Catcus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⣀⡴⠥⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠟⠓⠲⣄⠀⠠⣦⢞⠍⡠⠠⠀⠀⢈⠻⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠡⠰⠀⡇⡇⠐⡶⢁⢆⡼⢡⠃⡀⢰⠸⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢠⣡⠁⣸⢡⠏⡸⠁⡆⢰⠃⢸⡄⣧⠈⡗⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⢸⡈⣿⢰⡇⡞⢀⠇⡼⠀⠈⠀⢸⡄⢹⠀⣏⡴⠀⢀⡴⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⡈⢧⠳⠻⣸⢰⠇⡼⢠⠇⠀⡆⠀⠀⡇⢸⡄⣿⠀⡴⣡⢶⠖⠃⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⣛⠂⣿⢸⠀⡇⣼⠀⢠⠃⠀⢀⡇⢸⡇⣿⡸⣴⢣⠏⡴⣴⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⣿⣾⢸⠀⡏⠀⢸⡀⠀⢸⡧⢼⣅⣇⡇⡟⣸⣰⢣⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⢸⡇⠀⡿⠀⢀⡸⠄⠩⢕⣚⣻⣷⠟⣡⠏⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣿⡇⣿⠀⡇⠀⣇⡀⠀⣯⠠⣄⣒⣒⣫⢴⣚⠵⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⠀⣇⠀⡏⠀⢀⡏⢉⡏⠛⠛⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡇⢸⡄⢿⠀⡇⠀⡼⠀⣸⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠈⡇⢸⡀⡇⢠⠃⢠⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠲⠖⠒⠧⢻⠀⢿⠘⡇⠃⡞⢀⠏⡸⠃⠤⣀⠤⠒⠒⠒⠒⢢⣀⣀⡤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠸⡇⢸⠀⡇⢸⢁⠏⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⢙⣢⣁⡼⢰⠇⡿⣼⠀⢏⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣾⠤⠧⠷⠊⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢻⡟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠈⢹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⢾⡇⢰⠀⣧⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣸⡄⢿⠞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⣸⠀⠟⠐⣧⠀⠀⢠⣴⣼⣤⡀⠀⢠⠀⣿⠀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⠘⣾⠂⠾⢻⠀⢀⣛⣹⣿⣿⣧⡄⠈⢸⠙⠀⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⠀⣯⣶⣤⣦⣴⣧⠀⠸⣿⣿⣿⣧⣿⣷⡆⢸⠀⠂⡿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡇⣿⣧⢿⠏⡟⢙⢃⣦⣿⢸⣧⣧⣸⡏⠀⣸⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣿⡿⢾⢾⠀⠀⠈⡸⣿⡿⢸⡇⣿⣻⣇⠠⡇⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡇⠀⠸⠀⠀⠀⠁⢻⡇⣿⣿⣿⣷⣤⣼⣧⡄⣿⠁⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⡇⠉⢸⠀⡄⢰⠀⢸⣇⣿⣿⠝⠿⣻⡟⡇⢻⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢸⡀⠀⠸⠸⢈⣿⣿⠛⢸⠀⠸⠇⡇⡞⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢈⠘⡇⠀⢸⡀⢸⣽⣿⡇⡌⠀⠣⠄⠀⡁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⠀⣇⠀⠘⡇⢸⣿⣿⡅⢁⠀⢀⠀⠀⢇⡿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢃⢹⡀⠀⡇⢨⣽⣿⡇⠀⠀⡾⠀⠀⢸⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⠸⡈⣥⠀⡇⢸⣿⣿⡅⠀⠀⣅⠀⢃⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠁⠙⢠⡁⢰⣿⣿⡷⢘⠀⣿⠀⡌⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⡄⠠⢃⣇⠸⣿⣿⣿⢸⢠⡟⣰⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣠⡞⣧⣾⣿⣿⣿⣷⣾⣿⣿⣿⡿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⠉⠉⠒⠒⠂⠛⠓⠒⠂⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠂
⢶⣄⣀⡤⢤⡤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣭⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣧⣀
⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣦⣤⣄

⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠘⢿⣿⣤⣀⡀⠀⠀⣿⡇⠀⠙⣿⣯⣄⠀⠀⢸⡀⢠⡄⢠⣶⡄⣿⡇⢀⣤⣿⣿⢠⣿⣿⡆⣴⡆⢰⣷
⠀⠀⢾⣿⣿⣿⠋⢰⣧⣿⡇⠸⣦⣹⣿⣇⣰⡦⠘⣇⢸⠅⠀⢿⣷⣿⠀⢸⣿⣿⡏⠀⠀⠈⢷⣿⡇⢸⣿⣶⣦
⠀⠀⠈⠛⢛⠃⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠿⠼⠀⠀⠸⣿⠟⠀⠸⣿⡿⠁⣠⣄⡀⣸⣿⡇⠸⣿⣿⡇
⠀⠀⠀⠀⣾⡇⠀⠘⠛⠉⠁⠀⠸⣿⣿⣿⡇⠀⠀⣜⡞⣇⡞⣠⠀⢀⣀⣀⣀⠀⢺⣿⣿⠁⣿⣿⡇⠀⠉⡉
⠀⠀⠀⠀⢻⡇⠀⢰⣧⢰⣿⡄⣠⠈⠙⡉⡀⢀⡄⠀⣿⣿⣿⡄⠀⣾⣿⣿⣿⡇⢸⣿⣿⡄⠈⢋⣀⠀⢸⡇
⠀⠀⣸⡄⣼⡇⠀⣀⠙⢿⣿⣿⡿⠀⢱⣿⣿⣾⣠⠀⢻⣿⣿⠁⠀⠙⠿⠿⠿⠁⠈⣿⣿⣿⡀⢸⣿⡄⢸⡇
⠀⠀⢿⡇⣿⣇⠀⣿⡇⠸⣿⠀⠀⠀⠲⣿⣿⣿⠃⢀⠀⠙⠁⡴⣿⣳⠄⢠⣤⣤⣀⠸⣿⣿⠇⠘⣿⡇⣿⡇
⠀⣀⢸⡇⣿⣿⠀⣿⡇⠀⢀⣤⣤⡄⠀⠈⢉⠁⠀⣿⣷⣶⠆⠈⠁⠋⠀⢿⣿⣿⡗⠀⠉⢁⠀⢳⣿⣧⣿⠃
⠀⢻⡏⢿⣿⣿⠀⣿⠇⠀⠘⣿⣿⡛⣀⡀⢿⠇⢀⣾⣷⠁⢰⣿⣿⡆⠀⠘⣿⣿⠇⠀⠀⣾⡇⣎⢻⣿⡿
⠀⠘⣿⣼⣿⣿⡾⠟⢠⣾⡆⠁⠀⠀⠿⠷⢾⣦⢸⣿⡟⠀⠀⠛⠉⠡⡄⠀⠘⠃⠀⣿⢠⣿⣿⣿⠀⠀⣤⣤⡄
⠀⠀⠀⢸⣿⣿⠀⠀⣼⣿⣿⡆⠀⣴⣷⡄⠀⣿⣿⣿⡄⢠⣴⣧⠞⡀⣴⣾⣷⣦⡀⢸⣿⣿⢿⣿⠀⠀⣿⣿⡁
⠀⠀⠀⠘⣿⣿⠀⠀⠸⣿⣿⠇⠸⣿⣿⡿⠀⢿⣿⣿⠃⠰⣿⣿⠏⠐⣿⣿⣿⣿⡅⠘⣿⣿⣼⠏⠀⢠⣿⣿⡇
⣀⣀⣀⣀⣉⣁⣀⣀⣀⣈⣁⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣉⣁⣀⣀⣈⣉⣁⣀⣀⣀⣉⣉⣀
⣿⣟⣟⣛⣝⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣾⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠟⠀⠑⠀⡌⡆⠀⠀⠀⠀⠀⠀⢀⠤⠂⣈⠉⠹⢾⣮⡟⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠲⢄⠂⣠⡼⢠⠡⠂⣇⠀⠀⠀⠠⠁⡔⢈⠤⠂⢈⡠⠈⣷⡿⣟⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡐⠦⢬⣷⣽⣟⡥⢀⣊⣪⡻⡍⠲⢇⠎⠔⠁⠀⡰⠉⠀⠠⠀⠟⠺⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣚⠒⠸⢛⣿⢿⠫⢤⢝⡙⠁⠈⠄⠈⢋⠀⡠⠊⠀⠀⠀⠁⠌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣸⣫⠖⢃⠾⠀⠳⢼⡀⠃⢡⠀⠈⠄⠀⢇⠀⠀⠐⠀⣠⠌⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠒⠂⠼⠀⠉⢃⠰⣜⠀⢲⠆⠈⠃⠀⠀⠀⠀⠘⡀⠨⣄⡠⢀⣊⡡⠖⠁
⠀⠀⠀⠀⠀⠀⢀⡎⠤⠄⠀⠈⡋⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢸⠂⠒⠒⠀⠄⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠸⣅⠂⠠⠤⠤⠸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢅⣂⠀⣒⡩⡆⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢸⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠄⠈⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⢀⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣧⠐⠀⢀⠀⠀⢨⠀⠀⠀⠀⡄⠀⢸⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⡟⠶⠧⣤⣦⣴⣤⣧⣠⣤⣤⢦⠴⠷⢺⣏⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠛⠛⠒⠒⠲⠒⠚⠒⠒⠒⠒⠒⠒⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠐⠾⢋⡤⡴⣒⡀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢤⡤⣄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⢇⢠⡇⠀⣠⠀⠀⠀⠀⠀⠀⢠⠦⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄
⠀⠀⠀⠀⠀⠈⠙⠁⠀⠬⠇⠀⠀⠀⠀⠀⠀⢐⠁⣜⠀⢱⠀⠇⠀⠀⠀⠀⠀⢹⣤⣏⡇⠘⠇⢀⠄⡏⠀⠀⠀⠀⠀⠀⠇⠀⣶⠑⠀⠀⠀⠀⡐⡼⢹⠸⡟⡆
⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀⠈⠧⣰⡀⣸⣠⠃⠀⠀⠀⠀⠀⠘⡏⢣⡅⠀⣇⠀⠀⠆⠀⠀⠀⠀⣀⡘⠀⠀⢱⠁⠀⠀⠀⠀⠇⡇⢸⡀⡇⢋
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠈⠉⠉⠀⠀⡀⣀⡀⠀⠀⣳⡷⡀⡷⠀⡟⠀⣠⡤⠀⠀⠀⠀⢰⠁⠀⠀⠈⡄⠀⠀⠀⠀⡇⡇⢸⠂⣵⢸
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⢦⠀⢉⣿⣷⣵⣰⣇⡴⢧⡄⠀⠀⡖⡄⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣷⢸⡄⣿⠿
⠀⠀⠀⡀⠀⠆⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠶⠀⠀⡀⠀⠀⠸⠆⠀⠂⠀⣸⠃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢅⠡⡈⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡⢹⡀⡇⣹⡄
⠀⠀⠀⠡⠀⠈⢠⠀⠀⣼⠀⠀⢸⠀⡄⠈⡏⠁⢸⡉⠳⠀⡀⠗⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⠂⠀⠀⠀⢣⠄⠀⠊⡇⠈⢾⣃⣷⣿⠁
⠀⠀⠀⠀⠁⢀⢸⡇⠀⠇⠀⠀⢂⡼⠡⠊⠀⠀⠀⠙⣲⠋⠉⠉⢣⡀⠀⠀⠀⠀⠀⣀⣴⣾⣟⡤⣀⠀⠀⠀⠀⠀⠳⠌⠀⠀⠀⢪⠀⠈⠀⠃⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠈⠸⡇⠀⣀⡠⢂⠜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡃⠀⠀⠀⣰⠋⢠⠞⠉⠉⠳⣌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢨
⠀⠀⠀⠀⠎⠣⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⣊⠀⠀⠀⠀⣇⠀⢻⠀⠀⠀⠀⢻⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠇⠘
⠀⠀⠀⠀⠀⠠⡑⣆⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠉⢦⠀⠀⠀⠈⠳⠬⢦⣀⣀⡤⠟⠊⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⡈⢀⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⠀⡇⠀⠀⠀⠀⢀⡋⣠⠀⠀⡋⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⢀⠌⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⠀⠀⠞⠁⢙⣇⣤⠤⢧⡀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠈⠀⠀⠀⡷⠁⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠓⡴⠊⠀⡄⠀⠀⠘⢲⡤⠴⠋⠁⠀⠀⠀⠀⠀⡴⠁⠨⢥⠀⠀⠀⠀⠀⠀⢠⠼⣀⡇⠀⢠⠀⠀⠀⠀⢠⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⡄⠀⢀⡴⣤⠀⠈⢄⣘⡇⠀⢸⠀⠀⠀⠀⢨⡄⠀⠖⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡇⢀⠃⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⢆⡘⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⡅⢠⠀⠀⠀⠀⠀⠈⠦⣀⡀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⢸⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢦⠉⡁⣠⠁⠠⠀⠀⡔⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠡⡀⢸⡶⠛⠛⠂⣤⣰⠎⠀⠀⠀⠀⠀⠀⡁⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⣀⡴⢭⣥⣼⠿⠭⣉⠳⡄⠀⠀⠀⠈⠺⠁⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⢠⣄⠀⠎⠦⢀⡄
⠀⠀⠀⠀⠀⢀⡀⢹⢧⡇⢸⠀⠀⠀⠀⢀⠞⠁⡴⠁⠀⢸⠀⠀⠀⢣⠘⡄⠀⠀⠀⢰⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣧⣹⠀⢸⣣⡆⠠⠄
⠀⠀⠀⠀⠀⢸⢻⣸⠈⡇⢸⠀⠀⠀⠀⡎⠀⠀⠃⠀⠀⠀⡇⠀⠀⠘⠀⣧⠀⠀⠀⢸⣾⢉⡇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡤⠤⢌⣧⣿⠥⠶⣁
⠀⠀⠀⠀⠀⠸⠂⢿⠀⢡⢸⠀⠀⠀⠀⢧⠀⠀⡄⠀⠀⠀⡇⠀⠀⢸⠀⡏⠀⢀⣤⣬⣿⠎⢳⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠉⠑⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⢸⠀⠀⠀⠀⠘⣆⠀⢡⠀⠀⠀⡇⠀⢠⠇⢰⠃⠀⡏⠀⠀⠀⠻⡁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⢀⡄⣇⠀⠈⣸⠀⠀⠀⠀⠀⠘⣆⠀⠆⠀⠀⡆⠀⡞⢠⠏⠀⠘⡄⠀⠀⠀⠀⢧⢠⡅⠀⠀⠀⢀⡶⠒⠀⡸⣇⢀⡴⠒⠀⣿⢰⡆⠀⣦⠺⣄⡀
⠀⠀⠀⠀⠀⢹⢷⡸⠀⠀⣿⡴⠂⠀⠀⠀⠀⠈⢦⡘⢦⠀⡇⣼⣣⠃⠀⠀⠀⠱⡀⠀⠀⠀⣾⠘⠇⠀⠀⠀⠸⣧⣠⢠⡗⢻⡘⣧⣠⠄⢻⠈⣇⢠⡏⢤⣄⡽
⠀⠀⠀⠀⠀⠀⢫⢿⡆⢠⡿⡜⠀⠀⠀⠀⠀⠀⠀⠙⠾⠷⠷⠟⠁⠀⠀⠀⠀⠀⠱⡄⠀⠀⡏⣰⠀⠀⠀⠀⠀⠀⠀⠈⣀⢠⡅⠀⠀⠀⢀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠂⠿⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⡷⠃⠀⠀⠀⠀⠀⠀⢏⡐⠽⢛⡷⠟⠼⡁⢩⡀⠶⢏⡵⠏⠉⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⢀
⠀⠀⢄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠈⠛⠘
⠀⠀⢠⡄⠀⢀⡤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠀⡀⢠⡀⢀⠀⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣀⡆⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣅⠆⢧⠀⠈
⠀⠀⠐⠖⠂⠃⠠⠤⠀⠀⠀⠀⠀⢀⠀⠐⠤⠃⠀⠀⠸⠋⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⣉⠂⣠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣇⠀⠀⠈⢂⠀⣠⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠘⣀⠃⢠⠏
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠙⠓⢴⡏⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⠀⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⢤⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠸⢠⠀⠀⣰⠄⠀⠀⢰⡂⠀⠀⠈⠛
⠈⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠹⣿⣄⡀⣀⣴⠆⠘⠓⠚⠋⠀⠀⠰⡏⣼⠀⣿⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⢼⡇⣷⠀⣿⠧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡆⡾⣸⠇
⢀⠀⠀⠀⠀⠀⠀⢠⡷⠠⠄⠈⠀⠀⠀⠈⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠻⣿⣿⡷⠟⠀⠀⠀⣰⣆
⢠⡀⠀⠀⠀⠠⠀⠸⡷⠂⠔⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⠀⠀⠘⠃⠂⠁⠀⠀⠀⠀⢀⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠾⠃⣨⠁⢠⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢙⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣮
⠀⠀⠿⠆⡀⠀⠠⠀⣰⠀⠀⠀⠀⠰⠶⠿⠀⣀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠀⠀⠠⡄⠈⠓⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⢠
⠀⠀⠀⠷⠁⠀⣀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠓⣿⠆⠀⣻⠀⢀⡀⡰⠃⠀⠀⠀⠀⠆⠀⡆⡶⠀⠀⠀⢰⣴⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠈⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠿⣿⡴⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡔⠉⠁⠀⠀⢺⠀⡄
