Red hot chili peppers Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡰⠃⠀⠀⠀⢀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⣄⣦⣾⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⠉⠛⣥⡤⠀⢀⣀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⢤⡀⠐⠆⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣁⣀⣉⣀⣀⡀⡴
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⡖⠀⠀⠀⠒⠂⠀⠀⠀⠘⣿⣽⠿⣽⠿⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣙⠛⠿⣏⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡰⠋
⠀⠀⠀⠀⠀⣠⠀⠀⠈⠉⠀⠀⡀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠚⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠚⠺⢦⠆
⠀⠀⠀⠀⠐⢯⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢰⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣀⣈⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⠿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⢀⠀⠑⠒⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠒⠀⢠⡆⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠉⠉⠀⠀⠀⢀⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⣿⣿⣷⡟⠂⠀⠀⠀⠐⠊⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠨⠷
⠀⠀⠀⠀⠀⠄⠂⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣤⣭⠁⠀⠀⠀⠀⢴⢀⣴⣾⠿⠿⣷⡆⠀⡄⠀⠂⠀⡇
⠀⠀⠀⠀⠀⢀⣈⣤⣤⣤⣤⠀⠀⢠⠀⠀⢀⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⣬⡉⠀⠶⠶⠀⠀⡼⠁
⠀⠀⠀⠀⣸⣿⣿⡼⠿⠾⠛⢀⡴⠿⠿⠗⠸⡄⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢺⠏⠀⠒⠒⠀⠀⣰⠋⠀⠀⠀⠀⠘⠃⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠈⢠⣞⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠾⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⡄⠀⠀⠀⢠⠄⣄⣀⣀⡀⣄⡤⢰⠄⠀⠀⣀⠄⠀⠀⡠⢄⠀⠀⠀⠀⣀⡄⠀⠀⠀⢄⠀⠀⠀⠀⢠⠄
⠀⠀⠀⣠⠄⠚⣉⢉⡍⠉⣳⠶⣞⠉⢙⠃⠀⠀⠈⠀⠁⠘⠈⠁⠁⠀⠀⠀⠀⢀⣍⢀⡠⠀⠁⠀⠳⠄⣀⣀⠈⠱⠆⠠⡐⠂⠃⠀⢀⠹⠎⠁
⠀⢀⠞⢡⠔⠉⠀⠀⢀⠂⠉⠷⢏⠓⣝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣤⠀⠠⠀⠉⠈⢣⠀⠀⠀⢻⣆⠀⠀⡀⠈⠙⠓⠁
⠀⡸⠤⡞⠀⠀⠀⠀⠈⠀⠀⠀⠸⡄⠻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⡾⠡⠀⠀⢠⡴⠞⠋⣴⠖⣶⠎⠛⠀⠰⣿⠳⠄⠀⢀
⠀⠷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡄⢠⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠐⠀⠀⢀⡞⣳⠀⠀⣀⣀⠀⠀⠐⢞⠛⠁⠀⠀⠀⠀⠹⠀⢀⢶⠏
⠀⢐⣆⣱⣄⠀⠀⠀⠀⠀⠀⣠⠎⢀⡾⠁⠁⠙⠃⠀⠀⢠⠀⡀⠀⠀⠙⠁⣀⡄⠀⣾⢳⡇⠀⡞⠁⣼⠀⠀⠤⠋⣷⣾⢄⡤⡴⠰⠆⠀⢠⠏
⢀⡞⠙⢿⣍⠐⠄⠀⠀⠀⠈⢁⣴⠟⠁⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⣤⠛⡱⡙⠀⡄⠓⠀⠀⠉⠋⠵⠀⠈⠛⠉⠀⠅⠈⢊⠀⠀⢲⡄⠈⠀⢀
⠀⠱⠖⠋⠘⠐⠂⠴⠆⠐⠀⠉⣤⣤⣤⣤⣤⡄⠙⢞⡶⠀⣤⣄⣀⡤⢷⡮⠚⠁⠀⢀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠠⡞⣾⠞⠁⠀⠘⣌⢢⡀⢸
⠀⣤⢤⣤⣀⣠⣀⣀⣠⣤⣄⠀⠛⠃⠸⠘⠛⠃⠀⠀⠉⠓⠒⠒⠂⠈⢁⠀⡀⠒⢀⣾⠀⡅⣿⠀⠈⢷⣤⠀⠀⠀⢈⡡⢷⣠⠀⠀⠀⠈⠀⡇⠸
⠀⠿⠶⠏⢩⣯⠉⣯⣿⡶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⢀⡀⠀⣠⠀⡴⠻⠶⠚⠋⠉⠉⣠⡤⠀⠈⠑⠂⠐⠾⠛⠛⠉⠀⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⠄⣐⣣⠼⠁⠉⠁⠀⢀⡀⠰⠖⠂⠀⢀⡤⣤⣤⡀⠀⠀⢴⠟⣣⠆⠀⠘⠿⠿⠅⢀
⢠⠀⠀⡀⠐⠀⠀⣰⠖⠢⠈⠀⠀⠀⠀⠀⡄⠀⠀⠐⠚⠁⠉⠉⠀⢠⣄⡄⠀⠀⠀⠀⠀⠀⡔⠂⠘⣤⣇⢈⡌⣇⠈⠓⢯⣅⡀⠀⢀⡤⠶⡄⢸
⢘⣾⢦⣤⡶⣄⢨⣿⣴⡶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠰⠷⢌⡠⠴⠀⠀⠀⠸⠷⢺⠀⠀⠀⠉⠙⠑⠋⠀⠙⠐⡒⣮⡄⠸⠤⠖⠁
⢨⢻⡀⣾⣇⣘⢻⣿⢸⣏⣻⡇⠠⠄⢀⣀⡤⠀⣾⡗⡗⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⠏⠀⠐⡆⠀⢊⣇⡀⠀⠀⣀⠑⠈⢳⠀⠀⠀⠞⠢
⠀⡟⢣⠙⢿⠀⢺⣇⠈⣿⣚⡇⠀⠀⠀⢀⠄⠀⢯⡧⣇⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠉⠤⠤⠭⠤⠤⠌⠡⢤⡀
⠀⣍⣂⡛⢶⣿⡁⠸⢷⣌⣿⡅⠀⢀⣴⣿⡆⠀⠻⢻⣹⡀⠀⠀⠀⠀⠀⠈⠁⠠⠊⠄⠀⠀⠘⠀⠀⢸⣶⠒⠀⠀⠒⠐⠒⠒⠂⠐⠚⣿⠃⡆
⠀⣂⢽⡙⣿⡻⣻⣦⡀⠹⣿⠃⡸⣩⡿⣽⡇⠀⠀⠹⣭⢳⣄⠀⠄⠀⠀⠀⠀⠀⠀⣀⢤⡔⣀⠀⢀⡀⠻⣦⠀⠀⠀⠀⠀⠀⠀⢐⡿⠃⡠
⠀⠻⣤⣍⣚⡉⣩⣩⣩⡿⠟⠀⠀⠉⠓⡸⠁⠀⠀⠀⠈⠑⠿⣷⣄⣀⡀⢀⡠⠀⣠⠗⠈⠹⠶⠂⠘⣷⣆⠉⠳⢤⣀⣴⣾⣧⡶⠋⠁⠐⠁
⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣀⣀⣘⣀⣁⣀⣀⣀⣀⣀⣁⣀⣀⣀⣁⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⢿⣿⣛⣛⣛⣛⣛⣛⣿⣿⡷⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣛⣯⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣻⣽⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⢵⣫⣽⡶⠿⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⠶⣯⣝⡷⢿⣿⣿⣿⣧⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢯⣿⣷⡿⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦

⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣾⠛⠉⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⠤⠴⠶⠞⠛⠉⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠉⠉







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡉⠳⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⢷⡀⢀⣤⠶⠛⠛⠛⢳⡶⢶⣤⣤⠾⣿
⠈⠛⠿⣟⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣾⠁
⠀⠀⠀⠈⢷⡀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠙⠻⢯⣍⡉⠙⠳⢦⣄⠀⠀⠀⢠⡟⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣰⠏
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢷⣄⢶⣶⢦⡀⠀⠈⠛⢶⣄⠀⠉⠻⠶⠶⠟⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡆⢹⡆⢻⡄⠀⠀⠀⣹⠆⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⢿⡀⢀⣴⠟⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠈⠛⠛⠁⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⢋⣁⣀⣤⣤⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⣀⠤⢚⣋⣙⠳⡄⠀⠀⠀⠀⠀⠳⠀⠀⣤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⡠⠒⣩⠵⢺⠏⠠⠈⢻⡿⣆⠢⡀⠀⠀⢸⣦⡀⠻⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⢠⡄⢀⢠⡄
⢀⡴⣫⠀⠀⠀⣀⢁⡪⢽⠦⠁⡅⡟⠹⣿⠀⠀⡇⠀⠘⡏⠀⢣⢀⠴⢿⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡌⢩⠽⡊
⢸⣌⠘⠀⢀⣀⠠⠄⠀⡍⢈⡤⢂⠇⠛⠁⠀⠀⠐⠀⠀⢣⠀⢰⠏⠀⡸⠀⠀⠀⠀⠀⣌⠂⠀⠀⠠⠀⠊⠙⢻⢀⠃
⠀⠈⠉⠛⠒⠲⠦⠬⠵⠦⠖⠚⠉⠀⠀⠀⠀⠀⠀⢱⡀⡸⠀⣸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠁⣴⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣁⢤⠞⠡⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢸⠉
⠀⠀⠀⠔⠒⠲⠀⡀⠂⡢⠒⠢⠄⠀⠀⠀⠰⠒⠉⢈⡞⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⢀⣀⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⢆⠀⠈⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⢠⣄⣀⠠⠤⠄⠤⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⡀⠀⣀⡀⣀⣀⠀⡀⠀⠀⣀⠀⠀⣀
⠀⠀⢰⡀⠐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣙⣶⡷⢡⣿⣩⡧⣏⣹⢾⡟⣡⡟⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠈⢧⡀⣄⠀⠀⠀⠀⡸⠐⠀⠀⠀⠀⢸⠉⠀⠉⠁⣿⠀⠀⡯⠀⠀⠉⠁⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⢀⠼⣓⠀⢄⡠
⠀⠀⠀⠀⠉⠛⠤⠀⠄⠚⠊⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠹⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠅
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠂⠈⠉
⠉⠛⠻⣻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡀⠀⣀⡠⠊⠉
⠀⠀⠀⠙⢄⡀⠀⠀⠁⠀⠒⠒⠒⠋⠁⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠂⠀⠒⠒⠒⠂⠈⠁⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣠⡄⣙⡙⢮⡔⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⡽⣣⡌⢺
⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⠉⢦⡤⠆⠀⠀⠀⠀⠘⠁⢀⠋⠉⠉⠉⠙⠆⠀⢨⠀⠀⠀⢀⠂⣄⠀⠀⣠⠞⠁⠈⡿⣠⠂
⠀⠀⠀⠀⡀⠔⠁⠀⠀⢂⣀⠀⢃⢤⡀⣀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠈⢦⣘⡛⠉⠀⠀⠀⡼⢁⡇
⢤⣒⠚⠉⠀⣀⣤⠴⠞⠁⠀⠀⠂⢀⣹⠀⠲⠀⠀⡆⠘⠀⠀⠀⠀⠀⡆⢀⠆⠀⠀⠀⠀⣘⠤⣽⠘⠦⠶⠞⣡⠞
⠀⠈⠉⢿⣏⣁⣀⡐⢒⣁⣈⣐⣂⣪⠋⠀⠀⠀⠀⠘⢤⡄⠀⠀⠀⢀⣇⠌⠀⠀⠀⠀⠰⠏⠀⠈⠳⠶⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣰⣾⠾⣟⡿⠷⣄⠀⠀⠀⠀⠘⣣⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣭⠉⠉⠀⠀⠈⠹⡄⠙⣳⡀⠀⠀⠀⠀⢧⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢍⠀⠀⠀⢲⡀⠀⠙⠀⠘⢿⡄⠀⠀⠀⠀⠳⣄⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡠⡄⠀⠀⠱⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠈⠑⢤⡀⠂⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡖⡞⣀⡀⠀⠤⠀⠀⠀⢀⠙⢦⠀⠀⠀⠀⠀⠀⠈⠂⢠⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡩⠡⠀⠀⠀⠀⠀⠀⠐⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⡀⠀⠀⠀⠈⢙⣆⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣸⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠈⠀⠙⠓⣦⣄
⠀⠀⠀⠀⠀⠀⠈⢁⣘⡱⠀⠙⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠙⠛⠓⠢⣭⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠢⣁⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠨⠈⠒⢲⣁⣂⠠⠤⠀⠄⠘⢛⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡛⢻⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⠔⠶⣶⣶⣷⣶⣷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣴⣿⣿⣿⣶⠦⣽⣿⣿⣿⣿⣿⣧⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠉⠀⠐⠚⣿⣿⣿⣿⣿⣿⡀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⡁⠀⠀⠀⠼⣿⣿⣿⣿⣿⡿⠄⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡷⠀⠀⠀⠰⢿⣿⣿⣿⣿⡟⠊⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠗⠀⠀⠀⡀⠚⢻⣿⣿⣽⠂⠂⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⣀⣸⣿⣿⠿⠥⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⣸⣟⡻⠟⡒⠃⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣠⣀⣀⡛⠉⠉⠂⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣴⣿⣟⠓⢀⡠⠀⠀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠋⠉⣀⣴⠏⠀⠀⣀⣤⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⢁⣠⣴⣿⡿⢃⣤⣴⣿⡿⢋⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⢠⣴⣿⠿⠋⠁⣴⣿⣿⣿⠟⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠛⠋⠀⠀⣀⡾⠟⠁⢀⣲⣾⣿⣿⡟⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠤⠒⠐⠋⠁⠀⠀⠀⠀⠴⠚⠋⠀⢀⠰⣿⣿⣿⣿⡷⠛⠁
⠀⠀⠀⠀⠀⣀⣴⣾⠿⠏⠉⠀⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⠁⠀⢀⣤⣤⣶⣿⡿⠟⠛⠁
⠀⠀⠀⠀⣾⣿⠛⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣶⣶⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠻⠗⠐⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣿⣯⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣯⣽⣿⣿⣯⣭⣽⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠟⠛⠻⣷
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⢤⡄⠀⠀⢹⣇
⠀⠀⣼⣿⠿⠿⠿⣿⣿⣿⣿⣛⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀⣾⣿⣿⣿⣿⠋⠀⠉⠃⠀⢠⣤⣼⣿⡄
⠀⠀⠛⠀⠀⢀⡀⠈⠉⠙⠉⠀⢰⡿⣿⣿⡷⢀⣤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀⠘⢻⣿⣿⠃
⠀⠀⠀⠁⣰⡿⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠉⠻⠿⢿⣿⣷⣲⣶⡀⠀⣤⠀⢀⣤⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠤⣽⠇⣰⣿⡟
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⡿⠿⢷⣤⡀⠀⠒⢿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠐⠃⣠⠀⡀⢀⣿⡀⠀⠀⠀⡄⠀⠀⢀⣠⣄⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⡘⢿⣿⣿⣿⠿⠁⠀⠈⢹⣿⣿⣶⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠤⠾⡍⣹⣷⣆⠀⠀⢬⣠⣿⣿⣿⣷⣞⠛⢻⣿⣿⣿⣿⣿⣿⡗⢀⣠⣴⣿⣿⣿⣾⣿⢿⣿⣄⣀⢀⣴⣿⣿⣿⣿⣿⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡦⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⠙⠻⣷⣾⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣰⣿⣿⣿⣿⠟⠛⠻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣽⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⠰⠏⠀⢹⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⠛⠛⠟⢿⠟⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣀⠀⠀⠀⠀⣠⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠀⠀⢀⣼⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣀⣀⣤⣼⣿⣿⣿⣿⡿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣤⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣽⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠋⠀⣀⡀⣄⡉⢿⣿⣿⠀⠀⠀⠰⡄⠘⠿⣿⠿⢿⣿⣿⣿⣿⣿⣁⣲⣤⢠⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣺⡇⣤⠀⠀⢤⣬⣽⢯⡟⣸⣿⣿⣄⡀⠒⠀⠈⠳⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⢁⣠⣦⣤⠟⢛⣿⣯⠶⠄
⠀⠀⠀⠀⠀⢠⠚⠁⠀⠙⠷⡎⠀⠘⠛⢀⠀⣁⣿⣿⣿⣿⣿⣿⣶⣶⣼⡿⣿⣿⠿⠿⠋⣯⣿⣿⣿⣿⣿⣟⠁⠠⠚⣉⣴⡄⠀⠈⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡆⢀⣼⡟⠻⠿⡿⠿⢿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠁⡉⢿⠛⢻⣿⣿⣿⡅⠀⠀⠛⠀⠠⣤⣾⠿⣿⣷
⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⢀⣥⣾⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⢠⣴⡾⠀⠈⠀⣠⣿⣿⠆⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⣠⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣷⣀⣀⣀⠀⠐⠉⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣶⣦⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣶⣶⣶⣶⣦⣠⡄
⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣀⣀⠀⠀⢀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⠶⠞⠃⠀⠀⠀⠀⠀⠉⠙⢻⣿⣧
⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣾⣿⠿⠿⣿⣿⣿⣷⣶⣤⡀⠀⣰⡇⠀⠀⠀⢀⡤⠶⠤⣤⣄⣠⣤⣿⣿⣦
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠙⣿⣿⣿⠃⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⣠⠊⠁⠀⢠⡶⡮⠻⣿⣿⣝⢿⣿
⠀⢸⣿⣿⣿⠟⠉⠉⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡙⠂⢀⣀⣿⣿⡿⢀⣀⠀⠰⠟⡭⠍⢿⣿⣿⣿⣿⡄⢰⣧⣶⠖⠄⠸⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢸⡿⣿⣿⠃⠸⠛⠀⢀⠶⢶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢸⣭⣿⣿⣿⣩⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡧⢼⡇⠀⠀⢠⡴⠃⠀⠀⠀⣿⣿⣽⣿
⠀⢸⣧⠘⢳⠀⠀⢀⣀⣈⡁⠀⠀⣿⢻⣿⣿⣿⣿⣿⠀⠀⠠⠤⠾⢱⡾⠉⣿⣿⣇⠀⠀⠀⣴⠾⠧⢀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⢨⣄⣤⠏⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣷⡟⠀⠀⠀⠀⠈⡁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣇⢀⡀⠈⠁⢺⣷⣾⣿⣿⣿⣆⠀⠀⠇⢊⣥⠀⢱⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⣀⣴⣿⣿⣿⣿⣿
⠀⢸⣿⣿⢿⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣆⣀⣱⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿
⠀⢸⣿⣿⣦⡙⠻⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⠛⠋⡡⠀⠘⠿⣻
⠀⢸⣿⣤⡿⢷⣿⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⠙⠟⠁⠈⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣿⣏⡠⠀⡠⢶⣻
⠀⢸⣯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡠⠈⣿⣿⣿⣿⣿⣿⣧⢿⢿⣟⣦⡀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠿⣮⡻⣯⣾⣶⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⢉⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣭⡄⣉⣹⣿⣿⣿⣿⣿
⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠡⠁⠀⠡⠠⠤⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⢿⣿⡗⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢠⡾⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣷⣿⣿⡄⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣀⣼⣧⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⠀⠖⠀⠀⠈⠁⠀⠀⠹⡿⠋⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠙⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢈⠛⠤⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⣤⡀⣖⣦⣴⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠛⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠁⠀⣿⠀⠀⠀⠀⠀⣀⡀⣾⡿⠟⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⡄⢀⠀⣀⣿⣿⡿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣆⠐⠊⠁⣁⣨⣀⣀⡖⠉⠀⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡟⠡⣿⢆⣁⣀⣴⣿⣿⣿⠁⣠⣤⣾⣿⣿⣿⣿⣿⣿⠋⣿⠀⠀⠹⣿⠾⡭⠉⠈⠀⠀⠀⡢⠠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠰⣶⣦⣴⣿⣿⣿⣿⣿⣿⢴⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢀⠦⣰⡿⠀⠀⠀⠀⠠⠶⠟⠃⡤⠼⣅
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡴⢦⡽⢡⢀⣤⣴⠶⠀⠈⠃⠈⠀⠀⢉⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⠀⢼⣏⡀⠀⠈⠿⣥⣿⡿⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⠇⣿⢧⡄⠘⣿⠏⠀⠀⠀⠀⢤⣿⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣰⢇⡰⡋⠉⠡⢀⡀⠀⠟⣿⡇⠀⢹⣿⣿⣿⣏⡀⣼⣿⡀⠀⣦⣾⣧⠀⠀⢀⠄⠀⠀⠀⠀⡙⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⡞⠋⠁⠄⠀⠉⠀⠠⠆⢸⣿⡀⢸⣿⣿⣿⣯⣭⣼⣿⢡⠀⡏⢿⣿⠀⠀⢈⡗⠀⠀⢠⡾⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠈⠀⢀⣈⠀⢀⡀⠀⠀⠀⢺⣿⣧⠈⢻⣷⣿⣿⣦⡒⡿⠀⢳⡟⠘⢿⠀⠀⢀⣀⣶⡀⠀⠠⢀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠐⠾⠊⢱⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢸⣿⣿⡆⡀⢛⣛⠛⠃⠤⣄⣤⣼⠂⠀⠀⠀⠀⠙⠛⠛⠻⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠠⣶⡤⠀⣾⣶⠆⠀⠸⡟⢿⣿⣷⠄⠠⠀⢤⣼⠟⢿⣷⣄⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⣂⣠⣾⡟⠁⣼⣿⡏⠀⠀⠀⣿⣿⡿⣷⣄⠀⡀⠀⠀⠀⠀⠋⠁⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠃⠀⢹⣿⠀⠀⠀⠀⠸⣿⡇⠘⢿⣾⣿⣾⡗⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⠿⣷⡄⠀⠙⠟⠟⠀⠀⣠⣤⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⢠⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⡞⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠟⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⡇⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣿⣧⣿⠏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡆⢤⣀⢠⡄⣀⣀⣄⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⡀⢀⡀⣀⣀⡀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠂⠀⡇⢀⡸⡾⡟⢹⠁⡇⠹⡄⡜⢁⣀⢰⠦⡴⣄⢰⢶⠂⠈⣏⠳⠧⠷⠄⠀⡀
⠀⠀⠀⠀⠀⠛⣿⣯⣤⢠⡟⠋⠀⠀⡷⠋⢸⠓⣇⢸⠀⡇⠀⡝⠉⣁⡉⠈⡟⠉⡭⣸⣺⣴⡦⣯⣷⣶⣼⣾⠳⠃
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣧⠀⠀⠀⠃⢠⣿⠿⠿⣾⠂⠁⡜⠀⢙⣿⣿⣷⣾⠀⠷⣋⣫⠇⣰⣿⣿⢿⡟⣿⠇
⠀⠀⠀⠀⠀⢿⡿⣿⠏⣩⠛⠂⠀⠀⠀⢸⣿⣤⠤⢼⠇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠺⠿⣿⣾⣿⣯⣹⡄⢀
⠀⠀⠀⠀⠀⠘⣶⡿⠋⢁⠀⠀⠀⠀⠀⠀⢻⣞⢂⠈⣀⢀⡆⠀⠀⣿⣶⣿⡿⠱⣶⡶⠟⠘⣔⣽⣏⠛⢢⣀⡀⠠
⠀⠀⠀⡰⠒⣾⣿⣶⣴⡞⢻⡟⠤⠀⠀⣀⣾⣫⢿⡋⢡⠀⠃⢀⣴⣿⣿⣿⠀⣶⣤⣀⠀⣳⢹⣼⠛⡆⣞⣷⣼⡂
⠀⠀⠀⡇⠄⢻⣏⣀⣠⡄⢴⣷⣴⡃⠈⢿⡿⠟⣳⣥⡰⣿⣴⡿⣿⠛⠛⠉⠃⠈⠻⣼⡇⢸⠿⠁⠿⣷⠚⠉⠀⠟⠳
⠀⠀⢠⡇⢺⣾⡛⢉⣁⣤⡟⣾⣿⡇⣧⣠⣖⡛⣇⢿⣛⣿⢿⣿⢿⣿⣧⡼⠛⠾⣿⣿⡇⢸⠀⣢⡤⣥⣀⠀⣀⣘⣀
⠀⠀⢸⠇⣿⣿⡁⠀⣈⠀⠀⣿⣿⣟⣿⡟⠶⢣⢩⣞⠭⣹⢿⣿⢸⣿⡗⠀⠀⢫⣿⣿⡏⢸⣷⢟⣴⣶⣎⢷⡍⣽⠉
⠀⠀⡌⢸⣿⠇⠖⢫⣉⣀⠄⣿⢿⡏⣿⣿⣾⠾⠂⡷⣾⣥⠈⠛⣿⡏⢿⣿⡿⣽⣿⣿⣧⠘⡿⣞⣿⣿⡟⢈⡇⣿⡀
⠀⠀⣇⢸⣿⣤⣀⣒⣋⣯⣶⣿⢸⡇⣿⣥⣀⣰⣿⣿⣭⣿⣶⣿⣾⣆⣛⠛⠓⠈⢛⣽⣿⡀⠀⠘⠶⣍⣹⠏⠀⣿⡇
⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⠘⣷⠋⢹⣿⣻⣯⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⣶⣶⣤⣥⡴⠚⠘⠇
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⢸⠀⢸⣿⣿⡟⢿⡏⣿⠃⠉⠀⢿⣿⣿⣿⣿⣿⣿⣭⡟⣈⠿⠺⢿⡟⠀⡊⠀⡆
⠀⠀⠤⠤⠾⠿⠿⠿⠿⠿⠿⠦⠶⠼⠤⠼⠿⠿⠷⠼⠷⠷⠦⠼⠦⠾⠿⠿⠿⠿⠿⠿⠿⢱⠾⠚⠒⠚⠛⠒⠒⠂⠃
⠀⠀⠀⠐⠂⣶⣶⡆⣶⣶⡆⣶⣶⣆⡆⡶⣶⣶⢶⣰⣶⠀⠀⢿⣯⡇⠀⠀⠀⢾⣻⠆⠀⠀⠀⠁⢌⠥⠈
⠀⠀⠀⠀⠀⠉⠉⠁⣥⣿⣇⣩⣿⣫⣅⣤⣍⡀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⠄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣆
⠀⠀⠀⣰⣿⡿⠿⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣠⣾⣧⡿⠋⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⠿⣿⣿⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠿⣷⠆⠀⠐⠾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⡀⠈⣽⣿⠀⠀⠀⠘⢿⣿⣿⣿⠇⠐⠂⢰⠻⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠈⠶⠀⠀⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣶⠿⠶⣾⣽⣛⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⣦⣿⠋
⠀⠀⠀⠀⠀⠷⣄⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠈⢈⣛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠘⠟⠛⠶⠶⠄⠀⠀⠀⠀⠀⢸⣿⣶⡄⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃
⠀⠀⠤⠤⠤⠦⠀⠶⠤⠤⠤⠤⠤⠤⠄⠀⠀⠤⠌⠥⠄⢶⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⡤⠤⠤⣤⠄⢠⡤⠤⡤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⣠⣶⣿⣿⡿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣊⣽⣷⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⣤⠊⠉⠈⠙⣷⣄
⠀⠀⠀⢸⣿⣿⣉⠀⠀⠈⣿⡷⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⡿⠛⠛⠛⠉⢻⡆⠀⠀⠀⠀⢸⡏⣴⣶⣀⣾⣿⣿
⠀⠀⠀⢸⣿⣟⢹⡇⠉⠂⢹⠇⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠄⠧⠀⣿⡄
⠀⠀⠀⠀⠻⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⡟⠀⠘⠳⠄⠃⢸⠇⠀⠀⠀⠀⠈⠁⠀⠐⠒⠒⣠⡟⠁
⠀⠀⠀⠀⠀⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⣤⠀⢀⣠⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠘⠳⠦⠾⠿⣧⣤
⠀⠀⠀⠀⢀⣿⣿⡏⠁⢀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⢹⣷⣤⣭⡅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⡿⠏
⠀⠀⠀⡠⣭⠍⢭⠁⠠⢤⠡⣤⠀⠀⠀⠀⠀⠀⢠⠄⠠⡌⠙⡿⢯⠡⣤⡠⢀⠀⠀⠀⠰⠦⠆⠶⠐⢾⡰⠆⠶⠶⠴⠲
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠷⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦
⠀⠀⠀⠀⣠⢆⣿⣶⣦⣠⣤⣼⣷⡄⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣈⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣸⢸⡟⠛⣟⣻⡿⠿⣿⡇⠀⠀⠀⠀⠀⠰⣿⠀⠍⠁⠈⠭⢹⣧⠀⠀⠀⠀⠀⠀⢹⣿⠟⠛⠀⠙⠙⣿
⠀⠀⠀⠀⠇⣿⣇⠾⠉⠙⡶⣸⣿⣇⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠻⡀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀
⠀⠀⠀⠀⡇⣿⣿⣦⣀⣠⣶⣿⣿⣯⠀⠀⠀⠀⠀⠸⣿⣦⣤⣼⣧⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢠
⠀⠀⠀⢸⢱⡟⠛⠻⢿⣿⠏⢿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘
⠘⠓⠒⠚⣿⣿⣰⠂⠒⠀⠛⠻⣿⣿⠒⠲⠞⠒⠀⠸⠒⠒⠒⠂⠙⠃⠒⠒⠒⠒⠒⠀⠗⠒⠲⠂⠘⠐⠰⠒⠒⣐⠶⠒⠒
⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⠀⠙⠃⠀⠀⠀⢀⠴⠶⠖⠂⡀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦
⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⠻⣿⣿⣿⣷⡀⠀⠀⢠⣿⠏⠀⠀⠈⢻⣿⠂
⠀⠀⠀⠀⡟⢛⠛⢻⣿⣿⣏⠁⠀⠀⠀⠀⢸⡟⠛⠃⠈⠛⠀⠀⠀⠀⠸⣿⣤⡹⣿⣿⣿⡄⠀⠀⠈⢿⠶⠦⠀⠴⠂⠛
⠀⠀⠀⠐⠀⠀⠀⡀⠀⣼⠿⠗⠀⠀⠀⠀⠀⢹⡄⠟⠁⠀⠀⠀⠀⠀⠀⢯⠀⠀⠹⣿⡿⠃⠀⠀⠀⣀⡄⠀⡀⠀⢀⡀
⠀⠀⠀⠀⢀⣄⠀⠐⣰⣧⣤⣤⡀⠀⠀⠀⠀⣸⣿⣦⣤⣶⡇⠀⠀⠀⠀⠈⡤⠞⣿⣿⠁⠀⠀⠀⠀⠙⢻⣆⣀⣀⠎⣿⠧
⠀⠀⢀⣴⣿⡙⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⣀⣻⠟⠛⠋⠘⠃⣀⡀⠀⠀⠀⠘⢦⡴⠂⠀⠀⠀⠀⠀⠀⠀⠻⠿⠏
⠀⠀⠸⠹⠧⠥⠎⠸⠧⠶⠙⠿⠀⠀⠀⠀⠀⠀⠖⠰⠦⠆⠀⠀⠀⠶⠶⠶⠶⠦⠶⠶⠶⠶⠀⠶⠶⠖⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣺⣃⣾⡷⠀⡷⣶⢾⣳⢸⡇⠀⣞⡁⡷⣶⣶⣶⣀⡇⢰⡿⢺⣗⣺⠗⣾⠗⣾⣂⡾⡆⣷⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⡀
⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢗⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢙⠀⠹⣿⣿⣿⢿⣷⣦⣄⣀⣀⣠⣴⣾⣿⣿⣿⡟⠀⠀⠀⠉⠉⣷
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢀⣀⣤⣤⡠⣺⠃⠀⠻⣿⣷⣿⣟⣻⣿⣿⡿⢻⣽⣾⣿⣿⠟⠀⣀⣤⣤⣄⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⣠⠀⠄⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣠⣾⣿⣯⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⣀⣴⣿⣟⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⣀⠈⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⢠⣶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣵⣶⣤⣯⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠀⠉⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠈⡌⢿⣦⣐⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⡿⣦⣤⠀⠀⠀⠀⠑⢦⡈⠻⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠈⣿⡷⣼⡟⠀⠄⠀⠀⠀⠱⣄⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡻⣶⡤⡿⣿⡟⠎⠉⢾⣷⣠⡀⠀⠀⠘⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⡿⠷⠶⣴⡌⠠⣅⠀⠀⠀⢹⣿⣿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⡆⠀⠀⠀⠋⠹⠶⢋⣀⣤⣤⡈⢳⠀⢉⣷⢧⡶⣺⣹⡿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣀⣴⣿⣷⣿⣆⡿⣦⡹⠿⣿⣧⢹⡿⠾⠛⠁⢀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠘⠀⠀⠀⠾⠟⠉⣸⠛⠛⠋⢰⣽⣯⠈⠋⠙⠋⠀⠀⠀⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢠⣴⢆⡄⠘⠁⠀⠀⠀⠈⣿⡿⠀⠀⠀⢀⣀⡦⣀⣴⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢦⡀⠀⠀⠟⣀⡀⠀⠀⠀⢀⡼⠛⠠⣄⠢⢴⣿⣿⣧⡿⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⠀⠀⠐⣌⠻⢶⣤⣀⣘⠁⠀⠀⢀⣀⣨⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠸⣷⡀⠀⠉⠙⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢲⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠆⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢄⠀⠘⡣⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⢴⡈⠐⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠉⠀⣍⠉⠀⠀⠀⠀⠀⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢈⣦⠁⠀⠀⠀⠀⠀⣀⠄⠲⠼⣠⠋⡐⠠⠄⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡖⠈⠀⠀⡀⠀⠀⠀⡀⠀⠀⡈⠁⡓⢴⠉⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠁⠀⠿⠀⠀⠐⠀⠰⠔⡌⢡⡄⠠⠅⠀⡀⢅⠀⡈⠁⠀⠀⠀⠀⠀⠦
⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⢔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⠐⠒⡆⠀⠀⠁⠀⠀⠑
⠀⠈⢠⢈⠤⡀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠂⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⡰⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠒⡃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⠦⠄⡈⠀⠀⢀⠙⠻⡀⠀⠀⠀⡰⠁⡁⢴⢔⡄⠀⠀⠀⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠹⣄⢀⡔⠁⠀⠀⢐⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠄⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⢴⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠴⠄⠠⠤⠴⠴⠦⠤⠴⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠚⠉⠛⠉⠙⠛⠉⠳⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⣀⠀⢀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⣀⡴⠚⠉⠉⠉⠀⠀⠀⠈⠉⠋⠙⢦⣤⣄⡀⠀⢀⣧⡀
⠀⠀⠀⠀⠀⢀⡴⣇⣀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠻⡀⢹⡀
⠀⠀⠀⠀⠀⢸⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⡀
⠀⠀⠀⠀⢠⠏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠁
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣆⠀⢀⡰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢸⣿⣿⣟⣻⡇⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣸⠛⠛⠓⠚⣇⣀⣠⠤⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡾⠶⠭⣦⡀⢀⣜⣉⣠⡤⠴⢿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⡇⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠘⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⣼⣀⡤⠖⠚⣇⣸⡀⠀⠀⠀⠀⠀⢹⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠉⣩⡿⡄⠀⠀⠀⠀⠘⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⣇⠀⠀⠀⠀⣤⣶⣅⠀⠀⠀⠀⠀⢹⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢹⡖⠒⣛⣶⠒⠲⡖⣇⣀⣸⠷⢶⣶⣶⢤⣈⣇⡴⢻⢷
⠀⠀⠀⠀⡴⠒⠒⣲⡾⣭⣿⣿⠽⠋⠙⠤⠴⠃⠀⠉⠁⠀⢯⠀⣸⡇⠈⢿⡷⣿⠾⣷⡒⠒⠒⢦
⠀⠀⠀⣸⠃⣠⠞⠁⢠⣾⣷⣛⣦⡤⢖⣦⠀⠀⣠⣤⣄⠀⢈⣭⣭⣤⠖⢋⣴⡿⠓⡆⠙⢢⡀⠈⢧
⠀⠀⣰⠃⠀⢻⡀⠀⠘⢯⡙⠻⢭⣛⣛⣛⠓⠛⠓⠛⢋⣉⣉⣠⡤⠴⠚⣩⣾⣳⠋⠁⠀⣰⠃⠀⠘⣆
⠀⢠⠇⠀⠀⠀⠙⠲⢤⣀⡉⠓⠶⠤⣬⣉⣉⣉⣉⣉⣉⣉⣥⠤⠴⠒⠋⠁⠀⣉⣠⠴⠚⠁⠀⠀⠀⠸⡆
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠖⡡⠐⠒⠒⠠⡙⢦⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⡠⢂⠥⢂⠈⠌⢁⠠⠤⢀⠀⠀⠀⡀⠀⠀⠈⠂⢃⠀⢀⡀⢞⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡠⡪⢚⠕⠈⠀⠐⢊⡔⠂⠀⢨⡇⠢⠀⠀⠐⠄⠀⡀⠈⠀⠀⠹⡄⢣⠁⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠌⠔⠔⠑⠀⠀⠀⡀⠈⠂⢊⠔⠋⠈⠓⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠰⠀⠃⠳⡘⣆⣄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⡌⠀⠀⠀⠀⠀⠁⠀⠙⢄⡉⠀⠀⠀⠆⠀⠆⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠁⠀⠀⠀⠒
⠀⠀⠀⢁⠀⣤⠀⠛⣀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠙⠀⠘⠉⢼⣻⡆⠀⠀⠈⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⢼⠰⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢠⣻⠛⠀⠀⠀⠀⠀⠀⠒⢄⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠈
⠀⠀⢀⡀⠀⠄⠀⠀⠀⠈⠠⡄⠀⠇⣞⠄⠀⠂⠁⠀⠁⠐⢀⠀⠂⠐⠀⠆⠱⠠⠈⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⢄
⠀⠀⡜⠱⠀⢄⠀⠀⠀⠀⠀⠠⠖⠚⣿⢲⡦⢀⡄⢀⠄⠠⢂⠀⠀⠀⠀⡄⠃⠀⡀⠀⠀⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠈⠀⠁⠀⡀⠀⠀⠀⠀⠀⠉⢋⠉⠅⢀⠠⢊⠔⠁⠀⠀⠀⠀⢟⠀⠰⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠀⠀⡈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⢒⣀⠠⠐⠈⠀⠀⢀⡀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠌
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⢿⠀⠇⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⡆⠀⢀⠈⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠢⢤⠂⠐⢄⠀⠀⠀⠇⠄⠀⠀⠂⠃⠀⠘⠂⠃⠀⠛⠀⠀⠇⠀⠀⠀⠀⠀⢀⡤⣤⢤⡤⠄⣲⠶⡄⣀
⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠆⠀⠀⠀⠀⠀⠐⠐⠠⠒⠀⠔⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡀⠀⠀⠀⠈⠢⢬⣎⡢⠄
⠀⠀⢀⠄⠢⠎⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠈⠈⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⣠⠎⠀⢢
⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠙⠲⣄⢸⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠊⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢂⡵⢶⠒⢦⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⡂⢡⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠰⠦⢴⣒⣐⠀⡠⠶⠆⠀⠄⠀⠀⡐⡀⣄⣘⠶⢞⡴⠀⠑⡄⠀⣠⠇
⠀⠀⠀⠀⠀⠘⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⣯⠍⠄⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠺⠀⠀⠏⠀⠀⠀⠈⡁⠀⠀⠀⡼⠜⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⢰⠄⠉⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⢄⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠛⠄⠀⢌⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⡼⠇⠀⠀⢀⡠⠒⠉⣀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠚⠛⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠔⠒⠒⠶⠤⢀⠀⠄⠀⠀⠀⠀⠀⢸⠀⡏⠁⡇⠀⠠⠚⠁⠀⢀⠄⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠃⢀⠈⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠺⠄⡰⠃⡀⠰⠅⠒⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣴⠟⠻⣆
