Coat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢡⣦⣤⣤⣤⣤⣴⡈⠻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠋⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠙⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠘⠛⠒⣶⠄⢻⣿⣿⣿⣿⣿⠡⣶⡚⠛⠃⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢾⣅⠀⠈⢿⣿⣿⣿⠏⠀⢨⡷⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⠀⠀⠀⠙⢷⡀⠘⣿⣿⠏⢀⡴⠋⠀⠀⠀⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡇⠀⠀⠀⠀⠙⢶⣼⢏⡴⠋⠀⠀⠀⠀⢰⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⡀⠀⠀⠀⠀⣿⠀⣤⣄⠀⠀⠀⠀⢀⣿⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⢹⡇⠀⠀⠀⠀⣿⠀⠉⠁⠀⠀⠀⠀⢸⡇⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⣿⠀⣀⡀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡏⣸⠃⠀⠀⠀⠀⣿⠀⠛⠋⠀⠀⠀⠀⠈⣧⢸⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⡇⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣧⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⢋⣀⣀⣀⣀⠙⡏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠀⢿⠉⠁⠀⠀⠈⠉⡇⠀⢹⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⣀⣀⡸⡄⠀⠀⠀⠀⢰⢃⣀⣀⡇⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣨⠟⠉⠀⢷⠀⠀⠀⠀⡞⠀⠙⠻⣅⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠈⣇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣾⠀⠀⢹⡀⠀⠀⢸⡄⠀⠀⢰⡇⠀⠀⢀⡇⠀⠀⣿⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣿⠀⠀⠀⢧⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⡼⠀⠀⠀⣿⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣿⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⢸⠀⠀⢰⠃⠀⠀⠀⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢺⠀⠀⠀⠀⢱⡀⠀⡇⠀⠀⢸⠀⢀⡏⠀⠀⠀⠀⣿⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⣸⠀⡼⠀⠀⠀⠀⠀⣿⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠘⡆⣇⠀⠀⣿⢰⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⣠⢧⣀⠀⠀⡰⢻⠀⠀⠀⠀⠀⠀⢳⣿⠀⠀⣿⡞⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⣀⡼⣄
⠀⠀⠀⠀⠀⢰⠇⠀⠈⠙⢲⡇⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⡇⠸⡖⠋⠁⠀⠸⡄
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣄⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⠀⠀⢸⠤⠤⡇⠀⠀⠀⠀⢀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠋⠀⠀⠙⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢴⣖⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣠⣦⡈⠊⠻⣦⡄⠈⢳⣤⣀⡀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⡀⠀⢠⣷⣱⡏⠀⣰⢷⣌⢻⣆⢠⣿⣝⡻⣯⡿⣦⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠋⡁⢂⣩⣝⡻⠿⣯⡋⣶⣮⣿⣿⢈⢽⣯⡻⣼⡻⣦⡙⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠿⢷⡏⠀⢞⣯⢳⠛⢷⣟⠕⣄⡿⢿⣱⣞⠻⣎⢳⣌⢷⡐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣔⡳⠋⠴⣏⣴⣽⣷⣾⣿⣺⣿⠻⡦⣷⡝⢷⡝⣧⢹⡎⣿⡐
⠀⠀⠀⠀⠀⠀⠈⠛⠚⣆⠀⢖⡻⠁⠀⠀⢸⡇⠏⢣⢀⢸⣆⣻⣿⡿⣿⣈⣿⣾⣿⣿⡟⣿⠹⣷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⡕⡇⠀⠀⠀⢹⣧⣿⣦⣾⠻⡌⢣⣹⣷⡉⠿⡭⣕⢌⢮⠻⡜⣧⢻⠐⡄
⠀⠀⣾⡀⠀⠀⣤⠀⠘⠿⣦⠐⠻⠿⠶⣤⡄⠉⣿⣿⡌⣧⣿⣶⣏⠁⢧⡀⠀⢀⠈⠉⠁⢹⠸⣿⡆⠇
⠀⠈⣿⠅⠀⠀⠁⠀⠀⠀⠐⡣⢀⠔⣶⣻⣿⣆⣧⣻⣿⡻⠻⣏⠹⡆⢸⡿⢦⣄⠀⠀⢤⢸⠀⡇⣷⠀⠀⠀⡄⣾⢀
⠠⣤⡇⡾⠀⠀⠀⠑⣶⣦⣄⠱⠫⠷⠟⠓⠺⠯⢽⣛⣇⡙⢦⣝⣦⣹⣾⠯⡢⣝⠷⣄⡀⠘⡇⣇⢻⠀⠀⠀⡇⡇⣾
⠀⠀⠹⣠⡀⠀⠀⠀⢹⣿⣿⣷⣀⣄⡀⠃⠀⠀⠀⠀⠀⠀⠀⠣⢫⣿⡯⠳⣜⢮⡳⣌⠻⣆⠀⠙⠸⠀⠀⠠⢽⡿⡁
⠀⠀⡄⠹⣿⡇⠀⠀⠀⠈⠉⠙⢿⣿⣿⣷⣤⣢⣥⣤⣄⢀⣤⣠⢘⢋⣓⣤⠈⠁⠛⠛⠃⠉⠉⣠⠀⠀⢀⣴⡼⠃⡀
⠀⠀⠀⠀⠘⢿⢰⡀⠀⠠⡀⡀⠀⠉⠉⣉⠙⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠞⢇⣰⣴⣶⡄⠀⠁⠀⠀⡟⡾⢡⠟⠁
⠀⠀⠀⠀⠶⠾⠯⣤⣀⠀⠉⠙⠳⣦⣌⣻⡅⢀⣉⣉⣉⣁⣿⣿⡿⣛⠋⠑⠻⠿⠿⠿⠛⠀⠀⠀⠠⠄⢻⡵⠋
⠀⠀⠀⠀⠀⠀⠈⠈⠻⣷⡆⠸⠽⠛⠛⠿⣿⣾⠚⠉⢋⢻⢩⠉⠙⠋⣧⣀⣤⣴⠌⠔⠀⠀⣠⣆⣠⡼⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡷⠀⠀⠰⠿⠿⣢⣄⡈⣆⢧⢣⢀⡤⣾⡿⠷⠶⠀⢀⠀⣞⡿⢋⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⣻⣶⣶⣾⣷⣦⣀⠉⠛⢛⠛⠛⠛⠓⢋⣠⠴⣂⣄⣀⣴⡛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠈⠥⣛⡿⣼⡇⢀⠺⢯⣷⣛⣭⣴⣥⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠫⡞⢻⣝⠛⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠈⢧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡼⠁⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠈⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠁⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢦⣀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣀⡴⠋⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠳⢤⣀⠀⠙⢦⡀⠀⠀⢀⡴⠋⠀⣀⡤⠞⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣙⣦⣴⣋⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⣸⢧⣀⠀⠀⠀⠀⢀⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡟⢳⡀⠀⠀⠀⢀⣀⡼⣇
⠀⠀⠀⢀⡿⢤⣈⡉⠛⠒⢶⡞⠀⢽⠒⠒⠶⠶⠦⠤⠤⠤⣿⣿⠤⠤⠤⠴⠶⠶⠒⠒⣧⠀⢳⡖⠒⠋⢉⣁⡤⢿⡀
⠀⠀⠀⣸⡁⠀⠈⠉⠙⠛⡿⠀⠀⢾⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣀⣀⡿⠀⠀⢻⠛⠋⠉⠁⠀⢈⣇
⠀⠀⠀⣏⡉⠓⠲⠤⢤⣼⠁⠀⠀⣺⠈⠉⠉⠉⠙⠛⠛⠛⣿⣿⠛⠛⠛⠋⠉⠉⠉⠁⣷⠀⠀⠈⣧⡤⠴⠖⠚⢉⣹
⠀⠀⢰⡏⠉⠓⠲⠦⢤⡏⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⡤⠴⠶⠚⠉⢹⡆
⠀⠀⢸⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⢼⠛⠒⠒⠲⠶⠶⠦⠤⣿⣿⠤⠴⠶⠶⠶⠒⠒⠒⡟⠀⠀⠀⠸⣇⠀⠀⠀⠀⠸⣇
⠀⠀⢸⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢹⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⡟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡇
⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢾⠀⢭⠉⠉⠉⠛⠛⠛⣿⣿⠛⠛⠋⠉⠉⠉⡥⠀⣷⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣷
⠀⠀⠈⠙⠒⠒⠲⠚⠃⠀⠀⠀⠀⢽⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠘⠷⠶⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠾⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣶⣤⣤⣤⣤⣤⡿⡿⣤⣤⣤⣤⣤⣶⣶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣛⣿⣿⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⣿⣿⣿⣿⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣿⣿⣿⢻⢯⣿⣿⣿⣿⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢹⡿⣿⠋⠙⠻⠿⠞⠛⣻⠿⠟⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣷⡿⠀⠀⠀⢀⡴⠋⣡⠀⣠⠏⠁⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢿⣇⣀⣠⢶⡫⢠⡾⢃⣴⠏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠒⢂⣉⣥⣴⠏⣠⣾⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⣀⠀⠀⠘⡿⠛⢁⣼⠟⠁⣄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⣿⠙⠷⣶⣶⠏⣠⡞⠁⠀⠀⢹⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡎⠛⠶⠤⠴⠞⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⡃⠀⢸⣿⣿⣿⣿⠋⠛⠶⠶⢤⣤⣤⣤⣀⡈⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡇⠀⢸⣿⣿⣿⡿⠷⠤⣤⣄⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠁⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⣷⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⣀⣀⣿⣿⣿⠃⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣿⠀⠀⠈⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡏⢹⣄⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢱⠀⠙⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣾⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢲⠆⠀⠲⢶⣶⣶⠶⠶⠿⠛⢻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣰⠾⢥⣀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⡔⠀⠤⠄⣉⠛⢦⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡝⠿⣦⠀⠀⠈⢳⣦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠃⠀⠀⠀⣠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠻⠀⠀⠀⡠⠊⢁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⡄⠀⠀⠀⢀⣾⣀⠠⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣠⢾⠀⠰⢦⡟⢸⣿⣀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⡜⠀⣾⠃⠀⠈⢢⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣧⡀⠇⠀⠸⡗⠠⣤⣀⡆⠈⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡆⠀⠀⠹⣦⠛⠻⠿⠶⠶⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣰⠋⠉⠉⠉⠉⠙⣆⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠀⠀⢀⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠙⢤⣀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⣀⡴⠋⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⢸⡇⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣸⢇⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢰⠃⢿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠘⡆⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡷⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣇⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢠⡗⠦⢤⣄⣠⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠸⣄⣠⡤⠴⢺⡄
⠀⠀⠀⠀⠈⠛⠒⠶⠤⠟⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠻⠤⠶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⠤⠤⠤⠼⠧⠤⠤⠤⠤⠶⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢾⣏⣉⣉⣙⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⢸⠉⠉⠉⠉⣿⠀⢹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆⠻⣄⢸⠀⠀⠀⠀⢿⢀⡞⠁⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⡇⠀⣿⢸⠀⠀⠀⠀⢿⢸⡀⠀⡇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡇⢠⡇⢸⠀⠀⠀⠀⣾⠘⡇⢸⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡇⢸⡁⢸⠀⠀⠀⠀⣿⠀⣿⢸⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡇⠈⣧⢸⠀⠀⠀⠀⣿⢰⠃⠈⡇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⠇⠀⠘⣿⠀⠀⠀⠀⣿⡏⠀⠀⣷⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣿⠀⠀⠀⢹⡄⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡿⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⣇⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⢨⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⣽⣇⠀⠀⢸⠀⠀⠀⠀⢿⠀⠀⢠⣿⣽⡄⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⣿⣿⠈⢧⡀⢸⠀⠀⠀⠀⢸⠀⣰⠋⣿⣿⣧⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢰⣧⣀⠀⠀⣾⡇⠉⢧⠈⣧⣸⠀⠀⠀⠀⢸⢰⠇⢰⠋⠘⣿⡄⠀⣀⣨⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢻⠇⠀⢸⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⣿⠳⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⢻⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠀⣾⣿⠀⠀⠀⠀⢸⣿⠀⠸⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠁⠀⡟⡇⠀⠀⠀⠀⢸⡿⡇⠀⢳⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏⠀⢸⠃⡇⠀⠀⠀⠀⢸⡇⣷⠀⠘⣇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣄⠀⡟⠀⡇⠀⠀⠀⠀⢸⡇⢸⡄⢀⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠾⠃⠀⡇⠀⠀⠀⠀⢘⡇⠀⠷⠏⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠙⡇⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠤⠼⠇⠀⠀⠀⠀⠀⠧⠤⠤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡮⣝⡒⠒⣒⡯⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣯
⠀⠀⠀⣀⣀⣀⣴⣿⣿⣿⣿⣷⣶⣾⣏⡀⠀⠀⠀⠀⢰⣟⣧⠶⠶⣤⣠⣵⠶⠦⣞⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⠛⡿⠿⠿⠿⢛⡛⡇
⠀⠀⠀⠙⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣾⡇⠀⠀⣿⣞⢰⣿⣷⢸⣿⢰⣿⣷⡘⣷⡇⠀⠀⣠⣶⣴⣦⡀⠀⠀⠀⠙⠒⠓⠚⠃⠛⠚⠉
⠀⠀⡀⣠⣬⣿⣯⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣥⣀⠀⠹⣷⡘⠿⢋⡼⠻⣅⠻⠿⣁⣿⠃⠀⠻⠿⠛⠈⠻⠿⠃⠀⠤⣐⣶⣤⣄⣠⣤⡶⣦⣄
⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠙⢿⣷⡿⠷⡶⠾⢿⣿⠟⠁⣀⣀⣀⣀⣀⠀⠀⠀⠀⣤⣾⣡⣶⢛⣍⢯⣇⢻⣦⣻⡆
⠀⠀⠀⣙⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠄⠀⠀⠀⠀⣯⢍⣉⣉⣉⠭⡇⠀⢸⡿⠛⠛⠛⣿⡆⠀⠀⢀⢿⣿⣿⣿⣾⣿⣼⣿⣿⣿⣿⠗
⠀⠀⠀⠉⠉⠉⠉⠙⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⡀⠀⠀⠘⠲⠦⠤⠶⠖⠁⠀⣸⠃⠀⠀⠀⢸⡇⠀⢀⣴⡇⣩⠹⡛⡿⠻⡿⡻⣛⡙⢰⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢚⠛⡛⡓⠀⠀⠀⢠⣶⢤⠀⠀⠀⢻⠀⠀⠀⠀⠈⡇⠀⣼⣿⣾⣿⣰⣷⢰⣧⢸⣷⢸⣿⣼⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣄⢰⡛⢿⡇⠀⠀⠀⠀⠀⢁⣋⣕⡙⠀⠀⠀⠀⠣⡳⣑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡾⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⡸⠆
⠀⠀⠀⠀⠀⠀⣰⣿⣾⣸⣿⡞⣧⠀⢀⣀⡀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠿⣴⡇⣩⡍⢫⡟⢫⡝⢱⣄⡿⠞⠁⡄
⠀⢀⣄⣄⠀⢀⣿⣿⣿⣿⣿⣧⣿⠀⣼⣿⣿⠀⣰⣶⡆⠀⠀⣄⠰⣦⡄⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠈⠡⡄⠈⠻⢿⣧⣿⣧⣸⡿⠞⠉⢠⡄⠃
⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠀⢈⠉⠁⠀⢢⡘⣲⡈⠿⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠈⠉⠉⢀⠀⡄⠘
⠀⠸⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠁⠀⠀⣁⣤⡄⠂⠙⠀⠛⠀⠀⠀⠀⠀⠀⢹⣷⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠃⠸⠀⠈
⠀⠀⠙⠿⠿⠾⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⡄⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡛⢿⣇⡀⠀⠀⠀⠀⠀⠀⣠⢔⣒⣒⣒⡠⣀
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡌⠿⠟⣸⣿⣿⣷⣦⡀⠀⠀⣬⣷⣾⣿⣭⣿⣳⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣶⣄⠀⠀⠙⣿⣿⣿⣿⡿⢛⣹⣿⣿⠀⠀⢿⣿⣿⣻⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⣿⣿⣟⣡⣶⣿⣿⣿⡿⠀⠀⠈⠻⣻⠿⠿⠿⣻⠏
⠀⠀⠀⣤⣶⣿⣿⣿⡿⠹⣿⣿⣿⣷⣦⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠹⣤⣠⡤⠃
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⢼⣿⣿⣿⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣠⣠⣔⣶⣾⣄⡀⠀⠀⣠⠤⠚⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⣿⣿⣿⣻⣿⣯⣵⡤⣼⡟⣿⣾⣿⣿⣯⣈⣠⣾⠟⠋⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣿⣿⣿⣿⢿⡿⣃⡀⠀⠙⣾⣧⢤⣿⣿⣿⣿⣿⣶⡛⣿⡄⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⣶⣤⣴⣯⢳⣿⡟⣸⣿⣉⢣⣿⣇⠘⠟⠛⢁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⠈⠉⠻⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠉⠛⠛⠶⠰⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢛⣿⣿⣿⣿⣿⣿⣿⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢰⣿⡿⢿⡿⢿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣾⣿⣿⠿⣻⣿⡿⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠹⠻⠛⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣾⠟⠓
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠦⣴⣶⠲⢦⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣽⣯⣀⣾⣷⣾
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠙⠷⣬⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣁⡬⠀⣙⣿
⠀⣼⣿⣿⡿⠛⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠳⠛⠈⠋⠉
⢸⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣴⣶⡟⣂⡀
⢸⣿⣿⡇⠀⠀⠀⠀⣼⢋⣥⣭⢁⣦⡀⠀⠀⠻⣿⣿⡦⠤⠤⠤⠀⠀⠀⠀⣿⣾⣿⣿⣖⠀⠀⠀⣀⣀⡀⠀⢴⣭⣿⣿⣷⣄⡀⠀⣀⣤⣾⣿⣿⣿⣿⣿⡛⠙⣓
⢸⣿⣿⣇⠀⠀⠀⠘⣿⣿⣿⢵⣾⣿⣷⣶⣦⣤⣽⣿⣿⠶⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣷⡀⠀⠈⠉⠙⠁⠀⠀⢶⣽⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⡟
⠀⢿⣿⣿⡄⠀⠀⠀⠘⣿⠙⠋⠉⠉⠁⠀⠀⠀⠀⣀⣬⣁⣶⣶⣤⣤⣤⣤⣬⣭⣅⠀⣩⣤⣤⣤⣤⣤⡄⠘⠳⣾⡈⠙⠈⠛⠛⠻⠿⠛⣿⡿⢛⣡⡔⢶⡲⣦⠁
⠀⠈⠻⣿⣿⣦⡀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⣸⣿⣿⡟⠉⠀⠀⠀⠀⠀⢀⣿⣿⠿⠶⠈⣿⢫⠉⢹⣿⣷⣦⣀⣀⡁⢀⠀⣦⠀⠀⣀⣄⠉⠙⣿⣿⣵⣿⣿⣷⣠
⠀⠀⠀⠙⠿⣿⣿⣓⠤⣀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠀⠀⠀⠀⢀⣠⣤⣿⣿⠋⠀⠀⠀⢀⣿⣷⣿⣿⣿⣿⠿⢉⣀⣿⣠⣌⢛⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣶⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣷⣤⢸⣿⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣋⣘⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣷⡄⠈⠙⠛⠛⠁⠀⣠⣶⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢯⣬⣅⣨⣤⡀⠀⠘⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣿⣿⠶⢦⣬⡿⡿⠀⢀⠀⠘⠁⠟⠉⠀⢀⣀⣀⣤⣾⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣾⣧⣤⣇⠀⠯⡱⢀⣼⡷⣿⣦⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢠⣴⣿⣿⠸⣿⡖⢀⣰⣤⡟⠛⠛⢋⡙⠛⠛⠛⠿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⣧⣿⣀⣴⣿⣿⣿⣿⣷⡀⠀⣼⣿⣠⣦⠀⠀⠀⠈⠋⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢻⣿⣿⣿⣟⠁⠀⢙⣶⣯⡉⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣿⣿⣿⣿⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣿⠿⠿⠿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⢠⠀⠠⠄⠠⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠆⠀⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠁⠀⠀⢀⣀⣀⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⣠⠀⠁⠀⠀⠀⠀⣀⣤⠖⠋⠁⢀⠀⠀⣀⡀⠀⢀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⡂⢀⠈⣹⡋⢀⠀⡒⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢈⣁⡁⠈⠉⢹⠋⠉⠀⣁⣉⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠊⠁⠠⠁⠀⢀⣼⣄⠀⠀⠡⠀⠉⠢⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⣠⣴⣾⣿⣿⡇⠙⠃⣿⣿⣿⣶⣤⡀⡰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⣿⡇⠳⠃⣿⣿⣿⣿⣿⡇⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠙⠛⡛⠛⠉⠁⣴⣄⠉⠙⠛⡛⠛⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠄⠁⣼⣿⣿⡆⠁⢰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠃⠙⠛⠛⠃⠀⠈⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠂

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠴⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⠖⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠠⠔⠒⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⢠⡞⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⠄⠀⠀⠀⠀⢀⣀⣁⣤⣤⣽⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠉⡛⠷⣤⣀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠚⠉⠁⢀⣀⣀⣠⣤⠤⠶⠖⠚⠛⠋⠉⠉⠀⢀⣀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣹⣦⣈⠓⢬⣙⠻⣦⣄⠀⠀⠀⠀⠀⣠⠶⠚⢛⡉⠭⠥⠄⢒⣂⣀⣤⣤⡴⠶⠶⠟⠛⠋⠉⣛⠛⢶⡄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⠳⢦⣌⠓⠦⣙⠳⣦⣀⢀⡾⠁⠀⠀⠠⠖⣒⣛⣋⣭⡭⠥⠤⠤⠤⠀⢀⣀⣀⣠⣤⠈⠃⠈⣿
⠀⠀⠀⠀⢰⡏⠀⠀⠈⠙⠶⣤⡉⠻⢶⣄⡁⠊⠙⠻⢧⣄⣀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠟⠛⠛⠛⠉⢉⣁⡠⠄⢀⣼⠇
⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠙⠳⣤⡈⠛⢶⣤⡀⠀⠈⣩⡭⠭⠤⠄⠀⠀⠐⠒⠒⠒⢒⣒⣊⣉⣭⣭⣤⡶⣾⠋⠁
⠀⠀⠀⠀⠀⢀⡿⠷⣦⣄⠀⠀⠀⠀⠀⠉⠓⠦⠈⠛⢷⣤⣠⣤⣤⠶⠶⠶⠒⣚⣛⣛⣿⣭⡿⠿⠿⠟⠛⠛⠛⣻⡇
⠀⠀⠀⠀⠀⠈⢧⣈⠲⢭⡛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠉⢀⣉⣥⠶⠶⠚⣛⠛⠉⠉⠉⠀⢀⣀⣀⣤⣤⣴⡶⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣉⠳⢮⣙⢷⣤⡀⠀⠀⢠⠞⠉⠀⠒⣈⣉⣥⡤⠤⠶⠖⠛⠛⢛⣉⣉⠉⠀⠀⠀⠲⣎⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣌⠛⠮⣿⢶⣄⣿⠀⠀⠀⠈⠀⠀⠒⢚⣛⣉⣉⣉⣭⣭⣤⡶⠶⠶⠞⠛⢀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠈⠙⠻⠶⠶⠾⠛⠛⠛⠛⠉⢉⣉⣉⣀⣀⣤⠤⠤⠴⢒⣊⣥⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠒⠋⢉⣉⣁⣀⣤⣤⣤⡤⠤⠶⠶⠖⠒⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣰⣏⡭⠭⢍⢙⣓⡲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⢴⠄⠓⠳⢬⡫⡳⣌⢣⡁⡀⠑⡶⠛⣣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡶⠀⢀⠰⡴⣷⣂⣾⣴⠋⡔⢝⠵⡸⣄⣦⢈⠳⡃⣭⡻⣕⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠗⢂⠸⢣⡼⢭⠭⣞⡃⣶⣸⢜⠉⣦⡗⣲⢈⣯⢑⢽⣮⡻⣷⣷⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠠⠿⠲⡰⠁⢘⣫⣛⠁⣷⣸⡃⠊⡬⢆⣺⢉⡾⣿⣿⢟⢮⣻⠮⡛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣱⠇⢀⢃⠷⠻⢼⢉⣫⠴⠷⣡⠼⢡⡿⡛⠬⢎⢩⣤⢣⢰⢨⡉⡅
⠀⠀⠀⠀⠀⠸⠟⠆⡢⡀⡼⣡⠞⠁⠀⠀⢸⡿⣸⣿⢹⣿⡽⣰⡬⡆⠗⢍⡐⠮⣀⠳⣅⠑⢌⠳⡅⢳
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠃⣷⡇⣀⠀⣀⡀⠸⢛⠶⢇⣛⣤⣚⢿⣝⡄⢰⡀⠈⠑⢮⠱⣇⣿⣼⣸⣿⢸⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢀⠀⠘⢦⡢⢜⠲⠤⠤⠤⠌⡣⢀⠑⢬⡻⢟⡗⠼⡀⠜⣌⡆⣤⣀⠈⠁⠸⠘⣮⢻⡾⣼⠀⠀⡆⢸⢸
⢠⡏⣯⠄⠀⠨⢁⣂⠀⠈⡆⢧⠠⣾⣟⡴⣡⠯⣅⠣⠀⢦⡘⢝⠅⢠⡝⣣⡝⠿⣯⡢⢄⡀⠸⠈⠇⣷⠀⠀⡘⢺⡾
⠾⡒⡷⠀⠀⠀⠘⠶⡣⠶⣘⠲⠶⠉⠈⠉⠁⠀⠰⠬⠆⠂⠙⢖⢙⢠⡄⡨⡿⣳⢌⡙⠷⣏⣲⠄⠀⠋⠀⠀⠙⢀⠰
⠠⣽⢇⠾⠀⠀⠀⠾⡀⠀⠈⠯⣠⠄⡵⡍⠀⣀⣠⣀⣀⠀⢀⢀⠱⣼⣃⣁⢌⡛⠓⠉⢉⠀⢀⠠⠘⠃⢀⠄⡤⣾⡄
⠀⢀⣰⠶⣦⡄⠀⠀⠉⠳⠺⠠⣇⠀⠙⠁⡕⡏⠀⠄⢋⠂⡋⢩⠾⠟⠀⠜⢛⡝⠆⠔⢉⠑⠄⠃⠁⠀⠸⣶⣳⣿
⠀⠀⠸⢿⣉⠷⠀⡀⠀⠀⡀⢈⠉⠙⠋⢩⠅⠳⠤⢬⡤⢤⠶⡎⠀⢂⣈⢥⠞⠤⡬⠤⠤⠔⠉⠀⠀⠘⢂⠞⣙⠁
⠀⠀⠀⠀⢙⣺⣾⢃⣀⡀⠉⠉⠐⢩⠒⠨⠑⠤⠠⡒⠰⡖⣆⣇⣡⠏⢒⡆⠀⢄⠀⠦⠇⠀⢠⢴⡇⢲⠆⠀⠉
⠀⠀⠀⠀⠀⠈⠀⣙⣭⢧⣶⠀⠻⠇⠀⠒⠲⡄⠸⡇⠀⠙⡜⡖⠆⠀⠀⡇⣀⠣⣾⠀⢠⡄⢘⡤⢖⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⣌⣻⣸⠆⠀⠵⠃⡉⠁⠓⠢⠤⠬⠬⠤⠤⠛⠁⣠⠄⣒⠀⣀⠓⣉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢂⣴⣖⣛⣓⢋⡒⣲⠖⣂⢼⢰⠇⣖⠶⠾⣷⣭⠵⣛⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠁⠛⠁⢊⠔⣣⠞⣐⠲⠄⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣶⣄⣙⣼⣁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣾⣿⡇⢰⣦⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⠀⠀⠀⣰⣿⡿⠀⣿⣿⡏⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢰⣿⠟⠁⣰⣿⡟⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣴⣿⠟⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⣄⠈⢦⡀⠀⠀⠀⠀⠀⠠⣿⣷⠀⡏
