Washing machine Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⠙⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠦⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣄⣀⡀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠿⣿⣿⣟⢮⢆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⣿⣤⣽⣿⣿⡎⡟⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⡇⡇⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣜⣿⣿⣿⣿⣿⣿⣿⣡⠃⠃⠐⠈⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠎⠻⣿⣿⣿⡟⣟⣁⠀⠀⠄⠀⠀⢀⣀⠀⢀⠀⢀⣢⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡀⠄⠀⠀⠀⢈⣁⠉⢉⡉⠁⠸⠛⠲
⠀⠙⠻⠿⠿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡉⠡⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣭⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣶⣶⣶⣶⣾⡿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠉⠀⠀⠉⠉⠛⠛⠶⢶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣶⣶⣿⠿⠿⠿⢿⣿⣿⣛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣛⣛⣛⣻⣭⣭⣭⠭⠿⠶⣶⡶⠖⣛⠛⢻⡟⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁⠀⠀⠘⣿⠐⣿⣿⡿⠿⠿⠿⠇⢸⡇⠀⣾⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠄⠆⠂⠐⢘⠀⢸⡇⠀⠙⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣿⠟⠿⠿⠀⣿⠀⢀⣃⣁⣁⣬⣤⣤⡼⠷⠶⠖⠺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣶⣿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⢀⣠⣤⡶⣶⣶⡶⢶⣤⣀⠀⠀⠀⠀⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⡿⣫⣷⣿⣿⣿⣭⣛⠶⣝⢷⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢷⣻⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⡿⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠹⣿⣷⡽⢿⣿⣿⣿⡿⢟⣫⣾⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠘⠿⣿⣷⣭⣽⣿⣿⣭⠿⠛⠁⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⢀⣀⣠⣤⣶⣶⣾⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣤⣤⣴⣶⠾⠿⠛⠛⠉⣿⡇⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⣀⣴⣶⡷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠋⠉⠁⠀⠀⠀⣀⣀⣠⣄⣤⣤⡶⠶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣴⣶⣾⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁

⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⣴⣿⣷⡆⢠⣾⣿⣶⠀⣴⣿⣿⡆⢀⣾⣿⣷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠀⠙⠿⠿⠃⠈⠻⠿⠟⠀⠙⠿⠿⠃⠀⠻⠿⠟⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⠿⠿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢀⣤⣶⣾⣿⠿⠿⣿⣷⣶⣤⣀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⢹⣿⡄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⡿⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⢿⣷⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣿⡇⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⢸⣿⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⠃⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣧⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⡄⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢠⣿⠏⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠈⠛⢿⣷⣶⣤⣤⣤⣤⣶⣾⡿⠛⠁⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣶⣤⣤⣤⣤⣶⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⣿⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣿⣿⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠶⠶⠶⠖⠒⠶⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣿⣿⣿⣷⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠛⠻⢽⣓⣶⡶⣶⣶⣒⣚⣛⣿⣿⣯⣭⡿⠿⣿⠿⣶⠚⠛⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢹⡟⠉⠉⠉⠀⠘⣿⠰⣶⠿⠿⠿⠿⠃⣿⠀⢰⣿⠄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡀⠀⠀⠀⠀⢸⠀⢀⣀⣀⣀⠀⣿⠀⠐⢐⢐⢈⠨⠀⣿⠀⠀⣉⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡀⠀⠀⠀⢸⡇⠘⠛⣉⣋⣀⣿⣤⣤⣤⡶⠶⠶⠚⠛⠛⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡇⡇⠀⠀⢰⢸⡿⠿⠟⠛⠛⠋⠉⠉⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⡇⠀⢸⢸⢸⡇⠀⠀⠀⠀⢀⡴⣚⣭⣶⣶⣖⠮⣝⢿⣦⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⣷⢸⢸⢸⠸⡇⠀⠀⠀⢀⣞⣼⣿⣿⣿⣿⣿⣿⣎⢳⡹⣷⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⢸⢸⢸⢸⠀⣇⠀⠀⠀⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⣿⡇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢸⢸⢸⠀⣿⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⡿⢀⣇⣿⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⢸⢸⠸⠘⠀⣿⡇⠀⠀⠘⣞⢿⣿⣿⣿⣿⣿⠟⣡⢞⣾⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⠀⠃⣿⡇⠀⠀⠀⠈⠢⣝⡻⠿⠿⣗⣫⣷⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡄⣿⣧⡄⠀⠀⠀⠀⠀⠉⠙⠛⠉⣉⣀⣠⣤⣶⣶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠃⣿⣿⡇⠀⠀⣀⣀⣤⣤⣶⠾⠿⠛⠛⢹⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢻⣿⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⣀⣸⣧⡴⠿⠗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⢸⠀⢀⣀⣀⣤⣤⣦⡶⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠈⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⢾⡁⣹⠆⠀⠀⠀⣿⠁⠉⠈⠉⠉⠁⠉⣇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⢛⣋⣉⣉⣛⠓⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣥⠖⠛⠉⠉⠀⠈⠉⠙⠓⢦⣉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠏⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⢷⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⡄⢷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⡆⢷⠸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢷⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡴⠃⡟⢸⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢦⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣡⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⠓⠦⢤⣤⣀⣀⣤⠤⠖⢋⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠒⢒⡒⠲⠶⠤⠤⠤⢤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠔⠀⠀⠃⠀⠀⠀⠀⠀⠁⠉⠉⠉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠘⠚⠁⠃⠀⠀⠨⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠊⠀⠀⠀⣇⠀⠀⡅⢈⣉⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠊⢏⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠇⠃⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠆⠦⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠐⠀⠀⠀⠉⠓⠢⢄⡀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢉⠉⠀⢇⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢧⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡌⠀⢰⡘⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢱⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⢨⡃⠀⠀⠀⠀⠀⠇⡆⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣿⡀⠸⠀⠀⠀⠀⠀⠀⢀⢧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠷⡉⢀⠄⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠏⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠈⠽⣆⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢃⠀⠀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠊⠃⣀⠀⠀⠀⠉⠉⠀⠚⠛⠛⠉⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡆⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⠦⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠻⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠂⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⡀



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

⠀⠀⠀⠀⠀⢠⢤⣤⣤⣤⣤⣤⡤⢤⣤⠤⠤⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢤
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⣏⠉⣷⢾⠉⢹⣾⡯⡭⢭⢭⢭⡭⡽⣿⠀⢸
⠀⠀⠀⠀⠀⠰⠛⠒⠒⠒⠒⠒⠓⠛⠛⠓⠚⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠒⢺
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⡠⠼⠒⠂⠉⠀⡠⠤⠭⡓⠤⣈⣉⢴⡒⢦⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⡀⠀⢀⣀⠀⠈⠙⢦⡀⠀⠀⡬⠤⠤⠀⠀⠶⣮⣍⣀⣐⣒⣒⡽⠐⠒⠷⠶⠤⠿⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠞⠁⢀⠔⢋⣡⡤⠤⠤⣤⡉⠒⢄⠀⠙⢦⠀⡇⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠾⣇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢠⡏⠀⠰⠁⡴⠋⠁⠀⠀⠀⠀⠉⢳⡀⢣⠀⠈⣧⡇⠀⠀⠀⡼⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⢀⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠇⠀⢸⣧⠀⠀⢰⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⡄⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠘⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡄⠀⢸⠏⣄⢀⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣄⠀⠘⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠸⡆⠀⢣⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠏⡠⠁⠀⡾⠀⡏⣉⣀⣀⣀⣀⣀⣠⣠⣄⣀⣀⣀⣀⣀⡀⡝⠋
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⣄⠀⠑⢄⠙⠲⠤⣤⠤⠴⠚⢁⠔⠁⢀⡼⠁⠀⠇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢦⣄⠀⠉⠒⠂⠤⠄⠒⠊⠁⢀⡴⠏⠀⠀⠀⢠⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⢤⣤⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⢸⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⣀⢸⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢸
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡿⠀⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠨
⠀⠀⠀⠀⠀⠰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣂⣀⣀⣊⣁⡄⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⢸
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠋⠑⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠐⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣰⢀⣴⠟⠛⠛⠉⠉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣉⣉⠛⠛⠷⣦⡀⢦