⣼⠇⢀⡾⠃
⣿⠀⣿⠁
⢻⣆⣿⣀⣀⣀
⢀⣿⠋⠉⠉⠙⠻⣦⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣀⣀⣀⣠⡴⣷⡀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣠⡿⠁
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠒⠒⠒⠛⠻⣦⣀
⠀⠘⣷⡀⠀⠀⣾⠲⠶⠤⢤⣤⡽⠆⠀⠀⠀⠀⠀⠙⠷⣄⡀
⠀⠀⠈⢷⣄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠙⢷⣄⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠉⠻⣮⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⢶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠺⢷⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠢⠤⠋⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢄⣀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⡤⠖⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠙⠲⢼⡄⠀⠀⠀⠀⠀⠠⠀⠘⠒⠚⠉⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢣⡠⢦⡀⠔⢄⡀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠴⠗⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠛⠦⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠶⠤⡄⠀⠀⡤⡄⢀⣄⢀⡀⠀⠀⣀⣀⣀⣀⣀⣭⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⢠⣇⡤⠤⡆⠈⠁⠈⠁⡦⢤⣈⣏
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢰⠒⠞⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣄⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⠓⠒⠒⠋⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠢⢤⠀⢠⡠⠀⠀⣠⢀⡲⠶⠔⡉⢅⠉⠀⠀⢭⡉⠐⠦⡀⠀⠀⠀⠀⠨⠤⢉⡀⠄⠠
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠼⡋⠉⢹⠈⠑⠐⣀⠤⣶⣧⠴⠄⠊⢠⡦⢆⡷⠀⠽⠀⠀⡔⣩⣉⢀⡀⠴⣾⠇⣐⠀⠀⠀⠀⠤⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢄⠙⠟⠛⣆⣉⡔⣀⡠⣔⣎⠰⠤⠚⠁⠀⠀⠀⡂⠉⣁⠉⣠⣤⣀⠅⠉⣠⠒⠷⠦⠊⡶⠀⠒⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢆⠤⣄⡀⢌⡨⢵⠀⠌⢰⡀⢠⠰⠞⠁⠠⢁⣄⡘⠿⠈⡃⣠⠈⡛⢲⣋⡴⢣⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠈⠔⠂⡀⠰⣄⣈⠐⠀⡤⠃⠤⣈⣧⡀⠧⠭⠀⣀⣤⠃⠀⠉⠉⢉⠔⠁⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠢⢄⡄⠀⠐⠃⠀⠎⠙⠛⠛⣛⠉⡑⣲⠐⢀⣣⠀⠀⠀⡀⡄⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠐⢠⡠⠖⠀⠴⠆⣤⣤⣠⣤⠅⡥⢨⠟⠀⠀⠀⡆⣆⡗⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠒⠒⠂⡠⢀⣐⡐⠲⠔⠒⠚⢖⠦⠚⠃⠀⠀⠀⠃⠓⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠍⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡀⠀⠀⠀⠀⠈⣀⠤⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⢉⠁⠀⠀⠀⠈⡒⠰⢂⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠂⠀⠀⠀⠚⡉⠂⠀⠀⠉⠉⢉⢩⡅⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿⠆⠀⠀⠸⠿⠃⠀⠀⠀⠀⢱⡆⠃⣀⠔⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣈⢴⠊⠀⠐⠋⠉⢉⠍⣠⠞
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⢧⠀⢤⠤⠤⢀⡠⠄⠀⠀⠀⡀⠡⡼⢶⠶⠿⠭⠄⠒⠈⠁
⠀⠇⠀⠄⠋⠓⣦⢤⡀⠀⣠⣤⣷⡄⠻⠉⠹⠁⠀⠀⢀⡔⣀⣴⣿⣷⣤⣤⣀⡀
⠀⡄⠀⠀⠓⠀⡌⠀⢰⣾⣿⣿⡏⢹⡄⠒⠃⠀⣠⣴⡫⢕⡫⡾⠃⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠈⢦⡀⠈⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣶⢖⣋⠉⡀⠀⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣍⠽⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣷⡄
⡀⠀⠀⠀⠀⡇⠀⠀⣠⠶⠟⠋⠨⠟⠛⠛⠛⠛⠛⠛⠛⠳⣬⣙⠿⠿⢿⡿⠟⠛⢷⣽⣿⣿⠟⠋⠉⠙⢄
⡇⠀⠀⠀⢠⢂⠴⠋⠀⢀⠤⠤⣀⣈⣀⣤⡀⡠⣤⣠⣤⣾⣿⣿⣷⣿⠛⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠀⠀⠙⠢⢄
⠱⠤⠤⠄⠊⠁⠀⠀⠀⢸⣿⣿⣿⠿⣿⠿⡿⢿⣿⣟⣿⣟⡁⠉⠉⠙⢼⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⢿⣿⣽⣿⣿⣿⣿⣟⣳⣆⠀⠀⢀⠊⠐⠤⠐⠀⠂⠉⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⢄⠀⠀⢼⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠿⠁⢈⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠭⠭⠉⠭⠭⠽⠯⠥⠜⠂⠲⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⠀⠀⡈⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣻⡿⣿⠦⣿⢹⠘⢀⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠽⢩⠭⣿⠱⣟⠛⣿⡞⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠔⠀⠀⣠⣷⡷⣮⢱⠉⡎⢠⢴⠚⠠⠐⠀⠀⠀⢀⣀⣈⡑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣯⣿⣾⣿⢹⠛⣷⡟⣾⠀⠄⠀⠀⠈⠐⢻⣿⠏⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⣠⣦⣿⣽⡿⢋⠸⠀⠏⠷⠻⠀⣄⠀⣤⢀⣀⢀⡀⠄⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣾⠟⠋⠁⡀⠁⠄⠀⣞⠛⣇⣿⣦⣿⠀⣴⠀⢀⡤⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠹⣇⣀⣀⠀⠀⠀⠀⠻⣤⢧⢸⡼⢿⣄⡿⣰⠇⢀⣿⠡⠂⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣌⡙⢻⣿⡛⣿⣷⣖⡶⠒⠒⢶⣶⣶⣶⢠⣤⣤⡈⠉⢹⣥⣼⠎⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣿⣾⣟⣷⣏⣫⡀⠈⠀⢀⠙⢻⣷⡚⡟⡿⢷⡶⢾⣯⣼⣆⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣴⣇⣽⣬⡸⡿⠧⠐⣶⠿⠂⠘⠻⠗⠃⣇⣺⠅⠿⠘⣶⣠⣯⡳⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⠿⣧⣟⡿⣿⣟⠀⣠⠦⠄⠀⢀⡀⠛⠿⢿⣶⠂⢛⣿⡛⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡺⣿⠻⣿⠿⢙⢻⣧⡘⡛⠛⠙⠃⠀⣀⣀⠀⡨⢷⣶⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠘⢓⣟⡋⣉⠀⢁⡤⣤⠴⣾⣶⠿⠀⠠⠋⠙⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠛⠉⠙⠀⠋⠀⠁⠀⠀⠀⠀⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣛⣭⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣿⡿⠿⠿⢟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣀⡀⡀⠈⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⢻⠿⡤⠀⠀⠀⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣑⡒⠊⢀⡀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡓⠀⠉⠀⠀⢀⣤⠂⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢶⠿⣿⣧⣀⣀⣠⣴⠟⠁⢀⠀⢸⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢿⡇⠙⣿⡍⠁⢀⡄⠀⠀⡎⠀⠈⣏⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠟⠀⠀⢀⠀⠀⠀⠀⡀⠸⠇⠀⠈⣧⣤⠈⠀⠀⢸⠃⠀⠀⣿⠀⠀⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡁⠀⠀⠀⠀⠀⠉⠀⠺⠁⠀⣾⠠⠞⣿⣿⠢⡀⠀⡌⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠋⠑⣄⠀⠀⠰⠀⠀⠀⡄⠀⠀⠐⠀⠀⢿⡄⢀⣿⣷⡀⠀⢰⠃⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠼⠃⠀⢀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡇⠀⡎⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⠂⠀⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢰⠃⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⣄⠉⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣞⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⡼⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⡰⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠰⠁⠀⠀⠀⠀⣧⠀⣀⣀⣤⣤⣄⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⡋⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣀⣠⡼⠟⣿⠀⠀⠀⢰⡿⠀⠀⠀⠀⠸⠟⢠⡴⢀⣠⡄⠀⠀⢸⡇⠈⣿⣿⣿⡟⣼⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣉⣀⣀⣀⣿⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣿⣅⡉⠁⠀⠀⠀⡼⠧⠤⠬⠷⢤⡾⠿⠦⠴⠷⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢧⣀⡈⠓⠶⠶⠶⠶⠒⠀⠀⠀⠊⣉⣁⡤⣤⠤⠊⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠷⠿⠿⠿⠿⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⢀⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⢦⣄⠀⠀⢀⡀⠀⠀⠀⢰⣿⣦⣴⡇⣥⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢱⠁⠀⠀⠀⠀⠀⠀⢰⣾⣶⡆⣾⢫⣶⡿⠛⢿⣷⣝⣷⡀⣿⡇⠀⠀⠀⢸⣿⣿⢡⢳⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣾⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢸⡏⣿⣿⣧⠀⣾⣿⣿⢸⡇⢻⡇⠀⠀⠀⠈⣿⣿⢸⠸⣿⣇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⡹⣿⣿⣆⢻⣿⢟⣾⠃⢸⡇⠀⠀⠀⠀⠘⣿⣼⡀⠈⠿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠻⣮⣭⣟⣯⣵⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⢠⡰⡄⣎⡦⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⠼⣰⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⠆⡦⡖⠂⢀
⠀⠀⠀⠀⠀⢀⡾⠃⠁⢀⠠⡄⠈⠈⢳⡄⠀⠀⠀⠀⠀⠀⣴⠜⠚⢁⡠⢆⠉⠒⠡⣆⠀⠀⠀⠀⠀⠀⢠⠙⠟⠁⣀⠤⡉⠀⠋⢥⡀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⣿⠟⠀⠀⠀⢻⡄⠀⠀⠀⠀⣸⠃⠀⠀⢸⣿⡟⠃⠀⠀⠸⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⡿⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⠀⠀⠀⠘⣿⠠⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠹⣧⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠘⢿⡄⠀⢀⡼⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⢻⣆⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣨⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣥⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣡⡴⠞⠁



⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢟⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⡿⢟⢿⡿⣛⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⡿⢟⢿⡿⣛⣿⠿⡻⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⡇⠀⣼⡀⠠⣾⣿⣿⣇⠀⠀⠀⠀⢰⣿⡇⠀⣼⡄⠠⣾⠀⣠⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣷⡀⢿⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣷⡀⢿⣧⠐⣿⣆⠻⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣬⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣬⣿⣷⣼⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣬⣿⣷⣼⣿⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡿⡇⠀⡏⡇⠀⠀⠀⠀⠀⠀⢹⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⢁⡇⠀⡇⢷⠀⠀⠀⠀⢀⡀⠘⡇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⢠⠇⢸⠃⠀⣇⠘⡆⠀⠀⠀⠀⣿⡄⠸⡄⠘⢆⠀⠀⠀⠀⠀⠀⠠⡆⠈⡇⣇⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⡞⠀⣸⠀⠀⢹⠀⢱⠀⠀⠀⠀⡇⣧⠀⠹⡀⠈⢧⠀⠀⠀⠀⠀⢸⣷⠀⢧⠸⡀⠀⠀⠀⠀⠀⢰⢻
⠀⠀⠀⢰⠃⠀⣿⠀⠀⢸⠀⠈⡇⠀⠀⢀⡇⢸⠀⠀⢳⠀⠀⢣⠀⠀⠀⠀⡞⡿⠀⢸⡄⢧⠀⠀⠀⠀⠀⢸⠸⡄
⠀⠀⠀⢸⠀⠀⠹⣦⣤⠞⠀⠀⡇⣾⡀⠸⡇⢸⡀⠀⣸⠀⠀⠘⡆⠀⠀⢰⠃⡇⠀⠀⡇⠘⡆⠀⠀⠀⠀⠈⡇⢳
⠀⢸⣆⢸⠀⠀⠀⠈⠀⠀⠀⢠⠇⣇⢧⠀⣇⠈⠻⠛⠹⠀⠀⢠⢧⡇⠀⢸⠀⠹⣦⠾⠃⠀⢷⠀⢰⡄⠀⠀⢹⡀⠳⡀
⠀⢸⢹⠈⡇⢠⣆⠀⠀⠀⠀⡞⠀⠸⡌⣆⠘⢆⠀⠀⠀⠀⠀⡼⢸⣻⡀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠈⡿⡄⠀⠀⢧⠀⠙⣆
⡀⡏⢸⠀⢹⣼⠘⡆⠀⠀⣸⠁⠀⠀⢷⠘⡆⠈⢧⡀⠀⠀⢠⠇⠀⣇⢳⠀⣇⠀⠀⢰⡶⢦⣸⠀⠀⡇⢳⠀⠀⠘⡄⠀⠘
⣧⡇⢸⡀⠀⠻⠀⡇⠀⠀⡇⠀⠀⠀⣸⠀⢹⠀⠀⢳⡀⠀⢸⣦⣤⠿⠈⡇⠸⡆⠆⢸⡄⠸⠇⠀⢀⡇⢸⡆⠀⠀⣷⠀⡆
⢿⣇⠈⢷⣄⣠⣴⡇⠀⠀⢻⣦⣤⣴⡟⠀⣸⠀⠀⠈⣇⠀⠀⠣⠀⠀⢸⠇⠀⠰⠀⠄⠳⠄⠀⣀⠾⠃⢸⡇⠀⠀⣿⡄⣿
⠈⠻⠄⠀⠁⠀⠞⠀⠀⠀⠀⠫⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⢹⡆⠂⠉⠙⠉⠁⠈⢸⡃⠀⣠⣿⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠷⣦⣤⣾⣿⠀⠀⠀⠀⠀⢿⣄⣀⣠⡾⢿⠀⠀⠀⠀⠀⠀⡾⠛⠛⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠈⠫⠉⠉⠀⢸⠆⠀⠀⠀⠀⠜⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜

⠆

⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⣉⠰⢮⠉⣿⡇⠐⣤⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢠⣎⢉⣷⣾⣿⣿⣿⣿⣧⣼⠃⡀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⢠⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢨⣄⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣙⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡙⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⢦⠚⣻⠿⣿⣿⣿⡿⣏⣱⠎⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣠⣏⣸⡿⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠘⢿⡌⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠈⠙⠳⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡷⠻⣿⣿⡂⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢸⣿⣿⣿⣷⣤⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⣤⣽⣿⣟⡻⢿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⡼⠋⠁⠚⠭⠉⠉⠉⠉⠉⠉⠍⠂⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⢴⣦⣶⣦⡄⠀⠀⢰⠿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣦⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⣴⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢻⡇⠀⠀⠀⠈⢿⣶⣤⣀⣀⣀⣀⣀⣤⣾⣿⠏⠀⠀⠀⠸⣿⠋⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿
⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛






⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠒⠶⠋⠙⠚⠉⠙⠚⠋⠙⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣠⠦⠤⠴⠞⠲⠶⠛⢦⣄⣠⢤⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠲⣄⡀⢀⣸⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡤⢿⣀⣰⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢧⡀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⠃⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⡄
⠀⠀⠀⠀⠀⢀⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡦⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠃
⠀⠀⠀⠀⠀⠸⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠧⣤⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣴⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⠿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⣼⢿⣿⣿⣯⡽⡇⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣟⠲⠾⡀⠀⠀⠀⣰⠷⠖⠛⠉⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢹⠋⠙⠓⠻⢦⢀⡾⠧⠶⠶⠒⠋⠉⢿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡿⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⣼⣇⣠⠴⠖⠛⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢋⣩⣇⡀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢈⣉⣼⠃⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣸⣇⣀⣀⣀⣀⣼⠋⠉⢳⣄⠀⢀⣀⡀⠀⠸⡆⢀⣤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣰⣇⣨⣭⡽⣏⠀⠈⣿⠙⠦⠤⠞⠉⣩⠟⠻⢯⠛⢶⣷⣞⢁⡟⢳⡀
⠀⠀⠀⠀⢠⡟⠉⠛⣉⡿⠿⣶⠿⣿⡖⠋⠀⠙⠒⠚⠃⠀⠀⠀⠀⠀⢻⣄⣀⡼⠀⠀⢹⠞⢻⣟⠻⢿⣝⠉⠉⠙⢧
⠀⠀⠀⢀⡞⠀⣠⠞⠁⠀⣴⣾⣿⣉⣧⣤⠴⢛⣧⠀⠀⣠⣤⣤⣄⠀⠀⣠⣴⢤⣤⠟⢋⣠⣿⠟⢒⡆⠈⠳⡄⠀⠘⣇
⠀⠀⠀⡾⠁⠀⢿⡀⠀⠀⠻⣍⠛⠯⣝⣓⡛⠻⠿⠶⠾⠿⠒⠚⠛⠛⠛⢁⣀⣠⡤⠖⢋⣴⡛⣶⠋⠁⠀⢀⡿⠀⠀⠸⣆
⠀⠀⣼⠁⠀⠀⠀⠛⢦⣄⡀⠈⠓⠦⣤⣉⣉⠛⠛⠓⠒⠒⠒⠒⠛⠛⠛⢉⣉⣤⠴⠞⠋⠀⠙⠛⠀⣠⡴⠛⠀⠀⠀⠀⠹⡄
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣌⣉⣉⣛⠛⠛⠓⠚⠛⠛⠛⠉⠉⣁⣀⣀⣠⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⣙⣤⠀⠀⠀⠀⠀⠀⠀⢮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⣦⣫⡶⠋⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠿⣷⣋⡦⠀⠀⠈⢻⢲⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⠆⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡾⠀⠑⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡔⠁⠀⢀⠄⣢⡆⠀⠀⠀⠀⠀⠀⠘⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⢧⠀⠀⠀⡇
⠀⠀⠀⢀⠊⢠⠃⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣾⡇⠀⠀⠀⢠⣿⡟⠀⢳⠀⠀⡇
⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠘⠛⢁⠀⠀⡇⠀⡇
⠀⠀⠶⢀⡵⠀⠀⠀⠀⢨⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣖⣮⣽⣦⣤⣴⣦⣤⣇⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢄⡀⠸⡄⡇
⠀⢘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⠷⠟⠀⢻⡇
⠀⢨⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⣅⣀⠤⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠀⠀⠀⠰⠀⣠⡇⣸⡃
⠀⣈⡀⠠⠀⠀⠀⣸⡿⢳⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠒⠈⠙⠲⠤⠤⠤⡤⠤⠤⠔⠒⠚⡉⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⡷⠀⢀⡴⠏⢀⣼⣿⢠⠟⡇
⠀⡍⡄⠰⣴⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠀⠉⠀⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡤⠖⠋⢀⣤⣿⣿⢿⣿⢘⡇
⠀⠳⡙⡄⠈⢿⣷⣤⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣒⠋⠀⢀⣠⣴⣿⣿⣟⣵⣿⡇⢨⡇
⠀⠀⢹⣿⣷⣦⡙⢿⣿⣷⣤⣘⢮⣭⡹⠳⠂⠀⢀⢾⣷⠀⠀⠀⠀⠀⠀⠸⠶⠾⠿⠋⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠚⠀⢀⣴⣦⣴⣿⣿⣿⡅⣴⣿⣿⣿⠇⠰⡇
⠀⠀⠈⡄⠙⠿⣿⣜⠿⠿⠀⠙⢻⢞⡂⢀⡀⠀⠻⠞⣡⣶⡦⠀⠀⠀⠀⠀⠄⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⣀⣀⣠⣤⢰⣿⣿⣿⣿⡿⠟⠃⣼⣿⣿⣿⠏⠀⢸⡇
⠀⠀⠀⠱⡀⠀⠈⠿⢿⣶⣦⡀⠈⠛⢿⡿⣷⠿⠷⣾⣿⣯⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣯⣤⣴⣾⣿⣿⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⠿⣿⣦⣤⣤⣤⣤⣀⣀⡀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠻⠛⢛⣿⣋⣽⣷⣶⣬⣟⣛⣉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠉⠉⠛⠟⠿⢿⣿⣿⣦⣄⡀⠉⠛⠛⢉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣴⠀⠀⠀⠀⠉⠈⠛⠿⣿⣷⣦⣤⣶⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⣤⣤⣀⠀⠀⠑⠛⠛⢿⣯⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡄⣇⢠⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⣠⡇⠀⣷⣿⣿⣿⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣽⡀⣿⣿⡾⠿⠿⢿⣿⡅⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡈⣿⠿⠿⠿⠋⠀⠀⠀⠀⠘⢷⣾⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠙⠛⢷⣄⠀⠀⠀⠛⠋⠁⠀⢀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴⠞⣋⣁⣤⣤⣤⣀⣀⣽⠇⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣈⠒⠚⠁⠀⣀⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢰⠀⣧⠀⣿⠁⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⡀⠸⣷⣿⣤⣿⣼⠀⢹⡀⠀⢀⣸
⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣀⣼⣷⠀⣸⠃⡀
⠀⠀⠀⢸⡀⣇⠀⣿⡿⠛⠉⠙⠻⣿⣿⣰⣾⣾⡷⢁
⠀⠀⠀⠈⣿⣿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣇⣼⡀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠈⠀⢀⣤⣴⡶⠶⠶⠶⢶⣤⣄⡀⠀⠈⠙⠁⠀⠀⢀⣼⠟⠋⠉⠙⢿⣿⡀
⠀⠀⠀⠀⠀⢰⣇⢿⣇⣠⣤⣤⣤⣤⣤⣉⡛⢷⣤⡀⠀⠀⠀⠸⣏⠀⠀⣠⠀⣸⣿⡇
⠀⠀⣀⠀⠤⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠈⠓⠚⣁⣴⣿⡿⠃
⠀⠋⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠄⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠖⠉⡉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⢡⠖⠛⢛⢲⣞⠒⢇⠁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠋⠉⠉⠓⢦⠤⠤⣤⠶⠤⣤⠤⠖⢉⣨⠽⠛⣿⣆⠀⠀⠇⢴⠊⢱⠛⠉⠁⠀⢓⠩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⢀⣀⣈⣷⢖⣚⡷⢀⡔⠒⠛⠉⠀⢀⣴⡿⠋⠀⠀⠀⠘⠑⠎⡳⠖⢟⡠⠳⡄
⠀⠀⠀⠀⣠⣶⠿⠷⠈⠙⢷⣦⣀⡏⠉⠉⠁⠀⠀⠛⠉⠳⣄⣀⣤⡶⠛⢁⠀⣀⠤⠤⢤⡀⠀⠀⠁⢴⠈⢱⡆⣿⠐
⠀⠀⠀⠀⠛⣿⣄⠀⠀⠁⠀⡀⠉⠛⠷⠶⠶⢤⠶⠶⠶⠛⠋⢉⣀⣤⠖⠃⠰⢑⡄⠆⣤⢹⣄⡤⠦⠉⠙⠈⠡⠃
⠀⠀⠀⠀⠐⠈⠛⢷⣤⡀⣎⠉⠉⠀⠀⠀⠠⠀⠠⣄⢀⣠⣴⠿⠋⠁⠈⠀⠀⣈⠃⣄⠿⣸⠃⣠⠰⢤⡘⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣤⣤⣤⠴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⢿⢦⡀⠗⣤⡺⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣴⣻⡌⡇⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠚⢉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢟⢦⡀⠀⠦⠀⠀⠑⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡙⢄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠢⠥⠀⠀⢀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠠⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⡄⢀⡀⠀⠀⠀⠑⠢⠀⣀⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢋⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡰⠆⠐⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⢉⠷⠦⡀⠀⠀⠀⠀⠁⢸⣿⡀⠉⠉⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⢄⠀⠠⡚⢾⢌⠑⠦⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⢇⠸⠁⣤⠀⣄⠀⠀⠀⠀⠆⠀⠿⢷⠀⠘⣿⡿⠻⠛⠃⠀⠀⠀⣠⣮⠎⡡⡀⠘⠂⠋⢵⢆⠂⢵⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠘⣱⠂⣡⡈⠳⠢⢀⠀⡠⠒⢢⠊⠉⢣⠀⣿⡠⢐⡒⢄⠀⢀⠔⠀⠰⣾⠀⠀⠀⠀⠀⠂⠉⠘⠙⠉⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠡⣴⡇⠀⠀⠙⠀⠀⢨⠀⠀⢀⠀⠙⠀⢁⣠⡾⠶⠊⢀⡠⠂⠔⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⡈⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⣠⣀⣤⣤⡤⠔⠒⠠⢀⡴⠂⠈⠉⠈⠳⠤⠌⠀⠀⠈⣿⠦⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠸⢿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⣦⣤⣀⡀⠀⢩⡐⠘⠁⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡤⠖⠠
⠀⠀⠠⠄⠀⠀⠀⢀⣞⣠⣄⠀⠙⢄⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢿⣿⣿⣿⣿⣶⣼⣇⡇⠡⡀⠙⣧⠀⠀⠀⠀⠀⠰⡁⠈⡎⡆⠀⠀⡀
⠀⠀⠠⢤⡄⠐⠂⠈⠃⠀⠨⠁⠀⡌⠁⠀⠚⠂⠤⠶⢆⣠⢀⣀⢉⢀⡠⠊⠙⠛⠿⣿⣿⣿⣿⣿⣄⠘⠄⠈⠻⠗⢄⡀⠀⠀⠈⣵⢠⠠⠀⠀⡄
⠠⠞⣀⠄⠀⠰⠦⣀⠀⠀⣘⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠈⠑⢠⠋⢹⠿⢿⣿⣷⣌⠽⠃⠀⠑⡿⠆⠀⠀⠣⠄⠣⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠁⢀⠈⠑⢢⡴⡄⢀⣀⣀⡤⣴⠀⠀⠀⠀⢠⣄⡀⠠⠎⠀⡸⡀⠶⣷⠀⠉⠈⠢⠠⠀⠸⠿⠷⠄⣶⠄⠀⢀⠄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⠀⣸⠀⠀⢸⠀⢠⣠⠤⢷⠀⠀⣠⠲⠤⡄⣠⠊⢀⠀⠀⢠⠇⡄⣶⣼⣄⣀⡀⠀⠀⠀⠀⠀⠀⠮⠤⣄⠀⠈⠧⠢⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⠀⣸⠀⠀⡤⠂⡛⠀⢀⠃⠈⠤⢁⡌⠔⠁⠀⣴⣿⠾⠠⠆⠤⣇⠀⠀⠀⠂⠀⢄⠀⠰⠀⢠⡄⠑⠊⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣴⢏⠠⠊⠀⠀⠝⠁⠀⠳⣀⡀⠀⠀⢀⣤⠊⣡⣴⣾⠋⠈⡐⢾⠀⠀⠀⠀⠄⠀⠹⡘⢂⣟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⠿⣦⣆⠘⢡⢂⡀⡄⡲⢶⣼⠂⠁⠀⠀⠀⠀⠀⠈⠁⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣣⢸⠷⣮⣝⢰⣘⣂⣂⡅⠷⢶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⠒⠒⠒⠒⠒⠒⠒⠶⢤⣦⣶⠶⠠⢒⡆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠘⠧⣄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣶⡆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠀⣠⠞⠀⠀⠈⠓⣦⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠏⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠓⣄⠀⠀⠀⣖⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠀⠀⠤⠞⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣀⣀⠀⠀⠀⠀⠀⠋⠁⣀⣀⣀⠀⠀⠀⡼⠀⠀⡼
⠀⠀⠀⠀⣤⣤⠤⠤⠶⠶⡶⠋⠁⠈⠙⣖⠒⠒⠒⢲⠎⠁⠀⠈⠳⡖⢲⠇⠀⣸⠷⠶⠤⢤⣤⣄
⠀⠀⠀⠀⡏⠉⠉⠉⠉⠙⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⡇⠀⡴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢸
⠀⠀⠀⠀⣧⠘⣇⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⣠⠇⡟
⠀⠀⠀⠀⢹⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⠋⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣸⠃
⠀⠀⠀⠀⠀⢳⡀⠀⡤⠶⣄⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡤⠶⣄⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠳⣄⠳⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠣⡤⠞⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠠⣄⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⡔⢲⡄⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠓⠚⠚⠻⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠄⠐⠀⠈⠻⣝⠒⠛⣚⡚⢧⡄⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡏⢀⡤⢤⣉⠈⢷⡀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣔⣦⡀⠀⠀⠀⠀⠀⠀⢸⠹⠏⢱⠁⣾⣷⠈⣧⠈⣱⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢣⠁⠙⣄⣄⠀⠀⠀⠀⢨⠟⠚⠿⢄⡻⠏⣀⠟⠀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠛⠧⠉⠀⢷⢄⠈⢦⣦⠀⢀⣀⣱⠦⠀⠀⠈⠉⠀⠤⡚⠓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣆⠀⠐⢦⡤⠌⠁⠑⠿⠝⠒⠒⠦⣀⠀⠀⠀⠈⢉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⢲⠛⡖⡦⢤⡨⡙⠦⠤⣉⣀⡀⠻⠀⣀⢳⡢⠄⠈⢳⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠤⢤⣘⣖⣢⠣⣼⡠⢷⡀⠀⠀⠉⠉⡍⣖⣈⠂⠀⠀⢀⡜⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣑⠦⠤⠲⣤⣜⡉⢉⡟⠀⠀⠀⠀⠀⠳⣄⠈⠉⠉⠉⢉⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣉⣉⣁⣐⡢⠖⢋⠀⣀⣒⠀⠀⠀⢀⠜⠉⠉⢹⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⠤⢤⠤⠤⠤⠔⠲⡃⢀⡠⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⣎⣠⠀⠀⠀⠀⠈⠁⠀⠀⣇⠀⠲⠤⠤⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣟⣒⠒⠢⣌⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣰⠟⠉⠈⡇⠀⡟⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣤⣀⣠⠏⠀⠀⢠⡞⣛⣚⠁⠞⠙⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠱⡀⠀⢾⣸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠞⢅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠄⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢌⡔⠊⣠⣶⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⢘⡕⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠘⠁⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠐⡄⠀⠀⠀⠰⠀⡠⠄⡠⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠃⣠⠈⢢⠀⠀⠀⢲⠀⠠⣅⠀⠀⣠⢃⠠⠄⠒⠒⠈⠁⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠐⠀⢈⢹⣧⠀⠀⠀⠂⡼⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠔⡒⢆⡉⢰⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠂⠈⡀⠀⢠⠒⠖⠠⠤⢤⠠⣄⢀⡈⣙⣋⡉⠉⠀⠀⠀⣀⠰⠇⡾⠟⠣⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠓⠶⠤⠴⠄⠤⠄⠥⠠⠃⠀⠀⣀⡤⢎⣀⣀⣀⣀⡀⣀⣀⣀⡀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠥⠠⢍⡹⠯⠸⣁⡆⢺⡟⠳⠿⣿⡉⠶⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣮⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡤⠶⠚⠛⠛⠉⠙⠚⠾⠭⠶⣶⣿⣽⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⣿⣇⣃⡀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⣤⣀⣀⣀⣀⡀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢩⠈⠀⠀⠋⣨⠁⢃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⡆⢰⠉⢤⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠘⡀⠘⡁⢡⠌⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠣⢄⡉⢳⠀⠑⠊⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡠⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⠐⠣⢀⡀⠀⠀⡐⠤⠀⠠⢄⡀⠔⢊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⡀⠈⢹⢂⣍⠈⠁⠀⠈⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠒⠼⠀⠛⢃⠀⢠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⡀⠀⠀⠀⠀⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠠⠐⣄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠴⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⢁⠀⠀⠀⠀⠀⠀⠒⢺⠞⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠉⠿⠀⠐⠒⠒⠒⠒⠂⠀⠘⠒⠒⠾⠿⠽⠧⠤⠤⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡠⠋⠀⠀⡄⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡑⠀⠀⠀⠠⠀⠀⠁⠊⠉⠛⠳⠶⢶⣦⠤⢤⡀⠀⢒⠍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠁⠀⠀⢀⠐⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠌⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠁⠀⠀⢀⠄⠄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢡⠀⠀⠀⠡⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡳⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠐⠗⠂⠀⠀⠀⠠⠸⢂⠅⠀⠀⢸⣀⠖⢄⠀⠐⣬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠑⢢⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘⠀⠀⡠⠖⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⠀⠘⢄⠀⠀⠈⠂⠘⡀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡀⠀⠀⠀⠀⡐⠀⠀⠁⠀⢀⠅⠀⠀⣀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠌⠀⠑⢄⠀⠁⠢⡀⠀⠀⠐⠄⠀⠀⠀⠐⠤⠄⢀⢠⠔⠀⠀⠀⠀⡐⠀⠀⠀⡠⠀⠁⢀⠄⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠡⡀⠀⢈⠖⠈⠢⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠂⢤⠊⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⢁⠔⠈⠀⠈⠢⡀⠁⠀⡤⠠⠠⠄⡄⠀⠁⡠⠊⠀⠑⢄⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢁⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⢽⠁⠈⠀⠀⠀⠀⠀⠑⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠃⠐⠐⠨⠊⠀⡶⠦⢀⡀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⣦⠐⠀⠒⠀⠂⠎⠀⢦⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⢻⡄⠁⠸⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠱⣖⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣴⠀⢶⡄⠀⢸⡆⠀⠠⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠒⠈⠙⠀⠉⠙⠠⡀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠉⠉⠛⠈⠀⠈⠠⠀⠀⠀⠈⢄⠀⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⠠⠀⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠡⡀⠀⠀⠀⠈⠁⠐⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⢸⡗⠀⠈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠺⢦⣀⠀⠀⡠⠊⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣠⡀⢀⣬⠏⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠉⠙⠓⠤⠤⠀⣠⣄⠁⠀⣄⣀⢀⣀⣠⣄⣀⡠⠤⠶⠛⠋⠉⠁⡀⠠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠉⠒⢦⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⢄⠐⠀⡀⠈⣆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠀⢀⡆⠀⠐⠒⠂⠰⠦⠂⠀⠀⢸⡶⣌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢺⣀⠐⣯⠂⠾⠋⠀⡀⠲⣀⣤⠀⠀⠀⠀⢀⣼⢡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠈⢄⠉⢰⡞⠀⡾⢛⠛⠁⢀⣤⣤⣾⡿⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠉⠀⠀⣷⣾⣶⣶⣿⣿⡿⠟⠁⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⡦⠒⡂⢶⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠊⠢⡀⠀⠀⠀⠀⠀⠡⠀⢓⢈⠈⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⣀⠔⠉⠁⠂⠀⠀⠑⣀⡀⠰⠋⠢⡘⠀⠣⠁⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠖⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠅⠀⠢⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠚⡁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡶⠧⠶⠓⠒⠒⠛⠒⠒⠷⠴⠂⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠃⠀⡇⠀⠀⠀⠜⡄⠀⠀⡲⣤⡀⠀⠺⡄⠀⠈⠀⠀⠀⠀⠁⠒⠻⢧⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠤⣤⠶⠞⠃
⠀⠀⠀⠀⡰⠁⠀⠀⢡⠀⠀⡄⠀⢱⠀⠀⠙⣈⠻⣶⣄⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⡒⢲⠶⠒⠒⡒⠂⠢