⢀⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠹⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠙⠃
⠘⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡇⠀⠀⠀⡇⠀⠀⠀⠄⠉⢀⠠⠄⠀⠀⢷⣤⠶⠈⠓⠂⢀⣀⣀⡀⠂
⠘⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠁
⠀⠀⡀⠀⢣⢀⡇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡇⠀⠸⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣄⠄
⠀⠈⢀⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠛⡄
⣇⠀⠘⢖⠀⠀⡆⢠⠏⠀⠀⠀⠀⣺⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠣⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⡄⠋
⣍⢱⠆⢸⣄⠀⠀⠈⠆⠀⠀⢀⡤⡀⢁⡄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠄⢑⠙⠀⠀⠀⠀⠀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠁
⠙⢺⠀⠀⠁⠀⠀⠀⠀⠀⠀⢼⢰⡇⢸⡇⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⠀⢆⢱⡔⠀⠀⠀⠀⠀⠂⠠⣼⡇⠀⠀⠀⠀⠐⣤⣀
⢰⡈⠀⢀⣷⡀⠀⠀⠀⠀⠀⣾⣿⡇⡼⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣜⣆⣸⡼⠃⠀⠀⠀⠀⠀⠀⠰⢉⡀⠐⠀⠁⠀⠀⠈⣿
⡛⠁⠀⡼⠁⠐⠀⠀⠀⠀⠀⠙⠿⣿⠷⠋⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠄⠈⡁⠀⠀⢲
⠆⠀⢸⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⠂⢀⠀⣶⠁
⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣷⣖⣀⣴⠞⠁
⠈⠒⠊⠛⠁⠀⠀⠀⠀⠐⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⣄⣀⣾⠀⠀⠈⢉⡉⠁
⣿⣏⢹⣟⠻⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢐⣿⣿⡧⢙⣍⢫⣿⣿⡇⠀⠀⠈⠿⣾⣿⣿⣿⡆⠀⠀⠀⠀⢹⡿⣿⣽
⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠘⣿⣿⢧⣿⣿⢸⢻⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣏⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣻
⡶⠗⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣯⣭⣭⣭⣭⣽⣷⣷⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠸⢿⣿⣿⣿
⡇⠀⠀⢈⣻⡁⠀⠀⠀⠀⠀⣴⡟⣿⣧⣿⣿⡾⣦⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠘⠻⣿⣿⣿⠛⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠀⠀⣾⣿⣿⡄⠀⠀⠀⢸⣿⢽⣿⡿⣿⡷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠈⠛⠛⠛
⠀⠀⢈⣿⣿⣿⡇⠀⠀⠀⠘⣿⣺⣿⡷⣿⣯⣿⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢰⣾⣿⣿⣯⣿⣭⣯⣭⣤⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣶⣦⡈⡁
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣦⡀⠀⠀⠀⠂⢸⣿⣿⡅⡄
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⠀⣠⣶⣦⠀⠀⣿⣿⣿⡇⠀⠀⠀⠉⢘⣿⣿⠂⠆
⠀⢠⣶⣿⣿⣿⣶⠄⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣧⣿⣿⣿⠀⠀⣿⣿⣿⠃⠀⠀⠀⠉⢈⣿⣿⠅⡁
⠀⠈⠉⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢹⣿⣿⡟⢀⣼⣿⠟⠁⠀⠀⠀⠀⠉⢨⣿⣿⡆
⠀⠀⠀⣿⣿⡿⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠉⠉⠁⠀⢰⣿⣿⠂⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⢰⣶⣶⣾⣿⣿⣶⣶⡶⠀⠀⠀⠀⠀⠹⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢀⣤⣄⠀⠀⣿⣿⣿⡆⠀⠀⠉⢿⣿⣿⣿⣿⠉⠁⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠃
⣶⡄⠀⠀⠀⠀⠀⠀⠻⣿⣄⣿⣿⣿⠀⠀⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⢀⡀⠀⠀⠀⠀⠀⠉⢹⣿⣿⡟⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⢠⣤⠸
⠟⠿⣼⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠈⣙⣿⣛⠁⠀⠀⠀⠀⣾⣿⣷
⣿⣮⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⣏⣿⣟⣿⢿⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⠀⠀⠀⠀⣿⣿⡟
⣿⣵⡆⣿⠇⠀⠀⠀⠰⣿⣶⣶⣶⣶⣶⣶⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⡷⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢻⣿⣿
⣛⣛⣃⣫⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠄⢀⡀⠀⠀⢀⣼⣯⣿⣿⣿⣏⣟⣻⣧⡀⠀⢰⣶⣾⣿⣿⣿⣿⣷⣶⡶⠀⢀⣬⣿⣛
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢠⠁⣶⣦⡈⠅⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿
⣿⣿⣿⡿⠃⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠐⢨⣿⣿⡅⡤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠟⠁⠀⠀⠀⠙⢿⣿
⠛⠉⠁⠀⠀⠀⠀⠀⣙⣯⣟⡃⠀⠀⠀⠀⠀⠀⢉⢘⣿⣿⡂⠆⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢈⢈⣿⣿⡅⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣾⣦
⣆⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢨⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⣾⣿⡆⠀⠀⠀⠀⠀⣀⢰⡟⠀⢰⣿⣿⡿⠀⠀⠀⢀⣤⣾⣿
⣿⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠇⠀⠀⣶⣦⡻⣿⣿⡧⣤⣄⠀⠀⠘⣿⣿⣆⣤⣮⣟⠿⠁⠀⠀⠀⣾⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠆⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠀⠘⡆⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠈⠀⠀⠈⢃⡐⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⡏⠀⠀⠀⠀⡀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⡀⠁⠀⠀⠀⠀⠀⡁⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠙⠂⠀⠀⠘⠀⠀⢸⠃⣷⠀⠀⢰⠀⣿⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠸⠀⠀⠘⠀⠀⠀⠀⣸⠀⡿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣀⠒⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢱⡆⠀⡄⠀⠃⠀⠀⠀⠀⠀⡇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⣾⠁⢈⠁⠀⠀⠠⠀⠄⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢠⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠀⠜⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠛⢀⠀⠈⠦⢀⠀⠀⠀⠸⠀⠘⠀⠀⠀⣾⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢶⠀⠀⢰⡆⠈⠁⠀⠀⠀⢀⠀⠀⠂⢰⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠠⡀⠘⢧⡀⠀⠇⠈⠀⠀⠀⠀⠸⠀⢀⣼⠏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣀⡀⣸⣶⣤⣤⣥⣤⣥⣶⣤⣤⣤⣀⣤⣬⣥⣶⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣷⣤⣀⣠⣾⣶⣶⣶⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠙⠛⠋⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠘⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠶⢄⡀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠈⠀⠀⢠⣾⣿⢃⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⢻⡄⠀⠘⠀⠀⠀⠀⠈⠷⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠏⣸⣿⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⡇⡇⠀⠀⠀⢸⡏⠰⣿⡏⠀⢴⣿⣿⠄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀⣦⠀⠈⣿⣿⠃⠁⠀⠀⠀⢸⡇⠀⣿⡇⠀⢸⣿⠃⡄⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡄⠀⠀⣾⣈⣿⡇⠄⠸⣿⡀⠀⠂⠀⠀⢼⡇⠀⣿⡇⠀⢻⡟⢀⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰
⡀⠀⠀⣿⣿⣿⣇⠀⠐⣿⡇⠀⡤⠀⠀⣾⠇⢀⣿⠀⢀⣿⠃⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⡄⠀⠀⠀⠀⣼
⢡⡄⠂⣹⣿⡌⢻⡄⠈⢸⣇⠀⣧⠀⠀⣿⠀⢸⡏⠀⢸⠋⢠⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛
⠀⠱⡀⠻⣿⣿⡆⠹⣄⠀⣿⣀⠁⠠⠀⣿⠀⣾⠃⠀⠈⢠⣾⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠙⢄⠈⠻⣿⡄⢈⠆⠀⠋⠀⡀⠀⠉⢰⠟⠀⢀⣴⠟⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠱⣆⡈⠻⣦⡁⠀⢢⡄⠀⠀⠄⠈⠀⠸⠛⠁⡀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠈⠁⠀⠂⠈⠛⠳⢄⣙⠷⢦⡈⠄⠀⠄⠀⣀⡰⠶⠋⠈⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠠⠄⠀⣴⣶⣷⣦⣤⣤⣤⣿⣿⣷⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣇⡀⢀⣀⣿⣾⣷⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠏⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠚⠂⠙⠃⠉⠙⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢴⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠰⣧⣈⡖⢀⡄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠤⡄⠤⣤⠆⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⠃⡔⠋⠐⠒⣻⣌⡿⢉⡑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⠐⠠⠉⠁⠀⠁⠀⠀⢂⡀⠈⠁⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠉⡅⠀⢠⠂⣀⠈⠂⠒⢹⡍⣻⡌⡙⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠘⢁⠐⠈⢀⠂⠀⠁⠀⣠⡄⠻⠀⠉⠀⠁⠒⠉⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠓
⠀⠀⠀⠺⠀⣸⣀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⣀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢰⡇⠀⡅⠉⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠗⠂⠈⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⢂⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠰⠆⠀⢀⡀⠀⢢⠈⠀⠈⠃⠀⠀⠀⢠⠀⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⢰⡀⠘⡁⠀⠈⢥⠀⠀⠀⢂⠀⠀⠀⡁⠀⠀⡀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢠⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠘⢏⠀⠀⠐⡖⠀⠀⠀⠀⠀⡁⠘⠀⢁⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣄⠀⠀⢀⡀⠀⠀⠈⠀⠀⢸⠀⠀⠀⡀⠀⢀⠀⢀⡔
⠀⠀⠀⠀⠀⠺⠆⠀⠁⢄⣀⠈⢠⡄⠘⠀⢠⠁⠖⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠙⠋⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢎⣡⣄⣀⣁⣀⣠⣶⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣤⣤⣄⠀⠀⠀⠘⠀⢀⣠⣴⣤⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⠿⠿⠿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⣿⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⣿⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢰⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢹⣿⣿⢸⣿⣿⡀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⠀⠀⣿⡆⢠⠀⣿⢠
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢦⡀⣸⢰⢀⠇⠀⠀⠀⢻⣿⣏⣻⣿⣿⣿⣿⣿⡿⠀⠀⠀⢰⣿⡇⣸⡀⣿⢸⠃⢱⣾
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣇⣿⣸⣼⠀⡇⠀⠀⠀⠙⣿⣿⣿⠿⣿⣿⠟⠁⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠐⠀⠀⠀⣿⡏⠀⠀⠀⣿⣿⣿⣿⠏⠸⠇⠀⠀⠀⠀⣽⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿
⢸⣦⣼⣷⣧⣠⣿⣧⠀⠀⢄⣻⣿⣿⣿⠀⣆⣰⠀⠀⠀⢠⣿⣿⣿⠀⣿⣿⡀⢀⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠒⣿⣿⡶⣿⣾⣿⣿⣿⣿⣯⣿⣿⡧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⢯⣽⣿⣿⣿⣿⣿⣟⣙⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣏⣛⠽⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡙⣾⠛⣳⠯⠙⣿⣟⣿⡿⣭⣼⠏⠘⠃⢹⣿⠿⠿⣿⣿⡿⠶⣿⣟⠠⠋⠔⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢈⣿⣿⣇⠉⢓⠹⣧⠈⠀⠀⠈⠉⠉⠛⠛⠂⠀⠘⠛⠦⠀⣹⣿⣶⣿⣿⣿⣦⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿
⢸⣿⣦⠁⠱⠿⠋⠙⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠋⠉⠛⠉⠂⠙⠃⠀⠁⠈⠉⠉⠀⠉⠉⠙⣿
⢈⡏⣋⡁⢀⠀⢀⠔⠀⠠⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⣷⠀⣼⢀⡴⠎⠀⠀⠀⠀⢐⢺⡏⠄⠀⢀⠉⢲⠀⠀⠀⠀⠀⠙⠛⢶⣄⠀⢰⠟⠀⠘⣆⢣⣈⣴⢀⡔⠀⠀⠐⣿⣄⠀⠀⠀⢀⣹⣧⣤⣤⣤⣾⠟
⠀⠀⠀⠈⢷⣼⣼⣷⢟⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠻⣦⠓⠀⠐⡖⣲⠀⢟⢃⣿⡵⠂⠀⠀⢸⣿⣤⣶⣿⠿⠟⢛⠉⠉⠉⠁
⠀⠀⠀⣀⠀⠙⠿⠟⠛⠉⠁⠀⠈⢻⣏⡀⠨⣧⠄⠀⢆⢀⡀⠀⠊⠵⠀⠀⠀⠲⠀⠀⣟⠀⠀⠀⠐⠈⡖⣆⢨⠄⠁⠀⠀⢀⣼⣿⡿⠋⠀⣀⣤⣬⣷⣷⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⡠⠐⣷⠄⠘⣾⣫⠄⠀⠉⠐⣀⠀⠀⠀⡆⠀⠀⠈⠡⠀⠀⠘⠿⠿⢃⠀⠀⠀⢴⣿⣿⠏⠀⠀⣀⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⢁⠄⠀⢀⠀⠀⠁⠀⠀⠀⠠⠿⣬⣿⠊⢱⡿⠄⢀⠀⠀⠀⠉⠀⠤⠀⠈⣀⠠⠲⠀⠀⠀⠰⠖⠚⠟⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣹⠛⠂⢠⡉⠦⡒⠤⠄⠀⠐⡸⠐⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⣀⢀⡀⡀⠀⠀⢱⡄⠀⠇⠀⠀⠈⠿⠉⠁⠀⠰⢐⠣⠼⠀⠆⠠⠈⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠛⣿⡇⠀⣴
⠀⢀⣀⡀⠀⢀⡀⠁⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⣀⣤⣄⡀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣀⠀⠀⠀⠐⠂⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡀⠸⣿⣾⣷⠀⢨⣶⢾⣭⢴⡍⠀⢀⣛⣓⣉⣵⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠠⡄⠀⠐⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠⠀⠄
