Drug user Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠒⠒⠒⠲⠶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⣟⠉⠘⣧⠀⠀⡍⢩⠉⡋⢙⠉⡋⠉⡋⠉⠉⣁⡾
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⠈⠳⣄⠈⡟⠓⠷⠾⠤⠧⠬⠤⠧⠤⠷⠶⠚⡏⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣏⣀⣀⡀⠀⠀⠀⠀⠘⣧⡗⠢⠤⣄⣀⣀⣀⣀⣀⠀⠀⠀⢠⣿⠧⣤⣀⣀⣤⡼⣷
⠀⠀⠀⠀⢀⣴⡟⠉⠉⠳⡝⢦⠀⠀⠀⠀⠘⣷⠀⠀⠀⢠⠤⡄⠀⢽⠀⠀⠀⢸⣿⠦⠤⣤⣤⠤⠶⣏⡀
⠀⠀⠀⠀⡏⣼⠀⠀⠀⣀⣹⡌⢷⠀⠀⠀⠀⢻⠀⠀⠀⢸⢶⣡⠀⢹⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠘⡏⠙⠲⠤⣄⡀
⠀⠀⠀⠰⡇⢿⠀⠀⣏⣉⡹⣷⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠘⠉⠀⢸⡀⠀⠀⣿⢤⣀⣀⠀⠀⢀⣀⠤⡇⠀⠀⠀⠀⢉⡷⢦⡀
⠀⠀⠀⠀⢧⠘⡦⠚⠫⣽⢧⡏⣸⠁⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠉⠉⠉⠉⠁⠀⡇⢀⡄⠀⢀⠏⢀⣸⣇
⠀⠀⠀⠀⠈⢧⣑⣤⣾⣡⣾⡴⠃⠀⠀⠀⠀⢸⡄⠉⠓⠲⠶⠶⠖⠛⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⠀⡾⢰⡃⠀⣨⣳
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠦⣤⣀⣀⣀⣤⠴⠳⢤⣀⡀⠀⠀⠀⠀⢀⣀⡤⢿⣀⠀⠀⠀⠀⠀⠀⣠⡏⠛⠺⢤⣧⣤⠟⠲⠟⠋⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠋⠉⡧⠀⠉⠀⠀⠀⠀⠀⣈⣉⣉⣉⠛⠉⠉⠀⠀⠈⠳⢭⣟⣒⣒⣒⡿⠟⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⠄
⠀⠀⢠⡟⠉⢉⠋⠙⠳⣦⠚⠋⠁⠀⠀⢀⣀⣀⣀⣸⢗⣈⣉⣹⡇⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠉⠉⠉⢫⠉⠓⢦
⠀⠀⠀⠉⠓⠚⠶⠤⠴⠋⠀⠀⠀⠀⣜⠁⢠⠃⢈⣿⠲⠦⠤⣶⠗⠛⣅⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠾⠤⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣍⣩⡭⠞⠀⠀⢸⠁⠀⠀⣸⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣶⣿⣿⣿⣿⣹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⣿⣿⡛⣛⢛⢿⣿⣿⣿⢛⣟⢛⣻⣿⣟⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣤⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡿⣿⣿⢿⢿⡿⡿⣿⢿⣿⡿⣿⣿⢿⢿⡿⡿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⣿⣿⢸⣿⡇⡇⣿⢸⣿⡇⣿⣿⢸⢸⡇⡇⣿⣿⣸⠀⠀⢠⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⡰⠁⣶⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣛⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⠤⠭⠤⠤⠤⠇⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⣴⡆⠙⠛⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠘⢿⣿⣿⡿⠿⠿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⠀⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⢻⣿⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⣤⣬⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠁




⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠉⠁⠀⠀⠀⠀⠀⠉⠁⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢰⠀⠀⠀⠀⠀⠀⢎⣳⣛⣀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣂⡀⢀⠐⠄⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠳⢶⣄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢼⣯⡉⢿⣦⣶⣴⣿⣿⣿⣿⣿⣿⠀⣠⣤⣶⣾⣿⣿⣄⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⣿⣶⣶⣾⣙⣿⣿⣿⣿⣿⠉⠁⢺⣿⣿⣿⣿⡯⠈⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⣿⣿⠟⠛⠻⠟⠛⠀⠱⣌⠿⣿⡿⠟⠁⢠⣾⣿⣋⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠤⣴⣿⣿⠛⣦⣄⠀⠀⠁⠀⠀⠀⢀⣾⣿⡏⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⠈⠛⢃⢺⣸⣿⣶⣶⣦⡀⠀⠀⠀⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⠀⠀⣈⣿⢻⣿⣿⡟⢹⡃⣀⣀⢀⣀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⡇⠀⠻⢿⡌⢿⡯⢀⣀⡉⠉⠉⠉⠉⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣼⣧⠀⠀⠈⠳⠄⠀⠀⠠⢄⢉⠉⠈⠉⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠿⠿⡿⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣈⣷⢻⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠗⠦⢴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢩⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣷⡄⢄⣀⢀⣀⣄⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⡙⣿⣿⢆⠛⠛⠋⠀⠿⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⠛⣿⡆⢰⢛⠧⣴⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡟⣾⣿⣶⣤⣤⣶⣿⡿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⢙⣿⢋⣐⣟⣋⡰
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣭⣉⣩⣵⣾⣿⡿⣫⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣈⠀⢠⡿⣼⢏⣿⣿⣷⡿⠁
⠀⠀⠀⢠⣾⣿⣭⣭⣭⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣩⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⢷⡏⠀⢸⣿⣿⣾⢯⣾⠋⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢹⡄⢂⣹⡧⣿⡞⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⢻⣏⣿⣿⣿⠃⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠹⣭⡿⠉⢧⠈⠄
⠀⡟⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠻⣦⡓⢸⡇
⠀⠁⠿⠈⢹⣿⠁⠿⠿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠄⠀⠀⠀⠈⠻⣿⣿⡄
⠀⠀⠀⠀⠈⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⠔⠁⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠛⠉⠉⠃⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠷⠶⠖⠒

⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⠟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠖⢀⠀⠀⠀⠀⠀⠈⠁⠀⠻⣾⣿⣦⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⣷⣿⠀⠀⠀⠀⠈⠁⣤⡀⠰⢷⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣥⠀⠀⠀⠀⠀⠀⠀⠉⣲⣤⡤⠶⠾⠇⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠆⠘⠟⠋⠁⠀⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠷⡄⠀⠠⠄⢀⣤⡀⠀⠀⠀⠘⠃⠈⠀⠀⡄⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣾⠶⣃⠀⠀⠀⣈⠋⠀⠰⠆⠀⠀⠀⢀⣄⠀⢀⡀⠀⠀⠀⢀⠴⣶⣄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠋⠘⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⢿⡟⠀⠀⠀⠻⣶⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠶⢨⡕⠶⢌⡁⢀⠀⣴⡄⢠⣾⡟⠓⡀⠀⠀⠀⠀⠐⠰⠆⠘⠦⠌⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠀⢶⠀⠀⢀⠀⡅⠙⠁⠦⢀⠀⠡⠼⢶⣥⠀⠀⠀⠀⠐⠆⠘⠲⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠛⠿⠛⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⣤⡈⠅⣤⡐⠊⠀⣤⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠣⡀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⠀⠀⠉⠀⠤⠀⢠⡄⠀⠀⠠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⡠⠦⣤⣤⡶⠚⠛⢦⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣷⣬⣿⡶⠆⠁⢀⡀⢀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠘⢿⣷⡄⠀⠀⠙⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡏⣀⠿⡆⠛⠁⠀⠆⠀⠴
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠈⠳⣄⠙⢄⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿⣿⣿⣿⣟⣀⡁⠀⠘
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠳⣄⠑⢄⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣍⠋⠄⠀⠁
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠈⢷⣄⠳⣄⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⡛⠃⡀
⠀⠀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠙⢷⣌⠳⣄⣤⠶⠛⢉⣿⣿⣿⡇⣶⠄⢀⠈
⠀⠀⣧⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠹⣷⡇⠀⠀⠀⢸⣿⣿⣿⡆⠻⠀⠉⠁
⠀⠀⠹⣄⠀⠈⠓⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⡆⠀⢀⣠⠬⠟⠀⠀⢀⣼⣿⡿⢡⠀⠀⠀⠁
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠁⠀⠸⠟⠋⠉⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣻⣶⡤⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢉⢻⣿⣷⣿⣦⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⠸⣿⣿⣿⣿⣷⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⣱⣄⢀⠀⡀⠀⠀⠀⣨⣼⣿⣿⡿⠀⣀⣴⣾⣶⣤⣀⣀⠀⣠⣤⣘⠦
⠀⠀⠀⠀⠀⠀⠀⢱⢈⠻⣿⣶⣥⣀⣷⣺⣿⣿⡿⠋⢀⢸⣿⣿⣿⣿⡟⠉⣉⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢯⢧⡙⠛⠿⢿⣿⣿⣿⣿⠇⠀⠸⣜⠿⠿⠿⠏⠃⠀⠘⣶⡼⠿⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣳⣌⠃⢻⡿⠛⠛⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣷⣨⣵⠓⣦⣤⣤⣤⢤⣄⣀⠀⠀⠀⠸⡌⠿⠋⠀⡶⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣧⡐⠿⢛⣵⡷⣿⣿⣷⡄⠀⠀⠀⠀⠂⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⢿⣧⠀⠘⢿⡇⣿⡟⠈⠡⠰⢤⠀⢰⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡿⢫⡾⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⠀⠀⠐⣦⡘⠿⠋⠒⠀⠐⠀⠐⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣴⣏⡼⢛⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣧⣿⣄⠐⠀⠹⠃⠈⠂⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣽⣷⣏⢻⣼⣟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⣿⣿⣿⣿⣿⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣽⣿⠿⢯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠘⣷⣈⢙⣿⣿⣿⣿⣿⠎⢿⡷⠦⣤⣀⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢙⡾⠖⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⢰⣿⡌⠻⠾⣿⣯⣿⣏⡀⠀⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣞⠓⡴⠁
⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⣿⡀⠀⠀⠀⣿⣿⣿⡆⣨⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠘⠻⣼⣇
⠀⠀⠐⠋⣼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⡀⠀⠸⡻⢿⣿⣅⠀⢹⣿⣿⣿⣿⣶⣎⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⡀⠉⠃⢀
⠀⠀⠀⠀⠉⠉⠟⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⡀⠀⠈⢸⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣷⡹⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣤⡀⣈⡀
⠀⠀⠀⠀⠀⠠⣘⣽⣿⣿⣿⣿⡧⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣧⢻⣿⣿⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢽⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⡟⣻⣾⣿⣿⣿⣿⣿⢹⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣼⣽⣿⣿⣄⢻⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⡆⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠋⢿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠙⠿⠋⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣏⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⠿⠿⢿⠏⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣿⣿⣿⡻⣿⠛⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠋⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⡟⣻⣿⣿⡾⠃⠀⢰⣯⠀⢂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉
⣼⣿⣿⣿⣟⡷⠈⠋⠙⠉⠁⣁⠉⢁⡀⢀⣰⡇
⣿⣿⣽⣿⣿⡇⠀⠀⣶⣶⣷⣿⡇⢼⣷⣿⣿⠁
⣽⡟⢻⣿⣿⡟⠀⠈⣼⠢⡏⠝⡇⢾⡘⠫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⠇⢻⣿⣟⡃⠀⠀⠁⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠙⠻⡇⠀⠀⠀⠠
⡿⠀⠸⣿⣿⡇⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⠀⢰⡃⠀⠀⠀⠀⣷⡖
⠁⠀⠀⠘⣿⣇⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡙⠤⠄⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⢿⡏⠃⠔⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⡀⣀⣀⣀⠀⠤⠴⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠰⣿⠸⡗⠂⠁⠀⠀⠀⠀⡀⠀⠀⢴⣷⡦⢾⠦⠤⣶⠾⣟⡚⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠝⠠
⠀⠀⢠⢿⡀⢰⣶⠀⠀⣼⣷⣤⣧⠀⠀⠀⣰⣶⡀⠀⠀⠀⠀⢀⣀⠀⠠⠧⣷⠀⠀⢠⣷⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⢀⡆
⠀⠀⣿⣎⠡⣾⠛⡇⢠⠟⢿⣷⠙⠀⠀⠀⢘⣻⠀⢠⡤⢰⡆⢠⢿⡄⢠⣿⢿⡄⠀⢸⡿⠀⠀⣶⠆⢀⠋⠀⣴⡂⠀⡸
⠀⠈⠋⠉⠀⡏⠀⢀⠀⣴⣾⣿⣤⠀⠀⠀⠛⢹⣷⠀⠀⢸⣵⣿⣎⣉⢠⣿⣿⡀⣠⣿⣷⣶⣿⣦⣐⡺⠇⠘⠋⣿⢀⠁
⠀⠀⠂⠀⢰⡗⢀⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⣇⠀⠀⠸⠏⣻⣿⡟⢋⣼⣿⣿⣿⣿⠁⠀⠀⠀⣈⡀⠀⢀⡀⠁⠸⣰⠇
⠀⠀⠀⠀⠸⠇⢿⣿⣿⣿⣿⣤⣤⣶⣄⠘⢿⠠⠟⠀⠀⠘⠇⠉⢹⡇⣯⠀⠀⠀⢸⡿⠁⠀⠀⠀⠉⠀⠀⡈⠀⠀⣾⣿⣿⡦⠊
⠀⠀⣶⠆⠀⠀⠀⠉⠀⣸⣿⣿⣿⣿⡏⠀⢠⣤⠠⣀⡘⠒⢾⠀⢀⡑⣿⢀⠀⢀⢘⡷⢆⢀⠈⣉⣙⣷⢻⣷⣶⡆⢻⣿⣿⣛
⠀⠀⠀⠀⠀⠀⢀⠀⠰⠿⠋⠉⠉⠉⠀⠀⣼⣿⡠⣭⡄⠀⠼⠂⣨⣿⣿⣀⣀⣠⣴⡟⢉⣽⣾⣿⣿⡿⣸⣿⣿⣿⡘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣟⣶⣶⡆⠀⠀⠀⢸⣿⣿⣧⣿⣿⡇⠻⢃⠀⡻⠽⠿⠟⠛⣻⣶⣿⢿⠻⠟⣫⣾⣿⣿⣿⣿⣷⠘⣿⡿⠇
⣤⣤⣤⣤⣤⣴⣭⣭⣭⣼⣭⣥⣤⣤⣬⣤⣭⣭⣿⣭⣯⣧⣤⣤⣤⣤⣤⣤⣤⣬⣽⣯⣥⣤⣤⣾⣯⣭⣽⣿⣿⣿⣿⣥⣬⣥⣤
⣿⣿⣥⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⠳⣄⠀⠀⠀⠀⠀⢀⡟⠀⠉⠛⣶⣦⣄⣀⡀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣬⣷⣄⠀⠀⠀⣼⠁⠀⣠⡾⠃⠻⠉⠉⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠀⢰⠇⠀⠘⠋⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠁⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣭⣭⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⠀⠀⣦⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠌⠀⣻⣦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢲⠆⠀⠀⣡⣤⡤⠤⠔⠚⠉⠉⠉⠓⠒⠒⠶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣧⡀⠀⠀⠀⢀⣀⣤⡴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣶⣶⡶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠭⠽⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢹⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠻⣟⠟⣻⠿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠿⣤⣄⠄⠀⠀⠀⠀⠀⡀⠀⢿⡅⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠉⠉⠀⢠⠄
⠀⠀⠀⢀⣴⣄⠰⢀⣨⣌⠁⠀⠀⠀⠀⢸⢿⠛⣁⡰⠆⠀⣠⡄⠀⠀⠀⠀⠉⣙⠓⣃⠀⠀⢀⢀
⠀⠀⠀⠈⠉⠉⠁⠈⠙⠛⠁⠀⠀⠀⠀⠊⠘⠀⠻⠇⠀⠀⠈⠁⠀⠀⠀⠀⠁⠈⠛⠛⠀⠀⠘⠘

⠀⠀⠀⠀⠀⢀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡿⢿⣋⣭⣷⡟⠀⠀⠀⠀⠈⣦⡀⣿⢀⡴⠀⠀⠀⠀⠀⠀⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇
⠀⠀⠀⠀⣽⣿⣟⠉⠁⠀⠀⠀⠀⠀⠠⣬⣿⣿⣿⡥⠄⠀⠀⠀⠀⠀⣿⠋⣻⣇⠀⡀⠀⠀⠀⠀⠀⠠⣮⢿⠟⠁
⠀⠀⠠⠾⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠙⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣶⡆⠀⠀⠀⠀⠐⠞⠉⠁


