Curiosity Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣟⣻⣽⣟⣻⡿⠿⡟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⣿⣿⡿⢿⣿⣿⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⣛⠿⢟⡻⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⢎⣾⣿⢔⣮⣎⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⢟⢿⣷⣿⢟⣇⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣿⣿⣷⣕⣚⣒⣽⣾⣿⣿⢨⣽⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣷⣶⣷⣾⣦⡻⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠳⠿⠿⠿⠸⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠍⣹⣿⣿⣯⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⠞⠛⠀⠀⠀⠀⠀⠀⣿⣿⡄⠘⣧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣠⢤⢤⣰⣤⠘⣿⣷⠀⠻⣿⡛⢻⡀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⣚⢯⣴⣷⣾⣿⣶⡊⣦⡻⣿⡟⣿⣇⠀⣿⡇⢸⡧⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣭⣞⣿⠿⢞⡳⢿⣧⣿⣷⣿⣇⣿⣿⣀⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣠⣤⣀⣀⣀⣸⣇⣩⢽⣿⣲⣾⣷⣎⣁⣀⣄⣤⣌⣿⣿⣍⠸⣿⣿⣤⣠⣤⣤⣤⣤⣤⡊⠉⠀⠱
⠀⠀⠀⠺⣿⡭⢽⠏⠉⠉⠙⠛⠿⣿⣿⣼⣿⣿⣿⣯⣭⣭⣭⣭⣤⣼⣷⠶⠶⠆⠉⠉⠉⠉⠛⣛⣻⣿⣶⣶⣤
⢀⣠⣶⣶⣶⣶⣼⣦⢀⠀⠀⠀⠀⢈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢽⣿⢳⡄⢤⣶⣦⡄⠀⠾⣿⠗⠚⠛⠛⠁
⣾⣿⣿⡏⣹⣿⣿⣿⢠⣾⣿⡟⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⠇⠶⣿⣿⠁⠀⣰⣷⣾⣿⣿⣷⣶⣦⣄
⢻⣿⣿⡇⣿⣿⣿⡿⠘⠿⣿⡇⠈⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠰⠟⠛⠋⢸⣿⣿⡿⢛⣿⣿⣿⣿⣿
⠀⠉⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⢰⣿⣿⣿⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣻⣿⣿⣿⣛⣉⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢘⠀⠀⠀⠉⠆⠄⠆⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠢⠉⢁⢓
⠀⠀⠨⠀⠀⠀⠀⠐⠈⠀⠘⠁⠂⠀⠀⠈⠁⠐⠁⠀⠠⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠈⢚⡿⣿⡄
⠀⠀⢘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⢠⡔⢢⠀⠓⠋⠋⠉
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠀⢀⠀⢞⠀⢹⠄⠀⠁⠃⠀⠀⠀⠠
⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠁⢀⠁⠀⣉⠆⠈⠀⠁⠀⠀⠀⠁⠀⠉⠁
⠀⠀⢴⠙⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡌⢉⣍⠀⠀⠀⠐⢠⠄⠀⢀⡠⠂⠀⠊⠁⠁⠀⠀⠀⠀⠑⠦
⠀⠀⢨⢄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠄⠠⠂⠈⠂⠐⠀⣤⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠀⠁⠀⠀⠐⠛⠀⠘⠂⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⣀⠤⠤⠴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣁⠀⠈⠿⠂
⠀⠀⠈⠉⠁⠀⣇⠠⢠⠐⠴⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠉⣱
⠀⠀⠠⠤⡄⠀⢹⡤⠶⠒⠛⢋⡉⠦⠀⠀⠀⠀⠙⠑⠲⠀⠀⠀⠀⣡⠀⠈⠀⠀⠀⠀⠀⢀⠀⠑⡟⠁⣂
⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⣩⡥⠴⠀⠀⠃⠀⠀⠾⠏⠉⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⢠⠀⠀⠈⢹⠉⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⢀⡈⠐⠃⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠰⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⣀⠀⠀⠀⠈
⠀⠀⢨⠭⠭⠄⠀⢀⣤⡀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠀⠀⠀⠰⠀⠀⢀⡀⠈⠀⠀⠀⠠⠌⠬⠢⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠢⢠⠀⠀⠀⠂⠋⠀⢀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠐⠂⠀⠑⢆⢀⡀⠀⠀⠀⠈⢳⠠⠀⠀⠀⠀⠈
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⡈⠶⡄
⠀⠀⠀⠀⠀⣿⣶⣿
⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀
⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠆
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⡀⣠⣤⡄⠀⠀⠀⠀⣄⣀⡄
⠀⠀⠀⠀⠠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⣿⣿⡗⣿⣿⣿⠆⠀⠀⠺⣿⠿⠃⠀⠀⢀
⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⣿⣿⣷⣼⣿⣿⡀⢠⠀⣤⡆⠆⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣷⠀⠲⣿⣇⠀⠲⠀⠏⢸⠉⠛⡁⢡
⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⡀⣿⣿⣿⡇⠀⠀⣸⠉⣍⠸⡄⠀⠛⠀⠀⠃⢸⠀⢸
⠀⠀⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠚⠻⣯⣉⣿⠋⣿⡁⠐⠾⠓⠐⠛⠀⠈⠁⠠⠶⠾⠿⣿⠋
⠀⠀⠀⠀⠀⠃⠉⡿⠷⠒⠛⠛⠛⠛⠉⠉⠉⠀⠰⠦⣿⠯⠟⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠠⠄⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠉⠛⠷⣤⣀
⠀⠀⠀⠀⢴⡄⣀⣤⡴⠶⠿⠟⠛⠛⠶⠶⢿⣥⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠐⣶⣶⣶⣤⠀⠀⠈⠙⠳⣦⣠⣾⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⢠⣶⣾⣿⣿⣷⣶⣤⣄⠀⠀⠈⢷⡀
⠀⢴⡟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⣿⡟⠛⠛⠛⠻⢿⣿⣿⣦⠀⠈⣷
⠀⠘⣧⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⣤⡄⠀⠀⠹⣧⡀⠀⠘⢷⡀⠀⠀⠀⠀⠈⠻⣿⡷⠀⢸⡆
⠀⢠⣼⣧⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡁⠀⠀⠀⢠⣿⣿⣦⣀⠀⠙⠀⠀⢾⣷⣄⠀⠘⢿⡀⠈⣧
⠀⠈⠀⠘⢷⡄⠀⠀⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⣠⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠈⢻⡧⠀⠘⣇⠀⣿
⠀⠀⠀⠀⠀⢻⣦⣀⠀⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡇⠀⢀⣿⠀⣿
⠀⠀⠀⠀⢴⡿⠋⠙⠿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣏⠀⠀⣿⣿⣶⣾⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⣿⡄⠀⠉⠉⠉⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⡀⠀⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⢹⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠛⠃
⡶⣶⢶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⠶⠶⣶⣶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢖⣀⡈⠭⢥⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡅⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠶⢼⡁⠴⠠⠥⠑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠓⠲⠲⠔⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣏⢉⡅⣤⠤⡜⡄⠀⡇⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡰⠉⡄⢂⠈⡄⢱⠘⡄⡇⠹⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢇⠱⠘⣈⣆⡘⡀⢣⠸⣇⠼⠄⠤⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠆⢣⡉⡏⣧⠵⠤⡗⣇⠡⣖⠂⠉⣧⡀⠀⣸⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡫⢍⡣⠧⠏⠐⠒⠈⣁⡁⠳⠦⠙⠒⠊⠑⡏⠙⠋⢹
⠀⠀⠀⠸⡫⢕⠢⢄⠀⠀⢸⢸⠀⠈⠑⠶⢈⣉⠁⢤⠤⣐⢦⣬⠶⢄⡀⣑⠤⠤⠼⣄
⠀⠀⠀⠀⠐⣄⡉⠒⢌⣲⣼⢸⣅⠠⢴⡄⣤⠉⡞⠽⠗⠒⠂⠉⠉⠈⡇⠀⠀⢘⡀⡧⣑⠢⡀
⢠⡶⣆⠉⠒⠗⠋⠱⠦⣤⠸⡼⣡⡄⠼⣀⣨⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇⢖⢢⠈⠈⣷⣌⠑⢌⠲⢄
⣿⡠⡼⡄⠀⠸⠀⠀⡇⠣⡆⢡⠰⢱⠀⢳⠤⣀⡇⠀⠀⠀⠀⠀⠀⣀⣏⡌⡄⢧⢴⠃⠈⡇⠢⣑⢄⡑⣤
⢳⠦⣻⡇⢀⣴⠤⠒⠳⡚⠉⠢⣆⢣⢃⠀⢆⠀⠑⠒⠒⠒⠈⠉⠀⠀⠀⠰⠰⡘⣞⡇⠀⢸⠀⣇⠀⡅⢀⡄⢀
⠀⠀⠭⢠⡟⡇⣧⠀⠀⢱⠀⠀⠻⡈⠎⠆⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢠⢰⡆⠀⣼⡾⢏⠉⠉⢫
⠀⠀⠀⠠⠓⡙⣭⠀⠀⠀⠄⠀⠘⠃⢸⢹⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠦⢇⠀⣯⡰⡼⡆⠀⠀⡆
⠀⠀⠀⠀⢿⠙⣤⠀⠀⣸⢀⣠⣷⠲⠈⠙⠒⡋⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣸⠤⢧⡦⠚⡇⠀⠀⡇
⠀⠀⠀⠀⠈⠈⠛⠈⠉⠀⠀⢘⣨⣬⠇⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡚⢍⡻⠗⣀⡀⠥⢿⡁⠠⠴⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡐⠆⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⢬⡉⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢱⠂⣀⣀⠆⠤⠔
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣟⣿⣿⣿⣿⢇⣾⣿⣿⣿⡍⢹⣷⣶⣶⡖⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣱⡀⠀⣿⣿⣭⠏⠋⡹⣼⣏⢀⣿⣿⡇⢸⠉⠉⠉⣿⣿⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣐⣉⠉⠉⠉⠈⠀⠐⠐⠒⢒⢡⠍⠋⠉⠉⠛⠃⣘⡲⠶⠴⠿⠿⢄⣠⣹⠇
⠀⠀⠀⠀⠀⠀⣴⢶⠶⣿⣿⣿⣿⣿⣿⠛⣿⣹⠀⠈⢁⣀⣀⣀⣀⠀⠠⠔⠆⠀⠀⠀⠀⢠⠉⠉⠉⠉⠛⠛⠛⠛⠒⠒
⠀⠀⠀⠀⠀⠀⢹⣿⣀⣿⣿⣿⣿⣿⣿⣤⣾⣿⡇⣠⣿⣿⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠸⠇
⠀⠀⠀⠀⠀⠀⠈⠙⢏⠛⠛⠛⠛⢯⠛⠛⠛⢻⣿⠟⣩⣴⣶⣦⡝⢿⣇⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣫⣝⣷⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣯⣼⡟⣻⠟⡿⣿⣎⣿⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣾⡿⠿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⡇⠛⠀⠀⣿⣿⣿⣿⣿⣿⡏⠉⠻⠟⠛⢻⣿⣿⣿⠃⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠹⣿⣿⣷⣤⣀⣬⣾⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⠟
⠀⠀⠀⠐⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⠛⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⢸⡃⠈⡷⠴⡏⠀⢹⠀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⠀⠙⠛⠁⠀⠉⠛⠉⢀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⡀⠀⠀⠀⠀⠀⢀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠈⡟⠒⠶⠶⠶⠚⡏⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣻⠇⠀⢻⠉⣻⠿⡏⢹⠃⠀⢿⡳⠤⣄⣀⡤⠖⠚⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢴⡃⠀⠀⠈⣇⢳⣶⢋⡏⠀⠀⠀⣹⠄⣰⠋⠳⡄⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⢦⣀⠀⢹⡞⠘⣿⠀⠀⣠⠞⠁⢠⡇⣾⠁⢿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⢷⢰⢇⡴⠋⠁⠀⠀⠘⡇⠉⠀⢸⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠇⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣤⣤⠴⠞⠙⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢄⡀⠀⠀⠀⠠⠐⡦⠐⡒⡀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠐⠒⠒⢀⣒⡦⣄⠀⠀⠀⠀⠀⣀⠤⡤⢀
⠀⠀⠀⡰⢠⠀⠀⠀⢀⠔⠁⠑⢄⡈⠙⠀⠀⠀⠀⠒⠢⠢⠂⠡⣓⠀⠀⢀⠔⠈⠢⢸⠠⠉⡏⠅⠩⠀⠰⠄⢾⢠⠄⡀⠀⡰⡫⡣⠒⠰⢦
⠀⠀⠀⠈⠈⢀⡠⠚⡡⠆⠀⠀⠀⠈⠑⠢⢄⡀⠀⠐⠶⢠⡉⠦⢁⠄⠒⠁⠀⠀⠀⢸⠀⠀⡟⢘⢀⠓⠇⠓⣺⠈⠙⠀⠀⠱⠌⡪⣑⠠⠍
⠀⠀⠀⡀⠔⠁⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠄⡀⢀⠔⠁⠾⠵⡆⠀⠘⢄⢸⡉⠓⡗⠒⠓⠈⢉⣁⡽⠀⠀⠀⠀⠀⠀⠂⠛⠉
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠼⡁⠀⠀⠀⠀⡇⠀⠀⠀⠑⠌⠙⠓⠖⠉⢩⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⣁⣀⠠⢤⠄⠴⠳⡀⠀⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠄⡀⠀⠀⠀⠼⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣎⠡⠈⢆⠈⢆⠘⡄⢣⠀⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠁⠀⠒⠠⠄⡀⠀⢀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢇⠈⡆⢣⠈⡄⠈⡄⠘⡄⢳⡦⢠⣇⣀⡈⠐⠒⠒⠒⠀⠂⠀⢸⡀⡀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠁⠒⠂⠄⢀⠀⠀⠀⠀⠀⠀⠈⡎⢂⠘⡀⡟⡽⢳⠸⡀⢐⣀⡟⠥⣀⡀⠭⠶⡄⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠀⠀⠀⠘⣌⡦⠵⡇⡇⢸⢎⠉⣙⣢⠗⢌⣹⣂⡈⠤⠛⣢⣄⣰⠷⣤⡼⡆⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡯⡑⠢⢕⡓⠚⠀⢁⣀⠠⠤⠔⠐⠒⠂⠉⠁⠀⠀⢸⠀⢸⠀⡇⢀⣀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⢸⢓⠢⣉⠲⢄⡀⠀⠀⡇⢸⠀⠀⠈⡟⠫⣀⡠⠤⢴⡒⣎⡻⢭⣔⠓⢤⣀⣈⠱⠶⠀⡚⣧⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢢⣀⠉⠒⢌⡑⢤⣇⣸⣀⠀⣤⠧⢤⣼⠈⡟⢽⠿⠘⠛⠊⠉⠉⠀⡇⠀⠀⠀⠐⠀⡷⢌⠳⢄⠀⠀⠀⠂⠄⠒⠠⠠
⠀⠀⠀⣠⡰⡖⠊⠒⢼⠸⠉⠢⣤⣹⣀⣇⣨⢹⣀⣈⡅⠀⣹⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡇⣠⠒⡄⠐⠈⡷⣀⠑⢄⠑⢦⡀
⠀⠀⢰⡟⣇⣹⠀⠀⠀⡇⠀⠀⠆⢋⠇⠘⡌⢏⢇⠀⢫⣉⣹⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡏⠇⢃⠱⣀⣀⠟⠉⢗⢤⡙⠦⡈⠢⣄
⠀⠀⠀⡟⡋⣭⡇⠀⠀⢰⠀⢀⣀⣨⠼⢄⠱⠘⡌⡄⠀⢆⡉⡲⢇⣸⢀⣀⠠⠤⠀⠒⠒⠃⠹⡈⡆⢳⣹⡆⠀⠈⡄⠉⡒⠘⡶⠚⡇
⠀⠀⠘⢿⠙⣤⠇⢠⣾⢫⠉⠁⠈⢆⠀⠀⠱⣇⠱⡘⡀⠈⡄⠀⠀⠈⠀⠀⠤⠤⠀⠄⠄⣀⡀⢣⠹⡈⣷⡇⠀⠀⣇⣀⡦⠄⣿⣀⠟⠒⠢