⠀⠀⠀⠀⠀⠀⣤⣤⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⡄
⠀⠀⠀⠀⠀⢠⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⡗
⠀⠀⠀⠀⠀⢈⣿⣿⠀⢸⣿⣿⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣆⣿⣿⣿⡄⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⠤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣦⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣴⠻⣭⣬⣯⣶⣶⣧⣿⣬⣉⢢⣄⠀⠀⠀⠀⠐⡿⠟⠉⠁⠀⢀⡛⠛⠛⢋⠀⠀⠈⠙⠻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣆⠀⠀⠀⠀⠠⣄⣀⠀⠀⠙⠻⠿⠿⠟⠁⠀⢀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠛⠿⠿⠷⢶⣶⣶⡶⡾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⢨⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⣸⣤⣴⣷⡄⠀⢀⡴⠀⣄⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣤⣄⠀⢠⣦
⠀⠀⠀⠀⠀⣅⢛⠋⠿⠏⠿⠿⢙⢛⣬⠀⠀⠀⠀⢩⣼⠁⠦⠀⠀⠾⠿⣶⠿⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢰⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢻⡼⣿⣼⣿⣿⢸⣿⢹⠇⠀⠀⠀⠀⠀⠻⣷⣶⠇⠀⡐⠂⣸⡾⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠄⣾⣿⠇
⠀⠀⠀⠀⠀⠈⣧⢿⡟⣿⣿⣼⢏⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣦⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⠋⠷⠿⠇⢟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢨⣶⢻⢇⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⢠⣤⣭⠁⣉⣥⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⢻⣿⣿⡇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⢸⣿⣿⠇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠘⠉⠉⠁

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠙⣿⣿⡿⠶⣦⣤⣀⡀⠀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⠀⠀⠙⣿⣷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠙⠻⣦⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣰⣶⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣆⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⡀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣗⡀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣤⣦⣼⣿⣿⣿⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠟⠛⠻⢿⣿⡿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠐⠀⠀⡁
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢔⠉⢷⠀⠀⠀⠈⠐⠅⠂⠀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠑⠤⠄⠠⠊⠀⠀⠀⠀⠀⠀⠤⠐⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠁⠀⠐⠀⠠⠀⠀⠄⠀⠠⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⢈⠀⢀⡀⠀⠀⡀⠀⡀⠀⠀⠈⠀⠀⠀⢠⡆⠄⠀⡄
⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡢⡀⡀⠀⠀⠀⠁
⠀⠀⠁⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠇⠀⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠈⡀⠀⡁⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡂⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠁⡌⠀⠀⠀⠉⠶⠐⠒⠒⠁⠁⠁⠉⠉⠁⠀⠐⠋⠓⠟⠈⠀⠀⠀⠐⠄⠀⠀⠀⠐⡀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠄⠀⡁
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠄
⠠⠐⠂⠀⣄⠀⠀⠀⠀⠐⠒⠂⠤⡀⢀⠀⠀⠄⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢀⠀⠀⠂⠀⠀⠈
⠈⢢⠤⣀⡙⠶⣶⢆⢒⠋⡀⡀⠀⡴⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠄⠀⢄⠀⠁⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢴⢀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠰⠉⠉⠂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠄
⠀⢀⠔⠉⠀⠀⠀⠀⠁⠈⠉⠑⢦⠀⠀⠀⠠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢡
⠀⡁⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⡇⠠⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠐⠿⠏⠀⠀⡇⠀⠘⠆⠁⠀⠄⠀⠀⠀⠀⠃⠃
⠀⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠔⠁⡀⠙⢢⠀⠀⠀⠀⠀⢠⠃⣀⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇
⠀⠀⢨⠀⠠⠋⠓⠀⢣⠤⡄⢠⠒⣼⠘⠋⣤⡀⠀⢹⠀⠀⢀⡀⠤⢤⠐⠒⠒⣦⠀⠠⢠⣀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⡠⠀⠀⠀⠈
⠀⠀⢈⠀⢀⡾⠓⠀⢸⠀⣿⢨⠄⡟⠀⠠⣋⡉⠀⣼⠀⠀⡌⠀⡄⠀⠈⣦⠀⠀⠁⢄⠀⠀⡤⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⡀⠀⣰⢦⡀⢸⠀⡇⠀⠇⡇⠀⠴⣫⡓⠀⣿⠀⠀⢰⠀⠈⢢⠂⠀⠑⡄⠁⠀⢣⠊⠈⢴⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⡡⠶⠄⢸⡞⠀⠀⠈⣇⢀⣘⠥⢥⣀⣹⠀⠀⠀⠐⡄⠈⠑⣤⠊⠈⢢⡄⠈⠁⡠⡎⠀⠀⠰⠶⠦⠤⢤⣄⣀⡀⠀⠀⠀⠆
⠀⠀⢰⡗⢚⠃⠉⠉⠙⡇⠀⠀⠀⠸⡅⣠⢠⢠⡆⣸⠀⠀⠀⠃⠈⣦⠂⠀⢡⡀⠀⠈⢂⠈⠑⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠼⠤⡄
⠀⠀⠀⢿⣾⣼⣾⣇⣧⠇⠀⠀⠀⠀⠣⠽⠧⠼⠾⠟⠀⢀⣤⣧⡀⠀⠑⡤⠀⠉⢢⠄⠈⢣⣠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣩⣀⣸⢧⣀⣀⣀⣀⣀⣀⠀⢠⣾⠉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⠀⠀⢀⠀⠀⠀⠀⢽⠒⢻⡵⠊⠁⠀⠀⠉⠉⠉⠉⠛⣌⡿⠽⡇⠀⠀⠀⣴⣂⡤⢄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⣜⣛⣉⣉⣉⣉⣛⣛⣒⣒⣒⡒⠒⠾⠷⠴⡇⠀⠀⣸⠇⣏⠑⡞⠉⣴⡂⢀⡀
⠀⠀⠀⢀⠐⠷⠶⠶⢤⣤⣤⣤⣤⣀⣤⠞⢀⣆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⡏⠀⠀⣿⢠⢎⣩⠓⢠⠧⣸⠁⠲⢇⡴⢠⡄
⠀⠀⡀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠈⢆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⠟⠲⠤⣍⠸⠁⠶⢥⣝⣉⠖⢀⡟
⠀⠀⢆⡀⠛⠛⠛⠛⠓⠒⠶⠤⠤⠄⠠⣶⣦⡄⠼⡄⠀⢻⢻⡟⠉⠁⠀⠀⠀⠀⠒⠒⠒⠶⢲⠋⠀⢰⡏⠘⠢⣤⣀⠛⢱⠆⣼⠈⡏⢘⡏
⠀⠀⠀⠈⠁⠒⠈⠉⠁⠀⠀⠀⠀⠀⠠⠤⠤⠀⠠⠔⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢀⡴⠋⣤⠋⠰⢠⡍⢉⠓⠲⠤⣤⣁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣟⡶⠒⠂⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢤⣈⠑⠂⠠⠊⡨⠓⠦⢦⢨⠏
⠀⠀⠀⠀⡠⣶⣶⠯⠷⣻⣿⡿⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠤⢔⢢⠆⠐⠒⠬⡈⠓⠒⠤⠧⣏⡐⠀⡌
⠀⠀⠠⠊⠙⢯⣿⣾⣻⣯⠟⠁⠀⠤⢀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠌⡀⠴⠋⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠙⠛
⠀⠐⠀⠀⠀⣀⠀⠉⠁⡠⢀⡾⡻⣷⣦⣄⣀⠀⠙⠺⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠠⠀⠀⣶⡟⣽⣷⡀⠈⠀⠈⠳⣕⣦⡟⠁⠈⠁⠉⠉⠁⠊⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠱⡀⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⣀⠀⠀⡰⠃⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢄
⠀⠀⠑⣯⠉⠁⠀⠀⢧⠀⢦⡀⠀⠀⠀⠈⣉⠽⠪⣍⣀⠴⠊⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢌⠀⠀⠈⠻⠀⠀⠀⠈⢂
⠀⠀⠀⠙⠀⠀⠀⠀⠈⢧⠀⣈⠥⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠂⠀⠀⠀⠀⠐⢤⠔⠁⠠⡀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠄⠀⠀⣀⡀⣀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠈⢆⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠶⠤⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣴⣦⣦⣄⣤⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⣿⢏⡿⣷⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠙⢉⣁⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⣠⣯⠇⢱⣮⢷⢾⣿⣿⡗⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡜⢿⣻⣷⣾⣿⣿⣿⣿⣶⡀⠀⠈⠉⠛⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣷⣤⣀⠠⢀⡠⠂⠀⠠⢋⣽⣿⠿⠿⢿⣿⠿⠋⢹⣿⣿⣷⣦⣄⠀⢀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣦⡑⢶⠆⣽⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⣿⣿⣿⣶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣠⣀⡀⠀⠀⠀⠀⠀⠉⠛⢿⠟⣠⠾⣿⣿⣷⡲⠷⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⠿⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣩⡴⠶⠚⠛⠿⢿⣶⣤⠀⠀⣄⡴⢃⠞⣿⣧⢹⣿⡍⠐⠶⣤⣦⠖⠀⠚⠛⠉⠙⠛⠛⡛⠉⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠏⢠⡞⠡⠀⠈⠉⠉⠙⠲⢌⠙⢿⠆⠁⣼⣿⣷⢹⣿⡼⣏⣷⠄⢄⠈⠃⠀⠀⠀⠀⠁⠀⠑⠄⢈⣀⠈
⠀⠀⠀⠀⠀⠀⡜⠀⡟⠀⠁⠀⡀⠀⣇⣀⣈⠀⠿⠁⢀⣴⣿⣿⣿⡇⣿⣧⡚⣡⠇⣼⣷⣤⣄⠠⡀⠙⡖⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⣇⣸⡇⠄⠀⠀⢸⡏⢀⣴⣤⡋⠀⠰⠃⠹⣿⣿⢿⣿⠟⠹⣥⡸⣲⣿⣿⣇⣽⠓⠐⠂⠘⣶⣆
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠁⠀⠉⠹⣇⠸⣿⣶⡟⠶⠂⠃⠀⢿⡇⠉⣩⢾⣧⢼⡟⢙⢻⣿⠟⢎⢃⠀⠀⠀⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠄⠠⠊⠙⣦⣄⣉⡠⠆⡀⠀⠀⣸⣧⡈⣹⣺⢿⠀⡧⠺⣩⣿⣿⣿⡎⠄⠄⠀⠀⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣌⠠⡀⠰⠀⠀⠡⠀⠀⠀⡅⢀⣿⡇⠥⡷⠟⠛⠚⠓⢫⣌⢻⣾⣿⣿⢰⠈⠁⠀⠀⠀⠀⠀⠴⣶⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣌⡐⠀⠀⠀⠀⠤⠞⣠⣾⠟⠀⠀⡇⣴⣴⡆⢟⣤⣫⣾⣿⣙⣿⠌⠀⠀⠀⢸⣿⣿⣦⠀⠀⠈⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣶⣶⣶⣿⡿⠋⠀⠀⠀⠀⢄⠄⠠⠈⠙⢿⣗⢽⣯⡔⣶⣆⣶⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⣀⣭⣳⣿⣿⣻⢿⣩⡛⢏⠉⠄⠉⠙⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⡯⣝⠀⠀⢠⣤⢤⡀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⣿⣷⣦⡀⠁⠆⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡘⠿⣿⣿⡏⠲⣄⡀⠈⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠜⢻⣷⡁⠠⢀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠐⠈⢛⠀⠙⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡂⠀⡀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉

⡖⠒⠉⠉⠐⢄⡀
⠈⢲⠀⢐⠂⠲⢄⠙⠦⠠⢀⠀⣀⡀⠀⡰⠒⠒⠲⠄
⠀⠀⠆⢸⡀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠄
⠀⠀⢸⠀⢱⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢀⡠⢄
⠀⠀⠀⠑⠺⡑⢄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡜⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠃⠈⡆⠀⠱⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⢧⡁⠀⠑⡄⠀⠀⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠑⠒⢄⠈⢂⠀⠈⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠃⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⡀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡤⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠙⢦⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⡠⠤⢰⡉⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠈⠀⠀⠀⠀⣀⠤⠠⠊⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠲⣄⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⠉⠀⠀⠀⠀⡀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣄⡿⢻⡇⠀⣾⠟⢻⣦⠀⢿⡆⣾⠃⠀⣿⡇⠀⣾⡟⠛⠃⢰⡿⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠿⠃⢸⡇⠀⣿⡶⠾⠿⠀⠈⣿⡏⠀⠀⣿⡇⠀⣿⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⡀⠀⠀⠀⣼⠟⣿⡀⠀⣿⡇⠀⣿⡄⠀⠀⢸⣇⠀⣸⡇
⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣼⣧⣄⣽⣿⣿⣿⣠⣿⣤⣸⣷⣄⣿⣧⣤⣽⣿⣿⣧⣌⣿⣿⣿⣡⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤
⣿⣿⡟⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⢀⣴⣾⣷⣦⡀⣀⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣦⠸⠿⠟⠛⠛⠈⠉⠉⠉⠙⠁⠛⠛⠿⠿⠇⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⢸⠿⠛⣉⣠⣤⣶⣾⣿⡿⠟⢿⣿⣿⠛⢿⣿⣿⣶⣦⣤⣈⡙⠻⢿⢇⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⣠⣴⣿⣿⣿⡏⠀⣿⣿⣷⣤⣼⣿⣿⣤⣼⣿⣿⡁⢈⣿⣿⡿⣷⣤⣈⠛⢿⣿⣷
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠛⢁⣴⣿⣿⣇⢀⣹⣿⣿⡿⠿⠛⠻⢿⣿⣿⣿⣿⠿⠛⠻⠿⣿⣿⣿⣁⢀⣿⣿⣷⣄⡙⢋⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣿⣿⠟⢁⣴⣿⠋⠹⣿⡿⠟⢋⣁⠤⠤⢴⣶⡄⠈⣿⣿⣿⡇⠀⣴⣶⠤⠤⢀⡉⠛⠻⣿⡟⠉⢻⣿⣆⠙⢿⣿⣇
⠀⠀⠀⠀⠀⠈⠿⠋⣰⣿⣿⣿⣷⠞⢁⠔⢊⠁⠀⡰⢚⠕⣛⣁⣴⣿⣿⣿⣷⣄⣙⠓⢍⡲⡀⠠⢁⠂⠄⠙⢶⣿⣿⣿⣷⡄⠻⠏
⠀⠀⢠⣴⣿⡿⠁⣼⣿⡁⢈⣿⠃⡔⢀⡔⠁⡠⢎⠐⢁⣾⡿⣿⢉⢍⢰⡄⠩⡛⣿⣧⠀⠙⢈⠦⡀⠑⣄⠈⡊⢻⣏⠀⣹⣿⣆⠸⣿⣶⡄
⠀⠀⢸⣿⡿⠁⣾⣿⣿⣿⣿⡿⢡⠌⡉⠉⢉⡅⣸⠁⢸⣿⠀⣉⣊⣠⡞⠠⡱⡈⣿⣿⠀⢠⣯⠀⣉⠉⠉⡉⢠⠸⣿⣿⣿⣿⣿⣆⠹⣿⡇
⠀⠀⢀⣛⠃⣼⣿⠀⢉⣿⣿⣡⣟⡼⢁⠇⡼⢠⡏⡀⠀⢻⣷⣿⣿⡆⡉⠄⢠⢡⢹⠁⠀⢠⡀⢧⠸⡄⢣⠹⣌⣧⣹⣿⣯⠁⣸⣿⡄⢛⣁
⢀⣴⣿⡏⢠⣿⣿⣿⣿⣿⡟⢁⠉⠟⠻⠾⣧⢾⡴⣟⠀⡄⣹⣿⠟⠔⠐⢀⠌⣌⠃⢣⡄⠺⠷⣼⢧⡿⠾⠛⠋⢡⠈⣿⣿⣿⣿⣿⣷⠈⣿⣷⣄
⠈⣿⣿⠃⣼⡿⠉⢹⣿⣿⡇⣿⢸⢀⠇⢰⠀⡄⢠⣧⣤⣼⣿⢟⠓⠶⠒⠿⡾⢅⠈⢻⣷⣤⣧⠀⡄⢰⠀⢇⢸⠘⡇⣿⣿⣿⠉⠙⣿⡄⢹⣿⡏
⠀⢈⣛⠀⣿⣿⣷⣿⣿⣿⡇⡇⢸⢸⠀⡎⣸⢀⣿⣿⣿⠿⠧⢀⣹⢟⠉⢉⢿⡑⠑⠼⢿⣿⣿⣧⠸⡌⡇⢸⢸⡆⡇⣿⣿⣿⣷⣿⣿⡇⢘⣋
⢠⣾⣿⠀⣿⡟⠛⢿⣿⣿⡇⡇⣼⢸⢠⡇⡇⣼⣿⠉⣿⡯⢦⡧⡽⢎⡲⢞⡾⡅⢷⠾⣽⡏⢹⣿⡄⡇⣳⢸⢸⡇⡇⣿⣿⣿⠟⠛⣿⡇⢸⣿⣧
⠻⣿⣿⠀⣿⣧⣴⣾⣿⣿⣃⡇⣿⢸⢸⣇⣧⣿⣿⣤⢻⡟⡛⣉⠓⠻⠼⠭⠗⢋⡫⣙⣿⣃⣼⣿⣧⣇⢸⢸⢸⡇⣇⣻⣿⣿⣶⣦⣿⡇⢸⣿⡿
⠀⠈⢛⡁⢸⣿⡿⠿⣿⣿⣿⣿⣿⣾⣾⣿⣿⠯⠛⣍⣽⣿⠰⢎⡲⠤⠤⠬⠴⡊⠶⢸⣿⣏⡍⠫⢿⣿⣿⣾⣧⣿⣿⣿⣿⡿⠿⢿⣿⠃⣘⠋
⠀⢀⣿⣷⠈⣿⣆⣤⣿⣿⣿⣿⣿⡿⠟⣛⠻⣶⣾⣷⣾⠯⠿⢯⣿⣿⣿⣿⣿⣯⠽⠏⢿⣶⣿⣶⡾⠟⡛⠿⣿⣿⣿⣿⣿⣧⣄⣾⡟⢠⣿⣧
⠀⠸⣿⣿⣇⠸⣿⣿⡿⢿⣿⣿⣿⠱⢡⣦⣕⢌⠻⣿⣏⣶⣠⣰⠿⠿⠿⠿⠿⢧⣰⣰⣆⣿⡿⢋⠔⣡⣦⢱⢹⣿⣿⣿⠿⣿⣿⡿⠁⣾⣿⡿
⠀⠀⠀⠉⠉⣄⠹⣿⣄⣠⣿⣿⣿⣷⣭⢝⣛⠳⣽⢠⡏⣿⡝⢠⣶⣒⣒⣒⣒⣦⡘⣽⡏⣧⢸⡵⠚⣙⢭⣥⣿⣿⣿⣯⣀⣸⡿⠁⣘⠛⠁
⠀⠀⠀⠀⠀⣿⣆⠙⣿⣿⣿⣿⠻⢿⣿⣮⣥⣦⣽⣘⣣⣿⣧⠉⠉⠍⠿⠯⠍⠉⢥⣿⣧⣛⣰⣧⣤⣭⣾⣿⠿⢻⣿⣿⣿⡟⢁⣼⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣧⡈⠻⣿⣿⡀⢄⠈⠙⣿⣿⡿⠿⠛⠻⡿⠃⠀⠒⠀⠐⠂⠀⠺⡿⠛⢻⠿⣿⣿⡟⠉⢀⠄⣸⣿⡿⠋⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠁⢦⡈⠻⣷⡈⠳⣄⠈⢿⣦⣤⣤⣤⣦⡀⠀⠖⠀⠐⠂⠀⣠⣧⣤⣴⣤⣾⠏⢀⡴⠋⣰⡿⠟⣁⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣈⠛⢶⣬⣵⠦⠛⠛⠛⠛⠻⠿⢿⢟⣫⣙⢿⠿⠿⠛⠛⠛⠛⠣⢖⣩⣴⠾⢋⣠⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡷⢦⣼⠃⢠⠀⣠⣤⣤⠶⢖⣇⢾⣿⣿⢇⣗⠶⢦⣤⣤⡄⢠⠀⢫⣠⡶⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠘⠷⣤⣤⠶⠞⣋⡽⣦⢭⢥⡺⣌⡛⠶⣤⣤⡴⠟⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠒⠂⠲⠶⢿⣟⣰⠇⣾⡆⢳⡘⣿⡷⠶⠂⠐⠚⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠼⡁⡹⢦⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢲⣰⠄⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⡶⣦⠀⠀⣀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣃⢐⡂⣚⣻⣿⣿⣻⣛⠠⠄⠀⠀⠁⢨⣀⣀⣝⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⠟⢸⡿⣿⠏⠉⠉⠱⠜⢳⠞⣾⣿⢦⡶⠘⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠜⣿⣷⡐⣖⣻⣵⣶⣶⡗⣀⣠⣶⣾⣿⣾⣛⢋⣧⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⢂⣷⣸⣆⣖⣿⣼⣿⢷⣼⣿⣿⣿⡏⣩⣉⢣⣯⣹⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣿⣿⣿⣿⠟⢻⣿⠻⠿⢱⣿⠛⣇⢸⣹⣸⢉⠼⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣿⣿⣿⣿⣯⢁⡙⠛⠒⡛⠛⠛⠋⢿⣿⣿⣟⢿⠀⡀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⣶⢾⣤⢬⡤⢤⣤⡤⢤⣤⣶⣤⣤⣿⣿⣿⣿⡁⠐⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣶⢬⣭⣿⡆⡤⠐⠶⠤⠲⢴⣷⣴⣉⢀⣀⣉⣉⣉⣀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡿⠀⣬⡡⣠⣅⣈⠄⣐⡒⠰⡁⣿⣾⣧⢾⣾⣿⣭⡧⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⢋⣉⣉⡙⠉⡛⠋⢙⣛⢻⡻⠟⠻⠻⡟⢻⣻⢇⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠶⠿⠿⡶⢿⢿⣿⣿⣽⣥⣾⣤⣾⣿⣿⠿⡯⡟⢺⡁⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢘⠏⣉⡀⠀⠂⣸⣿⣯⣾⣷⣷⣷⣝⠛⡟⣓⢰⣶⡟⠁⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⠈⠙⠛⠐⠹⠛⠋⠉⠛⠢⠰⠂⠀⠛⠉⠛⠉⠀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠓⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠙⢿⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⢿⡿⠿⢿⡿⢿⠿⣿⠿⣿⠿⠿⢿⣿⠿⠿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡇⣿⣿⣿⣿⠀⣈⣁⢸⡇⢘⣻⡷⠀⠰⣿⠀⡏⢰⣶⣿⡁⢾⡆⢸⣿⣿⣿⡇⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⣿⣿⣿⣿⣴⣿⣿⣼⣧⣤⣼⣧⣾⣦⣽⣴⣿⣶⣤⣾⣷⣦⣴⣿⣿⣿⣿⡇⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣀⡲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣒⣤⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠒⢄
⠀⠠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠘⢦⡀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⣀⡀
⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡯
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢵⡪
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣖⢽⡪
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡫⢕⢽⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠽⣪⣕⢕⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⢠⡿⢖⡭⡪⣿⢕⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠭⡛⢗⢦⣄⣀⣟⣻⢕⣿⡪⣚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡺⢕⡪⡕⡜⡼⡜⠄⠈⠉⠺⢕⢽⣪⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣴⡫⢕⢪⣳⣹⢱⡱⠑⠈⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⣠⣖⠯⣓⢬⢢⢧⢇⠣⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣍⡎⡞⣎⠎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠜

⢻⠉⠉⠉⠓⠠⣀⡀
⠀⣧⠀⢹⡓⢦⡀⠈⠙⠢⢤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠙⡇⠀⣧⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠘⣦⠈⢣⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢸⣆⠈⢣⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠍⠀⠈⠙⣆
⠀⠀⠸⣍⠁⠀⠘⣧⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠈⠑⢦⠀⠈⢧⠀⠓⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⢳⡄⠈⡆⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠸⡁⠀⢹⡄⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠹⣄⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣹⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠠⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣀⣤⢠⡞⠀⠀⠀⠀⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠊⠁⠀⠘⠚⠁⣀⣀⣀⡠⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠤⣀⣀⠀⠀⠀⠀⢀⣀⣄⣀⣀⠀⠀⠀⣄⣠⠨⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠈⠀⠀⠀⠉⠳⣄⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠒⠚⠛⠓⠦⣤⠶⠖⢲⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣸⣦⣀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⡒⠊⠉⠉⢉⣽⠉⠉⠉⠙⠛⠒⠻⢷⡀
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢒⡎⠉⠁⣀⣀⠤⠕⠒⠊⠉⠉⠛⠓⠒⠲⠶⠤⢤⣤⣼⣇
⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⣀⡠⠄⢲⡎⠉⢀⣀⠤⠬⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄
⠀⠀⠀⡼⠉⠳⢤⡀⠀⡰⠁⠀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠶⠒⠛⠉⠙⡇
⠀⠀⠀⣇⠀⠀⠀⠉⠓⣧⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⣠⡤⠤⠶⠶⢺⡇
⠀⠀⠀⢘⣦⣀⠀⠀⠸⠀⢨⠓⢦⡀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠀⣀⣀⣠⡤⠴⠶⠒⠚⠛⠉⠉⠁⠀⣀⣀⣤⠴⠖⢻⡄
⠀⠀⠀⣾⠀⠈⠓⢦⣵⠀⢸⠀⠀⠉⠳⣄⡀⢠⡏⠀⠤⠖⠚⠋⠉⠉⠁⠀⢀⣀⣠⡤⠴⠶⠒⠛⠋⢉⣉⣀⣤⡤⠤⢾⡁
⠀⠀⠀⢻⡄⠀⠀⠀⡸⠳⢼⡀⠀⠀⠀⠀⠉⠛⣧⣤⡤⠤⠶⠖⠒⠛⠛⠉⣉⣁⣤⡤⠤⠶⠒⠛⠉⠉⠁⣀⣀⣠⣤⡞⠁
⠀⠀⠀⠀⠙⠳⣄⡀⡇⠀⡘⠉⠓⠦⣄⡀⠀⢰⡇⠀⠀⢠⡤⠴⠖⠒⠛⠉⠉⠀⢀⣀⣠⡤⠶⠖⠚⠋⠉⠉⢀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠇⠀⠀⠀⠈⠙⠶⣼⣄⠀⢀⣀⣀⣠⣤⠤⠶⠖⠚⠋⠉⠁⣀⣀⣠⡤⠴⠖⠛⠋⠉⠁⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠀⠀⢠⠏⠉⠉⠉⠀⠀⣀⣀⣤⠤⠶⠒⠛⠋⠉⠀⠀⢀⣀⣠⡤⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⢸⠀⠀⠐⠒⠛⠉⠉⠀⣀⣀⣤⡤⠤⠶⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠷⠤⠤⠶⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡮⣗⡒⠒⣒⡯⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣯
⠀⠀⠀⣄⣀⣀⣴⣿⣿⣿⣿⣷⣶⣾⣏⡀⠀⠀⠀⠀⢰⣟⣧⠶⠶⣤⣀⡵⠶⠦⣞⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⠛⡿⠿⠿⠿⣛⡛⡇
⠀⠀⠀⠙⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣾⡇⠀⠀⣿⣞⢰⣿⣷⢨⣿⢰⣿⣷⡜⣷⡇⠀⠀⣰⣶⣴⣦⡀⠀⠀⠀⠙⠘⠓⠚⠃⠛⠚⠉
⠀⠀⡀⣠⣼⣿⣯⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣥⣀⠀⠹⣷⡘⠿⢋⡼⠻⣇⠻⠟⣁⣿⠃⠀⠻⠿⠛⠈⠻⠿⠃⠀⠤⣐⣶⣤⣀⣠⣤⡶⣦⣄
⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠙⢿⣿⡿⠷⡶⠾⢿⣿⠟⠁⣀⣀⣀⣀⣀⠀⠀⠀⠀⣴⣾⣡⣶⢛⣍⢫⣇⢻⣦⣻⡆
⠀⠀⠀⢙⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠄⠀⠀⠀⠀⣯⢍⣉⣉⣉⠭⡇⠀⢸⡿⠛⠛⠛⣿⡆⠀⠀⢀⢿⣿⣿⣿⣾⣿⣼⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠉⠉⠉⠛⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⡀⠀⠀⠙⠲⠦⠤⠶⠞⠁⠀⣼⠇⠀⠀⠀⢸⡇⠀⢀⣴⡇⣩⠹⡛⡿⠿⡿⡿⡛⡙⢰⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣚⢛⡛⠳⠀⠀⠀⢠⣶⢤⠀⠀⠀⢻⠀⠀⠀⠀⠈⡇⠀⣼⣿⣾⣿⣰⣧⢰⣧⢸⣷⢸⣿⣼⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣄⢰⡛⢿⡇⠀⠀⠀⠀⠀⢉⣋⣝⡙⠀⠀⠀⠀⠣⡳⣱⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡾⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣱⠆
⠀⠀⠀⠀⠀⠀⣰⣿⣾⣸⣿⡞⣧⠀⢀⣀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠿⣴⡆⣫⡍⢫⡝⢋⡝⢱⣆⡿⠞⠁⡄
⠀⢀⣄⢄⠀⢀⣿⣿⣿⣿⣿⣧⣿⠀⣼⣿⣿⠀⣰⣷⡆⠀⠀⣄⠰⣦⡄⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠈⠡⡄⠈⠛⢿⣧⣿⣧⣼⡿⠞⠉⢠⡄⠃
⠀⢾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠀⢉⠉⠁⠀⢦⡘⣲⡈⠿⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠈⠉⠉⢀⠀⡄⠘
⠀⢸⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣤⣿⡿⠁⠀⠀⣀⣤⡄⠆⠙⠀⠚⠀⠀⠀⠀⠀⠀⢹⣷⣶⣾⣷⣦⡀⠀⠀⠀⠀⠀⠃⠰⠀⠈
⠀⠀⠙⠿⢿⠾⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⡄⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡛⢿⣇⡀⠀⠀⠀⠀⠀⠀⣠⢔⣲⣒⣒⡤⣄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣿⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡌⠿⠏⣸⣿⣿⣷⣦⡀⠀⠀⣬⣷⣿⣿⣭⣿⣷⣿⡄
