⣿⣽⡏⠀⢠⣦⣾⣿⣿⠞⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠋⠙⢤⣛⠳⠖⠢⠤⡥⣥⠤⠺⠃⠀⠉⠙⢿⣓⣻⣟⣿⣿⣿⣯⣿⣿⣿⣿⣷⡾⠋⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠿⠿⠿⠟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠾⠋⣄⡌⢄⠄⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢹⠏⠘⠀⢴⠄⠀⠀⠁⠐⠚⠲⠶⠖⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠟⣿⣿⢹⢿⢿⢿⢿⣿⠿⣿⡿⣿⢻⣿⢿⡿⢿⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣦⣿⣼⣼⣶⣼⣿⣦⣷⣼⣿⣷⣼⣼⣮⣿⣥⣼⣴⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⢸⡄
⠀⠀⠀⣀⣤⣤⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⡿⢆⠀⠀⠀⠀⠀⠀⠄
⠀⢀⠚⠁⠀⠀⠀⠀⠀⠐⠀⣠⡀⠀⢀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣷⠘⢇⠀⠀⠀⠀⡀⢀
⠀⠸⣦⠐⠀⠀⠀⠀⠀⢀⣧⡽⣇⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢀⣷⣜⢧⠈⠑⣎⠀⣸⣏⠈
⠀⠀⠘⢠⣔⠂⠀⠀⠐⠀⢹⣧⠸⡲⣤⣄⠀⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣿⣻⣙⣦⠀⡼⣡⣇⠸⢿⡂
⠀⠀⠀⢀⢭⣿⣯⣤⣴⣶⣿⠉⠃⠈⣌⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠸⣿⢂⠄⡽⠟⢰⣧⢄⡀
⠀⠀⠁⠀⠀⢿⣿⡉⢋⢙⠿⣃⠀⠲⣈⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢿⣯⡃⠋⠸⠊⣠⢏⣼⡬⣾⠅
⠀⠀⠀⠀⠀⠀⠙⠂⣘⠀⠛⠁⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡎⣿⠃⣠⠐⠊⣩⣾⠝⢡⡟
⠀⠀⠀⠀⠀⢀⠈⢁⠀⠈⠁⠀⣸⠶⡢⣴⣦⡖⠀⠀⠄⠀⠀⠀⡀⠀⢸⡿⣿⠌⠁⡰⢋⣤⡾⠟⣠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠏⠩⣙⠀⠉⢈⣐⣛⣛⡀⠀⡄⠀⠄⠀⠀⢀⣴⡟⠛⣨⡴⠟⠉⢨⡁⢻⠿⢛⠓⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠼⠟⠂⠀⡾⠟⢩⣿⣿⠀⠈⠀⠁⣀⣾⣿⡗⠀⢸⡻⠁⠀⠀⠀⠹⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⢐⡆⠘⠻⠛⠂⣷⠲⠾⠛⠛⣉⠡⡀⠈⠃⠂⠀⠂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠂⠁⠊⠀⠒⠀⠀⠑⠀⠀⠈⠀⠈⠀⠰⣶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⣇⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢹⣿⡆⣀⣄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⣠⠆⢻⣿⠀⠀⠘⣿⠐⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠲⠞⣸⠇⠁⠀⢸⣿⠀⠀⠀⡟⠀⠀⠀⠈⠉⠓⣂⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠠⠶⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢀⡀⣠⣴⣦⣾⣿⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣏⣽⣿⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣏⣽⣿⣷⠿⠟⠋⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣷⡾⢟⣛⠉⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠙⠛⣿⣿⣿⠟⠛⠉⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⢠⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶
⠀⠀⠐⢻⣶⣶⣶⠗⠂⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⢿⣦⠀⠀⠀⠀⠀⠀⠀⡿⠿⢿
⠀⠀⠀⡸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠃⣶⡞
⠀⠀⠀⠀⠁⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀
⠀⠀⠈⠙⠛⡟⠛⠉⠀⠀⠀⠀⠀⠀⣰⣿⣷⡀⠀⠀⠀⠀⠀⢠⣿⠟⣉⢻⣦⠀⠀⠀⠀⠀⠀⡸⣀⣀⣆⡁
⠀⠀⢸⣄⡄⠀⣀⣰⠀⠀⠀⠀⠀⢊⣿⣿⣿⣏⠂⠀⠀⠀⠀⠘⣧⣾⣋⣸⠟⠀⠀⠀⠀⢠⣤⣡⣟⣻⡿⠁
⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠁⠙⠛⠛⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠉⠁⠉

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⡔⢻⣿⣶⡄⠀⠀⠀⠀⠀⠀⣾⢸⣷⠶⠀⠀⠀⠀⠀⢀⡠⠂⢉⡭⡒⡄⠀⠀⠀⠀⢀⣀⣀⡠⠔⡄
⠀⠀⠀⡗⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣮⡿⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣴⠇⠀⠀⠀⠸⣿⣶⣦⣶⣾⠇
⠀⠀⠀⠑⠾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⣠⣿⣽⢧⣀⠀⠀⠀⠀⠀⢀⣀⡈⢀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡄⠀⠀⠀⠀⠀⠀⣠⠤⢴⠭⡒⡄
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⣔⣇⡀⣼⡿⢿⣷⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢰⠣⡑⢄⠑⣽⡼
⠀⠀⠀⠙⠿⠿⠟⠃⠀⠀⠀⠀⠑⢇⣀⡹⢿⣿⠟⠀⠀⠀⠀⠀⠀⡩⢯⠁⠀⠀⠀⠀⠀⠀⠓⠾⠦⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣦⣴⣧⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡟⠛⠛⠛⠛⠛⠛⢻⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠴⠶⠒⠶⠶⠶⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠒⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⣀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⢀⡴⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠉⠛⠦⢾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⡤⠶⠋⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⢦⣄⡀⠀⠀⠉⠙⠓⠒⠲⠤⠤⠤⠤⠤⠶⠒⠒⠛⠋⠉⠉⠀⠀⢀⣠⠞⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠈⠙⠛⠒⠒⠶⠶⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠒⠋⢁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠙⠓⠲⠶⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣈⣉⣉⣤⣤⠤⠤⠖⠒⠛⣉⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡶⠤⢤⣤⣄⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠒⠚⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠤⠤⠤⣤⣤⣤⣤⠤⠤⠤⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣴⣷⣿⣿⣦⡄⣤
⠀⠀⠀⠐⣜⣮⠯⠤⠤⢹⣏⢿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠇⢹⠇⢠⢶⣄⠀⠀⠀⠀⠀⣷⣾⡟⣋⣉⣉⡉⣛⣿⣟⡄
⠀⠀⠀⠘⠁⠉⠓⠀⠀⠚⠛⠋⠂⠀⠀⠀⠀⠀⠑⢾⣦⠀⠀⠀⣿⣽⠽⠃⠀⠀⢀⢀⣿⡀⠀⡀⠀⢀⡀⢀⡀⢸⣆⢀
⠀⠀⠀⢀⡀⠀⣠⠀⠠⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⣣⡞⠣⠤⠄⠜⣷⣌⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠲⣄⠀⠀⠀⠀⠀⠛⠚⣖⠒⠒⠒⠒⠒⠒⠒⠒⢒⡞⠚⠃
⠀⠀⠀⠘⠉⠈⠉⠚⠓⠉⠁⠉⠃⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠈⢳⣦⠀⠀⠀⠀⠀⠙⢶⡄⡆⠀⠠⠄⡠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠛⠋⠁
⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⡀
⠀⠀⠀⢀⣤⣾⣿⣿⡟⠿⢤⣄⠀⠀⠀⠀⠀⠀⢀⣠⡋⢁⣤⠈⣝⠿⣦⠀⠀⠀⠀⠀⢀⡢⣄⠀⢸⣿⠁⣰⢟⣿⣦
⠀⠀⠀⣿⣿⡿⡿⣿⠣⡅⣼⣿⡇⠀⠀⠀⠀⠀⠎⠈⠛⢌⠈⡵⠛⠓⢡⠀⠀⠀⠀⠀⠀⠉⣽⣶⣾⣿⣷⣶⣌⠹⠋
⠀⠀⠀⠙⠿⣿⣦⣿⣦⣾⡿⠟⠁⠀⠀⠀⠀⠀⡍⠀⢀⡠⠛⢝⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢸⣿⠉⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⢙⣴⠟⠀⠀⠈⠻⣦⡃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠍⡒⣒⢂⠩⠈⠁⠀⠀⠀⠀⠀⣠⣶⠙⠛⠛⠛⠛⠛⠫⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣶⣿⣿⣿⣿⣷⣷⣿
⠀⠀⠀⣀⠀⠀⠀⣀⣀⠀⠀⢸⣽⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⢋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⠀⠀⢰⣿⣿⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣿⣛⣁⣀⣛⣇⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠹⠰⠶⠿⠿⠿⠿⠶⠂⠏⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⣸⣷⡄⠀⣖⣖⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢧⣸⠁⢰⡿⢿⣷⣧⠈⣇⡼
⠀⠀⠀⢠⠠⣤⣤⣤⣤⣤⣤⠀⡄⠀⠀⠀⠀⠀⠠⢶⠁⡄⠀⠀⢡⠈⣶⣆⠀⠀⠀⠀⠀⠈⠓⠿⣇⠈⣿⠿⠚⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⢀⡤⢄⠀⣠⣤⠀⠆⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣞⠀⢀⠇⡷⠶⠀⠀⠙⠲⣆
⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠁⠀⠀⠒⠒⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠓⠉⠀⠉⠉⠁⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⠄⡴⡀⠴⢲⠀⠀⢰⡆
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠳⠉⠹⠚⠹⠀⠀⠪⠗⠇
⠀⠀⠀⠏⠙⢀⡦⢔⠂⢀⡠⢀⡄⠀⠀⢀⠤⠤⠀⢀⡈⠀⠀⢸⠀⠀⠀⢀⡀⢀⠀⣀⠀⣀⡀⡠⣀⢀⡀⡀⡀⢀⠀⡀⢀⠀⡀⠀⡀⣀
⠀⠀⡠⢜⡊⠁⠀⠈⠀⠁⣔⠉⠀⠀⠀⡋⠀⣀⢀⡠⢤⠆⠀⢺⠀⠀⠀⢸⠣⠎⡇⣇⠸⣀⡀⡷⢎⢪⣀⠄⢱⡜⢦⠃⠏⢳⠘⡜⠀⣗⡀
⠀⠀⠀⣸⠆⢀⠀⠀⠀⠴⠉⠀⠀⠀⠀⠈⠉⠡⠁⠀⠁⢀⡤⠆
⠀⠀⡰⠁⠄⠀⠁⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢈⢃⡅⢈⣀⣀
⠀⢠⠁⠸⣀⡀⢸⠀⠀⠘⡀⠀⠀⠀⠀⠀⢀⠎⠉⠁⠃⠀⠖⠉⠉⠳⠆
⠀⠸⢄⡀⣛⣓⡁⠤⠤⢰⠁⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠰⣄⢠⠴⡀
⠤⠄⢀⡆⠀⣀⣀⣀⣠⡸⢄⡀⠀⠀⠀⠀⣑⣖⣲⡒⣒⣒⣉⣈⡠⢥⠀⠀⠀⠀⢀⣀
⠀⠀⠛⠛⠒⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⢸⠲⢴⡂⠀⣒⢶⠂⠄⠀⠀⢰⣲⢖⠆⡗⠀⣗⡢⣀⡐⡆⠸⢰⡒⢔⡊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⣂⣐⣋⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣛⡂
⠀⠀⠀⠀⠀⠀⣤⣄⡈⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣿⢁⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣵⣶⣶⣶⣶⣶⣶⣶⣶⣮⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⠾⠧⠉⠏⠁⠈⠉⠉⠻⠧⠍⠏⠁⠈⠉⠉⠻⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠿⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠉⠉⠛⠛⠛⠛⠛⠉⠉⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⢓⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠾⠿⡿⠛⠻⣿⠿⠶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠛⠛⠛⠛⠒⠒⠒⠶⣦⠘⢻⡏⠁⢀⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠉⣿⠓⢦⣤⡀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣄
⠀⠀⠀⠀⢠⡆⢠⣿⣉⣉⣉⣉⣉⣉⣛⣛⠛⢛⣿⣧⢈⣁⣀⣀⣁⣀⣀⣁⣀⣀⣁⣀⣀⣉⣀⣀⡉⣠⣤⢤⣤⣶⣶⣶⣶⣶⡶⢶⣤⠀⢻⣿⣦
⠀⠀⠀⣠⣿⡇⠘⣿⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣿⡟⢘⡛⠛⠛⡛⠋⠙⡛⠛⠛⡛⠛⠛⠛⠛⠛⠁⠻⠿⠶⠿⠿⠿⠿⠿⠿⠷⠾⠿⠀⠘⣿⣿⣷⡀
⠀⠀⢰⣿⣿⡇⠀⣿⣥⣤⣤⣤⣤⣤⠤⠤⠤⠴⠟⠁⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿⠀⠀⣶⠀⠀⢰⠀⠲⣦⡀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⣴⣶⠀⠀⢰⠀⠀⢰⡆⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⢸⠀⠀⢹⣷⡀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⣾⣿⣿⠁⠀⢀⣀⣀⣰⡟⢻⠀⠀⢸⠄⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿⠀⠀⢿⠀⠀⣽⠀⠀⢸⠛⣷⡀⠀⠀⠀⠀⢹⣿⣿⡄
⢰⣿⣿⡇⠀⢰⠋⠀⢀⡏⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡈⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠟⠀⠀⠉⣀⣤⣤⣤⣤⣀⠀⠀⢸⠀⢸⣅⠀⠈⢳⠀⠈⣿⣿⣷
⣸⣿⣿⠁⢀⣿⣷⠀⣸⡇⠀⠀⣿⣿⣿⠿⠿⠿⣿⣿⣿⡆⠀⣿⣿⣿⡿⠿⠿⢿⣿⣿⣧⠀⠀⣴⣿⣿⣿⠿⠿⣿⣿⣿⣆⠈⠀⠈⣿⠀⢠⣿⣧⠀⢹⣿⣿
⣿⣿⣿⠀⢀⣿⣿⠀⣿⠇⠀⠀⣿⣿⣿⣄⣀⣠⣼⣿⣿⠇⠀⣿⣿⣿⣇⣀⣠⣼⣿⣿⠟⠀⣼⣿⣿⡟⠁⣤⠀⠈⣿⣿⣿⡇⠀⠀⣿⡆⢠⣿⣿⠀⢸⣿⣿
⣿⣿⣿⠀⢸⣿⣿⠀⣿⠀⠀⠀⣿⣿⣿⠟⠿⠿⢿⣿⣷⣄⠀⣿⣿⣿⡏⠚⠐⢪⣝⣷⣤⠀⢿⣿⣿⡇⠀⣿⠀⠀⣼⣿⣿⡇⠀⠀⣿⡇⢸⣿⣿⠀⠸⣿⣿
⣿⣿⣿⠀⢸⣿⣿⠀⣿⡇⠀⠀⣿⣿⣿⣀⣀⣀⣼⣿⣿⣿⠀⣿⣿⣿⣇⣀⣀⣠⣿⣿⣿⠆⠸⣿⣿⣿⣄⣀⣀⣴⣿⣿⡿⠁⠀⠀⣿⠇⢸⣿⡷⠀⠀⢿⣿
⢸⣿⣿⡄⠀⢻⠃⠀⢸⣧⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⣿⣿⣶⠀⢠⡿⠀⠈⢻⠃⠀⠀⣿⠛
⠘⣿⣿⣇⠀⠈⠓⠶⠦⣿⡄⣤⠀⠀⢰⠀⠀⢠⠀⠀⢰⡆⠀⢠⡄⠀⢠⡄⠀⠀⡄⠀⠀⡇⠀⠀⣶⠀⠀⣀⠀⠀⣤⠈⠙⠁⠀⣾⠧⠤⠴⠋⠀⠀⠀⣿⡇
⠀⢻⣿⣿⡄⠀⠀⠀⠀⠘⣷⣿⠀⠀⢸⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⢸⣼⡟⠀⠀⠀⠀⠀⣀⣾⣿⠃
⠀⠈⢿⡿⣿⡀⠀⠀⠀⠀⠘⣿⡄⠀⢸⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⡿⠀⠀⢿⠀⢀⣼⡟⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠈⣷⣼⡷⠀⣀⣀⣀⣀⣈⣛⣀⣘⣀⣀⠘⠀⠀⠸⠇⠀⠸⠇⠀⠸⠇⠀⠀⠇⠀⠀⠇⠀⠀⢋⣤⣶⠦⡤⠤⠤⠤⠬⠥⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠘⢿⡇⢰⣿⣏⣻⣿⣿⣿⣿⣿⣿⣉⣿⡷⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣿⣟⠀⣶⠀⣠⣶⠖⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟
⠀⠀⠀⠀⠈⢷⣄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⣭⣄⡀⢰⡄⠀⢠⡄⠀⢠⡆⠀⠠⡄⠀⠀⡆⠀⠀⡙⠿⠷⠶⠶⠦⠤⠤⠤⠤⠀⠀⠀⠀⣹⣿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠦⣄⣸⠃⠀⢸⡇⠀⠐⡇⠀⢀⣇⣠⣤⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣺⣿⣿⣿⣿⣿⣟⣛⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠾⢷⠀⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⡷⠶⢶⡥⣄⣉⠐⠀⠀⠀⣠⠬⢣⣶⡀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠿⠶⠶⠶⢶⠴⠶⠶⠶⠄
⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠙⣆⣶⣦⣄⣻⠟⠻⢁⣤⣀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⣤⢆⢪⣶⡌⡟⠏⠛⠒⣬⣐⡆⠺⡥⠰⠶⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⣹⣃⡙⠚⠛⢿⠷⣌⣡⡶⠇⠀⠀⠉⢦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠰⣊⠾⠁⠈⠁⠈⠀⠻⠄⠀⠀⠀⢘⣧⠀⠀⠘⠳⢤⣄⣀⣀⣀⣠⠤⣄⠀⡀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣀⡀⠀⠀⠀⠀⠀⣬⢱⡂⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣤⣄⣠⣈⣿⢋⣀⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠀⠀⠈⠲⣤⣀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⠒⢂⣰⠈⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡀⠀⠀⠙⠛⠾⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠠⡀⠁⠀⡀⠀⠀⠀⠁
⠀⠀⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣨⡧⡀⠐⣂
⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⠀⣻⣀⡝⠁⠰⣦
⠀⠀⠀⠀⠈⢳⡔⠄⠀⠀⠀⠀⠀⠀⡐⢃⠀⡠⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⡰⠈⠀⠄⠀⠀⠈⠊⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠘⠀⠁⢈⢹⡷⠀⠀⠀⠠⠦⣤⡀⠉⢀⣄⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠉⠂⠰⠛⠓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⢨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠴⠁⠀⢠⣶⢀⣆⢰⠇⠀⠀⠀⢀⣀⡀⡤⢄⣀⠐⠶⠶⠶⠶⠦⠤⠤⢷⣤⣤⣀⣸⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠽⠘⠀⠀⠀⠀⡶⠋⢉⠀⠀⠀⠀⠀⡀⠀⠄⠄⠀⠤⠆⠀⠐⠦⢌⢙⣻⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠒⢄⡀⠀⠀⠀⠀⠰⠂⢼⡓⠒⠀⠴⠤⢄⣤⣤⣠⣠⡤⢤⡤⠤⠤⠤⠾⠖⠋⣿⠀⠀⠈⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠎⡠⢀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠘⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡇⠀⠀⠃
⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠴⣁⠈⠼⠁⠀⠀⠀⠀⠄⠃⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⢠⠤⠤⣄⠀⠠⡄⢐⣈⡇⠀⠀⠀⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠈⠒⠒⠃⠀⠘⠁⠀⠙⢿⣄⠀⠀⠀⡇⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠀⡀⡀⠀⠀⠀⣀⠀⠀⠸⢧⡀⠀⢠⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣇⠁⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠚⠷⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣏⠠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢠⠈⠀⠀⠀⠀⠉⡸⠈⠂⡈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡆⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠇⣄⠀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠄⠀⠀⠀⠙⢦⡈⢀⡀⠾⠀⠀⢠⣡⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠀⠀⠀⡅⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠞⠁⠁⠀⠀⠠