⠀⠀⠀⠀⠐⠃⣾⠃⠀⢰⡟⠛⣛⣋⠉⠉⣉⣭⣉⠁⢠⣴⠶⠶⠶⠶⠶⠶⠶⣶⠶⣦⡀⢀⡤⠤⣄⠀⣠⣤⣌⠉⢹⣇⠀⠀⠸⣧⠈⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣼⣟⣻⣷⢰⣿⣋⣿⡧⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠓⠒⠃⠀⠻⠶⠟⠀⢸⡏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⠈⢻⣿⠋⠀⠙⢳⣟⠁⠀⢿⣤⣤⣤⣄⣀⣀⣀⣀⣠⣿⠃⠸⣏⣹⠇⠀⣟⣉⡿⠀⣼⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠷⠶⠶⢶⣶⣶⣤⣴⣶⣤⣶⣴⣦⢤⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠶⠛⠛⠷⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⢶⣴⡾⠛⢉⣩⡤⠖⠚⠉⠉⠉⠉⠉⠉⠛⠒⠦⣍⡙⠻⢶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢀⣴⠟⢁⠴⠚⠉⢁⣀⣤⣤⠶⠶⠶⠶⠶⠶⢶⣤⣀⠀⠉⠓⢦⡙⣷⡀⣀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠃⣴⠋⠀⣠⠾⢛⣩⠴⠒⠛⠉⠉⠉⠉⠉⠓⠦⣝⠻⣆⠀⠀⠻⡌⢻⡎⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⣸⠃⠀⣼⠏⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⣷⠀⠀⢻⠀⢿⡀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠘⣷⠀⢠⣤⣿⠀⡇⠀⠀⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡆⠀⠸⡇⢸⡇⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠁⢿⡄⡇⠀⠀⣿⠸⡇⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢿⠈⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢹⡇⠘⣧⢻⡀⠀⢸⣇⢳⡸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⢸⠀⣿⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣧⠀⢹⣎⢷⡀⠀⢻⣆⠱⣌⠛⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⡇⠀⠀⡼⢰⡟⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢲⠘⣷⠀⠙⠛⠛⠻⣆⢳⡀⠀⠙⢷⣌⠙⠲⢤⣄⣀⣀⣀⣀⣠⡤⠶⢋⣴⠟⠀⢀⡼⢃⡿⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠃⣿⠀⠀⠀⠀⠀⠹⣦⡙⢦⣀⠀⠙⠻⠶⢦⣤⣤⣤⣤⣤⣤⡴⠾⠛⠁⢀⡠⠞⣡⡾⠁⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣌⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⣠⡾⠋⠀⠀⠀⠀⢸⡇⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢤⣉⠻⢶⣤⣬⣉⣉⣛⣒⣒⣒⣋⣉⣤⣤⠶⠟⠋⠀⠀⠀⠀⠀⠀⣿⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡒⠚⠛⠛⠛⠛⠛⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠓⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣀⡀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⢿⡆⣾⡟⠙⢻⣇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣴⡿⠃⠻⣷⣴⡾⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠛⠛⠛⠛⠿⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⢋⣁⣤⣶⡶⠾⠿⠿⠶⣶⣦⣤⣈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣰⡿⠋⣠⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⡈⠻⣷⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣼⠟⢀⣾⠟⠁⣀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠘⢿⣆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡏⢠⣿⠋⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⡆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡿⠀⣿⠇⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣸⣿⣀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⡿⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠋⠙⠛⠛⠛⣿⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⡀⠀⠀⣀⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⣇⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⠛⣿⠟⠋⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⡄⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣼⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠹⣷⡀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣰⡿⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⢿⣄⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⢁⣼⠟⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠻⣷⣄⡉⠻⠷⣶⣤⣄⣀⣀⣀⣀⣤⣴⣶⠿⠋⣡⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣉⣉⠛⠛⠛⢋⣉⣁⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠟⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⢿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⢸⠉⡜⠛⠛⠛⠛⠛⠛⠛⠛⠛⡍⢉⣵⣿⣭⡉⠉⣩⣽⢿⣍⠉⢹⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⢫⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⠀⠈⣿⢰⣏⠀⠀⢹⡇⢸⡷⢶⡤⢴⡴⢤⡶⢤⡤⢴⡤⢾⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣧⣤⣠⣤⣤⣤⣤⣤⣠⣤⡇⠙⢷⣶⡾⠋⠀⠻⣶⣶⠟⠁⢸⣧⣴⣧⣼⣧⣼⣦⣼⣧⣴⣧⣼⣼⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠉⠉⠁⠈⠉⠉⠉⠛⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣀⠴⠒⠉⠁⠀⠀⠀⠀⠈⠉⠒⠦⣀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣠⠞⠁⢀⣠⡴⠶⠛⠛⠛⠛⠶⢦⣄⡀⠈⠳⣄⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⡜⠁⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⢣⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡿⠀⠀⠀⡜⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢣⠀⠀⠀⢿⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⢠⠃⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⡄⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠈⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⠁⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⠀⠀⠀⢱⡀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢀⡎⠀⠀⠀⣿⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠳⡄⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⢠⠞⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠘⠦⣀⠀⠉⠛⠳⠶⠶⠶⠶⠾⠛⠉⠀⣀⠴⠃⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠈⠓⠢⢤⣀⣀⣀⣀⣀⣀⡤⠔⠚⠁⠀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢦⣤⣄⣀⣀⣀⣀⣠⣤⣴⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣟⣉⣉⣉⣉⣉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣉⣉⣉⣉⣉⣹⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡼⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠶⠶⠶⠶⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢉⣀⣀⣀⣀⣤⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣉⠉⠉⠉⠉⡿⠁
⠀⠀⠀⠀⢰⡶⠒⠒⣲⡿⠂⠀⠸⡇⢸⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢙⡆⠀⣏⠉⢉⡇⠀⠀⡇⠀⢠⡴⢤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⢻⣀⡴⠋⠀⠀⠀⠀⣇⠸⡀⠀⠀⠀⠀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣥⣤⣀⣈⣉⣉⠁⠀⢰⡇⠀⠀⢹⡄⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠶⠦⠉⠀⠀⢸⡇⠀⠀⠀⠹⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⡠⠒⠉⠉⠛⠦⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠⠶⠗⠀⠠⠀⢸⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙⠛⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢦⣄⡀⠀⠀⢀⣠⠏⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢱⡀⠀⠁⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣤⣄⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠤⠤⠤⠤⠤⢐⣒⣒⣒⣛⣋⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠙⠛⠒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⣀⣤⣤⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⢳⣄⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡏⡽⠛⠛⠛⠛⠛⠛⠛⠛⢯⢉⣭⡿⣿⣍⠉⣩⣶⢿⣭⠉⡽⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⢿⠉⠉⢹⡂
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡏⠀⠀⣿⢶⣿⠀⠀⢹⡇⣯⡷⢶⠶⣶⠶⣶⠶⣶⠶⣶⠾⣼⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⣷⣤⣤⣤⣤⣤⣤⣤⣤⣼⣈⣻⣷⣾⣋⣀⣙⣷⣾⣟⣁⣿⣷⣾⣶⣿⣶⣿⣶⣿⣶⣿⣶⣿⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠟⠛⠛⠻⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⢀⡠⠴⠒⠚⠉⠉⠒⠒⠢⢤⣀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⣠⠞⠁⢀⣠⣤⡴⠶⠶⠶⣤⣄⡀⠈⠳⣄⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠏⠀⠀⢀⠞⠁⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠈⠳⡄⠀⠀⠹⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡟⠀⠀⢀⠎⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢻⡄⠀⠀⢻⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡇⠀⠀⢸⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣧⠀⠀⠘⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡄⠀⠀⣏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⠀⣸⣃⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⢸⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡟⠀⠀⢰⡟⠀⢸⠉⠉⠉⠉⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣧⠀⠀⠈⢆⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣸⠃⠀⠀⣼⡇⣀⣸⡟⠿⠿⠛⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣇⠀⠀⠈⢦⡀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⢀⡴⠃⠀⠀⣰⡏⢁⢀⡽⠉⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⢦⣀⠈⠙⠛⠷⠶⠶⠾⠛⠋⠁⢀⡴⠋⠀⠀⢀⣴⢿⠀⡎⡹⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠉⠛⠲⠤⣤⣤⣤⣤⠤⠶⠚⠉⠀⠀⢀⣠⠞⠁⢸⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣶⣶⣶⣶⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⣉⣩⠭⠭⣉⣉⣉⡁⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠒⠒⠒⠒⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⢉⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠤⠤⢤⣞⠳⠤⠤⠤⠤⠤⠤⠤⠔⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠑⢦⡤⠤⠴⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄⢶⠁⠉⠙⠛⠋⠛⠛⠛⠛⠋⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠖⠒⠒⠒⠒⠛⠃⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⣀⡀
⠀⠀⠀⡟⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠉⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠄⠒⢒⠒⠒⠂⡈⠉⠭⠭⠍⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠄⠒⠖⠒⠒⠒⠂⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠐
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⣠⠒⠀⢶⡄⠀⠀⡔⠢⠀⡖⠐⠀⢏⠈⠀⡇
⠀⠀⠀⡏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡅⠀⠀⠀⠛⠀⠀⠧⠀⠀⠳⠄⠀⠙⠂⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠴⠋⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⣤⠴⠶⠶⠶⠚⠛⠒⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢠⣤⠠⠤⠠⠤⠔⠒⠒⠒⠊⠉⠉⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠈⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡒⠷⠚⠛⠛⠛⠓⠒⠤⢀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡡⠊⠀⠀⠀⠀⣠⡤⢒⠂⠀⠀⠒⠤⣀⠀⠀⠀⠑⣄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡰⠁⠀⠀⠀⡠⠊⠀⠀⠀⠈⠑⠢⡀⠀⠈⢳⣄⠀⠀⠈⢆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠈⢺⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠹⠂⠀⠀⠘⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⡆⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⢡
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠀⠀⠀⠘⣕⠢⢀⣀⣀⡀⠄⠂⠀⠀⠀⡠⠁⠀⠀⠀⢀⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣣⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⢀⠎
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠉⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠤⠤⠤⠄⠒⠊⠁
⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠐⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠄⠒⠒⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⢀⣀⣀⣤⠤⠤⠔⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠒⠂⠀⠐⠛⠛⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⣉⣉⠉⠉⢁⣀⣀⣒⣒⣒⣒⣂⣀⣀⠀⠀⠀⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣀⣀⡀⠀⠀⠀⠸⠀⠀⣧⣀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠁⠀⠀⣀⣀⣬⣥⣈⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠐⠂⠈⠉⠉⠐⠒⠭⢁⠀⠀⠐⠒⠶⠶⠢⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠤⠤⠤⢄⣀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠋⠀⡀⢀⠔⠀⠀⠀⢠⠀⠈⠙⠢⡀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠃⠀⡞⡰⣡⠀⢠⢂⡤⠎⢀⠞⡆⠀⠈⢢⠀⠀⠀⢡⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡎⠀⡸⢰⠁⡇⠀⡞⠀⠤⠖⠁⠀⠘⠄⠀⠀⢃⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇⢸⠀⡇⠀⢱⠀⠀⣀⠤⠔⠒⠤⣄⣠⢜⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢁⠸⡀⠰⡀⠀⢣⡀⠀⠒⠒⠒⠒⠤⡀⢀⠃⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠀⠀⡀⢳⡀⠙⢄⠀⠙⠢⢄⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢂⠀⠈⢆⠙⢤⡀⠑⠢⠤⠄⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠑⠢⣍⡒⠲⠦⠤⠶⣒⠔⠊⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠄⢀⡀⠀⠠⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠦⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠲⠶⠤⠤⠤⠤⠀⠀⠠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃
⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠉⠉⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠈⠣⡀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡰⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠙⡄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠁⠀⢀⠃⠀⠀⠀⠀⢀⠀⠐⠀⠀⠂⠄⠀⠀⠀⠀⠀⢡⠀⠀⠸
⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎⠀⠀⡌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢇⠀⠀⢁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡄⠀⠈⠄⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠜⠀⠀⡰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠱⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⣠⠃
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠀⣀⡀⠠⠤⠔⠒⠉
⠀⠀⠀⠀⡃
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⣤⣤⣠⡟⠁⡴⠃⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡾⠋⠁
⠀⠀⢀⣀⠀⠀⠓⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢶⣤⣀
⠀⠀⣏⠀⠴⢤⠦⣾⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⠿⠆⠀⢰⣿⢐⡇⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣸⠀⠀⢀⣤⣤⠞⠋
⠀⠀⣀⣌⣤⠆⣼⠃⢸⣷⠀⢸⡇⠀⢰⡀⠀⠀⠀⠀⣠⠄⠀⢠⣿⠀⠀⣀⡈⠁⢀⣴⠟⠉
⠀⢰⡏⠀⠁⠀⢹⡄⢹⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⣼⡿⠀⠀⢸⡏⢀⡀⣨⠟⠀⣼⡟
⠀⠀⣿⠂⣀⣀⡀⢻⡌⢻⡀⢸⡇⠀⢸⡟⠀⠀⣰⡏⣴⠀⠀⣸⡟⠈⣹⠁⠀⣼⣿⡁
⠀⠀⠈⢻⡋⠀⠁⢀⣽⠶⢿⠈⣧⠀⣿⡁⠀⠀⣿⠃⢿⠀⠀⣿⣁⡿⠋⢀⣾⠟⢉⣷
⠀⠀⠀⣾⣧⡾⠀⣾⠃⠀⡘⣧⣹⡄⢸⣇⠀⠀⢿⡀⠘⢧⣀⡟⠈⣠⡴⠛⠁⠀⠈⢿⡀
⠀⠀⠀⢿⠀⠀⠀⣿⢀⡾⢁⠀⠉⢳⣜⣿⡀⠀⢸⡇⠀⠀⢉⣴⠾⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡷⠂⠀⢻⡾⣱⠏⠀⣴⡿⠉⠛⢻⡄⠈⣿⢀⣴⡾⠋⠀⠀⠀⠀⠀⢀⣷⠏
⠀⠀⠀⣼⠋⠀⠀⠸⢷⡟⢀⣸⡟⠁⢀⡖⠀⢻⣦⠟⠋⠁⠀⠀⡄⠀⠀⢀⣷⠾⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠘⠛⠛⠋⠀⠀⠻⠶⠶⠛⡉⠀⠀⠐⢦⡖⠃⠀⣀⡾⠁
⠀⠀⠀⠸⣧⡀⠀⡀⠀⠀⠀⢧⣠⠀⠀⢀⣀⣠⠷⣄⣀⣠⡾⠃⠀⠉⣿
⠀⠀⠀⠀⠸⣧⣴⠏⠀⠀⠀⠀⢙⣻⣷⡚⠉⠁⠀⠸⣏⠉⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠛⠋⣩⢙⠻⢷⣤⣀⠀⠈⠛⠒⠚⠋
⠀⠀⠀⢰⣞⣷⢸⣿⣄⡀⠀⠘⠶⠟⣠⠤⢤⡈⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠁⢸⡇⠈⠛⢶⣄⡀⠀⠙⠚⣯⣤⣶⣶⠀⠙⠻⢶⣦⣄⠀⠀⠀⠀⣏⣹⠆
⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⠋⡵⢶⣻⠆⠀⠈⠙⢻⣶⡄⠀⠈⠉
⠀⠀⠀⠀⣴⣋⠙⢷⣄⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⣀⣤⣤⡶⠞⠋⠉⡇⢀⡠⢤⡀⠀⠀⠀⡶⠛⡆
⠀⠀⣀⣸⣇⠙⢷⣾⣉⠳⣤⡀⠀⠀⠀⠀⠀⠈⠙⣿⠟⠋⠉⠀⠀⠀⠀⠀⣇⠈⣀⣨⡿⠀⠀⠀⠀⠉⠁
⠀⠈⢯⡽⠙⠛⣿⠀⢈⣷⠈⠙⢶⣄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠁⣰⠛⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⢺⠀⠀⠀⢀⣠⣴⠶⠛⠉⠀⠀⠀⠀⠻⠤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠂⠉⠁⣤⠔⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠈⠁⠢⢀
⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠤⠤⡤⠔⠈⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠒⠀⣈⡉⠍⠁⠀⢢⠀⠀⢀⠄⠐⠀⠀⢖⠒⠢⡴⠁⠀⠀⣀⠄⠐⠉⠀⠀⠀⠀⠀⠀⠁⠢⢽⡀
⠀⠀⠀⠀⠀⠋⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⢃⠔⢁⣠⠄⠀⠀⠀⠉⢹⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠃⠀⠀⠀⠒⠂⠀⠀⠠⢄⡀⠀⢸⣷⠟⠉⠀⠀⠀⠀⠠⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠒⠂⠠⠝⣂⣸⣧⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠈⠒⠒⡒⠢⣄⡉⠐⠢⢔⣋⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⣇⠀⠙⢦⣉⠀⠀⡸⡏⠉⠙⡏⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡏⠀⠉⢻⣏⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠸⣷⣤⡀⠈⢉⠿⢀⠈⠀⠀⢳⣶⣽⣷⣦⣄⣀⣑⡒⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠛⠉⠀⠀⣠⡟⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⠁⠸⠢⢄⣀⠀⠀⠇⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠲⣤⠀⠀⠀⠀⣇⣀⡤⠤⠒⢛⣿⠁⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠉⠁⠀⣀⣀⠀⠠⣄⡀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠈⣇⠀⠀⠀⡟⠀⡐⠀⡆⠈⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢃⠸⠀⠀⠀⠀⠀⢇⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⢹⠀⠀⠀⡇⢀⠁⢠⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⠀⢗⠒⠂⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⢰⠃⡌⠀⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠂⠀⡧⢀⢀⠴⡃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠱⠐⠁⢀⡁⠐⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⠀⠀⠀⠣⠀⠆⠀⠀⠀⠄⠀⠄⠀⠀⠀⠇⠄⠂⠀⠀⠀⢀⡀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡅⠑⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⢀⠊⢉⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢡⠀⢁⠀⠀⠁⠀⢸⠀⠀⠀⠉⠉⠁⠀⠀⢠⠀⠀⠀⠀⠘⠀⡌⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⡀⠈⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠂⢀⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠒⠁⠀⠘⡄⢀⠆⠀⠀⠀⠀⠀⠀⠀⢆⣀⠜⠀⠀⠑⢁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠑⠒⠃⠀⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣔⡒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⣿⣦⣌⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡻⣷⣦⡈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⡿⣦⡀⠙⢕⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⢎⠇⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⢤⣤⣄⡀⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠳⠀⠀⢀⢠⣤⣤⣤⣶⣾⣾⣼⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢠⣽⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣴⡏⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣶⣶⠟⠋⠁⣀⣤⠶⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣤⡴⠖⠋⠉⢀⣀⣠⠄⠐⠒⠒⠀⣀⠀⠀⢀⡀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⡾⠋⠁⠀⣠⡴⠾⠋⠁⢀⣀⣠⠤⠀⢈⡁⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⣀⡠⠴⠾⠟⠋⠁⣀⡤⠞⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠉⠉⠀⢀⣠⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⢩⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⠁⠀⣀⣠⡤⢼⣦⣄⡀⠈⠉⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠛⠉⠉⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⣼⠀⠀⠉⠓⠶⣤⣀⠀⠈⠉⠛⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠚⠋⠉⠁⠀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣠⣤⣤⣀⣀⡈⠉⠓⠦⣤⣀⠀⠉⠛⠳⣤⣀
⠀⢀⣠⡤⠖⠛⠉⠀⠀⣀⣠⣤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠦⣬⣷⠟⠁⠀⠀⠈⠉⠻⣄⡀⠀⠀⠈⠙⠲⢤⡀⠀⠉⠙⣳⢦
⠀⣿⠣⢤⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠶⠤⣤⣤⠽⠿⠚⠋⢁⣼
⠀⢹⣦⣀⡈⠙⠲⢦⣄⡴⠒⠛⠷⠶⠛⠉⠉⠳⣄⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠒⣶⠊⠁⠀⢀⣠⡴⠞⠉⣿
⠀⠈⣧⠈⠉⠑⠦⣄⡈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠈⠢⣄⣤⡤⠤⠶⠦⣤⣤⣤⣀⡀⠙⠳⣦⡤⠔⠚⠉⠉⢧⠀⠀⠀⢸⡦⠖⠛⠉⠁⠀⠀⠀⡏
⠀⠀⢹⡄⠀⠀⠀⢠⡍⡗⠦⣄⡉⠛⠶⣤⡀⠀⠀⠀⠈⠓⠲⠶⠒⠀⠀⠀⢀⡩⠿⠚⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣧⠀⠀⠀⠘⣿⡅⠀⠈⠙⠲⢄⡈⠙⠛⠶⣦⣄⡀⠀⠀⠀⣀⡤⠶⠋⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢻⡀⠀⠀⠀⠻⣕⢤⡀⠀⠀⠀⠙⠲⢦⣄⣀⠉⠛⢳⡖⠋⢁⣠⠴⠖⢻⡇⠀⠀⠀⠀⡄⠀⠀⠀⢸⡇⠀⣸⠀⢿⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠛⠾⢷⣶⣤⣀⣠⠟⠀⠈⠙⠲⢼⡗⠚⠉⠀⠀⠀⢸⠁⠀⠀⠀⡼⠀⡀⠀⠀⢸⡇⠀⠏⠀⢸⡆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⢠⠃⠀⠀⢸⡇⠀⠀⣀⣸⡇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡟⠀⠀⠀⠸⠀⡌⠀⠀⠀⠸⡷⠞⠋⠉⠁⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⣀⣴⠇⠀⠀⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⣠⠶⠶⠖⠚⠋⠁⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧⠶⠋⠁⠀⠀⢀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⢸⡏⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣼⣧⣤⠶⠚⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠿⡏⠉⠩⡈⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠀⠀⢀⠀⠁⠀⠀⠀⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣶⢠⡀⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⢠⡱⡆⠑⢤⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠙⡅⠀⠈⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢣⠀⠀⠀⡇⠄⠀⠀⡸⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⢀⢷⠀⡠⢿⠂⠀⠂⠀⠀⡀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠍⠉⠁⠈⠻⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⡀⠑⠀⠀⢀⠀⠄⣀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢆⠀⢀⠀⠸⡄⠙⠒⠁⠀⠀⠈⠙⠐⠄⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⠀⠀⠘⠆⠈⠄⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠂⠠⢄⡀
⠀⠀⠀⠀⠀⣸⣿⠀⡀⢀⠠⠀⠀⠀⠁⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠀⡆
⠀⠀⠀⠀⠀⠿⠘⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠤⠀⠀⠠⠁⠀⠀⡇
⠀⠀⠀⠀⠀⣷⠀⠁⠀⢃⠀⠀⠈⠀⠁⠀⠀⠈⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠧⠲⣄⠶⢏⣤⠐⠛⠁
⠀⠀⠀⠀⠀⡿⠀⠀⠀⢘⡷⠦⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠶⠒⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢃⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠐⠛
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠋⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣾⣷⣦⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⠈⠛⠓⠀⠀⠀⠈⢸⣿⡏⠉⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠰⠋⣁⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⠉⠁⠀⠀⠈⣹⠂⠀⠀⠀⠀⠀⠀⠀⢿⣥⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡻⠛⢷⣄