⠀⠀⠀⡰⠁⠀⠀⠀⢸⠀⡐⠀⢰⠸⡄⠀⢄⠈⠓⠀⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠈⠢⠌⠀⣰⡇⠀⠀⢁
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠴⠁⠀⠞⠀⠈⡲⢈⠏⢀⠀⠀⠀⠈⢃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⡀⠈⡁⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢶⡖⠒⣋⡵⢲⠀⠀⠙⢶⣄⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠐
⠀⢀⡜⣀⣀⣀⠤⣤⠒⠉⠀⠞⢁⡔⠁⠀⡎⠀⠸⡄⠀⠈⠻⢦⣀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⡄⠀⠀⠈⢠⡐⠂⠀⠀⠀⡀
⠀⠀⠀⠈⡁⠀⠀⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊⠈⠑⠒
⠀⠀⠀⠀⠑⠲⠄⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠉⠉⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣀⣤⣶⡶⣶⣶⣤⣔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⣀⣽⠻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠰⢰⡿⠁⠀⠀⢀⣤⠾⠁⠀⠀⠀⢹⣧⠀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠋⠀⢠⡿⠓⠘⠁⠑⠀⠀⠀⠀⠀⠂⠠⢀⢹⡆⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢸⡇⡰⠁⢠⣤⡄⠀⠀⠀⣤⣤⠀⠀⠘⡇⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢆⡁⠀⠀⠀⠁⡗⠀⠀⠘⠛⠀⠀⠀⠀⠛⠋⠀⠀⢸⡇⠁⠀⠀⠀⢻⠗⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠀⠀⠀⡀⠀⠀⠠⠴⡀⠀⠀⠀⠰⠖⠒⠢⠀⠀⠀⠀⠸⠄⠂⠀⠀⠀⠂⠀⢀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⢄⠈⠐⠄⠀⠀⠐⡀⠀⠀⠀⠳⠖⠃⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⠔⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠄⡠⠋⠀⠐⢌⠂⠄⣀⠀⠀⢀⠀⠐⠀⡠⠐⠁⠙⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠁⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⡀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢀⣀⠠⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠉⠠⡀⠀⠈⠆⠀⠄⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠐⢤⡀⠀⠁⠢⠀⠠⠀⠐⠀⢀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢬⠀⠀⠈⣷⠀⠀⠀⠀⢀⠂⠀⢀⣀⡥⠖⣀⠄⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⡐⠚⠛⠿⠿⠒⠌⠀⣤⠂⠠⣄⣹⣇⠀⠀⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠐⠀⠀⢀⠀⠀⠀⠈⠞⡁⢰⣤⣿⣿⣏⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡉⠆⠀⠀⠀⠀⠀⠈⡄⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⢑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠌⠀⢠⡴⣶⡶⢆⠀⡀⠀⠀⠀⠃⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡄⢁⠀⠐⠂⠠⠾⠚⠉⠀⠀⠞⠛⠛⠁⠀⢀⠀⠀⡠⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠋⠋⠉⠙⠓⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢏⣤⣀⣠⣀⣀⡀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠃⠈⠀⠀⢽⠎⠁⠐⠦⠙⣇⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⡠⣶⠾⡤⢪⣭⠒⡄⠸⢆⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⠓⡄⡀⠀⠀⠀⠀⢳⠭⢴⣇⢻⣿⠁⡸⠀⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡴⠷⡖⠃⢰⣌⠙⢆⣄⠀⠀⠘⣤⡀⠈⠑⠒⠊⢁⠴⠣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣤⡀⠈⢤⣅⡈⠋⠲⠿⡛⠦⠤⣀⠀⠀⠀⠐⠛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⢴⢳⠦⡤⣄⣙⠲⢄⣉⣀⡀⠲⠀⡀⢶⠤⠀⠑⡄⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠦⠤⢼⣞⣶⣣⣎⠼⡆⠀⠀⠉⠉⡭⢶⣙⠈⠀⢀⡰⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡸⢍⣒⡒⠳⠤⠯⠉⡹⠃⠀⠀⠀⠀⠱⣄⣀⠉⠉⢉⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠬⠭⠭⡝⠋⡆⠠⠭⠄⠀⠀⢠⡊⠀⠈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⢲⠗⠒⠒⠋⠙⠤⠤⠚⢱⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣚⡴⠂⠀⠀⠀⠀⠀⠀⠘⠦⢬⣍⣉⡚⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠒⢦⠈⡁⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⢀⠎⠉⠛⢩⠤⠤⠇⡠⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠸⠞⠑⠲⡀⠀⣻⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠿⡁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠶⣦⡀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⣋⣥⡶⠛⠛⢳⣬⣷⣀⣀⠀⠀⠀⠀⠀⢾⠀⠀⢹⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠂⠀⠀⠀⠠⠀⠀⠘⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠔⠛⢁⠚⠁⣤⡁⠠⠹⡏⢿⣦⡙⡄⠀⠀⢠⠞⠛⢦⣠⠽⢦⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟⣢⡠⢇⠿
⠀⠀⢀⡔⣡⣔⢀⠀⠀⢠⠄⢨⠅⢺⢟⡂⠘⡆⣾⢀⣝⡇⠀⠀⢸⠀⠀⠈⣧⠀⠀⣧⢠⠖⠛⣧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢴⠚⢇
⠀⠀⠸⣎⠀⠁⠀⣀⠀⠀⠤⠄⠀⣩⠀⢁⡴⢃⡷⠘⠋⠀⠀⠀⠀⢳⠀⠀⢸⡀⠀⢹⠃⠀⢀⡏⠀⠀⠀⠀⠀⠱⣌⠓⠀⠀⠠⣠⠤⠘⠁⠙⢻⠀⡘
⠀⠀⠀⠈⠙⠛⠲⠦⠭⣭⣭⣤⣶⣤⣤⠽⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠃⠀⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⢀⠟⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡟⠀⣰⡇⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⢀⡼⢫⠇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠣⠀⢄⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⣠⣤⢖⡏⠀⠜⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡂⢻
⠀⠀⠀⠀⠀⢀⠔⠉⠙⠇⢀⡠⠃⠱⠖⠒⠢⡄⠀⠀⠀⠀⠰⠒⠉⠀⢁⡞⠀⣼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠐⠈⠀⠀⠀⠀⢀⡀⣤⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠒⠚⢦⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠠⢄⣀⠀⣀⠀⠀⢀⣀⣀⣀⠠⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠰⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⠀⠀⠀⠀⢠⠤⣄⣠⢶⡄⣰⠶⢦⠀⣦⢤⡄⣴⢲⠄⣤⡴⣦
⠀⠀⠀⠀⠀⢿⡀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠁⠆⠀⠀⠀⠀⢸⣄⡽⢿⣋⣰⢿⣤⡾⠞⣧⡤⠟⢿⣉⡼⡏⠀⠉⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⢦⡄
⠀⠀⠀⠀⠀⠘⢧⡀⣤⠀⠀⠀⠀⠀⢀⠏⡜⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⢸⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⢸⠸⣛⡉⠁⣄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠹⢧⣀⣀⡠⠔⠓⠊⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⠇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠃⢲⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠤⠄⠲⠒⠉
⠀⠀⠤⣜⣦⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠊⠁
⠀⠀⠀⠀⠈⠳⣼⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠤⠚⠁⠀⢀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡔⣀⠠⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠂⠀⠠⠤⠤⠔⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠲⠒⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢇⢯⡑⢢⡀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠤⠤⡐⠒⣛⡶⡀⠲⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠐⢤⡀⢀⢛⠀⠀⠀⠀⠀⠀⡠⠒⠋⣱⠖⠿⣤⠽⢷⡆⠀⠀⢸⠀⠀⠀⠀⠀⢠⢊⠔⠀⣀⠀⢀⣴⠞⡡⢾⡟⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠻⡗⠋⠀⠀⠀⠀⠀⠈⠃⠀⢰⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⡄⠀⠀⠀⠀⠃⠘⣄⣀⣀⡴⠚⠁⠀⢀⡾⢠⡏
⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠀⠀⠀⢉⣠⡤⠀⣉⡲⣄⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢳⣄⢍⠉⠁⠐⢀⢀⠀⡾⠁⡸
⠀⠀⣠⠴⠖⠛⠉⠀⠀⣀⣤⡴⠞⠋⠐⠀⠀⠆⠀⠘⡟⠛⠶⠀⠀⢸⡀⠘⠇⠀⠀⠀⠀⠀⢸⠃⠀⡏⠀⠀⠀⠀⠀⠸⣃⣬⣷⠸⢤⣴⠶⠟⢁⡾⠁
⠀⠀⠈⠉⠓⢒⣲⠖⠋⠉⠁⣠⣤⠼⠐⠂⠰⠄⠴⣳⠃⠀⠀⠀⠀⠈⢣⡀⡄⠀⠀⠀⠀⠀⣸⢀⡜⠀⠀⠀⠀⠀⢠⡽⠁⠀⠹⣦⣤⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠒⠒⠒⠲⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢤⣀⢀⣀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⠘⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏⢸⡄⢻⠄⠀⠠⣎⠀⠀⠀⠀⠀⢀⣼⡵⣿⡶⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠛⠙⠈⠼⠓⠇⠀⠼⠧⠴⠖⠀⠀⠀⢿⠈⠁⢀⡇⠀⠠⠰⠆⠢⡀⠀⠰⢣⣟⣿⠞⠀⠀⠀⠀⠀⢸⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠈⠁⢀
⠀⠀⢠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠠⣤⣤⣦⠄⠀⠀⡀⠒⠀⠁⠀⠀⠀⢠⣤⣤⣴⡀
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠔⢰⡮⠃⠀⠀⠀⠶⠉⢀⠜⠁⠀⠀⠀⠉⠁⢀⠀⠀⣤⠞⣀⡈⠳⠀⠀⠈⢉⡻⠏⠁
⠀⠀⠀⡀⠃⠀⠀⠀⠘⠀⠤⠤⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠈⠡⢤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠉⠂⢀⠀⢠⡄⠘⠓⢠⠀⠀⠀⠉⠙⠀⠀⠀⠀⣀⡀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣙⡧
⠀⠀⠀⠀⣾⢴⡄⠀⠛⠀⢀⡀⠀⠘⠀⠈⠀⠀⠈⠀⠀⠀⢦⣤⣤⣤⡆⠀⠀⠐⠁⡠⡄⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠁
⠀⠀⣠⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠀⠀⠀⢠⠐⢄⣡⠀⠀⠀⢀⠀⢀⠀⠀⢀⣤⣤⣤⣀⡀
⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⣀⠀⢀⡀⡃⠀⠤⡥⢬⠖⠋⠀⠀⠅⡠⠀⣀⠀⠀⠀⠨⢉⠉⠁⠶⠋
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡇⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡙⠁⠀⠘⢀⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⢼⣵⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠁⠀⠀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢶⣴⣄⡇
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠀⠀⠀⢠⣴⢶⠶⣦⠀⠀⠀⢀⣀⠀⠀⠀⠠⠶⠀⠀⠴⠆⠀⠀⣠⠀⡛⡀⠀⠀⠀⢠⣤⣤⡄⠰
⠀⠳⢶⣶⣶⠶⠃⠀⠈⠛⠾⠿⠛⠀⠀⢄⡈⠀⣀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⢚⠟⢑⣇⣱⠀⠛⠣⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉
⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠶
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠓⠲⠂⠀⠀⠀⠙⢿⡉⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠾⠥⠀⠀⠀⠀⠰⣦⣄⣤⡾⠃
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠄
⠀⠀⢁⡐⠀⣨⠀⠀⢀⡠⠀⣤⠐⠀⠀⠀⢶⡌⠑⠄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⠶⠂⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠈⠐⢎⠹⠀⠀⠀⠁⠈⠀⠁⠀⢀⣹⢿⡟⣿⡄⠀⠀⠠⠸⠠⡔⠁⠀⠀⠶⠆⡀⢠⡀⠀⠀⡘⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠐⠂⠐⠁⠀⠀⠀⠀⠘⠃⠈⠁⠀⠀⠠⢀⣠⣀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢴⡄⠀⠀⣠⡀
⠀⠀⣩⣤⣦⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⡶⠟⠋⠁⠀⠀⠀⠀⠀⣦⡉⠀⠀⢀⠀⠀⡅⢠⠡⠀⠀⠀⠐⠀⠸⠃⠿
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠋⠀⠀⠠⡿⠟⠛⠛⠃⠀⠀⠀⠀⠎⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⢿⡿⠻⡿⢿⢿⠿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣾⣶⣾⣷⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣤⣼⣿⣿⣿⠶⠀⠀⠀⠐⠁⠐⡄⠀⠀⠀⡠⠤⠶⢶⣦⣀⡀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠠⠞⠀⠠⠞⠁⠀⠴⠋⠀⠄
⠀⠀⠀⠉⠉⠋⡁⠰⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠄⠀⢾⣼⣿⡇⠀⠀⠀⠀⣿⠀⠀⢰⣦⣤⣴⣦⣀⣰⣤⣀⣠⣤⣄⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠃⠀⠀⠰⠀⡿⠀⠀⠘⠛⠈⠡⠜⠆⠛⠰⠼⠧⠴⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠀⠀⢀⡀⠀⣠⡆⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠀⠈⠁⠀⠀⢀⣴⡿⠛⠛⠻⠛⠢⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣽⣶⣿⣿⠻⠿⠇⠀⠉⠉⠀⠁
⠀⠀⢀⠐⠄⠀⠀⠀⠀⠂⢈⠄⠀⠀⠀⢀⣽⠏⠁⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⡄⠀⡀⠀⠘
⠀⠀⣄⠀⠁⠒⠠⠁⠀⠖⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⠀⠀⠀⠀⠇⠀⠀⢰⠘⡆
⠀⠀⠓⠺⢿⣈⡢⠞⠁⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⠀⠀⠔⠀⠀⠀⠀⠂⠀⠀⣠⠁⢀⠘⠞⢣⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡷⠈⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⡅⠀⢠⡇⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣻⣿⣿⣟⣩⠁⠀⠀⠈⢂⠀⠀⠸⣿⣏⠰⡇⠀⠀⠀⠀⠀⢁⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⡀⠀⠓⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠿⠉⠉⠉⢙⠉⠹⠀⠀⠠⠀⠀⢻⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⡁⣹
⠀⠀⠀⠀⠈⢡⡆⢈⠜⢧⠠⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣄⣠⣄⠀⢀⠀⠀⣦⠀⠀⢆⠃⣿
⠀⠀⠀⠀⠀⠉⡤⠋⠀⠈⡆⠒⡀⠀⠀⠀⠀⢀⣠⠄⡐⢻⠷⠢⠀⠀⠀⠀⠀⠀⣸⠀⠀⡟⠛⠋⠉⠻⠀⠈⠙⠂⠀⠀⠀⢸⡃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⣮⣿⣷⣽⣭⣦⣴⣿⡤⠀⠆⠀⣠⠋⠀⠀⠷⠂⠀⠀⠀⠀⢀⡀⠀⠀⣀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣐⠶⢿⣯⣝⡳⣆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⠃⠀⠚⠀⠀⠘⠆⠀⠀⠀⠄⠀⣹⠀⢀⡳⢶⣶⡼⢷
⠀⠀⠀⠀⣀⠀⠀⠛⢷⣦⠋⠟⠁⠛⠁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⣴⠏⠀⠀⠉⠀⠋⠑⠚
⠀⠀⡆⠀⢹⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⢀⣤⢴⡶⠀⠀⠀⠀⠜⠀⣼⠇⠀⠀⠀⢀⡀
⠀⠀⡇⠀⠈⡱⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠜⠋⠀⠀⠀⠀⠀⠤⣴⠏⠀⠀⠀⠠⢸⢃⠐
⠀⢀⡇⠀⠀⡷⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⢀⡴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⡀⠀⠀⠀⡘⠘⠀⣇⡁⡐
⠀⠸⡇⠀⢀⡘⠂⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠁⠁⠈⢹⡷⠁
⠀⠀⡇⠀⢠⠟⠀⠀⠀⠀⣄⡀⣔⡾⢤⠗⣤⢠⣆⠤⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣶⡄⠄⠆⢂⢐⡐⡀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣾⡾⠂⠀⠀⢃⣀⠐⣛⣂⢛⡚⣘⣋⢳⠞⠋⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⡟⠒⠐⠂⠂⠃⠐⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⡉⠉⢉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠈⠤⠠⠤⠁⠀⠘⣿⢷⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠇⠤⠐⢠⠀⠶⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣍⢀⣈⣿⠓⠀⢀⠀⣈⠀⠀⠐⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣀⠻⢃⠘⢀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡀⢘⣿⠛⠂⠀⠀⠀⠀⠀⢱⡄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠈⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠄⠘⠳⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡈⢀⠁⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⠄⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠈⣦⠀⠠⠀⠀⢀⡀⢰⠀⣏⠀⠀⢠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠒⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢠⠌⠋⠐⠀⠤⠈⠷⠈⠁⣩⣅⠀⠋⢉⡴⠖⠀⠂⠀⠀⠈⠀⠉⠈⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠒⠆⠐⣿⣷⣽⣇⣴⣶⠆⠠⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠲⣿⣿⣿⣿⣿⣳⣦⠀⡤⢤⡀⠀⠀⠀⠀⣈⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⠀⠀⠀⠀⠀⠀⠀⢴⠔⠒⠚⠀⢠⣾⠿⣿⣿⣿⣿⠀⠐⢦⣄⠀⠀⠀⠀⢸⣏⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⢀⠀⠀⠀⠄⠀⣘⠛⡉⣠⠀⠀⠛⠛⠈⠩⢤⠳⡄⠀⠀⠀⠀⠰⠂⡘⡦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠛⠉⡁⠔⠁⠀⢀⣠⡄⠆⠘⠁⡰⠁⢼⠀⠈⡇⠈⠃⠀⠀⠀⡀⠀⠀⠀⠓⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠈⠀⠀⠀⠀⠸⢴⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣀⠀⠀⠀⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠄⠀⠀⠀⢀⠀⠀⠑⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠈⠙⠯⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠁⠀⠀⠂⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠢⣀⣀⣠⠤⠴⢚⣥⣤⣤⠀⠐⠀⠀⠨⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠀⠀⠀⠙⠿⠾⠿⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣤⣠⣠⣤⣀⣤⣄⣄⣤⣠⣠⣡⣤⣠⣤⣤⣠⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠋⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣿⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠂⠈⠁⠙⠟⠿⠿⠀⠀⠘