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠀⠊⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡟⠿⡿⠛⡿⠿⡿⡟⣿⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣾⣶⣾⣶⣶⣾⣿⣶⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣀⣠⣤⡄⣀⣀⣀⣔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠒⠈⠩⠁⡯⠐⠀⠀⣀⠀⠀⠓⠚⠁⠈⠉⡟⡝⢒⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⢁⠀⡀⠀⠀⠀⠈⠀⠀⠀⠐⠆⠀⠰⡠⡄⢄⡇⠀⠑⠁⠀⠒⠃⠈⣑⠪⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠦⠋⠘⠁⠀⠀⠀⠀⠀⠲⠉⠀⠀⠀⠓⠁⠔⢢⠀⠀⠀⣀⠆⠀⠄⠠⠃⢰⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⣳⠀⠀⠀⠐⠃⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⠤⠀⠀⡔⡄⠘⣼⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⡀⠀⠠⣤⠀⠀⠀⠀⢆⡄⠀⠀⠀⠐⠥⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢠⠉⠀⠀⠉⢋⡱⠀⢰
⠀⠀⠀⠠⡞⠁⢑⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡠⣷⣾⣷⣿⠉⡆⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠀⡠⠀⢰⣶⠢⡀
⠀⠀⠀⢣⣿⣿⣿⠏⠐⣿⣾⠨⣤⡾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣴⣤⡸⢿⣠⡿
⠀⠀⠀⠀⠈⣷⣶⣲⣄⣀⣥⣀⢀⡷⠶⢿⣿⡟⠚⣰⠶⣶⡂⢲⣤⣖⠐⡦⠐⣿⠈⣡⣴⡧⢤⣎⢑⠶⠶⢇⢰⣿⣭⠘⢛⣅⠀⠘⢄
⠀⠀⠀⠀⠀⠻⣿⣿⣏⠁⠀⠈⠁⠀⠒⣶⣿⣿⡟⠁⠀⠙⣷⠚⠖⠛⣿⣿⣶⠿⣤⣟⡭⠃⠈⢻⣾⣤⣤⣿⣶⡈⢁⣠⣿⣿⣗⣀⠌
⠀⠀⠀⠀⠈⢱⣦⠈⠉⠉⠛⠛⠛⢛⣉⣩⣭⣿⣤⣀⣀⣠⣿⣷⣶⣾⣿⣿⣿⣭⣉⡉⠛⠤⠄⠚⠛⠉⠉⣹⣿⣿⣿⣿⣿⣿⣦⠃
⠀⠀⠀⠀⠀⣾⣿⡄⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⡃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡀
⠀⠀⠀⠀⣾⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣛⣉⣭⣭⣤⣿⠛⠛⣿⡷⡰⡁
⠀⠀⠀⠀⠹⡏⢘⣿⠙⣦⠈⣭⠭⠍⣡⡤⣤⣶⣾⣿⠗⠠⣭⣌⣉⣉⣉⣉⣉⣽⡽⣾⣿⡛⠉⢹⣿⡿⠠⣿⣿⡿⠃⠀⣿⣛⡙
⠀⠀⠀⠀⠀⢹⣏⣉⡘⠻⣿⠋⢠⣤⡄⠀⠙⠟⠉⢸⣧⣨⣥⠀⠻⣿⠿⣇⠉⣯⠈⠛⢫⡅⢠⡶⠎⡷⠀⠉⠋⠴⣶⣦⣽⣿⡿⠊
⠀⠀⠀⠀⠀⠘⡉⠉⠓⠒⠛⠛⠛⠛⠿⣿⣶⡀⢰⣦⣴⣿⡃⠠⣤⣆⣤⣤⣄⣙⠥⣦⣤⣤⣼⣿⣬⣿⠿⢿⣷⡴⠞⠋⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠖⠋⠙⠿⠷⠖⠛⠛⠉⠛⠿⠿⠾⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⢄⣀⣲⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠨⠜⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠂⠂⠀⠀⠄⠤⠤⠀⠄⠀⠒⠂⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⠀⠄⢢⡶⠶⠶⠶⠄⠄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠄⠉⠀⠁⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠸⠏⠛⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠉⢿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠄⢈⣻⣷⣄
⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣁⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⢓⠶⣦⣄⣀⣀⣀⣀⣀⣀⣠⣀⡀⠀⣀⢀⡀⣉⣀⣀⣀⣄⣤⣤⣴⣾⣿⡿⣿⡟⢉⣩⡆
⠀⠀⠀⠀⠀⠀⣈⣿⣷⣤⣉⣉⣭⣝⣻⣿⡝⠻⠛⢻⣿⢿⣿⣭⣭⣿⠟⣓⣏⣁⣠⣟⠡⠚⠙⠛⢉
⠀⠀⠀⠀⠀⠉⠤⠌⠋⠃⡶⢿⣿⣯⣽⣿⣿⣶⡶⡟⠻⠯⠛⢉⠙⠿⠋⠈⠃⠘⠋⠛⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⣏⣷⣦⣤⡴⠗⠉⠀⠭⠄⠛⠃⣀⣀⣠⣤⣄⣠⣤⣤⣴⣶⣶⡶⢶⣿⡏⣿⣩⡟⡓
⠀⠀⠀⠀⠀⠀⣾⣦⡝⣻⣭⡻⣷⣤⡀⠀⣠⣴⣿⣯⣵⣿⣯⣾⢏⣼⠋⣱⡿⣿⢳⣟⣙⣿⣣⣿⢵⡃⢀⠘
⠀⠀⠀⠀⠀⠉⠀⣁⠙⠎⠛⠩⠏⠿⠷⣾⢿⠯⠉⣻⢿⡾⢿⡽⢿⡛⠛⠻⡵⡯⠼⠻⢿⠛⣿⣈⣢⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠂⠐⠢⣤⣶⠦⢶⢾⢿⣷⠤⠾⣬⣥⣴⡤⢶⡶⠶⠿⠒⠒⠷⢶⡟⠉⠉⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣈⣠⣦⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠶⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠶⠶⠴⠴⠶⠟⠓⠒⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠒⠒⠂⠀⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⢐⠀⠀⠀⠐⠂⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠁⠀⠢⠀⠀⠀⡠⠄⣄⠀⠀⠀⢀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡆⠴⠂⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠁⠀⠀⠋⠀⠈⠓⡂⠀⠀⠁⠀⡀⠀⠁⠀⠀⠈⠂⠀⢀⡄⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣷⣶⣤⣤⣖⡒⠒⠒⠛⠛⠉⠙⠋⠛⠓⠒⠒⠶⠤⣤⣤⣀⣀⣀⣀⣀⣠⠞⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⡟⠁⠀⠀⠀⠈⠍⠙⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣷⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⣤⣄⠀⢀⣤⣤⡄⠀⠁⠂⠬⡉⠲⢤⠴⠒⠂⠉⠉⠡⠄⠀⠀⠐⠒⣩⣥⢳⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠢⣝⣋⠀⠸⠿⠿⠃⠀⠀⠠⣤⣤⠁⠒⠀⠁⣾⡇⠀⠀⢿⣿⠀⠀⠠⠿⣃⢾⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⡟⢇⠀⠀⠉⡉⠉⠉⠐⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠚⠋⠉⢩⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⢦⡀⣸⠙⡆⠀⣤⢤⡀⠀⠀⠀⠘⡆⢀⡀⠀⠀⠘⣆⣴⠋⠙⠳⣤⡞⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠁⠀⢳⣀⣸⠆⠘⢦⣀⣀⣀⠟⠉⠹⣄⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣕⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠭⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠈⠻⠿⠿⠾⠓⠤⠀⢀⠀⠀⣠⡜⠋⠀⠈⠀⠉⠉⠙⠓⠲⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠿⡶⠾⠿⠟⠒⠲⣶⣧⣴⣶⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠑⠈⠀⠀⠀⠀⠠⠀⠀⠀⠐⡀⠀⠈⠙⠓⠦⣄⣀⡀⠀⠀⠐⠂⠉⠁⠀⠀⠈⠑⠀⣀⣀⣺⣯⢱⡛⠽⣿⢻⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣤⡄⠀⠈⠉⠀⡀⠐⠀⠈⠈⠀⡀⠈⠐⠔⣩⣿⣄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⣏⣊⣧⣖⢫⣿⣿⣿⠄
⢀⡀⣀⣤⣴⠎⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣛⠲⠶⠶⠶⣾⢤⠤⣤⣤⣶⣤⠤⡾⠾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠚⠿⠿⠟⠛⠛⠉
⣿⠿⡁⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣴
⣄⣈⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⣠⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣶⠧⠒⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠞⣡
⡿⠟⠁⠀⠀⠀⢀⣀⠀⢀⠀⠂⢒⣂⣀⡾⢃⢴⡡⠞⠋⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣿⣃⣴⠏⠀⠀⠀⠀⠀⠀⢠⢟⣠⠾⠋⠄⢈⠟⢋
⠶⠂⠀⣠⣴⣿⣿⣿⢷⣾⡿⠋⠉⠉⠛⡻⠛⠛⠓⣠⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢸⡏⢀⠀⠀⠀⠀⠀⠀⣠⡿⠛⡙⠛⣀⢠⣥⣴⡿
⠀⢠⣾⣟⣧⢽⠛⡉⣏⢭⣿⣤⡤⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠈⣧⢀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢈⡇⢸⠀⠀⠀⠀⣀⣼⢃⠴⣇⡀⠊⣠⡿⠛⠁
⠀⣿⣿⡿⣿⢫⣴⡌⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡁⣟⣿⠀⠀⠀⠀⠀⠀⠀⣼⣧⣦⣾⣇⠈⠀⠀⠀⠰⣟⠘⣁⠔⢠⣴⠾⠛⠨⠄
⠀⠈⠙⠛⠳⠻⠶⠞⠛⠁⠀⠀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠛⢻⣆⠀⠀⠀⢀⣼⡿⢯⠁⣼⣿⣅⠀⠀⠀⠀⣀⠹⠯⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣻⡇⣤⣬⠠⣇⠸⠀⠀⢸⣏⣮⠇⣁⢧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠁⡌⠩⠙⣦⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⢘⠛⠄⣿⠀⠀⠀⠸⡿⢛⣼⣿⣻⣿⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣹⠗⠀⠀⠀⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⢀⠀⡃⣼⡇⠂⠀⠈⣿⣿⣿⣶⡿⠋⠀⠀⠀⢀⣀⡀⠁⠄⠀⠀⠀⢀⣾⣿⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠲⣿⢻⠀⠀⠀⠀⠀⠀⠀⣽⡏⠸⠀⢷⢾⡇⣶⠁⠀⠘⠿⠿⠛⠀⠀⢀⣴⣞⠋⠉⠝⠺⡄⠀⠀⠀⢸⣿⡛⡆⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠅⠀⡂⠀⢀⡟⡘⠀⠀⠀⠀⠀⠘⠀⣾⡇⠐⠀⣺⢈⣷⠃⠀⠀⠀⠀⠀⠀⠀⡰⣻⠿⠇⠀⠀⠂⠀⢻⡀⠀⠀⠈⢧⣭⣸⣾⣿⠇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⡐⠘⠠⠁⣸⠁⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⡓⢺⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⠀⡞⠙⢻⡿
⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠁⢠⣰⡏⠀⠀⠀⢀⣶⣶⣦⣀⠀⢸⣧⣤⡆⢰⢸⣧⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠠⠁⠂⠀⢀⡞⠁⠀⠀⠀⠈⠁⢀⡼⢁⠄
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⢟⣿⣿⢿⣧⡀⠙⢿⣳⣤⡿⠃⠀⠀⠀⠀⣠⠀⢠⣿⠆⠀⠀⢂⠀⢀⡾⠁⠀⠀⠀⠀⠀⣧⣾⡃⠈
⠀⠀⠀⠀⠄⢽⠀⠠⠁⠀⢠⣿⡀⠀⡇⠀⠀⣿⣮⡜⢿⡧⣿⣿⡄⠀⢩⡀⠀⠀⠀⠀⠀⠈⠀⢀⣾⠁⠀⢀⠀⢀⢀⡞⠀⠀⠀⠀⠀⡄⣸⣟⠈⢿
⠀⠀⠀⠊⠀⣿⠀⠌⡀⢠⡿⠙⡇⠀⠀⠀⠀⣿⣽⠗⢀⣘⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣿⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠁⢀⡁⢰⠄
⠁⠀⠀⠀⠀⣿⢠⠀⣤⡿⠁⠠⠀⠀⠀⠀⠀⠘⢿⣧⠆⣉⣏⣽⣃⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠀⠀⠈⠉
⠀⠀⠄⠀⠀⢻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠟⠻⣯⠀⡀⠀⠀⠎⠀⠀⠀⠀⣼⣦⠀⠈⣠⠎⠀⠀⠀⠀⠘⢶⡤⣤⣀⣦
⠀⠀⠆⠠⠀⠈⠛⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⣽⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡾⠁⠀⠈⠀⠀⠀⠀⣈⣿⡆⠙⠻⣿⠿⢶⣈⡂
⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠙⢻⣦⣑⡦⣀⣶⣌⠻⣦⣄
⠶⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠌⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠙⠂⠀⠀⠀⠀⠙⠻⢷⣌⠙⢅⡉⠢⢉
⠰⣄⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢎⠒⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠻⢶⣶⣎⠒⠄
⠰⠞⠙⠢⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢷⠘⣇⠀⠀⠀⡄⠀⠀⠤⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣀
⠷⠄⠸⠦⠤⠾⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠦⠘⠄⠙⠷⠀⠐⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢛⣛⣛⣉⣉⡛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⣿⣿⣿⣶⡛⠀⠈⢳⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⣿⢻⣽⣿⣿⣷⣟⠀⠀⢸⣏⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⣠⠴⣲⡿⠋⠉⣠⠖⠋⠀⢀⣿⢻⣽⣿⣿⣿⣟⠀⠀⣸⣯⠟⠉⣩⠟⠉⠉⣹⠷⠦⣄⡀
⠀⠀⠀⠀⣾⣡⠞⠁⢀⡴⠛⠁⢀⣠⠞⢉⡇⠻⠿⠿⠿⠷⢟⣠⡾⠛⠁⣠⠞⠁⠀⣠⠞⠁⢀⡴⠋⣷
⠀⣀⣀⣀⣿⠓⠦⣶⣋⡀⣀⡴⠋⠀⣠⠾⠛⠛⠋⠉⠉⢉⡽⠋⠀⣠⠞⠁⠀⢀⡼⠃⢀⣴⣯⠴⠚⣿⣀⣀⣀⡀
⡞⢩⡤⠤⢤⣄⠀⠀⠈⠉⠙⠛⠒⠺⠷⠶⠤⠤⠤⠤⠴⠯⠤⠴⠾⠥⠶⠶⠖⠛⠛⠋⠉⠁⠀⠀⣠⣤⠤⠤⣬⠙⡆
⠹⣌⡛⣋⣩⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣭⣉⡓⣋⡼⠃
⠀⠈⠉⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣉⣓⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣚⣋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢩⡏⠀⠀⠀⠉⠻⡯⠭⣿⠛⠁⠀⠀⠹⡏⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⣏⠀⠀⠀⠀⠀⢷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠸⡆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡷⠦⢤⣀⡀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⢀⣀⣠⠴⠾⡆⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠶⢤⣄⣀⠉⠙⠒⠶⢤⣧⡀⣿⠴⠖⠛⠉⢁⣀⣤⠴⢷⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⡽⣿⡤⠴⠖⠋⠉⠁⠀⠀⠸⡆⠘⣇
⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣄⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⣨⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⡼⠃
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠉⠉⠰⠊⠙⢟⠟⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⢋⠈⣀⠀⡰⠀⠀⠀⠐⠀⢐⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠻⠀⠀⠈⠀⡄⠀⠀⠀⠀⢀⠀⢉⣙⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠶⠀⢠⡀⢀⡄⠘⢃⡉⠐⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣤⣤⣼⣥⣤⣭⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠭⢽⣿⣿⡿⠟⢛⣻⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠒⠛⠉⠉⣉⣉⠭⠭⠶⠿⠃⠀⣚⣩⡽⢟⣋⠉⡐⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⣴⣶⣶⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣌⣶⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣇⣀⣠⣤⣦⣼⣧⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⢄⣉⣛⣾⣿⣿⢿⠉⠉⣛⣿⠿⣿⣯⠭⠽⠿⣿⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡿⣾⠄⠴⠤⠴⠷⠦⠉⠚⠹⠶⠖⠢⢼⣲⣶⣶⣾⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣘⣁⣴⣿⣿⣿⣿⣿⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠟⠀⠀⠀⠀⠀⢀⠠⣂⡜⢣⠀⠣⡀⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠄⢣⠴⠀⡘⠈⠂⡠⢤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠐⡀⠀⠀⢠⠁⠠⠀⠀⠀⠡⠀⢡⠄⠂⣠⡉⠈⠂⠐⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠐⠁⢀⠔⠉⢡⡔⠈⠠⠄⠀⠈⢲⠈⡱⢅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠊⢀⠄⠒⢀⣰⠁⢈⠶⢀⠀⠈⡶⢁⡬⣀⡐⠀⠄⠀⠂⢈⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢁⠠⠁⠀⡀⡊⠀⡸⢅⠀⠀⢑⠒⢀⡈⠀⠘⠂⠀⠈⡀⠐⠁⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠁⠀⢀⡊⠀⠀⠃⠀⠀⠑⠄⠂⣀⠈⠀⡃⠀⢀⠄⠊⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠁⢈⠖⠈⠒⢄⣀⠔⢄⠠⠃⢄⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀⠀⠀⠀⠀⠰⠁⠁⡤⢆⠀⠀⠀⡠⠀⠀⡜⠀⢀⠄⢀⠊⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⢦⠂⠀⢀⠁⠀⠑⠁⡠⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⡯⠁⡀⠀⠀⡠⠁⠈⢲⠅⠀⠠⢀⠔⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⢢⠺⢀⠀⡠⠂⠀⣨⠔⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠐⠉⡈⠌⠉⠁⠐⠒⠃⠀⠎⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠐⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢀⠨⠉⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⡀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢀⠐⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⠊⠀⢀⠐⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠐⡀⠠⠋⠀⢀⠀⠂⠁⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠑⠠⠄⠈⠐⠠⠀⠀⠠⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡈⢦⢸⡰⢁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡾⡽⣷⢿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⢯⣿⣟⣿⣹⣥⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢤⣟⣿⢺⠧⢿⣤⣷⠶⢻⠀⠀⣴⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⢠⠓⡾⢤⣏⣹⣗⣻⣗⣛⣖⣩⣧⠞⢡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⣦⠀⣼⣩⡗⢺⡟⢾⢦⣼⣯⣩⣯⣠⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⢳⡗⢼⣍⣹⡇⠈⣧⠾⡦⠴⣷⠤⠾⡆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⢳⡀⢸⣝⣻⠤⢼⠇⠀⢸⣞⣟⠒⢻⡖⢺⣷⡷⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢻⡇⢸⠦⣿⣉⡿⠀⠀⢸⣯⣿⣒⣺⣏⣩⣿⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⣾⣓⣳⣼⠃⠀⠀⢸⠷⣿⢬⣽⡧⢤⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡬⣿⡏⠀⠀⠀⣾⣉⣹⠒⠚⣟⡾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⢷⢻⠇⠀⠀⠀⣿⢭⢿⡉⢉⡿⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⣿⠀⠀⠀⠀⣿⠲⢾⡽⠋⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡆⠀⠀⠀⢹⣽⠏⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢳⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡀⠀⠀⢸⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣭⣷⠤⣾⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠶⠶⠶⠾⠿⠶⠶⠶⠶⠶⠦⠤⢤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠿⠗⠛⣩⠍⠀⠀⠀⠚⠉⠀⠀⡄⠀⠠⠤⠀⠀⢦⠄⠀⠀⠠⡀⠈⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣋⡁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⣤⠀⠀⠐⠦⠀⠀⠾⠙⠳⢦⣄