⠀⠀⠀⠀⠀⢈⢳⣤⣤⡤⠤⢶⡖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣼⣜⣀⣠⡴⠶⣦⣀⣴⢟⠜⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⡾⣹⠿⠦⠤⠤⠤⠼⠧⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⠫⠂⠁⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⡇⣧⠀⢀⣀⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠳⣬⠟⠉⠉⠉⠉⢳⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣧⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠶⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢀⡴⠒⣄⠀⠀⠀⠀⠀⣀⣠⡾⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢠⣏⣠⠴⠃⠀⠀⠀⣠⡼⠋⠉⢻⡾⠃⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⣷
⡔⠓⠦⡀⠀⠀⢀⣄⡀⠀⠀⢠⡇⠀⢸⣀⣀⡉⠁⠀⠀⠀⠀⣀⣠⣿⡀⣠⠞⠛⠷⣄⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠙⠲⠤⣝⣦⠀⢯⡀⠙⡄⠀⢸⠇⠀⢸⣏⡉⠉⠛⠛⠛⠛⠋⠉⠉⠈⣿⠉⠀⠀⠀⠈⠻⣦⡀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣤⣾⠀⠰⣿⡙⠛⠳⠶⣤⣤⣤⣤⡴⠶⠶⠛⢷⣄⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣀⣤⣬⡿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠤⠤⠤⣄⡀⢹⣿⣭⣤⣤⠦⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠶⠶⠶⠛⠛⠷⠶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠲⠒⠊⠉⠀⠠⣿⣯⣥⠶⢖⣀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣀⠤⢖⡖⠀⠀⠀⠀⢀⣄⠸⠿⠶⢾⣟⣩⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣞⠁⣠⠞⠀⠀⠀⢀⠞⢉⡇⠀⠀⠀⠈⠉⠁⠀⠀⢰⡖⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⢶⣶⠶⠟
⠈⠉⠁⠀⠀⠀⠀⠻⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇

⣀⣀⣀⡤⠞⢧⣤⠤⢤⣀⡀
⢻⠁⢠⢒⢗⢦⠙⣦⠀⡇⢸⠉⠉⠉⠉⠉⠉⠉⠉⠛⣆
⢸⠇⠘⢮⣛⡼⣰⠁⣠⠧⠼⠒⠒⠒⠒⠒⠒⠲⣄⠀⢹
⠘⠲⡖⠲⢤⣄⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣤⠼⠲⡄
⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣉⣉⣉⣉⡇
⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠉⡇⠀⠀⢾⢣⠀⠀⣠⡲⠂⠀⢀⠞
⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣇⠀⠀⠈⠉⠀⠀⠈⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠄⠀⢸⠀⡏⠀⠀⡔⢩⢷⣄⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⢀⣡⠦⠶⣧⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡲⠶⠀⢀⠔⠉⠀⠀⠀⠈⠳⣄⡀⠈⠳⠤⠤⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⡇⠀⡧⠀⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠜⠀⢠⠁⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡜⠀⠀⡞⠀⠀⢻⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢦⣴⠇⣀⡀⣸⠠⡄⡽⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢮⣩⠵⠯⣽⣎⣡⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢜⣹⣷⡆⠀⠀⠀⠀⠀⠀⠦⠷⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣆⠀⠀⠀⠀⠀⡀⣸⡇⠀⠀⡀⠀⢀⣀⡠⡀⡘⢠⣿⣿⣿⣿⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⣀⣷⠜⢅⣸⣿⣿⣿⣿⣶⣭⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣧⡀⠙⢿⣻⣿⣵⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡟⢿⣿⣿⣿⢣⡰⢇⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣰⣃⡘⣿⣯⣾⢟⣿⣿⣿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡿⡿⣠⣤⣤⣄⣀⣀⣀⣀⣀⡈⠉⠙⣿⠉⡉⢿⣯⣆⢺⣥⣽⣿⣿⡟
⠀⠀⠀⣠⣼⣿⣿⣶⡞⠀⣩⣾⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⠿⣿⣼⣟⣿⣿⣿⠋⠉
⠀⠀⠐⣿⣿⣿⣿⣿⣶⣾⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣭⣽⣛⣛⣛⣟⣿⣿⣿⣿⣿⣄⡀
⢀⣤⣾⣿⣿⣟⣿⣿⡿⡿⣿⣻⣿⣿⣯⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢨⣿⣿⣿⡿⢛⣤⣚⣿⣭⣽⣿⣿⣿⢿⣿⣿⣷⣿⡛⠛⣿⡿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠿⣃⠄
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠂⠛⠛⠋⠉⠙⠛⠛⠳⠿⠶⣠⣻⣿⡿⢿⣿⣾⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠈⠀⠀⠀⠀⠀⠉⠀⠀⠠⠖⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⡠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡞⣠⠖⠉⠀⢠⡞⠁⢀⡾⠁⢀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣚⣠⠗⠁⠀⢀⡠⣾⠁⠀⣾⠀⠀⡼⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣩⣤⡤⠴⠒⠉⠀⣿⠀⣸⠇⢀⡾⠁⢠⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⣰⣯⡶⣋⠤⠚⠛⠳⠆⠹⣄⠀⡆⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⡀⠀⠀⠀⠈⢦⠀⠀⠾⠋⠀⠀⠉⠉⠉⠀⠀⡠⠀⠐⢤⠀⠘⣶⡇⢪⡖⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠂⣤⠠⠙⠒⠀⢠⢩⡆⠀⣠⣬⣌⠑⡄⠀⠀⠀⢰⣿⣿⣶⡀⠁⠀⠛⠁⠈⡛⠠⠞
⣀⡀⠤⠄⣠⠂⠀⠀⠀⠁⠀⠀⠙⢄⡀⠄⠐⠈⠀⠀⠑⠻⠀⠹⢿⣿⡇⠄⡠⠖⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⡜⢀⠀⠄
⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠚⢄⠀⠀⠀⠀⠙⠒⣀⢰⡄⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠉⠀⠀⠀⠀⣀⡤⢲⠙⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡀⠸⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢲⠶⡲⠖⠒⡉⠍⠀⠃⠀⠀⠀⢡⡀
⠀⠀⠀⡆⠀⠀⡀⠀⠀⠀⡇⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⡀
⠀⡇⠀⡇⠀⠀⠧⠆⠀⠀⡇⠀⣿⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠈⠄⠀⠀⠀⠀⠀⣀⣠⡤
⠀⣷⠀⣧⠀⠀⠀⠐⠀⠐⠓⠂⠉⠀⠀⠀⠀⡀⠀⠠⠤⢤⣀⣀⡠⠔⠁⠀⢑⣄⡄⠀⠀⠀⠀⣀⠜⠐⠂⠠⡤⠀⠀⠀⠈⢄⣤⠴⠒⠋⠙⠢⢄
⠀⢹⠀⢸⡀⠤⠄⠀⠀⣀⠠⠄⠂⢀⡀⢀⣀⠀⠤⠀⠠⠗⣴⠂⠀⢀⠠⠖⠋⠡⢑⠦⠂⠐⠈⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⣦⡀
⠠⠘⠉⠀⠀⠀⡠⠂⠁⡀⠀⠀⠐⠃⠀⠀⠀⢙⠁⠀⠹⢤⡙⡢⠈⠉⠒⠀⢴⡒⠈⡀⠀⢀⡀⠄⠐⠉⠀⠀⠀⠀⢀⠠⢖⠉⠄⣈⡱⠶⢖⡊⠉
⠀⠀⠀⠀⠀⠀⣄⠀⠣⡀⠀⠀⡈⠀⢠⠉⠑⠥⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠆⣠⠊⠑⠠⣀⢀⡀⠄⠒⠈⠀⠀⠀⠂⠌⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠈⠐⢄⡈⠑⣤⠀⠀⠆⠀⠀⣠⠼⠆⠘⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠏⠲⣄⣀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢌⣂⢐⠦⡀⠁⠀⢀⡰⠶⢃⡀⠁⠒⠠⣀⠀⠀⠀⠀⢀⠠⠀⠊⢀⡤⢺⠐⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠈⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡈⠑⠤⣀⠻⣀⡉⡼⠀⠀⠀⢀⣀⠦⠐⠈⣀⡠⠔⠊⠁⠀⠸⣠⡇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠉⠂⠤⠤⠄⠒⠈⢁⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢠⠌⠙⠤⠄⠀⠐⢒⣉⡠⠤⠛⠻⢅⡀
⣀⣤⠴⠖⠋⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠀⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡄⠀⠀⢨⣅⠀⠀⠀⠀⠀⠈⠙
⠧⣄⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡐⠳⡀⠀⠈⡄⠉⣒⣤⣤⠖⠊⠉
⠀⠀⢉⣲⠤⣔⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠗⠂⠔⠒⠈⣱⠀⣈⠢⠀⠙⠲⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂
⠀⠀⠀⠀⠀⠐⠶⠒⠄⠀⠠⠀⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣨⡡
⠀⠀⠀⠀⠀⡠⠠⠄⠀⠀⠠⣖⣒⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢨⠿⠀⣀⠀⠀⠠⠠⠀⠀⣀⠠⣮⠁
⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠐⣒⣒⡂⠸⡇⣠⡄⠀⡀⠀⠀⠈⠉⠀⠉⠁⠉⠉⠁⠉⠀⠀⠀⠀⠆⠒⢻⠽
⠀⠀⠀⠀⠠⠖⠀⠁⠀⠀⠀⠒⠒⠂⠈⠁⠀⣀⠐⠀⣉⠤⢉⠉⠉⠙⠙⢒⠒⠲⡒⠒⠀⠀⠀⣀⠈⡛
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⡀⠈⠃⡦⠄⡐⠀⠒⠒⡆⠉⠀⢀⠈⣡⠶⠖⠺⠀⢠⠤⠐⠠⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠂⠐⠆⠀⠀⠀⠀⢤⠤⡅⠀⠀⠀⡇⠀⠐⠦⡤⠤⡴⠀⢀⠆⠀⠀⠀⠈⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢢⠀⠤⠤⡇⠀⠰⠂⢀⣀⠘⠀⢄⠀⣄⡤⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⢔⡐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠨⠽⠈⠀⢤⣴⠀⠀⠘⠀⠸⠿⠆⠀⠀⠀⡈⣙⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⡎⢈⠀⢀⠰⡆⡄⠀⠀⠀⠠⠤⠭⠭⠤⠤⠤⠀⠠⠤⠀⠀⠠⠤⠬⠽⠖⠲⠲
⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁
⠀⠀⠀⢰⣰⠀⠀⢸⢾⡇⠀⠐⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠐⠀⠐⠀⠂⡰⠂
⠀⠀⠀⢸⢼⡀⠀⢸⢻⡄⠀⢸⣿⡿⣿⣿⣿⠇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⣳⣄⣀⣠⣜
⠀⠀⠀⡼⠘⡇⠀⠸⠻⠇⠀⢸⣿⣷⢾⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠟⠘⠇⠀⠀⠀⠀⠀⢸⣿⣿⣾⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢿⣋⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⠾⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠘⠓⠒⣄⣀⡀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠘⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠂⠒⠛⠓⠀⢰⣿⣿⢸⡀⠀⠀⠀⠀⢀⣶⠆⠀⣀⠁⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡄⠀⠘⣿⣿⣿⠁⢾⣦⠀⣀⠀⠁⠀⠸⠿⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⡀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⠀⠀⠁⠀⠻⠷⠀⠀⠀⡀⠀⠀⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣀⣠⣤⣴⡄⠀⠀⠀⢈⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣠⠖⢉⣉⣉⠑⢦⡀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⢀⣼⣿⣡⣤⣤⣿⣷⠀⠀⢠⠎⠈⠛⠁⠱⡄
⠀⠀⠀⠀⣼⢁⣾⡿⣿⣿⣿⠂⢱⡀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠟⠉⠁⠐⠃⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⡇⠐⣯⠀⠀⠀⢹⠀⢸⡇⠀⠀⠀⢀⣿⡟⠶⣄
⠀⠀⠀⠀⠘⣄⠙⠷⣶⡶⠟⢀⡞⠀⠀⠀⠀⢸⣿⣿⣦⣬⣷⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠈⠑⠀⠤⠀⠒⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠆⠀⠸⢿⣿⣿⣿⠟⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⢿⣇⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⢿⣿⠿⢿⣷⣼⣿⣦⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⣿⣇⠀⢀⣿⠀⠀⢹⣏⠀⣸⣿⢀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣼⡿⠛⠻⠛⠁⠀⠀⠈⠛⠻⠛⠻⢿⣯⣠⣿⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⣠⣶⡀⠀⠀⢀⣤⣤⣤⡀⠉⠻⢷⣶⣿⠋⠙⢿⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣀⣴⡿⠋⢹⣷⣠⣶⠟⠋⠀⢙⣿⣤⣤⣄⠉⠻⢷⣤⣾⠟⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⠟⠁⠀⢀⣾⡿⠛⠁⠀⢀⣴⡾⠛⠁⠈⣻⡇⠀⠀⠉⠻⣷⣄⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⣶⠟⠋⠀⠀⣠⣶⠟⠋⠀⠀⣠⣶⣟⠁⠀⠀⠀⠀⢸⣿⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣴⡾⠛⠁⠀⢀⣴⡾⠛⠁⠀⢀⣴⡾⠛⠉⠹⣷⠀⠀⠀⠀⣼⡟⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠉⠀⠀⠀⣶⠟⠋⠀⠀⣠⣶⠟⠋⠀⠀⣠⣾⣟⠀⠀⢀⣾⣯⣾⠟⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣤⡾⠛⠉⢻⣷⣰⣿⡿⠋⠁⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⣠⣴⠟⠋⠀⠀⣠⣾⣿⠟⠉⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣴⡾⠛⠛⠁⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣠⣴⠟⠋⢀⡀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⢀⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣏⣀⣤⣤⣴⣾⠇⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣶⣶⣶⠾⠟⠋⠁⠉⠉⠉⠉⠉⠀⢿⣦⣴⡿⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣾⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⡈⠉⠉⢳
⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡖⢲⢰⠊⡇⢰⠉⡇⠀⠀⢰⠧⠈⠁⠘⠦⠀⢰⡍⠉⠨⢷⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣸⠇⠙⠁⠈⠉⠁⠈⠈⠁⠀⠀⠘⢤⣆⣐⡶⠃⠀⠳⣤⡀⣠⡞⠀⢸⡆
⠀⠀⠀⠀⠀⠀⣿⠤⠤⠭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠿⠷⠶⠶⠾⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⣀⣠⣤⠤⢤⠤⢤⣀⡀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠴⡾⠉⡜⠁⣰⠃⢠⠎⠀⡜⠓⣦⡀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡴⢣⠞⣠⠎⢀⡴⠁⣰⠃⢀⡞⠀⣰⠃⢸⣆⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣼⡵⠃⡴⠃⢀⠞⠀⡴⠁⢀⠎⠀⡰⠃⣰⠋⢸⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⠀⠀⢠⠟⢀⡞⠁⣠⠋⢀⡞⠀⢠⠎⠀⡴⠁⣰⠃⣰⠋⣼⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⢠⠞⠀⡰⠃⢠⠎⠀⣠⠋⢀⡞⠁⡰⠃⡰⡥⠚⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠋⠀⡜⠁⡠⠃⠀⡴⠁⢠⠎⢀⡼⠁⡼⠑⣇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠀⢹⣀⠞⠀⡴⠁⢀⡞⠀⣠⠋⢠⡞⢀⡜⠀⠼⠉⡿⠲⡆⠀⢠⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⣏⢀⡜⠁⢠⠎⠀⡰⠁⢠⠏⢀⡞⠀⡼⢀⠖⠀⡶⠀⠀⠸⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⢿⡀⣰⠃⠀⡼⠁⣰⠋⢀⡎⠀⠜⢁⡟⢠⡿⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⠧⣄⡞⠀⡴⠁⢀⠎⠀⠌⢀⣏⠴⠋⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠉⠚⠓⠒⠛⠒⠚⠋⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⣿⠘⢯⣤⣤⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠁⠀⠀⠀⠀⠀⠀⢰⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠛⠳⠶⣤⣀⣀⣤⠤⢿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⠋⡴⠄⠀⠀⠴⠂⠈⡏⠀⠀⠀⢸⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⣀⣀⣀⣿⠀⠀⢻⡝⢣⡟⠀⠀⣿⡀⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡰⢋⡴⠖⠒⠻⢦⣐⣒⠈⠭⢐⣒⡿⠟⠛⠲⠶⠾⡇⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢄⠀⢸⡆⠀⡇⢸⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠒⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⡃⣞⠛⣋⣉⣉⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡹⢋⡞⢡⠄⠀⣄⢲⡹⣝⡆⠀⠀⠀⠀⠀⠀⠀⢠⡿⢛⡻⣿⠟⣛⠻⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡈⠀⠈⠀⠸⢘⡣⠘⠄⠙⠀⠀⠀⢰⣲⠀⠀⠀⠀⣿⠿⣯⡀⣇⠸⣿⢇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⠞⠁⡠⠀⢠⠀⠀⠀⠀⣄⠀⢠⡀⠀⠀⠀⠀⡠⣄⠀⣹⣧⢭⣥⠿⢷⡶⠻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣀⡀⠀⠰⠁⢀⡾⠛⠛⠳⣄⣸⣤⣄⢱⡞⢙⡇⠈⠂⠊⠀⣿⢅⡲⣿⢘⣻⡘⠟⣻⡽⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣉⣹⢆⡴⠚⠛⣷⠶⣤⡟⠻⣄⣠⢼⡇⠙⠋⠁⠀⠀⠀⠀⠻⣮⣥⣾⣶⣾⠿⠛⠉⣾⣿⡞⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⡁⢾⠀⣰⠶⣿⡀⠘⣷⠀⠙⣷⠀⠻⡟⠓⣦⠀⠀⠀⠀⠀⠈⠉⠋⣉⠀⠀⠀⠀⠉⠉⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠴⢿⡾⢧⣽⡄⠈⢧⠀⠈⢧⠀⠘⣇⠀⠹⣆⠘⡇⠀⢰⣷⠀⢀⡀⠀⣿⠀⠀⠀⠀⢀⣴⣶⠸⣷⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⠀⢀⡿⣞⠁⢻⡄⠈⢧⠀⠈⢷⠀⠈⠀⠀⠘⣶⠇⠀⢸⣿⠀⣼⣧⠀⣿⣀⣶⣶⣦⠘⠿⣦⡄⢿⣿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠙⣩⠖⠛⣰⠶⣿⡄⠈⠧⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⣿⣀⣿⠿⣷⣿⢿⣇⣾⣿⣄⣴⡾⠏⠘⠃⠰⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠁⠀⠀⢻⡄⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⠿⠟⣠⡉⢁⣈⠛⣋⣈⠛⣡⠀⣶⣾⣆⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣧⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢿⣇⣼⣿⣼⡟⢻⣿⣿⣀⣿⠻⣿⠏⠙⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠈⠳⢤⣤⣤⣶⣋⣷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠙⢛⣿⠙⠿⠿⢃⣙⠛⣿⣠⣿⡶⣶⡜⢿⣦⣍
⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⢸⡁⢈⡇⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠙⣆⠀⢸⣆⠀⢿⣿⠋⣴⣶⡀⢸⣿⣧⣿⡇⣿⡆⢸⣿⠀⠈⢻⣧
⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠘⣧⠸⣿⠀⢘⣿⡀⣿⣛⣿⡌⣿⡝⣿⣿⢸⣷⣾⢿⣦⣤⣼⡟
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣠⠏⠀⢿⡿⠛⢿⣇⣿⠟⠙⠿⢿⡇⠈⠛⠀⠛⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠤⠴⠚⠁⠀⠀⢸⣷⠀⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠉⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣚⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⣤⣴⡾⣿⣿⣛⢶⣄⠀⣾⢹⡷⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣦⣶⣮⡑⢤⣤⣤⣶⣶⣒⠚⠋⠉⠉⠉⠁⢀⣾⣿⢫⣾⣿⣿⣿⣿⣿⠀⠛⣿⣴⡆⢿⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⢿⡇⢿⣿⣿⣿⣿⣿⣿⣥⠼⣿⣤⡇⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠍⠛⠛⠛⠛⠛⠻⠟⠛⣿⣶⣶⣤⣌⡻⠎⠻⢿⣿⣿⣿⣿⠙⣆⣿⣄⡇⣼⣤⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣆⠀⢸⣿⣿⣿⣿⡇⢠⣷⡹⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⣿⣿⣧⢸⡇⠈⢦⣴⣿⠇⢹⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣿⢸⣷⣀⢀⣹⣷⠖⠒⠛⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢠⢸⣿⣿⣿⡞⡿⠟⠉⠙⠿⠀⠀⠀⢠⣗⣀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⢸⣿⣿⡟⡛⠃⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣶⡦⠤⠶⢶⠶⠶⠶⠶⠶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣾⡿⠁⢸⢸⣿⣿⣇⠁⠙⠃⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣥⣾⣿⢿⣿⣿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⣿⣿⣾⣿⣩⣽⣛⣁⣀⣘⣘⣛⣿⣿⣷⣶⢎
⠀⠀⠀⠀⠀⢠⡾⠯⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠏⠉⠩⠭⠭⠭⠭⠭⠭⠽⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡟⠋⠀⠂
⠀⠀⠀⣶⣶⣶⣶⡶⣶⣶⣶⣶⡟⡟⣿⣿⣿⢻⣿⣿⣿⣿⣶⣟⣷⣶⣶⣶⡶⣶⡶⣶⣶⣶⢶⡶⢲⣶⡶⢲⢲⠲⡇
⠀⠀⠀⡹⠊⠈⢻⠃⠏⠘⠟⢸⠃⠃⠀⠉⠇⠃⢸⢻⠿⠙⠿⠉⠈⢻⠙⠺⠀⠛⠃⠉⠋⠛⠘⠇⠀⠋⠛⠀⠀⠈⡇
⠀⠀⠀⠘⠶⠶⠶⠶⠶⠷⠶⠾⠶⠶⠶⠶⠾⠶⠾⠾⠶⠶⠶⠶⠶⠶⠷⠞⠛⠲⠶⠾⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠱⠤⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢈⠤⠂⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠚⠀⠀⠀⠁⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠒
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⡇⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⠀⠀⢠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠄⠃⠀⠀⠀⠀⠐⡀⠀⠁
⠀⠀⢀⠆⠀⠀⠀⠀⠀⠣⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢡
⠁⠀⠉⠒⠒⠶⠤⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠈⠁⡀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠠⠐⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠁⠀⠈⢆
⢘⠃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⠀⢀⣂⣰⠀⠄⠀⡂⠀⢠⠀⠀⠒⠊⠀⠀⡀⠀⠀⡀⠀⡆⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⢂⠈⡁⠀⠠⢀⣤⠤⠤⠃⠉⠀⠀⠀⠠⠀⠴⠀⠅⢤⡄⠴⠶⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⠀⢀⠴⣠⣤
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⠔⢊⠉⠑⣧⠞⢁⡸
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠴⠒⠋⠹⢓⠎⠁⠀⠉⠂⠀⠀⠀⠙⠀⠋⠘⠉⠿⣧⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠂⠉⢀⡀⠀⠀⠠⠄⢀⠀⠐⠐⠀⠠⠀⠀⠀⠀⠐⠂⠠
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⣀⠀⠀⠀⠉⠀⠂⠀⠀⡄⠀⠀⠀⠀⡁⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⢀⡼⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⠀⠀⠀⠁⠈⠄⠀⠀⠀⡀⠀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠻⠄⠀⠀⠃⠀⠀⠀⢀⠀⠃⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⡀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠
⠀⠉⠭⠩⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠠⠇⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⡧⠐⢿⠂⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⡉⠑⢾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢡⠃⠆⠠⣷⡄⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡹⠁⠀⣸⠷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢼⠘⠿⣲⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣁⣐⣂⣁⣤⢤⠛⢷⡀⠀⠀⠀⠀⣀⣤⣶⣦⡴⢁⣎⠉⠁⠀⠀⠀⢀⣴⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⢸⠃⠈⠁⠀⠘⠊⠉⠪⡑⠦⢐⡨⠿⣿⡯⣿⣷⣼⣯⣷⡄⠀⠀⣠⠏⠈⢯⣦⣿⠋⢹⡄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠀⣿⣿⣞⣯⣿⡼⢏⠳⢔⣫⡟⣴⠀⣸⢹⡀⢸⡾⡇
⠀⠀⠀⣛⡭⠭⠝⠒⠒⠉⠉⠉⠛⠓⠒⠲⠤⠤⠤⠀⣀⣀⣀⠀⠯⠽⣿⣛⣿⣿⡥⠄⠀⠉⢩⢎⡾⢹⠀⢸⡄⢳⢈⣧⡙⢦⡀
⠀⠀⢰⠋⡿⠿⢿⣶⣶⣶⣦⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡾⠯⠝⢻⣷⠁⠀⠀⠀⣇⣾⢁⡾⠀⢈⡇⢸⠸⢸⡎⣇⣷
⠀⠀⢸⠀⡇⠀⠀⠀⣀⣈⠉⠉⠉⠙⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡟⣿⣶⣿⣇⠀⠀⠀⠈⠉⠻⢧⣀⣼⣤⡷⠤⠼⠃⠈⠁
⠀⠀⢸⠐⡇⢀⡔⣫⠭⠭⡙⢷⡄⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣽⣻⠿⢿⣿⡆
⠀⠀⢸⠐⡿⣿⢸⠃⠀⠀⠘⡌⣿⣤⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣥⣹⣷⣶⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣀⣀
⠀⠀⢸⢸⡏⠹⡜⢧⣀⣀⡴⢠⡿⢭⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⣿⠉⠀⠀⠀⠀⠀⠀⢀⣜⣹⡭⢷⣿⠋⠁
⠀⠀⢸⢸⡇⠀⠈⠒⠭⠭⠔⠋⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡤⣤⠤⠿⠀⠀⣀⣀⣀⣀⣀⢎⣾⡿⢣⡿⠁
⠀⠀⢸⢸⡇⠤⠤⢀⣀⣀⣀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢇⣠⠔⠒⢉⣩⠭⠤⠒⠲⠏⢾⡷⢳⡿⠳⢤⡀
⠀⠀⢸⢸⡧⢤⣀⣀⣀⠀⠀⠉⠉⢹⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣧⡀⠔⠋⠁⢀⡀⠈⢀⡀⠤⠀⡉⠙⢂⣠⡏
⠀⠀⢸⢸⡗⠂⠤⠤⠄⣉⣉⠉⠓⢺⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢛⣏⠙⢛⣟⡲⠲⠶⠾⠗⠶⠚⠻⠿⣿⣏⠗
⠀⠀⢸⣸⡋⠙⠒⠂⠄⠤⠤⢈⣉⣹⡇⢸⠀⠀⠀⠀⢀⣤⣶⠋⠀⠀⠀⠟⠘⡆⠈⠻⢀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠛⠻⠿⢷⣶⣶⣤⣤⣄⣀⣸⡇⢸⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠢⣀⣀⠀⠀⠀⠀⠀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠉⠀⠀⠀⢀⣈⡙⠛⢄⡀⠀⠉⠑⠒⠲⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⣀⣈⡉⠒⠈⢉⡢⠖⠊⢩⢳⠀⢹⠙⠤⢄
⠀⠀⠀⠀⠀⠀⠀⡼⠶⠶⠶⠒⠒⠒⠒⢚⣧⣲⣤⣀⣀⣀⣀⣉⣉⣡⣖⣉⡉⠉⠛⠒⠚⠒⠒⠶⢇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣏⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣸⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠯⠭⠭⠭⠭⠭⠭⠭⠭⠽⠿⠭⠭⠭⠭⢽⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡆⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡸⠓⠒⠛⠓⠒⠒⠒⠒⠚⠛⠛⠒⠒⠒⠒⠒⠒⠳⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⠧⠤⠤⠤⠤⡤⠤⠤⠤⡤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠵⣄⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢙⠶⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠶⠒⠒⠒⠒⠒⠶⠒⠒⠲⠖⠶⠶⢶⠖⠒⠒⠒⠒⠒⠒⠒⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⠀⠘⠃⠂⠘⠛⠀⠛⠁⠀⠛⠀⠀⠀⠀⠘⢣⡤⠿⡼⠉⠿⣂⠉⠉⠉⣑⠳⠋⢢⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⢄⣠⠤⠤⠤⠤⠤⠤⠤⣄⠤⠤⠤⠤⠤⡴⠋⠀⠀⠑⠢⣄⡀⣩⠶⣍⢁⣀⠤⠜⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠹⡀⡏⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⣐⣂⣴⣐⣀⣐⣰⣖⣀⣀⣐⣦⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠺⠭⠭⠭⠭⠭⠭⠭⠭⠽⠯⠭⠭⣷⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣟⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡞⠒⠒⠒⠂⠀⠶⠶⠶⠶⠶⢾⣦⡷⠶⠶⠶⠶⠶⠆⠐⠒⠒⠒⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⢺⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⢺⡭⣷⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼⡤⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠀⠀⠐⠒⠒⠒⠒⢺⣷⡟⠒⠒⠒⠒⠒⠀⠀⠈⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣛⡭⢞⡳⢭⣛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⢠⣑⢾⣿⣿⠷⣊⡄⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣾⣿⣮⠻⣷⢢⡔⢾⠟⣵⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣾⣿⣿⣿⣿⡿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⡶⢿⣿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⢏⣾⢫⣾⣿⢹⣿⣦⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢸⣧⣿⣿⣿⣘⠿⣿⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣎⢿⣉⠹⣿⣿⣿⢟⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣮⣛⠷⣶⣶⣶⠿⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣶⢰⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢶⣾⣭⡍⠀⠀⠉⠉⠙⠛⠛⠿⠿⡿⢿⠿⠿⠛⠛⠋⠉⠉⠀⠀⢩⣭⣵⡶

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣲⡶⠶⠶⣶⣒⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣤⡇⠀⠀⠀⠀⠀⢠⡒⠒⠒⢲⠀⠀⠀⠀⠀⢀⡔⠒⠒⣎⠀⠙⠢⢄⣀⣠⠤⠚⠁⠘⡖⠒⠲⡄
⠀⠀⠀⠀⠀⡴⠒⠒⡟⠒⠒⠒⢳⡀⠀⠀⠀⠀⢸⠉⠉⠉⠉⡆⠀⠀⠀⢀⠎⠀⠀⠀⠈⠙⠲⢤⢴⠋⡦⠤⠤⠒⠋⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⡇⡎⡜⠀⠀⠀⠀⠀⢳⠀⠀⠀⣠⠞⠒⠒⠀⠚⢧⣀⣀⣠⣋⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣧⠟⠀⠀⠀⠀⠀⠀⠀⢣⢠⠎⠁⠀⣀⣀⣀⠀⢀⡈⢳⠖⠤⠤⠬⠭⠭⣉⣉⠭⠶⣆⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⠋⠁⠀⠈⡆⣿⢱⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣤⡿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⡇
⠀⠀⠀⠀⠀⠳⠦⠤⠤⠤⠤⠤⠤⠴⢲⡏⠀⡇⠀⠀⠀⠀⡇⣿⢸⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠯⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⡇
⠀⠀⠀⠀⠀⢰⠤⠔⠊⠉⠉⠉⠒⠒⣾⡇⠀⡇⠀⠀⠀⠀⡇⢿⣸⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣶⡟⠒⠒⠒⠒⠒⠒⠂⠀⠉⠉⠉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠀⠀⠀⠙⠒⢄⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠷⡿⠭⠭⠭⠭⠭⠭⠭⠭⠽⠿⠛⡆
⠀⠀⠀⠀⠀⣘⡒⠤⠤⠤⠤⠤⠤⠐⣻⡇⠀⡇⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠤⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡅
⠀⠀⠀⠀⠀⡇⠈⠉⠉⠉⠉⠉⠉⠁⠀⣇⠀⠈⠉⠐⠒⠒⠂⠉⠁⠀⡟⠒⠒⠲⠦⠤⠤⣧⠤⠲⣟⡿⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢀⠇
⠀⠀⠀⠀⠀⠳⠤⠤⢀⣀⣀⣀⠤⠤⠔⠻⠤⣀⣀⣀⣀⣀⣀⣀⣀⠴⠋⠙⠛⠓⠒⠲⠶⠾⠖⠚⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⡀
⠀⠐⢲⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀
⢠⣤⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⢸⢸⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣬⣭⣿⣭⣀⠀⠀⠀⠀⠀⠀⡟⣿⡂
⢸⢸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣾⡷⠟⡇⢸⡇
⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣀⡂⡇⠀⡇⣼⡇⢀⣀
⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⢇⡟⠛⡇⣿⡦⣾⣿
⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣇⡀⣿⣿⡆⡏⢻
⢸⢸⣿⣿⢫⢿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠙⠋⠛⣿⣿⡇⡇⣿⠀⣴⣿⠶⠿⢿⣿
⢸⢸⣿⣿⣾⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡃⣹⣿⡾⠁
⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⡏⣾⣿⣿⣤⣤⣤⣤⣿⣿⣿⣿⡿
⠘⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⣿⣿⠿⣿⣾⣿⣿⡿⠋
⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣸⣿⣿⢇⣿⣿⣿⣿⣿⠁
⠀⠀⡗⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⣿⣿⣿⡎⣿⣿⣿⣿⣿⣆
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣴⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣆
⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠭⠭⠭⠍⠩⠭⠭⠭⠭⠨⠭⠭⠭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠛⠛⠛⠛⠙⡇⠒⠂⣀⣀⣀⣀⣀⡀⠀⠀⠀⠻⠟⠛⠛⠛⡻⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⠀⠀⠀⡇⠀⣾⡇⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣚⡛⣶⣴⡇⠀⣿⣧⢠⣿⣿⣧⠀⠀⠀⠀⠁⠀⠀⢰⣾⣿⣝⣿⣄⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠷⠤⠤⠀⡇⠀⣿⣷⡆⠀⠀⠀⣼⣴⡆⠀⠀⠀⠀⣸⣿⣷⣾⣽⣽⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⠶⣶⡇⠀⡏⢻⡟⠀⠀⠀⠛⠛⡇⠀⣧⣤⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠈⣿⡇⠀⠛⠛⣃⣀⣀⣀⡀⠀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠛⠛⠛⠃⠀⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡄
⠀⠀⢰⣆⣖⣲⣶⣶⣶⣶⣶⡶⣶⠶⠶⠿⠿⠿⠿⠿⢿⣿⣿⠛⠛⠛⠛⠛⠋⠉⠛⠉⠉⠉⠉⠉⠏⢉⡏⠋⠉⡃
⠀⠀⢸⡏⣀⣠⡤⣠⠤⡶⠀⠀⠀⠀⠀⠄⢈⣙⣂⣀⢺⣿⣏⠀⠘⠋⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠡⠤⠤⠧⢄⣀⡀
⠀⠀⣼⣧⠠⠤⠤⠤⣤⣤⣤⣶⣒⠒⠒⠐⠀⠛⠛⠓⢺⠏⠛⠯⣉⠉⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣻⣶⣶⣤⣄
⠀⠀⣿⣿⣷⣄⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣈⣽⣶⣤⠤⠤⠤⠶⠶⠖⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⢹
⠀⠀⣿⠛⢿⣿⣷⠖⠒⠒⠒⠒⠒⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠴⠶⠶⠶⢾⠃
⠀⠀⣿⡇⠀⢿⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠤⠴⠶⠶⠖⠒⡿⠚⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣿⣷⠀⠸⡇⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⢸
⠀⠀⣿⣿⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⢼⢿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⢻⠘⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⣺⠀⢿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠈⠀⢸⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠐⣶⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡷⠀⠀⠀⡀⠀⠀⠤⠤⠴⠶⠒⠚⣀⣀⣀⣠⣼
⠀⠀⢾⡇⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠋⠀⠀⠠⠤⠄⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⢸
⠀⠀⠘⢧⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠤⠄⣾⡶⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠼⠆
⠀⠀⠀⠈⢳⡘⢿⠀⠀⣀⣀⣀⠠⠤⠄⠒⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣶⣶⡿⠿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠹⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣾⣿⠿⠟⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣠⣤⣤⣴⣶⣶⣶⣿⠿⠿⠿⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⢰⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢰⡀
⠀⠈⣤⣤⣤⣤⣤⣬⣭⡍⠀⠀⠀⢸⣿⡆⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠈⠁⠠
⠀⠀⣤⣉⡉⡉⢉⣩⣍⣀⠀⠀⠀⣼⣿⡟
⠀⠀⠉⠉⠉⠙⠉⠉⠉⠽⠆⠰⣿⠿⠿⠃⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠐⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⢸⡟⠀⢠⡆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠈⠉⠛⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⢰⠛⣿⣿⣷⡀
⠀⠘⠁⠀⠟⠀⣀⢀⡄⠀⠀⠀⠸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣾⣿⣿⠁
⠀⠀⠀⢀⠀⠀⠻⣤⣧⠀⠀⣀⡀⠙⠻⠿⢟⠁⠀⠀⠀⠀⠀⠀⠰⠐⠐⠇⠈⠀⠀⠉⠀⠀⠀⠔⠂⠈⢻⣿⡯
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀
⠀⠀⣠⣤⣠⣬⣌⢁⠀⠀⢴⠀⠀⠆⠀⣠⣴⣦⣤⣄⣠⣀⣀⣄⣀⣤⣴⣶⣿⣿⣷⡄⠀⠀⢸⣿⣿⣧⡀⠀⣀⣠⣤
⠀⠀⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⠇⢶⣿⣿⠿
⠀⠀⠀⠉⠉⠁⠀⠀⠀⣤⣤⡄⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢀⠀⠈⠉⠁⠀⢈⣉⠉
⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠂⠈⠙⠿⠦
⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣦⣤⠀⠁⠀⣀⣀⣀⣀⣀⠀⠀⢰⣿⣿⣽⡟⢀⣠⣦
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠀⠀⠀⠉⠙⠉⠉⠉⠀⠀⠸⠟⠟⠋⠁⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⠘⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠃⢰⣷⣤⣤⣠⣿⠃⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣀⢀⠀⡀⢀⢀⢀⣀⢀⠀⣀⣀⡀⢀⠀⠀⣀⢀⡀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠹⠃⠟⠆⠽⠘⠛⠇⠀⠏⠸⠼⠘⠤⠛⠛⠅⠘⠛⠖⠛⠾⠙⠆⠤⠇⠭⠆⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠈⠃⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠁⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠
⠀⠀⠀⢠⡖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢠⣶⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⡄
⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠈⠓⠚⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⠐⠂⠂⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠒⠀⠒⠀⠒⠂

⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢲⡄
⠀⠀⠀⠈⠓⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⢀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠰⠤⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠒⠒⠀⠂⠂⠒⠀⠂⠂⠐⠀⠐⠆⠀⠀⠰⠶⠶⠀⠶⠂⠐⠖⠤⠤⠶⠀⠀⠀⠀⠀⠐⠒⠒⠶⠒⠲⠖⠲⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⢠⣶⣢⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⡄⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠈⠓⠋⠠⠊⠈⠉⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⢀⠐⠀⠀⠀⠈⡓⠀⢠
⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠐⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠑⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⡀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣞⣼⣷⢽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠿⠦⣀⢀⣀⣿⣿⣅⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣦⡀⢰⣿⢻⣿⣯⣼⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣻⣿⠇⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣥⣼⣧⡌⣽⣿⣿⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⣶⣶⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣧⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣵⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡋⢩⠙⢻⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣫⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡢⣼⣾⣿⠀⢿⢽⣿⣿⣿⢿⣿⣿⡟⠷⣄⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣿⣿⣛⣿⡄⣶⣶⣿⣿⣿⣿⠿⠿⠃⠀⠙⠿⠲⠀⠤⠤⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣽⣿⣿⠟⢧⣿⣿⠉⠁⠙⠁
⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⢀⣸⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣵⣸⡷⣿⣟⣀⣀⣀⣀⡀
⠀⠀⠀⢀⡾⠋⠀⠛⢉⠂⠀⠤⠌⣽⡍⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣉⢢⣄
⠀⢀⠔⠁⢀⠀⠄⢠⡊⠀⠀⠀⠈⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⡀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡀
⡀⣀⣀⡀⠀⠀⢀⣈⣉⣉⣛⣛⣻⣿⣛⣉⣉⣉⣙⣋⣛⡋⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣿⣿⠿⠿⢿⣿⣿⣿⡛⠒⠃⠀⠀⠀⠀⠀⢀⡀⢈⣀⣙⣢⣀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣾⣿⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⣷⢷⣿
⢸⣿⣿⣿⣾⣿⣿⣿⣎⣉⣝⣙⣙⡫⣛⣛⣛⣛⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⡇
⠻⣿⣛⣛⣛⣻⣻⣿⣿⣿⣿⣿⣯⣽⣭⣾⣿⣿⣿⣿⣿⣷⣛⣛⣛⣛⣐⣋⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⠏⠁
⠀⠀⠀⠀⢤⣴⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠰⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⣠⣤⣧⣤⣾⡀⢀⣧⣤⣤⣤⣄⡀⠀⠈⠙⢷⣌⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣠⠖⠚⢯⣁⢀⣀⣀⡀⠉⠉⠀⢀⣀⣠⠬⣝⠳⣦⡀⠀⠛⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡖⠁⠀⢀⡸⠋⠉⠉⠉⠉⢉⣻⠟⠉⠉⠁⠀⠈⣇⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⣰⡶⠚⠛⠛⠛⢣⣀⣠⢿⣤⣀⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⢹⠄⠈⢷⣄⣀⣀⣀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣻⣿⡶⠶⠤⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠆⠘⢧⣀⣀⣤⠀⠀⠀⣠⣼⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠴⢧⣀⡀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠲⠤⠖⠁⠈⠷⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠾⡇⠀⠀⠹⡛⢻⡁⢀⡿⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠆⢨⠿⡟⢿⠄⠀⢀⣧⣄⣉⣉⣀⣀⣀⣀⡤⠤⠔⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠃⢪⡀⠀⢸⠋⢻⠛⡏⠉⡿⠛⠃⠀⠀⠀⠀⠠⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡍⠛⢿⡶⠾⠿⣶⣶⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⣀⣤⡶⠛⠛⠛⠓⠒⠶⠶⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣁⠀⠈⢳⡒⣦⣀⣀⣀⠳⠤⠴⢶⡀⠀⢀⣖⣋⣀⣤⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠉⠁⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠒⠋⢉⣉⡀⠀⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠒⠛⠉⠉⠀⠀⠠⣴⣶⣾⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⠿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠒⠋⠉⠉⠉⠁⠀⠒⣂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣋⡤⠔⠒⠒⠒⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⢀⡞⠀⠀⢀⣤⣶⣶⣤⣀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⣿⣿⣿⡿⠛⣁⠥⠤⠤⠴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡼⠀⠀⣴⡿⢋⣴⣾⣿⣿⣧⡀⠀⠀⢿⣷⠀⠀⠀⠀⣿⣿⡏⣰⠋⠀⢀⣀⠤⠴⠒⠒⠒⠚⠛⠛⠒⠒⠲⢶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢢⡇⠀⣰⡟⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⡇⠀⠀⠀⣿⣿⢀⠇⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⣀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢸⠀⠀⣿⠃⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⢈⡞⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⢸⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⢸⠀⣀⣤⣴⣶⣿⣿⡿⠿⠿⠿⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢸⢸⠀⠀⣿⡄⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿⡿⠀⠀⠀⣿⣷⡌⢻⣿⣟⣯⣥⣶⡶⡶⠷⠿⠿⣆⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠜⡆⠀⢹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⡇⠀⠀⠀⣿⣿⡇⢸⣿⢛⣭⡤⣶⡖⣶⡇⢾⣿⠰⠀⠀⢠⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢳⠀⠀⠻⣷⣈⠻⣿⣿⣿⡿⠁⠀⠀⣾⣿⠀⠀⠀⠀⣿⣿⣿⠈⣿⡟⣛⡁⣭⡄⣶⡆⣶⣖⢳⣶⣶⣾⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢧⠀⠀⠈⠻⠿⠾⠿⠋⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⣿⣿⣿⡄⢿⡟⣻⣅⣭⣤⢴⣆⢰⡆⢰⡦⣼⣿⣽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⢻⣋⢨⣥⢨⣦⢰⡦⢰⡆⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⣀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠈⣿⣿⣿⢈⣭⢰⣧⢰⣦⣼⡧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⣿⣿⣿⣉⣿⢨⣯⣸⣯⣼⡇⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⡇⢸⣿⣿⣏⣿⣭⣯⣼⣯⣽⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡄⡇⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠉⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣀⠤⢄⡀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡀⠀⠀⠹⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⣱⣤⣒⣤⡂⠀⠀⢸⣠⣖⣲⣤⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢹⠒⠒⠒⠚⡇⠉⢱⠀⠆⠀⠀⣎⠀⡜⠉⠉⢳⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⡎⢀⢀⡀⠀⢸⠖⠊⠉⠓⠒⠒⠊⠉⠙⠢⠐⠋⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠋⠞⢣⢦⡭⣷⢀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⢤⢦⠠⠕⠊⠁⠀⠉⠑⠂⠐⠒⠊⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠈⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠁⠈⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⣀⡠⠔⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠤⠒⠉⠁⠀⣀⠤⠷⡀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⣀⡠⠴⠒⠉⠀⣀⠤⠃⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡠⠤⢲⡋⠀⢀⣀⣤⠶⣛⡒⠬⢍⡐⠢⣄⣀⠤⠚⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠲⢄⡤⠹⢍⣁⠎⠀⠀⠑⠒⠂⠉⠁⠀⠈⢣⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠬⣑⠦⣈⣑⠒⢢⣧⡑⠢⢤⡂⠠⢄⣒⣊⡤⠃⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠙⠒⠤⠤⠥⠽⠍⠒⠲⣠⡖⠉⠀⠈⠀⠀⠀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⣀⣀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠧⣀⡠⠤⠒⠒⠒⠒⠊⠁

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⢀⡷⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠰⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠠⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠠⡀

⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⡅⠀⠠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠤⠤⠀⠐⠒⠀⠁⠀⠂⠀⠐⠂⠀⡄⣀⣠⠀⠀⠀⠀⠀⠄⠀⠀⢀⢉⢀⠄⢸⠀⠀⠠
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⠓⠠⠒⠌⠡⠀⠄⠂⠃⠉⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⠀⠀⠀⠀⠀⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠃⠀⠈⠀⠀⠀⠄⠁⠀⠀⠀⡈⢠⠀⠀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠁⠀⠀⡀⠀⡇⠀⠀⡄⢀⠀⠰⢀⠆⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠠⠀⠇⠸⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⢤⡤⣔⢲⣆⣲⠰⠯⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠸⢹
⠀⠀⠀⢀⠆⡃⡞⠙⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠡⠤⠠⠤⠐⠒⠒⠒⠢⠤⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⡸⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⢀⠠⠤⠐⠒⠂⠀⠀⠒⠒⠤⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠐⠒⢲
⠀⠀⠀⠀⢰⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⢇⡀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢸⠀⠠⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⡖⠉⠉⠀⠘⠀⠁⣢⠀⠀⠀⠀⠀⠀⠀⠠⢀⠒⠠⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡁⢘⠀⠀⠀⠀⢈⠀⠈⠉⠁⠈⠉⠉⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⣤⠀⠀⡀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠰⠀⠤⠀⡇⢰⠀⠀⠀⠀⠸⡀⢰⠁⠐⠒⠈⠂⢸⠀⠀⢀⠀⠀⠀⠈⠄⠈⡁⢀⠀⠠⠀⣊⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣧⠜⠀⠀⠀⢀⡔⠃⠈⠢⠨⠬⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⢌⠀⠠⠀⠀⠀⠊⠀⡀⠈
⠀⠀⠀⠀⠈⡗⠢⣤⠦⠒⠙⠀⠀⠀⢠⢊⡔⠊⠈⠉⠉⠁⠐⠒⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡐⠉⠁⠀⠀⠀⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⡄⠀⠀⠀⣀⣀⡀⠀⢘⢓⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢬⢠⡈⡰⠂⠤⠀⡤⠠⠔⡨⡤⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⡜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠌⠡⠁⠀⢀⢂⣤⠀⠀⠀⠀⠀⠈⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⠀⠐⠒⠀⠉⠀⠀⣀⠠⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠤⠤⠔⠒⠋⢉⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡋⠉⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠈⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⢠⣾⡿⠛⠛⢿⣷⡄⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⢀⣾⣿⠁⠀⠀⠈⠿⣿⣷⣦⡀⠀⠀⢿⣿⣁⣸⣿⡇⠀⠀⠘⢿⣷⣄⣀⣀⣠⣾⡿⠁⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⠈⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣴⣾⣿⣧⣄⠀⠀⠀⠀⠀⣴⣶⣾⣿⣧⣄⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⣠⣤⣶⣶⣦⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠉⠛⠋⠀⢰⣷⠆⠀⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠛⠿⣿⣿⣿⣿⠿⠛⠉⠉⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠿⣿⣶⣦⣴⣶⣿⠿⠛⠛⠛⠿⣿⣶⣤⣤⣶⣿⠿⠛⠛⠛⠿⣿⣶⣤⣴⣶⣿⠿⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣄⣜⡻⠛⢻⡛⡟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⣠⣤⡤⡤⣤⣤⣤⣄⣤⣤⢰⣤⣴⣶⣤⣀⣷⣤⣴⣿⣶⣶⡒⣿⡏⠉⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣟⡛⠛⢻⡿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣇⡟⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠑⢧⡙⠑⣾⠀⠘⢿⣿⣿⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡿⡿⣿⢿⣿⣷⣿⣿⣿⣾⠟⠛⠙⡇⠀⠀⠃
⠀⢀⣀⣀⣀⣀⣀⣀⣠⣿⣤⣐⣤⣷⣴⣿⣦⣤⣼⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⢿⣿⡿⣿⢿⣿⣏⡝⣒⡒⣺⣷⣒⣆⡇
⠀⠈⠉⠉⢹⠉⠉⠉⣹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠉⠁⠀⠀⠀⠀⠀⣁⣉⣉⣀⣿⣺⣷⣏⣿⣙⣿⣿⣱⣿⣿⣿⣿⡟⣿⣿⣻⣶⠄
⠀⠀⠀⠀⠀⠣⡀⠀⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⣯⠀⣴⣿⣿⣿⣯⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠈⣿⣿⣾⣿⣿⣿⡿⠿⣿⠶⠶⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠑⣄⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢭⠭⠽⠯⠭⠭⠽⠭⠥⠍⠭⡿⠚⢛⡛⣛⡷⣿⣿⣿⣤⢸⣏⣽⡏⢹⣯⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⣿⣿⠟⠛⣿⡟⣿⣿⣿⠀⣤⣤⣶⣶⣶⣀⣶⠶⠿⢾⣦⡿⢛⡉⢲⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁⣿⠹⣦⡀⣿⣇⣿⣿⣿⠀⣽⣿⣿⣿⣿⣿⣿⣶⣾⣏⠋⣿⣿⣽⣿⣿⡇⣿⣿⣿⣛⣻⡏⠉⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣶⣶⣿⡧
⠀⠀⠀⠦⢶⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠿⠿⠿⠛⠛⡛⡛⢓⣟⣉⣭⣽⠽⠿⠿⠛⠛⣛⣻⣭⡽⠿⠾⠿⠃
⠀⠀⢤⣄⣸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣉⣭⣥⠤⠶⠖⠒⠛⠉⠉⠁
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣯⠤⠤⠴⠶⠶⠿⠿⠿⠟⠯⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢀⠐⣀⠄⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢀⠀⢀⠠⠄⡤⣤⡒⢰⠏⢻⡽⠷⠼⠋⠀⢁⣽⣄⠀⣄⡠⢢⣼⡂
⠀⠀⠀⠀⡀⠀⢀⣈⠁⠆⢠⣶⣮⠁⢸⡿⢷⣾⠰⠛⠃⠀⠀⠀⢀⠀⠀⢀⠘⠈⣿⢏⡀⢻⣿⣀⣻⠓⠆
⠀⠰⢶⣦⡁⠀⠿⠿⠷⠄⠈⠉⠉⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣾⡷⣤⠙⡌⣇⢘⠢⢤⣄⣥⡇
⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⠰⠀⢡⣶⣶⣆⢸⣿⣧⣤⣤⡀⠠⠀⠀⢿⣿⣿⠠⣶⣄⡤⡛⠖⢻⣿⣿⣯⣥
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⣻⠿⠿⣿⠯⣿⣥⡴⠶⠠⣀⣠⣼⣿⣿⣿⣽⣗⡷⢶⣾⢿⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⠋⠂⠁⠛⠄⠸⢿⣸⣽⣧⢶⣿⣻⣿⣗⣾⣿⣿⣿⡭⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢐⣂⣬⣦⣶⣻⡿⢩⠶⠮⡭⠷⢾⡯⠴⠮⠽⠏
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠟⠛⠛⠛⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⢉⣡⣿⣄⡉⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣤⠶⠛⢋⣡⣤⣌⡉⠛⠶⣤⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣿⣤⡶⠚⠋⠁⠀⠈⠙⠛⢶⣤⢿⡟⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⢉⣤⠶⠈⣇⠈⠛⢦⣄⡀⠀⢀⣠⡴⠞⠁⢸⠇⠀⠀⠈⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠞⠋⠁⠀⠀⠙⣦⠀⠀⠈⣹⠿⣏⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡼⠃⣀⠈⢷⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠋⠉⠉⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⠶⠶⠒⠶⠶⣄⡀⣈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⣿⠀⠀⠀⠀⠀⣰⠏⠀⣴⠏⠁⠀⠀⣶⠀⠀⠠⢿⣿⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡟⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠿⢤⣄⡀⠀⢀⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⣿⠀⠀⠀⠀⠈⣧⠀⠀⣤⣄⡀⠀⠀⠀⠀⠈⠁⢀⣼⠃⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⠀⠀⠀⠀⠀⠘⣧⠀⠿⠻⣤⣀⡀⠀⢀⣀⣴⠞⠁⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠉⠉⠉⠉⠀⠀⣠⡴⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⡤⠴⠶⠛⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣸⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣤⣄⣀⡀⠀⢠⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠸⡄⠀⢀⣀⣠⣤⢾⡄
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠉⠉⢛⡟⠀⠀⠈⠉⠉⠙⠛⠛⠓⠶⢦⣤⣄⣀⣀⠀⣿⠀⣀⣀⣠⣤⡴⠶⠞⠛⠛⠋⠉⠉⠁⠀⠀⢻⡟⠉⠉⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠖⠛⠛⠉⠁


⠀⢀
⡏⠉⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⡏
⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⡔⠒⢤⢠⡄⠒⡖⠂⢰⡄⠀⡖⢢⠄⡆⠀⠠⠒⠂⠀⢠⡐⠂⠒⡶⠂⡴⠒⡄⣠⠒⠢⡄⣴⢠⠆⣴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⡇⠀⡸⢰⡇⠀⡇⢠⠇⠾⠀⡇⠙⠄⡇⠀⠀⠃⠀⠀⠀⠉⡦⠀⡇⠀⡼⠚⡅⢿⠀⢀⠇⣾⠳⡄⢸
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣿⣶⣾⣷⣶⣷⣿⣶⣶⣶⣿⣿⣶⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⣿⣶⣿⣶⣿⣶⣿⣿⣶⣿⣶⣿⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⡤⠀⠀⠒⠒⠂⠀⢀⠀⠀⠀⠀⠀⠀⠎⠉⠄⠁⠀⠀⠀⠀⡔⠀⢡⠄
⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠘
⠀⠀⠀⠀⠀⠒⠀⠀⠀⣄⡀⠈⠢⢤⣀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠍⠀⠁⠀⠈⣉⠂⡄⠀⠀⠰⠀⠀⠀⢀
⠀⠀⠀⠀⠈⣠⡀⠀⠔⠐⠋⣑⡀⠀⢀⡐⢍⠐⠈⠀⠀⠆⠀⠀⠀⠀⣶⠀⠀⡂⠀⠀⠀⠀⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠃⠀⠺⡧⠀⡀⠀⠀⢀⣒⠀⠀⠀⡠⣻⡀⠘⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠀⠈⢾⠀⠤⢐⠸⢧⠃⠀⢰⢩⠇⠀⡄⠂⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣽⠡⠂⠀⠀⠀⠖⠁⢠⢰⡡⠂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠠⠤⠁⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣨⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢄⠀⠀⠀⠠⡀⠀⠀⣠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⣄⠀⠈⠀⡀⣲⢃⣐⠄⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠲⠄⠀⠀⠈⠀⠀⠀⠀⠓⢰⡶⠒⠀⠘⡈⢁⡢⢀⠐⢄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡠⠄⠚⠋⣀⠠⠐⠂⠀⡞⢉⣤⡄⡀⠀⠛⠁⠡⠀⠁⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠙⠦⡈⠢⠁⠀⠀⢀⣀⠄⠤⣈⠈⢉⠧⠄⠃⠈⣀⠤⠔⠒⠋⢹
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠈⠢⣄⠐⢦⠄⠀⠀⠀⠃⢈⡁⠄⠒⠂⠉⠀⠀⠀⠀⢀⠰
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠈⠢⡀⠀⠀⠑⠪⠥⠐⠒⠂⠉⠀⠀⠀⠀⢀⡀⢤⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⢐⡀⠒⣄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⢀⠠⠀⢰⠀⠸⡁⠈⠄⣊⠐⡇⠐⠃⠀⢸⠁
⠀⠀⠀⠀⢨⠐⠀⠈⠀⠀⠁⠀⠀⠀⠀⡃⠀⠀⠀⠘
⠀⠀⠀⠀⣄⠀⠀⠐⠈⠀⠀⠀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⡇⡠⠂⠀⠀⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠽⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⡀⡨⠀⠀⠀⠊⠀⡖⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⠀⠊⠁⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⢀⠙⠐⢁⠤⢊⠂⠀⠀⣈⠂⠤⠊⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣉⡉⠙⠀⡇⠀⠀⠀⠀⠀⠀⠈⡠⠊⠀⠒⠓⠊⠀⠀⠒⣄⠀⡂⡂
⠀⠀⠀⠀⠀⠀⠠⠐⠊⠁⠉⣉⢀⡐⡲⠛⣈⠝⢀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣞⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⢄⣀⡠⠴⠮⠤⠤⠜⠀⡇⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠠⠤⢤⠐⠊⠥⣂⡈⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠃


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠙⠀⠉⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡁⠀⠀⠙⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠊⠀⠈⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠄⠀⠈⠀⠈⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⣉⣀⡀⠀⠀⠀⠀⠀⠂⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠒⠠⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠒⠚⠉⡉⡉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢲⢙⠠⢙⠃⠄⢡⡐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠰⠀⠐⣤⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠆⣀⠀⢳⡨⡀⠌⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠢⣁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡆⠀⠠⠄⠀⠀⢰⣲⠀⠠⠄⠀⠀⢠⣲⡄⠀⠤⠠⠀⠀⣆⡆⠀⠠⠄⠀⠀⢰⣲⠀⠀⠄⠀⠀⢠⣖⡄⠀⠤⠠⠀⠀⣔⡦⠀⠠⠄⠄
⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀
⠀⢹⣿⣿⡇⠀⠀⣠⣬⣉⣙⠷⠀⠀⠀⠀⣹⡿⠻⠄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⣿⣶⠀⠀⠀⠀⠉⣉⡻⠆⠀⠀⠀⢘⣿⣿⡇
⠀⠙⠛⠛⠀⡀⠀⣿⣿⡇⠀⠀⢀⠀⠀⠀⠛⠛⠋⠀⡀⠀⠀⠘⠛⠛⠁⢀⠀⠀⠈⠛⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠛⠁
⡀⠀⠀⠀⠀⠉⢶⣾⡿⠃⠀⠀⠈⢁⣄⡀⠀⠀⠀⠈⠁⡀⡄⠀⠀⠀⠀⠉⢠⢄⠀⠀⠀⠀⠈⢁⡤⡀⠀⠀⠀⠀⠉⡠⣄
⠁⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣆⠀⠈⢉⣵⣿⣿⣿⣿⣿⣧⡁⠀⠀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁
⠀⢺⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠰⠛⠓⠆⠀⠀⠀⠐⣿⣯⣤⠀⠀⠀⠀⢾⣿⣷⡄⠀⠀⠀⠐⣛⣿⡆
⠀⠺⢷⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠋⠀⠀⠀⠀⠀⠀⠽⡿⠏⠀⠉⠀⠀⠾⠿⠿⠁⠀⠀⠀⠸⢿⠽⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⠒
⢀⣀⣀⣀⠈⣉⣉⣉⣉⣉⣉⡉⠀⠀⠀⢉⣉⣉⣉⣉⣉⡉⠀⠀⢀⣀⣀⣸⠿⠿⠿⠄⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⣀⣀⣀⡀⠀⠈⠻
⣿⣿⡿⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠄⠐⢳⡆⠀⠀⠀⠈⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃⣠⣿⣿⣿⠗⠚⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠛⠛⠋⠁⠀⠹⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢼⣄⠀⠀⠀⠀⠀⣈⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠙⢷⡄⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣶⣀⣀⠀⡀⠀⠠⠿⠷⠯⠤⠤⠤⠄⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠐⠈⠀⠈⠈⠉⠉⠉⠉⠁⡆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢠⡴⠀⠀⠀⠀⢀⠄⠂⠀⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢄⠀⠀⢠⠀⡉⡯⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠣⠔⠐⠀⠀⢠⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠃⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠣⢄⣶⡆⠤⠂⠀⠀⠀⠀⠘⠠⠘⠿⠤⠈⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠤⠄⠀⣀⣀⣀⣀⣀⣂⣐⠀⠀⠠⠠⠄⠀⠀⠄⠀⢚⡠⠇⠀⡀⠄⣦⣀⠒⡢⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠆⢀⡐⠀⠀⠤⢉⡀⠒⠂⠀⠀⠀⠠⡄⠀⣤⣤⣤⠄⠀⠒⠀⠒⠈⠉⢀⢀⣠⡪⣴⠍⠊⠀⠁⠢⢸
⠀⠀⠀⠀⠀⠀⡇⠈⠉⠙⠓⠒⠭⣀⡖⣀⠠⠭⢐⡂⠀⠤⢄⣚⠃⠘⠛⠛⠀⠤⢄⣀⣤⣴⠮⡻⠕⠋⠈⠀⠀⠀⠀⠀⠀⢘⣦⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⢀⠉⠀⠀⠒⠦⢍⣐⠂⣠⠉⠛⣀⢀⣶⠾⣛⠟⠉⠂⠁⡤⠠⠊⡒⠒⠣⢄⡀⠀⠀⣨⠏⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⣲⠐⠀⠀⠀⠀⠀⠀⠀⠀⡐⠚⠲⠒⠒⡀⡉⠀⠀⠀⢠⡤⢂⠖⠁⠀⠈⠢⠈⡆⡰⣎⠥⠂⢀
⠀⠀⠀⠀⡠⠴⡇⠀⠀⢠⠲⠀⠙⣌⠄⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠆⠀⠀⠀⠀⢀⠃⡎⠘⠛⠒⡦⠄⠇⠁⣇⣇⢠⢀⠌
⠀⠀⠀⠰⡀⠺⣇⠀⠀⢠⠍⠁⢠⠲⣄⠀⠀⢠⡘⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠀⢀⠊⢀⠔⠀⠀⢻⣏⠤⠊
⠀⠀⠀⢀⠈⠢⢬⡝⣆⠈⠐⠃⠀⡍⠉⠀⠀⢖⠚⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣾⠃⠬⢅⠔⠀⠀⠀⢈⢸
⠀⠀⠀⠈⠢⡀⠀⣇⢸⠀⠀⠀⢇⡨⠦⠄⣀⣀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠋⠁⡀⣴⠄⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⡛⠛⠉⠀⠀⢀⠤⢄⠀⠀⠀⠑⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠰⠂⠴⠀⠙⠋⢁⠐⡂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⢦⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠹⠾⠘⠛⠀⠤⢤⡀⠏⠛⠈⠂⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠁⢒⠀⠄⡀⠘⠉⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠧⠉⠀⠉⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠀⠀⠀⠈⠐⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⡀⠄⢀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠠⢌⠐⣸⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⡁⢀⠀⡠⠀⢀⠄⠐⡠⠠
⠀⠀⠀⠀⠀⠀⠐⠈⠄⠐⡈⠀⠈⡁⠒⣦⠤⢄⣀⡀⠀⠀⠀⢳⡸⠃⠔⠸⢀⣀⠤⠠⠖⠈⢋⠔⡠⢊⠔⡡⠊⠔⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⠀⠐⠉⠄⢈⠭⠛⡠⠚⡒⠖⡂⠌⡉⠄⠈⠔⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⠿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣯⣭⣭⣭⣽⡇⣿⣿⠱⢌⡏⠶⢹⡇⠾⣫⡆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⠿⠿⠿⠿⠿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣮⣭⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣛⣫⣭⣭⣭⣝⣛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢋⣴⠿⣛⣭⡭⣭⣭⣝⡻⢿⣮⡻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣱⡿⣡⣾⢹⣿⢱⣿⣿⣿⡿⠶⡙⣿⣌⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢱⡿⣰⣿⣿⣧⠻⡸⡿⢫⣴⠾⣿⢱⣿⣿⡜⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⡇⣿⣿⣿⣿⡷⢾⣿⠵⣶⣿⣿⢸⣿⣞⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡸⣷⢹⣬⣭⣶⢞⣼⣷⡹⣮⠻⣿⡸⣿⣸⢣⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡹⣧⡹⣭⣶⣿⣿⣿⡇⣿⣇⡿⣣⣿⢏⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣝⠻⣶⣍⣛⡻⠿⣚⣛⣭⣾⢟⣡⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣭⣛⣛⣛⣛⣛⣭⣶⣿⣿⣿⣿⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡵⠟

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡅⡎⠉⠉⠉⠉⠉⠉⠉⠉⡆⣴⠞⠻⣦⡀⣴⠞⠻⣦⡀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣀⣀⣼⠃⣷⣀⣀⣼⠃⣿⠛⣿⢛⡟⢻⡛⣻⡛⣻⢛⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡧⠻⠳⠟⠛⠛⠛⠺⠒⠛⠣⠬⠛⠛⠡⠠⠬⠟⠛⠥⠠⠿⠛⠛⠛⠛⠛⠛⠻⠛⠿⠛⠛⠰⠀⢾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠴⠶⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣀⡤⠤⠒⠒⠒⠒⠤⢤⣀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⡴⠋⠁⣀⣤⣤⣤⢤⣤⣤⣀⠈⠙⢦⡀⠀⠀⠹⣦⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠃⠀⠀⡰⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠙⢆⠀⠀⠘⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡏⠀⠀⣰⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣆⠀⠀⢹⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠐⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⠂⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⠀⠀⣇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣸⠀⠀⢀⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣧⠀⠀⠘⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣠⠃⠀⠀⣼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣆⠀⠀⠈⢦⡀⠈⠳⢦⣄⣀⣀⣀⣀⣠⡴⠞⠁⢀⡴⠁⠀⠀⣰⠏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠙⠢⣄⣀⠈⠉⠉⠉⠉⠁⣀⣠⠔⠋⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠉⠙⠒⠒⠋⠉⠁⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⣤⣤⣠⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠣⢤⡤⠤⠤⠤⠤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⢤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠴⠄⠀⠀⢀⡀⣸⢼⠁⢷
⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠄⠀⠔⠀⠙⣿⡎⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠴⣾⡇⠀⢠
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠂⣖⠀⠀⠀⠀⠀⠀⠻⡾⡄⡼
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠁⠀⠀⠐⠁⠁⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠤⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⢀⠃⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⢀⠎⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⡀
⠀⠀⠀⢀⡎⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡀⠘⢦
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⢸

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