⠀⡀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣾⣆⠀⠀⠙⣿⣿⣿⣿⠿⢛⣹⣿⣿⠀⠀⢿⣿⣿⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⣿⣿⣟⣡⣶⣿⣿⣿⡟⠀⠀⠈⠻⣿⠿⠿⠿⣻⠏
⠀⠀⠀⣤⣶⣿⣿⣿⡟⠹⣿⣿⣿⣿⣦⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠹⣤⣤⡤⠃
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠉⠉⠋⠙⠀⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡍⠜⢤⣄⠀⠰⠶⠒⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⢃⠀⡀⠀⠀⠀⢀⡾⣿⣿⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠀⠀⠀⣠⣿⣿⣾⠀⠸⠄⠠⠄⢸⠘⠿⣿⣿⣿⣟⣷⡐⠦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠂⠀⠀⣴⣿⣿⣿⣿⠟⠀⣀⣤⣶⣦⣼⠁⡄⠛⣿⣿⣿⣿⣿⣶⡆⠈⣙⣦
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠹⢿⣿⣿⣿⠀⠀⣿⣿⣟⣿⡿⠀⣤⠀⠈⣿⣿⣡⣿⣿⠃⣾⣿⣿⣧
⠀⠀⠀⠐⢪⣣⣿⠟⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⠀⠀⠀⢸⣿⠃⠀⠀⢺⠀⢰⣿⣿⣿⣿⣿⣴⠇⣿⣿⣿⣿⡄
⠀⠀⠀⠗⠀⣿⡟⢠⣶⡆⢠⠀⣿⣾⣿⣿⣿⡿⠀⠀⠀⢸⣿⡄⠀⠀⠈⢠⣼⣿⡟⣿⣿⣿⡏⣠⡿⣿⣿⣿⣷⠁
⠀⠀⣾⢦⣸⣿⣿⡟⣿⡇⢹⢁⣿⣿⣇⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⠻⠛⢿⣿⡀⠙⢿⣿⣿⣷⡄
⠀⠀⠨⢿⣿⣿⡏⣠⣿⠃⠘⠏⠋⠀⣿⣿⣿⡇⠀⠀⠀⣾⢹⡇⠀⠀⠐⠀⠘⣿⣿⡗⠀⠀⠀⠹⣿⣤⣿⣿⣿⣿⣷
⠀⠀⠀⣠⣿⣿⣧⣼⣿⣀⠀⣴⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⣶⣿⣿⣿⣟⣻⣿⣿⡆
⠀⠀⠐⠈⣿⣿⣿⣿⣿⡿⢧⡼⡂⠀⢸⣿⣿⡇⠀⠀⠀⡟⢿⣿⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠠⢨⣿⣿⣿⣿⣷⣶⣿⣷⢆⣤⣿⣿⡇⠀⠀⠸⡇⣸⣿⡆⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⡿⢻⡿⣿⣛⣻⡿⠛⠉
⠀⠀⠀⠀⠈⣍⣽⠛⡿⠿⣿⣿⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡏⠘⣿⣷⠀⠀⣥⠈⠉⢉⡽⠋
⠀⠀⠀⠀⠀⢠⠀⠀⠈⠁⣨⣿⣀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⣿⡀⢀⠏⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⢿⣿⣿⣿⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣧⣴⠀⠟⠀⠎⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠸⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⡿⠟⡛⠀⡠⠚⡀⠰⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡛⢿⡆⠀⠀⠰⣶⣿⣿⣿⣿⠟⣟⣉⣁⠴⠖⠓⠈⠀⠀⠉⣶⡆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢠⠤⣼⠿⣿⣿⣿⣿⡀⠛⡻⠶⠂⠀⠀⣷⡄⠀⣼⣏⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⢸⠀⠤⠀⠘⣿⣿⣿⡿⠂⠕⢠⡖⠐⠋⢈⡗⠀⠁⣿⣿⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⣷⣦⣄⠁⠀⠈⡆⠀⢀⣤⣿⣿⠻⣿⡄⠰⠟⠀⠀⠀⠀⡇⡀⠀⢻⣿⡀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⣿⡆⠀⠘⠿⢦⣿⣿⣿⣿⠀⣿⣷⡄⠀⣿⣿⠀⣼⡇⣇⠀⢸⣿⣿⡼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⢇⣾⣿⣿⣿⣿⡇⠀⣄⡁⣼⣿⣿⣿⣿⠀⢸⣿⣿⣦⣿⣿⢀⢹⢄⢻⡄⠀⣿⣿⣷⢻⣿⡄
⠀⠀⠀⠀⠀⠀⣸⠏⣼⣿⣿⣿⣿⣿⡷⠀⠈⢻⣿⣿⣿⣿⣿⣤⠘⣿⣿⣿⣿⣿⡌⢸⢸⠘⣷⣤⣸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣰⢏⣼⣿⣿⣿⣿⣿⣿⡇⢶⠃⣸⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⡇⣾⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣰⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⡺⠀⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣻⠇⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⡆
⠀⠀⠀⣔⣡⣿⣿⣛⣋⣿⠿⠏⢹⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠗⠋⠈⢿⣿⣿⣿⣗⠈⠿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⣟⣿⣿⣿⣿⡟⠀⠐⠛⢻⡿⠻⢿⠟⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠃⠀⢙⠋⠹⣿⣿⣿⡇⠀⠀⠀⠈⢣⡀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀⠀⠀⠀⠙⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⢛⣩⠥⠖⠒⠚⠉⣉⣉⣉⡉⠙⠒⠒⠦⠬⣉⡛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⣩⠔⠊⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠉⠑⠦⣍⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠿⢋⠴⠋⠀⠀⠀⢀⣴⣿⣿⣿⣧⡻⣿⣿⣿⢟⣽⢿⣿⣿⣦⡀⠀⠀⠀⠀⠙⠦⡙⢿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⢣⠔⠁⠀⠀⠀⠀⢀⣾⣿⣿⡿⢷⣌⠳⣝⢿⣵⢟⣥⢞⣻⣿⣿⣿⣄⣀⣠⣤⣤⣤⣈⣢⡙⢿⣦
⠀⠀⠀⢠⣾⣯⣴⣧⣤⣤⣤⣀⡀⠀⣾⣿⣿⣿⣿⣶⣝⠳⣼⢿⣔⣫⣶⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠙⠛⠿⣶⣿⣷⡀
⠀⠀⣰⡿⠛⠉⠀⢀⣀⣀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣯⣿⣥⣴⠿⠿⠛⠋⠉⠀⣀⣠⣤⣴⣶⣶⣶⣶⣦⣄⡀⠈⠹⣿⣿⡄
⠀⣼⠏⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠈⣿⣿⡄
⢸⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣷
⢸⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠍⠉⡁⠀⠄⠀⠀⠀⠖⠀⠀⠀⠈⠃⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡟⣿
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡾⠿⠿⣿⣷⡄⠀⢠⣾⣿⡿⠿⢿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢇⢸
⣿⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡇⠀⠀⣠⣤⡤⠍⠃⠀⠈⠫⢤⣤⢤⠀⠀⢀⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⢸
⣿⡀⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⠐⠛⢺⡇⠀⠀⠑⠛⠛⠃⢸⠀⣾⠀⠛⠛⠃⠀⠀⣸⣿⠊⠃⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⢸
⣿⡇⣇⠀⠀⠈⠙⠿⣿⣿⣿⣿⣧⡘⢸⡇⠀⠀⠀⠀⠀⡠⢸⠀⣿⢠⡀⠀⠀⠀⠈⢻⣿⢘⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⡞⢸
⢸⣧⢸⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣾⡇⣾⣀⣔⣀⣤⣷⣾⣤⣾⣾⣧⣄⣰⣄⣿⢼⣿⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⡇⣾
⠈⣿⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡟⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⣿
⠀⠸⣷⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠉⠛⠉⠉⢐⣶⡖⠈⠉⠛⠉⠁⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣿⠇
⠀⠀⠹⣧⡘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠸⣄⣼⣿⣿⣄⡟⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣾⠏
⠀⠀⠀⠹⣷⡌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠷⣾⣭⣭⣭⣵⡶⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⣾⠋
⠀⠀⠀⠀⠘⢿⣦⡱⣄⠀⠀⠀⢀⣠⣤⣶⣶⣆⢿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⠇⣾⣶⣶⣦⣄⡀⠀⠀⠀⡠⢊⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣬⡓⢤⣶⣿⣿⣿⣿⣿⣿⣌⢿⣿⣦⣀⠀⢀⣠⣾⣿⢏⣼⣯⣾⣿⣿⣿⣿⣷⡤⢊⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣉⠻⢿⣿⣿⣿⣯⣻⣷⣌⡻⣿⣷⣿⡿⢋⣴⣿⢿⣿⣿⣿⣿⡿⠟⣩⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣌⣙⠻⠿⣷⣽⣿⣿⣮⣛⣫⣾⣿⣿⣧⡿⠿⠛⣋⣥⣴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⣶⣦⣬⣭⣭⣍⣩⣭⣭⣤⣴⣶⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠿⠿⢿⣿⠿⠿⠿⢷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠿⢿⣷⣄⣀⡀⠀⢸⣿⠀⠀⢀⣀⣴⣿⠿⠿⠿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠈⠛⠛⠻⠿⢿⣿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄
⠀⠀⣠⣿⢿⣦⣄⠀⠀⠀⠀⠀⣰⡿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣿⡄⠀⠀⠀⠀⢀⣠⣾⢿⣷⡀
⠀⠀⠻⣷⣦⡉⠻⢿⣦⣄⣠⣼⡿⠁⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠙⣿⣦⣀⣤⣶⠿⠋⣡⣶⡿⠃
⠀⠀⠀⠀⠙⠻⣷⣤⣿⠟⠛⠉⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠀⠀⠀⠀⠈⠉⠛⢻⣧⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠁⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⢸⣿⡿⠀⠀⢰⣾⣿⣿⠀⠂
⠀⠀⠀⠀⡐⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠸⣿⣿⣿⣿⠟⡐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⣆⢸⣿⠀⠀⠀⠀⠙⢿⡟
⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢀⠁⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⢿⡀⢻⣆⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣿⣿⠃⠀⢁⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠿⢷⣄
⠀⠀⠀⠀⠀⢧⠀⠀⠈⠒⢀⠀⠀⡁⠄⠀⠀⠀⠀⠸⡏⠀⠈⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⢈⣿⠆⠄⠀⣹⣿⠖
⠀⠀⠀⠀⠀⡌⠀⣀⣀⠀⠘⠀⠀⠆⢠⠀⠀⠤⠦⠠⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠐⢶⡀⠀⠸⠿⠀⠀⢠⣿⡟
⠀⠀⠀⠀⢀⠃⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⠁⠀⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⠇
⠀⠀⠀⠀⠘⠀⣿⣿⣿⡄⠀⠀⠀⠀⠉⠀⢠⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠘⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠠⠃⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣄⢀⠀⠀⠀⠀⠘⢋⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⢿⣄⣤⣿⡇
⠀⠀⠀⠀⡆⠀⠀⢀⠼⠷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠙⢧
⠁⢀⠀⠀⡁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠨⠀⠀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠄
⠀⠘⠙⢀⡁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠱
⠐⠈⠀⠁⠉⠐⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⡁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡀
⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠃⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠂⠈⠀⢘⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠄⠐⠈⠀⠀⠀⠀⠀⠈⠀⠀⠤⠒⠁⠑⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢂⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠀⠂⠀⢠⠀⠀⠀⠤⠤⠤⠀⠀⠀⠄⠀⠀⠙⠀⠀⠘⡀⠀⠀⠐⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⠃⠀⠀⠀⠢⠀⠀⠃⠀⢀⠄⠀⠀⢀
⠀⠀⠠⢀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠈⠒⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠈⡆
⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠌⠢⠰⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠆⠂⠀⠀⠀⠈
⠀⠀⠀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠈⠐⠂⠁⠂⠁⠀⠀⠒⣦⠠⡀⠄⢄⠂⠐⠔⠀⠀⠀⠀⠀⠥⠠⠠⠀⠠⡳⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⡀⠸⠀⡃
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢡⠘⠄⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠒⠀⠀⠄
⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠒⠒⠤⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠈
⠘⠄⢀⠀⠀⠻⡤⢀⢀⣀⢠⣴⠀⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠀⠈⠐⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠲⠐⠀⠀⠠⠀⠉
