Teeth Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣤⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠴⠶⠶⠞⠛⠛⠛⠋⠉⠉⠉⢻⡆
⠀⠀⣸⠋⠀⠀⠀⠈⠙⠛⠻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠇
⠀⠀⠸⢦⡀⠀⠀⠀⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠈⠉⠃⠀⠀⠀⢻⡆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣉⣉⠉⠀⢀⣀⣀⣀⡀⠀⢀⣾⠃
⠀⠀⠀⠀⣾⠀⠀⢰⡖⠒⠒⠒⠲⣶⠶⠒⠒⠒⠶⣦⠤⠤⠤⠤⢶⣶⠶⠶⠒⠲⣞⠋⠉⠉⢹⡏⠉⠉⠀⠈⣷⡾⠟⠁
⠀⠀⠀⠀⠙⠶⠶⢾⡇⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⢿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⢀⣽⡀⠀⠈⠀⠀⣸⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⣧⡀⠀⢀⣼⣷⣤⣤⠾⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠙⢿⠟⠶⠶⠶⠚⢿⣷⡶⠶⠶⢾⡿⠶⠶⠶⠒⠛⣿⠛⠛⠛⠙⣿⢀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣀⣠⡗⠀⠄⡀⠀⢸⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠆⠀⠘⡿⠛⢷⡄
⠀⠀⠀⠀⠀⢸⠋⠉⢿⣀⣀⣀⣀⣼⡀⠀⠀⢀⣀⣠⣿⡀⠀⠀⠀⣇⡀⠈⠀⠀⢀⣸⣆⣀⠀⢀⣸⣀⣀⣀⡴⠃⠀⠈⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠛⠛⠋⠉⠉⠓⠒⠛⠉⠀⠀⠉⠉⠉⠁⠉⠉⠁⣀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠛⠛⠛⠒⠶⠦⢤⣄⣀⣀⣀⣠⠴⣄⠀⠀⠀⠀⠀⠀⠰⠛⠳⣄⢀⣠⠴⠒⠖⠛⠁⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠘⠻⠶⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠘⠲⠋⠀⠰⣤⠆⠀⠀⠉⠉⠁⠀⢀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠷⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣭⠞⠛⠲⣄⠀⠀⠀⣀⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⢁⡾⠁⠀⠀⠀⠘⣷⡞⠋⠉⠀⠀⠀⠀⠉⡿⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⣿⣯⣀⠀⠀⣸⠁⠀⠘⣇⠀⠀⠘⣷⣤⣄⣀⡀⠀⠀⣸⠇⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣿⠀⠉⠻⣿⣿⠀⠀⠀⢹⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⠀⢀⣿⣧⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠻⢦⣀⠀⠀⢻⡄⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠙⠳⢦⣄⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣧⡀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠦⢤⣤⣤⣄⣀⣀⣀⣀⣀⣨⣿⡿⠿⠛⠛⠛⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠦⠤⠤⠤⠶⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⡞⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠙⡆
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠃⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠙⢦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠞⠁⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡎⠀⠀⠀⠘⠋⠉⠳⡄⠀⢀⣀⣀⠀⠀⣀⣀⡀⠀⡴⠋⠉⠙⠀⠀⠀⠀⣆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⢀⡾⡇⠀⠀⣠⣦⠀⠀⠀⠹⡞⠉⠀⠈⢳⠏⠁⠀⠙⠾⠁⠀⠀⢀⣦⣀⠀⠀⣻⣆⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠳⠖⠋⠁⠸⡄⠀⠀⢀⣦⠀⠀⠀⣠⡀⠀⠀⢀⣆⠀⠀⠀⣸⠁⠈⠓⠶⠃⠸⡄⠀⢸
⠀⠀⠀⠀⠀⠸⡇⣸⠃⡀⠀⠀⠀⠀⠀⠙⠦⠖⠋⠈⠳⠴⠚⠁⠙⠲⠴⠋⠈⠓⠦⠞⠁⠀⠀⠀⠀⠀⡀⢳⡀⡿
⠀⠀⠀⠀⠀⠀⣧⡏⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⠈⣧⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠳⡄⠀⢀⣠⡤⠤⠴⠶⠖⠒⠒⠶⠦⠤⠤⣄⣀⠀⠀⣰⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡞⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⣿⠉⠙⢲⡤⠴⠤⣄⡤⠴⠤⣤⠚⠉⢉⣟⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠈⠳⠤⠔⠲⢤⡤⠞⠦⣤⠴⠒⠦⠤⠋⠈⠛⠚⠋⠁





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

⠀⠀⠀⠀⣀⠤⠤⠤⠶⠶⠶⠶⠶⠦⠤⠤⠤⢤⣤⣀⡀
⠀⠀⠀⢰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣙⣛⠒⠶⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠈⠛⡮⢭⡵⣖⣒⣒⣒⣶⣶⣶⣒⣒⡯⡽⢶⠒⠒⠫⠭⠝⣛⣒⠶⠦⠭⣭⣍⣛⣛⣒⠲⠶⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠖⠚⢛⣧
⠀⠀⠀⣀⢀⠗⠘⠇⣰⣧⡆⠉⠉⠙⣦⠀⣗⠉⠙⢺⣤⠴⠖⠒⠶⠦⣄⡉⠉⠙⠒⠒⠢⠭⠭⢭⣉⣛⣛⡛⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⢉⡟
⠀⢠⠋⠀⠸⣄⠀⡼⠁⢀⠀⢀⠀⢰⣿⠀⠈⡀⠒⢬⡇⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠒⠶⠶⠦⠤⠤⢤⣤⣤⣤⣤⡤⠶⠋
⠀⢧⡀⠀⠀⠀⣿⡇⠀⠀⢸⡁⠀⠀⠉⠃⠈⢵⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⣸⠿⣶⣤⣤⡼⠿⣆⣀⣀⠽⢶⠀⠀⠀⢀⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⡿
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⢀⣠⠤⠊⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣷⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡟
⠀⠀⠀⠘⠧⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠈⠀⠈⠉⠉⠉⠀⠁⠐⠤⢄⡀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠈⠉⠉⠁⠀⠁⠐⠒⠂⠤⢀⣀
⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠤⢀⡀
⠀⠀⠀⣴⠊⢤⠄⠀⢤⠆⠀⢤⢤⣤⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⡀⡤⠠⠤⡤⠤⠤⡬⠒⣦
⠀⠀⠀⠹⡑⢆⡀⠀⡎⠀⠀⠰⡏⠀⠀⠈⠆⠠⠚⠛⠒⢶⠀⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠄⡶⠒⠛⠓⢄⡠⠉⠀⠀⢸⠆⠀⠀⢱⠀⠀⣰⡾⠃
⠀⠀⠀⠀⠑⡀⠙⢢⡅⠀⠀⢠⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢃⠔⠉⠀⠀⠈⠑⡄⢠⠊⠁⠀⠀⠉⠢⡘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⢸⡤⠊⡰⠁
⠀⠀⠀⠀⠀⠐⡄⠀⠈⠢⣄⣼⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣧⣀⡠⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠈⠙⢄⡀⠤⠚⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠒⠤⢀⡠⠟⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠲⢄⡣⠄⢀⣀⣀⣰⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⣆⣀⣀⡀⠠⢜⡠⠔⠈⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡰⠀⢀⡀⠄⠊⠁⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠬⠉⣀⡐⠒⠀⠁⠈⠐⢒⠀⠀⠨⠍⠒⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠄⣀⠀⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠤⢀⡀
⠀⠀⠀⠀⢀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⡀
⠀⠀⠀⣾⡉⣚⣀⡀⠻⠃⠐⠛⡰⠖⠶⢤⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⣤⠄⠲⢄⠒⠐⠒⡖⢒⣒⡒⢉⡿
⠀⠀⠀⠘⡌⠻⢕⠛⣧⠄⣀⡘⠇⠀⠀⠀⢣⠔⠉⠉⠉⠻⡀⠒⡲⠤⠤⢤⡤⠤⠤⢤⡤⠤⠴⢖⠒⢀⠟⠉⠉⠉⠢⡐⠀⠀⠀⠸⢃⣀⠤⣼⠛⢊⠝⡟⠁
⠀⠀⠀⠀⠈⠄⠈⠑⢏⠉⠚⢹⢖⠒⠰⣄⡸⠀⠀⠀⠀⠀⣡⠊⠀⠀⠀⠀⠈⢆⡰⠁⠀⠀⠀⠀⠑⣌⠀⠀⠀⠀⠀⢇⣠⠆⠖⡲⡏⠃⠉⢹⠖⢁⠌
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⠦⣼⠈⠀⠙⢁⡟⡎⡑⠒⢲⣀⡏⢀⣤⠀⠀⣀⠀⠘⠇⠀⡀⠀⠀⣠⡀⢩⣀⡖⠒⢊⢱⢻⡈⠉⠀⠁⣷⡤⠒⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠈⠲⢤⠂⠉⡇⠀⠀⠙⠂⠀⡍⢙⢀⡉⢉⠁⠦⠰⠆⠴⠈⡉⢉⣀⡏⢩⠀⠑⠋⠀⠀⢠⠉⠐⣠⠔⠋⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠙⠢⢕⠂⠠⠤⠤⠼⠀⠀⠁⠀⠈⠉⠀⢠⡄⠀⠉⠁⠀⠈⠀⠀⠧⠤⠤⠄⢐⡪⠔⠊⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠣⢀⣀⠀⠀⠀⠀⡘⢃⠀⠀⠀⠀⣀⡀⠜⢀⠠⠔⠂⠁⠀⠀⠀⠀⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠠⠤⠀⠀⠠⠀⠀⠀⠤⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠤⢀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠐⠂⠉⠁

⣶⣶⣶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣷⣶⣾⣿⣷⣶⣶⣶⣿⣿⣿⡿⣶⠿⠶⠷⠾⣶⡾⠷⠷⠾⠷⠶⠶⡶⠷⠶⠶⠷⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⣿⠓⠆
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢻⠁⠀⡟
⠐⠉⡟⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣶⠛⢩⡇⢀⡼⠀⠀⡇
⠀⠀⣧⠀⠀⣧⠀⠉⢹⠛⠒⢶⡤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⡾⠛⠉⠀⠀⣿⠀⢠⡷⠋⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠘⠳⢤⣼⠀⠀⢸⠀⠀⠀⠈⣿⠉⠉⠉⠛⠛⡟⠛⠛⠛⠛⢻⠛⠛⠉⠉⠉⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠶⠋⠀⠀⠀⠀⢸⠃
