High jump Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣀⣤⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⣿⠦⣤⣀⣀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆
⠀⠀⠀⠀⣿⠀⠀⠀⠉⣩⣿⣿⣿⣿⡿⣿⣿⣛⣉⠀⠀⠈⣽⠛⠛⣿⣿⣿⡿⣷⣦⣤⣄⣀⣀⣀
⠀⠀⠀⢠⣿⠀⠀⠀⢰⣿⣿⣿⠋⠁⠀⠀⠀⠀⠉⠉⠉⠙⣿⠀⠀⠈⠙⠋⠀⠀⠀⠉⠉⠙⠛⠿⠟⠒
⠀⠀⠀⢸⣿⠀⠀⠀⠈⠛⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣶⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⠸⠟⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⢀⢨⣧⣀⡀
⠀⠀⠀⠀⠀⠻⠱⢧⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡆
⠀⠀⠀⠀⠀⠈⠙⢆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠖⠒⣛⡿⠃⠠⡟⢢
⠀⠀⠀⠀⠀⠀⠀⠘⡄⢧⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⡤⠤⢤⣄⣤⡖⠚⠉⠙⢦⡀⠀⠀⠀⡀⠀⢀⠜⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡆⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠑⠢⡀⠉⠀⠀⠀⠀⢳⠀⢀⣠⠇⡰⠛⠉⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢹⠞⠛⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⡼⠚⣩⠏⣼⠃⠀⠀⣼⣠⠤⢖⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣰⣂⡠⠊⠀⠀⣠⠞⠁⠀⣴⠃⡼⠗⣒⣫⡭⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠯⢷⡖⢶⣶⡿⠵⣖⣊⡿⠁⡼⡟⠉⠁⡰⠁
⠀⠀⠀⠀⠀⠀⡔⢹⡇⠀⣤⠶⠶⠤⠤⣀⠀⢀⡴⣀⡧⢖⣚⣽⠥⢶⣞⣋⣩⠟⠀⡼⠁⡇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢷⣼⡇⡸⠁⠀⠀⠀⠀⢸⠀⠏⠀⠙⠛⠛⠋⠉⠉⣉⣉⣀⣀⣀⡴⠁⢠⡷⢴⠇
⠀⠀⠀⠀⣀⣀⡤⠽⢛⣳⣾⠀⠀⢀⡤⣼⣴⣄⣠⣤⠴⠶⠛⠛⢻⠉⢹⠉⠉⠀⠀⠀⡼⢁⡟
⢠⢖⣚⣩⡿⠶⠚⣻⠟⠉⡉⠉⠓⢾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⣇⠀⠀⣠⡞⢁⣼⡅
⠘⠉⠁⠀⠀⠀⠀⡇⠘⠛⠁⠀⠀⠀⠉⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣉⠵⣴⠋⣿⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⣤⠀⠀⡇⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⡏⠻⢧⡀⠛⡽⣄
⠀⠀⠀⠀⠀⠀⠀⢳⡐⠀⠀⠀⠂⡰⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠹⡄⠀⠙⢶⣄⡈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡐⠋⠁⠈⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⢰⡇⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⣻⠃⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣞⡁⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣉⡽⢁⡔⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣤⡤⠤⢤⠤⣤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⣄⢀⡀⠐⢦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣀⣨⠇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡄
⠀⠀⠀⠀⢀⣀⣀⣰⡿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢿⡿
⢀⠀⠀⠘⠋⠉⠉⠁⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣴⣿⣤⣼⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⡷⠿⠿⢿⡿⠿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿
⠀⠀⠀⠀⢀⣤⣤⣤⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠔⠊⠁⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⢀⣴⣿⣿⣿⠿⠛⠛⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠉⢻⣿⡿⠀⠀⠀⠀⠀⠀⢘⡿⠋⠻⣧
⠀⠀⢸⣿⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⣷⡿⠋⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⡟
⠀⠀⣿⣿⣿⣿⣿⣿⡿⢶⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⢻⢱⡧⠀⠀⠀⠀⠀⠘⣿⠀⢀⣄⡀⠈⠳⠄
⠀⠀⠙⠛⠛⠻⠛⠛⠿⣾⣿⣷⣄⣠⣾⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⢀⣴
⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⣰⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣿⡧⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⢹⡄
⠀⠀⠀⠀⠀⢀⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣬⠇
⠀⠀⠀⠀⠀⢸⡿⠋⢙⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠏
⠀⠀⠀⠀⣰⠟⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⡟
⠀⠀⠀⠸⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⠿⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⣦⣄⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣯⡙⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣌⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⢹⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣀⣀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⠟⣛⣛⣉⣤⣿⣋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠉⠉⠁⠀⠚⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣶⣆⣀⣀⣤⣤⡄⠀⠀⠀⠙⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠈⠛⠿⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣿⡏⠉⠁⠘⢿⣿⣦⣤⣤⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⢀⣀⣤⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣾⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⣻⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠁⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏

⠀⠠⣤⠀⠀⠀⠰⣤⣀
⠀⠀⠹⣷⣆⠀⠀⠈⠻⢶⣤⣄⡀
⠀⠀⠀⠙⢿⣶⣤⣄⣀⠀⠙⠻⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⣤⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠛⠛⠻⠿⣷⣾⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣤⣶⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⠟⠙⣿⣿⣿⣟⣿⣿⣿⣿⣦⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤
⠀⠀⣾⡷⠒⠒⠒⠒⠒⠒⠒⠛⠛⣿⣿⣿⣿⠙⠋⠉⠉⣹⣿⡟⠉⠉⠉⠉⠛⢿⣿⣷
⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠘⢿⣿⡄
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆
⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣴⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠹⠿⠿⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡉⠉⠉⠉⠉⠉⠙⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻

⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡄⠀⠀⠀⠀⣀⣠⡤⠶⠶⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⣶⣿⡿⠿⠿⠿⠟⠋⢉⣉⣩⠥⠴⠒⠛⠉⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣤⣶⡾⠿⠿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣇⣤⠤⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⢸⣃⣀⠤⠤⠔⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⣶⣶⣴⣷⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⣷
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⢿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴
⠴⠀⣠⠖⠀⠀⠀⣠⣤⠆⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⣀⣠⣤⣶⠶⠛⠋⠁⠙⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠟⠋⠉
⠠⣤⡟⠀⠀⠀⠞⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠉⠁
⣾⠟⠁⠀⠀⣤⡾⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣤⣤⣄⡀⠀⠀⠀⠀⣠⣶⣄⣀⣤⣦⡠⠿⠛⠋⠉
⠃⠀⢀⣶⡿⠋⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣤⣤⡄⢴⣿⣿⣿⠟⠋⠉
⣠⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣯⣽⣾⣷⣿⣿⣿⡇
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠛⠋⠁⢹⣿⣿⣿⣿⣿⣿⠿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⡀⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣀⣀⣠⣤⣬⣭⣭⣭⣟⣛⣛⣛⣿⣿⣿⣿⡿⠿⠶⣶⣾
⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠿⠿⠿⡿⠟⠋⠁⠀⠀⠀⠀⢀⣼⡿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣴⣾⣿⠄⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠟⠉⠁⠀⢀⡤⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦⣤⣄⣴⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣏⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⣤⡤⡤⠄⠀⢀⣠⣴⣿⠿⠋⠉⠈⠁⠀⠀⠀⠀⠀⠉⠉⠉⢿⠂⠁⢠⡐⢠⣄⣤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣛⣋⣠⣴⣾⣿⣟⣉⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣀⣋⣰⣿⣿⣿⣇
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⣼⣿⣤⣤⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢛⣿⣿⣿⠟
⠶⠶⠦⠤⠤⠤⠤⠤⢤⣴⣿⣿⣿⣿⣿⣿⣿⠿⠤⠤⠬⠭⢯⣿⣿⡿⠶⠶⢶⣾⣿⠿⠷⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⢀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠘⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠙⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠧⠧⠤⠀⠠⠐⠒⠉⠀⠈⡂⢀⣠⠶⢦⡄⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⢀⡷⠤⣄⣀⠀⠀⠀⣸⡀⠀⠧⡄⠸⡄⠀⢀⡴⠊⢉⡵⠉⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣀⡤⠞⠀⣀⡀⠈⠙⠢⡀⠁⡇⠀⠀⢰⠀⠘⡔⠁⣀⣀⠎⠀⠀⠀⢠⣄⠀⠈⢢⣤⡞⡆⠀⠀⠀⠃
⠀⠀⡞⠀⠀⠀⠀⠀⠒⠉⢙⠆⠀⢈⢴⣽⠂⠀⠀⠹⡼⠀⠀⠀⠘⠀⠀⢹⣉⠀⠘⡄⠀⠀⠠⢧⠞⠙⠂⢤⣀⣧⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢩⠁⢀⠀⠀⠀⣗⣒⣒⣠⠶⠀⠀⡘⠠⡈⢢⠈⢓⡶⠥⠀⠀⠤⠤⠤⠬⠩⢤⠤⠄⠠⡄⣄⠀⣀⣀⡀
⠀⢸⠀⠀⠀⠀⠀⠠⢞⠁⠀⠀⢄⠀⠀⢀⠈⢁⠀⠀⠧⠔⠊⡡⠂⠀⠀⡁⠀⠀⡠⠖⠉⠉⠉⠈⠉⠉⠁⠀⠀⠀⠘⠒⠒⠒⡇⠓⠀⠀⠤⠞
⠀⠀⢇⠀⠀⠀⠚⢄⡀⠀⠣⣸⡿⠁⠀⠉⠁⠁⣠⢻⣀⠀⠀⠁⠒⠒⠈⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠘⣄⠀⠀⠀⠀⠈⠑⠲⠤⠤⠤⠤⠤⠔⠊⠁⡰⠈⡏⠙⠲⠶⠎⢹⡆
⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠱⠤⠤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠙⠢⠤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢠⣤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠂
⠀⠀⠀⠀⠀⡀⠸⢖⠀⢜⡷⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⡀⠀⢿⣇⢨⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢈⡦⣤⣜⣭⡺⠗⠚⢶⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⣷⣾⣦⠟⠋⠀⠀⠀⠀⠀⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠛⠉⣤⡖⠀⠀⠀⠀⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⣰⠀⠀⠀⠀⠀⠠⠐⠂⠀⠒
⠀⠀⠀⠀⠀⢠⣤⣶⡀⡿⣘⡟⠃⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠸⡛⢹⡿⣿⠻⠀⠀⠀⠀⠀⢫⡤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⢆⣻⢿⡀
⠀⠀⠀⠀⠀⠐⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠛⠛⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⢀⡀⠘⠇
⠀⠀⠀⠀⠀⠠⠋⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡀⠀⢨⣹⣄⡀⠀⡀
⠀⠀⠀⠀⣄⣀⠀⢘⡏⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⡆⠐⠊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠟⣙⢉⡟⠃⠀⠁
⠀⠀⠀⠀⠛⠛⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣾⣷⣿⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠴⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⣀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢿⡿⠿⠿⣿⣿⡛⣹⣏⠁⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢋⣩⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠐⣿⣿⣿⡿⠻⡷⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⣿⣿⡅
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣿⣿⠃⠀⠀⠀⠁⢀⡰⠎⢠⠄⠀⠀⠀⠀⠀⠀⠐⠏⠀⠉⠹⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠎
⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡤⣶⣦⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣀⣴⣥⠞⠀⠀⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠲⣆⠀⠀⠀⠀⠀⠀⣿⣁⡈⢥⣈⡀
⠀⠀⠀⠀⠀⢸⣾⠟⠁⠀⠀⠀⠸⣾⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠉⠁⢀⣀
⠀⠀⠀⠘⠳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡙⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠓⠀⠐⢢⣦⣷
⠀⠀⠀⠀⠀⠰⣿⣧⣀⡀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⡁⠀⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡔⠂⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡿⢿⣿⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠤⠴⠆⢠
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠠⢜⢿⡿⠋⠙⠻⢤⡀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣾⣷⡀⠀⠂⢴⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢽⣶⠶⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠪⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣾⣷⣀⡄⠀⠀⠀⠀⠀⢀⣼⡿⣏⣀⣀⡀⠀⠀⠀⠀⠀⠘⣦⣤⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠋⠉⠀⠀⠀⠀⠀⢰⣿⣿⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣶⣄⠀⠀⠀⠠⠶⠾⠿⠋⠁⣀⡉⠛⠲⠚⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⢸⠛⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢷⣶⡄⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⣿⣶⡞⠋⠁⠀⠀⠈⠛⠉⠛⢶⣤⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⠀⠀⢰⣿⣏⠁⡿⠀⠀⢀⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⣶⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠘⢿⡆⠀⠀⠀⠀⠀⢙⣿⡿⠁⠀⢰⣿⣿⣵⣾⣿⣿⣓⣶⠀⠀⠒⠒⢒⣾⣿⠟⠛⢻⡟⢻⠟⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⢠⡖⠛⡟⠁⠀⠀⠈⠛⠛⠉⠀⠉⠙⠛⠃⠀⠀⢀⣀⣹⠋⠀⠀⠀⢾⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈

⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀
⠀⠀⢻⣿⠢⠀⠀⠀⠀⣹⡿⠤⠄⠀⠀⠀⡗⠀⠀⠐⠒⣿⠈⠀⠀⢸⣿⠀⠀⠀⠀⠂⠉⣿⡇⠀⢈⣿⠂
⠀⢀⡼⠛⢆⠀⠀⢀⠞⠋⠧⡀⠀⠀⠀⠸⢇⠀⠀⠀⢰⠋⡇⠀⠀⠈⡿⢷⠀⠀⠀⠀⢾⠟⠁⠀⢈⣿
⠀⠈⠀⠀⠈⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠃⠘⠀⠀⠀⠈⠀⠀⠀⢀⡀⠁⠈⠀⠀⠀⠀⢋⠀⠀⠀⠉⠁
⠀⠂⠲⣾⢇⡀⠀⣠⣷⠒⠂⢀⠼⣷⠖⠒⠀⠀⣾⡗⠊⠀⢸⣿⠉⠀⠀⢐⣾⣧⡀⠀⣾⣿⠉⠀⢳⣿⠤
⠀⠀⢸⣷⡀⠀⠀⡸⠛⣆⠀⠀⠀⣿⠁⠀⠀⠀⡻⡇⠀⠀⣰⠿⣇⠀⠀⣸⣿⠀⠀⠀⡸⡏⠀⠀⢸⣿
⠀⠐⠉⠀⠃⠀⠀⠃⡀⠘⠀⠀⠀⠘⠁⠀⠀⠀⠂⠃⠀⠀⠃⠀⠘⠀⠀⠃⠃⠀⠀⠀⠃⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⠀⠀⠀⠘⠶⣴⡶⡄⠀⣾⠿⣻⠃⠀⣰⡃⠀⣀⣤⡤⡦⠀⠀⢀⢄⡠⠀⠀⣀⠀⠀⠀⣀⣀
⠀⠈⢦⣎⣀⣀⡠⠄⠀⠀⠏⠀⠀⠀⠀⠀⠁⠀⢺⣿⡁⠀⠛⠉⠛⠁⠀⠀⢠⠟⠀⠀⠀⢻⣄⠸⠛⡏⠉
⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⢀⠀⢸⠙⣄⠀⠀⠀⠘⢹⠈⠀⠐
⠀⠀⢀⡤⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⢺⣿⠃⠀⠀⢀⣾⣆⠈⠀⠀⠁⣴⠇⠀⠘⠀⢀⣤⣤
⢀⣀⡿⠗⠦⣀⠀⠘⣿⠁⠀⠀⢀⣓⣻⡄⡀⠀⠠⠬⠽⣥⠀⠠⠞⠉⠈⠁⠀⠐⠚⢛⢲⠤⠆⠠⢴⠟⠃
⠀⠀⠛⠓⠂⠀⢀⡞⠛⣉⠀⠀⢀⠀⠀⢇⠀⠀⠰⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⠄⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠘⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠈
⢸⣿⡀⠀⠀⢶⣧⠀⠘⣴⡄⠀⠀⣴⣷⠀⠀⢰⡆⠀⠀⣴⡦⡀⠀⠀⠀⠀⠀⠠⣤⣆⡀
⢸⢳⠌⠂⣀⢾⡧⠀⠀⢹⢧⡀⠀⢸⣿⡀⠀⣽⣧⠀⠠⡼⡇⠃⠀⢠⣶⢻⠋⠀⠁⢸⣇⠀⠀⠀⣿⣿⣆
⠈⡀⠀⠀⠁⠈⠋⠁⠈⠛⠈⠅⠀⠈⠏⠀⠀⡇⠁⠀⠀⠑⠙⠦⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⠐⠀⠀⠈⠉
⠀⡠⣴⡀⠀⠀⣰⣤⠀⠀⠀⣰⠀⠀⢰⡄⠀⠀⣠⣆⠀⠀⢰⠄⠀⢀⣴⡀⠀⣰⣆⠀⠀⢀⣤⠀⡠⣄
⠀⢰⡟⠁⠀⠘⣿⣍⠀⠀⢈⣿⠃⠀⢸⣟⠀⠀⣾⠏⠀⠀⣿⡃⠀⢸⣿⠅⠈⢹⡏⠀⠀⢻⡟⠀⣘⣿⡅
⠀⡝⠁⠀⠔⠚⠁⠀⠅⠀⠘⠛⠃⠀⢸⠹⠀⠀⠏⠀⠀⡰⠯⠋⠀⠘⠻⠀⠀⡜⢇⠠⠔⠋⠙⠀⡏⠈⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠘⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠈⠣⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⢀⣨⠽⠓⣶⣦⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡖⠛⠉⠁⠀⠀⠸⣿⣿⠃⠀⠀⠀⢸⣇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⢀⣿⡈⠀⠀⠀⠀⠈⠙⢦⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣸⠿⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⢀⠟⠂⠠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣷⣴⣶⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠉⠉⠉⠉⠉⠛⠻⠿⠿⠶⠶⠶⣦⣦⡀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰
⠀⠀⠀⠀⠀⢰⣶⡶⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠙⣿⢳⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠨⣄
⠀⠀⠀⠀⠀⣼⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⣶⣿⢿⣶⡆⠄
⠀⠀⠀⠀⠈⠉

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣤⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣇⠀⡄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣴⢻⣿⡿⠀⠉⠉⠉⠉⠀⠀⠀⠀⢀⡞⠉⢹⣿⣿⠻⠇⠀⠀⠀⠀⠀⠈⠳⣄⣿⣂
⠀⠀⠀⠀⠀⢠⠇⣸⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠾⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠛⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈
⠀⣰⠷⢦⣤⣄⣼⡿⠁⠀⠀⠀⠀⠹⣶⠖⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠻⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠋⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⢸⡇⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣧⣴⣷⣶⣦⣤⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠔⢻
⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⠋⠛⣿⠏⢩⡿⠯⠤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠶⣦⣴⣦⣤⣄⣀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠸⡿⠏⠉⠀⠀⢠⡏⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⡴⠛⠛⠛⢿⡿⠿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⡤⠋⠀⠀⠀⠀⠀⡽⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⢸⠁⠛
⠀⠀⠠⠤⠴⠶⠒⢻⣿⣿⠳⠦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢁⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⢀⠀⠀⠀⠀⣰⣿⠿⠿⠛⠛⣷⡀⠀⠀⠀⠀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢠⣄
⠰⠛⠛⠛⠳⠾⠛⠁⠀⠀⠀⠀⠈⠻⡶⠂⠀⠀⠈⢳⣼⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣾⣿⢟⣿⠿⢿⣦⡀⠤⠤⠤⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠋⠀⢸⡇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⠇⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠻⠿⣿⣓⣄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣴⣿⣿⣿
⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣬⣛⠦⡀
⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣈⣙⣛⡤⣄⡀
⠀⢿⡽⡎⢢⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⣶⡤⡀
⠀⠀⠛⣿⠿⢿⣷⣶⣶⣶⣾⣿⣿⣷⣿⣿⣿⡀⠀⠹⡈⠻⣗⠈⢢
⠀⠀⠀⠉⠀⠀⠈⠙⠛⠻⠿⠟⠀⠻⣿⣿⣿⣿⠀⠀⠱⡀⠈⠳⢦⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣿⣀⠑⠦⣀⠀⠹⢮⣅⡐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣟⡥⠆⠀⠈⢳⡀⠀⠙⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣶⡆⠀⣸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣿⣿⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⠛⠉⠁⠀⠀⠀⢻⣿⣇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣤⣤⣉⠒⠄⡀⠀⠀⠈⢿⣿⣆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣷⣦⣭⣲⣦⣬⣿⣿⣦⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠋⣡⠟⠛⢿⣧⡀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢖⡴⠁⠀⠀⠀⠙⢿⣷⣤⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣌⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢛⡴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣷⣋⣀⣀⣀⣀⣀⣀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣶⣿⣾⡿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣿⣿⣿⠿⠿⠿⠟⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠰⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⡄⠀⡘⠀⠀⠀⠀⠀⣀⣀⡀⠄⠒⠀⣙⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣰⣿⠟⣻⣿⣍⠙⣿⣿⣿⣿⣿⣃⡄⢀⣀⠴⠒⠉⠁⣀⢨⣷⣾⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠾⣿⡏⠸⣿⣿⣿⡇⢸⣿⣿⣿⣶⠚⢡⣿⠀⢰⣶⣧⣾⣿⣿⣿⣎⡻⠿⠋
⠀⠀⠀⠀⠀⠀⡈⠀⠀⣉⣛⣛⣿⣮⡛⣿⣿⣁⠀⢨⡟⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢀⠄⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠓⠲⠞⠛⠋⠀⠀⠀⢹⣿⣿⢿⠁
⠀⣠⡞⠁⠀⠀⢀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⢿⡌
⢰⠏⠀⠀⠀⣠⠟⢹⣾⣿⣿⠁⠀⣠⣾⣶⣿⡇⠀⠀⠀⠀⣾⣿⣿⢿⡇
⣏⠀⠀⠀⠞⠋⠀⢸⡿⠛⣿⣤⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⢧⢺⡅
⠙⠷⠶⠤⣤⠔⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⡀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⡀⠀⠛⢿⣿⡇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣧⣀⡴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣿⣿⣻⣻⣛⣛⣛⣫⣭⣥⡀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⠋⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠷⠈⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⢀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠻⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⣀⣠⣬⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⡟⠁⠿⢿⣿⣻⢿⣿⣿⣿⡿⣫⡶⠟⠉⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢹⣿⣧⢻⡿⠿⢟⣩⣦⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡋⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⠟⣫⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣛⣥⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⡉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢛⣻⣿⣦⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⣤⣀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠓⠿⠛⠻⠟⣉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣛⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⠿⠷⠶⠞⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⡿⢿⠟⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠷⣤⣤⣤⣤⣶⠯⠓
⣤⣤⣤⣄⣠⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣜⣷⣶⣿⣛⣩⣄⣠⣄⣠⣄⣤⣤⣤⣤
⣿⠿⡿⠿⡿⢻⠿⢏⠻⠿⣿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣛⣛⣛⣛⣛⣿⣿⣛⣛⣛⣛⣛⣿