⠀⠈⠁⠈⠐⠆⠊⠑⢃⠓⡀⢂⠐⠀⠂⢂⠞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠒⠢⠠⠄⠀⠀⠀⠌⠀⠀⠐⠀⠠⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⢡⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠰⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⡄⠀⢰⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠁⠀⠀⠑⠄⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣈⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⢞⠸⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⣫⠤⣈⣃⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢿⣟⠋⠈⡆⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⣶⣶⣤⡈⠽⣵⡿⠉⠈⡿⠛⠋⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⣙⣶⣿⣿⣷⣉⢁⡴⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢾⣿⣶⣦⣴⠝⠽⢿⣿⣿⠹⣿⡗⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢀⣨⣿⢋⣮⠀⣌⣻⡷⠀⠀⡱⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡕⢻⣧⣞⣿⣿⠙⡇⢀⡈⡆⡇⣿⣹⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠙⠣⠛⠃⣿⣧⠀⢇⢫⡀⣿⣷⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣀⣼⡿⠉⠳⢾⣦⣤⣉⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠉⣿⡿⢿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣍⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢠⢼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣠⣄⣦⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠻⢼⡿⠛
⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠚⠙⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠔⠛⠉⠹⠶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢲⡉⠠⠤⠀⠒⠒⠀⠀⠀⠀⠐⠀⠄⠉⠀⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠤⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡗⠸⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠨⡗⢀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠳⣟⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣫⠾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣽⠀⢀⠑⠺⠯⢵⡶⢒⡶⠾⠙⠓⠉⠁⢀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠳⢤⡤⢀⣀⣀⣀⣀⠠⠄⠀⠀⡸⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣎⣁⣢⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠤⡤⢀⠀⢀⣤⣀⠀⠀⣤⢠⣿⣿⡛⠛⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣀⠀⠀⠀⠀⠀⣄⣀⣀⣼⣿⣿⣷⣴⣤⣔⡿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠑⠛⣩⣯⡿⠻⣿⢿⡿⣿⢿⣿⣿⡻⣿⣷⢿⣭⣡⣤⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢰⠋⢀⠁⠀⠘⡄⠀⡿⠀⠁⠿⡅⠹⠈⢢⠙⠻⣿⣄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⡇⠀⢰⠀⠀⠸⠁⠀⠰⠀⠃⠀⠉⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⡴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⢲⡀⠀⠠⣑⡀⠀⠠⡱⣄⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠀⠤⢇⠀⠀⠱⡀⠀⠀⠈⢆⠀⠀⡈⢆⠀⢉⠱⡀
⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠠⡄⠀⠀⠤⠀⠀⢀⠠⡆⠀⠀⠸⡇⠀⠀⢀⡁⢡⠀⠀⠠⠼⠀⠀⠀⢳⠀⠀⠀⠈⢷⡀⠀⠈⣧⠀⠁⣡
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⣚⠀⠀⠀⢐⠁⠀⠀⢘⠀⠀⠰⠒⡇⠀⠀⠀⠀⠸⠆⠀⠐⠂⡦⠀⠀⠄⢧⠀⠀⠀⡘⡇⠀⠠⠘⣇⠀⠄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠃⠀⠠⠎⡛⠀⠀⠀⣙⠀⠀⢈⣩⡇⠀⠀⠈⠀⢘⡂⠀⠀⠀⣿⠀⠀⡁⢸⡇⠀⠀⠀⢹⡄⠈⠁⢻⡂⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⡠⠀⡌⠀⠀⠐⢸⡇⠀⠀⠤⠆⠀⠀⠀⠴⠁⠀⠀⢈⡁⣉⡅⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⢀⠘⡇⠀⠠⢨⣇⠀⠁⣿
⠀⠀⠀⠀⠀⠀⠂⠤⢚⠇⠀⠀⣈⣨⠀⠀⠐⠒⠂⠀⠀⠀⠲⠀⠀⠀⠠⠀⢰⡆⠀⠀⠈⢸⠆⠀⠀⠀⣿⠀⠀⠐⠠⣏⠀⠀⠐⣿⠀⠀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡤⣤⠀⠀⠘⠛⠅⠀⠀⣉⣙⡀⠀⠀⠒⠒⢺⡇⠀⠠⠤⢼⡄⠀⢈⠒⠾⠀⠀⠘⢰⣯⣀⣤⡸⠷⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠈⠓⠳⠄⣀⡠⢨⡇⠀⠀⠈⢁⣼⠀⠀⠀⢀⣾⡀⠀⣀⠸⠛⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠂⠠⠀⢀⠢⠀⠀⠀⠠⠀⠀⠄⠂⠐⠄⠠⠐⠁⠀⠐⠔⠠⠂⠄⠀⠊⠐⠁⠂⡠⠀⢀⠆⠈⠀⠀⡐⡁⠀⠀⠌⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⠤⡀⠀⢀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⡐⠁⠀⠘⠂⢨⠂⠈⡄⠀⠀⠀⠀⠀⢀⠞⠁⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠒⡀
⠀⠀⠀⡇⠀⠀⠀⠓⠈⠀⡰⠀⠀⠀⠀⠀⠀⡼⠄⠀⠄⠠⠌⡆⠀⠀⠀⠀⠀⢀⠤⠼⠔⣀⡠⠑⠠⢄
⠀⠀⠀⢁⠀⠀⠀⠘⠀⠉⠀⠀⠀⢀⣀⠀⠰⠇⠀⠉⠈⠁⠈⠹⠄⠀⠀⢀⡀⠀⠂⠀⠀⠱⠀⠀⠀⡌
⠀⠀⠀⠀⠂⠀⠐⠃⠀⠀⠀⠀⠀⠈⢯⠉⠄⠀⠄⠀⠄⠀⠠⠀⠤⠈⠠⡼⠀⠀⢰⠀⠀⠀⠁
⠀⠀⠀⢀⠠⣠⠂⠤⠀⡀⠀⠀⠀⠀⠈⠑⠚⠋⠉⠁⠒⠒⠊⠙⠛⠓⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⢰⠮⠧⡙⢋⠕⣦⡙⢄⠀⠀⠀⠀⢀⠀⠄⡀⣠⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣀⠀⠁
⠀⠀⢀⡆⠀⠀⠈⢪⠞⠓⢻⠂⠀⢀⡤⢪⢀⣪⠫⠶⠋⠋⠳⠤⣩⠢⣀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣸⠀⠀⡀⠀⢸⠀⠀⡘⠀⢠⢚⠭⡿⠋⠁⠀⠀⠀⠒⠀⠀⠀⠙⢮⣢⠀⠀⠀⠀⠀⠀⡐
⠀⠀⡇⠀⠀⠀⠀⠘⠀⢀⠃⠀⠆⡟⡘⠁⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⢹⠁⠀⡠⠶⢄⡌⡀⠑⢠⢀⡀
⠀⢰⠃⠀⠀⠀⢀⠃⠀⡌⠀⠀⢃⡻⡃⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⡈⠤⠔⠀⠰⢱⠀⠈⠀⠙⠉⠙⠊⢡
⠀⢸⠀⠀⠀⢀⠌⠀⡐⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⡈⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠢⣄⣠⢊⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢂⢀⣠⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠆⠀⠀⠈⠀⠑⠢⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠎⠁⠈⠱⠀⠀⠀⠈⠢⠄⣀⠀⢸⠀⠀⡇⠀⠀⢀⡠⠂⠀⢘⡗⠄⢄
⠀⠀⠀⠀⡠⠂⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⣈⣁⢤⣀⠐⠐⠊⠁⠀⠀⠀⢸⠔⠚⠙⡄
⠀⠀⠀⠎⠀⠔⠒⢄⠀⢰⠀⠀⠀⡟⠫⠧⠄⠒⠒⠢⠭⠶⢹⠀⠀⣀⡀⠀⠀⢇⠀⠀⠱⢄⡀
⠀⠀⠀⡀⠀⠦⣀⠜⠀⡨⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡸⡠⠊⠀⠈⡀⠀⠈⠳⢄⣀⡀⠉⠙⠀⣒⠄
⠀⠀⠀⠘⠢⢄⣀⡠⠔⠁⠀⠀⠀⠘⠢⠄⡀⢀⡀⠀⠠⠔⠻⣀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡌⣿⣿⣿⣿⢡⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣎⠻⣷⡘⣿⣿⢃⣾⠏⣴⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢻⣿⣿⣿⣧⡙⣧⠹⠏⡼⢃⣾⣿⣿⣿⡟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡌⠇⠘⣡⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠸⣿⣿⣿⢸⣄⣨⣿⣿⣿⣿⠇⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⣿⣿⣿⢸⠟⠿⣿⣿⣿⣿⠀⠸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⣿⣿⡿⢸⣦⣴⣿⣿⣿⣿⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠘⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⣰⣶⣶⠀⣶⣶⣶⣶⢰⣶⢰⣦⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⣰⣿⣿⣿⠀⣿⠋⠙⣿⠸⠿⢸⣿⣧⠀⠘⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠀⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⣾⣷⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣧⣠⣥⣤⣦⣤⠉⠁⣰⡂
⣾⣿⣿⡿⢿⣿⣽⣿⣿⣾⣿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣶⣦⣦⣶⣶⣿
⣽⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿
⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⢣⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⢆⡴⢶⣎⢿⡄⣎⣧⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⡠⠂⢸⣵⣏⠊⠾⢋⠛⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⢀⠀⠃⣀⢈⠴⢛⢠⣀⠒⢶⡆⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣀⠀⠀⠀⠄⡀⠀⢁⣖⡻⠓⠀⠁⢀⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⢆⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠑⠢⣤⡀⠀⢀⢀⣤⡀⠓⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿
⠀⠙⠹⠛⠋⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⠿⣯⠅⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣶⠦⠤⠴⠶⠶⠶⠤⠤⠤⠤⠤⠴⠶⠶⠒⢒⣺⢏⣿⠳⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠿⣦⠈⠳⣶⠶⠶⠶⠶⠖⠒⢶⣶⠒⠒⡿⠋⢉⡵⢃⡎⠸⠃⠀⠀⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠳⢤⣀⠀⠀⠀⠀⠀⠀⢀⣡⠴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣈⠉⠛⠒⠒⠚⠉⢁⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⣠⡾⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠘⢷⣄⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠷⠤⢤⣀⣀⡄⠀⠀⢀⣀⣠⣤⠷⠴⠴⠧⣤⣄⣠⣤⠴⠧⠤⠤⠤⠤⠤⠶⠶⠲⠶⠶⠒⠚⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢢⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡐⠀⢉⠄⠀⠠⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠒⠄⠀⢄⠈⢁⡐⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠔⠈⠁⠤⢀⡀⠉⠢⠂⣀⠈⠁⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠈⠁⢀⡂⠁⠡⠄⠒⠀⢀⡁⠐⠄⡀
⠀⠀⠀⠀⠠⠊⠀⡖⠂⠴⣀⠠⠐⠂⠀⠀⠀⠀⠀⠰⢀⠑⠀⠀⠀⠀⠀⠀⠀⠐⠈⡰⡀⠀⠀⠀⠀⠀⠒⠠⢉⠀⢀⠀⠄⠈⠢
⠀⠀⠀⠀⢃⠆⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⡀⠀⠀⠀⠠⠀⠀⠀⠂⣁⠄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠐⠀⣂⠃
⠀⠀⠀⠀⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠋
⠀⠀⠀⠀⠀⠩⡄⢡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⣈⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠆⠐⠈⠀⡀⠠⠀⠀⡀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠐⠂⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠂⠁⢀⡀⠐⠀⢀⢬⠀⠀⡀⠐⠒⠂⠀⠀⠀⠀⠒⠒⠐⣀⠀⠉⢅⠀⠐⠢⣀⠀⠁⡁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⡐⠁⠀⠤⠂⠐⡀⠊⠡⣀⠔⠡⣀⠊⠢⡀⠀⠁⠌⠀⠑⡀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠤⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠂⢀⡀⣀⠠⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠐⠒⠒⠒⠈⠀⠈⠐⠒⠒⠒⠠⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠛⠛⠛⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣆⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⡉⠛⠛⣻⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⠛⠛⢁⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⢴⣿⣿⣿⣿⣿⣿⣿⣄⠀⣴⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⣿⣿⣿⣿⣧⡈⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠋⣁⣼⣿⣿⣿⣿⠀⣤⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣾⣧⠈⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⣿⣿⡟⠀⣿⣇
⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⣼⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⠟⠋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠀⢾⣆
⠀⠀⠀⠀⠀⣼⡟⠀⠀⣰⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⡄⠀⠈⣿⡄
⠀⠀⠀⠀⢰⡿⠀⠀⢠⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣷⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣾⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⢀⣿⠁⠀⢠⣿⣿⣿⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⠀⠀⢸⣧