⠀⢹⣿⣿⠇⢠⣿⡿⠃⠀⠀⢰⣿⡿⡦⠀⠀⠘⣿⠿⠷⠾⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⠿⢀⡤⠁⠀⠀⠀⠀⠀⣭⣻⡰⡞⠁⠀⢰⠶⢖⣻⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣿⡇⠀⠀⠀⠀⠀⠎
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠏⠋⠀⠀⠀⠘⢿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠃⠀⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⣶⣾⣷⣀⠀⢀⡀⠴⢃⡄⢀⣠⡄⠀⠦⠀⠀⠀⠐⣄⠀⠄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠑
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣴⡇⠀⡆⠀⠀⣿⣿⣿⣿⡀⢲⡙⡘⣆⣃⠀⡁⡦⢀⡃⠈⠀⠀⠠⡀⢂⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢶⠘⡁⠈⠁⠀⠘⡛⡴⠁⣠⣶⣤⠀⠈⠆⣡⠀⠠⢀
⠀⢠⣭⣏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⡏⠀⣀⠈⠁⠀⠈⠀⠀⠁⠀⢸⣿⣿⣿⡇⠀⠀⠈⠛⠟⠋
⠀⠈⠖⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⠀⠀⠀⢹⣿⣿⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄
⠀⠀⠍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠠⠄⠀⢸⣿⣿⣿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣠⣼⣦⠀⠀⠀⠐⠀⠛⡛⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣤⢀⡀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⢠⠰⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⣸⣿⡼⠇⠀⠀⢸⣇⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⡆⠉⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣀⡏⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠸⣿⣿⡯⠀⠀⢀⠀⢨⣷⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠖⠀⠀⠀⠸⣄⣧⢰⡄⣿⠃⡏⣤⠀⠀⠀⡄⢀⡠⠂⠀⠀⢀⣤⢄⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⢷⣘⣏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡄⣇⣿⢠⡇⣿⠀⠀⠀⢃⠀⢀⠀⠀⢀⠿⠇⡋⢿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣶⢿⠃⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢚⣇⠰⠄⠀⠀⠀⢣⢹⣿⣸⣇⠇⠀⠀⠀⡎⡀⣻⠀⠀⠈⡆⠃⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣌⡁⠀⢫⡔⡮⠁⠀⠀⠀⢻⣿⣿⠞⠀⠀⠀⠀⠰⣃⣿⠀⠀⠀⠑⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠠⠀⢀⡿⡿⢗⢐⡱⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣻⣿⠀⠀⠀⠀⠱⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⢾⠖⢺⠳⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠎⡀⠸⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣤⢾⠶⣤⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠇⢸⡀⠃⡇⠀⠃⡇⢻⡄⠀⠀⠀⢀⣰⣯⠇⠀⡄⢸⢿⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⠘⠀⡇⠀⢠⢸⠃⢷⠊⠀⠀⠀⡟⢸⠀⡄⢁⠈⡆⢷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠠⣼⠀⠀⡇⠀⠃⢸⠀⢸⠀⠀⠀⠹⡇⠺⡀⢀⢸⠘⠇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢰⡀⢸⢀⠀⡇⠀⠃⢸⠀⢸⡇⠀⠀⠀⡇⢀⡇⠀⠘⡀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢦⣾⠋⡟⢳⣄⣀⠀⠀⠀⠀⠰⡇⢸⡀⢸⠈⠀⠁⡄⠀⢸⠄⡸⣇⠀⠀⠐⣧⠈⠁⠀⡤⠁⢀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⡏⡁⢀⡗⠀⡘⣧⠀⡀⠀⢀⢐⡇⠘⠀⣸⠀⡄⠘⠁⠀⠈⠘⠰⡇⠀⠀⠀⣹⡄⢀⠈⢰⠠⡟⢠⡧
⠀⠀⠀⠀⠀⠀⣼⠁⡇⠀⠗⠀⡇⡿⡟⠁⠀⠀⠹⡇⠀⠀⢹⠀⠁⠀⠀⡄⢠⠀⢸⡇⠀⠀⠀⢻⠀⢸⠆⢸⢀⡇⣸⠅
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠸⢀⢴⠀⡇⣧⡀⠀⠀⢠⡇⡇⠆⢸⠀⡀⠀⠈⠀⠘⠀⣸⠇⠀⠀⢄⣸⠣⡄⠀⡘⢺⠁⡿
⠀⠀⠀⠀⠀⠀⣿⠀⡇⢐⠀⠸⠀⠷⣟⠀⠀⠀⠘⡇⡇⠀⢸⠀⠁⡄⠀⠀⣄⠀⢸⡂⠀⢀⣸⠇⠠⢃⣴⠃⡬⣴⠗
⠀⠀⠀⠀⠀⠐⣷⠀⡟⠤⠹⠀⡤⠆⡧⠀⠀⠀⠀⡇⣇⠀⢸⠈⠀⠃⡀⠀⡟⠀⢹⣥⣴⠟⣁⡴⠁⣠⣃⡰⣡⡏
⠀⠀⠀⠀⠀⠀⢻⠀⢇⠀⡧⠀⡇⢀⣿⠀⠀⠀⠘⡇⡏⠂⢸⢀⠀⡇⠃⠀⡇⠀⣾⣓⣊⡉⢤⣗⢊⡡⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠘⣇⠸⡂⢸⡁⢡⢸⢹⣀⠀⠀⠀⡇⡃⠀⢸⠈⠀⡇⠀⠀⣇⠀⣿⢤⡬⠄⢒⣊⡭⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢡⠀⢇⠘⣆⠣⣿⣶⣿⢷⡇⡇⠀⢸⠂⠀⡇⠣⠀⡿⠀⡟⡚⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠛⣧⠈⢷⠈⠢⡈⠓⠴⢤⠐⢈⣿⡅⢆⠀⠀⠀⡇⠀⠀⡇⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠷⢤⡤⡉⢈⣉⠥⣰⣿⡇⠈⠇⠀⠀⣧⠀⠀⡗⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⣤⣀⣤⣠⠶⠚⠁⢸⣧⠀⠃⢠⠀⡏⠀⠀⣧⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⢸⠀⡀⠀⠀⢃⠰⢀⠛⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠙⠆⢸⠀⢀⢸⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⡄⠀⢸⠀⠘⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠇⠀⢸⡀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣆⠀⢸⠇⠀⢸⢀⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠂⠑⠘⠀⠘⠸⢸⡇
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣧⠀⢸⠀⠀⡄⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⡒⢻⣿⠀⠉⠀⢸⠀⠜⡇⢸⠛⠶⠒⠶⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠀⠒⢀⡀⣼⣿⣀⠀⠘⢸⠀⠀⣇⡾⠀⢈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠬⠙⢧⣼⣀⣸⣴⠶⠋⠀⠠⠄⢀⡀⠓
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠉⠁⠀⢂⣀⠈⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢡⢁⠁⢡⢃⠂⠀⠀⠀⠀⠀⠀⠀⡠⠺⠩⠉⠉⢢⠀⠀⠀⠀⠀⠰⠀⡉⠘⠀⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠆⡀⠈⠀⢸⠈⢠⠀⠀⠀⠀⠀⠀⢠⠁⠁⡆⠀⢸⠈⠀⠀⠀⠀⢀⠂⠃⡇⠀⠁⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠁⠁⡆⠀⠸⠀⡄⡄⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⡈⢸⠀⠃⢠⢠⠘⠀⡆
⠀⠀⠀⠀⠀⠀⢰⢸⠀⡇⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⡇⢸⠀⠀⠘⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠘⠀⡇⠀⠸⠀⡁⡇⠀⠀⠀⠀⠀⡇⢠⠀⠀⠘⢸⠀⡇⠀⠀⠀⡇⢸⢠⠀⡆⢸⠀⡇⠀⠀⠀⠀⠀⢠⠶⢶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⢀⠀⠀⡇⢁⠀⠀⠀⠀⠀⡇⢸⢸⠀⡀⠘⠀⠃⠀⠀⠀⡅⢸⠘⢀⠁⠀⠀⡇⠀⠀⠀⠀⢀⠃⠁⠀⡀⠈⡄
⠀⠀⠀⠀⠀⠀⡄⢀⠀⡇⢸⠀⡀⡀⢸⠀⠀⠀⠀⠀⡇⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠃⡈⠀⢸⠀⠀⢠⠀⡁⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⡇⠃⢸⠀⠀⠀⠀⠀⡇⠸⠸⠀⠇⢠⠀⠆⠀⠀⢀⠀⠃⠀⢸⠀⡇⢸⠀⠇⠀⠀⠀⢸⠀⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠃⠈⠀⡇⢸⠀⠇⠀⠘⠀⠀⠀⠀⠀⠇⠐⠀⠆⢰⠈⡄⠰⠀⠀⢈⢰⠀⡆⢸⠀⠁⠘⠀⠀⠀⠀⠀⠀⢰⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⢸⠀⠀⢀⠀⡇⠀⠀⠀⠀⠸⠀⡄⢰⠈⡀⢡⠘⡄⠀⠀⢸⠀⡇⢸⠀⠀⠀⡇⢸⠀⠀⠀⡇⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢡⠘⡀⢆⠡⠈⢆⠘⢦⡄⢸⠀⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠃⠈⢀⠀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⢇⠑⡈⢆⠑⢄⠑⠠⣅⠀⠀⠀⠀⡀⢘⠀⡆⢰⠀⠀⢸⠀⡆⠸⠀⡇⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠸⠀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠑⢌⠓⢄⡉⠀⠿⠀⠀⠈⠀⡇⢸⠀⡇⠘⠀⠀⠄⢀⠃⡂⢠⠀⠆⡄
⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡑⠢⠌⡁⣛⠀⡆⠀⠀⡇⢸⠀⡇⠀⠀⢠⠃⡜⢀⠁⡘⠀⠂⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢼⠀⡇⠀⠀⡇⢸⠀⡇⢀⡠⠃⡰⠀⡌⢀⠁⢰⢰
⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⢸⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⡇⢸⠀⣇⠎⢀⠜⢁⠌⠀⡎⢀⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠇⠀⠀⡇⢨⡔⠁⡠⠃⡠⠊⠀⡜⠀⠎⢠⠃
⠀⠀⠀⠀⠀⠀⡇⠆⠀⡇⢸⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠎⡰⠁⡠⠊⠀⢠⠊⠀⠞⢠⠂
⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⢸⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⡞⠰⢀⠜⠁⢀⠔⠁⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠁⢸⠀⢰⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⡇⢰⠸⡇⠂⣀⠔⠁⡠⠊⢁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⢸⠀⠿⢎⠐⠒⣉⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠃⢸⠈⠅
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⡇⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⢰⢸⠀⢸⠀⠀⡆⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⡿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⡇⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠃⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢯⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠙⠷⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟
⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢸⡇⠀⠈⠳⢦⡀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⠦⣄⠀⣠⠞⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⡴⠋⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⢸⡇⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⢘⣇⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠛⠛⠛⠛⠛⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⢀⣤⣴⡶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣞⣛⣫⠭⠭⠭⠭⠭⠭⣍⡽
⢀⣤⢞⡝⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢶⣄⣠⣴⣾⡿⠿⠛⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⣀⡴⣡
⣿⣧⢍⣔⣂⣀⣐⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠬⠤⠒⣾⡯⠓⠉⠁⢀⣤⣶⣾⡿⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠋
⢸⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⡿⠛⠉
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⢞⡿⠋
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣾⠁
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠘⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁
⠀⠹⣮⡻⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠈⠙⠷⢧⣴⣂⣤⠩⠭⠍⠀⠀⠀⠀⠀⠀⠅⢀⣀⣠⣤⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠁⠒⢄⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠲⠆⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠢⣄⡀⠀⢀⣠⠔⠒⠈⢂⠀⠀⠱⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠉⠀⠀⡠⠁⠈⡆⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⣠⠖⠉⠀⠀⠀⢱⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⠀⣴⠻⡘⢇⣀⣶⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠚⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⠓⠶⠚⠁⠘⢄⠀⠀⠉⠙⠆⠀⠀⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⢰⠇⣀⠔⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣳⣤⣀⣘⣺⣦⣤⣀⣀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠲⠾⠐⠛⠂⠀⣀⣤⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣉⡀⢻⠈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠐⠃⠀⠁⢿⡀⣀⠜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠸⡿⢉⣽⢦⠀⠀⠀⠀⠀⠀⠀⣾⣷⡖⢢⡹⡶⠀⢀⡅⠀⠀⠀⠀⠀⠈⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⢳⠸⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⠟⠃⠀⢸⠀⠀⠀⠀⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠊
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⢇⡀⡸⠀⠚⠛⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠀⠀⠀⠀⠈⠀⠀⢀⣈⣉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠘⡈⠁⢧⠀⠀⠀⣀⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠈⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠒⢄
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⣀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⡴⠟⠛⠒⠛⢦⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢮⣋⠉⠀⢀⣀⣀⣠⣤⠶⠚⠹⡆⠀⠀⠸⣖⣋⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠱⣄⠂⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠
⠀⠀⠀⠀⠀⠙⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡇⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢢⡀⠀⠄⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⣹⡤⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⣿⡶⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠙⢦⣠⠎⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⢸⡇⢾⠀⠀⠀⠀⠀⠀⠈⢿⠀⣠⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢸⡧⠇⠀⠀⠀⠀⢸⡖⠊⠁⠀⠀⠀⠀⠀⠀⢸⠿⠿⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⢀⣀⡤⠔⠻⢤⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠉⠣⢤⣄⣀⡤⠴⠃⠉⠉⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠁⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠄⢀⡀⠀⠀⠀⠀⢀⠔⠈⠉⢀⣀⣀⡠⠤⢄⡀⠀⠀⠈⣆⡀
⠀⠀⠀⠀⠀⡀⠴⠒⠉⠙⠉⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⠒⠃⣠⠶⠚⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠉⢢
⠀⠀⠀⡠⠊⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢨
⠀⠀⡐⠀⡠⠊⠁⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠎⢠⢀⣀⡤⠤⠤⠤⠤⣄⡈⡆⠀⠀⠀⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠱
⠀⠀⠴⠊⠀⠀⠀⠀⠀⠈⠤⠤⠤⢄⣀⠀⠀⠀⠀⡇⡈⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢸⢄⡠
⠀⠀⠙⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠙⠢⣄⣠⠃⠃⠀⡇⠀⠀⠀⠂⠀⠂⠀⠀⠀⡞⠀⠀⠀⠀⠸⡄⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⡮⢎⠄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠽⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢸⣹⣄⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⢀⠞⠁⠉
⢀⣄⠀⠀⠳⣀⠀⠐⢄⡀⠀⢀⡠⠀⠀⢀⡴⠁⡀⣀⢡⠀⠀⠣⡀⠐⠄⠀⠔⢠⡞⠁⠀⠀⠀⠀⠀⠀⡼⠉⠳⢤⣀⡀⠀⠒⢂⣀⡤⠞⠁
⠈⠉⠓⠦⡤⠬⢑⡢⢤⣤⣉⣡⣤⡤⠚⣁⣠⠔⠋⠉⠀⠑⠒⠊⠉⠢⣄⣀⣀⣀⣈⡽⠶⠦⠤⠤⠤⢚⠀⠀⢀⡀⢠⡍⡋⠉⠉⠱⣤⠤⣄
⠀⠀⠀⠀⠢⢤⠔⠁⠀⠐⠀⠈⠀⠙⣭⠀⠁⠀⠀⣼⠖⠒⠒⡎⠀⡘⠀⠀⠠⢋⠘⡃⠈⢢⠤⠒⣂⢛⠥⠖⠺⠀⡔⠀⠈⠒⠂⠀⠈⢆⡜⠛⠛⠒⢴
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⠁⠀⠀⠀⠀⠀⢳⠒⠁⠀⠀⠛⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⡓⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⢶⡋⠉⠐⠠⢤⣀⡹⢫⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠛⡖⠂⠀⠀⠉⠈⠉⠉⠉⣉⡭⠶⡶
⠀⢠⡤⠷⠀⠀⠀⠀⠀⠀⠀⢁⡟⠁⠉⠉⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⣀⣠⠤⠬⠆⠀⠀⠀⠰⢦⡤⠤⠤⠤⠼⠖⠚⠉⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠋⠉⠉⠁⠀⠑⢄⢀⡖⢀⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡆⠀⠀⠀⠀⠀⠀⠋⠀⠀⠙⠳⠁

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣆⡀⠀⠀⠀⠀⣿⡇⠀⠙⣿⣿⣁⠀⠀⠀⢿⠈⢠⡄⠀⣤⡄⢸⣿⠀⣀⣰⣿⣿⢀⣾⣿⣧⢠⣤⠀⣾⣦
⠀⠀⢸⣿⣿⣿⡟⠃⣴⣆⣿⡇⢰⣦⢙⣿⣿⠀⣤⡀⢸⡆⢸⡃⠀⢿⣿⣾⡏⠀⣿⣿⣿⡗⠀⠉⠉⣧⣾⣿⠀⣿⣿⣤⡄
⠀⠀⠘⠿⠿⠿⠁⠀⣿⣿⣿⡇⠀⢉⣿⣿⣿⣿⠋⠁⠘⣇⣾⠀⠀⠸⣿⣿⠃⠀⣿⣿⣿⠁⠀⡀⠀⢸⣿⣿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⠀⠀⣿⣿⠿⠇⠀⢸⣿⣿⣿⣿⠀⠀⠀⢡⡠⡄⢠⠀⠉⠋⠀⠀⠘⠛⠁⣴⣾⣿⡖⢸⣿⣿⠀⠘⠿⠿⠁
⠀⠀⠀⠀⢸⣿⠀⠀⢠⡀⢀⣤⡀⠀⠻⢿⣿⠟⠀⠀⠈⠓⣧⣷⣦⡞⠁⢠⣶⣿⣶⣦⡀⣽⣿⣿⡀⠸⣿⠏⠀⠀⢰⡆⠄
⠀⠀⢀⡀⢸⣿⠀⠀⠸⣷⣼⣿⣇⣾⡆⢀⢠⣰⣆⣴⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠇⢸⣿⣿⣧⠀⠀⣶⡄⠀⣾⡄
⠀⠀⢸⡇⢸⣿⠀⢀⣤⠈⢻⣿⡿⠟⠀⠈⢿⣿⣿⣧⡖⠀⠻⣿⡿⠁⣀⣀⠉⠛⠛⠋⠀⠀⢿⣿⣿⣦⠀⣿⣿⢀⣿⡁
⠀⠀⢸⡇⢸⣿⡆⢸⣿⡇⠘⠿⠁⠀⠀⠘⢿⣿⣿⡟⢀⣤⡀⠈⠀⢾⣿⢿⡧⢀⣶⣾⣶⡄⠙⣿⣿⠏⢀⢻⣿⢸⣿⠁
⠀⣠⡘⣧⣸⣿⡇⢸⣿⠀⠀⢀⣶⣶⣄⡀⠀⢀⣀⠀⠘⣿⣿⣿⠇⠀⢉⠈⠀⠐⣿⣿⣿⡍⠀⠀⢀⡀⠸⣿⣿⣾⣿
⠀⢸⣇⢻⣿⣿⡇⢸⣿⠀⠀⠘⢿⣿⡟⢁⣀⠸⣿⠂⢠⣾⣾⠀⢰⣿⣿⣷⠀⠀⢻⣿⣿⠃⠀⠀⣼⡇⣴⠙⣿⣿⠏
⠀⠈⣿⣆⣿⣿⣷⡿⠟⢰⣶⡆⠁⠀⠀⠻⠿⢦⣷⡄⣿⣿⡿⠀⠀⠛⠋⠉⣤⡀⠀⠛⠁⠀⣿⠀⣿⡇⣿⡇⠀⢠⣤⣤⡀
⠀⠀⠈⠉⣿⣿⡇⠀⠀⣾⣿⣿⡄⠀⢠⣶⡆⠀⢹⣿⣿⣿⡄⢠⣠⣇⡴⠂⢈⣶⣾⣶⣄⠀⢻⣷⣿⡇⣿⡇⠀⢸⣿⣿⠁
⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⡏⢠⣿⣿⣿⡆⢸⣿⣿⣿⠇⢠⣿⣿⡷⠋⢼⣿⣿⣿⣿⡀⠸⣿⣿⣻⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠛⠛⠃⠀⠀⠈⠛⠋⠀⠀⠙⠛⠋⠀⠀⠙⠛⠉⠀⠀⠛⠛⠁⠀⠈⠙⠙⠛⠋⠁⠀⠙⠛⠛⠁⠀⠀⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢴⠖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣨⣠⣤⣾⠅
⠀⠀⠀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢋⠐⠂⣀⡀⠀⣀⣀⣀⡀⠠⠤⢿⡴⠋⠙⠉⠉⠀⠀⠀⠀⢀⡠⣴
⠀⠀⠀⢙⠉⠁⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣇⢸⠀⡏⢀⣀⠤⠠⠄⠒⠂⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢱
⠀⠀⠀⠐⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠉⠀⠀⢉⡉⠭⠙⠛⠉⣧⠂⡍⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠤⠒⡚⡆⠀⠀⢸⢠⢾
⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⣿⠇⠅⠀⠀⠀⠀⢢⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠁⣸
⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⣴⢛
⠀⠀⠀⠤⠠⣤⣠⣤⣤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡇⠀⠀⠀⠀⢘⠀⠀⠀⠊⠠⠀⠀⠀⠀⡇⢀⡀⣴⡷⡛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⡏⠩⢇⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⡴⠶⠚⠋⠁⠀⠀⠀⠈⠀⢄⠀⠸⠀⠀⣀⣀⣀⣠⠤⠴⠾⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⠿⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣍⣉⣉⣉⡉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⣴⣿⣶⣤⣰⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠷⢦⣄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢿⣿⠋⠉⢻⡿⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠻⣤⣄⢸⡇⠀⠀⠉⠉⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠉⢸⡏⠀⠈⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⢷⠀⣼⢀⣴⠞⠀⠀⠀⠀⢐⣺⡯⠄⠀⠀⠉⠲⠀⠀⠀⠀⠀⠙⠻⢶⣄⠀⢰⠟⠀⠘⡆⢡⣈⡴⢀⡆⠀⠀⠐⣿⣆⠀⠀⠀⢀⣹⣧⣤⣤⣴⣾⠗
⠀⠀⠀⠈⢷⣼⣼⣷⢏⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠀⠻⣄⡋⠀⠀⠖⢢⢀⠟⢃⣯⡵⠂⠀⠀⢸⣿⣤⣶⡾⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠙⠿⠟⠛⠉⠁⠀⠐⢺⣏⡀⢬⣧⠄⠀⢆⢀⡀⠀⠈⡬⡀⡀⠀⠔⠂⠀⡿⠀⠀⠀⠀⠀⡇⡆⢰⠂⠁⠀⠀⢀⣼⣿⡿⠉⠀⣀⣤⣤⣷⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣤⠀⣷⠄⠘⣾⡫⠀⠀⠉⠔⣐⠄⠀⠀⡀⡀⠀⠀⡅⠀⠀⡈⠿⠟⠁⠀⠀⠀⢴⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠷⣤⣿⠒⢰⠿⠄⠀⠀⠀⠐⠋⠀⠤⠀⠤⡀⢄⠔⠀⠀⠀⠐⠖⠒⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣹⠟⠒⢠⡉⠶⠒⠤⠀⠀⠀⢠⠒⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢱⡄⠀⠇⠀⠀⠉⡿⠉⠀⠀⠰⢑⠣⢍⠀⠆⢀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠓⣿⡇⠀⣴⠀⠀⠈
⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⢀⣤⣄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⢀⠀⠀⠀⠀⠂⠀⣠⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡄⠸⣿⣾⣷⠀⢨⣴⢾⣯⣴⡍⠀⢀⣋⣛⣊⣵⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠
⠀⢹⣿⣿⠇⠠⣿⡿⠏⠀⠀⢱⣿⡿⡦⠀⠀⠰⣷⣬⠿⠿⣟⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⡿⠀⣀⠉⠀⠀⠀⠀⠀⣭⣻⣠⡾⠁⠀⠠⠴⢶⣺⣭⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣻⡇⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠋⠀⠀⠀⠘⢟⣻⡿⠟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠢⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣲⣞⣦⡀⠀⠀⡀⠰⠂⡀⠀⢂⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⢀⠀⠀⢸⣿⣿⣿⠀⢠⡙⠰⡆⣁⠀⢠⠅⠀⠂⠀⠀⠀⠠⠀⠆
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢦⠘⡃⠘⠁⠀⢐⣒⡺⠀⣠⣴⣤⠀⠀⠂⢁⠀⠠⣀⠀⠀⠀⠀⠀⠀⠠
⠀⢠⣍⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⡀⠈⠁⠀⠈⠀⠀⠁⠀⢰⣿⣿⣿⡇⠀⠀⠈⠻⠾⠋
⠀⠂⠦⣯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠕⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠠⠄⠀⢸⣿⣿⣿⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣄⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠩⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠛⠛⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⢸⣿⣼⠏⠀⠀⢸⣖⢀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠤⠂⠐⠆⣈⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡀⡗⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠸⣷⣿⡟⠀⠀⢀⠀⢘⣧⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠱⣄⣧⢠⡄⣿⠃⡟⣠⠀⠀⠀⡄⣀⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⣷⣘⣛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡀⣇⣿⢠⡇⣿⠀⠀⠀⡇⠀⡉⠀⠀⠀⡟⡇⡟⢧
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⠿⠆⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⣁⠀⠀⠀⠀⠀⢧⢹⣾⢸⣇⡇⠀⠀⠀⣠⠀⣿⠀⠀⠀⡇⢁⠠⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⡀⠘⢋⣄⡜⠁⠀⠀⠈⢻⣿⣿⡞⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠱⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢠⣿⠿⠄⠈⢡⡿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠰⡄⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣶⣿⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⡀⠘⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠉⠠⠀⢠⠄⠀⠀⢀⡄⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠲⣄⣰⠠⠀⠀⠀⠄⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⢄⠀⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣐⠀⠂⠈⠀⣸⠀⠀⠀⠀⠑⠁⠀⠀⡀⢀⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⢀⠛⠃⠂⠀⠀⠉⠉⠁⠾⠛⠁⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⡀⠀⠀⠒⠂⠀⠀⠀⠒⡄⢀⣥⠆⠀⠛⠛⠂⠁⠀⠀⠀⡀⣀⠀⠀⢤⠀⠒⠀⣀⠀⠀⠂⢡⢠⣴
⠀⠀⣸⠁⠀⠘⠄⠄⠀⠀⠀⡤⠃⡜⠑⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠑⠤⢴⡀⣷⣀⡀⠀⠀⢀⠀⠀⠈⠁
⢀⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⠀⠀⠀⠃⠀⠈⠀⠀⠩⢤⡅
⠙⠟⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⠀⠐⠦⣧⣀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⡗⠀⠀⠀⠄⡅
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⡀⠀⠀⠀⠤⠃⢰⡀⠀⠀⠀⠈⠁⠀⠀⠰⠠⠈⠂⢠⠂⠀⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠀⠀⠐⡤⠤⠤⠤⠤⠢⣤⠀⠀⠀⠁⠀⠀⢀⣶⠒⣁⡀⣱⡇⠀⡁
⠀⣶⠀⠀⠀⠐⠀⠴⡶⠀⠀⣠⡄⠠⠐⠈⠐⠀⢲⡀⠀⠀⠉⠂⠖⠀⠀⠲⠀⠊⠉⠀⠧⠌⠀⡧⠞⠁
⣀⡘⣦⢊⣀⡀⣀⣀⣀⣀⣈⣙⣁⣀⣀⣀⣈⡓⠂⠓⣀⡐⠶⠶⠆⣀⣀⡐⠲⠶⠆⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⡋⠙⠎⠀⢻⠇⠵⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡛⢼⠀⠆⡰⠀⠀⠠⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⢳⣄⡀⢸⠒⢈⠓⣤⢤⣶⣟⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣁⠈⣩⠧⣀⢾⣧⡜⠃⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣼⠁⠠⣽⠉⠰⠈⣷⠦⡤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⢺⣙⣆⠀⢁⠟⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢄⠀⠀⠉⣿⡗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢤⠳⡄⠀⣿⡇⠀⠀⢀⡤⠒⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢦⠙⣄⣿⡇⢀⠴⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡂⢸⣿⣧⣮⡀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣿⠛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⠀⠀⠀⣀⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⠲⣾⣿⣻⣿⣛⣿⣿⣟⡏⡝⠙⢸⣻⣏⢉⠉⡉⠉⡉⠉⠉⠉⠛⠛⠛⢛⣿⡗⡆
⠀⠀⠀⠀⠀⠀⢹⠑⠒⠒⠒⠢⠤⠤⠤⠭⠍⢥⣉⣉⣉⣉⣉⣉⣉⢉⣭⣭⣭⡭⢭⡭⡭⡤⢶⡻⠁
