Stir Fry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢿⡆⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⠃⣼⡏⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⡇⠀⠀⠀⠀⣰⡿⠁⣰⡟⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⣿⠃⠀⠀⣠⡾⠋⢀⣼⠟⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣼⠏⠀⠀⣰⡟⠁⢠⣾⠋⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣠⡾⠋⠀⠀⢰⡿⠀⢠⣿⠁⢠⣴⠟⠉⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠸⠏⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣦⠀⢀⣤⡶⠀⢸⣧⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣰⡿⡋⠀⠀⠀⢿⣆⠀⢻⣆⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢰⣿⠈⢻⣦⠀⠀⠈⠻⣦⡀⠻⣧⡀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠸⠇⠀⠀⠙⢷⡄⠀⠀⠙⠻⣦⡌⠿⣦⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⠿⠛⠛⠿⠿⠿⣿⣿⣿⠿⣛⣋⣉⣙⡛⠿⣿⣿⣿⣿⠿⣿⠟⣋⣭⣉⡛⢿⣿⣿⣶⣶⣦⣤⣀⡀
⣴⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣷⣦⣷⡌⠛⣱⣿⣿⣿⣿⣿⣿⣷⣌⢻⡿⢡⣶⡆⣾⣿⣿⣿⣿⣆⢨⠹⣿⣿⣿⣿⣿⣿⣷⡆
⣌⠻⠿⣿⣿⣿⡟⣩⣅⢻⣿⣿⣿⣿⣿⣿⡃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠧⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⠆⣿⣿⣿⣿⡿⠿⢛⡁
⣿⣿⣶⣶⣬⣍⣁⣛⡛⠻⠿⠿⠿⢿⣶⣬⡍⠘⠟⠛⣛⣋⣩⣭⣭⣤⣶⣶⣶⣾⣶⡌⢿⣿⡿⠿⠌⠿⠁⣚⣛⣉⣭⣤⣶⣾⣿⡇
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡿⢛⣩⣭⣭⣭⣍⡛⢿⣿⡿⠃
⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣙⠳⣍⡛⢿⣿⣿⣶⣍
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠓⠀⠙⠲⢬⡛⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣙⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣝⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢰⣿⣷⡀⠀⠀⣰⣿⣿⡀⠀⠀⣰⣿⣷⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⣉⡑⠶⢎⡛⡿⣣⣿⣧⣻⣿⣿⣣⣿⣧⡻⢿⣋⡶⢖⡈⣉⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠁⢒⠛⠦⣄⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⢰⠃⠀⠀⠀⠐⠈⠣⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣷⡀⢀⠀⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠉⢉⠐⠢⡀⠉⠛⣾⠳⣆⠈⣟⠙⢦⡀⠅⠀⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡀⠂⣨⣆⡀⠀⠐⠉⠀⠀⠟⢻⣉⡴⠶⠀⣀⠊⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠁⠻⠋⠀⡀⠀⠀⠀⠰⠐⠃⠀⠁⠀⠶⠉⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠋⠈⠀⠀⢣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣄⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠱⣄⠀⠀⠀⠀⠀⠀⠻⠓⠶⠚⠁⣄⡀⠈⠀⢀⠤⠛⠉⣼⢻⢶⡄
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡤⣘⡛⠃⢄⠀⠘⠃⠁⠄⠀⠰⢠⡄⡠⠺⠉⠋⡄⣀
⣾⣿⠈⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡟⢸⡿⠷⠤⠈⢳⠀⠀⠀⢈⠀⢰⡞⠁⠀⣀⣀⣴⡃
⢹⣿⡄⠀⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡴⠋⠁⠀⠀⠀⢷⠘⠀⠀⢾⠁⢘⠃⠀⠀⠀⠀⠀⠛⢠⠄⠡⠙⠉⠁
⠀⠻⣷⣆⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠍⠋⠱⠢⠀⠀⠀⣿⢸⡀⠀⣸⡇⢰⡆⠰⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠈⠻⣶⣄⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠉⠠⣤⣴⡶⣦⡈⠆⠀⠹⣌⠻⠿⠟⣡⡾⠤⢀⣀⡀⠀⣏⠀⢸⡇
⠀⠀⠀⠀⠈⠹⣷⣄⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠀⡰⡟⢀⠐⠬⢱⠚⠀⠀⢈⣩⠵⣤⣀⠀⠀⠚⢤⡏⢉⣄⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡬⠁⠀⠀⠂⠀⢸⣰⠀⣄⠹⠁⠀⠐⠎⣀⠀⠀⠈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⠱⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠴⠀⡶⠀⡗⠀⠀⠀⠀⠀⠚⢻⠀⠃⠀⠀⠀⠴⣶⠀⠀⠀⣀⣀⠄⠀⠀⠀⢀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⢳⣄⠀⠀⢀⢠⡙⢁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢈⡤⠔⢴⣗⣀⣀⠙⡿⠋⠀⠀⠀⠠⠀⢴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⣟⠙⢂⡀⠈⡆⠸⠂⠀⠀⠈⠀⠀⣀⡴⠢⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠉⠀⠈⠁⠀⠀⠃⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⢹⣷⣾⣿⠶⢹⣿⣿⣾⣿⣖⠙⣿⢍⣐⣀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡟⣩⠞⠻⠛⠋⢨⡌⠉⡅⠉⠛⢾⡀⢯⡷⠾⠿⣶⣤⣔⡠⢂⣀⣀⡀⣠⠼⠟⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠠⠈⠁⠀⣀⡀⠹⡆⠀⠀⠀⠀⡹⠻⠛⠳⣿⡷⢉⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⢀⣠⠔⢶⣾⢷⣄⠀⠈⠀⣄⣷⣦⣤⣀⡞⢠⣶⣷⣶⣦⡛⣶⣕⢀⠀⢺⢠⣴⡞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣄⠀⠀⢀⣟⣉⡤⠾⣷⣧⣤⣄⠀⠀⠙⠉⠋⠻⠛⢧⠸⠏⠁⠀⣿⠃⢾⣿⣿⡷⣶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢋⠉⢛⠉⠁⠀⠀⣯⠽⢿⢹⣷⠶⣧⣴⣤⣇⡀⢰⣿⣧⣤⣄⣿⣧⣾⣽⣿⣷⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠀⠀⠀⠠⡶⠄⠤⣠⣤⣼⢿⣀⠀⣟⢿⣼⣄⣜⠀⠻⠿⠟⠛⣿⠿⠟⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⢀⡆⢀⠈⠀⠁⠨⠩⡀⢷⣿⣇⡼⠈⠛⠶⣶⠖⠛⠁⠀⠀⢠⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠈⠁⠉⠀⠀⠘⠀⢠⡅⢰⡇⢸⣧⠑⢀⣶⠏⣀⠀⠀⠀⠀⣸⠏⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⣠⣴⡿⢟⠳⣮⣴⣾⠿⢄⣿⣷⢇⠀⢠⡟⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠒⠤⡀⠲⢶⣿⣋⠀⠈⠲⣈⡉⠀⠀⣤⡟⠋⠾⠂⠀⣀⣽⠟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠁⠒⠨⠍⣃⣀⠂⠬⠽⠿⠿⠩⠴⠶⠶⠺⠛⡋⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⡀⠈⠉⢉⣙⣂⣀⣶⡶⠾⠛⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣁⣉⣏⣀⣍⣉⣭⣋⣭⣟⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠭⡍⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠈⣓⡿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⠤⣄⣀⡀⢀⣀⡤⠔⠋⠁⢀⡠⠖⠋⠁
⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆⠉⠛⠢⣄⢀⡤⠚⠉
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣰⢦⠙⣄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⠉⠉⠉⠉⠙⠓⠒⠶⠤⣀⠀⠀⠀⠈⠉⠀⣸
⠀⠀⠀⢻⣄⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠳⣝⠲⠼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠴⠚⣩⠏
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠈⠉⠙⠒⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠚⠋⠉⠁⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢣⡀⠀⠀⡰⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠛⠛⠉⠉⠉⠉⣉⡩⠝⠛⢉⡡⢤⣔⡀⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢹⠃⠀⠀⠘⣄⠀⠀⠙⣆⠀⣇⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⣀⣀⣀⣀⣠⡤⠤⠒⣋⡩⠤⠒⠚⢛⣉⣉⢉⣉⡉⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠸⣄⠀⠀⠀⠈⠳⡀⠀⢸⠀⠘⢦⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠺⡿⣭⣥⠴⠖⣂⡩⠤⠖⠚⡛⠋⠩⠉⠉⠁⠀⠀⠈⠀⠀⣀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⢣⠀⠀⠀⠀⢱⠀⡸⠀⠀⠀⠱⡀⡃⠀⠀⠀⠀⠀⠀⠀⠰⠿⡙⠂⠉⠙⠒⠲⠤⠤⠤⣤⣤⣀⣀⣁⣤⡭⠤⠴⠒⠉⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⠇⠀⠀⢀⣜⡴⠁⠀⠀⠀⢀⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠚⠁⠀⠀⠀⠋⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠒⢦⣀⣀⣠⡶⠶⠦⢤⣄⣀⠀⢀⡀⠀⠀⠈⠳⢤⣉⣙⡓⠒⠒⠒⠒⣚⣉⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠓⠲⢴⡞⠉⠉⠙⡟⠁⢀⡀⢀⣼⠁⠉⠈⠁⠉⣄⠀⣀⣀⣉⣹⣏⡻⢤⠤⠶⣆⠀⠀⠈⠁⠈⠉⠉⠉
⠀⠀⣀⣠⡤⠤⣶⣶⣾⠿⣧⣀⠀⠀⠉⠛⣦⣸⡷⣾⠁⢸⢋⡁⢙⠛⠛⠛⠛⢧⣠⠳⡈⠋⠡⣴⡿⡁⡙⠺⣏⣳⣶⣟⠒⠒⠶⢤⡀
⣰⠞⢉⡤⢶⡞⢏⣀⡅⠼⠏⠀⠀⡶⢶⣞⣻⣯⣀⣀⡠⠁⠞⢡⡉⠀⢠⡶⠦⣴⣧⠶⢿⠗⠀⠐⠁⠀⢀⣾⠈⡁⠀⡿⣿⡉⠳⡄⠈⢧
⢧⠀⠹⢄⣸⣄⡀⠻⣧⡀⣠⠤⠊⢰⡏⠉⠉⠛⢲⣊⠶⣌⡹⣍⣠⠤⠼⠧⣄⣀⣀⡤⠾⣄⣀⡔⠈⣳⠟⣛⢀⣢⢞⡵⢻⣇⡴⠋⢀⡼
⠈⠙⠦⣄⣈⢧⡙⠲⢬⣉⡛⠳⠶⠾⠿⣄⡀⠀⠈⠁⢀⣠⣿⡊⣀⠤⠤⣄⡈⢻⣁⣀⣴⣏⣈⣑⣠⠟⠒⣚⣫⠕⢋⣠⣞⣥⠤⠖⠋
⠀⠀⠀⠀⠉⠉⠙⠓⢦⣄⣉⣙⠓⠲⠶⠤⠭⢭⣭⣭⣭⣭⣤⣭⣭⣭⣭⣥⣬⣭⣭⣥⣤⠤⠭⠶⠖⣚⣋⣥⣴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣍⣉⢙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠦⠤⠶⠶⠶⠶⠒⠒⢒⠋⣉⣩⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⣀⠉⠩⠬⠭⠉⠁⣀⠂⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡑⠤⡀
⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢉⠁⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠐⢌⠢⡀
⠀⠀⠀⠀⠀⡠⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠄
⠀⠀⠀⠀⡐⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠄⠤⠀⣀⠀⠀⠡⠉⠀⠀⠒⠂⠀⠀⠀⠐⠌⢂
⠀⠀⠀⡐⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠐⠤⠁⠀⠀⠠⠠⠀⠤⠄⠀⠠⣀⠀⠀⡀⠐⠀⠐⡀⠀⠀⠀⠀⠘⠄⠄
⠀⠀⢀⠁⠂⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠣⠀⠂⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠢⠔⠀⠠⠀⠓⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡈⠠⠀⠀⠀⠀⠄⠀⠐⠁⠀⠀⠁⠠⡐⢆⡀⠖⠠⢀⡀⠀⡀⠀⠀⠀⢀⠐⠒⠒⠒⠓⠒⠠⠄⠀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⢄⠈⠢⢄⠀⠁⢐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠁⡇⠀⠀⠀⠀⠰⠇⠀⠀⠀⣌⢀⡠⠄⢂⡑⠀⣀⠀⠀⠀⠀⡤⠃⠀⠃⠀⠔⠐⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠖⠉⠀⢀⠐⠉⠀⠀⠈⡻⢁⠄⠊⠀⠐⠀⠀⡄⠀⢂⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⠀⠀⠀⠀⡨⠄⠀⠀⢈⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠈⠢
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠴⠊⠀⠀⠉⠁⠢⢴⡀⠊⠀⠀⠀⠔⠁⠐⠀⢁⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⠀⠀⠀⠱⠀⢀⢀⡀⠘⠢⠤⠄⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢄⠠⡀⠀⠀⠀⠀⠀⠁⠈⠌⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤

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

⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⠤⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠔⠂⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡸⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣄⠀⠀⠀⡀⠀⠀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⡄⠀⡈⠀⠀⢸⢷⣄⣀⣀⢶⣈⣫⣤⡾⠄
⠀⠀⠀⠀⠀⣀⣴⣫⣧⡤⠀⠀⠀⠀⠀⢀⠶⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠉⠀⠉⠋⠛⠉⠉
⠀⠀⠀⠀⠒⠈⡞⠫⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠚⠡⠀⠀⡹⠶⠲⠾⢾⣧⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⣀⠀⡀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢀⢄⡀⠀⠀⠀⠀⠀⡀⠀⠑⠾⠁⠐⣄⠂⠀⠀⠀⠀⠀⠀⠐⡚⣖⠰⡒⢲⠂
⠀⠀⠀⠀⠀⡀⠀⠂⠀⠈⢂⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢤⣄⣠⣀⠉⠁⢀⠇⠉
⠀⠀⠀⠀⠀⡹⣄⣠⣴⣤⡤⠷⠖⠚⠁⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠘⠗⠞⣈⣭⣿⢇⣁⡂⠀⠀⢀⢀⡄
⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⢼⠀⠀⠀⠀⠀⠒⠞⢀⣠⣾⣭⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⠢⢀⠀⠀⠈⠉⠀⠠⠅⠀⠈
⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠠⠀⠐⣢⠤⠠⠀⠐⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠈⠑⠪⢄⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠂⠒⠈⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠘⠄⡀⠂⢂⣴⠈⠀⠀⠈⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠤⠀⠒⠒⠒⠒⠒⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢠⠀⠀⢸⡆
⠀⠀⡠⠋⠀⠀⠀⢀⣀⡀⢀⣀⣀⢀⡀⢳⡄⠀⠀⠨⠤⠤⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠤⢰⡦⠄⠀⠀⠀⠀⡟
⠀⠀⡅⠀⣤⣔⡚⡿⡭⢵⣿⡎⡤⠤⢴⡚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠙⠲⢼⣛⢻⡙⠶⠾⠕⠞⣚⣥⠟⠛⠁⠀⠀⠀⠀⢀⠈⠁⠀⠘⡇⠐⠉⢉⠀⠠⠀⠀⠀⠀⠀⠀⠓⢄⡀
⠀⠀⠀⠀⠂⡈⠀⠉⠙⠛⠉⠉⢁⡄⠀⠀⢀⠀⠐⠀⠀⠉⠂⠀⡤⠜⠃⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠤⠄
⠀⠀⠀⡖⡦⣦⣠⣀⣠⣀⣤⣦⢆⣄⢠
⠀⠀⠀⠘⠁⠋⠛⠉⠛⠙⠚⠛⠛⠛⠙⠃
⠀⠀⠀⠀⠒⠠⠰⠂⠠⠤⠐⠦⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠛⢿⣄⠀⠀⡈⢡⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠑⣿⠀⢄⣀⣈⣟⢻⣿⡟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠶⡶⣟⣒⠚⠻⢆⠉⠻⣿⡷⠃⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠼⣀⠉⠙⠺⢤⡐⡘⣇⠀⡠⠒⢠⡀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠂⠄⠠⢬⢦⣄⣠⣄⣹⣤⡟⣦⣀⡀⠀⡃⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠚⠒⠄⠠⠀⣸⠉⠿⢠⡼⠋⢹⡄⡆⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠦⠀⠀⠀⠉⡉⠑⠀⠀⠀⠀⠾⢿⣧⣀⣄⣀⡀⠼⠒⢬⣆⠀⠔⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⡀⠀⠀⠀⠁⠙⠂⠀⢠⡄⢀⡌⠁⠉⠉⠛⢀⣀⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠈⠃⡶⠚⠃⠀⠀⣠⠚⠀⡀⠀⠀⠐⠷⢢⠛⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⡘⢀⠠⣄⣧⣀⠙⡅⠀⠻⣤⡤⠀⣀⣼⣄⣾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠅⠘⢧⡛⣿⠩⠀⠈⣻⠋⠀⠰⣾⠏⠁⠸⡀⠈⡹⠟⡿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢡⡈⠸⣿⡇⡏⢀⠀⠀⣹⡄⠀⠀⠘⢯⣂⠀⠈⠉⡵⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⠷⢹⠰⢡⡿⠒⢉⡥⠓⢦⣀⣀⡌⠀⠀⠐⠚⠒⠌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡷⠒⠛⠶⢾⡄⢧⡀⠀⠀⠀⠀⡦⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠊⢛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⣠⣿⡆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠃
⠀⠀⠠⣶⣷⣿⢿⣯⣿⣅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡰⣾⠅⠀⠐⢉⠡
⠀⠀⣰⣿⣿⣿⢦⣿⡯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠘⠁⠀⡏⠀⠀⡄
⠀⣰⢙⣽⢯⢻⣿⣣⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡆⠀⠄
⠜⠀⠠⢷⣶⣿⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠂⠀⠶⠁
⠀⠀⠀⠊⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠴⠖⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠑⢀⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣖⡶⠀⠀⠡⣄⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⣀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠡⢄⠀⣴⠉⡹⠈⠛⠿⣿⣾⣦⡈⠈⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢠⣴⠃⡀⠀⠀⠀⠠⠈⢀⠩⠻⠗⢀⢈⠀⢃
⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠐⠒⢻⡅⣀⠀⠐⠀⠐⢀⣀⡀⠐⠊⣹⣶⡁⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢼⣷⣼⣆⣠⠢⠾⢶⣊⢻⣵⡖⣽⠃⠀⠀⠈⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠈⣿⣿⣏⣶⢲⣍⣺⡶⣸⣿⠧⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠻⣿⣅⢺⣿⣷⠿⡝⠚⠃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠂⢁⠁⠋⠀⠁⠀⠀⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁
⠀⠀⠀⠐⠸⡆⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢰
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠈⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⡆⠀⠀⠀⠀⡜⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⡜⢁⠎⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢰⠃⠀⡠⠋⢠⠊⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡰⠃⠀⢰⠁⢰⠁⠠⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠀⢀⠀⢃⠀⡇⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠁⡔⠁⠀⠘⡄⠘⡄⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠸⠀⠙⢄⠀⠈⠦⡈⢦⡀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉
⠀⠀⠀⠀⢀⡠⠤⠖⠒⠒⢉⣉⣉⣉⠉⠁⣀⠤⠤⢀⠀⠀⠀⠉⢉⠭⢍⡉⠒⠒⠲⠄⢄⡀
⠀⠀⠀⣼⡁⠀⠀⠀⣀⡜⠁⠀⠈⠉⢳⠊⠀⠀⠀⠀⠑⡄⡎⠉⠃⠀⠀⠘⠓⡄⠀⠀⠀⢈⣧
⠀⠀⠀⡏⠉⠒⠲⠴⢥⣈⣀⣀⣀⠢⣽⣀⣠⠤⠤⠴⠒⠓⠛⢲⡀⣀⢀⣄⣴⠥⠤⠖⠒⠉⡹
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣔⢉⡉⠉⠒⢄⡴⠃
⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠵⠮⢕⠤⣀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢉⡉⠉⠉⢩⡉⠉⠉⢉⡁⠀⣠⡄⠀⠀⠀⠀⠀⠂⢑⡢⣀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣧⣼⠈⢦⢤⠃⠸⣤⡔⠁⣇⣜⣁⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠥⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠓⠚⠒⠚⠓⠛⠚⠓⠉⠁

⡆⢢⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡔
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⠀⢘⠁⠂⡆⢸⠁⡜⡄⡮⢅⠀⠀⠨⠀⠀⠪⡀⢹⠀⡅⡅⡎⠈⠆⡧⠁⡇
⣶⣶⡶⣶⣶⣶⣶⣶⣾⣶⣷⣷⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠖⠒⠒⠒⠦⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠔⣒⣊⡉⠉⠀⠀⠀⢀⣠⣴⣒⣒⣷⣦⣄⠀⠉⠉⢙⣒⣲⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠀⠀⡠⠞⠋⡽⠛⠛⢛⡶⠒⢉⡽⣋⣉⠙⢿⣶⣦⡙⣆⣴⡾⠋⣁⣄⠩⠑⠲⡄⠉⠉⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⠂⣀⣀⣀⣼⠀⣀⡼⢦⣦⡀⣾⢰⡶⣾⠉⠉⣉⠛⢦⣝⢯⣷⣯⢸⡀⡾⠁⠈⢳⣄⠀⠸⡶⠦⣌⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡴⣺⠭⠕⠋⢉⡻⠊⣁⣀⣴⣦⠑⡽⡌⠳⣼⡟⠳⣦⣙⠢⣝⢷⡝⣿⡆⢹⡇⡴⠋⠽⠿⣦⡠⣯⣄⡌⠳⣀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠞⢡⡟⡴⠁⠠⠀⢰⠏⡰⣫⠟⠀⠀⢸⠆⡷⠈⢲⣌⣻⣶⣦⣙⢷⣌⢷⣹⡎⡿⠸⣿⡀⠀⠀⠀⢈⣿⡷⢶⣟⣳⣮⣙⡆⠱⣄
⠀⠀⠀⠀⠀⡰⠋⠊⡸⡞⠀⠀⠀⢰⠇⡸⠑⠁⠀⠀⠀⠘⣆⡏⣹⡟⠉⠅⡐⢀⠉⠙⣿⣮⣿⠟⠙⠲⢧⡱⢤⡠⠾⣿⣩⡿⠷⠊⠉⠀⠈⠻⡳⣌⢢⡀
⠀⠀⠀⢠⠞⠀⠀⠀⢡⣷⠀⠰⠄⢸⡄⢇⠀⠦⠀⢀⠴⣲⡟⡿⢿⠀⠀⠀⢀⠰⠒⡀⢘⣇⣀⣤⠖⠶⠖⣛⣿⡛⠛⡾⠁⠀⠀⡁⠀⣀⠀⠀⠹⣽⡐⠙⢄
⠀⠀⢰⠃⠀⠀⢠⣴⣯⣛⢦⣀⣀⣀⣙⡮⣷⡶⣾⣵⣾⣯⠤⠧⠬⣶⢤⣀⠀⠄⣈⡴⠊⢸⣥⡦⠤⠔⠋⠁⠈⣿⠾⣇⠀⠀⠀⠀⠀⢀⠀⠀⢸⢃⡇⠀⠈⢳
⠀⠀⠸⡄⠁⢀⡿⣍⠳⣝⢷⡹⡿⠟⢡⡜⠁⡴⠁⠀⠀⠄⠀⢀⡀⠈⣗⣎⢉⡩⡥⣄⢀⠞⠀⠀⠀⠀⠀⠀⢀⣼⡲⣼⣄⠀⠄⠀⠐⣀⣀⠀⡸⣼⠀⠀⠀⡞
⠀⠀⠀⢳⠀⢸⣷⡘⢷⡘⢆⡻⢇⣠⠞⠀⠀⡇⠀⠡⠀⠁⠀⠄⠀⠀⢸⡞⠁⠀⢹⡌⡛⢄⠀⢀⣠⠔⠒⠋⠹⠀⢹⠘⡏⠓⢤⣔⡋⠉⣠⣍⠳⡁⠀⠀⣸
⠀⠀⠀⠈⡇⠘⣿⣻⡈⣷⠸⣷⠊⠁⠀⣠⣀⣧⠀⠄⠀⢀⠀⠒⡀⠀⡞⣇⠀⠀⠀⠱⣄⡘⣏⡟⠀⠀⠀⠀⡠⣠⠎⣰⢟⡼⠋⣩⠟⠛⣯⡙⡄⣷⠀⢠⠇
⠀⠀⠀⠀⠸⡄⢻⢿⣇⢹⡆⠉⣧⣤⡾⢧⡙⡟⠢⡄⠀⠠⠀⠀⣀⣼⡵⠉⢣⡀⠀⠀⠈⢳⡘⢷⠤⣤⠶⠯⠾⣥⡜⢣⣾⣷⢰⡏⡐⢰⡏⢻⡅⡿⠀⡞
⠀⠀⠀⠀⠀⢣⠘⡄⠹⣙⢳⡶⢳⣿⡒⢦⣻⡟⠀⠙⡦⣤⣴⣪⡔⡟⣇⠀⠀⣣⡀⠀⠀⠀⢣⣼⠞⠁⠀⠤⠀⠈⠻⣸⣿⡇⣿⠠⠇⣿⠀⡿⣿⠃⢸⠁
⠀⠀⠀⠀⠀⠘⡆⠘⢦⣙⣛⣀⣼⠉⢳⡌⣷⠷⠦⣤⡇⠀⠉⠠⣎⡀⢸⣶⢾⣋⡭⠶⢶⣾⣽⡏⠠⡀⠀⠂⠠⠀⠀⠈⢻⣷⢿⢸⡇⣿⢸⣿⡏⢀⠇
⠀⠀⠀⠀⠀⠀⢹⡀⢁⠀⠀⠠⡟⠻⣦⢻⡟⠀⠀⠙⢿⠖⢤⡀⢀⣠⢃⡇⠀⠀⠀⠀⡆⠈⣾⠃⠀⠀⡀⢀⠀⠀⠐⠀⢠⣿⡼⣏⣧⢹⣮⡿⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢷⣤⣁⠂⠀⠙⢦⣽⡿⣄⠀⠀⢀⡼⠀⢀⣿⣽⠁⡞⠀⠀⠀⠀⣀⢀⡴⢻⣄⠀⠉⠀⠠⠀⠀⠀⡠⣫⠏⠻⠬⠾⠟⢋⣠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠭⢗⣒⠤⣌⣑⠮⠭⢭⡭⠒⠊⠙⣄⠸⡜⠿⠒⠶⠾⠯⠒⣁⣴⠋⢹⠭⣝⣢⣤⣒⣚⡭⠞⢃⣈⠤⢔⣚⠭⠕⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠪⠭⣗⡲⠤⣄⡀⠂⠈⠳⣌⡒⠦⠤⠒⠚⣉⡥⣯⣤⠋⠠⠀⢈⣉⡥⢴⣒⡯⠽⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠮⢭⣒⡢⠤⣉⡙⠛⠉⠉⠁⠀⣀⡠⠤⣒⡪⠭⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠭⢝⣒⣒⣺⠭⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢶⣤⡀⠀⠀⠀⠀⣀⣀⣀⡀
⣰⡞⠛⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣤⡀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠛⠁⠀⠀⠀⠘⠋⠉⠉⠛⠷⡦
⢿⣄⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⢀⣤⣤⡀⠀⠀⢀⣤⣴⡶⠀⠀⠀⠀⣠⣤⣀
⠀⠙⠛⠛⠷⠶⢶⣤⣤⣄⣀⣀⠉⠙⠻⠶⣦⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⣠⡾⠛⠛⠻⣦⡀⠘⠃⠀⢸⣇⣨⡿⠀⠐⠛⠁⣀⣀⣠⣄⠀⣾⠋⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⢿⣧⣤⣄⣈⣉⠉⣿⡏⠛⠛⠻⠷⠶⣦⣤⣼⣧⣀⡀⠀⠀⠉⠉⠀⠀⣠⡶⠟⠋⠉⢹⡟⠀⠻⣦⣤⡾⠏⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠶⣦⣾⣯⣀⣀⡀⢠⡿⠁⠀⠀⠀⠀⢴⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠶⠶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⡉⠉⠙⠛⠛⠷⠶⢶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⠶⣦⣤⣤⣀⣀⡉⠉⠙⠛⠛⠷⠶⢶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠶⠶⣦⣤⣤⣀⣀⡉⠉⠙⠛⠛⠷⢶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠳⠶⠦⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⢳⡄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣸⠃⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠉⠁⠀⠀⢸⡇⠀⠀⠈⠉⠉⠛⠛⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣤⣍⣤⣮⣭⣧⣥⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣲⠀⠀⢀⣤⠀⠰⢴⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠾⣾⠏⢩⠙⣩⠁⠀⣠⢀⠁⠀⣋⡛⠦⡀⠆⠒⠀⠠⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⢰⡏⢀⡡⠤⢶⣂⣀⣉⠃⢀⣃⠀⢄⠀⣻⢠⠀⠀⠠⠤⠤⠠⡌⣐⡟⠁⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⠈⣰⣯⡔⣋⠛⠹⣿⠋⠸⠄⠈⢁⣀⠆⠀⣀⡁⡇⢀⠀⡀⠐⢔⡿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠛⣿⢸⠍⢠⣿⠘⣧⠈⠔⡁⠀⢀⠘⠏⢀⣻⡏⢀⡈⠀⣠⠶⠋⢼⢋⣤⡜⢀⡷⢀⡄⢀⣴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠔⢛⠃⠐⢋⡼⣏⠻⠶⣌⡙⠀⠚⢀⢁⡉⠙⠤⠚⠣⣾⠙⠂⠀⢠⡈⢻⡷⡀⠀⢸⣷⡿⢱⣮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠰⠙⣦⠾⡟⠁⢪⣿⠂⠉⣀⠐⠂⠐⠉⠀⠀⠀⠀⠀⠀⠄⠃⠀⣨⠎⠉⠑⢷⣢⣄⡿⡀⢁⠠⠆⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠠⠀⠎⠀⡀⠄⣤⡁⠀⢠⠋⠴⢛⠝⣄⠞⠀⠀⠀⣤⣤⣶⠴⠖⠀⠀⡘⣍⠀⠀⠀⠈⠑⣿⣿⠅⠊⠃⠙⠛⠂⠱
⠀⠀⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠐⠁⠀⠘⢡⠀⠀⠶⣿⠋⢠⢿⡄⠀⠀⢰⡟⠻⠁⠂⠠⠀⣼⡷⠉⣭⡠⠀⠀⠀⢻⣿⡇⠀⠁⠸⠶⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢁⡄⡰⢦⠶⠎⠠⠁⠀⠀⠀⢢⣠⢦⠇⠀⡁⠈⢏⠀⠈⡹⣷⡀⠴⢋⣥⠜⣡⡄⣤⡿⠓⠂⠀⢀⣌⡙⢇⡴⠁⣿⡉⠟⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣦⡄⣤⡀⠀⣀⣄⠈⠹⢿⠀⡀⠨⠀⠀⠫⠑⢦⡀⠈⢱⣦⣍⡓⠈⠁⠀⠀⠀⠀⠀⢀⠄⣿⡀⠀⢡⡶⠄⠀⣉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⠀⠀⠀⠁⠉⢀⣠⣶⣀⠾⠂⠒⠔⠠⢀⠀⠙⠖⠋⢀⢸⡽⢯⣭⠄⣠⠔⠋⢻⢿⣦⣤⠿⠷⠈⠻⢬⣄⣩⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠿⣯⣿⣁⠰⠟⠈⠁⣨⠉⠀⠁⠀⠀⠀⠀⠈⢇⡌⠛⠟⠹⠋⣀⠈⠤⢀⠆⠈⠀⠁⠀⠀⠀⠀⠀⢀⠉⣤⣤⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠒⡦⠀⢤⠟⠁⠀⡀⠀⢀⣀⠉⠀⢰⣶⡞⠶⣤⡠⠀⠀⢱⣀⠀⠀⣠⡏⠙⠙⠁⠀⠀⠀⠂⠠⢸⠀⢸⡀⠈⣠⠻⡷⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠆⡀⠀⣧⠐⠜⢋⠿⣤⠀⠈⠉⢳⣀⠈⢷⠀⠀⠈⢋⢠⡎⡈⢀⠀⠘⠁⠀⠈⠰⠀⠀⢸⠀⠸⢴⣻⡶⠋⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠇⠀⠁⠊⠀⠆⠀⠳⣳⣤⣤⢾⠋⠐⣤⢿⣶⠶⠛⣾⡇⠣⣘⡆⠀⠀⠀⠀⢀⣀⠸⠀⠀⢠⠈⠉⠁⠄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠘⣷⠄⠠⠐⠿⢾⡆⠀⠟⠫⡜⠘⠂⢸⡇⠋⣿⠒⠀⠋⡇⠀⢰⡇⠀⠀⠓⠂⠀⠍⢧⠈⠁⡈⠋⠐⠁⠀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡄⠀⠃⢀⠀⠚⣡⠄⢢⡄⠀⣜⠓⢈⣡⡔⡟⠀⢀⣾⠻⢿⠘⠁⠈⣧⣤⠈⣤⠄⢐⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡅⠈⡀⠃⠀⠰⣸⢧⡀⢋⠀⡟⡀⢹⣧⣤⣾⠧⠉⠈⠃⠠⡈⠙⣻⠶⠘⠗⠀⠀⠀⠘⠀⠈⠐⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⠀⠀⠀⠁⢠⢻⠃⢀⠄⢀⣤⢚⡙⠿⢼⠶⠀⢨⡇⣤⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠉⠀⢀⠐⠸⣇⠀⢀⡰⠀⠈⣀⡀⠀⠠⠰⠊⡘⠁⡙⠂⠺⢷⣤⣀⣀⡀⢀⠀⣀⡠⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠴⣤⠋⢯⡀⢈⢈⠀⠀⠀⣠⠘⣇⠀⡤⢁⡐⠀⠞⠊⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠂⠀⠚⠓⠈⠉⠀⠘⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⠀⠀⠀⠀⠺⣅⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠨⠗⠚⠜⠀⠀⠀⠀⠀⣀⢮⠳⠶⠖⠔⡇⣀⢀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣫⣥⡈⣆⠀⣀⣸⢠⣟⡿⠿⠿⣶⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣥⠾⣿⡿⠛⠁⠀⠀⠤⠶⠿⠟⠁⠀⠀⠀⠉⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⢀⣴⠲⡋⢀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⢀⠔⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡤⠤⠊⠉⠱⣬⣧⡸⠁
⠀⠀⠀⠀⡰⠋⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣮⢳⣀⠜
⠀⣠⠴⡶⠁⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⣠⠃
⡞⠀⢰⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢉⡴⠁
⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉⠁⠀⣠⠞
⠀⠳⣍⠑⠒⠶⠤⠤⠤⣤⣀⣀⣀⣀⣀⣤⣤⡤⠤⠤⠤⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⣠⠾⠁
⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⣠⠃
⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠀⢀⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠶⢦⣤⣄⣀⠖⡛⠛⠛⠛⠛⠛⠿⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠷⠦⣶⣄⣀⠉⠢⣄⠀⠀⠀⠀⠀⠈⠙⠻⢷⣷⣤⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⣀⠀⠀⠀⠉⠙⠿⣦⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠠⠄⡀⠀⠀⠀⠠⠽⣟⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⡠⠔⠒⠂⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⠿⠛⠛⠛⠛⠛⠶⢦⣤⣳⡀⠀⠀⠀⠐⠊⠉⠀⠤⠄⠀⠞⠐⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢥⣤⣀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣷⠀⠀⣠⡶⠿⠶⠾⠶⣶⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠄⣙⣧⠀⠀⠀⠀⣼⢫⣀⣨⣥⣤⣤⣭⣗⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣀⠀⠀⢈⡃⠀⠀⢸⣷⠟⠋⠉⠀⠀⠀⠀⣉⠽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠉⠻⢿⣦⣀⣿⡄⠀⠘⢿⠿⢶⡄⠀⠀⠀⡠⠤⠒⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⣽⠿⢟⣛⣉⣉⣩⣭⣙⣶⣄⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣀⣀⣉⣉⣉⠲⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⠭⠖⠊⠉⠁⠀⠀⠀⠀⡬⣻⣿⣿⠷⠾⠟⠻⠶⢷⣤⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⡿⠗⠢⡀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠺⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠷⠀⠀⢸⡆⠀⠀⠀⠀⣰⣿⣄⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢠⠏⠀⠈⣙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⢹⡄⠀⠀⠀⠀⠈⢀⡠⠘⠯⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠠⠖⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣶⠆⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣥⣰⣿⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⢸⣾⠿⢿⣿⣸⡇⢸⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠙⢶⣾⣿⠟⠀⢸⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠛⠁⠀⠀⠀⢻⣿⠟⠿⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠈⠀⢀⣤⣷⣷⣤⣄⠀⠀⠀⠰⠀⠈⠙⠻⢿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠘⢏⠹⣷⡶⠾⡇⠀⠀⣣⠄⠀⠀⠀⠀⠙⠿⢿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠐⠿⠿⠛⢋⣴⣾⣿⣦⡄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠋⠉⠉⣿⣆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡄⠀⠀⠀⠀⠀⠀⠀⡀⣴⡿⠁⣠⡴⠊⢹⠏⠀⠀⠀⠀⠈⠀⠠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣷⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣿⣦⡀⣠⡀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠈⠁⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣈⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡦⠀⠀⠙⠚⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⡷⠀⠀⠀⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠔⠀⠀⠙⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢩⡶⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⡴⡶⡛⣻⠉⠉⣿⢍⢟⢻⢶⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢿⡌⡜⡰⢸⡄⠀⣿⡌⣆⣣⠷⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠙⠲⠭⣝⣛⣻⠁⠀⣸⠭⠽⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡟⠀⠀⠀⠀⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢠⡇⠀⢠⠇⢀⡤⠖⠊⠁⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢶⣟⣹⡟⠉⣟⢒⣶⡄⢸⠄⠀⠀⠀⡞⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢭⡇⠀⣯⣭⠭⠴⠋⠀⠀⠀⡼⠁⠀⢰⠃⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⡏⠀⠀⠀⠀⠀⡝⠙⡶⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢳⠀⠀⠀⠀⠀⢀⡏⠀⠀⡾⠀⠀⠀⠀⢀⡞⠀⣸⠁⠀⣀⡠⠔⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠀⠀⠀⣸⠀⠀⢠⡇⠀⠀⠀⢠⠎⠀⣰⠃⢰⢋⣁⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠦⣄⠀⠳⡀⠈⢳⡀⠀⠀⡏⠀⠀⢸⠀⠀⠀⢠⠏⠀⣰⠃⠀⠈⠮⣓⣮⠋⣱⠦⣄⠸⡄
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠙⢦⠹⡄⠀⠹⣄⢸⡇⠀⠀⢸⠀⠀⠀⡟⠀⢠⠇⠀⠀⠀⠀⡸⠃⣰⠯⠭⠭⠞⠁
⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⢀⣀⡠⠞⠀⠹⡄⠀⠘⢾⡇⠀⠀⢸⡀⠀⣸⠁⠀⢸⠀⠀⢀⡤⠊⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠉⢇⠀⠀⠀⠀⢳⡀⠀⠘⡇⠀⠀⠈⣇⠀⡟⠀⠀⣿⣠⠖⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠳⢤⣀⣀⡀⢧⠀⠀⢳⠀⠀⠀⢹⡄⡇⠀⠀⢸⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣹⠺⡆⠀⠈⢧⡀⠀⣰⠃⢧⠀⠀⢸⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⢧⣀⣀⡞⠉⠉⠁⠀⠘⠦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢈⣡⣤⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⡿⠿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢤⡀⠒⠶⠾⢦⣔⢾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇⣤⣤⣤⣈⠻⢶⣶⣦⣶⣶⣤⣄⣤⣤⣴⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⣿⣿⣿⣿⣧⡄⠀⠉⠛⢻⣿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠶⢂⣤⣴⣶⢶⣾⣶⣶⣦⣾⠀⢠⡿⠛⣻⣟⣠⣿⠷⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡌⢿⡿⠟⠀⠃⠀⠈⣠⣾⣩⣹⡿⠑⡆⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⣶⠄⠀⠀⠀⠀⠀⠿⠿⠻⠛⠏⠁⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢦⠀⠸⠀⠀⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⡰⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠬⣠⣶⣧⣄⠃⠀⠀⣸⣶⡀⢸⣄⠀⢀⣠⠎⠀⠊⠁
⠀⠀⠀⠀⠂⠀⢣⡀⣰⡈⠛⢹⣿⣯⠤⢦⣿⣿⣷⣼⣧⣖⣼⡃⠄
⠀⠀⠀⠀⠀⠀⠻⠋⠉⣿⣿⣻⣿⣿⣷⣄⣿⣿⢉⠙⡀⠟⠋
⠀⠀⠀⠀⠀⠀⠺⣟⠁⠈⢻⢛⣾⣿⠋⡙⣛⠋