⠀⠀⠀⠸⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠋⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉
⠀⠀⠀⣿⠂⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⡆⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣶⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠶⠀⠒⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠀⢀⠤⠠⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠰⠂⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⢀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠒⡃⠀⢈⠒⠀⠀⠀⠰⠺⠄⡄⠦⠖⠀⠀⠀⠀⢄⣀⣀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠀⠀⠀⡀⠠⣌⣁⣀⡀⢀⡀⠀⠀⠰⠉⠉⠱⠀⠀⠀⠀⠀⠃⢀⠀⠃
⠀⠀⠀⠀⠀⢸⠀⠑⠤⠄⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁
⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡉⠈⠈⢀⡀⠀⠀⠀⠐⠙⣀⠉⠂⠀⠀⠀⠀⢂⣙⠚⡁⠂⠀⠀⠀⣀⠉⠋⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢠⡰⡀⠉⣀⢆⡄⠀⠀⣀⡼⠉⠀⠱⣠⠄⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢁⠌⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠓⠒⠒

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠒⠐⠆⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⡠⠂⢆
⠀⠀⠀⠀⢀⠀⠴⠚⠈⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠴⠂⠀⠀⠀⠀⠀⢃⠀⠁⠀⠀⠀⠀⠀⠁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠈⠂⠘⠉⠂⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡠⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠄⠀⠀⠀⠀⠀⡠⠢⠢⣀
⠀⠀⠀⠀⠘⠃⠠⠤⠈⠉⠇⠀⠀⠀⠲⠇⠐⠖⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⡃⠀⢁⠀⠀⠀⢀⣐⢑⢃⢄
⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠐⠀⠐⠀⠀⠐⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⠀⣆⠶⠐⠂⠾⣀⠀⠀⠀⠈⠘⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣰⣶⡴⠗⢠⡤
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⣠⣾⣿⡇⢀⣴⣿⣿⣤⣤⡿⢅⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄⠀⠛⠿⣿⣡⣾⣿⣿⣿⣿⠟⠛⠶⠠
⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣷⣄⡠⣠⠄⣸⣍⢻⡿⢡⠂⠀⡆⠑⡄
⠀⢀⣴⢖⣯⣷⣥⣤⣀⡀⠙⠻⣿⣿⣿⣇⠁⢨⣿⣿⣷⡈⢪⣟⣰⣦⣴⠃⡄
⢠⣿⠏⣸⡿⠛⠛⠻⠿⣿⣷⣤⡻⠿⣿⡿⢦⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣵⣦
⢸⡧⡃⣿⠀⠀⠀⠀⢠⣴⣿⣿⣷⣶⡟⠀⣼⣿⣿⣿⣿⣿⣷⣌⠙⢿⣿⣿⣿⣯⣄⣀⡠⢀
⢸⣿⢫⣿⠀⠀⠀⠀⣿⣿⣿⡿⠟⠻⣤⣰⡟⢿⣿⣿⣿⣿⣟⠿⣄⠈⢻⣻⣿⣿⣿⣿⣁⣹⡷
⠈⣿⣇⠾⣇⠀⠀⠀⢹⡟⢿⣷⣲⣶⡾⠿⣄⠈⣿⣿⣏⣸⣿⣷⣝⢳⣏⡀⣽⣿⣿⣿⣿⠋
⠀⠸⣿⣕⠛⣦⠀⠀⣸⣿⣮⣛⢿⣷⣾⣆⣹⣆⡀⠀⠟⠙⢿⣿⣿⣿⣯⣟⣋⡙⠿⢛⣭⣅⡈⠙⠻⠶⣦⡀
⠀⠀⠛⣯⣮⣙⣳⡄⠙⠛⠻⠛⠻⠿⠿⠛⢻⣿⣵⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢝⣲⣤⣍⠑⢄
⠀⠀⠀⠉⢿⣷⣦⡽⢦⣄⠀⠀⠀⠀⠀⠀⢸⣿⡿⡇⠀⠀⠀⠀⢠⣿⡿⣿⡿⠛⠁⠈⠻⢿⣿⣿⣧⣠⣽⣷⣤⡀⠹⣆
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣉⡳⢤⣄⡀⠀⣀⣼⣿⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣎⣋⠋⠉⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣧⣬⣉⣛⡛⣉⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣤⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠟⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠻⣯⢭⣤⣤⣤⣬⣭⡭⢽⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢀⡇⠀⢸⡆⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⡇⠀⢸⡇⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⢸⡇⠀⢸⡇⠀⠸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⢠⠀⠀⢠⡄⠀⢰⡄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢾⡉⠛⠷⠦⠼⠦⠤⠼⠷⠶⠚⠋⣹⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠁⠀⠀⠈⣙⡓⠲⠦⠤⠤⠤⠤⠶⠖⣒⣛⡭⠆⠀⠀⠉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡷⠶⢤⣤⣄⣈⣉⣉⢛⠀⠚⠛⠛⣋⢉⣉⣀⣀⣠⣤⡤⠶⡞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠉⠉⢹⡏⠉⠉⠉⠉⠉⡏⠉⠉⠁⢸⡇⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⢰⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠇⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠘⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢘⠃⠀⢰⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢾⣀⠀⢸⠃⠀⠀⠀⢨⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⢸⠀⠀⢘⣧⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠉⠓⠦⣤⣀⣀⠀⠛⠀⠀⠀⠀⠀⠈⠃⠀⠀⣀⣠⡤⠖⠋⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣈⣉⣉⠛⠛⠓⠒⠒⠒⠚⠛⢛⣉⣉⣀⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣶⣾⣶⣶⣶⣷⢷⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⢶⡿⠷⠿⠿⣷⣾⠿⣿⠷⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠛⢻⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⡝⣿⣿⡄⣼⣿⡟⣽⠿⣷⡄
⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣶⣶⡶⠾⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠿⠶⣶⣶⣶⣦⣤⣤⣄⣀⡀
⠀⣠⣶⠿⠛⣋⣉⣭⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣬⣍⣉⣛⠻⢷⣦⡀
⣴⡟⣡⣾⣿⣿⡿⠿⣿⣿⣿⡿⢽⣿⣿⣿⣿⣿⣧⣿⡇⣿⣧⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⡻⠿⣻⣿⣿⣦⡙⣿
⣿⣅⣿⣿⣿⣿⠙⣳⣿⣿⣿⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣖⣾⣿⣿⣿⣷⡟⢽⣿⣿⣿⡇⣹
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⣉⣭⣍⣉⠉⠉⠉⢉⣉⣭⣍⡉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠈⠻⣿⣿⣷⣭⣿⣿⣿⣿⠇⠀⠴⠟⠛⠛⠛⠉⠀⠀⠀⠈⠙⠛⠛⠛⠷⠄⠀⢿⣿⣿⣿⣯⣵⣿⣿⡿⠋
⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⠀⠀⠀⣼⣿⣿⣦⠀⢀⡇⣧⠀⢠⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠘⣿⠀⠀⠀⠙⠿⠿⠋⠀⠘⠇⠟⠀⠈⠻⠿⠟⠁⠀⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣿⡆⠀⢰⡀⠀⣠⣴⣾⣿⡇⣿⣿⣶⣤⣀⠀⣰⠀⠀⣾⣷⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠻⠿⠿⠿⠛⣋⣀⣈⡛⠿⠿⠿⠟⠋⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡄⡀⠀⠀⠘⣭⢿⢯⡝⠀⠀⠀⡀⣄⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣷⣄⡀⠀⠀⠀⠀⣀⣴⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣻⢿⣿⣛⠻⠿⠿⢛⣻⣿⢿⣻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢯⣗⢮⣗⢮⣻⢷⣤⣴⢟⣫⢞⣯⢖⣯⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣮⣝⢮⣗⣯⣿⠟⢿⣯⣞⣯⢞⣭⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⡿⠁⠀⠀⠹⣿⡾⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⡞⠋⠀⠀⠀⠀⠀⠘⢋⠉⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⡇⠶⠖⠀⠉⠉⠉⠲⢄⡇⠀⠈⢣⡀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡾⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⠀⠈⠻⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣠⣤⡀⠰⠗⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠈⠓⠒⠲⠖⢶⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠈⠱⢦⡀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡄⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣠⠃⢀⡞⠁⠀⠀⠀⢰⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠘⠀⠀⠀⠀⠀⠀⣴⠃⣠⠏⠀⠀⢠⡄⠀⠹⠸⠇
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢀⡜⢁⡶⠁⠀⠀⠀⡌⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠘⣇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⣆⢀⠞⠁⠀⠀⠀⠀⠀⠀⢀⣌⠀⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢰⠈⠉⠐⢦⡀⠀⡇⢸⠀⠀⠀⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠰⠀⡷⠀⠀⢸⠀⠀⠀⠀⡇⠀⢠⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣄⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⡀⢀⠀⢀⡆⠀⠀⢀⣼⣤⣤⣄⡘⠀⠀⠀⠀⠇⠀⠸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠂⠁⠤⠁⢉⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠏⠐⢦⡜⠃⠈⠁⣨⡿⡆⠀⠀⠀⢰⠀⠀⢃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡌⠸⡇⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣄⠀⣹⠀⠀⢨⣽⠁⡇⠀⠀⠀⢸⡆⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠇⠀⠙⣤⠄⠤⠀⠶⡶⢶⡖⠒⠒⠒⠒⠒⠒⠀⠀⡇⠀⠀⠙⡹⣦⡀⠀⠀⡄⢃⠀⠀⠀⢸⡇⠀⠸
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡞⠀⢀⡼⠀⢀⣠⠾⡄⢉⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⣟⠀⠛⠶⣤⣼⢸⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⠃⠀⣼⣥⡴⠿⠑⠂⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢘⠓⢦⡄⢀⡀⣾⢁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⠀⢠⠿⠉⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢸⡆⠀⠀⠉⠉⠁⣾⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠾⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡇⠀⢸⡇⠀⠀⢠⡄⢰⡏⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢸⡇⠀⠈⡇⠀⠀⠈⠇⠀⠀⠇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡌⡇⠀⡀⢠⠀⠀⠀⠀⠀⢰⢠⡆⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⣇⠁⠀⡇⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⢹⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠒⠢⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠇⣸⠀⠀⠁⠀⡄⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⡀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢿⡆⠀⠘⠀⡇⠀⢠⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡈⡇⠀⠀⠀⣿⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⡇⢸⡀⠀⠀⡇⠀⢰⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠸⠇⠸⢃⣠⡤⠇⠀⠀⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠒⠒⠒⠀⠤⠤⠤⠤⠔⠚⠁⠀⠉⠐⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠙⠀⠄⠀⠀⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠐
⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠁⣀⠐⡰⠊⠀⠀⡠⠊
⠀⢀⣀⠀⠀⠀⢀⡀⢀⠠⠀⠀⠀⠀⠀⡀⠀⠠⢀⠠⠦⠀⠀⠀⠀⠀⠀⣘⠀⠀⠐⠁⠀⠀⠰⠀⢀⣀⡀
⠀⠁⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⢀⠠⠊⡁⣀⠀⠀⢀⠀⢾⣿⡟⠹⢿⡿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠃⠆⠰⠀⠀⠄⢀⠀⠀⠈⠀⠀⠈⢀⠄⠈⢀⣿⣀⣀⣾⡀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢹⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠁
⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⢆⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠐
⠀⠸⠿⠃⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⣀⠀⠀⠀⠀⢀
⠀⠔⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⡸⠀⠀⠉⠙⣿⡟⠋⠁⠑⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠢⠀⠀⠀⠈⠈
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠
⠀⠀⠀⠠⠀⠀⢀⣠⡄⠠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠀⣤⠀⠈⠛⠋⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁
⠀⠀⠑⠂⠀⠀⠑⠀⠈⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠊⠀⠀⠀⠀⠈⡀
⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠃⠀⠀⠀⠀⢀⡄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⣶⣶⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠘⢿⣿⡄⢸⡏⢀⣿⡿⠃⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡁⠰⣿⣷⠀⠃⢸⣿⠂⢨⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣄⠙⣿⡆⠀⠟⢁⣴⣿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⣿⣿⣿⣆⠘⢧⠀⣴⣿⣿⣿⣿⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⣿⣿⣿⣿⣧⡈⠀⢸⣿⣿⣿⣿⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⣿⣿⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⠿⣿⡄⢸⣿⣿⣿⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣶⣿⡇⢸⣿⣿⣿⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠀⠀⠀⢀⣉⠉⢿⣿⣿⠿⣿⡇⢸⡏⠉⣉⡀⠀⠀⠀⠛⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇⠀⠀⠀⠘⠛⠀⣻⣿⣿⣴⣿⡇⢸⡇⠀⠛⠃⠀⠀⠀⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⠿⠿⠿⠿⠟⠀⠿⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠋⠀⠀⠈⢻⡏⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠏⠀⢸⣇⠀⠀⠀⠀⠀⣿⠀⠈⠻⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⢿⣥⣤⣄⠀⢿⡀⠀⠀⠀⣸⠇⠀⣤⣤⣼⡿⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⡾⠃⠀⠈⢷⡄⠀⣴⠏⠀⠀⠙⣧⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣇⠀⠀⠀⠈⠛⢶⣄⠀⠀⠻⠾⠃⠀⢀⣠⡾⠋⠀⠀⠀⢀⡿⢷⡀⠐⡧
⠀⠀⠀⠀⠀⠀⢀⣤⠀⢰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⢸⡇⠘⣷⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣼⠃⢠⡿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠸⣧⠀⢻⡄
⠀⠀⠀⠀⠀⣸⠇⢀⣾⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢹⡆⠈⣿
⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⢠⡟⠀⣾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣟⠀⣰⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢻⡄⠘⣧
⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⢸⡇⠀⠙⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢸⡇⠀⠉
⠀⠀⠀⠀⠿⠀⢸⡇⠀⠀⠀⠀⣾⢿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣿⢿⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡿⢸⡇⠀⠀⠀⢸⡇⠀⣴⠶⣤⠀⠀⠀⠀⠀⠈⠁⠀⣿⢸⣇⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⣼⠀⠀⠀⠀⢸⡇⠀⠿⣴⠟⠀⠀⠀⠀⠀⠀⣤⠀⢻⡄⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡆⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⢠⡟⢰⡏⠀⠀⠀⠀⣿⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⣷⠘⣧⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⣾⠃⠀⠀⠀⠀⣿⠀⢸⣏⣹⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⡄⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠀⠀⠀⠀⠀⣤⣤⣤⠿⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⢸⣉⡁⢳⡾⢸⣇⡞⠙⢢⡞⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠟⠿⠸⠤⠄⠞⠻⠼⠏⠧⠴⠊⠧⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠰⠂⣿⣿
⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⠛
⢹⣿⣿⡿⣶⣦⣄⡀
⠀⢻⣿⡇⠀⠈⣿⣿⣷⣶⣤⣤⣤⣤⣾⣿⣷⣦⡀
⠀⠘⢿⣧⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠙⣿⣅⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣠⣾⣷⣦⡀
⠀⠀⠠⣤⣿⣿⣆⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠈⠛⠻⣿⣦⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠐⢿⣿⠆⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⣀⣤⣤⣶⣤⣿⣿⣿⣿⠿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠉⠻⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠠⠖⠉⢷⠀⢀⣀⣀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣤⠶⠏⠀⣎⠁⠀⠀⠰⡟⢻⠏⢀⠌⠓⢬⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⠋⠉⠉⠙⣣⡀⠀⠀⢹⠁⠀⠀⡀⠘⢄⠁⠬⡖⠘⢂⡿⠀⠉⢳⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣠⣴⣾⣿⣿⣿⣷⣄⣈⡆⠀⠀⠀⢀⠉⠻⠶⡚⠉⠀⡈⠂⢴⠟⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢹⡀⠀⠀⠀⠠⡀⠀⠈⠙⠛⠀⠀⠀⢀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠓⠒⠲⢤⡀⢘⣆⠀⠀⢀⣀⡼⠛⠋⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠙⠓⢻⣍⠀⠀⣀⣤⣶⣾⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣾⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⡙⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⢿⣿⡿⣿⣯⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡟⠁⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⢠⣾⣿⠟⣻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣦⣄⣺⣿⣫⣴⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡙⠻⠿⢿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡛⣱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⢀⣟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢠⣿⡿⠙⠻⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡈⡙⠻⠿⣿⢾⡷⣾⣿⣾⣷⣾⣷⣿⢿⠟⠃⣾⣿⠁⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣦⣤⣠⣀⣈⣁⣈⣀⣈⣄⣥⣴⣆⣼⣿⡟⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣭⣿⣿⣿⣿⣿⣻⣟⣯⣿⣽⣶⣿⣿⣿⢇⣀⣤⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣹⣿⢫⣽⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠻⡟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣰⠀⡄⢀⢀⡔
⠀⠀⠠⠐⠈⠅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠃⠈⢠⠆⡄⡤⡀
⠀⠀⠐⠒⠒⠒⠂⠉⠉⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒⠚⠙⠓⠂
⠀⠀⠀⠀⢠⣟⠁⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠄⠀⠘⠣
⠀⠀⠀⠀⣸⠋⠀⠀⠉⣷⠀⠀⠀⠀⠄⠀⡜⠀⢠⢤⠀⡀⠤⢤⠀⠢⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠘⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⢀⡄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠔
⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠢⡀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⣽⠁⠀⢺⡋
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠆
⠀⠀⠀⠀⠀⠀⡀⠸⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠉⠉⣹⠐⠀⠀⠀⠀⠀⠀⡀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⣀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠰⠏⠀⠀⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠚⠛⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⠊⠀⠀⠀⠀⠀⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⠉⢻⡷⠦⠴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠉⢿⡛⢾⣷⣾⣿⣿⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣇⠀⠀⠀⠀⠀⢀⠉⢛⢿⣿⡇⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣦⠀⠀⠀⢀⣠⣕⣺⣿⣿⣆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣳⣄⢠⣿⣧⡀⠉⠻⣛⢿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣤⣍⡻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣹⠃⠿⢈⠛⠛⣿⡿⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣰⢻⡏⠸⠀⠈⠀⠀⠀⠙⣦⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⠇⡎⢀⣴⣾⣿⣿⣾⣦⡀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠁⡘⢠⣿⡉⣿⣿⠉⢹⣿⣷⡧⡸⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡴⠊⠀⢀⠁⢸⣿⣇⠘⣿⠀⣼⣿⣿⣷⢱⢿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠸⠁⠀⠀⡌⠀⣾⣿⣿⡄⢹⡇⣿⣧⢻⣿⣇⠈⢻⣿⡜⣧⡉⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⢀⡜⠀⣰⣿⣿⣿⡷⢼⣷⣿⣯⠀⣿⣿⡀⠀⣿⡿⡿⣷⡄⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠀⠊⠀⣾⣹⣿⣿⣿⠀⢸⣿⣿⢻⠀⢻⢹⣧⡀⣿⡅⠁⡈⢿⣆⢹⣷
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠀⢸⣿⡟⣼⡆⢸⢸⡎⠳⣜⣷⠀⠈⢮⢻⣿⠻⣦
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⣠⡟⣿⣿⣿⣿⣿⠀⢸⣿⠀⢸⠃⣸⢹⡇⠄⠏⠙⢿⣄⠀⢺⣿⠀⢹⡇
⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⢀⣿⢾⣿⣿⣿⣿⣿⡄⢸⡏⠀⢸⠃⣿⠄⢳⡀⠀⠀⠀⠙⣧⠀⢻⣇⢸⣧
⠀⠀⠀⠀⠀⠹⢦⣤⣀⣴⢋⣴⣿⡿⣿⣿⣿⣿⣧⣸⡇⠠⡏⠀⣿⢐⠈⡇⠀⢀⠀⠀⠸⡇⢘⣧⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⣿⣏⣿⡿⢹⠟⣧⠀⠀⠀⣽⣤⣴⣿⣄⠘⣿⠿⠟⠁⢻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠻⠿⠟⣧⡿⠂⢻⠶⠶⠶⠿⠋⠙⠛⠛⠛⠃⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠰⠾⠂
⣿⣿⣷⢿⣿⠶⣾⣿⣿⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣦⣶⣴⣶⣦⣾⣦⣾⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠻⠷⠶⣦⣤⣄⣀⣀⣠⣤⣴⠶⠾⠛⠛⠛⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠙⠻⠷⢶⣤⣤⣤⣤⣤⣤⡶⠾⠟⠉⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⢀⣤⣴⠾⠿⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠿⠷⣦⣤⡀
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⠙⠛⠷⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⡶⠾⠛⠋⠁⠀⠀⠀⠀⠈⠻⣦⡀
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⢸⡏⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢻
⢸⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣯⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠶⠶⠟⠛⣿⠀⢸⣿⠀⠀⠀⠀⢸
⣾⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸
⣿⣄⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠
⠈⠙⠻⠶⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣴⠶⠟⠋
⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠟⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