Calender Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣰⠚⠉⣙⣦⣄
⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⣤⡞⠋⠉⣉⣻⣥⣤⠤⠶⢻⠊⠉⢁⡟⠈⢧
⠀⠀⠀⠀⣀⣏⣠⠤⠴⣖⣛⣿⠿⠛⠋⠉⡏⠀⠀⠠⡿⠀⠀⠈⠁⠀⠈⢧
⠀⠀⠀⡏⡡⢴⡶⢿⠋⠉⢀⣼⠀⠀⠀⠿⠁⠀⢀⡀⠀⣤⣄⣳⡀⠀⠀⠈⢧
⠀⠀⢸⠃⡇⢸⡀⠘⡇⠀⠘⠛⠀⠀⠤⠴⡖⠃⣿⣿⣄⢹⡌⠙⠇⠀⠀⣀⡈⢧⡀
⠀⠀⢸⠀⡇⠀⡇⠀⢷⠀⠀⠀⠀⠀⠀⣀⣿⠀⠻⠀⠈⢀⣀⣤⠖⣚⣏⠥⢹⡄⢳⡀
⠀⠀⢸⠀⣿⠀⢳⠀⠸⡆⠀⠀⠀⠀⠀⠈⣀⣠⠴⠲⡋⡽⣆⣊⣧⡥⠚⢫⠁⢘⣆⠹⣄
⠀⠀⢸⠀⢻⠀⠸⡄⠀⢻⡀⠀⡤⠖⠚⡍⠥⠘⣎⡡⠷⡖⠉⢧⢀⣹⣤⠒⠻⣅⠈⣳⡈⢦⡀
⠀⠀⢸⠀⢸⠀⠀⢧⠀⠈⢧⠀⠸⣌⡥⠜⡞⠉⠙⣆⣀⠽⡖⠋⠳⡀⢈⣢⡤⠚⢫⡁⠙⣆⠙⢦
⠀⠀⢸⠀⠈⡇⠀⠘⡆⠀⠈⢧⠀⠹⡄⣀⡼⣖⠊⠉⢆⠀⣈⣦⠴⠛⢯⠀⠙⣄⡤⠝⢎⠉⠳⣌⠳⣄
⠀⠀⢸⡀⠀⣧⠀⠀⠹⡄⠀⠈⢧⠀⠙⣅⠀⢘⣦⠤⠚⠻⡁⠀⢱⣄⠤⠓⣏⠀⠱⣄⣀⠵⢶⡉⠳⣄⠑⢄
⠀⠀⠸⡇⠀⢸⡀⠀⠀⢳⡀⠀⠈⢳⡀⠈⢯⠁⠀⢣⣀⡠⠝⢞⠉⠈⠳⣄⡨⠷⣞⠉⠳⣄⡠⠽⠚⠉⠀⢀⡱⠆
⠀⠀⠀⣇⠀⠈⡇⠀⠀⠀⢳⡀⠀⠀⠳⣄⠀⠳⡖⠉⠙⢦⡀⣀⠵⢖⠋⠉⠳⣄⡤⠗⠊⠁⠀⢀⣠⠴⠊⠁
⠀⠀⠀⢹⠀⠀⢹⡀⠀⠀⠀⢳⡀⠀⠀⠘⢦⡀⠈⠢⡤⠒⠙⠢⣀⣀⠽⠖⠋⠁⠀⠀⣀⡤⠒⠉
⠀⠀⠀⠸⡆⠀⠀⣇⠀⠀⠀⠀⠳⡄⠀⠀⠀⠙⢆⡀⠈⠳⠴⠚⠉⠀⠀⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⢷⠀⠀⠘⡆⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠙⢦⡀⠀⢀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠸⡆⠀⠀⠹⡄⠀⠀⠀⠀⣈⡷⡄⢀⣠⠴⠚⠙⠚⠉
⠀⠀⠀⠀⠀⢳⡤⠤⠒⠻⡤⠴⠚⠉⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⠀⣀⣀⢀⣀⡀⢀⣄⡀⢀⠤⢄⢀⠤⢤⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⢠⣮⠭⢵⠾⠵⣿⠞⠒⣺⠛⢓⡾⠛⢫⠟⠉⠹⠋⠉⠉⠟⠉⠉⠟⠉⠩⠟⢧
⠀⠀⠀⠀⠀⠀⡞⣿⣿⠀⠋⠀⠀⢁⡤⢀⣄⢠⠀⢴⡂⢠⣄⡆⣖⢲⢰⣷⠰⡿⡆⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢠⠇⢸⣿⡇⠀⠀⠀⠹⠤⠘⠙⠘⠒⣘⣃⣈⣀⣁⣈⣁⡤⡤⠤⠤⡤⠤⢤⡔⠲⡄⢧
⠀⠀⠀⠀⠀⡼⠀⠈⣿⣿⠀⢰⣒⠉⠩⢽⡭⠭⠭⠽⡆⠀⠐⠺⡖⠒⠒⢛⢉⠉⣋⢉⢉⣏⣉⣧⠸⡄
⠀⠀⠀⠀⢠⠃⠀⠀⢻⣿⡇⠀⣧⠤⠤⠄⠗⠒⠒⠒⢛⠒⠀⠉⣏⢉⣉⣹⣅⣀⢸⡤⠤⢽⠤⠼⡄⢧
⠀⠀⠀⠀⡼⠀⠀⠀⠸⣿⣷⠀⢸⠄⠀⠒⢺⠒⠀⠀⢹⣉⣉⣁⣸⡀⠀⠤⡧⠤⠤⡆⠐⠚⡖⠒⢣⠸⡄
⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⣿⡆⠈⡧⠐⠒⠚⡇⠉⣉⣉⣧⠤⠤⠤⡆⠐⠒⢲⠒⠂⢻⠉⠉⣩⣉⣘⡆⢣
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⣿⣷⠀⢸⠂⠈⠉⢹⣁⣀⣀⢸⡤⠤⠤⢶⠐⠒⠚⡇⢉⣙⣍⣀⠼⠤⠤⠗⠘⡆
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣿⡿⡄⠈⡏⠉⢉⣈⣄⣀⠤⠤⠧⠒⠒⠚⠊⠉⠉⠉⣁⣀⣀⡤⠤⠤⠴⠖⢶⠃
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠈⠉⠉⠀⣀⣀⣀⡤⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⢸⣠⠤⠔⠒⠒⠉⠉⠉⡿⠟⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠴⠒⠒⠚⠉⠉⠉
⠀⠀⠀⠈⠉⠓⠒⠦⢤⣀⡀⢹⠀⠀⣀⣀⣠⠤⠤⠴⠒⠒⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⣆⠀⠀⠀⡴⠛⢶⠀⠀⠀⢠⠞⠳⡄⠀⠀⠀⡶⠛⢦⠀⠀⠀⣰⠞⢳⡄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⡇⠀⣿⣀⣀⣀⡇⠀⢸⣄⣀⣀⣸⠀⠀⣧⣀⣀⣠⡇⠀⢸⣀⣀⣀⣿⠀⢸⣇⣀⣀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⡇⠀⢸⡁⠀⠀⣸⠀⠀⣇⠀⠀⢈⡇⠀⢸⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⡇⠀⣿⡇⠀⣾⣇⠀⣸⣷⠀⢰⣿⡀⢀⣿⡆⠀⣾⣇⠀⣸⣷⠀⢸⣿⠀⢸⣿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠳⣽⣫⡽⠃⠀⠙⢮⣛⡥⠟⠀⠈⠷⣝⣫⠾⠁⠀⠹⢬⣛⡵⠋⠀⠘⢯⣝⣯⠞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⢸⡇⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⣤⣤⣤⣤⡇⠀⢸⣤⣤⣤⣤⡇⠀⢸⣤⣤⣤⣤⡇⠀⢸⣤⣤⣤⣤⡇⠀⢸⣤⣤⣤⣤⡇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⡄⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢠⡤⠤⠤⠤⡄⠀⢠⡤⠤⠤⢤⡄⠀⢠⡤⠤⠤⢤⡄⠀⢠⡤⠤⠤⢤⡄⠀⢠⡤⠤⠤⢤⡄⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⣄⣀⣀⣠⡇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⢸⣿⢀⣀⣀⣀⣀⣀⣀⡀⣿⡇⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⡇⢈⡿⠿⠿⠿⠿⠿⠿⣿⠀⢸⠿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⡘⠟⣸⣿⣿⣿⣿⣿⣿⣇⠻⢃⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⡟⠀⠘⢧⣴⠇⠀⠀⠀⠀⠀⠀⠸⣤⡼⠀⠈⣿⣿⣿⣿
⠀⠀⠀⢸⣿⠛⠛⠛⢛⣛⠛⣛⣛⠛⣛⡛⢛⣛⡛⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣿⣿⣿⣿
⠀⠀⠀⢸⣿⠀⠀⠀⢿⣿⠇⣿⣿⠸⣿⡿⢸⣿⡇⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣀⣀⣿⣀⣀⣇⣀⣸⣇⣀⣸⠀⣿⣿⣿⣿
⠀⠀⠀⢸⣿⢰⣶⡆⣶⣶⡄⣶⣶⢰⣶⣦⢰⣶⡆⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⢸⡏⠉⢹⠉⠉⣿⠉⠉⡏⠉⢹⡏⠉⢹⠀⣿⣿⣿⣿
⠀⠀⠀⢸⣿⢨⣭⡅⣩⣭⡁⣭⣭⢈⣭⣍⠈⠉⠁⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⢸⠓⠒⢚⡗⠖⣿⠲⢶⣷⠶⢾⣷⣶⣾⡆⣿⣿⣿⣿
⠀⠀⠀⢸⣿⠸⠿⠇⠻⠿⠃⠿⠿⠘⠿⠟⠀⠀⠀⣿⠇⠀⠀⠀⢸⣿⣿⣿⣇⢸⣥⣤⣼⣥⣤⣭⣤⣤⣿⣤⣼⣿⣿⣿⠇⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⣴⣦⠀⠀⠀⢀⣶⣆⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⣰⣶⡀⠀⠀⠀⣴⣦⠀⠀⠀⢠⣶⡆
⠀⢸⣿⡇⢸⣿⡇⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⡇⢸⣿⣿⢸⣿⡇⣿⣿⠀⠀⠀⠀⣿⣿⢸⣿⡇⣿⣿⡇⢿⣿⠃⣿⣿⡇⣿⣿⢸⣿⣿⢸⣿⡇⣺⣿⡇
⠀⢸⣿⣷⣜⣛⣱⣿⣿⣧⣙⣛⣼⣿⣿⣦⣛⣣⣾⣿⣿⣜⣛⣡⣿⣿⠀⠀⠀⠀⣿⣿⣌⣛⣣⣿⣿⣷⣜⣛⣴⣿⣿⣧⣛⣋⣼⣿⣿⣎⣛⣣⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⢠⣤⣤⡄⢠⣤⣤⡀⣠⣤⣤⠀⣤⣤⣤⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠇⢿⣿⣿⠀⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⣤⣤⡄⢠⣤⣤⡄⢠⣤⣤⡄⣤⣤⣤⠀⣤⣤⣤⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠺⠿⠿⠉⢙⣿⣿⡇⢠⣴⣾⣿⣿⣿⡇⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠿⠿⠇⠸⠿⠿⠇⠸⠿⠿⠇⠿⠿⠿⠀⠿⠿⠿⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣶⣿⣿⣟⡀⠸⠟⠋⢹⣿⣿⡇⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⣶⣶⡆⢰⣶⣶⡆⢰⣶⣶⡄⣴⣶⣶⠀⣶⣶⣶⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⡀⠈⠈⢻⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⠿⠿⠇⠸⠿⠿⠇⠸⠿⠿⠇⠻⠿⠿⠀⠿⠿⠿⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠻⣿⣿⣦⣤⣿⣿⠟⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⡇
⠀⢸⣿⡇⠀⣶⣶⡆⢰⣶⣶⡆⢰⣶⣶⡆⣴⣶⣶⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢸⣿⡇
⠀⢸⣿⣧⠀⠿⠿⠇⠸⠿⠿⠇⠸⠿⠿⠃⠻⠿⠿⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⠶⡶⢶⣶⢶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⢿⡆⠀⠀⠀⠀⢰⡿⠿⢿⡆⠀⠀⠀⠀⢰⡿⠿⢿⡆⠀⠀⠀⠀⢰⡿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⢼⡇
⠀⠀⠀⠀⣿⠛⠛⠛⠛⢻⡧⠀⢸⡟⠛⠛⠛⠛⢻⡇⠀⢸⡟⠛⠛⠛⠛⢻⡇⠀⢸⡟⠛⠛⠛⠛⢻⡇⠀⢼⡟⠛⠛⠛⠛⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠿⠶⠾⠇⠀⠀⠀⠀⠸⠿⠶⠾⠃⠀⠀⠀⠀⠘⠷⠶⠿⠇⠀⠀⠀⠀⠸⠷⠶⠿⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣾⠛⠛⠻⡧⣾⠛⠛⢻⡆⣾⠛⠛⢻⣶⡿⠛⠛⢿⣶⡟⠛⠛⣷⢰⡟⠛⠛⣷⢸⠟⠛⠛⣷⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣿⣀⣀⣀⣇⣿⣀⣀⣸⡇⣿⣀⣀⣸⣿⣇⣀⣀⣸⣿⣇⣀⣀⣿⢸⣇⣀⢀⣿⢸⡀⣀⣀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣉⣉⣉⣉⡁⣉⣉⣉⣉⡁⣉⣉⣉⣉⡁⣉⣉⣉⣉⢈⣉⣉⣉⣉⢈⣉⣉⣉⣉⢈⣉⣉⣉⣉⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⡇⣿⠀⠀⢸⡇⡏⠀⠀⢸⡷⡇⠀⠀⢹⣾⡇⠀⠀⢹⢸⡇⠀⠀⣿⢸⠁⠀⠈⣿⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠿⠶⠶⠴⠇⠿⠶⠤⠼⠇⠷⠴⠦⠾⠿⠷⠶⠶⠾⠾⠷⠶⠶⠾⠸⠶⠶⠶⠿⠺⠦⠶⠶⠿⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣶⠶⠶⠶⡆⣶⠶⠶⢶⡆⣶⠶⠶⢶⣶⡶⠶⠶⢶⣶⡶⠶⠶⣶⢰⡶⠶⠶⣶⢴⠶⠶⠶⣶⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢀⡗⣿⠀⠀⢸⡇⣿⠀⠀⢸⣿⡇⠀⠀⣸⣿⡇⠀⠀⣿⢸⡇⠀⠀⣿⢸⡀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣙⣛⣛⣛⡃⣙⣛⣛⣛⡁⣙⣛⣛⣛⡉⣛⣛⣛⣛⢉⣛⣛⣛⣋⢈⣛⣛⣛⣋⢈⣛⣛⣛⣋⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣿⠉⠉⠉⡇⣿⠉⠉⢹⡇⣿⠉⠉⢹⣿⡏⠉⠉⢹⣿⡏⠉⠉⣿⢸⡏⠉⠉⣿⢸⠉⠉⠉⣿⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢿⣤⣤⣴⡇⢿⣤⣤⣼⠇⣿⣤⣤⣼⠿⣧⣤⣤⣼⠿⣧⣤⣤⣿⠸⣧⣤⣤⡿⢸⣦⣤⣤⡿⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣉⣉⣻⣄⣀⣀⣴⣏⣁⣈⣿⣄⣀⣀⣠⣶⣋⣉⣷⣄⣀⣀⣠⣞⣋⣉⣻⣄⣀⠀⣠⡶⠛⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⠿⠿⢿⡟⠛⠛⠛⠛⠛⠛⣿⠛⠛⠋⠉⠙⠛⠋⢻⣏⠉⠉⠉⠉⠉⠙⢿⡛⠛⠛⠛⠛⠛⠛⢿⡿⠿⠿⠿⠷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠀⠀⠀⠈⠳⠶⠀⠀⠀⠈⣿⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⡤⠤⠤⠤⢤⣤⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⡀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⣿⠅⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⡠⠤⠤⣀⡀⣑⡶⠶⠶⣞⢈⡷⠶⠶⢶⡃⣑⠶⠶⠶⣎⢈⡶⠶⠶⠶⡉⣳⠶⠶⠶⡏⣳⣶⡶⠶⡏⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⣿⠂⠀⠀⠀⣿⡇⠀⠀⠀⡏⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣓⣒⣒⠒⡋⣙⣒⣒⣒⡊⠈⣓⣒⣒⣒⡁⣙⣒⣒⣒⡋⢈⣓⣒⣒⣒⡃⣓⣒⣒⣒⡋⣓⣒⣒⣒⡃⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠈⢸⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⡇⠀⠀⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⡷⠶⠶⢶⢊⣷⣶⠶⢦⠊⡨⠶⣶⠦⡔⢃⡷⠤⠶⢶⠊⣨⠦⡴⠶⡖⢉⣷⣶⠶⡴⢋⣧⡤⠤⡴⠃⠀⢰⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⡼⠀⠀⠀⢸⣿⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⢸⠀⠀⠀⢸⠀⡇⠀⠀⠀⡆⡞⠀⠀⠀⠸⡇⠀⠀⠀⡸⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣠⠽⠷⠶⢶⢊⡽⠶⠶⣖⢚⡀⢳⠶⢒⡒⣃⠈⢒⠲⣒⢚⣀⢑⣶⣶⠒⠁⠑⠒⠒⠒⠃⠑⠒⠒⠒⠃⠀⢰⡏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢠⡇⠀⠀⠀⡸⡜⠀⠀⠀⢸⢸⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⠹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⣿⡟
⠀⠀⠀⠀⠀⢾⣿⣅⣀⣀⣀⣉⣉⠉⠉⠁⠉⠙⠛⠒⠋⠈⠓⠒⠒⠒⠉⠓⠒⠒⠒⠋⠘⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠋⠉⠙⠛⠛⠓⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠋⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣠⣤⣤⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣟⣛⣛⣛⣛⣛⣛⣛⣯⣭⣭⣭⣭⣭⣭⣭⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠳⡄⠀⠀⠀⠀⠀⡶⠛⠳⡄⠀⠀⠀⠀⠀⡶⠛⠳⡄⠀⠀⠀⠀⠀⡶⠛⠳⡄⠀⠀⠀⠀⠀⡶⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⣠⠶⠒⠒⠒⠒⠒⠺⡇⠀⠀⡟⠒⠒⠒⠒⠺⡇⠀⠀⡟⠒⠒⠒⠒⠺⡇⠀⠀⡟⠒⠒⠒⠒⠺⡇⠀⠀⡟⠒⠒⠒⠒⠚⡇⠀⠀⡟⠒⠒⠒⠒⠒⠲⢦⡀
⣼⠁⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⠁⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢀⡶⠒⠒⠒⠒⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣠⠇⠀⠀⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠳⡆⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠋⠛⡆⠀⠀⠀⠀⠀⠀⡞⠛⠋⠛⠛⠛⠛⠋⠛⣦⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣴⠇⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣤⠇⠀⠀⠀⠀⠀⠀⢧⣄⣀⣀⣀⣀⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⣀⣀⣿⣀⣀⣿⣀⣀⣿⣀⣀⣿⣀⣀⣿⣀⣀⣿⣀⣀⣿⣀⣀⣿⣀⣀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠁⢹⠁⠈⠈⡏⠈⠁⢹⠁⠈⠈⡏⠉⠁⢹⠉⠁⠈⣿⠀⠀⠀⠀⠀⢿⣿⣧
⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣤⣼⣤⣤⣤⣧⣤⣤⣼⣤⣤⣤⣧⣤⣤⣼⣤⣤⣤⣿⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⡷⠶⠶⢾⠶⠶⠶⡷⠒⠂⢾⠶⠶⠶⡷⠶⠶⢾⠶⠶⠶⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⣿⠛⠛⠛⡟⠛⠛⢻⠛⠛⠛⡟⠛⠛⢻⠛⠛⠛⡟⠛⠛⢻⠛⠛⠛⣿⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⣿⣀⣀⣀⣇⣀⣀⣸⣀⣀⣀⣇⣀⣀⣸⣀⣀⣀⣇⣀⣀⣸⣀⣀⣀⣿⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⣿⠉⠉⠉⡏⠉⠉⢹⠉⠉⠉⡏⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⣿⣤⣤⣤⣧⣤⣤⣼⣤⣤⣤⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣦⣤⣄⣀⣀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⠼⠯⠼⣿⠼⣿⠼⣿⠼⣿⠼⢿⠭⢿⠭⢿⡯⢿⡧⢿⡧⢿⡧⢿⡧⢿⡯⠽⡯⠽⣯⠼⣿⠬⣷⢄
⠀⠀⠀⠀⠀⡆⠀⠘⠛⠛⠟⠙⠟⠛⠟⠛⠟⠛⠟⠛⠟⠛⠟⠋⠻⠋⠻⠛⠻⠛⠻⠛⠻⠛⠻⠛⠻⠛⠛⠛⠁⢸
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡿⠒⠚⠚⢲⣶⡶⣶⠶⢶⣶⠶⠶⠶⢶⡶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⣶⣶⣶⣖⠚⠒⠒⢺
⠀⠀⠀⠀⠀⡇⠀⠀⢀⣙⣒⣒⡒⣒⣒⣒⡒⢒⣒⣒⣒⢒⣒⣒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡏⠁⠀⠀⢨⡇⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⡇⣤⣤⣤⣔⢣⣤⣤⣤⢛⣤⣤⣤⡆⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸
⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⣻⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⢸⠤⠤⠤⡇⡦⠤⠤⢞⣳⠤⠤⢴⢙⡦⠤⠤⣎⡧⠤⠤⢴⢰⠤⠤⠤⣛⡧⠤⠤⣞⠀⠀⢸
⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⣇⡶⠶⠶⢾⡱⠶⠶⠶⣹⠶⠶⠶⣎⡷⠶⠶⢶⢱⠶⠶⠶⣏⡷⠶⠶⢾⠀⠀⢸
⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⣻⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠘⠒⠒⠒⠃⠖⠖⠖⢮⡱⠲⠖⠲⣨⠖⠒⠖⢎⡷⠖⠒⢾⠸⠲⠖⠶⣏⡗⠖⠒⢮⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⠈⠈⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⢀⡴⠖⠲⣦⡀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡈⢳⡀⠀⠀⠀⠀⢸⠁⠀⠀⡿⢹⡄⠀⠀⠀⠀⣼⠁⠀⢀⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⡀⠀⢸⣇⣀⣷⣀⣀⣀⣀⣸⠀⠀⢰⣇⣀⣧⣀⣀⣀⣰⠇⠀⢀⣾⣁⣿⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⣏⣉⣙⣇⠀⠀⣏⣟⣉⣹⣉⣿⣉⣿⠀⠀⣼⣙⣍⣉⣉⣉⣉⡿⠀⢀⣾⣉⣩⣏⣉⣉⣉⣉⡉⢹⡏⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⠉⠹⡄⠀⣯⠉⠉⠉⠉⠉⠉⢹⠂⢀⡏⠉⠉⠉⠉⠉⣹⠃⢀⡞⠉⠉⠉⣯⠉⣿⢹⡏⣧⣸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⣷⠀⣻⣦⠀⠀⠀⠀⢠⣾⡁⢸⣷⠀⠀⠀⢠⣾⣿⣀⣾⠀⠀⠀⠀⢿⠀⢹⠀⣇⢻⠿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⢸⠀⢸⡀⣿⢸⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢸⠀⢸⡇⣿⢸⠿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⣿⢸⣾⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⣿⢸⢱⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠀⣿⢸⢼⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⢀⡇⣿⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡟⢸⡇⡏⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡇⣸⢰⢇⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⠁⡟⣼⣾⢿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡟⢸⢇⣿⡟⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⠃⡾⣸⡿⠀⣼⡇⠀⡇