⠀⠀⠀⠀⠀⠀⠈⠟⠓⠀⢠⠨⠅⠈⠁⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣸⣄⠀⢆⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠛⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡿⠃⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣠⣿⡇⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⢻⣶⣿⢿⣿⣁⡿⠀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⢷⣤⣴⣿⡿⠃⠘⣧⣼⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠙⣿⡟⠁⠀⠀⢿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣀⠀⡀⠀⠀⠈⠻⠟⠈⠙⢿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠀⠀⢠⣾⣿⣿⣷⢶⡄⠀⠀⠀⠿⠀⠀⠈⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠘⣏⢻⣿⣴⣾⣿⠀⠀⠘⣡⡀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠘⢤⣾⣶⣶⡾⢂⣤⣾⣦⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢚⣻⡿⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⣿⠉⠀⠀⢸⣿⡇⠀⠀⠀⠈⠻⠄⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⢃⣀⣴⡞⠁⢿⠇⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠄⠄⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⣇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣆⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⣷⡄⢠⣄⢰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⠀⠉⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠀⠀⠀⠀⠀⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠾⣫⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⠂⠀⠀⠈⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣦⠀⠀⠀⣤⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠁⡀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠿⠋⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⠃⠀⣤⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⣧⠀⠀⠀⠀⣿⣤⠤⣄⠀⠀⢀⣤⡀⠀⢀⣤⣴⡇⠀⢠⣿⠀⣾⣡⡼⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢹⡆⠀⠀⢸⣿⣡⠆⠘⣧⣴⣿⡀⡿⢀⡾⢡⣿⠁⢀⣾⠇⠀⣿⠁⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⣾⠉⣟⠛⢻⡏⢾⣀⡿⠛⢹⣇⡞⢸⣀⡞⣿⠀⠀⠈⠛⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠘⣷⢀⡿⠀⠻⠶⠛⠀⠈⠋⠁⠀⠀⠉⠀⠈⠉⠘⠷⠶⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣀⣤⡤⠶⠒⢛⣋⣩⡍⠉⠉⠉⠍⠉⠉⠉⢩⠗⠋⡭⠛⠛⠛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉⠀⢀⣀⡀⠀⠀⠀⢀⣀⣤⣀⣠⠒⡏⢹⠛⣟⢦⡈⢢⡀⠀⠀⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣰⠋⢉⡉⠉⠓⢲⣯⠔⢶⡞⠉⣦⡑⢌⠲⣌⠳⡙⣄⢹⡀⠀⣀⠀⠀⣧⡙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣀⣤⣅⠀⠀⠀⢀⣠⠾⠾⠤⣾⢣⡘⢇⠙⢌⠳⣌⢣⡹⣌⢦⠳⠞⠉⠓⡚⢁⠛⢄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠐⠃⠀⣰⠋⠉⠀⢘⡾⠳⢖⡫⠭⠤⠴⠊⣉⣉⣧⢳⡈⢣⠀⠙⢎⢧⠉⠙⣆⠳⡀⠀⠯⣀⡁⠀⠈⢣⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣀⣀⣸⣠⠴⣻⠿⠶⣒⣋⣠⠴⠋⣉⡭⠤⠤⠜⣧⢹⠀⢙⡷⠛⠦⡓⢄⠸⣗⢭⡢⢄⠀⢹⠀⠀⢀⢧⢀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠐⣇⡔⣋⡥⠤⠤⣴⡾⠕⢒⣊⡵⠒⠒⢒⣫⠥⢖⡒⠂⢁⣹⡆⢧⠈⠓⢦⠀⠈⢢⡱⡌⢆⠙⣦⡱⡌⠑⢒⡡⠊⠘⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠊⠥⠒⠒⣫⡥⠖⠛⠦⣄⠀⣠⠞⣡⠖⣫⠥⠒⢊⡭⠂⣹⡌⢧⡀⠘⠢⠒⠚⣳⣝⡢⣥⣤⡾⠞⠛⠛⠒⠒⢤⡇⠠⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡩⢤⡟⠁⠀⠀⠀⠀⠈⢳⡏⠐⣅⡀⠓⠤⢤⣈⡳⣄⢣⠘⢦⣉⣓⣒⣈⡭⢶⠎⣩⠋⣼⠀⠀⠀⠄⠀⠀⠀⢳⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠸⡏⢷⣜⠀⣠⠞⠛⢦⡀⠀⠈⣿⠦⣄⣉⡉⠓⢦⡀⠈⢧⠹⡗⠤⠏⢉⢏⣠⠬⠥⢖⣡⠾⠖⠓⠒⢦⡀⠀⠀⢀⡾⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⢦⣇⠀⠀⠘⡇⠀⠀⣿⠈⣀⠒⠙⢳⣄⡑⠒⠚⠒⢿⣄⡰⣫⠏⡴⠚⠉⢹⠁⠀⠀⠀⠀⠀⠙⣆⡠⠚⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠷⣤⣀⡇⠀⠀⣿⠀⣒⠛⠛⠋⣊⠽⢛⢝⡛⢦⣉⠙⣁⣾⠴⠒⠒⠺⡄⠀⠀⠀⠁⠀⠀⢻⢀⣠⠞⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠈⠙⠳⢦⣴⣏⠒⠚⠿⠭⠭⢒⡪⢟⡭⠒⠉⠉⠉⡿⠁⠀⠠⠀⠀⢹⡀⠂⠀⠀⣀⣤⠾⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⣶⣭⣥⣖⣉⣀⣀⠀⠀⢰⡃⢀⣀⣀⣀⣀⣨⣧⡴⠞⠛⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠠⠄⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠉⠁⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡿⡿⠿⡟⢛⣋⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣤⣤⣴⣶⣶⣤⣤⣴⣶⣾⠿⠿⠛⣛⣋⣩⣭⣤⣴⣶⣿⡿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⠿⣿⢿⢛⡏⡟⡇⣿⣿⣿⣿⣶⣶⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⡏⢹⢸⠀⡇⢸⢰⡇⡏⡇⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⡿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⢾⢸⠀⡇⢸⠸⡆⡇⡇⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣾⢸⠀⡇⢸⢸⠀⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡏⢸⠀⡇⢸⠸⣤⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⢸⠀⡇⢸⢸⣿⡅⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⢸⠀⡇⣼⢸⢻⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣾⢸⡇⡟⢸⠀⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⡇⣿⢸⡇⡇⢸⠀⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣨⣿⡇⣇⣿⣸⣇⣧⣸⣀⣇⡇⣿⣧⣤⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣋⠭⢭⣉⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣯⣤⠤⠬⣝⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣾⣷⣾⣿⣿⣿⣥⣴⠚⣉⣉⣭⣉⣍⣉⣙⠒⠢⢬⡙⠿⣷⣶⣬⣷⣼⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⣋⡭⠥⠒⠒⠒⠒⠢⠤⢍⣉⠛⢿⣷⣤⠤⠤⠤⠤⢬⣉⡓⢦⣬⣷⡿⢛⣉⣉⣉⣛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⢠⣿⠟⣵⠚⣡⠖⣊⣉⠭⠭⠭⣉⡓⠒⠤⣉⠲⣌⢻⣷⡖⠒⠒⠒⠦⣍⣾⡟⣡⠞⣩⠤⠴⠤⢬⡙⢦⡙⣿⣆
⠀⠀⠀⠀⣠⣼⣿⣴⣧⣾⣵⣾⣷⣶⣶⣶⣶⣶⣿⣷⣶⣿⣷⣾⣷⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣼⣧⣶⣿⣿⣦⣽⣤⣷⣼⣿⣄⡀
⠀⠀⠀⠀⣿⣟⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠈⣿⡆⠛⠃⠀⠛⠛⠀⠘⠛⠀⠛⠛⠀⠘⠛⠀⠛⠃⠀⠘⠛⠃⠘⠛⠃⠀⠛⠛⠀⠘⠛⠀⠘⠛⠃⠘⠛⠃⠛⢃⣿⡇
⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣾⡿⠋
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠛⠛⠛⠿⠿⠿⠿⠿⢿⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⣿⡇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠃
⠀⢰
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⢄⣔⣣⠒⢛⣋⣛⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢨⣾⣯⣿⣥⢾⣟⣿⣵⣤⣤⣌⠳⢄
⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⣾⣿⣟⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⣬⠠
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣿⣿⣷⣿⠇⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠙⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣋⡻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣻⡉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣤⡀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⠆⡹⠟⠀⠀⠀⣀⣩⣵⠹⣿⣾⠧⠄⣶⣿⢋⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣞⠁⠀⠀⠀⠀⠀⠀⠐⠒⠾⠟⠀⠀⠻⠷⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢄⠶⡀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⠀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡆⠀⠀⠀⠀⠀⡀⠀⠀⢠⢭⡽⠇⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⣿⡀⠀⠀⠀⠀⠁⢴⣆⡀⠀⠐⠲⠎⠋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⢿⣄⠀⠀⠀⣀⠀⢈⣉⠛⠙⠀⢰⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠘⣾⣿⣷⣤⣀⣿⡀⠈⠻⠿⠟⢀⣿⠁
⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠇⠀⠀⠀⢨⠻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⡏
⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠃⠀⠀⠀⠉⠙⠂⢷⣬⣿⣿⣿⣷⣿⡟⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠻⣿⣿⣿⠿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢐⣤⣶⠾⠟⠛⠲⠦⢀⡀⠐⢄⠰⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠑⢾⡿⡝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠉⠺⣎⢧
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠈⢦⠳⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠁⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠶⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠦⢹
⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣦⣿⠀⠘⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⢀⢸⡆
⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣧⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡠⠀⠀⠀⠀⠀⠱⠀⠈⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣦⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠭⠙⠉⠉⠙⠓⢄
⠀⠀⠀⠀⣀⣤⣤⡤⣤⣴⣷⣿⣽⣿⣿⣿⣿⣻⡿⣿⣇⠀⠀⠀⠀⣀⠤⠒⣒⢀⣴⡂⠁⡡⠋⠁⠀⠀⠐⠲⠢⢄⠀⠂
⠀⠀⣰⣿⣿⣷⣾⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⡼⠁⠀⠀⠀⠈⠁⠠⢊⠀⠘⠀⠀⠀⠀⠀⠄⠈⡀
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡀⠶⠄⠀⠀⠐⠁
⠀⠀⠘⢿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⠀⠀⠀⠈⠙⡄⠀⠉⠀⠂
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⢐⣠⡀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣿⣶⣢⣴⣦⣄⣀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡁⣀⢀⠈⠉⠳⠛⠀⠂⢤⢴⣶⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⡆⠀⠀⠀⠀⠀⠈⠃⠀⠀⠨⠉⠖⢄⡀⠀⠀⠀⠛⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣟⣿⣿⢿⣿⣿⠿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠆⠤⢤⠤⢤⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠑⠀⠀⠀⠂⠠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠄⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⣿⣿⣿⣷⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡇⢠⡄⢸⠀⠀⠂⡛⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠛⠸⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠨⣛⣦⣷⣾⣴⡀⢰⠟⠋⠁⡈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈

⠀⠀⡀⠀⣀
⠀⠰⠷⠾⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣿⣭⣯⣶⡾⣿⣲⡿⠦⣿⣻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⣖⣿⣿⣻⣿⣿⣾⣿⣿⣻⣷⣦⣽⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⡿⣿⣿⣻⣿⣿⣛⣯⣽⣟⣿⣿⠿⢻⣿⣭⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⢿⣛⣛⣯⣟⠛⠛⠻⠿⠿⢿⣿⣷⣿⣾⣿⣿⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣾⡟⣷⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣴⣿⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⣼⣿⡿⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣮⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠿⠛⠛⣿⣷⣦⠀⠀⠀⠀⣰⣶⠟⠛⠿⢦⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢉⣻⢻⣿⢿⣿⣷⣾⣿⣟⣻⢿⣷⠀⠀⣿⣿⠿⣿⡷⣶⣤⣿⣿⣟⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⢿⣸⣿⡾⠉⠉⠛⠛⠿⠛⣿⣟⠀⢠⣿⣧⠲⣾⡶⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠿⣸⣿⣿⣿⠀⠀⠀⠀⠀⢀⡼⡟⠀⠸⣷⡟⠀⠀⠀⣰⣻⣿⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣍⣿⣿⣿⣇⠀⠀⠀⠀⠘⢴⣿⣀⣰⣧⣿⢀⠴⠚⠁⢀⣾⢿⣯⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⡀⣴⣤⣶⣶⣾⣿⣿⣧⣤⣴⠊⠀⢀⡴⣻⣿⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣿⡏⠂⠛⠿⠛⠓⠴⠦⠬⡿⣧⠀⢠⢾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⣿⣿⣦⣤⣽⣿⡙⣒⣒⣚⣻⣿⣷⣿⣾⣿⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠋⠉⠛⠛⠻⠛⠻⠿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣄⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⣤⣿⣿⣿⣇⣾⣿⣿⡿
⠀⠀⠀⠁⠠⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀
⠀⠀⠀⠀⠀⠠⢉⣿⣗⡚⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣽⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠘⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠙⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⠾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠻⠃⠘⡄⢈⣔⣵⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢺⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠒⣛⣉⣉⣀⣀⡀⠀⠀⠀⠀⠤⠤⠄⣀⣀⣈⠉⠉⠑⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠴⠊⣁⠤⠖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⢤⣀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⢀⡴⢁⡴⠊⠀⠀⠀⠀⠀⢀⠄⠐⠀⠄⠄⠀⢄⠀⠈⠁⠈⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠢⢄⠀⠑⡄
⠀⠀⠀⠀⢀⡎⢀⠎⠠⠀⠀⡂⠀⠀⡠⠋⠀⠀⠀⣀⡠⠂⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠳⠀⠘⡆
⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠈⠀⠀⡬⠡⠀⠤⠔⠊⠁⠀⢀⡠⠆⠀⠀⠀⠀⠀⠉⠐⠄⠀⠀⠀⠀⠔⠢⢤⢄⡀⠀⠃⠀⢱
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠠⠀⠠⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠒⠁⠀⠀⠀⠀⠘⠀⢸⠀⠘⡆
⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠢⣄⡤⠤⠴⠂⢰⠀⢀⠁
⠀⠀⠀⠀⠈⣇⠈⢆⠀⠀⠀⠀⠀⠄⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠘⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⠀⣍⢦⡈⠒⢄⡀⠀⠀⠂⢀⠀⠀⠀⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⣀⠀⠄⠀⠀⣀⡼⠁⣠⡇
⠀⠀⠀⠀⠀⠘⡀⠙⠢⢄⡈⠑⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊⢁⡠⠞⢱
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⠉⠒⠢⠤⣀⣈⣉⡉⠉⠑⠒⠚⠒⠒⠒⠀⠤⠤⠐⠒⠒⠒⠛⢉⣉⣀⡤⠔⠚⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠶⠒⠚⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠚⠉⠉⢉⡭⠭⠭⢭⡛⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⡡⠤⢤⡀⠀⠀⠀⠀⠈⠆⡀⣀⡠⠟⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⠤⠤⣀⠀⠑⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⡔⠉⠀⠀⠀⠈⡧⠀⠀⢠⠖⠉⠉⠉⠉⠉⠙⡆⠀⠀⢠⠞⠉⠉⠉⠉⠲⡀⠈⢦
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠣⠤⠤⠤⠖⠊⠁⠀⠀⡇⠀⠀⠀⠀⢀⣀⠴⠁⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠱⣄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠑⠒⠒⠉⠉⠉⠀⠀⢀⣠⣀⡀⠓⠤⠤⠖⠚⠁⠀⠀⢀⠤⣌⢧
⠀⠀⠀⢰⠃⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢘⡞⡆
⠀⠀⠀⢸⠀⠀⠀⢇⠀⠀⠀⠀⣀⡤⠔⠋⣀⣀⣠⡤⢤⡤⢤⢤⠤⢤⠤⣤⠤⢤⣤⣀⡀⠀⢰⠂⠒⢦⠀⠈⠉⠀⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠁⠀⠈⠉⣠⡴⠚⠛⢅⡀⠈⢦⠀⡇⢸⢸⢀⡆⡴⠁⡠⢊⠴⢊⡩⠓⢦⡑⠦⠞⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠳⡀⠞⠉⢱⠀⣠⠚⠡⢤⣉⡒⠦⢌⡓⢄⠣⣡⢈⣘⣸⡜⣡⡮⢖⡥⣚⡥⠔⠊⣁⡙⣦⠀⢀⠖⣳⡼⠁
⠀⠀⠀⠀⠀⠘⠢⡀⠁⠀⣇⣉⣉⣐⣒⣺⣷⣶⣦⡭⠟⠋⠉⠉⠉⠉⠙⠛⢯⣭⡶⠶⠟⠛⡒⠒⢸⡇⠐⣲⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣙⣦⡐⠒⢒⣒⡦⠽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣭⣉⣉⣩⣭⡴⠾⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠒⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣞⣿⠿⠟⠛⠛⠳⣄⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠵⠋⠁⠀⠀⠀⠀⠀⣦⡘⣧⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆⣧⠴⠶⠦⣤⣀⡀⠀⠀⠀⠀⠸⠇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠁⢧⡀⠀⠀⠀⠈⠙⠳⣄⡀⠀⠀⠀⣼
⠀⠀⠀⠀⣠⡴⢞⣛⣛⡛⠻⢦⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣴⠃⠀⠈⠳⣦⡀⠀⠀⠀⠀⠈⠳⣄⠀⣰⠏
⣀⠀⣠⠞⠁⠀⠋⠉⠉⠁⠀⢀⡽⢦⠶⠛⠉⠉⠉⠉⠛⠾⣅⠀⠀⡀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣽⠞⠃
⠉⢿⠁⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠁⠀⠀⠀⢀⣠⡤⠿⠿⠷⣤⣀
⠀⣾⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⢻⠀⢶⡤⠖⠋⠁⠚⠛⠛⠻⠆⠉⠳⣄
⠀⢹⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢿
⠀⠈⢧⡀⠀⠀⠀⠀⡟⠀⠀⢠⡾⣆⠻⣄⠀⠀⠀⠀⠀⠀⠀⠟⣸⠁⣿⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢸
⠀⠀⠈⠛⢦⣄⣀⣘⣇⣠⡴⠋⠀⠙⢦⡘⢷⣄⠀⠀⠀⠀⢀⡴⠃⠀⣧⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠲⠿⠷⠤⠴⠞⠋⠀⠀⠀⠹⡄⠀⠀⠀⡾⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣰⡇⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠒⠀⠶⢤⣀
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣲⠄⠐⠣⠀⢄⡑⠻⣿⣿⣷⣶⠤⣮⠋
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⣿⡾⠁⠀⠀⠀⠀⠀⠀⡀⠈⠱⣤⣬⣿⣿⡄
⠀⠀⠀⠀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯⣻⡅⠀⠀⠀⠀⠜⢠⠀⠀⠀⠀⢘⣛⣿⣿⣏