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

⠀⠀⠀⠀⣀⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢲⠰⢂⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡀⣀⡀⠀⢀⣾⠫⠇⡀⠀⠀⠂⢺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠘⡏⢼⡏⢠⡿⢖⣻⠠⢄⠃⠄⠐⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⢀⡴⣤⠀⢡⢼⡇⣼⠃⣄⠃⠠⠌⠀⠀⠨⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠸⢦⠈⠆⢸⢸⡇⣿⠍⣔⠃⠥⠀⡀⠀⠅⢠⣿
⠀⠀⠘⢧⠘⣼⡎⡇⢹⣆⠣⠀⢀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⢣⠘⢧⡇⠈⢷⣞⡈⠦⠂⡄⠆⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢣⡸⣿⡀⠈⢟⣦⣬⣐⡘⣾⠋
⠀⠀⠀⠀⠀⢸⢳⡄⠱⡀⠀⡆⠉⡵⠋
⠀⠀⠀⠀⠀⢸⠀⢳⡀⠙⣆⡇⢰
⠀⠀⠀⠀⠀⢸⠀⠈⢳⠀⠈⠳⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠘⣆⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠴⠎⠉⠀⠀⠀⠁⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⡈⣄⠀⠀⠈⢢⠀⠀⠀⠀⡰⠋⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⣿⡆⠀⠀⠀⢣⠀⠀⢰⠁⠀⢀⠠⠊⠀⠀⠀⢀⠄⠂⠀⠀⢀⣠⠧⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡆⠀⠀⠀⠳⡤⠒⠲⡈⠀⠀⠀⠀⠀⠐⢇⠀⠀⢠⠖⠙⡀⠀⠀⠀⠐⠓⢌⠐⣬
⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⡏⠉⠻⣦⠀⠀⠀⠱⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠑⡴⠁⠀⣰⣿⣿⣶⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⡇⠀⡔⠛⠑⢦⡀⠈⠣⡀⠀⠀⠘⡄⠀⢫⠀⠀⣐⠀⠀⠀⢀⣦⡠⠐⠙⢿⡿⠟⠀⡀⠀⡀⠐⠻⢿
⠀⠀⡜⠋⠉⠈⣧⠠⠷⠀⡀⠀⠉⠲⠄⠑⡄⠀⠀⠘⢄⠘⠹⡁⠀⠐⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡁⠀⠀⠀⢹⣄⡀⠀⠈⠑⠒⠀⠀⠀⢻⣄⠀⠀⠈⢢⣄⡑⢄⣀⣀⡀⠀⠓⠤⣀⣠⣴⣄⠀⠀⠀⡄⠀⠀⠀⢰
⠀⠀⠣⡄⠀⠀⢘⡈⢯⡢⣀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠱⠱⡄⠀⡠⠒⠂⠑⡄⠘⣿⣿⣿⠗⠀⠀⠀⠀⢠⣤⠂
⠀⠀⠀⠀⠀⠉⠀⠑⠆⠷⠏⡀⠀⠀⠀⠄⠀⠀⠐⡳⢄⣤⣨⠗⠃⠀⠁⠀⠀⠈⠉⠲⢉⠉⠙⢄⠀⠀⠀⡀⠞⠁

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

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

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

⠀⠀⠀⢶⡦⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠷⡀⠀⢀⠀⠀⠀⠀⣴⡄
⠀⠀⢠⣾⣿⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣤⣾⡇⠀⠀⠀⠀⠀⠚⣽⣟⠛⣡⣤⣿⢇⡀⣰⠶⠿⣤⠄
⠀⠀⠈⣿⣿⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡍⠙⠋⠀⠀⠀⠀⢀⡼⠋⠉⠷⢡⣿⣏⡉⠀⣠⡶⡆
⠀⠀⠀⠛⠛⠀⠀⠚⠻⠛⠙⠀⠀⠀⠀⠀⠦⠘⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠘⠃⠈⠁⠀⠻

⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠠⣶⠆⠀⠀⠀⠀⠀⣠⢤⣼⡿⡀⠀⠀⠀⠀⠀⢠⣠⣶⠄⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⡴⢾⡿⠦⠤⠠⠖⣾⡷⣤⠀⠀⠀⠀⠀⣰⠿⠯⡭⠁⠀⠀⠀⠀⠀⠈⢳⣿⡦⠤⠀⠀⠀⠀⢀⣬⢽⣶⣀
⠀⠀⢀⣠⠟⠛⠇⠀⢀⣰⠟⢻⠂⠀⠀⠀⠀⠴⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣼⠿⢦⡄⠀⠀⠀⠀⠀⠀⣸⠿⣄
⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠁⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠃⠀⠀⠀⠀⠀⠘⠉⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢀⡀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠰⠄⠈⣽⡿⣏⡿⠿⠀⠠
⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠐⠚⣻⣿⠋⠉⠀⠀⠀⠀⠀⠰⣾⣿⠛⠛⠀⠀⠀⠀⠀⠉⠁⠘
⠀⠰⠀⠀⠀⣰⠛⢷⡀⠀⠀⠀⠀⠀⠠⠶⠏⢳⡄⠀⠀⠀⠀⠀⠀⢀⣿⢿⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣿⡄
⠀⠀⠀⠒⠀⠛⠀⠘⠃⠒⠀⠀⠀⠒⠀⠀⠀⠈⠃⠐⠀⠀⠀⠂⠀⠘⠁⠘⠀⠂⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠇
⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣵⣤
⠀⠀⠀⠀⠀⢀⡟⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠺⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⢛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡛⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⣀⠴⢋⣡⠴⠚⣉⣩⡥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢬⣉⣙⠒⠦⣌⠓⢦⡀
⠀⠀⠀⠀⢠⠞⢁⠔⢋⡤⠖⣉⡥⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⣌⡙⠲⣌⡙⢦⡙⢦⡀
⠀⠀⠀⡰⠃⡴⢃⡴⢋⡴⠊⣡⠴⠒⢛⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡛⠒⠤⣉⠳⢄⠙⢦⠙⢆⠹⣄
⠀⠀⣰⢁⡞⢠⠏⣰⠋⡰⠊⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣌⠳⣄⠳⡌⢳⡈⢧⠘⡆
⠀⢠⠇⣼⢀⡏⣰⠃⡼⢡⠞⠁⠀⣴⢒⣒⣒⣒⠦⢄⡀⠀⡶⠒⢶⠀⠀⡖⠒⢶⠀⣴⢲⠲⡄⠀⣴⠒⢲⡄⠀⠈⢣⡈⣆⠹⡄⢳⠘⡆⢹
⠀⢸⠀⡇⢸⠀⡏⢸⠁⡞⠀⠀⠀⣿⢸⠁⡖⠾⡝⡆⢳⠀⡇⣿⢸⠀⠀⡇⣯⢸⠀⣿⢸⠳⣜⢦⣿⢸⢸⡇⠀⠀⠀⣧⠸⡄⢷⠘⡆⢻⠈
⠀⢾⠐⡇⢸⠀⡇⢸⠀⡇⠀⠀⠀⣿⢸⣄⣓⣚⡵⢃⡞⠀⡇⣿⢸⠀⠀⡇⡿⢸⠀⣿⢸⢠⣌⢣⡉⢸⢸⡇⠀⠀⠀⣸⠀⡇⢸⠀⡇⢸
⠀⢸⠀⣇⢸⡀⣧⠸⡄⢳⠀⠀⠀⣿⠸⠀⡖⣎⢣⠹⡄⠀⢳⡘⢦⣓⣚⡴⢃⠞⠀⡿⠸⢸⡏⠳⡙⢾⢸⡇⠀⠀⢀⡏⣸⠁⡟⢰⠃⡾⢰
⠀⠈⣇⢸⡄⢧⠘⣆⠹⡄⠳⣄⠀⠙⠒⠚⠁⠈⠓⠒⠛⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠙⠒⠚⠁⠀⠙⠒⠚⠁⠀⣠⠎⣠⠃⡼⢁⡞⢰⠃⡼
⣀⣀⣸⣄⣳⣌⣧⣈⣦⣈⣦⣌⣳⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⢊⣡⠞⢁⠞⢡⠞⣠⠏⣰⠁
⡷⠴⡧⠼⢦⠽⢦⠽⢦⡽⠶⢬⡽⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⣉⡤⠞⣁⠴⢋⡴⢃⡼⠁
⡗⢚⡗⠒⠚⠳⣞⠛⢶⣛⠓⢶⣟⣛⡓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣛⣉⣡⠴⠚⣡⠴⢋⡴⠋
⣏⣹⣏⣉⣉⣉⣉⣙⣯⣍⣙⣻⣭⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⠤⠴⠒⣋⡡⠖⠋

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠻⣿⣿⣿⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⣿⣿⡏⠸⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣆⢻⣿⣿⠀⠀⡄⠰⠓⠐⠚⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠘⢷⠰⡀
⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠮⠭⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⠀⡜⠀⠀⡆⠀⠀⠀⢀⣀⢀⣀⣠⠳⠤⠴⢇⣀⣀⠀⠀⠀⠀⠀⠀⡎⠀⠑
⣿⠀⠀⠀⠙⠉⠉⠙⠁⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁⠀⠀⢈⠉⠉⠉⠻⠀⠀⠀⣿⢠⠀⠀⠀⠋⠉⠉⠙⠁⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⡉⠉⠉⠙⠄⠀⠀⢁
⣿⣄⣀⣀⡀⠒⠒⠚⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠒⠒⠀⠀⣀⣠⣿⠘⢤⣀⣀⡀⠒⠒⠚⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠓⠒⠂⢀⣀⣠⠄
⣿⣿⣿⣿⣷⣶⣶⣿⣿⠉⡱⢤⣤⣴⡂⠘⣦⣤⣤⠶⠋⢹⣷⣶⣶⣶⣿⣿⣿⣿⠀⠀⠈⠉⠓⠒⠚⠙⣏⢈⠳⠤⣤⣶⡁⢑⣦⣤⠴⢚⣉⡿⠓⠒⠒⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡦⠋⠀⠀⡀⠀⠙⡇⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⡜⡉⠀⠀⠀⠀⢙⢆⣦⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠀⠀⠄⠀⠘⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠋⠁⠀⠀⠈⠛⢸⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠸⠂⠀⠀⠐⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢛⠁⠀⠀⠘⠏⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣷⣦⣤⣦⣴⣷⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣿⣷⣴⣶⣾⣿⠛⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠈⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡿⣿⡿⣿⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠘⡏⠸⡇⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡏⠀⢸⠁⢸⠀⢹⠀⠘⡟⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠁⢀⡇⠀⠁⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢱⠀⠀⠀⡸⡀⠀⠀⠀⠁⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣦⠀⢠⣾⣿⣄⠀⢠⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡆⠀⣼⠁⢹⡄⠰⡞⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠀⢸⣿⣿⣏⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⢸⡇⠀⠀⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣸⣿⣿⣿⡀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⢠⡇⠀⠀⣧⠰⢾⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⣷⠀⢰⡟⠀⠈⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠀⠸⡀⠀⢠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣸⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣤⠁⠀⠀⢣⡄⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠠⠀⠒⠐⠢⢄
⠀⠰⠁⠀⠀⠀⠀⠀⠀⢃
⠀⢁⠀⠀⠀⠀⠀⠀⡊⣾⣤⠠⢀⠤⣀⠤⢤⣀⡀
⠀⠀⢦⡔⠻⠛⠁⠀⠑⢞⣀⠵⠂⢰⠇⠀⠀⢫⡙⢦⡀
⠀⠀⠈⢷⣤⠀⠀⠀⢠⠀⠀⠠⠀⠘⡄⠀⠀⠀⠉⠢⣷⢄
⠀⠀⠀⠀⠻⣅⣀⠔⡏⠀⠀⠀⡀⠐⣘⠄⠀⠀⠀⠀⡨⠙⠷⣄
⠀⣀⡀⢀⣀⢸⡀⠀⠱⣄⣀⡠⠁⠀⠀⠙⠳⢤⠤⠐⠁⠀⠀⠙⢧⡀
⠀⡈⠩⣴⡦⠈⠙⡑⠒⠤⣀⠀⠀⠀⠀⢀⣀⡀⠵⠦⠴⠤⠄⠀⠀⠹⢦
⠀⢁⠌⣋⣈⡍⠀⠈⠢⣀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⢄⡀
⠀⠀⠁⠮⠄⠐⠒⠂⠤⠤⠱⢤⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠆⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⠀⠀⠉⠁⠀⠒⠒⣂⠩⢫⠔⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠒⠛⠓⠚⠓⠀⠉⠈⠆⠀⠀⠀⠀⠀⣤⣶⡤⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣀⣀⡀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡯⠠⠤⠤⠤⢉⣁⠒⠠⢄⡀⡁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢤⠿⠶⢎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⠐⠢⢀⡀⠀⠀⠀⠀⠀⠀⠱⡀⠉⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⠀⠔⠉⠑⢲⡄⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡜⣀⠀⠀⠀⠀⢀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⣻⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢀⢴⠏⠀⠀⠉⠁⠀⠐⡌⢢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠤⣄⡀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠚⠁⠀⣀⡠⠤⠤⠀⠠⣇⠌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⠤⠌⣷⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠱⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤⢼⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠠⠾⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⣄⡀
⠀⢺⣿⣿⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠙⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢯⣿⣿⣽⣿⣏⣿⣿⣟⣿⣿⣿⣿⣶⣄⡀
⠘⠻⣦⣀⣿⡿⢿⣿⣿⣿⣦⡀⣠⣴⣿⣿⠿⣽⣿⡿⢳⣿⣿⡏⣿⣿⣿⢹⣿⣿⣯⢿⣿⣿⡿⣿⣿⡲⣄
⠀⠀⠀⠙⠛⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣿⣯⣥⡘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉
⠀⠀⠀⠀⠈⠉⠉⢉⣿⠀⠘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠁⢀⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⡇⠀⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠠⠐⠊⠉⠉⠳⢦⣤⣤⣽⣿⣿⣷⠶⠶⠶⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠣⣄⢀⣀⣀⣠⣤⣤⣤⡾⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⢛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⣿⠿⠟⠛⠻⠿⠿⠷⠆⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠠⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⠟⠿⠉⠳⣼⡇⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢿⠁

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣦⣀⡀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠈⢿⣿⣿⣷⣶⣿⣿⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠋⠀⠈⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⠟⠁⢀⣠⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠟⠛⠉⠸⣿⣿⣿⠏⠉
⠀⠀⠀⣶⣶⣶⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟
⠀⠀⠀⠀⢿⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣶⣿⣿⠿⣷⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⠉⠁⠀⠸⠀⠀⠉⠉⠛⠻⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⢿⡟⠀⡴⣤⣀⣀⣀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠏⠁⠈⠉⢹⠟⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠂⠰⠾⠅⠀⠴⡤⠂⢺⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⢰⣦⣄⠀⣐⣤⣤⠄⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢀⡀⠀⠒⠀⣿⠈⠈⣳⣦⣴⣷⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠈⠀⢀⠀⢰⣿⣇⣷⡿⣻⣿⢿⣿⠧⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢰⡄⣠⢏⡞⢸⣿⠛⣿⠇⠃⡃⣹⢣⠀⠀⠙⢗⠀⠀⠀⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⢷⣿⣼⠀⣿⣿⡆⠁⡀⠀⣼⠃⡿⠀⠀⢐⡤⠛⠀⠀⠀⠈⣙⠂⠀⠀⠀⠀⠀⠀⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠈⣿⣿⠀⢿⣿⣿⠠⠁⣸⡏⡄⣿⠀⣴⠋⢀⡀⠀⠀⠀⠀⣌⠳⡄⠀⠀⠀⢀⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠈⢛⣿⠀⢈⣿⡇⠀⡸⢸⡟⡇⢻⢰⡇⣠⡞⠁⢀⡴⢠⠆⠈⠱⣿⠀⢠⣾⣿⡿⠋⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⢠⣸⣿⡾⣯⣿⠀⠰⠁⠀⠀⡙⣾⣿⣇⣿⠀⠀⣾⢁⣿⡄⠀⠀⢦⡾⠏⠁⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⣿⣿⣿⣷⡈⠻⢰⣶⣆⠙⢆⠻⣿⣿⣿⣿⡇⣷⡛⣈⠉⠁⠀⠀⠀⢁⠺⠀⠀⢠⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣸⣿⣿⠟⠉⠀⠸⠉⢻⣿⣦⠲⣄⠸⣿⣿⣿⣷⣿⠇⣿⡄⠀⢀⣀⣀⣀⡀⣦⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡁⠀⠀⠀⠀⢳⢾⡿⣿⣷⣌⡻⢿⣿⣿⣿⣯⡀⠻⠷⠛⠉⣉⣬⡭⢍⠳⣌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢹⣶⣄⠀⠈⣯⣙⣷⠀⠿⣿⣿⠓⠻⣿⣿⣻⣧⠰⠟⣡⡿⣉⠴⠂⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⣾⡞⠁⠈⠙⠿⠶⡌⢿⣿⣿⣿⠾⠿⢿⣿⣿⣿⣿⣿⡆⢰⣿⠾⠋⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⡿⠿⠿⢟⣛⣛⣩⣽⣷⠘⠃⣤⣾⣶⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠶⣛⣻⣿⡿⠿⣟⣛⣿⡇⠈⡋⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠛⠋⡉⠉⠹⠟⠀⠠⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷
⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣀⣤⣴⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣄⡀
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣦⡀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣿⡄
⠀⣾⡟⠩⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⡿⣸⡿⠁⣾⣿⣿⣿⣿⠿⣿⣧
⠀⣿⡇⠀⣿⣿⣿⣿⣿⠉⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⣿⣿⣿⣿⣿⠐⠿⠟⠋⠉⠀⣾⠇⠀⣿⣿⣿⣿⡿⠀⠈⠋
⠀⢻⡃⢲⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⣷⡄⢀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⡧⠀⣿⣿⣿⣿⣿⡀
⠀⢺⡇⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠑⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠀⠀⣿⣿⣿⣿⣿⡇
⠈⠢⠀⣾⣿⣿⣿⣿⣿⣿⠈⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠹⣿⣿⡿⣿⣿⡟⠀⠀⠀⠀⠈⠁⠀⠄⣀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠀⠁⠐⠀⠄⢀⠀⠀⠸⣿⡏⣿⣿⠁
⠀⠀⠀⠀⠙⣿⡷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢀⠀⢻⣿⡿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠺⠇⣽⣿
⠀⠀⠀⠀⠀⠻⠇⣾⣿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠐⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄
⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠈⠐⠠⢀⡀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⢠⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄
⠀⠁