⠀⠀⠀⠈⠂⠛⠒⡏⢹⢐⡵⠀⠀⠈⡆⠀⠀⠟⡀⢣⣱⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢣⠸⡇⡀⢴⡻⠊⢆⠀⠀⠈⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡏⢋⢩⣕⠀⠀⠀⡇⠀⠀⡛⠁⠈⠉⡇⠀⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠦⢧⠀⠔⣧⠧⠞⡆⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠈⠀⠁⠢⠞⡋⢣⡌⠀⠀⢀⠇⠀⡠⣗⠲⡉⠙⠓⢒⠁⠀⠐⠂⠐⠂⠐⠒⠒⠄⠂⠀⠀⠀⢡⠀⢈⡦⣤⣢⢤⠓⡁⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠪⠖⠐⠒⠈⠉⠁⡑⢁⢈⡆⠀⠀⠀⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⢖⡈⢯⡩⠀⠀⠉⣲⣷⠃⢀⣀⡮⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⣋⡸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡉⠲⠔⠒⠈⣁⡠⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡀⠀⠀⠀⢳⠛⣄⠍⠀⠀⢀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠉⠉⠀⠀⠐⠂⠄⠒⠀⠂⠤⠤
⠀⠀⢀⠠⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡢⣩⣀⠠⠤⠚⠒⠈⠁⠀⠀⠀⠀⠀⠈⠀⠉⠀⠉⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⠀⠐

⠀⠀⠀⠀⠀⠀⣀⠀⠛⠀⠀⠻⠀⣤⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⢀⠘⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠈⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣾⡆
⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣟⣻⣿⡑⠂⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠋⠀⠀⠀⠀⣀⠀⠀⠀⡀⢀⢀⣿⠿⠗⠀⠀⠀⠀⢠⣄⣤⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣍⣬⣴⠿⡀
⠀⠀⠀⠀⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠋⡤⠀⠀⠙⠉⠺⠿⣶⡄⠀⢠⢂⣴⠿⠟⠿⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣽⠃⠂
⠀⠀⠀⠀⠿⠀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢱⣿⣿⢶⡶⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠶⠀⠀⠀⠀⠀⠐⣞⠃⢈⠂⠁⢄⠀⠀⠀⠀⣼⠶⠘⠿⢷⣆⣤
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠀⠀⠀⠠⠄⡸⠖⠀⣠⠀⠀⠀⠀⠈⣯⠀⢸⡀⠀⠀⣄⠀⠀⠀⢸⠁⠀⢰⠈⠏
⠀⠀⠀⠄⠐⠎⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠙⣶⡔⣿⠀⠀⠀⠀⠛⡔⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⡤⠀⠁⠀⠀⣦⠀⠀⠀⠀⠀⠐⠻⠟⠃
⠀⠀⠀⠀⠀⠀⡀⠐⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠘⠀⡄⠀⣠⠀⢀
⠀⠀⠀⢠⠆⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⣦⣼⡇⠀⠀⠀⠀⡐
⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⣞⡉⡿⢿⣦⡠⠞⠃
⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠑⠲⡀⠀⠀⠀⠈⠋⠀⠀⢼⢿⣿⣷⢾⠆⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⣀⡖⣀⠀⠀⠀⠛⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⢯⣿⣽⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠛⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣦⠀⠀⠈⠀⢀⠀⠀⣤⠟
⠀⠴⠂⠀⠀⠈⠙⡆⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⡆⠀⠈⠀⠀⠲⣟⢷⣤⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠁⠀⠀⠀⡘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄⠀⠀⠀⠀⠈⠉⠈⠂
⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⣦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠀⡌⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢰⠉⠢⠀⠀⠀⠀⣀⠀⠀⠀⠃⢈⣹⣿⣿⣿⣋⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⢀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡋⡵⡆⠀⠀⠈⠟⠹⣿⡟⠋⠀⠀⠐⠁⠀⢀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⢀⠀⢸⣴⠃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⠳⠖⠀⠀⠀⠞⠀⠀⠀⠐⠀⠀⠀⢀⡀⠠⢴⣮⣿⣿⣿⣆⠀⠠⠄⠀⠸⡄⠀⠃⣾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠘⠟⠻⠻⠟⠁⠢⠄⠀⠀⠀⠁⠀⢀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⣵⡆⠁⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠒⠀⠀⠠⣀⡍⠀⠀⠠⠀⠀⡆⠀⠀⡀⠀⣼⡥⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢁⣠⠶⢚⣿⠏⠀⠀⠀⠀⠀⡆⠀⢀⡴⠀⠀⠀⠿⠀⠀⠀⠀⠀⢰⠇⠠⠎⠀⠀⠙⠁⠠⣤⠟⠏
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣀⡶⠋⣠⠴⠋⠁⠀⠀⠀⠀⠀⠄⢿⣿⣾⡄⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⠀⣰⣿⣖⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠉⠀⠒⠛⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⢠⣿⣀⣤⠶⠶⠶⠛⠋⠉⠉⠀⠉⠉⠳⣤⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⢿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣦⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⡿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡀⢀⣠⣴⣶⣿⣿⣿⡿⣿⣷⣶⣤⣙⠿⢋⣴⣶⡝⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢋⣴⣿⠿⣋⣭⣶⣶⡆⣶⣶⣦⣍⡛⢿⣷⣌⠻⣫⣾⣿⡟⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡙⢿⣷⡙⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣼⣿⣿⣿⣿⣿⣿⡏⣿⣿⡿⣫⣾⣿⣿⡎⢿⣷⡸⣿⣷⡀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⡇⠿⣫⣾⣿⣿⣿⣿⣿⠸⣿⡇⣿⣿⣿⣷⣶⣶⣿⣿⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢨⣭⣽⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣯⣭⠀⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⡟⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣌⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢛⣴⣿⠟⣴⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣭⣛⣛⣃⣛⣛⣫⣥⣶⣿⠟⣣⣾⣿⡿⠿⠿⣛⣫⣵⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠛⠉⠀⠘⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣭⣭⣭⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠒⠀⢐⠒⠒⠂⠀⠀⠀⣿⣿⡿⠣⠖⠂⠀⠀⠀⠤⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣽⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠠⠄⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⡽⠿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⡀⣠⡀
⠀⣴⣶⣾⣿⣿⣶⣤⠀⠀⡠⠀⣽⡄⠀⠐⠟⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⡿⠿⠋⠀⠄⠀⠀⣀⣀⣤⣤⣤⣤⣀
⣸⡟⣿⣿⣿⣿⣿⣿⣆⠀⠁⢠⣤⣴⣶⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠈⢻⣿⣿⣿⣿⡧⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣧
⣹⣠⣾⣿⣿⣿⣿⣿⣿⠰⡇⣾⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⡗⠀⠈⢹⣿⣿⣿⣿⡿⠀⠀⠀⣠⣤⡍⠀⠈⢻⣿⣿⣿⣿⣿
⣹⠈⢻⣿⣿⣿⣿⣿⣿⠀⢻⠃⢀⣿⣿⣿⣿⣿⣿⣿⣧⢘⣦⠀⠀⠀⠀⠈⢰⣦⣰⣿⣿⣿⣿⣿⠗⠀⠀⠸⣿⣿⣿⠀⠒⢸⣿⣿⣿⣿⣿
⠨⣷⣿⣿⣿⣿⣿⣿⡏⠀⠸⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠙⠻⣧⡀⠠⣸⣿⣿⣿⣿⣿
⠀⠙⠛⠻⠿⠛⠛⠉⠀⠀⠸⣆⠀⣹⣿⣿⣿⣿⣿⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⣀⣀⢀⠀⡀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠰⡄⠇⡰⢄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡿⠁⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠊⠀⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠂⠀⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠠⡀⡆⢠⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠈⠀⠘⡶⠁⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠇⡠⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡀⡇⢠⡀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢰⠂⠐⠂⠁⠬⠐⠀⠁⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⠂⠀⠱⣶⠃⠈⠂⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠂⠀⠀⡨⠠⠞⠀⠆⠇⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠦⠀⠅⠀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠈⡌⡔⠀⡤⠤⠤⢤⣀⠀⠀⠈⠀⢳⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣃⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠭⠭⣙⣒⠀⠸⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠭⢝⣒⣂⠀⠰⠿⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣊⣩⣍⣙⣓⣒⠦⠥⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣛⣛⣒⣒⣒⠭⠭⣓⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣒⣒⣒⣒⣒⡦⠭⢭⣒⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠙⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⣉⣀⣉⣉⣉⣉⣓⣒⣤⣼⣤⣤⣐⣀⣀⣀⣀⣀⣀⣀⣈⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣤⡄⣀⣀⠀⣤⠀⣠⡄⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠻⠆⣯⡅⢿⡼⠃⣿⠸⢧⡄⡾⠿⠼⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⢀⣠⡀⣀⣀⢀⡀⣀⢀⣠⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠇⡗⢯⠸⣔⡶⢸⣏⠸⠟⠿⠸⣄⠄⢹⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⡤⡤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣰⠒⣆⢸⢰⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠹⠤⢸⠯⠭⠭⠭⠭⢿⠭⡿⢿⢸⠉⠉⢹⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠁⠀⠀⠸⣶⡦⣏⣳⠤⠬⠥⠯⠼⠤⣎⣳⡺⠁⠀⠈⠓⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⢬⢧⡤⣤⣤⣤⣤⡤⡬⣄⠀⠀⠀⠀⣀⣤⣬⣀⠀⠀⢀⣠⣼⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⢸⠀⠀⢀⢞⠕⠋⠉⠲⣕⢖⡵⠊⠉⠓⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⡤⣄⠀⠭⣒⢤⠀⢸⢸⠀⠀⢸⢼⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣎⠀⣼⠁⠙⡎⣇⢧⢸⢸⠀⠀⠘⣾⢶⣦⠴⠭⠭⠭⠭⠷⢤⣶⢮⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠈⢦⡈⠳⣄⠤⣄⠀⢸⢸⠀⠀⠀⡇⠀⣀⣤⣀⠀⠶⠲⠶⠶⠶⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠙⠦⣄⡠⠞⠀⢸⢸⠀⠀⠀⡇⢸⣏⡀⣹⡇⠀⠤⠿⠤⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⢸⠙⢦⡤⡇⠀⠉⠛⠉⠀⠀⠩⠥⠍⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠀⠀⠀⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠤⢮⡁⠀⠈⠡⡍⠁⠉⢩⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠀⠠⢸⠗⡞⠉⠐⠲⣤⣜⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠒⣁⠀⣣⣀⣈⡰⠃⢏⡠⠔⣛⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠑⠬⣋⡀⠀⠀⣀⣀⠤⠴⠨⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡿⡕⠢⢀⠀⡀⠆⠀⠛⠋⠟⡡⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⢤⠄⠀⠈⠀⣸⠐⠀⠀⠁⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡗⠠⠀⠠⢰⠇⠀⠀⠧⠘⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠊⠀⠀⠀⢀⠌⠀⠀⠀⡰⠊⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⠀⢰⡊⠁⠢⡀⡠⠊⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠈⠙⡦⠤⢒⠁⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⢤⠒⠈⠠⠀⠔⠀⠀⠈⡂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠒⠠⠄⡼⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠣⣀⠀⠀⢀⡗⠂⠤⠀⣀⠀⠀⠈⠆⠠⠂⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂⠀⠁⠀⠀⢠⠈⠉⠈⠣⣀⡀⠀⠀⣀⡩⠟⠀⡆⠀⠀⠀⢠⠀⠌⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠄⠊⡐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣉⣀⣈⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠹⣿⡿⢀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣻⣿⣿⣿⣿⠟⠋⠉⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⠋⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡟⢢⠤⠤⠒⠒⢲⢉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⡜⡥⢱⡀⡈⡭⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⣇⣇⢸⠐⢌⡍⣑⣃⡁⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⢻⠀⠀⠀⠀⠀⣇⡉⢹⠋⠉⣉⣀⣠⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠤⠤⡀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠙⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⣉⣀⣠⢤⡤⠴⡶⢳⠀⠀⡟⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡜⠹⡀⢣⠀⠱⡀⠹⡄⢳⠀⣟⢒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⡎⠘⡄⢳⠈⢇⠀⢳⠀⢱⡀⢣⣇⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡄⠹⡀⢧⣼⣢⡄⢧⠀⢳⠈⣧⣔⠋⠉⠑⠢⣤⡀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⡀⢳⣸⢸⠁⣤⠼⠧⠶⡓⢿⠐⢭⣖⠨⠭⠑⣧⡀⠀⠀⣠⡇⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣟⡉⢹⣸⡀⡟⠲⠤⠤⠚⠃⠉⠒⠧⣐⣒⡨⠥⠼⠓⠢⡏⠙⡿⠋⡗
⠀⠀⠀⠀⠀⠀⣠⡴⠦⣄⡀⠀⠀⠀⠀⠀⡗⢦⠉⠓⠭⣉⣀⣤⠤⠴⠖⠒⠚⠉⣉⣀⣠⢤⡀⠀⠀⠀⣇⠀⡇⠀⣇
⠀⠀⠀⠀⠀⠀⣿⢫⠑⠦⣉⠓⢤⡀⠀⠀⡇⢰⠀⠀⠀⢸⠉⠲⣤⡤⠐⢒⣌⡹⣭⡝⢶⣊⢉⣳⣤⠤⠤⠙⠛⡀⢉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⣿⠀⢱⣄⡀⠙⠢⣌⣑⣤⡧⢸⣄⡤⠤⡼⣀⣦⣿⠈⡟⢫⠟⠓⠛⠛⠉⠁⠀⠀⢸⠀⠀⠀⠀⢑⡈⢺⢤⡙⠦⡀
⠀⠀⢀⣤⣶⡒⠛⠢⢼⡤⠟⠓⣤⡎⣁⢀⣇⣸⢉⡀⠀⣸⠀⠀⣿⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⢢⡀⠳⠌⢿⣄⠙⢦⡈⠳⢄
⠀⠀⢾⠻⡈⣷⡀⠀⠀⢧⠀⠀⢸⠈⡟⡏⠙⡌⢿⢻⠉⠘⣖⠊⣿⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢊⠹⡀⢧⠀⢀⡻⠚⢷⢤⡈⠲⣄⠙⢦⡀
⠀⠀⣿⠶⢳⣻⡆⠀⠀⢸⠀⠀⠈⠀⢱⢹⡀⢱⠘⡎⢧⠀⠸⡉⠻⢤⡇⢸⠀⠀⠀⠀⢀⣀⣀⠤⠼⠘⡆⢳⠘⣏⢻⡅⠀⠈⡆⠉⢲⠬⢷⣤⠬⢶
⠀⠀⢻⡾⢾⢹⠆⢀⣠⣼⠶⠒⠚⢻⠉⠉⠉⢢⣇⠸⡌⡆⠀⢳⡀⠀⠈⠛⠓⠚⠉⠉⠀⠀⠀⠀⠀⠀⠸⡈⣇⠹⣿⣷⠀⠀⢸⠀⢸⡀⠀⢸⠀⢸⣤⣄
⠀⠀⠘⢧⣘⣿⢃⣾⢿⠙⣇⠀⠀⠀⢳⠀⠀⠀⣻⡄⢳⠘⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⡄⢻⡟⠀⠀⣼⣖⣾⡉⠉⠛⠺⡋⠀⠀⠡⡀
⠀⠀⠀⠀⠉⠁⢨⢿⣼⢦⠞⡄⠀⠀⠘⡇⠀⠀⢸⡱⠀⢧⢼⠔⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢳⠈⠧⠐⢺⣻⢻⠈⢷⠀⠀⠀⢳⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣠⣰⠶⡇⠀⠀⠀⡇⠀⠀⠸⠀⢀⣸⣰⠀⠀⡧⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⠋⠻⡄⢸⡷⡞⠲⡋⡆⠀⠀⠘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡅⠹⣾⠃⠀⠀⣸⣃⣀⣠⣯⠝⣇⠀⠙⠋⢫⠁⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⡷⠼⣬⡴⣼⢛⡇⠀⠀⢰⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠿⠒⠒⠋⠉⠉⠀⢧⢉⡆⣏⡆⠀⠀⠈⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣌⠙⢭⣥⠇⠀⠀⢑⣾⣿⠁⢀⣀⣼⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠚⢙⣩⠃⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠙⢢⠴⠒⠒⠉⣁⣠⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠞⢎⠙⡄⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣆⡸⠧⠁⢀⣀⣼⠥⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠘⣿⡟⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⣿⡇⠀⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⠈⠻⠃⠀⠀⠈⠀⠀⠀⠻⠋⠀⠀⠀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣷⡄⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⣴⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⡟⠉⣠⣤⣴⣶⣶⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⡄⠀⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣤⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣛⣉⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⣉⣛⣛⣋⣙⣉⣙⣙⣉⣉⣛⣙⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⡀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠤⢆⡉⠉⠁⠩⡉⠈⠈⢉⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠠⢈⠗⡖⠃⠒⠲⣤⣌⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠒⡁⠀⣣⣀⣈⡠⠃⢍⡠⠔⣛⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠆⠀⠀⠈⠑⠬⣋⡀⠀⠀⣀⣀⠠⠴⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿⡑⠦⢀⠀⠀⠆⠀⠛⠀⠟⣡⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⢤⠄⠀⠈⠀⢸⠠⠀⠀⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡖⠀⠀⠠⢠⠆⠀⠀⠇⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠀⠀⠐⠄⠀⠀⠀⡠⠊⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⢠⡊⠁⠢⡀⢀⠌⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠆⠈⠘⡤⠤⠔⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢀⠀⠐⠀⠠⠤⠄⢤⠐⠊⠠⠀⠐⠀⠀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠒⠠⠄⡼⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⡗⠠⠄⣀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠈⠣⣀⠀⠀⠀⢁⡁⠟⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠤⠀⠠⠊⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣿⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡦⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡚⠐⠀⠐⠐⠓⣄⠀⠀⠀⠀⠀⣀⠀⠀⠠⠒⡄⠀⠀⠀⠀⠀⠀⠀⢿⠢⣀⣤
⠀⠀⠀⠀⠀⠀⠼⢰⣾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠈⣑⡂⠉⣉⠁⢰⠀⠀⠀⠀⠀⡛⠁⠲⣆⣀⢴⠄⣶⡄⠀⠀⢀⠴⠚⢿⡉⠁
⠀⠀⠀⠀⠀⠀⢷⠎⠑⠀⠁⠀⠀⢰⣶⡦⢀⠀⠀⠀⠀⠀⠀⠘⡤⠠⠄⣀⣀⠀⠠⡼⠀⠀⠀⠀⠀⡸⠶⡚⣴⡎⣲⣠⠊⠀⠀⠀⢸⣌⡒⣼⠇
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠇⢀⠀⠀⠀⢇⠰⣶⠉⠢⣀⠀⣀⠀⠀⠈⠲⢔⡀⠀⡠⠎⠀⠀⠀⠀⠀⠸⣀⣀⡯⠶⢴⡃⠈⢂⠀⢠⡖⠛⢿⡉⠁
⠀⠀⠀⢩⠙⡁⠀⠀⡘⢀⠆⠀⠀⠀⠈⢢⠀⠀⠀⠈⢦⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⠎⠈⠁⠁⠀⠀⠉⠊⠲⠇
⠀⠀⠀⠀⢢⣤⣷⣷⣴⡅⠀⠀⠀⠀⠀⠀⠟⢤⣀⣠⡾⠗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡄⠘⠛⠉⠉⠉⣁⣰⠀⠀⠀⠀⠀⢃⡆⠈⠫⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠘
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠢⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠐⠒⠒⠠⡀⠐⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡲⠶⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡲⠁⠀⠠⢀⠈⢻⢆⠀⠀⠀⠀⠀⠀⠀⡇⠒⠀⡏⠀⠀⠀⠀⠀⠂⠃⠀⣀⣠⢠⠀⠀⡆⡀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⡔⠁⠔
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠰⠁⠀⢀⠻⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡇⠀⠀⠀⠀⠀⠀⠘⠄⢸⠁⠁⠀⡔⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⣀⠀⣀⣠⠺⠁⠀⠀⠀⠀⠀⠀⠠⣀⣤⣤⡰⡀⠀⠀⠀⠀⠐⠁⢀⠈⠀⠐⢰⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⠉⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⡠⢉⠏⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣿⣿⣿⣷⡑⡀⠀⠀⠀⠀⠀⠘⠁⢀⡀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡜⢠⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡐⡀⠀⠀⠀⠀⠈⠓⠂⠀⠊
⠀⠀⠀⠀⠀⠸⣀⠏⠀⠀⠀⣄⣂⡡⠔⢇⠀⠀⠀⠠⣛⠛⣛⢛⠛⣻⡛⢛⠓⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠔⠉⠀⠶⠁⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠈⠱⠄⠀⠸⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸⣄⡀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠒⠀⠋⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠛⠓⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⠀⠛⢟⠻⠋⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚
⠀⠀⠀⠀⠀⠐⡎⠉⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣤⣾⡍⠉⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄
⠀⠀⠀⠀⢀⠄⠁⠀⠈⠚⡝⠁⠀⠀⠀⠀⠀⡜⠀⠈⢻⣿⠁⢀⣀⡀⢁⠀⠀⠀⠀⠠⣂⣽⠩⠽⠀⠸⡀⠀⠀⠀⠀⠅⢬⡑⢄⠀⠀⢀⠔⢊⡥⠂⢀⠄
⠀⠀⠀⢠⢁⡀⠄⠀⠤⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠿⣿⣿⡇⠘⠀⠀⠀⠀⠀⢹⠀⢡⠀⠒⠀⢡⠀⠀⠀⠀⠐⢌⠁⠾⣀⠠⢣⡟⠀⢀⠤⠊
⠀⠀⠀⠀⢆⠢⠀⣀⡀⠔⠜⠀⠀⠀⠀⠀⠀⠄⠻⣿⡿⠁⠀⠀⠉⢡⠃⠀⠀⠀⠀⠀⠀⢂⠀⢃⠰⣷⠄⠆⠀⠀⠀⠀⠀⠁⠀⠙⡷⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠁⠂⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠁⡀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘⡶⠿⡀⢀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣀⣆⣈⣿⣿⣿⣿⣿⣖⡀⠀⠀⠀⠀⡠⠚⢹⣿⣿⣿⣿⣿⣥⣬⠤⡄⠀⠀⢀⣔⣀⣽⣍⡀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣿⣿⣯⡭⠍⠩⠈⠁
⠀⠀⢿⢿⣿⣿⣿⣿⡿⣿⠿⠿⠛⠀⠀⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⠷⠖⠲⠀⠀⠾⡿⣿⣿⣿⣿⣭⣁⠚⠁⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠑⠊⠉⠉⠉⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠠⠀⢤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣿⠂
⠀⠀⠀⣀⣜⢂⣀⣏⣀⣹⡄⠀⠀⠀⠀⠒⢶⣶⣶⣶⣶⣶⣶⢰⣶⡒⠂⠀⠀⠀⠀⣀⣀⣾⣷⣤⡀⠈⣧⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣯⡝⢦⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠏⠀⠀⠒⠀⠾⠿⣿⣿⣿⣿⣿⣁⣠⣿⣷⣆⠀⠉⠉⢽⢿⡾⢿⣿⣿⣼⣁⣾⡷⢦
⠀⠀⠈⠛⠾⠋⠉⠉⠙⠷⠟⠁⠀⠀⠙⠼⠋⠉⠉⠉⠙⠧⠋⠈⠁⠀⠀⠀⠀⠀⠀⠿⠦⠟⠛⠉⠉⠉⠀⠧⠞⠀⠀⠀⠀⠁⠑⠚⠉⠉⠉⠉⠈⠓⠋

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣦⣤⣤⣤⣄⡀
⠀⠀⣐⣉⢹⣧⣿⠛⣷⠶⣤⣤⢀⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡂⠀⠠⠤⣤⣬⣭⣿⣿⣿⣿⠛⠛⣿⣷⠄
⠀⢰⣿⣿⣿⡹⣿⡛⢻⣦⣠⣷⠴⠛⢋⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⡅⢀⣀⢂⣰⣶⣿⣾⣿⣿⡟⠂⢀⣿⣄⡀⠐⠶⠾⠿⢿⣿⣿⣿⣶⣾⣿⡟
⠀⠈⠻⣉⡟⠃⠛⠛⠉⠁⠸⣉⡗⠀⠀⠠⠴⢾⣿⣟⣻⠛⠛⣟⣻⠃⠀⠀⠀⠀⢩⣿⣛⣿⠿⠿⠶⠟⢹⣛⡧⠀⠀⠀⠀⠀⠙⠿⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡀⢀⣄⡀⠀⠀⠀⡠⠀⢄
⠀⠀⣀⣀⣀⣠⡞⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡄⣶⠖⠀⠀⢠⣘⣿⣿⣿⣿⣿⣷⣿⣿⣿⠂⠀⣾⣶⣶⣶⣧⢀⣀⡀
⠐⣒⡿⢿⣿⣿⠀⠐⠆⠀⣿⣶⣶⠄⠀⠀⣀⣠⣴⣾⣿⣯⡤⣯⣤⠟⠁⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⢸⣉⣹⣄⣀
⠀⠀⠀⠀⠛⣹⣦⣄⣀⣴⣿⡿⠏⢀⡀⠬⢷⡾⣿⣿⣿⣿⣤⠟⠁⠀⠀⠒⠚⠛⠻⣿⣿⣿⡿⠿⣿⣿⣿⡿⠀⠀⣰⠿⣿⡿⢿⣿⣾⣿⣿⣿⢿⡿
⠀⠀⠀⠀⠀⠧⠊⠈⠉⠸⠤⠁⠀⠈⠀⠁⠐⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠤⠶⠛⠛⠋⠁⠀⠀⠘⠒⠉⠓⠋⠀⠀⠀⠀⠙⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣿⣵⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣾⣿⣿⣽⣿⣷⣾⣿

⠀⠀⠰⣿⣦⣤⣤⣀⣀⣀⡀⣠⣴⣿⣧
⠀⠀⠀⢸⣟⢷⣄⠉⠉⣩⡿⣻⡿⠁⠸⣇
⠀⠀⠀⠀⣿⡀⠙⢷⣾⣋⡾⠋⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣇⣴⢟⣽⠟⠁⠀⠀⠀⢰⡟
⠀⠀⠀⠀⣰⣿⣵⠟⠁⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢼⣿⡛⠁⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⣷
⠀⠀⠀⠀⠉⠛⠻⠶⠾⠻⣿⠉⠀⣿⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡆⠀⠀⠀⠀⣼⣿⠟⠷⣦⣄⣿⡀
⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢷⡀⠉⠉⠀⠀⠀⠉⠻⣟⠛⠛⠛⠛⠻⠶⣦⣄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠙⠻⣆
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣴⠶⠶⠶⢶⣤⡀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠇⠀⠀⠀⠀⣠⣴⠶⠶⠶⢶⣤⡀⠀⠹⣦⡀
⠀⣀⣤⣼⣧⣤⣤⣤⡾⠉⢀⣀⣤⣄⡀⠈⠻⣦⣤⣤⣴⣿⣤⣤⣼⣯⣤⣤⣤⣤⡾⠋⠀⣀⣤⣄⣀⠈⠹⣧⣤⣬⣿⣦⣤⣄⡀
⣼⠏⠁⠀⠀⠀⢠⡿⠀⢠⡿⠉⠀⠉⠻⣆⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⡾⠋⠁⠈⠙⣧⠀⠸⣧⠀⠀⠀⠀⠉⢿
⣿⡀⠀⠀⠀⠀⢸⣇⠀⢸⣇⠀⠀⠀⢀⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧⠀⠀⠀⢀⣿⠀⢀⣿⠀⠀⠀⠀⠀⣸