⠀⠀⢹⠀⠀⠀⠀⠀⠈⠳⠦⣼⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣇⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⣤⣤⡤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠛⠛⠒⠷⢤⡤⠤⠤⠾⠲⡞⠛⠋⠉⠁⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠋⠀⠀⠀⠀⣀⣀⣤⡤⠿⠶⠶⠶⠶⠶⠶⠦⠤⣤⣼⣁
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⢀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠁⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⣰⠞⠁⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠟⠁⣀⣰⣋⣀⣤⠤⠴⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⠤⠤⠴⢶⡞⠛⠛⠛⠛⣿⠉⠉⠉⢹⠛⠋⠉⢹⡖⠛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣟⠀⠀⠀⠘⡇⠀⠀⠀⠀⢻⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⢀⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣷⠀⠀⠀⠀⢸⡄⠀⠀⢈⣇⣀⣤⡼⠷⠛⠉⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣤⣤⣤⣤⣤⡤⠶⠖⠋⠉
⣿⣿⡟⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢂⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠜⠇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠙⡀⠐⢀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠂⠀⠑⠉⠂⠃⠄⠀⠐⠉⢱⠐⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠈⠀⠈⠀⠀⠀⠁⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠐⠨⡀⡀⠀⠀⠀⠘⢠⠈⠀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠘⢀⠀⠌⠀⠄⠀⠐⠀⠀⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠈⠑⠀⠑⠀⠈⠂⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠀⣀⣤⣶
⢁⠠⡄⠀⠀⠀⠀⣀⠀⠄⠐⠉⠙⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡀⠀⠀⠀⠀⠀⡤⠈⠉⠉⠛
⠀⠑⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠐⡄⠀⠁⠤⠐⠂⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠂⠄⡀
⠀⠀⠀⠰⠀⠀⠀⠠⠀⢀⡀⠀⡀⠀⠀⠀⢀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠁⠄⠀⠀⠡⡤⠀⠈⠁⠀⠀⠠
⠀⢀⠤⠚⣀⡤⠒⠈⠈⠀⠀⠀⠁⠁⠂⠄⠀⠠⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠑⠀⠐⠀⠁⢀⠆
⠀⠂⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠤⠀⠠⠐⠁
⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⣸⣯⣛⣿⣫⣫⣟⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⣤⢀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣠⢔⠊⠀⢱⠀⠀⠰⠀⠉⡖⠂⠶⠊⠁⡆⠀⠀⡀⠀⠈⠑⣤⡀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⣠⡎⠀⠈⢆⠀⠀⢣⠀⠀⣇⣀⣧⠀⠬⠀⣰⣀⡀⢠⠁⠀⢀⠞⠀⠈⣢⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡰⠁⠈⠢⢄⠀⢱⠤⠚⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠐⠲⢅⢀⠤⠊⠀⠑⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠤⡀⠀⢀⠗⠡⠀⠀⡆⢀⡠⠊⠀⠀⠀⠀⠀⠈⠒⢄⠀⡀⠀⠙⢄⣀⠤⠒⠙⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⣀⠀⠈⢱⠃⠀⠂⢀⡼⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡱⡄⢀⠆⠀⢣⣀⣀⡀⢧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⠉⠐⡎⠀⠀⣀⡌⡠⠔⢊⡥⠒⡉⠉⠉⢹⠓⠢⣄⠀⠈⠻⣎⠀⠀⠀⣇⣀⠀⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⢻⠤⢄⣀⠀⡇⢠⠀⢸⠋⠀⡰⢇⠀⠀⠇⠀⠀⠸⠀⢀⠋⠳⡀⠀⠘⣀⠔⠁⡇⠀⠀⢀⠋⠐⠢⠤⡀
⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠘⣄⠀⠀⠈⢃⠸⡀⠘⠀⢰⠁⠀⢢⠀⠸⠀⠀⡇⠀⡘⠀⠀⣵⠀⢢⡟⠀⠀⡏⠀⠀⡏⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢩⠈⠉⠁⠻⡀⠑⡆⠀⡗⢤⡀⠀⢣⠀⣃⢀⡅⢰⠁⡠⠊⠀⡆⠀⡇⠀⡸⠁⠒⢲⠁⠀⠀⠀⠀⠀⠀⠀⠈⣢
⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⢓⠒⠒⠀⢣⠀⠆⠀⣇⡀⠈⡲⠊⠁⠀⠈⠁⠣⡜⠁⠀⡠⢇⢠⠁⢰⠓⠢⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠘⡆⠤⠄⠀⡇⡀⢰⡀⠈⠹⠀⠀⠀⠀⠀⠀⠀⢱⡔⠉⠀⢸⠘⠀⠏⠢⣀⡎⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠰⡄⢀⣀⣸⢠⢸⡉⢑⠇⠀⠀⠀⠀⠀⠀⠀⠀⣆⡠⠊⢹⡆⠸⢄⡀⡘⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢣⡀⣀⣀⡃⢸⢈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠔⠋⡇⣄⠀⢨⠃⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⠣⣀⣈⣽⣆⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⠠⣷⠀⡱⠃⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠑⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠛⠉⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⢄⠀⢠⠀⠀⠀⠂⠀⠀⢄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠠⠄⠒⠁⡰
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⢀⣀⠀⠀⠠⠤⠤⠀⠈⡀
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠐⠀⠈⣀⡠⠃⠀⠀⠀⠀⣀⣀⡠⠤⠤⠔⠲⠒⠚⠁⢀⠀⢈⡀⢀⠀⠀⠄⠀⠂⡸
⠀⠀⠀⠐⠀⠀⠈⠐⢒⣈⡭⠥⠴⠒⠒⠊⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⠤⠤⠴⠖⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⣀⣠⠤⠤⠤⠤⠖⠒⠒⠒⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢀⣈⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢚⠄⠀⠈⠉⠉⢉⣛⡭⠉⠀⠀⠈⠙⠲⡄⠀⢠⠖⠋⠉⠀⠈⠉⠉⢙⣉⠭⠀⠀⠈⠉⠳⣄
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢹⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠸⡆⠀⠀⢀⡉⣀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⢸⠃⡇⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣧⠀⡐⠉⠀⠀⠈⠀⡠⠊⠀⠀⠀⠉⠀⠀⣸⠀⢷⠀⡐⠈⠀⠀⠈⠀⣀⠊⠀⠀⠀⠑⠄⠀⢸⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠰⣷⠆⡁⠀⠀⠀⣷⡆⢈⢀⡏⠀⠸⡆⠀⢾⡦⠀⠀⠀⡁⢾⡧⠀⠀⠀⢈⠀⡟
⠀⠀⠀⠀⠀⢧⠡⣀⠀⠀⢀⡄⠉⢄⡀⠀⠀⣠⠂⡼⠀⠀⠀⢷⠠⣀⠀⠀⢀⠐⠉⢀⡀⠀⠀⣀⠂⣸⠁
⠀⠀⠀⠀⠀⠸⡄⠈⠉⠉⠀⠈⠛⠁⠈⠉⠉⠀⢰⠃⢀⡀⠀⠘⡆⠀⠉⠉⠀⠈⠉⠀⠈⠉⠁⠀⢠⠇⢠⡦
⠀⠀⠀⠀⠀⠀⣷⢀⣴⠋⠀⢀⣀⡀⠀⠀⠀⠀⡏⢀⡾⠁⠀⢀⣿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣾⣴⠏
⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⢠⠏⠀⠹⡄⠀⠀⢀⡟⠋⠀⠀⣰⠟⢹⡀⠀⠀⢠⠏⠀⠹⡄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⢳⠀⠀⢸⡇⠀⠀⠘⠁⠀⢸⡇⠀⠀⡾⠀⠀⠀⢹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⢰⠇⠀⠀⠀⠈⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⠀⠀⢳⠀⣼⠀⠀⠀⠀⠀⠀⠀⣧⠀⡼⠀⠀⠀⠀⠀⢹⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠙⠞⠁⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠠⠤⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠤⠄⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⠀⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠄⢀⡀
⠀⠀⢀⡤⢂⡈⣀⣀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠁⡀⢤⡀
⠀⠀⠘⡂⢜⠀⠀⠘⠀⠀⢸⠌⠉⠉⠫⠀⠂⠶⠤⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠤⠴⠀⠂⠜⠉⠉⠡⡅⠀⠀⠃⠀⠀⢃⡴⠃
⠀⠀⠀⠐⡀⠑⢄⡀⠀⠀⠘⠀⠀⠀⠀⡖⠀⠀⠀⠀⠡⢀⠐⠉⠉⠉⠫⡉⢉⠝⠉⠉⠉⠂⡀⠈⠀⠀⠀⠀⢲⠀⠀⠀⠀⠃⠀⠀⢠⣀⠔⡡⠁
⠀⠀⠀⠀⠐⡀⠀⠑⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠘⠁⡔
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠣⢀⡀⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠄⢀⣀⠜⠉⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠑⠠⡀⠄⠀⢀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⣀⠀⡀⠀⠠⢀⠄⠊⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠩⠀⠀⣉⣁⣀⡉⠀⠨⠉⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠂⠈



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⣀⣤⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠙⠉⠉⠙⠲⣶⡶⠒⠞⠋⠉⠉⠛⡿⣿⣷⣶⣶⣤⣀⣀
⠀⠸⣿⢿⣿⣿⡿⠛⠟⠛⠛⢿⠿⠿⣿⣾⣶⣶⣶⣶⣶⣶⣿⣦⣶⣿⣿⣾⣿⣿⠿⡿⠛⢻⢿⢿⠿⣿⣿⣿⣿⣦
⠀⠀⠉⢷⡹⣿⡇⠚⠘⠀⢰⠁⠀⢀⠀⠀⠀⠠⠉⠉⠙⠛⠛⠛⠛⠉⠙⢠⠀⠀⠀⡧⠂⠀⠋⠘⠀⡖⣿⣿⡿⠟
⠀⠀⠀⠀⢻⣜⣿⣦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠁
⠀⠀⠀⠀⠀⢻⣿⠿⣿⡷⠰⠆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⡴⢤⣿⣟⡽⡿⠃