⠀⠀⠀⠀⢀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡟⢸⢇⣿⠃⣸⣿⡇⠀⡇
⠀⠀⠀⠀⣟⠛⠶⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣼⢁⡟⣼⡏⢠⡟⢸⡇⠀⡇
⠀⠀⠀⠀⠻⡄⠀⠀⠉⠙⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⠇⣼⢱⡿⢀⡿⠁⢸⡇⠀⡇
⠀⠀⠀⠀⠀⢙⣦⣄⣀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡟⣰⢣⣿⠃⣼⠃⢀⣾⡇⠀⡇
⠀⠀⠀⠀⢠⡟⠀⠀⠉⠙⠛⠒⠲⠶⠶⠤⣤⣤⣄⣀⣉⣉⣛⠒⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡾⢠⢏⣾⡏⢰⠏⢀⡾⢱⡇⠀⡇
⠀⠀⠀⠰⠯⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⣤⡤⠤⠤⢬⡭⣭⠭⢭⡿⢿⡿⣿⠿⠿⠷⠶⢶⡶⢶⡤⢾⡤⠾⠥⠿⠾⡿⢀⡟⠀⡾⢡⢹⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠴⠿⠤⠤⠤⠾⠧⠦⠤⠴⠦⠶⠤⠿⠦⠤⠴⠤⠼⠧⠴⠷⠾⠦⠤⠤⠤⠼⠧⠾⠧⠾⠧⠦⠾⠧⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⠀⢰⠙⢸⢹⡆⢘⡂⢺⡆⢰⢱⠀⡏⡆⡎⠆⡞⠃⡎⠃⠘⢃⢸⢩⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⢺⣼⡖⢻⣼⠺⣾⠃⠷⢷⡯⠿⣻⠼⠉⡧⢟⠳⠏⢧⣾⡧⢯⢩⣼⠽⣾⠏⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡄⠈⢠⠎⠉⠑⠀⠎⠉⠈⡄⠀⠃⢠⠈⠑⡄⢀⡔⠉⡐⠀⡅⠀⡀⡇⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠆⢲⠀⠀⠘⠀⠒⠀⠰⠀⡇⠀⠀⠲⡁⢸⠀⠻⠆⢦⠇⠀⡽⡄⢸⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠢⠘⠀⠘⠄⠚⠀⠴⠳⠤⠀⠼⠣⠤⠟⠢⠘⠊⠳⠶⠚⠁⠓⠒⠃⠑⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⢐⠀⠀⠐⠀⠈⢹⢌⢈⠃⡉⢈⢠⣀⡄⢈⠀⣈⠈⠀⡇⡂⠉⠀⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⠈⡀⣁⢁⠈⣁⡁⢀⢀⡀⣀⡀⠀⢀⡀⠀⣁⡀⠈⣉⠁⢈⠉⠀⢁⣈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⠤⠇⢇⣠⠀⣆⡸⠸⠤⠇⠄⠨⠀⣄⡸⠀⣁⡨⢈⣀⠇⠨⡈⠇⢄⠨⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠤⡄⠠⠤⡀⠠⠀⡀⠠⢄⠠⠠⡀⠠⠤⡄⡤⢄⠀⡤⡄⠀⠤⡀⠀⢤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠤⠄⠐⠀⠇⠐⠀⠇⠓⠐⠘⠲⠂⠰⠐⠃⠢⠚⠀⠂⠃⠀⠂⠃⠰⠔⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣐⣒⣒⡒⠐⠶⠶⠤⠤⠤⠬⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠉⠙⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠉⠉⢉⣉⠉⠉⠉⠛⠛⠿⠿⠛⠛⠛⠓⠂⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠯⠽⠶⠶⠶⠤⠤⠬⠭⠭⠭⡭⠭⠭⠭⠿⠿⠶⠤⠞


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢠⣄⠀⠀⠀⣤⠀⠀⠀⣠⡄⠀⠀⢀⣤⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⢾⡇⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡆
⠀⠀⠀⢸⣿⠀⠀⠀⣠⡀⠀⠀⢀⣄⠀⠀⠀⣠⠀⠀⠀⢠⡀⠀⠀⢀⣄⠀⠀⠀⣠⡀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠙⠁⠀⠀⠘⠋⠀⠀⠀⠛⠀⠀⠀⠘⠃⠀⠀⠈⠋⠀⠀⠀⠛⠁⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⡇
⠀⠀⠀⢸⣿⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⡟⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⢻⠀⣿⡇
⠀⠀⠀⢸⣿⠀⣇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣸⠀⣿⡇
⠀⠀⠀⢸⣿⠀⡟⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⢻⠀⣿⡇
⠀⠀⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⠀⣿⡇
⠀⠀⠀⢸⣿⠀⣷⠤⠤⠤⠤⠤⠴⡧⠤⠤⠤⠤⠤⢼⡧⠤⠤⠤⠤⠤⢼⡦⠤⠤⠤⠤⠤⣾⠀⣿⡇
⠀⠀⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣿⡇
⠀⠀⠀⢸⣿⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣸⠀⣿⡇
⠀⠀⠀⢸⣿⠀⡟⠉⠉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⢻⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢧⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣼⠀⣿⡇
⠀⠀⠀⢸⣿⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣿⡇
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⣖⣰⣄⢰⢰⣴⣶⣦⡆⠀⠰⡆⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣻⣿⣟⣟⣛⣿⣿⣿⣛⣛⣿
⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣞⣙⣆⣀⣜⣉⣦⣀⣴⣋⣳⣀⣰⣋⣳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠈⢩⠏⠉⠉⢩⠟⠉⠁⢉⡽⠉⠉⠉⡽⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⢠⠀⠀⡄⠀⢠⠀⠀⡄⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠈⠀⠀⠁⠀⠈⠀⠀⢁⠴⠚⢉⡉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠘⠀⠀⠃⠀⠘⠀⣰⠃⠀⠀⢀⡄⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⠰⠀⠀⠆⠀⠰⠀⡇⠰⠀⠀⣸⠇⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⡄⠀⠀⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣈⣁⡠⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⣿⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢸⣿⢠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢼⣿⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⣶⣶⡆⢰⣶⣶⡆⢰⣶⣶⡆⢰⣶⣶⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⡀⢀⣀⣀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⠛⠛⠃⠘⠛⠛⠃⠘⠛⠛⠃⠘⠛⠛⠃⠘⠛⠛⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣷⣶⡆⢰⣶⣶⡆⢰⣶⣶⡆⢰⣶⣶⡆⢰⣶⣶⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣤⣤⡀⢀⣤⣤⡀⢀⣤⣠⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⠛⠃⠘⠛⠛⠃⠘⠛⠛⠃⠈⠛⠛⠃⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⡤⡤⣤⢤⡤⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⠿⠷⠶⠶⠾⠮⠷⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢸⣝⣀⡀⣀⡀⣀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠄⠄⠠⠠⠇⡿⡄⠀⠀⠄⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠀⣦⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⡿⠀⠀⠀⠀⠁⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣀⣈⣁⣀⣀⣀⡠⠤⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⠈⠁⠀⠀⠀⢠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠅⠂⠀⠀⠈⠐⠀⠀⠀⠀⢸⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⣯
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⡧⠀⠀⠀⠠⠦⠄⠀⠀⠱⠆⠀⠀⠀⠈⠳⠀⠀⠀⠈⢼⠤⠤⠤⠬⠤⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢀⡀⠀⠀⠰⢀⠀⠀⠀⠐⢂⡀⠀⠀⠀⠆⡀⠀⠀⠀⠠⠈⠀⠀⠀⠤⠠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠉⠉⢹⠉⠉⠀⠈⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⡏⠉⠉⠉⠁⠉⠉⠈⠉⠀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠭⠤⠤⠤⠤⠬⠴⠤⠤⠤⠀⠰⠀⠀⠀⠈⠰⠦⠤⠤⠤⠥⠤⠠⠀⠈⢡⡄⠀⠀⢀⢈⣹⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⢸⢀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⡇⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠈⠀⠰⠂⠀⠀⠀⢰⠆⠀⠒⠲⠏⠁⠱⣤⠜⠉⢢⠤⠤⠌⠭⠦⠤⠄⠭⠤⠤⠤⠤⠄⠬⢡⠐⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢰⠀⠀⠀⠀⢘⠀⠀⠀⠀⢈⡦⠀⡠⢂⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⡀⠀⠀⠶⠨⠀⠀⠀⠰⠄⠀⠀⠀⠤⢎⠀⠄⠠⠒⡼⢣⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠐⠀⠈⠉⠁⠨⠥⠭⠍⠁⠈⠁⠭⠀⠈⠉⠉⠀⠀⠹⠚⠃⠀⠀⠀⠀⠃⠀⠐⠒⠒⠒⠒⠒⠒⠶⠶⡤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢶⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣥⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠄⢄⠠⡀⢀⠀⠀⠀⡠⠀⢀⠠⠄⢀⡠⢐⡠⠄⠠⠀⠀⠠⠀⠄⡀⢀⠄⠀⡀⢄⠀⠀⠔⠄⠀⠂⠐⠠⡠⡤⢄⢄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣠⡀⠀⠀⢀⣤⠀⠀⠀⢠⡄⠀⠀⠀⣤⡀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⢠⣶⣶⣶⣶⣾⣿⣶⣶⣶⣿⣷⣶⣶⣾⣿⣶⣶⣶⣾⣿⣶⣶⣶⣿⣷⣶⣶⣾⣿⣶⣶⣶⣶⣶⡄
⠀⠀⠀⢸⣿⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠘⠿⠀⠀⠀⠻⠇⠀⠀⠘⠿⠀⠀⠀⠸⠗⠀⠀⠀⠿⠃⠀⠀⠸⠟⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⢸⣿⠀⢠⠖⠒⠒⠒⠒⠒⢲⠖⠒⠒⠒⠒⠒⢲⡖⠒⠒⠒⠒⠒⠲⡶⠒⠒⠒⠒⠒⠲⡄⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠤⠤⠤⠤⠤⠤⢼⡧⠤⠤⠤⠤⠤⢼⡧⠤⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠛⠛⠛⠛⠛⠛⢻⡛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠸⣄⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣠⣧⣀⣀⣀⣀⣀⣠⠇⠀⣿⡇
⠀⠀⠀⠸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠶⢻⡇⠀⠀⠉⠉⠉⠙⠛⠛⠒⠲⠶⠶⠶⠤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⣸⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢸⣷⣿⣿⠓⠒⠒⠠⠭⠭⠭⢭⡭⠍⣉⣉⣉⣒⣒⣒⣒⣶⣦⣿⠄⠀⠀⢀⣠⣤⠴⠞⠛⠋⠉⢻⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡴⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⡇⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⣾⠛⣿⡀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⡇⠀⠀⠀⠀⣴⠾⠛⢻⡿⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣿⢃⣀⣀⡀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⢼⡿⠟⠉⠉⠻⣦⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠈⠳⣦⣀⠀⢀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠉⠛⣻⠇
⠀⠀⠀⠀⢸⣿⣻⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⢸⣿⣿⣇⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠺⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠈⣿⡸⣿⢳⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⣿⢇⡿⡞⡹⣹⡿⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⢹⣼⢱⢳⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⠿⢷⣄⠀⠀⠀⢀⣀⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠘⣯⣷⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠉⠓⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⠀⢸⢳⡆⠀⢰⠛⡆⠀⢰⠒⡆⢰⠓⡆⢸⠓⡆⢰⠛⡆⢠⠖⡆⢰⠟⡄⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⢼⣈⠤⢼⠰⠧⠄⠸⡁⡷⠐⠾⡀⡳⠰⣂⡗⠺⣀⡗⠺⣀⡷⠲⡀⡗⢺⣀⡓⢻⢘⡛⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠙⠁⠘⠋⠀⠀⠀⠉⠁⠀⠈⠃⠁⠀⠉⠁⠀⠀⠁⠀⠁⠁⠀⠃⠃⠀⠁⠁⠈⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠂⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠋⠙⢐⠁⢐⠀⠁⠈⠀⡁⠈⠀⡏⠀⡅⠊⠀⠀⠈⠀⠈⠰⠁⠈⡀⠈⠀⡆⠉⠀⠁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠉⠉⠀⠀⠀⠁⠈⠉⠁⠈⠁⠀⠈⠁⠀⠀⠈⠈⠀⠙⠒⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠁⡂⠀⠂⠈⠉⠂⡋⠉⠁⠈⠁⠆⢸⠁⠱⠐⠂⠐⠀⠂⠒⠀⢘⠐⠂⠈⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠀⠑⠒⠀⠈⠀⠁⠈⠀⠀⠈⠉⠁⠈⠀⠀⠈⠀⠚⠀⠓⠒⠀⠈⠀⠁⠈⠀⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡖⠀⠆⠘⠀⠐⠰⠉⠉⠀⠏⠙⠀⠉⢹⠀⠋⠉⠃⡊⠉⠀⠘⠉⡀⠐⠂⣂⢰⠀⠒⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠃⠈⠀⠈⠁⠉⠀⠁⠈⠉⠀⠁⠚⠀⠉⠉⠁⠈⠉⠀⠈⠉⠁⠈⠁⠀⠈⠁⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢤⠄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⣀⠀⠐⠒⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠤⠤⠴⠴⠦⠤⠭⣭⡭⠭⠥⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡆⠀⣄⠀⠀⠀⠀⢠⣤⡄⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠀⢸⡇⠀⡏⢀⡴⢦⠀⣿⢸⡇⣿⡾⠁⠀⣠⣄⡀⠀⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠀⢸⡷⠾⣟⣾⣥⠟⠀⣿⠟⠀⣿⠁⠀⢘⣧⣬⣿⠃⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠀⢸⡇⠀⣿⠘⢧⣴⠟⣿⠀⣠⡻⣦⠾⢸⡇⠀⣿⠀⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠓⠀⠙⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣦⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠋⢹⡇⠀⣶⢠⣶⡄⢸⡇⠀⣾⠀⢀⡶⠒⣦⠀⢸⡷⢶⡟⢠⡇⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣏⠀⣼⡇⢰⣿⡿⠈⡇⢸⣇⣰⣿⠀⣾⠁⢀⣿⠀⣸⠃⣾⠁⣼⠷⠟⣿⣠⡴
⠀⠀⠀⠀⢀⠀⠀⢀⣼⠃⠙⠛⠙⣧⡾⠻⠇⠀⢷⡟⠉⠉⠈⠛⠻⠶⠾⣿⣠⡟⠀⠻⠾⠃⠀⣠⣿⠉
⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣼⠋⡟
⠀⠀⠀⠀⠰⠶⠞⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⠶⠶⠶⠶⠶⠀⠷⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢺⠧⢤⣄⣀⣳⠞⠛⠉⠛⢦⣄⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢸⣦⠀⠀⠉⣿⠙⠓⠶⠶⣤⣿⣅⣀⣀⡀⠙⣦⠖⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠉⠀⠀⠀⢸⡦⠀⠀⠀⢸⡍⠉⠛⠛⠿⣿⣛⡓⠶⠤⢤⣄⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠲⢦⣤⣀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣿⠀⠉⠙⠓⣶⣶⣬⣍⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⠀⣼⠃⠉⣠⠾⡇⠀⢀⡀⠀⠀⠀⠀⢿⡿⠀⠀⢠⡇⠀⢹⠀⣹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢠⠶⠤⣄⣀⠀⠉⠛⠁⠀⡾⠛⠻⡇⠀⣾⢿⠀⣴⠀⠀⠀⠀⠀⠀⣸⠃⠀⡾⠀⣾⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⢯⣌⣓⡜⢭⡉⣳⠶⢤⣄⣀⠀⠀⠁⠸⠇⠘⣿⠇⠀⠀⠀⠀⠀⠀⡟⠀⢀⡇⠀⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣴⣃⠀⢠⠟⠑⠦⣴⣅⣓⡴⢥⡉⡿⠒⠦⣤⣀⡀⠉⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠃⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠞⠁⠈⡽⠓⠤⣠⡞⠀⢀⡝⠙⠲⡾⣉⣓⣰⠣⣌⡉⡿⠲⠦⣄⠀⠀⢠⡏⠀⠀⡟⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡴⠋⠑⣲⢮⣀⠀⡴⠋⠉⢹⠞⠤⣄⣜⠀⠀⣹⠋⠒⢦⣼⣁⠓⢂⡞⠀⢀⡾⠀⠀⢸⠃⠀⢠⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠾⠥⣀⡜⠁⠀⣨⠟⠓⢦⣴⡃⠀⢠⠎⠉⠙⡶⠧⣀⢀⡼⠁⠈⢙⡿⠁⢀⡾⠁⠀⠀⡟⠀⠀⢸⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣜⠁⢀⡴⠋⠙⢳⠶⣅⡀⣠⠎⠀⠉⡿⠳⢤⣀⡼⠁⠀⢀⡝⠓⠦⢤⡞⠁⢀⡾⠁⠀⠀⣼⠁⠀⠀⣾⠀⠀⣿
⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⢈⡽⠛⠤⣀⡴⠋⠀⢀⠞⠙⠲⣤⣞⠀⠀⣠⠏⠙⠒⢦⣾⣀⠀⢠⠞⠀⢀⡾⠁⠀⠀⣰⠃⠀⠀⢀⡇⠀⠀⡿
⠀⠀⠀⢴⣉⠀⠀⠈⠙⠲⠯⣄⣀⡴⠋⠉⣳⠶⣅⣀⣠⠞⠁⠈⢙⡾⠧⣄⡀⡰⠋⠀⠈⣱⠋⠀⢠⡞⠀⠀⠀⢠⠏⠀⠀⠀⢸⠁⠀⢀⡇
⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠉⠓⠦⣾⡁⠀⡠⠟⠙⠲⢤⣴⡋⠀⠀⣠⠟⠑⠲⢤⡜⠁⠀⣠⠏⠀⠀⠀⢠⡏⠀⠀⠀⠀⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠉⠛⠲⢤⣀⡔⠋⠀⠉⣳⠾⣅⡀⢀⡴⠋⠀⢀⡼⠃⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⠃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠈⠙⠲⠤⣎⡁⠀⢀⡽⠋⠁⠀⣠⠟⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡟⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠈⠉⠓⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣸⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⣀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠛⠳⢤⣀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠞⠁⠉⠓⠲⢤⣀⠀⢀⡿⣄⣀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠈⠉⠛⠁


⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⠛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠛⠛⠛⠛⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⢸⠻⠿⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⠟⡧⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠲⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠁⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡆⠀⢰⡖⠒⠒⢲⡆⠀⢰⠒⠒⠒⢲⠀⠀⢰⠒⠒⠒⢲⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠃⠀⠘⠓⠒⠒⠚⠃⠀⠘⠒⠒⠒⠚⠀⠀⠘⠒⠒⠒⠚⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣧⣀⣀⣀⡇⠀⠀⣇⣀⣀⣠⡇⠀⠸⣇⣀⣀⣸⠇⠀⢸⣄⣀⣀⣸⠀⠀⢸⣀⣀⣀⣼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡖⠒⠒⠒⡆⠀⠀⡖⠒⠒⠒⡆⠀⢰⡖⠒⠒⢲⡆⠀⢰⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠸⣧⡀⠙⠓⠛⠚⠃⠀⠀⠛⠛⠛⠛⠃⠀⠈⠛⠚⠛⠛⠁⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠟⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣤⣤⣄⣀⣤⣤⣤⣀⣠⣖⣦⣄⣠⣤⣤⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣰⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⣯⢽⣦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⢱⢻⡇
⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣫⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⠀⣉⡀⢀⣀⡀⣀⡀⢀⠀⡀⢀⣠⡀⢀⣀⢀⣉⡉⠉⠉⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢿⡼⠀⣷⡀⠸⣤⠀⢿⡄⢸⠟⢿⢸⣗⡇⢸⣂⢸⠷⡏⠀⠀⠀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢰⢒⣶⢲⠤⣤⠤⡤⠤⠤⣤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣷⡿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠒⢺⠒⠒⢲⠗⠛⠏⡦⠬⠭⠤⡇⢐⣒⣸⣀⣒⣈⡋⠯⢹⠇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⢀⣀⣜⣀⡀⢸⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⡆⠀⠀⠸⠀⠈⣹⠀⢸⢿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⡇⠀⠀⡏⠉⠉⢸⠓⠒⠂⡞⠒⠒⢲⠇⠤⠤⡧⠤⢤⡇⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡧⢄⣰⣁⣀⣀⠃⠀⠀⡇⠀⠀⢠⠃⠀⠀⢸⠀⠀⢀⠃⠀⠀⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⠃⠀⣸⠀⠀⡎⠀⠀⡜⠉⠉⢉⠋⠉⠉⡻⠀⠒⠒⠗⠤⠤⢼⠤⠤⢤⠇⢰⣿⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⡗⠂⢰⠧⠤⠤⡧⠤⠤⣼⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⢸⣿
⠀⠀⠀⠀⠀⣸⠁⠀⢸⠀⠀⠸⠀⠀⢰⠀⠀⠀⡇⠀⠀⢸⠉⠉⠉⡝⠉⠁⢸⠓⠒⠲⡇⠀⣿⡏
⠀⠀⠀⠀⢀⡇⠀⢀⡏⠉⠉⡏⠀⠀⡞⠒⠒⢲⠧⠤⠤⡦⠄⣀⣠⣇⣀⠀⡘⠀⠀⢸⠁⢠⣿⡇
⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⢸⠀⠀⢰⠁⠀⠀⡜⠀⠀⢠⠃⠀⠀⢸⠀⠀⠈⡏⠉⠉⡟⠀⣸⣿
⠀⠀⠀⠀⢿⣄⣀⡈⠉⠉⠛⠒⠒⠚⠒⠒⠒⠧⠤⠤⠼⠤⣄⣀⣌⣀⣀⣸⣀⣀⡰⢃⡤⣿⡏
⠀⠀⠀⠀⠀⠳⢶⣿⣭⣭⣽⣶⣒⣒⣒⣒⣒⣒⣲⣦⣤⣤⣄⣀⣀⣀⣀⣠⣤⡤⠔⠋⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠭⠭⠿⠛⠃

⠀⠀⠀⠀⢠⡶⡆⠀⢰⠓⡆⠀⠀⢰⠓⣦⠀⠀⡴⠶⣦⠀⣶⢲⠀⢰⡖⣦⠀⢰⠒⣆⠀⣴⢲⡄⠀⡟⣧⠀⡟⢳
⠀⣀⣀⣀⣸⡆⣻⣀⣸⠀⣇⣀⣀⣸⡄⣿⣀⣀⣏⠀⢻⣀⣿⢸⣇⣸⡇⢿⣤⣼⠀⣯⣀⣿⠈⣧⣤⡇⣿⠤⡇⠸⠦⠶⠶⠶⢦
⢸⠏⠉⠉⠉⡷⣮⠉⢸⢶⠋⠀⠀⠀⡖⡏⠀⠀⢸⠶⡮⠀⠸⡺⠅⠀⣗⡻⠀⠸⣒⡧⠀⢴⢰⠄⠀⣗⡷⠀⠩⠼⠆⠀⠀⠀⣸
⠘⡇⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⣳⢰⠃⠒⡄⠀⢰⠒⠲⡄⡴⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⠀⠛⠉⢁⡇⢀⠀⢱⠀⢸⠀⠀⠳⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡿⠀⢹⠀⡸⠀⠚⠂⠀⢃⢈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠊⠁⢀⡆⢠⠁⠀⢰⣆⠀⠈⢿⠀⢸⣦⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠞⠋⠀⠚⠛⠛⠋⠘⠛⠛⠛⠶⠟⠘⠓⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡆⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀⢀⣀⣀⡀⢀⠤⢤⡀⢀⣀⢀⡀⣀⠠⠤⡄⡠⠤⠤⡄⣀⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⡏⠉⢩⠀⡉⠀⢉⢸⠀⠀⠀⢰⡀⢀⡀⢰⠀⠀⡇⣇⢀⠀⡇⡇⠀⠀⡄⡇⠀⠀⡇⢈⠀⢘⠀⡀⠀⠀⡇⠀⠀⢸
⢸⡇⠀⠀⠀⠈⠛⠉⠀⠉⠉⠉⠀⠛⠛⠁⠈⠉⠉⠁⠈⠛⠋⠁⠈⠉⠉⠁⠈⠉⠉⠁⠙⠒⠒⠁⠈⠉⠉⠀⠙⠛⠛⠁⠀⠀⢸
⢸⡇⠀⠀⠀⢰⠒⠚⠆⠴⠒⠒⡄⠖⠒⢲⠀⡖⠒⠆⠰⠒⠲⡄⢰⠒⠲⡄⢠⠒⠒⡄⢰⠖⠤⡄⢠⠖⠲⡄⠰⠒⠒⡆⠀⠀⢸
⢸⠇⠀⠀⠀⠸⠤⠤⠇⠳⠀⠠⠇⠠⠤⠼⠀⠧⠤⠄⠈⠤⠤⠃⠸⠤⠤⠇⠸⢤⣀⠇⢰⣄⣀⠇⠸⠤⠤⠇⠠⠤⠤⠇⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⣀⠀⣀⣀⣀⠀⣠⣀⡀⢠⠤⣄⠀⢠⠀⣀⠀⣀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠁⠀⠉⢸⠁⠀⠈⡇⡇⠀⠀⡎⠀⠀⡇⢀⠀⠘⠀⡇⠀⢸⠀⡇⠀⡸⠀⡇⠀⣸⠀⡏⢉⡇⢸⠁⠉⡇⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠑⠊⠋⠀⠑⠈⠉⠁⠉⠉⠉⠀⠈⠉⠁⠈⠑⠛⠀⠉⠉⠉⠀⠈⠉⠁⠀⠉⠉⠀⠀⠉⠀⠀⠈⠉⠉⠀⠀⠀⠈
⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠺⣗⡒⠒⠒⠒⠒⠒⠒⠒⠶⠤⠤⣤⣤⡤⣤⣤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠒⠒⠀⠀⠤⠄⠄⠀⠀⠀⠐⠒⠒⠒⠒⠆⠈⠉⣸⠃
⠀⠀⠙⢶⣀⢀⢀⣐⣒⣒⣒⣒⣒⡒⠒⠒⠒⠒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠒⠂⠀⠀⠀⣀⣀⣀⣐⡂⠀⠉⢀⡞⠁
⠀⠀⠀⠀⠙⢦⡤⠤⠤⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⣲⣶⣒⣒⣒⣒⣉⣉⣀⣡⣤⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢀⡔⣂⠀⠀⠀⠀⡂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠐⠀⠀⠀⣰⠛⠤⠀⠀⠀⠀⠉⢢⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⠼⠑⠄⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠀⠀⠀⠀⠀⠀⠙⠙⠂⠀⠀⠀⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡎⡖⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⢚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⣤⠀⠀⠐⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⡀⠀⠃⠀⡀⠀⠀⡠⠀⢓⠴⠊⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⡠⠀⠀⠑⢤⠠⣡⠜⠉⠀⠀⠀⠀⠀⠀⠀⣠⡄⡠⠒⠰⠈⠁⠛⠁
⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡠⠀⠴⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠲⠀⠀⠉
⠀⠀⠀⠀⠀⠂⠂⠀⠐⠁⢀⠀⠊⠀⠈⠠⠄⠈
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠐⠁⠀⠀⠂⠀⠀⠀⠈⠁
⠀⠀⠀⡰⠁⠈⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⢰⣧⣡⠥⠒
⠀⠀⠛⠉

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

⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠂⢰⠃⠀⢀⠀⠀⠀⢀⣄⣄⡰⢂⢂⠼⡦⠘⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠄⡀⠠⠁
⠀⠀⠀⠀⠀⠓⠰⡜⣀⡏⡡⡅⣜⠄⠈⡆⠀⢁⣀⡼⠁⢀⠀⠁⢲⡀⡈⠃⢀⣀⠀⡀⠤⢤⠄⠤⠤
⠀⠀⠀⠀⠸⠱⠀⠐⠃⠈⠀⠀⠒⠀⢀⢁⢀⡄⠀⠀⢄⣀⡤⢀⡈⠀⢸⡸⢷⣁⡁⢟⢸⣸⠸⠅
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠒⠄⢸⢤⠦⡻⣘⣨⢋⡹⠁⠈⠈⠃⡙⠁⠀⠉⠐⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢠⣤⡀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠐⠂⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠀⠈⠀⠃⣀⠈⣡⣄⡠⠤⢦⡀⠀⠀⠀⢴⠂⡄⠀⠀⣀⠀⠀⠸⡀⠀⢀⠀⡄⢲⠢⠄⣀⣤⢤⣀⠰⠞⡆
⠀⠀⣵⢋⣡⣴⣶⠿⡁⡄⢠⣰⠋⢦⡀⠁⢠⣾⡆⣀⠀⠀⠀⣬⣤⣌⣦⠀⢀⣀⠀⢹⣠⣧⡦⣦⣾⠰⠒⡇
⠀⠀⢰⣯⠛⢨⢸⡆⠘⢠⠃⡗⠱⠛⢧⡀⣘⠰⠙⠋⢣⢄⣾⣏⡋⢁⣿⢓⡯⠈⠀⡟⡼⡏⠡⢁⣿⣇⢠⠇
⠀⠀⠁⠈⠳⠒⠋⢠⠚⡁⠁⣧⡀⢀⣿⡞⣻⣰⠛⡀⡎⣀⡭⡿⣭⡋⠘⠁⠙⠶⣿⢮⡐⣛⣿⣿⠿⣯⣿⢻
⠀⠀⠀⢅⣀⡴⡊⢉⣠⣽⣦⠀⠙⡛⠹⡋⠈⠀⠱⡡⢻⡁⠆⠀⢸⡅⠀⢸⣭⣤⡥⢀⡥⡭⠭⢩⢾⡇⠸⠹
⠀⠀⠀⣰⡍⠉⢻⠋⢽⠄⣹⠀⢸⠀⣧⡋⠛⢻⠳⡏⠀⠳⡤⡖⢉⠛⠄⣾⡿⠛⣿⠉⠘⣇⠞⢀⣼⡁⠀⠇
⠀⠀⠀⢡⣴⠄⢬⣷⡴⡾⠃⢐⣩⣤⣼⣇⣐⣃⡞⡑⣠⡾⠁⠘⢻⣆⢰⠉⡟⠝⣺⡠⠂⠈⠛⠋⠀⠀⡰
⠀⠀⡈⠉⢂⢀⠴⠟⢳⡄⠀⡷⠟⠹⣿⠽⠙⣡⣄⠁⠫⡿⠊⠘⢛⡆⢩⡛⠖⠾⠉⠠⠄⢀⡆⣷⠀⡅
⠀⠰⡏⢣⠈⢻⣀⣀⡹⣧⠄⢻⣄⣠⡯⡀⢲⢧⠚⠀⠀⢹⠤⠤⠼⡀⡃⠌⠀⠀⣀⡠⠤⠊⠀⠁⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⢰⢦⠀⢠⢦⠀⢠⢤⠀⡤⡄⠴⡄⢠⢢⠀⠤⠀⡴⠄⡖⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢇⡶⢸⡸⠒⠚⣸⠒⠚⣀⠒⢣⠗⢣⡗⢲⢼⠒⡄⠓⣧⡃⠃⡍⠉⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⡤⠅⠀⠐⠀⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡅⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠦⣤⠴⠁⠤⠤⠳⠤⠧⠼⠧⠠⠄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠠⠄⠄⠄⠄⠀⠐⠒⠀⠒⠂⠐⠐⠀⠂⠀⠐⠐⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠈⠈⠀⠁⠀⠐⠀⠀⠁⠁⠐⠒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠁⠅⠁⠈⠀⠀⠁⡀⢈⣉⠀⠁⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠄⠄⠀⠀⠀⠠⠠⠀⠄⠀⠠⠠⠀⠄⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠂⠀⠀⠂⠂⠀⠀⠂⠀⠐⠀⠒⠂⠀⠈⠀⠀⠁⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠶⠶⠖⠒⠒⠒⠒⠀⠀⠀⠐⠒⠒⠒⠒⠲⠥⠀⠐⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⢰⡄⠁⠀⠉⠤⡀⠀⡀⠀⣴⣾⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⣄
⠀⠀⣦⠀⣰⠀⠋⡀⠀⠀⠀⣤⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠃⠀⠀⣤⠀⠋⣤⠀⠀⠐⡟⠀⡀⠀⠛⠀⠀⠀⢠⡀⠀⠀⠘⢦⠀⠠
⡳⣄⠀⠀⠀⠀⠈⠁⡀⠀⠀⡿⣀⠀⣴⡀⠀⢘⠋⠀⢣⠀⠀⢱⡄⠀⠾⠀⠀⠀⠋⠀⠈⠛⢻⡄⠀⠀⠀⠿⣦⡀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠀⡄
⠀⢈⡀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⣄⠉⢳⡀⠈⠇⠀⠺⠀⠀⠘⢀⣄⠀⠀⠀⢀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣿⠀⠀⠀⠀⢀⣧
⣀⣸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣟⣸⣀⣀⣻⣀⣀⣢⣀⣂⣀⣁⣈⣿⣄⣀⣀⣸⣀⣀⣀⣟⣀⣴⣀⣀⣀⣀⣆⣀⣀⣉⣀⣀⣉⣆⣀⣀⣀⣘⣃⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣦⠀⡴⠶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠈⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⣸⣧⡀⠀⠀⢻⣷⡄⠀⢀⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⠀⢨⣿⠇⠀⡿⠉⠻⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⠿⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⣴⡆⠐⢂⣼⣿⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠙⠓⢿⣦⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢄⣘⢿⡀⠀⣽⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠈⠁⠀⠘⣿⣧⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠀⠙⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⣯⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠓⡦
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢦⡀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠿⣿⣿⣄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⢀⡠⠴⠚⠋
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠈
⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣡⣤⣠⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣠⣤⣠⣠⣤⣠⣤⣄⣤⣀⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣿⣽⣭⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣭⣿⣿⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣦⣦⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⣿⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡿⢹⡇
⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣾⡇⠀⠀⠀⠀⣿⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⢰⣷⣼⣧⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⢸⣿⣿⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⣭⣭⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠏⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠉⠉⠉⢿⡀⠀⠀⣿⠛⠛⠻⣦⡟⠉⠉⢹⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⠀⠀⣿⠛⠋⠀⣼⠃⣠⢶⡀⠸⣧⠀⠀⣿⠀⠀⠀⠹⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣤⣤⣀⣿⠀⠀⣿⠀⠀⣰⡏⠀⠙⠛⠃⠀⢻⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣯⠀⠈⠛⠁⠀⠀⣿⠀⢀⡿⠀⠀⣤⣤⡀⠀⠈⣷⡀⣿⠀⠀⣴⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⢀⣼⠃⠀⣼⣇⠀⣼⠁⠈⣧⠀⣀⡼⠃⢿⠀⠀⢻⠛⣦⡀⠀⢀⡇⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠉⠛⠛⠃⠀⠀⠘⠛⠋⠀⠀⠘⠛⠛⠛⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡾⠇
⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡟⠋
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉




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

⠀⠀⡔⠉⠩⠁⠒⠛⠒⢶⠒⢢
⠀⠀⢇⠀⠘⢄⠀⠀⠀⡘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠈
⠀⠀⠈⢂⠀⢀⠀⠀⢠⠀⠜⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⡠⠨⣄⠀⡀⢀⠀⡀⠀⠀⢠⢄