⠀⠀⣤⢂⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢠⣄⣠⡉⠁⢹⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⡀
⠀⠛⠿⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⠻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣴⢖⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣉⢀⣼⡟⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣿⣿⡇⢸⠃⠀⠀⠀⠀⠀⢀⣾⣡⣼⢿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣿⢧⠀⠀⠀⠀⠀⣠⡴⢶⣎⠱⡈⢿⢀⣃⠴⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠈⠀⠀⠀⠀⠀⣠⡿⠛⠉⣰⠟⠉⠁⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⣿⢿⡈⠁⠀⠀⠀⠀⣯⠰⡟⠘⡃⢈⡾⠃⣿⠠⣿⠄⡇⠀⠀⠀⢀⣠⣄⠀⢸⡏⢷⡄⠀⠀⠀⠀⠀⠰⠏⠀⢠⣾⢁⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢯⡛⢦⣀⠀⠀⠀⠘⠲⠴⠞⠀⠀⠀⠀⠙⠳⠶⠞⠁⠀⠀⠀⠸⣿⠟⣠⠟⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠶⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠟
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⣄⣰⠶⠶⠶⢶⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢇⣴⣶⣄
⠀⠀⠀⠀⣄⣲⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡄⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣯⣉⣿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⢙⣿⡟⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⢐⣀⣤⣾⣿⠿⠃⠈⠁⠀⠀⠀⠀⠀⠀⣼⡟⢿⣷⠀⠀⠀⠀⠀⢠⡾⢻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣾⠟⣿⡀⠀⠀⠀⠀⠀⠙⠻⢶⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣹⠆⠀⠀⠀⠰⠿⠇⠈⠛⣿⡿⠿⠾⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣀⡀⠀⢀⡿⣸⠃
⠀⠀⠀⠀⠀⠴⠿⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡍⠈⠋⠈⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣄⠀⢀⣻⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⡀⠘⣏⠀⠀⠀⠀⡶⠀⢰⣿
⠀⠀⣠⣾⣿⣿⠛⠛⠛⠉⠉⠁⠈⠁⠀⠀⠀⠀⠈⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢶⣶⣾⣷⢶⣤⣤⣤⠤⠆⠀⠀⠀⠀⠉⠀⠀⢹⣦⣶⢄⣼⠁⠀⠙⠋
⠀⢰⠏⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠈⢀⣿⠿⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⢀⡼⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣸⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⢿⡆
⣰⡋⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠈⣇
⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠳⠄⠀⠘⠂⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡐⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣶⣶⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⣧⣀⣠⣞⣠⠁⠀⠀⠀⠀⠀⢀⡤⠶⠖⢛⣿⣿⣏⠀⣠
⠀⠀⠀⠀⠀⣶⡆⢀⡞⢁⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿⣿⣿⡟⠻⣆⠀⣀⡰⠏⠀⠀⠀⠠⠆⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠻⠷⠃
⠀⠀⠀⢀⣾⣿⣿⣯⣤⠤⣤⠀⠀⠀⠀⠀⠀⢹⡄⢽⣿⣿⣷⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣶⡀
⠀⠀⠀⠸⣿⣿⠂⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠈⠻⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⣴⠏
⠀⠶⢶⢶⠿⣿⣿⢿⢶⠆⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠘⠷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣴⣁⣀⣀⣀⣀⣳⣄⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣈⣉⡉⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠈⠁⠒⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣵⠃⠠⣢⠄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡴⢲⣶⠿⠻⡆⠀⠀⢈⡏⡈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⠟⠊⠀⠈⡀⠠⢳⡤⡀⠐⠏⡸⠆⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠏⠀⠀⠀⠀⡇⠀⠑⠝⠚⠶⠞⠁⣸⠀⠀⡘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠶⠚⠁⠒⠒⠂⠀⠤⠤⠤⡷⠂⠡⣶⣿⣗⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⠈⠂⢄⠈⡍⠙⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠈⠒⠀⠀⠒⠒⠀⠉⠁⠀⢀⠃⠀⠉⠐⠓⠲⡃⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣋⠣⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢾⠒⢄⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⠄⠊⠁⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠑⢄⠑⣄⢢⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⠉⢀⠌⠈⠁⠐⠂⠀⠤⢀
⠀⠀⠀⠀⣀⠤⢊⠕⠙⠀⠀⠀⠀⠀⠱⡈⠆⢣⠀⠀⠀⡠⠊⠀⠀⠀⢰⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡉⠳⣄
⢀⠔⠈⢀⠄⠊⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠸⣌⣀⣀⣜⠁⠀⠀⠀⠀⡄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢢
⠆⠀⢠⠁⠀⠀⠀⡠⠃⠀⠀⠀⠀⢀⡀⠤⠐⠉⠉⠁⠀⠈⠁⠂⠤⠤⣅⣸⣀⣀⠀⠠⠄⠠⠄⠀⠤⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠠⠘⠋⠑⠒⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⠀⠈⢢⡀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⠒⢒⣩⠏⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠔⠁⡌⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⣠⠞⢀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧⣴⣁⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣄⣠⡶⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡖
⠀⠀⠀⠀⢠⢶⣿⣄⠀⠀⠀⠀⠀⠀⠼⢻⣿⣅⠀⠀⠀⠀⠀⠀⣠⣶⠿⠤⠄⠀⠀⠀⠀⠀⠀⣾⣟⡓⠚⠀⠀⠀⠠⣶⠿⠛⠻⢾⣃
⠀⠀⠀⠀⠈⢸⣯⡈⠁⠀⠀⠀⠀⢀⣀⣿⣇⠈⠉⠀⠀⠀⠀⠐⠿⠟⠲⠶⠄⠀⠀⠀⠀⠙⠛⢡⠀⠙⠃⠀⠀⠀⠘⠛⠇⢸⠀⠀⠈
⠀⠀⠀⠀⠠⠟⠈⠧⠀⠀⠀⠀⠀⠀⠉⠁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬

⠀⠀⠀⠀⠀⢠⡄⠀⢀⠠⠀⠀⠀⣠⡄⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⢠⡄⠀⢀⣄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣀⡗⣤⡀
⠀⠀⠀⢠⢶⣾⡗⠛⠉⠀⠀⠀⠀⠨⣷⡟⠉⠁⠀⠀⠀⠀⢀⣠⢴⣾⠗⠚⠃⠀⠀⠀⠀⠙⠤⣽⣴⠖⠒⠀⠀⠀⠈⠹⣿⣥⢾⣄
⠀⠀⠀⣨⠾⣏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠈⢁⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⢂
⠀⠀⠈⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⢳⡀⠀⠀⠀⠀⠐⠛⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢶⣠⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠠⢤⣤⣼⡃⠀⠀⠀⠀⠀⢀⡀⠉⢳⣶⡛⠀⠀⠀⠀⠀⣀⡀⢻⡟⢀⣀⠀⠀⠀⠀⢀⡴⠾⢻⡉⠀⠀⠀⠀⠀⠀⣾⣆⣀⣀
⠀⠀⠀⠀⠀⢹⣿⣤⡀⠀⠀⠀⠀⠉⠛⠿⠿⡷⠶⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠒⠋⠀⠀⣤⣷⣤⣄⠀⠀⠀⠀⠃⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠏⠉⠀⠁⠀⠀⠀⠀⠶⠷⠶⠶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠆⠰⣤⡴⠂⠰⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠤⢴⣧⠤⠀⠀⠀⠀⠀⠈⠓⡟⠁⠀⠀⠀⠀⠀⠀⠀⠒⢲⣾⠷⠒⠂⠀⠀⠀⠒⠢⣼⣧⠔⢲⡀⠀⠀⠴⠞⠋⠛⠻⡟⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⣀⡀⠀⠀⠐⠖⠒⠚⠛⠒⠲⠂⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⣽⣤⡀
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄

⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣰⢰⠆⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢀⣿⣴⠶⠈⠀⠀⠀⠀⠀⢹⡿⠖⠋⠀⠀⠀⠀⠀⠀⣿⡷⠋⠀⠀⠀⠀⠀⡀⠈⢳⣾⣃⡄⠀⠀⠀⠀⠀⠸⠿⢿⡾⠁
⠀⠀⠀⠀⣠⡾⠧⣄⠀⠀⠀⠀⠀⠀⣴⢿⡇⠀⠀⠀⠀⠀⠐⠦⣤⠿⠧⣤⠀⠀⠀⠀⠀⠙⠶⢿⠇⠀⠀⠀⠀⠀⠀⡒⠒⠒⠛⢛⡖
⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⡄⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢰⢀⡞⠀⠀⢠⠀⠀⠀⠐⠀⠀⢀⢀⣠⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠋⠹⠟⠳⢆⣠⡆⠠⡀⠀⠀⠀⠀⠀⠲⢶⡄⠀⠉⢰⣾⣿⡶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣅⢴⡿⣿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣿⡟⠁⠀⢀
⠀⠀⠀⠀⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠿⣿⠀⠀⢀⣦⣿⡀
⠀⠀⠀⠀⢹⣿⡄⠀⣀⣤⠤⠛⠓⠾⠿⢮⣕⢾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠉⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠻⡄⠀⠀⠀⠀⢀⡰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣧⣾⠃⠀⠀⠰⣿⡄⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠉⠲⠖⠉⣷⠀⢀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣷⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⡈⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⣿⠇⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⢠⣤⠤⠶⠶⠒⠂⠀⠤⠀⠸⡟⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣼⣿⣦⣴⣼⡟⠀⠀⠀⠀⠀⢰⠟⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⠀⠀⣠⣴⣚⡿⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣾⣉⣢
⠀⠀⢀⣀⣀⢀⣼⠟⠉⠉⠉⠛⠻⣿⣿⣿⠃⠀⠀⢀⣀⣀⠉⣦⣤⣤⡄⠀⠀⠀⢀⠀⠀⢙⠂⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⢠⠏⠉⠉
⠀⠀⠘⠛⠻⠾⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠈⠉⠉⠈⠛⠿⣶⣀⣀⠐⠋⢺⠆⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠿⢯⣭⣯⣽⣾⣶⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡆⠀⠀⣼⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠋
⠀⠀⠀⠀⠀⠀⠀⠇⠀⢙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢩⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠝⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣾⣿⣶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⠈⠿⠿⢷⡺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⣶⠄⠀⠀⠀⣠⣾⣿⣿⠟⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣦⣤⠀⢾⡟
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢣⣟⠀⠀⠀⢠⣿⣿⠋⠁⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠛⠁
⠀⢰⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣔⣶⡆
⠀⠘⠃⠀⢶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠄⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⡀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠶
⠀⠀⠀⠀⡠⠑⣷⣤⡶⠚⠙⠀⢸⣿⠉⠀⠀⠀⠀⠀⠘⣾⡡⠟⡻⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⡀
⠀⠀⠀⡤⣤⠾⢿⣿⣧⠀⠀⠀⠸⡿⠀⡆⠀⡀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⢾⠿⢷⣶⡄⠈⠻⢿⣿⣧
⠀⠀⠂⠀⠀⠀⢨⣿⣿⣦⣄⠀⠰⠙⠦⠈⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠁⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⣠⡿⠋⠁⠉⠙⠻⣦⣀⠀⡀⢸⣿⠀⠀⠀⠀⠠⢠⡄⠀⠀⣰⠂⠀⠀⢠⡀⠀⠀⠀⣴⡿⣿⣿⠃
⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⣿⠀⢀⠀⠀⢀⣀⣷⠀⣠⣟⠀⠀⢀⣸⡀⠀⠀⢠⡟⠀⠈⠻⢦
⠀⠀⢀⣠⡔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠼⣷⠀⣼⠀⠁⠀⠀⠁⠀⠠⠀⠀⠁⠀⠙⠛⠀⠀⠀⠀⠘
⠀⠈⠉⢉⣿⢧⡀⠀⠀⣿⡖⡄⢼⡷⢄⠀⠀⠦⠚⠋⠉⠀⡤⠀⢀⣀⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⣤⠀⢀⡄
⠀⠀⠀⠀⠉⠆⠉⠢⠀⣴⣿⠀⣤⢷⡀⠀⠀⠀⠀⠀⣠⣶⣿⣦⣼⣯⣀⣸⣧⡀⣴⣾⣷⣤⣶⣶⣯⣾⣾⣷⢄
⠀⠄⠦⣾⠗⠂⠀⠀⠀⠀⠈⠑⠬⠂⠈⠓⠀⠀⠀⠠⠁⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⣿⡀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⣤⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⣿⡿⠀⣿⣿⣧⡿⣿⠁
⠀⠀⠾⠏⠀⠀⠀⠀⠈⢨⣿⣅⡀⠀⠀⣠⣿⣉⡀⠀⠈⠻⡇⣿⣿⡇⣼⣿⣿⢹⡿⡿⠁⠀⡿⣿⠹⠃⡇
⠀⠀⠒⣲⣾⣄⣀⠀⠂⠉⠀⠈⠉⠀⠚⠋⠋⠋⠁⠂⠀⠰⠁⡟⠃⠀⣿⠻⡟⢸⠱⠇⠀⠀⠃⡟⠇⠰
⠀⣀⠴⠿⣅⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⡿⠀⠀⠼⠀⠀⠀⠀⠸

⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⡆⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⡇⠀⠀⣠⣴⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⢹⣿⣿⣿⣇⠀⠀⣿⠀⣿⣿⣿⣇⣤⡦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣠⣴⠆⠀⠀⠀⠀⣼⠃⠀⠀⣿⣿⡿⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣯⠀⠀⣼⣿⣿⠋⠿⠖⠀⢹⣦⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣸⣿⣿⣇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣦⠀⠀⢀⣿⣿⠟⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⣠⣴⣄⣀⣀⣀⠀⣿⣿⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠁⠀⢉⣿⣷⣶⡿⠟⠁⠀⠀⠈⣿⡿⠀⠀⠀⠀⣀⣀⣼⣿⠏⠈⠻⣿⡆⠰⠟⠉⠉⠙⠛⠻⠿⠿⠃⠀⠀⢿⣿
⠀⠀⠀⢰⣶⠞⠋⠉⠀⠀⣿⡿⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣶⡶⠿⠿⠛⠛⠋⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠟⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⠄⠀⠀⠀⠀⠀⠀⠸⠿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣿⡿⠃⠀⣰⠆⠀⢠⡶⠶⠶⠿⠛⣿⣿⣿⣿⠉⠉⠙⠛⠶⠆⠀⠠⣶⠶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⡿⠟⣿⣇⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣅⡀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⢛⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠈⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠋⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣶⡾⠟⠛⠋⠉⠀⠐⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠸⠿⠶
⠀⠀⠀⣤⣤⣤⣤⣾⣧⣤⣾⣿⣤⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠋⠀⠁⠈⠀⠁⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠉⠀⠉⠉⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠤⠀⠄⠠⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⢖⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣶⣶⣦⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡟
⠀⠀⠀⢀⣴⣶⣾⣶⣄⣀⠀⢠⣾⣿⡿⠿⠿⠿⠛⠋⠉⠙⠿⣷⣦⣀⣀⣴⡆⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠁⠀⠀⠈⠙⠿⣿⣾⣿⠏⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣀⠀⣠⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡛⠉⠉⠉⠉⠐⢊⡟
⣿⣉⣉⣉⡀⣀⡀⠄⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