⠀⠀⠀⠀⠀⠀⠸⣤⡀⠉⠓⣦⣄⣁⠉⠙⠚⠀⠠⠀⠀⠀⠤⠀⠀⢠⠤⠴⠀⠉⣀⣠⡄⠐⠉⢀⢼⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠈⠋⠉⠉⠙⠓⠒⠐⠲⠤⢤⠴⠔⠶⠖⠒⠐⣺⠡⠌⠅⠁⠀⢠⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⢀⣰⡆⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣴⣦⢀⣤⣤⣰⣠⣦⣴⣰⣷⣷⢾⣛⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢿⡿⣿⠟⠿⠟⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠐⠀⠀⡀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⢀
⠀⠀⠀⢀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⡀
⠀⠀⠺⢁⣐⣀⡀⠟⠀⠀⢂⠔⠒⠦⠠⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠄⠤⠒⠲⡐⠀⠀⠶⢀⣀⡂⢈⠗
⠀⠀⠀⠂⠙⢅⠋⣷⡢⢄⡈⠀⠀⠀⢠⠄⠀⠀⠈⢩⠀⡀⠖⠒⠲⢄⠀⠀⡠⠖⠒⠲⢀⠀⡝⠁⠀⠀⠠⡌⠀⠀⠀⢁⡠⢔⣾⠙⠈⢙⠍
⠀⠀⠀⠀⢂⠀⠘⠢⡀⠁⡿⠉⢀⡢⢬⢀⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢁⡈⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⡀⡥⢔⡀⠉⢿⠈⠀⡠⠃⢀⠂
⠀⠀⠀⠀⠀⠡⠀⠀⠈⠲⠅⠀⢀⠠⠆⠡⠌⢉⡑⢰⠄⡐⠀⠀⠤⠄⢈⠁⠠⠤⠀⠔⢂⠠⡆⠊⡉⠡⠌⠰⢄⡀⠀⢨⠖⠈⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠙⠀⡀⢀⡀⠀⠀⠀⣈⠀⠣⠒⠀⠤⠏⠈⠉⠩⠤⠀⠒⠜⠀⠁⠀⠀⠀⢀⠀⢀⠀⠋⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠁⠢⢁⠀⠀⢁⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⡈⠀⢀⠈⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠂⠠⠀⠀⢐⡒⠂⠁⠈⠐⣒⠂⠀⠠⠀⠂⠈⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠶⠚⠛⠛⠛⠶⢦⣄⣀⣀⣠⡴⠶⠒⠓⠒⠲⠶⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠰⣶⣿⣧⡤⠤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⢦⠶⠶⠶⠶⠛⠛⠋⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠘⢿⡻⢧⣀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣠⡿⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠳⢦⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠴⠛⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠉⠛⠶⣾⣧⣄⣀⣀⣀⣄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢀⣄⣀⣀⣤⣾⡿⠷⠋⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣷⣶⣶⣾⣷⣶⣶⣶⣾⡿⠿⠟⠛⠉⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠂

⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠠⠀⡀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣀
⠻⢠⡥⢤⡘⠀⠈⡥⠉⠑⢂⠂⠠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⢐⠒⠈⠣⡍⠀⠙⣠⢤⢅⡼
⠀⢀⠀⠠⡝⠡⠤⣄⠄⣀⠀⠆⠀⠀⠀⢀⡀⠈⠉⠉⠃⡁⡁⠋⠉⠉⠀⣀⠀⠀⠀⠀⠎⢀⡀⢄⡤⠤⠘⣅⠔⡑
⠀⠀⠀⠀⠈⠂⢠⠁⠀⠒⢙⠒⠂⠠⣄⣸⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⡀⢘⣀⡤⠀⠂⢚⠑⠂⠈⢡⡀⠐⠁⠔
⠀⠀⠀⠑⡀⠀⠀⠑⠄⡊⢉⠀⠀⠐⠀⡈⠙⡀⠀⡁⠀⠀⠀⠀⡁⠀⡘⠉⡀⠐⠀⠀⢈⠉⠂⠄⠈⠀⢀⠊
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⠀⠁⡀⠂⠂⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠓⠐⢂⠀⠁⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣂⣤⣤⣤⣤⣤⣤⣤⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣷⣆⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⡏⠀⢀⡀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀⠀⠀⠈⠁⠀⠀⡇⣼⣿⣧⣴⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣈⡙⢦⡀⠀⠀⠀⢳⠻⣿⣿⠿⠁⠀⠀⣸
⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠚⠛⠿⢿⡄⠀⠀⠈⢧⡀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠾⠟⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⣷⢽⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡿⢤⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡃⠉⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠉⠉⠉⠛⠉⠉⠉⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠙⠒⠒⠒⠒⠛⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⣀⡀
⠀⠀⠀⢰⠋⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⢢
⠀⠀⠀⢰⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡴⠚⠉⠓⢤⠀⠀⠀⣠⠤⢤⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢠
⠀⠀⠀⠀⠣⣄⠀⠈⠢⣀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡜⠀⠀⣤⡀⠈⢳⠀⡞⠀⢠⣀⠈⢦⠀⠀⠱⡀⠀⠀⠀⠀⠀⡠⠊⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⠙⠢⡀⠀⣰⠁⠀⠀⠀⡇⠀⣿⣿⡿⠀⢸⠀⠀⠸⢿⡿⠀⢘⠆⠀⠀⢱⡀⠀⡠⠖⠉⠀⠀⢀⡎⠁
⠀⠀⢀⡤⠒⠉⢁⣀⣀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠱⣄⠀⠁⠀⢀⡜⠀⠢⡀⠀⠀⢀⠜⠠⣄⡀⠀⡇⡸⠀⠀⠀⠀⣀⡀⠉⠓⠦⡀
⠀⠀⢈⠀⠀⠀⠁⠀⠈⡇⠀⠀⠀⣿⠁⠞⠧⣄⡀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠉⠉⣁⣤⡖⠋⠃⠀⣿⡇⠀⠀⠀⡎⠀⠈⠉⠀⠀⠘
⠀⠀⠈⢢⣄⣀⣀⣠⠔⠑⣆⠀⠈⠃⡇⠀⠀⠈⠻⣗⠒⠦⢤⣤⣤⣤⣤⡤⠶⠚⠋⣡⡞⠀⠀⠀⠀⡇⠗⠀⢀⡔⠳⢄⣀⠀⣀⣠⠞
⠀⠀⠀⠘⢄⡀⠀⠀⣀⡴⢉⣦⣠⠂⢳⠀⠀⠀⠀⠈⠻⣶⣦⣤⣤⡤⠤⢤⣤⣶⣿⡿⠀⠀⠀⠀⢰⠃⢂⣀⣎⠳⣀⠀⠈⠉⢁⡸
⠀⠀⠀⠀⠸⣉⠉⠉⣁⡠⠞⣰⠁⠀⠀⢣⡀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠀⠀⣉⡿⠁⠀⠀⠀⣠⠃⠀⠀⢹⠘⢦⡈⠉⠉⠉⡹
⠀⠀⠀⠀⠀⠀⠙⠫⠥⠐⠊⠁⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠙⢥⣀⣀⣈⡽⠋⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠑⠢⠬⠭⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠴⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠂
⠀⠀⡤⠆⠄⠀⢤⠄⠠⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠠⡤⠀⠠⠠⢤
⠀⠀⠈⠐⢟⠲⣆⢀⡀⠟⠀⠀⠑⡀⠈⠛⠒⠆⠀⢠⠤⢄⣀⠀⠀⣀⡠⠤⡄⠀⠲⠒⠚⠃⢀⠊⠀⠀⠳⢀⠀⡱⠖⠛⠶⠃
⠀⠀⠀⠀⠀⠑⠎⠁⠊⣷⣂⠀⢄⠃⡀⠀⠀⢠⠌⠀⠀⠀⠀⢂⡐⠀⠀⠀⠀⠠⡅⠀⠀⢀⠘⡠⠀⣐⣾⠑⠈⡱⠆⠠⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠲⠀⠀⠀⠤⠉⠌⢀⡂⢸⢀⠀⠀⠠⠄⠈⠁⠠⠄⠀⠀⡀⡇⠘⡀⠡⠉⠤⠀⠀⢀⠶⠊⠀⡐
⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠁⠄⡀⠀⠀⠀⠀⡄⠘⠐⠂⠠⠌⠈⠁⠡⠄⠐⠂⠃⢠⠀⠀⠀⠀⠀⠠⠈⠁⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠈⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠍⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠁⠀⠀⠀⠀⠂⠠⠄⣀
⠀⠀⠀⠀⠀⡀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⢀
⠀⠀⢠⠶⠡⠄⠀⢠⡤⠀⠤⠄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠤⣤⠤⠤⠬⠔⢦
⠀⠀⠈⠅⠺⡏⠲⢮⣀⠀⠀⡟⠀⠀⠈⠆⠠⠘⠓⠒⢦⠀⠤⢀⣀⣀⣀⢀⠀⠀⢀⣀⣀⣀⠠⠄⢠⠖⠒⠛⠡⠀⠌⠁⠀⠘⡇⠀⢀⣨⠶⠊⢺⢴⠃
⠀⠀⠀⠈⠄⠈⠢⡜⠓⠨⢓⣥⠄⠀⡀⠸⠁⠀⠀⠀⠀⢃⠔⠁⠀⠀⠈⠡⡀⡠⠋⠀⠀⠀⠑⢄⠃⠀⠀⠀⠀⠹⠀⡀⠀⢤⡕⠫⠐⠋⡄⠔⠡⠁
⠀⠀⠀⠀⠈⢆⠀⠈⠑⢄⣸⠙⠐⠂⠋⠳⡔⠢⠤⢄⠀⡋⠀⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡇⢠⠤⠤⠒⠔⡋⠣⠒⠘⢹⣀⡠⠊⠀⡰⠁
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠙⠠⣀⠄⠚⠃⠁⠁⠒⠌⠈⠓⠺⠈⠀⠒⢉⠄⢤⠄⠌⠑⠂⠈⠸⠒⠇⠈⠔⠂⠁⠁⠛⠂⠀⣀⠜⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠐⠄⡁⠄⠀⠀⠀⢰⠀⠈⠉⠁⠐⠚⠀⢰⠀⠘⠒⠈⠉⠉⠀⢰⠀⠀⠀⠀⠄⡀⠔⠈⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠑⠀⢄⡀⠀⢄⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⢀⣀⡄⢀⣀⠄⠀⠁⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣷⡀
⠀⣠⣶⣶⣤⣤⣦⣄⢺⣿⣿⣿⣿⣷⣄⠠⣴⣾⣿⡷
⠀⢿⣿⣿⣿⣿⣿⣿⣦⢻⣿⡿⢿⣿⡿⢹⣿⠃⠈⠁
⠀⣼⣿⣿⣿⡅⠈⠻⣿⣿⣿⠁⣸⣿⢣⠟⢉⣡⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠻⣿⣿⣿⣿⣶⣄⢹⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣶⣄⡀
⠀⣀⣤⣤⣭⣭⣽⡿⠇⢴⡿⢟⣛⣉⡉⠉⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣤⡀
⣾⣿⣿⣿⡟⠁⠀⢀⣴⣦⡘⢻⣟⡻⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⡀
⢘⣿⣿⣿⣧⣤⣶⣿⡿⣿⣿⠀⠙⣿⣶⡙⠿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⣾⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⠈⠻⠛⢹⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⠿⠏⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⢠⣿⣿⠏⠀⠀⢿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷
⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿
⠀⢹⣿⣷⠀⠀⠀⠀⠠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠈⠁⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣤⣤⣤⣤⣤⣤⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⣤⣀⣀⣤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⢺⣟⡟⣓⣲⠖⣒⠒⠒⡖⠒⠒⠒⠒⠒⢲⠖⠒⠒⠒⠒⠒⢲⠒⠒⣒⠲⡖⡚⢻⣻⡗
⠀⠀⠀⠀⠀⠘⡎⠻⣬⣽⡟⠯⠽⠶⡧⢴⡏⠉⠉⣇⣸⣄⣼⠉⠉⢹⡤⢾⠶⠯⠽⣻⣯⣥⠟⢱⠃
⠀⠀⠀⠀⠀⠀⠹⡄⠈⠑⢾⣛⢲⡾⢷⣬⣉⣉⡉⠁⣸⣇⠈⢉⣉⣉⣤⡾⣷⣖⣛⡳⠞⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠈⠛⠿⣿⡿⢾⢽⣛⣿⣽⣯⡟⢻⣭⡧⢿⣽⡿⠟⠋⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠉⠙⠛⠻⠯⠼⠧⠭⠿⠞⠛⠉⠁⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⢠⣾⡿⠿⠟⣻⣿⠿⢻⣿⣇⣿⣷⣿⣷⣦⣼⣿⣀⣀⣤⣾⣿⠿⢿⣿⣶⡀⠀⠀⣿⡿
⠀⠀⠀⠀⠈⢿⡄⠀⠈⠛⣡⣤⣼⣿⣿⣿⢿⣷⣬⣙⣿⣿⣿⣿⣿⣏⣀⣀⣀⣼⣿⠃⠀⢀⣿⡇
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⠟⢹⣿⣿⡟⢀⣩⡝⠻⠿⣿⣿⣿⡟⠻⠿⠿⠿⠟⠁⢀⡀⢸⣿⠁
⠀⠀⠀⠀⠉⠉⠻⣿⠉⢿⣏⣀⣼⣿⣿⣇⣸⣿⣧⣄⣀⣈⣹⣿⣿⣄⡀⠀⠀⢀⣠⣿⢃⣈⡉
⠀⠀⠀⠀⠀⠀⠀⠹⠇⠈⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠿⠛⠁⠙⠻⠿⣿⣿⠿⠟⠁⠸⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣛⣟⢻⣛⣿⣷⣿⣻⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⡿⣻⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⢡⣟⢻⢿⠟⡇⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣸⣷⣾⣾⣼⣧⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡟⡿⡟⣿⢛⢟⡿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣷⣵⣿⣾⣿⣧⣧⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠦⠤⡤⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡛⡫⠅⠒⠊⠉⠉⠉⠉⠁⠒⠪⠭⣛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⠕⠊⠁⠀⢀⣀⡠⠤⠤⠤⠤⠤⣀⣀⠀⠀⠉⠠⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⠔⠁⠀⢀⠔⣂⣬⡶⠞⠛⠛⠛⠛⠻⠶⣮⣕⠢⠀⠀⠀⠑⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡱⠃⠀⢀⠖⣵⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡑⣄⠀⠈⢪⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡁⠁⠀⣰⢣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣌⢆⠀⠀⢣⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⠉⠉⠉⠉⠍⠛⠩⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⡙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⣤⣤⣤⠄⠀⢠⣤⡀⠀⠀⠄⠀⠀⠀⣠⣴⣤⡀⢠⣤⣤⡤⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⣿⣧⣤⠀⢀⣾⠻⣧⠀⠀⣾⡇⠀⠀⢿⣦⣉⠁⢸⣯⣀⡄⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⣿⡏⠉⠀⣼⠟⠛⢻⣆⠀⣿⣇⣀⠀⣤⣈⣹⡇⢸⣿⣉⠁⠀⠀⠀⠀⠀⠃⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠉⠁⠀⠈⠋⠀⠀⠀⠙⠀⠙⠉⠉⠀⠈⠛⠋⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠿⣿⡷⡿⠶⠷⣿⢯⣾⠷⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠷⠿⠿⢾⣿⢶⠽⠾⢾⡿⣷⠿⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡑⡄⠀⠈⠢⡙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⡵⠃⠀⢀⢞⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠎⠢⠀⠀⠈⠒⠍⠛⠷⠶⢤⣤⣤⣤⡶⠾⣛⡩⠔⠉⠀⢀⡴⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡲⢄⡀⠀⠀⠀⠀⠀⠐⠂⠀⠊⠉⠁⠀⢀⣠⢔⣩⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣮⣕⣒⠤⠤⢀⣀⣀⡀⠠⠤⣐⣪⣭⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠶⠖⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣀⠀⠀⠀⢀⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⣡⣤⠶⠿⠿⠿⣿⣶⣄⣀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠋⠉⠉
⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢲⡶⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠎⠀⠘⠉⠀⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠃⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡇
⠀⠀⠀⠈⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣷
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣿⣿⣇
⠀⠀⠀⠀⢀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡇⣿⣿⣿⡀
⠀⠀⠀⠀⠘⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣽⣷⠾⠿⠛⠛⠁
⠀⠀⠀⠀⠀⢧⠀⠀⠱⣤⣤⣶⢶⣿⣿⣿⣽⠿⠿⠛⠛⠉⠉
⣀⣠⣴⣶⣤⣼⣟⣀⣴⣾⣷⣿⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⣤⣀⣤⡴⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣛⣙⠛⠿⠟⢛⣙⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣀⣐⣚⣉⣀⣀⡀⠀⠀⠉⠀⠀⠀⣀⣀⣉⣓⣂⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠭⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠮⠽⠿⢿⣿⣿⣿
⠀⠀⠀⠀⡙⢧⡍⠙⠙⠟⠻⡿⠿⢿⠿⠿⠟⠻⠋⠋⢩⡼⢋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠳⣦⣶⣄⣤⢀⣬⡉⣩⣄⢀⣤⣴⣦⡶⠛⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠸⡄⠙⠶⣄⢄⢀⠀⠀⠀⠀⠀⡀⡠⣠⡴⠋⢠⠎⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡻⣷⣍⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢋⣵⡿⢳⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⢦⡀⠈⠙⠲⠧⢤⣭⡤⠼⠖⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡝⢿⣿⣶⣬⣉⣛⠓⢛⣛⣩⣵⣾⣿⠟⣵⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⡀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⣃⣉⡛⠿⣿⣿⣿⣿⣿⡿⠿⣛⣵⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣤⣤⣬⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠠⣖⣶⡦⠀⠤⠠⣤⢤⡀⠀⠈⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⣀⡀⠀⠀⠆⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⢺⣌⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠁⠀⠀⢀⡀⠠⠄⠘⠚⠃⠀⢀⣃⣀⣀⣠⣤⣤⣷⣶⣶⡶⣶⣶⠿⣷⣶⡀⠐⠀⠀⠙⣿⣿⠃
⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠐⣀⠰⠝⠋⠀⢀⣤⣄⣤⣴⣿⡿⠿⠿⠟⠉⠉⡉⡁⢠⢴⡄⠀⢠⣤⣈⢁⣀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠈⢿⣦⣀⣤⡖⠈⠀⣠⣤⣴⣤⣾⡿⠟⠋⣉⣁⣀⣠⣤⣦⣼⣷⣧⣶⣤⣶⣴⣶⣶⣾⣶⣾⣿⣷⣶⣦⣾
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣶⣿⣿⣿⣯⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁

⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠶⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠄⢀
⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠄⢀⡀⠀⢀⡀⠠⠀⠀⠀⠀⠈⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠆⠈⠛⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠋⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠙⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠛⠁⠰
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠠⠂⠀⠀⠀⠀⠀⠀⠢⡀⢀⠔⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠠⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠠⠀⢀
⠀⠀⣴⠂⠄⠀⡤⠀⠤⣠⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⣄⡤⠠⢤⠀⠠⠔⡤
⠀⠀⠈⠙⠠⡀⠀⠀⠸⠁⠀⠈⡄⠈⠉⠓⠀⠒⠦⠤⠤⠀⠀⠤⠤⠴⠒⠀⠚⠉⠁⢠⠁⠀⠈⠇⠀⠈⠀⡠⡛⠁
⠀⠀⠀⠀⠄⠈⠢⡀⡀⠀⠀⠀⠃⠀⠀⠀⠼⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠧⠀⠀⠀⠈⠀⠀⠀⢀⢀⠀⠋⠔
⠀⠀⠀⠀⠈⢀⠀⠈⠑⢤⠀⠚⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡓⠀⡠⠘⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠈⠀⠄⠀⠀⠐⡁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢈⠂⠄⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠁⠂⠀⠀⠀⡀⠀⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠⢀
⠀⠀⢾⢁⣆⣀⡖⠀⢒⡖⠲⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡤⠄⢲⡖⠀⢲⣀⣰⣊⡗
⠀⠀⠀⢊⠁⢍⠷⢴⢼⡀⢀⠀⠆⠀⠀⠈⢂⠄⠛⠐⠒⠀⢀⠒⠀⠛⠠⡀⠁⠀⠀⢰⠀⡀⢀⡥⠆⠾⡉⠄⠍