⠀⠀⠀⠀⣠⡀⡀⠀⠀⠐⢺⣶⡅⠀⠀⠀⠀⠀⠀⠀⠘⣯⣹⣷⡄⠀⠀⠀⣠⣾⠿⢿⣷⣶⣿⣿⡿⠛
⠀⠀⠀⠀⣿⣿⣿⡀⣤⡀⡠⣞⣳⡄⠀⠀⠀⠀⠀⠀⠀⠉⠫⢬⣽⣛⡿⣵⣿⡇⠀⣡⣾⣿⣿⡋⠁
⠀⠀⠀⢰⣦⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢀⠛⣍⠉⡁⠀⠼⡿⢻⣿⠃⠀⠀⠀⠀⣠⡴⠲⢶⣶⣤⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠘⠩⢿⢽⣿⣶⣿⠟⠉⠀⠀⠀⢀⣾⠏⢀⡀⣼⣿⣯⡁⡀⠀⠀⣀⠀⠀⢀⡔⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⣠⠆⠀⠠⠺⣿⣿⣭⣿⣿⣟⣿⡟⠁⠀⠀⠈⣷⡄⠘⠇⠀⠀⠀⢨⡿⠃⠂⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢨⣿⣿⡟⠛⠁⠀⣻⣦⠄⠀⠀⠘⡇⠀⠀⠐⠚⠚⠙⣇⠀⠀⠀⠀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢀⣀⣘⣣⣼⣿⣿⣇⣀⣴⣶⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠙⢿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣆⡀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠁⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢂⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣍⢻⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣤⣿⢹⣟⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡏⡾⢸⢿⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⡾⣡⠏⣼⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⣫⡴⣫⣾⣛⣛⠷⣤⡲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡲⢾⣉⡞⣵⢫⡞⠋⢩⠾⠿⣿⢮⣻⣯⠍⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣈⠳⣬⣙⠒⢸⡇⣧⡻⢮⣽⢳⡎⠃⣼⣛⠿⢧⣛⠩⠶⢋⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣶⣿⣿⣤⣿⣮⣉⣻⣿⣟⣥⣞⣩⣿⣻⣶⣼⣷⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣤⣀⣉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⢉⣀⣠⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣋⣽⣿⣧⠴⣶⣤⣀
⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⣰⣿⣆⣀⣠⣤⣁⣤⣠⣶⣄⣀⣄⣉⣈⠁⢀⣀⠐⠂⠈⠛⣦⣄
⠀⠀⠀⠀⣰⣏⡴⡛⠛⠉⠀⠈⠪⣻⠁⠙⡭⡹⢹⣹⢹⡙⡏⣉⢋⢋⠟⡯⢴⣦⣀⡉⡤⠈⢣⡀
⠀⠀⠀⠀⡟⠁⠀⠀⠄⢀⠂⠄⡐⠈⢶⣄⠌⣱⡾⣏⣧⣕⣼⣏⣡⣪⢊⡴⠓⠉⡹⠶⣗⣄⠀⢱⡀
⠀⠀⠀⠀⢷⡀⡀⠀⠀⠠⠬⣒⣬⣑⣦⣜⡷⠿⠷⢿⣿⣿⣿⣿⣥⣿⣥⢤⣴⣮⣴⣵⣮⠿⣌⣋⠡
⠀⠀⠀⠀⠀⠻⣤⠒⣒⠺⠷⢶⣬⣽⣻⣿⡇⠀⠀⢰⡟⢿⣿⣶⣦⣤⣄⣀⡤⠍⠉⢉⡬⠟⢻⣥⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢬⣥⠶⢒⣛⣻⣿⠀⠀⠀⢸⠀⢸⣧⣙⠡⡉⠙⡻⠽⢍⠛⡻⠶⠄⣼⡛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢾⣿⠀⠀⠀⠀⡆⢻⣿⣿⡀⠀⠀⠈⠂⡀⣑⣌⣢⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡇⣼⠻⢽⣧⠴⠖⠚⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠠⣶⣾⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⣠⠂⣤⡀⡻⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⣵⣿⣾⣿⣿⣷⣮⣬⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣀⡀⣤⣀⣼⠟⠋⠁⠸⠸⡟⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⣗⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣠⡏⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⣀⣻⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⢿⢿⠻⠏⠿⠿⢿⢿⣷⣦⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠟⠛⣉⣡⣌⣤⣤⣤⣴⣶⣶⣄⣄⠁⠛⠙⠿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢋⣈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣬⣍⡻⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣟⠋⣟⠈⣋⠡⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⢟⡀⣽⡧⠈⠘⠁⠴⢧⣬⣿⡿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣛⣽⣧⣶⣙⣿⣿⡆⢰⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠏⣇⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣂⣉⣙⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠀⠁⢸⡟⠻⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⣴⣷⣾⣿⣿⠿⣿⣿⣿⠿⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣡⣤⣶⣶⣤⣄⣀⠢⡀
⠀⠀⣠⢔⣾⣿⡿⠋⢀⣉⣤⣶⣤⣴⣦⣴⣶⣤⣮⣙⡻⠆⠀⠀⠀⠀⠀⣧⠀⢠⣿⠀⠀⠀⠀⢀⣠⠀⠀⡰⠶⠿⠿⣿⠿⠿⠿⠿⠿⠿⢿⣷⣝⢢⡀
⠀⢰⣵⢿⣫⣥⣤⣾⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡇⠐⢸⣿⡀⠀⠀⠀⣿⣷⣶⣷⣶⣶⣶⣷⣶⣷⣶⣛⣿⣻⣗⣾⠶⠤⣬⡙⣆
⠀⡟⢋⣼⣿⣿⣿⣻⣻⣤⣬⣥⣿⣿⣾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⡁⠀⠀⠐⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡿⣖⠠
⠀⠰⣽⣿⣿⣿⠿⠿⠛⠉⠛⠻⡯⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⢹⡇⠀⠀⠀⢋⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⠿⠟⢻⣿⣿⣿⣿⣷⣞⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢡⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠀⠀⡷⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠀⠉⢻⡾⡇⢰⣾⣧⣶⣿⣿⣿⣿⣿⣿⣆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠀⢸⣷⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠇⠸⠟⠉⠙⠻⠿⢿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣴⣾⣹⣟⡻⢿⣛⣿⣻⣦⣄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣣⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣾⡷⢿⡿⠿⣿⡿⢛⣿⣿⣛⣋⣋⠃⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣿⠠⠈⠳⡀⠀⠀⠀⠀⠠⢽⣠⠀⣷⣾⣿⣿⣿⠿⣿⠎⡿⣿⣿⡿⠿⠇⠀⠀⣿⡇⣀⠀⠀⠀⠀⢠⡀⣟⠉
⠀⠀⢸⠇⠃⣠⠀⠀⠀⠀⢒⠀⢁⠀⠘⣿⣧⠸⣗⠀⠀⠀⠀⢈⢻⣠⡄⣿⡙⣿⣿⣿⠀⣹⢷⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢹⠄⠀⠀⠀⠘⡿⠟
⠀⠀⠠⡴⠆⠉⢀⣄⠀⠀⠘⠁⠀⠁⠀⠈⢿⣦⡙⡄⠀⠀⠀⢉⢹⣀⣀⣿⠃⠁⠋⢻⠀⣿⢸⠀⢠⣿⡀⠀⠀⢀⣾⡯⠀⡰⠀⠀⠐⣿⣾⣷
⠀⠀⠀⠀⣤⣤⣼⡍⠀⠀⠰⠡⠤⠁⢁⠀⠀⢻⡗⠈⢮⣂⠀⢉⣹⡅⠉⣿⠂⠀⠀⢸⠀⡿⢸⠀⠲⣿⡅⠀⢀⣾⡿⠁⢰⠃⢀⣤⣄⣸⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠛⠉⠀⣤⡖⠀⠀⣲⠀⠘⣀⠀⠀⢻⡀⠘⠿⢣⠈⠙⡧⠄⣿⠀⢸⠁⣼⢀⣷⡟⠀⣛⡇⠀⢀⣾⡏⢠⠰⡞⠀⠀⠀⣿⠛⢋⠀⠒⠡⡀
⠀⠀⠀⠀⠀⠀⠒⢃⡱⠁⠤⡄⠰⣂⢼⠿⠀⠀⣀⢷⠾⢤⡈⣷⣴⣧⣤⣿⢠⢺⣧⣿⣾⠃⡇⠀⠉⡟⢳⣿⠟⠀⠀⡘⠀⢸⣇⣠⡶⢀⡈⠛⡀⠒⠑
⠀⠀⠀⠐⠶⠀⠰⢣⠕⠀⣺⣏⠈⢛⠂⢀⣤⢀⣽⣷⠶⢼⡗⣼⢿⣿⣿⣯⡼⢸⣿⡹⡟⢠⡍⠙⢀⣧⣾⢏⡜⠀⡾⢠⡄⠾⣾⡇⠀⢺⠔⡠⢁⢀⡀
⠀⠀⠐⠷⠈⢠⡄⠉⢙⡚⣥⢾⡧⠰⢂⣌⢙⠉⣰⣟⠀⣺⣿⣸⣷⣿⣿⣿⡇⣿⣿⣷⢂⡼⢳⣾⣿⡟⢇⡾⠑⢸⠋⠀⡗⠀⠘⣇⣟⡀⢛⢀⡘⠚⠃
⠀⠀⠀⠀⠀⠛⢼⠧⠘⡻⠏⡄⢱⠀⠀⣻⢦⣤⣽⣯⠀⣿⠏⠁⠉⣿⣿⣿⣿⣿⠋⣡⣾⣧⣿⣿⡿⢀⢾⠃⢠⣾⣷⣴⣳⡾⢄⠈⠀⡟⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣁⢐⠀⢛⠀⡽⠃⣩⣤⣿⣿⣧⣠⣿⣦⣠⡀⣿⠋⠈⣿⡧⢾⣿⣿⣿⣿⣿⠃⠀⠠⢀⣼⣿⣿⣿⣿⣿⣾⣧⣼⣇⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⣧⣶⣿⣿⣿⣻⣟⣹⣿⡉⠈⢷⣿⣆⣼⠏⠀⠀⢠⣾⣿⣿⣟⠀⠄⠀⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡷⢦⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⣮⢹⣿⣠⣴⣶⣿⣿⣿⣿⣿⣤⣶⣿⡿⣿⣿⢿⣿⣿⡿⠿⠿⠋⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠛⠿⣿⣉⣻⡿⢿⣿⣿⡿⠧⣀⣀⣾⣎⠹⣯⣀⡀⢹⠈⠛⠛⠀⠈⠉⠋⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠁⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠤⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠢⡄⠀⠀⠀⢀⠤⠒⢈⠌⢃
⠀⠀⠀⠈⠂⠀⠈⠐⠊⠂⠀⠀⠃⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡌⠸⡄⠈⢄⠀⠀⡌⠀⢀⠎⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢱⡀⠸⠀⢸⠀⢠⠟⠀⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠠⠦⠴⠠⠄⠢⡀⢡⠀⠇⡀⢀⠎⢀⠔⠀⢀⠤⠒⠃⣁⡠⠤⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢍⡉⠉⠉⠑⠀⢄⣹⣦⣣⡀⣇⡞⠀⢂⠔⣊⡡⠶⠂⠉⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢐⠂⠀⢀⠈⣌⣿⣿⣿⣶⠾⠲⠋⣉⠀⠒⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠾⢿⣶⣌⣡⠾⠛⠛⠛⢿⣝⢿⠟⠊⠫⡭⣿⠠⣁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠁⠀⠀⢙⣿⡇⠀⡀⠀⠀⠀⢈⣧⢂⠀⠀⠀⢿⠆⠹⠶⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢄⠀⠬⠼⢀⡀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⣿⣦⠄⣀⣸⡏⡀⢀⡇⠀⡙⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⢢⡀⡻⡀⠀⠐⢀⡀⡝⣿⡃⠛⢿⣷⣦⣄⣀⣶⣞⠻⡋⠉⠁⠉⠀⠁⠘⠂⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠱⣦⢀⠀⠈⢀⠇⠀⠁⠀⠁⠈⠙⠉⠉⠙⠉⠀⢠⠈⠄⠀⠈⠀⡀⠓⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠄⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⢨⠄⠀⣤⣤⣄⠀⠀⠀⠀⠀⢀⡴⢧⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠄⢤⠄⠀⠀⠀⠀⠀⠀⠀⡦⠶⠓⠦⣤
⠀⠀⠀⠀⠀⠘⢿⣀⡠⣬⡿⠾⠀⠀⠀⠀⢠⠏⠀⠀⠻⡅⠠⠀⠀⠀⠀⠀⠀⢰⣏⡀⠀⠀⣹⠃⠂⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⣯⠂
⠀⠀⠀⠀⠀⠘⠉⠉⠈⠀⠀⡘⠀⠀⠀⠀⢀⢙⡦⣤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠮⣘⠏⢀⡆⠀⠀⠀⠀⠀⢹⣦⣄⠀⢀⣠⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠈⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⢼⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣽⣿⣅⠀⠀⠀⢠⣽⣤
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣿⣿⡟⠀⠀⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⡖⠀⠐⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣦⣶⢠⡀⠀⠀⣀⣠⣿⣿⣿⣦⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⡠⠿⠟⠛⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣺⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠕⠊⠁⣀⠤⠒⠉⣀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠭⠒⢉⡠⠤⠒⣉⠤⠔⣂⠥⠄⠺⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡪⠕⢊⡠⠄⣂⠥⢔⣂⠥⠐⣊⣁⣤⣴⠦⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠝⠊⣁⣴⠮⢙⡂⠥⠒⠈⣁⡀⠤⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠮⢛⣩⡴⣞⠫⠕⠂⢉⡡⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⣺⣿⣽⢿⠅⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣏⣿⢧⣿⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⡽⣟⢯⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣳⢯⣟⡾⡽⢤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠛⠉⠉⣉⣉⣤⣤⣤⣤⣤⣤⣧⣏⣿⣾⣽⠁⢀⣀⣀⣀⣀⣀⣀⠉⠉⠉⠉⠛⠓⢲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣉⣠⡴⣞⣿⢽⣷⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⢤⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠂⠭⣙⡛⠛⠾⠿⠿⠶⠶⣿⣿⣷⣶⣿⣭⣟⣶⣝⣳⣽⣿⣿⣿⣿⣿⠭⠿⠷⠾⠟⠛⣛⡋⠥⢐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠬⠅⠀⠀⠉⠉⠐⠒⠒⠂⠠⠶⠤⠤⠤⠤⠀⠀⠠⠆⠀⠀⠠⠆⠀⠀⠐⠒⠒⠈⠉⠁⠀⠀⠨⢽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡒⠒⣂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠔⢉⠄⠒⡒⡀⠉⠪⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡬⠐⠈⠀⡜⠁⠈⢣⠁⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⡀⣼⣀⠈⠁⠀⡤⢀⠌⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⠢⢈⣉⣀⡉⠄⡪⠊⠀⠀⠀⠀⠀⠀⢀⡀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡒⠤⠤⣀⣀⣀⠀⠀⠀⠉⠒⠂⠐⠒⠉⠀⠀⣀⣀⠀⠤⠄⢀⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⢭⣭⣭⣭⣭⣭⣭⣭⡥⠤⠤⠶⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡤⠄⠀⢀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⠊⢉⢠⡄⣀⠔⠁⠀⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡶⠿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⣤⢴⡾⣿⠶⠚⠛⠶⣶⣤⣄⣀⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡴⢋⠔⠁⠀⣰⠤⠿⠛⠛⠛⠛⠛⠓⠒⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠟⠡⠃⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠠⣊⠔⠁
⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⡿⢿⡟⠇⠀⣤⡀⠤⡴⣴⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠉⠁⠀⠀⠁⠀⡄⠀⢁⠀⠀⠀⠒⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠈⠀⠀⠸⠄⣶⣇⣄
⠀⠀⠀⠀⠀⠀⢤⠀⢻⠘⡀⠘⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠙⠏⠁
⠀⠀⠀⠀⠀⠀⢀⡆⠘⢁⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⡄⡄
⠀⠀⠀⠀⢸⡴⠈⢠⡆⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢤⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⢀⣾⡟⢀⠈⡁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠆⢀⣀⣴⣶⣶⠶⠒⠀⡤⢸⠀⢸⣿⡇
⠀⠀⠀⢸⣟⠃⠆⠀⠁⠀⠀⠀⡸⣶⠂⢀⣤⣤⡤⠶⣶⣺⣿⡿⢹⠵⠛⠁⠀⠀⠔⠀⠀⠃⢸⣿⣧
⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⣀⣼⣧⡴⢞⣩⣿⣿⣾⣾⣿⡿⠟⢭⣶⣾⣶⣤⡤⠂⠀⠀⠀⠱⢼⣿⡇
⠀⠀⠀⠘⣿⡇⣀⠀⠀⢸⣿⣿⣟⡉⠉⠉⠓⣹⣛⣥⣤⣤⣴⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⢿⣿⡀⠀⠀⠈⠛⠻⠛⠿⠦⠠⠞⠛⠛⠛⢿⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⠀⠀⠈⣿⣷⡄⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⣀⠕⠀⠂⠀⠀⠀⢀⣸⣿⡿
⠀⠀⠀⠀⠀⠈⢿⣷⣨⠃⢄⡑⠀⠢⡄⠀⠀⠀⠀⠆⢰⡅⠀⣾⣿⡀⠀⠀⠀⠀⠞⢹⡏⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⣜⠁⢦⢰⣿⣇⣤⣤⡀⠁⠀⢻⠆⠘⠿⢷⣶⣤⣄⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠖⣻⣿⣯⡿⣿⡭⠛⢺⣇⠀⢚⡡⠀⢀⡟⢩⣧⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢀⠁⣷⣿⣿⣿⣿⣄⣴⠾⠷⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣯⣢⡀⠀⠀⠀⠀⣠⠴⣉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡓⢬⠖⢱⡀⠀⠀⣔⠻⣄⡙⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⠻⡖⢋⡅⠀⣴⠹⣆⣍⣉⣩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣓⠟⢊⣴⣸⡉⢧⣌⣉⣩⠋⠀⢀⣤⢤⡖⣶⣲⡶
⠀⠀⠀⠀⠀⠀⢐⡦⣾⣿⣟⠋⠽⢵⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠭⣛⣩⢼⣇⠹⠾⠤⢴⢎⢴⢻⠁⡿⣸⣵⠛⡺⠃
⠀⠀⠀⠀⠀⣴⡿⢱⣿⣿⡛⢴⢄⠄⣥⣈⢁⡆⠀⠀⠀⠀⠀⢠⣤⣶⡖⠖⢻⢲⠤⡄⠀⠹⣗⢾⡤⡾⣈⠟⡓⣳⢟⠁⡿⣸⣴⡛⠧⣌⠋⠁
⠀⠀⠀⠀⢤⢿⡇⣸⣟⣿⠗⣀⠠⡄⠁⠦⠠⠽⡄⠀⠀⠀⠀⠀⠘⣯⠟⡟⣺⢼⣄⡆⡟⣦⣻⣻⣿⣻⠯⢍⣽⣇⣸⣴⠛⠧⣀⠩⠒⠁⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⢀⣿⡆⢸⣷⣿⡇⠙⢢⡀⢘⣘⠓⣸⠇⠀⠀⠀⠀⠀⠀⠀⠙⠲⣇⣾⣸⢫⡟⡿⣾⣿⣿⣿⣿⡿⠷⣛⡶⠄⠛⠁⠀⠀⠀⣀⣠⠤⠄⠒⠒⠁
⠀⠀⠀⠀⠈⢻⣷⠸⣿⣿⣷⡄⣠⣡⣦⢽⣅⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠟⢛⣿⣿⣿⣿⣿⣿⡶⢲⡦⢤⣄⣠⠞⠉
⠀⠀⠀⠀⠀⠈⠹⣷⣝⢿⣿⣦⣽⣷⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⢿⣛⣟⣾⣵⡾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠾⠿⠿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠲⠿⠥⠤⠤⢄⣄⣶⠯⢥⣿⢻⣯⣾⣿⣿⡯⢤⡄
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⣀⢠⣔⣢⠭⠥⠤⠵⠶⠶⣯⣓⣶⠋⠉⠉⠉⢀⣠⣶⣾⣧⣿⢿⡟⠏⢉⠛⣼⠃
⠀⠀⠀⠀⠀⠘⡏⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⣦⢐⡐⠆⣽⢳⣄⠀⢀⣴⣿⣿⡍⢻⣽⡟⠠⣅⠈⠋⣈⢡⡽⣄
⠀⠀⠀⠀⠀⡀⢸⣼⠶⢧⡶⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡁⣪⣾⡿⣿⠟⢨⡷⢿⡿⢇⡂⡄⢼⣧⡆⠀⢥⡘⠃⣬⠀⠁⠻⠂
⠀⠀⠀⠀⣰⣟⣉⡓⢿⣶⣶⣿⣷⣯⡻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢜⣾⣿⡍⣰⣇⢬⠐⣷⣼⣿⠆⣁⡄⣾⣏⣷⠑⢊⡘⢣⡄⠸⠧⣿⠂
⠀⠀⢠⣾⣿⡏⠁⠀⠈⣿⡏⠀⠉⠛⢫⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣺⣿⣿⡿⣥⠀⢴⢠⡿⣿⣿⣧⡄⢠⣿⣿⢷⣴⢺⡁⣤⢠⡄⣶⠛⣅
⠀⠀⣿⣿⣿⡇⠀⠀⠀⣿⣿⡀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣌⣤⣸⣧⣿⡇⣹⣭⢟⣃⣛⣿⠿⢳⣾⢻⣷⠚⠷⠭⢿⠼⠟⠃
⠀⠀⢿⢿⣿⡧⠀⣄⣠⡘⣿⡇⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣻⠟⢻⠏⡯⣄⣔⠻⣿⠹⡷⣎⠛⣹⣍⣦
⠀⠀⠙⣎⢿⣿⣷⣿⣿⣿⣿⣧⣀⣠⣼⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣼⠾⠉⠀⢸⡋⢀⡦⠤⣕⡏⢿⡑⠸⠻⣤⠶⢾⢿⡀
⠀⠀⠀⠉⡿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⢿⢁⢵⡦⠄⣧⠀⠈⠻⣬⣹⡛⣶⣞⢇