⠀⠀⠀⠀⠀⣠⣦⣼⠂⠀⠀⠀⠀⠀⢀⣔⠰⠶⢖⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠄⠀⠀⠀⠀⠀⢀⡀⢶⡦⠤⠤⠤⠤
⠀⠀⠀⡠⠚⢿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⢯⣿⡽⢀⠀⠀⠀⠀⠀⣿⣇⣤⡄
⠀⠀⠺⣷⣦⣀⡽⠋⠀⠀⠀⠀⠀⠠⣤⣤⣤⠀⣶⣶⡆⠀⠀⠀⠀⠀⠛⢦⣤⡴⠛⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠉⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀
⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⡄⠚⢢⠀⠀⠀⠀⠀⠀⠀⢸⡦⠶⢾⠃⠀⠀⠀⠀⠀⢼
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⣄⠹⢿⣎⠉⢃⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⡇⠀⠀⠀⠀⠀⢤⣶⡆⠀⠀⠀⣀⡀
⠀⠀⢐⣋⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⡀⠘⢾⠀⠘⠁⠀⠀⠀⠀⠀⢸⢨⠁⢶⡇⠀⠀⠀⠀⠀⢀⣽⣷⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣤⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆
⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⣀
⠀⠀⣷⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⢎⠀⠀⣹⢟⠅⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⣃⣤⣴⡶⠟⠋⠁
⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠈⠓⠊⠁⠐⠎⠜⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⠉⠁

⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦
⠠⣶⣿⣿⣿⣿⣿⡟⣻⣿⣿⡏⣿⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿
⠀⣿⣿⡿⣷⣷⠾⣷⣿⣿⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠿⣾⣧⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⡀⠀⢹⡏⠉
⠀⢻⣿⣷⣿⣿⡆⢿⣹⣿⣿⡈⣿⣿⡄⠀⠀⣴⣆⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⢠⡟⠀⢀⣤⣤
⠀⢸⣿⣶⣿⣾⣿⣞⣿⠛⣿⣷⣧⢹⣷⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣾⠀⠀⣿⣻⣿⡧
⠀⠈⣿⣇⣯⣟⣻⣽⣞⣿⣿⣾⣾⠷⠟⠃⠀⠙⠋⣀⡘⠦⠀⠀⣰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠸⣇⠀⠀⠙⣏
⠀⠀⢹⣿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢻⡄⠀⢀⡟
⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠈⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠇⠠⠾⠁
⠀⠀⠀⠆⠸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣴⡾⣿⣿⣿⡛⣿⣷⣄⠀⡀⣶⠎⢻⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠠⣶
⠀⠈⠁⠀⠀⠢⠀⠺⠿⠇⠀⠀⠀⠴⠀⠀⢀⣾⣿⢡⠇⣷⣿⣽⣿⢻⣿⡄⠸⡌⠓⢦⡑⣜⡀⢀⡶⢶⡶⢶⢲⣶⡟⠟⢉⠋⣠⣈⡷⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢈⢸⢿⣯⡟⡇⣿⣿⡇⠀⠘⡄⠀⣿⠌⠃⠀⡇⢀⠐⠇⠈⢿⡇⠀⣿⡷⢬⡛⢷⣄
⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⡟⣟⣿⢹⣷⢰⣿⣿⡇⠀⠀⠈⠋⠀⠀⠀⠀⡇⠸⠀⢀⠀⠀⠀⠀⠈⠁⠈⠀⢀⣿
⠀⠀⠀⢀⠠⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣻⡿⣾⣿⣸⣿⡟⠀⣿⣿⠀⠀⠀⠀⠀⠀⣷⡤⠶⠼⠷⠷⠞⠓⠶⠶⠛⠛⠛⠁
⠀⠀⠀⠸⠄⠀⠀⢠⣤⡄⠀⢀⣀⣠⡄⠀⠘⢿⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⣿⣿⠀⠀⣠⡀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖
⠀⠶⠶⠿⢿⣿⣿⠾⠟⠁⠀⠀⠉⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⣴⣿⣿⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢀⣴⣶⣮⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⡄⠀⠀⠀⠀⢸⣦⠀⠀⠀⢀⡄⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⢿⣿⡌⠉
⠀⠀⠀⢠⠤⠖⠒⠉⠁⠀⠀⠀⢘⡄⠀⠀⠀⢸⣿⡆⠀⢀⣾⡇⠀⠀⠈⢿⣿⣿⡟⠀⢀⣀⣀⣀⣀⣀⠀⠀⠚⠀⠲⠀⠀⠿⠀⠁
⠀⠀⠀⠸⡀⠀⠀⢀⣀⡤⠴⠚⠉⠐⣦⣄⡀⠈⢿⣿⡀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⢿⣿⡟⣿⡆⠀⠚⠀⠲
⠀⠀⡀⠀⠓⠊⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡈⢿⣷⡿⢁⣠⣴⡾⠋⠀⠀⠀⠀⠸⣿⢩⣾⡇⣇⣿⡇⠀⠚⠀⠒
⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣽⣿⣿⣷⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣇⣿⣹⣧⠀⠀⠀⠀⠀⠂⠉⠙⠒⢦
⢀⣀⣠⡤⠴⣦⠀⠀⠀⣀⡀⠀⠀⠐⠛⠛⠛⠉⣹⡿⢱⠉⠙⠷⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠼⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠇
⠻⣥⣤⠀⠐⠙⠷⣤⣾⣯⣿⡆⠀⠀⠀⠀⠀⠰⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠸⣏⠀⠀⠒⠀⠄⠙⠁⢻⣦⣤⣤⣄⣠⣤⣴⣄⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⣤⢰⡆⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠇
⠀⠀⠈⢳⣏⡀⡀⠋⠀⠀⣾⠃⢠⠀⠘⠇⠀⠎⢻⣆⠀⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⢿⡿⢴⡆⢿⣶⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠈⢻⣏⠛⣠⣄⠁⠀⣰⠀⠰⣦⠀⢸⣄⣿⠆⠈⠀⠀⠀⣶⡄⠀⠀⠀⠀⠘⣷⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠄⠒⠓⠘⠉⠈⠉⠁⠛⠃⠲⠆⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠉⠁⠀⢀⣀⢀⣤⠀⠤⠄⢤⡄⢀⣀⠀⠀⠀⠘⠓⠀⠀⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠋⠀⠀⣀⠰⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠀⠀⠀⣠⠞⠁⣰⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠋⠀⢀⡴⠈⠁⠀⣀⣤⠶⠒⠛⠛⠋⠛⠛⠀⠀⠀⠀⣀⡤⣤⠞⠁⡀⠀⣏⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠴⠃⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⢀⡴⢾⠛⠲⣴⠞⠉⠀⣸⠃⠀⠉⢤⡈⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⠞⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⣴⠻⣆⠈⠳⣄⠈⠳⢤⡾⠁⠀⠀⠀⠈⢡⡀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⢀⡍⠀⠀⠞⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡴⢯⠙⢧⡈⠷⣄⠈⠳⣄⡀⢳⠀⠀⢰⡄⠀⠀⢡⡀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⣨⠁⠀⠸⠂⠀⣸⠁⠀⠀⠀⠀⢀⣴⡛⢧⡈⠳⣄⠙⠦⠈⠀⠀⠈⢙⡞⠀⠀⠀⢳⠀⠀⠈⣅⠀⠀⣦
⠀⠀⠀⠀⠀⠀⡋⠀⠀⡶⠀⠀⠏⠀⠀⠀⢀⡴⢿⡈⢳⡄⠛⢦⡈⠃⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠸⡇⠀⠀⢉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡃⠀⠀⡆⠀⠀⠀⣤⢀⡴⢏⠀⠈⠻⣤⡈⠳⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠇⠀⠀⣦⠀⠀⠀⠈⢿⡀⠈⢧⡀⠲⣌⠁⠀⠀⠀⣠⡾⢃⣤⠖⠛⠋⠉⠛⠲⢦⡀⠁⠀⠀⠚⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠻⠀⠀⠈⠀⠀⠀⠀⣨⠷⣄⠀⠙⢦⣈⢷⡀⣠⠞⠉⣠⠏⢀⡴⠛⠉⠉⠛⢦⡄⠙⣆⠀⠀⠋⠀⢀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠞⢁⣴⠟⢳⣄⡀⠉⣳⠟⠁⠀⢠⡏⠀⡞⠀⠀⠀⠀⠀⠀⢹⡄⢸⡆⠀⠀⠀⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠙⢾⡁⠰⠟⢁⡴⠋⠈⠙⠻⣧⠀⠀⠀⠸⡇⠀⢳⣴⣒⣶⢴⡒⣶⣼⠁⢸⡇⠀⠀⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡴⠋⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⢳⡀⠸⢬⣍⠱⠒⢩⡥⠟⢀⡾⠀⠀⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣹⠇⠀⠀⠈⠙⠓⠶⠦⢤⣤⠤⠄⠙⢦⣀⡉⠛⠛⠋⣀⡴⠟⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⢠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣄⠀⠀⠀⠀⠙⠃⠒⠒⠐⠒⠀⠋⠀⠀⠀⢀⣠⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠦⠄⣤⡀⣀⡀⣀⣄⠠⠤⠐⠛⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠀⠀⠀⠀⠀⢀⣉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣉⠉⠉⠉⢙⣻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣽⣛⣫⣿⣞⠛⣫⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠉⠻⠉⠋⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯⠄⠀⠠⣄⡀⠀⠐⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠉⢻⡁⣄⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⠀⡤⠀⠟⣇⠾⠈⠙⠗⠊⢁⣤⠭⣀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢭⡙⠳⠪⠄⠁⣀⡴⠁⠀⣤⣾⣿⡟⠏⠻⢆⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡟⠒⠲⠀⢭⣹⢃⡀⠶⠂⠉⢿⣾⣟⣶⣶⡶⢆⡀⡐⣿⣿
⠀⠀⠀⠀⣤⣶⣶⣯⡲⠴⠠⢴⣴⡷⢾⣈⣽⢻⣦⡄⠀⣱⠂⠉⢹⣿⡿⣶⡎⣩⠀⣡⢼⣿⡀
⠀⠀⠀⠀⠱⣭⣭⣭⣭⢭⣭⣤⣤⠆⠀⠈⠙⢶⢿⣙⣧⠉⠁⠀⣌⣿⠛⣬⠻⢿⣼⡵⠛⠋
⠀⠀⠀⠀⠀⠘⠋⠋⠉⠉⠉⠁⠊⠀⠀⠀⠀⠈⠃⣹⠻⡤⠛⡶⢌⡰⠉⣠⢜⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠘⠉⠰⣆⣠⠖⠁⣠⣾⠗⢱⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠰⡄⠉⢀⣴⡾⠋⣀⣤⣿⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡨⡶⠕⣫⣴⣧⠿⣿⣫⣿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠋⠀⠀⠀⠁⠈⢀⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣉⣐⠀⠀⠀⠐⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠖

⠀⠀⣀⡿⠗⡀⠀⠀⠀⠀⢻⢿⠿⠀⠀⠀⠀⠀⠀⣽⣿⡷⠀⠀⠀⠀⢺⣿⠗⣠
⠀⢰⣿⣿⣾⡟⠀⠀⠀⠀⠻⢿⣃⡤⠀⠀⠀⠀⣼⣿⣟⠀⠀⠀⠀⠰⢾⡛⠾⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡠⣭⡕⠀⠀⠀⠀⢪⣒⣀⠀⠀⠀⠀⠀⣰⠾⠷⣆⠀⠀⠀⠀⢿⡿⣿⠇⠀⠀⠀⠀⠀⢾⣷
⠀⠠⣿⠿⢁⣠⠄⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⢩⡏⢹⡍⠀⠀⠀⠀⠀⢙⢌⡂⠀⠀⠀⠀⢀⣠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣟⣰⡆⣀⠀⠀⠀⠀⠺⢯⡹⠗⠀⠀⠀⠀⠈⣀⣤⡀⠀⠀⠀⠀⢀⠸⣟⡛⠀⠀⠀⠀⢘⣿⣇⡀
⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⠗⠀⠀⠀⠀⠀⠀⠙⢁⠀⠀⠀⠀⢿⣧⣿⡇
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣴⣶⠀⣷⡄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢠⠀⢀⠈⠀⠀⠀⠀⢰⣶⣶⣦⡄⠀⠀⠀⠀⢾⣿⣿⠇
⠀⢠⣶⣷⡟⠃⠀⠀⠀⠀⠀⢯⡶⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠈⠉⠚⠹⣿⠛⠀⠀⠀⠀⠶⣢⠄
⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢧⡼⠀⠀⠀⠀⠀⠀⣽⡷⠋⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⣠⠦⢘⣧⠀⠀⠀⠀⣠⣶⣿⣇
⠀⠀⠳⣼⣧⠞⠀⠀⠀⠀⢜⣿⣄⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⢼⣿⠆⠿⣾⡃⠀⠀⠀⢻⣿⣻⡟
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⡀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠻⠭⢍⣉⣉⡉⠛⠓⠒⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣞⣋⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡵⢶⠋⠁⢹
⠀⠀⠀⠀⠀⢀⣤⠤⣤⠶⠿⠥⢤⣤⣤⣀⣀⣈⡉⠉⠑⠒⠒⣢⣴⠞⠋⠁⠀⢸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⡴⠛⣿⣿⣻⣿⡟⠳⣼⠀⠀⠀⠀⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢀⣠⣴⣚⣋⣿⣯⣭⣽⣿⣿⣿⡇⠀⢸⡀⠀⠀⠀⠀⡇⣠⡼⠃
⠀⠀⠀⠀⠀⣿⠀⢠⠿⠚⠉⣾⠭⢍⣉⣹⣯⣟⡛⠛⣻⣿⡇⠀⢸⡇⠀⠀⢀⡴⠟⠁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠀⢙⣶⢦⣤⣬⣭⣿⣛⣉⣙⡲⠶⠶⢚⣻⠃⠀⢸⣇⣤⠞⠉⠀⠀⠀⣠⠴⠚⢉⣬⣽⡶⣄⡀
⠀⠀⠀⠀⠀⠸⣶⣋⣁⠀⠛⠻⠭⠽⠋⠻⢭⣭⣭⢟⣩⣽⠀⠀⢸⠋⠀⠀⢀⡤⠖⢋⡥⣤⣾⣭⡿⠛⣃⣤⣙⢦⡀
⠀⠀⠀⠀⢀⣠⠞⠋⠉⠉⠛⠓⠒⠒⠶⠦⠤⠴⠞⠫⢥⣼⣤⡤⠞⢀⡤⠞⢉⣠⣤⣿⡶⠿⠃⣠⣶⣾⣿⠿⢋⣤⠏
⠀⠀⢰⡞⠛⠓⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⢞⣩⣤⣄⣿⣀⣶⣟⣀⣰⣯⣭⣽⠏⣡⠴⠋
⠀⠀⠈⠓⠲⠶⠤⣤⣀⣀⡀⠉⠙⠓⠦⡄⠀⣠⠟⠁⠀⢶⡋⠰⣯⠤⣤⣺⣇⣉⣼⣯⣠⣼⡏⢉⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣭⣝⡓⠲⠦⢿⠞⠁⠀⠀⠀⠈⠛⢦⡉⠉⣽⣋⣉⡩⣿⠉⢉⣡⠞⠉
⠀⠀⠀⠀⠀⠀⢰⢏⣁⣸⣇⣠⠝⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⠒⠛⣁⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠖⠛⢁⣠⠴⡶⡖⠶⣤⡀⠀⠀⠀⠀⠀⠙⠦⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣑⣚⣛⣃⡭⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⢀⣀⡀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⣀⡀⠀⣀⣀
⠀⠀⣿⣯⣬⣉⣉⣥⣾⠗⠚⠛⠀⠀⠀⠀⠀⠰⠄⠀⠀⢻⡏⢉⠀⢼⣇⣦⠀⣿⡅⢻⠁⣺⠏⢍⠈⣯⣔⠢
⠀⠀⠛⠛⠛⠛⣛⣋⣡⡄⠀⠀⠀⠀⠀⠀⠐⣦⡄⠀⠀⠈⣿⡶⢀⣼⣧⣦⡀⢸⡇⠞⡀⢻⣾⡟⠂⢬⣝⣿⡀
⠀⠀⠀⠀⠀⣻⣷⡿⠿⠷⠶⠒⠐⠒⠒⡐⠀⠉⠀⣤⡆⠀⠛⠉⠀⠈⠁⠈⢩⠀⠉⠋⠁⠀⠉⠋⠀⠈⠛⠋⠁
⠀⠀⠦⠃⠀⠀⠀⠀⡀⢄⡀⡀⠀⠘⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⡀⡀⠀⠨⠀⠀⠀⠀⣰⣎⠑⠠⢾⡿
⠀⠀⠂⠉⠀⠑⠀⠉⠉⠁⠀⠀⠀⠀⢰⣻⣿⣿⣻⣿⣿⣧⡁⣈⣑⣖⡀⠀⢠⣴⡄⠀⢉⣀⠶⠴⠊⠀⡄⠒⠠⠇
⠀⠀⠀⠀⣼⠄⠀⠀⠀⠉⠉⠁⠉⠉⠈⠛⠛⠛⠛⠿⠿⠷⠦⡯⠝⠋⠀⠀⠺⠞⠀⠀⢰⠯⠇⣠⣤⣄⠈⡅⠀⡀
⠀⠀⣶⡀⣿⠀⣠⡆⠀⠀⠀⠀⢒⣈⡉⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⡀⢀⠀⣄⠀⠀⠀⠀⢀⣠⣈⠉⠉⠉⠀⢀⡰⠠⠤
⠀⢠⣽⣷⣿⣾⣿⣶⠏⠀⠀⠀⠉⠠⠂⠀⠀⠀⢀⡴⠋⠉⠀⠉⢙⣃⣘⠷⣌⣙⠀⠀⣾⣿⣿⡿⠀⠀⣾⡓⠊
⠀⠀⣙⣿⣿⣿⣿⣭⡄⠀⠀⠀⣤⣾⠻⣼⡄⢀⡎⠀⢠⠤⣤⢤⣿⣿⣻⣷⡍⠋⠀⠀⠀⠋⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠙⢿⣦⣉⣛⡿⠁⠀⠀⠀⣿⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠺⣧⠀⠀⠀⠀⠀⢠⠂⠒
⠀⠀⠀⠀⡄⠀⢀⣶⣄⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣿⣿⠈⠟⠟⠟⢋⣠⡾⠋⠀⠀⠀⠀⢱⠤⠄⣴⣶⢃
⠀⠀⠀⠀⠀⠀⡘⣿⣽⢉⣼⠟⠆⠀⠀⣼⠉⠢⠀⠀⠀⣿⡿⠀⠀⣠⠀⠀⠉⠑⠀⠐⠈⠀⡀⠁⠀⠀⠈⠉⠹⣆
⠀⢠⣬⡀⡀⠈⣛⢻⡿⣿⠁⢀⠀⠀⣨⡍⡆⢠⠦⡀⠀⠿⠃⠀⠀⠀⠄⡀⠠⠀⡀⠀⠀⠀⢳⡀⠀⠀⠀⡀⢀⠜⠉⠉
⠀⠘⠿⠷⠖⠀⢹⣟⠀⠈⠻⡿⠃⠀⢹⣶⡷⢏⡇⠀⠀⠀⠀⠀⠀⠆⠆⠉⠠⠘⠁⠀⠀⠀⢾⡗⠐⠶⢾⣷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠾⠿⠿⠿⠛⠛⠘⠓⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠙⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠟⠁⠀⠀⠉⠉⠓⠦⣄⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡾⠁
⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁
⠀⣴⠟⠁⠈⠁⠀⠉⠉⠛⠶⣄⡀⢹⣤⣤⣤⣄⣠⣤⣤⣤⠤⠤⠶⠖⠒⠛⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⣼⡏⠀⠈⠳⣄⠀⠲⣄⠀⠀⠈⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⢹⡀⠀⠀⠈⠳⢄⠈⠢⡀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⢻⡀⠳⡄⠀⠀⠀⠀⠑⢤⡈⠢⡀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⢠⠀⠀⠀⣴⠃
⠈⢷⡀⠘⢦⡀⠈⠰⠀⠀⠙⢦⡈⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⢀⡾⠃
⠀⠀⠻⣆⡀⠙⠦⣄⡀⠀⠀⠀⠙⢦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠈⠙⢦⣄⡈⠉⠓⠲⠶⠶⢖⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠞⠛⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠀⢀⣤⠟⠋⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⠟⠋⠀⠀⠒⠀⢀⡤⠞⠉⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣀⣠⡤⠞⠋⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢀⡠⠒⠉⢀⣠⠞⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠒⠒⠲⠶⠶⢤⣄⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠖⠋⠀⣀⠴⠋⠀⠀⠁⠁⢀⡴⢋
⠀⠀⠀⠀⢠⣶⣏⠉⠛⠦⢤⣀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠲⢾⣁⢀⣠⡞⠁⠀⣀⣀⡤⠴⠚⠁⣠⡾
⠀⠀⠀⢰⡏⠀⠈⠛⠶⣤⣀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⠉⠉⠉⠉⢉⣁⣀⣠⣤⠴⠞⠉
⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠉⠛⠢⢄⡀⠈⠙⠲⢤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠸⣇⠙⠦⣄⡀⠀⠐⠀⠀⠀⠉⠛⠶⣤⣀⠈⠙⠲⢤⣤⢿⡇
⠀⠀⠀⠀⠹⣦⠀⠀⠉⠛⠒⠠⠤⣀⣀⣀⣀⣀⣩⡿⠶⠒⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠻⣿⣶⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠈⠙⠻⣿⣿⣟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣦⣄⠀⠀⠀⠀⠙⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠻⣿⣶⣦⣄⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⣿⠏
⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⡿⠿⠿⠶⠶⠾⠛⠋
⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⢀⣼⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡏⠻⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣤⣴⣿⠟⢸⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣄⡀⠉⠛⠿⢿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣽⣿⡿⠋⠁⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⣿⣿⣿⢩⡍⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⢩⣭⣼⣧⣭⡍⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣶⣦⢸⡇⣶⣶⣿⣿⡇⠀⠀⣿⡇⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⠿⠿⠿⠿⠶⠶⠿⠿⠿⠿⠇⠀⣠⡿⠟⠉⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠞⠛⠙⠛⠛⢻⣿⣿⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠤⠤⠤⠤⠤⠤⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⢷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠲⠿⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠁⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠉⠛⠒⠒⠶⠤⠴⠤⠶⠶⠖⠚⠛⠃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠢⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡠⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣧⢸⡇⠀⢾⣉⣈⢿⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⣇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢀⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀⠉⠉⠉⠉⠀⠀⡷⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⣴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠒⠲⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠛⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡙⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤
⡞⠋⠉⡟⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⠹⠉⠓⢦⡀
⠉⠒⠲⠦⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠁⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⣭⠇⠀⠀⡼⠁⠀⠀⣸⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣄⠀⠀⡄⠀⠀⠀⠀⢀⡠⠤⠴⣶⠖⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢶⣶⣦⠀⠀⠀⠈⣇⠀⠀⢰⡟⢛⡄⢰⠁⠀⠀⠐⠉⠁⠀⠀⣰⠇⢀⡤⣴⠾⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣟⡆⣴⢋⣉⣤⣼⡙⡅⠀⣰⣿⡀⠸⡄⠀⠸⡄⣠⣷⢸⠀⠀⠀⠀⠀⣠⣤⡀⠉⠀⠘⠋⠁⢀⣼⠗
⠀⠀⠀⠀⠀⣀⣠⣽⣾⣯⠥⢈⡟⠻⠿⠟⠛⣿⣃⠞⢁⠅⢧⠀⢡⠰⣶⣧⠙⠛⠀⠀⣠⣶⣿⣿⠿⠿⠟⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠛⠋⢹⡘⢇⣠⠞⠁⠀⠀⠀⠀⡧⠋⠀⢸⣀⣘⡆⠈⣆⠀⠁⠀⠀⣠⣤⠟⠉⠁⠀⠀⣰⠞⠂⠀⢀⡟⠋
⠀⠀⠀⠀⣀⠀⢀⠎⠉⠁⡽⠀⢠⡀⠀⠀⠀⣿⣿⣿⡿⠿⠿⣷⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⡶⠛⡀⠹⣄⠖⠱⡄⠙⠛⠛⠲⣄
⠀⠀⠀⠀⠉⢁⣾⣶⣿⣿⠇⠀⠀⠙⠂⢀⢞⣭⠖⣀⠀⢀⡞⢉⡠⡀⠀⠀⠀⠀⠀⡹⢿⣇⠀⠉⠁⢠⡌⣣⠀⠘⡄⠀⠀⠀⡟
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡌⠁⠸⠫⠆⠀⠳⡀⠀⠙⣆⠀⠀⠀⠀⢳⡀⠉⠀⠀⡄⠈⠉⣹⡄⡀⣷⠀⠠⠞
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⢀⣀⠀⠀⢈⡿⣄⠀⠀⠀⠀⠒⡊⢐⡆⢹⡀⠀⠀⠀⠀⠉⠛⢧⡀⢣⡀⢿⡿⠂⣧⣯⣤⣤⣤⣤⣤
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠘⠒⠁⠀⠘⢦⡒⠀⠀⡇⠲⢯⣶⣿⡏⢸⡇⠀⢀⡀⠀⢀⣴⣶⣏⠒⠬⣤⠶⠾⠋⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣤⠀⠀⠀⠀⠀⠀⠈⠛⠳⣜⠦⣀⠉⢉⠀⣼⣃⣴⣿⣿⣶⣿⣿⣿⣿⣆⢠⣌⣢⣘⣴⣿⣸⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⣦⡀⠀⠀⣹⡉⠓⠶⠶⠛⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⠛⠿⣯⣿⡿⠿⣟
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⡄⢳⣦⣼⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠿⠃⠀⠠⣎⠹⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡵⠶⠶⢦⡀⢹⣿⠿⣿⣿⣿⣿⣿⡄⢻⡟⠉⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣤⠈⠩⢭⣉⠓⡆
⠀⠀⠀⠀⢠⣦⠀⠀⣾⡡⠔⠀⠀⠀⣡⡿⠋⠉⠲⣍⢻⣿⣿⣿⡄⠁⢰⣢⠀⠻⠉⣩⡍⠉⠻⠿⢿⣿⠟⠻⠂⠀⠁⠀⠀⠀⠀⣱⠇
⠀⠀⠀⠀⠀⠁⢠⡞⠉⠀⠀⠀⠀⠘⠁⢀⡀⢠⠖⠚⣦⡻⣿⣿⣿⣆⠀⠀⠀⣀⣀⣉⣁⣐⣟⣀⣀⣀⣀⣀⠀⢠⡤⠀⣀⡴⢋⠏
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⣾⡫⠀⠀⠀⣾⠟⠤⣈⠹⣿⣿⡆⠀⠀⠙⠣⣟⠒⣦⠐⠒⢒⣶⠟⠉⠀⠀⣠⠞⣉⠔⢁⡀
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣰⠯⢟⣀⡀⠀⠀⠉⠀⠀⠚⠁⠙⠛⠛⠀⠀⠀⠀⠈⠑⢯⡠⠶⣯⠀⠀⠀⠀⣾⡣⠊⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠀⡏⠙⠻⠀⠀⠀⠀⢠⣞⣃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣗⡴⡼⠀⠀⠀⣸⣏⠀⠀⠲⢤⣄⡀
⠀⠀⠀⠀⢠⡀⠀⠻⣿⣄⠀⠀⠀⠀⠙⢦⣤⡴⠀⠀⠀⠀⠀⠁⣠⠀⠀⠀⠀⠀⠀⢀⠎⣠⠿⠿⠀⠀⢀⠀⢿⡘⠳⣤⡀⠀⠀⠉
⠀⠀⠀⠀⠈⢿⣶⣄⠹⣿⣦⠀⠀⠀⠀⠀⠀⠲⣤⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀⢀⠎⡼⠁⠁⢘⡀⠀⠛⠁⠀⠙⠢⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠈⢧⠙⠇⠙⣿⣷⡀⠀⠀⡄⠀⠀⢸⣷⢸⠁⠀⠀⢀⣠⠴⠒⠂⠀⡎⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡑⠄⣿
⠀⠀⠀⠀⠠⣶⣾⣧⠀⢀⣘⣿⣷⡄⠀⣧⣄⣠⣼⣿⠀⠆⠀⡴⠋⠀⠀⠀⠀⠀⢷⠀⠀⡟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⢻⣿⡀
⠀⠀⠀⠀⠀⠈⠛⠋⣴⡿⠃⠈⢿⣿⣆⢷⡈⠉⢉⣿⠀⠈⣾⠁⢀⡤⠚⠉⠙⢷⣌⣇⠀⢣⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣠⡿⡋⠙
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⣠⣤⠀⠻⢿⠦⠙⠾⠿⠋⠀⠀⢹⣾⠋⠀⠀⠀⠀⠀⠙⣿⡀⠀⠂⠀⠀⠠⣶⠀⠀⠙⣤⣾⠏⡰⠁
⠀⠀⠀⠀⠀⣠⡄⠘⣿⣧⣿⢸⡆⣰⣶⣆⣀⣿⡆⠀⠀⢀⣿⠷⣄⠀⠀⢄⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣀⣤⠶⢋⢳⡎
⠀⠀⠀⠀⠀⠉⠁⠀⠈⠛⠻⣿⣿⣿⠋⠉⠛⠉⠀⠀⠀⢸⣿⠀⠈⠛⠶⢤⣵⣄⣀⣀⣀⣁⣤⡤⠴⠖⢛⡉⠄⠊⠁⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⢭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣭⣭⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⠙⠳⠦⢤⣤⣄⣀⣀⣀⣀⣉⣁⣀⣠⣤⡤⠾⠛⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⡶⢶⣶⣦⣤⣤⣭⣭⣭⣥⣤⣤⣴⣶⡶⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣧⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣼⣧⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠷⢶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⣿⡇⠀⠀⠀⠀⢀⣴⠟⡽⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣶⣦⣤⣄⡀⠀⠀⢸⣿⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣿⣇⠀⠀⠀⣰⡿⠛⠳⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⠒⠲⠍⣿⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠄⠀⣿⡀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣶⣦⣶⠟⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢿⡟⠛⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠉⢹⡇⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠂
⠀⠀⠀⠰⠤⠄⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⡁⠀⠀⠀⠀⠐⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⠠⣀⠀⠀⠀⠐⠃⠀⠀⠀⢉⠀⠀⠀⡘⠁⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠒⣀⠀⠀⠛⠀⠘⠀⢈⡀⠀⠴⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠈⠦⡀⠚⠀⠀⡀⢈⡁⠐⠃⠀⠀⠀⠐⠀⠀⢀⡀⠒⠈⠀⠀⠀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠱⡄⢃⠀⢠⠀⡀⠚⠀⡀⠀⡜⠀⡄⠒⠀⠀⠀⠀⢀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⠢⡘⠧⡖⢰⠈⢉⡁⡰⢁⢎⡔⠃⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠱⣄⡈⢂⠻⡡⣬⣡⡀⣁⠾⣀⠄⢊⡀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢤⡄⢠⠠⠤⠤⠀⢀⠄⠀⠀⠂⠠⠀⠀⡀⠀⠀⠀⠀⠙⠢⣁⢵⣽⡤⣶⠽⠎⠐⢈⠁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⠚⣾⠿⣿⡑⠒⠚⠓⠚⠀⠁⠈⠁⠁⠘⠂⠲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠒⠂⠀⣸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣂⣡⣠⡠⠓⠐⡟⠸⣌⠑⠉⠳⢒⠰⠠⠆⠤⠠⠄⠠⠠⠄⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠿⠭⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡸⠀⠠⠈⢣⡄⠀⠂⠐⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⣸⠈⠁⠄⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠄
⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⢄⣀⡠⠀⠀⠀⢀⣀⣀⢠⡤⠤⠤⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢯⣠⣾⠏⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠤⠔⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⡌⢢⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⢀⠀⠸⠀⡀⠀⠀⠐⠁⠀⢸⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠒⠊⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⠀⠈⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠶⠶⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠚⠋⢿⡄⠉⠉⠋⠛⠓⠒⠒⠒⡖⠒⠒⠛⠋⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠈⠳⣄⠈⢳⠶⢤⣤⣄⣀⣀⣀⣀⣃⣀⣥⣤⠴⡞⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢷⣸⡄⣀⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣷⣞⠉⠉⠉⠉⣙⣷
⠀⠀⠀⠀⠀⣀⣴⠷⠛⢿⡓⢦⠀⠀⠀⠀⠈⢿⡇⠀⠉⠉⢙⣛⠛⠛⣷⠀⠀⠀⢀⣿⣈⣉⣉⣉⣉⣉⡼
⠀⠀⠀⠀⣰⢫⠇⠀⠀⠀⠹⡌⢷⡀⠀⠀⠀⠘⡇⠀⠀⠀⣯⡬⢃⠀⣿⠀⠀⠀⢰⠏⠀⠉⠉⠉⠉⠀⠙⡖⠶⢤⣀
⠀⠀⠀⠀⡇⢸⠀⠀⡠⠖⠲⣿⠈⣇⠀⠀⠀⠀⡇⠀⠀⠀⠉⠽⠫⠀⢻⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⣇⠸⡆⢀⡵⠶⣞⢹⠀⡟⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠉⠒⠶⠶⠶⠶⠖⠋⣿⠀⠀⠀⠀⢠⠞⠉⢳
⠀⠀⠀⠀⠸⣆⢿⡁⣠⠟⢉⡟⣸⠃⠀⠀⠀⠀⣿⠲⢤⣀⣀⣀⣀⣀⣼⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡖⠀⢀⡎⢠⠂⠛⢢⡄
⠀⠀⠀⠀⠀⠈⠳⠯⠿⠶⠿⡚⠁⠀⠀⠀⠀⠀⣻⡀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣇⡇⢸⠀⢻⣄⣰⣷⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠬⣟⠲⠶⠶⠖⠛⠉⠉⠓⠦⢤⣤⣤⣤⡤⠤⠖⠋⠹⣶⠤⣀⣀⣀⣀⣀⣴⠏⠀⠈⠙⠛⠓⠋⠀⠉⠁⠀⠈⠙⠲⠦⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣋⠀⢘⣀⡼⠁⠀⠀⠀⠀⠀⠀⣠⣒⣲⠶⢦⡀⠀⠀⠀⠀⠀⠈⠛⠲⠾⠶⠷⠚⠉⠀⠀⢀⣤⠤⠤⢤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢧⣀⣀⠃⠀⠈⢻⠉⠁⠀⠀⠀⡠⠴⢶⠶⢤⣟⠲⠤⠤⢞⢇⣠⠶⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⡇⠀⠉⡧
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⢸⠆⣀⣎⣀⡴⡏⠉⠛⢋⠟⠋⠉⢆⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠓⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠦⠶⠚⠁⠀⠀⣯⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣩⡛⣉⣝⣙⣯⣏⣿⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠐⢎⠂
⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠁⠀⡁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⠢
⠈⠐⡆⠀⠀⠀⠁⠀⠀⠀⠦⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⢠⡄⠀⢅⡂⠀⠀⠀⠐⢠⠀⢀⡀⠐⠠⠀⠚⠲⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⣼⢢⡄⢀⠀⠀⠀⠂⠜⢦⠀⣤⠤⠇⠰⠃⣅⠀⢠⠀⠀⡦⠍⠈⢀⡖⠀⠀⠀⠀⢹
⠀⠀⡎⠀⠀⠀⡀⠄⢁⠰⠉⠉⠀⠨⠂⠂⠀⠘⠋⠐⠃⠀⠀⠀⠈⠄⠐⠖⠊⠑⠀⡇⠀⠂⢀⣿⠧⢄⠀⠀⠘
⠀⠌⠀⠀⠀⠀⠡⢄⢀⠀⠀⠀⠀⡦⣂⠍⠂⢀⠀⢀⠀⠀⠀⠀⢀⠔⠀⠁⡔⠁⡎⠑⢄⠀⠋⢛⠟⠛⠉⠦⡀
⠀⢐⠀⠀⠀⠀⡄⠈⢢⠑⠀⢀⠈⡠⠊⠀⢉⡟⢀⠿⠀⠠⠒⠀⠀⣠⡆⠀⢀⠌⠁⠀⠈⡀⠀⠀⠀⠀⡀⠀⢃
⠁⠈⠉⢲⠀⠀⠎⠢⠀⠂⠔⠡⠊⠅⠀⡐⠀⠀⠀⠀⢆⡀⠈⠐⠂⠁⠩⡀⣀⣀⣀⠀⢰⣾⠀⡀⣀⠀⡀⠀⢸
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠂⠐⡁⠀⢀⠎⠀⠐⠤⠤⠔⠃⠀⠤⠀⠀⠀⠀⠑⠒⠳⠤⠤⠤⠋⠙⠃⢀⠀⠓
⠀⠀⠘⠀⠀⠀⠂⠐⠂⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠑⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠉⠉⠛⢶⣄⡀⢀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢘⣷
⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⢳⡀⠀⠀⠀⠀⠈⠷⢄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⠋
⡟⠀⠀⠘⡄⠀⠄⠀⠀⠀⢹⠈⠙⢄⠀⠠⠊⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀
⠹⡄⢀⠀⠘⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢲⠷⣶⠿⠟⠋⠁⠀⠀⠀⠀⣀⣤⠔⠊⠉
⠀⠹⣤⣇⠸⣿⡄⠀⠀⠀⣼⣾⠀⠴⠾⠙⠵⢦⣼⣷⣶⣶⣞⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⣉⡄⠀⠀⢀⣠⠼
⠀⠀⢻⣿⣆⠹⣿⡄⠀⠘⡃⠀⠀⠀⠀⠀⠀⢠⠃⠉⠙⠛⠭⢆⠀⠀⠀⠀⠀⣇⣤⣶⣿⣿⡷⠖⠚⠉
⠀⠀⠀⢻⣿⣦⠟⠇⣀⡀⠈⠓⢤⡀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠉⠉⠀⠀⠣⣀⠀⠀⠒⣽⣶⣄⠀⠀⠀⠀⠐⠚⠈⠀⠀⢴⡖⢄⠀⠀⠀⠀⠀⠀⠀⣄⠊⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠐⠒⠂⡌⠙⢶⣿⣍⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⢷⡀⠀⠀⠀⠀⠀⠈⠛⠲⠦⠤⠤⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠉⠻⣷⣦⣈⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣢⣄⣄⡠⢤⢐⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⢷⠒⠒⠒⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡆⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠤⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠄
⠙⠒⠚⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤
⠀⠀⠀⠀⠀⣀⠤⠤⠄⠒⠒⠉⠉⡍⠉⠁⠐⠒⠒⠐⠀⠡⣆⠀⠀⠀⠀⢰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀
⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠿⠀⠀⠀⠀⠈⠐⠀⢳⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⢠⣀⠠⠂⠀⠀⠀⠀⠀⣠⢴⠊⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠔⠀⠀⠀⢠⠐
⠀⠀⢀⣀⡠⠤⠔⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠊⠀⠀⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠀⠀⠁⠀⠀⠀⠀⠐⡄
⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠔⠒⠒⢒⣤⡀⠀⠀⠀⠀⠀⣽⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠈⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠀⠉⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⡤⠊⡁⠀⠀⠉⠀⠀⠒⡀
⡀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠇⠤⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⢈⢦⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⡸⠃⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠐⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠁⠀⠑⠀⠀⠀⠑⢄⠀⢀⣠⠴⠊⠀⠀⠀⠀⠠⡀⠀⠀⠀⡠⠒⠒⠒⠒⠀⠄⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠐⠒⡂⠉⠁⠀⠀⠀⠈⠰⡄⠀⠀⠀⠀⠀⢸⣀⠠⠄
⠀⠀⠀⢃⠀⠀⠀⠀⠓⡉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠇⠈⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠤⠊⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠱⣤⣠⠤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⡀⠤⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠙⠉⠁⠶⠤⣄⢀
⢣⡀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠈⠐⠠
⠀⠁⠀⠀⠈⠀⠀⠀⣠⠞⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠧⠤⢤⡀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⡰⠊⢀⠁⠀⠀⠐⡄⠀⠀⠀⠊⠀⠀⡷⠐⠒⠀⠤⠤⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⠆⠀⠀⠀⠀⠀⠀⠠⠀⣀⠋
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡰⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢤⠄⣀⠀⠀⠀⠀⠤⠄⠀⠀⠀⣀⣀⣀
⠈⠢⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠰⠁⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠆⢀⠁
⠀⠀⠑⣤⡀⠀⢀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢰⠀⡅
⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸⡀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠤
⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀
⣆⣀⣀⡀⣀⣀⡀⠈⣀⠀⠀⠀⠀⠐⣏⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⣼⣄⠒⠈⠁⠀⠀⠀⠀⠀⣀⠐⠉⠀⠀⠀⠉⠉⣻⠀⠀⠀⠀⠀⠀⣀⠊
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠊⠉⡇⠁⢐⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡴⠋⠘⡆⠀⢉⢶⠲⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣧⠔⠁⠈⣇⢀⠔⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠋⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡰⠁⢀⣀⣰⢇⠞⠉⠳⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠋⡜
⠀⠀⠀⠀⢸⠁⠀⡸⠉⣀⡜⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠘⠤⠤⡄⠈⠙⢦⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⡼
⠀⠀⠀⠀⡌⠀⠀⡇⠸⣅⡀⡗⢤⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⠳⡀⠀⠀⠈⣧⣀⣠⠴⡆⠘⢣
⠀⠀⠀⠀⣇⠀⠀⢳⠀⢸⡇⠳⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠙⢆⠀⢠⣄⡀⣀⡔⢰⠚⠁
⠀⠀⠀⠀⠘⢦⡀⠀⠉⠚⠀⠀⠀⠉⠀⠧⢄⠀⠀⠀⠀⢰⢢⠀⠀⠀⠀⠈⠢⡀⠀⠉⠋⠀⠉⠁⠀⠳⠦⡄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡞⠘⡄⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠃⠀⠸⠀⠀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠀⡜⢆⠀⢳
⠀⠀⠀⢀⣀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠠⠤⣄⣀⡰⠃⠀⢇⠀⡸⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⣀⠇
⠀⠀⠀⢸⠀⠀⣽⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⢤⠒⠋⠁
⠶⠶⠖⠚⠂⠀⠻⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⠈⠒⠒⠂⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⠶⠶⠶⠶