⣀⠀⣀⠀⠉⠀⠀⢀⠇⡼⠋⢀⡞⠓⣇⠀⠙⠀⠀⣰⠇⠈⢢⠊⠉⠶⠁⠱⠀⡊⠀⠀⠎⠀⡌⠀⠸⠇⠀⢩⢄⠱⡇⠀⡇⠀⠀⠆⢀
⡁⠀⠀⠁⠀⠀⠀⡌⡼⠁⢠⠃⠆⠀⠹⠀⠀⠇⢰⡿⠀⢠⡏⠀⠘⢐⡀⠀⢃⢡⠀⠀⠀⠰⠀⢠⢁⠆⠀⠎⠀⠉⠹⡀⠀⠀⡘⠀⠎
⠇⠀⠀⡇⠀⠀⡘⠜⠃⢀⠆⣠⠶⠀⢠⢠⠀⣠⣿⠃⠀⠼⠁⢀⣴⠃⠠⠀⠸⣴⢇⠀⣀⠂⢀⣧⡎⠀⡜⡔⠒⠄⠀⠱⡰⡠⠁⠌
⠘⡀⠀⠁⠀⢠⡟⠀⠣⠸⠞⠁⠀⢃⠈⠀⠣⠘⠇⠀⡘⠘⠤⠟⠁⠀⠀⠡⠤⠋⠀⠑⠋⠑⠚⠁⠑⠊⠀⢁⠀⠀⠀⠀⠈⠏⠜
⠀⠱⣀⠣⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠣⠽⠃⡘⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡄⠀⠀⢌⠌
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡠⣀⢎⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣤⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀
⣿⣿⡋⢙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠂⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠐⢁⠄⠀⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠐⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠐⠄
⠀⠀⢀⡀⠄⠄⠀⠀⠂⠀⠁⠀⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⢀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣐⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⡀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⢀⠀⢀⠔⡀⠀⠀⢀⠄⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠂⠀⠀⠀⠀⠒⠀⠀⠃⢠⠆⠈⡄⠀⠀⠀⠀⠀⠠⠀⠠⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠄⠃⡠⠄⠀⠀⠀⠖⠂⢀⡄⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠐⠁⠀⡈⠀⡠⡄
⠀⠀⠀⠀⠀⠔⠁⠀⠀⢈⠐⠂⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢁⠈⠠⠈⠢
⠀⠀⠀⢀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠠⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⡀
⠀⠀⢀⠂⠐⠀⠀⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠄
⠀⠀⠂⠀⠀⠀⠠⡀⠀⠄⠀⠀⠂⢠⠀⠄⠀⠐⠀⢠⠀⠀⠂⢰⠀⠐⠀⠈⠄⠀⠈⠀⠀⠐⠀⠀⠀⢀⠂⠀⣴
⠀⠈⠈⡀⠀⠀⢀⠃⢠⠀⠀⠀⠰⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠂⠀⡀⠀⡀⠈⡀⠀⠀⢀⠁⡀⠁
⠀⠆⠀⡀⠈⡄⠘⡄⠀⠀⠐⠃⠀⢳⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⢀⠃⢀⠁⠈⠀⡆⠈⠀⡀⠃⠀⠰⠀⢀⠄⠀⠁⠠
⠀⠀⢈⠁⡂⢡⠀⢀⠀⠀⠀⠠⠀⢸⠀⠀⠠⡄⠀⣿⠀⡆⠀⠀⣿⠀⠈⠀⠀⠃⡇⠀⠀⢃⠀⠀⠀⠀⡌⠀⡄
⠀⠀⡄⠀⡀⠈⠀⠈⡇⠀⠀⠀⠀⠈⡄⡀⠀⠀⠀⠸⠀⠀⠀⠀⠟⠀⠀⠰⠀⢀⡇⠘⠀⠀⠂⢰⠀⠀⠀⢨⡠⡈
⠀⠆⡇⠀⡀⢀⠃⠀⢒⠀⠂⠀⡂⠀⢴⠉⠄⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠈⡇⠰⠀⠂⠀⢠⠀⠀⠀⠈⠀⠀⠰
⠀⢀⢀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠃⠀⢠⠀⠈⢀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠀⠀⠠⡃⠀⠂⠀⠀⠘⠇⠀⠀⠀⠆⠀⡀
⠀⠀⠌⠂⠄⠀⠀⠀⠂⠈⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠠⠀⠀⡠⠂⠀⠀⠀⠀⡐⠂⣀⠰
⠀⠀⠐⠄⠀⠀⢠⡀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡂⢨⡄⣀⡤⡄⠀⠀⠌⠀⠀⠀⠀⢠⢀⡀⢀⠠
⠀⠀⠀⠈⢄⠐⢉⡀⠌⠀⠈⠀⠀⠀⠀⠀⢡⠀⠀⠓⡀⠒⠋⡁⢀⠠⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⡄⠈⠀⠠⠁
⠀⠀⠀⠀⠀⠢⡘⠁⠁⠀⠠⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠰⠁⠀⠀⠀⠁⢀⠀⠈⠀⠀⠀⡠⠎⠠⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢄⠀⠀⠀⢀⠄⠀⠄⠀⠀⢠⠐⠀⠀⢸⠀⠁⠐⠀⠸⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠐⠭⠂⠨⠀⠀⠀⡘⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠀⠈⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠐⡀⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣻⣿⣟⣿⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣟⣢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⣏⡛⠻⠿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠛⠃⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⣶⣤⣄⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⡶⠦⠀⣀⠀⠀⠀⠉⠛⠻⣿⣿⣟⣷⣷⣤⣀
⠀⠀⠀⠀⠀⢀⠏⢀⣤⣀⠀⠀⠀⠐⠒⠃⢠⠾⣽⠀⣰⣆⠀⡀⠀⢹⡦⠈⠉⠛⠻⢿⣿⣆
⠀⠀⠀⠀⠀⡞⠀⡜⠙⢺⠯⣷⣲⠤⣄⡀⠀⠀⠈⠀⠃⠘⡾⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⢸
⠀⠀⠀⠀⢰⠃⢰⠉⢑⠗⠤⣠⡏⠙⠳⣼⣉⣖⢢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠈⣇
⠀⠀⠀⢀⡏⢀⣏⡉⡾⠤⢄⣜⠈⠙⢲⠧⢄⣈⠟⠚⠦⣽⣓⡶⢤⣀⡀⠀⠀⢰⣿⠁⠀⠀⢹
⠀⠀⠀⡼⠀⡼⣄⣸⠓⠲⣼⣉⠉⢒⠧⢤⣀⡎⠉⠒⣴⣅⡈⠉⡞⠺⢭⡇⢀⣿⠏⠀⠀⠀⠈⡇
⠀⠀⢰⠃⢰⠧⢄⣏⠙⢲⠧⢄⣉⡟⠢⢤⣜⠉⠑⢲⢧⣀⠈⡝⠓⠤⡼⠀⣾⡟⠀⠀⠀⠀⠀⢹
⠀⠀⣞⠀⠘⠒⠼⣁⣉⠟⠢⢄⣼⠉⠒⡾⢥⣉⢓⠾⢤⣀⣹⠓⠦⣤⠃⢸⣿⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠻⢽⣓⠦⢄⣀⠉⠑⠲⠤⣇⠉⢲⠧⢤⣀⡝⠓⠢⢤⣏⠑⢲⡎⢠⣿⣏⣀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠉⠓⠺⢽⣒⠦⣤⣀⠉⠛⠢⢄⣸⠉⠒⢢⠯⣀⠉⡞⠀⣾⣿⡀⠈⠉⠒⠦⢄⣀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠯⢽⣳⣦⣤⣀⠉⠓⠺⠤⣀⣹⠁⣼⣿⡇⠈⠑⠒⢤⣀⣠⠤⠭⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⢽⣓⠦⣤⣀⠀⢠⣿⡿⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⢽⣛⣻⣧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠔⠈⠁⠀⠉⠐⢄⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡠⠒⠉⠀⠈⠁⠢⠀⠀⣀⠀⣀
⠀⠀⢀⠔⠁⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠈⠢⡀
⠀⠀⠆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠐⡀
⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠃
⠀⠀⢃⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⢲⠄⣀⣀⠠⡔⠊⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠙⢢⢄⣀⡀⢤⠐⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠈⠑⠀⡤⠀⠐⡁⠐⠀⠒⠐⠟⠂⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠉⠒⠀⠤⠀⢊⠀⠈⠀⠂⠒⡛⠂⠀⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⢆⢠⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⢎⠘⠓⠂⠀⠀⠀⠀⢰⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡰⠦⠀⠀⠀⠀⠰⡂⠛⠠⡀⠀⠐⠛⠯⡀⠹⠋⠓⠀⠀⢔⠒⠇⢀⠀⠀⠀⠀⠀⠤⢆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠗⠂⢀⡀⠀⠀⠀⠁⠐⣦⠤⡀⠆⠰⠆⢸⠀⠴⠀⢄⠀⢼⠑⢰⠂⠀⠀⠀⢀⡀⠐⠺⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠲⡤⢚⠁⠀⠇⠀⢸⣤⣀⣀⠀⢀⣀⣀⣼⠀⣨⠀⠠⠏⠲⣤⠶⠋⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠉⠁⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⡿⠀⠉⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠴⢤⠀⠙⢧⠀⠈⠀⣠⠟⠁⠀⡠⢤⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⠀⠈⡆⠀⠀⠀⡏⠈⢳⠀⠀⢀⠇⠀⢣⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣀⠇⠀⠀⠀⢇⠀⠀⢀⠇⠀⠈⢦⣀⠜⠀⠀⠀⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠤⢤⣀⢀⢀⣠⠤⠤⠤⠴⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣾⣧⠀⠀⣿⣾⣿⣿⣿⣦⡀

⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠⠒⢤⡀⠁⠀⠀⠀⠀⠀⠀⠦⠨⠀⡇⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠁
⠀⠀⠀⠁⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢰⣀⣀⠀⣁⣩⡄⠀⠀⠀⠀⠀⠘⠁⡠⠈⠀⠈
⠀⠀⠀⠱⠆⡇⢠⡛⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣸⢒⢒⢒⢰⢶⢆⡀⠀⠀⠀⠀⡠⠿⢀⡀
⠀⠀⠀⠃⠀⣀⢤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⡠⣀⠈⣀⠤⠀⠀⠀⠀⠀⠀⠈⠁⠂⠉⠀⠀⠀⠀⠀⡔⠀⠀⢀⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⢰⠈⠁⠁⡆⠀⠀⠀⠀⠀⡂⠐⠀⠀⠄⡁⠀⠀⠀⠀⠏⠀⠤⠀⠕⠊⠀⠀⠀⠀⠀⠄⡀⢀⣀⠀⢞⢒⡀
⠀⠀⠀⠁⠰⠙⠂⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠀⠙⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠐⢂
⠀⠀⠀⢀⡀⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠎⠀⠀⠀⠀⠀⠀⠅⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠐⠰⡂⠂⡀
⠀⠀⠀⠀⠄⠀⠄⠇⠀⠀⠀⠀⣀⣄⣀⣀⣠⡨⠄⠀⠀⠀⠀⠀⠂⠘⢀⡀⠳⠟⠀⠀⠀⠀⠀⠄⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠲⠐⠠
⠀⠀⠈⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⣇⠀⣞⠄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠊⢐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢋⠁⠀⠀⠈⠙⠋⠉⠈⠀⠠⡐⠀⠀⠀⠀⠈⠟⠋⠁⠀⠙⠟⠉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⣻⣿⣿
⣿⣿⣿⡷⠀⠀⠐⡀⠀⠀⠀⠄⠀⡀⠁⠠⠤⠀⠤⠀⠀⠀⠀⢵⠀⠀⠰⠦⢄⠀⠀⠀⠀⣆⡀⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⢿⣿⣿⣿
⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣯⡀⠀⠀⠀⠀⢀⢠⠀⠀⠠⠆⠀⠀⠀⡄⠀⠄⠃⠠⠀⠀⡀⠀⠄⠤⠠⢀⣠⣤⢠⠄⣵⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⣿⣿⣿⠗⠀⠀⠀⠂⠈⠀⠀⠐⠀⢿⠀⠀⠚⠃⡘⠁⠂⠀⠀⠀⠀⠀⡠⠐⠂⢻⣷⠃⡘⠻⠿⢏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿
⡿⠋⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⠁⠠⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⣿⣷⠶⣤⣤⡄⠀⠨⠀⠀⠀⠀⠁⠀⡀⠀⠀⠰⡄⠁⠀⠈⠀⠀⢠⠀⠀⠀⢰⡶⠀⠈⠀⣀⠀⠖⠆⠀⠠⠀⠀⠀⠀⠀⠀⠠⠶⣶⣿
⣿⠛⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠃⠈⠀⢀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣠⣤⣦⣴⡶⠿⠿⠷⣶⡿⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣠⣤⣤⣤⣄⢀⣴⠾⠛⠛⠛⢷⣴⠾⠛⠛⠿⣟⣉⣁⠈⠙⢿⣤⡄⠈⢳⡶⣤⠀⠈⢻⣆⠀⢻⡆
⠀⠀⠀⠀⠀⠀⢠⡾⠛⣉⡉⠛⢷⣿⠋⣠⣤⡀⠙⣿⣇⣠⣶⣶⡄⠀⣿⠶⢶⡀⠀⢹⠋⠙⡧⠀⢸⣋⣿⠀⢸⡧⣼⡇⢀⣾⣟⣀⡾⢻⣦
⠀⠀⠀⠀⠀⠀⣿⠁⣾⣿⣿⡆⠈⣿⠾⠿⠿⢿⠀⣼⠉⠉⠉⢀⡇⠀⣿⢀⣠⡇⢀⡾⠶⣾⡃⣠⡞⠙⠿⠤⠟⠀⠙⠛⠋⠁⠉⠉⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣰⡿⠿⠿⠛⢛⣿⠀⣇⣠⣤⣴⠋⢠⡷⠶⠶⢶⣾⢃⡴⠋⠉⠻⠶⠞⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣴⣿⠋⠙⠷⠼⠋⠁⠀⠉⠛⠋⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⡏⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣷⣿⣿⡏⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣿⡿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⣴⡶⠶⠶⣶⡄⠀⠀⠀⣿⠋⠉⠉⠻⣆⣿⠀⠀⢹⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢰⣿⢇⣿⣿⠀⠀⠀⠀⠀⠀⣤⣶⠶⠶⠾⠟⠛⠛⠋⠉⢹⡆⣿⠀⠀⠀⠈⢿⡄⠀⠀⢿⡄⠀⠀⠀⠹⣿⡇⠀⠘⣷⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⣸⣿⢸⢸⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⣿⠀⠀⠀⠀⠈⢿⡄⠀⢸⣧⠀⠀⠀⠀⠈⠁⠀⠀⢻⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⡟⡏⣾⣿⠀⠀⠀⠀⠀⠀⢻⣷⠿⢿⡆⠀⠀⣾⠿⠛⠋⢡⣿⠀⢀⡟⣦⠀⠈⢷⡀⠀⣿⡀⠀⠀⣶⡀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢸⡇
⠀⠀⢸⣷⣇⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣷⠀⠀⢿⡄⠀⠀⢸⡏⠀⠘⠷⠟⠀⠀⠘⣷⠀⢸⡇⠀⠀⣿⣷⡀⠀⠀⠀⢿⡄⠀⠀⠀⢸⣇
⠀⠀⣾⢹⢹⢻⢿⣿⠀⠀⠀⠀⠀⠀⣿⡟⠙⢿⠟⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢠⣄⠀⠀⠀⠸⣧⠘⣷⠀⠀⢸⡇⠛⣷⣄⡀⢸⣧⠀⠀⠀⢸⣿
⠀⢠⡟⣾⣼⣼⢸⢹⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⣿⠃⠀⠀⣿⠁⠀⠀⣾⠻⣧⣀⣀⣤⣽⡧⢿⡶⠿⠛⠃⠀⠈⠛⠛⠻⠋⠀⠀⠀⠀⣿
⠀⣼⡇⡇⣿⡇⣾⢸⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⣰⡟⠀⠀⠸⣿⡶⠶⠿⠟⠀⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⢸⣷⣿⠃⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡏⣸⣸⣿⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⢹
⣿⠃⣿⡿⡟⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⢸
⣿⣀⣿⡇⡇⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⠶⠟
⠉⠙⢿⣿⡇⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⡶⠶⠾⠿⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠉⠻⠿⣧⣤⣿⡀⣀⣀⣀⣀⣀⣠⣤⣶⣶⠶⠾⠿⠿⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠲⣦⣄⡀⠀⠀⣠⠚⠉⠉⠉⠙⠲⡄⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣠⠞⠋⠉⠉⠉⠁⠺⠗⠛⠉⠉⠙⠒⢤⡀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⡖⡖⡴⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⠔⠚⠉⠙⠛⠲⣄
⠀⠀⠀⠀⠀⣠⠾⠚⠛⠓⠲⢤⡇⠀⢀⣄⣠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠉⠁⠃⠋⠛⠸⠅⠀⠀⠀⡠⠂⠁⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢀⡟⠀⠀⣀⠉⠊⢷⠠⢀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⢀⡀⡄⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠑⠙⠳⢂⠄⢈⠛⢳⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣟⠁⠀⠀⠀⠀⠘⠈⠚⠈⠁⠀⠀⡾
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣄⡀⢀⣀⣀⣤⠴⠖⠛⢿⣿⠁⠀⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠈⢠⠇
⠀⠀⠀⢳⠈⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠻⣿⣿⡿⠁⠀⠀⠀⠀⠙⠲⠤⣄⣀⡀⠀⠀⠀⢀⡠⠤⠶⠶⢿⣄
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠭⠭⠭⠟⠉⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⢠⠀⡒⠢⠄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠐⢤⠪⠂⠛⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠙⠖⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠑⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠐⠢⣀⠀⠀⠀⠀⠀⠈⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠔⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⡀⠤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⡤⠠⡄⠀⠀⠑⢄
⠀⠀⠀⠀⢇⠀⠈⠀⢠⠂⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣠⠂⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⡔⠂⣄⠄⢤
⠀⠀⠀⠀⠈⠢⡀⡰⢃⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠌⠀⠀⠀⠀⠀⠀⠀⠘⠦⠖⠁⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⢣⠀⠀⠀⡰
⠀⠀⠀⠀⠀⣀⠜⠊⠀⠀⠀⠀⠀⠀⠀⡠⠀⢤⠔⠂⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠳⣀⠜
⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠳⡀
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢀⠇⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠆⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⠲⠉⠑⠄⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⣘⡠⠖⠉⠀⠀⢀⡀⠀⢀⡀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠁⠀⠀⠀⠀⠰⡀⠈⠛⠀⢹⠀⠀⠀⠀⠙⠢⡀⠀⠠⠲⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⣀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠑⢄⠀⣠⠃⠀⠀⣀⠠⠂⠁⢉⣢⡈⠢⡞⣀⣀⠤⠀⠀⠀⢠⡄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠁⢀⠜⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢀⡠⠊⣡⠔⠚⠉⠈⠀⠙⠂⠉⠉⠀⠀⠀⠀⠀⡐⠀⠠⠍⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠙⢇⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠁⠀⠀⠀⠀⠀⢣⠈⢢⡀⠄⠒⠀⠈⠁⢀⠀⠀⠈⠁⠐⠒⠤⣀
⠀⠰⡂⠒⠐⡆⠀⡘⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡄⠰⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⢣⠀⢂⠀⠀⠀⠀⠀⠉⠉⠒⠒⢢⠀⠀⠀⠀⠑⢄
⠀⠀⠑⡤⠊⠀⢠⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠠⠀⢀⢀⡏⠀⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⢣⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠱⡀⡘
⠀⠀⠀⠀⠀⠀⡆⢀⡃⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⠑⢧⡀⠀⠀⡀⣿⠀⠀⠃⣨⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡀⠀⠀⠀⠀⠱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⢀⡡⠊⠉⠉⠁⠐⠢⢄⡀⠈⠠⡀⢀⠔⠀⠈⠢⠎⢠⠁⠀⣰⢂⠡⠐⠂⠉⠉⠁⠀⠈⠉⠘⠣⡀⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⡄⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠘
⠀⢀⢀⣀⡀⢸⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⡇⢰
⠀⠘⢄⡠⠃⠈⡀⢰⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡈⠀⠑⠶⠠⠄⠀⠀⠀⠀⠤⠔⠊⠁⠀⠀⠀⠀⠇⢸⠀⠀⠋⠁⠒⠉⢰
⠀⠀⠀⠀⠀⠀⢃⠀⠆⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⠀⠱⡀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⡄⠘⡄⠀⠀⠀⠈⢓⡒⠂⠠⠄⠓⠒⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡄⠀⠀⠀⠀⠉⠂⠤⣀⣀⣀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠉⠀⢀⠌
⠀⠀⠀⠰⡀⠒⠂⡰⠆⠀⠈⠢⣀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠉⠉⠉⣀⣀⠀⠤⠤⠔⠒⠁⠀⠀⠰⢍⠐⠂⡠⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⡒⠒⠒⠒⠒⣒⠶⠒⠒⠒⠂⠈⠉⠙⠥⣀⣀⣀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢡⡀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡙⢦⡽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂⠀⠁⠛⢻⣿⣷
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠒⠁⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠠⣿⣿
⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⢠⡰⢖⡖⠊⢻⠈⠀⠉⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⢶⣤⣤⣤⠴⠺⠏⠙⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠙⢿
⠀⠀⢀⡄⠀⠶⠸⣯⠑⠁⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⢳⡀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡦⠆⣒⣶⠖⣻⠏⢡⡦⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠙⡄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠀⢢⣥⠽⡰⠋⣴⠋⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠈⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠁⠂⠀⡞⣰⣧⡜⣣⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠾⡀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣽⡆⠀⠀⠀⠏⠀⢚⣿⠅⠶⠱⡃⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡐
⠀⠀⠀⠀⠀⠀⠈⢆⠹⠿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⣻⡀⠀⣞⠭⣦⢚⠁⠈⠁⠀⢀⣥⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠴⠖⠋⠩⠤⢀⠀⠀⣠⢤⢖⡡⡤⠶⢾⣥⠼⢫⣾⣏⠄⢐⣂⢢⠀⠘⡈⢏⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠑⠤⢘⡇⢘⣛⣄⡀⠀⠷⢀⣈⡩⣶⠚⠛⢯⠀⣆⠠⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠈⠛⠋⠡⠶⠞⠙⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠂⠈⣧⠀⣀⠀⢀⢲⡘⡧
⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡄⠀⢀⠠⣦⠸⣿⢁⡠⣿⡀⢿⡻⣜⠾⢻⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢹⠀⣾⣆⡘⣆⠘⣮⠳⠏⠳⠬⠀⠈⠀⢈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⢲⡟⠆⠹⠿⣆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢺⡄⠀⠀⠀⠀⠙⠘⠃⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⣷⠀⢀⣤⡀⣄⢤⡘⣾⠱⡜⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡁⠘⣇⠸⣯⢳⣽⡄⣷⢹⡟⠃⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣧⠀⠙⠖⠀⠀⠉⢿⡀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠚⢥
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠈⠉
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠰⢛⣇⣠⡾⡿⢍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢸⡇⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⢠⢟⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠁⢨⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣤⡀⢸⣿⣶⠟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⣷⣼⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠀⠀⢹⠇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⣾⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠻⠷⣤⣆⢸⣿⠺⣴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⢙⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠁⠀⠛⢧⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣹⣦⣤⣤⣀⢁⠀⢠⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⡻⣦⣿⠿⠧⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡆⠁⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⣝⡀⠀⣹⡏⣠⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⡿⣿⣿⣿⣷⠿⠍⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣬⠃⢽⣿⠏⠈⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣆⣒⣿⠀⣀⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⢧⡿⣋⣿⣟⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠌⠁⣿⠏⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠈⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿

⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣤⡔⣤⢖⡆⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡖⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠂
⠀⠀⠀⠢⢩⠘⢤⡀⠀⠀⢿⣵⠥⠊⠀⠀⠀⠀⢀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠢⢄⡀⠀⠀⠈⠉⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠱⣄⠘⠆⠀⠁⠀⣠⢚⠁⠀⠀⠀⠀⠶⠭⣡⡄⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠴⠀⠀⠀⢀⣤⡜⢠⣾⡿
⠀⠀⠀⠈⠃⠀⠀⣠⠞⡉⢺⡇⠀⠀⠀⠀⠰⠾⠡⠤⠤⠄⣈⡑⠀⣌⠉⠉⠐⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⢶⣞⢒⣻⠞⠀⠘⠛⠁⠀⠉
⠀⠀⠀⠀⠀⣠⠞⠁⢄⠘⣾⠃⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀⠀⠀⠢⣄⠀⠀⠰⠞⠉⠓⠦⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠞⠡⡈⠲⡄⢳⣼⠀⠀⠐⢯⠇⠀⠀⢈⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠊⠀⢀⣈⠣⡀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠏⠈⠙⣷⠆⣉⡁
⠀⢠⡾⠥⠴⣄⣘⣦⠘⣆⣿⠀⠀⠀⡟⣧⠀⣰⢫⡇⠀⠀⢀⣴⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡇⠉⠳⠀⠀⢀⡀⠈⣄⠴⠛⢏⠀⠀⢀⠇
⠀⠈⠳⣄⡀⠀⠈⠙⠦⣼⡟⠀⠀⠀⡇⠘⠿⠁⢸⣇⣠⠔⣺⠟⠁⣠⠖⢛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⣠⠔⢋⠀⠀⠉⠀⠀⠈⠉⡹⠉⢄⡀
⠀⠀⠀⠀⠉⠛⠲⠶⠦⠾⠃⠀⠀⢸⣗⣒⣒⠶⢬⣍⡀⢠⠏⠀⠀⠉⣿⠔⡹⠫⢛⡶⠦⣤⣤⣀⣀⣠⣤⣤⡴⠚⡟⣄⠀⣬⣆⠀⠀⠫⣭⣴⣌⠁⠂⠀⢈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣭⣉⠓⢮⣹⠏⠀⢀⡀⠀⠀⠀⠣⠤⠊⣿⠄⢸⠀⠃⡌⣧⠃⢸⠘⢦⡇⠈⠳⠇⠀⠀⠀⠀⠀⢀⠆⠐⠒⠀⢸⡀⡁
⠀⠀⠀⢀⣀⣤⡤⠤⠤⢤⣤⣄⠀⠈⠓⠭⣓⣛⣻⣦⠁⢠⠞⣉⣉⠳⣄⠀⠀⠀⠀⠉⠀⠸⠋⠑⠇⠘⠲⠞⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⢠⣊⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠘⢦⡀⠀⠀⢠⠾⠥⣬⣇⠀⠀⠀⠀⠀⠉⠀⠀⢾⢸⠃⠈⠳⡜⡄⠀⣠⣾⢯⡛⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⡦⢰⠔⠀⠀⢀⡠⠞⢁⠜⡽⠒⠦⠄
⠀⠀⠀⠀⠀⠳⣄⠀⣿⡊⠁⢀⣈⣙⣦⣄⠀⠀⠳⡶⢤⣘⡞⣧⠀⠀⢹⡇⣸⡟⡁⠀⠸⢸⠇⠀⡀⠈⠻⡄⠀⠀⠀⠃⣀⡀⠀⠀⠯⠡⠖⣡⠊⢀⠌
⠀⠀⡤⡤⣀⠀⠈⠳⢯⡙⣲⣍⠀⠀⠀⠈⠳⣄⣀⣬⠦⠈⠙⠮⣷⡸⡄⣿⣿⠎⠀⢐⣡⠟⠀⣈⠉⠉⢀⡤⣄⣰⠛⠛⠉⠉⠀⠀⠀⠀⠀⠧⠔⠃
⠀⠀⣦⣈⠠⠇⠀⡴⣄⠉⠁⠈⢳⡎⠉⠉⢉⣻⣇⠉⠙⠒⠶⢤⣌⣻⡟⠛⢧⣤⠶⠛⠛⠉⣿⡁⠀⠀⡞⠓⠤⠌⣽⠂⠀⠀⣆⠀⠀⠀⣠⠔⢊⠉⡁⠒⢄
⠀⠐⣁⣙⠓⠀⠀⠱⣮⠆⠀⠀⠀⢻⡤⠞⣉⣩⡿⠀⠀⡏⠉⠉⠉⡛⠉⠂⠚⠛⠛⠛⠻⠍⠂⠛⠂⢰⡗⠀⠀⢠⢦⠀⠀⠀⡟⠀⠀⡴⠋⠀⠀⢀⠀⠀⠈⢃
⠀⠀⡟⠢⠽⠀⠀⣴⠾⡦⠀⠀⠀⠈⠛⠛⢻⡅⠀⠀⠀⢳⠤⠤⠤⡇⠀⠀⡤⠤⠤⣀⠼⠀⠀⠀⠀⠸⡇⠀⣠⠃⠈⠳⢤⠼⠁⠀⢠⠆⠀⠀⡀⠀⠀⠀⠀⢸
⠀⠀⠁⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⡇⠀⢰⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣝⠋⠁⠀⠀⠀⠈⣾⠀⠀⠸⠀⡔⠁⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢠⣞⠛⠙⢧⡼⠉⠁⠒⣤⠀⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⡇⠀⡆⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠘⠀⢀⠔⠈⠀⣠⠊
⠀⠀⠀⢸⡈⣩⡛⢛⡛⠛⣛⠉⡅⠀⠀⢀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⢠⠁⠀⠀⡸⠀⠀⠀⠀⠀⠶⠿⡄⠀⠀⠀⠀⠀⣴⠾⠓⠚⢀⣸⠦⠼⠤⠚⠉
⠀⠀⠀⠘⡷⠃⠙⠋⢣⣤⠁⢰⠁⠀⠀⣼⡛⠿⣿⠀⠀⠙⠚⠒⠚⠓⠚⠦⠤⢤⠇⠀⠀⠀⣀⣠⣤⣤⣀⣀⣤⢤⡤⢤⣀⡀⠀⠀⠙⠶
⠀⠀⣴⠚⢷⡀⠀⠀⠀⠀⢀⡟⠠⡀⠀⠘⣳⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠃⠀⣠⢴⣶⣬⣉⠀⢀⡦⡍⡆⢀⠂⠀⠀⠀⠀⢠⢤⣀⣀⡀
⠀⠀⠙⠲⢤⣭⣛⣒⣒⣚⡩⠤⠖⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡴⡇⠀⠀⢀⠀⠀⠀⠀⡇⢸⠀⢸⢱⡏⣴⣶⡌⢧⠸⠵⢯⠁⡌⠀⠀⠀⠀⣀⣎⡀⣉⡽⠛
⠀⠀⠀⠀⠀⠙⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠠⡀⠀⢇⠘⢎⠢⡀⠑⢄⠀⠀⣧⢸⠀⠘⢾⣧⡻⠿⣣⠟⠀⢀⠆⠰⠀⠀⠀⣠⢎⠀⠈⠻⡍
⠀⠀⠀⠀⠀⣠⠶⢮⡙⢢⡀⠀⠀⠀⢀⣀⡀⠀⡇⠳⡔⢄⠈⠢⡀⠑⢄⠉⠓⢤⣬⡿⡷⠈⠻⢷⣄⣀⠀⠉⠉⠁⠀⢀⠜⠀⡘⠀⠀⣰⠧⡀⠙⠒⢴⠏
⠀⠀⠀⠀⡞⠁⡄⠀⢹⣄⡧⠤⠴⠒⠻⣆⡷⠀⠈⠢⡈⠂⠥⣀⣸⣶⣦⠑⢄⠛⠛⠀⠈⠄⠀⠀⠀⠈⠉⠉⠛⠓⠚⠉⠀⠀⡇⠀⠀⣯⡓⠬⢑⣰⠋
⠀⠀⠀⠀⢳⡀⠓⠶⠛⠋⠀⠀⣀⣠⠴⠋⠁⠀⠀⠀⠈⠢⡐⠾⣿⠉⠑⡀⠀⠑⠂⠀⠊⠀⠀⢀⠀⠠⡄⠀⡏⢣⠀⠀⠀⠀⠣⠠⣞⠡⢛⠖⠊⠁
⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠔⠀⠀⠀⠀⠀⡠⢄⣀⣨⠧⣀⠟⢤⡈⡾⠒⠂⠀⠀⠀⠀⠉⠷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢳⠀⠀⢀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡿⠀⢠⡟⠀⢰⢉⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢸⡇⣰⠋⠀⠀⡟⡸⠀⣾⠇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣿⠋⠁⠀⡀⠀⣷⠃⢀⣿⠀⠀⣿⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⣿⠀⢸⡡⠋⣰⡇⠀⢸⣿⠀⠀⡿⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⢻⡄⠀⠁⠉⠀⡇⠀⠈⣿⠀⢰⠇⠀⠀⣠⠠⡄
⠀⢀⣤⠖⠲⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢿⠀⠀⠹⣧⠏⠀⠀⠀⢧⣀⣼⠔⠚⣻⡆⠀⠀⠀⠀⠀⠀⡀
⣰⠟⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⠀⠀⣿⢣⣶⣠⡴⣺⣶⠉
⠻⠀⠀⠀⠀⠀⢹⣇⠀⠀⢀⡤⠄⠀⠀⣤⢀⢾⡇⠀⣰⡆⢠⣶⢠⣿⣱⣇⠀⣰⠃⠀⢸⣿⠈⠙⢉⠞⠁⣿
⠀⠀⠀⠀⠀⢀⣸⣿⠊⠁⣿⣡⢿⣀⠜⣿⡎⣸⡇⠀⣿⠷⠋⢹⠘⠛⠃⠙⠊⠁⠀⠀⠸⣧⠀⠀⡏⠀⣼⠃
⠀⠀⠀⢀⡴⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⣰⠋⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠋
⠀⣰⠃⠀⠀⠀⣸⡏
⠀⡏⠀⠀⠀⢠⡿
⠀⣧⠀⢀⣴⠟
⣶⣾⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠛⢛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⠀⠰⣶⣶⣆⠈⢻⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡋⠉⠁⠀⠀⠀⠀⠀⠈⠙⠀⡀⢻⣿⣿⣿
⣿⣿⠟⡡⠂⠑⠀⠀⠄⠀⠢⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣄⣿⣿⣿
⣿⣏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠔⠀⠙⠒⠤⢄⣀⠀⠠⣤⢠⠴⠓⢏⠻⠿
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠈⣥⣤⣴
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠠⠘⠁⠀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⣀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠈⢻⠟⠿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⠤⠤⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⢀⢄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⡏⠀⠐⡀⠒⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠁⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⠿⠿⠻⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠐⠀⠀⠀⠘⠠⠄⠐⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡘⠂⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣥⣤⣵⣢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⠀⠀⠕⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣹⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣶⠊⠀⠀⠀⠀⠀⠀⢸⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣌⣀⣠⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠠⠄⠀⠤⠀⠸⠀⠀⠀⠀⠠⠜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⢀⠄⠣⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⠀⠀⣈⣁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⡀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⢁⠠⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⣦⠂⠀⠀⠀⠀⣿⡷⡀⢀⣶⣄⢀⣶⠀⠀⡢⠃⠁