⠀⠀⠀⠀⢂⠀⠑⠄⡜⠀⠒⢁⢦⠂⠠⣄⡚⢀⡀⠀⠀⠐⠂⠀⠀⢀⡀⢃⣠⠄⠐⠾⡋⠒⠀⢣⡠⠂⢁⠊
⠀⠀⠀⠀⠀⠡⡀⠀⠈⠲⢌⠩⠀⠀⠉⠀⡍⠁⠄⢄⡐⠒⠒⢂⠠⠠⠌⢸⠀⠉⠀⠀⠍⠀⠖⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠁⠀⠈⡀⠈⠄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠠⠁⢀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂
⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠄⠀⡔⠂⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⣁⠂⠱⠄⠀⢵⠉⣡⡰⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣤⣤⠀⠠
⠀⠀⠀⠀⠀⠙⠛⠢⠀⢀⠠⠀⠸⠌⠿⢁⠀⠀⡔⠐⠀⠑⠠⠀⠉⠐⠀⠀⢀⠀⢀⠀⢆⣂⠀⢠⣤⣤⡀⠈⢡⠈
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢸⣾⡷⡄⠈⠁⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠘⠀⠉⠉⠁⠀⠈⢿⣄⡀⢘⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠃⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣏⠁⢺⠄
⠀⠀⠀⠀⠀⡑⠈⢆⠰⡇⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠤⠀⠀⠀⠈⢀⣉⣽⣧⣄
⠀⠀⠠⠐⠀⡈⠁⠀⠀⠙⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠄⠀⠀⣒⣦⡀⡤⡀⢂⠀⠙⠒⠂⠼⣿⣿⢿⡟⠂⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠓⠁⠀⠀⠙⠎⠀⠠⠄⠀⠀⠀⠀⣬⣤⡇⠀⠀⠀⠀⠁⠀⠈⠀⠀⡀⠀⠀⠀⠀⠆⠆⠀⣿⣿⠛⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠂⠀⢠⠀⠀⣠⣿⡇
⠀⠀⠀⠐⠐⠄⠀⠠⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠐⣿⣿⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡌⠀⣄⣠⣤⠐
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢠⡟⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⠟⠛⠀⢸⣏⡽⢞⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠍⠉⠛⠀⢨⠔⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⣤⣀⠀⣀⣀⣀⣄⡀⣀⣀⣀⢠⡀⣀⢀⡀⡀⡄⡀⣀⣀⣀⡀⢀⣀⣀⡄⠀⣀⣠⡄⠀⣀⣀⣠⢄⣠⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡤⠶⠒⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠶⢦⣄⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠲⠶⣤⡀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠶⢦⣄
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢸⡇⠀⠐⠟⠀⠐⠟⠀⠀⢹⡄⠀⠀⣿⠀⠀⠻⠃⠀⠺⠃⠀⠈⡇⠀⠀⢸⡇⠀⠘⠟⠀⠘⠟⠀⠀⢹⠀⠀⠀⣿⠀⠀⠻⠃⠀⠻⠃⠀⠘⡇
⠀⠀⠸⣇⠀⣤⡀⠀⠀⢀⡄⠀⣼⠁⠀⠀⢿⡀⢠⣤⣤⣤⣤⣤⠀⢠⡇⠀⠀⠸⣇⠀⠀⢀⣀⣀⡀⠀⠀⣼⠀⠀⠀⢿⠀⢀⡴⠖⠒⠶⣄⠀⢰⡇
⠀⠀⠀⠙⢦⣈⠙⠓⠚⠋⣠⡼⠃⠀⠀⠀⠈⠳⣄⠉⠛⠛⠛⢁⣤⠟⠀⠀⠀⠀⠙⢦⡀⠈⠉⠉⠀⣠⡾⠃⠀⠀⠀⠈⠷⣌⠀⠀⠀⠀⢈⣴⠟
⠀⠀⠀⠀⠀⠉⠛⠓⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠛⠉

⠀⠀⠀⠀⣤⠖⠛⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⣤⠞⠛⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⠙⠳⢦⡀
⠀⠀⢀⡾⠁⢀⣀⠀⠀⣀⠀⠘⣧⠀⠀⠀⣰⠏⠀⣀⡄⠀⣀⡀⠀⢻⡄⠀⠀⢀⡞⠁⣠⣠⡀⣠⣤⡄⠘⣧⠀⠀⠀⣰⠋⣴⢋⡉⠛⣉⢳⡄⢻⡄
⠀⠀⢸⡇⠀⠉⠉⠁⠈⠋⠀⠀⢸⡆⠀⠀⣿⠀⠀⠉⠀⠀⠈⠉⠀⠀⡇⠀⠀⢸⡇⠀⠙⠋⠁⠈⠛⠁⠀⢸⠄⠀⠀⣟⠀⠹⢦⣥⢦⣥⠼⠃⠈⡇
⠀⠀⠘⣧⠀⢶⣄⡀⢀⣠⠆⢀⡾⠀⠀⠀⢻⡄⢠⠞⠋⠉⠛⢦⠀⣰⠇⠀⠀⠘⣧⠀⢶⣄⡀⢀⣠⠆⢀⡾⠀⠀⠀⢻⡀⠀⢀⣶⣶⣦⠀⠀⣸⠇
⠀⠀⠀⠈⠳⣤⣈⣉⣉⣁⡤⠞⠁⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⠈⠳⣄⣈⣉⣉⣁⡴⠟⠁⠀⠀⠀⠀⠙⢦⣈⣙⢛⣋⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⡶⠋⠉⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠈⠙⠳⣄⠀⠀⠀⠀⢠⡶⠋⠉⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠈⠙⠳⣄
⠀⠀⢠⡟⠀⢰⣴⠆⢰⣶⠆⠀⢷⠀⠀⠀⣼⠁⠠⣴⡤⠀⣴⣦⠀⠹⡆⠀⠀⢠⡏⠀⣠⢤⡀⣠⣤⡀⠈⢷⠀⠀⠀⣼⠁⠀⣤⡄⠀⣤⡄⠀⠹⡆
⠀⠀⢸⡇⠀⠈⠉⠁⠈⠉⠁⠀⢸⠇⠀⠀⣿⠀⠀⠉⠁⠀⠈⠉⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⣿⠀⠀⠈⠀⠀⠈⠀⠀⢀⡇
⠀⠀⠈⢷⡀⠀⠰⠶⠶⠂⠀⣠⡟⠀⠀⠀⠹⣆⠘⠷⣤⣀⣤⠞⢀⣼⠃⠀⠀⠈⢷⡀⠻⢦⣤⣤⡤⠁⣠⡟⠀⠀⠀⢻⣆⠀⠰⠿⠛⠛⠁⢀⣾⠃
⠀⠀⠀⠀⠙⠶⣤⣤⣤⡤⠞⠋⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⠴⠛⠁⠀⠀⠀⠀⠀⠙⠶⣤⣤⣤⡤⠾⠃⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⠶⠛⠁

⠀⠀⠀⠀⠀⣠⡤⠴⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⢤⣄⡀
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⢀⡾⠿⠿⠿⠿⠿⠿⠿⣦⠀⠀⠀⠀⣰⠟⢁⠀⠀⠀⢀⠉⢳⡄⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠈⠙⣦
⠀⠀⢰⡟⢻⣿⣿⡟⢻⣿⣿⠛⢻⡀⠀⠀⣾⠁⠀⠶⠆⠀⠴⠆⠀⠘⡇⠀⠀⢰⡇⠀⢾⡷⠀⠰⣿⠆⠀⢻⠀⠀⠀⣾⠀⠐⠦⠖⠐⠦⠶⠀⠘⡇
⠀⠀⢸⡇⠀⣉⠉⠀⠀⠉⣁⠀⣸⠃⠀⠀⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⡇⠀⠀⢸⡇⠀⠈⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⣿⠀⢀⡀⠀⠀⠀⢀⠀⢠⡇
⠀⠀⠀⠻⣄⠙⠳⠶⠶⠞⢁⣴⠏⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠻⣄⠀⠘⠛⠛⠁⢀⣴⠋⠀⠀⠀⠘⢧⡈⠛⠶⠶⠖⠋⣠⡞⠁
⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣐⣒⣢⢤⡉⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠳⣌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣹⣿⣧⣼⣿⣿⣿⣿⣿⣿⢿⣿⣆⢰⣝⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⣿⣿⣿⣿⣿⣿⠯⣿⢷⣽⣫⣿⣿⢨⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡄⢸⡏⠉⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⡾⠘⣼⢳⣇
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡴⢁⣷⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣽⠿⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠇⠈⣇⣀⡀⠀⠀⠀⣤⣶⣾⣛⠓⠤⠀⢻⣿⣿⣛⡶⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⣯⡉⠀⠀⠀⠉⠘⠉⠙⠻⠆⠀⠀⢿⣿⣯⣉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡳⣤⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⣿⣮⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠒⠃⠀⠀⠈⠙⠋⠀⠀⠀⠀⣿⣿⣿⡟⠥⡟⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠇⡇⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⣿⣿⣿⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢿⡒⠦⠤⠤⠔⠊⠁⠀⠀⢸⣿⣿⣿⣿⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⡇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⢡⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⠐⡀⠣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣅⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⠀⢀⣑⠦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢁⢈⠻⢷⣤⣀⡀
⠀⠀⠀⣠⢔⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⠎⠉⠁⠱⡄⠀⠀⠀⠀⢀⣿⣿⣿⣷⡀⠁⠁⠈⠻⣷⡄
⠀⠀⠈⠐⠒⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠑⠂⠀⠹⡄⠀⠀⠀⠞⣿⣿⠉⢻⣷⡀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⡈⢯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠌⢀⡿⣁⣤⠄⠻⡇⠲⠛⠉⠈⠋⠓
⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡞⠀⠀⠈⠀⡿⠉⠙⠋⠀⠁⠈⠂
⡜⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢀⠀⡤⠀⢠⠃⠀⠀⠀⢀⣀⣀⣀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠻⢿⠟⡿⠿⠿⠿⣿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠤⠐⠒⠀⠉⠉⠁⠀⠀⠉⠁⠒⠤⢄⡀⠀⠀⠀⠀⣀⠤⠐⠂⠉⠁⠀⠉⠉⠁⠐⠒⠠⠤⢀⢀⡀
⠀⠀⠀⠀⢀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⡀
⠀⠀⠀⣖⠓⡖⠒⠒⡶⠒⠒⠖⡦⠤⣤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣤⡔⠒⠲⡖⠒⠒⡆⢓⡆
⠀⠀⠀⠸⡙⢧⡀⠀⠇⠀⠀⡸⠀⠀⠀⠑⡠⠊⠉⠙⠳⡐⠒⣠⠤⠤⣤⡀⠄⠄⣠⡤⠤⢤⡐⠒⡰⠛⠉⠉⠢⣐⠁⠀⠀⠸⡀⠀⠀⠇⠀⢀⢷⠏
⠀⠀⠀⠀⠑⡀⠈⠲⡀⠀⠀⠇⠀⠀⠀⠸⠃⠀⠀⠀⠀⢣⠎⠀⠀⠀⠀⠑⣄⡔⠁⠀⠀⠀⠈⢦⠃⠀⠀⠀⠀⢻⠀⠀⠀⠀⡇⠀⠀⢰⠔⢁⠎
⠀⠀⠀⠀⠀⠐⡄⠀⠈⠲⣴⡆⠀⠀⠀⡈⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢘⡀⠀⠀⠀⢦⡠⠚⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠑⠤⡒⠉⠅⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠋⠐⡢⠔⠉⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠈⠒⠬⡒⠠⠤⠤⢼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠺⠤⠤⠤⠐⡪⠔⠊⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠈⠑⠂⠄⣀⠢⠄⢀⣀⣀⣀⣀⠞⢄⣀⣀⣀⣀⡀⠤⢂⠠⠐⠂⠁⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠀⠠⠀⠀⠀⠒⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⠄⠀⠀⣀⡀⠀⠠⠤⠄⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠒⠒⠂⠀⠈⠉⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠉⠀⠒⠒⠂⠤⠄⣀⡀