⠈⠻⢦⣤⣤⣤⣤⣿⣄⠀⠙⠷⢶⠶⠟⠁⢀⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣆⠀⠙⠷⠶⠶⠟⠁⢀⣼⣧⣤⣤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⣀⣠⣴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠢⢈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠛⢄⠀⠀⠈⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⢴⡁⠀⠀⠀⠈⢺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠑⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠤⠄⠠⠄⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠁⡠⠐⠢⡀⠙⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢃⠀⢠⡀⣀⠄⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠢⢀⣈⣁⡠⠊⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⠐⠠⣤⠀⠀⠤⠔⠚⠣⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡃⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣙⠳⣤⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠄⠤⠄⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣭⠆⠀⠈⢩⠋⠝⣋⡛⢍⢫⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⢁⢠⠸⡘⢅⠸⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⢀⠔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡜⢠⣤⡄⠊⠀⡈⢆⠢⢍⣒⣒⡡⠊⠳⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢄⠁
⠀⠀⠀⠀⠀⠀⡜⠠⠁⠀⠀⢀⠀⠘⡌⢆⠀⠀⠉⠢⡀⠀⠈⠢⡀⠀⢀⠊⠀⠀⠀⢠⠊⠉⠑⡄⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡼⠠⠁⠀⠀⠀⠑⠃⠀⠘⡌⢆⠀⠀⠀⠈⠦⡀⠀⠈⢦⡌⠀⠀⠀⠀⠐⢄⣀⡠⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⡰⢡⠃⠀⢠⡆⠀⠀⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠈⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⡰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣦⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⣀⡀⠀⢤⣄⣀⡠⠤⠿⠐⠒⠺⠄
⠀⠀⡰⢁⠂⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⠀⠀⠱⡘⣄⠀⣀⣀⡀⠤⢤⣗⠒⠦⠭⠙⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢰⢃⠂⠀⢠⢢⠀⠀⠀⠀⠈⠛⠁⠀⡠⠠⡀⠱⡘⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⢠⢃⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠁⠀⠡⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⣣⣤⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣍⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠆⡄
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠙⠣⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣦⠀⠀⠀⠀⠀⢀⠀⢄⠁⠂⢀⡜⠀⠠
⠀⠀⠀⠐⢄⡀⠀⠀⠸⠒⠂⠀⠀⠀⠀⣤⡄⠀⠀⠀⠰⠀⡑⠒⠂⠉⠒⠀⠀⠠⣀⠀⢠⠛⠣⠐⠠
⠀⠀⠀⠀⠀⠈⠒⠄⠄⢁⠄⠠⠀⠏⠀⠣⠤⠤⠤⠤⠧⣤⡹⠞⠭⠉⣁⢀⠀⠀⣀⣶⠃⡄⠨⠀⣈⣁⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠐⢐⠄⠀⠀⠀⢀⡦⠐⣑⠄⠀⠀⡴⠋⢀⡎⠀⠀⠀⢂⠀⠀⠔⠋⠛⠁⢁⠀⠹⢉⠁
⠀⠀⠀⠀⠀⡀⠀⠰⣚⡀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠘⠡⣤⠀⢀⢀⢀⠀⠄⣠⠀⡀⠠⠶⠚⠃⠀⠀⠈
⠀⠀⠚⠉⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⢀⠀⠁⠄⠀⠒⠊⠃⢠⠈⠓⠂⠀⠐⠀⠈⠒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠘⠒⠁⠀⠈⠛⠐⠃
⠀⠀⠀⡔⢙⢿⠗⡒⣶⢆⣤⣰⡀⠀⠉⠀⠵⠀⠀⠀⠒⠐⠂⠐⡚⠀⠘⠦⡤⠀⢀⣀⣀⡀
⠀⠀⠀⡷⣿⣾⣴⣷⢼⠃⣀⠹⡍⡞⠊⠻⡝⢄⢲⢨⠄⡄⠀⠠⣴⣶⠀⢤⠘⠰⢋⠁⠈⢧
⠀⠀⠀⠱⣘⣼⡍⠛⢹⢾⣿⡇⣿⢁⣤⢄⢹⡈⡄⠄⠀⠈⠪⠤⠈⠓⣔⣀⣌⢶⠐⠀⠠⣼
⠀⠀⠀⠀⠀⠀⠈⠒⠛⢇⠀⢠⣿⡟⠿⠴⢺⠥⡔⡂⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠓⠷⠶⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⡀⢀⣜⣰⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠀⠀⠀⢀⣠⡤⠖⠚⠛⠉⠉⠙⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⣀⣠⡤⠤⡤⠤⣤⣀⡀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡼⠁⠀⢀⡴⠛⠉⠀⠀⠀⡇⠀⠀⠈⠙⠳⣄⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⢠⠟⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⣧
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡞⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⠀⠀⠀⠹⡆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣤⠧⣴⠋⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣅⢀⡽⠒⠒⠒⠒⠒⠒⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠸⡇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⣠⠤⠶⠶⡶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢳⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰
⢠⠏⠁⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠋
⡏⠀⠀⡄⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠙⠲⢤⣀⣀⡀⠀⣀⣀⣠⠴⠚⠁⠀⣠⠞⠁
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠛⠦⣄⡀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⡤⠞⠁
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠶⠖⠚⠋⠁⠀⠀⠀⢠
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⡴⠃⠀⠀⣠⣄⠀⣏⠀⠀⢹⠀⣠⣄⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⣰⠃⠈⠙⠃⠀⠀⠘⠋⠁⠘⣆⠀⠀⠘⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⣀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⣤⠖⠋⠀⠀⠀⢿⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⣶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠘⣆⠀⠀⠘⣦⣠⠶⡇⠀⠀⣸⠶⣄⣴⠃⠀⠀⣰⠃⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠘⢦⠀⠀⠈⠀⠀⣧⣤⣤⣼⠀⠀⠁⠀⠀⣰⠃⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸
⠻⡄⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⢠
⠀⠙⠲⣤⣤⣤⣧⣄⣀⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣀⣄⣼⣤⣤⣤⠖⠋
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠠⣦⣋⣀⡙⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠰⠆⠀⡔⠁
⠀⠀⠀⢀⡴⠁⢫⣿⣽⠉⢦⠀⠀⠀⠀⠀⠀⢦⣴⡿⠂⠀⠀⠀⠀⠀⠛⠛⢿⣿⣏⣽⣿⡄⠀⠀⠀⠐⠀⡀⢀⣾⣿⣧⠁⢀⡄⠂
⠀⠀⢀⡞⣠⡔⠈⠻⠉⠢⣌⢳⡀⠀⠀⢠⣀⣾⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠈⠠⡁
⠀⠀⠀⠉⠉⠉⠙⠛⠒⠚⠛⠚⠃⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⡿⠂⠀⠀⠀⠰⠄⠋⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣤⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣤⣤⣄⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠄⠂⢀⠐⠣⣀⡀⠀⠶⠀⠀⠀⢠⠁⠀⢻⣿⠇⠀⠱⡀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠠⣀⠀⡸⢄⢀⠜⠂⣆⣤⠀⠀⠀⢀⣴⣶⡦⠷⣴⣶⣦⠀⠀⠀⠀⠀⠀⢺⣝
⠀⠀⠀⠀⠀⠻⠿⠿⡿⠿⠿⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⢸⡋⠀⠀⠈⠻⡋⠀⠀⠀⠀⠀⣤⣾⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠉⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⣆⠀⡅⠀⠄⡀⠀⠀⠀⠀⣀⡙⢠⣤⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢲⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇⠀⠀⠀⠀⠛⠣⡀⠀⡶⠀⠶⠀⠀⠀⠀⠀⠀⠀⡼⠿⠿⡄⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠰⠳⠄⠃⠀⢰⡆⠀⠀⠀⠀⢀⣀⠼⠿⠀⠐⢷⠀⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣀⠀⠀⢀⡇⠀⠈⠁⠀⠀⠀⠀⠘⠋⠀⢸⡆⠀⠀⠗⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠛⠛⢻⡀
⠀⠀⠐⠿⠿⠶⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⢰⣶⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⡀⠀⠀⠀⠀⢀⣠⠤⠶⠤⣤⡀
⠀⠀⠀⠛⢛⡿⠛⣷⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣄⢀⣤⣄⢠⣤⠀⠀⠀⠀⠀⣀⣨⠟⠛⢿⣷⠀⠀⠀⠀⢊⣾⡡⠄⢀⣴⡙⡀
⠀⠀⠀⠀⠾⣥⣴⣧⣤⣤⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣾⣇⣠⣼⡿⠀⠀⠀⠸⢏⠉⠙⣀⠋⠁⠉⠇
⠀⠀⠀⠀⠀⠰⣟⣁⣁⣨⣇⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠈⠈⠐⢿⣿⡿⠛⠁⠀⠀⠀⠀⢂⢠⣀⣿⣀⡴⡠⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠩⠟⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠈⠙⠂⠘⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠀⠀⣀⣠⣤⣤⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⣉⠉⠉⠉⢁⣴⠾⠋⣉⣤⣤⣤⣤⣤⣉⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣉⡀⠀⣰⡟⢁⣴⠿⠋⠉⠀⣿⠀⠉⠙⠻⣦⡈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⠉⠁⣸⡟⢠⡿⠃⠀⠀⠀⠀⣿⠀⢀⣴⠄⠈⢿⡄⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⣿⠁⣾⠃⠀⠀⠀⠀⣠⣿⣴⠟⠁⠀⠀⠘⣿⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠀⣿⠀⣿⠀⠀⠀⠀⠀⢿⣤⡿⠛⠛⠛⠛⠛⣿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⢿⡆⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢠⡿
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⣿⠉⠉⢹⡏⠉⠉⠉⠉⠁⠀⠈⢿⣄⠹⣧⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⢠⡾⠃
⠀⠀⠀⠀⠀⠀⢰⣿⠀⣶⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢀⡀⠀⠈⠻⣦⣌⠙⠿⢶⣤⣤⣤⡶⠾⠋⣁⣴⠟⠁⣶⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⣠⡾⠟⠁⢀⣀⣀⡈⠙⠻⢶⣦⣤⣤⣤⣴⡶⠟⠋⠁⣤⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⠀⣼⠟⠀⣴⣤⣿⡏⢹⣿⣤⣦⠀⠀⢀⠀⢀⡄⠀⠀⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⢸⡟⠀⣼⣏⡈⠛⠃⠘⠛⢁⣹⣧⠀⢻⡇⢸⡇⠀⠀⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⢸⡇⠀⣤⡿⠟⠃⠀⠀⠘⠻⢿⣤⠀⢸⡇⢸⡇⠀⠀⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⠈⣿⡀⠘⢷⣶⣿⡇⢸⣿⣶⡾⠃⢀⣿⠁⢸⡇⠀⠀⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⠀⠈⢿⣄⡈⠀⠻⠿⠿⠟⠀⢁⣠⡿⠃⠀⢸⡇⠀⠀⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠙⠻⠶⣦⣤⣤⣴⠶⠟⠉⠀⠀⠀⢸⡇⠀⠀⣿⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠉⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠉⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠤⠤⠶⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠻⢷⣶⣤⣴⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣤⣦⣠⣤⣤⣤⣬⣭⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠑⠂⠀⠀⣸
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠒⠒⠲⠶⣤⣤⣀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢻⣿⣿⣿⣿⡟⠩⠐⠆⢻⣿⣿⠇⠀⠀⠀⠐⠛⠻⢷⣤⣄⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⣆⣴⠀⠸⣿⣿⠀⠀⠀⠀⠀⠲⠆⠀⢸⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⢸⣿⣿⣿⣿⡆⠸⠇⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠙⠻⢿⣿⣿⣿⡿⠠⡄⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⠆⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠲⠄⠀⠀⠀⠀⠀⠀⣈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⠀⠉⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠓

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⠿⠛⠛⠛⡛⢛⠟⠿⠿⢿⣿⣷⣦⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣽⠿⢛⣻⣯⣷⠾⠗⢛⡛⡛⠛⠛⠛⠛⠛⠷⠶⣦⣌⠉⠛⠷⣧⣗⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⣫⣴⠞⢛⣉⣥⡶⠖⠛⠛⠉⠋⠀⠀⠀⣛⠒⠒⠶⢤⣌⡙⠻⢦⣤⣉⠻⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢆⣽⡿⢋⣴⠟⣋⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠑⠲⠿⢶⣦⡈⠙⠷⣀⡙⠿⢇⣄
⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⣁⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠈⠻⣦⡈⢻⣧⡀
⠀⠀⠀⠀⣀⣾⠟⣰⡟⢁⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠈⢣⣄⠈⢿⣆
⠀⠀⢀⣾⡿⠋⣼⠏⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠙⢦⠀⢹⣦
⠀⠀⣼⣿⢃⣾⢋⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠘⣷⡀⢿⣆
⠀⠐⣿⠇⣸⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣧⠈⣻⡆
⠀⣴⡟⢸⡟⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⡄⢿⡆⠈
⢰⣿⡇⣼⢃⡇⢠⣤⣤⢠⣤⣤⢀⣤⣤⣤⣤⡀⠐⠀⣀⣤⣤⣀⠀⢀⣀⣀⣀⠀⠀⣀⡀⢠⣤⡄⣤⣤⣤⣤⣬⡀⣤⠤⡄⢸⣇⠀⣶⠀⢦
⣶⠟⠀⣿⣸⠁⢸⣿⣿⢸⣿⣿⢸⣿⣿⠛⣿⣿⠀⠘⣿⡟⣿⣿⡇⢸⣿⣿⠿⠂⣤⣿⣧⢸⣿⡇⠛⢿⣿⣿⠛⠃⢸⣯⡅⠀⣿⠀⣿⠀⢺
⣿⡆⠸⣯⢹⠀⢸⣿⣿⢸⣿⣿⠀⣿⣿⣶⣿⡟⠀⣿⣿⡇⣛⣛⡃⢸⣿⣿⣤⠀⣿⣿⣿⣿⣿⣇⠀⢰⣾⣿⠀⠀⢸⣿⠀⠀⣿⠀⣿⡀⢸
⢻⠟⠀⣿⢸⠀⢸⣿⣿⢸⣿⣿⡄⣿⠿⡯⣿⢿⡆⣿⣿⡟⣿⣿⡇⢸⣿⣿⠉⠀⣿⣿⡿⣿⣿⡇⠀⢸⣿⣏⠀⠀⢸⣿⠀⠀⣿⠀⣿⠁⣸
⠈⢶⡆⣿⡘⡇⠘⢿⣿⣾⣿⡿⠁⣿⣷⡄⣿⣿⡀⢿⣿⣧⣿⣿⡇⢸⣿⣿⣶⡆⣿⣿⠇⢿⣿⡇⠀⢰⣿⣿⠀⠀⢰⣶⡆⠀⣿⢀⡿⠀⣿
⠀⠀⣄⢸⣧⢻⡀⠀⠉⠉⠉⠀⠀⠉⠈⠁⠉⠁⠀⠀⠉⠉⠁⠉⠀⠈⠉⠉⠉⠁⠉⠉⠀⠈⠉⠁⠀⠈⠉⠉⠀⠀⠀⠉⠁⢸⡏⣸⠃⢰⣿
⠀⠀⠈⡄⢿⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡏⠀⣾⡏
⠀⠀⠀⣭⡈⣷⡌⠳⠈⠁⠠⠄⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡾⠁⣼⡿
⠀⠀⠀⠈⣷⡈⢻⡄⠀⠀⠘⠀⠀⠀⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⡾⠃⣰⠿⠁
⠀⠀⠀⠀⠹⣷⣄⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣰⠟⠁⣼⠃
⠀⠀⠀⠀⠀⠙⣻⣧⡘⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⠊⣠⡾⠉⣰⣾
⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⡙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠉⠚⢉⡤⠾⠋⣠⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⠘⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⣀⣤⠾⠋⢁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣬⣙⠛⠿⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠶⠞⠛⢋⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣶⣤⣬⣍⣉⣉⣉⣉⣋⣉⣉⣥⣤⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠀⠘⣟⠛⠛⠃⠐⠄⠀⠀⠀⣶⣄⢀⡀⠀⠀⢰⠒⠢⣤⠂⠐⡄⠀⠀⡹⠒⠊⣁⡀⠄
⠀⠀⠀⠀⠤⠀⠟⠀⠀⠀⠤⠀⠀⢀⣴⡆⠀⠑⡀⠀⢀⠜⢖⡚⠓⠓⢦⢶⢄⣉⠀⠀⠸⢀⠝
⠀⠀⠀⠀⠀⡜⠉⠀⠀⢇⠀⢰⢙⠟⠁⠰⣴⣾⠁⠀⠈⠳⢄⣗⣄⠚⠀⡿⡀⢉⠆⠰⠽⢂⠔⡳
⠀⠀⠀⠄⣸⣶⣾⣷⣿⣿⣆⠀⣿⢣⠀⠀⠬⠬⡀⠀⠀⠀⠂⢣⠈⢙⠾⠥⠏⠀⠈⢀⠔⡣⠊
⠀⠀⠀⢠⢹⣿⣿⣿⣿⣿⠏⡆⢸⠤⠧⠤⠭⠭⠽⢄⠀⠈⠃⠀⠉⠁⢀⣤⠤⡀⠶⣿⠋⠀⠊⢹⡂
⠀⠀⠀⢀⡑⠚⠉⡉⠑⠒⠈⠈⠈⠂⠤⠤⠤⠴⠐⠋⠀⠀⣤⠀⠀⣴⢋⠔⡒⢢⠱⠈⡄⠀⠃⣸⡉
⠀⠀⠀⠈⠁⠀⠀⠻⠇⠀⡀⡀⠀⠀⠀⠀⠐⠊⠢⠔⠀⠀⠈⠀⠀⣇⠸⣨⡋⡱⢡⠀⡇⠀⡄⣷
⠀⠀⠀⠐⢃⠞⠉⠳⡄⠈⠉⠉⠀⠀⠀⠀⠈⠉⠒⠒⠁⠀⠶⢦⠰⠈⠲⣀⣄⣀⠡⠊⠀⠀⠓⠋
⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⢒⣠⣀⠀⠀⢀⠀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡉⠉⠉
⠀⠀⠀⠀⣀⠀⠀⢹⡆⣰⠃⠀⠈⠧⠀⢹⠀⠀⣾⠉⠉⠀⢀⣷⠀⢀⡇⢠⠞⠉⠷⠀⢸⠖⠒⠂
⠀⠀⠀⠀⢘⠶⠤⠞⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⣿⠴⠶⠀⢸⡇⢧⢺⡇⣾⠀⠀⠀⠀⢸⣤⡤⠤
⠀⠀⠀⠀⠈⠀⠀⠀⢠⠹⣄⠀⣀⠄⠀⣿⠀⠂⢿⣀⣤⡀⠼⠀⠘⠾⠀⠘⢤⡤⠞⠁⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠉⠁⠀⢈⡉⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⢠⣢⢤⡠⠀⡠⣊⠅⢌⠑⡔⠂
⠀⠀⠀⠀⣦⠀⣁⠀⠀⡸⠀⢀⡈⠀⠈⠫⣀⠎⠁⠂⠮⢈⡉⠉⠁⠀⡤⠀⠠⣄⡾⠖⠁⠀⡠⢀⠇⣴⠄
⠀⠀⠀⢀⣀⣸⣓⣇⣸⣹⣀⣏⣇⣀⠀⣠⠁⠂⠀⠀⠀⠈⠁⢶⣶⠀⡙⢦⡸⠍⠀⠀⠀⠸⠷⢊⣀⠋
⠀⠀⠀⠈⣿⠗⣇⡏⢹⣽⠉⣯⣿⠋⠀⠈⢢⠀⠀⢀⡀⠀⡀⠀⠁⢀⠵⠋⠈⠱⢄⠀⠀⠃⠀⡀⢻⠗
⠀⠀⠀⠀⣿⠀⣿⡇⢸⣿⠀⢿⣿⡄⠠⠒⠁⠱⠆⠒⠂⠈⠁⠀⠤⠎⠀⠀⠀⠀⠀⡧⡄⠀⠀⣷⡷
⠀⠀⠀⢴⣿⣶⣿⣷⣶⣶⣶⣶⣿⠷⠆⠓⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠢⡁⠀⠀⠀⠀⣀⠀⠀⠀⠈⡉⠰⠄⢀⡰⡈⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢦⢫⠻
⢀⡀⠄⠂⠀⠀⠀⠀⣀⠐⡄⠀⡅⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⢚⣛⡧⢄⠐⢀⠀⢀⠀⠙
⠈⢆⠀⠀⠀⠀⠀⠀⢘⡂⠱⡀⠘⠦⢤⣀⣀⡤⠤⠀⠀⠚⠀⠀⠀⠀⠀⠴⠂⠒⠤⠓⠊
⠀⠘⠀⠀⠀⠀⠀⡀⠤⢈⣂⣱⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⡀⢘⠧⡦⠚⠁⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠂⠀⠀⠀⠣⡡⣀⣠⣄⠀⣀⡤⢠⠎⠀⠀⠀⠀⠀⢀⡌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⢃⣀⠉⡩⠙⢧⠀⠀⠀⠀⠀⢠⠮⠀⠈⠠⠃
⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠃⡀⠀⢠⠀⠀⠀⠠⠄⠐⠀⠠
⠀⠀⠘⣼⡤⠤⠄⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡤⠤⣠⠁⠀⠀⠀⠄
⠀⠀⠀⠈⢷⠀⠀⠀⠈⠊⠑⠲⢤⠀⠀⠈⠢⡀⠀⠀⠘⣣⠀⣀⡤⠤⢄⠐⡤⠆⢀⡡
⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⣃⠢⢤⢤⡜⠂⠀⠀⠁⠘⡟⢶⠓⠐⠊
⠀⠀⠀⠀⠀⠀⠓⠊⠁⠀⠀⠀⠀⠈⠁⢢⠁⡤⠀⠀⠀⠀⠀⠀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣈⠀⠀⠀⠐⠊⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢤⣄⠀⣀⣀⣀⣀⢈⣉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠀⠈⠁⠈⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⡠⠂⢆⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠚⠀⠀⠀⣅⠀⢀⡅⡠⠂⠤⠤⠤⠤⠤⠀⠄⠀⠀⢠⠀⢄⠀⠀⠀⠀⠀⢀⠊⡠⠒⠀⠐⠢⡈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⢀⠇⠀⠀⠀⡇⠀⢀⡁⡅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡼⠀⠀⠀⠀⡄⠀⢠⠃⠑⠤⠤⡤⠤⠤⠤⠤⠂⠀⠀⡀⠀⠀⠀⠀⠀⡠⠔⠚⢄⠑⢄⠀⢀⠔⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠄⣠⠊⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠁⠁⠀⢀⡞⢳⡀⠄⠂⠉⠑⠠⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢗⠀⠀⠑⡀⠀⠀⠣⠀⠀⡜⠀⠀⠀⠀⡇⠀⣀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠃⡠⠖⠑⠢⣀⠇⠀⠀⡳⠀⠀⠌⠀⡠⠔⠂⠉⠈⠉⠉⠉⠉⠈⠃⠺⢄⠀⢸⠀⢸
⠀⠀⡤⠤⡌⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⠀⠱⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⢸
⠀⠀⠒⠒⢊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠺⡀
⠀⠀⠀⠀⠀⠉⠉⢋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢀⠔⣈⣁⠰⠀⠀⢆⠁⠢⡀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⢨⡔⢈⠉⠉⠀⠼⢟⠳⡄⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠔⢅⠔⠁⠀⠀⠀⠀⠀⠉⠣⡈⢢⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⢁⡀⠀⠀⢆⠀⠀⠈⢢⡀⠔⢊⠃⠀⠀⠀⠀⠀⠸⣀⠎⠀⠠⣀⠀⠀⠀⢀⡀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣐⢅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠉⠑⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠤⠂⠉⠀⠀⠀⠀⠀⠀⢐⠉⢂⠀⠀⠀⠀⠈⠀⠀⠀⠀⡰⠀⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠣⡚⠳⢄⡀⠀⠀⠀⠀⡠⢬⢀⠌⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠂⠍⠈⢱⠀⠉⠃⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⠒⠆⡐⠀⠂⠐⠀⡀⠖⠲⢀⠀⠐⠀⠀⠐⡀⠖⠒⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠉⠒⠈⠀⠀⠀⡌⠐⠈⠑⠆⢡⠀⠀⠀⠎⠐⠈⠁⠂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠢⠀⠔⡠⠀⠀⠀⠣⡐⠄⠠⢂⠌⠀⠀⠀⢣⡐⠄⠠⢂⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡶⣆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠄⠀⠀⠀⠀⢀⠠⠄⠀⣃⡃⠀⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢰⡅⠈⠘⡦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⢠⠀⡔⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⢀⠀⠀⠀⡀⠀⠂⠂⡰⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠈⠱⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢤⡔⠁⠀⠈⡠⠒⢤⠀⠀⠀⠀⡴⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⠂⠀⠂⠔⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠈⠉⠉⠀⠓⠤⠞⠀⠀⠀⠀⠀⠀⢤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⡁⠊⠀⠀⠀⠄⠀⠇⠀⠈⠉⠉⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⢀⣀⡈⠂⠁⠀⠂⠀⢠⠤⠤⠴⠧⠤⠤⢤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⢃⠀⠀⡠⠀⠀⠀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠶⢀⠆⠀⠠⣀⠀⠒⣒⠚⡛⢛⠛⠛⡉⠂⠀⢀⠂⠀⠀⠐⠀⠀⢱⣄⠀⠀⠁⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢊⡁⠀⠊⠰⠀⠀⠂⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⢴⡦⢀⣤⣀
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⢤⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠰⠏⢉⠉
⠀⠀⠀⠀⠤⢆⡕⠀⢀⠀⠀⠈⠋⢰⡟⣶⠀⠸⡟⠂⢀⡶⠛⢷⡀⢰⡇⠀⠀⠀⣴⠛⢳⡄⠀⣴⠛⠻⠆⠀⠻⣆⢀⡾⠁⠀⠀⠘⠒⠖⠉
⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⢸⡷⣯⠀⠀⣿⠀⢸⡇⠀⢸⡇⠘⣇⠀⠀⢸⡏⠀⠈⣿⢰⡇⠀⠰⣦⠄⠀⠹⣾⠃⠀⠀⠀⡆⠀⠄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡼⠃⢠⣿⠄⠘⢷⣤⠾⠃⠀⣷⣤⣤⠈⢿⣤⡾⠃⠀⢷⣤⣴⠟⠀⠀⢸⠇⠀⠀⠀⠉⠀⠈⠂⡀⠈⠉
⠀⠀⠀⠀⠀⠤⢀⠒⠀⢃⠀⠂⠀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡅⠀⠈⡢⠠⠇
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⠀⠀⠣⣀⡸⠀⢀⠜⡁⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠐⠂⠚⢃
⠀⠀⠀⠀⠀⠠⠐⠓⠄⠓⠂⠀⠈⠙⠀⠀⡠⠁⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⡄⠀⠂⠀⠀⠀⠐⢂⠀⠈⠑⠂⠁⡀⠀⡈⠁⠉⠠
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠃⠀⠡⠀⠀⢰⡒⠀⠀⢈⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠴⠀⠀⡘⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠆⠠⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠆⠀⠀⠀⠾⡂⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠠⠄⠄⠀⠀⠀⠀⠀⠀⢰⠄⢠⠄⠀⡄⠀⡄⠠⢐⡀⢀⡀⠀⢀⠊⠀⠤⠀⠀⠀⠀⠘⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠤⠠⠀⠀⠀⠐⠚⠲⡀⠀⠀⢠⠤⠇⠀⠈⠀⢸⠢⢤⢈⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠀⠀⠈⠀⠂⣄⡂⢐⡀⠀⠀⠀⠀⠀⠈⠂⠢⠤⠤⠴⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠘⠒⠀⡀⠀⠉⠁⠀⡈⠘⠂⠀⢀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠲⠁⡚⠦⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠉⠙⠉⠉⠠⠦⠄⢀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠈⠉⠙⠉⠛⡀
⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠰⠧⠤⠄⣀
⠀⠀⢀⣠⡄⠒⠛⠓⠒⠒⠒⠒⠒⠂⠀⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠑⢢
⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠛⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣌⠳⠆⠈⠉⠉⠉⠉⠠⠾⢋⡴⢆⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠴⠖⠉⠁
⠀⠀⠀⠀⣿⠛⡟⠀⠠⠤⠤⠤⠤⢀⡴⣛⡾⠁⣀⡀⣀⠀⢀⠀⠀⠀⠀⠀⠠⠴⠶⢌⡷⡄⠚⠛⠋⠁⠈⠻⢄⣘⡷
⠀⠀⠀⡌⢿⠏⠀⠀⠀⠀⠀⠀⢀⢮⡙⠁⠀⠀⠀⠀⠀⢰⠄⠀⢴⠄⠀⠀⠀⠀⠀⠈⠳⣡⡄⠀⠀⠀⠀⠀⠀⠹⠇⣴
⠀⠀⣴⠃⠘⠀⠀⠀⠀⠀⠀⢠⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠋⡸⠂⠀⠀⠀⠀⠀⠀⢸⠉⡆
⠀⠀⣅⢠⡆⠀⠀⠀⠀⠀⠀⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣴⠀⠀⠀⠀⠀⠀⢸⠀⡘
⠀⠀⠈⠲⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠟⠁
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠻⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⢰⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢴⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡝⠃⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⢾⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⠓⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣀⠀⠀⠀⠀⠙⠿⣦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⣴⠷⠋⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⡀⠀⠀⠀⠈⠛⠛⢷⡾⠷⠾⠟⠛⠉⠀⠀⠀⠀⢀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠂⢤⣤⡄⠀⢸⡂⠀⠀⣿⠂⢠⣤⡤⠰⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢹⠃⠀⠀⣟⠀⠀⠀⠀⢀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⡁⠀⠀⠉⠉⠉⢹⡇⠀⠀⣿⣉⡉⠉⠉⠀⠙⣧⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⠘⣇⠀⠀⠟⠈⢡⠀⢀⡴⠛⠋⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⡌⠀⠀⠈⢳⠄⢀⡜⠛⠳⠤⠀⠀⠈⠾⠯⠤⢀⣸⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣼⣧⣤⡤⠰⠛⠲⠞⠙⠲⠀⠀⠀⠀⠸⠀⠀⠀⠈⠉⠑⠒⢠⣄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠷⠶⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⠆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠤⠤⠀⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠈⢤⠤⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⡀⠀⡀⠀⠀⣇⣀⣀⣀⡈⠉⠿⢂⠒⠒⠀⢤⣤⣄⣀⡀⡀⢀⡀⢀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⣟⠉⠉⢻⠋⠹⠟⠛⢩⣽⠛⠏⣭⡅⠴⡉⢹⠖⠒⠐⡟⠈⢿⡁⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠒⠋⢉⠉⠹⢇⠿⠲⠶⢶⡄⠀⠀⣰⠴⠶⢧⣸⠇⠀⠈⠙⠆⠛⢃⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⣄⣠⣾⡦⢾⣿⣦⡀⠀⠀⠀⣠⡟⢹⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠠⣿⡟⠛⠿⠀⠙⠁⣠⡛⠀⠱⠀⠀⠀⡛⠁⡾⢷⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢿⣥⠄⠒⠒⠈⢀⣍⠉⠀⢿⠀⠀⣠⠃⢸⠀⠀⠳⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠲⠂⠈⠉⣹⠏⠉⢹⣿⠀⢠⡋⠀⠿⢢⡄⠀⢣⣀⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠛⠉⠠⠷⠤⠰⠾⠛⠳⡄⠙⠾⠆⠾⠇⠀⠈⠁⠖⠁⠶⠶⠄⠀⠀⠀⠀⠠⠶⣷
⠀⠀⠀⠀⠀⠀⢰⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠
⠀⠀⠀⠀⠀⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡄
⠀⠀⠀⠀⠀⡌⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⡀
⠀⠀⠀⠀⠀⠏⠀⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠸⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠧⠤⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⡀⠐⠀⣠⣄⣠⣀⣀⣀⣀⣀⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⢞⣛⡿⢿⠿⣛⣛⣫⣿⣬⡁⣿⡏⣨⣿⣯⣛⣛⣛⠿⠿⢿⣛⠢⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⠶⢂⣀⣀⣀⣀⡰⠶⠬⠓⠉⠘⠫⡴⠖⣀⣀⣀⣀⣀⠶⢦⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⣖⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣀⣀⣀⠤⣴⣒⣾⡍⣿⣶⣿⣿⢹⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠿⢿⡅
⠀⠀⠀⣽⠋⠛⢳⡟⠛⠛⢣⡿⠀⢸⠿⡼⣿⣿⣿⠿⢻⣿⣋⠉⠁⣿⣧⣄⡀⠈⣿⡀⠄
⠀⠀⠀⣿⠀⠀⢸⠃⠀⠀⢸⡇⠲⠾⣤⡇⠳⡤⠬⠯⠭⠌⠉⠉⠻⠛⠓⠶⠿⠶⠾⠽⢠
⠀⠀⢀⣓⣀⣀⣈⣡⣥⣤⡆⠀⠀⠀⠸⡿⠼⠐⠒⠂⣤⠄⠀⣠⡤⣍⡽⣟⡟⣛⣓⣶⣶⣶⣶⠶⠶⢶⢦⡀⠀⢀
⠀⠀⠛⢛⡟⠉⠉⠉⠉⠀⠶⠆⠀⠀⠀⠣⠀⣤⣤⣤⣤⣤⠙⣿⠙⣯⠐⢨⡇⣿⣿⣿⣿⣿⣿⣿⣿⢰⠋⠑⣷⢿⣇
⠀⠀⡔⠊⣰⣶⣦⠐⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣤⣤⣀⣿⣋⣑⡇⠿⣿⣿⣿⣿⣿⣿⣿⢸⠶⠎⡅⢸⣇
⠀⠀⠅⣀⣿⠿⢿⡆⡄⠀⠀⠀⠀⠀⠙⠀⡟⣩⣤⣌⠙⢿⣿⣿⠀⠉⠉⠉⠁⠀⢡⡞⠉⠉⠙⠛⠛⠛⠋⣹⠓⠉⠉⠈
⠀⠀⠠⠿⢱⣿⡈⣷⣷⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣆⡠⡄
⠀⠀⠀⠸⣽⣿⡇⣿⣿⣿⣭⣿⣿⣿⣿⣗⣿⣿⢹⣿⣷⠐⢗⠲⣛⣿⣿⣶⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⠲⢑
⠀⠀⠀⢸⠘⢿⣇⣿⣿⣿⠀⠈⠙⠛⠋⢷⣿⠹⣞⣽⠏⢨⣭⣽⣷⠟⠋⠀⠀⠙⠛⠛⠉⢹⣿⣿⣿⡿⢟⣿⣿⣯⣉⡯
⠀⠀⠀⠈⢧⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⠈⣯⡳⠤⢀⣬⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠶⠶⣶⣶⣶⣶⣶⣒⣒⡲⠖⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠯⣺⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣛⣠⢤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣠⣤⣤⣄⣀⣀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⡀⣿⠇⢠⡛⣯⣭⣩⣽⣅⣾⣻⣼⣿⣳⢻⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢨⠄⢧⣟⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⠠⡅⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⠂⢾⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⡷⠐⡶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠞⠁⠘⡀⣻⣐⣐⣿⣴⣦⣿⢻⠛⡟⣿⣿⣿⣟⢀⠃⠈⠳⢰
⠀⠀⠀⠀⠀⠀⠀⢘⡟⢘⠓⢦⠈⠈⠀⠀⠉⠉⠉⠁⠀⠈⠁⠀⠁⠀⠁⠁⡴⠚⡃⢻⡃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢸⡁⡄⠖⡆⢤⠸⠇⠟⠀⠀⠀⠛⠰⠄⠀⠀⢀⢄⢀⡠⠀⠀⠀⡰⣆⠀⠀⡔⠉⠀⠀⠀⠀⡄⠀⣀⠂
⠀⠀⢦⠀⢠⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣿⡄⡽⠉⠀⠀⠀⠘⠁⠈⠃⠸⡅⠀⠀⠀⠀⡰⠃⢰⢹⠇
⠀⠀⠀⢧⠸⠀⠀⠀⣤⠀⡴⠀⠀⠰⢶⡀⢄⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀⠤⠒⠖⠒⠷⣆⠒⠋⠉⠀⠀⢸⢸⡀⢀⠴⣾⠂
⠀⠈⠣⡘⡇⠀⠠⡴⠁⠉⢶⠀⠀⠀⠀⠀⢀⠵⠒⠒⠒⠤⠶⠆⠾⠀⠀⢰⠋⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⢦⣉⣁⠤⠊
⠀⠀⠀⠘⣇⠀⢠⠜⣤⣠⠾⠀⠀⢰⡆⠘⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⠣⡀⠀⠀⠀⣀⡴⢃⣴⠶⠆⢠⡄
⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣠⡾⠋⣰⠒⠉⠉⠉⠉⢣⡉⠉⠁⠀⡎⣏⣀⢠⠃⣇⢞⠆⣠⣤⡀
⠀⠀⠠⢄⢸⡞⠀⢀⣀⣀⡀⣀⠤⠢⡀⠀⠀⠀⢀⣀⣀⣉⣀⠀⠱⡄⠀⠀⠀⠀⠀⡣⠀⠀⠀⠓⠴⠊⡧⢤⢀⡎⠀⠻⠿⠂
⠀⠀⠀⠀⢺⡇⠀⢋⡀⢀⡜⠑⠢⣤⠁⠒⠰⠚⠋⠁⠀⠈⠁⠉⠛⠛⡖⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢊⡴⠲
⠀⠀⠀⠀⢈⠂⠀⠈⠳⣞⠀⠛⢠⡎⠳⡀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡰⠃⠀⠀⠀⠠⡶⡄⢰⢶⠄⢠⣤⠄⠀⢸⣿⢠
⠀⠀⠀⠀⠘⠀⠀⠉⢸⠀⢉⡲⠯⠄⠤⠃⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣧⡇⢸⣾⠀⢸⢷⠀⠀⠈⠣⢸
⠀⠀⠀⠀⠀⣀⡀⠀⠈⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⡖⡄⠀⠀⢰⠒⣄⠀⠀⣿⠁⢸⣿⠀⢸⣼⠀⠀⠀⡀⢸
⠀⠀⠀⢠⠀⡏⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠒⠃⡇⠀⠀⡦⢙⢘⠀⠀⠟⠀⠘⠛⠀⠐⠛⠀⠀⠸⣇⣸⢠⠄
⠀⠀⠀⠀⠀⣯⠀⠈⠀⠀⠀⠀⠀⠐⡶⠶⡖⠀⠀⢸⢸⠉⢢⡄⠐⡄⠣⣉⠞⠀⠀⠀⡺⠀⠀⠀⠀⡀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢰⠀⠀⠀⠋⠀⠈⠁⠘⠁⠀⠀⠀⠀⠀⠾⠧⣠⣤⠔⠊⠉⢢⡔⠁⠀⠑⢦⠄
⠀⠀⠀⠀⣠⠊⢆⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⢣⠀⠀⠀⠖⢠⠄⠀⠒⣒⠒⡆⠀⠀⠀⠀⠈⠑⣤⠀⠀⠀⠀⠀⠨
⠀⠀⠀⢰⠓⠩⠾⡆⠀⠀⠀⠀⣼⣦⣶⣷⣶⣾⡆⠀⠀⠀⢸⠀⠀⠀⣿⠀⣉⠉⢉⡍⠉⠙⣆⣀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠸⡀⠀⢀⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠄⢼⠀⠀⠀⣿⠀⣿⡇⢠⡇⠀⣠⡀⠀⠈⣭⠉⢩⣇⠀⠀⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⣠⡀⠛⠿⡿⠿⠿⠿⠿⠛⠃⠀⠀⢸⠀⠀⠀⡏⠀⡏⠀⢈⡇⠀⡟⡇⠀⠀⣿⠀⠸⢻
⠀⠀⠀⠀⠀⢀⣯⣦⡤⠜⢳⡶⠒⢻⣷⠒⠒⠀⠀⠀⠀⠐⢸⠀⠀⠀⡇⡀⡇⡀⢀⣇⠀⣇⡇⠀⠀⣿⡀⢀⣿⢀⡀⣷
⠀⠀⠀⠾⠟⠉⠀⠘⠁⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠸⠂⠉⠙⠉⠉⠉⠩⠉⠉⠉⠉⠍⠉⠩⠩⠉⠹⠉⠉⠉⠉⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⣀⡀⢀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠤⠤⠤⠀⠀⢀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠩⠉⢉⣁⣀⠀⠠⢼⡯⡀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠉⠐⢄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣒⣒⡒⠒⠆⠀⠀⡜⠧⡀⠰⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠄⠀⠠⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠀⠤⠭⠭⢀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠁⠀⠀⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠉⠉⢁⣐⡒⠢⠠⠭⣁⣺⢀⣀⠀⠀⠀⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣒⡒⠒⠢⠬⠍⣉⣒⠒⠼⣿⠉⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡠⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠤⠤⠤⠭⠍⣁⣒⠂⠠⠬⢹⠿⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠐⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠃⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠙⠒⠂⠤⢤⡨⣄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢻⣿⣿⣿⡟⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⢻⣿⡍⠋⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠠⢀⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⠃⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⢠⠀⡆⠀⠚⡁⠙⠋⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⠷⠋⠀⠀⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⡇⣄⣴⣾⣿⣿⣿⣶⡀⠀⠀⠀⢰⣧⠀⢸⣿⣿⣿⡀⠀⢀⣸⠟⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⡇⠸⠃⣹⣿⣿⣿⣿⡇⣢⠀⠀⠈⠱⣤⣾⣿⣿⡿⠀⠀⣾⣿⠄⠂⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠃⠈⡀⢻⣿⣿⣿⣿⡗⠘⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠹⣦⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⢉⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠙⡞⠟⠾⠳⠿⠁⠀⠎⠹⠓⠇⠟⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣤⣤⢤⣤⣤⣤
⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣶⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠠⠂⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠠⠄⠀⠰⠂⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠀⠀⡜
⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠁⠀⠠⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠐⡀⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⢀⠀⠘⠀⠀⠐⠀⠂⠀⠀⠀⠀⠉⠋⣀⡞⠈⢀⡏⢈⠫⠀⡐⢰⢠⠂⢁⡛⠁⠐⡆⠀⠀⢄⠀⠶
⠀⠐⠐⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠊⠑⠂⠀⠒⠐⠃⠊⠀⠐⠁⠒⠂⠀⡂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠉⠂⠀⠈⠛⠃⠘⠛⠘⠛⠛⠋⠙⠛⠃⠀⠛⠛⠚⠃⠀⠁⠀⠶⠀⠂⠈⠆⠀⠠⠂
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠐⠛⡀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡠⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⣀⣴⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣄⡀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠻⠟⠀⠸⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣠⣤⣶⣶⣤⣼⣿⣿⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣿⣿⣿⣶⣦⣤⣄⡀
⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⢰⣿⣿⣿⡿⠛⠉⠉⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠉⠉⠻⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⠟⠋⠉⠙⠻⣿⣿⣿⣷
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿
⢻⣿⣿⣿⣄⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⢀⣼⣿⣿⣿
⠈⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⠏
⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠟⠁
⣶⣶⡶⠶⣶⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⢒⣟⠮⠛⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢀⣊⠬⠚⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠂⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠚⠉⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢤⣴⠿⡞⡃⠀⠀⠀⠀⠀⠈⢪⡀⣈⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠤⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡦⢻⣽⣬⣿⣆⠘⡜⡄⠀⠀⠀⠀⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣒⣤⠹⣯⠤⡄⢫⢛⠻⣝⣆⠘⠛⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢀⣐⠀⡰⠀⢀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣐⡌⢞⢄⣥⣦⠹⡩⣤⣤⠱⠃⠈⠀⠀⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠈⠑⠳⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢆⢹⢡⠹⡱⡾⣶⡌⢼⢬⣿⠇⠙⠉⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀⠀⠀⠀⠀⠀⠀⠈⢮⡆⠱⣣⠹⣷⡘⠾⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠀⠀⠈⠜⠰⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢠⠜⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠤⠀⠀⠉⠓⠶⠶⢦⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⢿⣷⣶⣄⣀⠀⠀⠀⢠⠈⣧⣄
⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠻⢗⢒⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠘⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠅⠓⠁
⠀⠀⠀⠀⠀⠀⠠⠚⡄⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠀⠂⠂⠘⠈⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠠⠊⠁⠀⠄⠀⠀⠀⠈⢀⠀⠄⠠⠀⠰⠀⠂⠐⡀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠅⠰⠂⠀⠐⠈⠀⠉⠀⠀⠀⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠂
⠠⠐⠀⠂⡠⠈⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⠿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⢀⣤⣶⠿⠟⠛⠛⠛⠛⠛⠻⠿⠷⢶⣶⣤⣤⣀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣀⣠⣤⣴⣶⠶⠿⠿⠟⠛⠛⠛⠛⠿⠷⣶⣄⡀
⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡿⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⠉⠛⠿⢶⣦⣄⡀⢀⣠⣤⣶⠿⠛⠉⠁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣨⣽⡿⢿⣿⣅⡀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠈⠙⠻⢷⣦⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣄⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⣤⡾⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⢷⣦⡀⠀⠀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⡿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢻⣶⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⠿⣦⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣴⡿⠋⠻⣷⣄
⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠈⠻⢷⣤⡀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣤⡾⠟⠁⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣶⣦⣄
⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢹
⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣤⣤⣾
⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠛⠿⣶⣤⡀⢀⣠⣴⡾⠛⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠿⣿⣥⣀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣀⣠⣴⣶⠿⠛⠉⠁⠀⠀⠀⠉⠛⠻⢷⣦⣤⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢿⣦⣀⠀⠀⠀⠀⣴⡿⠛⠻⣦⡀⣀⣀⣤⣤⣶⢿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⡿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿
⠀⠀⠉⠛⠻⠿⠷⢾⣿⠀⠀⠀⣿⡟⠛⠋⠉⠁⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠷⠶⠶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⢀⣠⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⡉⠭⠍⣁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠊⠁⠀⠀⠀⠀⠉⢢⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⣂⠉⠉⠉⠉⠉⠉⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡑⢌⠢⢄⣀⣀⠤⢊⠜⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣁⠂⠀⠀⢂⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠉⠉⠉⠢⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⠉⡉⠉⢹⡁⠀⣀⠀⠀⠀⠀⢸⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢤⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⠘⠋⠀⠀⠈⠁⠢⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠂⢀⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠱⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠢⣀⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡎⢐⠄⢀⠠⡀⠀⠀⠀⠘⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⢀⢀⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠃⠠⡄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠉⠰⠒⠉⠑⠂⠀⠁⢠⡍⠉⠒⠊⠉⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⢎⠈⡳⠸⠏⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠋⡀⢸⠀⠀⠀⠀⠀⠀⠀⡠⠋⠑⢌⣉⡥⠚⠀⠤⢄⡀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢄⠀⠀⠀⠀⠁⠀⡀⠀⠀⠘⠤⢂⢌⠔⠀⢸⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢀⠌⠀⠀⠀⠀⠀⠈⠑⢠⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠈⠢⣑⠤⣀⠀⠀⢎⡰⠀⢀⡠⢐⠥⠊⠀⠀⢸⠀⠀⠀⠀⢠⣎⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠙⡀
⠀⠀⠀⠀⠀⠘⡤⠤⠤⠤⣬⠃⠀⠀⠀⠁⠒⠨⠭⠬⠭⠭⠐⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠪⣓⢦⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠱
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠇⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠈⢁⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀
⠀⠀⠀⠀⠀⡰⠡⢤⠬⠥⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠂⡶⡰⣒⠂⠲⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⡜
⠀⠀⠀⠀⡰⠱⠁⠀⠠⡄⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠃⡣⡘⣢⡀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠤⣀⠀⢀⠔⠁⢀⠜
⠀⠀⠀⠰⠡⠃⢀⡀⠀⠀⠀⠐⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠛⢊⡁⠈⠓⠤⣀⠜⠁⠀⠀⠀⠀⠀⠀⠑⡁⠀⡠⠊
⠀⠀⢠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠲⢄⡀⠸⠀⠀⠀⠔⠁⢑⠀⠀⠀⢰⠈
⠀⢀⢂⠂⠀⠀⠀⠀⠰⣉⡁⠀⠀⠑⡐⡤⠠⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠸⠤⠤⠀⠤⠄⢤⠀⠀⠀⢙⠀⠀⠀⠈⠐⠈⠀⠀⠀⢸
⢀⢂⠂⠀⠘⠃⠀⠀⠀⠀⠀⠰⠉⠆⠱⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣆⣘⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣁⣵⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⠁⠛
⠀⠀⠀⠀⠀⠀⠀⡀⠌⣀⢈⡀⠀⣇⠙⠊
⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠨⠀⠀⢀⣠⣀⠀⠊⢁⡠⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⢀⡀⠀⢈⠁⠀⡆⠀⣀⠉⠑⠒⢤⣤⠀⠀⢀⡤⠶⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠠⢤⢀⠀⠀⢐⠇⢀⠠⠄⠀⠀⠀⠐⢀⠀⠀⠀⠀⠠⠄⠑⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣔⡀⠐⡈⠀⠀⠊⠀⠀⢀⠀⣀⠀⡀⠀⠀⠂⠀⠀⠀⣀⠀⡞⠄⠐⠄⠀⠈⠀⠀⠙⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠜⣧⢀⡄⠀⠀⡠⠀⠲⡐⠀⠀⠀⠙⠀⠀⠨⠀⠀⠀⠈⠒⢣⢷⡃⢀
⠀⠀⠀⠉⠁⠀⠀⠀⠈⢷⠀⢠⠀⠀⠀⠀⣤⠀⠒⡐⠀⠀⠀⠀⠀⠘⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠁⠀⠀⠀⠀⠜⣇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠩⠅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠛⠤⠰⠾⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠯⣄⠀⠐⢶⡔⡿⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠍⡀⠀⠀⠀⠀⠉⠁⠠⡀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡴⠁⠀⠀⣑⠢⡄⠠⠆⠉⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢤⠘⠀⠀⠀⠀⠀⢀⠂⠀⢣⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢀⠐⣀⠀⠀⠂⡼⠁⠀⠀⠂⠀⡐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠀⠀⡰⠂⡀⠈⠂⠀⠀⠀⠀⠄⢤⢀⡎⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠢⠤⢴⠁⠀⠀⠀⠀⠀⢁⠀⠀⠉⠉⠀⠢⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢛⠣⡀⠶⢴⠁⠀⠀⠀⠀⠀⠀⠈⣅⠀⠀⠀⢀⣀⠳⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡦⢬⡂⠈⢅⠀⠀⢀⠀⠀⠀⠀⠈⠙⠶⡬⠖⠁⣠⠃⠐⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠈⠀⢘⠀⠑⠀⠀⠀⠀⠀⠉⠲⠽⣞⠕⠁⠀⠠⠀⠁⠒⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢰⢄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠀⠀⠀⠀⠀⡰⢧⡌⠉⠂⠌⡒⠄⠀⠀⠁⠀⠀⠚⠀⠀⠉⠁⢀⡤⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⢸⠉⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⠂⣁⠀⠀⠠⡄⠀⠀⠀⠐⠂⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⠀⢀⠈⠣⣀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢄⠀⠀⠀⡼⠀⠀⢸⠀⠈⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⠁⠀⢰⠃⠀⠀⠈⠁⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⠒⠐⠀⣠⣀⢘⠀⠀⠀⠀⠊⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣠⡦⢀⠠⣤⣤⣬⡏⠤⠌⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠷⣚⣧⠴⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢸⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠒⠀⡠⠐⠒⠒⠒⠒⠒⠒⠂⢄⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⢀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⢪⠔⠋⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢡⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣧⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡠⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗

⠀⠀⠀⠀⠀⠈⣩⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⡁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⡍⠛⠓⣒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠇⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀
⠀⠀⢸⠀⠀⠀⡐⠉⠿⠓⠀⠼⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠾
⠀⢰⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⡎⠀⠀⠐⠁⠀⠀⠀⢰⢅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠛⠉⡁⠀⠀⠀⠈⢢⣀⣀⣠⡾⡁⠀⠀⠀⠀⢠⠒⠐⢀⠀⠀⠀⠀⠸
⢠⠁⠀⠀⠠⢀⡀⠀⠀⢸⠀⢁⠠⢄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠼⠦⡀⠀⠟⠙⠒⡄⠀⠀⠘⢄⣠⠋⠀⠀⠀⠀⠀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠸⣀⣀⠇⠀⠳⠤⠔⠃⠀⠀⠀⠀⢸⠖⠂⠄
⢀⠔⠒⢆⠀⠀⠀⠀⠈⠻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡼
⠘⠦⠤⠞⣤⠄⠒⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠔⠦⡀⢰⠃⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⡀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣀⠞⠘⢦⡀⣀⠜⠁⠀⠀⠀⡎⠈⣣⠀⠀⠀⠀⠀⡔⠁⠀⠊⠀⠀⠀⠀⠀⠀⠠⡑⣄⠀⠀⢀⠠⣶⠄⢸⣀⠀⠀⠀⠂⠀⠀⣠⡄⠀⠀⠀⠘
⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠐⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠙⠁
⠀⣠⠄⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠐⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘
⠋⠁⠀⠑⡀⠀⠀⢇⣀⡽⠒⠠⡎⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠙⠤⣤⠼⢃⡤⠂⠰⡄⠀⢀⡠⠀⢄⠀⠀⠀⠒⠲⠛⢹
⠀⠈⠄⠀⠀⠀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣸⠀⠀⠣⠤⠜⠀⠀⠀⢩⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡀⠀⠀⠀⠀⠈⠒⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠱
⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⣅⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢰⠀⠀⠀⢠⠐⠒⠒⠦⡀⠀⠀⠀⠀⢀⣀⡳⠆⠊
⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠁⠀⡁
⠀⠀⠀⠀⠈⠒⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⢠⠖⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠇⠀⠀⠈⡓⠶⠒⢫⣥⣀⡀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠢⣤⠸⠦⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⡊⠉⢳⠀⢎⠀⠀⡹
⠀⠀⠀⠀⢀⠔⠐⠄⠀⠀⠀⠀⢨⡀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⠊⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠰⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣺⣭⠿⠷⠶⠶⠾⠯⣿⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡫⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠔⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⣯⢧
⠀⠀⠀⠀⠀⠀⢀⡴⣞⣯⣾⣷⠶⠶⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣶⣄⢸⡾⡆
⠀⠀⠀⠀⠀⢀⣏⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣉⡁⠀⠀⢻⡿⢻⣿⢣⠇
⠀⠀⠀⠀⠀⠘⣎⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠛⠀⠀⠈⣿⡾⣿⣘⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠈⠑⠲⡯⣿⠀⠀⠀⠀⠀⠀⠀⠒⠛⢡⣿⡅⠀⠀⠀⠀⢸⣿⡿⡡⢀⢹⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⣿⡇⣴⣿⣿⡶⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣿⡿⠈⣼⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⡇⠈⠁⢸⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠃⠀⣼⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⣆⡇⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡼⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⡇⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣷⠀⠀⠀⡤⠘⠃⠂⠐⠛⠉⢙⠢⡀⠀⠀⠀⢀⡀⣷⣬⣭⣭⣟⢦
⠀⠀⠀⠀⣠⢖⣻⣭⣽⣗⢿⢻⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢆⠙⣤⠄⢲⡀⠠⠤⠤⠄⠀⣿⣸
⠀⠀⠀⡼⡷⢩⠋⠀⠂⡍⢷⡤⡽⣦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢦⠈⠓⠸⡄⠀⠀⠀⠀⢠⡟⣿
⠀⠀⠐⣷⡇⢠⠀⠀⠀⠐⢸⡇⡿⢮⡳⣤⡀⠀⠀⠀⠘⢧⠀⠀⢘⠳⣄⡀⠙⠀⠀⠀⢀⠞⢳⡞⡆
⠀⠀⠀⢳⡳⣄⠑⢦⠶⣣⡾⣳⠃⣰⢣⣿⣿⣶⣤⣀⣀⣀⣳⡀⠈⣆⠀⠉⠐⠛⠓⠛⠁⡴⠻⣞⢧
⠀⠀⠀⠀⣹⢞⣹⡧⣾⢻⣜⡇⠀⠈⠓⠮⣽⢛⣿⣿⣿⣿⡏⡁⠀⣏⠁⠀⠀⠀⠀⠀⢀⡆⠀⠘⣯⢣
⠀⠀⠀⢸⡷⣏⣡⡕⢸⠈⢧⡳⣤⢤⣖⣫⣶⣿⣿⣿⣿⣿⣟⣇⠀⠹⡦⠀⠀⠀⠀⠀⢨⢳⡀⠀⠘⣯⢧
⠀⠀⠀⠐⡗⣯⡤⢮⠸⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣏⠠⠀⠙⠦⣄⡀⠀⠀⠀⠀⡅⠀⠀⢸⡎⡆
⠀⠀⠀⠀⢯⢻⡄⢛⣶⠀⠀⠈⠉⠛⠟⠀⠈⠛⠻⠿⠛⠉⢰⠘⢄⣀⡠⠀⡀⠉⠉⠒⠒⠶⡆⠀⠀⣼⣿⣸⡀
⠀⠀⠀⠀⠀⠳⣽⣟⢻⠁⠙⠺⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⡼⠃⠀⡰⢻⣿⣧⢧
⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⡜⠀⠀⠀⠀⢠⢞⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠁⠒⠛⠀⠖⠋⠀⣿⣿⣿⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢯⡳⠾⠶⣶⣶⣶⠒⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣿⣿⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢟⣾⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⣿⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠴⣺⣵⣾⣿⣿⡟⣠⠁⠀⠀⠋⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠤⠆⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣎⢿⣿⣿⡿⢟⣉⣏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⣿⣿⣿⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⠭⠭⠖⠉⠳⣝⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣿⣿⣿⣿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠯⣽⣟⣲⡶⠦⣤⣤⣬⣥⣤⣴⣦⣭⣤⠤⢶⡖⣿⣿⡿⣣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠒⠒⠒⠛⠛⠋⠉⠙⢾⣫⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣒⣒⣈⣉⣭⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⠁⣀⡄⠘⢒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⢸⠡⢑⠋⣛⣘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢹⠀⠀⠀⠀⠨⣉⣹⠋⣉⣉⡀⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠔⠲⡄⠀⢸⣀⣸⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⡦⢴⠒⢲⠚⢏⠱⡀⢸⣀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡡⢣⠘⡄⢣⠀⢇⠈⢆⢱⢸⠒⢺⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡱⡀⢇⠱⣀⣦⡈⣆⠘⡆⢻⣃⠼⠖⠤⢄⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢱⠈⣆⡏⡏⢹⣘⠤⣼⢾⡋⢕⣦⡒⠊⢹⡀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢗⡉⣇⣇⣸⠲⠤⠄⠛⠉⠒⠿⣔⡒⠮⠬⠓⠢⡏⠛⡞⢻
⠀⠀⠀⢀⣴⡒⠤⣀⠀⠀⠀⠀⡟⢢⠉⠒⢥⣤⠤⠤⠒⠂⠉⣉⣁⡤⠤⢤⡀⠀⠀⢧⣀⡇⢸⣄
⠀⠀⠀⢰⠑⠌⠑⠬⣑⠢⢄⠀⡇⢸⠀⠀⠀⡇⠉⠶⢮⣭⢿⣞⣷⣏⡿⠧⠬⢷⠒⠒⠉⢩⠋⢸⠲⢄
⠀⢀⣀⣨⣄⢸⠓⡤⣀⢱⢶⠛⡗⠺⢶⠈⢻⠍⠛⡇⢸⠈⡏⠉⠀⠀⠀⠀⠀⢸⠀⢀⡀⠠⣒⢸⠑⢤⡑⢤⡀
⣰⢿⢳⡄⠀⠉⡏⠀⠈⡟⡾⡖⢳⠺⡾⡖⠒⡤⠤⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⣔⢣⠹⡀⠀⢸⠵⣤⡉⠢⡈⠢⣄
⣿⡼⠾⣧⠀⠀⢸⠀⠀⡶⠸⣰⠀⢧⢱⢱⠀⠸⡒⠧⣸⠀⡇⠀⠀⠀⠀⢀⣀⡸⠬⡌⠆⢳⠲⡏⠀⠘⡌⠢⣌⣢⣌⡱⣄
⢻⡷⡞⡿⠀⣠⣼⠤⠒⠻⡊⠉⠑⢼⡄⢃⢣⠀⢱⠀⠈⠑⠓⠒⠈⠉⠉⠀⠀⠀⠀⢱⠸⡈⢿⣷⠀⠀⣷⠀⣇⠀⢸⠀⢨⠤⡀
⠘⢧⣼⡇⣼⢿⠙⣧⠀⠀⠘⡄⠀⠈⣷⠈⡎⢆⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢱⠘⡟⠀⢀⣷⡾⣏⠉⠉⠛⡁⠀⠈
⠀⠀⠀⠀⠺⠶⢳⡋⡄⠀⠀⡇⠀⠀⡦⠃⢸⠺⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣇⣹⠈⢹⡏⣃⣸⡆⠀⠀⢱
⠀⠀⠀⠀⢐⡾⢮⣹⠇⠀⠀⡇⠀⢀⡧⣤⠜⠦⡤⡼⠋⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⢇⢰⡝⡇⣯⡆⠀⠀⢸
⠀⠀⠀⠀⠈⠳⣬⣿⡠⠤⠴⠓⠒⡯⢫⠩⠆⠀⠀⠰⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢷⡖⡏⠉⠛⢭⣦⡇⠀⠀⣸⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠜⠞⣧⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢍⠑⠦⣉⠤⠔⠒⠊⣹⠓⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⠶⡋⠛⠀⠀⢀⠇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠧⠔⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢄⢟⡆⣀⡀⠼⠤⠖⠊

⠀⠀⠀⠀⠀⢉⠧⡀
⢀⣀⠀⠀⠀⠣⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠆⠉⢩⠕⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢸⠀⠀⠀⠠⣤⣄⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⡇⠀⠀⠨⠀⠈⠁⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⢸⠀⠀⠀⠀⠢⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠉⠲⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰
⠀⡎⠀⠀⠔⠀⠀⠈⢠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠲⠂⡠⠀⠀⠀⠰⣀⠀⢀⣰⠃⠀⠀⠀⠀⡠⠂⢄⠀⠀⠀⠀⡞
⢠⠁⠀⠠⡀⠀⠀⠀⢐⠈⠀⢄⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠭⣉⠁⡱⠓⠢⡀⠀⠀⢇⣀⡜⠀⠀⠀⠀⢅
⠁⠀⠀⠀⠀⠀⠀⠀⣨⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢇⣀⡸⠀⠑⠤⠔⠁⠀⠀⠀⢀⠖⠒⢄
⢠⠊⠑⡄⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⡜
⠈⠢⠔⢫⠖⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⢢
⠊⠑⡄⣌⠀⠀⢀⡄⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠂⠀⠀⠀⠑⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠤⠞⠁⠈⠢⠔⠊⠀⠀⠀⠀⠦⡠⠃⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠛⠃⠒⠀⠤⠀⠀⠀⠀⢴⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠄
⠖⠋⠐⠄⠀⠀⣔⠉⣢⢀⢠⠔⠉⠒⡄⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠒⠒⠂⠈⠁⠀⠀⠀⠀⠈⠡
⠠⠀⠀⠈⢂⠀⠈⠉⠁⠀⠈⠣⣀⡠⠇⣠⠤⢤⡀⠀⠀⡠⢀⠀⠀⢀⠤⠴⠖⡢
⠀⠑⠀⠀⠀⠑⠄⠀⠀⡀⠀⠀⠀⠀⠀⡅⠀⠀⡹⠀⠘⠄⠠⠃⠀⠀⢁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠑⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡷⢤⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡁
⠀⠀⢃⠐⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⡰⠈⠉⠉⠲⡀⠀⠀⠀⡠⠤⡝⠈⠁
⠀⠀⠈⠣⢀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠱⣄⣀⣀⡴⠁⠀⠀⠀⠆⠠⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⢰⡁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡠⠾⣍⠀⡔⠓⠲⡀
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡎⠀⠉⡇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠜⠀⠑⠤⠚
⠀⠀⠀⠀⢂⠀⡨⠀⠀⠀⠀⠙⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣴⣿⣿⣶⣶⣶⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠻⠿⠤⣭⣿⣏⣿⣿⣻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣤⣠⣀⣀⣀⣛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⢿⣿⡿⠛⠛⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣿⡇⣠⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⣿⢿⣿⣟⣿⢿⣾⣿⣿⣿⢯⡿⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⢯⣾⣛⣾⢯⣼⣹⢏⣾⠃⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢀⣠⡴⣾⠟⠿⣩⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⣳⣾⣭⣿⠻⣾⣼⡏⣾⣇⣀⣠⣤⣶⢶⣿⣷⣾⡇⣷⣠⠾⠋⠡⢞⣡⠤⠊⠁⣰⢯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⣿⣿⣿⣷⣿⣛⡿⣶⣿⣼⣿⡿⣟⡵⣛⣿⣾⣿⣿⡿⣷⣿⣧⠀⠀⠈⠩⠔⠀⡠⢞⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⣿⣿⣿⣿⣏⣻⢷⡿⣽⣿⣿⣿⡻⣶⣿⣉⠶⣿⣿⡋⣽⣿⣿⡀⠀⠀⣀⣀⣬⣶⢟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢻⣇⣿⣿⣿⣯⣿⢻⡿⣼⣿⣻⣿⣟⣻⣿⣿⣿⣶⣝⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣷⣿⣻⣿⣿⣿⣿⣷⣿⣫⡿⣱⣿⣿⣫⣶⣾⣛⢷⣝⣻⣿⣿⣿⣿⣿⣿⡿⢟⣻⣽⣿⣿⣿⣿⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣭⣿⡿⢿⣿⣿⡿⣀⣿⣵⣿⣿⣟⣛⣶⣞⣻⣷⣿⣿⣿⣿⠿⣿⣿⣵⣟⣿⣯⡿⣿⣯⡽⣶⣛⣿⡟⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣜⡻⢷⣿⣻⡇⡇⠸⣇⠐⡟⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⣟⣋⠿⣾⣯⠿⣿⣛⣿⣶⡟⣻⣭⡿⢿⣏⢿⣦⢻⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣬⣙⠃⡇⡘⠛⢿⡏⣿⣿⣿⠿⢟⣻⣭⠷⣿⣿⣽⠿⣿⣯⡿⢿⣯⣻⣶⣞⢿⣯⣽⢿⣎⣻⣷⣿⣻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⢿⣿⣇⣿⣦⣽⣆⣿⣿⡿⣿⣭⣿⢿⣿⣯⣝⢿⣿⣯⣝⢿⣯⣍⣷⣾⣿⣷⡽⢷⣛⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⢯⡿⡿⣹⣧⣸⣯⣿⣿⣿⣿⣽⡻⣿⣿⣭⡿⢿⣭⡽⠿⣿⣦⣜⢿⣷⣿⣿⠷⣺⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣳⢿⣿⣾⣿⣿⣿⣟⢿⣿⣿⣿⡄⣿⣷⣭⡻⢿⣧⣭⣿⣿⣟⣭⡷⢞⣻⣿⣿⠟⡋⠁⠈⣷⢰⣴⡶⣶⡿⣛⣦⡀
⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠈⢿⣽⢿⣿⣽⣿⣛⣛⡋⢹⣿⣯⣉⣡⣼⠿⣿⣿⣷⣾⣿⣿⣫⣭⣶⣿⠟⠻⠛⠁⠀⠀⠀⠀⣿⣿⣯⡟⣢⣿⣿⣿⣿⣧
⠀⣴⣿⢿⣟⠾⣿⣿⣦⣀⣤⢞⣵⡿⠛⠙⠛⠿⣿⣙⣷⡝⢧⣝⢻⣿⣻⣶⣝⣿⣿⡿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡳⢰⣿⡏⡄⠈⣿⣿
⣾⠷⣝⡳⢭⣿⡿⢟⣭⣭⡾⠛⠁⠀⠀⠀⠀⠀⠈⠛⠿⠿⣶⣿⣿⣿⠟⠛⠛⠛⠛⠀⣿⣿⡀⣀⣤⢶⣶⢾⡳⣤⡀⠀⠀⣿⣿⢯⢸⣿⣷⣠⣴⣿⡿
⣿⣷⢮⡛⣾⣯⣁⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻⡙⣿⣷⣝⢓⣭⣶⣿⣿⣿⡄⠀⠘⠿⣕⣺⣿⣿⣿⣿⠟⠁
⠹⣏⠲⣭⣻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢤⣿⡿⠛⠉⢻⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠙⠻⣶⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣯⣸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣶⡿⢯⣛⢿⣵⣆⠀⠀⠀⠙⢷⣸⣿⣿⣷⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣝⣛⣷⣿⣿⡿⣿⣷⡀⠀⠀⠀⠙⠛⠻⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢾⣽⣿⡿⢉⠑⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢺⣿⣇⠈⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣿⣿⣿⣿⠟⠁
⣿⣿⣿⢿⣿⠿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣧⣴⣯⣶⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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