⣿⣿⠟⢿⢛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢀⣤⡏⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⡞⠁⠌⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⠦⣄⡀
⠀⠀⣠⣴⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠠⣿⠀⠀⠀⣠⡶⠶⢦⡀⠀⠀⠀⠀⠹⣏⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⠘⢧⡈⣷
⠀⠠⣟⢠⡟⠰⢈⡷⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⢸⡏⡛⠲⢮⣷⠀⠀⠀⠀⢠⡟⠉⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠻⣤⣀⣀⣹⡿⠶
⠀⢀⣽⢿⣤⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣁⣀⣴⣿⣤⣤⡤⢤⣼⣇⡶⢶⢹⡆⠀⠀⣀⣤⣴⣿⡆⢹⡯⣭⡿⠂⠀⢀⡾⠋⣉⣻⡄
⠐⠛⠁⣾⡁⠙⢦⡀⠀⣠⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣼⠇⣠⡗⢀⡼⢿⣿⡇⢸⡀⣿⠀⠀⠙⣿⣺⣟⠁⠿⣿⡿⣄⠀⠀⣿⢡⡾⠋⣿⡇
⠀⠀⢰⡟⢷⡀⢀⣹⣾⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢃⡶⢮⣴⢏⣴⠿⣅⢸⡍⣧⠸⣧⣼⣦⠴⠞⠋⣿⠟⠃⢀⡏⠙⢮⡳⠦⠿⠛⠀⣸⠟⡇
⠀⠀⢸⣇⣠⣵⣿⡷⠛⢷⡄⠀⠀⣀⡀⠀⠀⢾⣟⣉⣭⡭⠴⠟⣱⣿⡵⢿⡅⠀⢹⣿⡇⠙⢦⣄⣠⣤⣤⣤⠴⣿⠀⠀⠙⠃⠀⠀⠙⢲⡦⠤⠾⠋⢠⡇
⠀⠀⠈⠛⠛⠛⢷⠀⠀⠀⢻⡶⠛⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢀⡿⠀⢀⣿⡇⠀⠀⠀⢰⠀⠀⠀⢠⣿⠄⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣸⠷⢦⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣁⠀⣼⣿⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣽⠂⢠⡟⠀⣾⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣰⠟⣿⢹⡏⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡟⢠⡟⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠸⣏⣸⣧⡿⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡞⠀⢰⠀⡇⢸⡇
⠀⠀⠀⠀⠀⢀⣾⢡⡟⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣉⣿⣿⠁⠀⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⢁⡀⢸⠀⡇⢸⠁
⠀⠀⠀⠀⠀⣼⢃⡾⠁⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢷⡄⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡏⢸⠀⣸⢠⡇⣿
⠀⠀⠀⠀⣰⠏⣼⠁⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⡇⢻⡄⢹⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⣀⣸⣀⣿⣸⣇⣿
⠀⠀⠀⢠⡟⣼⠃⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⢿⡏⢸⣷⠟⠁⠸⢦⣤⣤⣬⣿⣦⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⣽⣟⣋⣉⣿
⠀⠀⠀⣾⣱⠇⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢸⣿⣿⡾⠆

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⢀⡤⠤⠦⠴⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⢸⣉⣉⣀⣉⣉⡇⠀⠀⠀⠀⠀⢸⣃⣀⣀⣀⣀⣀⢀⣻⠀⠀⠀⠔⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⢼⡁⠀⠀⠀⠀⢀⡴⠃⠈⠀⠀⠀⠀⠈⠳⢄⠀⠸⡣⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠒⡂⡐⠈⡇⠀⠉⠒⠦⠤⠤⠒⠋
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠆⡬⠀⠙⠒⠐⠀⠀⡀⡀⡇⠀⡴⠒⠒⠛⠛⠻⣿⣿⣿⣶⣆
⠀⠀⠀⢸⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⡇⠄⡋⠀⣀⣾⣆⡀⠀⡘⠀⡇⠸⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠠⠃⠀⠉⢿⠏⠁⠀⠅⠂⡇⠀⠉⠛⠒⠒⠒⠛⠛⠛⠛⠉
⠀⠀⠀⣼⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠙⠤⠤⡠⠤⡠⠔⠁⠂⡇⠀⡔⠋⠉⠉⠉⠉⠉⠉⠉⠒⡄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡇⠁⠈⠓⠖⢂⡈⠡⡃⠂⠀⡇⠘⡅⠀⠀⠀⠐⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣻⠀⠀⠀⠀⢶⣿⠶⠀⠀⠀⠀⡇⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠀⠈⠉⠛⠓⠒⠒⠒⠒⠋⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣤⠤⠲⠤⠠⠴⠲⡤⠤⠶⠒⠖⠲⠖⠒⢲⠲⠶⠒⠒⡶⠦⡀
⠀⠀⠀⣿⣶⢶⣦⣶⣦⣤⣤⣶⣶⣶⣖⡇⠀⠀⢀⡞⢡⣀⠀⠛⣄⡀⠈⠃⢥⡄⠀⠉⢠⣤⠀⠈⠀⢦⠀⠀⠁⡼
⠀⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⡇⠀⢀⠎⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⡄⢀⠀⠀⣠⠀⠠⠀⠀⣀⠀⡰⠁
⠀⠀⠀⢻⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⢟⠇⢠⠋⢠⣤⠀⠋⢤⠄⠈⠁⢢⡆⠀⠀⠰⠖⠈⠈⠀⠲⡖⠈⠈⣰⠃
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠒⠒⠛⠉⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⠴⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⡤⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡧⢥⣸⣨⣅⣇⠧⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠂⠠⠤⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣶⣽⡖⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⢀⡠⠔⣊⠡⣾⣲⠏⠉⠁⢠⡶⢮⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠻⢄⣘⠯⠟⠀⣀⣀⡸⠽⠟⠈⡡⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣈⠉⠁⠀⠀⢀⢤⢄⠀⠉⠲⢄⡙⠚⢃⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣝⠋⠘⠿⠃⠀⠘⠋⠛⢠⣶⣦⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣠⠤⡄⠀⢀⣈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠨⠒⠁⠘⢅⣸⣈⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠐⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⣀⡉⠙⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠷⠆⠀⠀⢀⠀⠀⣤⣶⡧⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠿⠋⠀⠀⠀⢠⣄⣄⣀⡏
⠉⠀⠃⠀⠀⠀⠀⠀⠀⣼⣟⡀⠀⠰⡄⠁⠀⣿⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠛⠻⣿⡅⠀⠘⠀⣄⡀⠀⣤⠄⠛⠁⠀⠀⠀⠀⠀⠀⣿⠟⠋⣉⣀
⠀⣀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠃⠀⠀⠀⠀⢰⠁⠸⠀⠀⠀⠀⠃⠀⠀⠀⢸⣧⠀⠀⠀⠸⣿⠀⠀⠀⠀⠉⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣠⣾⠿⠿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡄⢸⣶⣶⣄⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣀⡀⣠⣮⠀⠀⠀⠀⠀⠸⠇⢠⣴⠶⠀⠀⠀⠀⢠⣿⢻⡿⠁⠈
⠐⠋⠀⠀⠀⠀⠀⢀⣰⣾⣿⠿⠟⠋⠉⢓⣟⣋⣉⣽⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⢻⣷⣿⠁⠀⠀⠀⠀⠀⠀⢿⠼⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠇⠀⠀⠀⠀⠘⠿⠛⣿⡿⠋⠉⠀⠀⠹⡆⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠘⣿⡄⠀⢀⣀⣀⣀⣀⣀⠀⠀⣤⠀⠀⠰
⠀⠀⠀⠀⠀⠐⡶⢶⣀⣤⠀⠀⠀⠀⠀⢠⣤⣤⣿⡇⠀⠀⠀⠀⠀⣷⠀⠀⢀⣄⣠⣘⡀⠀⠀⠀⠀⠀⠀⠀⡎⠰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣽⡆
⠀⠷⠀⠀⠀⠠⠷⠾⠏⠉⠀⠀⠀⠀⠀⠸⠿⠿⠏⠇⠀⠀⠀⠀⠀⠷⠶⠶⠾⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠸⠘⠁⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣚⠉⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣫⠵⠊⠁⠀⠀⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⠥⢖⡩⠔⢀⠀⠀⢀⣠⢴⡺⠟⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⢀⡤⠖⠋⠀⠀⣁⡴⣚⠽⠊⠁⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡫⠀⢀⡤⠞⠉⠀⠀⣀⣴⡾⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⡠⢞⡩⠖⢋⠤⠚⢉⠤⢊⣠⣴⡾⠛⠁⠀⠀⠀⢀⠀⠀⠀⢠⡞⠋⠉⢳⡄⠈⢧⡀
⠀⠀⠀⡞⠉⠐⠉⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⣇⣀⣠⡼⡷⠀⠀⠹⣦⡀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⣀⡤⠤⣄⣀⣤⣤⣀⡤⢶⠿⣿⠷⠊⠁⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠙⣦⡴⡪⠟⠁⠀⠀⠀⠀⠀⠀⡞⠢⠤⢤⣌⣿⠀⠀⣾⠀⢸⠀⢸⡏⠙⣢⠤⠤⣄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣄⣀⣠⡴⣿⣤⠖⢿⣦⣼⣦⡞⢡⡎⠉⠲⣤⡾⡆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡼⡏⠣⡈⠙⣦⢰⡇⢿⡴⠋⣷⠀⠘⣬⠿⠿⢾⣋⣩⠴⡧⠶⠶⣄⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢷⠳⣄⡙⢆⡿⠈⣧⣈⣳⣤⠟⠀⣾⠓⠲⢖⣰⢿⠀⢸⡄⠀⠀⣸⡇⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠳⠮⠽⠟⢡⠾⡀⠉⢍⢱⣴⡟⠻⣿⣭⣭⠵⠋⠀⠘⠮⣭⣭⡽⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠈⢧⣉⠓⢶⣿⡘⢿⢦⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣽⡉⠁⠀⢸⡆⠑⠿⠞⠃⠀⢀⠤⠶⢤⡀⠀⠀⠀⠀⢀⣴⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢧⣙⡲⢶⡿⠁⠀⠀⠀⠀⢠⣇⠀⠀⣨⡇⠀⠀⠀⢐⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠉⠀⣠⠴⡶⢤⡀⠈⠻⢿⡭⠟⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢰⡇⠀⡇⢀⣿⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠸⣿⣶⣷⣻⠏⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠉⠉⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⣀⣀⡀⡀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⣧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠘⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠛⠀⠀⠉⠁⠀⠀⠀⠀⡦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⢱⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠖
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⣂⡀
⠀⠀⠀⠂⢀⠀⠀⣀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠚⠳⠤⠀⠀⠄⠀⠀⠀⠀⠐⠁⠈⡄

⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢰⣿⣟⡑⠐⠒⠒⣩⣴⣶⣴⢾⠷⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⢰⣶⠒⠲⠄⢸⣿⢩⡍⠂⣿⡆⢰⡖⢂⣴⡟⣛⠢⠸⡟⠭⣅⡀
⠀⠀⢺⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠘⢻⣇⣙⠀⠈⣿⢘⠋⠀⢹⡇⢨⡇⠘⣾⣡⣼⣆⠈⠿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣤⣤⢶⣶⣶⡆⠀⠀⠀⠀⣀⠀⢀⡀⢙⠿⠃⠀⢀⠀⢺⣿⣟⠠⠚⣿⠻⢷⣄⠘⢷⣙⣡⠆⠙⢿⣗⡤⠈⢿⣶⣿⡗
⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠟⠛⠛⠋⠁⠉⡉⠉⡀⠀⠀⠀⠘⢶⠟⠀⠀⠉⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠉⠁
⠀⠀⠹⠜⠁⠀⠀⠀⠀⢀⢀⢄⡀⡀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⡀⠀⠀⠇⠀⠀⠀⠀⢀⣰⣍⠘⠀⠴⣿⠟
⠀⠀⠐⠐⠓⠊⠁⠊⠁⠛⠛⠂⠀⠁⠀⠀⠀⢠⡟⣿⣿⣟⣿⣿⣿⣷⣐⠒⠘⠳⣴⠀⠈⠀⢀⣤⡄⠀⠈⠉⠁⢴⣀⠴⠋⠀⡤⠤⠒⣸
⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠐⠒⠒⠂⠐⠒⠂⠹⢿⣿⣿⣿⣿⣿⣿⣿⣟⣀⡟⣛⠿⠍⠈⠠⣭⣥⠃⠀⠀⣞⡟⡆⠀⠀⠀⠀⠳⠆
⠀⠀⢀⡀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢤⠐⠂⠀⠀⠀⠀⠀⠀⠉⠉⠯⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠉⠁⠰⠿⠽⠧⠤⠛⠀⠱⡄
⠀⠀⢸⣿⡄⣿⠀⣴⡿⠀⡀⠀⠂⠀⢨⡤⠤⠄⠀⠂⠀⠀⠀⠀⢀⣠⡤⠴⣦⣤⣤⠀⣤⠒⢦⣄⡀⠀⠀⣀⣤⣶⣶⡄⠀⠀⢀⡀⢀⠴⠋⠉⠉
⠀⠰⣶⣿⣾⣿⣾⣿⣾⣿⠃⠀⠀⠁⠀⠀⠒⢁⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⢈⣁⣤⡙⢷⣄⣬⡁⠀⠸⣿⣿⣿⡿⠃⠀⠰⣿⣣⠁
⠀⠀⢙⣻⣿⣿⣿⣿⣭⣥⡀⠀⠀⠀⢠⣰⣿⢻⣵⣇⠀⣠⡋⠀⠀⡤⣄⣤⢠⣿⣿⣟⣿⣦⠙⠋⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠙⠛⠋⠟⠻⠏⠉⠉⠀⠀⠀⠀⠈⢿⣿⣄⠙⠿⠿⡻⠁⠀⠀⡃⢸⡇⢸⣷⢿⣭⣟⣿⡇⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀⠈⡥⠤⠤⠤
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠛⠁⠀⠀⠀⣧⣼⡇⠘⣿⣿⣶⣿⠟⠀⣠⡶⠀⠀⠀⠈⠉⢣⡀⠀⠀⢀⣄⣼
⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⠶⣶⠰⣠⡄⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣿⣿⡇⠀⠁⠁⠈⠀⠰⢿⣏⠃⠀⠀⣠⠀⠀⡠⠋⠉⠁⠻⣿⣬⡄
⠀⠀⠀⢀⡀⠀⢀⣤⣹⣷⣧⣠⣾⠋⠙⠀⠀⢀⣾⡁⠈⠃⠀⠀⠀⣿⣿⠇⠀⠀⢰⠂⠀⠀⠀⠀⠈⠀⠁⠀⠠⣴⠁⠀⠀⠀⠀⠀⠈⠻⣆⣀⣀
⠀⢀⣮⣤⢀⡀⠀⢉⡙⣿⢟⣟⠁⢀⣀⠀⠀⣴⢄⢿⠁⣴⠲⡀⠀⠹⠟⠀⠈⠀⠀⠰⢂⡀⠰⠀⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣀⠀⡰⠋
⠀⠈⢷⣿⣶⠖⠀⠙⣿⡃⠀⠈⢻⣾⡿⠀⠈⢻⣦⣼⢴⢽⡆⠀⠀⠀⠀⠀⠀⠀⢤⠰⠈⡇⠡⠸⠇⠀⠀⠀⠀⢼⣷⠀⠦⠦⣾⣷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢉⠀⣠⣄⣼⣿⣿⣶⣿⡷⠶⠆⣶⠄⠀⠤⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠈⠉⠹⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠆⠀⠀⠀⠰⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣿⣿⣿⣿⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡄⠀⠀⠀⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠻⢻⣿⣿⣿⡟⠛⠛⠛⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢈⡉⢠⣿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⢶⣿⠃⢀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⣷⡄⠁⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠿⠀⢻⣷⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⣀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣭⣤⠀⠀⠀⠀⢀⣼⡿⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡜⠀⠀⠠⠖⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠀⠀⠀⠠⣶⠠⡀⠀⠀⠀⠈⠀⠹⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⠀⡀⠀⠀⠠⠋⠓⠷⠂⠉⠐⠀⢠⠀⠀⢈⠆⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⠀⠀⠊⢆⠀⠑⠀⠀⡤⢈⡀⠠⠀⠀⠠⠀⠀⠘⠂⠀⠀⠀⠀⠼⠆⢀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠀⠀⠁⠀⡠⠀⠀⢠⠀⠀⠀⠈⡀⠒⠀⠀⠸⢲⠀⠎⠐⠚⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣀⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠠⢺⠀⠀⠒⠚⠀⠁⠁⠀⠀⠀⠀⠊⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢌⡀⠐⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠈⠁⠂⠉⠲⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠤⠘⠀⠀⢀⠀⠀⠀⠉⡀⠀⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⡀⠀⠈⠆⠀⠀⠀⠈⣤⣤⠀⠀⣀⣠⠀⠀⠆⠀⠀⠀⠀⠠⡁⠀⠈⣀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⢣⠀⠀⠂⠀⠆⠀⢠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠠⡤⠶⠂⠄⠁⠀⠄⠁⠡⠇
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣿⣶⣿⣿⣶⣶⣶⣶⣿⣶⣶⣷⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣦⣾⣵⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣮⣭⣽⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⣿⣿⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣿⠀⠀⣿⣿⣿⣿⣷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⣤⣤⣬⣽⣿⣄⠀⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣤⣬⣭⣽⣙⣩⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⣿⣿⣿⣿⠟⢿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣥⣿⠅⠀⢴⣿⣿⣿⡿⢧⡈⠻⢿⡿⠶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⠀⠙⠀⠀⠁⠀⠀⣈⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⣽⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠈⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⢻⣿⡶⢿⡾⢿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣏⣿⣷⣯⣽⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣼⢿⣌⢁⠾⣧⣾⣟⣿⣯⣤⠀⠀⠀⠀⢼⠷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⡟⣿⣷⡚⢛⣧⢛⣹⣿⣿⡄⠀⠀⠀⠘⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣴⢻⣷⡉⣿⣷⡋⣹⣿⣯⣾⣿⣆⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢡⡿⣷⣀⣿⣿⣯⣽⣯⣼⣿⣿⠀⠀⠀⠀⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣶⣦⣵⣶⣦⣽⣿⣶⢿⣷⠿⣿⣷⣿⣿⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⢻⣿⣷⣿⣿⣿⣿⣿⣿⣮⣻⣿⣿⣾⣿⣿⡀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣷⣼⣿⣿⣿⠛⢻⢿⣿⣿⡟⣿⣸⣿⣁⣟⣿⡯⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠄⠻⠁⠀⢸⣿⣿⣧⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡏⣾⣿⣿⣼⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⡙⡏⢀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⣿⣿⣿⣛⣿⣌⣙⠟⠃⠸⢟⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡷⣦⣤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣾⣿⢶⣶⣿⣧⣴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠋⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣈⣙⡛⠿⠿⠻⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⣉⣁⣴⣾⣿⣿⣿⠟⠉⣹⠙⠋⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡿⠟⠛⠒⠦⠤⠦⠀⢴⠶⣶⠟⠛⠛⠛⠻⠿⠿⠿⠟⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣷⣶⣷⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣷⣶⣶
⣿⣿⣿⡏⠀⠉⠀⢀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠛⠒⠦⣄⠀⢀⠜⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠀⠒⠂⠠⡀⢀⡞⠁⠠⣶⣶⣿⣿⡆⠀⠈⢳⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢷⣾⣶⠶⠄⢠⣄⣄⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠈⠁⠀⣀⣠⣌⠭⠖⢋⡁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣓⠭⢟⣋⣭⣴⠶⠿⠟⠛⢆⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⣒⣫⣭⠭⡄⠰⠖⠒⠒⢚⠉⠀⠀⠀⣈⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠋⠳⡀⢀⠀⠀⠀⠠⠞⠘⢇⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⣀⣀⣀⠌⠀⠀⠙⡏⠀⠄⠀⠀⠰⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢀⠔⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡀⠀⠀⠀⠀⢹⠏⠀⠀⠀⣸⣤⣤⠋⠀⣀⣤⣷⡀⠀⠀⠉⠒⠤⢄⠀⠀⠀⠀⢐⠫⠔⣊⡤⠖⠛⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠁⠀⠀⠀⣼⣿⣿⣿⡀⠀⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢣⡅⡜⢁⡴⠊⠁⠄⢐⣶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣆⠀⠈⠀⠀⠀⠀⣧⣿⣿⣗⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠆⠀⠂⠀⠀⢀⠟⣿⡗⠀⠙⠦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⢃⡆⠎⠙⣼⡄⠀⠙⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣾⣶⣶⣾⣾⡇⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡇⣼⡇⢸⣿⣿⣿⡄⢀⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⡴⢧⢹⡇⢸⠿⠿⠿⠿⠿⠿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠶⠾⠶⠶⠶⠾⠶⢶⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠿⠓⠛⢛⠇⠘⢆⠒⢂⡛⢻⣛⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢠⣀⠀⠁⠀⠀⢸⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣠⡔⠋⠀⣀⣈⣓⠦⠄⣴⠁⠈⢆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⡇⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⠒⠂⠂⠛⠒⠐⠓⡰⠒⠋⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⢷⣶⣷⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠙⠃⠉⠉⠉⠁⠀⠍⠉⠉⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⠀⣀⣀⠀⠀⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⠶⠶⠶⠶⠶⢶⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⠀⡇⠀⠀⣿⠉⠉⠉⣻⠉⠉⠛⣻⠉⠉⢙⡏⠉⠉⢹⠉⠉⠉⡏⠀⢰⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣷⣤⣧⣤⣄⣿⣀⣠⣀⣼⣀⣀⣀⣿⣀⣀⣸⣇⣀⣀⣸⣄⣤⣤⣧⣤⣼⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣤⣌⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣈⣭⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣸⣯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠶⠶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠛⠛⢶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢶⡄⠀⠀⠀⠀⢠⣤⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠇⠀⣾⠋⠉⠉⠀⠸⡇⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⣿⣄⣀⣀⣠⣤⣧⣤⣤⣤⣴⠟
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣍⣉⣉⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣤⣤⣤⣀
⠀⠀⠀⠀⢰⡟⠉⠉⠉⢩⡏⠉⠉⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠻⣿⡁⠀⠈⢙⣿⣦⣀
⠀⠀⠀⠀⠸⣧⡀⠀⠀⢺⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣴⠟⠛⠛⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠦⣄⠀⠀⣼⢿⣄⣰⠋⠁⠈⠙⢷⣄
⠀⠰⠀⠀⠀⠈⠻⠶⢶⣼⣦⣤⣤⣤⣤⠞⣃⣠⣤⣤⡀⠸⣧⠀⠀⠀⢀⡤⠟⠷⣦⡀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠘⣷⡾⠋⠀⠙⠻⣤⡀⠀⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣭⡿⣿⠋⠁⠀⠈⢻⡄⠙⢷⣄⣠⠏⠀⠀⠀⠈⠻⢦⡄⠀⠀⠈⢷⣄⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠈⠻⢶⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠈⢳⡀⠀⣠⡾⠃⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⣀⣼⡷⠟⠋⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣀⣼⠏
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁
⠀⢰
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣌⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⣽⣿⠻⣷⣮⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⣤⢀⡟⣁⣄⡘⣿⢸⣞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣶⠤⢤⠠⢤⠤⠤⣄⡀⠀⢀⡯⣽⣿⢸⡿⠋⠉⢻⡏⣻⣿⠒⡆⠀⠀⢀⡠⡤⠤⢶⢶⣂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⠿⠿⢿⣄⠻⣷⣦⢉⠶⣸⡦⢻⣿⣸⠃⢰⢤⡈⠇⣿⡏⣬⢇⡴⣊⣥⣶⢖⣴⠿⢿⣿⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠵⣿⡇⢠⡶⠾⣧⡙⣿⡆⢳⢉⣏⣁⠹⣷⡀⠈⠀⢀⣰⡟⣔⣶⠯⢹⣿⡟⣴⡿⢶⣄⢀⡿⣣⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣹⣬⡻⣾⣇⠠⠌⠁⢘⣿⡀⠀⡏⠳⣖⣘⢿⣿⣾⣿⠿⣉⡾⣯⠁⣸⣟⡞⣡⣶⠄⣹⣿⣳⣿⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⢿⣿⣷⣝⣓⠈⠀⣸⣿⡧⣼⠃⡶⢬⡙⠛⣾⡾⠚⢋⣡⣆⢳⣂⢿⣿⣆⡙⠉⠰⣿⣿⡿⢣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣈⣳⣼⢉⠙⠛⠻⠿⠿⢫⡴⠃⢸⠃⠀⠈⣄⢧⢸⢠⠏⠀⢸⡆⠻⣌⡻⢿⣿⣿⠿⠛⣁⢢⠙
⠀⠀⠀⠀⠀⢀⣴⣻⣾⣷⣦⣄⣀⠉⠹⢿⠾⠓⠖⠶⠚⠹⡥⠒⡜⣆⠀⡀⡇⣄⡀⢸⢀⠀⣸⢁⢊⠋⠙⠳⠦⢥⡦⢴⡾⢗⢻⣼⣍⣛⢲⣤
⠀⠀⠀⢀⡠⢏⣮⣭⠭⢽⣭⣿⡽⠻⣶⡍⣧⠐⢖⠚⠛⠒⢤⡲⣼⠌⠛⠀⠉⠈⠁⠈⠒⠾⣅⠐⣡⠖⠋⠉⢉⠏⣰⡛⢈⣴⡿⢿⣛⣛⣉⣬⡱⣄
⠀⠀⠐⢠⡽⣿⣟⠁⢴⡋⠀⡆⠒⡆⢹⣿⣺⠀⠈⠢⡀⠀⢄⡽⣠⠴⠦⠶⠶⠰⢦⠠⡄⠀⠀⠻⡥⠀⣀⡴⠋⢰⣣⣿⣿⠋⠘⠛⠻⣯⡉⠛⢿⣾⣉⠆
⠀⠀⠀⠀⠳⡘⣟⡳⠦⣵⣦⣬⣉⣠⣿⠟⣼⠷⡃⠀⢊⢲⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠓⠄⠀⠀⢘⡋⠍⡀⠐⣾⡞⣿⣿⡀⠻⠛⢀⣿⣃⣴⣿⢣⡏
⠀⠀⠀⠀⠀⠳⣹⢿⣿⣶⣷⠾⠟⠋⠑⡼⠃⣠⠔⢚⡯⠋⠀⣠⡶⠟⠋⠓⠆⠀⢰⣆⠀⠀⡁⠀⠀⣋⣭⣍⣀⠈⢷⡹⠿⢷⣤⣟⣏⣍⣭⡍⢩⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠪⠧⣴⣰⣮⣶⡛⠠⠾⣁⣠⡻⠁⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢀⡷⠀⠀⠈⠓⣦⡙⠧⣄⣨⣹⣛⣋⣧⠼⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⣯⣇⣉⣘⣱⣳⢦⡀⢩⠁⠀⠀⣿⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠼⡻⠛⠛⠛⢉⣤⠶⠛⠋⠙⣹⡭⠁
⠀⠀⠀⠀⠀⠀⢠⣏⣵⢛⣩⡭⢟⡉⠛⣿⣿⣿⣎⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠠⠂⠀⠀⡐⠓⣷⣟⣵⣿⠿⢻⡟⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⣾⢰⣾⢟⣏⠐⢿⠈⠑⠚⠛⣿⠟⣆⠀⠀⠈⢦⡐⣄⠐⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠁⢠⡿⣼⣿⠟⢠⣦⡙⣿⡶⣌⣘⡆
⠀⠀⠀⠀⠀⢠⠷⣾⣯⣈⡻⣶⡶⡆⠀⠀⢠⡟⣼⠈⢧⡀⠀⠀⠁⠺⣀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⠀⠀⠸⣧⢻⢿⡗⠬⣍⣴⡿⠇⠘⣷⣺
⠀⠀⠀⠀⠀⠉⠛⠳⣭⣫⠉⠁⠀⠛⠢⠀⡾⢰⡿⣇⠀⣧⠀⠀⠀⠀⠀⠀⡍⠳⡤⢀⠀⠀⠀⠀⢸⡤⠒⠀⠉⠀⣾⠻⢶⣤⣍⡛⠿⣟⡯⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠘⢧⢸⣿⣿⡀⣺⠀⠀⠀⠀⣀⣠⡿⠄⠘⡌⠂⠀⠀⠀⡸⠀⠀⠀⠀⢀⡏⠉⠚⠾⠼⠚⠚⠁
⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢿⡿⠓⠹⡷⣌⣈⣁⣁⣀⣠⣤⣤⣘⣄⠀⢀⡜⠁⠀⠀⠀⢀⠜⠀⠀⠀⠀⠄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡉⠒⠒⠀⠐⠒⠀⠀⠠⠄⠒⡀⠀⠹⡌⠲⢤⣀⡀⠀⠀⠀⠀⠁⠀⠸⣄⠠⠐⠒⠒⠋⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠕⢲⣮⢦⡀⠀⠀⢙⡀⠀⠀⠀⠀⢦⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢒⣄⣨⡁⠀⠀⠀⠀⠀⠈⠓⠀⠈⠒⠠⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠤⠤⠤⠤⠤⠤⠐⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⠶⠤⠤⠤⠤⡴⣶⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣤⣤⢤⡄⣤⣥⣾⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣮⣭⣵⣿⣭⣍⣩⠼⣯⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⠉⠀⠐⠃⠉⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠣⠄⠁⠀⣤⣀⠀⠈⠐⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⠁⠀⠈⠉⠀⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠟⠛⢳⡖⢂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡔⠀⠀⠀⣸⢿⢈⡽⠓⠶⣤⡴⠆⢀⣐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⠷⣴⣉⡠⠈⠸⠊⠁⢀⠔⠁⠀⣀⣽⣯⣽⡷⣷⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣤⣉⣁⠓⢤⣰⣶⠃⠀⠀⠚⠿⣿⡿⣉⣃⡈⠑⡀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠿⠍⠉⣙⠁⠰⣶⣿⢰⠀⠛⠁⣀⠘⢿⣿⣭⣿⣿⡟⠛⣤⡀⠜⡿⣾⣇⠀⠀⢀
⠀⠀⠀⠀⢠⣶⣾⣿⣯⡖⠶⠓⠒⢒⣼⠿⢿⣥⣠⣮⢹⣶⣆⠀⣩⡗⠐⠀⣸⣿⡿⣷⡿⢅⡥⠂⣠⢞⣿⡆
⠀⠀⠀⠀⠈⢲⣭⣭⣭⣭⣭⣭⣥⣤⣴⡖⠁⠀⠉⠻⡞⢿⡙⣧⠍⠉⠐⢀⣈⣽⠛⣡⠛⠿⣧⣽⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⡛⡛⠩⠍⠙⠀⠀⠀⠀⠀⠘⠂⢛⢿⣄⡰⢶⣆⣍⡠⠊⠁⣡⢞⣽⢿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠰⠛⠠⣼⠀⡘⠑⠛⠉⠐⡛⠛⢹⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⢀⡄⡙⠒⠇⣀⣰⡛⠋⠁⣰⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣀⡠⢾⠿⣋⡄⣶⣾⣿⠧⣼⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡔⠛⠛⢡⡾⠿⠿⠚⣿⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠏⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣬⣍⣈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⠀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⡁⠀⠀⠑⠀⠀⠠⠂⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣧⢠⣶⣶⡀⠀⣠⣶⣶⡀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⢀⠒⢧⠀⠀⠀⠐⢄⠀⠀⠀⠀⡀⠂⠀⠀⠐⠄⠀⠛⠋⠁⢠⣿⣒⣄⠀⠀⣿⣿⣿⠈⢻⣿⣿⣶⣿⣿⠟⠀⠀⢸⠄⠀⡇
⠀⠀⠀⠀⢀⠂⢀⠂⠀⠀⠀⠀⠀⠁⢢⡄⠈⠀⠀⠀⠀⠀⠊⠀⢱⣶⢦⡻⠿⣿⠏⠀⠀⣿⣿⣿⠀⠀⣹⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⢀⣿⣷⠃⠀⠀⠀⠀⡠⠔⠲⡅⠈⢄⢀⠴⠶⠀⠀⠑⠠⢿⣿⣿⢷⣶⡀⠈⠀⠀⣿⣿⣧⢀⣼⣿⣿⠿⣿⣿⣦⠀⠀⢸⣄⣠⡇
⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠁⠀⣠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠧⠐⠁⠀⢿⣿⣿⠈⠻⠿⠃⠀⠙⠿⠟⠀⠀⠀⣿⣿⠃
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠂⠀⠀⠀⠀⠀⠰⣄⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣮⢥⡤⠄⠼⣉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠔⠋⣈⠷⡀⢸⡇
⠀⠀⠀⣦⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡅⠰⠚⢀⠠⣤⠣⢸⡇
⠀⠀⠀⠉⠀⠚⠉⢀⠀⢀⠲⢶⣶⠶⢖⠀⣸⠟⠁⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⠠⠴⠃⢉⣀⢆⡓⠋
⠀⠀⠀⣀⣀⠀⣀⢀⡀⠀⠉⠀⢦⣉⡉⠀⠐⠀⠼⢋⡼⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⣁⡠⠐⢺⡔⠺⠉⠠
⠀⠀⠀⡇⠈⠉⠉⠈⡇⠀⡄⠀⢨⠳⠇⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠟⠈⢋⣌⠙⠁⠀⠀⠀⠀⡀
⠀⠀⡇⡇⠀⠀⠀⠀⡇⠀⡇⠀⢘⡓⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣿⠃⠀⡐⠀⠀⠀⠀⠀⠁⠝⠁⠀⠀⠀⠀⢀⢠⣌⠀⠳⡀
⠀⠀⠳⢧⢶⡴⠒⠞⠁⠀⠑⠖⠾⠥⠂⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠿⡄⠀⠘
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠂⡠⣄
⠀⣾⣀⠀⠴⢂⠘⣢⠀⠀⢤⣄⠈⣥⠞⠋⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⣠⠁⠀⠀⠀⠀⠠⠤⡤⠦⠐⠃⠀⡜⢠⠁⣼
⠀⠈⡛⠟⠣⣤⡾⠟⠀⠀⠀⠈⢉⠹⠦⠀⠈⠁⠀⠀⠀⠀⡀⠀⢀⠈⢳⡀⠀⠻⣷⣿⢿⣮⡁⠀⠀⡈⠬⠭⠄⠁⠀⢀⡀⠤⠊⠀⣘⢀⡇
⠀⠰⣦⣤⣤⠆⢠⠀⠀⢠⠀⠀⠘⠓⠂⠠⣤⡤⠀⠀⠀⠘⠟⠃⣸⡟⠁⠃⠀⠒⣫⣴⣿⣿⡿⠀⠐⠀⠀⣀⣤⣦⣴⣶⡄⠀⠀⠀⠇⢸⠃
⠀⠀⠀⠈⠀⠀⠘⠻⠶⠟⡀⠀⢀⣾⣷⠄⠀⠀⠀⠀⠸⢿⣦⠀⠙⠃⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠸⣷⣷⡟⠛⣷⣿⡿⠃⠀⠀⢠⢓⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢦⡈⠁⠙⢦⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⣷⡤⠀⠀⠀⠀⣀⣀⡀⢀⣌⣿⣷⠶⣾⣿⡇⣀⡀⠀⠸⣭⡇
⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠛⠛⠃⠀⠛⠛⠉⢠⡄⠘⠿⣿⡿⠂⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⠃⠈⠻⣦⡀⠀⣾⠟⠋⢀⠠⡄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⢽⣿
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢈⢁⣀⡀⠀⠈⠁⠀⣧⠀⡀⠶⣠⣴⡁⡐⠚⢸⣿⠑⠊⠉⡇⠀⠀⢀⣿⣧⠀⠀⠀⠀⠸⣼⡇
⠀⡇⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⢰⣴⢶⡜⣦⡆⠀⠀⠀⢀⡀⠮⣩⣞⣃⠶⣠⠴⠤⣸⣿⠀⠀⠀⡇⠀⢠⡋⣼⣿⣷⠀⠀⠀⢰⡟
⠀⣇⠀⠀⠀⡸⣤⣀⣀⣀⣆⠀⢸⡿⢾⡇⢿⡇⠀⠀⠀⠈⠙⡛⠦⠈⠋⢛⠷⠀⠉⢹⣿⣤⣀⣴⡇⠀⠸⣿⣿⣿⡿⠀⠀⠀⣼⠇
⠀⠀⠉⠉⠉⠀⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠖⠈⠁⠐⠒⠂⠙⠛⠛⠛⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠛

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠠⡀⢀⡀⠀⠀⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢁⣒⠦⣄⠀⢤⠤⡼⡛⠧⠉⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⡀⠀⢠⣄⣀⠐⠙⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⢸⠄⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠰⠁⠀⢸⠁⡃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣠⠞⠑⠲⠶⠄⠀⠀⢀⠇⠀⣀⡿⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠐⠶⠻⠆⠀⠁⡀⡀⠀⠀⣸⠀⠀⠀⠠⠖⠐
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⡵⣧⢀⣀⣀⢠⡀⠀⠀⠀⠐⣼⠶⡤⠞⢙⣤⡀⢀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⡿⠁⠀⠘⣎⣹⠋⠈⠑⡀⣶⣦⡀⣌⣀⣀⣠⣼⣅⠀⠀⠉
⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠑⠤⠴⠶⠋⠛⠀⠀⠀⠸⣏⢉⣉⣟⣿⣯⠄⠀⠆⢁⠄
⠀⠀⠀⠀⠠⠄⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣰⣉⣯⣉⠉⠛⠻⣆⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠒⠊⠀⠀⠀⠐⠈⠰⡆⠠⠄⡀⠀⣈⠢⢀⠜⠹⠓⠟⢿⡃⢀⣀⡸⠂⠀⠲⠄⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠀⠃⠀⠀⠀⠈⠑⠀⢀⡄⠀⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⢰⠋⠀⠏⠃⠀⠀⠂⢀⡅⠀⠀⣀⠀⠀⠈⠀⢀⠜⠃
⠀⠤⠂⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⢋⠔⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠷⠞⢫⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠸⣇⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⡢⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠂⠀⠀⠀⠀⢶⡦⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⢌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠙⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢴⠆⠀⠀⠨
⠀⠀⡕⠀⡀⠀⠀⢰⣶⠀⣦⠀⢀⣇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢠⠀⠀⢸⡿⠀⠘⢦⣘⣟⣠⠞⠀⢰⡄⠀⠰⠀⠀⢰⠄⠀⣆⠀⠀⡆⠀⠀⠀⠀⡄⠀⢀⠦⠀⢰⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⡄
⠀⠘⠀⠀⠾⡿⢀⡼⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⢳⣄⢻⣟⣠⠟⠀⠀⠹⣄⡺⡿⣀⣀⠀⠀⠻⣄⡘⣿⣂⡾⠀⠀⠐⢿⣇⣀⡼⠃⠈⠳⣤⣀⣻⠿⣀⡾⠁
⠀⠀⢰⡟⣿⣿⡏⠀⠀⠀⠀⢠⡿⠻⣧⠀⠀⠀⠀⠉⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⡏⠉⠻⠆⠀⠈⢹⣿⣯⠀⠀⣠⠞⣿⣿⡅⠀⠀⠀⠀⠀⢹⣿⣿⠉
⠀⠀⠀⠳⣿⣿⡇⠀⠀⠀⣰⡟⠀⠀⠘⢷⡀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠘⠇⢸⡿⣧⠀⠀⠀⠀⢀⣿⣿⣿⡆⠈⠃
⠀⠀⠀⠀⣿⢸⡇⠀⠀⠘⠋⠀⠀⠀⠀⠈⠛⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠉⣿⢻⡏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠈⢻⢻⡟⠁
⠀⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠀⠀⠀⠀⠀⠀⠿⠸⠇⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠾⠃⠼⠃⠀⠀⠀⠀⠸⠸⠇


⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠘⡒
⠀⠀⠀⠀⠀⣠⣬⣭⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣃⠀⠀⠀⣠⡄⠈⠁
⠀⠀⠀⠀⠀⢿⣿⡿⢿⡿⢶⡤⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣷⢶⣯⠅⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡆⠀⢠
⠀⠀⠀⠀⠀⠀⢻⡥⣮⡁⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣀⠀⠀⠘⠉⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⡄⠀⠑⠀⠀⠁⠀⠁⠀⣷⡆
⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⠈⢹⣧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⢧⡜⠀⣴⣿⣷⣤⣤⣠⣿⠁⢀⣀⡄
⠀⠀⠀⠀⠀⢀⣿⠁⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢀⣼⠇⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠾⡆⠀⠀⠌⣧⣄⢙⡿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠉⠀⠀⠀⠀⠀⣿⢿⣇⠀⠀⣿⣿⣷⠀⠀⢰⡄⠙⣿⣷⣻⣿⣿⣧⣦⡄⠈⠓⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠙⣷⣶⣮⣩⣥⣴⠇⣝⣝⣄⣿⣿⣧⣿⠙⢿⣿⠟⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡻⠿⢿⣿⣿⣿⠀⠿⣿⠟⣿⣿⣾⡻⢷⣶⣶⣾⡿⠛⠉
⠀⠀⠀⣰⣷⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣹⠾⣿⣾⣿⣿⡟⣿⡇⢸⣿⣿⣿⣷
⠀⠀⠀⢈⣭⡁⠀⠀⠈⠀⠀⠀⡀⠀⠀⢈⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢸⣿⣼⣿⣦⣿⣿⣿⣿⡇⣿⡇⣸⣿⣿⣿⣿⣇
⠀⠀⠀⢸⣿⡟⠶⠶⠛⠂⠀⠀⠛⠲⠶⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢸⣿⡇⣻⣯⣿⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⣿⣿⣿⠸⣿⡇⣿⡆⣿⡏⣿⡟⠃⠙⠋⠉⢹⣿⢹⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠿⠗⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⢸⣿⠁⠈⢸⣿⡇⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⢸⣿⠀⠀⠀⠉⠀⠉⠀⣿⡇⣿⡇⠀⠀⠀⠀⠸⠟⠘⠿
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠿⠇⠿⠇

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢀⡔⣂⠀⠀⠀⠀⣶⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠙⠟⠀⠀⠀⣠⠛⠦⠀⠀⠀⠀⠉⠻⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⢀⠼⠑⠆⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠀⠛⠙⠂⠀⠀⠀⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠁⠀⠀⠀⠀⠀⢠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⣦⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⢚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣤⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠗⡀⠀⠁⠀⡀⠀⠀⡠⠀⢓⠴⠊⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠈⣠⠀⠈⠑⢤⢠⣩⠚⠋⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⡖⠰⠿⠁⠛⠁
⠀⠀⠀⠀⠀⢠⣿⠋⠀⢀⣾⣿⣷⡤⠀⠶⠚⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠏⠀⠉
⠀⠀⠀⠀⢀⣾⠃⢀⣴⣿⣿⠿⠋⠀⠈⣠⣄⡈
⠀⠀⠀⠀⣼⠃⣠⣾⡿⠛⠁⣀⣤⣶⣿⠿⠛⠋⠁
⠀⠀⠀⣸⢃⣾⠿⢋⣠⣴⠾⠟⠋⠁
⠀⠀⢰⣷⣿⠵⠞⠋⠉
⠀⠀⠛⠉