⠀⠀⠀⠀⠀⣴⡶⠛⠁⠀⠈⠊⠀⠀⣤⠄⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡀⠀⠀⢤⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠰⠦⠙⢳⡀
⠀⠀⠀⠀⣴⢋⠤⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠔⠀⠀⠀⠀⠶⠙⣦⡀
⠀⠀⢀⣾⢣⠈⠁⠀⠀⠈⠀⠀⠘⠁⠀⠀⢀⠔⢄⠀⠀⡀⠀⡀⠀⠠⠢⠀⣀⠠⠂⠈⠂⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⢀⡀⠀⠈⢷
⠀⠀⢸⡧⡃⣄⠄⠀⠀⠀⠀⠀⢀⠠⡀⠠⠋⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⢄⡀⠀⢀⠀⠀⠀⠁⠀⠀⠘⡇
⠀⠀⢸⢇⣾⣆⢀⡤⢤⡄⠀⠀⢀⣴⢠⢀⣦⣇⣧⣦⣼⣼⣼⣿⣼⣾⣶⣾⣶⣶⣴⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⣿⢿⠿⢣⣰⣿⣿⣢⣼⣾⣾⣿⣿⣿⠿⠿⠛⠛⠛⢋⡉⠉⣉⣉⣉⣉⠉⠉⠉⠉⣩⣿⣽⣛⠛⠛⢳⣶⠶⠶⢦⣤⣤⣤⣤⣤⣀⣀⣤⠏
⠀⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢀⣤⠶⠛⠛⠓⠲⠋⠙⠛⠉⠉⠈⠉⠙⠛⠲⠞⠁⠀⠀⠉⠉⠙⠉⠉⡓⠛⠶⣄⡀⣀⣈⣉⡉⢉⣉⠳⣄
⠀⠀⠀⢈⡽⠿⣟⣛⣭⣥⣤⣤⣤⣄⣀⡴⠋⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠻⠏⠉⠙⠲⢿⢻⡞⠛
⠀⠲⠛⠋⣶⣿⠿⠁⠀⣔⠀⠀⢀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⢀⡤⠀⠀⣿
⠀⠀⠀⠀⣿⣀⣬⣀⠀⠀⠀⠀⠙⠀⠀⣠⣾⣛⣛⣛⣯⣤⣤⣤⣤⣤⣤⣤⠀⢀⡀⠀⠀⢀⣀⢀⣶⣾⣶⣶⣶⣦⡄⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⣴⢦⠾⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⡄⢰⣿⣿⣿⣁⣀⡀⠀⠈⣻⣧⠀⣴⣦⡾⠛⠟⠻⠷⣶⣾⠋
⠀⠀⠀⠀⠀⠘⣿⣻⣿⣠⠃⠀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠴⠶⠶⠶⠒⠚⠛⠛⠛⠿⠿⠞⠛⠋⠀⠀⠈⠉⠉⠙⠛⠛⠒⠷⠦⠤⠤⣄⣀⣀⣠⣟
⠀⠀⠀⣠⣴⠿⢿⡿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⣼⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⠴⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⣦⣠⣶⣤⠀⠀⠀⠀⢠⣼⣧⡀
⠀⢨⡟⢉⠉⠳⣶⠖⠉⠈⠙⠛⢻⣶⣤⡀⠀⠀⠀⠸⣇⡄⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⣇⠀⢰⢦⡍⠈⠙⣷
⠀⠈⣷⣦⣤⣼⣷⠆⠀⢠⡀⠀⠀⠈⠙⠻⣷⣄⡀⠀⠉⠀⠀⢀⣠⣼⠏⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠟⠀⢀⡀⢠⡇
⠀⠀⠈⢻⣿⣮⣤⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣿⣶⡄⢀⣾⠋⠀⠀⠀⣈⣳⣄⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀⣉⣀⣀⡀⢀⢀⣀⣰⣦⣀⣀⣀⣀⣴⠟
⠀⠀⠀⣿⣿⣿⡛⠙⢹⡿⣿⣯⠟⠋⠻⣿⠽⠿⣿⣿⣿⣿⣾⡟⠛⣿⡟⠛⠉⢉⠉⠉⢹⡏⠁⣽⠋⠉⢻⠟⢿⣍⣛⣻⠟⠛⣿⠛⠻⠻⣩⡿⣯⣿⠇
⠀⠀⠀⠛⢹⣿⣿⣤⠏⠀⠈⠀⠀⠀⠀⢻⣄⣠⠋⠉⠛⠛⠋⠀⠀⢸⡇⠀⢰⠋⢷⡴⠋⠀⠀⣻⣦⣤⠏⠀⠀⠉⠉⠁⠀⠀⣿⡆⠀⢀⡟⠀⠉⣿
⠀⠀⠀⠀⢸⣿⣽⣥⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠃⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠳⠶⠶⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠖⠒⠛⠋⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠛⠒⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣡⠔⠊⠀⠠⢄⠠⠤⠤⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢹⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠠⠖⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣸⠁⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⣸⠁⢀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⠁⠀⠀⠀⠀⣟⢸⡇⠀⣼⠁⣿⠸⣇⠀⡿
⠀⠀⠀⠀⠀⢰⠃⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⣸⠃⠀⠀⠀⠀⣷⠘⠧⠆⠻⠎⠿⠀⠸⠇⠳⠄
⠀⠀⠀⠀⠀⡾⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡾⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣇⠀⠁⠁⠀⢠⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⠇
⠀⠀⠀⠀⠀⠈⠑⠲⠤⣤⢀⣈⣉⠀⠀⠠⠀⠀⠀⣵⡀⠀⣰⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠳⠦⢤⣀⣈⠙⠃⠋⠀⡿⠁⠀⠀⠀⢀⣠⠔⠒⠛⠉⠉⠈⠉⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢀⣀⡀⠀⠉⠉⠛⠒⠚⠁⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⣠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢏⡀
⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢰⠃⠀⠀⠀⠀⢀⠀⠄⣀⠃⠀⠀⢆⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⢆⠀⠀⠀⠀⡎⠀⡸⠀⠉⠓⠒⠢⡌⢁⠀⠀⠀⠀⢣
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⠏⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡰⢠⠄⠃⠀⠀⠀⠘⡆
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⢨⠀⠀⠀⠀⠴⠘⠠⢀⣀⠀⢼⠃⡀⡑⠀⠀⠀⠀⠀⢹
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠐⡄⠈⢍⡁⠠⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⡤⠴⠃
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠉
⠀⠀⠀⠉⠙⠒⠒⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⢀⣀⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠢⠤⣄⣀⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠋⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣢⡉⠙⠓⣲⡶⠶⢦⠤⡦⣤⡤⡤⢤⢤⡤⡶⠶⠶⠶⠲⠛⠛⣉⠁⠀⢀⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠩⠿⠻⠋⠿⢦⣀⠀⢀⣠⣶⠿⠶⣤⡀⠀⣠⠞⠶⢤⣠⡾⠉⠹⡶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠼⠛⠻⣥⣀⣀⣀⣠⣽⣻⢿⣀⣀⣀⣀⣀⣀⣤⠟⠻⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣝⣒⡒⠖⠚⠁⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣀⣠⠼⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣒⡶⢿⣭⠭⠭⠭⠭⣭⣉⣉⣙⣛⣻⣛⣛⣛⣛⣛⣉⣉⠭⠭⠥⠴⠖⠒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠳⠤⠴⠚⠋⠛⠦⣄⠀⠀⠈⠁⢀⣤⣄⢀⡴⠒⠦⣤⠴⢻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⣀⡀⠀⠈⠙⠓⠒⠒⠋⢀⣈⣉⣁⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣴⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠻⠿⣿⣿⣿⣯⠉⠽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠍⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⡉⠉⢻⡏⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡁⠀⠀⠀⠀⡛⠻⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢤⣤⣤⣤⣤⣤⣤⣴⡶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠛⢦⠤⠤⠤⢷⠖⠛⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣽⣭⣹⣛⣛⠿⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⣾⣳⣦⠀⠀⢸⠄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⢭⣭⣛⣛⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠿⣿⠿⠁⠀⠘⣗⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢟⣻⣿⣴⣿⣯⣭⣿⣿⣷⣾⣭⣭⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢠⠶⠾⣧⡀⠀⠀⠠⠀⠀⠀⠠⢿⠄⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠸⣄⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠺⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠟⠻⠛⠿⣿⡿⠛⣏
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠤⠂⠀⠀⢸⠇⣤⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣇⠀⠀⠀⠀⠀⠈⣎⠙⢛⠛⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠽⠷⣤⣄⣀⣀⣀⣨⡤⠾⠗⠻⡅
⠀⠀⠀⠀⢠⡿⢻⡇⠀⠀⠀⠀⢀⣠⡤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⣤⣾⣄⠀⠀⠀⠸⡆⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⣿⣹⠁⠀⠀⠀⣴⣏⣷⣿⣿⣿⣿⣿⣾⣹⢦⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⣯⣿⣿⣧⠀⠀⢀⣷⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⢹⡏⠀⢤⠤⡼⣷⢹⠓⠣⣷⠛⠹⡩⠚⢝⣾⢷⠤⣤⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠚⡿⣿⠿⠃⠂⡀⠈⢽⣃⠔⣀⠈⠀⢳⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⢰⡇⢿⢸⠀⡃⣿⠘⢣⡇⣿⢸⢺⢸⡇⡇⠀⠀⣿⠀⠀⠀⠀⠀⣠⡶⢿⣿⣤⠈⠔⠂⠐⡡⠈⠀⠀⡐⠂⠼⣇⠀⢁⠐⠀⠀⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠸⠄⣧⣿⢸⡀⢃⣿⢘⣣⣇⠋⣘⣸⣸⠇⠧⠀⠀⣿⠀⠀⠀⠀⠐⣏⠀⠄⠘⣷⡇⠐⠁⠀⠠⠈⣀⠀⡀⠂⠠⢯⡴⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢯⡦⣶⣶⣶⣷⣾⣯⣵⢛⣸⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠶⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠯⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⡀⠄⠒⠂⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⠢⢄
⠀⢸⠋⠉⠉⠉⠙⠛⠒⠀⠀⠀⠀⠚⠀⠉⠉⠉⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠱⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣀⣢⣀⡀⠀⠀⠀⠀⠀⠘⢆
⢸⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠆⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⠀⠀⠀⠘
⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠆⠀⠀⠀⠋
⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⠓⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡼
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡾⠁
⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⠒⠒⠒⠲⠶⠶⠶⠶⠶⠦⠤⠤⠶⠞⢃⡴⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠿⣭⣭⣥⣤⣤⠤⠴⠶⠶⠶⠾⢿⣿⣭⣐⣒⣒⣂⣀⣀⣠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠉⠛⠓⠶⠶⠶⠶⠶⠶⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠻⣤⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠒⠒⠒⠛⢧⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠉⠒⠦⢤⣀
⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⢀⣆⠈⠙⠓⠶⠶⠶⠶⠶⠤⣤⣤⡤⠶⠶⠶⢿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠈⠙⠓⠻⠦⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⢧⣀⡀⠀⠀⣄⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠳⠶⠶⢿⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠈⠉⠛⠛⠛⠶⠦⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣄⣹⡄⠀⠘⠦⠀⠀⠤⠤⢀⣀⣀⠤⠂⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⠤⠄⠀⠀⠈⠉⠀⣀⣀⣀⣤⣤⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⡀⣺⣦⠀⠀⠀⢹⡿⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠛⡋⡁⠀⣠⣤⡘⣿⠣⡇⠀⣴⡄⡆⠜⢡⡄⠀⡇⡏⣿⠇⠀⢀⡀⠀⣀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠻⣠⣫⣷⣼⣧⣾⣷⣸⠦⡷⠛⠛⠉⠙⠿⠋⠀⠈⠳⠶⢏⣼⡧⣾⣯⣼⡛⣇⢘⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡶⠃⠉⠁⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⠛⠛⢾⣤⠖
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢰⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⣆⡀⢀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠐⠀⠀⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⢿⠧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⣀⣀⣀⣀⡀⢁⠶⠭⣓⠦⡀⠀⠙⠔⢅⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠖⠀⠠⠖⠛⠉⢉⡔⠣⢌⢙⠣⣍⡒⢌⠳⡄⣄⠀⠀⡀⡀⡢⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠴⠐⠁⠀⠀⠀⠀⠀⠑⠰⢯⡈⠑⠠⣁⠡⡄⢉⠀⢣⠙⣌⠳⣄⠀⠘⠄⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠑⠈⠢⠑⡇⠘⡄⠠⡀⠑⢬⣑⠲⣄⠀⠂⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⡀⠀⠘⡀⠡⡘⢤⡘⠂⡀⡀⠂⢤⡑⣌⢣⠁⡀⠈⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡁⠑⣄⠳⡜⢆⠱⢌⠢⢤⡂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⡙⢅⠈⢢⠙⠀⡑⠦⡽⠊⠀⢦⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⡀⢡⠈⠢⢌⡀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⡐⠀⠌⠀⠀⠀⠈⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢆⡈⠑⢢⠍⠀⠀⠀⠀⠐⠀⠑⡀
⠀⠀⠀⠀⠀⠌⠀⠘⠄⠀⠀⠀⠀⠠⠀⢳⡀⢀⠀⠤⢤⠤⠂⠀⠲⠂⠰⠂⠐⠢⠄⢀⣀⠀⠀⠀⢠⠏⠢⠌⠛⠀⠀⠀⡀⠀⠀⠀⠀⠄⠈⠄
⠀⠀⠀⠀⠌⠀⡐⠀⠘⡀⠀⠀⠀⠀⡡⠤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠰⣏⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⢂⠈⠂
⠀⠀⠀⠐⠀⡐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠈⢄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣤⣤⣤⣄⣀⣀⣀⠀⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⡷⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢋⡀⠤⠖⠋⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⣀⠔⠊⡡⠒⠉⠀⠀⠀⠀⠀⠀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⠀⣠⣴⣾⣿⣿⠟⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣠⠖⠁⠈⠛⠿⠿⠓⠀⠀⠀⣰⡏⠐⠻⠿⠟⠋⠀⠑⢦⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⡀⢠⣿⡇⠀⠀⣠⠀⠀⠀⠀⠀⠙⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢹⠇⣼⣿⣇⠀⠰⣿⠀⢠⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⡄⢠⣷⡿⠀⠀⠀⣿⣿⣿⡄⠀⠃⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡄
⠀⠀⠀⠀⠀⢀⣴⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣿⣿⡇⢸⣆⢰⣿⣿⣿⣷⢠⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⣄
⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣼⡇⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦
⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠿⢿⣿⡟⢻⣿⠟⣛⡛⣿⢛⣛⠻⡟⣛⣛⣿⢛⡛⢿⠻⣿⡿⡿⠿⠿⣷⣶
⠀⠀⠀⠀⢤⣴⣶⣶⣶⣶⣶⣿⣿⠀⣛⠠⣿⠱⠆⢿⡇⣭⠡⣿⢨⣭⠘⡇⢨⣽⡇⢺⣿⢾⠐⣿⡇⡇⢘⣻⣿⣿⣶⣶⣶⣶⣶⣶⡤⠄
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣀⣛⣥⣧⣿⣿⣼⣷⣿⣷⣿⣶⣶⣾⣷⣶⣶⣿⣦⣵⣾⣦⣭⣼⣧⣘⣛⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠴⠿⠿⠿⠟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠿⠿⠿⠦
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣟⢽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⠭⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⡄⠀⢨⡯⠿⢹⡅⠀⢠⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⢿⣿⡗⣺⣒⡖⢺⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣚⣃⣛⣘⣃⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡈⣿⠥⠽⠤⡧⢼⡟⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⢽⠥⣭⢬⡧⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⡒⣛⠒⡓⢺⠃⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⡓⣿⢚⢃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠈⣇⣭⣉⡭⡼⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡩⣿⢍⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣭⣥⡀⠉⣤⢰⡶⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠙⢢⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡠⠀⡀⠀⢀⠢⢤⡀⠀⠀⡏⠀⢻⢀⡤⣠⠊⠉⠀⣀⠤⠄⠀⢞⢡⠀⠑⢆⠀⠐⠤⡀⠀⠀⡞⢳⡄⠀⢠⠟⠓⠦⣔⠒⠓⠦⣄⣀
⠀⠀⢀⠰⢀⠑⣄⢻⠀⡠⠓⠀⠀⠈⠓⠁⠸⡀⣀⠇⠀⢸⣇⠀⠀⠀⠈⠉⠁⠉⠁⠤⠤⠒⠳⡄⠀⣧⣸⠃⢀⡟⠀⠀⠀⠈⠙⠒⠶⢤⡈⠉⠉⢱⡀
⠀⠀⠀⠂⢢⣽⣿⡻⠋⡠⠔⠒⠉⠉⠓⠦⣀⠀⠀⠀⠀⢸⣧⠤⢄⣀⡀⠀⠀⠀⠈⢉⣀⡈⢽⡃⠀⠼⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢀⡟⡄
⠀⠀⠀⢊⢀⠔⠁⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡅⢀⡀⠀⠈⣈⡉⢉⣉⣀⠀⠀⣰⠇⠀⠀⣠⠞⠀⠀⠀⠀⠁⠀⠀⣠⢎⡵⠁⠀⡼⡸
⠀⠀⠀⠀⠁⢀⡎⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⣇⠀⠙⠒⠦⠬⠤⠤⠄⠀⢀⣀⠠⠤⠘⠁⠀⠀⣧⣀⠀⠀⠐⠀⠀⠀⣰⢣⠏⠀⠀⢠⢇⡇
⠀⠀⠀⠀⠀⠸⣇⠠⡀⠀⠀⢀⡞⠁⠀⠀⠙⢦⠀⠀⡿⠀⡴⠾⠶⡆⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠀⠘⠫⢽⣲⡦⣄⠀⢠⠇⣾⣀⣀⣠⡼⢸⠁
⠀⠀⢀⣤⣄⠀⠙⢦⡀⠀⠀⠘⣇⠀⡀⢀⡄⣸⠀⢠⠇⢸⠁⠀⣰⠏⠀⢠⠒⠒⢦⡀⠀⠀⠈⣧⣀⣀⣀⣀⣀⡈⠙⠲⣝⣫⠞⠓⠶⠶⠶⠖⠋
⠀⠀⣾⠁⠈⠳⣄⠀⠉⢦⡀⠀⠈⠳⠬⠵⠞⠁⢠⠟⠀⠘⠒⠚⠁⠀⠀⠘⢮⣀⣠⡇⠀⢰⣯⣽⣏⣀⣠⣤⠤⠽⠇⠀⠀⠀⠀⠀⢠⠖⠒⠲⡄
⠀⠀⣿⡄⠀⠀⠈⠑⢤⣀⠑⢄⡀⠀⠀⢀⣠⡴⢋⣠⠴⠖⠒⢛⡓⠒⠲⢦⡀⠀⠀⠁⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠏⠀⠀⠠⢹⡀
⠀⠀⠸⣷⡀⠀⢀⣤⣤⡈⠑⢦⡈⠉⠉⠉⠁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠲⢄⡀⠀⠸⣄⠤⠤⢷⡤⠤⠤⣤⡇⠀⠀⠀⢠⣾⠀⠀⠀⠀⠃⢦⡀
⠀⠀⠀⡟⣧⠀⢻⠀⠀⡝⣦⠀⢹⡄⠀⠀⡞⠀⠈⣧⠈⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⢙⡆⠀⣟⠒⠒⠚⣷⠚⠛⢉⡇⠀⠀⠀⠸⡍⢙⠋⠙⠉⠉⣩⠁
⠀⠀⠀⢿⠘⣇⠀⠳⢤⣤⠟⠀⢰⠇⠀⢰⠳⣕⠀⠘⣆⢀⣒⣒⣀⣀⣸⣇⣀⠐⣡⠞⢳⠀⢻⠀⠀⠀⠸⣆⠀⢸⠃⠀⣀⡀⠀⠙⠾⣷⣤⡤⠞⠁
⠀⠀⠀⠈⢧⣈⠳⢤⣀⣀⣠⣴⠟⠀⠀⢿⣐⣨⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⢧⣀⣸⠇⠈⢧⣀⣀⣀⣉⣠⠜⠀⢯⠉⢧⠀⢀⣠⡴⠀⠢⣄⡀
⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠋⣁⣀⣀⡀⠀⢉⣁⡀⠀⠀⠀⠸⡳⣶⣄⡇⠀⠀⠀⠀⠈⠁⢀⣴⣦⣍⡉⠉⠀⠀⠀⠀⠈⠓⠻⣄⣈⡓⠶⠴⠶⠞⠃
⠀⠀⠀⢰⡒⠦⣴⡒⠋⢉⣉⣀⠠⠀⠉⢶⡁⠀⡝⠀⠀⠀⣠⠽⠾⢿⣧⣠⠤⠤⣄⡀⠀⢸⣝⡻⠷⣯⣭⣍⣉⣉⣉⣛⠲⢤⣀⠈⠉⠓⠦⣄
⠀⠀⠀⠘⣧⠀⠱⢭⣒⣤⣀⠀⠠⠄⠀⠀⠱⡀⢨⠆⠀⣼⢡⠊⠈⠀⠈⠁⠀⠀⢠⠹⡄⠈⠻⢿⣷⣶⣶⣯⣭⣭⣽⣛⡻⠶⣌⢳⡄⠀⠀⠘⣆
⠀⠀⠀⢰⡿⡦⢤⡘⣿⣭⢻⢷⣦⣄⡀⠀⠀⠑⣌⠆⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠶⠤⢤⣉⣉⣉⣉⡉⠛⠻⢷⣼⠋⠀⠀⠀⠀⣿
⠀⠀⢀⣀⠓⢬⣒⢵⡀⠛⠉⣟⠀⠛⢿⢗⠦⣄⡈⣧⠀⠸⡆⠀⠀⠀⠏⠘⠆⠀⠀⢰⠁⠀⢸⠭⠶⠶⠶⠶⠶⠦⣭⣍⡓⠤⡉⠀⠀⢰⠋⠉⠉⣹⠂
⠀⠀⠀⠈⣳⡀⠈⠑⠮⣓⢦⣈⠉⠳⡀⢀⡙⠲⠽⠇⠀⠀⠹⣔⠤⡀⠀⠀⠀⠄⣠⠏⠀⠀⠘⠿⢿⣒⣒⣒⣒⣒⠢⠌⡙⣾⠀⠀⢠⡟⡶⠒⢲⣿
⠀⠀⠀⠑⢿⣧⣤⡠⠴⡌⠑⢬⡓⢦⣉⣁⡸⠂⠁⢀⣀⠀⠀⠈⠓⠒⠛⠓⠒⠛⠁⠀⣀⣤⠴⠶⠲⠶⠦⣄⡀⠈⠙⢦⣄⣷⠀⠀⠸⠶⢷⣬⣿⣸
⠀⠀⣠⢾⡿⠋⠛⠒⠋⠀⠀⠀⠈⠓⠖⠋⢀⡠⠞⠉⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢉⢳⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠉⢁⡤⠤⠤⠄⢤⣄⣤⠤⠤⡀⠀⠀⡿⠤⠤⠤⠤⢤⡴⢦⣄⣈⣓⠲⢄⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⡰⡠⠃⢀⡴⠞⣻⠋⠉⠉⠉⠓⢦
⠀⠀⡎⢹⠉⣿⠛⠛⠛⠛⠛⠛⠛⡏⠀⠀⣛⣷⠀⠀⣀⠀⠙⠋⠀⠀⠉⠉⢻⠀⠈⢧⡳⢤⡀⠀⠀⠀⠀⠀⢸⠁⢀⡞⠀⢎⠉⣠⠶⢶⣄⠀⠈⢧
⠀⠀⠹⣼⣧⠘⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣯⡀⠀⠸⠽⠂⠀⣠⣤⣄⠀⠀⢳⠀⠀⠀⠙⣆⢷⠀⠀⠀⠀⠀⠘⡇⠸⡇⣠⠊⠘⣇⠀⣸⣽⠀⠀⣸
⠀⠀⠀⢠⡛⣦⣀⡀⠀⠀⠀⣠⠗⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⠛⠶⠟⠀⠀⢸⠀⠀⠀⠀⢿⢸⡆⠀⠀⠀⠀⠀⢹⠀⢷⡸⢄⣠⣌⢉⣩⣁⡖⣲⠏
⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠙⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠳⣧⣄⣀⣠⣤⡤⠞⠀⠀⠙⠶⣤⣈⣉⣠⡭⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣿⣛⣻⡿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⣭⠈⣽⠀⢸⡥⠨⣮⢹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⡦⠠⡼⠀⠘⣗⠀⣻⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⡝⢹⠧⠠⣞⠃⠙⣧⠀⣽⡋⣧⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠲⠇⢰⠆⠠⠞⠁⠘⡧⠀⢴⠆⠲⠺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢺⠆⠲⣄⣀⡜⠃⠚⢇⡀⣴⠂⠸⠇⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠻⠦⢄⠀⠀⠱⠆⠰⠄⠀⠀⠦⠴⠛⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣠⣀⡈⠁⠈⢣⡀⢠⠎⠁⠙⣄⢠⡌⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠲⣇⠀⠘⠖⠒⢆⡀⢀⡶⠂⠲⡀⢀⡽⠚⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣿⣷⢤⡏⠉⢳⣄⣠⡌⠉⠉⣡⣄⣤⠋⠉⢳⡤⣿⡇⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⣛⣛⣛⠛⠿⣿⣿⣇⢀⠷⠲⢮⠀⠀⡸⠒⠒⢃⠀⢀⠗⠒⠿⣀⣼⣿⡿⠟⢛⣛⣛⣛⠛⠿⢿⣶⣦⣄
⠀⠀⠀⠀⣠⣾⠿⢋⣥⠶⠚⢩⣭⣭⣭⣍⡓⢦⣹⡏⢉⣄⣀⣜⠉⠉⢡⠤⢤⡎⠉⠙⣤⠄⣴⠉⢹⣯⠴⢚⣩⣭⣭⣭⡍⠓⠦⣌⡛⢿⣷⣄
⠀⠀⠀⣼⡿⠡⠖⢛⣋⣛⡛⠲⢬⣙⢿⣿⣿⣶⣽⠗⠚⡀⠀⠘⠒⠒⢆⣀⣀⠐⠂⠚⣀⠀⣈⠓⢻⣧⣾⣿⣿⠟⣫⡴⠖⣛⣋⣛⡛⠢⠙⢿⣷⡀
⠀⠀⣼⣿⣴⡾⠿⠟⣻⣿⣿⣿⣦⣍⢳⡝⢿⣿⣿⡆⢼⠉⠈⢹⡤⠤⡌⠀⠈⣠⠤⢴⠉⠀⠙⠤⢼⣿⣿⡟⣡⠞⣡⣶⣿⣿⣿⡛⠿⠿⣶⣤⣿⣧
⠀⠸⠟⠋⠀⠀⣰⣾⠟⣋⡭⠤⠤⣍⡀⠹⡎⢿⣿⣀⣰⠗⠒⢷⣀⣀⡘⠋⠙⢃⣀⣀⠛⠐⠻⣀⣠⣿⡟⣴⠃⣈⣭⠤⢬⣍⡙⠿⣷⣄⠀⠙⠻⣿
⠀⠀⠀⠀⢀⣾⡟⢡⠞⣡⠖⣛⣓⠶⣍⡳⣄⠘⣿⠁⢉⣤⣤⣜⠁⠈⠱⠦⠴⠋⠁⠉⡦⠤⣴⠁⢈⡿⢁⡴⢚⡥⠖⣛⣓⠶⣝⢷⡘⢿⣧⠀⠀⠈
⠀⠀⠀⠀⣼⡟⢠⢏⣾⣥⠤⢭⣍⡛⢮⡙⣮⠳⣌⠛⠛⣀⣀⡘⠓⠘⢃⣀⣀⡞⠓⠛⣄⣀⣀⠛⠛⣡⢏⡴⢋⡴⢛⣭⡭⠤⣼⣧⢳⡈⢿⣇
⠀⠀⠀⢰⣿⠁⡟⢈⡵⠖⣛⡓⢦⡙⣦⠻⣎⢳⡜⢆⠐⠉⠉⢱⠄⠠⠎⠁⠈⠠⠀⠴⠉⠀⠉⢀⡜⢡⢏⣴⢋⡴⣫⠔⣚⣛⠲⣬⠀⣧⠸⣿⡀
⠀⠀⠀⣼⡏⢸⣧⠏⣰⡿⠟⢿⣦⢹⡌⣦⢻⣧⡹⣎⢧⡀⠐⢣⣄⣀⡌⠀⠘⣠⣀⣠⠋⠀⢠⡞⣴⢣⣾⡏⡾⣱⠋⣾⡿⠻⣷⣌⠳⣼⡀⣿⡇
⠀⠀⠀⣿⡇⢸⠏⣼⡿⠁⠀⠘⣿⡇⢷⢸⡌⣿⣷⡘⣆⢳⡀⢮⠀⠀⡱⠆⠶⠁⠀⠈⠶⢠⠏⡼⢡⣿⣿⢸⢇⡏⣸⡿⠀⠀⠘⣿⣆⢻⡇⢻⡇
⠀⠀⠀⣿⡇⡟⣰⡿⠁⠀⠀⠀⢹⣿⢸⡎⣇⢻⣿⣷⡘⣆⢳⡈⠋⠉⢣⣄⣠⠞⠉⠙⢠⠏⡼⢡⣿⣿⡇⣿⢸⢃⣿⡇⠀⠀⠀⠘⣿⡆⠇⢸⡟
⠀⠀⠀⢹⣇⢠⣿⠃⠀⠀⠀⠀⢸⣿⡄⡇⣿⢸⣿⣿⣷⡘⣎⢣⠀⠰⢆⠀⢀⡰⠄⢀⡏⣼⢡⣿⣿⣿⢃⡇⣿⢸⣿⠀⠀⠀⠀⠀⢹⣿⠀⣿⡇
⠀⠀⠀⠘⣿⣾⡟⠀⠀⠀⠀⠀⠀⣿⡇⣿⢸⡘⣿⣿⣿⣷⠹⡌⣧⠀⡌⠉⠉⢡⠀⡾⣸⢃⣿⣿⣿⣿⢸⡇⡇⣸⣿⠀⠀⠀⠀⠀⠀⣿⣶⡿⠁
⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⣿⣇⢸⢸⡇⣿⣿⣿⣿⣇⢻⡘⡆⠐⠒⠒⠀⣸⢡⠇⣾⣿⣿⣿⡿⢸⢹⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⡎⡇⢿⣿⣿⣿⣿⡎⣧⢹⠀⠤⠤⢠⠇⡞⣸⣿⣿⣿⣿⡇⣿⢸⠁⣿⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⡇⣿⢸⣿⣿⣿⣿⣷⠸⡄⣇⠀⠀⡞⢸⢁⣿⣿⣿⣿⣿⠇⡟⣾⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢿⢹⡌⣿⣿⣿⣿⣿⡇⣧⢹⡀⢰⠇⡏⣼⣿⣿⣿⣿⣿⢸⢇⡏⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠸⡎⣧⢻⣿⣿⣿⣿⣷⢸⡌⡇⣼⢸⢃⣿⣿⣿⣿⣿⠇⡾⣸⢃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢻⡜⣧⠻⣿⣿⣿⣿⡈⡇⣷⡇⣼⢸⣿⣿⣿⣿⢏⡼⣱⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡙⣎⠳⣌⡻⢿⣿⡇⠷⠾⠶⠇⣸⣿⡿⢛⡵⢟⡴⢃⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⡛⢮⣝⡳⠮⣭⡘⣿⡟⢣⡭⠶⢚⣩⠴⢋⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣬⣉⢻⠠⣇⣙⣃⣼⢰⠋⣩⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡘⠷⠬⠭⠭⠥⠞⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣶⣶⣶⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⢀⣤⣀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣴⣿⣿⣿⡆⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠒⠤⣀⣀⣀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡼⠀⠀⠀⣀⣤⡤⠤⠶⠤⣄⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⢺⡆⠀⠀⠀⠀⠀⢨⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠒⠒⠒⠒⢠⡀⠀⠀⠀⠀⠀⢀⡤⠼⠧⠤⠤⠤⠤⠤⠼⠼⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃
⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⢀⣀⡠⠤⠔⣊⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⠀⠐⢬⠭⠉⠉⠭⠭⠁⠤⠐⠂⠉⠀⡂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠘⡄⢀⣀⣀⡀⠤⠤⠀⠐⠒⠈⢹⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⢀⣀⣀⣀⠀⠻⣃⣟⠘⠃⠀⣠⠒⠢⠤⠭⠍⠉⠐⢲⠋⡇
⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⣤⣦⣄⠀⠀⠀⢸⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠐⠒⠒⠒⠒⠒⠐⠀⠐⠃⠀⠀⡇⠀⠀⠢⠠⠐⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⢱⠀⠀⠰⣿⢿⣽⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⢀⡀⠀⠠⠤⠤⠄⠚⠃⢰
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⠟⠋⢀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣔⡉⣑⢏⡠⢶⠀⠀⠀⠀⠘⠁⢠⢰⡴⠄⠶⠦⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠐⢖⠒⠒⠂⠈⠉⠀⠀⠀⡄⠀⠀⠀⡠⠠⠤⢊⠭⠠⠕⠀⣈⠔⠨⠥⠄⠒⠤⠀⠀⠀⠀⢰⣈⡡⡀⠤⠤⠤⠤⠒⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⣀⡠⠄⠊⠀⠀⠀⠀⡗⢒⡒⢁⠔⠒⠊⠀⠀⠀⠀⣀⠀⠀⡀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢰⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠂⠑⢊⣐⢂⡮⠭⠱⢞⢄⡨⠮⡀⢴⠀⠀⠀⠀⠆⠀⠐⠒⠂⠀⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠐⠠⣀⠀⠀⠀⠀⠀⢸⣁⢉⡈⡡⠤⠤⠊⠑⠒⠉⠑⠀⠒⠢⠼⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠤⡐⠜⠋⠁
⠀⠀⠀⠀⢀⠴⠈⠠⠤⠤⠄⠤⠤⠤⠤⠄⠤⠤⠤⠬⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠧⠤⠶⡈⢁⡀
⠀⠀⠀⠀⠘⣷⣮⡴⡤⠰⢶⣤⣤⣄⣄⣠⣡⣤⣐⣲⣶⠃⠀⠀⠀⠀⠀⠀⠀⣔⠈⡡⠄⠰⡀⠠⡤⢀⣐⠢⠤⣄⡉⢲⡄
⠀⠀⠀⠀⠀⢏⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⢋⡁⠃⠀⠀⠀⠀⠀⠀⠀⢙⠛⠠⠬⢵⣏⣘⣏⣁⣬⣡⠦⠶⠚⢛⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⣀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠷⢶⣤⡀⠀⠀⢀⣤⡶⠾⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠴⣶⡄⠀⠀⠀⠀⠀⠀⢠⠶⣦⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⢿⠿⠃⠀⠀⠀⠀⠀⠀⠘⠿⡿⠃⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠛⢛⣁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⣿⣿⡇⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄
⠀⠀⠀⠀⢃⣑⡒⢂⡀⠀⠀⠀⠀⠀⠀⣐⣊⣡⡞⠀⠀⠀⠀⢳⡾⠶⣦⢀⠀⠀⠀⠀⠀⣀⠴⠂⣳⡶⠁
⠀⠀⠀⠀⣜⠛⠿⠿⢿⠷⠾⣿⡾⠿⠿⠿⠛⠋⡱⠀⠀⠀⠀⢜⡛⠷⠾⠿⡿⠶⣤⡶⠿⠿⠿⠛⠛⢩⠆
⠀⠀⠀⠀⠸⡑⠒⠓⠒⠲⠤⠴⠦⠤⠚⠓⠊⣩⠇⠀⠀⠀⠀⠘⣝⠒⠓⠒⠒⠤⠤⠦⠤⠒⠛⠚⢉⠏
⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⠤⠤⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⠤⠤⠖⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠄⠒⠒⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠳⣖⠟⠴⢄⣐⠒⠒⠒⢒⣂⠶⠊⣰⣶⠃
⠀⠀⠀⠀⢮⣵⡦⣤⠄⠀⠀⠀⠀⠀⠠⡤⠄⢮⣭⠂⠀⠀⠀⢰⣉⠛⠛⠻⠿⠿⠶⠶⠿⠿⠛⠛⢛⣁⠇
⠀⠀⠀⠀⡸⠷⣤⣼⣿⣶⣦⣀⣤⣶⣷⣷⠶⠿⢓⡄⠀⠀⠀⣔⡻⠿⣿⣷⣶⣶⣴⣶⣦⣾⣿⣿⠿⢛⡄
⠀⠀⠀⠀⠸⣷⣤⣶⣤⣤⣀⣀⣄⣀⣴⣶⣴⣶⡎⠀⠀⠀⠀⠸⣤⣤⣁⣀⡠⣈⠉⢉⣠⣔⣠⣬⣤⣾
⠀⠀⠀⠀⠸⡀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⠇⠀⠀⠀⠀⠀⢇⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⡜
⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⠤⠤⠤⠤⠤⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣤⡴⢖⣚⣛⣉⣉⣉⣙⡓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⣠⣴⠟⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣴⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡟
⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠟⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢋
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣫⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⣠⡾⠁
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣻⣼⠟⠁⢀⣴⣶⣶⣶⣦⣄⠀⢰⡏⢠⣾⡿⠁⣠⣴⣶⣿⣿⣿⣷⣦
⢀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⣫⣾⠟⠁⠀⢀⣿⣿⡿⠛⠛⠿⣿⣷⡈⢠⡿⠋⣠⣾⣿⣿⣿⠟⠉⠀⠀⠉
⣼⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣵⡿⠋⠁⠀⠀⠀⠈⢿⣿⣧⣠⠀⠀⢹⣿⡇⠘⢁⣾⣿⣿⣿⠟⠁
⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣸⡟⠀⣠⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣀⣾⣿⣿⣿⠟⠁⣀⣤⡴⠶⣒⣀⣀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢟⣯⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣠⣴⣾⣿⡿⠿⠋⣡⣴⣿⠟⠉⠐⠊⠉⠉⢙⣿
⠈⢿⣿⣿⡿⣟⣋⣭⡶⢟⣻⣵⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠩⢭⣤⣴⡾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠈⡿⠿⠿⣛⣯⡵⠞⠛⣉⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠉⠛⢋⡩⣴⣶⡿⠿⠛⠛⣩⣟⠛⢁⣤⠖⠀⣠⡞⠀⢠⡾⠠⠀⣶⠀⠈⢯⡉⠉⢿⡟⠿⠿⢷⣦⣤⡀
⠀⠀⠀⠀⣏⢼⡋⠀⠀⣠⡴⠛⠁⢀⡴⠟⠁⠀⣴⠏⠀⠀⣼⠇⠀⠀⣿⡅⠀⠈⢷⡀⠀⠙⣦⡀⠀⠈⠙⢯⡂
⠀⠀⠀⠀⠹⣾⣿⣴⣿⣁⡀⣠⡼⠋⠁⠀⢠⡾⠋⠀⠀⢰⣿⠀⠀⠀⢹⡇⠀⠀⠘⣷⡄⠀⠈⢻⣦⣠⣴⣿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣦⣤⣾⣧⣤⣤⣤⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⡿⠟⢛⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣭⣽⣛⣛⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⣾⡇⢸⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡾
⠀⠀⠀⠀⠀⠀⠹⣎⢿⣿⣿⡉⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣿⣿⣦⣬⣭⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠈⠉⠉⢹⣿⡏⠉⠉⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣤⣶⣶⣶⣿⣿⣇⣿⣿⣸⣿⣿⣿⣷⣶⣶⣦⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠈⠻⠿⣿⣿⣛⣿⣿⢻⣛⣻⣛⠿⠍⠁⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡅

⠀⠀⠀⠀⠀⢀⡀⢠⠄⣠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣼⣱⣿⣆⠫⣆⠀⠀⠀⣰⣿⣿⢦⡀⠀⠀⢀⡾⢡⡀⠀⠀⠀⣠⣾⠆⠀⠀⠀⣠⡾⡀
⠀⠀⠀⠀⢿⡿⣮⡈⡼⢢⢟⡆⠀⠰⣏⡻⣴⡾⡷⠀⠀⢼⠿⣆⣿⠀⠀⠘⢿⣏⣠⠇⠀⠀⢿⡱⢹⠆
⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⢀⡖⣩⣦⣭⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⢀⣹⣆⢾⡄
⠀⠀⠀⠀⠈⢰⣿⣿⣿⣗⠘⠀⠀⠀⠀⠀⢀⣠⣾⣟⣿⣦⣀⠀⠀⠀⠀⠀⠀⢠⣿⢈⡸⢿⢻⢸⣷⣠
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⣰⣿⡿⣿⡿⡿⣿⣿⣷⠀⠀⢀⣀⢀⣟⣻⣎⣻⣆⣾⣾⣹⣟⡁⢀⡀
⠀⠀⠀⠐⣒⠀⠀⠀⠀⠉⣙⣓⠀⠀⠀⣿⣯⡇⢺⡇⢸⢱⢸⣿⡇⠀⠀⠘⠻⡍⢿⢹⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣷⣧⣵⣯⣜⠎⡰⣿⠃⠀⠀⠀⠀⠙⢮⣣⣻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠤⠠⠩⠉⠉⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢈⠟⠉⠉⠉⠛⡃
⠀⠀⠀⠀⠀⢰⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⡜⠒⠒⠲⠶⠒⢳
⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠠⢤⣿⢾⣿⣦⠄⠀⠀⠀⠀⠀⠀⢠⠄⠐⠀⠠⡀⠀⠀⠀⠀⢰⡉⢹⡆⠄⠀⠀⠀⠄⠀⠸⣄
⠀⠀⠀⠀⠀⠈⡿⠿⢿⠁⠀⠀⠀⠀⠀⣠⠔⣡⣶⡶⢶⣦⡈⠢⡀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⡆⠀⠰⢱⣿⡍⠀⠀⢰⠀⠀⢘⠡⣴⣿⣿⣤⣼⣿⣿⣲⠉⠂⠀⠀⠀⠀⠠⡀⢸⣭⢀⣤⡀
⠀⠀⠀⠣⢠⣃⡈⠀⣉⣻⡇⠜⠀⠀⠲⣄⠙⣿⡏⠏⠻⣻⡿⢚⡴⠂⠀⢀⡀⠀⣀⣙⢦⣥⢚⣋⠀⠀⣀
⠀⠀⠀⢰⣰⣮⡅⠄⢸⣅⣦⡦⠀⠀⠀⠈⠀⣈⠛⠛⠛⢋⡠⠊⠀⠀⠀⠈⠉⠉⠉⣩⠞⡟⢺⣍⠉⠉⠉
⠀⠀⠀⠈⠀⠒⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠇⠀⠙⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠶⠶⠦⠤⣤⣄⣀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠴⠀⢀⠀⠒⠀⣀⠀⠶⠀⠈⡙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⠘⠀⠀⠒⠀⠀⠠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣶⣶⠬⢭⣙⣓⠒⠒⠶⠶⠶⠦⠤⠤⠤⠤⠴⠶⠶⠖⢒⣛⠭⠵⢒⡶⣶⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⣙⡒⠒⣛⣉⣳⣶⣤⣀⠀⢀⡀⢀⡀⢀⣠⣶⣏⣉⣉⣉⣩⣥⣾⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣦⣍⣡⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠍⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣆⠈⠀⢀⡀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣀⠠⡤⢀⣤⣄⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣀⣚⣤⣴⣦⣤⣀⣤⣾⣿⣿⣿⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠛⠉⠉



⣿⣿⢛⢿⠛⡟⣿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⢚⠛⡦
⠀⠀⠀⠀⠀⠀⠎⠉⠉⠙⠢⢄⣀⣀⣀⣀⠀⠀⠀⠀⢀⠤⠚⠉⠐⠄⠠⠀⢀⡎
⠀⠀⠀⠀⢀⡴⠀⠀⠀⣠⡇⠀⠃⠱⠀⠈⢧⠀⡠⠚⠉⠐⠈⠀⡄⠁⠀⢀⡞
⠀⠀⠀⠀⠏⢀⣠⠞⠉⢩⠃⠀⠀⠀⠀⢀⠼⠋⠀⠀⡀⠀⠑⠊⠀⠀⣐⣏⡠⠤⠒⠊⠙⠦⠒⠒⢄
⠀⠀⠀⢰⡴⠁⠀⠀⢠⠃⠀⠀⠀⢀⡴⠋⡀⢀⠨⠀⠤⠈⠠⠀⢐⡰⠋⠀⠀⠀⡠⣤⠶⠒⠒⠒⠺⠒⣄
⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⢀⠄⡠⠎⠀⠀⠈⢈⡠⠁⠀⠂⠀⣠⠎⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣆⠜⠁⠀⠀⢀⡐⠂⠀⠀⢀⣠⣜⡡⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠏⠀⠀⠀⠠⠂⠀⢀⣠⠴⠚⠉⠁⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⢠⠋⠀⡏⠠⠀⠀⠀⣀⡤⠚⠋⣁⣀⣀⣠⣴⣞⣉⡤⠤⠤⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡌⠀⢸⠃⠀⣠⢴⣊⠥⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠒⠒⢒⠦⠴⢄
⠀⠀⠀⢀⣀⣴⣡⣆⣧⡤⠞⢋⣁⣠⠤⠴⠖⠒⠚⠛⠋⠛⠙⠙⠓⠒⠒⠶⠤⠤⠤⠤⠤⢤⣀⣸⠀⣄⣈
⠀⠛⠛⠻⠲⠶⡦⠤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⣠⠖⠒⠛⠉
⠀⠀⠀⠀⠀⠀⢊⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠤⠒⠋⠁⢀⣀⠴⠚⠁
⠀⠀⠀⢈⣤⣤⡵⠊⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠋⠉⢁⣀⣠⠤⠖⠊⠉
⠀⠀⠀⠀⢀⡤⢭⡹⠋⣠⠤⠖⠛⠓⠒⠒⠒⠶⠶⠖⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢾⢉⣤⣴⣷⣶⣶⣶⣤⣀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣭⣽⣥⣄⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⢄⣉⣠⠆⠀⠀⠀⠀⠀⠀⠀⣾⣧⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⢋⡅⢠⡆⢸⣾⠃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⢚⣋⣉⣀⣀⢶⣾⢿⠿⡷⢾⡿⢿⣿⣂⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⢖⡞⣻⠏⡹⠋⡽⢋⡿⢛⡶⢦⣤⡆
⠀⠀⠀⠀⠈⢿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⣿⣒⣷⠾⠷⠾⠴⠾⢶⣟⣺⡏⠙⠃
⠀⠀⠀⠀⠀⠈⢷⣌⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠿⠿⠿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠙⠛⢛⡛⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠸⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣷⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣸⡿⠉⠉⠉⠉⠉⠉⠉⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡶⢲⢞⡿⢻⣿⡳⢲⠖⣾⣧⡀
⠀⠀⠀⠀⠀⣿⣛⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠶⠧⢮⣴⣥⣿⡴⠧⠾⠖⢿⡁
⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣠⠔⠊⠁⠀⠉⠑⢦⡀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣀⣀⡯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣧⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢠⠞⠁⠸⣆⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠔⠉⣠⡟⠀⣆⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠈⠓⠶⣄⠙⢷⣄⠀⠀⠀⠀⡠⠐⢁⣠⣶⠟⠋⢀⣼⠇⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠈⢀⠀⢀⠀⠉⠙⠳⣎⠳⣆⢀⣉⡵⠞⠋⢁⣡⠴⠞⠋⠁⠈⣠⢏⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠈⠙⠉⠀⠀⣰⠟⠁⠀⠀⠀⠀⣰⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⣀⡤⠖⠛⠁⠀⠀⠀⠁⠀⣼⣳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⠀⠀⠀⠀⠀⢀⡾⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣧⣄⣤⣗⣉⠙⠛⡛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠻⠾⢿⣦⣴⣖⣭⠻⢻⡲⢦⢤⣄⣄⣀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢤⣬⣆⡐⠈⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠿⠛

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠉⠉⠉⠉⠙⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⢀⡴⠞⠲⣄⡀⢀⣴⠖⠲⣦⡀⢀⣠⠖⠳⢦⡀⠀⣠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠙⠉⠀⠀⠀⠈⠙⠉⠁⠀⠀⠈⠉⠋⠁⠀⠀⠀⠉⠋⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠉⠉⢩⣍⣉⠉⠉⠉⠉⢩⣍⣉⠉⠉⠉⠉⠉⢉⣩⠉⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠒⠛⠋⠙⠓⠶⢤⠴⠋⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣤⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⣀⣀⠤⠄⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡔⢲⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠓⠲⢄⠀⡀⠤⠒⠒⡲⠦⣀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠋⠀⠑⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⠁⠀⠀⠀⠀⠀⠘⣦⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢠⠀⠀⠀⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠠⠀⠛⠺⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣀⡀⣀⡀⠻⠗⠀⣣⠈⠀⠀⠀⠑⠄⣀⢀⠀⠀⠀⠀⠀⣴⠋⠊⢉⠉⠣⣀⠀⠀⡀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⠁⣠⢄⠹⢶⠤⠾⠃⠦⡀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣰⣾⡀⠀⠀⠈⠀⠀⡤⠑⠛⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠠⣀⡩⠞⣼⠁⠀⣠⠀⠘⢂⡤⠐⠒⠀⠐⠒⠠⢄⣹⡞⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡠⠄⠠⣄⠸⡀⣶⢌⢁⣠⡞⠉⣠⠀⠐⠀⡒⠀⠀⠀⠉⢧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢸⡆⢧⣅⣀⢀⡀⠀⠀⠈⠣⠈⠀⠁⠔⠁⠀⠀⠈⣳⣦⠤⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠥⠎⠀⡟⠁⠀⠈⡇⠀⣀⡈⠁⠀⠀⠀⠐⢂⠨⠓⠝⠋⠀⠀⠀⠀⢘⠀⡠⠂⠀⠀⠉⠒⠤⠤⣀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⣇⠸⠖⠀⣣⠀⠀⠤⠂⠀⡐⠠⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠾⠀⠓⠒⠒⠙⢄⠀⢂⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⣡⠀⠀⠀⠤⠐⢞⠈⠑⠤⣀⣀⠀⣀⣳⡀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢿⠁⠁⠀⠠⣄⠀⠀⠀⠀⠀⢨⠀⠀⠈⠢⠵⠀⣠⣄⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⡀⠀⠉⠉⠳⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠈⠐⠂⢤⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⢀⣀⠤⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠐⢄⣀⣀⣀⠠⠜⢗⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣁⠠⠊⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⣠⠴⠖⠒⠉⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠁



⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣴⣿⣷⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⣟⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠛⠉⠀⠀⠀⠀⢀⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢀⣀⣀⠤⠔⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡭⢝⣛⣳⣬⣽⣿⣿⣯⣴⣾⣿⣯⣽⣒⣲⡦⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⠽⣗⣾⡿⣿⣷⣾⡿⣿⣷⣺⡽⣿⣷⣺⡿⠽⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣭⣿⣿⣯⣭⣵⣿⣯⣭⣽⣶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⠻⠿⣿⠿⠟⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⣤⣿⣤⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠙⠓⠦⣤⣿⡤⠶⠛⠉⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠠⣸⣹⠇⠀⠀⠀⠀⠀⢀⣴⡧⠁⠸⣿⣎⠈⣿⡟⣧⠘⣷⡿⣶⣞⠀⠁⡚⣸⢻⣿⣿⣿⣿⡟
⠀⠀⠀⢀⠀⣠⣤⣤⠹⣿⣼⣿⣦⣰⣾⣶⣿⠂⠀⠀⠀⢻⣿⣷⠘⠏⣿⡎⣿⡇⠈⠛⢅⣿⡇⡿⣿⢿⣿⣿⡿⢦⢀⡀⠀⡀⣨
⠀⢀⣠⣾⢼⣿⣿⣿⠑⠜⢿⣿⣻⡙⢻⣿⠎⠂⠀⠀⠀⢸⠘⣿⣧⣤⢻⡷⣿⠂⠀⠀⢠⣿⢫⢷⣿⣿⣿⣿⠁⠀⢻⣷⡿⣫⠟
⣀⢀⢙⣽⣼⣿⣿⣿⡧⢀⣜⣿⡯⢿⣧⡈⠲⣤⣿⣆⠀⠘⣇⠘⢿⣿⢸⣟⣿⠀⠀⢀⠟⣿⣾⣺⡏⣿⣿⡏⠀⢼⠟⢉⠿⣷⣀
⢻⠟⣛⣩⣿⡿⣿⣿⢿⠀⢿⡾⣿⣌⣿⣷⣄⠈⠛⢿⣆⠀⢻⣤⡈⣿⣿⡇⣿⡇⠀⡼⠀⣿⣿⡟⣸⣿⠟⣒⢷⣇⡲⠁⠀⠀⠑
⣴⢺⠟⠉⠀⣿⢿⣸⡌⠃⠀⠀⠈⠙⣏⣿⣿⣷⡄⠀⠉⢳⡈⣿⣧⡈⣿⡇⣿⡇⣰⠃⢰⣿⡿⣱⣿⣿⣿⣾⣽⣿⣯⣐⣠⣀
⠈⠪⠀⢀⠀⣿⡘⣯⢧⠁⠋⣀⠠⡑⡜⣞⣿⣿⣿⡀⠀⠀⠁⠘⣿⣷⣿⣇⣿⣇⡟⠀⣸⡿⢀⣿⢷⣿⣿⣿⢋⣰⠄⣀⠉⠻⣆
⠀⠀⠀⡜⠀⢸⣷⣿⡏⣧⢰⠸⡌⢧⢱⠘⣼⣿⣿⡇⡄⠀⠀⠀⠘⢿⣿⡿⠹⣿⡇⠀⣽⢣⣿⡟⣹⣿⣿⢏⣾⢇⣾⣿⠀⠀⡼
⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⢘⡀⢫⠉⡌⢧⢹⣞⣿⣧⣿⡒⢠⣶⣶⣤⣿⣿⣿⢿⠇⠀⡟⡼⢏⡸⣿⣿⣏⣼⣏⠌⣿⣿⡀⡰⠁
⠀⠀⠀⠀⠀⠐⠋⣵⣿⣿⣇⢹⡈⡧⠼⡽⣆⢽⡞⣿⣿⣿⣿⡛⠯⠟⢛⣛⡛⠛⠃⠀⢬⣣⣼⣿⣿⣿⣿⡟⡜⠀⡿⠫⢠⠇
⠀⠀⢀⣴⠅⠀⡼⡿⣿⣿⣿⡂⠳⢘⡥⢪⠹⣊⣿⢻⣿⣻⣿⣧⠀⠀⠀⠨⣻⣿⠙⣳⡶⢿⣿⠿⢿⣿⢋⠎⠀⠀⣠⠀⡘
⠀⢰⣯⣿⢀⡾⠀⢻⡍⠟⣿⣷⡈⠄⢻⠄⠣⢰⡸⡿⣿⣟⢿⣿⡆⠀⠀⢈⣿⣿⡀⢺⡏⣾⣿⣷⣷⣵⡁⠀⣠⣾⢯⠀⡇
⠀⢸⣿⡏⣗⡇⠀⠈⣟⡜⠸⣿⣷⢩⠄⣧⠘⡭⢆⢿⢻⣿⣸⣿⣿⡀⠀⠀⣾⣿⡐⡸⣡⣿⣿⡿⠃⠈⢓⣻⣿⣿⣧⢻⠁
⠀⢸⣿⣷⣿⡇⠀⠀⠸⣷⠐⢹⣿⡎⠥⠘⡥⢻⠵⣊⢿⣿⣿⣿⣿⡇⠀⠀⢾⣿⣷⣃⣿⢿⠟⠁⠀⢠⣿⣿⣿⣏⢾⣿⠃
⠀⠐⣿⣿⣿⡇⠀⠀⠀⢹⣷⡀⢿⣷⠩⡏⢷⠈⢧⠵⡊⢿⣿⣿⣿⣿⠀⠀⡬⡿⢛⣫⠔⠁⠀⠀⢀⣾⣿⣿⣿⣟⣾⡏
⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⢻⣧⠸⣿⣇⠽⠄⢏⠉⡧⢒⡨⣿⣿⣿⣿⡇⠀⠈⣱⣿⠇⠀⠀⠀⠀⠜⡟⣱⡿⠭⡎⣼⣧⣴⠃
⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠈⢿⣵⡽⣿⣆⢯⠽⡇⢹⡄⢗⠹⣿⣿⣿⣷⠀⢀⣿⣿⠀⠀⠀⢀⠆⠀⢠⡏⠀⠀⣰⣿⣿⣿⣶⠞
⠀⠀⠀⣿⣿⢹⠀⠀⠀⠀⠀⠀⢻⣾⡝⣷⡌⢧⠸⡀⢧⡘⡏⣫⣿⣿⣿⣇⣰⣿⡇⠀⠀⠀⠂⠀⢔⠎⠀⠀⣴⡟⠁⢈⠞⠁
⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡭⢧⢻⠈⣇⠹⡺⣿⣿⣿⣿⣼⣿⡇⠀⠀⣰⣴⣿⣿⡣⢀⣼⣿⢇⡴⠃
⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣽⣂⢣⣸⡎⢣⣿⣿⣿⣿⣿⣿⠇⠀⣬⣿⣿⣿⣷⣷⣿⣿⣿⡿⠁
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣿⣮⡇⢽⣸⢽⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⡿⠁
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣝⣧⢻⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⠋⡴⠁
⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⠙⢹⠁⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠏⠉⠙⠃⠐⠀⠀⠂⠀⢀⠉⠉⢉⠓⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⠉⠀⠂⠀⠀⠀⠐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢒⡫⣚⠄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⢏⠉⠑⢒⡲⡤⠤⠤⢤⣄⣄⣀⣀⣀⣀⣀⠤⣤⣤⠤⢤⣶⣒⣪⣭⣋⠡⠭⠍⠓⠉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠪⢷⣮⣭⣥⣤⣽⣿⠶⠿⠟⢻⡙⠳⠤⠤⠤⠤⠷⢄⣀⣉⣀⣁⣀⣀⣠⡤⠤⠴⠒⠚⠉⣇
⠀⠀⠀⠀⠀⠀⣀⠀⢳⠚⠉⠉⠉⠉⠓⠺⢖⡢⢄⡀⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉⠉⢀⣄⣐⣂⣐⣒⣒⣒⣒⣂⣀⣸
⠀⠀⠀⠀⠀⠀⡏⠉⠺⣄⠀⠀⠀⠀⠀⠀⠀⠉⠢⣍⠢⡀⠀⠀⠀⣀⠠⣀⡤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢥
⠀⠀⠀⠀⠀⠀⣹⠄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⢄⡠⢊⡵⠊⠁⠀⠀⠀⠐⠊⢀⣉⣁⠔⠒⠲⠤⣀⡠⠇⠈⡇
⠀⠀⠀⠀⠀⠰⠧⠤⢤⡀⠈⠳⠤⢶⣤⣤⣤⣀⡀⠀⣀⠳⢤⠔⠋⠀⢀⣀⡤⢄⡀⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⢤⡀⠀⠀⠀⠀⠀⢀⣉⠉⠉⠉⠉⠉⠙⢋⣉⡴⠢⣄⣩⣀⣀⢀⣠⠖⠒⠤⢤⠤⠤⠤⢤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠓⠤⠖⠒⠦⠔⠋⠀⠉⠙⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠠⠾⣿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⢢⡀
⠀⠀⠀⠀⠀⣀⣠⣴⡿⢠⣿⠇⠀⠠⢶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠀⠀⢀⠇⠀⠠⢶⠒⠦⢄
⠀⠀⠀⣠⣿⣿⡏⠀⠐⢿⣯⣤⣤⣴⠿⢹⡿⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠋⠀⠀⠀⠰⠯⠤⠤⠐⠉⠀⠀⠘⠄⡀
⢀⣠⣾⣿⣦⣿⣶⣶⣶⣷⡟⣳⣾⣿⣶⣶⣰⣾⣮⠇⣶⣠⣠⡀⢀⣀⢀⠋⠀⠀⠠⠒⠂⠐⠐⠠⠄⠀⠀⠀⠐⠀⢀⠅⠀⣀⣀
⠀⠈⡟⠙⠻⣿⡿⠟⠛⠛⠃⠛⠻⠿⠿⠿⠿⣿⠏⠉⣿⠳⠴⠃⠀⠈⠎⠐⠒⠀⠀⠂⠂⠀⠂⠐⠀⠠⠀⠠⠤⡀⠈⠈⠞⠁⠤
⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⣿⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣤⡀⣿⠀⠀⠀⠀⠀⢐⠀⠀⡤⠆⠨⡁⠀⠀⠐⣂⡉⣭⠙⠃⠐⠠⡀⠅
⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿⡿⢿⣿⣷⠏⠀⠀⠀⠀⠀⠐⢦⡈⠤⣄⠀⢅⠤⠀⠀⠀⠊⡀⢂⠀⠀⠆⢰
⠀⠀⠈⠙⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠌⠑⠪⠄⠀⣀⣁⣀⣀⣀⡁⠤⠥⠒⡝⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⢀⠄⠀⠀⠀⡀⠀⡠⠊
⠀⠀⠀⠀⠀⢠⣯⡽⠿⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡙⠲⢼⢨⣤⡤⢴⣶⡋
⠀⠀⠀⠀⠀⣾⠋⠛⠛⠾⣿⢿⠟⠛⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠐⠀⠸⢸⠭⠅⠘⠀⠁⣆
⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣿⢸⡆⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢆
⠀⠀⠀⢰⡏⠀⠀⠀⠀⢸⡇⠈⠁⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡆
⠀⠄⠠⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠠⢈⠓⡄⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⠀⢴⠿⣶⡀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⢠⡏⠼⣿⣿⣳⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣿⣿⡆⠁⡽⣤⣼⣽⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠇⣿⣿⠃⢘⠃⢀⣐⣗⣲⠺⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⠘⣿⡏⣤⠈⡃⢸⠁⠭⠽⣯⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢆⠀⠀⠐⣿⠧⠬⢁⡍⢉⣁⣭⣉⣟⣛⡺⣿⡇⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠡⡀⠀⠛⠐⠓⠀⠃⠐⠖⠺⡴⠧⣽⢍⣻⡇⠀⠀⠀⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⣄⠀⢘⡃⣘⠁⢐⣋⣉⡿⠲⠷⠶⢾⠀⠀⠀⣠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⢨⡅⣨⠀⢈⣁⣀⣋⣈⣛⡛⢻⠀⠀⣰⣿⢿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⢠⡀⢴⠀⢠⡅⢨⣏⣉⣉⣉⣛⠀⣰⣿⡏⣼⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡴⠂⠶⠀⠰⡦⢤⣍⣤⣽⣩⣉⣳⣿⣿⠙⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠙⠀⠐⠂⠶⠦⠤⣼⠤⢯⣿⣿⣏⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠀⢚⠂⠒⠃⠐⠾⠖⠦⣿⣿⣿⣆⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⣉⣉⣏⣙⣺⣛⣟⣿⣿⣿⣿⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠄⢠⣯⣭⣽⣭⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⢴⠀⠰⡶⠶⢶⠶⡿⣿⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⢸⡇⠈⣟⢚⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢸⡇⠠⠧⢤⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢸⡇⢹⡏⣽⣷⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⡇⢸⣃⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣷⢸⣷⡾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣷⣿⡇⢿⠛⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠸⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠇

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣀⣀⣀⣠⣤⣤⠴⠶⠶⠗⠛⠛⠛⠛⠛⠉⠛⠉⢙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⡿⢛⡉⠩⢥⠀⠀⠉⠁⠐⠂⠀⠒⣂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡠⠊⠄⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢃⣀⡀⠠⠀⠐⠀⠉⠁⢀⣀⠀⠤⠀⠀⠀⠀⠀⠉⠭⠁⠀⣴⣿⣿⣿⠀⠀⠀⠀⢀⠔⠀⢠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠂⠠⠤⠀⠀⠀⠀⠈⠉⠀⢀⡀⠠⠄⠀⠀⠂⠠⠤⠄⠀⠀⠐⢩⣭⣿⠀⠀⠀⡰⠋⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡶⠀⣉⡁⠀⠀⠉⠉⠄⠀⠀⠀⢀⣐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⠀⠀⣀⠠⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣋⢉⡀⠀⠀⠤⠄⠀⠀⠤⣀⠡⠤⠄⠀⠈⠉⠐⠒⠒⠀⠀⢻⣿⣿⡇⢀⠄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠉⠐⠂⣀⠀⠀⠉⠀⠀⠐⠀⠀⠀⣉⣀⣠⣔⣂⠤⠒⠤⢢⣰⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⡮⠉⣀⣀⠀⠀⠀⣐⣂⣐⣤⣄⠔⠲⢭⣶⣬⡳⠯⣔⠊⠀⣩⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣴⣤⣾⣷⣶⣿⣿⡿⠿⠛⠛⠛⠛⠲⢦⣼⡄⠀⢀⢀⣿⣤⣾⡿⢃⣿⣿⣿⣷⣖⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⢾⣿⣿⣿⣭⣿⢶⡶⣿⣿⡿⣽⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣟⢟⣿⣿⡿⣿⣷⣶⠶⡶⣖⣺⣺⣭⣿⣷⣾⣿⣟⢟⡿⣻⣟⣿⡷⣜⡫⠿⠛⠉⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣷⣝⡻⣽⡶⢶⠾⣿⢿⡿⣿⢿⣿⣿⣿⢿⠿⢏⣛⠿⠍⠚⠊⠁⠀⠀⢀⡶⣶⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡇⠇⡏⣿⣮⡙⢾⡑⠮⢷⣙⠯⠏⠝⠉⠐⠃⠈⠀⠀⣀⣶⣶⠀⠘⠃⠀⠘⢷⡿⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣦⢇⡌⡏⡟⣾⡟⠉⣀⣄⣀⠀⣴⣻⡆⠀⠘⠃⠀⠘⠿⠏⢀⠀⠄⠄⢴⣖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠓⠧⣀⢿⡇⠀⣿⣼⣿⠀⠙⠛⠁⢀⣀⠠⠄⢲⣶⠁⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡽⠀⠀⠀⠀⠈⠹⡇⠀⣈⡙⠥⠐⠂⠀⠈⠀⠀⠀⠀⣀⣿⣆⡀⠀⠀⠀⠀⢻⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⣀⡤⠤⠖⠚⠋⠉⢹⣿⠐⠍⠀⢀⠠⢸⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⠀⠀⠀⠀⠀⢀⣀⡄⣷⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢈⠐⢗⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣧⠴⠖⠒⠋⠉⠉⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣃⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠭⣒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠒⠈⠁⠈⣿⡄⠀⠀⠀⠀⠀⠘⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠉⠒⠤⣁⠒⠄⣴⣠⡠⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠉⠉⠀⠐⠒⠒⠂⠠⠤⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁
⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣆⣠⠃
⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡟
⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢡⠞⠙⠒⠦⣄⡀
⠀⠀⡟⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⡰⠋⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠣⣀⡀⠀⠀⠈⠉⠀⠒⠲⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡔⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⢀⠟⠑⠢⢄⣀⣀⡀⣀⠀⠀⠀⠀⠀⠉⠉⠐⠢⠄⠄⠀⣀⣀⠠⠊⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠓⣄⡀⠀⠀⠀⠀⠉⠉⠉⠁⠶⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⣠⡾⢽
⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠲⠶⠖⠒⣉⣀⡤⠤⠤⠀⠀⠀⠀⠀⢀⠞⣿⡯⡅⠿⡿
⠀⠀⠀⠀⠐⣄⠀⠄⡄⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⣀⠀⠀⠀⠀⢀⡠⠖⠁⢀⡿⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠑⢄⡁⠠⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⠂⠀⠀⢀⣀⠤⠔⢊⠁⡐⡀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⡇⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢊⢩⠀⠀⠀⠀⢄⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢇⠀⠀⠀⠀⠈⠑⠒⠒⠒⠉⠁⠠⣧⠘⡈⠀⣃⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⡀⢀⠀⠰⠀⠸⠀⣁⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⠼⢤⡤⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠊⠉⠉⠀⠀⠀⠈⠉⠉⠐⠒⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡠⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⢉⡀
⠀⠀⠀⠀⣠⠾⣅⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢰⠖⠋⠀⣠⢾⠃
⠀⠀⠀⢰⣇⠀⠙⣌⠳⣦⡀⠀⣀⢴⡾⢉⠛⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⢶⠗⠒⡷⠒⣳⠿⣷⡟
⠀⠀⠀⠀⠛⠷⢶⣬⣵⢦⣭⣟⡋⠀⠤⣤⣷⡀⠘⡏⠓⠒⠒⠲⣤⣤⣠⠞⣹⠃⠀⡀⠁⢀⡴⠣⡎⢉⡴⣘⡅
⠀⠀⠀⠀⠀⠀⢮⠑⠻⡫⢭⡛⠒⣦⢾⡶⠆⣴⣤⡟⠤⠀⠰⣟⣋⡉⣉⡿⠥⠠⠴⠛⣫⣟⣒⢒⣛⠭⠎⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣸⣷⣄⡈⠑⠒⠒⠒⠛⠥⠆⣺⣷⣕⠦⢲⡀⢲⠌⡻⠥⠤⢦⣶⣒⠝⠀⠀⠀⠀⠀⠀⣀⣴⠿⢿⡄
⠀⠀⠀⢀⢴⡞⢷⡹⡿⣿⣗⣦⣄⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠐⠒⠀⠀⠀⠀⢀⣀⠠⠤⢒⣾⠿⢤⣀⣼⠷
⠀⠀⠀⣯⡈⢧⣴⠑⡌⠐⠉⠙⠿⢤⡙⢿⣶⣒⣒⣤⣤⣤⡤⠤⠤⠒⢒⣒⣻⠋⠭⢿⡿⢶⡴⠯⠑⠉⠀⣀⣬⠟
⠀⠀⠀⠈⠉⢿⡹⣄⣈⢒⣒⢒⣤⣀⠈⠙⠦⣍⠛⠋⠉⠀⢹⠭⢤⠦⠛⠉⠉⠉⠁⠁⠁⠀⣀⣠⣴⣖⠚⣡⡞
⠀⠀⠀⠀⠀⠀⢷⣀⣩⠞⠉⠉⠻⣙⠒⠶⣅⡢⢍⣒⣤⣰⢏⣀⡵⠋⢉⠉⣑⡷⠳⢦⡖⠉⠡⠋⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠐⠙⠷⣄⡀⠀⢀⡾⠞⠋⠉⠉⠉⠉⠁⠒⠛⠈⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠂⠀⠤⠄⠤⠀⠀⠀⠀⠀⠄⠤⠄⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣌⡷⢆⠁⠄⣸⣽⢿⡏⠙⠉⠙⠂⠠⠄⠅⠆
⠀⠀⠀⠘⣠⣀⣠⣀⣀⣀⣬⣅⡩⠕⣖⠲⢦⠤⣤⠄⣤⡞
⠀⠀⠀⠀⣽⢟⣦⣤⣤⣶⣴⣮⣶⣶⣾⡼⡇⠊⠉⡦⣿⡧⠀⠀⠀⢠⠛⠘⠒⠠⣄⠄⢠⠀⡄⢠⢀⡀⣠⡀⢤⠄⠠⠖⠃
⠀⠀⠀⠀⠙⠓⠷⠶⠶⣾⣾⣭⣬⡶⢯⣿⠿⠟⠛⠛⠙⠁⠀⠀⠀⠀⠈⣁⠾⠇⢠⠠⢀⣠⠀⠠⠘⠃⣤⡀⣠⠤⠿
⠀⠀⠀⢀⢤⣄⣀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠪⠄⠤⠀⠶⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠈⠐⠛⠛⠉⠙⠑⠒⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠏⠉⠉⠁⠲⠞⡄⠁⠃⠄⠀⠀⠀⠀⠀⠀⠘⠿⣿⣯⣿⣶⣤⣤⣶⣿⣟⣿⣻⣝⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠐⠄⢄⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⣤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠀⠀⠀⠈⢻⡄⠀⠀⢀⣤⠤⠖⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠒⠂⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠀⠀⠀⢸⡟⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠚⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠂⠀⠀⠀⢻⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷⠀⢳⣄⠀⠀⠀⠀⢀⣀⡤⠖⠊⠁⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠙⠷⠶⠖⠛⠋⠁⣀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⣿⣿⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢿⣿⣦⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⢻⣿⣇⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⢹⣿⡆⠀⠈⣿⣿⠀⠀⠀⣾⡇⠀⣿⣿⠀⢀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠹⣿⣧⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⣿⡇⠀⠀⢹⣿⠀⠀⠘⣿⣧⡀⠹⣿⣧⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠘⣿⣇⠀⠙⣿⣦⠀⠀⠀⠀⢰⣿⠇⠀⢰⣿⠇⠀⠀⣾⡿⠀⠀⠀⠈⠻⣿⡄⠙⣿⣇⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⢸⣿⠀⠀⢹⣿⠀⠀⠀⢠⡿⠃⠀⠀⣾⡏⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⣹⡇⠀⢸⣿⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣸⡏⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⡟⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⣿⠁⠀⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⢠⡿⠁⠀⠼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠟⠛⠛⠛⠉⠉⠉⣉⣉⣉⣁⣁⡠⣤⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⠙⠛⠛⠻⠷⢶⣦⣤⣀⡀
⠀⠀⠀⠀⢀⣠⣤⡶⠟⠛⠉⣉⣁⡤⣴⠶⢂⣶⣾⡿⠛⠻⣿⡿⠛⢉⣩⣿⠟⠁⣉⡼⠛⢿⡉⢉⣭⡯⠟⠉⢀⣿⡾⠷⠢⣤⣤⣌⡉⠛⠿⣦⣄⡀
⠀⠀⣠⡶⠟⢋⣡⠤⠐⠛⣡⣽⡯⠛⢁⣴⡿⠛⠻⣷⣄⢀⡼⣠⣴⠿⢋⣡⡴⠛⢿⣦⡀⢠⣿⠿⠋⠀⣠⡴⠛⠿⣧⡄⢀⡼⠛⠉⡹⢿⣶⡀⠉⠻⣦
⢠⣾⠋⢀⡴⠋⠁⣀⣤⣾⣽⣧⣴⡞⠉⠛⣷⠆⠀⢀⣤⣿⣿⣿⣿⠛⠛⢻⣷⠀⠀⣉⣼⣟⣡⣴⡚⠛⢻⣷⠄⠀⢈⡴⠋⢀⣤⣾⠟⠁⠀⢱⠀⠀⢸
⣾⠇⠀⠸⣄⣠⣾⠿⠋⣹⠁⠀⠹⡿⠂⠀⣁⣤⣾⣿⢿⠟⠁⠈⢻⠷⠀⠈⣁⣤⡾⠋⠝⠁⠉⢹⡿⠀⠀⣁⡤⠞⠉⢀⣴⡿⠛⠁⢀⣀⠴⠃⢀⣠⣾
⣿⣆⡀⠀⠙⠛⠧⣤⣴⠿⢄⣀⣀⠤⠞⢋⣤⡿⠛⠁⠈⣦⣀⣀⣀⠤⣴⣿⠟⠁⢀⣴⡷⣄⣀⣀⣤⡶⠟⠁⠀⢀⣴⣿⡟⠤⠖⠛⠉⣀⣤⣶⣿⣿⣿
⢻⣿⣿⣷⣦⣄⣀⡈⠈⠙⠛⠛⠣⠴⡾⠿⠃⣀⣀⣤⣾⣋⣁⣀⣤⣾⣏⣁⣠⣾⣟⣁⣀⡀⣴⠿⠿⠤⠶⠐⠚⠛⠋⣁⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⣀⣀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠉⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠋⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢠⣿⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⢻⣿⠛⢻⡿⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⣿⠁⣀⣀⣤⡤⠶⠛⠛⠉⠉⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠉⠙⠛⠶⣤⣄⣀⠀⠀⠸⣷⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣿⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠦⣿⡆⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢰⡿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣾⠇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⣇
⠀⠀⠀⠀⠀⢰⡟⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣾⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠸⣧
⠀⠀⠀⠀⢰⡟⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢻⣆
⠀⠀⠀⠀⣿⡃⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⣿⡀
⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣚⡉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⠰⢤⡐⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢀⣉⠛⣖⣉⠽⢦⡔⠃⣞⢈⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⡆⡩⠔⢁⠿⢤⠚⣉⠴⣥⠔⠃⣈⠒⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠂⡎⢻⣤⠂⢹⠧⣤⠋⣩⢯⡤⠛⣅⢡⣜⣒⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢻⡕⢃⡼⠈⣇⣤⠋⡹⢤⡎⣁⠼⢤⠔⠃⣄⠒⣀⡲⣔⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⢦⡤⠀⠨⠿⠭⠤⠞⣅⣜⣘⣀⡜⢉⣧⣤⢊⡩⠧⡤⠚⣠⠐⢊⣆⠉⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢩⣀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣉⣙⣉⣛⣓⠊⠽⠧⣤⠘⢂⡜⡆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣄⡙⠢⣠⣀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠯⢔⣀⠈⠁⠐⠻⢴⡀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⣹⢉⣓⡸⠀⡭⢴⢀⣆⠽⢓⡦⠥⠾⠒⠑⠂⠲⠤⣀⠀⠉⠒⠤⠀⠀⠉⠂⢤⣀⣄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⣥⡎⢩⠗⢻⠔⣼⣡⠜⢀⠖⣠⢏⡉⢮⠔⠊⠍⠓⠲⢯⣶⣤⣀⡀⠀⠀⠀⠀⠈⠻⣷⡵⡀
⠀⠀⠀⣀⠠⠀⠀⠀⠠⢱⠠⠴⣀⠋⡻⠰⢧⣴⣁⡜⢉⡝⢺⠅⢺⣥⡞⣁⠖⣰⠯⣔⣋⠞⢙⢪⣟⣿⠶⣕⣤⡀⡠⡈⠻⣷
⠀⠀⠈⠉⠉⠉⠒⠢⢄⡀⠛⡔⡉⡕⠣⠴⡁⣼⠁⡙⢛⠖⢦⣴⣃⣰⢁⡜⢺⠧⣎⢤⡎⡩⠗⡤⠚⣷⡳⠄⠁⠻⣖⢌⢷⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡡⠔⡜⢄⠦⢨⡎⠳⠚⠤⣆⢠⠁⡹⠋⡗⢧⢴⣁⡜⢉⠗⢹⠗⢾⠤⣿⡄⠀⠀⠀⡙⢾⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⣈⣢⠧⣰⠈⣲⢣⡼⣀⡅⢙⡊⣣⣆⣰⣁⣟⣙⡖⣧⢴⣇⣴⠉⣇⢀⠀⠀⠈⢧⣻⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢻⣿⣿⣷⠦⡒⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⡒⠦⢄⣠⣸⣿⣧⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠐⣊⠝⡩⠂⣁⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣝⣿⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⣢⡶⠟⠒⠐⠒⠒⠓⠒⠂⠒⠠⢌⣑⠂⠄⠦⣄⡂⢕⡢⢀⠠⡀⠀⠀⠀⠀⠀⢹⠇⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡈⠛⠷⣮⣕⣯⣶⣭⣒⣀⣠⣴⣟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠬⣖⣿⣿⣿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⣄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⣀⡀⠀⣄⣀⣠⠈⠐⢄⠀⠀⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠘⠛⠂⣠⢈⠀⣠⡔⣮⠉⢳⣤⣭⠠⠀⠀⠘⠁⡁⡀⠄⠀⢠⡿⠀⠀⠠⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠠⠟⠓⠠⣀⣉⡤⠔⢈⡭⣬⣈⣻⡆⢀⡀⠁⠀⠀⠀⢷
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⢲⣿⣿⠿⠃⠀⠀⠃⠀⠀⠀⠀⠀⠉⠁⢀⡜⠀⠁⠀⠀⠐⡒⠉⠀⠐⠈
⠀⠀⠀⠀⠀⠙⢀⣠⣥⣤⣬⣉⣡⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣮⣤⣤⣄⣀⠀⠉⢀⡶⣿⠟⠹⣿⠿⠆
⠀⠀⠀⠀⠀⠈⠀⠙⠩⠼⠿⢿⣿⣟⠛⣿⣿⣧⣀⣤⣾⠿⣛⣛⣿⣿⢩⣽⣿⣿⣽⣦⣭⡴⠟⢓⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠀⢀⣀⣀⣴⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠂⠈⠉⠁⠉⠉⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣖⣛⡻⠭⠽⣟⣓⣒⠦⣤⣀⠀⠀⢀⣠⠴⢖⣚⣛⡯⠭⠽⣟⣓⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠕⠋⣁⡤⠤⢤⣄⣀⠀⠈⠉⠒⠮⣝⣛⠭⠒⠋⠉⠀⢀⣀⡤⠤⢤⣌⡉⠲⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⡱⠃⣠⠊⠁⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠉⠉⠛⠓⠒⠒⠛⠉⠀⠀⠀⠀⠀⠙⢦⠈⢳⣹⡄
⠀⠀⠀⠀⠀⠀⢸⢣⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⢀⣀⠀⠀⠀⠀⣈⠀⢀⠀⡀⠈⡇⠀⡇⣷
⠀⠀⠀⠀⠀⠀⢸⢸⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠥⣄⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⢐⠄⠉⠀⢀⡇⠀⡟⣿⠀⠀⠀⢠⠖⠢⡴⠋⢳⣀⣀
⠀⠀⠀⠀⠀⠀⠘⣇⢇⠀⠹⡄⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠑⡄⡴⠂⠐⠢⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⢣⡏⠀⢀⠤⢼⡀⢀⡇⠀⡸⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠙⣎⢦⠀⢹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⣻⠀⡄⠀⠀⢱⠀⠀⠀⠀⠀⠀⣼⠀⢠⢫⡞⠀⠀⠸⣄⠀⠙⠒⢄⠉⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠀⢘⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡼⠁⠀⠀⠀⡄⠀⠀⠓⠦⠤⠶⠋⠀⠑⠦⠤⠞⠁⠀⢠⠄⠀⠀⠀⢹⡀⠸⡟⡇⠀⠀⠀⠀⠀⡇⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⣼⠁⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⢳⠀⡇⡇⠀⠀⠀⣠⠞⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⢸⢳⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠤⠤⠤⠤⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⠒⠒⠋⢁⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢿⢹⠒⠚⠋⠉