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢠⠆⡄⢰⢁⡞⡜⡰⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⢄⡄⡄⡔⡰⢡⢏⡞⡰⢃⠎⡜⡰⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠹⣻⢲⢶⠤⡴⣥⢥⠥⡬⣬⣤⢤⡥⣭⠾⡴⢳⠿⡾⢻⠟⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠈⠀⠁⠊⠘⠰⠱⢃⠞⡠⢃⠜⡡⢋⡞⢡⢏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⡡⢋⠞⡡⠋⡰⠃⠊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡱⢋⠞⣡⠎⡠⢣⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⢋⡴⢁⢜⡵⣣⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡴⣡⠎⡴⣣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠜⣡⢊⡜⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⠞⡱⣫⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠄⠀⡀⢀⣨⠞⠡⠾⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢄⡤⢂⠤⠀⡠⢀⡀⢀⠄⣀⠄⡠⠀⡀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠑⠋⠔⠁⠐⠂⠔⠡⠖⠡⠊⡠⠊⡤⠊⡔⣡⠜⡵⣡⢢⠆⠔⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣛⠛⠂⠀⠀⠉⠛⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣁⠀⠀⠀⠀⠀⣠⡶⠟⠋⠙⠻⣦⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡁⠀⠙⠳⣄⠀⢠⡾⠋⠀⢀⣀⣠⣤⠘⢿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⣾⠟⠛⠳⣦⠈⢷⠏⠀⢠⡾⠋⠉⠉⠙⣷⡈⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣾⠁⠀⠀⠀⠘⣧⠀⠀⢠⡿⠁⢀⣀⠀⠀⠘⣷⠸⣇⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡇⠀⢠⣴⣦⡀⢸⡆⠀⣾⠃⢠⣿⠛⢷⡀⠀⣿⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠀⢀⣿⡏⠈⢿⡄⣇⢀⣿⠀⣿⣿⠀⢸⡇⠀⣿⠀⢹⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⣿⡇⠀⢸⡇⣿⢸⡇⢸⣿⣿⠀⢸⡇⠀⣿⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡄⠸⣿⣿⣄⣸⡇⣿⢸⡇⢸⣿⣿⣷⣿⠀⣸⡇⠀⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡘⣧⠀⢿⣿⣿⣿⣇⣿⣀⣿⣸⣿⣿⣿⠏⣠⡟⠀⣼⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡘⢷⣌⠻⣿⣿⠟⠛⠟⢉⣙⡛⠿⣏⡼⠋⢠⡾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠻⣦⡉⢻⡿⠁⠀⠀⢀⣴⢿⢛⠃⣹⠀⣶⠋⠀⠀⠀⠸⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⣾⣥⣤⠶⣾⢿⣁⡟⣼⠋⠁⠀⠈⢷⡀⠀⠀⠀⠀⠈⠛⠻⢿⣶⣤⣤⣀⣀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿⠀⠀⠀⠀⠀⢻⣜⢛⣴⠃⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣩⡿⠛⣡⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣆⣿⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠘⣷⠀⣦⣤⣀⣀⠀⠀⠀⠈⠉⢉⣁⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢹⠉⠛⣻⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡻⣯⣁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⠛⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣭⣉⣁⣤⣴⠿⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠷⣶⣤⣤⣤⣤⣤⣴⣶⠾⠛⠋⠉⣭⣭⣉⣙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣉⡤⠖⠀⡀⠈⢩⡟⠁⠈⢳⣄⠀⠀⠰⢤⣄⡀⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⡴⠋⠁⣠⡿⠁⠀⠀⠀⠙⢿⣦⣄⣀⢈⣿⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠺⣧⣤⣼⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⡻⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠶⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢇⡄⠀⣰⠆⠀⠀⣺⠁⠀⡀⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠹⠿⠦⢤⣴⡞⠀⠙⠉⠁⠀⠀⢸⠃⡆⠘⣷⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⢸⣇⣧⠐⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢢⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⣿⣿⣶⣧⡟
⠐⠀⠀⠀⠀⠀⠀⣿⣁⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠛⠋⠀⠀⠀⠘⠗
⣸⠇⠠⠄⠀⠁⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡦
⠁⠀⣧⠀⠋⠀⡀⢠⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣀⠀⠦⠄⠀⠀⠀⠁⠀⠀⠀⢀⠀⡀⠀⠀⠈⠉
⠀⠀⢸⡖⠂⠈⠀⡼⠀⠀⠀⠀⠀⠀⠰⢼⣦⠀⢸⡇⠀⠀⢀⠇⠀⠀⠀⢨⠁⢢⢠⠀⠀⠀⢸⣀⠀⠀⠸⠶⠃
⠀⠀⠀⠀⠰⢪⡿⠃⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⢾⣧⣼⠷⠃⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⡤⠚⠋⠀⠀⡆⢠
⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠘⣧⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⢛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡅⠀⠀⢸⠀⠀⠀⠈⠋⢀⠠⠀⠀⠰⣄⡴⠀⠓⠂⢀⣀⣀⠰⠁
⠸⡤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡀⠀⣆⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢰⠀⡀⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⡄
⡀⠀⣀⡀⠀⠀⠀⢠⠂⠀⠀⠀⣠⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠧⢀⠈⣇⠀⠘⠠⡇⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠀⠀⢦
⢷⣸⠀⠹⠃⠀⠀⠁⠀⠀⢠⢏⡆⢰⡞⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⢀⠠⡁⠀⠀⠀⠀⠀⡀⠀⢸⠇
⢀⠹⠀⢠⡄⠀⠀⠀⠀⠀⣹⣼⡆⣾⢰⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⣧⢡⠀⣇⡿⠀⠀⠀⠀⠀⠀⣘⠟⠀⢀⠠⠀⠀⠙⣿
⠾⠃⠀⡾⠛⠀⠀⠀⠀⠀⠻⣿⣷⣷⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠳⠷⠋⠁⠀⠀⠀⠀⠀⢀⡀⠈⠀⣀⠀⠂⠀⠀⢻
⡅⠀⢸⠃⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠀⠀⢠⡜⠀⠀⠈
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⣥⠞
⠐⠀⠚⠛⠁⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠦⠄⠈⠉⠛⠛⠛⠛⠋⠉⠰⠶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢠⣤⢀⣀⣤⣴⠶⠛⠛⠛⠛⠛⢿⣿⠳⢦⣤⣀⣸⣇⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡀⠀⣀⣴⡿⠷⠛⠉⠀⠀⠀⠀⣠⡶⠶⠶⣆⡙⠀⠀⠀⠉⠻⠿⢧⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠏⠉⠈⠉⣠⠶⠛⠛⠷⣄⠀⣸⠃⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠀⠀⠀⢠⠋⠀⢀⣤⣤⣿⠀⡇⠀⢀⣴⡟⠓⣿⡄⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⣬⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⠀⢸⠀⠀⣿⣿⣠⣿⠀⣇⠀⢸⣿⣧⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠟⠃
⠀⠀⢀⡶⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠘⢷⣀⢻⣿⡿⠋⠀⠙⢧⣼⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠋⠻⣿
⢀⡞⠛⡆⠀⢻⠙⢣⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢉⣻⣯⣤⠾⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇
⣰⡇⠀⢷⠀⠀⡇⠀⣶⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡶⠟⠁
⡏⢸⡆⠘⣇⠀⠰⠀⢸⡆⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠻⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⢣⠀⢷⠀⠘⠀⠀⠀⠈⣧⡴⠶⠦⣀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠘⣇⠀⠀⠀⢀⣀⣀⣰⡏⠀⣀⠤⠿⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠸⣇⠀⠰⠋⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢿⣅⡀
⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣶⣦⣤⣤⣤⣤⣤⣴⣶⠾⢻⣿⠁⠀⠀⠹⣿⠳⣦⡀
⠀⠀⠀⠀⠀⠙⠛⣷⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⢋⠛⠀⠀⢫⡍⠉⠉⠁⠀⠀⢀⣼⠇⠀⠀⠀⠀⢹⣇⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣤⠞⠉⠀⠀⡿⠀⠀⠀⠀⠻⢦⣤⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢱⡀⠀⠀⣀⣤⢶⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠈⣧⣤⠞⠋⠀⢸⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣦⡀⠀⣿⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⠁⠀⣠⡴⢿⣃⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⠛⢶⣿⡄⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣤⠶⠟⠉⠀⠈⠋⠉⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢻⣄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠹⣆⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠋⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣠⠋⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⡜⠁⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⡿⠀⠈⣦⢴⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⠶⠤⠤⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠈⣿⠀⠀⠀⠀⠿⠞⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢤⣄⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢻⡇⠀⢀⣀⣀⣀⣀⣤⣤⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡿⠛⠛⠻⣷⡶⠶⠾⠇⠀⠀⠀⠘⠛⢻⡟⠛⠛⠉⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡾⠃⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣀⣀⣀⣼⠏⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠒⠒⠀⠉⠉⠉⠉⢩⣭⣽⠿⣦⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠉⠉⠙⢦⠀⠀⠀⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠳⢦⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⣀⣀⣠⣤⡤⠤⠶⠶⠶⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣉⠛⠛⠒⠠⠤⠤⠤⠴⠤⠶⠆⢘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⢿⣀⣀⣀⣀⠀⣀⣀⣀⣀⣠⣤⡶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣤⣤⣤⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣹⡿⢋⡽⠋⠀⡟⠉⢿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡜⣀⠀⢰⡇⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣶⣤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠸⡇⢸⡄⢸⠁⠀⣶⢸⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⠁⢸⡇⠈⣿⣿⡋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠇⠀⠸⢣⠀⠀⣫⠀⠀⠀⠈⡆⢨⣿⡀⠀⡀⠀⠀⠀⠰⣴⡟⢷⡏⠀⠀⢣⠀⢸⠉⣿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣼⠈⣷⠀⡇⠀⠀⢠⡄⣿⠆⠘⣷⠞⠀⠀⠀⠀⠀⣿⠃⢸⡇⢦⡀⢸⠀⠈⣧⠸⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⡀⣿⠀⠀⠀⡇⠀⠀⣼⠁⣿⠀⠀⣿⠀⠀⠀⠀⠐⢶⣿⠠⣼⡇⠈⠁⠸⡀⢰⣇⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡇⣿⠀⠳⣿⠀⠀⠀⡇⠀⠈⣀⠀⣯⠀⠀⢿⣆⠀⠀⠀⠀⠈⣿⠀⠹⡇⠀⢠⡄⣷⠈⢹⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⣿⡄⠀⣿⢀⠀⠀⢧⠀⠀⠿⠀⡿⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⡄⣱⠀⠘⠃⣿⠀⢸⡆⢠⣿
⠀⠀⣀⠀⣼⣶⠶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⣿⠁⠀⣿⠈⠷⠀⢰⠀⡀⠀⠀⣟⠀⠀⢸⡇⠀⠀⠀⠀⣀⣿⠀⠙⣿⠀⠀⠀⣿⠀⢸⡇⠘⣿
⠀⠀⢸⣿⣿⠁⠰⡇⠈⢿⢷⣄⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⡟⢴⠀⣿⠀⠀⠀⢸⣄⠇⠀⠀⣿⠃⣰⠸⣧⡀⠀⠀⠀⠈⢿⡆⠀⢸⠀⢠⡞⣧⠀⣸⡇⠀⣿
⠀⢴⡿⠁⡇⠀⠀⡟⠀⢸⠘⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⣷⠀⠀⣿⠀⢀⡀⢸⡏⠀⠀⠀⣿⠀⠃⢸⡏⠀⠀⠀⠀⠀⢸⣷⠀⢸⠀⠈⠀⣿⠠⢿⠁⢸⣿
⠀⣾⡧⢀⡇⠀⢻⣇⠀⢸⡇⢹⣷⣤⠎⠀⠀⠀⠙⢾⣿⠀⡿⠀⠘⢿⡀⠘⠃⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠐⢾⡏⠁⢸⢠⠀⠀⡏⠀⡞⠀⢸⡇
⠀⣿⠀⢸⡇⠀⣾⠀⠀⢸⠃⢸⢹⡇⠀⠀⠀⠀⠀⠸⣿⠀⡇⠀⠀⢸⠁⠀⠀⢸⡇⢀⡟⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⠀⢸⠈⠃⢀⠇⢰⡇⢀⣾⠇
⣸⣿⠀⢸⡏⠀⣿⢀⣴⠿⠀⢹⢸⣷⠀⠀⠀⠀⠀⠐⣿⠀⡇⢶⠀⢸⠀⠀⡆⢸⡇⠈⠀⠀⣿⠀⠀⣸⡟⠀⠀⠀⠠⡄⢸⡏⣇⣸⠀⠀⢸⠘⢯⠃⢨⡿
⢸⣧⠀⢸⡇⠀⣼⠈⠀⢰⠀⢸⣸⣿⠁⠀⠀⠀⠀⠸⣿⠀⡅⠀⠀⢸⠀⠸⠇⢸⠁⠀⠀⠀⡇⠀⠀⢻⡇⠀⠀⠀⠀⢱⣿⠁⢠⡟⠀⢀⡜⠀⡿⠀⣼⡇
⢸⡟⠃⢸⡇⠀⢹⡄⠀⢸⠀⢸⢹⣿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣾⠰⡀⠀⢸⠀⠀⠀⠀⣷⠀⠀⣿⡇⠀⠀⢠⣤⡾⠃⢀⡞⣡⠴⣿⠁⢸⠇⣺⡟
⠸⣿⡄⢸⡏⡆⢸⠱⠀⢸⡄⢾⢸⡿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠛⠀⢸⠀⡀⠀⢠⠿⠀⠈⣿⣥⣤⣴⠾⠋⣀⣴⡏⠀⢀⡞⠁⣠⠏⣰⣿
⢤⣿⠀⠸⡇⠀⢻⢀⠀⢸⠃⢸⠸⣿⠀⠀⠀⠀⠙⢶⣿⠀⡿⣄⠀⣹⠀⠀⠀⣼⠀⡇⠀⢸⠀⠀⠀⣿⣯⣥⡼⠗⠊⠁⣚⣤⠶⠛⢊⡽⠃⣰⠟⠁
⠀⢻⡆⠀⣧⡀⠀⡟⣧⠘⡆⢸⣴⣿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⠀⣿⠀⣶⠀⡡⠀⠁⠀⢸⠀⠀⢤⣿⠤⠤⣴⠶⠒⠻⢯⣤⣤⡞⢉⣤⠾⠋
⠀⠘⣷⡀⢸⡳⠄⢷⡉⠀⢿⠈⡇⢻⡄⣀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠁⠀⡇⠀⠀⠀⢸⠀⠀⠸⣿⣀⣀⠴⠤⠖⠛⢋⣁⣴⡿⠛⠁
⠀⠀⢻⡇⠀⢳⡀⠘⣟⠀⢸⡇⠱⡌⢿⣯⣀⣦⣴⣤⣿⠀⡇⠀⠀⣿⡄⠀⠀⣧⠠⡄⠀⢸⣼⠃⢸⣿⣤⣼⠷⣶⠶⠟⠻⠏
⠀⠀⠘⣧⠀⠈⣧⠀⠹⣄⠀⠻⣄⠉⠲⠿⠛⠿⠛⠛⣿⠀⡇⠀⠀⣿⠀⠀⠀⡏⠀⠉⠀⢸⠏⠀⢸⣇⡤
⠀⠀⠉⢻⣆⠀⠘⣷⠀⠘⢦⣀⠙⠳⠦⠶⣴⠒⠚⢉⣿⡆⡇⠰⡀⣿⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⣾⡏
⠀⠀⠀⠀⢻⣿⠅⢘⣦⡀⠀⠈⠓⠒⠒⠆⠛⠒⢊⣩⣽⡇⣿⠀⢷⡎⠀⠀⠀⡗⣠⠀⠀⢸⢠⡆⣿⠁