⠀⠀⠀⠀⠀⠈⠉⠙⠻⠛⠟⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡜⢳⢢⡃⠀⠀⠀⠀⠉⠙⠑⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡄⡤⣘⣁⡀⠀⢄⡤⡞⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⡈⢀⠋⠐⠋⢣⡭⣤⡾⠁⢀⣀⠨⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠲⠀⢶⡰⣤⠅⠃⣦⡗⢀⢂⡤⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⢉⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠙⠄⠃⠸⣧⠘⠢⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⢻⡶⠓⠆⠀⠋⠀⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⢀⠺⠃⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⡄⠀⡀⠀⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠈⠂⠀⠀⠀⠀⣼⣅⠂⠀⠼⣄⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠁⠰⠀⠀⠀⠀⣀⠄⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠴⠚⡤⠀⠄⠀⠀⡀⣠⠄⢸⡧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡇⢀⠳⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠⠞⠠⢶⣦⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠈⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⣈⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠒⠀⢠⠀⠀⠀⡀⠊⠀⠀⠐⠂⠈⠀⠀⠀⠀⠑⠀⠆

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠄⠀⣐⣂⣀⣀⣀⣠⣤⠤⠤⠤⠤⠶⠶⠒⠒⠒⠚⠚⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣛⣚⠀⡄⣇⣩⣉⣩⠩⠅⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠶⠧⠦⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡡⢭⣍⠂⠘⠒⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⡇⠛⠀⠠⠥⠀⢄⣍⡐⡠⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⣄⠄⠘⡇⠀⢤⡤⡄⢴⡄⠈⡆⠄⡈⡴⡂⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣍⢀⡘⡙⠀⠄⠓⠟⠁⠓⢄⠻⢋⠤⠣⡀⠀⣀⣱⠈⢑⣤⡉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢀⠭⢄⠁⠂⡀⠉⣐⡂⣮⠤⠶⠞⣠⣀⡀⠃⠉⢉⣀⡄⢍⡸⢼⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡐⠏⡣⡁⠬⢧⡀⠀⣀⡀⠋⢐⠁⣈⡢⠊⠬⠂⠛⠶⡄⡘⢂⠂⣇⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡛⢷⣾⣤⣃⣀⣚⠂⠊⠀⠀⡀⠴⡄⢾⢗⣀⣀⣄⣠⣬⣥⡶⠾⢛⣭⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠳⢦⣭⣉⣙⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣉⣥⡤⠶⠛⠉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⢉⠉⠉⠛⣿⠟⣿⡿⠟⠿⣿⠿⠿⢿⣬⠻⣷⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠿⣛⣛⣛⠿⣾⣯⣼⢯⣼⢟⡟⠖⣾⠿⣶⣽⣧⣽⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢛⣉⣙⠻⢾⡷⡿⡿⣻⢿⢻⢣⠇⠹⣟⣉⣉⡙⢷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣉⣙⢿⡬⡇⣼⡳⣛⣾⣺⣿⡿⣧⡞⣉⣉⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⢸⣧⣹⣟⢿⣮⣻⡷⠿⢃⣿⢰⡟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡿⣮⣝⣧⣿⢏⣴⠞⣛⣡⡾⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⠿⠿⠾⠿⠾⠟⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣧⣀⡀⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⡁⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣦⢀⡈⠙⣶⣤⣤⣴⣶⣾⣿⣿⡿⣿⣿⣧⠀⠀⠙⣿⣿⡃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠹⣆⠀⠀⠈⠻⣇⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⢀⣬⣿⡿⢿⣿⡿⢻⣿⣷⣆⠀⣿⡄⠀⠀⠀⠈⠻⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀⣴⣿⣿⣿⣧⡾⠿⡷⠦⠉⡈⣉⢑⣿⣿⠀⠀⠀⠀⠀⠙⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⢰⠉⠛⣹⣿⠁⣴⣿⣿⣢⠍⢹⣿⡞⠱⢻⣧⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢰⠇⠀⠀⠸⣿⣷⣏⣛⣛⢿⣆⣾⣿⢿⣶⣿⣿⣧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣠⣖⠀⣠⣿⣿⠙⣿⣿⣿⡿⠿⠋⣾⡿⣿⣿⣿⣆⠈⣷⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⢿⣿⣿⠇⠀⠷⠉⠁⠀⠀⢰⣿⣿⣿⡟⣛⠙⢠⣼⣿⡏
⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠘⣷⡶⠀⠈⣹⣯⠙⣿⠇⠀⣽⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⡜⠂⢦⣀⠀⡿⠀⠀⢸⠃⢳⡄⠀⠉⢀⣠⣾⣿⣿⣧⣿⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠱⣾⣷⣿⢃⣀⡇⣦⣐⣿⣿⣦⣤⣾⣽⣿⣡⣿⣿⣿⣷⡇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃⣼⢹⠖⠩⠟⠀⠉⠉⠛⠵⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⡏⣿⠆⠀⠀⠀⠀⠀⡀⠠⡌⠻⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠉⢿⠋⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠻⠶⠦⢤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⠀⠀⠀⠉⠒⠄⠀⠀⠉⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠰⢶⣄⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⡀⠄⠂⠊⠀⠀⠀⠀⠀⠐⠛⠻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⢀⣠⡤⠄⠀⠢⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⣤⠴⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⣠⣺⣵⠾⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣀⣀⣤⣤⣤⣴⣶⠎⠉⢷⣤⣾⣿⢟⡁⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⠀⢀⣰⡾⣿⡿⡆⠀⢸⣿⣟⣩⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠊⠄⠇⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠈⠈⢿⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⠇⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠀⠛⠿⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣠⣄⣀⣈⡑⠠⠀⠀⠀⠀⠀⠐⢀⣴⠏⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢽⠀⠹⣦⡿⠓⠼⠖⠀⠀⣮⣿⠔⠈⠀⠀⠀⠂⠺⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠄⡲⣶⡞⠉⢱⡶⠚⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢹⡀⠀⠀⢈⣧⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠳⠆⠴⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⣤⡀
⠀⠀⠀⠀⡤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡠⠬⢍⣔⠵⢀⠊⢴⡈⠅⠠⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠂⠀⠘⠄⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣀⢠⣀⠜⠫⠛⠁⠀⣨⡗⠁⡙⡉⠒⠤⣶⡍⠓⣀⡀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢀⠒⢀⡤⠧⠦⣮⠁⢉⡏⢀⣀⣋⢄⢈⠢⣑⠶⡼⢀⠋⢩⠀⣀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠰⡀⠀⠀⠀⢸⠃⠀⠀⡠⣮⠀⡞⢋⠓⣄⡌⠀⢸⣌⢲⡂⢒⡡⠂⡎⠀⠀⣅⡫⠂⠈⠠⠊⠑⣀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣿⠀⠀⡜⠀⠀⣸⠁⢰⠂⡉⠀⠀⡁⠀⠉⡋⣱⠄⠀⣩⡀⠀⣀⣀⢠⣶⠊⠔⠃⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢢⠀⠀⢹⣄⠨⡇⣰⠛⠉⢆⢂⠠⠐⠢⠰⢆⠖⡉⢹⢹⡜⡲⢧⣀⡀⢉⠔⠊⢐⠈⣿⡶⠿⠩⠢⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢣⠀⠘⣿⣨⣵⣏⠀⢠⡟⢹⠛⠲⡤⠀⡇⢀⠞⢣⢸⢄⠀⢸⣭⣉⣊⣀⡀⠴⠀⠈⢸⠑⡂⢄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏⣙⣲⣬⢥⣄⠑⠀⠰⢄⣼⣾⢂⠨⠘⣃⣀⠠⠨⢈⣛⡞⣐⡨⠀⠀⠖⠄⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠆⠀⠈⢷⣆⡎⠈⣄⠁⠬⣡⣄⣠⠉⠈⠳⣄⣦⡦⠛⠉⠍⢉⢘⠀⠉⡔⠣⣀⢈⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠆⠀⠈⢋⠻⣶⣄⢙⠖⠋⣀⣈⡄⠔⠀⣥⠦⢤⣄⡐⢆⠲⠆⢂⠜⡀⢀⣴⠟⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠱⡄⠙⠻⢶⣬⣁⣩⢀⠁⢊⠲⠇⠀⢒⡑⣠⣋⣩⣥⡶⠟⡋⢐⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⠈⢦⡀⠀⠀⠉⠙⠛⠻⠿⠿⠷⠿⠿⠿⠛⠛⠉⡑⠂⠅⣪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠉⠀⠈⠂⠀⠀⠀⠀⣂⡤⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⠀⠀⠀⠀⣟⡳⠦⣤⣄⣀⣀⣤⣀⣀⣤⡴⢞⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⢳⠀⡄⠀⠀⠀⠻⣿⣷⣶⣬⣭⣭⣭⣭⣴⣶⣾⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡜⡆⢻⠹⡄⠀⠀⠀⠈⠑⠪⠭⣭⣭⣭⣭⡭⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⡄⢧⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣴⣿⣶⣶⢦⠀⠀⠰⢶⣟⣛⠳⠦⠀⢀⣿⡿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠏⢨⡴⠟⠛⢻⣷⠂⠀⠀⡛⠙⠛⠙⠂⠀⠈⣿⢱⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⣲⣶⢠⠀⠠⠆⠀⠰⣄⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣻⣿⣿⣍⣉⣉⣁⣤⡿⢹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⣾⣿⣿⣿⣿⣰⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣭⣭⣭⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠂⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⡁⠀⠀⠈⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿
⠀⠀⡀⢶⡄⠀⠂⠄⣦⠀⣿⣧⡹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢰⡏⣸⡇⠀⠀⠀⠀⢀
⠀⠀⢿⣎⢿⣆⠀⠀⣿⣦⢸⣿⣷⡘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢰⡟
⠀⠀⠈⢿⡎⣿⣤⡄⢹⣿⣼⣿⣿⣿⣎⢻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣱⠟⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠘⣿⡸⣿⣧⢸⣿⣿⠻⠛⠋⠙⢷⣝⠿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣾⠏⠀⠀⠀⠀⠀⠀⡎⢸
⠀⠀⠀⠀⣿⡇⣿⣿⢸⢽⣿⡀⠀⠀⠀⠀⠙⠷⣮⣙⡳⠶⢤⣤⡶⠾⢛⣩⣴⢟⣥⠠⠀⢀⣀⠀⡀⠰⣷⣼
⠀⠀⠀⠀⢹⡇⢸⣿⢠⣾⣯⢷⡀⣀⣤⠴⠂⠀⠈⠙⠛⠿⠷⠶⠾⠛⢛⡩⢎⢿⣿⣷⣿⣿⣷⣿⣶⣾⣿⣿
⠀⠀⠀⠀⣼⡇⢸⣿⢀⠈⠛⠩⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⢸⠲⢭⠿⢻⠛⠿⠟⠹⠿⢻⡄
⠀⠀⠀⠀⣿⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⣆⡀⡄⣸⣧⡤⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⠁⠙⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠈⠁⠈⠉⠉⠉⠉⠁⠉⠉⠁⠋⠙⠒⠁⠀⠀⠙⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⢐⠀⠈⡐⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⣢⡶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⠐⡖⣔⢀⢀⠄⠂⡸⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠹⡄⠀⢿⡇⠀⠒⢄⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠐⢶⢦⣔⡀⡀⣺⣾⡎⣡⢂⡨⠐⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣶⣿⣤⣼⠃⠀⠀⠈⠂⠀⡀⠀⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⠘⠭⠿⣿⣿⣿⣿⡕⡀⠀⢀⠄⠀⠀⠀⡠⣾⡿⡉⢘⠀⡀⠀⠈⠛⠛⠓⠋⠁⡀⠀⠀⠀⠀⠘⡀⡀⠃⡱⠀⢀⢄⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠙⣿⣷⣾⣿⣧⠀⠀⠀⠀⡇⣿⣏⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⣄⠀⡀⡘⣅⣀⠯⠀⣀⠆⠈
⠠⠀⠀⠄⠀⠐⠒⠲⣴⠀⠈⣠⣴⣷⡿⠛⠉⠆⠀⠀⠀⢣⡻⣿⣄⣴⣥⠎⠀⣠⡤⢖⡲⢤⡀⠀⠀⠀⠘⠱⠢⣷⣝⣗⣃⣬⠁
⠀⠀⠀⠀⠀⡴⣡⡶⠞⠱⢾⠏⠁⣿⠀⢄⠀⠈⡃⠀⠀⠀⠈⠘⠛⠉⠀⠀⢰⣏⡀⠃⣡⣼⡇⠀⢠⡀⠢⠄⠠⢸⠿⠟⠿⢶⡀⢀⢄⡀
⠀⠀⠀⠀⠀⢵⣿⠦⠀⣼⢿⣇⣰⣿⢥⣀⣄⣤⢂⠀⠀⠀⢠⡴⠾⣷⣦⠀⠘⢯⣾⣁⣼⠿⠃
⠀⠀⠀⠀⠀⠀⣼⣶⡿⠛⠚⠙⣟⠯⠛⠓⡈⠉⠉⠀⠀⠀⣿⡀⠣⠐⣷⣧⠀⠀⠉⠉⠀⠀⢰⣶⣶⢶⣴⣶
⠀⠀⠀⠀⠀⠀⠟⠋⠀⠰⣀⡄⡈⠁⠬⣫⣽⡀⠀⠀⠀⠀⠹⢿⣶⣎⡹⠃⠀⠀⠀⠀⠀⠀⠘⢶⣣⢠⣰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠉⠛⠛⠋⠉⠉⠳⣄⠀⠀⣴⠏⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣉⣤⠶
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠋⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⢁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠟⠉
⠀⠀⠀⢀⣠⣤⢶⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⣰⠟⣰⡟⠉⠙⠛⢶⡄⠀⠀⠀⠀⠀⢀⣠⡶⠛⣉⣤⠾⠋⠁
⠀⢀⡴⠛⣁⣤⠾⣗⠶⠀⠀⣤⠶⠄⠀⠀⠀⠀⠿⠀⠀⢀⡾⢋⣼⠋⠀⠀⠀⠀⠀⡿⠳⣦⣀⣴⠞⢋⣡⡴⠛⠉
⣰⡏⣠⡾⢯⡜⠓⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡿⠁⠀⠀⠀⣀⠀⢘⣻⡶⠟⣉⣴⠞⠋⠁
⣿⠀⣿⣹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠏⠀⠀⠀⠀⣀⣼⠷⢋⣥⡶⢻⡏⢸⡇
⢻⣦⡟⠷⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠞⣩⡴⠞⠋⠁⠀⢸⡇⢸⡇
⠈⣿⣿⣗⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⠶⠛⠉⠀⠀⠀⠀⠀⢈⣹⣿⠁
⠀⠘⣿⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠃
⠀⠀⠘⢷⡝⠶⠍⠛⠻⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠀⣼⠏
⠀⠀⠀⠈⠻⣾⠛⠦⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠙⠷⣝⡛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠚⠉⠁⢀⣀⣠⣷⠾⠃⠀⠀⠀⡠⠖⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢯⡶⣤⣤⣤⣤⣶⣤⣶⣿⣿⣾⣷⣶⣶⣾⣿⣿⠵⠚⠁⠀⠀⠀⠀⢸⣷⠀⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠈⠙⢦⡉⠙⠿⣿⣿⣿⣿⣶⡾⣭⣾⣄⣀⣄⠀⠀⠀⠈⠻⠿⠾⠷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠣⡀⠀⣤⠸⣿⠲⣤⣄⣉⠛⠳⠯⢜⣾⣎⣍⠿⠟⠋⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡵⠳⣌⡲⣿⣿⣿⡟⣿⣿⣿⣿⣷⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠟⠋⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⠁⠀⠀⢨⣿⢨⣭⣛⣛⣻⠟⣿⣿⣿⣿⣿⡿⠿⠿⣟⣰⣤⡀⠀⠀⠘⣷⡀⣀⣠⣾⠁
⠀⠀⠀⠀⠀⠠⣼⡯⠁⠀⠀⠈⢳⡀⡀⢸⡿⣼⣿⣿⣿⣿⣿⢿⠛⠙⡙⠿⣿⣷⣄⡀⠩⠛⡩⠄⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠰⣿⣿⠂⠀⠀⣠⣾⡿⠉⠛⠹⠿⣿⣿⣿⣻⣟⠄⠀⢳⣤⡀⢘⣿⣿⣿⡶⣤⣀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⠀⡹⣿⣿⣿⣷⣞⣀⠀⣻⣿⣾⣿⣿⡟⢏⣻⠿⠗⠂⠀⠀⠀⣠⣶⠦⣶⠦⣿⣿⣆⠺⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠁⠙⠉⠹⣿⣷⣷⣶⣾⣿⢀⣿⣿⣿⣿⣿⣿⣿⣷⠟⠛⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⣿⡇⣸⡏⣢⣿⣿⢿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⣀⡀⣄⣀⡀⠀⠙⠿⣿⣿⣿⣷⣾⣿⣿⡇⠿⣿⣿⣇⣹⡆⠀⠀⠀⠀⠀⣠⠶⠒⠒⢤⠀⠀⢹⣿⣷⣿⣿⣿⣿⡿⣷⣌⣿⡇
⠀⠀⠀⢠⣮⠱⠛⢟⣻⣿⡀⠀⠀⠈⠀⠉⠀⠙⢿⣿⡃⠀⠀⠉⠛⠓⠃⠀⠀⠀⠀⢰⡇⠀⠀⢼⣿⡇⠀⠀⠙⠻⠿⠿⣿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⢿⣯⣤⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⠿⠿⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠋
⠀⠀⠀⠈⠛⠿⠿⠿⠟⠁⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠄⠀⠀⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢠⣟⠡⣀⠑⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠤⠼⠧⠖⠶⠧⠟⠶⠾⠿⠄⠀⠀⠀⠀⠀⠀⠈⣿⣆⣹⣤⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡾⠛⠉⠙⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠋⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣈⣻⣿⡀⠀⠀⣀⣀⣤⣤⣴⣦⣶⡀⢸⠟⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣻⣭⣶⣿⣿⣿⣿⣿⣿⡗⠀⢠⣿⣿⣿⣤⣍⡙⠛⠀⢿⣾⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠃⠀⢯⣹⣿⣿⣿⠾⠛⠋⠀⠚⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠉⠉⢻⣿⣿⣿⣿⣿⠀⠀⠸⣿⡛⠙⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣭⣟⡓⢶⡆⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⠻⠫⢄⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣀⣨⣵⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⣩⣇⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢿⣄⠀⠈⢣⠀⠀⠀⠀⢠⡟⠀⠀⠀⣴⡟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡌⠓⢤⠀⠣⠀⠀⠀⠉⢳⣦⡜⠀⠀⠀⠀⠰⢍⠉⠉⠉⡇⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⢏⡀⠀⠀⢣⠀⠁⠀⣀⣀⣀⢿⡷⠃⠀⠀⠀⠀⢲⡄⢀⠀⢷⠀⠐⢂⠔⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠎⢴⣇⠀⠀⠀⠤⢸⠆⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⠞
⠀⠀⠀⠸⣄⠈⠇⠀⠀⠀⠲⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠓⠦⣤⣤⡤⠞⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣤⣤⣠⣀⠀⠀⠀⠀⢀⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣾⠋⠙⢻⣾⣶⡄⠀⠀⠀⢀⢊⣹⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣻⣽⣇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀⢸⡇⠀⠀⠁⣿⣿⣅⠀⠀⠀⣯⡀⣙⢿⢻⣿⣿⣧⠀⠀⢀⢀⣯⣿⣿⣿⣔⠉⢹⢁⣈⣗⣦⣤⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⠈⢷⣀⣀⣼⣿⣿⡟⠀⠀⠀⢂⣀⣤⠭⣯⣽⣿⣿⡆⠀⡰⢼⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠈⠓⢬⣿⣿⣿⣿⣿⣷⠀⠢⣾⣿⢟⣷⣷⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣽⣿⣿⣿⣿⣿⣧⢍⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣹⣿⡿⣿⣿⣿⣿⣿⣿⣼⣧⣿⠿⠟⠛⠉⢉⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢆⡀⠀⠀⡀⣏⠀⣜⣷⠄⠀⠀⠀⠀⠀⠀⠘⢯⣁⣸⣿⣿⣿⠿⠟⢛⣿⣿⣴⣖⣒⡺⠾⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣞⠋⢈⢳⡆⠀⠀⣯⡑⣿⠏⢀⢀⣠⣶⡴⠎⠀⠀⠀⠉⠀⠈⠁⠀⠀⠠⠋⣽⢻⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣐⣊⣻⣄⠈⢾⣿⢁⣿⣻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠙⠿⢿⡈⠙⠿⢿⠿⠟⠁
⠀⠀⠀⠀⢀⠠⠀⠀⠺⠢⡽⡲⢿⣿⣿⣼⣿⣿⣷⣿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠃⠀⠀⠀⠁
⠀⠀⠀⠲⣮⢤⡤⠁⣤⢀⣀⣮⣤⣢⣭⣳⣿⣿⣿⡯⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠠⠂⠀⠀⣒⠠
⠀⠀⠀⠀⠑⠆⠀⠀⠀⣫⣾⣿⣿⣿⢿⢿⣿⠿⠟⠟⢷⠒⢦⣀⠀⠀⠀⣠⣤⣶⣤⣤⣤⣄⡆⠀⣤⠰⠁⠀⠀⠈⠑⠘⢄
⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠋⠉⣀⠶⡞⣻⠆⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⢻⣿⣿⣿⣶⣷⣤⠀⢀⣀⣀⠀⠀⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠶⠛⠃⣐⠶⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢸⣷⣤⣿⠿⢿⣿⣿⣿⣿⣇⠙⠁⠀⢀⠜⣠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠙⢿⣿⣠⣿⣿⣿⣿⣿⠿⣤⡀⠀⣡⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠻⢿⣿⣿⠿⠿⣍⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠶⠶⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠛⠛⠉⠉⠉⠉⢹⣏⠉⠛⠛⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠆⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠙⣷⠀⠀⠀⠀⠀⠈⠿⣦⣤⣤⣴⠿⠁⠉⣻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⢿⣆⠀⠀⠀⣠⡿⠀⠀⢀⣤⣶⣶⣦⣄⠉⠉⠀⠀⠀⣾⠏⠁⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠙⠻⠿⠟⠛⠁⠀⢀⣾⠋⠀⠀⠈⢹⣧⠀⠀⠀⠘⣿⡀⠀⠀⠀⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢿⣦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣿⣄⣀⣀⣀⣸⣿⡀⠀⠀⠀⠈⠻⠶⣶⠾⠟⠁⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⣀⣿⣧⣶⣶⠿⠿⣿⠛⠛⢻⡟⠛⠛⣿⠟⠛⠛⢻⡟⠻⠿⢷⣶⣶⣤⣄⣀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡿⠿⣿⡉⠁⢻⡄⠀⢻⡀⠀⠘⠇⠀⠀⠹⠀⠀⠀⢸⠃⠀⠀⡾⠀⠀⢨⡟⠛⠻⣷⣦⣄⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠈⠳⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡼⠋⠈⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣯⡉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣾⣇⣀⡀⣠⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠰⣄⢀⣘⣧⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣷⣿⡟⠀⠀⠀⠀⢀⠈⣿⣷⣾⣿⡿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠸⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠈⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⢰⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⡄⡸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡗⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⣸⢱⠁⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⢰⠃⣼⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⢀⡏⠀⠃⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⡾⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠈⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣄⣀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠐⠀⢉⠑⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠫⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠈⠄⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⢀⣄⣸⣃⠀⢀⡠⣀⡠⣀⣀⠌⣀⣀⡠⣀⣠⣀⣌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢛⡉⠉⠉⠈⠉⢻⠀⠈⠉⠀⠀⢀⣋⣀⣠⠠⠭⠝⢛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⣏⠤⠤⠢⡤⢄⣈⡇⠀⠀⠀⠐⢈⠀⠀⢀⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⣠⠤⣶⠤⢤⣤⣄⣀⣈⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢣⠀⠱⠊⠉⠙⠢⢬⠀⠀⡏⡉⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⠏⢠⡢⠀⢀⣤⠴⠆⣧⠀⣷⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⢀⠎⠀⢆⡤⢾⡇⠀⢷⣳⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠐⢁⡎⠀⠀⠈⠒⠤⡇⠀⢸⡃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡀⠀⠀⠀⠀⡘⣇⠀⠀⠀⠀⢠⠇⠀⠘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡃⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠸⣤⣄⣠⢇⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⡟⠻⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠿⠛⠉⠀⠀⠈⠛⠿⢿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣄⡀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣷⣄⡀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⡀⠀⠙⣿⣿⣦
⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠈⢿⣿⣧
⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠈⢿⣿⣇
⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠸⣿⣿⡀
⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⢸⣿⣿⠀⠀⢀⣠⣶⣿⣿⠿⠛⠋⠉⣤⡄⠀⠀⢠⣤⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣦⣄⠀⠀⠀⠀⢠⣿⣿⠃
⠀⣿⣿⣇⣴⣿⣿⠟⠋⠁⠀⣀⡀⠀⠙⠃⠀⠀⠘⠛⠀⠀⠀⡉⠁⠀⠀⢰⣦⠀⠀⠀⢿⡗⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⡀⠀⣾⣿⡏
⠀⠘⣿⣿⣿⡟⠁⠀⠀⢀⠀⠛⠋⠀⠀⢀⣀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⣠⡈⠛⢿⣿⣾⣿⡟
⠀⠀⠘⣿⣿⣆⠀⠀⠐⠿⠇⠀⠀⠀⠀⠘⠿⠀⣤⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⠿⠃⢠⣶⡄⠀⠀⠉⠀⠀⠀⠛⠃⠀⣠⣿⣿⡟
⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠙⠋⠀⠀⠀⠀⠘⠟⠁⠀⣾⡧⠀⠀⠀⠀⠉⠀⠀⠀⠐⠿⠇⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣤⣀⠀⠁⠀⠀⠀⣶⣦⠀⠀⠰⣿⠇⠀⠀⢀⡀⠀⠀⣠⣀⠀⠀⠸⣿⠆⠀⠀⠀⣀⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣶⣦⣤⣬⣀⣀⣀⡀⠀⠀⠀⠀⠻⠟⠀⠀⠛⠋⠀⢀⣀⣀⣤⣴⣶⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠄⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣶⢶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⢒⠒⣒⣒⣒⣒⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠠⠤⠴⠒⠒⣚⢒⢒⣐⣐⡇⠀⠠⠤⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠂⠠⠬⠭⠭⠭⠭⠍⠉⣹⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣋⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠶⠶⠶⣶⡶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⡾⠿⠿⣦⣶⠿⠻⢿⣶⡿⠻⢿⣭⣭⣉⣉⣩⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡅⠀⠀⣿⠃⠀⠀⢰⣿⠀⠀⣾⣏⣉⣉⣉⣉⠁
⠀⠀⠀⠀⠀⠠⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣇⠀⠀⢿⡇⠀⠀⣸⡇⠀⢠⣿⣋⣉⣉⣉⣹⣷
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡄⠀⢸⣷⠀⠀⣿⡇⠀⢸⣿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⡿⠀⠀⣿⡇⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣾⡇⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⡇⠀⢰⣿⡀⠀⠀⣼⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠉⠁⠀⠀⣿⡇⠀⢸⣿⠻⣷⣴⡿⠁⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣿⡿⠁⠀⠀⣠⣴⡾⠟⠻⣷⡀⠀⢿⡆⠈⢻⣧⠀⠀⣰⡿⠁⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢰⡿⠁⠀⢠⣾⠟⠁⠀⣠⣴⣿⡇⠀⠸⣷⠀⠀⢻⣇⣴⣿⡿⠿⠛⠛⠛⠛⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣠⣾⡇⠀⠀⣿⠃⠀⢀⣾⠏⠁⣼⡇⠀⢀⣿⠀⠀⢸⣿⠋⠁⢀⣀⣤⣤⣤⣀⡀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢰⡿⢿⡇⠀⠀⣿⠀⠀⠸⣿⠀⣰⡿⠀⠀⣼⡟⠀⠀⣼⣧⣴⠿⠛⠋⠉⠉⠉⠙⠻⢷⣄⠀⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠸⣿⡀⠀⠻⣷⣄⣠⣿⡿⠋⠀⢀⣼⠟⠀⠀⣰⡿⠋⠁⣀⣤⣶⠾⠿⣷⡄⠀⢸⣿⠀⠀⠀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠶⠶⠿⠷⠶⠿⠿⠶⠶⠾⠿⠿⠿⠶⠶⠶⠿⠿⠶⠶⠾⠿⠷⠶⠾⠿⠿⠶⠶⠶⠿⠷⠶⠿⠿⠶⠶⠶⠶⠾⠿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠆⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣷⠀⠀⠀⣴⠟⠉⠉⠙⠛⠓⠂⠀⠀⠀⠀⠐⠒⠛⠛⠻⠷⣦⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢿⡄⠀⠀⢀⣴⡾⣿⣿⠻⣷⡆⠀⠀⠀⠀⣠⠶⣾⣶⢶⣄⠀⠀⠀⣼⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⢸⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⡀⠀⢀⡀⣰⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⣀⣈⣀⣄⣀⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⣼⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⢸⠱⠟⠛⢋⡉⠉⠙⠛⠛⠿⢷⣦⢠⡀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠸⣿⢭⣅⣉⣉⣉⣱⣶⣶⠈⠘⠀⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣴⣆⠀⠈⠳⣤⣤⣤⣤⡵⠋⠁⣠⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⡀⠀⠉⠉⠛⠉⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣿⣤⣠⣴⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠡⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⢀⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠠⠁⠰⠀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠂⠄⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠄⠀⠀⠆⠀⠀⠀⢀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⢘⡇⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠈⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠸⠤⠈⡠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠑⣬⣡⠀⠀⠀⠀⢄⣀⠀⢀⣀⢀⠤⠖⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⣏⠁⠁⠀⠀⠐⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠟⠿⠿⢿⣿⣿⣿⣷⣷⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢀⠀⠀⠉⠀⠐⠀⠀⠉⠈⠉⠙⠿⠿⠿⠛⠟⠛⠻⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀
⠀⢀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡎⠀⠀⢿⣿⣿⣿⡇
⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣻⣿⣿⣿⡀⠠⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣇⠀⠀⠻⠿⠁⣤⣴⡆⠀⠀⠀⠀⠀⣀⣐⣿⣿⣿⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠙⠋⣀⣤⣰⣶⣶⡿⠟⠃⠀⠀⢀⣤⣜⠉⢽⡷⣿⣋⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠍⠁⢸⣿⣿⠀⠀⠀⠀⠴⣷⣽⡋⠉⠀⠀⠈⠉⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢚⣿⡆⠀⠀⠀⢶⡦⢀⡉⠀⠰⢦⡀⣠⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⢿⣷⠀⠀⠀⠀⠀⠉⠁⠠⠄⠈⣃⠙⠃⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣷⠀⠀⠀⠀⠀⠒⢲⣦⠀⠀⠈⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡄⠀⠀⡀⠀⠀⠾⠃⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢺⣿⣧⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡏⣿⣿⡄⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⣿⣇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⠍⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢷⢫⢺⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠛⢶⡟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢟⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣽⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣴⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣻⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣲⣾⠿⢿⣛⣿⣿⣯⣿⣯⡭⡭⣍⣽⡿⣿⣯⣽⢿⣿⡿⣟⠿⠿⣷⣶⣦⣤⣀
⠀⠀⢀⡤⢖⣯⣷⣛⣩⣥⣶⣿⢿⣿⣿⣿⣯⣿⣿⣹⣾⡿⣗⣶⢖⢾⣻⣷⣛⣿⣵⡵⣶⣶⣮⣭⡛⠾⣽⡲⢄⡀
⠀⡴⣫⣾⢛⣽⣿⣿⣵⣿⡯⣺⣿⣿⣿⣿⡿⣿⣷⢿⡟⡟⣿⢿⡞⣟⣽⣵⢞⣯⣽⣿⣺⣿⣿⣿⣽⢢⣌⠛⣷⣝⢦
⡼⣱⣿⡱⡿⢿⡶⣿⣿⣿⣟⣽⣿⣿⣿⣯⣿⣿⣿⡜⣺⣿⣿⡞⣿⣻⡿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⢽⣣⣈⢿⣎
⡇⢿⣇⠓⠻⣿⣿⣶⣽⣿⢿⣿⣿⣿⣮⣛⣿⣿⣆⣿⣿⣟⣿⣞⣯⣯⢻⡜⣿⡿⢿⣿⣟⣿⡿⣿⣿⣯⣾⣿⣿⣸⡿
⠹⡜⢿⣄⠀⠻⠿⣿⢿⠿⣯⣿⡿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢗⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⣫⡿⢣
⠀⠈⠢⣝⠷⣤⣀⠻⣿⣭⣷⣾⣿⣿⣾⣿⣿⣿⣿⣟⢭⣝⣿⣿⣿⣿⣽⣿⣷⣿⣿⣿⣻⣯⣿⡿⠟⣋⣤⠾⣫⠔⠁
⠀⠀⠀⠈⠙⠲⢽⣛⠶⣬⣍⣉⡉⠛⢿⣷⣾⣽⣿⣿⣛⣥⣿⢿⣿⣿⣿⣿⣽⣿⠿⢛⣛⣡⣤⠶⣛⡯⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠭⠭⣛⣓⣺⡿⠿⠶⠦⠤⠤⠤⠭⠥⠶⠶⢶⣖⣛⣛⠭⠭⠓⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡒⠈⠀⠀⠀⠀⠉⠀⠐⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠄⠀⠀⡹⠋⠉⠙⣦⣀⠀⠀⠄⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢸⡄⠀⢋⣧⣠⡼⡲⠖⠐⠀⠀⠀⠓⠂⠄⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠁⠙⢺⠋⠓⠀⠈⢫⠈⠂⣀⡀⠀⠀⠀⠀⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠑⢄⠀⠙⠚⠀⠶⠀⠘⣿⠈⠉⠋⠁⠀⠀⠠⠔⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠐⠀⠢⠀⠀⠠⣡⠡⠀⠤⠐⠂⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠒⠠⠀⢠⠠⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠡⠀⠊⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠐⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠄⠀⡴⠚⠉⠁⠈⡰⠂⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⠠⣿⡆⣢⠷⠒⠈⡷⣶⠁⠀⠰⠄⠀⢈⠃⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⡄⠀⠆⠺⠟⠁⡩⣔⡳⣖⢒⡬⠩⢦⠐⣰⡶⠿⠂⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠺⢭⣀⡘⢄⣿⣿⣦⠏⠤⠤⠼⠚⠋⣀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠉⠉⠛⠒⠓⠒⠒⠛⠉⠈⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣠⠞⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠒⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠴⠤⢄⣤⡄⢀⡀⠠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢸⣃⠠⠤⡀⣬⣠⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠐⠼⠃⡀⠊⢰⣷⡌⡰⠀⢀⡀
⢀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠶⠟⠉⠁⠁⢰⢈⠆⡴⠓⡆⢜⠩⠀⠁⠀⣆⠠⡀
⠀⠀⠀⡈⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠐⠁⠄⠎⠀⠚⢣⣨⠀⠄⠀⢰⣀⡰⢄
⠶⠞⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢤⣀⠀⣀⣦⠀⠃⠃⠞⡀⠄⠺⢃⠔⢤⡓⠄⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⡮⢊⠀⠔⠂⠄⢀⡌⡀⠀⠦⠀⠀⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣀⢤⡞⠁⢀⠀⠁⠀⠁⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠇⠸⠀⡴⠁⠀⠀⠀⣴⣦⢚⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢃⠀⠀⠀⠀⢡⠀⠀⠀⠀⠘⠋⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢁⠃⠀⠀⠀⠂⠳⠀⠰⠃⢈⣆⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡆⠘⢯⠀⡁⠀⠀⠀⡇⠠⢀⠀⢠⠳⡷⣄⠈⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠉⠁⠠⡇⢀⠆⡼⠀⠀⠀⢈⠆⠔⠉⠂⠈⡟⣀⠀⠆⠰⠈⡛⠻⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⠐⠚⢩⠂⠀⠐⢱⠛⠚⡁⠊⡐⠁⠀⡂⠰⡇⠂⢠⢄⠤⢯⡠⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⡸⠃⠀⢀⠼⡄⡄⠀⡃⠀⠁⠀⡖⠡⢦⠘⠀⠀⠏⠎⡇⠉⠐⠄⣘⡁⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⡀⠀⣁⠆⠐⠉⠀⠍⢀⡐⢧⠰⡀⠀⠀⠘⠺⠀⠀⡜⠠⡄⠈⢶⡄⠸⠑⠐⠡⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢳⢰⣏⡼⣨⢂⠀⠀⠀⣱⡈⡇⠡⠀⠀⡠⠘⡐⠞⡁⢠⠹⡀⢰⢥⠘⢠⠐⠀⡋⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣾⠤⠊⠐⡉⠄⠀⠀⠈⠽⡇⡃⠅⠀⠈⠀⣆⠉⡞⠀⣠⣜⣀⣎⡤⠗⡄⢚⢸⠄⠈⠂⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠐⡄⢠⣡⡤⣤⠂⠀⢢⠀⠀⠀⡴⠡⠁⠐⠠⠠⢀⡿⠃⣷⢀⣐⡀⠀⡀⡠⠊⠀⠲⣄⣯⡰⠜⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⠘⢄⢲⠰⡇⠀⢀⢰⠆⠐⠀⠤⠀⢀⡋⠉⢁⡈⠀⠠⠟⢧⡞⠁⠁⣡⣛⠃⠀⠄⠨⣟⠏⣆⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⢈⠓⡹⠀⠚⠦⣀⡴⡲⠶⡒⢇⠚⠛⠂⢶⣈⠣⠀⠀⣀⡴⠊⠁⠩⠀⠀⠀⠓⢤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⡳⢬⣀⡠⠶⢦⡈⠀⢀⣘⠃⠄⣀⡤⢈⠀⠈⠁⠀⠀⠀⠇⠀⠀⢈⣃⣠⣴⠾⢛⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠉⠛⠿⠶⣶⣤⣌⣁⣀⡀⡀⣇⢀⢀⢁⣐⣦⣤⣌⣤⣴⡶⠿⠛⠋⢑⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⢐⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠐⢂⠨⠀⠈⣂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣈⡑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠊⠁
⣿⢿⢿⠿⣿⢟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣟⣟⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠿⢷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⣄⠈⠉⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠁⠒⠂⢀⢀⢸⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣰⡄⢠⣼⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣦⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠠⠀⠠⠆⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⢿⣿⣿⣶⣤⣈⢻⣿⣿⣿⣟⡉⠉⠉⠙⢻⣿⣿⣷⣧⠀⠀⠀⢀⡴⠠⠠⠀⠀⠀⠀⠀⢀⠀⣿⠁
⠀⠀⠀⠀⠠⣴⣾⣿⠿⠋⠁⠀⠀⠲⠛⡉⠟⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠹⣿⣿⣿⡂⠀⠀⡋⠂⠀⠀⠀⠀⠀⠠⠀⣁⣿⡶
⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠠⢴⣤⣄⣠⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⠁⣴⣾⡇⢀⣀⣤⡴⠂⠉⣰⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣟⣦⡀⠀⠀⠀⠉⠙⢿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⣾⣿⣿⣾⣿⣛⣤⣄⡒⣾⣭⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣤⣀⠀⠀⡀⢈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣠⣾⠿⠟⠛⠃⠁⠚⠛⠛⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠾⠷⠶⠿⠾⠖⠛⠛⠛⠛⠿⠟⢛⣻⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢾⠟⢋⠟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠄⠁⢠⡏⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⡼⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⢀⡷⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣠⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣿⣿⣷⣾⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠛⠻⠿⢿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⡿⣷⣦⠀⠘⠀⠀⣠⢼⣻⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢂⣥⣬⣥⣝⣻⣲⣿⣿⣆⡀⠠⠃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡋⣐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⡿⠿⣟⣧⣿⣿⣿⣿⣿⣿⡿⣿⢇⣼⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣥⣾⣻⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣴⣾⠟⠋⠉⠉⠉⠁⠀⠀⠈⠉⠉⣭⠉⠉⠙⠛⠛⠻⠿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣏⣵⣿⣿⣿⣷⣾⣷⠀⠀⠀⢀⡀⣛⠀⣀⠀⠀⢶⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢺⣉⣷⣿⣧⣿⡿⠁⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⠶⠶⠟⠙⠁⠀⠀⣁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢲⣾⡿⢿⣷⣀⣾⡿⣿⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣦⣙⣾⣾⣿⣹⣿⠃⣿⡇⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⢿⣿⣿⣿⣿⣿⡿⠟⡏⣽⢏⣿⣯⣿⣣⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣻⠿⣿⣿⣭⣶⣶⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣟⣉⣉⠉⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⢄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠒⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠖⠒⠒⠢⠤⣤⡀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣠⠁⡤⠀⠀⡀⢀⠔⠉⡆⠀⠀⠀⠀⠀⠀⣰⣿⣶⡄⠀⠺⡶⢶⣦⡘⠳⠀⣷⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⢠⣼⣧⣾⣧⣤⣶⣿⣥⣶⡆⠀⠀⠀⠀⠀⠀⢀⡿⣻⠋⠀⢈⠛⠿⠷⠎⠀⠀⠀⣾⠀⢀⣀⠀⠀⣼⠃
⠀⠀⠀⠀⠾⢿⢾⣏⠟⠻⠟⢹⠉⡞⠀⠀⠀⠀⠀⠀⢸⣃⣛⣚⣓⣋⣠⡀⠀⠀⠀⠀⢀⣿⠞⣩⡟⣿⡾⠃
⠀⠀⠀⠀⠠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⣠⣿⣏⣀⣾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣿⣇⠙⣿⢿⣶⣿⣿⡿⠟⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣾⡿⠿⠛⠵⠞⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⣶⣾⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣶⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣶⢶⣾⡿⠁⠈⢰⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠿⠋⣹⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠞⠉⢀⣿⣿⠁⠀⠀⠘⣿⣿⣄⠉⠉⠑⠲⠛⠉⠉⢀⣠⣴⣾⣿⠿⠋⠀⣴⣾⡿⠋⠁⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⣾⣿⢣⣄⣀⣀⣠⡙⠿⣿⣿⣶⣦⣴⣶⣶⣿⡿⣿⢿⣥⣴⠲⣦⣾⣿⣯⠤⢤⣤⡀⠀⠐⢮⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⣾⣉⣹⣿⡟⠛⠛⠋⠉⠀⢀⣠⡌⠉⠉⠛⠛⠉⠉⠁⢠⣇⣿⣤⣿⣷⣿⣿⠓⠒⠒⠒⡆⡇⠀⠀⠈⠃⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⣇⠁⣿⡟⠀⢠⣤⡤⠞⣛⡉⠁⣤⣤⣄⡀⠀⣠⡀⢀⣬⣋⣙⡛⠿⠛⣿⣿⠶⠶⠖⠺⡟⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⠯⠿⢻⡁⠀⠀⠀⢶⣿⣿⣿⣤⣿⣿⣿⣧⣼⣿⣫⡾⣷⣦⠀⠀⠀⠀⣿⣿⣟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠇⡀⠀⠀⠀⣷⢰⣶⣶⣶⠿⠟⢋⣡⣤⣤⣤⣬⣍⡙⢿⣶⣿⡋⣰⣦⡀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢀⡟⢠⡏⠀⠀⠀⢸⣦⣿⠟⣁⡴⠞⠉⠁⠀⠀⠀⠀⠈⠙⢷⣄⠹⢏⣽⡾⠗⠀⠀⠘⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠤⠤⠤⢤⣤
⠀⠀⠀⠀⠀⢀⣴⣛⣛⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣼⠃⣠⠞⠉⣁⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣠⣤⣤⣀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⡾⠁⢀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣼⣣⠴⠚⠉
⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠒⠚⠛⠛⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⣶⠀⡴⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡄
⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⣹⠇⠀⣴⢋⡞⠁⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⣻⠏
⣴⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠶⠞⠁⢀⡾⣱⠋⠀⠀⠻⠶⠦⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠁⢀⡴⠋
⢧⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠋⠀⠳⣶⣦⡤⠤⠦⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣦⡶⠶⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣠⣤⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⢃⠁⠄⡀⠀⠀⠀⠈⠙⠯⣟⡶⣥⣒⠠⣀
⠀⠀⠀⠀⠑⢄⠈⠒⠄⣀⣀⣀⣠⣤⡽⢿⣭⣻⣷⣮⣔⡠⢤⣀⣀⡀
⠀⠀⠀⠀⣠⡤⠧⡀⠐⠚⠻⣄⠀⠀⠀⠀⠀⠈⠙⠳⢭⣋⠗⡲⢭⣓⠿⢳⠶⣤⣀
⠀⠀⠀⡎⠋⠀⠀⠀⠀⠀⠀⠘⣧⣤⣴⣶⠖⣶⣶⣲⡶⠮⣿⣶⣥⣊⠝⡲⠦⣄⡛⠷⢀⡀
⠀⠀⠀⡗⢦⣠⣴⣧⣸⣄⣀⣠⡞⣎⠙⣷⢿⢿⣿⣽⣾⢾⣯⣽⣷⣿⣿⣶⣌⢐⠠⢦⡔⠠⠅⡐⠠⠀⡀
⠀⠀⠀⢡⠀⠉⠙⠛⠿⠶⠿⢦⣏⣧⣮⣮⣷⣷⣿⣷⣯⣩⣿⡿⠿⢿⡿⠻⠍⠓⠫⣒⠨⣐⠠⠀⠈⠀⠆⠇
⠀⠀⠀⠈⡍⠐⠠⠄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⠠⣴⣮⡏⠈⠐⠨⣐⣬⡇
⠀⠀⠀⠀⠘⣏⠩⡳⡦⠀⠩⡴⠶⣆⠐⠒⠒⣒⣶⣒⠐⠒⠒⣰⡞⠿⢦⠤⡺⡡⡞
⠀⠀⠀⠀⠀⠈⢮⣾⣮⣶⡾⠏⣂⢴⣦⣭⣟⠫⠉⣳⣬⠀⢙⢕⣪⣲⣿⣷⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠑⢿⠐⠚⠂⠕⡪⠩⠩⢵⠫⠿⠿⣿⡛⣿⡛⠝⠂⢈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣖⡂⠀⠤⠤⠤⠤⠤⠤⠤⠀⠐⡒⣲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠛⠋⠁⠀⠐⠛⠚⠒⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⠉⠉⠉⠉⠈⠉⢉⡶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠫⢈⣈⣧⣶⣿⣿⣷⣶⣶⣕⠂⡁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡝⣶⣿⡿⠛⢹⣿⣿⣿⣶⣾⢷⠎⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⠤⠜⣾⣟⡇⠀⣸⣿⣿⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠤⡸⣧⣀⣿⣯⡻⡟⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣴⢦⣀⣀⣴⣾⡻⣏⣋⣝⣟⡧⠠⠄⠠⠎⢼⣿⣿⣿⣿⣿⣖⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠁⢠⠀⠐⠂⣶⣿⣭⣯⡷⢷⣿⣿⣡⣤⡀
⠀⠀⠀⠀⠀⠈⠀⠈⠩⣿⣿⣿⣿⣿⣯⠁⠀⠀⠐⠀⠀⢠⡟⣿⣿⣵⣿⣿⣦⣄⡈⠩⢻⣿⣷⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⠈⠟⠃⠀⠀⠀⢀⣴⣄⠃⠀⣫⣿⣿⡟⣿⣿⠏⠀⠀⣼⣿⣿⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⣤⣶⣿⣿⣿⣦⡉⠀⠀⠸⠡⡟⠀⢁⣠⣾⣿⣯⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠨⡐⠿⢿⣿⡽⠟⠁⣰⡟⠐⠁⠀⠺⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠏⠁⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡁⠀⠀⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⢸⢿⠃⠀⠀⠎⠀⠀⠀⠛⠿⣿⣿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡄⢠⡀⣾⣿⠊⣀⡟⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢰⣧⠘⣷⣿⢄⣿⣿⣰⣿⠃⡀⠀⠀⠀⠐⢤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⣿⣏⢸⣼⣿⢧⣿⣿⡏⠀⠀⣀⣠⣤⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣤⢿⡿⠛⢻⢿⡋⢹⡟⠳⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠙⢉⡱⠟⠻⣇⡹⠀⢈⡏⠙⢿⠛⣿⡟⡟⢁⣾⠀⠀⣆⣼⠂⠘⠣⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠉⠑⠀⣀⠍⠛⢀⠀⣰⠂⢈⡆⡸⢧⠀⠀⠁⠀⡜⠉⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⣸⠀⢣⠀⢆⠈⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠈⠆

⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡀⠖⠒⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠐⠿⢿⣿⣿⣷⡀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠨⡟⠊
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠃⠀⠀⢀⡀⠀⠀⠀⢀⡀⢩⣶⢰⣿⣿⣷⣀⠀⢀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠒⠀⢌⣑⡶⠀⠈⣧⠈⣭⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠃⠰⢀⣿⡀⠹⣿⣿⣿⣿⠇⠀⢸⣆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢁⡐⠀⢀⡀⠀⠀⣾⣿⠃⠀⠙⢿⠿⠋⠀⠀⣸⢿⡇⠀⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠈⠁⠙⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⠀⠀⠀⣀⡸⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠒⢄⣀⡀⠙⠀⣸⠀⠘⠻⣿⣿⡟⠁⠀⠀⡼⢻⣷⠀⠀⠀⠀⠀⠂
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠻⠟⠀⠀⠀⠀⠀⠉⢩⠀⠁⠈⢤⡀⠀⠀⠈⠀⠀⠀⣼⠁⢰⡿⠃
⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠀⠀⠀⠀⠀⢰⡿⣠⠂
⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⢾⡿⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣃⡀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋
⣿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠒⠒⢠⡀⢁⠁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⣄⠔⠋⠀⢁⠕⠢⠤⡀⠀⠀⠀⠀⣁⠐⠐⢦⡄⠤⠠⠀⣀
⠀⠀⠀⢀⠤⠖⠚⠉⠁⠀⠀⠀⠐⠁⠈⠀⢀⠂⠀⠀⠀⠐⠈⠁⠂⠂⠀⠈⠠⢄⠀⠀⠀⢄⠀⠈⠙⠂⠤⡀
⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠐⢄⠀⠨⠒⠂⠀⡄⠈⠐⢀⢀⠠⠄⠒⠂⠀⠀⠈⠛⠩⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠈⠓⢄⡀⠀⠀⠔⠉⠑⠁⠁⠀⠀⠔⡁⠠⠀⢘⡀⠀⠠⠐⠨⠀⠀⠀⡀⠈⠀⠀⠢⠀⠀⠀⠀⣀⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠑⠓⠦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠚⠀⠀⠐⠀⠀⠀⠁⠀⠪⠀⣀⣀⣀⣠⣤⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣍⡉⠉⠙⠛⠛⠛⠛⠒⠓⠒⠖⠛⠒⠛⠉⠉⣉⡽⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⢤⣤⣤⡬⠯⠤⠤⠤⠴⠒⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣽⣿⣿⣯⣿⣽⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⢿⠛⣷⠶⠶⠿⠛⠟⢿⣿⢙⣿⣿⣷⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠇⢀⠈⣀⣬⣤⣤⣤⢴⣤⣬⣤⣄⣾⣿⣵⣶⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡓⠒⠏⠉⣧⣦⠖⣄⣼⣿⣿⣶⣾⣽⣿⣧⣏⡟⣗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡁⠟⠈⠆⢿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠜⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠩⣹⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⢀⣼⡿⣳⣟⣹⣿⣿⣿⣿⣿⣿⣿⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣼⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⢛⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡨⠅⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⣉⣦⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⠶⠛⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⣠⡴⠞⠋⠉⠀⠀⢀⣀⣤⠶⡞⠋⢉⣹⠆
⠀⠀⠀⠀⠀⠀⢰⡶⢤⣤⣤⣄⠀⠀⣀⣤⠶⠛⣁⡤⠶⠛⠉⠀⠀⢀⣀⣤⠶⠚⠋⣁⣸⡤⠷⠛⠋⠁
⠀⠀⠀⢠⡾⢋⢻⢥⣂⣰⡄⢸⣷⣛⣩⡴⠖⠋⠉⠀⣀⣠⡤⠶⠛⠋⣁⣤⡴⠞⠋⠉
⠀⠀⣰⠏⣤⡍⢊⠀⣉⡙⠙⡄⢸⡏⠁⢀⣠⡤⠶⠛⢉⣡⣤⠶⠚⠋⠉
⠀⠈⢻⡆⢔⣩⠖⢢⡄⠰⣌⣡⡼⠷⠚⢋⣡⣤⠶⠚⠋⠁
⠀⠀⠈⣷⠰⢍⣡⡼⠶⠛⣉⣡⡴⠶⠛⠉⠁
⠀⠀⠀⠈⢻⣏⣥⣶⠾⠟⠋

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠷⣐⠟⠂⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⡾⡻⣄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢚⠁⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣥⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠠⠠⣄⣀⠀⢀⣤⣴⡇⠈⠉⠸⠀⣰⣔⣶⣤⢤⣤⠄⠠⢄⡀⠀⢡
⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠈⠛⠆⡾⡏⠡⣁⠀⠐⠀⢖⠁⢹⣿⡁⠀⠀⠀⠀⠀⠁⠀⠠⣧
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⣀⠀⠀⢂⠁⢄⣠⠤⠱⡄⠃⠟⠀⠀⠸⣼⠀⠀⣠⣄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠉⠀⠉⠉⠈⠉⠛⡓⠄⡄⠃⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠏⢢⣈⣿⠋⠙⠲⠷⠧⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠈⠈⢁⠠⢀⡆⠐⡀⢀⡂⠀⠀⠙⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⡁⠆⡨⠗⠎⠀⠌⠸⠀⠈⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⢀⣴⣾⣿⣿⣿⣶⣄⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⣿⣿⣴⣿⣿⣟⣿⢿⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠉⠿⠇⠀⠈⢸⡇⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡜⠉⠀⠀⠀⠀⠺⢷⠀⣠⡾⠀⠀⢠⡿⠟⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⣴⣬⣿⣷⠀⠀⠀⠀⠀⡨⠂⠐⣿⡅⡀⠀⠈⠀⠀⠀⠠⢂
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣋⢹⡿⢾⣮⠻⣝⠀⠐⠊⢽⡦⠞⢛⢛⡑⢶⣶⣤⣾⢄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⠂⠅⠀⠄⠀⠀⠀⠀⢠⢺⣿⣦⣠⣾⡗⡂⠀⠀⠀⠀⠙⣟⠻⡷⣶⣊⠁
⠀⠀⠀⠀⠀⠠⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠃⠀⢀⠀⠀⠀⠀⠉⠀⠁⡿⠃