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠠⢄⡀
⠀⠀⢀⡴⠊⡥⠀⠠⣤⠀⠠⡤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⡤⠤⢤⡤⠀⠠⡅⠲⡄
⠀⠀⠀⢹⠲⢷⠳⡶⣇⡀⠀⠸⠁⠀⠈⠢⢈⠝⠓⠒⢦⠠⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠠⢤⠖⠒⠛⢍⠠⠋⠀⠀⢹⠀⠀⣀⡷⡖⠗⡧⠞⠁
⠀⠀⠀⠀⠡⠀⠑⢤⠛⠪⠗⣧⠤⢀⣀⢸⠇⠀⠀⠀⠀⢃⡔⠁⠀⠀⠉⠣⡀⡠⠋⠁⠀⠀⠑⣀⠃⠀⠀⠀⠀⢿⢀⣄⡠⢤⡟⠧⠚⢣⡤⠊⠜
⠀⠀⠀⠀⠀⠱⡀⠀⠑⠤⣠⡌⠂⠒⠎⠹⠴⠢⠤⢤⡀⡘⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠘⡀⣠⠄⠴⠢⠾⠙⠔⠀⠊⣤⣀⠔⠋⢀⠎
⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠈⠣⣄⠤⠒⠃⠉⠉⠓⠜⠉⠟⢺⠉⠁⠐⠙⠄⢼⠄⡎⠑⠀⠉⠱⠚⠏⠙⠖⠈⠉⠠⠓⠂⢄⡠⠚⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠑⠢⣐⠤⠄⣀⣀⢰⠀⠈⠉⠉⠙⠒⠀⢸⠀⠐⠊⠉⠉⠈⠀⢰⢀⣀⡀⠤⢘⠠⠒⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠁⠒⠤⣀⠀⠄⣀⠀⠀⠀⠀⠀⡼⡄⠀⠀⠀⠀⢀⡀⠆⣀⠠⠔⠊⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠬⠉⢩⠅⠀⠀⠍⠉⠭⠄⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠠⠄⢀⣀⣀⡀⠀⣀⣀⣀⡀⠠⠄⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠤⠒⠛⠛⠒⠒⠛⠛⠒⠤⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣭⣵⣦⣭⣭⣴⣮⣭⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣻⠿⠶⠶⠶⠶⠿⣟⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⣿⣦⡈⣢⢤⣬⣉⣉⣉⣉⣥⡤⣔⢁⣴⣿⣿⣿
⠀⠀⠀⠀⠘⢆⠙⠶⣍⣝⢫⡝⣫⣩⠷⠋⡰⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⡻⣦⣝⠲⢿⣼⣧⡿⢖⣫⣴⢟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠉⠉⠉⢉⣀⡤⠞⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣮⡻⢿⣷⣶⣶⣾⡿⣟⣵⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⡶⢶⠾⣷⢶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠒⠒⠦⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⢠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⡄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⢀⡀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⣀⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠉⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠉⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⢿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⡿⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⢍⡉⠛⠛⠛⠛⠛⠛⠛⠟⠉⡩⠋⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣤⣤⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠶⠶⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠲⠦⠤⠤⠤⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⠄⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠶⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠐⠙⠀⠁⠒⠈⠉⢮⡂⣂⣰
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⡌⢀⣾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠰⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣒⣶⣶⣶⣒⣖⣲⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠋⠋⢉⡉⢉⣹⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠛⠛⠛⠛⠻⠟⠛⠻⡷⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄⠀⠀⠀⠀⠀⠀⠘⠛⠒⢲⣶⣾⣿⣷⣿⡿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠙⡇⢹⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣽⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢿⠘⢹
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠉⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⡟⡆
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡇⡅⢡
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢀⣆⣀⣀⣀⢠⡀⣂⡀⠀⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡇⠫⠄⠀⠀⡄⠀⣤⠄⢞⠘⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣴⣿⡟⣿⣿⣿⣿⣿⣷⣄⣀⣀⡠⡼⠀⠀⠀⠀⠠⠃⠈⣯⡆⠈⡄⠡
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣻⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠘⠆⠱⡀
⠀⠀⠀⠀⠀⠀⢸⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡤⠠⣄⠤⢤⣤⣠⣤⣤⣤⣴⡆⣴⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠛⠛⠛⠛⠓⠛⠟⢻⣿⣿⣿⡄⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⣀⡴⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠶⣤⡀
⠀⠀⠀⢽⡿⣶⣤⡘⠀⠀⢰⠆⠀⠈⠫⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠍⠉⠀⠠⡆⠀⠀⢃⣤⣶⢿⡋
⠀⠀⠀⠈⢿⣦⡀⠹⠿⢶⢼⣠⡀⢀⠀⡖⠀⠀⠀⠀⠠⠀⠉⠉⠉⠛⠛⡛⢛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢲⠀⡀⢀⣀⡷⡶⠿⢏⠀⣠⠞
⠀⠀⠀⠀⠈⢿⣿⣶⣄⠀⡘⠛⠛⠿⠒⢆⣤⣀⣀⡀⠸⠃⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠘⠇⢀⣀⣀⣤⡰⠒⠿⠛⠛⢀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣅⡀⣀⣤⣾⠘⠛⠛⠿⠃⠙⠠⣿⣶⣦⣶⡆⢠⡄⣰⣶⣴⣶⣿⠄⠋⠘⠿⠛⠛⠃⣷⣤⣀⠀⣸⣷⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣟⣿⣄⣀⣀⠀⣀⡆⠈⠛⠉⠉⠻⠃⢀⡀⠘⠟⠉⠉⠛⠀⢰⣀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠲⠤⣄⣀⣀⡤⠖⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⣀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢧⣯⠡⣄⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠌⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠙⢿⣯⢉⠍⡭⠉⠀⢄⡀⠈⠙⢭⡍⠁⠲⢢⡀⠀⢠⠐⣢⢺⣽⣿⠟⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠉⠒⠆⣍⡀⠀⢺⠂⡀⡲⢼⠤⠖⢀⣿⠆⠀⣹⣂⣤⠝⠋⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠉⠉⠛⠲⠶⠶⠾⠶⠶⠶⠾⠛⠛⠉⠉⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⢫⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡠⣴⣒⢖⡈⡀⠀⠄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢬⡭⠃⡉⢶⡇⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⡊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿
⣶⣾⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⢀⣀⣠⣤⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⠿⠿⠛⠋⠉⢻⣿⣧
⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⡿⠿⠟⠛⠋⠉⠀⠀⠀⢀⣀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⢿⣿⣿⡿⠿⠛⠛⠉⠉⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⣀⠀⣤⣤⣶⣶⣿⣿⣿⠄⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⣀⣠⡄⠀⣠⣾⣿⠏⠀⢻⣿⣿⣉⣁⣤⣤⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢿⣿⣷⣰⣿⣿⠃⠀⠀⠘⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⣿⣿⡏⠁⠀⠀⠀⣀⣠⣤⣴⣶⣾⣧⠀⢀⣿⣿⣷⣄⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠀⠀⢻⣿⣿⣤⣶⣶⣿⣷⠀⠀⠀⣿⣿⡆
⠀⠀⠀⢻⣿⣧⠀⠀⠀⠈⣿⣿⣿⠛⠋⣉⡁⠀⢸⣿⡟⢿⣿⣷⡀⠀⢻⣿⣿⠁⠙⢿⣿⣷⣄⠈⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⣸⣿⡗
⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⡿⠷⠀⣿⣿⣧⣶⣿⣿⣿⣦⡘⣿⣿⠇⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⠿⠁
⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⢰⣿⣿⠟⠉⠉⠙⠛⠉⠁⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⡿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠸⣿⣿⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⣀⣠⣤⣴⣶⣶⣦
⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⣆⣀⣀⣤⣤⣶⣶⣿⣿⣿⠿⠿⠛⠛⠉⠉⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣾⡿⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠙⠉⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣶⣷⣸⣿⡇⠀⠀⠀⠀⠀⣠⣾⡟⠁⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⢿⣿⣿⡇⠀⠀⠀⢀⣴⡿⠋⠀⠠⣿⣿⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠘⣿⣿⡇⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⣾⣿⣷⣶⣶⣶⣶⡆⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠉⠉⣽⣿⠁⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠿⠿⣷⣦⣤⣤⣤⣶⣾⣿⣿⢃⣴⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣰⣿⣷⣿⠟⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣼⡿⠛⢿⣦⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⡿⠁⠀⠈⣿⣧⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢰⣿⠇⠀⠀⠀⢸⣿⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⣸⣿⠀⠀⠀⠀⠀⣿⡇⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣿⡟⠀⠀⠀⠀⠀⢽⣿⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⡛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠻⠻⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠢⠄⡀⠀⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣀
⠀⠀⠀⠀⠀⠠⠀⠘⠁⠀⠀⣀⣰⣴⣶⣿⣿⣿⣿⣿⣦⣷⣆⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣶⣾⣶⣬⣄⡀⠐⢤⢦⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⡀⠀⠀⠀⣴⣾⣿⣿⣿⠿⠟⣿⣯⡀⢸⠀⠉⠛⢿⣶⣬⣃⡀⣀⣀⣀⡀⣼⣿⣿⠿⠛⢩⠁⢀⣀⠉⣟⣷⣶⠬⢬⣵⣆⣛⡁
⠀⠀⠀⠀⠁⠠⠄⠠⠙⢻⣯⣅⣀⠀⠀⠛⠿⠀⠙⢲⣿⣇⣸⡀⠀⣀⠀⠉⠉⢉⣁⠉⠉⢠⣴⣆⣸⡀⣿⣿⠖⠛⠿⠟⣀⣤⠿⣿⢝⠇
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠛⢿⣿⠿⣷⢖⣶⢤⡤⢌⣙⠃⠈⠀⠀⠛⠂⠀⠀⠸⠿⠃⠀⠀⠙⠃⢀⣀⣈⣩⣤⣶⣶⣿⣿⠋⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠉⠳⢇⣘⠁⠚⠓⠨⠃⠀⡀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠉⠘⠛⠛⣻⠿⠛⠁⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⣤⡀⠀⠀⠀⢀⡴⠹⡿⢀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⠿⢿⣿⣿⣿⣷⣿⠾⠶⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣠⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣸⢰⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡰⡔⡞⣎⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣧⣄⣃⣘⠻⠀⠄⡄⡆⢶⠴⠀⠿⣿⢹⣇⣃⣧⡷⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠷⠷⠷⠾⠶⣶⠶⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠀⠀⠐⠂⠄⠠⠐⠂⠀⠀⠀⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠔⠀⣀⠠⠀⠐⠂⣈⡉⠀⡠⢀⠀⠀⡨⠩⢁⠀⢀⠌⠉⡉⢉⠭⡉⢉⠴⣀⠀⠀⠀⠀⠠⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠡⡘⢤⠂⠐⠎⠰⠀⣀⣙⢀⣄⠑⡎⢀⣄⡀⣶⣁⣠⣄⢰⡆⣤⢰⡄⣄⣇⣀⡏⠀⢡⠔⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠑⢶⣏⢉⡍⠉⣯⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⢸⡀⠀⢸⣄⢀⠇⢀⡥⠛⠁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠑⠈⠉⠀⣉⠀⠉⠉⠀⠒⠂⠉⠐⠒⠂⠉⠀⣉⠁⠀⠀⠂⠁⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠤⠤⠀⠀⠤⠄⠀⠂⠈







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠟⠛⠛⠚⠷⢻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣧⣤⣶⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠶⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠻⠟⠉⠀⠀⠀⠀⠀⠙⠻⣷⣶⣄
⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣰⡞⠋⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣧
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⣿⠀⣿⠃⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠘⢦⡀⠀⢀⡔⠀⠀⠀⠀⠀⢸⡇⢠⣿
⠀⠀⠀⢠⠏⠀⣤⡀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀⡏⣠⣿⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠙⣦⡞⠀⠀⠀⠀⠀⠀⢸⠇⢼⡧
⠀⠀⠀⣿⠀⠀⠸⣇⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⡀⠀⠀⠀⠀⠀⣼⣼⣿⠁
⠀⠀⠀⢻⡆⠀⠀⠽⣄⣠⣼⠛⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠹⡄⠀⠀⢀⣴⢿⠟⠁
⠀⠀⠀⠸⣷⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⣀⣤⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉
⠀⠀⠀⠀⢹⣷⣠⣀⣀⣠⣀⣀⣤⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⠿⠉
⠀⠀⠀⠀⠀⠹⠝⠾⠭⡿⢿⠹⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣟⣗⣻⣿⠿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢩⠽⠅⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣵⣶⣶⢶⠦⣤⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⢾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⣠⣾⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠈⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⠀⠀⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣷⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣇⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣿⡄⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠋⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⡉⣄⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⢀⣀⣠⣶⣿⡿⠟⠀⠀⠀⠀⢀⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣷⣤⣀⠀⠀⠀⠉⠙⠛⠃⠙⠙⠋⠉⠀⠀⠀⠀⢀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣶⡝⢿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢭⢭⡟⠛⠋⠉⠉⠿⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠛⠛⠳⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢀⣠⡶⣿⠟⣩⣭⣤⣤⣤⡈⠉⠻⣿⢶⣄⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣰⠟⠁⢰⡟⠰⣿⡀⣹⡇⠈⠻⣆⠀⢿⡄⠙⢷⡀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢻⣄⠀⠘⣧⠀⢻⡟⠋⠀⠀⢠⡿⠀⣾⠃⠀⢈⡿⢶⡄⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠙⢷⣤⣹⣦⡈⠛⠶⠶⠶⠟⢁⣼⢏⣀⣤⣾⣧⡾⠇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⣤⣤⡆⠀⠈⠙⠛⠿⠷⠶⠶⠶⠶⠿⠛⠛⠉⠀⠀⠀⠰⣦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⢀⣤⣽⣷⠄⠀⣀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⢀⣄⠻⣦⠘⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⢀⣼⡏⠀⠀⣠⡾⢋⣡⣤⣤⣄⡉⠻⣦⠀⠀⢹⡇⢹⡇⢹⡇⠀⣿
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠘⢛⡿⠃⢠⡿⢀⡾⠋⠀⢀⢈⣻⡄⢹⡇⢀⣼⠃⣼⠇⣼⠃⢰⡟
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠛⠁⠀⢸⡇⢸⣇⠀⣀⠙⣛⡋⠀⠀⠀⠀⠁⠾⠋⣴⠟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠈⣿⠀⣿⡀⢻⣆⠉⣻⡆⠀⠀⠀⠀⠀⠘⠋⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⠀⠀⠀⠀⠹⣧⡈⠻⣦⣉⠛⠋⠀⠀⠀⠀⠀⠀⣀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠈⠻⢶⣄⠉⠀⠀⠀⢰⡆⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⡄⠀⠙⢷⣤⣤⣤⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣛⣯⣝⡻⢷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⢳⣿⣿⣿⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠱⢶⣶⡝⡎⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⢟⣼⣿⣿⣿⣎⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⡾⢣⠿⣣⢇⣿⣿⡆