⠀⠀⠀⠀⠀⠙⣧⡈⠉⠙⠲⠧⠥⠤⠤⠤⡖⢛⣩⡴⢿⣷⣗⠀⠀⠇⠀⠀⠀⣧⡙⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣈⡻⢶⣦⣄⣀⣠⣄⣀⣴⡿⠟⠉⠀⢸⣟⣿⠀⠀⡇⠰⡄⠀⣿⠀⠀⠀⢸⡆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉⠉⠀⠀⠀⠀⠀⢺⡟⢏⡀⢀⣧⠀⠋⠀⣇⢀⣀⠀⣸⣧⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡀⠀⠉⠀⠀⠚⠋⠀⠙⢁⣿⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢹⡇⠠⠶⠶⠄⠲⠆⠀⢠⠼⡿⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⣶⠀⠀⢰⡄⠀⢴⠀⣤⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢈⠀⢠⣏⠀⠀⢸⠀⠀⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠘⠀⠀⡇⠀⠀⢸⡄⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⢰⣿⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠳⣄⠀⢸⠇⠀⢠⢸⡇⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣿⡇⠀⠀⡇⠈⠃⢸⠀⠀⠈⢰⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠰⣇⠀⠀⢸⠀⠀⠀⢸⠇⢸⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⡀⠀⢸⠀⠀⢠⡿⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠟⠛⠛⣿⡇⠀⠀⡏⠀⠀⢸⠀⠐⠃⣿⠀⢸⡏⠛⣛⠛⠻⠶⢶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⣠⡤⠀⠀⠁⠀⣿⡟⠀⠀⣧⠘⠇⢸⠀⠀⠀⣿⢀⣾⠃⠀⠐⠲⠂⠰⠄⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠄⠀⠀⠒⠀⠻⣿⣿⡵⠆⣿⠀⠀⢸⠀⠀⠀⣿⡾⠃⠀⠠⠔⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⠄⠙⠷⣤⣿⣀⣀⣼⣤⣾⠿⠋⠀⠀⠀⠤⠄⢀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠩⠥⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢀⣄⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡶⠶⠶⠶⠶⠿⠛⠛⠛⠋⠉⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣬⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠘⣷⡀⠀⢀⣀⣀⣠⣤⣤⣴⠶⠶⠞⠛⠛⠛⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠐⠂⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠤⠴⠶⠶⠒⠒⠛⢻⠻⢭⣀⠀⠈⠙⠳⣦⣄⡀
⠀⠀⢠⣴⡶⠶⠶⠶⣿⡶⠒⠚⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠳⢤⣀⠀⠀⠉⠛⢶⣤⣀
⠀⠀⠀⠙⢷⣤⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠈⢙⣻⣦⡀
⠀⠀⠀⠀⠀⠈⢻⣦⣄⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣤⣤⣤⣴⠶⠾⠿⣿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠙⢷⣤⡀⠀⠀⠈⠙⢦⣄⣀⣀⣤⣤⣴⠶⠶⠶⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠛⠛⠛⠛⢻⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡶⠶⠶⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣴⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡻⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⣤⣄
⠀⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⣾⡄⠀⠀⠀⠘⣤⣀⣰⠇⠀⢀⡯⠀⢀⠈⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⢶⣾⠁⠈⠉⠀⠀⠀⢸⢱⡃⢸⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⣸⣿⣇⢸⢹⡏
⢀⠀⠀⠀⠀⠀⢰⡆⠄⠐⠀⠀⠀⠛⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣿⠞⠀⠀⢀⣄
⢠⡄⢀⠀⠠⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⠀⠘⠃⠀⠀⠀⠀⠀⢠⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡁
⠛⠁⡆⠠⠄⠀⠁⡁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢅⠀⠐⠀⡇⠀⠀⠀⠀⢀⣀⠀⠈⠛⠣⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⢫⠠⠀⠒⢠⠇⠀⠀⠀⠈⠉⢁⣠⡀⠠⣟⠀⠀⠀⡇⠀⠀⠀⠓⢠⠉⡀⠀⠀⢰⠀⠀⠀⢦⡴
⠀⠀⠈⠁⡴⣲⠞⠀⠀⠀⠀⠀⠀⠀⢸⣥⣴⣇⣠⣶⠎⠀⠀⠀⠀⠀⠀⠷⠁⠀⢀⠼⠋⠀⢠⡀⡀
⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠓⠇
⢛⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣼⠀⠀⠸⠇⠀⠀⠈⠋⠀⠄⠀⠈⢦⡴⠄⠓⠂⣀⣀⣀⠄
⠸⠶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⠀⠸⣤⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠾⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⠀⠀⠀⠀⠀⠰⡆
⡄⠀⢧⠀⠀⡄⢰⠃⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⡀⠀⠀⠀⠀⠀⠲⠟⢀⠀⠀⠀⠀⠀⢀⠸
⣟⣴⠀⣧⠀⠁⠹⠀⠀⠀⡤⡈⣁⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠁⠀⣠⠀⠀⠀⠈⠁
⠙⢳⠀⢀⠀⠀⠀⠀⠀⢰⣱⠁⣾⣸⠂⠀⠀⠀⠀⠀⠀⢸⣣⡄⠀⢢⢱⡄⠀⠀⠀⠀⠂⢤⡿⠀⠀⠀⠀⢠⣤
⣴⠄⠀⡾⠄⠀⠀⠀⠀⢺⣿⣧⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣥⡼⠚⠁⠀⠀⠀⠀⠀⠋⠠⠀⠀⢀⠀⠀⢸
⡃⠀⣼⠁⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⢀⡈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠁⣰⠂⠀⠈
⠁⠀⢹⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⢀⡴⠋
⠐⠤⠚⠋⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣰⠀⠀⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡍⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⡲⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⡇⠀⠀⠀⠀⠀⣠⢊⠜⠁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⡀⠀⠀⠀⠀⠀⠀⡸⢸⠁⠀⠘⢄⠀⠀⢀⡔⣡⠏⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠫⡲⣄⠀⠀⡠⠚⠁⢸⠀⠀⠀⢸⡏⠉⠁⣰⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢮⡳⣄⢱⡀⠀⢻⠀⠀⠀⠀⡇⠀⢰⠇⣠⡦⡀⡸⠀⠀⠀⣀⣤⠖⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠙⣎⠉⠈⢆⢸⡄⠀⡤⠜⠀⢀⣏⢔⡟⢠⠃⠳⣄⡠⣪⠗⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⢳⡀⠘⣜⡇⠀⡆⠀⠀⣸⢏⡞⢀⠎⣀⠔⣩⠞⠁⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⢶⣄⠀⠹⡄⠈⠙⢢⠱⡀⢀⢏⡞⠀⠘⢎⢀⡾⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠫⡳⡄⠹⣄⠀⠘⡔⠁⠁⡼⠁⠀⢸⣴⠟⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠳⢶⢄⡀⠀⠀⠘⡄⠙⢎⠢⠿⣆⢰⡽⠀⣸⠁⠀⠀⣸⠏⠀⠀⡠⠔⠊⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠙⠮⡓⢤⡤⣇⠀⠈⢳⡀⢸⡾⠇⢀⡇⠀⠀⠀⢙⠀⢀⣨⠦⣒⠽⠋⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⣄⢘⠄⠀⠀⢳⡀⠳⢤⣸⠀⠀⠀⣠⠞⠉⣡⠴⠋⠁⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⢾⣄⠀⠀⠀⢳⡀⠀⡇⠀⠀⢸⠁⣠⠞⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣄⠀⠀⢳⡍⢢⠀⠀⢳⠀⡇⠀⢀⣴⠟⠁⠀⢀⣀⣀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢤⣀⡀⣹⡗⣄⡀⢈⣷⣅⡔⣻⡃⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⢈⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠠⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠐⠀⢰⡄⠰⠀⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠀⠸⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡧⠀⠀⠀⠁⠸⠀⠀⠜⠀⠁
⠀⠀⠀⠀⠀⢀⠸⣄⠀⠆⠀⠀⠀⠀⠄⠀⣴⠃⠀⠁
⠀⠀⠀⠀⠀⠈⣤⣬⣤⣬⣥⣤⣤⣀⣠⣾⣥⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣴⣤⣦⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⢼⡿⣱⡄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡇⠀⠀⠀⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠁⣼⡏⠀⠀⠀⣼⠁⣿⠁⢤⣿⠇⠀⢀⠀⠀⠀⠀⠀⠘⠀⡇
⠀⠀⠀⠀⢠⢰⣮⠈⣿⡇⠀⠀⠀⣽⠀⣿⠀⢸⡏⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⢸⣿⣿⠀⢼⡇⠀⠀⠀⣿⠀⡿⠀⣼⢁⣿⡿⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡀⢸⣷⡙⣆⠀⣷⠀⠀⠀⡏⢸⡇⠀⠏⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇
⠀⠀⠀⠐⡌⠻⣷⡈⠢⠉⠆⠀⠀⠇⣼⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠰⣌⠻⣦⡀⠢⠀⠀⠀⠀⠘⠋⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠁⠀⣝⣣⠈⠀⢀⣤⡖⠯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣞⣀⣀
⠀⠀⠀⠀⠀⠒⠀⠀⠚⠛⠻⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠘⠛⠛⠗⠚⠛⠛⠛⠛⠚⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠰⠆⠀⠑⠒⣯⣽⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠋⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠂⠀⠂⡖⠰⠀⢈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠰⠀⣆⠀⠄⠀⠀⠈⠁⠀⢀⠘⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠒⠀⣈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠅⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⣄⠀⠁⠀⠆⠀⠀⡀⠁⠈⡀⠒⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠉⡀⠀⠄⠀⠀⡀⠀⠀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣄⠁⢀⠈⠃⡀⠀⠀⡉⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣉⣄⣉⣀⣠⣴⣤⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⢀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠛⠛⠛⠛⠋⠙⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⠉⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⢀⠆⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣔⣶⡄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣨⣀⡄⠀⡘⠀⠀⢃⠀⠀⠠⠀⠀⠀⠐⠀⠀⢀⠀⠈⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡒⠊⠀⠀⠂⠈⠻⡇⠀⠀⠸⠇⠀⠀⠐⠀⠀⠀⠀⡬⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡰⠃⠐⠁⠠⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⢀⠏⠁⠀⠀⠉⠀⠀⡯⢈⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠂⢀⠀⠀⠀⠀⠀⣠⠄⠀⠁⠀⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠁⠒⡆⠒⡈⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⡀
⠀⣠⡴⠶⠛⠋⠉⠉⠉⠈⠉⠉⠉⠙⠛⠷⣦⡀⠀⠀⠀⠸⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⠉⡁⢈⣉⣭⣹⡷
⠺⠿⣀⠒⠒⠛⠛⠛⠶⠶⠦⢤⣀⣠⠀⠀⠈⠻⣦⡀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⢀⣠⣴⠶⠟⠛⠉⢡⡼⠋
⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⠐⠈⢻⡄⠀⠀⢹⣿⡄⠀⠀⢀⣴⠟⠁⠀⢀⣶⠿⠟⠋⠁⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠐⠒⠒⠛⠿⣧⡀⢿⡀⠀⠀⣿⡇⠀⢠⡾⠁⠀⣠⡾⠟⠁⢀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⣿⡇⢠⡟⠀⣰⣾⠿⠗⠛⠉⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠶⠶⠶⠶⠾⢿⣦⠀⣿⠁⣼⢁⣴⠟⠁⠀⠀⠀⣀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⠀⢻⣾⣣⡴⠶⠶⠾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⣿⣿⠷⠿⠿⠿⠿⠿⠷⠶⠶⢶⣦⣤⣤⣀⣀
⠀⠀⠀⢀⣀⣤⣴⠾⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⢦⣤⡀
⠀⠀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷
⠀⠀⣿⠻⢶⣤⣄⣀⣀⣀⠀⠀⢀⣀⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⣿⢿⡷⠶⠶⠶⠶⠦⠤⢤⣤⣀⣀⠀⣀⣀⣠⣤⡾⠛⠉⢹⡀
⠀⠀⢿⡄⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⢶⠶⣶⣶⠿⠾⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⣿⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏
⠀⠀⠀⠀⠈⠉⢿⠓⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠚⢻⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠤⡤⠄⣀
⠀⠀⠐⠀⠈⠁⠄⠀⠀⠀⠀⠨⠀⠂⠄⡄⠀⠀⠀⠀⠀⠀⠋⠀⠁⡄⠌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣤⠀⠌⠁⠀⢨⠠⡆
⠀⠀⠃⠄⠈⠈⡀⠆⠀⠀⡀⠀⠄⠁⠂⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠐⠈⠃⠀⠈⡀⢠⡄
⠀⠀⠀⠁⢀⠀⠀⠐⡀⢀⠀⡀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠗⢲⠴⠻⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⠀⠠⠄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠐⢠⠅⣈⠀⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠚⠀⠂⢁⠘⠆⠀⠀⠀⠀⠀⠀⠈⣀⠘⠂⠀⣀⡀⠀⢘⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠡⢈⠘⠀⠀⠀⠀⠀⠀⠀⠠⠆⠘⠃⠀⠐⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠓⠚
⠀⠀⠀⠀⠀⠀⠠⡄⠀⡁⠐⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠄⠀⠠⠆⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡀⠀⠀⡄⡁⢠⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢦⠀⠈⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠒⠀⠨⠁⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈⠀⠒⡇⠇⣀⠀⠀⠀⠀⠀⠀⠋⠁⠄⡁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⡆⠀⠉⢠⠁⠀⠀⢐⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⠀⡴⠛⢛⠦
⠀⠀⠀⠀⢠⠀⠇⠞⠆⠀⡀⠼⢁⠊⠀⢠⡄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⢈⠀⠁⡀⠀⠈
⠀⠀⠀⠀⠀⣄⠸⣄⠰⠨⠀⠀⠑⡠⠂⣸⠜⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠃⠁⠀⠄⠀⠀⠀⠀⢡⠇
⠀⠀⠀⠀⠀⠘⠁⠠⠁⠀⠀⢠⠠⢣⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠇⠀⡀⠀⠄⢰⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢐⣘⡇⠀⢗⣄⢠⠾
⠀⠀⠀⠀⠀⠠⠠⠀⠀⢀⠀⢀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⢀⢀⢀⢠⢀⠠⢠⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣁⠀⠁⠁⠁⣈⣁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢐⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡇⠀⠀⣤⡀⠄⣴⡄