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⣤⣀⣀⡀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⣻⣳⠀⠀⠀⠀⠀⠀⠀⠚⠉⡹⢻⣿⣧⣿⣿⣷⣦⠼⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢀⣨⣠⣾⣿⣿⣿⣫⠔⠛⠿⠆⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣴⣶⣶⣷⣄⢾⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⠀⠀⠁⠀⠈⠛⠻⣿⡿⠋⠀⠀⠀⠀⣤⣄⣄⣀⠀⢁
⠀⠀⢸⡳⣿⣟⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠙⠻⠾⣽⣛⣻⠿⣿⠷⢿⣿⣿⣿⣿⣿⣧⣶⡦⡀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣤⣴⣾⣟⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠷⠿⠿⠥⠤⢼⣭⣯⣷⣭⣶⠤⠀⠴⠷⠾⠿⠟⠛⠛⠉⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣻⣟⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣊⡀⠘⠄⠱⠀⠀⡀⠀⠀⠀⣠⠊⠁⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠴⠴⣌⠀⠑⢄⡌⠉⠉⢲⢃⡆⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⢀⠤⠤⣽⡇⠀⠀⢡⠀⠀⠾⡆⡁⠤⠊⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠠⢀⣂⠑⢤⠀⠀⠐⠌⣩⠈⠁⠀⠀⠀⠑⠀⠘⠓⢒⡒⠈⠉⠉⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠈⢢⡰⠁⠀⢀⠔⠁⠀⠀⣀⠤⣀⡖⡰⠂⡤⣈⡁⠂⠀⠀⡤⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⣗⡤⠐⠁⠀⢀⡤⠊⢀⠀⠀⠈⠑⠚⠤⢆⡨⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠹⣇⠀⠀⢠⠿⢦⣀⠄⠺⣀⢀⡐⠀⠘⠀⠟⠀⠤⠠⡀⢄⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠋⠁⠀⠀⠀⢃⠢⡀⢗⠈⠦⠔⢨⣠⣋⠀⠈⠠⠒⠉⠑⠄⠣⠀⠀⠉⠁⠀⠈⠁
⠉⠤⢀⠄⢒⡤⠛⢉⡹⠔⠚⢆⠀⠀⠀⠀⠀⠀⠀⢂⠙⠦⡑⠛⠫⠧⠇⠚⡤
⠀⠀⠒⠐⠙⡀⡴⠋⠀⠀⠀⠀⠑⢄⠀⠀⢠⢄⠀⠈⠑⠒⣬⠒⠀⠀⣠⢎⠑⠒⡰⣆⠀⠀⠀⢰⡡⣬⡂⣤
⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠈⠢⣀⣮⠁⠀⠀⠀⠀⠸⢅⠼⠳⡀⠀⠀⠀⠘⠐⢮⠥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠘⠓⠂⠄⣀⡀⠠⠌⣈⣄⠀⠀⠀⡠⠁⠰⠀⣕⡹⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⡀⠈⢦⣀⠤⠤⠤⣤⠀⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⢀⡀⠔⢹⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⣀⡴⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠤⠤⠦⠀⠤⢤⠦⠴⠦⠤⠤⡤⣤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢢⢠⢤⠀⠀⠾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⡠⠃⠤⢀⣦
⠀⠀⠀⠀⠀⡸⠁⠋⠰⢆⠀⣉⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢈⣶⡆⢰⠾⡏
⠀⠀⠀⠀⠀⢁⣯⠁⠀⡀⠀⠁⠀⠒⡨⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠛⢀⣠⣈⠈⠉⠀⡅⢈⠘⠁⠁
⠀⠀⠀⠀⠙⠴⠄⠀⠂⠀⠡⠘⠒⠞⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠡⠄⠘⠚⣀⡄⣡⠋
⠀⠀⠀⠀⢠⣐⢄⠨⠄⡤⠂⠢⢉⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡕⠀⠂⢀⣤⣤⣤⣈⣁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⢀⠈⠀⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣹⠀⡤⠰⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣻⡤⡀⠱⡅⢄⣨⠼
⠀⠀⡀⡀⠀⠴⠀⠁⡀⠊⢀⡀⢀⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠠⡈⠙⠖⡂⠮⢑⠀⢠
⠀⠘⠀⠑⠈⠀⠀⠅⠙⠂⠠⠝⠁⠀⠉⠠⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠁⠐⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠃⢀⣀⡀⡀⠀⠀⠀⠀⠈⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⣀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠁⠲⣄⠀⠀⠈⣄⠀⠀⠈⠁⠸⠄⠀⠀⠀⠀⠀⡈⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⣤⠀⠀⣠⣤⣤⣤⡉⠢⢀⠘⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⣼⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠍⢠⡄⠀⢈⣤⠀⠀⠉⠂⠀⢷⡄⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠁⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠉⠂⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⠐⠢⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠁⠈⠄⠁⠤⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢄⠀⠀⠀⢀⣠⣤⣴⣆⣀⡀⠀⠀⠀⠀⢸⣤⠀⣈⠆⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠂⠠⠄⠀⡀⠂⠀⠈⠙⠻⠯⣭⠍⠿⠛⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠴⠋⠀⢰⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠦⠤⠶⠒⠁⠀⠀⡰⠋⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢲⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠓⠦⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠒⠁⢠⠋⠀⠈⠸⣖⣤⣤⣤⠠⠄⡐⡅⠀⢀⣠⠂⣠⡊⠀⠀⠈⡉⣲⠶⢄⠀⢰⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠞⡵⠃⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⢉⠀⠐⡎⠃⢰⡟⠀⣦⠀⡾⢰⠃⠀⠀⠑⢬⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠔⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠀⣤⣼⠁⠀⠁⢸⠃⢀⡔⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠁⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⡏⡜⠀⡠⡿⢸⣿⡧⠊⠀⣀⣈⢢⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⢹⢹⡇⣼⢡⠇⡾⡏⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⠚⠀⠀⢸⣿⠃⠸⠈⢱⡇⠀⠁⡀⠀⡂⠀⠰⡀⠀⠀⡰⠀⠦
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⢰⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡏⠀⠆⠀⠀⢧⡀⠋⣀⣾⡗⠄⠀⢈⠉⠉⠀⢀⢰⠂
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⡀⣿⢣⠐⣄⠀⠻⣆⠀⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⡀⠀⠀⠀⠀⠀⠇⠹⡈⡄⠈⢗⠀⠙⠂⠀⠀⡐
⠀⠠⠇⠀⠀⠀⠀⠀⠀⢀⢮⠀⢈⡇⠘⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡇⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⡞⠀⠀⠀⠛⠒⠠⠀⠀⠀⠐⠈
⠀⡧⠘⠀⠀⠀⠀⢀⡔⠁⠰⠰⠊⡅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⣽
⠀⠸⡀⠃⠀⠀⡠⠋⠀⠠⠃⡦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠃
⠀⠀⠑⣦⠤⠐⠁⢀⡴⠕⠊⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠒⠶⠒⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃

⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣳
⢰⣩⡤⣌⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧
⠀⠀⠀⠈⢳⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠘⣆
⠀⠀⠀⠀⠀⢳⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠤⣤⣀⣤⠤⢧
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡴⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢸⠦⣄⣠⣤⠴⠫⢀⠔⠂⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣉⣳⠀⢠⠓⠐⣶⠁⡂⠐⡄⠀⢸
⠀⠀⠀⠀⠘⡄⠀⠀⡁⠰⠀⠈⡆⠃⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠎⠀⠀⠀⠰⡀⠀⣸⠤⠀⠔⢁⡄⢸
⠀⠀⠀⠀⠀⠱⡀⠠⣔⢂⠀⠊⠘⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢸⠀⠀⠀⠀⠀⢸⠛⠒⠒⠂⠉⣀⡆⢸
⠀⠀⠀⠀⠀⠀⠹⡀⢡⣀⠉⠉⠉⠁⣁⣀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠘⢆⠀⠀⠀⠀⠀⢻⠃⠀⠈⠀⠐⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡜⠳⠤⣄⣀⣀⣸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢸⠈⢯⠀⠀⠀⠇⠀⢩⠀⢠⠊⡉⠉⢣⡤⠒⠠⢄⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⢸⠀⠰⡀⠀⠀⣈⠀⠀⠁⢈⠀⣰⠁⠢⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠣⡀⠀⠀⡠⠂⠁⠀⠈⠉⡏⠉⠒⠄⠔⣊⢰⠃⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣤⣀⣈⣀⣤⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠟⠙⠋⠛⡿⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣾⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠚⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣈⠽⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⠀⠒⠂⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠼⠄⣀⡀⠀⠀⣤⣀⣀⣀⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠄⠀⡄⠀⡠⠈⠑⢢⡘⠿⠿⡿⠟⠛⠿⠖
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠠⠀⠒⢘⠄⠀⠀⠤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠁⣀⡰⠉⠢⡀⠀⠀⠀⠀⠀⠀⢎⢹⠄⣀⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⡜⠁⠈⠀⠄⠀⠀⠀⠠⠤⠒⠉⠀⠀⠀⠂⠀⣎⠙⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠀⠈⠀⡔⠐⢦⢈⣧⢾⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠜⠀⢀⡤⠋⠁⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠉⠻⣅⠉⠂⠤⠒⠁⠀⠀⠉⣉⠥⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠒⠒⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀⠀⢀⣠⣤⡀⠀⠀⠀⠴⢤⠀⠀⠀⠀⣤⠀⠀⠀⢠⡀⠀⠀⣀⠀⠀⠀⠀⢀⣄⣀⡄⢀⡀⠀⢀⣀⣠⠠⣤⠠
⠀⠀⢀⡠⠒⡩⠄⠴⠂⠩⣟⢿⣅⠈⡇⠀⠀⠀⠁⠀⠑⢀⡤⡔⠉⠓⠀⢤⡀⠀⠀⠀⠟⢁⠄⠈⠀⠘⠀⢸⠁⠹⠋⠛⠈⠃⠉⠀⠁
⠀⢀⡎⣠⠊⠀⠀⠀⠎⠀⠈⢡⡈⣷⡀⠀⢰⡂⠀⠀⠘⠀⠀⣈⡦⠀⠀⡈⣷⡀⠀⣤⡀
⠀⢘⠉⠋⠀⠀⠀⠠⠀⠀⠀⠈⢳⠈⡄⠀⠲⠄⣠⠇⠀⠒⠛⠉⠰⢋⣽⠏⠀⠁⠀⢷⡈⠃⢀⣠⠀⠀⠀⠀⠀⢀
⠀⠈⣄⢠⡀⠀⠀⠔⠀⠀⠀⣠⠋⣸⠃⠀⠉⠉⠀⣠⠶⣦⠀⠀⢙⣦⣀⡀⠀⠀⠀⡈⠃⠀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⣰⠟⣿⡗⠤⠀⢀⡄⠄⠛⢁⡴⠋⠀⢀⢀⠀⠀⢅⡤⠋⠀⢠⣏⠼⠻⠷⣞⠞⠈⡋⠀⠰⠃
⠀⠹⠆⠜⠙⠠⠀⠤⠀⠄⠀⠁⠀⠀⢀⠀⢲⠀⠀⠀⠀⠋⠀⠀⠀⠀⢈⣨⣿⡆⠀⠸⡳⡀⠀⠰⡆⢀⠀⠀⠀⠁⠂⠤⠄⠀⢠⠠⣴⡀
⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⣶⢠⠤⡄⠀⢻⠆⠀⠀⠰⣄⠀⠀⠀⠀⠷⢚⠋⠀⠀⠀⠑⠜⡆⠀⠹⣆⢥⡀⠀⠔⠒⠒⠢⣀⠘⠀⠘⠃
⠀⠀⠀⠀⡔⠈⠀⠄⡟⠦⠀⠀⠄⠈⠂⠀⠀⣤⠀⠃⠀⠙⠳⠄⠀⢀⠒⢉⡿⠃⠀⢠⣄⡄⠁⠀⠀⠙⢧⡙⢶⠀⠀⠀⠠⣼⠖⠶⡂
⠀⢀⣤⣦⣤⡆⠀⠀⠿⠂⢀⠀⠀⠀⠀⠢⡀⣿⠀⠀⠀⣀⣀⣀⠀⠀⢀⣤⠤⡠⠀⠈⠻⠷⠶⠀⢀⡤⡀⠻⡏⠉⠀⠀⠀⣟⡌⢳⡸⡆
⠀⢸⣧⡇⢸⠇⠀⠀⠀⠁⡀⠣⠀⠀⠀⠀⠈⢿⠠⠀⠀⢧⣏⢉⡱⡄⠲⢵⡚⠁⠀⠀⣀⣀⡀⠸⡙⣧⠅⢀⡀⠈⠀⠀⠀⡄⣆⢘⡀⡇
⠀⢸⢣⣿⢼⡇⠀⠀⠀⠀⠈⠢⢡⡀⠀⡈⠠⢀⡔⠀⠀⠀⠈⠙⠘⠁⠘⠮⠭⢧⡀⢠⣁⡠⠇⠀⢈⡡⣎⡜⠀⣤⠀⠀⠀⠀⠙⣸⠇⡇
⠀⠸⣾⣿⡌⢧⠀⢘⡟⠒⠶⢤⣀⠉⠀⠈⠓⠸⡇⠀⠀⠀⠠⢶⠀⠀⠀⠀⠹⠝⠳⡀⠀⠀⠀⢰⡸⠀⠩⠧⣴⢶⣶⠆⠀⠀⠘⣷⢸⠅
⠀⠀⠙⢈⣶⡘⣆⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣛⠀⢠⠼⠧⠤⣬⠁⢀⡀⠀⠸⠵⠋⠀⠀⠉⠋⠁⠀⢀⣀⡜⢁⡆
⠀⠀⠀⠈⢧⣬⢩⣧⡀⠀⠈⠠⣄⠀⠀⠀⣠⠀⠀⠀⠀⢿⡧⠄⠀⠀⠀⠴⠶⠆⠰⠶⣾⠇⠐⠣⡄⠀⠀⠀⠀⠀⢀⠐⠛⠻⢁⠞
⠀⠀⠀⠀⠈⠙⢦⣽⣹⣦⡀⠀⠀⠉⠚⠛⠃⠀⠈⠀⣀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠈⠓⠀⠀⠀⢀⡬⠟⣃⡥⠾⠋⢠⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣶⣤⣤⣤⡴⠋⠀⠀⢿⣶⠀⠙⠦⣄⣠⣶⣿⡶⠚⠁⠀⠀⠠⠶⠞⠛⠒⠚⠛⠛⠉⠁⠀⠀⠰⠳⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⡔⠁⡀⠀⠀⠄⠀⠁⢀⠌⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠁⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢈⡠⠔⠊⠁⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢀⡤⠤⠤⣶⡌⢥⠈⡢⣠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠈⢣⡀⠶⣅⠙⠦⠌⣠⢆⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⣤⠐⠟⠁⢉⠉⠁⠂⠀⠊⣉⠢⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠈⡄⢠⡀⠀⠘⠀⠀⠀⠄⠀⡓⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠁⠀⠰⠋⠙⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡩⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢈⢀⠀⠊⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠠⠄⠲⠎⠀⠀⠀⠀⠀⠀⠘⠆⠀⠓⠄⡠⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠒
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠠⠤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠐⠠⠀⠀⢀⠀⠀⠓⡀⠀⠀⠀⠦⠐⠊⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠂⣉⣆⠀⢀⠄⠰⢤⡀⠀⠀⠸⡀⠀⠀⠀⠐⢰⢔⠋⢤⡄⢀⡹⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡢⠐⡉⠠⢨⡗⠁⢀⠴⠈⠀⠀⠀⠀⠳⡀⠀⠀⡀⠀⢀⡤⠐⠁⢠⡇⠈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢰⠋⠐⠁⠀⢠⠔⠁⢰⠁⠠⠂⠀⠀⠀⠀⠀⢱⡀⠀⠑⠒⡁⠈⠑⣀⠈⠦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠈⠀⠀⠄⠠⠈⠀⢀⠊⢀⡔⠀⠀⠇⠀⠀⠀⠀⠀⢀⠊⠉⠈⠁⠘⠂⠙⠁⠁⠀⠀⢹⠹⠒⠠⢤⣀⡀⠀⠀⠀⠣⠀⠀⠀⡀⠀⡈
⠀⠀⠀⠀⠀⠀⣀⠐⠀⢁⠀⠠⠾⠛⠰⠛⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⠂⠀⠂⠒⠒⠀⠀⠀⠀⠀⠈⣆⢀⠀⠀⠘⠉⠙⠦⣄⠁⠐⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠑⢄⡀⡀⠀⠀⢠⠔⠊⠀⠀⠀⠀⠀⡴⠁⠀⠑⣀⠀⠒⠒⠀⠀⠀⠀⠀⠀⢈⠇⠑⢄⠀⢀⠀⠀⠙⠦⣀
⠀⡀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⠰⠛⠒⣀⠴⠃⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⢱⠤⣉⣉⣁⣀⣤⠴⣶⡒⠃⠀⠀⠀⠀⠀⠁⠲⣞⠀⠈⠲⢤⣄⡀
⠀⠁⠀⠔⠀⠀⠀⠀⡈⠀⠀⠀⠀⢠⠄⠀⠀⠆⠀⠀⠀⣠⠎⠉⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠙⠢⣴⠂⠀⠀⠀⠀⠀⠀⠙⠲⠶⠒⠚⣛⣳⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠔⡁⢦⡀⢴⠀⠀⠀⠀⢦⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⡄
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠖⠁⠀⢿⣳⣤⢴⠀⠀⠀⠀⠸⡆⠀⠜⢀⠎⠀⠀⠀⠀⠀⠀⠰⠉⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠈⢢⠀⢸⠟⠁⢸⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⣿⡇⠈⠙⠦⣄⡀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠸⡰⠋⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠟⡇⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠴⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢠⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⠗⠰⠦⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠠⡄⠀⠀⣙⣆⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣦⡀⡉⠛⠉⠀⠀⠀⠀⠀⠀⡉⢹⣆⠀⠰⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⣽⣿⠊⣢⡄⢀⠄⠠⡀⠀⠀⡘⢺⡿⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠟⠀⠀⠻⢿⢻⣿⣇⠜⣀⠀⠑⠠⢤⣴⣿⣿⠖⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣴⣿⣰⠆⠀⣸⣿⣿⣿⣶⣦⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠻⣿⣿⡿⡻⣿⣶⣷⣶⣿⡏⡉⠛⢻⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠐⢻⠁⠀⠀⠀⠻⣿⣿⣇⣴⣿⣿⣿⣿⠿⠋⣥⡤⠆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢙⣛⠿⣷⣾⣿⢿⠧⠀⠀⠀⠀⠠⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣠⣴⠶⡶⠋⠉⠻⣮⣿⣡⣌⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠉⢸⠟⠀⠀⠈⣳⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⣴⣦⠰⣤⠔⠚⠋⠁⠀⠙⠂⠀⠀⠐⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⣾⣿⣿⣷⡄⢀⣠⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⢠⣿⣿⣿⣿⣴⣿⣷⣻⢠⣤⣤⣄⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⠻⡟⠉⠯⠉⣿⡿⠀⠀⠀⢻⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠃⠀⠄⠀⠃⠰⠟⠁⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⣤⣶⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣻⣾⠿⠏⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠋⠁⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡛⠿⣦⣌⣉⣉⣉⡉⣻⠉⠉⠉⠉⠉⠁⠀⠀⠀⣉⣈⣀⣀⣠⡤⠤⠖⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⡍⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣀⡀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣿⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣶⠿⠶⢷⢶⣶⠶⠾⣿⠿⠋⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣅⣀⠀⠈⠉⠀⠀⠁⠠⠴⠀⠈⠀⠰⠒⠀⠀⠳⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⢻⡛⠭⠽⠋⠿⠿⣷⣦⣀⢀⡀⠀⣀⠀⢀⣀⣠⣤⡶⠖⠛⠛⠛⠉⠉⠁⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⣦⠄⣀⡀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣾⡿⠛⠛⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⡟⠅⠁⠀⠀⠀⠀⠀⠀⣠⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣭⣟⠉⠉⠙⠙⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⣁⣤⣄⣤⣤⠶⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⡳⠦⢙⠻⢿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣦⣶⣶⣶⣾⣷⣾⣿⣿⠿⠛⠋⠡⠀⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣈⡙⠛⠲⠶⠍⢉⡛⠛⠛⠛⠉⠉⠋⠙⠛⠛⠛⠛⠛⠋⠀⠐⠊⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠁⠀⠀⠀⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⣀⣀⣐⣒⣒⣂⣀⣀⣠⣠⣤⣤⣤⣀⡄⡀⢠⣤⠤⠤⠤⠤⠐⠒⠉