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁

⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠻⠏⠁⠀⠀⠀⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠐⢶⡀⠀⠀⠸⣧⣄⡀⢠⣾⡇⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣧⠀⠀⠈⡀⠀⠇⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣰⣦⣾⡷
⠀⠀⠀⠀⠀⢠⣴⡄⠀⠀⠀⡆⠀⣾⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠛⠿⠀⠀⠀⢀⠫⠄⢂⠁
⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠈⠛⠁⠀⣴⣦⣶⣆⠀⠀⠀⣿⣿⣇⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣦
⠀⠀⠀⠀⠻⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢸⣿⡇⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢻⣿
⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢠⡤⠀⠀⠀⡀⠀⣿⠃⠈⣿⡁⠀⠸⠝⢛⣛⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⢀⡀⢀⡀⠀⢸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠿⡿⠟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣴⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠉⠹⣦⣤⠁⠀⠘⡟⠙⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣤⣄⣴⣿⡏
⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠋⣁⠀⠀⠀⠀⠀⠀⢀⠏⠘⠀⠀⠀⠀⣻⣦⡄⠀⠀⠀⠉⢻⠟⠋
⣰⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⣼⡁⠀⠤⠄⠀⠸⠛⠇
⠿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⣿⣦⣠⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶
⠀⠀⣰⣷⡀⠀⠀⠀⠀⢀⡀⠉⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⣦⠀⠀⠷⠀⠀⠀⠀⠹⣿⣿⡇⠀⣠⣤⣴⣶⣦⣤⣼⣿⣿⣿
⠀⠀⣿⣿⣿⡄⠀⠀⠀⡚⠉⣷⡆⠀⠀⠀⠀⠄⠀⢠⡤⡀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⢰⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿
⢀⣴⣿⣿⣿⡇⠀⠀⢠⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣼⣿⣿⣿⣿⠏⠁⠀⠈⠙⣇
⣿⣿⣿⣿⡿⠁⠀⠀⠀⡀⢸⣏⣿⣿⠀⠀⠀⠀⠀⠐⠀⠀⣠⣄⡀⣰⠒⢲⣾⣆⠀⠀⠀⣀⣿⣿⣇⡈⠃⠀⠀⠐⠀⠘⢿

⠀⠀⠀⠀⠀⠄⠀⠠⠠⠀⡀⠀⠀⢀⡀⢀⣠⣤⡟⠀⠀⠀⢀⣀⣤⢀⠀⠀⠀⠀⠀⠀⢠⡤⡄⠀⠀⡀⡐⢀⠤⢤
⢠⢀⠀⠂⠃⠀⢃⠀⢀⣐⠁⠈⠁⠀⠛⢹⠖⠚⠃⠀⠀⠀⠀⠉⣀⠀⠁⠀⣤⠶⠓⠂⠈⠀⢠⠀⠀⠀⠠⢈⠀⠐⠂⠀⠀⠁⠆⠁⠀⠉⠀⠀⢀⣐
⠘⠀⠀⠀⠁⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⡈⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣀⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢠⠈⠁⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢈⣙⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⢸⣶⣂⠀⠂⣽⡟⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣤⠄⠉⠉⠀⢠⢿⡏⣶⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡄⠀⠀⢀⡿⠐⣿⠛⠀⠀⣀⠞⣯⠳⡟⠘⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠋⣹⣿⡇⠀⠀⡍⠀⣠⡽⣿⠿⣿⠋⠀⡿⠊⢀⣸⣯⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠊⡀⠂⢸⣿⣿⠀⢠⡶⡖⠃⣿⠋⠁⠀⠉⠀⠀⠑⠀⠅⠚⠉⠹⠾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠈⠀⠄⠀⢈⣿⣿⠉⠀⡀⢛⣁⣨⡟⠀⠀⠀⠀⠀⠀⠃⢄⠻⢆⣛⠤⠀⣽⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡠⠂⠈⠛⠋⢳⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠓⠤⣀⣶⠿⠿⢶⣿⢿⣾⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢧⠀⠈⠃⠼⣷⣠⠀⠀⠀⠀⠄⠀⣻⣯⣄⠀⠀⢉⡿⠋⡄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠤⣿⡁⢀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⢀⠐⠞⠋⣻⡅⠈⠁⠈⣡⣶⣶⣤⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣤⡀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠜⠀⣠⣾⡿⠃⠀⣠⣾⣿⣿⠟⠓⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⣿⠁⣀⣤⢠⣀⡘⣀⣁⣀⡁⣉⣀⡀⠀⠏⣠⣾⣿⣍⠃⠀⠈⢻⣼⣿⠛⠂⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠻⠃⠀⣰⣀⣿⣿⣀⣭⣿⠟⠆⠒⠀⠃⢠⣿⣯⣭⠙⡃⠀⠀⣮⠉⠈⢀⡀⠀⠀⠀⠻⡄⠀⠀⡀⠉⢀
⠀⠀⠀⠀⠀⠀⣾⠂⠀⢰⣿⢿⡿⠅⣿⣿⠀⣧⠄⡄⢀⣞⣻⡿⠁⠀⢀⠀⠀⠈⠳⠄⠜⠁⠀⠀⠀⠀⠹⠆⠀⠈⢦⠀⠳⣄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠿⣺⢋⡤⣿⣿⠀⠈⠘⠃⣶⣻⠟⠁⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣾⡟⢁⢿⡏⠀⠀⠀⠚⠋⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠐⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠆⠸⣝⣨⡇⣿⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢹⡆⠀⠀⢠⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⢀⢠⣜⣿⣿⣧⡏⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢠⣶⠀⠀⠑⡀⠘⡀
⠀⠀⠀⠀⠀⠀⢸⠀⢰⣿⣿⣿⣿⡧⡇⠀⠀⡀⡆⢸⣟⡏⠈⣿⡄⠐⠀⢶⣤⣤⢤⣠⣤⣤⣤⡴⠶⠶⠊⠀⠀⠀⠸⢿⣆⠀⠀⠹⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠼⣿⣿⣿⣿⣿⡇⠀⠀⠃⠀⢸⣽⠃⣸⣿⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠔⢏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢩⠿⣿⣿⣯⡇⠀⠀⡀⠄⠘⠃⠐⢿⡃⠀⠀⠀⠀⠀⠀⢰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⣖⣿⣿⣿⡇⠀⠀⡇⡆⠀⠀⢠⠀⠈⡉⠀⠀⠀⠂⣤⣤⣿⣯⣀⣥⣤⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⡇⢀⣀⡇⠀⠀⠥⢤⠀⣠⣤⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣧⡼⡇⠀⠘⠆⠀⠀⠁⡛⣰⡗⠀⠀⢀⠀⠀⠈⠿⣿⣿⠹⡏⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠰⡀⠀⠀⣯⠃⢀⣀⣁⣀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢻⠀⢻⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠂⠀⢴⠊⠁⠀⠀⣋⡇⠈⠉⠻⠋⠁⠀⠂⡤⢤⣄⣀⡶⢄⣸⡀⠈⣇⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⣤⡴⣿⣷⣴⠟⠓⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠒⢀⠀⠀⡟⠁⢲⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⢠⣿⣷⢶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⡟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈

⠀⠀⢰⠒⡆⣴⢳⡄⡆⢰⢠⡞⠢⠀⠀⢰⡆⢆⣄⠆⢰⡆⢰⡞⣦⢰⣛⠂⣶⡀⡆⣾⡓⠀⣞⠂⢴⡓
⠀⠀⠸⡤⠇⠟⠹⠆⠣⡼⠘⢧⠟⠀⠰⠟⠷⠸⠻⠇⠟⠳⠸⠋⠧⠸⠤⠄⠿⠹⠇⠿⠤⠀⢤⠟⠢⡼⠃


⠀⠀⠀⠀⠀⠘⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠐⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣅⣤⣤⣤⣤⣾⣿⠀⠀⣀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⠟⠛⠀⠀⢠⣦⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠹⡿⠋⠀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠷⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠇⠀⠀⠀⠛⠛⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣀⡀⠀⠀⢿⣿⠿⠀⠀⠀⠀⠛⠛⠛⠀⠀⣀⣠⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠸⣿⠿⠗⠀⢀⣀⡀⠀⠀⠀⢾⣿⣦⠀⠠⣶⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠌⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠚⠿⠿⠃⠀⣠⣶⣶⠀⠘⢿⣿⠗⠀⠀⠈⠛⠉⠀⠀⠉⠙⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣀⠀⠀⠀⠀⠰⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⠷⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣛⣿⡿⠟⠛⠿⢿⣿⠛⠛⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⣿⠀⠀⠀⠀⠈
⠀⠀⠐⠂⠛⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠐⠂⠐⠒⠚⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿



⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⡀⠦⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣤⡄⠀⡀⢀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠿⠟⠁
⢠⠀⠀⠀⠀⠀⠒⠒⠃⠀⠉⠀⠀⠀⠈⠑⣿⠊⢠⣦⣼⠃⠀⠀⢺⠟⡀⢿⢋⠁⠘⣕⡏⣱⣶⡦⠀⠀⠀⠁⠀⢰⡿⠃⠀⠀⠀⠀⣤
⢚⣶⣦⠀⠀⠀⠰⣦⠘⣧⠀⠀⠀⠄⠀⠀⣀⡀⠿⠃⠋⠀⠀⠀⠀⠀⢱⡏⠀⠀⢸⣟⠀⠸⠟⠁⠸⠇⢀⣀⢀⡜⠁⠀⠀⢤⠔⣆⣿
⢀⣽⣿⣆⠀⢀⡋⠁⠷⠈⠀⠀⠀⠀⠀⣿⣿⣿⠆⡘⠃⠀⠀⠀⢸⣶⠀⠈⠡⠄⢀⠈⠀⠶⠀⢠⣖⠀⠀⠹⡿⠷⠾⠀⠀⠉⠠⢿⡶
⠛⠛⠋⠁⠀⠈⣇⣤⣶⣷⠀⠀⠀⣀⣀⠻⠿⠛⢸⡃⠀⠀⠀⠀⠘⡥⢂⡀⠀⣰⠀⠀⢠⣾⣷⡌⢿⡦⠀⠐⠀⠀⣴⣦⡀⠀⠀⢀⡀
⠀⠀⠀⣴⠃⠀⣿⣿⣿⡿⣀⣶⣾⣿⣿⣿⣶⣶⡿⠋⠀⠀⠀⢀⡀⣴⠛⠛⢠⠟⠲⣶⣾⠟⠋⠀⠀⠀⠀⢰⡶⠿⠚⢿⣿⠉⠻⣭⡀
⠀⠀⠀⠻⢿⣴⠟⠻⣿⣄⣿⣿⠟⠿⠿⠿⠟⣻⠁⠀⠀⠀⠀⠀⠀⠛⠶⡖⠻⠂⠀⠀⠁⠃⠀⠀⠀⠀⠀⠸⡶⢰⣄⠈⠁
⣀⣀⣀⣀⣠⣗⣀⣀⣹⣿⣿⣃⣀⣠⣿⣶⣾⣃⣀⣀⣀⣀⣀⣴⣗⣈⣀⣀⣀⣠⣆⣀⣀⣿⣦⣀⣀⣀⣀⣢⣀⣀⣀⣿⣀⣀⣀⣀⣾
⣿⣿⢛⠻⠟⡛⢻⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⣀⠑⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣞⣿⠟⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠠⣾⠂⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⠀⠁⠺⠁⠀⠀⠀⠈⠄⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⢀⣤⣀⠋⠉⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠀⣠⠀⠀⠀⠨⠀⠀⢠⣶⠀⠀⠀⠀⠄⠠⠄
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⣥⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⠀⠀⠀⠀⠀⢰⣋⠀⠀⠀⠀⠀⠂⠀⢀⠁⡁⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠤⠊⠕⠀⠀⠀⢠⠂⠀⣀⠠⡀⠀⠀⢀⣤⠀⡠⠀⠒⣾⠇⠀⠀⠀⠀⠀⠁⠰⠂⠀⠁⣀⠀⠀⠀⠀⠀⠀⠒⠀⢭⡓⠶⣄
⠀⠀⠠⠂⠀⠀⠀⠀⡠⠢⠄⠜⠀⣨⠀⠀⠀⡇⠀⡘⠃⠀⡀⠀⠀⠀⠀⠀⠑⡄⠀⠘⠄⠠⣤⡢⠀⣠⣵⠤⡂⢀⡢⢄⠙⢦⡀⠀⠀⠀⠻⠃⠀⣿⠄⠘⡆
⠀⠀⠀⠂⠀⠀⠀⠀⠙⠃⡀⠀⢀⠠⠂⠀⠀⡇⢰⡁⠙⠬⠁⡆⠀⠀⠀⠀⠀⠘⢄⠀⣠⡀⠻⠐⠀⢹⠚⢀⡁⡠⠀⡘⠀⢆⢣⠀⠠⢇⠄⠀⠀⢀⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠘⠦⠘⠀⠂⢤⠀⢣⡐⠎⠑⠢⠞⠀⢠⡐⢢⠀⠀⠀⠈⢆⠀⠀⢀⠀⠂⣁⠎⠀⠭⣤⠜⠀⢀⡸⠙⠀⠀⠂⣠⠤⣊⠎⣡⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠖⠁⠀⠀⠈⢇⠀⠈⢰⣒⠀⢰⠀⡎⠀⠈⡄⠀⠀⠃⠀⢮⠀⠀⠗⠤⣀⠀⠀⠀⠊⡰⠋⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡇
⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡀⠉⠨⡄⠈⠑⢤⡁⠀⠀⠀⡐⠀⢹⠺⡀⠀⠀⠉⠁⠠⠭⠤⠤⠐⠉⠀⠀⠀⢀⣠⠴⠂
⠀⠀⡘⠀⡘⢃⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣄⠘⢇⠀⡇⠀⠀⠁⠀⠀⠀⡹⠀⠀⠠⠀⣤⠀⠣⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠃
⠀⢀⠃⢀⠃⠸⡀⠀⠀⠀⠀⠤⣭⡭⠰⡍⠙⠂⠀⠁⠷⢀⣀⣀⠔⠉⠉⡄⠀⠀⠐⠊⠉⠀⠀⠱⡄⠀⠪⡙⠒⠤⣤⠔⠚⠉⠀⠀⠀⠀⠀⡠⠁
⠀⠘⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠙⠛⠒⠀⢄⠀⠒⢂⠐⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡁⠘⢆⣴⡡⢄⢀⠎⠀⠀⠀⠀⠀⠀⢀⠴⢤⡤
⠀⠘⡄⠐⠓⠤⠵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡀⢃⠀⠀⠀⠀⠀⡤⡠⠙⣄⠀⠀⠀⠀⢧⡄⠀⣼⡦⠀⠏⠀⠀⠀⠀⠀⠀⡴⠓⠊⠁
⠀⠀⠈⠢⡀⢠⠾⠕⢰⠆⠀⠀⠀⠀⠀⠀⡴⠾⠃⠀⠘⠄⢆⡴⣿⡟⠚⠹⠟⠂⠈⢦⠀⠀⠀⡇⠀⠀⠈⠉⢙⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⠢⡀
⣀⣀⣀⣀⣀⣁⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣎⣴⣋⣀⣀⣀⣒⣃⣀⣘⣆⣀⣀⣇⣀⣀⣀⣀⣸⣀⣤⣄⣀⣄⣀⣀⣀⣀⣀⣀⣘⣦⣀⣀⣀⣀⣀
⣿⣿⡟⡛⠿⠛⡻⠻⣟⢟⣿⢟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⡆⠀⡖⠀⣶⠀⣶⠀⢰⠀⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣧⣤⣧⣤⣧⣤⣿⣤⣿⣤⣼⣤⣼⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠉⢉⣉⠉⠉⠉⠉⠉⠁⢸⡇⠀⠀⠀⠀⡠⠊⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⡏⠉⠙⡆⠀⠀⠀⠀⢸⡇⠀⠀⡠⠊⠳⢄⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣟⠛⢻⡁⣠⠀⠀⠀⢸⡇⠀⣼⠁⠀⠀⢈⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠁⠀⣠⠟⢧⠀⠀⠀⢸⡇⠀⠘⠦⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠉⠉⠀⠈⠉⠉⠉⠀⢸⡇⠀⠀⠀⢠⠴⠒⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠉⠉⠀⠈⠉⠉⠉⠀⢸⡇⠀⠀⢰⠃⠀⠀⣠⠞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠂⢸⡇⠀⠀⠸⣄⣠⠞⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠃⠀⠀⠀⠘⠳⠤⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⠀⡀⠀⠀⠀⡀⠀⢀⢀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠘⠀⠚⠀⠂⠈⠁⠈⠁⠈⠀⠀⠒⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠂⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⢀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠈⠀⠊
⠀⠀⠀⠀⠀⠀⡴⠿⠿⠿⠿⢿⢸⠿⠿⠿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠻⢿⡿⠃⠘⠿⣿⠿⠛⠛⠛⠛⣻⠋
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡼⠸⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣠⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⢷⠀⠀⣠⠞⠀⠀⠙⢆⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠁
⠀⠀⠀⠀⠀⠀⠘⣧⡴⠁⠀⠀⠀⠀⠈⠳⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠐⠺⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠷⠦⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤
⢀⣠⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣶⡦⢶⣶⣾⣿⣿⣿⣿⣿⣿
⣼⡏⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⣤⢢⡄⠀⠀⠀⠀⠀⠀⠸⣏⠉⠉⣿⡄⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⣿⠁⠘⣯⠉⠉⠉⠉⠉⠉⢹⡆
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣸⡇⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸⡇
⢿⣆⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⣷
⠀⠙⢻⡿⠀⠀⠀⠄⠀⠀⠀⣾⠁⠀⢹⡄⠀⠀⠠⠁⠀⠀⢸⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣧⣄⣀⣀⡀⠀⠀⢀⡿⠀⠀⢸⣇⠀⠀⠀⣀⣀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢀⣽
⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣿⠿⠿