⠀⠀⠀⠀⢀⣠⠴⣾⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢸
⠀⠀⢀⡴⠋⢀⡤⣿⣾⠀⢸⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⡆
⠀⠀⡞⠀⢰⠋⠀⡇⡆⠀⣸⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⢸⡇
⠀⢸⠃⠀⣿⠀⠀⡇⡇⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⢏⡇
⠀⢸⠀⠀⠙⢢⠀⢷⢱⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡸⢸⠃
⢰⠃⠀⢀⠀⠘⠒⢮⢧⡳⣌⡓⠢⠤⠤⠤⠶⠒⠒⠲⠤⣄⣀⣀⣀⣀⣠⡤⠔⠒⠒⠲⠤⠤⠤⠴⠒⣁⠔⣱⠃
⡟⠀⢰⠻⡑⠲⠶⠋⠀⠙⠲⢭⣝⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡭⠵⠋⠁
⢧⣀⡼⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢹⠉⣿⢹⠉⣿⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠛⠛⠛⠒⠦⣼⠀⣿⢸⠀⣿⡤⠖⠚⠛⠋⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡜⢫⡞⠁⢗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠢⠄⣈⠧⠀⣘⠃⠯⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⠒⢤⠓⠤⠓⠀⣤⠶⢨⡂⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠲⠄⣸⠁⠐⠛⠀⢠⣌⠀⠢⢈⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣼⠓⠤⠣⢤⠛⠀⢤⡤⠁⣙⡃⢦⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⣙⠉⡲⠓⠤⠚⠂⠀⡴⠆⢀⣈⠁⠓⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣑⠦⢀⡘⠓⠢⠞⠢⢄⣀⠓⠂⢴⣁⡙⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠓⡶⢀⡈⠉⠲⠾⠂⠀⢀⡜⠁⠲⡆⢀⡛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢍⠧⢀⡘⠓⠠⣴⠄⠀⠀⣈⠁⠲⠶⢤⣈⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⢄⡠⠆⢀⣠⠄⠀⠀⢨⡇⠁⡒⠃⢤⠌⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠒⠂⢤⠆⠀⢀⡀⠀⠀⢘⡆⠀⣨⠉⢐⡞⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢉⠓⠲⡎⠁⠐⣎⠁⠀⠐⠧⠀⣀⣍⠁⠺⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠃⠚⠂⠄⠁⠐⠊⠁⠁⠐⡾⠀⢀⣭⠀⠈⠇⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠉⠛⠃⢶⡁⠀⡒⠁⠀⠠⡴⠀⢀⣨⡀⠀⡛⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢈⠓⠀⠦⠄⣠⠋⠐⠀⣴⡆⠀⠀⠥⢀⣙⠓⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡊⠁⡲⢄⣀⡰⠄⠀⢀⠿⠀⣈⠿⠄⣤⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢤⠄⣨⠤⢀⣨⣀⠀⢀⡟⠀⠠⠜⠠⡄⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣈⡁⣀⡧⢀⣈⡁⠀⠈⣏⠀⠐⣖⠓⢠⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠴⠆⠸⠆⢠⡁⠀⠀⣫⠀⣀⠶⢀⣉⡋⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡒⠲⠖⠠⡌⠁⠀⠶⠣⣀⡛⠠⣤⠓⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡁⡘⠂⢰⠉⠁⣲⠃⠠⣬⡁⠲⠆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⡉⣉⣀⡤⠀⣈⡛⠰⠶⢄⣬⠁⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡾⠴⣇⣰⠏⣁⠉⢠⠒⢤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣬⣗⡯⢶⣭⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠑⠃⠐⠀⠀⠀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⠀⠂⢀⡀⠘⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⡠⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⢀⠀⠈⠁⢀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠸⠀⠀⡤⠀⠀⠀⡀⡀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡆⣡⢤⠤⡀⡒⢀⠐⠀⠒⠀⠀⠶⠦⠴⠶⠒⢀⠀⠒⠂⣄⡀⠘⠐⠐⡀⠀⡰⠆⠁
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢈⠉⠉⠉⠚⠒⠀⡓⠛⠈⠙⠃⠁⠈⠀⠘⠃⠃⠈⠉⠉⠉⠉⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⢍⠣⠲⡀⢄⢤⠠⡀⣞⢁⠀⠀⡘⣀⣀⡀⠠⢃⡀⠀⣀⣉⡀⠀⠀⠡⠀⠀⠐⠋⢉
⠀⠀⠀⠀⠀⠀⣀⡑⠒⠬⠦⡓⣕⣜⢮⣂⣀⣀⠀⢀⣀⡀⡀⡀⣀⣀⣀⠀⣀⡀⣀⢀⢀⣠⡤⠤⢨⠄
⠀⠀⠀⠀⢀⣈⡉⠄⠀⠀⠀⠒⠂⠠⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠄⠠⡤⠤⠖⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠰⠁⠘⠀⢀⠴⡀⠈⡠⢖⡤⠀⢀⢺⠁⢰⢢⡀⠈⢰⠢⡀⠀⠁⠀⠜⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢯⡀⠠⠍⠀⢤⡚⠊⠐⠒⠃⠁⠀⠀⠾⠈⠀⠀⠀⠈⣆⠂⠉⠛⠀⠁⠤⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠠⠀⠈⠀⠀⠤⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠉⠀⣈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠐⠆⢀⡀⠀⠀⠆⠀⡀⠈⠀⣀⠀⠄⠠⠄⠀⠠⠀⠀⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢦⡔⢀⠎⠀⣤⢀⠄⠀⡱⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠁⠊⠀⢀⠁⠈⠀⢀⠅⡀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⢤⣡⠎⠀⢀⠀⠄⠀⢀⢎⠜⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⡄⠀⢀⡖⠀⠀⠀⡠⠂⠀⢀⠔⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡃⢐⠎⠀⢀⠊⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠐⠀⠀⠀⠀⠁⠀⠠⠔⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⡀⠀⠀⠀⡁⠀⢀⢂⠅⢄⠈⠒⠀⢠⠄⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⡀⢖⠁⠄⠀⠀⠁⠀⢨⡌⠓⠃⠀⠀⠀⠈⠡⠂⠀⠀⠇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⠸⠒⢁⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣀⡄⠤⢉⢀⡔⠘⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠈⡀⠀⠀⣰⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⡀⢉⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⢀⠄⠉⠁⠻⣚⠠⠧⠄⣄⠀⠘⢆⠀⠀⠀⠀⣀⠀⠁⠈
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⡠⠇⠀⠀⠀⡁⠀⠀⢄⡀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠴⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡇
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠍
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠎
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⢄⡀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣿⣿⣻⣿⣿⣟⣻

⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣤⡸⠋⠿⢳⣾⣀⡄⠀⠀⠀⠀⠀⣀⠸⣿⣆⢲⡄⠀⠀⠀⠀⢄⠙⢦⡀⠀⠀⠀⢰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢠⡴⢼⣦⣤⣤⣤⣤⣿⣤⣤⠀⠀⠀⠀⢿⣦⣿⣿⣿⡿⠀⠀⠀⠀⠈⠳⠞⢇⠀⠀⢀⡼⠿⠿⠋
⠀⠀⠀⠉⠈⣧⢸⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢠⣆⣸⣿⣿⡟⢹⣧⣼⡀⠀⠀⠀⠀⠀⠀⢑⣴⠋
⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⣿⡟⠻⠀⠁⠀⠹⡿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣸⠁⠉⠉⠉⠁⢱⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡢
⠀⠀⠀⠀⣠⣮⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣼⣄⠀⢀⣾⡀
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣰⣿⠟⠋⠁⠈⠙⢻⡿⣄⠀⠀⠀⠀⢸⣿⣿⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡆⢰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⡄⢴⠀⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⢀⠞⣤⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠗⠸⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠃⠚⠀⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠛⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡦⣄⣀⣀⣠⢼⡿⠋⠀⠀⠀⠀⠘⠛⠛⠀⠛⠛⠛
⠀⠀⠸⡏⣿⣿⡿⠋⠀⢂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠋
⠀⠀⠀⢻⣌⡟⠁⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣀⣻⡶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣿⣿⡿⠏
⠀⠀⠀⠀⠀⢷⡸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⡏⠉⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⠁⠀⠸⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠧⠤⠤⠤⠤⠤⠤⢷⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠀⠈⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⣴⠥⠀⠰
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⣒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠂

⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣆⠄⢀⠀⠀⠀⢰⠀⣰⠀⠀⠀⢰
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠏⠾⠈⠳⠁⠼⠸⠇⠘⠠⠿⠑⠼⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠱⡀⠈⠁⣀⣼⢀⡀⠜⠀⠀⠀⠀⠀⠀⠇⢀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠀⠀⠀⠀⠀⠀⠈⠉⡋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣀⠄⠐⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠠
⢀⡀⠀⢰⢁⡈⢀⡶⢾⣹⡾⡿⠂⠀⠀⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢐⣒⠀⠂
⠈⠻⠀⠈⠁⠠⢭⣙⣤⣄⣘⣭⡼⠶⠞⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠪⢙⠒⠀⠤⠤⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠉⠂⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡆⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣠⡴⣫⢞⡽⠱⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⢿⣟⡽⣣⠞⣵⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢀⣮⡿⡻⢫⠊⣱⢏⡾⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⣰⡿⣛⠞⡳⢁⠞⡡⢗⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠘⠀⣀⣼⢯⣝⢫⠟⠩⡃⣜⣰⡟⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⠀⢀⠿⣱⢏⡶⢁⠬⣑⠮⣝⠏⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡐⢣⡟⣉⠮⣑⠎⣱⢮⣛⠊⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡎⠀⣿⠯⡼⢇⡹⢉⡰⢍⡲⢥⡟⠁⠀⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⢰⠁⠀⣏⠶⣉⠮⣁⠾⢁⡶⡽⣹⠃⣰⠋⣩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠂⠀⣟⣤⡉⠢⠍⣰⠮⡽⣵⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⢹⢦⣜⢓⣤⡭⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣦⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠐⠾⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡷⠶⠤⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⣴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠅⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⡀⠞⠁⡄⠀⠀⣀⣤⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠀⠈⠈⢹⠟⠉⠀⠉⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠠⠞⠶⣆⠀⠀⠁⢛⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⠁⠒⠒⠒⠂⢤⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⣴⣏⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣧⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠢⢄⡀⠀⠀⠄⠂⠐⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣸⡧⡀⠀⠠⠐⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡥⠂⠒⠣⠤⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡿⠀⠙⢄⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘⠿⣤⢸⠀⠀⠀⠀⠀⠠⡀⠀⢸⠁⢸⠁⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡇⢸⡆⡠⠊⠀⠀⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⢠⡤⠤⢤⣤⢀⣀⢀⣀⢀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢚⡇⠁⠀⠀⡠⠊
⠀⠀⣠⠴⠚⡃⢀⡹⣿⣿⡿⣿⣷⠆⠶⠶⠶⠶⠾⠟⣃⡉⠁⠘⠳⢤⡀⠀⠀⠀⠀⠀⠀⣏⡯⡀⣀⠴⠋
⠀⠘⣷⣔⣿⣿⣿⡿⠿⣀⣀⣤⣴⣴⣶⠷⠀⠀⠾⣿⣿⣿⠿⠆⢀⡴⡇⠀⠀⠀⠀⠀⢸⡿⣄⣸⣿⡀
⠀⠀⠃⠈⠉⠙⠓⠲⠶⠾⠭⠭⠥⠤⣤⡤⠤⠤⠦⠶⣒⣒⣾⣭⣷⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⣼⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡇
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣸⣿⣿⣿⢟⣼⡿⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠈⠲⣄⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢟⡿⠋⠸⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠓⠯⢿⣿⣶⣶⣶⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠉⠉⣻⡏⠉⠀⢻⡆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⠤⠿⠇⠀⢀⣀⣿⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢰⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⢿⣿⣷⣆⣀⣀⣀⣬⣿⣷⠀⠀⠀⠈⠙⣾⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠑⠸⢿⣿⣿⣿⣿⠿⠛⠁⠸⣇⠀⠀⠀⠀⣿⠹⠿⢿⣷⣶⣦⣤⣤⠇⠀⢇
⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢹⠀⠀⠀⠹⡏⠉⠉⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠈⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢴⠶⠖⠲⠛⡛⠯⠽⠛⠿⠛⢛⡛⣿⣶⣶⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⢋⡉⠰⠅⠚⠶⠉⠁⠈⠉⠉⠀⠒⠒⠒⢒⠶⠬⠄⠉⠧⣭⡹⢿⢿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠃⢥⡄⠾⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠄⡀⠉⢸⡻⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣈⡭⠁⠑⠒⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠰⣂⣽⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡓⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠌⠀⠛⡶⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣄⠾⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠐⢡⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣆⠑⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠂⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡧⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠌⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣂⡭⣄⣼⣟⢁⣀⣁⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢦⣿⣿⣿⣿⡿⢀⡀
⠀⠀⠀⠀⢀⡤⢚⣥⣶⠏⠁⠈⠓⠻⠿⠶⠶⣴⣿⣝⣀⣴⣄⠐⠲⠂⢀⡂⠤⠀⣀⠀⠀⠀⠰⠀⠂⢈⠞⣆⣸⣿⣿⣿⣿⡧⢀⠈⠁⠂⠄⡀
⠀⠀⢀⡴⣫⣾⠟⠙⠻⠛⠒⠒⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢶⣿⣥⣄⣀⡁⠒⡒⠐⢎⣹⡈⠀⣠⣼⣿⣿⣿⣿⡁⠀⠨⢑⠢⢄⠨⢑⠢⣀
⠀⢠⠎⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⣿⣭⣖⣥⣿⣿⣿⣿⣟⣤⠑⠂⠀⠘⠋⠀⠀⠱⣮⣗⢄
⢀⡏⣸⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠠⠐⢢⠤⣤⣄⡀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠐⠊⠒⠀⠀⠀⠈⠈⢻⣯⡳⡀
⣸⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠐⠒⣀⠽⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢄⠀⠀⠀⠀⠘⣷⡹