⠀⠀⠀⠀⠠⠔⢶⠀⠀⠀⠈⠙⢲⣤⢀⣀⣀⣤⣤⠶⠛⠉⠉⠁⠀⣀⣴⡀⠀⠀⠀⠀⠐⠉⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⢍⡉⠁⠀⠉⠉⠀⠀⢀⣀⣤⣤⣖⣋⣁⡀⡁⠂⢐⠀⣋⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡎⢭⠀⠀⠒⠬⠍⠉⠓⠒⠒⠊⢉⡀⠤⠛⠉⠉⠩⠉⠉⠻⠄⠀⡠⠂⠀⠹⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⣠⣴⠶⡋⠉⠉⠉⢀⠀⢀⠀⠀⠀⢀⣀⣀⠰⠀⢠⠀⠀⢀⡀⠄⠁⢀⣀⣀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠴⢋⠉⠙⠂⠈⠛⠛⠒⠀⠀⠘⠁⠤⠄⠈⠀⠀⠂⠀⠐⠶⠚⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠛⠇⠀⠀⢠⠶⠶⣿⡆⠀⠀⠀⢀⠴⠖⠶⠄⠀⢀⠞⠳⠄⠀⠟⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠀⠀⠐⠤⠐⠁⠀⠀⠈⠃⠐⠂⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⢀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡤⢄⡀⠀⠀⣀⠀⠀⡀⠀⡀⡀
⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢏⠉⠉⡏⠈⠉⢻⢩⢿⡭⢿⡟⢻⡏⢻⡉⠉⢹⠏⠉⠉⢉⣉⠉⢉⠉⠉⣉⣭⡍⠉⢭⡟⢻⣹⠏⣿⠉⠉⠉⠉⠉
⠀⠀⢸⠀⠀⠀⢠⣄⣄⣠⣄⣀⠀⢀⣀⣤⠈⠀⠀⡇⠀⣠⠞⡟⢸⡇⢸⠇⢸⠃⠀⢳⣠⣏⣤⠤⡤⠸⡏⣳⣏⣳⠀⣧⢻⠀⠀⠀⣧⡘⠛⠚⢉⡉⣅⠰⡆
⠀⠀⢸⠀⠀⠀⠀⠛⢻⣿⣯⣤⡀⣼⠛⠋⠀⠀⠀⣿⠋⠀⢰⠋⠙⡇⢸⠀⢸⠀⠀⣰⠏⠀⢀⢀⠀⠀⢛⠃⢨⡥⣄⢾⣻⣶⣳⡼⣧⣿⣶⣶⣼⣷⡟⠒⠃
⠀⠀⢸⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣟⡀⠀⠀⠀⠀⠿⠀⢀⣿⣶⣦⣷⣼⡆⠈⠀⢰⠇⠀⠳⣿⣿⣿⣧⣼⡇⠈⣧⡼⠹⢟⡦⠉⢸⣿⣿⣿⣿⠿⣿⣿⠇
⠀⠀⢸⠀⠀⠀⠀⣾⣿⣿⡿⡟⠿⢿⢗⡀⠀⠀⠀⠀⠀⣿⣿⠍⠁⠈⢻⣖⠀⠀⠻⠀⠀⠘⣿⣿⡿⣿⣿⣷⠀⣨⣶⣶⣿⣀⣴⣿⡿⣿⡇⠛⠃⠺⠋
⠀⠀⢸⠀⠀⠀⠀⣿⡟⠻⣿⣃⣀⡾⠈⠁⠀⠀⠀⠀⠀⢿⣿⢿⡆⠛⢺⠟⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⣿⣿⡇⠉⠟⠋⣿⠿⡿⣿⣷⡤⣿⡀⠨
⠀⠀⢸⠀⠀⠀⠀⠘⣷⣶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠛⠀⠈⢀⣀⢐⡆⠀⠀⠀⣿⣿⣾⣿⣿⡟⢴⣆⣧⠿⠿⠀⣇⠱⣽⣷⠙⠛⢧⣀⣀⠀⢰⢀
⠀⠀⢸⠀⢀⣠⡤⣼⣿⣏⣄⣠⣤⡿⣶⣶⣀⡀⠀⠀⠀⠀⣸⡿⣛⣭⡾⢻⠁⠘⠇⠀⠀⢠⣿⣿⣿⣿⡏⢠⣤⡋⠁⠀⠀⢦⡘⣷⢹⡽⢦⡀⡼⢿⡍⣷⢸⢠
⠀⠀⢸⠀⡎⠀⠀⣿⣿⢹⠚⠛⠻⠁⠟⢟⠀⢡⣀⠀⢴⣾⣿⣶⣭⡵⣄⠘⠓⣤⠀⣠⣶⣿⣿⣿⣿⣿⡇⠈⢿⣟⠓⣤⠀⠸⣦⠾⠿⣤⣿⡀⣳⣾⠗⠳⣾⣘
⠀⠀⢸⠐⡇⠐⠀⢹⣿⣠⢀⣼⢲⠂⣿⣿⣧⣾⠁⢀⠈⢿⡟⠿⣉⣵⣶⣄⠳⣿⡆⡿⡟⣿⡉⠉⠉⠔⠈⡈⠂⡈⣷⣿⡄⢰⡟⡇⠀⠻⢿⣯⠁⠀⠀⠀⢻⢸⠓
⠀⠀⢸⢠⣿⠠⣿⣾⡛⠋⢈⡁⣀⣤⡷⣴⣿⣿⡆⣾⡀⢠⡖⠞⢿⡄⢿⠟⢿⣼⣿⣿⣷⢿⣿⣿⣀⣼⠟⢷⣼⣿⣿⣿⡆⢸⡇⠘⣆⣠⣌⣀⡀⠀⠀⠀⢸⢸
⠀⠀⢸⢸⡏⢰⣿⣿⡇⠀⠘⠙⠋⠙⠠⣿⣽⣿⣷⢾⡷⢿⣙⡷⣈⢗⣬⠾⠛⣿⣌⣷⡿⢼⣿⣿⣍⠁⢠⠠⡶⣻⣿⣿⡇⢸⣷⣰⣿⢁⣈⡍⡹⢷⡜⠛⢻⢻⠃
⠀⠀⢸⢸⢁⣼⢹⡿⢰⢀⣤⣦⠂⠀⠠⢿⣿⣿⣧⢸⣿⣀⢉⠀⣏⢹⣷⠋⣡⡏⠋⣿⣿⣿⡿⢿⣀⣀⣤⡀⣾⢿⣿⣿⡇⠸⣿⣿⢱⣟⣿⡟⣷⠩⣿⠀⣾⢸
⠀⠀⢸⡈⠸⣿⡸⠃⠘⠋⣤⣠⢁⣰⠀⣾⡟⣿⠇⢼⣻⡿⣿⡿⠟⠀⣿⢻⡷⣧⠀⢸⠸⣯⡇⠘⣿⣾⡿⢧⣿⣿⣿⣿⣇⠀⢻⠻⣎⣿⣿⣣⡟⠀⣸⠀⣿⣼
⠀⠀⢸⣇⠀⣿⣿⣀⠀⠸⠴⠛⣻⣡⣦⣿⠃⣿⡀⢿⣿⡁⠀⢠⣶⣷⣽⡟⣋⣿⡤⣼⣧⣸⡇⠰⠿⠿⠛⠦⠘⠛⢛⣿⣿⡀⠈⠀⠙⢦⣍⠋⢻⡾⠃⠀⣿⣿
⠀⠀⢸⢻⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⡇⢸⠟⣿⣿⣾⢿⠟⢻⡿⣿⣿⣶⣿⣿⢿⣿⣿⣶⣦⣤⣤⣴⣶⣿⣿⣿⡇⢠⣀⣀⣀⣍⠛⠟⠀⣀⣤⠻⣿
⠀⠀⢸⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠏⣿⠘⠀⣿⣿⣥⣿⣻⣿⣧⣼⣿⡏⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⠘⢿⣯⠻⣿⣶⣒⠟⠉⣀⠀⢸
⠀⠀⠸⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⠀⠀⣿⣿⣿⣾⠋⢿⣿⢸⣿⠃⠉⢠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣿⢀⡜⢿⢩⠖⢿⡍⠆⢐⠀⠀⢸
⠀⠀⢠⣀⣀⣠⣻⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣄⣸⣀⣀⣿⣿⣽⣿⣆⣸⣿⣘⣇⣄⣀⣺⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣬⣷⣶⣴⣄⣼⣿⣣⣼⣤⣄⣸
⠀⠀⠀⠀⠀⣠⠀⡀⣀⣀⠀⢀⣀⣀⡀⣀⣀⣀⡀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠰⠒⠢⠄⠀⠦⠴⠠⠄
⠀⠀⠀⠀⠈⠉⢰⣿⣧⣿⠇⣿⣿⣿⡁⣏⣿⣿⣇⡏⢸⢻⣖⡟⡿⢻⣸⣟⣧⠀⠀⢸⣿⣶⣿⠀⠀⠀⠀⠀⢿⣽⠟⠀⠀⠀⠀⠀⠐⢓⣞⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣼⣿⡅⢀⣼⣵⢃⣄⣠⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠻⠿⢻⢿⠿⠻⠿⠛⠉⠩⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⠻⠿⣿⣿⡿⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⣀⣀⠀⠀⢀⠁
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⣿⣿⣷⡎
⠂⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣶⣵⣿⣿⠀⠀⠀⠀⠹⣿⣿⠇
⠈⡄⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠘⠿⣿⣿⣿⣦⠀⠀⠀⠀⠉⢿
⠀⠈⢄⠀⠀⠀⠀⠁⠂⠤⢀⠀⠀⠀⠀⠀⡀⠠⠐⡸⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⡄⠠⢀⡀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠑⡀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈
⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠁⣀⡀⠀⠀⠀⠀⣀⡀⠀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⣀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠂⠁
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠈⠳⣄⢀⣠⣤⣴⣦⣤⣶⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⢀⡼⠋⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣥⣤⣤⣴⣾⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡟⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠻⣿⡈⠻⣿⣿⣧⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠉⠙⠃⠀⠀⢸⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⢿⣿⡇⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⣠⠶⠦⣄⠀⠀⢸⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢀⡞⢹⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣯⠙⡆⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⣿⡇⠸⣇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⡇⠀⠀⣿⣿⣿⡿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⡇⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⣤⣤⣤⣠⣤⣤⡤⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣇⠀⠀⢸⣿⡇⠳⣄⠀⠀⠀⠘⢧⣀⣀⣀⡽⠃⠀⠀⢀⡴⠃⣿⡟⠀⠀⠀⠀⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣿⣿⠻⢶⣴⣿⡀⠀⠈⠳⢤⣀⠀⠀⠉⠉⠁⠀⢀⣠⠴⠋⠀⠀⣿⠇⠀⠀⠀⢰⡿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⣋⣉⣭⣉⣛⣶⡀⢀⣬⣽⣛⣒⣒⣚⣻⣯⣄⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢉⣉⣉⣉⣭⣽⣿⣿⣦⣄⡉⠉⠉⠉⠁⠀⣈⣳⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠠⠤⠤⠴⣶⡿⠉⠉⠛⠿⣿⣷⣦⣠⠖⠻⢉⢁⠬⠬⠕⠠⠲⢭⡩⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⣲⠞⠋⣽⠁⠀⠀⠀⠀⠀⠉⣹⢃⢃⠖⠉⠀⠀⠀⠀⠀⠀⠀⢹⡞⢚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠉⠉⠛⠛⣷⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠹⡜⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⣹⠦⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣥⣂⣄⣀⣀⣀⣠⣤⣲⡴⡾⢋⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⡧⠞⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠦⣍⣉⠉⠉⣉⣡⣴⡯⠴⢋⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⠻⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣀⠄⠀⠀⠍⠄⠠⣝⠅⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠠⠀⢀⡐⡁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡏⣼⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠋⡋⠉⣠⣤⣴⣿⠃⠸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢿⣷⣾⣿⠿⠟⠃⠀⢸⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⡔⠁⠀⠢⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠋⠀⠀⢠⠄⠀⠐⡂⡘⠀⠘⠧⠤⠤⣀⣰⡀⢀⠄⣠⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⢆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⠀⠜⠁⠀⠐⠀⠀⠀⠀⠰⠀⠁⣰⠇⠘⢰⠁⠀⠀⠀⠀⠙⠂⠠⢶⣎⡁⠀⣤⡶⠿⠿⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣠⡏⡄⠀⠀⠀⢰⣿⣦⣡⣾⢿⡇⠀⣸⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠰⠃⠉⣷⠁⠙⠁⠀⠀⠀⣿⢏⣿⣿⡿⠀⠙⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⠀⠸⢇⠀⠈⣿⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⢀⠔⠟⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠀⠹⣿⡷⠿⠿⠞
⠀⠑⠄⣀⣤⣶⣊⡤⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢷⡈⣻⠷⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠾⠟⠁⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠿⠦⣤⣌⣉⠛⠶⣦⣄⠀⠀⠀⢀⣠⣤⡤⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠈⠙⠻⢶⣄⠉⠛⠶⠶⢿⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠻⢦⣼⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠲⠶⠒⠒⠒⠒⠲⠶⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡾⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣄⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⡟
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶

⠀⠀⠀⠀⠀⢀⣤⣔⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡀⡀⠛⠀⠠⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠦
⠀⠀⠀⢠⡶⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠐⠋⠀⠀⠀⠘⠋⠉⠀⡀⢀⠄⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠁⠀⢀⣤⢀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠀⠀⢀⠀⠀⠘⡻⠋⠀⠀⡔⠁⠀⣾⠖⠀⠀⠀⠀⣀⡀⠉⠁
⠀⠀⢸⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣀⠴⠂⠀⠀⠀⠀⡛⠁⠀⣤⣄⣀⠤⠚⠁⠀⠀⢰⡗⠃⠀⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⡀⣠⣆⢒⣈⣀⣤⡤⠟⠉⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢃⠀⠀⠀⠀⠚⠛⠃⠀⠀⠰⡿
⠀⠀⠘⠻⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠀⠉⠁⠀⠀⠀⠀⠞⠀⠘⠟⠀⠀⠀⣠⣤⣄⠀⠀⣠⣤⣤⣤⣀⡀⢀⣾⢃⣼⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠘⠲⣿⠆⠀⠀⠈⡁⠀⠐⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣠⣿⠃⠘⠟⠛⠙⠛⠛⠛⣿⡟⣛⡁⣘⠁⣤⢤⢿⣼⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢸⣿⠇⢀⣶⠲⡄⣼⡏⢹⢠⣿⣏⣼⢣⡿⢸⡧⢊⣔⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠛⢂⣾⣯⣠⣧⣿⠣⡼⢻⡟⢿⣄⠘⢓⣉⣙⡉⢸⣇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⣠⠞⠻⣧⠟⠁⠙⠚⢁⣀⣥⣼⠿⢿⣍⣁⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠈⠿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠞⠃⠀⠈⠉⠁⢀⡀
⠀⠀⠀⠀⣴⠆⠀⠀⣤⠀⠀⠀⠈⠙⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠒⠓⠚⠃⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⡾⠖⠋⠉⠁⠙⠒⠀⠀⠀⠰⠒
⠀⠀⠀⢠⠀⠘⠷⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠉⠉⠀⠄⠀⠀⠀⡠⠂⠛⠁⠀⠐⠟⢃⡀⠀⢀⣤⡀⢀⣀⠀⠀⠀⠀⠘⢿⠁⣠⣤⠀⣀⣘⣀⣀⠠⣤⠀⠀⢤
⠀⠀⠀⣿⣧⠀⠀⣠⣄⢠⣴⣦⠀⠀⢠⣶⣤⠀⠔⢠⠆⠀⠀⣼⠃⠀⢛⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⢦⡤⠒⠉⠉⣉⠉⠉⠉⠓⢄⢀⡀⠁
⠀⠀⢰⣿⣿⣿⣧⣤⣤⣄⡀⢤⣄⣀⣀⣀⣀⣀⣴⡏⠀⠀⢀⡴⠀⠀⠙⠁⠀⠀⠀⠤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣀⠀⠀⠋⠀⠀⢀⡀⠀⠈⠡
⠀⠀⠘⢿⣽⣋⡉⣉⡉⠹⠿⠟⠛⠉⠉⢉⣽⡷⣀⣶⠀⠀⠈⠳⠀⠀⠦⢀⠐⠀⠈⠀⠁⠚⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⣏⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⢰⣿⣿⣿⣭⢤⣦⣦⣤⣤⣴⡷⠾⠿⠛⠙⠋⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠉⠀⣀⠀⠀⠤⠀⠀⣀⡀⠀⠀⢸⡇⣴⠄⠀⠀⠀⠀⢴⣆⠀⠀⠀⡀
⠀⠀⠀⢨⣥⣌⣉⠀⠀⣀⣀⣀⢠⠾⠆⠀⣀⣠⣤⣴⡛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⣿⠀⠀⣤⡀⠀⠀⠀⠀⠀⢠⡄⠛
⠀⠀⠀⢉⠾⠋⠉⢭⡉⠉⠋⢹⠟⢻⡏⠉⠉⠉⢈⣉⣤⠀⠀⠀⠀⠀⣀⣀⠀⠰⠖⠒⠒⠀⠉⠈⠁⠀⢠⡀⠀⠀⠀⠀⠘⣇⠀⠈⠁⠀⠶⠂
⠀⠀⢠⣿⡟⢛⡶⠶⣤⣤⣤⣤⡶⠶⠶⠞⠛⢋⡉⠡⢄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢴⣦⡄⠀⠀⠀⠙⠁⢠⡆⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⢶⠆⣀⠤⠔⠁
⠀⠀⠀⠨⣷⣿⣿⣄⣀⠺⠷⠀⠀⠀⣀⡀⠀⣛⣣⠴⠊⠀⠀⠀⠀⠀⠀⠈⠁⣀⡀⠀⠀⠉⠁⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⠀⣸⠃⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠛⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⢳⣄⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⡾⠁⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠳⣦⡀⠀⡾⠁⠀⠀⣀⠀⠀⠀⠀⢻⣤⡴⠋⠀⠀⢀⡀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⣶⡇⠀⠀⢰⠛⢦⡀⠀⠀⠈⠏⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠀⠀⠙⢦⣀⣀⣤⡤⠶⠛⠁⠀⠈⣧⠀⠀⠀⠀⠀⠘⣷
⢿⣶⣄⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠉⢀⣀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⣧
⠀⠹⣎⠙⠛⠶⣤⣼⣇⠀⠀⠀⠠⣤⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡼⠋⠉⣽⠃⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠹⡆⠀⠀⠀⠉⠛⠀⠀⠀⠀⣯⠉⠳⣤⠏⠀⠀⠀⠀⠀⢰⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡟⠢⣄⡀⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢷⠀⠀⠉⠙⠲⣿⡀⠀⠀⠀⠀⠀⢴⡿⠖⣷⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠿⠶⣤⣀⢸⡇⠀⠀⠀⠀⣠⠼⠷⣤⣀⣉⣉⣹⠛⠛⠳⣦⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠈⠉⠁⠀⠀⢠⡞⠁⠀⣀⠀⠈⢉⣩⣤⣤⣀⠀⠈⠳⡄⠀⠀⠀⡇⠀⠀⠀⣼⣏⣀⣠⣤⠶
⠀⠀⠀⣿⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡾⠀⢠⡞⢉⡙⢶⠏⠀⣠⠀⠈⢷⠀⠀⢱⡀⠀⣰⠃⠀⠀⠀⠈⠉⠉⠁⠀⣰
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⡇⠀⠘⣧⡈⠁⣸⡆⠀⠉⠀⠀⣸⠃⠀⠈⡇⠀⠛⠶⣤⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⢹⡄⠀⠈⠉⠉⠁⠻⠦⣤⡤⠖⠋⠀⠀⠀⣿⣀⣤⠞⠃⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡙⢦⡀⠀⠀⠲⢦⣤⣤⣤⡴⠞⠀⠀⠀⡟⠉⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⣄⠀⠀⢻⡀⣸⠀⠀⠀⠀⢰⠃⠀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⠀⠀⠀⠀⠀⠙⣦⠀⠘⡏⢻⠀⠀⠀⣠⡿⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⢻⡆⠀⢳⡘⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠻⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢤⡶⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣠⡤⣼⠆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⡀⠈⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠳⢤⣤⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⣀⠀⠀⠀⣀⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠈⠁⠀⠀⠀⠈⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⣿⠁⠀⠀⠢⠂⠀⢠⡅⠒⠀⠀⣷⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⢎⠻⠆⠀⠀⡀⠀⢤⣸⠇⠀⠀⠀⣿⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡆⠀⠀⠐⢧⡀⠀⠀⠀⣠⠀⢀⡏⠀⠀⠹⡟⠁
⠀⠀⠀⠀⠀⠀⠰⠾⣉⡉⠓⣻⣄⠀⠀⠀⠈⠉⠉⠉⠀⠀⣼⠁⠀⠀⢀⣿⢲
⠀⠀⠀⠀⠀⠀⢠⠾⣉⣩⠿⠁⡏⠳⢤⣀⡀⠂⢒⣂⡠⣾⡁⠀⠀⠐⢹⡟⡻⣄⡤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣉⣀⡀⠇⠀⢠⡟⢹⠉⢹⡀⠑⠸⡝⢦⠀⠀⢣⡻⠖⣨⠟
⠀⠀⠀⠀⠀⠀⢠⠿⢻⢩⢨⡛⣧⣠⡟⠀⠊⠀⠈⣁⢦⢠⡹⣌⣳⡄⠀⡇⣾⠁
⠀⠀⠀⠀⠀⢀⣿⡄⢸⢸⢸⡇⡇⣿⠀⠀⠘⡝⣤⠁⠛⢪⣃⠙⢏⠀⢠⠃⢸
⠀⠀⠀⠀⠀⡞⢽⢸⣼⠘⢸⡇⣅⡶⠃⠀⡆⢰⠀⢀⣠⡼⠚⠀⣸⡀⡎⠀⢸
⠀⠀⠀⠀⢠⣇⢸⢸⢿⣨⣴⠛⠁⢰⣄⣠⢷⡌⢠⣏⣠⢶⠳⡖⠃⠙⠃⠀⣸
⠀⠀⠀⠀⢸⡟⢸⢸⢸⠉⠻⣆⠀⠀⢧⣠⠏⢀⠋⢩⣵⡟⠀⠈⢢⠄⣚⠈⠉⠑⠂⠠⣀
⠀⠀⠀⠀⢸⣧⣼⣸⢸⠀⠀⠙⣦⠀⠈⠁⠀⡼⠀⣌⣿⠇⢀⣀⣶⠠⠤⠄⠒⠒⠉⠀⡿⣿⣿⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⡏⠉⠙⠛⠛⠻⠷⠿⢷⡀⢀⣼⢶⣿⣿⣿⣿⣿⣏⠈⠦⣀⢀⢀⣀⡤⠞⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣬⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣀⣠⣤⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣿
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠳⣌⠙⢻⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⣤⣤⣤⣿⣄⣀⠀⠀⠈⢧⠈⣇⣨⣽⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢳⡄⠀⠈⣷⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⣦⣾⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡿⣋⣶⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⡤⢒⣋⣉⡳⣄⠀⠀⠀⠀⠘⠃⠀⢤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⡀