⠀⠀⠀⠀⠀⠀⢠⡄⠀⣾⡟⢉⣭⣤⣾⣦⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠀⢿⠇⠀⠿⠇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⢙⣡⣿⣿⠟⣛⣫⡄⠀⠀⠀⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠁⠐⠦⢤⡀⠀⠀⠀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠟⣡⣿⣟⡛⠀⠀⠠⠀⠀⠀⠠⡀⠂⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⢀⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠄⠀⢃⠀⠂⠀⠀⢇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡⠄⠀⠹⣄⠀⠂
⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⢸⠀⡼⠷⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂
⠀⠀⠄⠀⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠜⠀⢷⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠐⣿⣴⠤⣤⡄⢶⣯⣷
⠀⠀⡀⢡⣄⠀⡀⠀⣐⠀⠂⠀⠀⠀⣠⡤⠀⠀⠀⠈⣉⠉⠃⠈⢃⣽⣿⣿⣻⣿⣿⣿⣻⣻⣿⣿⡇⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⣿⣇⣾⢏⣩⡄⠈⣿⡀⠀⠀⠁⠐⠃⢠⣤⢀⣤⡄⠻⠃⠀⠀⠉⣿⣿⣽⣿⣻⡿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣈⣛⡃⠙⠛⠃⠀⢸⣧⠀⢀⠤⢄⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⡰⠄⡀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾
⠀⢩⡉⠛⠀⠀⢀⠄⠐⠉⠑⠏⡀⠀⠑⢄⠂⠀⠀⠀⠂⡌⠈⠐⣄⣀⠈⠹⣿⡿⠋⠹⣿⣿⣛⠖⠈⠉⢉⡐⠎⠀⠀⠀⠁⠀⠀⣴⣿⣿⣿⠷
⠀⠀⣙⠛⠧⠔⠁⠀⠀⠀⡀⠀⠈⢆⠀⠈⠄⢘⠹⡢⡀⠇⣠⠂⠉⠀⠀⠀⠀⠉⢢⠀⣿⣿⣇⠂⠀⠁⠀⠈⠀⢰⠲⠤⠀⠒⠀⠄⡀⠹⠇
⠀⠀⠘⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠰⠢⠈⡥⢱⡘⠁⢀⡀⠀⠀⠀⢀⠀⠀⢱⠟⠛⠛⠄⠠⠀⠉⠄⡠⠋⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄
⠀⠀⠰⠀⠀⠠⠄⠘⠛⣄⠀⠀⠀⣀⣤⣤⣼⣟⢄⣘⣽⠁⠀⠘⠛⢀⣳⡂⠘⠋⠀⠈⠄⠀⠀⡀⠀⠀⠺⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠄⠀⣀⠄⠀⠀⠀⢥⣰⣿⣿⣿⡟⠛⢿⣷⡈⠉⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣂⠀⠻⠃⠀⠀⣀⡘⣄⠀⠀⠀⠀⡛⠁⠀⠶⠀⠀⡁
⢀⡀⠀⠈⢢⢄⡀⢀⠀⠀⢨⣿⢀⡌⣿⡇⠚⢸⣿⣧⡀⠈⠇⢄⢀⡀⠀⠀⢀⣠⠖⠉⠙⠀⠀⠀⠀⠰⣿⣿⣯⡢⠀⢀⡀⠀⠀⠀⠀⢀⠐
⠀⠛⠦⡈⢇⡀⢈⠀⠀⢀⡀⢿⣆⣀⠁⠀⢂⣼⣿⡇⠕⠀⠈⡇⠀⢀⡠⠤⢤⠻⠴⠤⣐⠃⢀⣀⡀⢀⠿⠋⠁⠐⠀⠀⣈⠰⣶⣶⣶
⠀⠀⠀⠡⢀⡇⣠⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠁⠀⠃⠀⠀⡰⢏⡲⠁⠀⠀⠐⠀⠀⠀⠀⠉⢆⠀⢨⡁⠀⠀⠀⣀⡀⠀⠀⠁⢹⣿⠇
⠀⠀⠀⠀⣠⣿⣿⣿⠿⡟⠉⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡇⠀⠀⠀⠀⠀⢄⠀⢧⠓⠀⠀⠀⠠⣼⡋⠀⠀⠀⠘⠤⡀
⠀⠀⠀⣾⣿⣈⣼⠁⠈⠃⠀⢾⣿⡿⣷⡄⠀⢠⣄⠀⠀⢠⡤⠀⠀⠁⠒⢁⠀⠀⠀⠀⡀⠀⠀⡄⠑⣄⢠⡀⠀⠀⠁⠀⠀⠀⠀⢸⠶⠈⡆
⠀⠀⠀⢿⣿⣿⣿⣄⡀⢀⣠⣿⣷⣤⣿⡇⠀⠀⠉⠐⠖⠈⠀⠀⢀⠔⠀⠘⠃⠀⠀⠘⠁⠀⡠⣤⡚⠉⠉⠣⣤⣀⣰⡤⠴⠉⠐⢎⠀⠆⠈⠢
⠀⡐⣆⢤⡽⠿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣈⠐⢢⠄⠀⠀⠀⡤⠐⠉⠢⢀⡀⠀⠀⠀⢀⡠⠖⠀⢿⣿⠀⢰⣶⡁⢸⣿⡗⢲⣤⡞⢩⠃⠐⠠⠄⠧
⠀⣭⣈⣺⣀⠀⣤⠈⠉⠉⠉⠁⣤⠀⠘⠋⣿⡆⠀⠀⠀⠀⠐⠀⠀⠀⢀⡜⠉⠉⠉⢃⠀⠑⢀⢼⣿⠀⠊⠀⠈⠉⠀⠑⣾⣿⠁⡎⠀⠀⠀⢠⠒
⠀⠀⠆⠀⡨⠟⠻⣷⣷⣤⣸⣶⣿⣧⣤⣶⠟⡃⠀⠄⠐⠀⠀⠣⠀⢠⠋⠀⢠⢀⠀⠸⢄⠇⢀⢸⣿⡄⢢⡀⠀⠀⢀⠴⣿⡏⢰⢤⣀⠀⠀⠁
⠀⠀⠀⠸⡀⠀⠀⡿⠿⢿⠿⠿⣿⠀⠀⣸⠉⠟⠒⢆⠔⠠⡊⠑⣧⠚⡰⠂⢼⡴⠤⡞⠙⠤⠈⠺⣿⡇⢸⣿⠒⢴⣿⢸⣿⠇⡌⠀⠠⣖⢀
⠀⠀⠀⠀⠈⠑⠚⠒⠒⠚⠖⠐⠛⠢⠚⠁⠀⠓⠀⠉⠀⠐⠓⠴⠛⠄⠐⠦⠜⠓⠴⠛⠀⠃⠀⠀⠉⠉⠉⠉⠃⠛⠛⠘⠛⠐⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠂⠉⠳⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠐⠒⠀⠀⠀⠀⣀⠄⣀⠴⠒⠦⣄⡀
⠀⠀⣀⡤⠴⠒⠋⠉⣀⡤⠤⢒⣊⠭⠕⠓⢉⠉⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣀⣠⠤⠖⠛⢍⡺⠁⠀⠀⠀⠀⠉⠒⢤⡀
⡰⢻⠲⣄⠤⢖⣺⠭⠖⠚⠉⢁⣀⡤⠴⡶⠃⠀⠀⠀⠀⢀⠔⢁⣠⠤⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⡇⡁⠀⣧⠞⠟⣦⣀⠤⠖⠚⠉⠁⠀⣈⠭⢦⠀⠀⡠⠔⠁⠀⡎⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀
⡇⡇⢠⣿⠀⠠⢹⠀⠀⠀⠀⢀⠴⢋⣁⡲⣬⣠⡞⠐⠀⢀⡒⠹⣄⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠖
⡇⡇⢸⢿⢸⠀⢸⠀⠀⠀⠠⣡⠴⠋⢀⣉⣟⡕⠒⠢⡁⠂⠌⠢⠜⣢⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⡴⠚⢉⡷⣀
⡇⣇⢸⢸⢸⠀⣾⠀⢀⡴⠚⠿⠴⠊⠁⠉⠒⠛⠲⢤⣀⠀⡄⢰⡈⠄⠳⣄⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣤⠖⠋⢁⡠⢖⡥⠚⠧⣄⡀
⠓⠓⢾⣸⢸⠀⡏⠀⣨⣿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⡈⣗⡥⠖⠛⢦⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⡶⠛⡠⢔⡩⠖⠉⠀⠀⠀⠈⢙⣶
⠀⠀⠈⢹⠼⢤⡷⣋⠙⢭⡲⢄⠉⠳⢤⣀⠀⠀⠀⠀⢀⡤⠚⢹⡏⠳⣄⠀⠀⠳⣄⠀⠙⡤⠴⠖⠚⠛⠉⠉⣀⡠⠴⣚⣻⠮⣖⠋⠀⠀⠀⠀⣀⡴⠞⢿
⠀⠀⠀⠀⠀⠘⣷⢏⡙⠲⢌⡲⢍⡢⣄⠈⢙⠦⡤⠚⠉⢀⡤⣊⠷⢄⠀⠙⠦⣀⠘⢦⣾⠩⣁⠨⠴⢒⣊⡭⠴⠒⠉⠁⠀⣀⣬⠗⢀⣤⠶⠛⠁⣀⠴⣊⡽
⠀⠀⠀⠀⠀⠀⠈⠓⢍⡢⢄⠉⠓⠿⣦⣅⡂⠨⣿⡠⠞⣩⠞⠣⣄⠀⠑⢦⡀⠈⠳⢦⡉⠒⠒⠚⠋⠁⠀⠀⠀⢀⣠⠴⠛⢁⡿⣾⠉⠀⢀⡴⢊⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢕⡢⣄⠀⠝⣏⠉⣁⠴⠋⠘⢆⡀⠈⠳⢤⡀⠈⠳⢄⡀⠉⠳⢤⡀⠀⠀⣀⡴⠞⠉⢀⡤⢚⡵⠊⣹⡶⢚⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠱⠿⠚⠁⠀⠀⠀⠀⠙⠦⣀⠀⠙⠲⣄⡀⠙⠦⣄⠀⠉⣶⡫⠅⢀⡠⢒⡡⣞⡥⠖⠋⣯⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠈⠙⠦⣄⠈⠓⢦⣯⠂⣂⡥⣲⠽⠚⠉⢀⡤⢚⡵⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠈⠙⠦⣄⢀⣭⠞⠋⠁⢀⡠⢒⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⢸⠯⠒⠉⡠⠖⣩⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣞⣂⡥⠖⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡄⠀⠀⠀⠲⡦⠀⢠
⠀⠀⢀⠀⠀⠀⢀⡆⣰⠃⡀⠀⠀⠀⠀⠀⢠⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀⢼⣣⢀⡓⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠈⠳⠥⠅⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⢠⣉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠁⠀⠀⠀⢙⣋⠠⠤⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠂⠀⠀⢀⠠⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⢢⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠌⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⡴⠀⠀⢰⣿⠃⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⢀⠠⠋⠀⡈⠈⠀⠀⢁⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⡀⠀⡇⠀⠀⢀⣸⣀⠀⠀⣱⢶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠎⠀⠀⠀⠀⡀⢠⠸⡇⢀⡇⠀⠀⠀⠉⠉⠀⠀⢹⢸⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢇⢐⣠⡗⠚⠁⠰⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢀⠆⡄⠀⢄⠀⠀⠜⢀⠄⠈⢺⢸⠁⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠽⠿⠟⠀⠀⠀⠁⠁⢀⠁⠀⠀⠸⢼⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⣙⡁⠀⠸⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⢸⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢣⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠙⢦⠀⢃⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢉⠉⠒⢦⠀⠀⠀⠛⠀⠀⠀⠀⠓⢬⣼⡦⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠇⠀⠀⠀⠀⡀⠤⠒⢒⡶⠿⠿⠯⢍⣉⣉⠑⠂⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠃⠀⠀⢀⠌⢀⠜⠀⠀⢀⠔⠉⠀⠀⠔⠁⠀⠀⢡⠀⠀⠀⠈⠉⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠓⠊⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠰⡆⢄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⣼⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠣⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⢿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠲⠤⠀⣀⣀⠀⠒⠠⠄⣀⠀⠀⠑⢄⠱⡄⠀⠀⡄⠀⢀⠅⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⣧⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠛⠶⣄⡈⠢⡘⡄⠀⡇⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠘⠀⠈⠳⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡓⠸⣷⡀⣃⠇⠀⠀⠀⢠⠀⠀⠀⠀⣀⡤⠔⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠤⠙⠚⣻⣯⠀⠀⠀⠀⣼⠆⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⢣⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠁⢙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠀⠋⠀⢨⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠑⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⣀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠚⠋⠉⠀⠀⠀⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠖⠒⠒⠉⠉⠁⠀⠀⢸⠀⠀⠀⠉⠉⠑⠒⠒⠦⠤⢤⣀⣀⡀
⠀⠀⠀⠀⢀⡴⠚⠛⠻⠥⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠼⠛⠛⢲⣄
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠢⠤⠤⣼⡤⠤⠤⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⠳⡀
⠀⠀⠛⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡷⠚⠂
⠀⠀⠀⠀⠀⠀⡏⠉⠉⠓⠒⠦⠤⣄⣀⡀⠀⠀⠀⠀⡰⠁⢸⠈⣆⠀⠀⠀⠀⠀⣀⣀⡠⠤⠴⠒⠒⠋⠉⡏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠁⠀⢸⠀⠘⠶⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⢄⣀⡀⠀⠀⢸⠀⠀⠀⣀⣀⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠺⠒⠚⠉⠁

⡶⠒⢶⠶⠶⠶⠶⣶⠶⠶⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⠶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⣻⣿⡿⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣧⢹⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠻⣧⡀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠿⠃⢀⣿⠷⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡶⠟⠁⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⣀⣤⡶⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡆
⠀⠀⠀⢠⣾⠋⠁⢾⣿⣿⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣄⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠷⢶⣬⣿⠀⠀⠉⠛⠻⢿⣿⣿⣛⣻⣶⣶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⢛⣋⣭⡶⠟⠋⢹⣇⣉⣉⣉⡟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⣿⣋⣭⣀⣀⣀⠀⣾⣏⣽⠟⢋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⡉⠉⠉⠙⠛⠛⣋⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣘⣿⠛⠛⠛⠶⠶⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠉⠁
⠀⢠
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠲⣄⠀⠀⢸⠀⠀⠘⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⡄⢹⠀⠀⢸⠀⠤⠀⠈⢠⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⢸⠀⠀⢸⠃⠀⠀⠀⢰⣠⠠⢻⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢸⠀⢴⠷⠄⠀⠀⠀⠸⠁⢀⡜⢀⡞⠉⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⢈⠀⠈⠧⠀⠀⠀⠀⢠⠒⠁⠀⢸⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⢰⢶⡄⠀⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠠⠀⠂⢸⠀⠀⠜⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢈⡀⠀⢠⠀⠀⢘⠀⢨⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢀⠀⠈⢧⣀⣳⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⢀⠉⠁⠀⠀⠈⠀⠸⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⠀⠀⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢰⠀⢰⠀⠀⢀⠎⠀⠀⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠃⠀⢸⠀⢸⣤⠴⠚⠁⢀⠊⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⠀⠸⠀⠀⠀⠀⠠⠀⠁⠀⠠⢢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠠⠀⠐⠀⠀⠀⢀⡠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠸⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⡁⠦⡃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⢄⠀⠀⠀⠀⠀⡰⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⢆⠀⠀⠀⢠⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠑⢄⠀⡇⠀⠀⠀⠈⠆⠀⠀⡂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠊⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⠢⣁⠀⠀⠀⠀⠘⡀⢀⠃⠀⡀⠀⠀⢸⢀⠔⠉⠀⢹⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢹⠀⠠⡀⠀⠀⢡⢸⠀⠀⠁⠀⡀⢰⠋⠀⠀⠀⢸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⡄⠀⠈⠁⠰⠈⣮⠀⠀⢀⡐⢡⠃⠀⠀⠀⠀⣬⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠒⢆⡴⠢⣄⠈⡆⠀⢹⠀⢠⢸⢀⠇⠀⠀⠀⠀⠀⠇⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡅⠀⠈⢧⣡⠀⠘⡄⠀⣆⡈⠀⠀⢨⢀⠄⡸⠊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢃⠀⡀⠀⢻⣀⠄⡷⠀⣴⠁⠀⠀⠎⠁⢠⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⠈⢲⠈⠏⠀⡀⢁⡏⠀⠀⡞⠀⢀⡇⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⡄⠓⠆⡸⠀⡿⢰⡇⠁⠰⠕⢂⢏⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣜⣔⣼⣀⣿⣧⣸⣁⣠⣁⣠⣶⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⡀