⠀⠀⠀⠀⠀⠈⢿⣏⢾⡛⢿⣿⠟⣻⠇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣵⣿⡞⣵⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣷⣵⣶⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠻⠿⣣⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⢛⡛⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡰⣇⣸⢟⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢸⣿⠟⣛⣛⠿⣶⣶⣿⣿⡿⡛⣿⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠸⡏⣾⣿⣿⣿⣶⣭⣭⣵⣾⣿⡌⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣿⣾⡟⣥⣶⣶⣶⣝⢶⣶⣍⢻⣿⡷⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠈⠻⣸⣿⣿⣿⣿⣿⢸⣿⣿⡇⠋⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡄⠀⠀⠀⠀⢀⣿⢿⡻⢿⣿⡏⡾⣿⡻⣿⡀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠠⢋⠞⠉⢀⣠⣶⣶⡿⣼⡇⣏⣉⡇⣿⢱⡱⣏⣹⢎⣇⢿⣶⣦⣄⠈⠑⣌⠦
⠀⠀⠀⠀⠀⠀⠀⠏⠀⣠⣿⣿⣿⣿⢣⣿⣿⣮⣿⣾⡏⢸⣷⣮⣵⣾⣿⡼⣿⣿⣿⣷⡄⠈⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠑⠢⡀⠀⣀⠤⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢒⡲⠇⠀⠀⠀⡗⠉⠀⠀⠀⠀⠈⢇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠙⠢⠤⠀⠤⠞⠁⠀⠀⠀⠀⠀⠀⢸⠙⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⢸⢀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⡄⠀⠀⠀⠀⡖⢲⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢘⡄⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢏⠈⢆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡰⠉⢣⠀⠀⠀⢸⠦⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣸⡄⠀⠀⢰⠋⠉⠊⠳⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠑⠒⠐⠋⠀⡇⠀⢀⡇⠀⠀⠀⠀⠱⢄⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠞




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠟⠛⠛⠛⠛⠿⢿⣶⣾⠿⠟⠛⠛⠛⠛⠷⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠸⣝⢿⣿⣿⢻⡟⠻⣿⠛⣿⣶⡶⣶⣤⣶⣶⣶⣾⡟⢻⡿⠛⣿⢻⣿⣿⢟⡽
⠀⠀⠀⠀⠀⠀⠙⣧⡙⠻⣿⣷⠶⣿⣦⣼⣯⣤⣤⣹⢡⣤⣬⣿⣤⣼⡷⢶⣿⡿⠛⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠈⠙⠷⣿⣦⣼⣏⡙⠋⣹⡉⠛⣉⣿⣤⣾⡷⠟⠉⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠋⠁⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣴⣶⣦⣄⣠⣴⣶⣦⣤⣤⣴⣶⣦⣄⣠⣴⣶⣦⣤⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠉⠉⠉⠁⠀⠈⢻⣿⠁⠀⠈⠉⠉⠁⠀⠈⣿⡟⠁⠀⠈⠉⠉⠉⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⣿⣇⣀⣠⣾⡿⢿⣷⣀⣀⣸⣿⣀⣠⣾⡿⢿⣷⣄⣀⣿⣇⣀⣀⣾⡿⢿⣷⣄⣀⣸⣿
⠀⠀⠀⠀⠀⠀⢻⣿⠉⠙⢿⣷⣾⡿⠉⠉⣿⣿⠉⠉⢿⣷⣾⡿⠉⠉⣿⣿⠉⠉⢿⣷⣾⡿⠋⠉⣿⡟
⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣀⡀⠀⠀⣸⡿⣿⡇⠀⠀⣀⣀⠀⠀⢸⣿⢿⣇⠀⠀⣀⣀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⣾⡟⢿⣇⠀⣿⡇⢸⣿⠀⣾⡟⢻⣧⠀⣿⡇⢸⣿⠀⣼⡟⢻⣧⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢰⣿⠁⢸⣿⣸⣿⠀⠈⣿⣆⣿⠃⠸⣿⣰⣿⠁⠀⣿⣇⣿⡇⠘⣿⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠀⠀⠻⠿⠃⠀⠀⠘⠿⠟⠀⠀⠻⠿⠃⠀⠀⠘⠿⠟⠀⠀⠻⠿⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡤⠶⢦⣤⠴⠶⢤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠹⡇⠈⠙⠦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠀⠀⠀⢹⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠷⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣄⡀⣀⡞⠛⠻⣄⡀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣀⡴⠋⠙⠋⠁⠈⠉⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠘⠦⢀⣀⣀⣤⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣉⣁⣀⣠⣞⣶
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⠀⠖⠚⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠓⠀⠀⠀⠀⠚⠋⠉⠁⠀⡟⠀⠀⠀⠈⠉⠀⠀⠉⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⣤⡤⠴⠖⠛⣉⣉⣀⣀⠀⠀⠉⠉⠁⣀⣠⣄⡀⠈⠉⠉⠀⠀⢙⡦⠀⢛⣭⣍⡉⠙⠓⠒⠛⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠈⣭⠙⠂⠀⠀⢸⣍⠓⢦⡙⢦⡀⠀⠀⠀⡟⠀⠀⠸⠀⢦⠉⠳⠦⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉⣶⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠸⣌⠛⢦⡙⢦⡙⢾⣏⠳⣽⠄⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⡀⠀⠀⠀⢸⣇⡀⠀⠐⣏⠳⣄⠙⣆⠙⠆⠙⢦⡙⢦⠀⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡤⠴⠋⠀⢻⢦⣄⠈⠳⡌⢧⡈⠳⠀⠀⠀⠓⠈⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⣆⠐⢀⠀⠀⠄⠀⠰⠀⢰⠀⡄⢠⠀⠂⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠴⠤⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣤⣤⣤⠀⢠⣤⣄⣀⠀⠀⠀⣠⣤⣄⠀⣠⣤⣤⠀⣠⣤⣄⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⣿⣿⣿⠀⣾⣿⡿⣿⣷⡀⠀⣿⣿⣿⠀⣿⣿⡟⠀⣿⣿⣿⢿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⢹⣿⡇⠀⣿⣿⣿⢰⣿⣿⠃⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣷⣶⣶⠀⠀⣿⣿⠁⢸⣿⡇⠀⣿⣿⣿⣾⣿⣿⠀⠀⣿⣿⣿⣶⣶⠂
⠀⠀⠀⠀⠀⠀⣲⣿⠀⠀⢸⣿⣿⡞⠛⠛⠀⢠⣿⣿⣷⢸⣿⣿⠀⣿⣿⣿⢹⣿⣿⡀⠀⣿⣿⣿⠙⠛⠃
⠀⠀⠀⠀⠀⠰⢾⢿⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⠛⢸⣿⣿⠀⣿⣿⣿⠀⣿⣿⣇⠀⣿⣿⣿⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⢸⣿⣿⠀⢸⡿⠻⠀⢸⣿⣿⠀⢻⣿⣿⡀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠁⠈⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠻⠻⠿⠛⠛⢿⣿⡿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣛⣛⢘⠻⢦⣄⣀⣤⢠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⣿⣿⣶⣭⣭⣅⣴⡆⣬⣝⠂⠀⢠⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⢁⣛⣭⠭⢭⣝⡻⠿⠇⠿⠿⠃⠀⠀⠻⠿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⡿⣓⣤⡄⣀⠠⠤⠠⣤⢤⣜⠿⣿⣿⣿⠀⠀⠀⠀⠙⠻⠟⠋
⠀⠀⠀⣼⣿⠟⣼⢟⣭⣾⡿⠿⣿⣿⣶⣷⡎⢷⡝⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢨⡵⣫⣭⣼⣿⣿⠇⠀⠀⣸⣿⣷⣾⣷⣭⢳⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⣿⣇⢿⣿⠟⠻⣿⣷⣶⣾⣿⣿⢿⠋⠙⢿⣿⣿⡀⠀⠀⣠⣶⣾⣿⣿⣶⣶⣭⡛⢿⣿⣿⡆
⠀⠀⠀⠈⣱⣾⣿⣷⣾⣿⣿⣿⣿⣿⡀⠀⠃⠀⠀⠺⣿⠃⠀⠀⢿⣿⣿⠏⠀⠀⠀⢹⣿⣦⢻⣿⣿
⠀⠀⠀⣿⣜⠻⣻⣿⠋⠀⠀⠈⣿⣿⣧⡄⠀⠀⠀⢀⡏⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⣸⣿⣿⢸⣿⡟
⠀⠀⠀⠹⣿⡸⠿⢿⣦⣄⢀⣼⡿⣿⣿⣷⣶⣤⢶⣿⢇⠀⠀⠀⠀⠀⠈⠻⢷⣶⣾⣿⠿⢣⠿⠛
⠀⠀⠀⢻⣌⡻⢿⣎⡻⠿⡻⠿⡃⢿⣿⢏⡭⣁⣭⣵⣿⠃
⠀⠀⠀⢸⣿⣿⡷⠶⠎⠙⠛⠛⠛⠑⠒⠋⠼⠿⣿⣿⣿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⢰⣿⠍⠉⠉⠏⠉⠙⡛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⡛⠛⠉⠏⠉⠉⢹⡶
⠀⠀⠀⠈⢿⣄⠀⠐⠀⠀⠀⠇⠀⠀⠀⣀⠂⠀⠉⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠁⠀⢀⡀⠀⠀⠀⠇⠀⠀⠰⠀⠀⣨⠃
⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⢂⠂⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⠀⠀⢀⣦⡾⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡼⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⣄⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣾⣿⣿⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣸⣿⣷⣦⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣟⡷⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣾⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⢀⣴⠶⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠷⢦⣀
⠀⠀⠀⠸⣟⠷⢦⢤⠁⠀⠀⡆⠀⠀⠩⠉⡙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⡉⠩⠁⠀⠀⡆⠀⠀⢡⣤⠶⢿⡋
⠀⠀⠀⠀⠹⣷⣄⡈⠛⠻⠶⣥⣄⣀⡀⠖⠀⠀⠀⠀⢀⡠⠈⠉⠉⠉⠉⡉⡉⠉⠉⠉⠉⠠⣀⠀⠀⠀⠀⠐⡆⣀⣀⣤⡴⠾⠟⠋⣀⣤⠞
⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⣰⠙⠛⠻⠃⠦⣶⣤⣠⡀⠸⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠹⠀⣤⣀⣴⡦⠇⠹⠛⠛⢱⡀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣄⣠⣴⣾⠀⠉⠙⠛⠁⠙⢰⣿⣷⣶⣿⡄⠠⠀⣼⣷⣶⣿⣷⠈⠅⠹⠛⠉⠁⢸⣦⣤⣄⣨⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣻⢦⣤⣀⣀⣠⡇⠀⠉⠈⠉⠛⠀⢠⠀⠘⠋⠉⠈⠁⠀⣧⣀⣀⣀⣤⢾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⡀⠀⠀⢀⣼⣄⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