⠀⠀⠀⠀⠀⠠⠤⠤⡀⡄⣀⢤⡄⠠⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣲
⠀⠀⠀⢀⢄⢣⢠⠆⣑⠤⠒⠀⣜⡂⠜⠏⠁⣛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠂⣤⢠⣄⠂⣴⠂⠀⠀⠀⠀⠀⠀⠉⣠⠹
⠀⠐⠿⢩⡀⢻⢀⠚⢩⡘⠂⠐⠁⢠⠁⢄⠀⢅⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣡⠃⣤⢰⠄⠈⣠⡀⣊⣺⠱⠍⣄⡨⢅⣈⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿
⠀⠀⡴⠉⠣⣌⣠⣧⣰⡄⣦⠠⠋⠀⣉⢈⠏⣠⠞⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⣾⣿⣇
⠀⠀⠗⠰⡦⢤⠔⠨⢷⢣⡈⣴⠧⢊⣡⠀⠂⣡⡄⢆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⡁
⠀⠀⠀⣊⠀⡊⢞⡅⢸⠡⢠⠡⡀⣄⢹⡔⠒⣬⡇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⣿⡄
⠀⠀⠀⠉⠉⠻⠖⠓⠟⠣⠚⠇⠈⣀⠼⢘⠊⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠶⠚⠂⡬⠀⢠⡄⠘⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠉⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⢀⠀⢠⠈⠂⣤⡀⠄
⠀⠀⡠⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠖⠁⠂⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡇⠘⡀⣿⣿⣷⣤
⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢳⠄⣀⠀⠠⢰⠀⠀⠈⠈⠁⠈⠑
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣄⠀⠀⢄⣀⡰⠖⠒⠀⠀⠀⠈⢆⡀⠀⡠⠂
⠀⠀⢄⠶⠴⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⢬⠴⠶⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⠚⠰
⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠠⠔
⠀⢰⠀⢀⠀⡀⢠
⠀⠀⡀⢇⣖⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠂⠀⣀⡀⠀⠀⠀⢄
⠀⠀⠈⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠈⠀⣀⣀⡠⢄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠉⠒⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠄⠐⣂⠈⠭⠍⢀⡐⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡄⠀⠀⡠⢈⠔⠊⠁⠀⠀⠀⠀⠀⠀⠁⠢⡈⢂⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⢠⣎⢱⡄
⠀⠀⠀⠀⢴⣶⠀⠸⠈⢛⠀⠀⠜⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠃⠀⠆⠀⠀⠀⢀⠉⠀⠀⢸
⠀⣶⣶⠀⠿⠻⠀⠀⢱⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠀⠀⡈⠀⠀⠀⢸
⠀⢹⡛⠀⠘⡎⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠀⠀⠀⠀⠁⠀⠀⠀⢨⠀⢀⡀
⠀⢸⠅⠀⠀⢹⠀⠀⢸⢰⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡄⠀⡁⢸⠀⠀⢙⢰⠀⠀⠈⢻⡛
⠀⢸⡀⠀⠀⠀⠀⠀⢰⢈⠀⠀⢡⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡐⠀⠀⡇⠘⠀⠀⢸⠸⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠒⠀⠀⠘⠄⠀⠀⠀⠑⢌⠂⠤⣀⠀⠀⠀⠀⢀⡠⠐⡡⠊⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢀⡸⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⠉⠉⠁⠠⠐⠁⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠉⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡄⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠃⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢢⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠸⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⢋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣼⠀⠀⢀⠄⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢱⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡄⠐⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡐⠛⢦⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠑⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠙⡆⠈⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠏⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⡸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢄⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠈⠛⠋⠀⠀⠈⠚⠂⠀⠈⠘⠂⠀⠀⣀⣀⠀⢀⣀⠀⢀⣀⡀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⣴⣦
⠀⠀⢀⣶⣶⣶⣆⠀⣀⣀⣀⡀⣀⣀⣀⡀⠀⠁⠈⠀⠈⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤
⠀⠀⠈⣿⣿⣿⡏⠀⣿⣷⣿⡇⣿⣧⣿⡇⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⠀⢀⣀⣀⠀⢀⣉⣉⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣶⣤⠰⣶⣶⡄⠀⣤⣄⠀⢠⣤⡀
⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠀⢀⣀⣀⡀⣀⣀⣀⠀⠸⠿⠀⠀⣠⣤⣤⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⣠⣄⠀⢸⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⣤⠤⣤⠀⣤⢠⣄
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣀⣀⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣀⣉⣉⣁⣀⣀
⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣹⡍⠁⠀⠀⣤⣤⡄⠀⠀⣤⣤
⠀⠀⠀⠛⠓⠀⠚⠓⠀⠀⠀⣰⣾⣿⡄⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠂
⠀⠀⢰⣖⣶⢰⣶⣶⡆⠀⠈⠙⠟⠛⣴⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣟⢻⡇⠀⢸⡟⣻⡆⠀⠀⠀⢀
⣀⣀⣈⣉⣉⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢰⡇⣿⡿⠟⢸⣿⢸⣿⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⣿⡇⠀⠈⣿⣾⡿
⠿⠿⠟⠟⢀⡦⠀⢀⡄⠒⠶⠶⣴⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⣾⣦⣸⡇⣾⣥⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠛⠀⢠⠏⣀⠀⣀⡀⠈⢣⡈⢃⠀⠀⠀⠀⠀⢹⠀⠀⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣷⡿⢻⣿⠋⠒⠶⠱⡌⠀⠀⠀⠀⠀⠈⠀⢰⣿⠛⣿⣇⣿⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⡏⣿⣿⡯⡿⣿⣿⢿⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠁⣀⠀⠀⠀⠀⣴⢷⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⣉⣉⣉⣀⣉⣁⣈⡠⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠿⠛⠃⠚⣿⣿⣴⣿⢿⣷⡿⡏
⠀⠀⠀⠪⡀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠐⢶⡤⠉⠁⠤⠤⠤⠄⠀⠀⠀⠀⠒⠲⠟⠁⠀⠀⠀⠀⠀⢐⠀⠉⣀⣠⣤⣄⣙⡿⠛⠛⠓⠚⠗⠺
⠀⠀⠀⠤⠇⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⣴⣋⣽⠽⠷⠾⣿⣿⡧⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠠⡏⠬⠉⡁⠀⠀⠀⠀⠀⡼⢀⡏⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠉⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⢂⠠⠀⡐⠑⢦⣤⠄⣆⢟⠀⠐⠌⢀⡦⠝⣢⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⢠⡤⠋⠀⠀⠌⠠⠤⠤⠠⠬⡄⠃⠋⢀⠈⢁⡄⣁⠀⠀⠀⠀⠀⢠⡴⣿⠯⠽⠿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⣀
⠀⠀⠐⣯⠴⠲⠜⠀⣇⠀⠀⠀⠀⠀⡄⢂⠠⠀⣠⣾⣿⣧⠀⠀⠀⢰⣿⣿⣷⣿⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢉⠥⢘⡶⠉⣿⣿⣿⠀⠀⠀⠀⠙⠻⢿⣿⡶⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⣠⠀⢆⠀⠀⠀⡀⠀⠠⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠄⠀⣑⠀⠀⠠⠤⠤⣮⣦⣼⣶⣶⣾⣿⣿⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⢹⡋⠿⠈⣶⠈⠳⣴⣆⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠘⠉⠂⠀⠀⢀⠠⣤⣤⣦⡄⠦⠠⢿⣶⣴⣧⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣀⣴⠋⣁⠀⠆⢀⡀⠃⠘⣿⠛⣧⢠⢤⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠄⠀⢀⡀⣠⠤⢤⡀⣁⠀⠒⠩⠀⣰⢬⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠟⠉⠉⡄⠉⢀⣀⠈⡅⠀⠁⣼⡟⡇⠀⠀⠁⠄⠤⠁
⠀⠀⠀⠀⠀⢸⣄⠁⢀⣢⣄⡓⠙⣘⣀⠀⠄⠀⠀⣘⠬⠻⣈⡁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⢰⠄⠀⢤⠀⠂⠈⠉⣀⠀⠀⠓⠈⣿⡇⠀⠀⡀⠀⡀⠴
⠠⠀⡶⠆⠠⠦⠾⠀⠠⠥⣼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠶⠀⠀⣀⠀⠄⠰⣷⠀⢀⡀⠃⢘⠁⢻⡇⠀⠀⠈⠀⠁
⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⢀⣤⣤⣍⣀⠴⠀⢀⣄⠠⠁⠄⠉⠀⠈⠁
⠀⠀⠀⠑⠀⠐⠀⠀⠀⠐⠆⠀⠀⠀⠶⠀⠀⠀⠦⠀⠠⡆⠀⠐⣤⠀⠀⠀⠀⠀⠀⠈⣷⠟⠻⣿⣿⣿⣿⣦⢀⡄⠴⠛⢆⠀⠄⢰⠴⠆
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⡀⢀⡁⠀⠀⠀⠶⠂⠀⠀⠀⢀⣘⢁⡀⠀⠀⠙⢿⣿⣿⠈⢀⡂⠀⢈⡀⠀⢀⠀⢴⠀⠀⠀⠀⢠
⠤⠄⠂⠈⠁⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣦⣤⡔⠀⠀⢬⡁⠀⠀⠀⠈⠁⢸⢿⠏⣾⣿⣿⣿⣿⣿⣿⣿⡀⡼⠀⠀⠀⢀⣾⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⡶⠾⠿⠿⠿⠃⠀⠀⠐⣿⡟⠁⠀⠀⠘⡧⢀⡀⠀⠀⢀⣤⠄⠀⣻⡟⠛⠉⠉⠛⠀⣿⠀⠠⠤⠤⠤⢤⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠟⡄⢰⣿⣧⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢠⠤⠞⠛⢢⣤⡾⣧⣿⠁⠀⠀⠀⠹⣿⣿⣀⠀⠀⠀⡜⣸⣿⣇
⡄⠀⠀⢀⣴⣶⣶⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⣴⣶⣶⡂⠀⠉⠀⢸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢻⣿⣿⣀⠀⣀⣀⣴⣿⠋⠛⠳⢄⠠⣷⣿⣿⣿
⠉⣀⡀⢈⣉⣉⠉⣁⣀⣀⣉⣉⡉⠉⡁⢀⡘⡛⢉⡉⠃⢀⣾⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠻⣿⣏⠉⠉⠉⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠘⠅⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡿⠀⠀⠀⢨⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⡄⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣧⠀⢠⠦⠀⣴⢖⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠆⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋⠿⠷⣨⢻⡀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡟⡸⡘⡼⡏⣯⣦⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢲⣾⣯⣶⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠓⠛⠛⠁⠉⠀⠀⠀⠀⢠⠱⢠⢣⢡⢳⢰⣿⠸⠸⣷⠢⠄⠀⠀⠀⠀⠀⠀⢰⣶⠚⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣀⡀⣀⣀⣀⣒⡀⠒⠂⠂⠘⢘⠀⡀⠂⠐⠰⠀⠀⠐⠒⢀⣀⣨⡇⡆⡜⡄⡈⡆⣼⢸⡇⠟⠘⡀⠀⠀⠀⠀⠀⠀⠀⢫⣥⣸⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠃⠀⠸⣿⣿⣿⠋⠈⢿⢡⡇⣿⣿⠋⣿⢸⣇⢿⣿⡿⠃⠙⣿⣿⢰⢀⢣⠀⢷⢀⡇⣇⢷⡸⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠹⡿⠁⠀⠀⠀⣼⢀⡿⠃⠀⠘⡼⣿⡸⡿⠁⠀⠀⠸⣿⢘⢸⡜⢸⡈⢸⢰⣹⣸⣇⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣅⠛⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣪⠭⠭⠭⢑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡸⢇⠸⢄⣀⣀⡠⠜⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠀⠒⠒⠈⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠒⠒⠒⠒⠊⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠒⢬⡑⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠴⢒⢤⠀⠱⡘
⠀⠀⠀⠀⠀⠀⡗⢦⡀⠀⠀⠀⠀⠀⢀⣀⠤⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣠⣾⡵⢻⠇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠂⢬⡉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⠀⡠⠚⣡⣴⡿⠟⣋⠴⣁⣀⣠⠗
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢉⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠉⠲⡝⢦⣾⠟⢋⡤⠊⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣗⠠⣀⠇⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠧⠚⠉⠉⠉⠑⢄⠘⡞⣧⠔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⢀⣀⠴⣪⠃⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢍⣉⣉⣉⣉⡡⠤⠊⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠈⠉⠢⡀⠀⠀⢀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠐⠒⢄⠀⠀⢱⠀⠀⣨⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡍⠢⣀⠜⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠖⠛⠊⠁⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⢀⡠⣞⠵⠊
⠀⠀⠀⠀⡠⢖⡽⠊
⠀⣀⢔⡫⠖⠁
⣾⠕⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠤⢬⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⠖⠾⣦⠀⠀⢀⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⣐⣢⣭⣉⡛⢳⠀⠀⠳⠶⢺⠏⢡⠉⠛⠖⠈⡄⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠛⠛⠿⠟⠀⠀⠀⡀⠀⠀⠀⣥⣀⠀⣀⠸⠜⢧⡀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⢱⡄⠀⠀⠀⢀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⠤⢄⣀⣾⠈⡿⠁⠀⠀⠀⠀⡐⠶⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⡇⠀⠀⠀⠀⠁⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀⡟⠀⠷⠀⠀⠠⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣀⡜⠋⠒⠺⣿⡷⠆⠀⠀⠀⠀⢠⠇⠀⠀⢀⣼⠇⠀⠐⠲⣄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠲⠛⠁⡆⠀⠀⠀⠀⠀⠊⠀⢂⣀⣴⣟⡄⠀⠙⠋⠉⠀⠀⠠⠂⠀⠁⡌⠀⠀⠐⠀⠀⢀⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣂⠈⠀⠁⠰⣆⠀⠉⠁⠘⠁⠀⠀⠀⢢⣀⠎⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠛⡁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠀⠀⡠⠀⢀⣴⢟⣧⣄⡀⠀⠀⠀⢤⡀⠀⠀⠈⠀⠀⠐⢢⣿⡿⢤⠾⠟⠂⣓⣦⣄⠀⣀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣷⡶⠁⠀⠀⠻⡌⠛⢻⡿⠁⠚⢷⡀⠐⣤⣄⠀⠀⢘⠇⠀⠀⠑⠀⢠⣿⠡⢌⡁⠁⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⢀⣷⣾⣿⠀⠀⠀⠀⠹⣤⣿⣿⣷⢖⣽⣷⣤⣴⠶⠺⠛⢎⠣⡀⠀⠀⢀
⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⠳⠶⠶⠻⠟⠋⠈⠁⠀⢀⠀⠀⠂⢹⡅⠀⣀⣒⣫⣭⣭⣽⣶⠄⠀⠘⡆⢀⡵⠆⠂
⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠉⢿⡋⠉⠋⠻⠿⠿⣧⠐⠂⠁⠘⠞⠀⢀⠀⠈⠆
⠀⠈⠀⢀⢀⡀⣰⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⢀⠀⠀⠈⠐⢾⠀⠀⠀⢀⣼⣿⠟⢻⣟⣷⣤⠀⠀⠀⠙⠳⡀⠀⠀⢀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠐⠉⠀⠀⠹⣿⠀⠲⠦⢀⡀⣀⢀⣀⠓⠦⠤⠜⢁⡞⠋⠙⠙⢿⣹⢁⣠⣄⣤⡼⠃⠤⠄⠙⠷⠤⠀⠊⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡀⠀⠘⠀⠀⠀⠀⠀⠉⠉⠱⠀⠀⢀⡀⠀⠀⠀⡇⠀⡸⠋⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠀⠤⠄⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠠⠀⣠⡷⠀⢀⡞⡇⠀⠀⠀⠁⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠈⢤⡠⠚⠁
⠀⠀⠀⠀⠈⡦⠀⠀⠀⠀⠘⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠠⠀⠘⠀⠁⠀⠀⠀⠀⢀⣀⡼⠀⠀⠀⠀⡤⠄⠂⠀⠀⠀⠀⢀⠴⠋⠀⠸⡄⠀⠔⠉
⠀⢠⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠒⠁⠀⠀⠀⠀⢀⣿⠟⣠⠤⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠂⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⠀⠀⠀⢀⣧⢤⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⠿⢷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢈⣵⣶⠾⠟⢩⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠋⠉⠀⠀⠀⢸⡇⢹⡇