⠀⠀⠀⠤⢀⠤⠀⠀⠀⠀⠀⠀⠠⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠃⠖⠂⡐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⡁⠀⠡⠏⠉⠙⠀⣀
⠀⠀⢠⠀⠀⠄⠨⠁⡀⠀⠀⠐⠄⠁⠠⠀⠁⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃⠀⠠⡄⠀⠸⠂⠉
⠀⠀⠀⢈⠀⠂⠀⠄⢁⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣤⠀⠀⠀⠀⠀⠀⣦⠀⠗
⠀⠀⠀⠀⠀⠅⠐⠈⠈⢆⠐⠆⠄⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣋⠙⠛⡙⢂⡀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐⠂⠀⢀⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠉⠰⠂⠤⠀⡁⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠁⠀⠉⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠀⠀⡠⠄⠀⢠⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠠⠈⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢘⠀⠀⠐⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠀⠂⠐⠀⠀⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⡈⠐⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⠀⠀⠀⣦⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠀⠀⠚⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⠐⠂⠅⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⢠⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠉⠁⠐⠲⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠱⠀⠀⠀⠀⣃⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠂⠠⠀⠀⡁⠀⠞⠋⠙⠓
⠀⠀⠀⠀⠀⠄⠘⡀⠏⠇⠀⣀⠢⠃⡐⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠈⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⢀⡀⢵⡀⢠⢀⠁⠀⠈⢄⠰⠊⣸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠈⠀⢠⠀⠀⠁⠀⡂⠁⡄
⠀⠀⠀⠀⠀⠀⠻⠂⢈⠀⠀⠁⠀⡀⡸⣤⠞⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠈⠈⠀⠐⠇⠀⠀⠀⡁⢀⡅
⠀⠀⠀⠀⠀⠀⠒⠃⠲⠶⠆⠀⠰⠂⠰⠓⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢸⠀⠀⡦⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠈⠈⠀⠀⠁⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⠐⠀⠀⠀⠀⠈⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠐⠂⠁⠂⠂⠐⠘⠐⠊⠁⠃
⠀⠀⠀⠀⠀⠀⡅⡀⠁⠈⠈⠀⠈⢈⠈⡀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⡀⢠⢀⢀⢀⠀⠄⡀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⣀⣠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⣀⣀⣀⣠⣤⣽⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣏⣥⣤⣴⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⢀⣶⣶⣶⣶⣤⣤⣀⢀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣤⣤⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣾⣷⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⣿⣆⠀⠀⠀⠀⠀⣸⣷⣾⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⢹⣿⡧⣷⣿⠀⠀⠀⠀⢀⡟⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣏⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⡟⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⢸⡿⣿⢿⡇⣿⣿⠀⠀⠀⠀⣾⣿⡿⣿⢼⣿⣇⣿
⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⣸⣷⡿⣿⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⢸⣿⡿⣿⠀⠀⠀⠀⠀⢸⡇⣿⣿⢻⣇⣿⠀⠀⠀⠀⣿⣿⣿⣧⣿⣼⣏⣿⠀⠀⠀⠀⢸⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⣿⣽⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣾⣧⣿⡆⠀⠀⢀⡿⣿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⢹⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠸⣿⢹⡟⣧⣿⣹⣧⠀⠀⢸⡇⡿⣿⣽⣿⢻⣿⣿⡄⠀⠀⠀⣿⣼⣿⡏⣟⣇
⠀⠀⠀⠀⠀⢸⣿⢻⡇⣿⢻⣿⣿⣼⡇⠀⠀⠀⠀⠀⢿⣟⣷⢿⣽⣟⣿⣄⠀⣼⡇⣷⣿⣿⣿⣼⣿⣿⡇⠀⠀⢀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⣿⢻⡇⠀⠀⠀⠀⠀⠈⢿⡿⣞⢷⣻⣞⢿⣦⣿⡧⣿⢹⡿⣿⣿⣿⣿⡇⠀⠀⢸⡏⣿⣿⣧⣟⡟
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣼⣇⠀⠀⠀⠀⠀⠀⠈⢿⡽⣯⢷⣽⣻⠾⣿⣇⣿⣾⣿⣿⣿⡟⣿⡇⠀⠀⣼⣧⣿⣿⢻⡿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡳⣯⣛⣿⣿⣷⣿⣿⣿⣿⣿⡇⣿⡇⠀⢀⣿⣿⣧⣿⣾⢿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣯⣽⣿⣿⣿⣿⣟⣿⣿⡇⣿⠀⠀⣼⢿⡿⣽⣇⣿⣼⠁
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣼⣇⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣇⣿⣠⣾⢯⣾⣳⣿⣽⣏⡿
⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣧⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⡿⣿⣿⣏⣴⣟⣵⡿⣵⣿⣳⡿⣼⠇
⠀⠀⠀⠀⠀⠀⣿⣻⣷⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⣟⣿⣡⣿⣯⡾⣫⣾⡿⣷⡿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣸⡿⢻⣯⣿⣫⣾⣿⢿⣾⣿⣽⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣇⡘⣿⣽⣿⢟⣵⡿⣫⣾⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⣿⣿⣇⠙⢯⣷⣻⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡟⣿⢸⡧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⣿⢹⣧⣿⣭⣯⠉
⠀⠀⠀⠀⠀⠀⣿⣧⣿⢸⡇⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣼⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⢻⡧⣿⣸⡇⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⡿⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠸⠇⠿⠻⠛⠇⠿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⠻⠸⠗⠿⠻⠇

⣿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠖⠛⠓⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⠼⠛⠻⠶⣤⣀
⠀⠀⠀⢰⣶⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⣶⡄
⠀⠀⠀⢸⡟⠿⣶⣄⡀⠀⠀⣀⣤⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⢻⣷
⠀⠀⠀⢸⢿⡄⠈⠙⢻⣾⣏⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠀⢸⣿
⠀⠀⠀⢸⡇⢳⡀⠀⢸⠀⠙⠻⢷⣤⣠⣤⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⡆⠀⢳⡄⢸⠀⠀⠀⣠⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⡇⠀⠀⠙⣾⣤⠴⠚⠁⢸⡏⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠘⠛⠶⠀⠀⢸⣿
⠀⠀⠀⢸⡗⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠀⣀⣀⠀⠀⠀⢀⡴⠒⢦⣀⠴⢺⣿
⠀⠀⠀⢸⡇⠀⠈⠑⠢⢄⡀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣉⠉⢳⡀⢤⣾⠶⢆⠀⡇⠀⢸⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠑⠢⣼⣧⠤⠤⠐⣿⣯⣬⡇⢸⠇⢰⣿⣷⠟⢀⡇⠀⢸⣿
⠀⠀⠀⠸⣇⠀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⡟⠋⢀⡞⠀⠈⠳⢤⠴⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⢀⠷⠀⣙⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢧⡀⠙⡀⠀⠀⠀⠀⡠⠃
⠀⣠⢚⣡⣶⠋⠁⠁⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣳⡄⠳⣤⠎⠀⢾⡥⠂⠈⡩
⡜⢁⡞⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⣿⡉⠁⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⢸⡟⢦⡀⠀⠀⠀⠀⠀⡅⠀⠀⣸⠀⠀⠀⢀⣴⠋
⣇⠸⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡏⠙⠦⢤⣤⣤⠤⠖⠚⠉⠁⠀⠀⠀⢸⡷⣦⣉⠓⠢⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⢤⡔⠒
⠈⠲⣌⣁⠛⠒⠂⠤⡀⠀⢀⡠⠔⢺⡧⢄⠘⣇⠀⠤⢤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠉⠛⠶⠶⢤⠤⠴⣆⠀⠀⣀⣠⠴⠦⠤⠼
⠀⠀⠀⠈⢿⢹⡇⠀⠘⠆⠁⠀⠀⢸⡇⠀⣉⠺⢗⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢸⡾⣇⠀⠀⠈⡄⠀⠀⢸⡇⠀⠉⠓⠶⠏⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡼⢇⡽⠃⠀⠀⢠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⢹⡆⢤⣢⣆⣄⡜⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⢸⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣸⣿⠀⢀⣀⣠⣤⣶⡾⠿⠛⣿⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⠟⢿⠋⠉⠀⠀⠀⣠⠟⠀⠉⠛⠛⠛⠛⠛⠛⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠻⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠀⠉⠉⠉⠉⠉⠉⠛⠲⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣧⢙⣍⢋⣿⣿⡇⠀⠀⠀⠻⢧⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡿⣯⣿
⠁⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠘⣿⣿⢧⣿⣿⡸⠿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣼⡇⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠨⣿⢿
⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣭⣭⣽⣫⣽⣭⣭⣶⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠰⢶⡶⠿⠿
⡇⠀⠀⠈⣻⡋⠀⠀⠀⠀⠀⢀⣾⢯⣿⣽⣟⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢿⣿⣿⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⣿⣟⣿⣿⣽⣿⣽⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠘⠿⠿⠿
⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⢿⡧⣿⣿⣼⣿⣺⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿⣿⣿⣺⣟⣻⣗⣛⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣬⣀⠚⠂
⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣟⡛⠋⠀⠀⠀⣴⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⡍⢰⣿⣿⠂⠁
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣀⣀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠆⢸⣿⣿⠅⣉
⠀⢀⣀⣿⣿⣿⣇⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣇⣸⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠂⢺⣿⣿⠂⠆
⠀⠀⠿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⠋⣿⣿⣿⠃⠀⣼⣿⡿⠃⠀⠀⠀⠀⠖⢺⣿⣿⡉⡁
⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣾⠟⠉⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣧⣤
⠀⠀⠀⠻⠿⠿⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣀⣈⣿⣿⣿⣁⣀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠹⠿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⣤⣤⣤⣭⣭⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢠⣶⣷⡆⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⢹⣿⣽⣭⣽⣿⡏⠉
⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⡇⠀⢸⣿⣿⠏⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⢠⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣶⠀⠀⠀⠀⠀⣶⣶⣘
⣭⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣿⣿⣟⣯⢷⡄⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠟⣿⣿⠀⠀⠀⠀⣀⣀⣈⠻⠿⠿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣷⣿⣿⢿⣟⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣯
⣿⣷⣷⣿⡇⠀⠀⠀⠀⠿⢿⣿⣛⣛⣛⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⢿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣿⣿
⣯⣭⣭⣽⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠰⠀⣠⡀⠀⠀⢠⣾⣷⣿⣿⣾⣯⣽⣽⣿⣦⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢰⣾⣿⣭
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣿⣶⡀⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⡃⢸⣿⣿⠄⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠙⢿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⣈⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⣁⣸⣿⣿⡑⡂⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣶⣿⡆
⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⡂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⢀⡀⣿⠃⠀⣼⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿
⣿⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡶⣶⡆⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠃⠀⠀⣶⣶⡙⣿⣾⣿⢠⣤⠀⠀⠀⢻⣿⣷⣠⣶⣯⡻⠟⠀⠀⠀⠀⣿⣻⣿⣾