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⡀⠀⠀⠀⠀⢻⣟⢥⡸⣧⡠⢖⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⢸⡃⢨⣴⠟⣇⣨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⣧⡼⠻⡇⠈⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣴⠀⣿⡇⠀⠀⠇⠀⢠⠟⡷⠀⠙⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⣿⣇⣀⠀⡀⠠⠂⡴⠀⠂⠠⠆⣡⠁⠀⠀⠀⠀⠙⣤⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠾⡇⠀⣿⣿⣻⣷⣧⣤⣼⠷⠀⠀⣀⠛⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡼⠀⢀⣿⠟⠁⠀⢿⠛⠳⠦⠤⠟⠛⢧⡀⠀⠀⠉⠗⠦⠤⠄⠠⠾⠃⠀⠀⠀⠀⡀⠤⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠁⣸⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠠⠃⠀⠘⡅⠀⣶⠁⠂⠀⠀⠀⠀⠀⠀⠀⡆⠘⢀⠀⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⡀⠛⠁
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠁⠀⡰⠀⡴⠐⠄⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠇⢨⡅⠀⢄⣿⣿⢼⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⡆⠀⠀⠀⠀⠀⠴⠀⢠⠟⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⢠⠀⢀⡀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⡗⢀⣺⣿⣿⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⣄⠀⠀⠀⠀⢀⠀⣩⢦⡀⢠
⠀⠀⠀⣀⠀⠀⠈⣿⡀⠈⡅⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠸⣆⣹⣿⡿⢿⣤⣄⣤⣀⣀⣀⡀⠀⢀⣼⡆⢀⡛⠳⣶⡶⢊⠌⠴⢃⠜⢡⡿⠆⣴⢶⣶⣆
⠀⠀⠀⠛⠀⠁⠀⠈⠓⠄⠐⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠸⣿⣿⡷⣿⠆⠀⠀⠀⠀⠉⠉⠉⠉⠹⢧⡄⣿⠀⠀⠴⢋⠟⣠⠋⣴⢋⣰⠶⠬⣭⣙⢻⠅
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢃⠣⡦⡤⢡⡎⣠⠟⢰⣿⢏⡑⠶⢶⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⠄⣀⠀⠀⢀⡀⢀⢰⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠔⢱⠂⣧⠼⠉⣴⢽⠟⠛⡂⠘⣃⣠⡅⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⢼⠦⢄⡙⢄⡍⣶⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⣦⡉⡖⢸⢴⡞⠉⠀⠀⣾⠁⠀⠈⢿⠀⠀⠳
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠐⠀⠻⡦⡏⡶⢗⢻⣾⣿⣿⡆⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⢳⡿⠟⠓⡘⠈⠀⠀⠉⢤⣼⡄⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠠⣈⠀⠙⠄⠀⠀⠀⠀⠀⢑⡹⢰⣬⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠓⠚⡀⢒⠒⣒⡒⣒⣆⣽⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠤⠝⠳⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⢱⢮⡩⠌⠀⠀⠀⡿⠹⠟⣀⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠘⣠⣴⣧⣑⢂⡤⣼⠛⢿⡿⠀⠈⠢⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⡀⢀⠲⠷⠷⠾⠿⠷⠿⠞⠏⠉⠙⠒
⠀⠀⠀⢀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢠⠄⠀⠃⠈⠀⢸⣿⢻⣿⣿⡷⠲⠶⣾⡇⣶⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⢀⡐⠀⢀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠌⠠⢿⣷⣦⣄⣀⣀⠐⢦⡀⢀⠀⠀⣘⡿⠈⢿⢻⡇⠀⢠⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⡠⡀⡀⠘⠀⠀⠡
⠀⠀⠀⠀⢤⠄⠀⡀⠯⠀⠀⠴⡢⣟⢶⠦⠤⣤⣇⣤⣿⣡⠆⢠⣿⣿⢰⣾⡤⣷⠀⢸⣿⡄⠀⣳⡀⠀⠀⠀⢄⠀⢠⣤⠤⣈⠶⣉⠀⠒⢉⡴⠚⢣⡀
⠀⠀⠀⠀⢠⣶⣾⣷⣶⣴⣶⣾⣿⣿⣿⠶⠶⣮⣉⣏⡷⠄⣠⣾⣿⣿⣿⣿⣷⣿⡄⢸⣿⣿⠲⣿⠀⡀⠀⠀⠀⠀⠈⠈⠑⢈⠷⠔⣦⠃⢠⡤⠉⢈⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠛⠙⠻⢯⠻⠿⠛⢿⣿⣿⠷⠯⠭⠉⠀⠉⠉⠉⠉⠉⢀⣼⡟⠀⢸⠉⢡⣴⣃⣀⣀⡀⠀⢀⠀⠀⠒⠺⡏⠒⠗⠉⡴⣁⣤⣾⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠰⡀⢀⠘⢃⣦⠀⠀⠸⠧⣦⣠⠄⠀⠻⠷⣶⠯⢀⡀⠀⣀⠈⠉⠈⠉⠉⣉⣤⠀⠀⠀⠈⠹⠿⠶⠼⠟⠛⠉⠀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠁⠘⠀⠊⠂⠐⠁⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠄⡀⠀⢤
⠀⠀⢏⢀⠀⠀⠀⠀⠀⠒⠁⠀⠀⣀⠀⠀⡼⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠠⠘⠆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠙⣆⠀⠀⠀⠠⡠⡄⠀⠀⠀⠘⠉⠂⠀⠀⠀⢇⡠⠀⠈⠉
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠅⠤⠒⠁⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠂⣤⠁
⠀⠈⠀⠀⣴⠀⠀⢀⡀⢰⡆⢢⠀⠀⢠⠀⠀⠀⡤⠠⡀⢰⡄⣀⢀⠀⢤⠄⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠙⡀
⠀⠀⠀⠀⡟⠀⠃⣼⢡⠀⡇⠁⡆⠀⠈⣧⠀⠀⢿⠐⠄⢸⠀⣿⠀⠀⢸⠀⡏⢀⠸⡆⠀⢠⠄⢳⡐⠀⠀⠄
⠀⠈⠀⠀⠁⠀⠘⠃⠀⠀⠁⢠⡇⠈⠀⠇⠀⠀⠸⠤⠂⠈⠀⠟⠀⡀⠈⠀⠃⠀⠀⠃⢠⠟⠂⠀⡇⠀⠰
⠀⠀⠀⠈⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠆⡄⡈⠀⠐⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⡄⠀⠁
⠀⠈⠀⠀⠀⠆⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢗⡂⠨⠈⠐⢱⠀⠀⠀⠎⠑⠊⢁
⡀⠀⢀⠀⢀⠖⠁⠤⡀⠀⠀⡤⠀⠀⠈⠂⠐⠄⠄⠀⠀⠀⠀⢠⣤⠴⠦⠒⠛⠁⠀⠀⠈⠢⠠⠁⠀⣀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡁⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠠⠀⠀⠀⡐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡀⡠⠎⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠒⢠⠁⠰⠁⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠃⡀⠀⠈⠀⠀⣠⠆⡠⠁⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡇⠈⠁⠊⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠐⠊⠀⠠⠂⠀⠔⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡜⠋⢀⡔⠀⢀⠠⠊⠁⢀⠀⠂⠀⠀⠀⢀⠔⠀⠀⢉⠀⠀⡴⢈⣁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⡁⠀⢐⣊⠁⢨⠂⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⡔⠁⣦⢃⠀⡾⠀⡁⠀⠐⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠤⠀⢄⠈⢃⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⠀⠜⠀⠀⠃⠈⢆⠑⠒⠁⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠈⠁⠒⠒⠂⠁⢄⠣⠤⢀⠀⡄⠰⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡾⠁⠠⠔⠁⠀⠈⢢⠀⠀⠀⠀⠀⡏⠉⠁⠈⠁⠀⠀⠈⠀⢄⠁⠀⠀⠀⢠⠀⡄⠀⠀⠀⠉⠀⠀⠘⠄⠉⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢀⠎⠳⡀⢀⠒⢢⠉⠂⠈⠹⠀⠈⠠⠀⠀⠀⠂⠀⠀⠀⠈⠒⣀⠀⠤⠤⠤⠀⡀⠀⠈⠀⠤⠀⠠⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢄⠰⠀⠠⠀⠀⠸⠠⡀⠈⢎⠓⠃⠀⠀⠀⠀⢃⠀⠀⠡⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠂⠀⠀⠈⠀⠀⠀⠑⠠⠤⠜⠛⢄⡀⠰⣎⡆⢸⠀⠀⠀⠁⢄⣀⣀⡀⠄⠐⠀⠁⠀⠀⠀⠀⠱⡀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠐⠁⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⢈⢓⡤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠘⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⣰⢇⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⠡⠦⠐⠂⠁⠀⠆⢲⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣠⡅⠀⢠⣧⣀⠤⠤⠔⠒⠂⠉⠉⠀⠀⠀⠀⠀⠈⠡⠀⠀⠜⠀⠀⠀⠇⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡸
⠀⠀⠀⠀⠘⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⢀⠀⠀⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠆
⠀⣍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠈⠉⠉⠉⠉⠉⠉⠀⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠙⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢏⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⣀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠄⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⣀⡀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢀⠄⠐⠂⠀⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⡀⠄⠖⠋⢢⡀⠔⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰
⠀⠀⠀⢀⠔⠉⠀⡂⢀⡴⠛⠑⠂⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡠⠁⠀⠀⠀⢀⠋⢀⠄⠀⠀⠒⢌⡄
⠀⡰⡐⠉⠉⢁⡠⠁⠀⠂⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⢀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⢠⠁⠀⠀⠀⣼⠁⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡋
⡄⠈⠣⠄⠰⡇⠀⠀⠀⠀⠈⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣁⣀⡸
⡇⠀⠀⠀⢠⠉⠁⠀⠒⠒⠒⠀⠀⠤⠬⠶⢆⠀⠀⠀⠀⠀⠉⠉⠓⠄⠀⠀⠀⠀⠀⠀⡠⠔⢹⣀⠅
⡇⠀⡠⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠈⢲⠖⠒⠁⠀⠀⠀⢀⠤⠊⠀⠀⢸
⢠⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠒⠊⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⣈⣀⣀⡀
⠀⢫⢄⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢀⡤⠒⠁⠀⠀⠀⠀⡀⠠⢰⠁⠀⠀⢻
⠀⠈⢆⠈⠉⠀⠳⠒⠒⠀⠀⠤⠤⢤⡤⠀⠀⠀⠐⠂⠉⡏⠉⠁⠈⡆⠐⠂⠀⠉⠀⠀⢀⠎⠉⠀⠀⠙
⠀⠀⠀⠱⣄⠀⠀⠱⡀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠚⠃⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠑⠤⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢈⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠉⠁⠐⠂⠀⠀⠰⠆⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠙⠉⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⠀⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⠀⡖⠀⡖⡗⢠⡖⠀⣴⢢⢰⢢⢰⠂⢰⢲⢠⢲⢠⢲⢰⢢⣀⠔⠁⠀⠀⠀⠀⠑⢂
⠀⠀⠀⠀⠀⠀⠘⢆⣀⠀⢰⠂⠚⠣⠋⠧⠋⠈⠥⠁⠩⠸⠉⠞⠉⠌⠉⠼⠉⠼⠉⠾⠉⠮⠉⠀⡇⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢬⣷⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⢪⣀⣈⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠁⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡀⠀⣀⠠⠊
⠀⠀⣀⢀⣀⡀⠀⠀⠀⠉⢹⠃⠀⠀⠀⠀⠀⠀⢄⣀⣠⢁⣀⡰⣀⣱⣰⣆⢀⠀⠀⠀⠀⠀⠀⠀⡘⠐⢌⠉⠀⠀⠀⢀⠄⠠⠀⢄
⢠⠘⠀⠀⠀⠈⠁⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡸⠀⠀⠀⠊⠁⠀⠀⠀⠀⢱
⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⢀⠴⠀⢠⡇
⠑⠤⡀⠀⢀⠀⠄⠊⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠀⠐⠆⢀⠀⢀⠔
⠀⠐⠨⠍⠀⠀⡎⠁⢢⠀⢸⠀⠀⢀⠀⢀⠈⠀⣀⠈⣉⠀⣀⠀⣉⡁⠁⠈⢀⠀⠀⠈⠀⣀⡀⠀⠀⠀⠀⠐⠒⠃⠀⠠⠂⢠⠈⠁
⢎⣀⠀⢐⠀⠀⠂⠒⠂⠀⢸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠨⠀⠀⠠⠀⠠⠄⠀⢇⣀⡀⠀⠀⠀⠀⠐⠄⠔
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠐⢐⣀⠀⣒⠆⠆⡄⣖⠦⠀⣶⠠⢌⡃⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠳⠀⠇
⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠠⠀⢂⣠⠆
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠺⣦⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠀⠒⠒⠀⡰⠓⠒⠒⡡⠤⣀
⠀⠀⠀⠀⠀⠈⠣⡄⠀⠀⠀⠀⠙⣦⣀⣀⣠⣤⣤⣤⣤⣤⣄⣤⣀⣤⣤⡤⣤⣤⣤⣬⣥⠤⠜⠈⡱⠀⠀⠃⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⣀⣀⠔⠀⠀⠈⡆⢁⡤⠂⢀⠴⠀⠠⢌⠀⠀⠀⠀⠀⠀⡄⠑⠤⠢⠤⠜⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠒⠑⣄⠀⠈⠉⠀⠀⠐⠄⠀⢀⠆⠀⠂⠠⡀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠈⠐⠁⠀⠄⠂⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣇⠀⣠⠀⠀⠀⠀⠀⠘⣯⡷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⢲⡶⣮⣹⣞⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣛⣻⡇⢪⣹⡏⠻⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢀⡠⢿⠁⠀⠚⠳⣺⣽⡧⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠘⠛⠤⠀⣀⠋⠈⠁⠀⠀⠀⠀⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠛⠾⣆⢠⡀⣤⠶⠘⠖⠀⠀⠐⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠀⠀⠀⠛⠉⠀⣀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⢀⣠⡴⠟⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠂⠹⡇⠀⡀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⣄⣡⠛⠛⠛⠓⠟⢧⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄⣀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠚⠙⣟⠓⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠆⠈⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠞⠀⠀⠀⠀⠛⠯⣄⠀⠄⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠀⣀⣠⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⣠⣾⡿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⣿⣿⠏⡟⠂⢰⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣿⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠇⣧⢸⡄⢻⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⡿⠸⡇⢺⡗⡖⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣠⠆⠀⡧⠀⣇⠘⢁⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠁⠈
⠀⠀⠀⠀⠀⠀⣀⣄⠀⣴⠟⠀⢀⠜⢀⣱⠟⠀⡼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⣾⡇⠠⢦⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⡨⠄⠱⠤⠄⠠⢷⡴⠞⠁⠠⠜⣡⣘⣦⠀⠀⠳⣀⠀⠀⠀⢀⡤⠀⣰⡾⠀⠀⠘⠾⠀⠁⠛⠠⡌⢀⣁⡀⢠⡀
⠀⠀⠀⢠⡔⠊⡉⣶⠉⠔⠀⠠⣄⠀⠰⢛⠓⠨⢝⣍⠉⠀⢀⣠⣀⡉⠀⠀⠋⢁⠈⠉⣅⡀⢀⡀⠘⠃⠜⠠⠀⠈⢁⡄⢉⡠⢄⠂
⠀⠀⠀⠈⠤⣌⣀⣀⡀⢠⠀⠀⠈⠃⠐⠺⢎⣦⡄⢈⠁⠁⠈⠁⠀⠈⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠚⢀⣀⠋⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠩⢀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⡠⠄⠰⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⣀⠀⢀⣤⣤⣄⠀⣠⠤⠤⣄⣠⠤⠤⣄⢠⠶⠶⢦⡀⢠⠖⠛⠲⣄⣰⠚⣛⣳⣄⣞⣋⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣉⣉⣙⣦⣾⡥⠤⢼⡷⠿⠶⠶⣾⠷⠛⢒⣚⡟⠛⠛⣛⡟⠋⠉⣩⡿⠋⠉⠉⢉⣽⠋⠉⠉⢩⡟⠉⠉⢉⣽⠋⣧