⠀⠀⣀⠔⠉⠵⠺⠟⣀⠂⡹⡟⣦⡢⡄⠀⠀⠿⢦⣘⡧⡀⠀⠀⣜⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠠⣄⡠⢴
⢠⢊⣤⠀⠀⠠⠅⠄⢺⢗⠀⠇⡏⣬⠆⠀⠸⡀⠀⢻⠀⢸⣠⠖⢻⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⣆⣼⢺
⠘⠦⣥⣀⣤⠤⠋⠀⠒⢠⣞⡵⠃⠁⠀⠀⠀⠁⠀⢸⡄⢸⠃⢀⡞⠀⠀⠀⠀⠐⢌⡀⠀⠐⠂⠀⠀⣅⡐
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃⡸⠀⣼⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⣠⠞⡅⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀⡤
⠀⠀⠀⡀⠤⡄⠀⠠⢀⡀⢀⠀⠀⠀⠀⣰⠥⠒⢋⠇⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠕
⠀⠀⠀⠀⠀⠀⠸⠄⠰⢄⠀⠑⠀⠀⠀⠀⠀⠴⠉⠀⠁⠀⠀⠀⠀⠠⠀⠀⢀⡀⣉⠁⠀⣀⡀⣀⠴⠞⠋⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢟⢳⣾⠏⣼⣉⣧⣞⣹⣾⠟⣰⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠘⢧⣠⡀⠀⠀⠀⡰⡁⠀⠀⠀⠀⣈⠁⠈⠉⢸⠉⠀⣿⠀⠀⠉⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠰⢸⡓⠀⣄
⠀⠀⠀⠀⠉⠓⠠⠀⠊⠉⠀⠀⠀⠀⠀⠛⠀⢀⠀⠘⠀⠀⠛⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢁⠴
⣀⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠈
⠀⠉⠻⣝⠁⠀⠀⠄⠀⠀⣀⣀⣀⠄⠒⠁⠀⠀⠠⠎⠀⠀⠀⠀⠀⢀⣀⠠⠔⠊
⠀⠀⠀⠈⠲⠤⢀⣀⣀⡀⠀⢀⠀⣀⡀⠠⠔⠊⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠭⡀⢄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⣤⠄⠸⣦
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⣄⣀⡇⠀⠀⠀⠀⡔⠊⠱⠒⠷⠽⠷⡀⠀⢱⠀⠀⠀⠀⢢⠀⠀⠀⣰⠞⠑⡿⢠⠃
⠀⠀⠀⠀⢀⡴⠊⠀⠠⠀⠈⠯⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢱⠀⠸⠀⠀⠀⢢⡈⠶⠖⠋⠁⠀⡰⠃⠇
⣀⠤⠐⠊⠁⣀⣠⠴⠚⠉⠀⠌⠉⢿⠙⡄⠀⢠⠀⠇⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⣏⣵⠰⢤⣤⠴⢣⠞
⠈⠉⠡⣶⣋⠉⡁⠰⠈⢀⣐⡂⣪⠋⠀⠀⠀⠈⠢⣄⠀⠀⠀⢀⣇⠌⠀⠀⠀⠀⠾⠁⠈⠳⢤⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠓
⠀⠀⠀⠀⠀⠀⠀⢾⣽⢿⡁⠀⠀⠀⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⣦⠀⠀⠀⠀⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⣧⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⢠⣿⣿⣷⣄⠀⠘⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡄⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⡄

⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠉⠀⠀⣰⢣⠇⠀⠀⠀⠀⠀⠙⠳⣄⠈⠓⢦⡈⠉⠀⠀⣀⣠⡞⠁⠀⠀⠀⠀⢀⣴⠾⢳⣞⣉⡴⠛⠋⠁⠀⠉⠁
⠀⢸⠆⠀⠀⠀⢀⡿⠀⠀⠀⠀⡏⠀⣀⣤⣤⣴⢻⡟⠀⠀⠀⢀⡤⠤⠄⣀⣘⣷⡀⠀⠉⠲⢶⣛⠉⠁⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠈⣹⠇
⡀⢸⡀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⡼⠛⠁⠀⠙⢿⡇⠀⠛⠀⠋⠙⠲⣤⣄⣈⣉⣙⣦⣀⠀⠀⠉⠉⠉⠛⠉⠉⠁⠀⠀⠀⠀⢀⣠⠼⠋⠀⠀⢴⡆
⠁⠸⡇⠀⠀⠀⣿⠁⠀⠀⢠⡿⠋⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠿⢶⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣚⣉⣀
⠀⢰⡟⠀⢀⣼⠃⠀⠀⢀⣾⠃⠀⠀⠀⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡲⠶⠤⠤⠤⠴⠶⠾⠛⠛⠉⠋⠉⠁⠀⠀⠀⠉⠛⢻⣄⣀⣀⡀⢤⣐⣲⣄
⠀⣾⢁⣤⠟⠁⠀⠀⣠⡾⠃⠀⠀⢠⣾⠟⠁⠰⡦⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣸⣧⠿⠖⠛⠉⠁⠉⠁
⠴⠛⠋⠀⠀⠀⣠⣴⣿⠁⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡆⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠁⠀⠲⠆⠀⢀⣀⣠
⠀⠀⢀⣠⣶⡿⠋⡼⠃⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⠀⠛⠂⠀⠀⠘⡌⣧⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠁
⠛⣻⠟⠉⠁⢀⡼⠁⠀⣠⡾⠋⠀⠀⠀⠀⢰⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⣞⣥⡴⠶⠶⠖⢻
⡴⠋⠀⠀⡰⠋⣀⣤⠞⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠖⢉
⠀⢀⣤⣚⣥⡾⠋⠁⠀⠀⠀⠘⢿⡻⢦⡀⠀⠀⠀⠀⠳⡽⣧⣀⡀⢀⠀⠸⠗⠀⠀⠀⠀⣰⣯⣽⣷⣄⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢀⡞⣡⡴⠿
⡀⠙⠉⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠙⣦⣙⢧⡀⠀⠀⠀⠙⣌⠉⣿⠏⠛⠷⣦⠀⠀⠀⣼⡏⠉⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣹⣶⠶⣶⣤⣘⣶⠟⠀⠀⠀⠈⢳⣄⠀⣿⠋⠀⠀⠀⠈⣿⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⣠⡤⠶⣶⡶⠀⠀⠀⠀⠀⡀⠀⢸⡟⠁⠀⠀⠈⠻⢿⣄⠀⠀⠀⠀⠀⠹⣦⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠁
⡴⠖⠋⢉⣠⠔⠋⠁⢀⣠⡴⠶⠖⣪⠇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠸⣿
⠀⢀⡴⠋⣀⣀⣠⣴⡋⣈⡤⠖⠊⠁⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠘⣷⡄⠀⠀⠈⢿⡆⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⣰⠞
⣰⡿⠶⠟⠋⠉⠉⠉⠉⠙⠛⠒⠶⠶⠶⡴⠆⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⢹⣷⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠀⢀⣠⣶⠟⠁
⠉⠀⠀⢀⣠⠴⣶⠆⠲⠶⠶⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠈⣿⡀⠀⠀⠈⣿⡆⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠀⠀⣴
⠀⣠⠞⠋⢀⣴⠃⠘⠃⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠳⢦⣤⠀⠀⢸⡇⠀⠀⠀⣿⢿⡄⠀⠀⢸⣧⠰⠗⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⢀⣤⡾⠁
⣼⠋⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⣷⠀⢸⡇⠀⠀⣸⣿⠈⣷⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⣾⡷⠿⠶⠾⠚⢩⠟
⠃⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⠃⠀⠀⢬⣿⠀⠸⡆⠀⢸⡇⠀⠀⠀⠀⣠⣯⠋⠀⣀⠀⠀⢠⠏
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⢠⠏⠀⠀⢀⣿⠏⠀⠀⡟⠀⣼⡇⠀⠀⠀⠻⠐⠁⠀⠀⠀⠀⠀⢸⡇⠀⡀⢰
⠀⠀⠀⣸⠃⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⡾⢿⡀⠀⠀⣿⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢋⡝⣿
⣀⣀⡴⠃⣾⣷⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣴⣿⠀⢸⡇⠀⠀⣽⣸⡟⠀⠀⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⣠⢿⠎⠀⢻
⠏⠉⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠏⠀⣠⡾⠁⣿⠀⢸⣧⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠰⣷⠏⠀⠀⢰
⠀⠀⠀⠀⣧⣸⠀⠀⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣾⠀⣴⠏⠀⠀⡏⠀⣽⡏⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⣠⢴⡶⠀⢀⡇
⠗⠀⠀⣠⣯⣿⡀⠀⠀⡼⣾⠁⠀⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⣧⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⡴⣋⡴⠋⠀⠀⢸⣿
⠀⢠⡞⠉⠁⠈⢿⡄⢰⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡆⠀⠀⠘⠇⠀⠀⠀⠀⠘⠿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠙⣷⠏⠁
⠀⣿⠀⠀⠀⠀⠸⣷⠿⠾⠛⢻⣆⠀⠀⣀⠀⠀⠀⣰⣱⠋⠀⠀⠰⠶⡖⠶⢤⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⣰⠟⠀⢀⡠⠴⣶⠄⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣶⣻⣿⣯⣭⣿⣦⣶⣶⣶⣿⣿⣯⣭⣿⣿⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⣿⠿⢿⣟⣻⣛⣛⣛⣛⣻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⣝⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣕⣭⡿⠾⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠷⢼⣭⣳⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠷⠿⠋⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡾⠛⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⣺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠉⠛⠲⠦⠤⣤⣤⣀⣀⣀⣤⣤⠤⠤⠶⠖⠛⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠠⠤⠄⠤⠠⠄⠤⠄⠤⠤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠹⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡤⠤⣤⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠛⠃⢆⡁⢀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⣶⣾⡁⠀⠂⠀⠀⡄⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠹⣦⣾⣧⠄⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⢠⡀⡆⢻⠀⢀⣶⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⣤⡁⡀⢡⣄⣰⡆⣀⡀⠋⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⣬⣿⣿⣿⣿⣥⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠦⠒⠒⠀⠰⠿⣿⡿⣿⠏⠀⠦⡌⠀⠀⠀⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⡀⠄⠀⠀⠀⠤⠉⣡⠄⡀⢈⠁⢀⠲⡝⠂⠀⠀⠀⠚⢠⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡐⢲⠀⠀⠀⠁⠘⠀⠈⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠲⠖⠊⠉⢹⣿⣿⡆⠀⠀⠄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠐⠀⠈⠀⠈⠀⠘⠂⠀⠈⠐⠊⠐⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠿⠛⢉⣡⣶⣾⣿⣿⣿⡆⢠
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⢀⣠⡴⠟⠉⠁⠈⣉⣉⣉⣀⠈⠂
⠀⠀⠀⠀⠛⠻⠿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⢉⣩⠴⠶⠶⣶⣶⣶⣾⣿⠟⢁⣠⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⡀⢢⠀⣶⡿⠛⠛⠿⢿⣶⣦⣤⣴⣶⠾⠋⠁⠀⠀⠀⣀⣠⣭⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠸⡄⠁⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⠈⠁⠁⠀⠀⠘⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠄⣀⠤⠶⠒⠀⠤⡀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠘⠁⠀⠀⠀⠀⠀⠢⢀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢶⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠈⠻⣿⣿⢦⡀⠀⠀⠀⠀⠀⠂⢠⠚⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠀⣿⠿⢿⠳⢄⠀⠀⣸⣿⣷⡄⠀⣠⠟⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠚⠁⣀⣠⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⢃⡄⣷⠚⢄⣀⣀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠔⠉⠀⢈⠀⠀⢲⣦⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠛⠔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠃⠀⠀⢀⠂⠀⠉⠁⠙⠿⠷⣤⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⣬⡗⠠⠤⠤⠄⠒⠉⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢰⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⢀⣡⣄⢠⡤⠎⠁⠀⢣⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⠀⠀⠀⠀⢠⡂⠀⠁⠀⠀⠀⠀⠀⠀⠙⢦⣸⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⠢⠄⠀⢠⣿⠁⡆⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⢩⡍⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⡐⠀⠸⠀⠀⠀⠀⠀⠈⠉⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠑⣄⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠀⠀⠀⡸⠀⠀⡄
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠉⠀⠈⠒⠂⣴⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣴⡾⠃⠀⠀⡇
⠀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠃⠀⢸⣿⠁⠀⠀⠀⢹
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠁⠀⢀⡽⢰⠇⠀⠀⠀⠀⢸⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⡇
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⢈⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⡇
⠀⠀⣆⠀⠀⠀⠀⠠⠔⠊⣡⢀⡄⣸⠔⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠙⠢⠤⠴⠶⣶⠾⠷⠛⠉⠀⠀⠀⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠁⢁⠀⠀⠀⠀⠀⢠⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠐⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠑
⡿⢿⠿⠿⡿⣟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣻⣿⣛⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⠛⢦⠀⠀⠀⢀⡤⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣀⣃⠀⠇⠀⢀⣿⡷⠄⠀⢿⡄⣠⣾⡟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠏⠀⣾⣿⣷⠛⢂⣸⣿⣿⠁⠀⠈⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠘⠇⠀⣸⣶⣿⣿⡛⠟⠛⣿⣿⣿⠶⠦⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠯⠠⡹⢿⠛⣄⠴⡇⠿⠛
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⣿⣿⣿⡿⠛⠙⢾⢲⡆⠀⠀⠀⢨⣴⠁⠀⠀⠀⠀⠀⠚⣶⠂⢤⣀
⠀⠀⠀⠀⠀⢻⣄⣤⣶⣗⣬⠙⢻⡏⠛⠷⣦⠀⣾⡇⠐⢠⢀⣾⣇⠀⠀⠀⠖⠀⠀⠀⠘⠛⠙⠛⣇
⠀⠀⠀⠀⢸⣾⣥⠀⠄⢹⣿⣧⣮⣄⣦⣲⣾⣴⣿⣷⢊⣡⠋⠉⠉⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⣠⣜⢟⣰⡄⠀⢸⣛⠀⠟⠫⣞⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⢠⡀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⣻⡄⠀⢸⣿⣤⣮⣵⣟⢤⡀⠨⣭⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⠀⣳⣄⣿⡀⠰⠂⢀⠀⠀⠀⠀⠀⢣⣸⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠄⠀⠐⠂⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠒⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢳⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠒⠒⠒⠚⠉⠉
⠀⠀⡀⠀⠀⣀⣀⣤⠮⠤⣘⣆⣀⡠⠴⠒⠉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠓⠛⠛⠉⠉⠀⠀⠀⠀⣀⡀⠠⠚⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠒⠒⠒⢀⡢⠏
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⢣⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣉⡉⠉⠙⠛⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠉⠛⠷⣦⡀⠀⠂⠠⢄⡀⠀⠀⣠⠠⠔⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⢀⡴⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡲⠒⠉⠁⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠹⣳⡧⣌⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠁⠙⣧⠀⠀⠘⠟⢺⣔⠶⠆⠄⠀⠀⠀⠀⣠⣤⡴⠶⢏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⢷⢶⣄⠀⠀⠈⢿⡂⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠹⡃⠂⠀⠀⢀⣴⠞⠉⠀⠀⠢⡘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠻⣤⠀⠈⢷⡀⠀⢀⣀⠎⠁⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠸⣷⠀⠀⠙⠛⠷⠒⠲⢦⣿⣄⡀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡞⠉⠉⠉⠛⠳⣄⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⠆⠀⠀⢀⡴⠫⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⢸⡧⠤⠦⠔⣹⠃⠀⠀⠀⠀⠀⠈⠳⠮⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⢀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣝⣋⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣉⡀⠀⠀⠀⠀⠀⠀⠠⢄⣠⡶⠛⠁⠀⠀⠀⣰⠟⢃⡴⠾⢟⣡⠤⠤⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣐⣲⣄⣀⣀⠠⠄⠀⠀⠀⠈⠀⠉⠛⠛⠒⠒⠒⠒⠛⠋⠁⠀⠀⠀⣀⡠⠴⣵⣿⡫⠶⠄⣀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠷⠚⠋⣩⠙⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠙⠦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢁⠆⡄⠙⣦⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠼⠠⠋⠄⣿⠁⠀⣰⢯⣅⠹⡹⣆⠀⣴⢫⣍⠝⢟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⢀⡤⣴⣤⡀⢀⣀⡀⠈⠙⠓⠒⠒⠛⠁⠀⠀⣏⢨⣠⣦⢰⢿⠀⡇⢰⣉⡚⠸⠀⠊⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢹⡆⣿⢠⢢⢈⢻⠏⠉⢙⡳⢤⡀⠀⠀⠀⠀⠀⠀⠹⣌⠢⠝⣉⡾⠀⢷⡘⠃⡠⠁⠀⠀⠀⠀⠹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⠀⢸⡇⣿⠸⠕⢈⢸⡀⡘⠋⢰⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣠⡴⠟⠛⠋⠀⠘⢦⣥⣦⠞⠳⣬⣢⣉⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣶⣥⠴⣬⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⡤⠄⡲⠖⠂⠦⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣴⡟⠉⣹⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠞⠋⡵⠋⢠⠜⠃⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠠⠃