Thereon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢀⣠⠴⠖⠛⠉⠉⠉⠙⠋⠉⣹⡏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠈⠙⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⡟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣿⠁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢠⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣼⠏⣼⠇⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢰⡟⣰⡟⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣿⣡⡿⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⡇⡼⠃⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⣤⠶⠚⢛⣉⣉⣛⣳⣶⣶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢤⣤⣷⣠⡾⠿⠖⠛⠉⠉⠉⠀⣀⣀⣀⣀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢹⡀⠀⠀⣀⣠⣤⣶⠿⠿⠒⠛⠉⠉⠉⢹⡇⠀⣀⣠⠤⠖⣚⣋⣭⣭⣽⠶⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣌⣳⡾⠟⠛⠉⠁⢀⣀⣠⡤⠤⠶⣖⣶⣾⣷⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⢀⣀⡤⠴⣒⣋⣭⣵⣶⠶⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⢘⣆⣀⡤⠀⢀⣇⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣼⣧⣤⣠⣟⣠⣿⣿⢿⡿⣿⣿⣿⣟⣻⣿⠟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾⣿⣿⠿⠛⢻⠟⢿⣿⣿⣿⣏⠳⠚⣿⡿⠵⠿⣿⡁⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠳⠀⠀⠰⣴⣿⡟⡹⢿⣿⣿⡟⢻⣿⣏⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠙⣷⣤⣿⣿⠋⠀⠀⠀⠀⠀⠀⣠⣿⣿⠤⠠⠶⢿⣿⡷⠚⠛⠻⡏
⠀⠀⠀⠀⢀⠀⢠⣿⣿⠋⠙⠀⠀⠀⠀⠀⠀⠈⠙⣿⣧⣠⠆⢤⣾⣿⡟⠒⠀⠀⠁
⠀⠀⠀⠀⠈⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⣿⣿⣷⣿⣿⡟
⠀⠀⠀⠀⢰⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠉
⠀⠀⠰⠒⢿⣿⣿⣤⣀
⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣻⣿⣷⣄⡴⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⣸⣄⣠⣄⣤⣿⣀⢀⣴⠆
⠀⠀⠀⠀⠐⠋⠛⣿⣿⣿⣦⣤⣀⣷⣀⣀⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⠆
⠀⠀⠀⠀⠀⠀⡰⠛⠙⠻⣿⣿⣿⣿⣿⣿⡿⣿⡟⠛⢉⡉⠻⠀⢰⡀⠀⣹⠟⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⢻⠉⠀⠀⠈⠃⠀⠀⢻⣶⣶⣿⣷⣤⡴⠂⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⡙⢻⣿⣷⣀⣚⠛⣿⣿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⡄⢀⡋⢉⣿⣯⢥⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣙⣻⣿⣿⣠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠐⢋⠄⢉⠻⢿⣿⣿⣿⣿⠟⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣾⣯⣤⣨⣷⣾⣿⣏⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣯⣍⣿⠛⠻⠿⢿⡟⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⣄⣉⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢹⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣯⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣶⠶⣤⡀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣉⣉⡿⣿⣯⣅⣻⠿⠻⣿⣿⣿⠁⠀⠀⠀⣼⣿⢿⣻⣟⣟⣿⣄⡀⠙⠀⠀⣿⣿⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⣸⣿⠀⠀⠀⠈⠉⡚⠛⢉⣿⣿⣿⣿⣿⠆⠀⢰⣿⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠚⠿⠛⠛⠁⠀⠀⠀⣸⡿⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣄⡀⠀⠀⠀⠀⢀⣴⣽⣿⡀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⡀⠀⠀⠸⣿⣿⣿⣿⣶⠴⣷⠌⢧⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠻⠿⣷⣄⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠂⠀⣀⣀⣀⣤⣿⠋⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡀⡀⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⠀⢀⣤⣀⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⠈⠉⠛⠛⠛⣻⠟⠉⠙⠋⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣷⣶⣶⣶⠾⠁⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⠀⢞⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣰⣷⡿⠟⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄
⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣙⣿⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⣿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⢿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡟⠻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⡅⠰⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠘⣯⠹⣿⣷⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣍⣥⣤⣿⣧⡾⠃⠘⢷⣽⣿⣿⠣⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣦⣝⣛⣿⢿⣟⣛⠛⠛⠋⠉⠉⠉⢹⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠁⣽⣿⣿⣽⣿⢟⣿⣿⣶⣮⣽⣿⣷⣶⠀⠀⣀⢿⣿⣿⠃⠈⠳⠀⣰⣶⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⡎⣹⡟⣿⢿⣿⣿⣿⣿⡠⢀⡇⢸⣿⣿⣿⣷⣤⣄⣻⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣱⡟⢹⢹⣾⣿⣿⣿⣿⠡⢘⣿⣾⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⢿⣿⣷⣿⣾⣷⣿⣿⣿⣿⣷⣿⣿⣿⣷⣈⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⣾⣿⣿⣿⡉⠀⠀⠀⠈⠙⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢿⣿⣿⣿⡿⠁⠀⠀⢀⣀⣀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣃⣀⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⡇⠀⠹⣿⣇⡀⠀⠈⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⢸⣿⣿⣿⡏⢷⠿⠟⠛⠛⠿⢿⣿⣿⣿⡉⠀⢸⣿⣧⣀⠀⠀⠈⢛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠃⠀⢸⣿⠋⠁⠀⠀⠈⠲⠀⠀⠈⠛⠩⠉⢙⡿⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢤⣼⡋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⢸⣿⠁⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠘⣖⣒⣲⣀⠀⠁⠈⠈⠛⠂⠀⠤⠀⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠛⠛⠂⠰⠖⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⠀⠒⠤⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠔⠂⢇⣁⣄⠀⠀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢐⡖⣂⡨⠤⠐⠆⠒⣒⣤⣤⣀⠈⠲⡂⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣉⣈⠉⠉⣉⣁⣉⣉⣀⣀⠀⠀⣀⣈⣱⣄⠈⠳⢦⡠⡄⢡⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⢱⠶⠋⠁⢀⡀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢤⡀⠁⠒⢬⣳⡀⠹⡄⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⡀⠂⡽⠋⢀⡤⠀⡠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣁⡈⠢⠄⠀⠑⠀⠑⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠄⠎⠀⡠⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⣀⢑⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢦⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠁⢤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠌⠙
⠀⠀⠀⠀⠀⠀⠠⢤⡀⠁⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⠸⡇
⠀⠀⠀⠀⠀⢽⢀⡄⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⠁
⠀⠀⠀⠀⠀⢴⠊⢀⠚⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⠀⣼⢁⠚
⠀⠀⠀⠀⠀⠀⠠⢨⠧⠠⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠁⡰⠃⠚
⠀⠀⠀⠀⠀⠀⡆⡰⢤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡴⠈⢠
⠀⠀⠀⠀⠀⢴⡇⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⣠⠂
⠀⠀⠀⠀⠀⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣾⠃⡸⢓
⠀⠀⠀⠀⠀⠀⢉⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠁⠘⠂⠁
⠀⠀⠀⠀⠀⣤⠈⣙⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠛⠁⠊
⠀⠀⠀⠀⠀⠹⠎⠉⠄⠀⢧⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢠⡾⠀⠎
⠀⠀⠀⠀⠀⡀⠚⢀⢤⠀⠸⣗⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡆⠝⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⡛⠯⢄⣀⠀⠀⠀⢂⠀⠀⠀⢀⢰⡀⠀⠠⠤⠄⠀⠀⠀⣀⠄⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠘⡧⢠⣌⣙⠒⠛⠞⠒⠒⠚⢯⣄⣀⣀⣀⡠⠴⠭⣹⡿⠁⠂⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠴⢿⡛⠋⠷⡒⠂⠤⠴⠶⠈⠿⠿⢏⣁⢠⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⠒⠒⢟⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠙⠢⢥⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠
⠀⠀⠀⣶⡏⢩⠀⠀⠀⣀⠴⠤⣀⠀⠀⠀⠀⢀⢸⡈⢁⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⡇⠀⠀⢀⠤⠀⠀⠀⠀⠈⠳⠀⠀⠀⠰⠒⠒⠠⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠉⠀⠀⠀⠀⢹⢀⠀⠀⠀⠀⢞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠘⠀⠀⢠⠶⠤
⠿⠿⠿⠶⠶⠾⠙⠸⢻⠒⠒⠒⡨⠶⠊⠁⢠⡄⠀⠀⠀⠀⠀⠀⡘⢀⡓⣓⣾⡇⣀⣠⣀⣼
⠀⠀⠀⠀⠀⣹⠀⢀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠴⠀⠀⢀⡿⡏⠉⠉
⠀⠀⠀⠀⢀⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠶⠖⠶⡏⠈⢶⠒⢲⠒⠒⠂⠐⠀⠀⠚
⣀⣀⡤⠚⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠐⠓⡋⠀⠀⢰⠎⠀⠀⠈⡄⢘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠺⣧⠀⡀⠈
⠀⠀⠀⠠⠄⠀⡦⠠⠄⠀⠀⣀⠀⠀⠀⣏⠲⠷⠖⠰⣿⠤⢧⡀⠴⠐⠠⠖⣻⠿⠆
⠀⠐⢃⠤⢤⣴⣶⡾⠛⠛⠁⠀⠀⠀⠀⢹⠀⠀⠀⢴⡗⠎⠁⠀⠀⠀⣀⣀⠀⢠
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣆⠈⠄⠀⡞⣉⣇⠀⠠⠀⠀⢺⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢻⣄⣌⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢦⡀⠉⡽⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣼⣿⣄⣴⠀⠀⠀⠀⠐⠷⠾⠁⢀⣴⡁⠀⠸⣿⣄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠓⠶⠤⠤⣀⣠⣄⢠⣾⣻⡛⠓⠶⣬⣄⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠲⠤⠤⠍⠉⢛⡛⣒⠂⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠂⠤⠤⠀⠄⠀⠀⡀
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣄⠀⠀⢠⣤⣠⣤⠀⠀⡀⠀⡀⠀⠀⡀⠀⡀⣀⣀⠀⣀⢀⡀⢰⣶⣦⠖⠀⠀⠘⠓⠿⢸⠋⠿⠣⠞⠀⠀⡦⣼⠇
⠀⠀⠀⠀⠀⠟⠛⠀⠂⣤⢿⣏⠁⠈⡈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡁⠀⠀⠀⠀⠀⠀⠸⠀⠼⠇⠀⠀⠀⠀⢸⠇⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⣧⠀⠀⣸⣧⣤⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⠀⢀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢾⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡗⠀⢐⣿⣈⠉⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠐⠐⠀⠁⠀⠀⠀⢰⠀⣤⡂⠀⠀⠀⠀⣨⡄⠀⠀⠀⠀⢠⡶⣿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠯⢾⣄⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠾⣿⣷⣀⢸⠷⣶⣶⣿⠇⠐⢂⣰⣟⣿⣿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡆⠈⠛⠛⠛⠛⢦⣂⣀⠀⢀⣀⣐⠺⣿⣿⣼⢶⣀⡁⣰⠀⣘⣀⡐⠻⠔⠋⠙⠛⠳⣶⣀⡉⣀⠀⢰⢿⣿⠇⠀⣸⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⡿⠻⠿⡿⣿⣿⣿⣿⠛⠉⠛⠛⢿⣿⣿⣿⠈⢻⣷⣿⣶⣜⣴⣀⠀⣿⣭⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡇⠀⠉⠙⢟⠛⠟⠿⠟⠛⠀⠀⠀⠀⠀⠓⠂⠀⠀⠈⢻⣿⣫⠖⠀⠀⠤⢼⡟⠛⢻⠀⢸⣿⣿⣿⡿⣿⣿⣿⣷⣾⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⠥⠀⠀⠀⠂⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠆⠀⠀⠲⡜⠀⠀⠠⢹⠀⢸⣿⡛⠙⢩⣿⣏⠈⠉⠿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠇⠀⠐⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⣿⣠⣾⡆⠀⠉⣀⣀⡀⢸⠀⢹⣿⣿⣿⣟⢿⣿⡿⣤⣶⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠂⠀⠀⠹⣿⠿⢗⢈⡁⠀⢸⠀⠙⢷⡿⣷⡘⣣⡈⢠⣌⡀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⠶⡶⣦⠀⠀⢟⡋⠁⠀⢸⢀⠹⠆⠰⠬⠿⠿⠿⠿⠯⢿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠛⢾⣷⣿⠃⠀⣼⣿⣀⡄⢸⡆⢰⣶⣶⣶⣶⣶⣶⠶⠀⠆⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠾⠷⢦⠾⣿⣿⣶⣤⣈⣯⢉⠛⣿⠇⠈⠉⠉⣉⢿⣟⡿⠘⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡘⢀⡶⠛⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⣿⣿⠛⠛⠻⣟⠀⢹⠀⠀⠀⠀⠿⢺⠁⠀⢘⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡇⢸⣿⡿⠄⠀⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠃⠀⠀⠈⠁⢘⡇⠀⠀⣸⡄⠶⠀⠀⢈⠀⣿⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢳⢸⣿⣿⣶⡆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡆⠀⠀⠀⠈⠀⠀⠀⢠⡄⡀⢸⡇⠀⢀⠃⢠⡌⠀⠀⢸⠀⣏⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠌⠀⠁⢻⡐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣠⣤⣦⠴⠠⠄⢀⡈⣫⣴⣧⣿⠁⠀⢸⡆⢸⠇⠀⠀⠈⠀⠈⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⡍⠁⠀⣠⢠⠀⠩⡏⠀⠸⣿⠀⠀⠸⠿⣸⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⡐⠀⢰⡆⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠙⢸⣴⣶⣿⣧⣄⣿⠀⠲⠶⠶⠿⠀⠀⠀⣀⠀⠀⠠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⢰⢿⣼⣷⣤⡤⣬⣄⣰⡆⠂⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠐⣤⣽⠯⠹⠯⠉⡏⢢⠄⢀⣤⣤⣤⠀⢠⣤⣄⡄⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣼⣿⣧⣿⠀⠈⠙⢃⣠⡄⠀⠀⠀⠀⠀⠨⣷⡾⡿⣹⣿⣾⣿⢩⣦⡀⡀⠀⡇⢀⡾⣿⣿⣿⡟⠷⣤⣿⣞⠃⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠰⠀⢸⣿⣟⣧⣌⡀⠀⠀⠀⠐⠻⡄⠀⠀⢀⡠⢀⠉⠁⠀⠉⠉⠩⠟⢛⠉⠛⣟⠀⡇⢸⣿⣇⣹⣿⣿⣷⣬⣿⣿⡆⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠀⢠⣟⣫⣿⣹⣇⢠⣾⡆⣾⠀⢇⣀⣄⣸⣋⣉⣤⠤⠖⠒⢛⣿⢺⣥⣽⣠⣦⣬⡇⢸⣏⠉⢣⣶⢿⠿⢿⣿⡟⡇⠈⠋⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠁⠀⠉⠙⠛⠛⠛⠓⠒⠚⠛⠋⠉⠉⠙⠋⠿⠊⠉⠇⠸⠋⣶⣾⣅⢰⣆⢸⢃⢻⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⢠⣄⣰⠀⠈⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⣿⠃⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢠⡟⠙⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⢠⣄⣀⡀⣀⣄⣄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⢀⠈⠻⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣆⠀⠛⣝⠻⠟⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠁⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣀⡄⠀⠀⠈⠁⠀⠀⠀⠀⣠⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⣼⠧⠤⠠⠶⠆⢀⠰⣿⠾⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠏⠀⠀⠀⠀⠀⣠⡤⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⠀⢠⢠⠀⠁⠀⠁⣐⠃⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡆⠀⣘⠀⡽⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⣉⢡⣬⣥⣤⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠀⢠⠆⠄⠱⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⢀⠀⢶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠐⣶⣤⠴⠀⠀⠀⠠⠂⠰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⣾⣻⣷⣿⠀⣻⣦⣀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠿⠇⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣹⣿⡕⢻⣿⠀⡾⣏⢻⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠀⢠⣴⣶⣶⢶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣧⠀⣶⣈⡛⠀⠟⡋⠀⠠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠐⠋⣀⠀⡀⠀⡙⠉⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠄⠚⠧⠀⠀⣀⡽⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣩⣤⣤⣄⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠔⠀⠀⠀⠀⢸⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠋⠉⣩⣿⣦⡀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣿⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣉⣋⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠶⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣻⣻⣟⣿⣻⡗⠎⣻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣼⡷⢢⡤⣀⠀⠀⠙⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠀⠀⠀⠈⢀⣿⣿⣤⣻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢡⡟⠀⠋⠀⠀⠀⠀⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣠⠞⢁⣥⢀⣤⢰⣾⣿⠟⠀⠙⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⠀⠐⣀⣠⢄⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢀⠁⢈⣰⣊⣾⡿⡻⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣉⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠐⠋⠀⠐⣃⣾⣿⡿⢉⠃⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⣈⠻⠟⣀⢠⣾⣼⣿⠿⠟⣵⡟⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣧⣼⠆⠀⠀⡀⣤⢸⠷⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣝⣷⣠⣬⡿⢄⣾⣿⠷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣮⣿⣿⣿⠟⠁⠀⠉⠓⢤⣶⣦⡄
⠀⠀⠀⠀⢀⡂⠀⠉⠻⠇⠀⠈⠙⠛⠠⣌⣻⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣱⣻⠟⠃⠀⠀⠀⠃⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠙⠂⠁⣠⡤⣠⠀⢰⡆⠀⠈⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠁
⠀⣸⣷⣦⣔⠀⠀⠀⠙⠛⠃⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⣄⠀⠀⠀⢀⡈⠁
⠀⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⢈⣴⠞⣦
⠀⠈⢻⣿⣿⣿⣿⣿⣷⣤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣾⣿⣴⡉⠁
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠁

⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⢐⣿⡟⢉⣉⣉⠉⢉⣉⡉⠛⠛⠻⣿⡙⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡇
⠘⣿⡇⢾⣥⠙⠷⠟⠀⢻⡄⢀⣀⣈⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢠⣿⡇⢠⡿⠀⠀⠀⠀⣾⠁⡟⠉⠉⠻⠛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠘⣿⡇⠘⣷⣄⣠⣤⡀⠻⡴⠇⠀⠀⠀⢾⡏⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⡇⠀⢀⣭⠥⣬⠟⠀⠀⠰⣦⣄⣀⣼⠇⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⡇⠀⢺⡇⠀⠀⠀⠀⣶⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⣿⡿⣦⣾⢃⣀⡀⠀⢠⡟⣿⢠⡿⠀⢀⣀⡀⢀⣀⣀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⣿⡇⠈⠻⣿⡋⠛⠶⠛⠁⣿⢸⡇⢰⣿⡉⠿⠟⠉⢹⡇⣰⡶⢶⣌⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⣿⡇⠀⠀⠘⢿⣦⡀⠀⠀⢻⣿⣧⡈⣽⡇⠀⠀⠀⢸⡇⣿⠀⠀⠉⢉⣽⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣿⡇⠀⠀⠀⠀⠙⢷⣦⠀⠀⠉⠙⠁⠻⣧⣤⣤⣤⡈⠻⠟⠀⠀⠀⠈⣿⡄⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⣿⣧⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⢠⡶⠷⠶⠾⠃⠀⠀⠶⣦⣤⣤⡾⠃⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠸⣧⠀⠀⠀⠀⠀⣿⣦⠈⢿⡁⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣿⢁⣄⡀⠀⣠⡇⢹⡇⣿⠇⢀⣀⣀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠋⠙⠛⠉⠀⢸⡇⣿⠠⣿⣍⢻⣾⠟⠻⣦⢀⣠⣄⡈⢻⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠘⣧⣿⡀⣸⡏⠀⠀⠀⢀⡿⣼⠋⠉⠻⢾⠟⣿⣦⡀⠀⠀⠀⢰⣿⡇
⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠙⠁⢿⣆⠀⣀⡀⠸⣧⣼⠀⠀⠀⠀⣾⠋⠈⠻⣦⡀⢀⣿⡟
⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣙⣛⣋⣻⡆⠈⠁⣠⣀⡀⢀⣿⠆⠀⠀⠈⢻⣾⣿⠁
⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢰⣏⠉⠉⠉⠀⠀⣶⣌⠙⢿⡏⠁⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣿⠆⣀⠀⠀⠀⣹⡟⣷⠘⣿⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⣦⣤⣴⠟⠀⢹⡅⣿⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠈⠀⠀⠀⠈⢷⣿⣦⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠈⣡⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣄⣀⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⠉
⣿⣿⣿⠿⣿⡿⢿⢿⡿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣶⣿⣶⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠛⠛⠻⠿⠿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⢳⡸⣧⡈⢷⡄⠸⣧⡀⠀⢷⡀⢰⡄⠀⣤⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣃⣼⣷⡌⢿⣄⡘⢷⣄⠈⢷⣄⡙⣦⣈⣷⡀⣷⠀⠀⠀⠀⠘⣷⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣀⣴⠟⢋⣡⡾⠟⢁⣼⠟⢡⠞⠉⠸⠛⠉⠁⠀⠀⢀⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠐⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣻⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣼⠇⢠⡿⢰⠀⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣰⠀⢀⡾⢀⣿⠃⣸⡟⢀⣾⣧⡟⠳⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣷⠀⠀⠀⠀⠀⢀⡶⢠⣿⣠⡾⢧⣾⠳⣾⣍⠙⠻⣦⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⠀⠀⠀⢸⣦⣜⠛⠿⣄⠙⠻⣄⠙⠷⣄⠙⢦⠀⠈⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣄⡀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⠟⠛⠉⠉⠉⠉⠙⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠉⣀⡀⠰⣤⡘⢳⣄⠐⣆⢀⡀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣄⡲⣤⣝⣷⠆⣿⠟⡼⠛⠹⠾⠇⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠡⠋⠘⣁⣀⣀⣀⡀⣀⣀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠿⠟⢿⣷⣶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⡿⠁⠈⠃⠀⣄⠀⠀⢹⣏⢺⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⡛⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡏⠀⠀⠀⢉⠘⣩⢛⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡿⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡼⠃⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢆⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠟⠀⠹⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠏⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⠋⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣻⣿⣦⠀⠀⠀⠀⠀⢠⠀⠀⢰⡏⠀⠀⠀⠀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠙⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢻⣇⠀⠀⠀⠀⠀⠀⢸⡘⣿⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⢹⡜⢷⣄⠀⠀⢠⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⣧⣿⣿⣯⡟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠱⣤⣀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠈⠻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣧⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠸⡿⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣽⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⣠⡾⢦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠞⡁⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡄⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡴⠿⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⡠⢾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣿⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣀⠀⠀⢁⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣦⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠤⠂⠀⢀⡀⢠⢄⣠⣷⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⣿⣦⣼⠽⣿⡅⣄⣈⣳⣾⠿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⣿⣿⣷⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢟⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢆⠀⠀⠀⠀⠀⠀⠰⡀⣤⠤⠤⣶⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⣞⠉⠀⢉⡯⡅⡀⠀⠀⠀⠀⠀⠀⣘⢆⡸⣇⠀⠀⠀⠀⠈⠁⠜⢧⣄⣀⡼⢟⣌⠁⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠬⠘⠙⠛⠋⡑⠀⠀⣀⠀⡶⠀⠀⡼⡓⠀⠁⠌⢧⠀⠘⠂⠀⠁⠀⢡⡘⡄⣠⢆⡀⠤⣾⠋⠀⠀⠠⣄⠲⡄⠐⡖⠞⡭⣤
⡤⠜⠈⠆⡄⠀⡴⡀⢰⡄⠀⠀⢰⡢⢄⣀⡐⣰⢪⡆⠉⠁⠍⠸⠀⠀⢿⣹⡛⠀⠀⠈⣷⡌⠂⠁⠠⠈⠉⠢⢇⣏⡴⠛⡥⢰⣌⣠⡁⠀⠊⠙⢦⡇⠈⣿⣀⠞⠉
⠐⢢⡄⢰⠃⠀⠟⡙⠠⠄⣠⠠⠄⡉⠂⠀⠀⠈⣻⠁⢀⡖⠨⠈⠂⠀⠸⡦⡓⠀⠨⠻⢠⠀⠀⠊⠡⠑⠦⠀⢸⢋⣠⡴⣾⡾⣿⠿⣷⢦⣤⡶⢛⣠⣼⡶⠋
⠀⠀⠹⢤⣦⢀⠁⠙⣂⣀⣪⠶⠻⢫⠟⠛⠒⠦⢄⠁⣘⠶⢄⠃⢀⠀⢘⡏⡈⠀⠐⠀⠀⡠⠀⡠⠀⢰⠀⣄⡴⠋⠀⠍⠙⠓⠀⡆⠁⠓⢙⢿⣧⣤⣤⠤⢔⡟
⠀⠀⡀⠀⠉⣉⣩⢩⣵⣫⡄⠀⢠⢮⡇⢁⠀⢀⠁⣥⢻⣧⠈⠀⠀⠀⣸⢏⡀⠀⠀⠀⠀⠱⡀⠐⠁⣠⢰⡟⡘⠁⡚⣄⠰⢋⡇⠁⠧⢐⠀⠠⡺⣟⠢⣀⣎⠛
⠀⠀⠠⠆⡀⣀⠈⣼⣉⠞⠀⡀⢸⡀⠀⠂⡀⠎⠠⠈⣏⢿⡌⠅⢀⡴⢋⡜⠀⠀⠀⠀⢀⣀⡀⠦⣀⡁⣿⠀⠀⠒⠁⠁⠂⡉⡠⠂⠐⠈⡥⠘⣿⣙⡆
⠀⠀⠀⠈⠁⠁⠀⡇⣅⡘⠁⠄⠀⠱⣤⠔⠃⠀⠀⣡⢨⠺⡟⡾⠯⣶⣩⣤⠔⠦⣾⣷⠨⢥⡤⢵⠞⡃⡿⠖⠋⢳⠀⠀⡜⡵⠁⢀⡀⠤⠕⠶⠃⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡗⢁⡐⠚⠀⢀⠀⢸⠃⠈⡀⠠⠂⠀⠀⣇⢄⣤⡏⠀⢺⡎⠘⠚⠂⢾⣈⣁⣻⣤⠂⣿⡊⠙⠃⠡⢈⣣⠼⣄⡼⠹⠀⡤⢂⠔⣼⠃
⠀⠀⠀⠀⠀⠀⠐⣿⣌⠀⠈⠀⢍⢦⡜⠑⠀⠁⠀⠀⠁⠐⢥⠈⣼⠏⣿⢏⠉⠀⡘⠁⠀⠈⣿⠹⢻⢠⠏⠀⠀⡤⠖⡆⠀⠢⠇⠚⠰⢡⣈⣥⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠹⣗⢌⠉⡔⠀⠋⠐⠁⠀⢀⠰⢐⠂⣀⠀⡷⢶⢶⣟⣚⠀⠀⠀⣀⣀⣠⠹⢦⡞⣻⠆⡴⡆⢣⡇⢼⠀⢄⡒⢄⣀⡠⢟⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠢⢈⢀⠀⠀⡴⠋⠀⠃⠥⠘⢿⡟⣷⡰⠄⠈⠉⠀⠀⢠⣼⠏⣱⠏⢀⣁⣭⡶⣿⣮⣦⣀⣠⣄⣶⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢤⣠⠠⢤⡴⢾⠳⢶⡒⢦⡦⠤⣄⠙⠻⢿⣷⡄⠀⠀⣠⢞⡵⠞⢡⡾⣫⠎⢁⠌⢃⠨⣟⠭⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠬⠛⠁⢠⡀⠀⠀⠙⡄⠀⢛⡆⢕⣀⢐⣎⠀⢠⡇⠄⢣⡔⢂⡴⠴⠴⣦⡀⠀⣿⢢⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠂⠀⠀⡤⢆⠈⠀⠀⠈⠀⡀⣠⣧⠀⣿⠁⠀⠀⠀⡯⡷⢸⢆⠀⢀⠀⢀⠀⢁⣼⢲⡇⢠⢣⣀⣉⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡁⠀⡀⡀⠘⣀⠀⡌⣈⠱⠀⢨⠂⡁⡟⠀⡽⠶⠖⠒⢾⢛⡅⠈⢧⣦⣹⠀⠬⠁⠀⢑⣽⣣⡾⠟⠉⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠲⣦⣳⡄⠀⢌⠉⠀⣨⣥⠖⣱⠶⠛⠛⠳⢒⠛⠛⠋⠛⣠⠙⠲⠶⣶⣾⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠸⠀⠀⢀⣠⠄⠤⠤⣞⡁⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⢄⣥⣆⠼⢷⣶⠶⠫⠥⣄⠠⠼⠿⠛⠹⠯⠑⠲⡷⣄⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠊⡀⣨⣎⣀⠵⠋⠀⠀⠅⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠔⠀⠉⠉⠉⠻⣤⣻⠑⡀
⠀⠀⠀⠢⣴⡆⠊⠀⠀⠂⢀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠂⠀⢀⠀⢀⡀⠀⠼⡐⡌
⠀⠀⠀⠀⠈⠧⣁⣠⣤⣀⢐⡒⠤⣥⣏⠠⢔⡀⠐⠒⢀⡐⠀⣠⡤⢆⡠⣄⣘⡤⢊⣴⣦⡉⡰⠁
⠀⠀⠀⠀⠀⠀⠈⠉⡀⠬⢅⠹⣧⡮⣗⠿⣗⠠⣤⣶⠌⣉⣱⣄⡚⠟⠋⠁⣈⠔⠁⠀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠁⠠⡀⠀⠈⠉⠉⠐⠂⠠⡐⠉⠁⠈⠉⡇⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠐⠒⠺⠬⠦⢄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠄⠿⣥⡔⠒⠈⠉⠩⠵⠶⠦⣄⠙⢧⣀⠘⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡤⠄⠒⠒⢒⠒⠶⠖⠂⠐⠐⠒⠲⠂⠘⠓⢀⠙⠳⢕⡀⢄⠐⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡴⠂⢉⠀⢠⠒⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠒⢀⢉⠛⢧⠈⠇⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢠⠊⠀⡴⠃⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠰⣦⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⠁⠸⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢠⠚⠂
⠀⠀⠀⠀⠀⠀⠠⡄⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠖⡇
⠀⠀⠀⠠⠸⢃⡔⢀⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⣼⠀⠃
⠀⠀⠀⠀⠰⠋⢠⡏⠀⠼⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠆⢠⠇⡌⠁
⠀⠀⠀⠀⠀⠀⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠋
⠀⠀⠀⠀⢀⡆⠂⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠋⡀⠆
⠀⠀⠀⠀⠸⣇⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣠⡞⢰⣠
⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠰⠃
⠀⠀⠀⠀⢠⡄⢑⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⠃⡐
⠀⠀⠀⠀⠘⠇⠉⡀⠈⣦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠇⠰⠁
⠀⠀⠀⠀⠠⠈⠠⡰⠀⠸⣏⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠙⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠈⣏⠒⠤⣄⠀⣄⣅⢀⣀⣠⠀⠆⠀⠒⠒⢀⣀⣀⡤⠆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠸⣪⣶⠤⣌⣉⡉⠉⠉⠙⢶⣤⡴⠖⠈⠉⠴⠟⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠉⢣⡄⢉⡦⣌⠉⠉⠀⠈⠉⠁⠒⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠈⠉⠉⠉⠉⠉⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⢿⣿⣿⣿⣿⣿⢿⡿⠿⠿⣿⣿⣿⣏⣩⣍⠩⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣽⣿⣿⠿⠟⢻⣟⣓⠙⠻⠧⡉⠛⢿⣿⠃⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣯⠁⠀⠀⠀⠀⠀⢠⠶⠄⠈⠑⣀⠙⣧⡄⠊⠉⠁⠄⠈⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡱⣶⠦⣄⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠈⠛⣶⣀⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠠⠀⡆⢀⣄⣠⣠⡤⠴⠤⠕⠂⠀⠐⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⣧⣀⣀⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣘⣷⣀⣼⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠿⠇⠂⡰⢶⣮⣽⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⣀⣸⡟⠉⠓⢛⣿⣿⣿⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⢯⣴⣶⣾⡏⠁⠀⠚⠉⠈⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣤⣀⣀⣘⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣌⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡖⢾⣿⡇
⠀⠀⠀⠀⠀⠀⣄⠀⣠⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣏⡇⢸⡇⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡿⣿⡟⠇⢸⡇⠲
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠿⣿⣿⠿⠿⡷⠒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⣯⣼⠻⠇⡄⠸⠷⠖
⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⣿⡋⠰⠆
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⡃⣿⣩⡇
⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠐⢾⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⠀⠀⢠⡄⠠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⣀⣼⣿⣿⣟⢓⣤⠠⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣷⣾⣷⣶⣺⢧⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣶⣦⣤⣶⣿⣿⣭⣿⣬⣦⣤⣤⡶⠤⠶⠆⠀⠀⠀⠀⠈⣈⠻⠧⣿⣿⣿⣍⠶⣽⡆⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣈⠉⠋⠈⣿⣿⣿⠿⠁⠈⠂⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠈⠿⢿⣷⣌⠻⣤⠀⠀⠀⢨
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡉⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢈⣿⣿⡿⣿⡀⠀⠀⠘⠃⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠄⠀⠀⠀⠀⠀⠈⣧⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢻⢟⣉⠛⢿⣿⡄⠀⢘
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠠⠘⣿⠀⣠⠄⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡆⠀⡀⢴⣄⠁⠓⠠⣯⠀⠀⢠⡄⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡈⠀⠀⢸⣷⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⠀⣠⣶⠻⠏⠈⡁⢤⡟⠁⠀⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀⠁⠀⠀⣘⢛⣣⠈⢿⡏⠗⠀⡇⠀⠀⠀⣆⡨⢻⡗⢰⠇⠀⠾⠁⠀⠀⠋
⠀⠘⠀⠀⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢠⠀⢠⠈⢴⡙⠿⠿⠁⢸⣏⡄⠀⠀⠀⠀⠀⠈⠁⢸⡆⢈⠁⠀⠀⠀⣄⠀⠀⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠂⡀⠁⢀⣿⣿⣶⡀⣠⣶⡈⡃⠀⠠⠈⠀⠀⠀⠀⣿⡄⠀⡄⠀⢠⣴⡟⢀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠛⣤⠈⢿⣿⣿⣴⣎⠈⣁⣄⡀⠀⠀⠀⠀⠀⣠⣿⢿⡆⣸⣃⣴⣿⠖⢁⣤⠖⠀⠀⠀⢀⣤
⠀⠀⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠑⣦⡙⠋⢋⣩⣶⣿⣿⡁⠀⠀⠂⠀⢠⣿⣿⡛⣿⡿⠋⠞⢡⡴⡟⠀⠀⠀⠀⠀⣿⡁
⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣦⠐⠆⢀⣿⠉⢽⡿⢸⡇⠀⠀⠀⠀⣾⠉⢿⡦⠉⠀⡀⣶⡿⢟⠇⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠈⠙⠙⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⡌⠻⠇⠰⢿⠋⠁⣀⡣⠸⠃⠀⠀⠀⠀⢾⠓⠿⣠⡼⢃⡐⠉⣴⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡧⠀⠀⠀⠀⠀⢇⣀⠀⠁⠀⣆⠀⠿⠳⠚⠀⠀⠀⠀⢰⣤⡄⠚⣅⢠⠾⠁⢰⣇⠈⠃⠀⢀⣤⣦⣤⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣴⡇⠀⠀⠀⠀⠀⡘⠛⠃⠀⡾⠆⢰⣄⠳⣶⠀⠀⠀⠀⠸⣿⠀⡀⠟⠀⠀⡶⠀⢠⠿⠀⠀⣾⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣷⡄⠀⢀⠀⢠⣴⠏⠹⠟⠀⠀⠀⠀⠀⡤⢾⡇⠀⣠⡆⢀⠐⣀⡀⠀⢸⣿⣿⣿⠁
⠀⠀⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⡜⢻⣧⠀⠿⠷⠘⢋⡀⠐⠀⠀⠀⠀⠀⣠⠄⠀⠀⠆⠀⣠⠠⠶⣿⠇⢀⣿⣿⣿⡏
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣤⡀⢀⣴⡿⠃⣤⣆⣠⣀⠀⠀⠀⣠⠔⠁⣠⠞⠁⠀⡼⢁⣿⣼⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠛⠋⠱⣦⠀⠘⠛⠈⠁⠀⠖⠋⢿⣾⣿⢿⣷⠊⢁⣠⠞⣠⣆⡀⠊⠀⡸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⣷⡆⠀⠀⠸⠿⠀⠀⣀⢽⡿⠿⣿⣶⢟⡡⠚⣠⡞⠁⠀⠀⢱⣿⡇⠈⠛⠛⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠳⠶⣦⡤⣤⣶⣈⡿⠎⠃⣿⣏⣛⣿⣷⡎⣠⣤⣼⣿⣶⠛⠋⠀⠀⠀⠀⠀⠈⠹⠿⠿⠇
⠀⠀⠀⠀⠀⠦⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⡄⠸⠓⠜⢂⡅⠀⠀⠀⠈⠙⠛⣉⠛⣛⠿⠏⣉⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠿⠷⠶⠶⣤⣤⣀⠒⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠤⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠐⠒⠒⠀⠠⠤⣄⣀⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡀⠀⡄⠀⠀⡆⠠⠀⠀⠀⣄⠰⡆⠀⠀⣶⠀⠀⡇⢰⢐⠂⡆⠠⠀⠀⢸⠀⡀⡐⢰⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⠀⠀⡀⠐⡰⠆⠰⠄⠠⠄⠀⠂⢠⠀⠀⠀⠀⠀⠐⠀⠀⡆⢸⠰⡆⡦⢰⠀⠀⠀⡆⢰⠀⠂⠄⢸⠀⠀⠛⠀⠂⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠛⢉⣭⢆⣤⡾⠛⠿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⡗⢰⡆⢲⠄⢀⢴⠀⠀⡆⠀⢀⣻⣭⣵⡞⢵⠿⠿⣠⣀⢀⣀⡛⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⡀⣤⡆⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⢠⡈⠂⣬⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⢀⡀⠀⠀⢀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢄⠉⢳⣝⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠈⠃⠀⠀⠙⠀⠀⣿⣷⠶⣶⠀⠀⣴⡟⠛⣛⠉⠀⢰⣹⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠲⠠⠶⠰⠶⠀⠀⢰⡿⢻⣿⣿⡇⠀⣼⣿⣅⣸⣗⠀⠀⠙⣿⣿⣿⣹⡧⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄⠠⡄⠆⠀⠀⣾⣷⠘⠀⢺⡇⠀⠀⠩⠅⠉⠉⠀⠀⢸⣡⣿⣿⣻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠐⠀⣤⠄⣀⠀⢰⢻⣿⠃⠀⢸⠁⢠⢠⡀⠀⠀⠀⠀⣾⡾⠃⢻⣥⣿⣿⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢤⡀⠦⢤⠀⠸⣸⣿⡆⠀⠉⢙⠓⠋⠁⠀⠀⠀⠀⠰⠀⢰⣿⣿⣿⣾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀⢸⣿⣿⣦⠠⠀⠀⠀⠀⠀⢀⡿⠏⠿⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣿⣿⣷⣄⠙⠷⠒⠀⠀⠀⠀⠀⢀⡞⠁⠀⢰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⢻⡜⠙⠟⣿⡦⠀⠀⠀⠀⠐⠀⢀⡾⢃⣼⢐⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢟⠀⢸⢟⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⡟⣛⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣤⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣇⣁⣨⠝⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⣤⣈⣥⣮⠭⠝⣛⢶⣌⠐⢦⢼⣶⣶⣆⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣯⣽⣶⠟⠛⠛⠛⠛⠛⠛⠻⠿⢶⣤⣍⡛⣽⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠤⣶⠖⣻⣷⡟⠛⠃⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠽⠿⢾⣿⣦⠀⢱⡄⠀⢸
⠀⠀⠀⠀⣠⠞⢡⣤⢞⣿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⢹⣿⣷⣌⣧⠀⢸⡇
⠀⠀⠀⡸⣁⢴⣶⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣯⡻⣿⡄⢐⡇
⠀⠀⢠⣽⡵⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⣷⣼⣇
⠀⠀⡼⠻⢱⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣿⡏⠳⡀
⠀⠄⢰⢗⡿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⠢⡀
⠀⠂⠊⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠱
⠀⠀⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⡇
⠀⠑⡄⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠐⣿⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠐
⠀⠀⠑⢾⣿⡢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⠁
⠀⠀⠀⠀⢹⣟⢺⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡉
⠀⠀⠀⠀⠈⢿⣿⣄⠘⣝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⠤⠾⠟⠋⡴⠁
⠀⠀⠀⠀⠀⠀⠙⣷⣦⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡗⢋⠠⠈⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠻⡽⢷⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⡖⣿⠶⠖⠳⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣉⠻⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣀⣠⠾⣺⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠛⠛⠿⢿⠶⠤⣤⣄⣤⣦⡿⠿⡿⠛⣃⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣷⣾⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡏⠀⠉⠈⠁⢸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣄⢷⠀⠀⠀⠀⡼⢘⡷⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠻⣌⣳⡀⢀⣼⡵⠛⠁⢠⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡼⣷⢬⡓⠦⣄⡙⣷⣾⢋⡤⠴⠖⣻⣚⣵⢶⣀⣀⣀
⠀⠀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⣋⣉⣉⣀⠈⠛⣏⠛⠛⣛⣾⣿⡛⠛⢉⡽⠋⠉⠀⠀⠉⠉⠻⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢠⣾⡿⠻⣏⣩⣝⢶⡀⠀⢀⡴⢟⣆⣴⡯⠴⠚⣉⡉⠉⠉⢉⡽⣷⣮⠷⣾⣏⠁⠀⢹⣷⠾⣤⣴⣞⡋⠉⠉⠙⢓⣲⢤⣽⣆⢰⡇⢶⡄⠀⠀⣠⣞⣛⣋⣽⣶⣄
⣾⢻⣄⠀⠈⠁⠈⣿⠛⠶⢾⡵⢞⡿⠋⠀⠀⣼⣯⣥⡤⠰⠟⠐⠿⠈⠳⢤⣥⡤⠤⣤⣤⠾⢩⣿⠆⠉⠲⠤⢤⡿⣹⠂⠈⠙⢦⠙⠶⠿⠶⠻⣿⠋⠉⠉⢀⣸⣿
⣿⠀⣹⠇⠀⠀⣾⡁⠀⠀⠀⠀⣾⡴⠚⠲⠋⠁⣠⣤⡤⢤⣄⡀⣴⠻⠇⠀⢻⠉⠉⣿⠁⢰⣶⡄⠀⢀⣀⣀⣀⣀⠈⠳⣦⣤⢬⣷⡀⠀⠀⠀⠙⢦⣄⢀⣿⠉⢀
⠹⣾⣇⠀⠀⠀⣉⣁⣀⣀⣠⢾⢿⡄⠀⠀⢠⡞⠋⠁⠉⠳⠴⠛⢿⡀⠀⢠⡟⠀⠀⠹⡄⠀⢰⣷⠿⠿⠦⣴⣋⣉⠱⣄⠀⠀⢸⡟⣷⢦⡄⢤⡀⠛⠋⠀⣹⣦⡾
⠀⠘⠿⢦⣶⣟⣥⠤⠟⠋⢁⣿⠀⠙⠳⣤⡞⠐⣯⠟⢳⣤⠤⣤⣀⣧⣴⣟⣀⣀⣀⣀⣙⣦⣿⣁⣠⡤⣴⣏⠙⠿⠇⢸⣦⠶⠞⠁⣿⠀⠙⠳⠿⣶⣶⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢻⡄⠀⣶⠾⢧⣀⠀⢀⣿⠃⢰⣦⢿⡗⠒⠛⠛⠛⠛⠛⠛⠛⠛⣿⣧⣤⠸⣽⣆⣀⣀⡼⢿⠃⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡀⠈⠳⣄⠈⠙⠘⣿⡉⠁⠙⠶⣄⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣡⡴⠋⠉⣩⠷⢦⣼⠇⣠⠞⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢯⣳⣤⣀⠈⠙⠷⠤⣶⡾⠟⢻⣇⢰⢶⡄⣴⢲⢀⡞⡇⢠⣿⠛⠻⣶⡴⠾⠃⢀⣀⣤⢞⣿⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠻⢧⡼⣿⣼⠻⣾⡆⣧⣿⢸⢸⢿⣣⠿⣇⣻⣷⡶⠟⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠧⠤⣍⣦⡘⢷⣿⣻⡟⣸⣿⠋⣴⡯⣄⡞⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠽⠋⢧⡤⠤⣄⠀⠈⣷⠿⣿⠯⠽⣯⢿⣾⠃⠀⣠⠤⢄⣴⠋⠻⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⡷⠛⡴⠚⣿⠀⠘⡇⢠⡇⠀⢿⠓⢦⡝⢶⣀⡿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣶⢿⡾⠁⠀⠀⡭⢼⡇⠀⠈⠳⣼⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣘⢧⣶⣤⣼⣁⣀⣷⣤⣾⣶⣧⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠻⠹⣷⣛⣒⣒⣒⣓⣒⢚⣛⣻⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠿⠷⢤⣔⡯⢁⣴⣾⠿⢿⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣱⣟⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣽⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣮⣄⣈⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⡀⠀⠀⠀⣶⡃⠀⠀⠂⢲⠀⠀⣴⣿⡶⠃⠀⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣻⠀⠀⠀⢈⠛⠀⠀⠀⠃⠀⢸⣿⣿⠿⠔⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢼⣿⣿⣤⣤⣶⡗⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠘⣾⠆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣫⠻⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣠⣶⠟⠋⠁⢸⣿⣷⣂⠀⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣤⣿⣿⣦⡄⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢿⠀⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣍⣼⣯⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣗⢸⣿⢳⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢻⠁⠙⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠈⢺⣶⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣧⠀⢀⣘⡿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⣄⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠷⢦⣄⣰⡶⠶⣄⡀⢦⠀⢩⣿⠏⠁⠀⠉⠩⠽⠿⠷⣦⣴⣄⣤⡤⣤⣀⡀⠀⠀⢀⣤⠖⠋⠉⠛⢦⡀⡄
⠀⠀⠀⠀⢠⡾⠛⠶⣤⣀⢈⡿⠀⠠⠀⠀⠈⣹⣿⣶⣶⠿⠿⣾⣷⣿⣏⣀⠀⠠⣤⣀⣤⠶⢛⣥⡿⠛⢿⣝⠶⣬⣻⣦⡶⠋⢠⣀⣀⣀⣨⣶⣿⢿⡀
⠀⠀⠀⠄⣼⣷⣤⣶⡾⠿⠟⠷⢶⡶⠾⠿⣿⠟⢩⠟⠷⣤⣤⡾⠛⣧⡟⠋⠛⢛⣋⣩⣤⡾⢿⠋⠀⠀⠒⠛⠛⢛⡿⠋⠻⣿⣟⠛⠋⠉⠉⢸⠏⣸⠇
⠀⠀⠀⣾⠃⢻⡟⣿⣙⣷⣄⡀⠀⠀⢴⣾⠋⠀⠀⠀⠀⠀⠉⠀⠈⠠⠻⠷⠶⠿⠟⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣷⣤⡏⣰⡏
⠀⠀⠀⣿⢀⡟⢣⠘⢧⡀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣄⡀⡀
⠀⠀⠀⢘⣿⣇⠀⠃⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢧⠙⢻⣷⡀
⠀⠀⠀⠀⢿⡉⠻⣄⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠃⣼⡷⠀⣿⠇
⠀⠀⠀⠀⠈⢷⣤⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⣿⣥⠞⠃
⠀⠀⠀⠀⠴⡟⢷⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡟⠛
⠀⠀⠀⠈⠀⠻⣾⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠏⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣤⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⡿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⢹⣇
⠀⠀⠀⠀⠀⠀⣸⠇⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⣷⡆⢸⡟
⠀⠀⠀⠀⠐⢺⣯⣴⠟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣟⠙⣿⣇
⠀⠀⠀⠀⣠⣾⡏⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢿⡏⠹⣧
⠀⠀⠀⠊⣿⢻⡿⡀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠁⠀⢹⡆
⠀⠀⠀⠀⢿⡈⡗⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢿⡆⠀⣼⠁
⠀⠀⠀⠀⠈⣿⣇⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⠈⣷⣼⠃
⠀⠀⠀⢀⣼⡿⠹⣆⠀⢈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣶⣏⣿⡀
⠀⠀⠀⠉⣸⣇⠀⣿⣆⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡀⢈⣿⢀
⠀⠀⠀⢠⣿⠀⠀⢀⡿⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣼⠋⠁
⠀⠀⠀⠌⢻⣆⣴⢿⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣽⣧
⠀⠀⠀⠀⣀⣿⣥⡾⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⢛⡇⢹⣆
⠀⠀⠀⠈⣹⣿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣾⣧⠀⢻⡄
⠀⠀⢀⠔⣿⣇⢸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣿⣷⡀
⠀⠀⠀⢰⡏⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢹⣷
⠀⠀⠀⣿⠃⣼⠏⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⢸⡿
⠀⠀⢸⡏⠀⣿⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣸⠃
⠀⠀⠸⢻⣄⠸⣧⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣠⡿⠁
⠀⠀⠀⠀⣹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣼⣯⡔
⠀⠀⠀⣰⠏⠔⢩⡿⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢸⢋⡿
⠀⠀⣸⠷⠀⠀⣼⢧⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⢻⣿⠁⢀
⠀⠀⠸⣦⣄⣰⣏⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠟⣯⠻⣮⡆
⠀⠀⠀⣠⣬⢿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⢻⡇⠈⢷
⠀⢠⡾⠋⣠⣾⡏⢨⡟⠀⠀⠀⠀⠀⠀⢀⣤⣴⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠙⣦⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢀⠀⢸⣿⡀⣘⣧⠈⣿
⠀⣿⠓⠀⠰⣿⠀⢸⡇⠀⣀⠄⠀⣀⡴⠋⠀⠀⣠⡾⠛⢿⣷⣄⠀⠀⠀⠄⣰⣯⠄⣰⣿⣶⣛⠛⠛⠿⡛⠶⣤⡜⣠⣞⡡⠀⠉⠻⣦⣘⣿⣷⣈⣿⣾⠗
⠀⠘⢷⣄⡀⠙⠷⠶⠿⣾⣯⡶⠟⠛⠶⣶⣦⣾⠇⠀⠀⢀⣙⣮⣿⣦⣾⣿⣿⣥⣴⡋⠀⠀⠉⠛⣶⣾⣶⣾⡿⣿⣿⣥⣤⣤⡴⠂⠀⠉⣋⣿⠏⢉⣷⠂
⠀⠀⠀⠙⢏⠙⠛⠗⠒⠚⠿⣤⣄⣀⣤⣾⠟⠉⠻⢟⠛⠛⠉⠉⠉⠛⠻⠯⠛⠋⠉⠛⠛⠶⠖⠛⠋⠉⠈⠉⠒⠂⠈⠛⢯⣭⣉⣹⣿⣿⣿⣷⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⢁⠔⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⢀⠋⠓⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠠⠄⠀⠀⣀⣼⣿⡦
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⠁⣀⠀⠀⠀⠀⢆⣾⢞⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠘⡄⠀⠓⡆⠀⠀⠀⠀⠀⠀⠀⠠⠊⢧⢀⠎⠀⠁⠀⠀⠀⡠⠞⠁⠀⠑⠽⡖⠚⠓⣆
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠄⢡⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⠁⠀⣌⠻⠀⠀⠀⠀⡱⠋⠀⠀⠀⠠⠂⠀⢹⢶⡀⠈⢉⣶
⠀⠀⠀⢀⣀⣰⠖⠻⢄⠀⠀⠀⡇⠈⢹⠀⠀⠀⠀⠀⠀⣈⢀⡣⠈⠀⠀⠠⣈⠎⠀⠀⠀⠀⠀⣇⠀⠀⠸⠀⢻⣇⠀⠈⢳
⠀⠀⢈⠟⠀⣀⣀⣠⣀⣧⡀⠀⢡⠀⡼⠀⠀⠀⠀⠀⠠⠟⠉⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⣄⠀⠀⠈⠂⠙⠆⠸
⠀⠰⣁⡈⠉⠀⠁⠀⠀⠉⠙⠲⢼⣜⠀⠀⠀⠀⢀⠔⢁⠀⠀⡀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠉⠛⠲
⠀⠀⠀⠩⣄⣀⣠⡄⠀⣀⣠⣤⠎⠹⣷⠀⣀⠔⠁⠀⠀⡠⠚⠧⠧⢔⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡰⠚⠻⠁⠀⠀⢀⠼⠍⣁⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡹⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡰⠁⠀⡠⠂⠀⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⢠⠀⢙⠒⠢⠀⠀⠀⠀⣠⡾⢟⡲⠃
⠀⠀⠀⠀⠀⠀⢘⠀⣀⡽⠁⠀⠀⣠⠞⠉⠉⠁
⠀⠀⠀⠀⠀⢀⠎⠉⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⡴⠃⠐⠒⠀⠀⣰⠋
⠀⠀⠀⠞⠀⠊⠁⠀⠀⡴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢹⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⡏
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⢃⠀⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⡇⠻⢸⠉⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣠⢀⣀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣷⠀⡍⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠋⣸⠬⡇⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢦⠏⠀⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠿⠛⠛⠋⠁⢰⡶⠂⣀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⢠⢾⠿⠿⣳⣷⠏⠉⠉⠉⠙⠛⠙⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠋⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⡄⠴⠠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⢀⡀⠀⣀⠀⢀⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢈⡀⠀⣁⠀⢀⡁⠀⠀⠀⠀⣸⡇⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⣀⣴⠏⣴⠟⢉⡁⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⢷⣄⢰⡟⠛⠋⠀⣼⣃⣠⡾⠻⢦⣄⣀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⠀⠀⠀⣿⠋⠉⠀⠀⠀⠉⠙⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠻⣦⣀⠀⠀⠀⣠⡾⠟⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⣿⠇⠀⠀⠀⠀⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡿⠀⣼⣯⣤⡀⠀⠀⡀⠀⠀⠀⠀⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠺⢶⣿⡇⠀⠀⠀⠾⠷⣶⢀⣼⠏⠀⠀⢸⣿⣶⠇⠀⠀⠀⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠙⢷⣄⡀⠀⠀⢀⣿⡾⠃⠀⢀⣠⡾⠋⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⣸⡿⢦⣄⠘⠟⠀⣀⣴⠿⣇⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠈⠛⢶⣾⡋⠀⠀⢹⡇⠀⢸⡏⠀⠀⠙⣷⣶⠛⠁⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡉⠀⠀⢸⡏⠻⢦⣤⡾⠃⠀⠘⢷⣤⡴⠟⢹⡇⠀⠀⠉⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣦⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣼⣿⣋⣈⣿⣜⣷⣤⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣻⡟⢉⣶⡿⠉⠙⠙⠛⠛⠛⠻⣿⣶⠞⢻⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣼⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣾⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣷⢿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⣰⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠿⣶⣾⣷⡶⠿⣿⡿⣿⣿⣿⣦⣤⣾⣿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⡿⢶⣾⣿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠤⣤⡼⢷⠶⠶⣄⡀⣴⣠⡤⣄⣴⢀⣤⣤⡼⢦⣼⣠⠴⣛⢚⣶⢶⡶⠮⣀⣨⠷⢤⡤⣤⣀⣀⢀⣧⣀⣠⡀⠀⠀⢀⡠⠦⣤⠖
⠀⠀⣨⠷⢬⠔⠓⠈⠉⠓⠟⠒⢶⠋⠛⠲⠮⠴⠦⣤⠽⠛⢭⣸⣯⣾⣃⣚⡽⠗⡶⢤⡴⠿⠴⠋⡿⠶⠤⠿⡾⠛⠳⣭⣤⣧⡼⠧⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡈⢀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡆⣬⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣴⣿⢔⣀⠀⠀⠀⠀⠀⠹⣧⣤⣄⣀⣀⡀⠀⢀⣤⠤⡤⢷⣄⣀⣀⢘⣄⣀⣀⣀⣀⣠⠤⠔⠊⠁⠀⣠
⠀⠈⠳⣄⡀⠀⠀⠀⣅⣸⣾⣭⣭⡟⣯⣷⣷⣿⣶⣵⣶⣿⡿⠿⠿⠿⠿⠿⠟⠿⢿⣿⣫⣭⣿⣿⠿⢿⣋⣵⣾⣿⣤⣤⣄⣀⢠⣾⠝⠋
⠀⠀⠀⠘⠿⣦⢬⣿⣿⣿⣿⣿⠟⠒⢿⡉⠉⠛⠒⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⢟⠾⠿⠶⠿⠷⢿⣿⣿⣿⣟⣋⡔⢿⣦⣄
⠀⠀⠀⠀⢀⣘⣿⢿⣟⡯⣭⣤⡤⠒⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠛⠻⠶⣴⣏⣿⡶⠶⠃
⠀⢀⡤⠾⠛⣟⠃⣧⣵⡟⠛⠋⠈⠑⣦⣄⡀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⢿⣿⣷⣄⡀⣠⣤⠄
⠀⠀⠀⠀⢠⡋⢳⣬⣹⡇⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢀⡴⠛⢟⢿⣿⣿⡁
⠀⠠⠶⣲⡿⠗⠲⢖⡋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡄⠀⠰⠋⠘⠁⠉⠛⣿⣿⣿⣦⣤
⠀⠒⣙⣩⠛⢹⣚⣋⡭⣾⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⢉⡟⠉⠉⠙⠋⠂⠞⠓⢦⣥⢻⢡⡇⠙⢦
⠀⡶⢫⠇⠀⠀⠙⣭⠓⣬⣹⣾⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣤⣷⣸⡿⢾⡟⠁
⣾⠁⡖⠀⠀⠀⠀⠈⠱⠿⠻⢢⣆⣶⣿⣇⣒⢤⣄⣀⠠⠤⢤⢤⣀⠀⠀⠀⠀⠀⣶⠹⢄⣈⢳⣄⣇⣀⡴⢦⡠⠤⠤⢀⣤⣤⣤⣤⢾⣷⠶⢾⣌⠿⠀⡀
⠣⠘⠁⠀⠀⠀⠀⠴⠒⠋⠈⡴⠋⠳⠿⠿⠿⠿⣿⣤⣾⣿⣏⠙⢳⡖⠲⠤⢔⣭⣶⣧⣮⣿⡧⢉⣉⣽⣇⣻⣿⣆⣼⣿⣟⣿⣿⣷⠿⠷⠞⠃⠈⣦⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠉⠉⠛⠟⣛⣩⢖⣿⣿⠋⢉⡉⡋⠉⠩⠉⠙⠉⣹⣿⢻⡅⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⡠⠃⠺⢷⣈⠉⠀⠀⠀⠀⠀⢀⣨⠴⠻⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠺⠈⠙⠓⠲⠷⠐⠒⠉⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣧⣤
⣿⣛⣛⣛⣿⣍⣝⣻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣽⣿⣿⣭⣭⣭⣭⣽⣭⣭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⣀⣀⣤⣤⣶⣶⣤⣄⣴⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⢾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⣾⣿⣿⣾⣿⣿⡿⠟⠻⠉⠉⠉⠁⠀⠀⠀⠉⢩⠋⠉⢩⡿⣶⣍⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢘⣶⣿⣟⣿⠿⠋⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠙⢷⣬⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⠟⠁⣽⠯⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⣿⡻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣏⣿⠃⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠻⣷⣸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣺⣿⣿⡿⣶⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢰⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣹⠉⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡾⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⣿⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⢿⣧⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣳⡾⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣠⡾⠏⣰⣿⡞⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠟⢿⣮⡻⢿⣶⡴⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣋⡤⣾⡿⠋⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠻⢿⣦⣝⡻⣿⣷⣦⣴⣤⣤⣤⣀⡀⣷⡀⣀⣤⣶⠿⠛⣉⣉⣤⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡿⠿⠿⢿⣷⣶⣶⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡠⠴⠛⠉⠙⠛⠛⠋⠉⣇⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⣤⡀⠀⠀⠀⠰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡄
⠀⢀⠀⠀⠀⢰⠿⠛⠻⠰⠄⠀⠀⠀⠀⠘⢊⠈⠁⠀⠀⠀⠀⠀⠀⠤⣄⠀⠘⣿⠀⠀⠀⠶⣿⡽⣿⣤⠀⠀⠈⣾⣧⡀⠀⠀⣰⣿⣿⣿⠗⠀⠀⠀⢈⣿⣶⡄
⠀⠚⢃⠀⠀⠀⠀⠀⢀⣤⠄⡁⠦⠀⠀⠀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡀⠀⠀⠈⣿⠓⠀⠀⠿⣿⣟⠉⠀⠀⠀⠀⠩⠿⠚⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⡄⠀⠀⠀⠀⠈⠑⠆⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠠⠀⠘⢶⢶⣤⠄⠐
⠀⠀⠀⠀⠐⡇⠠⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡿⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠹⡦⠀⠀⢈⡆⠼⠒⠒⠀⠀⠀⠙⠛⣯⣥⡃
⠀⠀⠀⠀⢸⣇⠁⠀⠀⠀⢰⠅⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠐⣂⠐⢾⣿⠆⠀⠀⠀⠀⠀⠀⢦⣤⠀⠀⣠⠆⠒⢻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⣨⠀⠀⠀⡀
⠀⠀⠠⣶⠃⠀⠀⠀⠀⢠⠂⠆⠀⠀⣀⠀⠀⢰⣿⣿⣿⡄⠀⠐⢀⢑⣬⣤⡤⠀⢤⣄⣀⠀⠈⠿⢟⣷⢺⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣠⠀⢠⡄⣀⠜
⠀⠀⠀⣿⠀⠀⠀⠀⡰⢋⠃⠀⠀⠀⠔⡞⠂⠴⠹⢿⡟⡿⢀⡀⠀⠀⠘⢿⠗⠰⢺⣯⢿⣦⠀⣰⣮⣤⣬⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⡿⡈⢺⠀⣬
⠀⠀⠀⠃⠀⠀⣠⠞⢡⠁⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⡁⠶⠤⡖⠠⣀⠰⣀⠂⠈⠛⠻⢿⡟⠉⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣬⣼⡎
⢀⣀⣀⣀⣴⣋⡠⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠚⠙⠛⠁⣡⣶⣾⣾⡷⢤⡈⠛⢄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⣿⡇
⠀⠉⢣⣠⠌⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⡿⠟⠉⠀⠙⢆⠘⣆⣰⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠁⠉⠙⣤
⠀⠀⠀⠙⢤⡀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢶⣛⣉⠉⠈⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠱⡄⠂⠀⠀⠈⠓⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣶⠞⠋⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⣗⠒⡀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠴⠠⡀⠀⠂⣀⠀⠀⠿⠀⠀⢀⠀⠀⠀⠀⠀⣀⡈⠁⠀⠀⠀⡰⠒⠀⠀⣀⣀⠴⠴⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢴⠒⢄⠀⠀⠘⠁⠀⠀⠀⡽⠋⠁⠀⠀⡐⠋⠉⡴⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠌⠂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠑⠃⡀⠀⢀⡞⠁⠀⠀⢀⣆⡱⠂⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢣⣠⠞⠀⠀⢀⣠⠚⠁⠀⠀⠀⣨⠆⠀⠀⠀⠀⠀⣀⢀⠆⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣀⠀⠀⡀⠀⠀⠀⠀⠙⢾⠋⣆⣀⣜⠁⠎⠀⡄⠀⣄⢀⣸⣤⡀⠠⣤⡴⠂⠉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁⠺⡉⠘⢇⣄⠀⠀⢸⡦⠞⢙⣤⠼⠐⢲⠆⠙⢿⣤⢿⡄⢀⡴⠁⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡇⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢤⡀⠀⠀⠀⠀⢰⡇⠀⠀⣷⠀⠀⠀⡟⠁⠉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢧⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⡟⠀⠀⢸⠃⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠹⡄⠀⠀⢸⠇⢀⠀⣿⠀⢸⠃⠀⠀⣿⠀⠀⢠⡞⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢻⡀⠀⢸⠀⣾⡆⢿⠀⡿⠀⠀⢀⡇⠀⠀⠟⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠈⢧⠀⢸⠀⡿⣧⠈⠸⠇⠀⠀⠘⣁⡴⠃⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢀⠘⣇⣸⠀⡇⡙⢻⡇⠀⠀⣠⢾⡿⠁⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⡀⠀⠀⠀⠀⠀⢻⡛⠛⣇⠈⠁⠈⠋⣿⣸⠁⠠⢾⣅⡛⢶⡄⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠳⣄⠀⠀⠀⠈⠟⠳⣽⡄⠀⠀⠀⢸⡟⠀⠀⢀⣞⡵⠋⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠘⢧⡀⠀⢰⡆⠀⠙⢷⠀⠀⠀⠘⠃⠀⢠⠿⠋⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠙⠓⠛⠀⠀⠀⢀⣤⠶⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠖⠛⣛⠛⢦⡌⠳⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢰⡇⢸⠃⡴⠋⠉⠙⣆⢹⡄⢹⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⡇⢸⡀⢷⣀⠀⣠⠟⢸⠇⣸⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠳⣄⠻⢦⣉⣉⣡⡴⠋⣰⠏⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠳⢦⣤⣤⣤⠴⠚⠁⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠖⢦⣀⣤⣤⣭⣤⣤⣤⣭⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣥⣀⣀⡰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣄
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⠈⠴⢿⡇
⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠭⠀⠀⠠⠊⠁
⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⡿⢿⣿⡿⡻⣿⡟⡿⣻⣿⡿⣛⢻⡟⢻⣻⣿⢸⣿⠁⣠⠄⠒⠤⠀⠀⠀⢀⣤⢀⡀⢘⣦⣀
⠀⠀⡀⠀⣿⣿⡇⠗⣼⣿⢰⣷⢹⡡⣿⣿⡇⡸⣿⣿⡇⣿⢇⡇⣶⠁⣿⣾⣯⡀⠉⠉⠲⡂⠀⠀⣠⣾⠟⢡⣧⣏⣾⣿⡇
⠀⠀⡇⠀⣿⣿⣇⣷⣮⣻⣦⣥⣾⣷⣭⣾⣿⣿⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠶⠀⠀⠐⢧⠀⣼⠛⠓⠀⠸⠿⠛⠹⠂⠁
⠀⠀⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣤⣤⣶⣾⣿⣦⣤⣤⣤⣦⣤⣶⠃
⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡏⢿⡿⠤⠉⢉⣙⣣
⠀⠀⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⣾⣿⣿⣿⣟⢹⢸⠰⠄⡟⢤⠶⠞
⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⡿⣇⠈⠈⠀⠀⢧⢀⠄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⢀⠽⣽⣿⣿⣿⣿⣿⡷⠘⢃⣽⢻⡟⠛⣿⡁
⠀⠀⢠⠀⣿⣿⣿⣿⠿⠟⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣻⣿⣿⣿⣿⣿⣿⠿⠒⠋⠀⠁⠀⠛
⠀⠀⠸⠟⠋⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣀⠀⠀⠀⠀⠤⠶⠿⠅⠀⠀⠀⠒⠒⣿⣿⣿⡿⠒⠺⠛⢶⡶⣤⣴⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣟⣭⣵⣒⣀⣀⣀⡤⠤⠠⠄⣤⠠⣶⣶⣾⣽⣿⣿⠇⠀⠀⠘⠓⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠉
⠀⠀⠀⠀⢀⣄⣀⡄⢀⣀⣀⠀⣀⣀⡀⢀⣀⡀⢀⣀⣀⣠⢀⣄⣀⠀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠁⢠⣀⡀⢨⣄⣄⡀⣀⣄⣀⣀⣄⡍⠤⠄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄⠀⠀⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣷⡀⠀⠀⢹⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣇⠀⣴⠾⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠶⠞⢷⣄⠀⠈⢻⣿⣿⣏⠉⠉⠀⠘⣧⣰⡶⠾⠇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠈⠳⣤⡀⠙⢿⣿⡀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣅⡀⢴⣾⠛⠀⠀⠙⠇⠀⠀⢀⣀⣈⣁⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣄⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠉⠙⠻⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢀⡙⠻⣤⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣽⣿⣶⣤⠀⠀⠀⠙⠓⠀⠙⣦⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣀⣀⣈⣋⣋⣉⣉⣉⣉⣉⣉⣡⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣤⡄⢀⡤⠖⠚⠛⠒⠦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⢉⡴⠶⠦⣤⣋⣀⣙⠓⢦⣄⣉⣉⢰⡉⠙⢦⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣬⠥⠤⠤⠤⡴⢞⠁⠀⠀⠹⠀⠀⠀⠈⠉⠉⠀⢳⡜⠃⢻⡠⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⠋⢱⢂⣠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠝⠶⢸⡇⠈⢿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⠆⣻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢦⡈⡇
⠀⠀⠀⠀⠀⠀⢀⡶⠋⣦⠀⣿⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠹⣆
⠀⠀⠀⠀⠂⢌⣾⠀⠀⢸⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⢸⡏⢧⡐⠀⡀
⠀⠀⠀⠀⠀⠀⢻⢀⡴⠂⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡅⠈⣷⠋
⠀⠀⠀⠀⠀⠀⢠⡞⡁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠻⡄
⠀⠀⠀⠀⡀⠀⣾⠀⢳⡀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⢞⡁⣿
⠀⠀⠀⠀⠈⠓⣿⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠸⢇⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠼⣆⠾⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣠⠞⠓⠤
⠀⠀⠀⠀⠀⠀⢀⢨⡓⠦⣥⣀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠀⠁⣞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⡆⠉⠻⣇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡶⠋⠁⡿⢀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠓⠾⣄⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⣋⣀⢀⡾⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⣄⠀⢲⠙⢂⣀⠼⠦⠿⠤⠤⢀⣤⠶⠞⠛⢡⡟⠁⣉⣴⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢬⣤⡜⠄⠶⠶⠶⠬⣭⣀⡈⠉⢡⡟⠐⠛⠁⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⡞⠁⠀⢀⠏⠉⠁⣾⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘

⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠙⢷⢦⡀⠀⠀⠀⠀⠀⣀⠤⠤⠀⠀⠘⠎⠦⣀⠠⠤⠀⢀⣀⣀⠜⣏⠤⠒⠒⠒⠒⠀⠤⠤⢤⣄⣒⣒⣺⣷⠀⠤⠤⣄⣀⡀⠀⠀⣰⠆
⠀⠀⠀⠀⣎⡁⠬⣭⣶⣴⣬⠾⣿⣟⡛⠉⠉⢛⢶⣦⡈⢻⠛⠒⠒⣤⣈⡈⠓⢿⡏⠉⠉⢩⡇⢋⣶⠶⣬⣓⡤⠜⣁⡉⣭⣵⣶⣶⣬⡁⡴⠁
⠀⠀⠀⠀⡈⣿⢻⣶⢦⣬⣻⣵⡿⢟⣻⣭⠟⣡⣿⣁⠙⣦⣣⠔⣩⣾⣏⢉⣲⣄⡉⠲⡸⣏⣴⣯⣵⣿⠟⢉⣴⣾⣥⣀⣀⣉⡩⡾⣿⡷⠃
⠀⠀⠐⠛⠳⠿⣆⠛⠟⠛⣉⣵⣞⠩⢽⣵⣟⣉⣙⠶⠄⠋⢡⣾⣙⠻⠿⠧⠤⠾⠿⣷⢮⣫⢭⣝⣋⡻⠒⢉⣙⡿⠝⣹⣿⣿⣅⣡⠖⠚⠚⠒
⠀⠀⠀⠀⠀⢀⡼⠟⠛⠻⢿⡿⡿⠿⠗⠲⠤⣤⡔⠒⠻⠛⣜⠉⠉⠉⠉⠉⠛⠛⠛⣻⠟⠙⠷⢬⠭⠭⠽⠶⠤⢶⡎
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠒⠒⠒⠒⠒⠒⠒⠀⢲⡖⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢅⡤⠗⠀⠤⠔⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⡇⠒⠒⠂⠀⠒⠐⠒⠂⠐⠀⠀⢺⣁⠉⠉⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⣁⠈⠓⠬⠓⣤⣀⠀⠀⠈
⠀⠀⠒⠀⠀⠀⣠⠂⠀⠀⠤⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣠⢴⠢⡀⢀⣄⠀⠀⠀⠢⠤⠐⠛⠇⠀⢀
⠀⠀⡠⡀⠀⠀⠰⠂⠀⠀⠀⠀⠄⠐⡒⡄⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠠⢮⣀⣨⠌⠁⠀⠀⠀⠉⠁⠀⠀⢀⠀⠸
⠀⢸⠀⠈⠀⠀⠄⠋⡀⠀⠀⠐⢦⠒⠁⢸⠀⠀⠀⠀⠀⠉⠀⠂⠶⠀⠀⠒⠐⠚⠚⠒⠂⠐⠀⠈⠉⠀⠀⠈⠁⠈⠉
⠀⡄⢇⠀⠀⢈⠀⠀⡙⠐⠂⠀⠉⢆⠣⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⢆⠀⠀⠀⠀⢡⡀⠀⢠⠀⠀⠈⠷⠴⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠸⡀⠀⡆⠀⠂⠀⠀⠀⢀⠔⠛⢁⠁⠀⢢⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡄⠀⣧⠜⠀⠀⠀⠄⠀⡀⠨⢷⡀⢸⣶⡀⢸⢳⡰⠃⠀⠀⠀⠀⠀⠀⠤⠅⠀⠤⠤⠄⠐⠀⠂⠤⠀⢈⠰⠦⠄
⠀⣀⢀⡀⠸⠄⠀⣁⡀⠀⢠⠀⠀⢸⡇⠘⠧⢥⠸⢉⣧⠤⠞⠡⠤⠤⠄⠐⠂⠠⠴⠶⠶⠒⠒⠂⠐⠒⠒
⠀⢀⡤⠤⠀⢰⡀⠈⠉⠑⠂⠀⠒⡾⠘⠀⠀⠘⡈⠈⠿⡀
⠀⠀⠀⣀⡀⠂⢧⣀⣀⡀⠀⠀⠍⢀⣰⡀⠢⠞⢐⣨⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠓⠂⠉⠈⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⡀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⣀⡀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠈⠀⠈⠁⠀⠀⠀⠀⠉⠀⠁⠀⠁⠀⠀⠈⠈⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣧⡟⣠⠀⠀⠀⣠⠀⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⣸⡰⢋⣠⠀⣠⢋⣼⠶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣧⡟⣴⣸⠋⣴⡵⠿⠔⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⢠⡘⣿⢸⡷⢣⣧⠾⠥⠴⠶⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣣⢠⣷⠄⠀⠻⣿⠘⣼⣡⣟⡥⠤⠶⢿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⢌⣻⣄⠹⡀⢼⣦⠘⢆⢹⠁⣠⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣄⡉⠳⣧⠈⢧⢰⣌⢿⢀⡿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠳⣼⡏⠻⣺⠎⢀⣾⠇⠀⠀⠀⠀⢀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⠶⠤⠤⢤⣹⣄⠹⡆⡸⠁⣀⡄⠀⠀⢰⡿⢀⣾⡁⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣷⠃⢀⡿⣣⡄⢀⠎⣠⠾⠛⣋⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣶⡄⠀⢸⢀⠎⠀⡟⢁⣾⠾⠗⢚⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠸⡏⢰⣷⢡⣞⡥⠔⠒⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠈⠳⡇⡜⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠀⠀⡿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⣿⠁⢠⣶⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡀⠘⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠈⡆⠀⠀⠀⠀⢸⠚⠁⠀⠀⠀⠜⠁⠀⢡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣢⠀⠀⠀⡎⢠⠀⠀⢀⠄⡔⠀⠀⠀⠈⣰⠄⣀⢀⠤⠤⠀⠀⠀⠀⣱⠀⣰⠃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢠⠆
⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠹⣯⠇⢰⡧⡐⠁⠾⣄⣠⣄⣾⣇⣹⡋⠉⠀⢀⠀⠀⠀⢀⠀⡁⣹⠏⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡰⠃
⠀⠀⠈⢦⡈⠑⠲⢴⣀⡀⢶⡸⣣⣿⡟⣰⣟⠛⠻⣧⣟⡛⠫⣝⣛⣼⣿⣿⣿⡶⢳⣂⣄⣧⣬⠵⠶⣿⣇⠂⠀⣀⣠⣬⠃⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠩⡢⣀⠀⠈⡻⢿⣮⡿⡻⢿⠟⠋⠉⠙⠙⠉⠉⠉⠉⠉⠉⠉⠙⠃⠻⠿⠉⠛⠟⠷⠛⠛⠋⠫⣿⢶⣾⣶⣶⣤⣬⣭⣥⡀⠀⢰⠀⠀⢠
⠀⠀⠀⠀⠀⠘⢮⡑⠪⣀⢈⣿⠙⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠰⡀⠀⠀⠀⠀⠀⠈⢤⣥⠏⡫⣯⠀⠀⠈⠙⠶⣮⣦⠔⡍
⠀⠀⠀⠀⢀⣀⣀⣙⢾⡅⢙⡿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⡿⢢⣤⣤⣤⣤⣶⣿⣦⣾⡱⣬⣷⣤⣤⠤⠾⢫⠿⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢠⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠔⠚⠑⠚⠉⠉⠉⠋⠒⢿⡟⠋⡟⠺⣿⠈⢻⣿⣧⠈⢾⡦⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⢀⠀⠞⠁⢊⢃⠘⣷⠒⣜⠋⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢆⠀⠀⠀⠈⡆⢹⡴⠋⠋⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⡀⢒⣶⢤⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠹⡎⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⢿⣉⠉⠉⠁⣀⠤⣉⣉⡤⠰⡻⠿⠓⠒⠶⣖⢶⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⣲⠇⣤⠄⢤⠔⠨⠅⠚⠳⠟⠛⠋⠓⠒⠂⢬⣿⣿⡽⠛⠋⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠙⠍⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣤⡺⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠣⣄⠄⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠇⡈⠂⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠴⢷⡜⣢⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠞⠁

⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠐⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃
⢀⣴⠟⢻⣿⣿⣿⣦⡀⠀⠀⢀⠀⣠⣴⡆⠀⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠉⠀⠀⠀⠙⢿⢿⣿⡄⠀⠀⢼⢴⣿⠤⠤⠤⢴⣿⣷⡶⠶⠀⠀⠀⠀⣴⠟⠁⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠘⠈⠛⢛⣛⣛⣻⣿⣿⣇⡀⠀⠀⢠⡞⠁⠀⠀⠀⠙⣆⠀⠀⠀⠀⠸⠇⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⡴⠋⠀⠀⠓⢦⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠈⠓⠲⢼⣦⡀⠀⠀⠀⢠⡿⠃⠀⣠⣴⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠀⣀⠀⢀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠝⠀⡀⠀⠉⠀⢰⡾⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣿⣷⡀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠻⣿⡿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⢿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠶⣶⣶⡶⠶⠶⠒⠶⠒⣲⣾⢗⠀⢻⠻⠛⠛⠿⠉⠉⠙⠁⠈⠉⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠐⠛⠃⠀⠀⠀⠀⠀⠘⢿⣇⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣿⡆⢀⣄⣤⣤⣤⣤⣴⠶⠖⠂⠐⠒⠚⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠃⢓⣛⣻⣋⣀⣌⣉⣲⣭⣼⡿⠯⠆⠀⠓⠐⠛⠒⠀⠁⠈⠁⠀⠀⠀⠀⢹⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠠⠀⠀⠀⠀⠀⠀⠈⠤⠴⠑⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⣀⣀⣀⣀⣀⣀⣤⡔⣠⠥⢼⣿⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠤⠟⠛⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠻⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅
⠀⣿⠀⡀⠀⡀⠄⠀⣀⡤⣀⠀⢦⢤⠀⣤⢀⠀⣀⢀⡀⠀⣤⢀⢀⡄⠀⢠⡄⢀⡀⣠⡄⠀⢠⡄⠈⢣⠀⢸⡆
⠀⣿⠀⡁⠀⠋⠀⠀⠉⠁⠘⠂⠀⠚⠀⠐⠋⠛⠉⠘⠃⠀⠀⠈⠙⠃⠀⠀⠀⠙⠈⠀⠛⠀⠈⠁⠀⢸⠀⢸⡇
⠀⣹⠀⡇⢤⠸⡧⠼⠶⠿⠷⠄⠠⠷⠀⠏⠸⠍⠾⠳⠀⠘⠾⠠⠸⠟⠆⠸⠛⠾⠁⠻⠋⠧⠘⠛⠆⢸⠀⢸⡇
⠀⣿⠀⣇⢦⠒⣴⡦⢤⢲⢶⡆⠀⢢⠖⠰⡆⣴⠶⠀⠀⣄⢰⢦⡶⡴⡆⠰⢶⢦⣔⡆⠇⢴⠀⡶⢦⡇⠀⢸⡇
⠀⣿⠀⡍⢠⣄⡀⢤⡀⣌⠠⢨⣄⡀⠆⡅⢈⣤⢠⡄⠀⡠⣠⠄⡀⢠⢨⡠⠄⡄⣤⠀⡶⠀⠀⠀⠀⢸⠀⢸⡇
⠀⢾⡀⢆⠉⠈⠁⠊⠓⠙⠐⠊⠉⠁⠀⠁⠈⠂⠈⠂⠀⠀⠉⠈⠁⠀⠈⠁⠀⠀⠈⠀⢠⣴⣤⡈⢢⠘⠀⢸⡇
⠀⣹⡇⢰⡿⡗⠀⠀⢸⢿⡇⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⣿⣷⣾⣿⣿⣆⠘⠀⠀⢸⡇
⠀⢿⡇⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠻⣿⣿⣿⡿⠋⠀⠀⠀⢸⡇
⠀⢺⡇⢸⣿⣿⡆⢰⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⡷⠠⡄⢀⡀⠀⠀⠀⠈⣆⠀⠈⣟⣻⠟⠁⠀⠀⠀⠀⢸⡇
⠀⢾⡇⠘⠿⠿⠇⠸⠿⠿⠃⠀⠀⠀⡆⣷⣿⡟⠛⠘⠓⠀⠂⠀⠀⠀⠀⠀⠰⡁⠀⡉⢧⠒⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠁⠀⠀⠀⢃⠘⠀⠀⠀⠈⠀⠀⠃⠀⢛⠙⠂⠀⠀⠤⠄⠀⠀⠀⢣⢤⠢⣌⢲⠐⠃⠀⠀⠀⠀⡀⢤⢸⠇
⠀⣿⠀⠀⠀⠀⢸⠆⠀⠀⢀⣀⣀⢀⣠⠀⠈⠐⠄⣠⣀⣴⣆⠀⠀⣀⠘⣧⡖⢨⠁⠀⠀⡇⠀⠀⠸⡆⠎⢸⡅
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢳⠁⠀⠀⠀⠻⣿⢿⡇⢂⢀⡇⠓⣒⠟⠈⡄⠀⠀⠀⠤⠒⠉⣿⣀⣼⡄
⠀⣿⠀⠀⠀⠀⣠⣀⡀⠀⢸⣿⡇⠀⡆⠀⠀⡁⠀⠀⠘⢻⠇⠘⣿⡄⠀⢤⡼⠀⠈⡢⠀⢒⠀⠀⣼⣿⣿⢸⡇
⠀⣿⠀⠀⣰⣿⣿⣟⣳⠄⣼⣿⡇⠀⠃⠀⠐⠥⡀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠁⠀⢰⠀⠀⠉⠀⠐⢿⣿⡟⣸⡇
⠀⣿⠀⠀⣿⣿⣿⣍⠀⠠⣾⣿⡇⠀⡀⠀⠀⢠⡿⠋⠢⡀⠀⠀⣧⣀⢀⡆⠀⢀⠃⠀⠀⠐⢦⣽⣿⣿⠣⢸⡇
⠀⣿⠀⠀⠙⣟⠛⠠⣠⠊⢸⣿⣿⣶⣤⣌⣝⠛⠇⠀⢠⣦⣤⣼⣿⣿⣿⠟⡆⠈⠢⣀⠀⠀⣾⣿⣿⠏⠁⢸⡇
⠀⣿⠄⠤⢠⠈⠈⠀⢛⡀⢼⣿⣿⣿⣿⣿⣿⠀⠛⣾⣿⣿⣿⡧⣿⣿⣿⣇⠃⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⢸⠇
⠀⣿⠀⠀⠆⠀⠀⠀⠠⢱⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⢹⣿⣿⣟⣾⣿⣿⣷⠀⠀⠀⠀⡇⢈⠀⠠⡆⠀⠀⢸⡇
⠀⣿⠀⠀⡀⠀⠠⡀⠀⣦⢻⣿⠿⢿⣿⣿⣿⠀⣀⣠⣼⣿⣿⣧⣿⣿⣿⣿⠄⣠⠤⢤⣥⣴⡀⣠⠀⠀⠀⢸⡇
⠀⣿⠀⠀⢘⣶⣾⣷⣾⣿⠘⠿⢼⣿⣿⣿⣿⠈⣿⣿⣿⡿⢿⣟⣉⠉⣙⣯⣵⡷⢴⣁⠀⣀⣉⣀⠄⠀⠀⢸⡇
⠀⣿⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠉⠋⠉⠛⠛⠛⠋⡄⠄⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠸⢉⡿⠿⠛⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠁⠙⠘⠙⢀⡧⠈⠋⠙⠈⠉⠀⠀⢸⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠴⣿⠦⠄⣤⡤⣤⢠⡄⠰⢾⠶⠆⡠⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⣸⡀⠁⢀⣇⠀⢸⡃⠸⣟⡛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠈⠉⠁⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⡀⠀⡀⠉⠁⣀⡀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘⠀⠋⠀⠸⠆⠀⠀⠰⠀⠘⠳⠇⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠠⠀⢄⣄⣤⣠⣠⡤⢤⡀⣠⣠⠀⢠⣀⠀⢤⠀⠀⣀⣀⣄⡐⢠⡄⢄⠀⡖⠠⡄⠲⠀⠂⡄⠀⢸⡇
⠀⣿⠀⠀⠐⠂⠚⢉⠉⠉⡈⠁⠉⠉⠉⠀⢁⠉⠉⣀⠉⠀⠃⠀⠉⣈⠁⢉⠀⡁⠉⠉⡀⢀⠉⠈⠁⠀⠁⢸⡇
⠀⣿⠀⠀⠰⠋⠞⠡⠘⠓⠙⠂⠘⠀⠛⠈⠈⠀⠘⠛⠘⠁⠘⠐⠀⠛⠚⠘⠘⠋⠛⠂⠓⠊⠒⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠒⠦⠶⠄⠀⠀⠦⠀⠃⠼⠆⠄⠸⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣦⣤⣀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠐⢀⣠⡟⠃⠠⠀⢌⡝⡇⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠁⠀⠀⠀⠀⣤⡘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢠⡇⣿⣿⡇⠀⣀⠐⢽⠓⢻⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⣤⣌⢁⣀⠀⠀⠀⠀⠀⠘⠧⡠⢃⠔⢲⡖⡽⠛⣟⠛⢳⣶⣤⣄⡀⠀⠂⠄⠰
⠀⢠⣎⢻⣟⢎⣩⣄⢴⠅⠠⠝⣧⢙⠄⣀⡠⠒⠀⠀⠀⠙⡦⡀⠀⠈⠞⡏⠁⠱⣤⠀⠀⠀⠀⠀⡎⠀⢸⣌⠁⠀⣩⣤⣤⣍⡿⣿⠉⡄⠂⠂
⠀⢘⠀⠈⠹⡌⠋⠳⢺⠆⣁⠀⢿⣇⣸⢉⠡⡄⢀⡐⠫⣀⣦⣤⠀⠄⢰⢇⣤⣤⠿⠆⠀⠰⠀⢸⡧⡤⣼⢿⣇⠀⢻⡉⠉⢹⠃⣟⢠⣵⠈
⠀⠈⢷⠋⠠⣜⢦⡄⠃⠀⢸⠃⠹⡯⠝⠖⠀⢰⡄⠑⣄⠹⡖⠖⠂⢤⣼⢈⠉⠛⡄⠀⢣⠤⣿⠿⣄⣁⣽⣿⣿⡵⡾⢦⢼⢤⣴⢿⣿⣿⣇
⠀⠀⢠⠵⠊⠀⠈⠙⠘⠊⠛⠀⠀⠈⠑⡇⠀⣸⣙⣧⣼⣀⠸⣄⡀⠀⠀⡾⠄⠀⠀⠀⠘⣧⢺⣄⣽⣉⣩⠟⠋⠙⠓⠾⠿⣷⣷⣿⣿⣏⣿⠛⣦
⠀⠀⡤⠀⢀⠀⣀⣧⠀⠀⠸⠀⠀⠀⠀⣤⡈⠀⠈⠠⠂⢁⡄⢘⠃⠛⢦⠤⠠⡤⠶⣆⠘⡿⠗⠂⠄⠸⠭⡀⠀⠀⠀⠘⢀⠬⣙⡹⠗⢛⣿⣤⣽⠃
⠀⠀⠐⡤⠸⡏⠈⠁⠀⠀⠀⠀⠰⠉⠈⠀⠠⠀⠀⠀⠰⠈⠀⢙⠋⠂⠀⠀⠀⠤⢦⡦⠄⠳⠾⠿⣄⠀⠒⣧⡀⠀⠠⣿⣿⣆⠻⣴⣾⣿⡉⠀⠀⠴
⠀⠀⠀⠱⡂⣱⠀⠄⠀⠀⠀⠀⠀⢀⣤⡤⠞⠀⠀⢀⠐⡷⣏⠺⡀⠀⠀⠀⠁⠀⣸⡀⠀⠀⠀⠀⠈⠀⢰⢟⠄⠒⠠⣯⠟⢟⠳⢂⡀⣰⣏⡀⠠⠴⠆
⠀⠠⠆⠐⢉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣀⣈⣮⣦⡀⠀⠀⠀⠰⣖⠋⠋⠺⡶⠂⠦⠁⡏⢾⣟⠀⣖⣴⠃⣰⠎⠀⠈⣿⠏⣀⢠
⠀⠈⠒⠒⣶⣶⠈⣽⣦⢠⣂⡄⠀⠀⠁⠀⠐⠛⣖⣧⣯⠉⡙⣻⣵⣄⠀⠀⠀⠾⠆⠊⠘⠁⠀⠀⠀⡥⣾⣿⣕⣷⠛⠀⠳⠌⠀⢺⠻⠲⣍⡖⠁
⠀⠀⠀⠀⢽⣼⣵⣿⣿⣾⣿⡷⣦⣀⣠⠇⠀⠀⠀⢻⡇⢶⣭⣽⣿⡉⢳⡄⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⣉⣁⣀⣠⢦⡄⠀⢀⠑⡀⠈⠧
⠀⠀⠀⠀⡾⠋⠉⠹⣷⣧⡤⣘⢿⣿⡕⡌⠁⢰⣾⠻⣷⣆⠤⣴⣧⢽⡋⡚⡽⠆⠀⠀⣀⢀⠀⠀⠀⠀⠐⠺⣿⣩⣍⣹⢷⣇⠀⣀
⠀⠀⠀⢸⡇⠀⣠⡴⣿⣛⠏⠉⡝⢻⡿⡵⣴⠾⠿⠄⠸⣿⢄⣼⠟⠈⠁⠹⢫⣿⣦⣀⠋⠩⠅⠀⠀⢀⣰⡇⣿⠲⠤⡯⢬⡁
⠀⠀⠀⡄⠀⠈⠀⠀⣬⢯⣥⡖⠁⢾⠿⣈⢩⣀⠉⢀⠀⠸⠉⠀⣈⡑⠄⣁⠒⠉⢿⣿⡆⠀⠠⣰⣀⢠⣿⣄⠻⡾⠾⢿⠀⠁
⠀⠀⠀⠠⠤⠐⠻⣿⣇⠀⠂⠛⣠⠿⣿⣿⣿⡊⠀⢈⣠⠃⢀⣶⡁⠀⠀⢀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠹⣏⠸⠆⠀⠀⢸⠾⠷
⠀⠀⠀⠀⠀⠊⠀⠀⠑⣮⣉⣭⠃⠈⠐⣟⡿⠛⢰⠊⣹⠀⢀⡀⢈⣹⡂⠉⠁⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠙⣁⠀⠀⣾⣦⣠⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣆⠠⠆⠀⡨⡄⠘⠁⣸⠑⠂⡼⠋⠉⠐⠈⠙⠂⠘⠉⡶⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⢀⠈⠉⠉⠋⠀⠀⠀⠁
⠀⠀⠀⠀⢇⠀⢰⠁⠀⠀⠀⠀⠆⠄⣠⠿⠖⠶⠁⠀⠀⠀⠀⠀⠀⡟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠦⠀⠀⠀⠁⠈⠀⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢾⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⣤⣴⣶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢛⣩⡄⠈⠙⠛⠶⣄⠀⠀⠀⠀⠀⢀⣨⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢡⡿⢋⣤⣶⣶⣄⠀⠘⣧⠀⠀⠐⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢻⣧⠹⢿⣿⣿⡿⠁⠀⣼⠁⠀⠠⢤⣄⣀⣀⣿⡿⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⡙⠿⣶⣤⣴⡦⠀⠞⠁⠀⠀⠀⠀⠈⠉⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣴⣾⣷⣤⡀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠋⠁⣀⣭⡟⢿⣶⡿⠿⠿⣶⣦⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⣿⣿⣿⣶⣶⣿⠟⠉⠀⠈⢻⣷⣦⣀⣀⡹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢰⣿⠀⠀⠀⠹⠃⠀⠀⠀⠀⠘⠛⠉⠙⠛⠛⣿⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⣾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣧⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⢠⣿⡷⠖⠁
⠀⠀⠀⠀⠀⠀⢀⠴⢾⣿⠃⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢻⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡿⢻⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣿⣿⣤⣤⣄⣠⣤⡄⠀⠀⠀⠀⢠⣆⠀⠀⠀⣿⢇⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣎⠉⠉⠻⢿⣧⠀⠀⣀⣴⣿⠿⠿⣿⣿⣿⠿⠿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠻⠿⣶⣶⣾⠿⣷⣼⣛⠉⣀⣠⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠈⠛⢿⡿⠟⠋⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣼⢋⣀⣀⣠⡴⠂⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠟⠙⠛⠸⠛⢀⣀⣠⡗⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡴⢡⠆⠀⠀⠀⠀⢺⣿⠉⠸⢄⣂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣈⣦⠤⠄⠀⣠⣄⠠⢤⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠻⢷⠟⢁⣤⣤⣶⠛⠿⠀⠓⠖⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⣶⣤⣾⣿⣏⠑⠦⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⣿⣿⣿⣿⣿⡷⢤⣤⠖⢫⡠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⣿⣿⣿⣿⣿⠷⠘⠷⣠⡇⠠⠻⠇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⣠⣷⡟⠹⣿⣯⣴⣧⡀⢸⡖⠁⡸⠖
⠀⡴⢀⡞⠀⡀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠴⣦⢰⣿⣤⣶⣿⣿⣤⣤⣾⣿⣿⣏⡛⠉⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠸⠀⠀⡄
⢸⣇⣼⣟⡀⠀⠀⣠⣄⣸⠟⠋⠀⠀⠀⠀⠀⠀⣀⣴⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⢠⠀⡸
⣿⢻⠛⣿⣗⣶⣿⣷⣾⣧⣾⣮⣴⣂⣀⠀⠀⣴⣿⣁⣴⠟⣙⣿⣿⣟⣿⣿⣿⣿⡟⣽⡏⠁⠻⡟⢿⡄⠀⠀⠀⠀⣄⡠⢦⣤⣿⡆⣀⠠⠻
⣷⣼⣶⣆⣾⣿⣿⣿⣿⣷⣮⣭⣛⣿⣿⣷⣶⣿⣿⠋⠁⠀⣿⣼⣿⣿⣿⣿⣿⣿⣛⡿⠏⠀⠀⢧⠘⣿⡀⣠⢷⣸⣭⣶⣿⣿⣿⣿⣿⠃⢠⣴
⠹⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⠀⠀⠀⠙⠻⢿⣯⣼⣿⣿⣿⣧⣤⡄⢀⠀⣀⣱⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⢷⣿⡃
⠀⠈⠛⢡⣿⣿⡿⠛⣻⡿⢿⣿⣿⠿⠋⣻⡇⠀⠀⠀⠀⠀⠀⡄⣾⣿⣿⣿⢿⡿⣿⣿⣿⣷⣾⡟⢻⣿⣿⠿⠿⠾⢿⠟⠟⢛⡿⠅⢀⡸⠿
⠀⠀⠀⢸⡟⠁⠀⠀⢿⡀⠀⢿⣃⠀⠈⠻⢧⡄⠀⠀⠀⠀⣤⣽⣿⣯⣿⢣⣾⣼⢿⠋⠹⠞⠿⣛⠷⢤⠉⠑⡾⠛⢻⡁⢸⠂⠑
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠑⠠⠀⠉⠛⠛⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠻⠿⠿⢿⣶⣿⢀⠀⠀⠻⣶⠤⠤⡤⠏⠀⠎⠐⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢩⣼⣿⣿⣿⣄⠀⢀⣾⣿⣿⣼⡆⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣼⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣷⡟⢄⠀⢸⣟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣺⣿⣿⣿⣿⡿⠋⠀⠀⢈⣿⣿⣿⣷⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⣰⠀⢀⣿⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⠓⢟⣻⣿⣿⣧⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⠃⠀⢸⣿⣿⣿⣿⠝⡃⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⢿⡿⣿⠀⠀⠳⣠⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢿⣳⡄⠀⡼⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣿⢀⣠⣾⢀⣀⣰⠟⡵⠁
⠀⠀⠀⠀⠀⠀⣰⢀⡀⠀⠀⠩⣃⠈⠙⣧⣾⣡⣿⠃⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⢿⣧⣀⡄⠁⡴⠊
⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠉⠓⢶⣾⣿⡟⢩⠂⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣫⣿⣿⣦⣝⣯⠀⠀⠁
⠀⠀⠀⠀⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⠏⠙⢷⣌⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡋⣷⠈⡗
⠀⠀⠀⢀⣴⣼⣿⣧⣦⡄⠀⠀⠀⠀⣾⡀⠀⢸⣿⣿⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢹⣿⣤⣾⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣼⣿⣿⣿⣿⣿⣿
⢀⣬⡙⠋⠹⣿⣿⣿⣿⣟⣿⡇⠀⠀⢀⣿⣿⣿⣷⣼⠻⠟⠷⣤⠀⠀⠀⠀⠀⠀⠎⣉⢾⣿⠏⣹⣿⣿⣿⣿⢿⣷⣄
⠌⣿⣷⣦⣄⣀⣾⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⢿⣎⡁⠀⠀⠀⠀⠀⠀⠈⠀⣴⠋⢀⣿⣿⣿⣿⣏⠉⠀⢿⡟⡇
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⢿⡇⠹⣿⣿⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⣾⠟⣹⣿⣿⣿⠀⠀⢸⡇⠘⡆
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡆⠀⡘⠿⢸⣷⡀⠈⣿⣷⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⡟⣹⣿⠿⠇⠀⢸⣿⡇⠀⠈⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣄⠀⡦⣠⣄⣄⣤⠀⣤⢄⣄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣈⣀⣉⠨⣁⡁⢈⣠⡀⢁⢀⠉
⠀⠀⢦⣦⢲⣄⣤⡆⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡉⠉⢀⠉⡁⢈⠉⢉⡉⠋
⠀⠀⠀⡤⣤⢀⣠⠄⡄⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠫⠉⠉⢷⠀⠀⠀⢛⠋⠙⠛⠋⠙⠈⠻⠃⠉⠉⠙
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⡿⠋⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⡞⠀⠀⠀⠘⠛⠛⠛⠛⠉⠫⠟⠛⠘⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠁⠀⠀⠀⠐⠓⠖⡆⠐⠧⠷⠶⠗⠲⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠻⣲⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣙⣛⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⠻⠛⣿⠿⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣻⠦⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢚⣁⣭⣍⣛⣒⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠭⠍⠁⠂⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢈⣟⣒⣪⡹⠿⠷⠋⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣭⣿⣿⣗⣀⠀⠀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠘⠻⠀⠙⣿⣿⣿⣿⣿⣿⣒⠂⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣛⣛⣛⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁⢨⠀⠀⠀⠀⠀⠀⢹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠲⠶⠶⠶⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢭⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠃⠀⠙⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⠀⠀⠀⠀⠈⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠰⠰⠆⠐⠖⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣽⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠻⠿⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⢀⣤⣴⣿⣿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⢸⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⣀⣀⣠⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⣿⣿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⢀⣀⣀⣼⣿⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠘⣿⣿⠿⠟⠛⠃⠀⠀⣀⣠⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣾⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⢀⣴⣶⣾⣿⠿⠟⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣿⡿⠿⠟⠛⠋⠉
⠀⠀⠀⣀⣠⣾⣿⣋⠀⣰⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁
⠀⣴⣿⠿⠛⠛⠛⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣠⣤⣶⡆
⣼⣿⠃⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⣀⣴⣿⣿⣦⡀⣠⣾⣿⣷⡄⢀⣴⣿⣷⣄⠀⢀⣴⣾⣿⠀⠀⠀⠀⠈⠿⠛⠉⠁
⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣾⡿⠟⠁⠙⢿⣿⣿⠟⠉⠻⣿⣿⠟⠉⠙⢿⣿⡿⠟⣻⣿
⠸⣿⣧⣀⠀⠀⠀⣠⣾⡿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣷⡖
⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠄⠀⠀⢑⢀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢐⣛⣃⠤⣶⠄⠀⢀⣑⡠⢤⣖⠂
⠀⠀⠀⠀⠀⠀⠈⢣⠠⡀⢔⠥⠼⢟⡥⠚⠻⢿⡿⠛⠋⠁⠐⠀⡤⠘⠛⠋⠐⠈⠐⠠⢦⣅⠠⡀⢤⡠⡀⣠⠄
⠀⠀⠀⠀⠀⠀⢰⡦⣾⠖⠁⠐⠂⠈⢀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⠀⠉⠉⠉⠪⢿⡇⡨⠁
⠀⠀⠀⠀⢀⡤⠄⢧⣃⡀⠀⡀⠄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⠀⠀⠲⡀⠀⠀⠀⠀⠀⢣⢣
⠀⠀⠀⠀⠀⠀⠀⠲⣾⣟⠝⡁⡀⠀⠀⠠⣴⠤⣒⡡⠤⠄⠠⢌⣀⣠⡀⡁⢄⡴⠒⢃⡶⢀⣴⠖⠙⢋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢄⠀⠀⠂⠬⠕⡊⣻⣗⡠⠶⣎⠀⠈⠹⠟⣪⣴⠏⠀⢊⠄⠉⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠉⠉⠉⢲⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⢿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⠿⠿⣿⣿⡿⡻⠆⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣉⠇⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⠄⢠⠀⠄⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⢘⡿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠲⠉⢀⡸⠂⠀⠆⠠⠀⠀⠀⠈⠀⠀⠀⠀⠈⢱⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢯⣀⣔⡡⠄⠐⠒⠀⠚⠢⡀⠀⠀⠣⣀⣀⡠⠂⢸⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣀⡠⠙⠀⠀⡀⠑⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⠀⠀⢠⡎⠀⠀⣰⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣱⡶⠠⠖⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⣈⣡⣤⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠐⠋⠁⣀⡘⠷⠀⡀⠀⠀⣤⡤⢴⣿⡿⣽⠛⢻⢛⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠨⠀⠐⠊⡏⢤⠄⠿⠣⠀⠀⣧⠀⠸⣿⣷⣠⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡰⠊⠀⢠⠀⣿⣿⣫⣴⡾⣿⢋⣸⣿⣿⣯⠉⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⠄⠀⠀⠀⣠⠔⠁⠀⠀⣠⡄⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠼⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠤⢦⡀⠀⡠⠊⠁⢀⡠⡔⢋⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⢋⣀⣀⠠⠤⠴⠒⠋⠉⠀⣨⠼⠀⢡⢀⣿⣿⣿⣿⣿⠟⠋⠀⢀⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠉⠛⠉⠉⠰⠖⠂⠉⠁⠈⠉⠁⢸⠀⣾⠟⢁⣀⣉⣉⣡⣤⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠐⠘⠛⠛⠉⠻⠿⠛⠛⠉⠉⠉⠋⢰
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣛⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠴⡀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⡇⢠⠆⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠂⠲⣀⡀⠀⢀⠀⣀⣀⠤⠚⠢⡀⠀⠀⢦⠀⠀⠀⠀⠔⠀⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⣀⡀⢀⣀⣀⠀⠤⠚⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⠁⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣯⠟⠅⣀⠄⠐⠒⢶⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠈⢠⣿⡆⠀⠀⠀⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⢃⣾⣿⢻⡇⠀⠀⠸⡇⠀⠀⠰
⣿⣿⣿⣿⣿⣿⣿⡾⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆⠀⢷⠀⡀
⣿⣿⣿⡿⠟⠛⠉⠊⠜⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⠀⢸⣾⡇
⠛⠋⠈⠀⠀⠀⠀⠀⢸⣏⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠐⠆⠀⠘⢿⣦⣿⣿⡿⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⢸⣿⡟⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠰⠄⠀⣽⣿⣿⠀⣀⣿⣿⢧⠀⢻⣿⠋⢻⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⣿⣿⣿⣿⣷⣀⣴⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢻⣿⣿⣦⠇⣽⣿⡂⠈⢿⡌⢿⣿⣿⣿⣇⣸⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠘⢿⣿⣿⠀⣿⣿⣆⠀⠀⠻⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣿⡀⣿⡇⠈⠀⠀⠀⠈⠙⣿⣿⣯⣍⣻⣿⣿⣧⣽⣷⡀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⢹⣿⣷⡌⠛⠂⠀⠀⡄⠀⠀⠸⣿⡏⠛⢻⣿⣿⣦⣙⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⡄⠀⠀⣾⣿⣿⣀⠀⠀⢘⠀⢻⣿⡇⠀⠀⠀⠸⡇⠀⡀⢰⣿⣿⠀⣿⣿⣿⣌⠛⣿⣿⣏⠀⢻⡆
⠀⠀⠀⠀⠘⣇⠐⠀⠈⠙⠿⣍⠉⠀⢸⣤⡾⢿⣷⡀⠀⢀⡀⢳⠀⠙⢿⣿⣿⣿⣿⢿⣿⡟⢷⣿⣿⣿⣧⣾⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢠⡟⠉⠓⡾⢿⣧⠐⢤⣙⣆⢳⠦⢄⠉⢹⣿⡟⠀⣿⣷⣾⢿⣿⣿⣿⣿⣦⣎
⠀⠀⠀⠀⠀⠀⠀⠙⡿⢦⣄⠀⠈⣻⠗⢦⣄⢸⡄⠹⣷⣤⣿⣿⠀⣷⠀⡈⣿⣿⣷⠀⣼⣿⣏⣼⠇⢻⡿⢿⣿⣿⣮⡆⢁
⠀⠀⠀⠀⠀⠀⠀⢠⣯⠀⠙⣧⠀⢸⡀⠀⣼⡇⣵⡀⢻⣿⣿⠫⡇⢸⠘⣿⣿⠈⣿⣷⣿⣿⡿⡇⢠⣾⠏⣸⣿⡇⢸⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠁⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣺⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⣿⣿⣷⣶⣭⣭⣿⡛⢿⣯⣷⣄
⠀⠀⠀⠀⠀⢀⡤⠚⠁⠂⠭⠩⠶⢬⡭⠉⠽⠋⣛⡿⠻⠷⣮⣟⣧⡀
⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠉⠉⠀⠀⠀⠀⠻⣿⣮⣦⡀
⠀⠀⠹⣦⢤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⣀
⠀⠀⠀⠈⠳⣷⣶⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⠉⠉⠙⠛⠷⠂
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡿⠟⠛⢿⠟⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡗⣈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⢫⡀⠀⠀⠀⠀⠀⣀⣬⠂
⠀⠀⠀⠀⢀⣠⣴⣾⣾⣿⣦⣿⣿⣿⣿⣦⣀⣄⣠⣴⣶⣿⣿⣟⡛⠋⠁⠀⠈⠠⠄⠐⠒⣥⣾⣿⣏⠀⠀⣠⣶
⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣬⣶⣶⣾⣷⣤⣤⣀⣀⢀⣤⣤⣔⡛⠋⡿⠋⣠⣾⣿⡿⠃
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣠⣾⣿⡿⠋
⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⢋⣤⣾⣿⡿⠋
⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠙⢷⣤⡼⠳⣄⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣶⠚⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠟⠺⢷⣄⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢀⣤⣞⣣⡽⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠈⠁⠘⣆⡀⣠⢞⡯⢽⡲⡄⢀⡼⠁⠚⠋⠉⠁⢀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⣀⣸⡇⣭⠿⠟⠛⠓⠀⠀⠀⠁⡇⣏⠀⠀⡷⣿⠈⠀⠀⠀⣀⣀⣀⣠⡧⢩⠿⠟⠛⠒
⠀⠀⠀⠀⠉⠉⠉⠛⠒⠺⠂⠀⠀⠀⡀⢠⠞⠁⠙⢮⣓⣺⠵⠃⠈⢳⡀⠀⠉⠉⠉⠛⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣲⠿⠛⠁⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠙⢶⣤⣀⣴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⣘⣧⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠙⢮⣁⡶⢿⣆
⠀⠀⠀⠀⠀⠀⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠃

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