⣿⢸⣿⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠽⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⡇⢸⡜⡆⠀⠀⠀⠀⠘⡇
⡿⢸⣿⢅⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⢰⣥⡧⠶⠤⣤⡀⠀⢹
⣇⠈⣿⡡⢒⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣂⠉⢀⠀⠀⠀⠀⠀⠀⠚⢧⡀⠘
⣿⠀⣿⣎⠥⢂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣇⣸⣇⣰⣖⣀⣀⣤⣤⡶⡊
⢹⡄⢹⣷⣊⠥⠒⡀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠛⢋⢹⠀⡇⡿⠛⢥⡤⠀⢀⣇
⠈⢷⣄⠙⠷⣶⣩⡔⣊⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠰⠛⠁⠀⠀⠠⠀⣼⣿
⠀⠈⠙⠿⣶⣤⣉⡛⠻⠶⣦⣴⣀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣾⠋⡶⡄⠀⠀⣰⣿⡏
⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣤⣬⣉⡛⠻⠷⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣻⣀⣷⣇⣤⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⣶⣤⣬⣉⡉⠐⠃⠒⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣁⠀⠀⠀⠀⠀⠀⠀⢔⣊⡽⢿⣟⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣯⣥⣤⣤⠤⠤⢒⣐⣩⣭⡷⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠷⠶⢶⣦⣤⣤⣤⣤⣴⠶⠶⠿⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠁⣠⠈⠀⠈⣡⠀⠉⢉⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣡⠀⠀⠀⠈⢁⠀⠁⠀⣄⠀⠀⠦⠀⠉⠀⠀⠀⣀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠴⠀⠀⠋⢀⡀⠀⠀⣀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠖⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠐⠆⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⢦
⠀⠀⠻⣍⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡴⠁
⠀⠀⠀⠈⠳⣄⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠱⣄
⠀⠀⠀⠀⠀⡸⠓⢄⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡰⠁⠀⠀⠑⢄⡈⠑⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⠯⠤⠤⠤⠤⢤⡤⢄⣘
⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⡍⠭⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁
⠀⠀⠀⣤⠄⢺⡀⠈⠉⠐⠂⠀⠙⠢⡀⠀⠀⠀⣀⡠⠤⠔⠒⠉⠉⡹⡁⠲⢄⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠄⠒⠊⠉⠀⢠⠦⣀
⠀⠀⠀⠈⠉⠲⠋⢲⠂⠀⠀⠐⠐⠂⠙⠒⠛⠋⠁⠒⠒⠐⠀⠂⠉⠀⠉⠒⠒⠛⠒⠒⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⡃⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠣⣀⠈⠦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⣫⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠟⠒⠂⠀⠀⠒⠀⠤⣤⠤⠀⠒⠒⠒⠂⠀⠀⠀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠤⠒⠚⡷⠒⠒⠀⠒⠒⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⢀⣀⠭⠶⠤⠤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⠄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠤⠤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁



⡿⠉⢙⡟⡿⠻⠿⠟⠿⡛⠿⠻⠿⠿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣴⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⡴⠚⠉⠉⢙⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣴⠋⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⢀⠸⠅⠈⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣠⡎⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣴⣃⣀⣀⣤⠀⣀⠀⡀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣻⣯⣯⣿⡅⠈⢠⣀⢀⣌⡞⡿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⣿⣿⣿⣟⢛⣡⣻⢆⢗⡼⣫⣿⣿⣷⣍⡷⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣻⠿⠷⣿⣿⣟⣵⣿⣿⣿⡿⠽⢛⣯⣞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣗⠖⠀⠰⠖⠒⠒⠒⠀⠛⠙⣿⡟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣄⣀⠁⠀⠀⠀⢀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⢿⣿⣿⣷⡾⣾⣿⡿⣏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣿⡟⠛⢁⣻⡿⠤⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠙⠧⣤⣀⡽⠃⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⢖⣿⡓⢤⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢀⡤⠖⠋⠛⠿⠛⠙⠓⠤⣀⡀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣦⣽⣷⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣾⡿⣼⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣛⣛⣟⣹⣛⣟⢛⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠒⣶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢠⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⡷⠦⠤⢾⠧⢴⠚⠻⠛⠶⠤⠤⠤⢤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠠⠀⡸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠳⢤⡤⠃⠀⡎⠠⠀⡤⠄⠰⣄⣠⡀⠀⠙⣆⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⡀⣤⠔⢀⣀⢴⠾⠀⠙⠀⠓⡘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡷⡇⠘⠛⠋⡀⢀⠀⢀⠀⠀⣅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⡼⠂⠀⠘⢛⠘⢻⡀⢋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⢀⡇⠳⡄⠀⠈⠈⠁⠉⠉⠉⠁⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠇⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⡀⠀⠀⡇⠘⢄⡀⠀⠀⡠⠻⣀⣀⡠⠏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢄⠀⠀⠑⠢⠄⣀⠀⠀⠀⠀⣾⠈⠭⠍⠩⠍⠁⠀⡇⠀⣀⢀⢉⣉⣀⡀⠀⣀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠠⡀⠀⠀⠀⠉⠁⠐⠾⠿⢀⣟⡀⠘⠓⠀⣠⠀⠀⢩⡄⣬⠩⠉⠁⠁⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣀⣀⡑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠧⠰⠴⠶⠶⠶⣦
⠀⢀⡴⠛⠛⠙⠋⠁⠉⠙⢶⣄⠀⠀⣿⠶⠛⠋⠉⠉⠉⠙⠲⢬⡒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡌⠀⠀⣀⣠⡀⢸
⢰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠉⠉⠙⠂⠚⠉⠉⢀⠀⢻⠋⠀⠀⠈⢋⣉⡡⠼
⡏⠀⠀⠀⠀⣰⠋⠉⠙⢳⣶⡿⠘⠁⠀⣠⠖⠓⠉⠙⢦⡀⠀⢀⣀⡿⠷⠤⠴⠆⠀⠲⠒⠴⠶⠦⠤⢤⣴⡟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⡀
⠃⠀⠀⠀⠀⠇⠀⠰⠊⣸⡏⠀⠀⠀⠀⠻⣀⡀⣀⡤⠞⠋⠉⠀⠀⢀⣀⣀⠤⠤⠤⠤⠤⠄⣀⣀⡀⠀⠀⠉⠙⠒⠤⣀⠀⠀⠀⢀⡴⣋⡿⠷⢦⡀
⠰⡄⠀⠀⠀⠈⠓⠲⠟⠛⢧⠀⠀⠀⠀⠀⡼⠛⠁⠀⣀⡤⠖⠊⠉⢈⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠒⠦⢄⡀⠀⠀⠑⠢⣴⣩⡟⣹⠤⠖⣶⠟⢧⣀
⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⡷⢦⣀⡰⠋⠀⠀⡠⠊⡥⢤⣀⡔⠊⠉⠙⣿⠯⢤⣞⣿⡾⣻⣏⢉⡵⣶⢦⣀⠀⠉⠒⣄⠀⠀⠈⠻⣿⡧⣶⠋⢉⣽⠛⢯⣧
⠀⠀⠀⠀⠉⠑⠒⠒⠒⠚⠉⠀⠀⡟⠀⠀⢀⠞⠀⢀⡴⠾⠿⡆⠀⠀⣴⠃⠀⢠⠋⠉⠉⢉⠏⠀⠀⠘⡟⠋⠑⢦⠀⠀⢳⡀⠀⠀⠹⣿⣛⣻⣋⣉⣩⠟⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡎⠀⣰⢻⠀⠀⠀⣸⣏⣉⣽⣇⡴⡞⠀⢀⡰⠛⢳⡤⡤⣾⠥⠤⢄⡠⢳⡄⠀⢷⠀⠀⠀⢋⣸⣏⣋⡽⠉⠙⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢠⣏⠙⠤⡤⠴⠛⠌⢻⡶⣏⠀⠈⠉⣁⣹⣀⣸⣄⠑⣷⠀⠀⠘⡷⠋⡿⣄⢸⠀⠀⠀⢸⣇⣀⣝⠹⢓⡶⠧⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢯⠹⡏⠹⢶⣿⣻⣦⠀⣀⣽⠛⢋⣩⣿⣏⣿⢯⢤⠀⣑⡛⡶⡖⣾⣁⣼⣾⣇⡎⠀⠀⠀⣾⣻⣏⡉⣹⢿⢦⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣀⣀⣈⣿⣷⡧⠴⢟⡛⣛⣉⠉⣉⡀⠘⠻⠾⠀⠈⠁⣼⣼⣭⡟⠓⢻⣁⠀⠀⣸⠟⠀⠀⠀⣼⠉⠑⣴⡙⠙⢳⣾⣁⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⢉⣩⢭⣭⣵⠶⠒⠛⢿⣍⠁⢽⠁⠀⠈⠛⡿⠟⠉⠒⠒⠚⡄⠀⠀⣷⠤⠿⣯⡷⠛⠁⠀⠀⣠⣞⠛⢳⢶⠋⢉⠟⢧⣀⡝⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠒⢄⡀⠀⠈⠑⠂⠕⣶⣿⠞⢣⣜⠄⠒⠒⢲⣧⣄⡴⠥⠔⠊⠁⠀⢀⣠⣴⠿⡁⢈⠷⣅⢀⡽⠧⢤⣀⠟⠦⣤⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠄⠀⣀⠀⠀⠀⠀⠉⠈⠁⠉⠀⠀⠀⢀⣀⠠⠤⠒⢊⠉⠉⠑⣤⡜⢧⣀⣼⢋⠛⢣⡴⠛⣆⡠⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠒⠒⠀⠉⠉⣁⡀⠀⠀⠀⢮⣋⠆⠀⠈⠣⣤⣏⡽⣻⡔⠛⢧⡠⠚⢷⡤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣈⡼⢟⠻⢳⠀⣡⠦⡄⠀⠀⠀⠀⠟⠉⣀⡡⠋⠉⢳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣩⠟⠓⠋⠉⠁⠀⠛⠴⠀⠀⠀⠀⠀⠱⣴⠿⠧⣄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⣔⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠿⣛⣫⣭⣭⣥⣭⣭⣭⣛⠻⢿⣿⣿⣷⣴⠞⠋⢺⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣫⣴⠿⠛⣩⡵⠛⠁⣠⠘⠛⠙⣻⣶⣍⠻⣿⣿⣷⣄⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢋⣾⠟⣁⣴⠟⠉⣀⣴⠞⢡⢇⣴⠞⢋⢄⣽⢷⣌⢻⣿⣿⣦⡴⠟⠛⠃
⠀⠀⠀⠀⠀⢀⣿⣿⡿⢡⣿⣥⠞⠋⢀⣤⠾⠋⢀⣄⣼⠈⢀⡀⡞⠈⢁⣠⣿⣧⢻⣿⣿⡆
⠀⠀⠀⠀⠀⣸⣿⣿⢃⣿⠋⣱⢯⣙⡒⢧⡠⡶⠛⠁⡙⣷⣶⠞⣡⡴⠛⠁⣠⣿⡆⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⢸⣯⢤⣿⣓⠲⢭⣿⣷⡀⠴⠟⢡⣏⣴⠞⠉⢀⣴⠞⠋⢸⣿⢸⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⢸⣏⢈⡓⠦⢭⣽⠿⠋⠉⢛⠲⣾⣬⣄⣀⡚⠋⠀⣠⠾⢻⡿⢸⣿⣿⠇
⠀⠀⠀⠀⠀⢹⣿⣿⡌⣿⡋⢁⣠⡶⠊⢀⣠⡶⠋⣼⢇⡶⠉⠛⠿⢿⣿⡦⣠⣾⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣷⡘⣷⡟⠁⣠⡴⠟⠁⡀⣸⣿⠀⣀⡴⠟⠁⣀⣼⠞⣽⡟⣼⣿⣿⠇
⠀⠀⠀⣤⢤⡾⠛⢿⣿⣷⣌⢿⣾⡉⢀⣴⠞⢱⣿⡏⠞⠋⢀⣤⠞⠋⣠⡾⢋⣼⣿⣿⠏
⠀⠀⠀⠹⣷⡷⡀⠈⢻⣿⣿⣷⣝⠻⣿⣤⣠⡶⠉⢀⣠⡾⣋⣡⣴⠾⣋⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠘⢿⣿⣄⣴⠟⠻⣿⣿⣿⣶⣭⣝⣛⣛⠛⣛⣛⣛⣭⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⢋⣍⢉⡉⠓⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣀⣠⣤⣤⣀⡀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡴⣫⣅⢄⣰⠠⠈⠝⢦⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡞⢼⣊⠊⠜⠇⠁⠈⠁⠦⢹⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠓⠱⡠⠁⡅⠂⡀⠀⠈⢠⠷⠶⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣄⡀⠀⠀⠀⣇⠀⠀⠀⢳⡄⠔⠈⣈⢄⠐⠊⠌⣀⣼⠟⠛⠁⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⣤⠤⠴⠶⠶⣶⣶⣶⣤⣄⣀⠀⠀⠉⠒⢤⡀⢸⣄⠀⠀⠀⠙⠶⣼⣂⡪⣁⣮⡵⠛⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣤⣶⣿⡛⠓⢦⣤⡄⠸⣷⢄⠐⢈⢻⡈⠙⠲⣄⠀⠘⢉⡻⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⣠⠊⠀⠀⣠⣶⡏⠀⣹⠛⠻⠶⢿⣤⡇⠀⠙⢮⡧⠄⠁⠑⢦⡀⠀⠙⢦⡈⠁⠈⢻⣿⡶⢄⣀⡀⠰⠆⠖⠀⣀⣠⠔⠋
⠀⠀⡴⠁⠀⢀⣼⠿⣽⡧⢤⣿⠦⣦⡄⢀⡍⠛⢓⢆⠈⢷⡂⢡⡀⠠⠙⡆⠀⠀⠑⣄⠀⠀⠹⡇⠀⠈⠉⠉⠉⠉⠉⠁
⠀⡸⠁⠀⢠⡏⣸⣠⡇⢀⣠⡃⢀⣼⣽⣷⠲⡀⠄⠉⠛⠶⣿⣿⣬⡤⠀⢹⣦⡀⠀⠘⣆⠀⠀⠹⡀
⢰⠃⠀⢀⣿⣧⠋⠉⣹⠁⠀⣿⣏⠀⣼⣃⠀⠈⠻⢧⣙⣶⢤⡘⠻⢦⡀⠀⠀⠻⡄⠀⠘⣆⠀⠀⢧⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠓⠒⠤⣄
⡾⠀⠀⣸⡿⠻⣤⠼⢻⠶⠚⠋⠉⠉⠙⠛⠛⠦⢤⣀⠀⠉⠛⢿⣴⠄⣗⠄⠒⠀⢹⣄⣀⣿⠀⠀⠸⣄⣀⡴⣪⠅⠀⠀⣀⣀⣤⠴⠚⠉⣹⠀⢠⠶⡝⠦⡀
⡇⠀⠀⣿⣇⡀⣸⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⠄⠈⠙⠶⣽⣦⡂⡄⠀⠳⡽⠟⢦⡀⠀⡿⠋⠘⠁⣠⠖⢋⡽⠋⠁⠀⠀⢠⠟⢿⠏⠀⢹⠀⠈⢦
⡇⠀⠀⣿⠉⢿⠋⠀⠀⠀⠀⣠⠴⠖⠒⠒⢦⠀⠀⠂⢸⡙⠂⠀⠀⠀⠀⠈⢷⡘⡆⠀⢻⣿⣫⠇⠀⡇⠀⣠⣾⡵⠚⠁⠀⠀⠀⠀⢀⠏⢠⠏⠀⠀⠸⡇⠀⠀⢳
⢷⠀⠀⢿⠙⣿⡀⠀⠀⠀⡾⢱⠀⠀⠄⢂⢘⣇⡴⠒⠚⡛⠛⠉⠓⢦⠀⠀⠀⢹⡄⠠⠀⣿⠃⠀⢰⠁⢸⡟⠁⠀⠀⠀⠀⠀⠀⢀⡎⢀⠏⠀⠀⠀⠀⣷⡀
⠸⡄⠀⠸⡇⠜⣧⠀⠀⠀⢷⡈⠀⡀⠆⢀⣸⠟⢀⡤⠥⠦⣤⡀⠀⠀⢳⣀⠀⠸⣌⣅⣠⡟⠀⠀⡜⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⡼⢀⡞⠀⠀⠀⠀⠀⢹⣇
⠀⢱⡀⠀⠙⣦⣈⣦⡀⠀⠀⠈⠓⢳⡿⠛⠁⣰⠯⡀⠀⠐⠠⠙⣆⠀⠀⢹⣆⠂⡈⣹⠟⠀⠀⣰⠁⠘⣯⣿⣇⠀⠀⠀⠀⠀⡜⢁⡜⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢳⡀⠀⠘⢖⡐⡛⡄⠀⠀⠀⢸⠀⠀⠀⢿⡣⠐⠠⠐⢀⠂⡿⠀⠀⠈⢷⣬⣶⠋⠀⠀⣰⣷⠀⠀⢹⣽⣿⡀⠀⠀⠀⣰⢗⡾⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠙⢄⢀⡈⠳⣄⠿⢦⣀⣀⣼⣧⠀⠀⠈⠳⣤⣁⣵⣥⠖⠁⠀⠀⠀⠈⢿⠁⠀⢀⠞⠁⠙⡆⠀⠀⢻⣷⣹⡄⠀⢰⡏⡼⠁⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⢰
⠀⠀⠀⠀⠀⠻⢵⡆⠈⠑⠦⣈⠉⠀⠈⠣⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⣀⠔⠁⠀⠀⠀⠘⢆⠀⠀⠙⣧⣇⢠⣯⣥⠃⠀⠀⣀⣀⣠⣴⡾⠟⡡⠆⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠉⠑⠲⠤⠶⢭⣽⠷⠶⠶⠦⠤⠤⠖⠊⣉⡥⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠿⠿⢾⣷⣶⣶⣿⠧⠴⠚⠉⠀⠀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⠀⠈⠁⠀⠀⠀⠀⣀⣠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠦⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠋⠡⠀⠀⠀⠀⡠⢒⠤⢈⣄⠀⢀⠐⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⡀⠀⡐⠀⠀⡀⠀⡐⠁⡱⠂⡤⢄⠀⢑⡎⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡐⠀⠀⣡⡋⠀⣸⡊⠁⠖⠄⠀⡰⢀⠘⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⢁⠈⠀⢠⠊⠀⠘⠊⣀⠘⠓⢄⣀⠝⢠⠈⠰⠁⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⡖⠁⠀⠈⠀⠰⠚⢀⡔⠉⠂⢄⡀⠉⠲⠓⢔⠂⢀⠈⠠⢀⠴⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡤⠘⠢⡀⠐⠢⡠⠘⠃⢀⠀⡘⠁⡲⠡⡠⠀⠀⢀⠠⠂⠁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠢⣀⡠⡀⠀⠀⢀⠁⠈⡖⠀⠀⠀⢀⠔⠁⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠁⠀⠀⠀⠖⠇⠀⠠⠁⠀⠀⠑⠐⠁⠰⠀⠀⡐⠁⡠⠁⠀⢀⠊
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⠑⠠⡀⠀⠊⠀⠔⠃⢄⠔⠀⠌⠀⠀⠔⠁
⠀⠀⠀⠀⡐⠁⠀⠀⡐⠁⠀⠀⠀⠀⡴⠰⠀⠀⠀⠀⠜⠠⣀⠄⠀⢀⠄⠠⠂⠀⡠
⠀⠀⠀⠌⠀⠀⢀⠈⠀⠀⠀⠀⠀⠰⠋⠉⠂⢀⣠⠊⠀⠀⠜⠁⠲⢀⠔⠁⡠⠊
⠀⠀⠌⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠼⠀⠐⠒⠊⠀⣠⣎⢁⡠⠊
⠀⡈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡬⠒⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⡀⠔⠈
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠊⠀⠀⡠⠂⠁⠀⠀⠀⢀⠔
⡇⠀⠀⠀⠀⠀⠀⠀⠠⢁⠠⠊⠀⢀⠄⠀⠀⠀⠀⠀⠠
⠁⠀⠀⠀⠀⠀⠀⡰⠂⠁⠀⠠⠂⠁⠀⠀⠀⠀⡠
⠈⠄⠀⠀⠀⢀⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⡠⠊
⠀⡈⠑⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊
⠀⠐⢄⣀⠐⠂⠀⠀⢀⣀⠀⠄⠂⠁
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⣿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⠊⣠⠖⢉⡤⠝⣷⣤⣀⠀⠀⢀⣴⠟⡹⠋⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣱⣱⣃⡞⣡⠞⣁⠔⢋⣡⣬⡿⠃⢀⡾⢃⡞⠀⣰⠋⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠩⠭⢝⣛⡻⢾⣥⣖⣉⢤⣿⠀⢀⣾⢁⡞⠀⣰⠃⣠⠎⡴⣿⠏
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠉⠑⠮⡙⢷⣾⠃⠀⣼⢇⡞⢀⣼⠃⣰⠇⢀⡾⠃
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠣⡙⢷⣤⣿⣟⣤⠟⣡⡾⢃⢠⡿⠁
⠀⠀⠀⣤⣿⠀⠀⠀⠀⢼⣟⣹⡄⠘⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⠭⠖⢁⡿⠁
⠀⠀⠀⣿⡙⠶⠂⠀⠀⠈⠛⠋⠀⠀⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣒⣒⡂⢸⡇
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⣤⡑⠢⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠄⠐⠁⠀⣠⡾⣿⠮⣛⢶⣄⠀⣀⣴⣿⢧⣄⠈⢿⣿⡳⣦⡙⠢⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿⣋⣀⣈⣿⣮⣿⣿⣾⣏⠑⢬⡓⣭⣿⠌⢿⡻⣆⠙⢦⡀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢏⣿⣯⡙⢮⡑⢝⢷⣹⡶⠟⠋⠁⠀⠈⣷⡘⢷⡈⠻⡄⢈⡲⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣷⡙⢦⡙⢮⣻⣿⠀⠀⠀⠀⠀⠀⠘⣷⡈⢳⡀⠙⣆⢹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢮⣿⣦⡙⢦⡙⣿⡄⠀⠀⠀⠀⠀⠀⠘⢷⡄⠳⡄⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⣯⡢⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