⠀⠀⠀⠀⠀⠀⢫⣀⣀⠀⠀⠀⠀⣴⣀⣂⠞⠉⠉⠹⡀⣤⡀⠌⠀⠀⠀⠈⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠷⠶⠞⠚⠁⠀⠀⠀⠀⠑⠌⢿⣦⣰⣤⣀⢀⢀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣷⣿⣿⣿⣶⣿⣾⣓⡞⠀⠤⠐⣤⡄⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣬⣶⡿⠟⠶⣛⠯⢴⣖⢠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⢺⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠂⠀⠈⣝⣺⣝⠛⠷⣥⣽⡖⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠁⠀⠼⠛⠅⠘⣿⠟⠉⠈⠙⠹⠿⠿⣿⠟⠋⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠙⠛⠻⢯⡬⣑⡢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠻⢷⣤⣬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣑⣦⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣶⣤⣤⣤⠤⣄⣀⣒⣒⣃⣀⣀⣀⣈⢿⠿⣿⣿⣿⡄⠀⠀⠀⠀⣀⣀⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣷⣾⣾⣿⣿⣿⣿⣿⡿⠛⠟⠛⠀⠀⠹⣿⣿⢷⣾⡿⢜⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⡶⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠁⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⠆⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣙⣟⣛⡻⣋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡵⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡂⣠⠶⠆⠲⠀⠺⢿⣿⣿⣶⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠉⣻⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠻⣿⡎⠸⠀⠀⠀⠀⡅
⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⣼⣿⡙⠁⠀⠀⡞⠉⠁⠿⣷⣦⣦⣀⣠⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⢸⡄
⠀⣰⣿⡏⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⡿⠻⢿⣤⣤⣼⣿⣧⢤⣴⣄⡀⠀⠀⠉⢆
⠀⣿⣿⠀⠀⠀⣠⡴⣾⣿⣿⡇⠀⠀⠀⠀⠸⡄⠀⣼⣿⡏⠀⠀⠀⠸⣿⣿⣿⡇⠈⠈⠹⠇⠀⠀⠀⠀⠳⠀⠀⠀⠀⡚⢰⡏
⠀⢻⣿⣀⣹⣿⣿⠀⠀⠙⢿⣷⣦⣦⣤⣀⣸⣯⣼⣿⣁⠀⠠⠀⢀⣀⣿⣿⣧⡀⠞⠛⠻⣦⠀⠀⡀⠀⠀⢁⠀⠀⣈⠃⣾⠀⢀⡤⠀⠀⠁
⠀⠀⠉⠉⠀⢻⣿⡀⢀⣠⣴⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⢧⣼⣿⣿⣿⣿⣿⣦⣀⡀⠃⣠⣄⣤⣧⣾⣾⣤⣀⣁⣠⣿⠀⣥⣴⣠⣠⡄⢀⣀⠄
⠀⠀⠀⠀⠀⠠⢿⢿⣿⡟⣟⠋⣋⡀⢘⡿⢿⠿⠿⠟⠛⢻⢿⠻⢿⠡⠾⠛⠛⢿⢿⣶⣷⣶⣿⣿⣾⣿⣿⣿⣿⣯⣭⣿⠹⡾⠋⢹⠿⠛⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁⠈⠁⠁⠀⠋⠈⠛⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⢸⢸⢸⢸⣟⠛⣷⣄⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣴⣶⠶⠶⠶⠶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣻⣿⢸⢸⢸⢸⣿⠀⠈⠛⣛⣛⣛⣛⣛⣉⣉⣉⣁⣀⣀⡀⠀⠀⢀⣀⣀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⢸⢸⢸⣿⣀⣠⡿⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢸⢸⢸⢸⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⢸⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⢸⠀⣿⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⣿⣾⣾⣾⣤⣿⣴⠾⣛⣛⡭⢍⣛⣛⠻⣶⣄⣀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⣠⡾⢋⣥⣶⡾⢛⡩⠤⠒⣒⣒⣒⣒⠬⢝⡻⣾⣥⠖⢒⣒⠒⠬⣹⣾⠟⣛⡩⠭⠭⠭⠭⠭⣙⡻⢶⣤⡀
⠀⠀⠀⠀⢰⡿⢰⢣⣿⢃⠞⣡⢒⣩⠭⢒⣒⣒⣨⣍⣓⣌⣢⣻⣯⣭⣭⣍⣿⣟⣰⣊⡵⢚⣩⠭⠭⠭⢍⡒⠬⡳⣝⢿⣆
⠀⠀⢰⣶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠷⠿⠿⠿⠿⢶⣶
⠀⠀⠀⠹⣷⣜⠛⠀⠛⠛⠀⠚⠃⠀⠒⠓⠀⠐⠛⠂⠘⠛⠃⠀⠛⠋⠀⠘⠛⠁⠘⠛⠀⠘⠛⠀⠚⠓⠀⠐⠒⠀⠶⠶⣠⣾⠏
⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣋⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣉⣉⣉⣉⣉⣉⣹⡏
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣉⣌⣹⣿⣿⡿⠗⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣴⠖⠀⠀⢀⣠⣻⣿⣷⣿⣿⠇⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣻⡵⢀⠀⢀⢉⣹⣿⣿⣿⣿⣿⢀⠀⠠⣀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠹⣂⢱⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠶⣔⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣽⣿⠇⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⣠⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣀⣤⣾⣿⣶⣾⣾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢀⠄⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡼⢋⣿⣭⣿⣿⣿⣿⣿⣾⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⣀⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠐⢯⠎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠙⠣⣴⣙⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⣄⣬⠙⠛⠻⠾⠿⡯⣽⣿⣿⣛⣿⣩⢎⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⡛⢿⣶⣦⣼⡦⢶⣿⣯⡻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠌⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠐⠀⠀⠈⣀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠔⠛⠲⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⠃⠀⠀⠈⠁⠀⠀⠀⠀⢀⡤⠔⠒⠉⠉⠉⠉⠑⠒⠤⢺⠋
⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠙⠁⢘⣏⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢙⣿⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⠀⠀⠀⠀⠀⠀⠀⢀⢻⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠣⠹⣿⣗⡆⠄⠀⠀⠀⠀⠀⢂⡇
⠀⠀⠸⠷⠶⣤⣀⡠⣠⣴⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⠿⣿⡁⢀⠀⣀⠀⣢⠞
⠀⠀⠀⠐⠤⣁⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⡀⡄⠀⠀⡀⠀⠀⠀⠑⠺⠾⠾⠶⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⣀⣤⡄⣬⣪⡷⣾⢸⣟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣙⠀⣷⣾⠟⠉⣻⣷⣯⣯⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣭⣜⠿⣿⣿⠀⣼⡿⠿⠟⠳⠦⣍⠲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢠⣮⠎⡺⣷⣞⡖⣸⣿⣥⣀⠀⠀⠀⠈⠛⣮⣷⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⢛⣻⣿⢿⣾⡿⢠⣿⠛⠙⠻⢧⣤⣀⠀⣠⠈⢹⡖⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⠌⢩⣶⣿⣖⡎⣸⣇⠂⠀⠀⠀⠀⢿⣧⣸⠀⣼⠇⢀⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣏⣽⣯⣥⠞⡧⣾⡏⠀⠀⠀⠀⠁⠈⠻⣿⣷⡃⠀⠀⠀⢀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣮⡈⣻⢿⣿⣅⠘⢷⣧⣠⣤⣤⣦⠶⠟⠛⣉⣩⣥⣀⣰⡮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠚⠻⣯⣭⣹⢦⣄⣈⣩⣭⣴⣶⣶⡶⢛⣿⣿⣿⡿⠧⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡱⠾⢿⣿⣿⣿⣿⡏⣽⣷⡿⣶⣯⣭⠈⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠓⡫⢾⡵⣅⣿⣿⣿⣿⠳⡟⠫⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢿⠹⠃⠻⡟⢉⡏⠀⡛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⢚⣂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠞⣛⣩⣥⠴⠶⠚⠛⠉⠉⣀⣠⣤⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢛⣋⣩⣤⠶⠞⠛⣉⣁⣤⣤⣤⣶⡿⢿⣛⣻⣭⡽⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡾⣡⢞⣫⣍⢹⡶⣤⣠⡤⠶⢞⣋⣩⣥⠶⠞⠛⣉⣉⣤⣴⡶⠿⢿⣛⣛⣭⡽⠷⠞⠛⠉⠉⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⡀⠀⣀⣄⣼⠿⢿⣷⣿⣼⣿⣿⣾⢿⣯⣷⠖⠛⣉⣉⣤⣤⣶⠾⣟⣛⣭⡽⠶⠚⠛⠉⠉⠁⠀⠀⣀⣀⣤⣤⠶⠶⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠈⢠⣞⣭⣾⣿⣿⣷⣿⣿⡿⣯⡻⣏⢷⡹⡏⢿⣟⣿⣿⠿⠟⠛⠛⠉⠁⢀⣀⣀⣤⡤⠶⠶⠚⠛⠋⠉⠁
⠀⠀⠀⢰⣿⣿⡿⠿⢛⣋⣩⣿⣿⣿⣎⣷⢻⠈⣿⣷⢸⣏⣁⣀⣠⣤⠴⠶⠟⠛⠋⡉⠁
⠀⠀⠀⣼⣿⣵⣶⣿⣿⣿⡿⠷⣿⣿⡟⣿⢸⣼⣯⣇⣼⣿⠉⠁
⠀⠀⢰⣿⣿⣿⣛⣩⣥⣴⣶⣾⣿⡿⣹⢇⣾⣽⣿⣿⡟⢯⣷⡄
⠀⠀⢾⣼⠃⠉⠉⠘⣿⣷⣿⣿⣿⣹⢻⣿⡿⣿⣿⡟⣧⠘⠿⠃
⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿⢹⣿⡧⡏⣾⢸⣿⣿⣿⣿⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡿⣧⣿⣧⢿⣿⡿⣿⡏⣿⢉⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣼⣷⣿⣿⣹⣧⡻⣷⣿⢷⡹⣿⠿⢻⡇⡿
⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣯⣷⣜⣿⣿⣳⣼⢷⡌⢿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⢻⣿⣿⣿⣿⣿⣞⣿⣿⢿⣧⣿⠀⠙⢿⡝⣦
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣷⣿⣿⡙⢧⣽⣿⣿⣿⣷⡟⠀⠀⠀⠷⠟
⠀⠀⠀⠀⢀⠀⢿⢻⡄⠀⠀⣿⣿⡇⣿⡷⢾⢿⡟⠉⢿⣷⡀
⠀⠀⠀⠀⠈⠣⠈⢷⣿⡄⠀⣿⣿⣇⣿⡷⢏⡼⠃⠀⠈⢻⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢿⡙⣿⡿⢳⠏⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣫⣾⣟⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⣳⢿⣿⣿⣿⣷⣶⣟⣳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣽⣾⣿⠛⠁⠀⢻⣿⣄⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⠀⠀⠀⠀⠹⣟⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⣾⣿⣿⣾⡿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢿⣿⣿⣿⣟⢿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣻⣷⣄⠀⠀⠀⠘⠿⢿⣷⣿⣿⣿⠿⣿⠿⠟⠛⠋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⠀⣠⣶⣿⠿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⣿⣿⣿⣯⣾⣿⡗⠀⣠⣾⡟⣿⣷⣇⠀⠀⣿⣼⣿⣿⣷⣴⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡏⠹⡏⠉⠉⢠⣾⣿⣷⣦⣾⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⣦⡀⠀⡇⠀⡇⠀⣰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⢿⣿⣾⣿⣿⣿⣾⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣷⣄⢛⡀⠿⠀⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣸⠉⠉⡹⠉⠉⢹⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣼⣿⠷⡿⠿⠟⡈⠃⠀⣀⠈⠉⠉⠉⡟⠉⠛⡟⠙⠋⠁⡿⠀⢀⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠶⡖⠢⢯⠀⠀⠀⠀⠇⠀⠀⠇⠀⠀⢀⡇⠀⣸⠈⠀⢠⣇⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣤⡀⠸⡄⠀⡆⠀⠀⢀⡆⠀⢸⢀⣤⣶⣌⠀⢠⠇⢀⣴⣿⣿⢛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⡿⣿⣿⣷⣇⠀⢸⠀⠀⢸⠁⢀⣴⣿⣶⣿⣿⡆⠎⠀⠸⣿⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡿⡿⠛⡄⠀⣦⣤⡜⠀⢸⡟⡿⠿⣾⢿⡿⠀⠀⢠⠏⠄⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡄⣱⡀⢇⢰⣿⣽⣿⡆⢸⢃⠃⠀⣧⠞⠁⠀⢠⠎⡸⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣆⢳⠈⢷⠸⠀⢘⠁⡇⠀⣾⠎⠀⡾⠁⠀⢀⢢⠺⣄⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾⢿⡁⢣⠈⢳⡇⢸⠀⡇⢀⡟⠀⣸⠃⠀⢔⡵⠃⠀⠀⡳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠳⡈⢧⠀⠙⢾⠀⣇⠜⠀⣰⣏⠀⠄⠁⠒⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣳⡆⠀⠀⠈⠂⠙⠀⠓⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠔⠊⠀⠀⠀⣴⡇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⡿⠇⢀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⢀⠀⠻⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⢀⣶⣿⣿⣷⣆⠀⠀⠀⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠁⠀⠁⢸⣿⣿⣿⣿⣿⠀⠁⠀⠙⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢲⠀⠸⡇⠈⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠸⠁⠀⠈⠄⠀⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠃⠀⠀⣳⠀⢀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠠⠢⡉⠀⠈⠁⠉⠀⠀⠀⠂⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⡇⠀⢀⡀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⡐⡄⠀⠙⣁⠈⠅⠼⠟⠒⠢⣀⢬⠔⢂⡀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⠄⠄⠸⠄⠤⠲⠀⣵⠁⡬⢀⠀⡌⡶⢦⣄⠐⠀⠐⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠁⠀⠀⢰⢀⢁⠀⠚⡛⠒⡠⠞⠹⠁⠔⠉⢠⣆⠀⡀⡀⠜⡏⠓⠊⢀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠈⣬⢈⠄⢀⠀⠘⡺⠦⠠⣤⠤⠊⠁⠀⢰⠆⠀⣐⠀⣠⠴⠀⢀⠀⠀⠀⡘
⠀⠀⠀⠀⠸⡄⠀⠐⠈⠛⠈⠁⡰⠠⠄⠔⠂⠈⣛⠲⠧⢴⠾⣂⠀⠀⠀⠆⠀⠀⠁⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠂⢤⠂⡀⠀⠀⠤⠂⠈⠁⠀⠰⠔⠓⠂⠔⢶⠂⣠⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠁⠠⢄⠐⠀⡐⠂⡀⢶⠂⠀⠀⠀⠀⠁⠈⠁⠀⡀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⠋⣻⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⣻⣿⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⠿⣿⠟⠛⢿⡛⠻⡟⢿⠛⠿⠿⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠛⠁⠀⣀⡤⠬⣙⡢⢝⣆⢘⣸⡐⠠⣣⠖⡡⢔⠨⠂⡉⠽⠛⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠒⠈⡉⠭⠀⠂⢀⡨⠿⣿⡿⠟⠋⠙⠛⢻⣧⣖⣢⣵⣶⣥⣦⠤⠤⢭⣉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⢮⣤⣴⣬⣿⣇⣎⠓⢊⠀⢼⣿⠿⠿⠶⠶⠶⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡍⠀⠠⠈⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣶⣶⣴⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⠀⠀⢠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡆⠀⠀⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠠⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣰⠇⠀⠂⠀⣀⠀⠘⠀⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢠⡏⠀⠰⠀⣰⡏⠀⠀⠀⣿⢀⡴⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⢻⡟⠀⣾⠀⣸⢻⠃⠀⢰⡿⢿⡾⢁⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣷⣾⡅⢰⡿⣅⡏⣸⣰⣆⣎⣤⣾⡴⢋⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣽⡙⣿⢾⡇⣿⠁⣿⡿⣿⠟⢿⠋⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠃⠘⠊⠁⠀⠀⠉⠀⠁⠀⠀⠀⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠧⠀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣴⣆⣀⣠⣿⣿⣦⡀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠋⠉⠛⢶⡄⠀⠀⠀⠀⢀⣠⡤⣤⣿⣿⡿⣿⣿⣿⡿⠛⠟⠙⠚⠋⠻⠷⢦⡀
⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⣤⡼⢤⣥⠀⠀⢠⡾⠿⠛⠀⠀⠘⠿⢿⣧⣽⣽⣗⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣼⣿⠇⠀⠀⠀⢠⣿⣵⣆⡀⠀⠊⠀⠀⢚⣿⠏⠈⣿⣷⣆⡀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠸⣅⠀⠀⠈⠳⣄⡤⣤⣾⠋⠀⠀⠈⠛⠛⠓⠲⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠤⠀⢀⣽⠿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡀⢀⢀⠀⠀⠀⠀⠀⠐⠥⢈⡐⠀⠀⣐⡂⠀⢀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⠉⠉⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣠⣤⣤⣶⡆⣴⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⠤⠤⢤⢄⣀⣀⣀⡀⠀⠀⠀⢀⠤⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡠⠊⠀⠀⠈⢫⠑⢲⢃⢔⡲⠦⣈⣧
⠀⠀⠀⠀⠀⠀⢀⠜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠰⠁⡠⠄⠠⢄⠀⣧⢃⢎⠎⡠⢤⡈⢻⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠈⢿⣿⣿⣿⣿⡿⢋⡤⠤⠤⢍⡇⢸⠁⢴⠀⠈⡆⠰⣪⢎⡜⠀⠀⢱⢸⢷⡀
⠀⠀⠀⠀⠀⢂⠀⢀⠔⢉⡡⠬⢍⡡⠔⢁⠔⠂⠒⠢⢧⠀⠳⠤⠤⠞⢀⡞⢁⣇⠔⠲⠤⢧⣌⠎⠃
⠀⠀⠀⠀⠀⢸⢄⡌⢰⠃⡠⠒⠒⠒⠒⢁⡞⠣⣈⣉⣢⣑⡂⠒⢢⡴⢏⠣⡸⠴⡻⡿⢷⡌⣻⠀⡆
⠀⠀⠀⠀⠀⠸⡈⠳⢇⡜⡠⠊⡩⠭⢍⡓⢌⠒⠤⠤⠤⠤⢌⠑⢾⡉⢫⣾⣋⢱⡿⡶⢿⣁⡧⢚⠇
⠀⠀⠀⠀⠀⠀⢷⣄⠀⠉⠓⠮⢴⣒⠲⡝⠦⣉⣒⣉⡑⠢⣄⠑⡄⠱⢻⡗⢺⡌⣉⠵⠞⠉⠀⡸
⠀⠀⠀⠀⠀⠀⠈⡄⠑⠢⢄⡀⠀⠀⠉⠉⠐⠒⠒⠦⠬⠷⠼⠦⠞⠒⠛⠃⠉⠁⠀⠀⣀⠴⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠈⠉⠒⠂⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠒⠚⠉⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣖⠠⠤⠤⠀⣀⣀⠠⠤⠤⠄⣒⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠀⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣃⠀⠠⣽⢦⣀⣀⡀⠀⠀⠃⠉⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢿⡯⣬⢰⢿⣾⣷⠉⠁⢤⣦⣾⣿⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣟⠁⣺⡿⣿⣧⠀⠈⠙⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢻⡇⢸⣋⣁⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡰⣛⣋⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡰⣷⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡯⠴⢤⣭⣿⣿⠟⠛⠛⠛⠛⠛⠛⠋⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣅⣲⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣶⣿⣿⡿⠿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⡟
⠀⠀⠀⠀⠀⠀⠀⡠⠀⣼⣿⣿⡿⠛⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢂⣴⣾⡿⠛⠉⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣆
⠀⠁⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄
⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⠿⠷
⣶⠈⠈⠛⠛⠋
⠁