⠀⠀⠀⠀⠀⠀⣠⣴⡟⣿⡉⢡⡴⠃⠀⠀⠰⠟⠀⠀⠀⠛⠃⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⣈⣀⡀⠀⣤⡀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢀⡏⠸⣧⣿⣇⠀⠀⠀⠀⠀⠀⣠⠴⠆⢀⣶⡄⢰⡆⠀⢸⣯⠅⠀⣿⢦⣹⠀⣯⢈⡷⢰⡧⢿⠀⣷⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⠇⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⢿⣀⡄⢸⠛⠷⠈⠧⠤⠘⠓⠒⠀⠛⠀⠙⠀⠙⠋⠁⠈⠀⠈⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡀⢸⡆
⠀⠀⠀⠀⠀⡿⠀⠀⢹⣿⡟⡇⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠤⠴⠶⡶⠖⠒⠒⠛⠛⣿⠛⠛⢉⣉⣹⣉⣉⣉⣭⣯⠤⠤⠤⢽⠤⠤⠼⡇⠀⣷
⠀⠀⠀⠀⢰⠇⠀⠀⠘⣿⣷⢻⠀⠀⢸⣍⣡⣤⡤⠤⠼⡦⠤⠴⠶⠒⠒⢻⠒⠒⠒⠒⠛⢻⠉⠉⠉⠉⠉⡇⠀⠀⠀⣸⣀⡀⣀⣘⣆⣀⣀⣻⠀⢸⡄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⢿⣿⡿⡇⠀⠀⣧⠀⣀⣀⣀⣀⣷⣀⣤⣤⠤⠤⠼⡧⠤⠶⠒⠒⠚⡗⠒⠛⠋⠋⢻⠉⠉⠉⠉⡏⠉⠉⠉⣿⣉⣁⣘⡆⠀⣧
⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⣿⣿⢿⠀⠀⢸⡍⠉⠁⠀⠀⠸⡆⠀⠀⠀⣀⣀⣷⣀⣀⣠⡤⠤⢿⠤⠴⠶⠖⠺⡖⠒⠒⠛⢻⠉⠉⠉⠹⡍⠁⠀⢻⠀⢸⡄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⣿⡿⡇⠀⠀⣷⠴⠒⠒⠒⠚⢿⠉⠉⠉⠉⠉⠸⡀⠀⠀⠀⢀⣸⣄⣀⣠⣤⠤⣧⠤⠤⠴⠾⡖⠒⠒⠚⢿⠉⠉⠙⣇⠀⣷
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢹⣿⣧⣷⠀⠀⢹⣀⣀⣀⣀⣠⢼⡤⠴⠒⠒⠒⠛⣟⠉⠉⠉⠉⠀⣇⣀⣀⣀⣀⣸⣤⠤⠤⠤⢷⠒⠒⠒⢻⡖⠛⠋⢻⡀⠸⡆
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠸⣿⡿⣾⡆⠀⠈⣏⠉⠀⠀⢀⣀⣧⣀⣠⠤⠤⠶⠺⡖⠚⠉⠉⠉⢹⡉⠀⠀⠀⠈⣇⠀⠀⣀⣸⣀⣠⣤⠤⣧⠴⠶⠞⣇⠀⢷
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣇⣧⠀⠀⢹⡛⠉⠉⠉⠁⢹⠀⠀⠀⠀⢀⣀⣧⣀⣤⠤⠤⠼⠷⠲⠒⠒⠚⢻⡋⠉⠁⢸⣇⣀⣀⣠⣽⣤⣤⣤⠿⠄⢸
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⡄⠀⠈⡷⠶⠶⠖⠒⠚⡏⠉⠉⠉⠉⠀⢹⡀⠀⣀⣀⣀⠶⠤⠴⠶⠶⠾⠓⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡎⣇⠀⠀⢻⠀⢀⣀⣀⣤⡽⠤⠴⠶⠒⠒⠛⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠶⠶⠚⠛⠛⠋⠉⠉⠉⣧
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢻⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠶⠖⠒⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⢿⣿⡼⣇⣀⣀⣤⣤⡤⠤⠶⠶⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠶⠖⠚⠛⠉
⣿⣤⣶⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠸⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠶⠖⠒⠛⠋⠉⠉
⠀⠀⠉⠙⠓⠲⠦⣤⣀⣀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠶⠖⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⣼⣧⡤⠤⠶⠖⠚⠛⠉⠉⠉

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠈⠢⠀⠀⡀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠡⠄⠀⠁⠐⠀⠄⠀⠘⠀⠀⠀⠉⠀⠄⠀⠈⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠠⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡴⠀⡈⠉⠀⢱⠀⠀⠀⠰⠀⡈⠀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠐⠀⠃⠂⠀⠀⠁⠐⠂⠀⠀⠀⠀⠂⠀⠀⠠⠤⠄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠖⠂⡀⠀⠀⠀⠐⢈⠀⠢
⠀⠀⠀⠀⠐⠖⠆⠀⠀⠀⠠⠀⡀⠀⠀⡠⠄⢁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⢴⢱⠂⠱⠀⠀⠀⠀⠄⠐⠀⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢅⠁⠀⠁⡖⠁⠄⢀⠀⠀⠀⠠⠉⡐⠀⠀⠁⠀⠄⠈⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⢡⠄⠰⠀⠀⠀⡂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⠤⠀⠂⠈⢁⡈⠀⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠐⠀⠀⢀⠉⠀⠑⣄⠠⠀⠀⠀⠀⡄⡨⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⡅⢋⠠⢀⠰⠠⠈⡀⠀⠀⠀⡠⡀⠀⢂⣁⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠀⠧⠜⠀⠀⠀⣁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠈⠃⠀⠁⠀⠈⠡⠄⠀⠀⡼⠈⠀⠈⠈⠀⠀⡀⠀⣀⠂⠈⢂⠈⢀⠀⠀⠂⠀⠀⠈⠀⠀⠐⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁⡠⠀⠀⠀⠀⠀⠁⠁⠀⠀⣀⠘⠀⡀⠠⠡⠈⢆⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠡⠄⠆⢠⠀⡦⡀⠁⠀⡀⠄⠀⠀⠀⢀⢀⠀⠀⠤⠄⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐
⠀⠀⠀⠀⠈⠁⠢⡀⢀⠀⠂⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠤⢇⡑⠠⠄⡀⠀⠀⠀⠠⡂⠆⠰⢀⢀
⠀⠐⠀⠀⠐⠀⠐⠃⠀⠓⠀⠘⠀⠀⠠⠀⠀⠠⠀⢂⠀⢀⠓⡰⢤⠃⠒⡀⠀⠠⠍⣤⠘⠃⠚⢀⡐⢃⠀⠀⠀⠀⠀⠘⠁
⠀⠠⡄⠀⠀⠀⠠⠄⠀⡤⠀⠀⠀⠀⠜⠀⠀⠀⠁⠀⠀⠀⠀⠅⠒⠈⠀⠀⠀⡕⠠⡆⢀⡀⣀⠀⡄⠠⡀
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢔⠂⢀⠠⠆⢀⠑⠁⠀⠠⢄⣉⠀⠄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠁⠴⠀⠆⠔⠈⠀⠀⠈⠤⠈⠒⠁⡄
⠀⠀⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠄⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠐⠦
⠀⠀⠀⣶⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠀⣾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣽⢷⡀
⠀⠀⢠⢽⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⡟⠷⡄⠂⠀⠀⠀⠀⠀⠀⠀⣿⠄⣿⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⣸⡇⣸⡇
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠉⣠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⣽⣿⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣇
⠀⠀⠀⠀⠀⣿⣿⠈⣿⣷⠀⠀⠀⠀⠀⠸⢿⣿⣷⣶⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣦
⠀⠀⠀⠀⠀⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠾⠁⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆

⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠂⠀⢀⣀⠡⠠⠂⡀⠀⠀⠀⠀⠀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⣈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠀⠐⡈⡀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠤⠀⠄⠁⡠⠀⠄⠀⠈⠑⠠⡄⠈⠂⠤⠐⠉⠀⠈⠀⠀⠀⠐⠁⠹⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⡀⠂⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⢀⢀⠀⠀⠀⠦
⠀⠀⠀⠀⠐⠂⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠂⠰⠊⠀⠀⢸⠁⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐
⠈⠀⠀⠀⠀⠀⠠⠼⠁⠀⡀⠀⠄⠀⠰⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠈⠧⠄
⠀⠀⢄⠰⢀⢀⠀⠀⠀⡀⠀⠀⣀⠀⡀⠀⠀⠀⠠⢀⠀⢨⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠐⢂⠀⠀⠒⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠑⢈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠂
⠀⠈⠀⠁⠈⢀⠀⠠⠀⠀⠀⡀⠐⠂⠐⡀⠀⠀⠀⡒⠒⠚⠓⢒⠂⢀⡐⠀⠐⠂⠐⠂⢢⠀⠄⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠰⠀⡆⠂⢈⠐⠂⠆⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣂⠀⠀⠒⢉⠀⠂⠁⢈⡈⠀⠀⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⠘⠂⠀⠀⠘⠃⠀⠀⠐⠃⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠄⠀⠀⡠⢠⠐⡄⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⢬⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠠⠐⡀⠐⣀⡖⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠠
⠀⠀⠀⠀⠀⠠⡁⣀⠅⠀⠨⢀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠈⠁⠈⡠⠠⠈⠀⠉
⠀⠀⠀⠀⠀⠈⢒⣀⠴⠀⠣⢀⡐⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⠀⠀⠰⠄
⠀⠘⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠐⠆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀
⠀⠀⠁⠂⠉⠐⠉⡀⠀⠀⠀⠀⠀⡀⠴⠐⠀⠠⣀⠀⣰⠄⠠⠰⠀⠀⢀⠄⢠⠀⠀⠠⠀⠀⠀⠀⠘⡌⣰⠢⠌⡀
⠀⠈⠀⠄⠀⠠⠁⠁⠀⠄⠀⠀⠀⠥⠐⠀⠐⢀⠀⠀⠀⢈⢁⠀⠀⠀⠈⠐⠀⢆⠁⠀⠀⠀⠀⠀⠘⠠⠈⡈⠠
⠀⠀⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠀⠃⠀⠐⠀⠐⠘⠀⠈⠀⠀⠐⠘⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠁⠀⠒

⠀⠰⡀⠀⡐⠀⠀⠀⢠⠀⠀⠀⠀⢔⠀⠀⢤⠀⠀⣀⠠⡄⡀⠤⡀⠀⠀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠄⢠⢀⡄⣠⢀⡀
⠀⡔⠃⠠⢊⡐⠄⢀⠰⠄⡀⡄⡂⠊⠀⠐⣓⡦⠘⢆⠁⣸⠀⡠⠃⢢⠀⣿⢠⡝⣘⢃⢼⣶⣯⢹⣿⢀⠔⠀⠂⣀⠠⠄⣀⠤⠄⣀⠔⠀⠢
⠀⠀⠀⠈⠁⢂⠂⠈⠄⠃⡐⠇⣐⡁⠀⠂⢡⠐⠀⡮⡹⠇⠹⢦⡄⠰⠁⠻⠿⠿⠿⣿⡿⠿⠿⠛⠋⢘⠀⢧⡄⠃⡠⡆⠘⣠⣄⠘⠀⡦⡆
⠀⠃⠘⣀⠁⠀⣞⠰⠁⠁⠀⠀⣁⠉⠀⠑⠐⠀⠀⢀⡧⠁⢠⠊⠁⢀⠔⡤⢀⠀⠀⠋⠀⢋⠀⠀⠔⠈⠢⣉⡠⠄⠙⢁⣌⠉⠉⡰⢄⣈⠔
⠀⠀⡀⠎⢀⡀⠂⢀⠀⢘⠆⠂⡄⠌⠂⠀⠰⡣⠀⠀⢀⢀⠃⢠⠂⠁⠀⠀⠀⢲⠀⠀⢰⠝⠆⢀⡲⣁⠀⠀⠀⠀⠙⠁⠀⠈⠃
⠀⠊⠐⠣⡀⢨⢃⠂⠐⡩⡕⡇⡀⠖⡈⠐⠪⢅⢢⠀⠀⠁⢀⢼⡆⠁⠀⠀⣀⠨⠁⡂⢸⠀⡄⠸⠀⣸⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⡠
⠈⠢⢁⠡⠃⠀⠆⢀⢡⠤⡄⠄⢁⣈⡀⠄⠃⠠⠠⠀⠉⠁⠐⠠⠉⠉⠩⢤⠀⠂⠈⠀⡄⠀⡇⢀⠅⢸⠀⠂⢛⠀⠈⠒⠁⠀⠀⠃⢣
⠀⠀⠀⠀⠀⠄⡀⠠⢅⠒⢈⣆⠀⠐⠁⠈⠐⠂⠁⠀⠈⠁⢀⣀⠀⠄⠤⢸⡇⠀⠀⠀⢈⠉⠠⢘⠆⠓⠀⠄⠀⠐⠀⠐⠀⠀⡞⡄⠀⠣
⢰⠂⠀⠐⢂⠌⠀⣠⣤⣥⠁⠛⠘⣍⠉⠝⠩⠉⢉⠝⢍⠁⡹⠑⢄⠀⠆⠀⡀⢠⠀⡐⠁⠀⠀⠀⢁⠀⠠⠀⠲⣀⠐⢆⠀⠘⠠⠀⠄⠂⢁
⠠⣶⣶⣶⠀⠐⠜⢿⣿⣿⠀⠀⠀⠈⠊⢤⠀⠑⠊⠀⠀⠑⠁⠀⠀⠉⠀⠀⠁⠈⠀⡁⠀⠀⠀⠀⢠⡀⡀⠦⠠⠀⠀⠈⠁⠛⠀⠀⠀⠒⠈
⠀⢻⠿⡿⠀⠀⠀⠈⠉⠙⢦⡀⠀⠀⠀⣿⠀⠀⠀⠂⠀⡠⠒⠚⠙⠉⠉⠋⠓⠰⢢⡀⠄⣀⣀⠐⠃⠀⠀⠈⢣⠂⠠⡘⠀⠀⠀⢠⣤
⠀⠀⢸⠀⠀⠀⢀⠚⠐⡀⠎⠕⠠⠐⠒⠾⠒⠀⠀⠀⢐⠃⠀⣀⢀⢀⠘⡀⡇⢠⠈⠕⠀⠉⠀⠀⠀⠀⠀⡄⠀⢳⠀⠇⠀⠈⢀
⠀⠂⠙⠉⠂⠀⠨⠀⠀⠘⠄⢀⠔⡀⠀⠀⠀⠀⡆⠀⢘⠀⠘⠀⠄⠁⠈⠀⠃⠘⠀⠀⠀⠀⠈⣤⠄⠀⠊⡀⣀⠀⠀⠀⠀⠙⡀⠁⠀⠈
⠀⠀⠀⢠⣆⠀⢇⠀⠐⢀⡃⢸⠠⠔⢑⠈⣀⠉⢄⡃⠘⣁⢐⠀⠐⠔⠢⠄⠀⠬⢀⡸⠀⠀⠀⠀⠀⠀⡦⠀⠠⢆⠀⠀⢀⠀⠙⠂⠙⠆⠁
⠈⡡⠀⠜⠘⡄⠘⡀⠀⢨⠀⢶⠀⠄⠀⠀⠀⠀⢀⠆⠀⠈⠃⠄⠤⠤⠤⠠⠤⠄⠋⠁⠀⣶⠀⣶⣶⡖⠂⠀⠀⠘⢶⣶⡆⠀⠀⠒⢂⠀⠂
⠀⠁⡼⠀⠀⠈⡄⠑⠒⠈⠀⠓⠌⢀⡀⠀⣀⡀⠥⠊⢀⢀⠀⠀⠀⠀⡀⢀⠒⠒⡠⠆⠀⠀⠀⢈⠿⠀⠄⠀⠀⠀⢸⠏⠀⢀⡠⠀⠄⠠⢄
⠀⢰⠃⠀⠀⠀⢱⠀⠀⣔⠘⠛⠀⠺⠂⠄⠀⠀⡰⠂⢪⠃⠐⠀⠄⢘⣐⡠⢤⢊⠔⠃⠸⠵⠀⠀⠘⠀⠀⠀⠀⠀⡘⠀⠀⠁⠢⠠⠤⠓
⠀⠈⠐⠃⠚⠁⠈⠁⢠⠇⢀⠠⠠⠠⠀⠂⢀⡜⠁⠈⠄⠐⠰⠏⠁⠀⠃⠈⠉⠇⠀⠸⠀⢀⢨⡄⠀⡊⢑⣆⣶⠋⣀⠀⠀⠓⠀⠀⠀⠀⠊
⠀⠀⠀⠠⡶⠄⠀⠀⢤⡀⠌⠀⠨⠘⠀⠀⡎⣀⣠⠤⠆⠉⠁⠀⠀⠀⠀⠢⠄⣀⡠⠀⣰⡆⠁⠈⠈⠛⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⢀⣶⠄
⠀⣠⠆⣤⣤⠈⣃⠀⠀⠈⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⡤⠒⠂⢆⣠⠤⠤⠀⠀⠀⢀⠀⠐⠃⢸⠉⢩⡏⠃⠁⠐⢰⢒⠒⠋⠃⠀⠩⠀⠈
⢀⠭⠒⠊⠚⠝⣂⢹⠀⡀⠁⡡⠀⠠⡄⠁⢀⠄⠀⡛⠤⣀⡀⠉⡇⠀⠀⢀⠀⠀⠂⠰⠀⠀⠰⠒⠲⠀⡄⠤⡘⢸⠴⠦⠀⠠⠐⠠
⢀⠄⠀⢸⠂⠁⠀⢸⠀⣀⠈⠀⠀⠀⠸⣔⡖⠀⢠⠁⠁⠀⠀⡭⢡⠫⡄⠈⢠⠀⠀⠀⢀⣀⢀⡀⢀⡀⠀⠀⢀⡀⠀⣀⢀⡀⣀⠀⢀
⠀⠙⠆⣀⡀⠥⠖⠂⠈⠈⠉⠀⠀⠁⠀⠀⠀⠀⠈⠨⣉⠑⠰⠀⠰⠀⠧⠀⡺⠀⠀⠀⠀⢐⠂⡇⠄⠠⠀⠀⡃⠅⢈⡣⠋⠎⠁⠀⢀
⠀⠤⠀⠀⠀⠀⠐⡄⠀⡰⠆⠀⠀⠀⠀⠸⠀⠀⠠⢀⠁⠠⠁⠀⠀⢙⠀⢀⡅⠀⠀⠀⢀⠀⠀⠁⠀⠀⠁⢈⡁⣀⠉⡀⠀⠃⢀⡀⠀⡀⢀
⠀⠀⠀⠢⡈⠁⠀⡅⠀⠀⠈⠀⠀⠠⠀⠀⣀⠀⣀⣀⣀⣀⣀⣨⡵⠄⢢⡰⠀⠀⢩⠀⡄⠀⣘⢠⠀⠀⠚⠀⡓⠈⠄⠀⠑⠀⠀⠄⠀⠣⠁
⠀⠓⠀⠀⠀⠀⠐⠁⠀⠑⠂⠀⠁⠁⠀⠀⠋⠀⠑⠒⠒⠒⠒⠒⠐⠂⠀⠀⠀⠉⠀⠀⠙⠀⠋⠘⠁⠘⠀⠐⠁⠈⠉⠓⠁⠈⠀⠈⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠢⠄⠀⡀⠀⠀⠀⢀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⡀⠈⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⣳⠀⠀⢀⣀⣀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠢⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠉⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠘⠁⢀⠁⠠⢸⡄⠈⣠⢀⠀⠠⠀⠂⠀⠋⠈⠉⢃⠀⠀⣌⡜⣡⡁⠀⢠⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠘⠄⠀⠉⠁⠐⡀⠈⠁⠀⠀⠀⠀⠈⠘⠁⠉⢀⣼⠏⠀⠄⠀⠀⠙⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠁⡀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠠⠀⠀⣈⠀⠀⠈⠀⢠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠠⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⢠⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠒⠀⠈⠀⢀⡀⠀⠀⢠

⠐⠤⠤⠃⠰⠂⠀⠂⢠⠀⠀⠈⠀⠈⠀⠀⠐⠒⠀⢰⠀⠀⠀⠀⠀⠀⠐⠤⠤⠃⠰⠁⠀⠂⢀⡀⠀⠈⠀⠈⠀⠀⠐⠂⠀⢰
⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⡠⠀⠀⠀⠀⠀⠈⢦⠀⡸⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠒⠂⠤⠁⡠⠄⠀⠀⠀⢄⠀⢤⠀⡸
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠤⢤⡀⠑⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⡀⠈⠀⠀⠀⠀⠄⠀⠉⠂⠈
⠀⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠘⠉⠐⠁⠀⠀⡀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠀⡀⡀⠆⠀⢁⠄
⠀⠀⠀⠀⠈⣋⣀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⣠⠰⠀⠀⠀⠀⠀⠀⡀⠤⠤⠄
⠂⠀⠆⠈⠢⠭⠤⡤⠀⠀⠀⠀⠀⠀⠱⣄⢀⡰⠂⠀⠠⠄⡀⠀⠀⠠⠂⠀⠆⠀⠢⢥⢤⠜⠀⠀⠁⠀⠀⠀⠱⡀⢀⠠⠂⠀⠠⠄⠀⠀⡀
⠘⠏⠀⠀⠀⣀⠀⠀⠠⡀⢠⠤⢀⠂⠀⡈⠁⠀⠀⠘⢄⣀⠔⠀⠃⠴⠘⠋⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢀⠄⠀⠈⢁⡀⠀⠐⢄⣀⠐⠀⠃
⠀⠀⠀⠀⠀⣀⢀⠀⠀⠙⠢⠄⠁⠀⠀⣀⠠⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠘⠢⠄⠁⠀⠀⣀⠠
⠀⠀⠀⠘⡄⠉⠉⡡⠀⠀⠀⠀⠀⠀⠠⣀⠀⢀⠃⡃⠄⣀⠀⠰⠀⠀⠀⠀⠀⠘⣄⠀⢈⡴⠀⠀⠄⠀⠀⠀⢄⠀⠀⢠⠁⢊⠄⠈⠁⢠
⠢⡀⠂⠀⠈⠒⠊⠀⠀⠀⢀⠐⠄⡀⠀⠀⠉⠉⠀⠀⠀⠈⠈⠀⢰⠁⠑⢀⠀⠀⠈⠓⠁⠀⠀⢀⠀⠈⠆⡀⠀⠉⠒⠁⠀⠀⠀⠙⠐⠊⡜
⢀⡈⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⠠⠄⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠉⠢⠈⠢⢄⠔⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠐⠀⠀⡠⠀⠀⢀⠄⠀⠀⠀⠀⢀⡀⠀⠃⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⡠⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠁⡀⠀⠄
⠠⠒⠁⠃⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠐⢁⠄⢤⠂⠁⠀⠀⠒⠁⠀⠀⠀⠀⠐⠀⠀⠠⡄⠆⠀⠀⠀⠀⠀⠀⠀⠁⠤⠴⠀⠁
⠐⠤⠐⠃⠰⠁⠀⠀⢠⠀⠀⠘⠀⠐⠁⠀⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⠄⠰⠃⠰⠈⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠈⠉⠀⢲
⠀⠀⠀⠀⠀⠀⠐⠂⠔⠀⡤⠀⠀⠀⠀⡀⠢⡀⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠚⠂⠢⠁⡤⠀⠀⠀⠀⢀⠈⢦⠀⡸⠀⢀⡀⠀⢀
⣄⡀⠰⠀⠀⠀⠀⠀⠀⠈⠠⣀⡈⠀⡀⠀⡀⠈⠀⠃⠀⠀⠀⠉⠂⠀⠰⠦⠄⠈⠀⠀⠀⠀⠀⠀⠤⣀⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠐⠁⠀⠀⠀⠀⠀⠆⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠉⠐⠁⠀⠀⠀⠈⠂⠀⠠⠂
⠀⠀⠀⠀⠈⣉⣀⠠⠀⠀⠈⠀⠀⠀⠀⠠⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣠⠘⠀⠀⠈⠀⠀⠀⡄⠤⠤⠄⠀⠀⠈
⠀⠀⠄⠀⠲⠥⠀⠴⠀⠀⠀⠀⠀⠀⠱⣄⠀⡴⠃⠀⠠⠄⠀⠀⠀⠐⠀⠀⠀⠀⠲⠥⠠⠔⠀⠀⠀⠀⠀⠀⠱⣄⠀⡠⠂⠀⠀⠄
⠚⠃⠀⠀⠀⡀⠀⠀⠠⡀⢠⠄⢠⠀⠀⠈⠁⠀⠀⠘⢄⢀⠔⠁⠀⠈⠑⠦⢀⠆⠀⡀⠀⠀⠀⡀⢠⠤⢠⠄⠀⠈⠁⠀⠀⠐⢄⢀⠔⠀⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠢⠔⠁⠀⠀⣀⡀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠈⠢⠔⠁⠀⠀⣀⡀⠄⠀⢠⠀⢀
⠀⠀⠀⢠⡈⠉⠉⡠⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠃⠁⠂⣀⠀⠐⠀⠀⠀⠀⠀⢰⡈⠉⠉⡠⠀⠀⢀⠀⠀⠀⠠⣄⠀⢀⠃⠡⠂⣀⡀⠸
⠢⡀⠀⠀⠑⠔⠊⠀⠀⠀⠀⠘⠄⠆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⢰⠀⠲⠀⠀⠀⠑⠔⠊⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠃⡜
⠀⠀⠀⠀⠀⠠⠀⠈⠂⠀⠢⢄⣀⠄⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠸⣄⡀⠠⠄⠀⠀⠀⠀⠈⠢⠀⠠⢄⡀⠄⠀⠄⠀⠀⠠⡀⠀⠀⠀⠀⢄
⠠⠀⠀⠀⠐⠀⠈⡠⠀⠀⠀⠄⠀⠀⠀⠀⣀⡀⠀⠃⠖⠁⠒⠀⢀⠀⠤⠀⠀⠀⠐⠀⠈⡠⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠁⠆⠀⠒⠀⢀
⠐⠒⠀⡃⠀⢀⠀⠀⠀⠀⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⢀⠑⠚⢂⡀⠀⠀⠂⠁⣀⠀⢀⠀⠀⠀⠀⠀⡄⠆⢀⠀⠀⠀⠀⠀⠀⢀⠓⠚⢂⠈
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠐⠃⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠚⠀⢀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⡦⠀⠀⠀⠂⠀⣀⠀⠈⠀⠀⠀⠀⣾⠃⠉⠀⠀⠀⢀⡀⠠
⠀⠀⣿⣷⡔⠆⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⡀⢀⣤⣭⠀⠀⢠⣤⠀⢀⠀⠀⠀⣠⣤⡀⠀⠸⠀⠀⠀⠀⠉⠀⠀⢠⣤⠀⠀⠀⠈⠀⢀⡀⠀⣻⠟⠠
⠀⠸⠿⠛⠁⠀⠀⢰⣶⡆⠀⢤⣤⠀⢰⣶⡀⠀⠘⠈⠁⠀⠀⠀⣠⡄⠈⠁⠀⠀⠙⠛⠀⠀⠐⠀⠐⠂⣶⠄⠀⠀⠀⠁⠀⣀⠀⠉⠀⠌⠁⠀⠀⠂
⠀⠀⠀⠀⡰⡶⠀⠀⠉⠓⠀⠄⠀⠀⠀⠉⠀⠀⣠⡄⠐⢺⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣶⡦
⠀⣠⣾⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⢠⣶⠀⠀⢀⣄
⠀⠈⠉⠙⡀⠀⠀⠀⠀⠀⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉
⠀⠶⠀⣈⣁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀
⠀⠀⠸⣿⡿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡀
⠀⡀⠀⢀⡀⠀⠀⠀⠀⣦⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⠃⠀⠿⠷
⠐⠟⠃⠘⡿⠆⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠄⢠⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⡄⠀⠻⠛⠉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴
⠀⡁⠀⠀⢠⡆⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠩⠄⠈⣀
⠀⡃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⡉⠀⠀⠀⠀⠀⠉
⠀⡀⠰⣿⡿⠀⠀⠀⠀⠛⠀⠀⠰⠆⠀⠀⠀⠀⠀⣀⠀⢠⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠀⠀⢰⣦⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠁⠀⠀⣤⡄
⠀⠆⠀⠀⠉⠀⠁⠀⠀⠀⠚⠀⠀⠀⢠⣦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⣤⡀⠀⠀⠀⣀⣀⠀⠀⠉⠀⠀⠀⠀⢰⠀⠈⠀⠛⠁
⠀⡆⢴⡶⠀⠀⢠⡶⠆⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣄⡀⠀⠀⣶⡄⠈⠉⠀⠀⠾⠂⠙⠃⠀⢰⠆⠀⠐⠂⠛⠀⠀⠀⠀⠀⠀⠆⠘
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⢴⡆⠾⠂⢀⠀⠀⠀⠘⠉⠀⢀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣰⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠶⣦⣤⣀⠀⠀⢸⡇⠀⣸⡇⠀⠀⣀⠀⠀⣼⡟⣻⡇⣿⢁⣿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠆
⠀⠀⠀⠀⠀⠀⣀⣀⠉⠙⠁⠀⢸⡇⠀⣿⡇⣰⡿⢛⣷⠀⣿⢡⣿⠁⣿⡾⠃⠀⠀⣴⡶⣦⣄⠀⠙⠉⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠀⠀⢻⡿⠛⢿⡇⣿⣧⡾⠋⠀⣿⡿⠁⠀⣿⠁⠀⠀⠈⣿⣦⣾⣿⡏⠘⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠀⠀⢸⡇⠀⢸⡇⠹⣧⣀⣴⡖⣿⡀⠀⢀⢻⣦⣠⡾⢺⣿⠀⠀⣿⡇⠰⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣧⠀⠸⣿⠀⠉⠛⠉⠀⠹⣷⣴⠿⠁⠉⠉⠀⠈⢿⣦⣴⠟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣶⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⣿⢠⣾⠋⠉⣿⠀⠀⢰⡆⣠⣶⡄⠀⣿⡇⠀⢰⣷⠀⠀⣠⡶⢶⣦⠀⠀⣿⣷⣤⣾⠇⢀⣿⠀⢠⣿⡇
⠀⠀⠀⠀⠀⢀⣿⣼⡇⠀⢀⣿⠀⠀⣿⣷⡿⠈⣿⠀⣿⡇⠀⣾⡇⠀⣼⡏⠀⢀⣿⠀⠀⣿⠇⢰⡟⠀⢨⣿⣠⡿⣿⠁⢀
⠀⠀⠀⠀⠀⢸⣿⠸⣧⣠⣾⣿⠀⣸⣿⣿⠇⠀⣿⢀⣿⣧⣴⠿⣷⣠⣿⡇⠀⣸⣿⠀⢠⣿⠀⣾⡇⣠⡿⠛⠋⠀⣿⣶⠟
⣀⠀⠀⠀⢀⣾⠇⠀⠈⠉⠀⠻⣷⠟⠙⠟⠀⠀⢿⡾⠃⠀⠀⠀⠈⠉⠘⠻⠾⠛⣿⣀⡾⠃⠀⠙⠿⠛⠁⠀⢀⣾⣿⠁
⠙⠻⠷⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⣰⡿⢹⡟
⣀⣠⣤⣤⣶⡶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠶⠶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣄⠀⣿⣀⣼⠇
⣿⣿⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣽⣽⣿⣿⣿⣿⣷⣶⣼⣿⣿⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⣄⣤⡄⠀⠠⠶⠎⢀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⣠⠀⠠⠛⠀⠁⣀⠀⠀⠀⠀⢄⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠰⠞⠉⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⡄⠀⠀⠉⠉⠀⠰⠒
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⡀⠀⠈⠀⠐⡄⠀⠀⠀⠀⠀⠀⠈⣆⢀⢀⡄⠤⠖⠁⢲⠐⢀⣄⠀⠀⠀⡐⠀⠰⠀⠀⡔
⠀⠀⠀⣀⠀⠀⠀⠀⢀⡤⠀⠀⣦⣄⡠⠂⠈⠁⠈⠀⡄⠀⠀⢈⠄⠀⠀⠈⠛⠶⡦⡀⠀⠀⡌⠀⠀⠘⠒⢶⡄
⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠨⠛⠈⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠒⠱⣎⠀⠈⠋⠀⠀⠠⠄
⠀⠀⠀⠀⢀⣠⡄⠚⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⣂⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠂⠰⠀⢠⡅
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢃⡔⠀⠠⠶⠒⣤⡤⠄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠦⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣠⡴⠶⠂⠀⠶⢄⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⢀⣿⠟⠀⢀⣤⡶⠐⠚⢶⣄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⣼⡏⠀⠀⣿⠋⠀⠀⠀⠀⣿⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⡐⢻⣷⣿⣿⠆⣤⣤⣿⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣿⢏⢹⣦⡍⠡⣶⡏⢻⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⠛⢿⣶⣴⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣛⣟⣹⠏⠃⠀⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣾⣿⣿⢃⣴⣿⣿⢋⡟⠘⠂⣼⢿⣿⣿⣇⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣦⣹⡏⣼⣷⣿⣿⣾⠃⠀⠀⠛⠀⣩⣿⣿⣿⣿⡵⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣻⣿⣇⠙⣿⣫⣾⠛⢿⣷⣤⢤⣴⡾⠁⠼⣿⣿⣾⡏⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠻⣯⣻⢿⣿⣦⣈⠙⠛⠒⣸⣉⠍⢛⠉⢁⣠⣺⣿⣿⣿⣿⣼⣃
⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣧⠸⣿⣷⣼⣿⣿⣿⠛⢉⣿⠿⢞⢧⣰⣿⠛⠉⠛⠻⡆⢹⢿⣿⣇
⠀⠀⠀⠀⣰⣿⣿⣿⣾⠛⣿⣧⠈⣿⡿⣿⣿⣿⣶⡿⠋⠀⠉⠈⣿⢃⠠⣤⠘⡂⣹⣿⣿⣿⢸⣦
⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣷⣍⣵⣿⣿⠿⠉⠀⠀⠀⠀⣴⣾⣏⣳⡽⠟⣹⣿⣿⠿⣧⣿⣟⠃
⠀⠀⠀⠀⣀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠰⣦⣤⣤⣾⡍⠻⣧⠿⣶⠾⡿⢾⣿⣾⣿⣿⣿⡀
⠀⠀⠀⠀⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠏⣿⣷⣶⣿⣟⡻⣿⣦⣿⡏⡀⠀⠀⠀⠀⠀⣹⣿⣿⡟⣷
⠀⠀⠰⣿⣷⣿⣿⣿⣿⣛⣿⣿⣿⣿⠏⡖⣿⣿⣿⣧⡌⢿⡴⢬⢿⡧⣿⠀⣐⠋⣸⣧⣿⣿⣟⣵⢿
⠀⠀⢰⣯⣿⣿⣾⣿⡿⣿⣿⣿⣿⣏⣠⣷⣿⣿⣿⣿⣿⣼⡅⠀⣠⡀⠁⣼⣽⣿⣿⠛⣭⣍⢿⣿⣶⣷
⠀⠀⢸⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⣠⣿⣿⣿⠿⠟⠻⢛⢻⣞⠛⠟⠙⢿⣧⡀
⠀⠀⠀⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⠜⠃⠀⠙⣧⠀⠀⢶⡄⠙⣷⡀⣷⣷⠙⣿⡦
⠀⠀⠀⠘⣿⣿⣿⣿⡇⢨⣿⠹⣿⡟⢿⣾⣿⣿⣝⠋⢿⣚⣻⡉⠀⠀⣤⣾⣧⠀⢈⡛⣤⣼⣿⣿⢿⣮⣴⡏
⠀⠀⠀⠀⣿⣿⣯⣿⡇⣸⣿⢀⣼⡇⣀⣿⣿⣾⣫⢆⣿⣷⣾⣷⣶⣾⣿⣿⣿⣤⣶⣷⣿⣟⢹⠿⡋⢿⡿
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡏⣸⣿⣿⡯⣿⣿⡿⢁⣾⠋⠀⣿⣟⣿⣿⣿⣿⣿⣿⡿⢹⣏⠹⣏⡀⣷⣈⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣾⣯⣶⣼⣿⣼⢿⡿⣿⣿⣿⣿⠹⡆⢿⡀⠸⣷⢸⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣻⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⢃⣿⣸⡇⣿⣿⣿⣿⣄⣿⡼⣿⡄⢿⣎⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⠏⣸⢷⣿⢱⡏⣺⣿⣿⣿⣿⣇⢿⣿⡘⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⡟⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⡌⣿⣧⡹⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⢀⡴⠛⠛⠛⢶⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⡴⠶⠶⠶⢤⣴⠛⠁⠀⠀⢉⣻⣥⡤⠶⠒⠛⡏⠙⣆
⠀⠀⠀⠀⣠⠶⠋⠉⠉⠉⠛⣾⡋⣀⣀⣠⣤⣴⣿⡶⠶⠛⠋⠉⢹⡇⠀⠀⢀⣼⡇⠀⠘⣆
⠀⠀⠀⣸⣃⣀⣤⡤⠶⠖⢚⣛⣿⠽⠟⠛⠉⠁⢸⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⠉⠀⠀⠀⠘⣆
⠀⡞⠋⣉⣩⣤⣶⣶⠚⠋⠉⠁⢸⠆⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⡆⠀⠀⠀⠀⠘⣦
⢸⠇⢸⠁⢸⠉⠁⢹⠀⠀⠀⣾⣿⠄⠀⠀⠀⠈⢀⣀⡀⢰⣶⣄⠀⠸⣟⠳⣮⣿⡀⠀⠀⠀⠀⠘⣧
⣼⠀⢸⠀⢸⡄⠀⢸⡄⠀⠀⠈⠁⠀⠀⠀⠶⠟⢿⡏⠁⢸⣧⡿⢷⡄⢻⡆⠀⠉⠁⠀⠀⣀⣀⣄⠘⣧⡀
⣿⠀⢸⠀⠈⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠸⠇⠀⠈⠁⠀⢀⣀⡤⠶⠚⢿⢩⡤⠙⣦⠈⢷⡀
⣿⠀⢸⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⣀⣠⠴⠖⢿⣉⣠⠳⡐⠋⣈⣷⡖⠚⠉⢧⡀⢻⡄
⣇⠀⢸⡆⠀⢸⡄⠀⠈⣧⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⢺⡋⣁⡈⢦⠚⣋⣷⡤⠖⠛⣏⠁⠀⠹⣄⣠⠴⢳⡄⠹⣆
⣿⠀⢸⡇⠀⠀⣧⠀⠀⠸⡆⠀⠀⣴⠚⠋⢉⢧⠠⠶⠂⢳⣡⠤⠞⢯⠉⠀⠳⡄⢀⣨⢷⡖⠋⠉⢦⡀⠀⢙⣦⠈⢳⡄
⣿⠀⠈⡇⠀⠀⢸⡄⠀⠀⢻⡄⠀⠘⣇⠛⣉⣨⢷⠖⠋⠉⢳⡀⠀⢈⣧⡴⠒⠛⣇⠀⠀⠹⣄⣀⡤⠿⣞⠉⠈⠳⡄⠙⢦⡀
⣿⠀⠀⣷⠀⠀⠀⢧⠀⠀⠀⢻⡄⠀⠘⣏⠁⠀⠈⢳⡀⣀⡤⢷⡋⠉⠀⠳⡄⠀⢈⣣⡴⠚⠉⢧⡀⠀⠈⢳⣄⡤⠟⢦⡀⠹⣦⡀
⣿⠀⠀⢸⡀⠀⠀⠘⣆⠀⠀⠀⢻⡄⠀⠘⣆⡠⠴⠚⢫⡁⠀⠀⠹⣄⣀⡤⠿⢞⠉⠀⠙⢦⠀⢀⣹⢶⡒⠉⠉⢦⡀⠀⠹⣄⠈⠻⢦⡀
⢻⠀⠀⠘⡇⠀⠀⠀⢹⡄⠀⠀⠀⢻⡄⠀⠘⢧⠀⠀⠀⢳⣤⠤⠒⠛⢧⡀⠀⠈⠳⣄⡤⠖⠻⣍⠀⠀⠑⣄⠀⣀⡽⢶⡋⠉⠳⣄⠀⠙⢦⡀
⢸⡀⠀⠀⢿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠻⣄⠀⠈⢳⡖⠋⠁⠙⣄⠀⠀⢀⣳⣤⠖⠋⠉⢦⡀⠀⠈⢳⣤⠴⠚⠻⣅⠀⠀⢉⣦⡴⠞⠃⠀⠀⠙⢦
⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⢷⡀⠀⠀⠀⠹⣆⠀⠀⠹⣄⠀⣀⡬⢷⡚⠉⠀⠈⠣⡀⠀⣀⡼⠶⣎⠉⠈⠳⢄⣀⣨⠷⠚⠉⠀⠀⠀⠀⣀⠤⠚⠉
⠀⣇⠀⠀⠀⣧⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠘⢧⡀⠀⠈⢯⡁⠀⠀⠙⢦⣀⣠⠴⠛⠫⣁⠀⠀⠈⣳⣤⠶⠛⠉⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⢻⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠻⣄⠀⠀⠙⢦⣠⠴⠚⠙⠦⣀⠀⢀⣈⡷⠖⠋⠁⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⢸⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠙⢦⣀⢀⣠⠼⠛⠉⠁⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⣷⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⢸⡆⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣀⣤⠴⠚⠋⠁
⠀⠀⠀⣷⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⢀⣠⠴⠛⠳⠖⠋⠉
⠀⠀⠀⠸⡆⠀⠀⠀⣀⣷⡀⠀⠀⣀⡤⠴⠚⠋⠙⠧⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⣠⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣱⡞⠀⠀⠀⠀⠀⠀⠈⠢⠃⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣓⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡼⠅⢀⣐⡇⠀⠀⠀⠐⠢⡄⠀⠀⠀⠢⣀⣸⡕⠀⠀⠀⠀⠀⡠⠄⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⣉⡀⣒⠒⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⠁⢀⣀⠆⠚⡆
⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠈⢉⠉⠀⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⢁⣀⡤⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡜⠀⢠⣄⠀⠈⣷⠀⢀⡇⠀⠀⠀⠸⣆⠀⠀⡄⠀⠀⠙⠧⡀⠀⢀⠆
⠀⠀⢠⠒⠢⠔⠈⢢⠀⠀⢸⡗⠒⠒⡇⢀⡾⠙⡄⠀⣿⠊⠉⢰⡖⠒⢄⠀⢻⣄⡜⠀⠀⠀⠀⠀⠀⠹⣣
⠀⠀⠀⠣⡀⠀⢀⠇⠀⠀⢼⠇⠀⢸⠁⣼⠋⠉⢣⠀⢸⡄⠀⢸⡇⢀⡼⠀⠈⡟⠀⠀⠀⢎⢒⡅⠀⠀⠘⡄
⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠈⠂⠀⠀⠀⣼⠉⠁⠀⠀⠸⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠐⣖⠂⢀⡤⢤⡀⠠⠤⣶⠒⠂⠀⠉⠀⢰⡖⠢⡀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⢿⠀⢀⡇⠀⢰⡇⠀⢸⡇⣠⠇⠀⠀⡿⠀⢸⡇⠀⡆⢸⡇⠀⢹⠀⠀⡀⠘⣧⠀⢰⠁⠀⡆
⠀⠠⢄⣄⠀⢸⡏⠉⢲⠀⢸⡇⠀⢸⡟⢄⠀⠀⠀⡇⠀⣿⠦⠤⡇⠘⣧⠀⡼⠀⣾⢣⠀⠸⣧⠃⠀⠀⢃
⠀⠀⠀⠀⠀⢸⡇⠀⡰⠀⠉⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⡿⠀⢠⠃⠀⠛⠋⠀⣼⠓⢺⠀⠀⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠀⣖⡄⠀⠘⠁⠀⠘⠀⠀⠙⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠉⠂⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠓
⠀⠀⠀⠘⠁⠀⢸⠑⡖⢤⣀⠘⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡸⠤⠄⢢⠀⠈⠢⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠕⠒⣒⡒⠥⠘⡄⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠛⠀⠀⠀⠈⠀⡰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠁⣀⡀⢤⢤⣷⠄
⡠⠔⠒⢄⠀⠀⡰⠋⠀⠀⠀⠀⠀⣶⠠⣄⠀⠀⠀⠉⠀⠀⠀⠸⠝⠚⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⢠⡞⢭⣱⠂⠀⠀⠀⠀⠀⣿⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⢻⡿⠆⠀⠀⠀⠀⢀⡴⢯⣍⡢⠁⠀⠀⠀⠀⠐⠛⠻⣿⠟⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠞⠣⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡈⠳⠃⠀⠀⢀⠤⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠳⠎⠀⠀⠀⠀⢠⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡋⠁⠀⠀⢎⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⠂⠀⠀⠀⠀⠀⡔⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢙⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠢⢄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡄⠀⠀⠀⠀⠀⣤⠰⠃⠑⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠈⠢⣄⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⣔⠲⠈⢃⠿⠟⠀⠀⠀⠀⠀⢙⣀⠤⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠓⢄⠀⠀⢈⠀⠀⢸⠀⠀⠀⢀⡤⢤⠀⠙⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠈⠢⡀⠀⠑⠚⠙⢄⣀⠤⡈⠻⢸⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⣴⣿⠙⠬⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣠⣿⣦⡀⠀⠀⠀⠙⡆⡹⠶⠃⠀⠀⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⠀⣴⠛⠫⣸⡿⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢀⣼⣿⣿⣿⣿⣦⡀⠰⠿⠟⠣⡀⠀⠀⠀⠀⢂⠀⢀⡄⠀⠀⠀⠀⠘⠺⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣴⣿⣿⣿⣿⡿⠋⠁⠈⠲⢄⠀⠀⠘⢄⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣠⣾⣿⣿⣿⠟⠉⠀⠀⠀⣀⣤⣶⣿⣦⣤⣨
⠀⠀⠀⠀⠀⠀⣼⡿⠁⢀⣼⣿⣿⡿⠋⠁⠀⢀⣠⣴⣾⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⢰⡟⠀⣴⣿⣿⠟⠁⠀⣠⣴⣾⣿⡿⠟⠋⠉
⠀⠀⠀⠀⢠⡟⣠⣾⡿⠋⣁⣤⣶⡿⠟⠛⠉
⠀⠀⠀⢀⣿⣼⢟⣩⡴⠟⠛⠉
⠀⠀⠀⣾⠿⠛⠉⠁


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