Strawberry dog! Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⣷⣶⣶⣤⣤⣤⣤⣤⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠁⠀⠞⠋⠉⠀⠀⢚⣻⡿⣿⡿⠛⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⠟⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣼⣿⣶⣶⣷⣶⣦⣄⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⢀⣤⣶⣿⣶⣿⣿⣿⣿⡷⠆⠀⠀⠖⠛⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠋⡿⢻⡿⠟⢿⣿⣿⣿⣷⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠮⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠘⢫⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠹⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⠗⣒⠾⠁⠀⠤⢙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣖⠒⢾⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠉⠘⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢣⣀⡦⠐⣳⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠛⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠙⣆⠀⠀⠀⣸⠿⣶⣄⠀⠀⠀⠀⠀⣴⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠘⠦⢤⠀⠻⡘⠛⡫⠀⠀⠀⠀⠀⠈⢉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠐⢫⡀⠀⠉⠁⠀⠀⠀⠀⠈⠓⢒⡟
⠀⠀⠀⠀⠀⠀⢀⠖⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⡴⢫⡄
⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡴⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡤⠚⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠸⡀⠑⢤⣀⠤⠖⡲⠒⠒⠒⠒⠤⠤⠄⣀⡀⡇⠀⠀⠀⠀⢀⠆⣸⠁⠀⠈⢩⠯⠤⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡔⠁⠀⠀⢃⠀⢀⠀⠀⠀⠀⡠⠂⠀⠙⢄⠀⠀⠀⠸⣄⣯⡙⠢⠤⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠢⠀⠠⠔⠀⠀⡀⣀⠀⠉⠒⠒⠒⠚⠉⠈⠱⡖⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡔⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⣧⠆⡐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⡧⠤⢤⣀⡀⠀⠈⠁⠔⠂⢡⠀⠀⠀⣆⡤⠺⡍⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣠⠞⠀⢀⡔⠃⠈⠉⠉⠛⠛⠛⢻⠀⠀⠀⢳⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠙⠒⢤⡀⠀⢬⢹⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠣⢄⠀⢉⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⣂⣹⠧⠤⠼⠛⠁⠀⠀⠀⠀⠀⠈⢦⡀⠀⢘⣆⡿⠤⠼⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⡆
⠀⠀⠀⠀⣠⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮
⠀⠀⠀⠈⢉⡿⠟⠛⢹⣶⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾
⠀⠀⠀⠀⢸⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⣿⡁
⠀⠀⠀⠀⠀⠻⣄⡀⠸⢛⣛⣛⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⡷⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠐⠋⠉⠀⠀⠙⠛⣿⠿⢤⣱⠀⠀⠀⠀⠀⠀⠀⠐⠚⣙⣧⣦⡖⠀⠀⠀⠀⣾⠁⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠻⣧⠀⠀⣀⢠⡟⠀⠀⠀⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠀⠀⠉⠀⠀⠀⠀⠐⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⢀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⣿⣿⣿⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣦⣿⣷⣷⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡟⣭⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣾⣿⣭⣽⣿⡅⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡤⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⢠⠟⣙⣙⣄⣹⠴⠶⠿⠓⣴⡆⣠⠊⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣿⣳⠽⠗⠚⠟⠉⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⢞⠵⠟⠑⢄⠀⠀⠀⠀⡠⠐⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⠄⠀⠈⠀⠀⢀⠊⠔⠉⠉⠛⠦⣄⣀⣀⣤⢤⡶⣞⡷⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢀⠤⡄⠀⠀⠀⠂⠀⠀⠀⠠⡀⠀⡙⠀⠀⠈⣗⡷⢊⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⡋⣤⡷⠀⠀⠀⠀⣠⠖⠶⣄⠀⠀⠇⠀⠀⠀⢹⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠘⠛⠁⠀⠀⠀⠀⠁⢶⣾⣿⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠐⢖⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠠⡄⢿⣭⡦⠀⠀⠀⠡⠚⠻⠃⢀⡠⡄⠤⠤⢴⠇⠀⠀⠀⠀⠀⠀⢺⠆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠣⠤⢅⠀⠀⣀⠆⠀⠀⠀⠀⠀⠑⠀⢀⢀⠞⠀⠀⠀⢀⡀⠀⠀⡸⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠂⠉⠉⠀⠀⠀⠀⢀⠀⣠⣧⠔⠓⡿⠒⠔⠒⠊⠁⠉⠉⠋⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠳⠤⠰⣄⣴⡠⠔⠓⠊⠁⢀⡤⠊⠀⠀⠠⢅⠀⠀⠀⠀⠀⠀⢰⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⢦⡴⠖⠒⠋⠁⠀⠀⡀⠀⠂⠀⠑⠠⠀⠠⠐⠀⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⢦⡀⠀⢀⠀⠀⠀⠘⡷⠀⠀⠀⠸⡀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢳⡾⠀⠀⠀⢀⡷⠒⠺⠚⢏⡙⠦⣀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⠚⠀⠀⢀⡨⠇⠀⠀⠀⢸⠀⠀⠀⡴⢒⠁⢀⡠⠟⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣀⣀⣀⣇⡆⣰⠀⠀⠀⡞⠀⠀⠀⢧⣇⣀⣾⡆⣴⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠶⠚⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⣦⡬⣧⣾⡤⠶⣶⣒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠚⣱⠋⠀⣠⠋⠀⠀⠀⠀⢳⡀⠀⠈⠳⣄⠈⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⡾⠁⠀⠀⡏⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠸⡟⠒⠺⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⠓⠒⠚⠋⢷⠀⠀⠀⣠⠖⠁⠈⠙⠛⠛⠚⠃⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣤⠀⠀⠀⠈⢣⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠀⠀⢠⣦⠀⠀⠀⢠⡄⠀⠀⠀⣶⡄⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⠋⠀⠀⠀⢰⡆⠀⠀⠀⠀⢴⡆⠀⠀⠀⠛⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⡀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠉⠁⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢰⡆⠀⠀⠀⠀⢰⡆⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢰⡆⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠈⠁⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠛⣩⡽⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠛⠉⠀⠀⠀⠀⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠷⣶⠶⠛⠋⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⠶⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⠆⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢿⡀⢸⣇⠀⠀⠀⠀⠀⠀⣴⠟⣷⡏⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⣸⠃⠀⡴⠟⠛⠷⠄⠈⢷⣼⡿⣦⡀⠀⠀⠀⣸⠇⠀⠉⠀⠀⠠⠞⠛⠳⠦⠀⠀⢹⡀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢠⡾⠁⠀⠲⠂⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠈⠙⠷⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠰⠒⠀⠘⣧⡀
⠀⠀⢀⡿⠁⠀⠀⠀⠀⢠⠁⢸⡇⠀⠀⣠⡶⠛⠛⢷⣦⡀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⢀⣴⡿⠛⠻⣶⣄⠀⠀⠀⢻⡄⢠⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣾⠃⠀⠀⠀⠀⠀⡈⠀⣾⠀⠀⣰⣿⣇⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⣸⣿⣧⠀⠀⢸⡇⠈⡄⠀⠀⠀⠀⠀⠸⣇
⠀⣸⠇⡀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣿⠀⠀⠈⣷⠀⠁⠀⠀⠀⠀⠀⠀⢹⡄
⢀⡟⢠⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢫⠙⣿⣿⣿⣿⣿⣿⠇⠀⠀⣀⣀⣀⣀⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣶⡈⣷
⢸⣷⢿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠼⢧⡙⠻⠿⠟⣻⢏⡴⠚⣉⣥⣤⣤⣤⣌⣉⠓⢦⡙⣝⠻⠿⠿⢛⡵⠧⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣿⣷⣽
⠸⡟⠸⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠉⠉⢠⠞⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠱⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠈⣿
⠀⠁⠀⢿⡀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠻⢿⣿⡿⠛⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢰⡟⠀⠘
⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠙⠷⣦⣄⣸⡇⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⣶⣤⣤⡴⠞⠋⠈⠙⠶⢦⣤⡤⣶⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁⢻⣆⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⠾⠛⠋⠁⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠈⠉⠙⠻⢿⣛⣛⣛⣛⣛⣛⣭⠟⠋⠁⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠠⢀⣀⡴⣫⠖⠒⠒⢦⡙⣄⢀⡠⠄⢀⣠⠶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠙⠶⣤⠟⣴⠉⠰⠄⣀⠤⢻⡌⢻⣤⠖⠋⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠉⠳⢬⣓⠦⣄⡤⢖⣫⠴⠚⠁⠀⠀⠀⠀⠸⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠠⣿⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡇⠘⡀⠀⢹⡇⠀⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⠀⡀⠐⠄⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⠒⠢⡀⢸⡇⠀⠀⠀⢸⠟⠶⣤⣤⡾⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠦⢿⠀⠄⠠⠂⠀⠀⢸⣿⡿⠳⠶⠶⠶⠶⠶⣿⠀⠀⠀⠄⠀⠁⢸⡧⠤⠄⠀⣿⣦⣤⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⢸⡅⠠⠤⠤⠄⠀⣼⠙⢷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠤⠤⠄⠀⢸⡁⠀⠀⢀⠈⠻⣆⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣇⡼⠋⠀⠀⠀⠀⠀⠀⠈⢻⣾⡇⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣦⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⣰⠀⠀⠀⠀⡄⠀⠀⢻⡇⠀⠀⠀⣾⠁⠀⠀⡦⠀⠀⠀⢰⡀⠀⢸⣶⠶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣄⣿⡀⠀⠀⢀⣟⣄⣀⣼⠇⠀⠀⠀⢻⣤⣀⣄⣧⠀⠀⠀⣸⣇⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠤⢤⡄⢤⣦⣤⡖⠲⣶⠠⣤⣦⣤⠒⠲⡦⠰⣶⣶⠖⢤⡀
⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢀⣤⡀⠀⣿⣿⡇⢀⠈⠁⢸⣿⣿⡇⠀⠈⠀⢻⣿⣿⠀⠀⠁⠀⣿⣿⠀⠀⡇⠀⣠⣤⠀⢀⡀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⣾⣿⠛⠿⠿⠟⢿⣿⠇⠀⣿⣿⡗⡿⠀⠀⠀⣿⣿⡗⠿⠀⠀⢸⣿⣿⠲⠇⠀⠀⣿⣿⠀⠀⡟⠀⢿⣿⠟⠛⠛⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠷⠀⠀⠀⠼⠿⠿⠷⠤⠾⠀⠾⠿⠿⠧⠴⠇⠾⠿⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡖⠰⡆⢰⡆⣴⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⢤⡀⠀⣿⡇⠘⡗⢸⡇⢹⡇⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣺⡆⠀⢮⣢⡈⠁⠀⠉⠈⠁⠈⠁⣠⠛⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⣇⠀⠀⢻⠱⠀⠀⠀⠀⠀⠀⢠⢻⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⣼⣁⡐⢒⠁⠀⠀⠀⠻⠿⡗⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡴⠎⠋⣡⣭⣾⣷⡄⠳⣀⠀⠱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣡⡆⢔⣵⡞⢁⣀⣴⣤⡺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣈⣭⣿⢀⣿⡀⢘⣿⡀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⣼⢿⣿⡄⠛⣷⣼⣧⡁⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠈⣯⡄⣏⣿⣿⣟⣻⣿⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠘⣿⣿⣿⣿⣶⣜⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠛⢲⡄⠀⠀⢀⣶⣿⡿⠛⢦⡀⠀⠀⠀⣠⣼⣿⠟⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢿⠀⠀⣼⣿⡿⠀⠀⠀⣿⠀⠀⣼⣿⣿⠃⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣼⠀⢸⣿⣿⡇⠀⠀⠀⢸⠀⢰⣿⣿⣿⠀⢠⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⡿⠀⠸⣿⣿⣇⠀⠀⠀⣾⠀⠸⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢀⡾⠁⠀⠀⢿⣿⣿⡀⠀⣰⠇⠀⠀⠹⣿⣿⡀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠏⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠀⠉⠛⠿⠷⠛

⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣤⣴⣦⣤⣶⣶⣶⣶⣶⣦⣶⣿⣿⣿⣷⣤⣤⣤⣤⣀⣀⣀⣀⣀
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⣼⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠉⠙⠋⠈⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠉⠛⢿
⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠦⢼⣿⣁⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣯⠴⣦⣠⢤⣀⡶⢼⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⣶⠆⠀⠘⢁⠀⠉⢁⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⣀⠀⠐⠿⠃⠀⠙⠃⠸⠿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠸⠋⠀⢀⠀⠀⠀⣤⡀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠐⠿⠃⠀⠀⠛⠁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣠⡄⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⣠⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠒⠐⠂⠠⢀⠀⡀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠔⢰⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠔⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⠐⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢀⠆⠀⢂⣁⠀⠀⠀⠀⠀⠀⠑⠀⠘⢇⠀⢀⡱⠄⠐⠊
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢁⠀⠀⢡⣰⣷⠀⢀⠀⠐⡡⣬⡓⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡩⢫⣾⣛⣦⠐⠿⠛⠃⠀⠀⠀⠰⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⡀⠀⠀⠙⡛⠁⠀⠀⠡⠀⠁⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⢲⠦⠤⠤⠤⠔⠠⠔⠊⠀⠈⠉⠓⠈⠠⡶⠿⡖⣩⣷⣇⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢤⠀⠀⠀⢀⠄⠀⠈⠂⣤⣤⠈⡍⢉⣀⠀⠸⠏⠉⠹⢠⢴⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⣤⠀⠀⠀⠀⠷⣤⠠⠄⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠂⠀⠠⠞⠀⠀⢑⡆⠀⠀⠀⠠⢀⣀⠐⠀⠀⡈⠋⠂⠰⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠄⠠⠚⡁⠀⠀⣠⣂⢀⣁⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡠⠔⠊⠁⠀⠀⡀⠀⠀⠈⠐⡤⠐⢂⡉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢘⢀⠃⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠆⠀⠠⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⢀⠀⠒⠄⠀⠀⠀⠀⠀⠀⡠⠀⢄⠈⠀⠀⢁⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠂⠈⢀⣉⡀⠀⠀⠀⠔⠁⢀⣈⠒⠘⠳⡀⢀⣀⠡⠐⠂⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⢁⠀⠀⠁⣐⣿⡆⠀⠀⠀⠈⡡⣤⡹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢉⠝⣱⡖⢻⣄⠚⢿⠿⠃⠀⠠⠀⠀⡄⠀⠀⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⡀⠀⠠⠘⠻⠟⠋⠀⠀⠢⠀⠂⠁⢀⠜⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠱⠈⠂⠦⣄⣈⣀⠀⣀⡠⢁⡠⠤⠊⠉⠁⠂⣄⠀⠀⠠⠎⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠐⢇⠀⠉⠉⠉⠀⢀⠅⠐⠄⠀⠀⢀⠈⠃⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⡘⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠒⠛⢈⠀⠀⠀⡜⠈⠫⣉⡁⠀⠀⠀⢸⠀⠀⠀⠀⠠⠠⢀⣄⣀⠀⡂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⣰⠇⠀⠀⠀⢸⠒⠢⠌⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠊⠡⢄⢀⣀⡰⠦⠤⠤⠄⠀⠀⠀⢁⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣀⡠⠚⠓⠀⣠⣄⠐⠻⠆⠀⠠⡀
⠀⠀⠀⠀⡁⢶⠄⣀⢀⣌⣥⠶⠄⠤⠀⣁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⠀⣀⣤⡤⠶⣶
⠀⠀⠀⠀⣀⠠⠆⢁⠤⠄⠰⠄⠴⢤⠐⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠼⠛⢉⣠⣶⠿⠷⠒⠒⠲⠤⣤⣀
⠀⠀⠀⠀⠉⠰⡶⠀⠀⠀⠀⠂⢤⠄⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠴⠋⡏⠀⣀⠀⠀⠀⡀⢄⡐⠂⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⡀⡇⢸⡇⠀⢠⠊⣼⠛⠃⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⠀⠇⠁⠘⣇⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⡴⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠰⠈⠀⢰⠈⠃⠹⣇⠀⠀⠀⠀⣰⡾⢿⣶⣤⡀⠀⠀⢰⠀⠀⠀⠀⠼⠿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠇⠀⡀⠃⠘⡀⠆⠘⡄⠙⣦⠀⠀⢸⡟⠀⣴⣿⣿⣷⠀⠀⢈⠀⠀⠀⠀⠀⠀⠉⡸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⢡⠘⡀⢡⠘⢂⠰⡀⠘⢧⠀⠈⢇⠀⠊⠉⠁⢘⠀⠀⠸⠀⠀⡐⠶⠤⣉⣋⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡀⠠⠀⠄⠈⡄⢆⠈⡄⠡⠀⠈⣧⠀⠈⠑⠒⠒⠒⠁⣀⠔⠁⡠⠒⠀⣴⣒⣽⣿⡇⠀⠁⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣹⠀⠀⠀⠀⠀⠀⠀⠸⡇⢡⠀⢆⠈⣀⠰⡈⢦⠘⡀⠘⡀⠘⣧⠀⠀⠠⠤⠀⠁⠀⠀⠎⠀⠀⠀⠙⠛⠻⠛⠀⠀⡙⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠢⠈⠄⠈⠄⢡⡀⢃⠐⠄⠱⠀⣿⠀⠀⠀⠀⠀⠀⢀⠉⠀⠴⢇⡀⠀⢀⣠⠛⠦⠴⢃⡼
⠀⠀⠀⠀⠀⠀⠀⣿⠠⠐⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢣⠈⢀⠘⡄⠲⡀⠆⠈⡄⠃⢸⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠉⠓⠉⢁⡠⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠄⢂⡈⠷⣄⠀⠀⣀⣠⣄⣤⣀⣀⢻⡄⢣⠀⠆⠰⠄⢡⠈⠂⠰⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠃⠄⠀⣀⣀⣠⣤⡶⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣶⠉⡠⢊⣭⠟⠋⠁⡤⠈⠁⠀⠀⠈⢳⡀⢠⠘⡀⠰⠀⡄⠘⡀⢆⣿⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⣶⠞⠟⠉⡄⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⠟⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢷⡀⠆⢁⠀⡆⠀⠀⠃⣸⣏⣉⠉⠉⠉⠉⠉⢋⣀⣠⡴⢿⡅⢨⡀⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠈⠀⠀⠈⠂⣸⠏⠀⠉⠙⢻⠛⠛⠛⠟⡉⠁⠘⡀⠙⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠳⢀⠀⠀⠀⠀⠀⢀⠻⣾⣀⣀⣠⣤⠿⠁⠀⠀⡇⠀⠄⠀⠠⠁⠀⠈⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⣧⠆⠀⢈⠀⠀⠋⠈⠑⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠈⠀⢠⠆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⣰⠟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠉⠑⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⡴⠚⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⠓⠦⠤⢤⣠⡇⠀⠀⠀⠀⠀⠀⢸⡧⠔⠛⢻⠁⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⢹⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣧⣀⡀⠀⠙⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣳⡄⠀⢻⡀⠀⠀⠀⠀⡀⠤⠐⠻⠤⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠠⠀⢁⠀⠀⣈⠳⡄⠈⠳⣄⠀⠀⠀⣽⠀⠀⠀⡀⠄⠁⠀⠀⠀⢉⡓⣾⣧⠀⡠⠄⠁⠀⠀⢤⣀⠲⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠀⠀⠀⠀⣧⠀⢸⣆⡿⠀⠀⠉⠻⣭⣄⣨⣷⠐⠁⠀⠀⠀⠀⠻⡄⠈⡧⢸⡟⢧⡀⠀⠀⠀⠀⠀⢹⠄⣸⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⢤⣤⡴⠧⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⣀⣼⣁⣴⠷⠋⠀⠀⠉⠓⠦⠤⠤⠴⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠰⠤⠔⠂⠼⠦⠄⠖⠒⠀⠀⠂⠈⠜⠠⠴⠤⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠁⠾⠹⠇⠀⠰⠁⠾⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠀⡠⠛⠛⠉⠀⣦⣄⠐⠻⠯⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⢤⣀
⠀⠀⠸⢃⢥⡀⠀⡀⣀⡛⣃⣄⣀⣀⣀⣀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣀⣀⠀⠠⠉⠳⣤⣀
⠀⠀⡆⠛⠨⡱⠌⠀⠛⠉⡉⡀⣉⣉⠀⡁⢑⢇⠀⠀⠀⠀⠀⢲⣤⠊⡏⠀⢀⣀⣠⠤⠤⢤⣤⣧⡞⠁⠈⠱⣄⠉⠂⠁⠀⢉⠗⠲⡄
⠀⠀⠰⣦⣑⣃⠋⠍⠉⠁⠀⡁⠉⠙⠅⣬⣡⠊⠀⠀⠀⠀⠀⢸⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠘⢦⠀⠀⠀⠸⡀⠀⢹⡄
⠀⠀⠀⠀⠨⠟⠂⠐⠀⠀⠐⠒⠲⠖⠀⠙⠛⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠙⢦⠈⢧⡀⠀⠀⠈⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠳⣄⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡹⣄⠈⠓⠦⣤⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠧⡘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣤⣆⠱⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠔⠁⠈⠑⡄⠀⠳⡄⠀⠈⠀⠀⠀⠀⣰⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠞⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢄⠀⠀⢀⠆⠀⠀⠙⢦⠀⠀⠀⠀⣼⠛⠉⡙⠢⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠁⠈⠁⠀⠀⠀⠀⠈⢳⡀⠀⠸⣷⣷⣴⣮⠂⢱⠀⠀⠀⠀⠀⣼⣡⣿⠃⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⠉⢂⠀⢷⠀⠀⠹⣿⣿⣟⡤⠎⠀⠀⠀⠀⠀⠉⠉⠋⣀⣠⠃⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣀⣀⠀⠀⢨⠀⠀⠀⠀⢸⠀⠘⣇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣾⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡎⠀⠀⢱⠀⠀⠑⠤⠤⠔⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠽⠂⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣤⣀⣀⠀⣠⣟⠓⠦⣤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠋⠀⠙⠢⣄⡉⠙⠒⠠⠤⠶⣴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⢤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠔⠒⡄⠀⢀⠊⠉⠉⢢⠀⡂⠉⢘⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠈⠢⠤⠃⠀⠘⡀⠀⠀⡠⠀⢑⠀⠈⠁⠰⢧
⠀⠀⠀⢶⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠒⠒⠦⣀⠀⠀⠀⠉⠉⠀⠀⠈⠁⠉⠲⠁⠘⣇
⠀⠀⠀⠀⠳⡄⠱⡄⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⢀⡠⠤⢄⠀⠀⠀⠈⢻⡄⠢⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠹⣀⠸⣄⠀⠀⠀⠀⠀⢸⠁⢈⠄⠀⡎⠀⠀⠀⢱⠀⠀⠀⠈⡧⠤⠃⠀⠀⠀⠀⠘⡏⠀⠀⢠⠒⢺⢧⡀
⠀⠀⠀⠀⠀⠀⢿⡐⠉⠲⣄⣀⣀⣀⣼⡉⠁⠀⠀⠡⣀⣀⣀⠌⠀⠀⠀⠀⢹⡀⠀⢀⠀⡀⠀⠀⠱⡀⠀⠀⠒⠊⠀⠹⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠸⡀⠀⢸⠘⣧⠂⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⣈⣇⠀⠠⠀⠔⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⣈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢬⣬⣤⣤⠼⢧⡀⣀⠇⠀⠀⠀⠀⢀⠴⠚⠉⢉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⣄⠀⠀⠀⠀⢸⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⡄⠀⠀⠀⠀⠀⢦⠀⠘⡄⢸⡦⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠦⠤⠤⠤⠴⠾⠓⠋⠙⢦⣀⡀⠀⢀⣼⣀⣠⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⣀⠀⢀⠜⠂⠀⠀⣀⡀⠀⠀⠀⢀⣤⠉⡏⢳⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠏⠙⢾⡆⣸⡞⢁⡸⠀⠀⠀⠀⢸⢸⠀⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠄⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢠⣾
⠀⠀⢀⠠⠜⠷⢾⣿⣿⡿⠋⠁⢀⡀⠀⠀⠸⢸⢠⡄⡇⠄⠀⠀⠀⠀⣴⣶⣿⡿⣿⣿⣿⣿⡖⠚⣿⣛⣆⡀⠀⠀⠀⠀⠀⢀⣸⣦⣷⣿⣿⣷⡁
⠀⠀⠈⠐⢶⡶⢿⡿⣿⡷⢶⡀⠀⠀⠀⠀⠀⣆⢸⠀⡇⠢⡇⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣟⡟⢛⣉⠩⠤⠃⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⣋⠠⠻⡇⠈⠻⠄⣱⠀⠀⠀⠀⣧⣿⣿⣿⣷⣷⡇⠀⠀⠈⠹⠿⣿⡯⠡⠌⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣀⠠⠜⠃⠘⠂

⠀⠀⣾⠟⣳⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⣄⡀
⠀⠀⠻⠧⢿⣷⠛⠁⠉⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡽⡅⢬⡇⣐⣟⢻⡝⣦⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⠛⠛⠟⠳⣶⣤⡀
⠀⠀⠀⠀⠀⣿⡀⠀⣾⡇⠀⠀⠀⢸⣟⠛⠛⠁⢲⣶⣤⠀⠀⠀⢸⡟⣯⣭⣁⣸⣗⣏⣭⠾⠱⣼⣇⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⢻⣿⣆
⠀⠀⠀⠀⠸⣯⠁⢀⡿⠀⣀⡀⠀⠀⠹⣆⠈⠀⠈⠁⠀⢱⠀⠀⢸⡷⣟⢦⣹⣿⣿⣿⣿⣆⡱⣿⣿⠀⠀⣠⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧
⠀⠀⠀⠀⢶⡟⠀⣾⢠⡞⣉⠝⠀⠀⠀⠹⣆⠀⠀⠀⢀⠎⠀⠀⠘⣷⣹⡿⣽⣽⠟⢯⣚⠲⢍⣿⠇⠀⠀⠛⢤⣥⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡾
⠀⠀⠀⠀⠀⣿⠚⠿⢏⠀⠁⠀⠀⠀⠀⠀⠈⠒⠴⠒⠋⠀⠀⠀⠀⠘⢿⣵⡶⢧⣼⣮⡿⣲⡿⠋⠀⠀⠀⠀⠀⠙⢿⣵⣄⢀⣀⣀⢒⣀⣤⣤⣴⣿⠟
⠀⠀⠀⠀⠀⢿⡄⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣽⣿⡿⠅⢀
⠀⠀⠀⠀⠀⢀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡤⢤⡤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠻⠿⠟
⠀⠀⠀⠀⢠⡅⢀⣭⣴⣤⡀⠀⠀⠀⠀⠀⢐⢾⣸⠿⣼⣼⣿⢁⡀⠀⠀⠀⠀⠀⢰⣬⣖⠉⠀⢹⠀⢈⣶⣶⣾⡿⢷⡄⠀⠀⠀⠀⣳⣄⠸⢀⣤
⠀⠀⠀⡘⠉⠉⣾⣷⠻⣯⣭⣥⡖⠀⠀⡬⠉⠹⣏⢀⣿⣇⠀⣿⡛⠂⠀⠀⠀⡰⠋⠀⠀⢀⣰⣾⣷⣿⣿⣿⢿⡷⠾⠃⠀⠀⠐⠾⠿⠿⠶⢿⣷
⠀⠀⠨⠟⢛⡿⣿⠈⢻⠃⣤⡜⠀⠀⠀⠀⠀⠀⠘⠿⠻⣿⡿⣿⡟⡧⠀⠀⠔⠁⠀⠀⠀⣴⡟⠛⢿⣿⣿⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢨⣻⣿⡗⠸⠃⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠉⢹⣿
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢠⣀⣀⣡⣀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠒⠒⠒⠀⠑⠉⠉⠓⠈⠑⠢⢀⠊⠀⠀⠀⠀⠀⢸⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⡆⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⢀⡴⠋⢋⢣⣄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⠉⠓⠁⣠⠄⠀⠀⠀⠠⢀⠶⢀⡴⣦⠙⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⣦⡿⢛⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣇⠀⠘⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡟⢡⠞
⠀⠀⢀⡤⠊⠁⠀⠀⣀⡀⠀⠑⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢸⡁⢤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦
⠰⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠳⡄⢣⠈⠳⠖⠤⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⡀
⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⢡⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⡌⠀⠀⠀⠀⠀⢰⠁⠐⠂⠤⠤⢀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠒⠊⠁
⠀⢣⡀⠀⠈⠢⠄⠀⠀⠤⠐⠁⠀⣠⠊⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠈⠢⠄⣀⡀⠀⢀⣀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⣠⠁⠛⠶⢤⣤⡀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢄⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠂⠀⢀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠑⠂⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⣄⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠐⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⢀⡎⠀⠀⠀⠀⠀⡈⠋⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠈⣀⠀⣀⠔⠉⠀⠀⠀⣠⠔⠁⠀⠀⢀⠀⡔⠁⠀⠀⠀⡜⠀⠀⠀⠀⡠⢊⡉⠡⡶⠖⠂⠉⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⢀⡠⠚⠁⠀⠀⠀⡠⠃⠀⠀⠀⠈⠉⠏⡀⠀⠀⠒⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⠤⠄⠀⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⠴⠉⠀⠀⢀⡠⠴⠋
⣷⣿⣷⡾⣶⣿⣶⣷⣶⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣾⣿⣾⣶⣶
⣿⣿⣿⣀⣀⣤⣤⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⢳⡀⠀⠀⠀⠀⢂⢄⠀⢀⡛⣣⣀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⡴⠱⡀⡇⠀⠀⠀⠀⣈⠀⠢⠈⠄⠀⠰⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠁⣠⢬⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣜⠁⠀⠇⢻⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠰⠀⠙
⠀⠀⠀⠀⠀⠀⢠⠃⢀⡗⠀⡉⠦⡑⣄⠀⠀⠀⠀⠀⡸⠁⠀⢸⣁⡀⠈⢃⢸
⠀⠀⠀⠀⠀⠀⡸⠀⠈⡇⠈⢀⠔⠙⣌⠣⣠⡤⠒⠒⠓⠒⠒⠛⠢⠤⣀⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⠐⠀⡠⠂⠉⡆⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⣆⠊⢀⠔⠁⠀⠀⠀⠀⠀⠁⠐⢄⡀⠀⠀⠀⠀⠀⠉⢣⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠻⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠈⠉⢧
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠞⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠚⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⣉⣷⡄⠀⠀⡇⠀⢀⠡⣾⡗⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⣬⣿⣿⠀⠀⠇⠀⠈⠛⠭⣀⣝⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢣⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠺⠟⠁⠀⠰⠀⠀⠀⠠⣶⣯⣿⡇⠀⠀⡍⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣗⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠮⣀⣀⡈⢹⠞⠀⠀⡳⠇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⣀⠴⡋⠀⠀⢀⡇⢀⠒⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡶⠶⣤⣂⣈⣀⣀⣠⣤⣤⠶⠚⠉⠀⠀⠈⢳⡤⠞⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠲⠤⣦⣀⣀⣤⠤⠞⠁⠀⠀⠀⠀⠀⠄⠀⢳⠀⠀⠀⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⠀⡤⠀⠀⠰⠀⠀⠀⠀⠀⡠⢼⠀⢸⡇⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠲⢤⠼⠀⠀⢀⠐⠀⠀⠀⢠⠀⢀⠎⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠉⠦⣀⠀⠀⠀⠘⡄⠀⠀⠀⠈⣴⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡏⠉⠒⡶⠲⡇⠀⠀⠀⠀⢹⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⠀⠀⡇⡴⠚⠁⢰⡦⠤⠤⠄⠀⢸⡄⠀⠀⠘⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢜⠀⣴⠀⠀⠀⣠⠃⢇⣧⢰⡇⢰⠀⠀⡄⠀⢸⡆⠀⠀⢰⢈⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠦⠼⠶⠒⠚⠁⠀⠀⠉⠉⠳⠼⠦⠤⠽⠖⠊⠉⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠠⠆⠤⠀⠄⠀⠀⢰⠂⢀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣉⡠⠠⠀⡀⢗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡷⠞⠉⠁⠀⠉⠉⠉⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠁⠈⢧⡀⠀⠀⠀⠀⣀⠔⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡉⠉⠢⢄⡨⠷⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⢀⣩⡿⠟⠛⠓⢤⣞⠉⠒⠲⢤⡀⠈⠙⢦⣱⣄⠀⢄⠀⠀⠀⠀⠀⠀⢸⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠷⣴⡟⠁⠀⠀⠀⢠⠋⣷⡑⢤⡀⠀⡹⠀⠀⠀⠛⠈⠓⢦⣑⡄⠀⠀⠀⢸⣸⠣⡄⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⠎⠀⠀⠀⠀⢀⠇⢰⠁⠹⡦⡽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⢀⣾⡃⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡎⠀⠀⠀⠀⠀⢸⠀⠈⡄⠀⢇⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⢀⣇⡴⠛⠄⣧⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠋⠁⡏⢀⣤⡶⢿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⢠⠇⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⣿⣤⡀⢹⠀⠀⠀⠀⠀⠀⢠⣿⠀⢫⡞⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠻⣿⣟⢉⡘⠀⠀⠀⠀⠀⠀⠘⣿⣧⠙⢧⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠴⡆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠐⣄⠀⠑⢼⡀⠀⠀⠈⠀⠀⠀⠀⠀⣁⠀⣀⠀⠀⠀⠀⢸⡆⠀⣸
⠀⠀⠀⠀⠀⠀⢠⠏⠘⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⣀⠀⠀⠻⠷⠋⠀⠀⠀⠀⣸⠁⠀⢹
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠘⢦⠀⠀⠀⠈⠒⢤⣰⠆⠒⠁⠀⢀⡼⠃⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠙⢦⡀⣀⣠⠤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⣧⣀⣀⣀⡀⢀⣐⣀⣠⠤⠞⠉⠀⠀⠀⠀⢀⢈⢦
⠀⠀⠀⠀⠀⠀⢶⢷⠀⠀⢀⡴⠋⠁⠀⠀⠀⢰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢙⣉⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠱⡬⠂
⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⡜⠀⠀⠀⠀⢀⣤⣏⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠻⠿⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠇⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡼⢧⡀⠀⢀⣸⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡽⠁⠀⠉⠉⠙⠦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠸⡀⠀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡞
⠀⠀⠀⠀⠀⠀⠙⢓⡎⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡇⠀⠀⠀⠀⠀⠀⡸⢁⠀⠀⠀⠀⠀⢧⡜⠀⠀⣧⡀⠐⡄⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡙⢦⡘⢦⡀⠀⠀⠀⠸⣾
⠀⠀⠀⠀⠀⠀⠀⢨⣸⠀⠀⠀⠀⢀⠄⠀⠀⡇⠰⡀⢈⠳⢄⡀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢳⣀⠉⠑⠛⠓⠒⠲⠶⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣠⠖⠋⣠⠞⣰⠓⣶⣹⠿⠛⠦⣌⡉⢲⠊⢁⡞⠀⠀⢀⣄⣠⠟⠒⠛⢿⡉⢉⠉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢭⣖⠒⠉⠉⠉⣸⣀⣷⠗⠲⠦⠶⠿⠛⠙⣠⠏⣀⠄⣠⠞⠉⠀⠈⢦⠈⣧⡇⢈⡇⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠊⠙⠲⠤⠤⠴⠟⠚⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢗⠀⠀⣠⡀⠄⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠊⠐⠉⠛⠘⠁⠛⠘⠃⠛⠑⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠲⠄⢲⡀⠀⠀⠀⠀⠀⠐⠃⠚⠗⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠈⠀⠀⠈⠛⠧⡀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠀⠀⠀⡁⠘⢂⡀⢀⠉⠀⠀⠡⠀⠀⠀⠀⢰⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠐⠀⠀⠱⣄⠙⠶⠾⠟⢯⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡆⠀⠀⠀⢸⠃⢳⠠⣾⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠁⠀⣈⣀⣘⢷⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⣒⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠒⢂⡼⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⡴⠋⠀⠀⠀⢀⡤⠤⠤⠐⠶⡉⢠⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⡃⠲⠀⠀⠔⠁⠀⠀⠀⠀⣀⠀⢺⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠲⠀⠀⠀⠀⠀⠔⠋⣀⠈⠸⣿⣿⣷⣴⣷⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠶⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣆⠀⠀⠀⠄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡄⠀⢸⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠃⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣉⡟⠻⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢸⣿⣿⣿⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣷⣤⣤⣤⣤⣤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣤⡴⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠉⠀⠀⠀⠈⠁⢀⠈⠦⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⣠⣈⣀⣀⣈⣄⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡛⡏⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡹⠃⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⣸⣿⣿⣇⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢂⠀⠀⠙⢛⠛⠛⠛⠃⠀⣀⣀⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠉⠐⠠⠤⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣥⣴⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣦⠂⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣷⠀⠀⠀⠀⠈⢀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⣾⠻⣿⡟⣻⠦⠤⠤⢀⣸⡇⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⡇⠀⠀⢀⠀⠀⣿⡟⠀⢀⣴⣾⣿⣿⢃⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠙⠁⢠⣤⣾⣶⣷⣿⣿⣶⣾⣿⣿⣿⣧⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣴⣄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠶⠓⠒⠒⠊⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠃⡀⡄⠀⠀⠀⠀⠀⠈⠓⠒⢦⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠀⠈⠀⢄⠃⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠁⢠⠡⠙⢆⠀⠀⠘⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠗⠀⠀⠀⠀⠹⡖⠼⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠀⠓⠒⡤⠂⠈⠀⠀⠹⢶⠼⡦⡴⠀⠀⠠⢂⠆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⢰⡀⣠⢀⠀⢤⠀⣠⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡰⣂⣽⢦⡀⠀⣡⣶⡄⡀⢀⣠⣌⠀⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⣃⣠⡈⠉⠁⠀⡐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡁⠀⠂⠂⣀⠙⠋⠙⣀⠈⠛⠋⠀⠠⠃⢦⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⡁⠀⢀⢀⡄⠈⢀⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢠⠂⠀⠈⢻⣷⣠⠀⠀⢀⡀⠀⠀⡄⠐⡌⢢⡃
⠀⠀⠀⠀⠀⠀⠘⠀⢀⢤⣳⠥⠬⠦⠥⠴⣫⢖⡄⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⢄⡣⡧⠬⠴⠌⣴⡥⣶⡀⠀⡸⠁⠀⠈
⠀⠀⠀⡀⠀⠀⠀⢀⠮⣗⠯⠭⠭⠭⠭⠽⠉⡷⢖⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠫⡳⢻⠭⠭⢽⣿⣿⡟⢔⡻⠄⠈
⠀⠀⠀⠀⠆⠀⠀⠶⡽⠃⣏⣉⣉⣋⣉⣙⠛⢭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠳⠝⠀⣬⣭⣭⣭⣭⣭⣇⠈⢪⠽
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⠉⢉⣩⢉⣤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⠀⠓⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡄⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠰⠟⠀⠨⠅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠰⠠⠳⠜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠅⠽⠈⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⢀⠜⠙⠉⠁⣰⣦⠀⠛⠏⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣀⣠⢤⡄
⠀⠀⠈⡤⢢⠀⡠⢠⣌⣡⡴⣤⢤⠤⡄⣀⡛⠀⠀⠀⠀⠀⠀⢀⡜⠡⠗⠋⣩⡶⠿⠒⠒⠢⠤⣄⡀
⠀⠀⠂⢁⣀⢓⡀⣈⠄⠤⠤⡤⣦⠀⢄⠜⡁⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠘⠃⢤⣆⠀⠀⠠⢀⣀⣀⡈⠀⢶⡞⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⢀⣞⣠⠶⠂⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠏⠀⠀⢠⡆⠀⡠⢢⠶⠒⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠇⠀⠀⠀⠘⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡰⢿⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠰⠈⡀⠂⠀⠹⣄⠀⠀⠀⣴⠞⢿⣶⡄⠀⠀⠀⠀⠀⠀⠗⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⡀⢃⠠⠀⠈⠄⠘⣆⠀⠸⡇⢐⢿⣿⢿⡄⠀⠀⠀⠀⠀⠀⢀⠠⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠰⠀⠄⠂⠀⠘⠄⠈⢧⠀⠱⠄⣀⡀⠄⠁⠀⠀⠀⠐⢉⡩⢤⣤⠀⠈⣳
⠀⠀⠀⠀⠀⠀⢀⡴⣷⠀⠀⠀⠀⠀⠀⢿⠀⠘⡀⠡⠈⠄⠄⠣⠈⠄⠘⣆⡀⠀⣀⠠⠄⠂⢀⠐⠁⠀⠛⠿⠿⠏⠀⢲⢸⡆
⠀⠀⠀⠀⠀⢀⡞⢀⡏⠀⠀⠀⠀⠀⠀⠸⣆⢂⠐⡀⠡⠀⠈⠄⠡⠈⠄⢹⡀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⡐⠢⡤⠎⡼
⠀⠀⠀⠀⠀⢸⡅⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣆⢢⠐⡀⠁⠀⡈⠄⠡⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠠⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠸⡆⠁⠘⡳⢄⣀⡤⠤⡤⠤⠤⠼⡄⢣⠘⡀⠀⢡⠈⡄⢃⢸⠃⠀⠀⠀⠀⠀⠀⠁⠂⠀⣠⣴⠶⠛⡿
⠀⠀⠀⠀⠀⠀⠹⣤⢊⡴⠋⠁⢠⠊⠀⠀⠀⠀⠸⡄⢂⠀⠐⠀⠆⠰⠀⡾⠲⠶⠴⠶⠶⢶⠒⠒⣻⠋⠙⠀⠄⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀⡀⠀⠆⢠⠀⡾⠃⠒⠦⡤⠤⠤⡶⠒⠛⠃⠻⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢈⣧⡀⡀⣀⣰⠞⠁⠀⣀⢀⠁⠀⡀⠀⠑⢀⠐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠙⠛⠉⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠂⢰
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⠀⣰⠀⡆
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⣠⠿⣤⣀⣀⠀⢸⠀⠀⠀⠀⠀⠀⣇⣠⡤⡴⠊⠁⠀⠀⠀⢳
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⡤⠞⡷⠀⠀⠀⠉⠉⣻⠀⠀⠀⠀⠀⠀⣯⠀⠀⢷⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡇⠀⠀⢳⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠹⣤⣀⠀⠳⡄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠳⣄⠈⡇⠀⠀⠀⠀⠤⠀⠛⠦⣄
⠀⠀⠀⠀⠀⢳⣀⠠⠀⠀⠀⣄⠀⢤⢱⡄⠘⢦⣀⠠⠘⣇⢀⠠⠀⠁⠀⢄⠀⢢⡙⡿⡄⠐⠁⠀⠀⠐⢦⠙⣎⣷
⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⢀⣼⢀⣼⠼⠁⠀⠀⠉⠓⠒⠛⣇⠀⠀⠀⠀⢈⡇⢠⣧⠇⠙⠦⣄⣀⣀⣀⣼⡤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠛⠓⠉⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢰⣶⣶⣶⡄⠀⠀⠀⢀⣀⠀⣴⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⢺⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⡁⠀⠀⠀⢿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣠⣤⡀
⠀⠀⢠⣀⡠⣦⡀⣸⣶⡄⠀⠀⠀⣠⣀⠀⠀⠉⣴⣦⡀⠀⠀⠀⣠⣶⣾⣶⣦⣈⣉⣭⠉⠀⠀⠀⢰⣶⣷⣶⣄⣤⣀⠀⠀⠀⠀⠿⡿⠇
⠀⢀⣸⣇⣀⣈⣛⢹⣿⣷⠀⠀⣀⣿⣀⣤⣴⣾⢻⣿⡇⠀⠀⢀⡿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⠉⠛⠋⠁⠀⠀⠀⠀⢐⣿⣷
⠀⢹⣿⣿⣿⣿⡿⢹⣿⡟⠀⠀⢹⣿⣿⣿⣿⡏⢸⣿⠇⠀⠀⢸⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⡟⣿⣿⡆⡤⢄
⠀⢈⡉⠙⡋⠉⠁⢸⣿⠀⠀⠀⢈⡉⢙⠋⠉⠀⢸⣿⠀⠀⠀⠀⠁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠟⠀⠀⢸
⠀⠀⠣⠴⠁⠀⠀⢸⣿⠀⠀⠀⠈⠣⠜⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⢄⠀⠀⠀⢦⣸
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⢿⠟⢿⠇⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⡿⠀⠀⠀⠀⠀⠀⠘⠛⠀⠄⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⣠⣼⣧⡄⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⡶⠶⠛⢷⡀⠀⠀⠀⠀⠀⢀⣘⡿⠿⢃⣀
⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠶⠶⣷⣄⠀⢹⣦⠀⠀⠀⢠⣿⣿⠛⠛⠛⠉⣲
⠀⠀⠀⠀⠻⣦⣰⣿⣿⠷⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡆⣿⣿⣷⠈⡇⠀⠀⠀⢸⣿⣿⣄⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠙⣷⣭⣥⣶⠿⠁⠀⠀⠀⠀⠀⠀⢸⡇⢀⣆⣀⣀⣤⣭⣭⣤⡀⠀⠀⠀⠀⠀⢹⣿⡀⠀⡇⠙⠛⠋⠀⡇⠀⠀⠀⠀⢹⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠋⠉⠉⢹⣿⣿⡿⣷⠀⠀⠀⠀⠀⠈⣿⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⠙⢿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⢸⣿⠁⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠀⢸⣿⣿⡇⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⢸⡿⢿⡇⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣤⢺⣿⣦⡄⠀⠀⠀⠀⠀⣿⣿⣦⣼⣟⣳⣤⠀⠂
⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣬⣭⣵⣿⣯⣯⣬⣿⡄⠀⠀⠀⣠⣬⣭⣤⣿⣯⣥⣼⣧
⠀⠀⠀⠀⠀⢀⣨⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠙⢛⡛⠛⠉⠐⠀⠀⣸⣿⣿⣿⣿⠛⢻⡛⠋⠁⠂
⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣠⣤⣴⣤⣤⣄⠀⠀⢻⣿⣿⣿⣿⣤⣤⣥⣤⣤⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣭⣄⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⠛⠛⠀⠀⠀⢸⣿⣿⣿⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⣤⣭⣟⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⣨⣽⣿⡛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿
⠀⠀⠀⢸⣿⣿⣿⡄⠀⠹⠟⢀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿

⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠛⠛⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀
⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⢣⣤
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢴⣿⣿⣿⡥
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢞⣛⢿⣿⣶⣀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⣣⡔⢲⣿⣿⣿⣻⠞⠁
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⠽⣷⡞⣟⣏⣯⣮⡤
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⣦⣿⣻⣤⣾⣯⢘⣿⡿⣿⠛
⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⡷⣾⣿⢿⣏⢹⡿⢿⣋⣴⣚⠇
⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⡾⢒⣾⡭⢷⡤⣿⠛⢿⢧⠜⠛⣿⣯
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢃⡿⣥⡋⡟⣌⣦⣧⢸⠙⢄⡟⠍⣡⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⣍⣿⡏⠳⡬⠿⢯⡭⢊⡜⡼⢀⠞⣧⠞⢿⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⡠⠄⢀⢐⠛⢏⣇⣰⡇⠸⡦⠬⣯⣉⡩⠝⣩⠗⢁⡠⣿⠒⢂⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠐⢷⣾⣾⣸⣶⣊⣉⣹⡟⢢⣍⣒⣦⠦⠔⠚⢓⡪⢿⢭⠈⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣌⠙⣿⣿⣯⣉⣡⣿⣿⢀⡞⠙⠒⢋⣱⢶⡲⢭⠥⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠋⡽⠁⣻⡇⣯⠤⢴⣒⣪⠟⠓⢤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠟⠁⠛⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠲⡄
⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⢪⠐⠇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠛⣠⠞
⠀⠀⠀⠀⠀⠀⡞⠓⢤⡜⠀⠀⠀⠸⡆⠀⠈⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢸⠃⠀⠘⠦⣄⡀⠀⠀⢳⠀⠀⢻⠀⡏⠀⠈⠉⠉⠙⠛⠲⣤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠙⡆⠀⠈⣇⠀⠸⡆⢹⠀⣰⢲⠶⠤⣤⠟⠁⣀⡴⠋
⠀⠀⠀⠀⠀⡇⠀⠀⡠⠐⠢⠄⢸⣀⡠⠞⠉⠙⢧⡏⢠⡏⢛⡶⠞⢁⡴⠮⡉⠳⡀
⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠈⠄⢫⠀⢠⠖⠉⠁⠀⠈⠳⣏⡠⠴⠿⠓⠒⠛⠉⠉⠱⡄
⠀⠀⠀⠀⠀⠈⢧⠀⢇⠀⠀⠀⢸⠈⢆⡜⡔⠉⠉⠒⠢⠀⢸⠀⣀⠤⠴⠒⠒⠒⢄⠀⣧⡤⠖⠲⢤⣀
⠀⠀⠀⠀⠀⢀⣸⡄⠈⢦⠀⠀⣸⠀⠘⣤⠁⠀⠀⠀⢠⠀⢸⠀⠇⠀⠀⠀⠀⠀⠈⡄⢏⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠰⣅⠀⡱⠀⠀⠉⠉⠁⠀⠀⠈⡀⠀⠀⠀⠸⢀⡏⡀⢀⠀⠀⠀⠀⠀⠀⠇⢸⠀⡠⠖⢆⠐⡆⢳
⠀⠀⠀⠀⠀⢹⠂⠉⡑⠒⠒⠒⠒⠒⠠⠤⠼⠤⠤⠤⠧⠼⠽⠧⠼⠤⠤⠤⠤⠤⠤⠼⠤⠯⠔⢀⡸⠀⠇⠈⣇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⢸⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣧⠀⢸⢦⣠⠇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⢻⡀⡸⠀⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡙⢦⡀⠀⠀⠀⠀⢻⡄⢙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠘⢦⣉⠓⠶⢤⣄⡀⠙⢦⣍⠐⠮⡙⢦⡀⠀⠀⠀⡠⠚⠁⠀⣀⣠⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠻⢷⡀⠈⠙⠓⠲⠮⣉⠳⣦⣙⣷⡀⢹⡆⢻⠀⣠⠎⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣤⠆⠀⠀⠙⢦⣀⠀⠀⠀⠈⠑⠄⠙⢿⣧⢸⠁⢸⡞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⠀⠀⠙⠧⢠⠟⢀⡼⠛⣋⣉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⡿⠛⠁⠻⣤⠟⣀⣉⣉⡉⠙⢆⠹⣄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⣰⡾⠀⠀⢀⡾⠋⢀⠔⠁⠀⣾⠀⢙⠻⢭⡙⠷⣦⣁⠈⠓⣦⡄
⠀⠀⠀⠀⣰⠏⠀⣠⡆⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⡾⠀⢠⠋⠀⢀⣼⣿⣆⠀⠙⢦⡉⠳⣄⠉⠙⠛⠉
⠀⠀⠀⢰⡏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡇⠀⠃⢀⣠⡾⠋⠈⢻⣆⠀⠀⠹⣄⠈⢷⡀
⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠀⠈⣇⢀⡴⠛⠁⠀⣠⠀⠀⠻⣦⡀⠀⠙⣄⠀⢳⡄
⠀⠀⣸⠃⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠁⠀⠀⠾⠋⠀⠀⠀⠈⠻⣦⡀⠈⠢⣄⠙⢦⡀
⠀⢀⡟⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⣀⣀⣉⡷
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⣰⡏⠀⢸⡏
⢀⡟⠀⠀⢀⡄⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⢸⡇⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⣠⡾⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠋⠀⢀⣴⠿⠋
⣿⡀⠀⠠⡿⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠁⠀⠀⠀⠀⢀⣤⡾⠟⠁
⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋
⠀⢻⣦⡀⠀⠀⢀⡤⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠉
⠀⠀⠙⢿⣦⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⠀⠉⠻⠿⣶⣦⣤⣤⣤⣤⣶⣶⡿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢻⣿⢸⣿⡗⣻⡥⣏⣹⢾⡷⣿⣸⣿⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⣀⣀⣨⡀⣀⣡⡄⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠀⠿⠘⠧⠷⠿⠿⠧⠿⠻⠿⠿⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢯⣙⡆⢙⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠼⠤⠤⢬⣍⡙⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⠴⠒⠒⠒⠒⠠⢀⠙⣆⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠚⠋⢸⠀⢟⠀⠀⠀⠀⠀⠀⢸⠀⣹⡼⠑⠛⠴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠈⢧⣈⠓⠒⠒⠒⠒⠚⣁⡴⠃⠀⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠤⠤⠤⢀⠈⠉⠉⠉⠉⠉⠉⠉⣀⣀⣀⣀⣀⣀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⣖⣲⠲⣄⠘⢦⡀⠀⠀⠀⠀⢸⣭⠶⠶⠶⡶⡾⠃⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡶⠄⡄⣤⠀⠈⢣⡀⠙⠆⠀⠀⠀⢠⢦⣀⣰⣟⣛⣛⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣡⣈⠀⠀⠀⠙⢦⡀⠀⠀⠀⣏⢀⡿⠁⠉⣉⠉⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⣚⣷⣐⣚⣓⣒⣲⡀⠀⠁⠀⠀⠀⠈⠉⡇⠀⠸⣽⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠴⠶⠾⢿⡵⢶⡇⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⣒⡒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠭⣭⢭⡿⣭⢏⡀⠀⠀⠀⠀⠀⣰⡇⣇⣀⣀⣉⣀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠁⠀⠈⠻⠦⣄⣀⣤⡞⠃⠀⠿⠭⠩⠉⠭⠥⠾

⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣷⢸⣟⣛⡃⣾⡟⢻⡆⣾⣟⡛⠂⣶⠟⠻⣦⢸⣿⣆⢸⡇⢀⣾⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠉⢸⣯⣭⡁⣿⡟⢿⡁⣬⣍⣿⠇⢿⣤⣤⡿⢸⣿⠙⣿⡇⣼⠷⠾⣧⢸⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣸⡆⢷⣄⣾⢃⣴⠟⠳⠆⢸⡆⣾⡟⣛⢰⣷⣆⢸⡇⣼⡟⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢻⡇⠀⣿⡇⠘⣿⣌⣻⡇⢸⡇⣿⣏⣉⢸⣿⠹⣿⡇⢽⣏⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠈⠀⠀⠀⠉⠁⠀⠈⠀⠈⠉⠉⠀⠁⠀⠈⠁⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡟⠛⢻⣆⠀⠻⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⢻⣦⣤⣿⣄⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣉⠀⠀⠿⠋⠀⠀⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣤⡾⠛⠛⠛⠛⠛⠛⠛⠓⠀⠦⠀⠀⠹⣦⠀⢴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣦⣴⠄⣿⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢻⡆⢈⣷⢀⣤⣆⠀⢀
⠀⠀⠀⣀⣠⣿⠟⠛⠉⠁⠀⠀⠀⣿⡀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣸⣧⡾⠃⠀⠉⠙⠛⠿⣦⣤⡄
⠀⢀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠈⠻⢦⣤⣤⣤⣤⣤⣤⣠⣤⣤⠾⠋⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤
⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠐⢿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣾⡇⠀⠀⠀⠀⢰⣿⠉⠉⠉⠉⠉⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⠀⣾
⠀⢀⣿⣄⠀⠀⠀⠈⣿⡟⠛⢿⡟⢷⣄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣴⡶⠶⠶⠶⠶⣶⠶⣶⠾⠃⠀⣴⣿
⠀⠀⠉⢹⣧⣄⠀⠀⠙⠛⠛⠛⠁⠀⠙⢧⡀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠀⠀⠀⣤⣤⣿⣤⣿⣤⣤⠘⠋
⠀⠀⠀⠈⠁⢹⡷⡦⢰⡗⠀⣷⠀⠀⠀⠈⠻⣦⡀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⣰⡿⣷⣀⣀⣀⣏⣀⣀⣀⡀⢀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⠀⠻⠆⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠘⣿⡛⠉⠉⠉⠉⠉⠉⠙⠉⠋⢻⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢻⣇⣀⣀⣿⠃⠀⠀⠀⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⣠⣤⣶⣶⣿⣧⡄⠠⣶⣾⣿⣶⣶⡶⣦⡄⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⠀⠀⠀⣼⠏⢹⡆⠀⠀⠀⢸⡇
⣴⣶⠟⠁⠠⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⣦⣴⣶⣶⣶⣾⣷⣴⣶⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠾⠿⠿⠷⠿⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣴⣿⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢸⣿⠀⠀⠀⠐⠶⠶⠆⠀⠀⠀⢸⡇
⣀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣴⣿⣤⣴⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠙⠻⢶⣤⣤⣤⣤⣤⣤⣤⣤⣼⠟⠀⠀⠀⠀⣽⣷⣄⠀⠀⠀⠀⠀⠀⢀⣠⣿⡁⠁⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣶⣦⣤⣶⠶⢿⠏⠈⠀⠀⠈⠛⠛⠛⠃⠘⠃⠘⠛⠛⠛⠛⠛⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠄
⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⣿⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⡆
⠀⣀⣀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⡇
⠀⠀⠈⠉⠁⠒⠢⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠻⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋


⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⡿⠀⠀⠀⢠⢞⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⢠⡷⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠇
⠀⠀⣼⡇⠀⠀⢠⢿⡿⠃⠀⠀⠀⠀⠀⠀⠁⠗⣠⠃⠀⢠⠋⠇⠀⠀⠀⠀⠀⠀⠸⢷⢿⣿⠛⠉
⠀⠀⣿⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⠀⡴⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠈⠓⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠀⠀⠀⢀
⠀⠀⠀⠀⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⠇⠀⢀⡴⠋
⠀⠀⠀⠀⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢠⡏⠀⣰⡿⠁
⠀⠀⠀⠰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⡏⠀⠘⠊
⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⢰⣿⣿⣿⣿⡟⠿⠋
⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣤⣀
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⠛⣿⣿⣿⣿⣿⠈⠙⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣯⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣄⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷
⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣷⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⡿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣼⣿⣿⠃⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢰⣿⣿⡇⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⡇⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠈⠉⠉⠛⠛⠛⠻⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢿⣿⡇⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⡇⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣶
⠀⠀⠀⠀⢠⣿⡇⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⡀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣧⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿
⠀⠀⠀⠀⠃⠹⣿⣧⡀⠀⠘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⢿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⡿⠟

⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⡾⣀
⠀⠀⠀⠈⠀⢈⠈⢀⡔⠊⠁⠀⡘⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⡀⢀⠄⠀⠀⠀⠀⠀⠛⢂⠀⢀⣀⣀⠀⣠⠄⠀⠘⢁⡄⢀⡘
⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠔⠤⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠘⠃⢀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⡔⠬⠟⢛⡓⠋⠈⠁⡠⠋⠀⠈⠁
⠀⠀⠀⠀⠈⢲⡀⠘⠂⣘⠆⣰⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⣇⠲⠛⠀⣧⠠⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣠⡀⠀⠀⠐⢠⡌⠀⠀⠀⣼⢇⡄
⠀⠀⠀⠀⠂⠘⢀⠙⠀⠑⠠⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡃⠀⡸⣧⢄⠘⠃⠀⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣩⡀⠀⣀⣀⠘⣞⠣⣽⣿⣿⡷
⠀⠀⠀⠦⢠⠤⠄⠀⢀⠠⡶⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⡇⠞⠛⠋⠈⢉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⣁⠀⠁⠘⠃⠈⢣⡈⠉
⠀⠀⠀⢠⡀⠀⣦⠀⠈⢊⡱⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠁⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣀⠀⢂⣈⣴⡎⢻⡀
⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⠍⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠈⣤⣬⣿⣿⡗⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠸⠛⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣎⠀⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⢛⡌⡝⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠜⠀⠠⠆⠨⢸⡓⠀⠀⠀⠀⠀⠄⠀⢀⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣠⡴⠀⠀⡰⠃
⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⣨⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡄⢀⡋⢁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠞⠁⠀⠠⣞⡀⠀⠀⠄
⠀⠀⢀⢠⠀⠀⠊⠀⠀⠀⠰⠃⠈⠙⠳⠄⠀⠀⠀⠀⠀⡄⠘⠀⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠒⠀⠒⠒⠂⢳⡾⠀⡀⠘⠳⡀⠙
⠀⠀⠈⠀⠀⠀⠀⠀⢲⠶⡾⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⢦⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⢠⡅⠀⠀⠀⠀⠀⠀⡠⠊⣰⣧⠈⠁⠐⢄⠟⠣⠔
⠀⠀⠀⠀⠀⢀⡰⡶⢁⠀⠚⠆⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢀⠐⠂⠀⠀⠀⠀⠀⢀⠞⠁⡴⠋⠀⠈⠠⢀⣾⡀⠀⠄
⠀⠀⠚⠿⢤⡀⠀⠐⠧⠀⠫⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠂⠀⡀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢰⠱⡈⠀⠤⣀
⠀⠀⠀⠲⢻⠃⠀⠌⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢠⠢⠄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⢳⠀⠀⠀⠉
⠀⠀⠁⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢉⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣄⠸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡶⠀⠀⠀⠀⣕⠡
⠀⠀⠀⠈⠀⢰⠐⠃⡄⠀⠰⠀⠐⠁⡀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⡄⠀⢐⡖⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⡀⠾⠂⢀⣿⡁⢂⡀
⠀⠠⠆⠀⠀⢁⢀⡟⠃⠀⠄⠀⡄⡄⠀⠀⡠⠐⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠙⠶⢄⣁⣠⠀⠀⠀⠀⠀⠀⢀⠠⠄⢠⡅⢧⣸⡿⠋⣉⡄
⠈⠧⠀⠠⠷⠛⠋⠀⠀⠀⠀⢲⡾⠀⠀⣀⠀⠀⠁⠀⠀⠀⠠⢦⣀⠀⠒⠦⠀⣀⡤⠆⠴⣆⡀⠀⠀⠉⠉⠙⠀⠀⠀⠀⠈⠙⢓⢦⠿⢖⢦⡿⣠⣼⣷⢚⡁⢠⡀
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⢊⠀⠀⠀⠋⠱⠐⡤⠆⠐⠂⠀⠀⠀⠀⠀⠺⢶⣮⡀⠀⢼⣿⠿⠟⠻⣿⡛⠀⠁
⠀⠀⠀⠀⠀⣠⠀⠈⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡖⠀⡁⠀⠀⠀⢀⠀⡀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠄⠉⠀⡀⠀⢀⢿⣇
⠀⠀⠀⠈⣽⣟⠉⠀⠀⠑⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢉⣁⠗⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠟⠀⠀⠀⠀⠀⠀⠀⠻⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠻⠇⠀⠀⠀⠘⠡⠟
⣶⣶⣤⣦⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣦⣶⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣴⣤⣶⣶⣶⣦⣤⣶
⣿⣿⣏⣀⣁⣈⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣶⣶⣤⣤⣤⣤⡤⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⣀⡄⢊⢀⠄
⠀⠀⠀⠘⣵⣾⣯⣽⣿⣥⣤⣤⠶⠋⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⠀⢀⣀⣀⣤⣀⠀⠀⠀⠀⢠⡿⣻⣿⣛⣛⣋⣭⣴⠆⡄⠈
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣶⡦⣤⣌⡐⠄⠀⠀⠀⢸⣿⣿⣷⠿⠟⠛⠉⠻⢿⠄⠀⠀⠀⠈⢱⣿⣿⣿⣿⣿⣷⣦⣤⣈⡉
⠀⠀⠀⠀⠀⠀⠋⠛⠿⣿⣿⣿⣿⣛⠲⠦⠄⡀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⠶⣭⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠶⡍⠙⠂⡠⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣍⠛⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⣾⠟⠉⠉⠻⣷⠀⠀⠀⠀⠀⠊⠁⠀⢀⢀⡤⠒⠚⠛⠛⠛⠙⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⢸⡿⠀⢀⣤⣶⣿⣷⣤⡀⠀⠀⠀⠀⠀⠇⡎⠀⠄⠁⠀⠀⠀⠈⢢⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠠⠉⠉⠉⠉⠉⠉⠉⠰⠀⠀⠐⠁⠀⡇⠀⡀⠀⠀⠀⠀⠀⢰⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⡇⠀⢼⠀⠷⢰⡇⢾⠘⠂⠀⠀⠐⠀⠀⠱⣄⣈⠀⡐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣾⢷⣶⠶⠾⢟⣋⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣥⣬⣤⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣶⣶⣶⡶⠾⠃
⠀⠀⠀⠸⣳⣿⣿⣿⣿⣿⣯⣁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠉⢻⣿⡇⠀⠀⠀⠀⠈⠻⢿⣿⣿⣾⣿⣿⣷⢶⣤⣄⡀
⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣝⡛⠲⠀⠀⠀⠀⠀⠀⠀⣼⡏⠠⣾⡦⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣩⡯⠻⣿⡿⣫⣿⠶⣬⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡻⢦⣍⠛⠀⠁⠀⠀⠀⠀⠀⣿⣇⡀⠈⠁⣀⣿⡇⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠙⠻⢯⡙⠳⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡆⣿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡋⠋⠛⠛⠛⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⣿⣿⣿⣿⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⣿⣿⣿⡿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⡉
⠀⠀⠀⠀⠀⢠⣾⣷⣆⠸⡆⠀⡿⠁⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡏⣿⣿⡏⠀⣷⠀⡇⣀⣤⣤⣶⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣶⣧⡘⣧⡀
⠀⠀⠀⠀⠀⠸⣻⣿⡟⢀⡇⠀⣿⢻⣿⣟⣻⣄⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡶
⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠀⠀⣿⣸⣗⣷⣹⣽⣿⣿⠁⠀⠀⠀⢰⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡘⣿⣆⠀⠀⠀⠀⠀⠀⠀⣇⢠⡇
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡘⣿⡄⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠙⠛⠛⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡘⣷⠀⠀⠀⠀⠀⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡘⡇⠀⠀⠀⠀⠀⠙⠙
⠀⠀⠀⠀⠓⠒⠶⠶⠶⢤⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡈
⠀⠀⠀⠀⠤⠤⠶⠶⠶⠟⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⣾⠂⠀⠈⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⡏⠀⠀⠀⢃⠀⠀⠁
⠀⠀⢀⣀⣤⣤⣤⣤⣴⣾⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠚⢃⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠸⠟⠿⠟⣿⣿⠿⠿⠿⠟⠻⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⣀⣾⠁⠀⠀⠀⠈⠛⠿⢿⠿⠿⣿⠟⠛⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠠⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⢁⠀⠛⠋⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢀⡀⠀⠀⠀⠀⣿⣟⠀⠐
⠀⠀⠀⠀⠠⣤⣤⣼⣶⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡄⠀⠀⠀⠀⠀⣒⣶⠶⠶⢶⣖⠀⢠⠀⠀⢸⡏⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠴⠶⠾⣿⣿⣿⣿⣶⣤⣤⣶⣴⣧⣤⠾⠯⠍⠀⠀⠀⠀⠀⠀⠀⡪⠭⠭⠭⠭⠵⠀⠈⢧⡀⠀⠻⠶⠂⠀⠀⠹⣿⣄⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⣽⣯⡭⠭⠳⠶⠞⠓⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠈⣿⣶⣦⣴⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⢀⣠⣴⡿⠟⠀⠰⣿⣿⢻⣿⡿⣿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠛⣿⣾⣿⣿⡜⣦⡹⣿⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣷⣽⡇⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⠀⠀⠀⠀⠀⢸⣿⠙⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣷⣄⣀⣀⡀⣀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⡀⢀⣠⣄⣀⣀⣀⣀⣐⣦⡄⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⠟⣼⣿⣻⣧⣄⣙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠋⠀⢚⣿⣿⣿⣿⣿⡿⢟⠋⠙⠂⠀⣀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢰⣦⣾⣿⣿⣿⣿⣿⣟⣀⡄⢀⡀⠀⠀⡹⣷⣶⣶⣦⣄⣀⠀⢀⢀⣾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣿⣴⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⠅⠀⠈⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢂⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣂⣤⢀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡆⠈⠁
⣗⠀⠀⠀⠀⠀⣄⣐⣀⣀⢀⡈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⢡⣸⡇⣀⣴⣿⣄
⣿⣿⣦⣄⣠⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠋⠀⠙⠟⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣋⣧⣿⣶⣦⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣠⣼⠽⠿⠦⠼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠛⡍⠀⢠⠭⠁⠀⢐⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠬⠶⡄⠀⠈⠚⠁⣀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⠢⣄⣀⣀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠈⠊⠓⢾⣆⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⠽⠃⠀⠀⠀⠀⠀⢀⡀⠁⠀⠙⣆⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡞⠁⠀⡤⣶⠻⠀⠀⡔⠁⠈⡆⢠⠀⠸⡄⠀⠀⠀⠸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠳⡀⠀⠳⡇⢀⣀⣼⠔⠂⠀⡇⡾⡁⠀⠽⠦⠄⣀⣠⣤⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠹⣄⣀⠷⢚⡄⠸⢄⣀⡴⠁⡿⣜⡂⠤⢀⡀⢡⠊⣄⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⡋⣁⣤⢴⠟⠲⣄⣀⣀⣀⢧⠀⠉⠙⠲⢆⡽⠤⢿⣤⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡝⠋⠉⢸⠀⢰⡏⢁⡄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠘⠁⠀⠀⠈⠳⡈⢣⣾⠆⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢰⢹
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣶⣄⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠏⡄
⠀⠀⠀⠀⠀⣠⠞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢳⠈⡓⠀⠀⠀⣸⠀⠀⠀⠀⠀⢓⢡
⠀⠀⠀⢀⡞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣇⠀⢀⡌⢠⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⣸⠀⢀⠀⣄
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⣾⢀⡏⣀⣀⣀⣐⣳⠐⢯⠍⣰⠖⠀⢱⠀⠈⢟⣉⡓⢲⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⣳⣜⠯⣝⣓⠠⠤⠬⣓⡦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠴⠋⠀⠀⢈⡉⣉⠍⢥⡀⠀⠀⠀⡤⠶⠋⠛⠒⢲⡄
⠀⠀⠀⠀⠈⠙⠲⢤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⡅⠙⠄⠀⣀⠅⠀⠀⠘⠓⠒⠢⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠐⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠚⠚⠋

⠀⠀⠀⡤⠚⢩⣭⠉⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠀⡤⠀⠀⠀⠀⠀⠀⣠⠒⠒⠒⠒⢲⡶⠒⢢⡀⠀⠀⠀⠀⣖⠛⡆⠀⠀⣀⣀⣀
⠀⠀⡞⠀⠀⣠⠁⢰⢾⣧⡘⡆⠀⠀⠀⠀⠀⢠⠖⠛⠛⠲⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡇⢶⠆⡇⠀⠀⠀⢀⣬⡉⢰⣯⠎⠷⠆⢀⡗
⠀⠀⡇⣀⣰⣾⢖⣁⡊⠁⠀⡇⠀⠀⠀⠀⠐⢿⣂⡀⠀⢀⣥⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⡷⣄⡴⠃⠀⠀⠀⠀⢉⡔⠋⠰⠆⣨⣶⣿⠟
⠀⠀⠳⣀⠜⣱⠛⠈⠀⠀⡰⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⡇⠁⠈⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣴⣴⣾⣿⠟⠁
⠀⠀⠀⠈⠲⠬⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠁


⠀⠀⠀⠀⣶⠛⠛⠛⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡟⢀⣀⣀⣷⡶⠂⠀⠀⠀⠀⢀⡤⣤⠤⢤⡀
⠀⠀⠀⠀⢸⠀⣠⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠽⣿⡟⠉⠉⣿⣿⣿⡆⠀⠀⠀⠀⠀⠓⠋⠀⢀⠏⢳⡀⡀
⠀⠀⠀⠀⠸⡄⠈⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠙⣫⠇⠀⠀⠀⠀⠀⠀⠀⠸⠃⢳⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⢻⣶⣾⣿⣷⣴⣾⢯⠃
⠀⠀⠀⠀⠀⢷⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠰⣇⡀⠉⠉⠁⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣿⡿⠃⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠼
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠠⣶⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠻⠿⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⡤⣤⣤⣤⣤⣤⡄
⠀⠀⡰⠒⠲⠤⣤⣼⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⡤⠖⠒⠋⠀⠈⠓⠒⠦⡄⠀⠀⠀⠀⠙⢻⠀⣿⣿⣿⣿⣿⡟
⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠓⠶⠶⠤⣤⡤⠤⠶⠖⠃⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⡇
⠀⠀⢿⣿⣿⣿⣿⣿⣛⠛⢋⡇⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠒⠐⠐⢂⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠛⠛⠛⡟⠁
⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣠⢖⣒⡒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⢰⣦
⠀⠀⠀⢰⡗⡿⠋⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣼⡁⠀⠀⠹⡄
⠀⠀⣤⣤⣥⣤⣤⣤⣤⣬⣤⡄⠀⠀⠀⠀⡀⠀⡰⠓⠦⣄⣠⡤⠤⠀⠀⠀⠀⠀⠀⢀⡭⠿⠯⣅⠀⠀⠀⠀⠀⠀⠀⢹⠉⠓⠲⢤⣳⡀
⠀⠀⢸⣿⣿⣟⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠹⡉⠉⠘⠒⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⡻⠗
⠀⠀⢸⣿⣿⣷⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠸⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡾⠶⠟⢿⣿⠟⠛⠻⠤⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡂⠒⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⣷⣀⢐⣶⡁⠢⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠀⠀⠉⠛⡟⠉⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⣤⡄⠀⠀⠀⠈⠋⠸⠟⠋⠉⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⡀⠀⠀⠿⣿⣆⠀⠀⣦⣄⠀⠀⠀⠀⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠙⣿⢿⡇⠀⠀⠀⢿⣿⣦⣤⣬⡿⠞⠁⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡴⠆⠠⠉⠉⢄⠀⠀⠈⠼⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⢋⣷⡄⠀⠀⠳⠂⠓⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⢋⣿⠁⠀⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣾⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⣿⢹⡿⠻⡟⠀⠐⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠸⣿⠊⠀⠀⠀⠀⠀⣻⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢀⣀⢀⣀⢀⣀⢀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠸⠥⠸⠻⠨⠷⠻⠼⠻⠹⠧⠟⠇⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡄⣤⢆⡔⡂⢶⢠⡆⢰⣤⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠙⠁⠉⠈⠁⠈⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠉⠉⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⣄⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠤⠌⠉⠩⠍⠹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠘⡟⢆⠈⢀⣸⡈⠀⡼⡟⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠸⡘⠉⠍⠆⢉⠩⡤⠁⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⢈⠑⠒⠓⠒⠋⠁⠀⡀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⢭⡭⢭⠭⡏⠉⢹⢹⠉⡇⠀⠀⠀⠀⣽⠉⣽⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⠴⠦⢼⠤⡇⠀⢸⢸⠀⡇⠀⠀⠀⠀⣿⠀⢺⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠺⠗⠺⠒⡇⠀⠈⢸⠀⡇⠀⣠⡄⠀⡾⡒⠚⣁⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⢇⣈⠀⠘⣀⠇⢰⠹⡀⠀⢸⢸⠠⠌⡖⢲⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⠈⠉⠉⣨⠚⠁⠑⠷⠆⡌⢸⠀⠐⠨⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠
⠀⠀⠀⠀⠈⠀⠈⠠⠒⠁⠀⡉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⣦⣄⣀⣀⣠⠀⠈⣁⠀⣜
⠀⠀⠀⠀⠀⠀⡁⢠⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠠⢴⢠⡀⠀⠀⠀⠀⠀⠴⠶⠟⠉⠉⠒⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠆⠃⠀⠘⠠⠧⠁⠀⠀⠀⠀⠀⠀⠀⣠⣞⢀⢷⢄⠘⠁⠿⠀⠀⠀⠀⠀⠀⠠⢈⣁⠀⢀⡈⢲⠢⣾⣿⠇
⠀⠀⠀⠀⠒⠒⢒⠀⢄⢞⠺⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⠉⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⡄⠀⠈⢀⢱⡄
⠀⠀⠀⠀⠈⣀⠛⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢂⣴⣿⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢒⡚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢦⠀⠀⠀⣠⠔⠁⡐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠔⠦⡄⠀⠀⠀⠀⠀⠀⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣑⣄⡘⠁⢠⡺⠤
⠀⠀⠀⠀⠈⠀⠀⠀⡤⣶⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠃⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⢀⡔⢨⡅⠂⠀⡰⠢
⠀⠀⠀⢀⣀⠀⠴⠆⡀⢺⡀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠆⠎⠀⠀⠀⠀⢠⠊⠰⠃⠀⠀⢠⠇
⠀⠀⠀⠀⠩⡿⠀⢸⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠻⡆⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⢠⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂

⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠦
⠀⠀⠀⠀⠀⠀⠀⣥⠄⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⢆⡀⠇⠀⠀⠀⠀⠀⠐⠀⠀⢁⢸⣧⠴
⠀⠀⠰⡄⠀⠶⠖⠁⠀⠀⣬⠁⢀⠈⠐⠀⠀⠀⣄⠀⠠⠄⠀⣀⠄⣤⠈⠁⠒⠓⠀⠀⠀⠐⠦⢥⠿⢤⣿⣠⣾⣔⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⡹⠆⠀⠈⠀⠀⠈⠑⠲⠂⠒⠀⠀⠀⠀⠻⣯⡀⠸⠿⠻⢻⣿
⠀⠀⠀⠀⠀⣶⡖⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢣⠄⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠐⠆⠀⠀⠘⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⠋⠀⠀⠈⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡖⠁⠀⢠⢤⠀⠀⠀⠀⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢚⠀⠀⡜⢀⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣭⠃⠀⠙⠋⢁⠀⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠸⣦⣀⡼⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⡀⠀⡉⠑⠒⡄⢀⠀⠀⠀⡰⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢒⠏⠻⠤⠕⠀⢾⣿⣿⣿⢖⠝⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣴⣶⣤⣴⣿⣿⣿⡷⡍⣴⡁⠀⠀⠀⣀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣯⢟⠞⠱⡄⠈⠓⣖⠉⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⢿⣿⣿⣿⡿⡣⢯⠶⠚⠙⠦⣤⡼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣹⠊⠀⢀⢞⠞⡔⠛⠿⣬⡉⠁⠀⡶⠒⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠰⣇⢀⡰⡻⠃⠀⢸⠀⢀⣨⣿⡆⣸⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠙⢦⠌⡐⣟⠀⠀⢠⠃⠀⢻⣿⡿⠙⠋
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣢⠾⠁⠀⡰⠁⠠⣾⣿⡟
⠀⠀⠀⠀⢠⡏⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠜⠁⠀⢀⠜⠀⠀⣤⣾⣿
⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡡⠋⠀⠀⢠⣾⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⢀⠤⠒⠤⣾⠝⠀⠀⠀⠐⠛⠛⢻⠉⠙⣯⠉⠙⣇
⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⢀⠔⠡⢄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⢇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⠄⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢣⢀⡇⠘⡄⢸
⠀⠀⠀⠀⠀⠠⠴⠚⣉⠄⢀⠅⠀⡠⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⢣⢸
⠀⠀⠀⠀⠀⠀⠠⠭⠒⠭⡀⢄⣪⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠈⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠢⢀⡀⠄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠠⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⡀⠚⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡃⠀⠀⠀⢤⡆⠀⠘⠠⠄⠁⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠀⣠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⠃⠀⢤⠊⠈⠁⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠠⠌⠁⠈⠄⠤⡀⡹⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⢧⠄⡰⠓⠀⠀⠀⣄⣀⠼⠦⣀⡉⢀⠀⠐⠂⠴⠆⣀⠀⠀⠀⠀⠀⢸⠁⠠⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⢹⠃⠀⠀⠁⠀⡞⠁⠀⠀⠁⠀⠁⢤⠀⣄⠀⠀⠁⠙⢏⠀⠀⠀⠈⢇⡐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠈⠚⠐⠂⠈⠂⠀⠀⠐⢾⠀⠀⠀⠀⠺⡄⠀⠀⢀⠈⠈⠁⠠
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠋⠀⠀⠀⢸⡇⠀⠀⠂⢸⡇⠠⠠⡄⠀⠀⠀⠀⠈⠐⢀⠀⠀⠀⣼⢂⡀⠡⠀⠀⡷⠀⠀⠠⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠒⠀⠠⠨⣈⣷⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣤⡏⠀⠀⠀⠀⠄⣿⡤⠀⡐⠆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⡇⠀⠀⠰⠀⠈⢿⠖⠀⠀⠀⠈⢳⣤⠄⠀⢴⠀⠀⠀⠀⢁⠄⣠⠾⠀⠀⠀⠀⠈⢡⡟⠀⠀⢹⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠦⢾⡆⠀⠀⠀⠠⠀⠙⠳⣤⡟⠀⠀⠀⠀⣤⠾⠋⠀⠀⡀⠀⠀⠀⢼⡗⠃⢀⣼⠃⠀⠠⠤
⠀⠀⠀⠀⠀⢀⠐⠀⡀⠉⠉⠖⠲⣤⡀⣼⠃⠀⢀⠀⠂⠄⠈⠇⠉⠛⠷⣤⣽⡞⢡⠀⠀⠀⢠⡈⠠⠃⠀⣼⠃⣰⠾⠁⡶⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠻⣿⠀⠀⢠⠀⠀⠀⡀⠀⣰⣴⠾⠋⠉⠛⠿⢶⣤⣩⡊⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠢⡤⠀⢀⣵⣾⣋⡁⡐⢂⡄⠠⠀⠀⠛⠙⠻⣶⣮⣀⢸⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡀⠈⢹⣧⠀⠀⣠⣴⠟⠁⠀⠈⠀⠁⠈⠀⠀⠀⠀⢐⠄⢺⠉⠙⢿⣿⣿⣧⠀⠀⠲⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢃⠀⠀⠀⠀⣿⣆⣹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠈⠐⠂⡀
⠀⠀⠀⠀⠐⠐⣄⡀⠠⠄⠀⠀⠀⣄⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢁⠀⣾⣿⣿⡀⠀⠀⢰⡏⠉
⠀⠀⠀⠀⠀⠀⠀⢈⣳⡆⠀⠀⣰⠅⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏⠀⣲⡴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣹⣇⣠⣀⠀⢘⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠻⠦⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⣔⠓⠀⠀⠉⠉⠉⠛⢷⣬⣿⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⢰⣿⡿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣧⠀⣽⣿⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⡿⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣠⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠈⢻⣿⡟⠁⢹⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠈⢿⣷⡀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⢠⣟⢹⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣷
⣤⣤⣤⣤⣤⣄⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣦⣶⣿⣿⣷⣤⣤⣦⣶⣿⣿⡿⠿⠿⠷⠶⠶⠶⠶⠶⣤⣤⣄⣀⣀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⣀⣴⣞⣡⡄
⠀⠀⠀⠀⠀⠀⡔⣿⣿⣮⢞⡵⣫⠝⠁
⠀⠀⠀⠀⢠⢖⡣⣞⡿⠁⢀⣜⣡
⠀⠀⠀⠀⣎⣿⣿⣿⣷⣠⠜⠻⡀⠀⠀⢀⡀⠀⠀⠀⠈⠁⢀⣀⡀
⠀⠀⠀⠀⠙⠿⣿⣿⠿⣇⠀⠀⠱⣄⠀⢉⡤⢤⣀⠀⢀⠞⠁⠀⢸⠂
⠀⠀⠀⠀⠙⠓⣼⣅⠀⠀⠑⢢⡄⠀⠙⠺⣆⠀⠈⠳⣼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⡎⢻⣷⣄⠀⢀⣭⡓⢤⡀⠈⢣⡀⠀⠈⢳⡭⠥⠤⠤⠤⠤⠔⠒⠚⠉⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠳⢿⡈⢮⣑⢮⡀⠈⠙⢿⣦⡀⠙⠲⢤⠤⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⡤⢔⡛⠿⠆⠀⠀⠀⠃⠀⠀⢹⡉⠁⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠋⣉⠴⠚⢇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⠻⡖⠚⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠓⠿⣶⡄⢀⣤⣶⠿⠛⣁⣸⠾⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⡭⠞⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⣄⠀⠀⣾⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠷⢖⠤⣈⣋⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⡼⠂⠀⠙⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠔⣊⡥⠄⠒⠂⠀⠀⢲⡀⢱⠀⠁⠀⠱⢬⡑⢤⡀⠀⠀⠀⠀⠀⣈⡦⡇⠀⠀⠈⠳⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⠳⢄⡠⢊⡵⠊⠁⠀⠀⠀⠀⠀⢰⡣⠷⠞⠀⠀⠀⠀⠈⢯⠓⢬⡒⠒⣒⡩⠥⠒⠊⠹⣤⣀⡀⠠⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠑⣒⣻⡀⠀⣀⠉⣉⣉⡹⠂⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠕⠊⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣀⣀⣀⣀⣀⣀⢤⠤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠧⡔⠈⢋⠫⠏⠉⢖⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⠋⢀⢿⣾⣿⡛⠺⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⠷⠞⠿⢳⣾⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⡴⢩⠃⠀⠀⣠⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡀⠈⣛⣦⣀⡀⣀⣨⠇⣴⡉⠀⠀⢉⣑⣾⣖⠒⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣏⡫⢟⣽⡩⠊⠀⠀⠉⠒⠭⣓⠿⣏⡩⣟⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⠷⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣀⣛⣛⡛⠻⠿⢯⣛⠿⢦⠀⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢁⣀⠀⠀⠚⠋⣉⣩⣭⣟⠛⠶⠀⠈⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣿⣡⠴⠀⠀⠸⠟⣦⣀⣀⣠⣴⣶⡄⠀⠀⠀⠀⣠⡶⠶⣤⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡟⣡⠾⠋⠀⠀⠀⠀⢉⣩⢴⣿⡽⠂⠀⠀⠠⡾⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢸⠃⣠⠆⠀⠀⣀⣾⣯⣶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣴⠶⣠⣾⠃⠀⠀⠀⣉⡵⢞⣽⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⡶⠿⠦⠀⠙⢷⣄⠀⠀⣠⣄
⠀⠀⠀⣀⡴⠿⠀⠀⣠⢴⡟⠀⢸⠇⡿⠀⠀⠀⠀⠉⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⡟⠉⠻⢶⣤⡶⢶⣄⣀
⠀⠀⣾⠋⣰⠟⢡⣾⡟⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠙⠷⢾⣧⣽⡿⣦⠀⠀⣠⠶⡆
⠀⠸⣏⠀⠿⠀⡿⠘⠇⠀⠀⠰⣄⡀⠀⠀⠀⠲⣦⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣞⣡⠞
⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣤⣴⢿⣯⣩⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣙⠶⢤⣤⣤⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢧⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡖⢀⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠻⠶⠖⠂⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠿⣤⡌⠻⠓⢶⣦⣤⣀⡀⠀⠀⠀⢠⡏⢀⡾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠈⢻⡄⠀⠀⠓⠀⠈⣹⠟⠲⠦⣼⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⣶⣶⠶⠛⠁⠀⣀⣼⣄⣠⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⣿⠆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠛⠉⠈⠙⢷⣶⣶⣤⣴⣟⠉⠙⠛⠓⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠶⢦⣤⣄⣀⠀⠀⠙⠿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⠛⠂⠀⠀⣀⠀⠀⠈⠙⢦⠀⣤⣿⣧⡀⠀⣀⡠⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠴⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢶⣶⡉⣿⠟⢋⣡⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠗⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⢻⣽⡏⠀⡈⢻⡿⠳⠶⢦⣤⣤⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠛⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠛⣅⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣼⠂⠀⠀⠀⠀⢿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣗⠀⠈⠙⠷⣦⡀⠀⠀⢀⣴⣿⠋⠀⠚⠁⠀⠀⠀⠀⠀⠈⢿⡉⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⣷⠀⠈⠙⠆⣴⡟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢶⡶⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠿⡅⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⣀⡞⠁⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣷⡆⢸⣿⠛⠛⠀⣼⡿⠻⣷⡆⢠⣾⠛⠛⠇⢠⣶⠟⠛⣷⡄⢠⣿⣧⡀⣾⡇⠀⢠⣿⣷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠿⠃⢸⣿⠛⠛⠀⣿⡿⢾⣟⠁⠈⠛⠿⢿⣦⢸⣿⠀⠀⣸⡿⠠⣿⠙⣷⣿⡇⢀⣿⣇⣽⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠘⠿⠷⠟⠀⠻⠃⠀⠛⠗⠘⠳⠶⠟⠃⠀⠙⠳⠾⠛⠁⠀⠟⠀⠈⠻⠃⠘⠋⠀⠈⠻⠂⠻⠻⠾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⢰⣶⠀⢶⣄⢀⣶⠆⢀⣴⠶⠶⣦⠀⣶⡶⠶⠶⠠⢶⣶⠆⠀⣶⣦⠀⢰⡆⢠⣶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⢾⣿⠀⠈⢿⣿⠋⠀⣾⡏⠠⣦⣤⠀⣿⡷⠶⠆⠀⢸⣿⠀⠀⣿⠻⣷⣾⡇⢸⣿⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠸⠿⠀⠀⠸⠿⠀⠀⠘⠿⢶⡾⠿⠀⠿⠷⠶⠦⠠⠾⠿⠦⠀⠿⠀⠙⠿⠇⠸⠿⠶⠶⠆



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⣿⠖⠚⠛⠛⢻⡷⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣿⠀⠀⠀⢀⣼⠇⢀⣴⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⣿⠀⠀⠀⠛⢿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⢠⣾⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢹⡇⣿⠀⠀⠀⠀⢹⡇⠀⣿⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⣿⠂⣿⠀⠀⠀⠀⢸⣧⠾⠋⠀⠀⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⢁⡀⠀⠀⠀⣼⠇⣿⠛⠛⠛⠛⠿⠃⠀⠀⠀⠀⢰⡄⠀⠉⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⣠⡾⣿⠃⠀⠀⠀⠙⢧⡈⢳⣄⠀⠀⠀⠀⢶⣄⠀⠀⢸⠇⠀⠀⣠⠆⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⣸⡏⢰⡏⠀⠀⠀⠀⠀⠈⣿⠀⠙⣧⠀⠀⠀⠀⠙⠃⣠⣴⣦⣄⠚⠁⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀
⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢠⣤⣤⠀⣾⠁⠀⠀⢹⡆⢠⣤⣤⡄⠀⠀⠀⠀⠀⠈⠛⠷⣤
⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢻⣄⠀⠀⠀⠀⢠⡿⠀⠀⣿⠀⠀⠀⠀⠀⡙⢷⣤⣤⠞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⣀⣤⣤⣤⣤⡤⣤⣤⣤⡀⠀⠀⠀⠀⠙⢷⣄⣙⣶⣄⡀⠀⢸⡇⠀⠀⣿⠀⠀⠀⣠⠞⠁⠀⢠⡄⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠰⣾⣋⣡⡴⠶⣶⡶⢶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⢸⡇⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⢸⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠈⠛⠉⠀⠀⣿⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⢰⡞⠛⠛⠛⠛⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠲⠶⣤⡀
⠀⠀⢀⣼⣧⣤⣤⣤⣤⣤⣤⣼⣧⡀⠀⠀⠀⠀⠀⠀⢸⣟⣛⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠈⢻⡄
⠀⣰⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣄⠀⠀⠀⠀⠀⢸⣿⣉⣻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⢀⣤⢤⣄⠀⠈⣷
⠀⡿⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣿⠀⠀⣤⠶⠶⠛⠉⠉⠉⠙⠳⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⢸⡇⠀⣿⠀⠀⣷⣄
⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⡇⠀⣀⣀⣴⠟⢶⣄⣀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⢰⡏⢨⣿⠀⣸⡇⠀⣿⡀⠀⣿⠈⣷
⠀⣿⠀⠀⠀⠀⣤⠶⠶⣄⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠉⠻⣤⡾⠋⣿⡇⠀⣿⠀⠀⠀⠀⠀⢐⡟⠀⢹⡆⢸⡇⠀⣿⢰⡏⠀⠀⠈⣷⠀⣿⠀⣿
⠀⣿⠀⠀⢀⣘⣿⡀⢀⣽⣀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⠶⠶⠶⠄⣿⡇⠀⣿⠀⠀⠀⠀⠀⠘⣷⠞⢻⡇⢸⡇⠘⣿⠘⣧⠀⠀⢠⡟⠀⣿⠀⣿
⠀⣿⠀⠀⠈⠉⠉⠛⠛⠉⠉⠁⠀⠀⣿⠀⢸⡇⠀⣿⠀⠰⠶⠶⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠘⣷⠶⢿⡇⠘⣧⣘⣿⠀⢹⡇⠀⣿⠁⠀⣿⣠⡿
⠀⣿⠀⠀⠾⠿⠿⠿⠿⠷⠾⠷⠀⠀⣿⠀⢸⡇⠀⠻⠿⠿⠾⠷⠷⠿⠃⠀⣿⠀⠀⠀⣰⠟⠠⣧⡴⢿⡇⠀⠈⠛⣿⠀⢸⡇⠀⣿⠀⠀⣿⠉
⠀⣿⠀⠀⠀⠘⠛⠃⠘⠛⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠋⠀⠘⠿⣶⠾⠇⠀⠀⠘⣿⠀⠈⠛⠛⠋⠀⢀⡿
⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⡇⠀⠰⠶⠶⠶⠶⠶⠶⠶⢶⣿⠰⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⢀⡼⠃
⣀⣻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣟⣀⣈⣻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣁⣀⣀⣀⣀⣀⣴⣾⣃⣀⣀⣀⣀⣀⣀⣉⣻⣶⣶⣾⣋⣁⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣏⠈⠉⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣿⠿⢟⣛⣿⣮⣛⠻⠿⠟⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣾⣿⡟⢡⡾⣫⡿⣿⣿⢿⡿⣿⡿⣯⣻⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣳⣤⣽⣿⡿⢱⣿⣿⡟⣰⢏⣿⣹⣗⣿⢷⡙⢿⣮⣛⠶⣿⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣩⣽⣿⣿⣿⠃⣼⡿⣹⡇⣿⣿⢿⠙⣿⣽⣆⣿⢦⡙⢿⣷⣮⠻⣿⣷⡶⣆⠀⠘⠻⠶⠶⠾⠟
⠀⠀⠀⠀⠀⣠⣤⠖⠛⠉⢱⠞⢻⣿⡽⢟⣡⠞⣽⣿⣿⡇⣿⣿⣿⡆⣿⣿⢿⣧⣾⠻⣆⠹⣎⢷⠘⣯⠻⣟⠛⠛⢶⡄⠀⣤⠶⠖⠛⠻⢦⣄
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠘⠻⣯⣭⠶⣻⣿⠾⢋⡾⣡⣿⣿⣏⣼⠇⣿⣿⡘⣏⢹⣧⣹⠌⣿⢿⡆⢿⡛⠋⠀⣴⣟⣁⠀⠙⠛⠛⠛⠛⠛⠋
⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⣰⣟⣫⡾⢿⡏⣿⣿⡟⣰⡏⣿⣇⢿⡿⣿⣿⠀⣿⣌⢳⣼⣿⡆⠀⠀⠀⠉⢻⡆⠀⠰⣾⣿⠆
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⢻⡆⠀⢾⣿⣧⠾⠷⠞⠻⣷⢿⣟⣱⢿⡇⢿⣿⣎⢻⣿⢿⡶⣷⠾⠀⠉⠋⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣹⣾⠟⠋⠀⣿⣼⠁⣿⢻⡇⠘⠷⠛⢀⣀⣠⣤⡴⠶⠛⢉⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠛⠓⠒⠛⠛⠛⣋⣉⣩⣉⠛⠦⣤⣤⣤⣬⣅⡀⢙⣋⣡⡤⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣤⠴⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⢤⡀⢀⡠⠐⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣇⠀⣠⠀⠀⠀⢠⣤⠀⠀⠀⠔⠀⠉⠁⠢
⠀⠀⠓⠃⠀⠀⢰⠁⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢁⣀⡀⠀⠉⠉⠀⠀⢀⡀⠈⠀⠀⢘⢀⡄⠀⠀⠀⠀⡔⠁⠉
⠀⠀⠀⠀⢠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⠀⠀⠀⠀⢀⡜⠢⡠⠚⣄⠀⠀⢀⡴⠥⠄⠠⠤⢄⡀
⠀⠀⠀⠀⣈⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠥⢀⠀⠀⠀⠀⠀⠃⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠒⠈⠀⠀⠀⠀⠒⠎⠀⠀⣠⣒⡒⠦⠔⠒⠢⠤⡄⠀⠈⠑⢄⠒
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡇⠰⡞⡵⣶⡦⠀⠀⣬⣭⣁⠁⠀⠀⠀⣸
⠀⡏⢉⠉⡉⠉⡉⢉⠉⣀⣀⡄⠬⠤⠄⢀⡀⠀⠀⠁⠀⠇⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⢹⢶⠀⢏⡻⡇⠀⢸⡸⣿⠁⢃⠒⣄⡴⠃⡖
⠀⡇⠀⠀⢀⢸⡀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠛⢭⠭⠍⠀⡥⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⢸⠈⢆⠀⢰⡥⠤⣴⠉⠁⢀⡌⢴⠉⠀⠆⡗
⠀⡇⢀⠀⡰⠊⠀⠀⠤⠤⢤⣄⠀⠐⠒⣠⢄⡀⢣⡠⠀⡇⠰⠐⠒⠐⠂⢲⠒⠂⠀⠀⢸⠀⠨⠷⡦⢭⣨⡥⡴⢚⠉⡹⢋⢧⣁⣤⣷
⠉⠀⠉⠀⡇⠀⠀⠀⠉⠐⣚⣧⠀⠀⢴⣻⡄⢃⡿⢤⠀⡇⢀⠀⠀⠀⠀⢸⠀⢀⠀⠖⠁⠁⠐⡞⠀⢰⠀⠅⢀⢸⠊⠐⠁⠈⡇⡐⡒
⣀⡄⠉⠁⠳⢦⠃⡵⠇⠀⣌⢫⠇⠀⣩⡛⡣⢸⠃⠜⠀⠃⢸⠀⠀⠀⠀⢸⠀⠈⠀⠐⠂⠈⠀⠳⠄⣨⡀⢘⢇⣀⠉⠒⠒⠘⣧⠆⢇
⢀⣠⣤⠦⠄⠠⠛⢦⠀⠀⠈⡵⢦⣤⣷⠍⠀⠌⠀⣁⠀⡁⢸⠀⠀⠀⠀⢸⡔⠁⠠⠔⠀⣰⢯⢻⡄⢙⡷⢡⠞⡀⠈⠑⠒⠒⠙⡀⢸
⠈⡆⠀⡬⢤⢰⣪⠞⠓⢤⣀⠘⠂⢐⣋⣤⠞⢋⡡⠜⡇⡀⢸⠀⠀⠀⠀⢸⠐⠤⢄⣀⣄⣀⡄⠀⣠⢈⣱⡁⠀⣣⣀⣀⣀⠠⠔⡇⠸
⣀⣿⠀⠇⠲⡼⡅⠀⠀⡇⠉⢛⠫⠚⡩⠔⠊⠁⠀⠰⠁⡀⠗⠠⠦⠠⠄⣸⠄⠂⠌⠣⠸⠄⢤⠔⡹⡏⢸⠁⠀⠀⢳⠀⠀⠀⠀⣭⢉
⠤⠘⠀⡇⡘⢰⣀⡀⠠⢼⢠⠋⡝⠁⠀⠀⠀⢀⠠⠺⣒⣊⡉⠔⠓⡄⠢⠔⠢⡀⠈⡉⠤⠶⣭⠊⠀⡆⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⠄
⠒⠉⠀⢹⠁⠈⠲⠒⠛⢋⡇⠸⠀⢀⡠⠔⢊⡡⢐⠩⠐⠉⡠⠔⠊⢳⠴⠒⠛⠩⠀⠀⠀⠀⣿⠈⠀⠉⢸⠀⠀⠀⡞⠹⡄⠀⠀⢸
⠀⠶⠄⠱⢤⣀⡀⠑⠢⢄⡑⠦⣮⣅⠴⠮⡔⠊⣀⠤⠂⠁⠀⠀⠀⠸⡄⢀⣀⠀⠀⠀⡐⠀⢸⠠⠶⠄⠸⣽⣖⣱⠇⠀⢳⡁⢮⡼⢀
⠀⠀⠀⡐⠁⠀⠈⠉⢲⠚⠻⣄⣠⣏⠀⠂⠓⢎⠀⠀⢠⠊⣿⠽⠂⣄⢗⠝⠁⠀⠀⠠⠀⠀⣴⠀⢀⣄⢰⠃⠄⢇⠀⠒⣂⢇⡀⣇⠈
⠀⠀⠀⡇⠀⠀⠀⢰⡟⠈⠀⠘⢟⠋⠀⠀⠀⠈⠄⠀⠠⢡⠀⢀⡶⣼⠚⡤⠖⠤⠒⣦⣐⠊⡿⠴⣥⠤⠥⠤⠤⢬⡖⠛⠚⠀⠀⢈⡆
⠀⠀⠀⡇⠀⠀⠀⠘⢹⠀⠀⠀⠘⡣⡀⠀⠀⠀⠈⠀⠘⢯⣉⡜⠂⠁⠀⡛⢄⢠⡾⠜⣹⡦⣤⡔⠉⠉⠈⠈⠁⠉⠓⠀⠈⠉⠓⠒⣁
⠀⠤⡄⡇⠀⠀⠀⡇⠈⡆⠀⠀⠀⡗⠓⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠜⠉⠛⠉⠙⢎⠀⠀⢙⢆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⡧⠤⠤⢤⡇⠀⢸⡄⠀⠠⡇⠀⠈⢢⡀⣀⠀⠈⡄⠀⠀⠀⠀⠎⠀⡘⠀⠀⠈⡈⢣⠀⠀⠁⢻⠉⠙
⠀⠀⠀⢹⣁⣹⣉⡀⠀⠀⠹⠤⠽⡥⢄⠀⠋⣕⢄⠱⡀⠘⣄⣀⠤⢸⠀⢠⠀⠀⠀⠀⠰⠈⡆⢀⠈⠈⡆⠀⠀⠀⠀⠀⠐⠓⠶⠳
⠀⠤⠤⢾⣀⠀⠁⣈⣧⠒⢷⢄⣀⣀⠠⡧⠡⣑⣀⡤⠋⠀⠉⠀⠀⢸⠀⠘⠄⠀⠀⠀⠀⠀⢡⣀⣙⣀⣱⣄⡀
⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣐⣲⣆⣀⣀⣀⣀⣀⣘⣙⣁⣘⣒⣒⣔⣒⣒⣚⣒⣒⣚⣃⣀⣀⣈⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠶⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡛⠁⠀⡀⠀⠄⠀⠀⠘⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⣶⢀⢼⣿⠀⡐⠀⣠⡀⣹⣿⡆⠀⠀⠉⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡼⣿⣾⣿⣿⠟⠹⠈⣿⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⡏⠙⠃⠉⠁⠀⢠⡀⢁⠀⠀⠒⡄⠀⠠⢦⡀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠉⠙⠛⠁⠃⠀⠀⠀⠀⠈⠂⠉⣈⡀⠀⠀⠐⢤⣄⡀⠑⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣨⡇⠰⣀⢧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡄⠀⠀⠐⠅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡙⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢼⠂⠹⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣾⡿⠳⠾⣿⣠⠘⠮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠃⠀⠀⠀⠈⠙⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⡼⠃⠀⠀⠈⡌⢹⠋⣄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣴⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⢠⠜⢻⠟⠀⠀⠀⠀⠀⢧⢸⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⡀⠀⠀⠀⠀⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢻⠀⠀⠀⠀⠀⠀⠀⢀⠱⡸⣧⠀⠀⠀⣤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⡐⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⡆⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⣴⠟⢹⠳⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⠿⣤⠀⢀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣿⡏⢠⡄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠾⠁⢠⡇⠀⠀⣀⠤⠖⠈⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠉⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡇⠀⠀⠠⠄⢀⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⣿⣿⣏⠁⠀⠀⡶⠤⠤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣷⣴⣦⣤⣦⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡿⣿⠛⠟⠛⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠀⠠⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⣶⣶⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠏⠀⠉⠙⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⡋⠁⠀⠀⠀⠀⠠⣿⡃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡟⠃⠀⠀⠀⠀⠀⢀⢀⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠤⢀⣿⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡀⠀⠀⠀⠀⠀⠘⣿⣿⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢛⠄⠀⠀⠀⠀⠀⠀⡏⣿⡇⢻⡇⠀⠀⠐⠀⢀⠀⠀⠀⣾⠇⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⢠⠘⡄⠀⠀⠟⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠘⠃⠀⠀⠀⠀⠀⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡙⣉⡉⣿⠁⣽⠉⣩⡍⡋⣭⡟⢩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⠤⣤⣄⠀⣤⣤⣤⠤⠤⣤⠀⣤⣤⣤⡤⠤⣤⡀⣤⣤⣤⠤⣄
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⣿⣿⣿⠀⠀⠛⠀⣿⣿⣿⠀⠀⠙⠀⢻⣿⣿⡄⠀⠙⠀⢸⣿⣿⠀⠘⡇⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣾⣿⡃⠀⣿⣿⣿⣴⠃⠀⠀⢸⣿⣿⡄⣆⠀⠀⢸⣿⣿⣄⣶⠀⠀⢸⣿⣿⠀⠀⡇⠀⣻⣿⣷⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠛⠁⠀⣿⣿⡇⠘⠀⠀⠀⢸⣿⣿⠂⠀⠀⠀⢸⣿⣿⡇⠈⠀⠀⢸⣿⣿⠀⢰⠇⠀⠙⠋⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⣸⣿⣿⣆⠀⣰⠀⣸⣿⣿⣇⠀⣰⢀⣸⣿⣿⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⡉⢉⡉⢀⡉⠉⡉⢉⠉⠉⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡁⢸⡇⢸⡏⢸⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⠉⡲⢄⠀⠿⠇⠸⡇⢸⡇⠸⠿⠠⢀⡶⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣸⣿⠀⠈⢪⣳⡀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠱⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⣻⡄⠀⠀⣇⠡⡀⠀⡀⠀⠀⠀⢠⣫⣇⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠰⣏⢄⡙⣻⡁⠀⠀⡀⠙⠛⢿⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣰⠾⠉⠋⣡⣥⣿⣽⡄⠱⣄⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣯⣠⡢⢞⣵⡞⣁⢀⣴⣤⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⣉⣭⣟⢈⣿⡄⠈⣿⡂⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠆⢀⣽⣿⣿⡀⠿⢷⣈⣿⣉⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠳⣎⣉⡟⣶⣿⣿⢻⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⢹⣷⣿⣿⣿⣭⡹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⠿⠛⠊⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠐⠀⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⢻⡄⠀⠀⣾⣿⣿⠃⠀⠙⣧⠀⠀⠀⣴⣿⣿⠟⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⣇⠀⢰⣿⣿⡏⠀⠀⠀⢸⡇⠀⣼⣿⣿⡏⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢰⡇⠀⢸⣿⣿⡇⠀⠀⠀⢸⡇⠀⣿⣿⣿⡇⠀⠲⠲⣶⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣼⠃⠀⢹⣿⣿⣇⠀⠀⠀⣼⠁⠀⢻⣿⣿⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣀⡾⠃⠀⠀⠀⢿⣿⣿⣄⢀⣼⠃⠀⠀⠈⢿⣿⣷⣀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⢀⠔⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣀⣤⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢠⣿⠃⠀⡴⠋⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣥⣀⡀
⠀⠀⢀⣴⠞⠀⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠈⠛⠛⠷⣄
⠀⠀⢸⣇⠀⡸⠛⠿⠟⢿⣿⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠙⢿⠷⠄⠀⠀⣾⣿⠀⣷⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠘⠆⣀⡀⢰⣿⠁⢸⣿⡀⠀⢹⣧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠴⠋⠀⠀⣠⣾⡿⠛⠉
⠀⠀⢠⡾⠿⠾⠟⠁⢺⡇⠀⣾⣿⡇⠀⢸⣿⠀⠀⠀⣧⡀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣿⡇⠀⠀⠸⢷⣄⠀⠀⣼⣿⠋
⠀⠀⢿⡇⠀⠀⠀⠀⠘⣷⡀⢻⣿⡇⠀⠀⣿⠀⠀⢰⣿⡇⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⣿⡇⢠⣀⣀⣾⠋⠀⣰⣿⡏
⠀⠀⠀⣿⠇⠀⣀⣀⠀⠸⣷⡈⢻⣇⠀⢠⣿⠀⠀⢸⣿⠃⠀⠀⠀⣾⠏⣰⡄⠀⠀⢠⣿⡇⠈⢹⡏⠀⠀⢰⣿⣿
⠀⠀⠀⠻⣦⣾⠋⠙⢷⠀⠘⣷⣤⣹⣆⠘⣿⠀⠀⣼⡏⠀⠀⠀⣸⣿⠀⣿⡇⠀⠀⣾⡟⠀⣶⡾⠃⠀⣰⣿⡿⢻⣧
⠀⠀⠀⠀⢸⣷⠀⣀⠀⠀⣴⡿⠉⠉⣿⡀⢻⡆⠀⢻⣇⠀⠀⠀⢿⡇⠀⢸⣇⠀⠠⣿⠷⠶⠛⠀⣠⣾⡿⠋⠀⢸⣿
⠀⠀⠀⠀⣸⣿⣶⡿⠁⢰⣿⠁⠀⢀⠘⢷⣸⣿⠀⢸⣿⡀⠀⠀⠸⣧⠀⠀⠻⣦⣠⡿⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⢿⡄⠀⠀⠀⢸⣿⠀⣴⠟⠀⠀⠉⠻⣦⡀⢿⣧⠀⠀⠀⣿⡆⠀⠀⠈⠉⣡⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠈⢣⣤⡀⠀⢸⣯⣼⡏⣠⡟⠀⠀⣠⣿⠿⣾⣿⣦⠀⠀⢻⣧⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣄⣼⠃
⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣹⡟⣰⡟⠀⠀⣾⣿⠏⠀⠀⠀⢹⣷⠀⠘⣿⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⠟⠁
⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠻⢷⡿⠁⢀⣴⡿⠃⠀⢀⣼⠃⠀⢹⣷⣼⠟⠉⠀⠀⠀⠀⢠⡀⠀⠀⠀⣸⣷⡾⠋
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠘⠿⠿⠿⠟⠁⠀⠀⢿⣥⣤⣶⡿⠟⠁⠀⠀⠀⠰⣤⣤⠿⠁⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⡇⠀⠰⠶⣶⡟⠁
⠀⠀⠀⠀⠀⠻⣶⡀⠀⢶⡄⠀⠀⠀⠈⠳⣶⣆⣀⡀⠀⣤⣤⣴⠞⠻⣦⣤⣴⣾⠟⠁⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣧⣤⡾⠃⠀⠀⠀⠀⠀⠈⢉⣻⣷⡚⠋⠁⠀⠀⠀⠸⣯⡀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣤⣤⣴⠶⠟⠛⠋⠛⠿⣶⣦⣀⠀⠀⠀⠙⠻⠦⣤⡤⠾⠋⠁
⠀⠀⠀⠀⠀⣀⣤⣀⠀⣾⣿⠋⠉⠀⠀⢠⣀⠘⣿⠙⠂⠈⠙⠛⠷⣦⣄
⠀⠀⠀⠀⠰⣿⣩⡿⠂⣿⡿⣦⣄⠀⠀⠀⠙⠛⠁⣴⠟⠛⣷⠄⠀⠈⠙⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⡇⠈⠙⢿⣦⣄⠀⠀⠀⠙⠟⣛⣥⣤⡶⢶⣶⠀⠈⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⢺⠁⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⠛⠿⣶⣄⠀⠀⠀⠀⠈⡿⠟⣡⣤⡶⢦⡄⠀⠉⠛⠿⣷⣦⣄⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣤⣿⡄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠙⠉⠙⠛⠛⠁⠀⠀⢀⣀⣤⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⣰⣿⣄⡀⠙⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⣀⣴⣶⣶⠾⠟⠋⠁⠀⠨⡷⠀⡤⠶⠶⣄⠀⠀⠀⠀⠸⡏⣀⣿⠄
⠀⠀⠀⠀⠀⣿⠀⠘⢿⣾⣋⡉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣇⠘⠁⡀⢀⣿⠇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢺⡟⢳⠿⠷⠶⣾⠏⠉⠙⣷⡀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠛⠛⠀⢠⡴⠶⠶⣤⡀
⠀⠀⠀⠙⠛⠀⠀⠀⢿⣄⣀⣤⣿⠃⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⠶⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⣟⢀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠁

⡎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢠⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⣠⣾⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠛⣿⡟
⡇⠀⠘⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⢠⣿⣿⠿⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠿⠿
⡇⠀⠀⠀⠈⠛⢿⣧⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⡇⠀⠀⠀⠀⢸⣿⡏⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄
⡇⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⣿⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⣾⣷⣾⣶⡇
⡇⢀⣄⣀⡀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣫⣳⣿⡇
⡇⠀⠀⠉⠉⠙⠓⠒⠤⣄⡀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠸⣿⡟⠁⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡘⠻⠿⠿⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠐⠒⠀⠀⠀⠀⠀⠐⠂⠐⠀⠊⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡆
⡇⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⢀⡼⠋⣹⠇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣤⣶⣶⣿⣷⣶⣶⣿⡀
⡇⠀⠀⢠⣿⠇⠀⠀⠀⠀⢀⡾⡕⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠢⡀⣀⠄⡞⠁⠀⠀⣰⢿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣟⣻⣿⣿⣽⣾⡿⠛⠉⠁
⡇⠀⠀⣸⣿⠁⠀⠀⠀⢠⡞⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡀⠔⠋⢠⡎⠀⠀⠀⡴⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⠿⠿⣿⣿⠉⠁
⡇⠀⠀⣿⡗⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢉⠂⢀⡾⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⣿⡀
⡇⠀⢸⣿⠃⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⢠⠋⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣿⣷⡀
⡇⠀⠈⠙⠂⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠻⡇
⠇⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠉⠈⠉⠈⠀⠈⠉⠉⠁⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠁

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠒⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣤
⡇⠀⠀⠀⠀⠀⠀⣰⣷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠤⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠁⢠⡆⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⢊⡴⣶⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡄⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣾⠃⢠⡟⠀⠀⠀⢀⣴⠟
⡇⠀⠀⠀⠀⢀⢰⣔⣿⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣾⠃⢠⡿⠁⠀⠀⣠⣾⠏
⡇⠀⠀⠀⠀⠀⣾⣿⣏⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡼⠃⢠⣿⠃⠀⢀⠞⡽⠃
⡇⠀⠀⠀⠀⢰⣿⣛⣭⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⠁⢀⣼⠁⠀⠐⢯⠞
⡇⠀⠀⠀⠀⠘⡻⠿⠿⠿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⢀⣾⠇
⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠈⠋
⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣿⣿⣾⢿⠿⠿⠿⢿⣿⢿⠿⠿⠿⢿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠦⠖⠦⡀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣷⠀⠀⡷⡇⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⡯⡀⠄⣐⡑⡘⢦⡀⠀⠀⠀⠀⡼⢡⣤⡌⣧⠀⡇⡇⠀⠀⠀⠀⠀⣿⣿⣶⣄⣠⢤⣼⡟
⠀⠀⠀⢀⣰⠛⠉⠙⢦⡄⠀⠀⠀⠀⠀⠙⢶⣄⠉⣡⠽⠊⠀⠀⠀⠀⠀⡇⠈⢭⠀⣿⠀⣱⡇⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠙⠓⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⠛⠚⣿⣤⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠉⠉⠛⠋
⠀⠀⣠⠔⢒⡒⠒⢤⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢶⣶⣤⣤⡄
⠀⢸⡇⡈⠀⠒⡃⠴⠃⠀⢸⠀⠀⠀⠀⣀⠴⢊⠅⣢⢟⠎⠳⡄⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡛⢑⡀⢃⢲⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢐⡧⢀⠋⠾⠓⡁⠔⣨⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⠈⠀⢸⢸
⠀⠸⡇⠀⠀⠀⠀⢠⣄⣀⡟⠀⠀⠀⠀⡷⣄⠑⣖⣡⠴⠋⠀⠀⠀⠀⠀⢀⣠⠔⣒⣿⡟⠉⢳⡆⠀⠀⠀⠀⠀⣷⣽⢀⠀⠀⣿
⠀⠀⠈⠒⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣳⣄⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠙⠾⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢠⣴⡳⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠞⠓⡆
⠀⠀⠘⣎⢳⠘⠉⠸⣿⡀⠀⠀⠀⢀⡤⠴⠉⠀⠀⠀⠀⠈⢓⣢⠀⠀⠀⠀⡶⣯⣶⡯⠕⠒⠢⣄⠀⠀⠀⠀⠀⠀⡨⠷⠾⣄
⠀⠀⢴⡚⠂⠀⠀⠀⢻⠃⠀⠀⠀⢸⡕⠀⢄⡀⠀⢀⣠⠒⢁⣼⠀⠀⢀⡴⢇⣻⠀⠀⣀⣴⣾⣿⠆⠀⠀⠀⡴⠋⠀⠀⠀⠀⠳⡀
⠀⠀⠀⢹⠓⢄⠀⠀⠈⢳⡀⠀⠀⠸⣧⣄⠀⠈⢙⠁⣀⣴⠟⠋⠀⠀⣸⣻⣦⣤⣴⡞⣣⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢼⣀⣈⣆⣀⣤⠾⠁⠀⠀⠀⠀⠙⠻⢶⣶⣶⠞⠁⠀⠀⠀⠀⠈⠙⠾⣽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⢀⢀⡞
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣠⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠘⣇⣀⡼⣏⠀⠀⠀⠀⢰⠛⢦⣀⣀⡀⠀⠀⠀⣠⢶⡄⠀⠀⢀⡤⠖⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢀⡿⠛⣧⣞⣲⣦
⠀⠀⠀⠀⠀⡿⠙⡇⠈⠀⠀⠀⠀⠈⣧⡾⠀⠈⠉⠉⠉⠉⢧⢸⠇⠀⠀⠙⡟⠒⠶⠶⠶⠒⡿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⡄
⠀⠀⠀⢠⣎⠀⠀⢙⡆⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢻⠢⠤⠤⠴⢺⡇⠀⠀⠀⠀⠀⢸⡏⠈⠉⠉⠁⠹⡇
⠀⠀⠀⢸⣇⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠈⠳⠤⢤⡤⠞⠀⠀⠀⠀⠀⠀⢫⠢⠤⠤⠤⠤⠒⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠕⠆⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⡏⢡⡀⠑
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠉⠒⠉⠉⡠⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢐⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⢠⠂⠂⠒⠀⠀⠀⠀⠀⢤⢀⡗⠈⠢⠤⠄⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠉⢀⠽⡽⠋⠒⠂⠀⠀⠀⠀⠤⠐⡇⠀⠀⠀⠀⠀⠀⠈⠆⢄⠀⢄⢀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠲⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢠⡃⠀⢱⠂
⠀⠀⠀⠀⢬⠇⠀⠀⠀⠀⠀⢸⠌⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡶⢫⣜⠒⠊
⠀⠀⠀⠀⠂⠲⢁⠀⠀⠀⠀⠇⠀⠠⠒⠎⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡰⠡⠃⠀⠉⡆
⠀⠀⠀⠀⠀⠃⠈⡄⠲⠀⠴⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠰⠖⡐⠠⠁⠀⠀⠠⠁
⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⡰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠏⡐⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⡠⠄⠒⠀⠈⠀⠈⢸⠄⠀⡠⠂⢸
⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠀⢀⠼⠠⣀⣀⡀⠀⢠⡁⠊⠆⠀⠠⠀⠀⣉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣀⣶⡿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢧⣼⠻⡿⠎⠿⣿⢿⣏⠩⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠹⢳⣿⣷⣶⣌⣷⡉⠃⢀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣔⡢⡀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠁⠀⠉⠉⠳⠶⠟⠛⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡞⠿⠙⠁⠉⠉⠁⠀⡀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡐⠻⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⢿⣿⣛⡛⡡⢀⣀⡄⢠⣳⣦⣶⡔⠀⠀⠀⢙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢈⠛⢳⠀⣥⡇
⠀⠀⠀⠀⢀⣴⡿⡟⠛⠁⠒⠀⠛⠋⢁⢠⠆⠀⢸⣮⣝⠉⠙⡄⠀⠀⠀⠻⠮⡇⠀⢠⣤⣀⡀⠀⠀⠀⠀⢀⣲⣌⢣⣹⣿⣿
⠀⠀⠀⢀⣾⣿⣿⣧⠰⣶⣴⢂⣴⠂⢸⣿⣧⣶⡼⠛⠀⠀⠀⠘⠀⡘⠀⢀⠜⠀⠀⠀⣯⣉⠙⠷⡄⠀⠀⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⣾⣿⣿⡿⠋⠀⢀⣥⣿⡟⠉⠉⣿⣿⣧⠄⠀⠀⠀⢠⠞⠇⠁⠠⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⠿⠛⢟⡛⣿⠏
⠀⠀⢸⣿⣿⣿⡇⠀⢠⣿⢿⠿⠀⣀⡀⣿⠿⢿⠀⠀⠀⢰⠁⣰⠇⠈⠐⢄⠉⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡇
⠀⠀⠘⣿⢻⣿⡀⠀⠈⢧⣸⣄⣾⡿⠘⠱⣾⣶⠅⠀⠀⠁⠀⠀⠀⠀⠌⠀⠉⠲⠤⠄⠀⡄⠀⠀⠀⠀⠀⠐⠋⡁⠔
⠀⠀⠀⣿⣇⢿⠏⠀⠀⢾⣷⡸⣿⡷⠄⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠞⠐⠈
⠀⠀⠀⢹⣿⣌⣣⣴⡄⠀⠀⣠⣿⠇⠀⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠐⢭⠁⠀⠀⠀⣀⣀⡤⠤⠔⠊⠁
⠀⠀⠀⠈⢿⡞⣿⣿⡇⠀⢰⣾⡇⠐⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠉⠁
⠀⠀⠀⠀⠈⠋⠈⢿⣿⣌⠺⢿⣭⣴⡖⠒⠤⠞⠀⠀⠀⠀⢀⣀⡠⠔⠊
⠀⠀⠀⢦⣇⣴⣷⢈⣹⡿⢥⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠸⡻⣿⣿⣼⣯⣉⣭⣿⣿⠏⠁
⠀⠀⠀⠀⠈⠀⠀⠚⠻⠿⠟⠋

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⢷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠈⢉⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣷⣤⣤⣴⣶⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠿⠿⠿⠟⠛⠛⠛⠻⢿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⣀
⠀⠀⠀⣀⣤⣶⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢷⣶⣤⡀
⠀⠀⣼⡟⠉⠀⠀⠀⢀⣠⣴⣶⣾⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⣶⣶⣤⣄⡀⠀⠀⠈⠙⢿⣦
⠀⠀⣿⣷⣤⣀⠀⢰⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡆⠀⣀⣤⣾⣿
⠀⠀⣿⡏⠙⠻⠿⣿⣿⣷⣶⣤⣤⣀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⣠⣤⣤⣶⣿⣿⡿⠿⠛⠋⢹⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⣿⡇⠀⣿⡏⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠙⠿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣷⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣶⣶⣶⣴⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣤⣶⣶⣶⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣿⣿⣶⣶⣶⣶⣶⡾⠟⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣠⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⡦
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⣖⢒⡇
⠀⠀⠀⠀⢸⠀⣴⡜⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠿⠯⢼
⠀⠀⠀⠀⠘⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂


⠀⠀⠀⠀⠀⣀⣀⣀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢠
⠀⠀⠀⠀⢰⠁⠀⠨⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠸⠘⠄
⠀⠀⠀⠀⢇⠀⠀⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⠓⡆
⠀⠀⠀⠀⠀⠁⠒⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⣰⣁⣰⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠄
⠀⠀⠀⠀⢸⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠱⠋⠉⠉⠉⠉⠙⡗⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠘⡀⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⣇⡇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣾⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀⣤⣀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠈⠻⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⢠⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠈⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠼⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄⢠⣾⣶⡄⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠾⣟⡛⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠡⠀⠠⢴⡾⢶⣿⣿⣿⠛⠡⠤⢤⣙⢿⣿⣿⣿⡆⣿⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠠⠦⡌⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠒⠉⢀⡚⠒⠛⠳⢝⢿⣿⠰⠻⣡⡀⣘⡇
⠀⠀⠀⠀⠀⣰⠀⠘⣇⠹⣿⢿⢷⣶⣄⡀⢀⠀⠀⣰⡇⠰⠂⠈⠙⢦⣄⣀⣐⣄⣄⠀⢣⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢷⣤⣌⣳⣶⣤⠦⣉⠻⣿⣮⡟⠛⠟⠀⠀⠀⠀⢶⣄⣬⠉⠉⣿⣿⡄⠞⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠢⠌⠳⣦⣴⠾⢃⡀⠀⠀⠀⠀⠛⠯⠀⡀⢀⣿⣿⣧⠈⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣀⠀⠀⠀⠀⠁⠀⢤⡶⠟⠛⠶⠀⠀⠀⠤⠶⠾⠋⡼⢻⣿⣿⠀⣿⣿⡀⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡞⠁⣼⢿⡏⢠⡘⠿⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⢳⡄⠀⠀⠀⠀⢠⠞⣷⣦⡀⠀⠀⠀⠀⠀⢡⡌⢻⣁⣾⠧⣄⣙⠳⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠿⣧⠀⠀⠀⠀⠀⢤⠿⠛⠁⠀⠀⠀⠀⠀⢲⡄⢸⣿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠙⠂⠉⠀⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢫⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠠⣴⠶⠶⠦⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⠛⠛⠁⠀⠀⠀⣴⣊⠉⠁⠀⠀⠀⣀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣽⠀⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠾⣅⢘⠀⠀⠀⠀⠀⢀⡀⣀⠜⠚⢻⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠈⢿⡅⣀⣙⠀⠏⢉⡽⢁⠄⣠⠞⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡆⢀⣒⠚⠇⢹⣿⡗⠀⠉⢚⣿⠋⣠⠔⣡⠾⡄⠀⢀⡴⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⡟⠀⠀⠈⠙⣿⣾⣿⣿⣧⠰⢻⣷⡞⣡⠞⢁⣴⡷⠖⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⢠⡟⢰⡟⠀⠀⠀⠀⠀⢈⣿⣿⣋⠁⢀⠈⠹⣿⢧⠾⠋⣡⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⡟⠠⣾⣃⠀⠀⠀⠀⠀⠘⡿⠿⠟⠃⠘⠳⠟⠛⠃⢰⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠏⠀⠀⣈⣛⡛⣦⠀⠀⠀⠐⣿⣿⣽⣧⣿⣴⣷⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠈⣍⡉⠙⢧⠀⠀⠀⢻⣿⣄⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⣄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠟⠛⠿⢃⣠⠟
⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⣰⡟⠀⠀⠚⠋⠁
⠀⠀⢀⣀⣿⠃⠀⠀⣀⣤⡾⠋
⠀⠀⠛⣩⣿⣄⠀⠀⠈⣿
⠀⠀⠈⢧⠼⢿⣷⣤⣀⠁⣼⢿
⠀⠀⠀⠀⢶⣼⡟⢳⡇⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠿

⠀⠀⠀⠀⢀⣤⣶⣤⣤⣤⣤⣠⣾⣿⣶⣄⣤⣤⣤⣤⣶⣤⡀
⠀⠀⠀⠀⣿⡃⠀⠀⠈⠉⣉⣉⣉⣉⣉⣉⡉⠉⠀⠀⠀⢹⡷
⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠛⢻⡟⠙⣿⠛⠛⠛⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣷⣴⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⣿⠟⠛⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠿⠿⠶⣦⣤⡀
⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠉⠛⣷⡄
⠀⠀⣿⣤⣤⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⡀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠈⠉⠉⠉⠙⢷⣄⣀⠀⠀⠀⠀⠀⡀⢀⣀⣴⡿⠋⠉⠙⠻⣦⡀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠘⣿⣀⣀⣀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⢶⣶⣶⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠛⠘⠛⠛⠙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠛⠻⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠺⠺⠿⠺⠺⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠺⠺⠷⢾⠺⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠶⠰⠖⠶⠲⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⣹⡇⠀⠀⢠⣴⠿⠛⢷⣆⣤⡶⢶⣦⡀⠀⠀⠀⣠⣶⠶⠿⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠛⠛⠋⠀⢀⣴⠟⠁⠀⠀⣠⠿⠋⠀⠀⣹⡇⠀⠀⢰⡟⠁⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠙⣷⡄⠀⠀⢀⣠⣼⣟⣵⡾⠟⠛⠻⢿⣦⣀⣠⣾⡿⢷⣄⠀⢸⣧⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⡇⠀⣰⡟⠉⠉⠙⣩⣶⣦⣄⠀⠀⠈⢋⡉⠉⠻⣾⣿⠀⠀⠙⠿⣶⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢀⣿⣡⡾⢛⣷⠞⠷⣾⣏⠀⠈⠙⢷⣤⣾⠛⠻⣷⣄⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⣸⣿⣿⡇⠸⣿⡀⠀⠈⠻⣷⣄⠀⠀⠙⢷⣄⠀⠈⠻⣷⣄⠀⠻⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⢻⣧⣽⡷⢀⣽⣿⣦⡀⠀⠈⠻⣷⣄⠀⠀⠙⢷⣄⠀⠈⠻⣷⣄⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣿⠏⠀⣿⠋⠀⠙⢿⣦⡀⠀⠈⠻⣷⡄⠀⠀⠙⢷⣄⠀⠈⠻⣷⣤⣿
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠙⢷⣄⠀⠀⠙⢿⣦⡀⠀⠈⠻⣷⣄⠀⠀⠙⢷⣄⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠸⠟⠻⣦⣤⡀⠙⢷⣄⠀⠀⠙⠿⣦⡀⠀⠈⠻⣷⣄⠀⠀⠙⠁⠀⠀⠈⠛⢶⣀
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢷⣄⠀⠀⠙⢿⣦⡀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠙⢷⣄⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠿⣦⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⢟⣵⠾⠟⠻⠿⢾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠋⠀⠸⣿⣄⣀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄
⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠈⠻⣷⣄⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷
⠀⠀⠀⠀⠀⠀⠈⠻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡾⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠉⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢸⣤⠴⠚⠉⠉⠛⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⣴⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠲⢤⣀⠀⢹⣆⠀⢀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠳⠦⣤⣬⣵⣎⠉⡳⠮⣅⣀⡀⠀⠀⠤⣄⠰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣤⡾⠟⠉⠀⠀⢀⡽⡖⢄⡀⠀⠉⢳⡄⠀⠈⠳⡟⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⣇⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⢻⠟⠀⠀⠀⠀⢀⡞⢀⠟⢦⡙⢦⣀⡼⠁⠀⠀⠀⠀⠀⠈⠙⢮⣧⠀⠀⠀⢐⣮⠃⠑⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⠏⠀⠀⠀⠀⠀⣸⠁⢸⠀⠈⡟⠛⠋⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣠⠟⣧⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠀⠈⡆⠀⢱⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠞⠉⠃⢸⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⡄⣸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠉⠀⡟⢀⣴⠾⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢠⡏⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⣿⣧⣤⠀⡇⠀⠀⠀⠀⠀⠀⢠⣿⡀⢩⣾⠁⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠻⢿⣿⡃⣠⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⡌⢻⡀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠆⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠑⣼⡀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣀⠀⣀⠀⠀⠀⠀⠈⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠈⠳⡄⠀⠀⠀⠀⠀⡀⠀⠘⠿⡶⠟⠀⠀⠀⠀⢠⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⠀⠀⠀⠀⠱⠤⣄⣤⠀⠴⠂⠀⠀⣠⠟⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⢷⡀⠀⠀⢀⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣧⡀⠀⠀⠀⠀⠈⠡⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⢀⣸⡄⠀⠀⠀⣩⠷⠛⠉⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⠙⠛⠷⢒⡶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⡕⢌⣢⡄
⠀⠀⠀⠀⠀⠀⠈⠫⣍⠀⠀⡾⠁⠀⠀⠀⠀⠀⡼⢃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣤⡶⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⢸⠇⠀⠀⠀⠀⠐⣻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠁⠈⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡾⠑⠳⠤⠤⢖⠛⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⡄⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⣠⢔⡉⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⢧⠀⣰⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠉⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⡀⠀⠀⠀⠀⠀⠀⡜⢠⠀⠀⠀⠀⠀⠘⣶⠁⠀⠸⣷⡀⠈⢆⠀⠀⠀⠀⠀⠸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢿⡙⠶⣌⣣⣄⡀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⠀⠀⠀⠀⣠⠆⠀⠀⣾⠀⣧⡀⣝⠳⣤⣀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢳⣄⣈⠉⠛⠛⠛⠒⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢀⡤⠞⠁⣠⡞⣡⡟⢲⣎⡿⠟⠓⢦⣉⡉⣳⠊⢁⡞⠀⠀⠀⣠⣡⡜⠓⠒⠛⢯⡉⢈⠉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⣥⣒⠚⠋⠉⠉⢨⡇⣸⡾⠶⠶⠤⠾⠿⠛⠙⣠⠞⢀⠄⢀⡾⠉⠀⠀⠹⡆⢸⣾⠇⢨⡇⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠳⠞⠛⠶⠤⣤⣤⡴⠷⠚⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡆⠀⠀⢀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠧⠔⠡⠛⠷⠠⠆⠺⠁⠶⡰⠖⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡤⠤⣀⠀⣀⠀⠀⠀⠸⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⢠⠏⠈⠑⢦⠀⠀⠀⠉⢱⠖⠒⢲⠤⡤⠤⠤⠤⣤⠒⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠃⠀⠀⡠⠋⠑⠢⣄⠀⡸⢀⡴⠋⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡄⠄⠀⠤⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡔⠁⠀⠀⠀⠀⠙⢳⠉⠀⢀⠜⠓⠢⠐⠒⠛⢆⠀⠀⠀⡤⠒⠉⠉⠉⠉⠉⠁⠉⠉⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⡸⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⠴⠒⠚⠛⠉⠙⠛⠒⠒⢤⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⣠⡄⠀⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣷⠒⠒⠶⠶⠦⠴⠾⠤⠧⠤⠷⠤⠼⠦⠤⠤⠤⣄⣀⣀⣀⣀⣀⣼⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣏⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡹
⠀⠀⠀⠀⠀⠈⢣⠤⠤⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡞⠁
⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡎⢹⠀⢰⠋⢱⠀⢰⠉⣧⠀⢸⠉⡆⠀⡞⠙⡆⠀⡎⠙⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⢸⠀⢸⠀⢸⠀⣿⠀⢸⠀⡇⠀⡇⠀⡇⠀⡇⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⡇⠀⡇⠀⡇⠀⡇⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⡇⠀⡧⠀⡇⠀⡇⢰⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠉⢱⠒⢲⠤⠤⠄⢶⢲⡶⠢⡤⡤⡤⠤⡤⢤⡤⠛⡇⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⡇⠀⠁⠀⡇⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⢸⠀⣿⠀⢸⠏⡇⠀⡇⣧⡇⠀⡇⠀⡇⠀⡇⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⢸⣀⡇⠀⣤⠴⡇⠀⡇⣸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⢸⠀⢸⣄⣗⠀⢸⠀⡇⠀⡇⢿⡇⠀⡇⠀⡇⠀⡇⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⢸⠀⡇⠀⡧⠀⡇⠀⡇⣿⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠓⠊⠀⠈⠒⠋⠀⠘⠒⠃⠀⠙⠛⠁⠀⠑⠚⠁⠀⠓⠚⠀⠈⠓⠊⠀⠈⠒⠋⠀⠘⠒⠃⠀⠙⠒⠁⠀⠙⠛⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠄⠒⢒⣒⡠⠤⢄⡀
⠀⠀⢀⣀⢰⣠⠖⠉⠀⠀⠠⠐⠉⠉⠁⢀⣈⡁⠀⠈⠳⣄⡠⢀⡄
⠀⠐⢯⡁⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠀⣀⠴⠒⠋⠥⣪⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢀⠞⠁⠀⠀⠀⠀⠠⠄⠀⠀⠠⠤⠐⠒⠉⠀⠀⣀⡴⠚⢉⣇⠀⠀⠀⢀⣀⡠⢂⡭⠚⠋⠉⠀⠀⠉⠑⣢⣄⣠⠖⡒⠲⣄
⠀⡞⠠⠀⡰⠀⠀⠀⠠⠀⠠⠤⠤⠤⠤⠴⠖⠚⠋⠁⠀⠀⠘⣾⠀⢠⢞⠁⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡿⡄⠔⠈⣇
⢠⡇⡇⠀⠃⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡟⢠⡏⡈⠀⠀⠀⠀⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⣹⣹⠀⠁⡿
⢸⡇⢳⢀⠆⣀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢼⠆⠀⠀⠀⠉⠀⡇⣼⠇⠳⣄⣀⣀⣀⠀⠐⠒⢤⣀⠉⠒⠦⣤⣤⡴⡃⣯⡡⠔⠁
⠀⣧⠀⡎⡞⣡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⢠⠃⠸⣌⡧⠄⠉⡅⠈⠉⠲⣄⠀⢈⠳⡀⠀⠀⠀⠊⣠⡆
⠀⠹⡆⠀⠙⠮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠎⠀⠀⠸⡇⠄⠀⠀⠀⠀⠀⠘⢸⢇⢡⠀⠀⠀⠀⣰⢃⡇
⠀⠀⠹⣆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠤⢔⡵⠃⠀⠀⠀⠀⢇⠁⠀⢀⠀⠀⠀⠀⠀⠘⠃⠀⣀⠠⠚⢡⡾⠁
⠀⠀⠀⠈⠑⠮⠽⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⢤⡄⠀⠀⠀⠀⠈⢻⡋⠁⠀⠀⠀⠀⠀⠘⡀⠀⣀⠤⢔⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⡄⢲⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠈⠒⠤⣄⠀⠀⣀⣀⣧⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠑⠈⠉⠢⣄⠀⠀⠀⠀⢠⣾⣿⣦⣤⡀⠀⠀⠀⣀⠜⠤⠜⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⢀⠜⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⢠⠸⣀⠀⠀⠀⠈⠻⠿⠁⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠂⠀⠀⠀⠀⠀⡆⠀⠉⠒⠲⢴⠖⡤⠤⠔⠋⠙⠀⠀⠀⠀⠀⢧⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠸⠾⠤⠔⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⣀⣣⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠊⢂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠋⠷⠤⣤⠹⠷⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠢⠤⠤⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡚⢒⠀⠓⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠃⡤⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠓⠦⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⣝⠻⠖⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠞⠀⠀⠀⣠⢾⡷⡾⢀⡜⠙⣆⠀⠉⢫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣃⠀⢀⡠⢞⣁⠀⠀⠷⠋⢀⣀⠘⢆⣦⢀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⡹⡴⠋⠀⠈⠈⠁⠀⠀⠀⠈⠈⠀⠈⠙⡶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠀⢠⠄⠀⠀⠀⠰⡦⠀⠀⠀⡟⠱⡄⠀⢀⠜⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣇⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡷⠚⢁⡴⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠢⣤⠔⠀⠀⠀⢀⡴⠓⠋⠻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣀⣀⣀⣀⣠⣤⡖⠻⡇⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢙⠲⠋⠀⠳⠋⢘⡶⡹⠓⠒⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⢸⡀⠀⡠⠔⠶⣯⢾⣁⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠙⠲⣇⠀⠀⣸⠘⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢤⣀⠜⡽⠋⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⣄⣀⠀⠐⣏⠙⠒⢢⠀⠀⠀⠀⠀⣿⣷⡶⣫⣾⣶⣶⣶⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠉⠰⢧⡐⢥⡄⣰⠇⢀⣤⢖⠒⠒⢿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⠀⢀⣠⠇⠀⠉⠁⡴⠋⠘⠦⣳⢄⠀⠹⡟⢻⠛⠉⠛⢿⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠱⠤⠞⠁⠀⢀⡤⢊⠀⠀⢀⠀⠉⠻⣷⣤⠇⢸⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣔⠋⠀⠀⠀⡸⡏⠉⢹⡀⠀⠀⣸⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠴⣗⣋⣉⣹⠇⠀⠀⠿⢝⣛⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠤⣤⣤⣤⣤⡶⠶⠒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣠⠞⠋⠉⠁⣐⣒⡒⠾⠿⣟⡶⢦⠠⣤⡇
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣁⡄⠀⠚⢉⣩⣭⠭⠛⠒⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢠⡞⠁⠀⠀⣴⡋⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠘⣇
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢺⢗⣩⠄⠀⠁⠙⠲⢒⣯⣟⠇⠀⠀⣠⠞⠉⠙⠃⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⡞⢁⠄⠀⢀⣴⣾⣽⣫⠅⠀⠀⠀⠁⠀⠀⢶⠀⢻⡄
⠀⠀⠀⠀⣧⠀⠀⠀⣠⡶⢦⢶⠃⠀⠀⢈⡵⢫⡟⠁⠀⠀⠀⠀⠀⠳⠶⠾⠓⠀⠛⢦⡀⠀⣤⣄
⠀⠀⣠⠖⣻⢀⣠⢶⠏⠀⡏⠻⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠈⠛⢶⣛⣷⢶⣄⡀⠀⠀⢀⡀
⠀⢸⠇⢾⠁⡞⣿⠘⠀⣀⠀⠀⠀⠀⣄⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⠃⠀⠀⠀⠀⠉⠙⠻⣯⣷⣀⠔⡩⠃
⠀⠘⢧⡀⠈⠁⠀⠀⠀⠈⠛⠶⣤⣤⣬⣽⣟⣋⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣤⡀
⠀⠀⠀⢻⠀⠀⠀⠀⣝⠶⠤⡤⠶⠋⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣤⣤⣤⠤⠤⠤⠤⠤⢀⣠⣀⣀⡴⢀⡟
⠀⠀⠀⠘⣇⠀⠀⠀⠈⠙⠛⠁⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠶⡎⠋⠛⣶⠶⢤⣄⣀⠀⢼⢁⡞
⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣤⠞⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢹⣦⠀⠀⢀⡴⠋⠉⠙⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⠙⠻⠛⠙⠳⣤⣤⣄⣰⡞⠒⠶⠦⢤⣤⣤⡶⠏⠀⠀⠀⠘⡇⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠰⠶⣤⣄⣀⠀⠙⠿⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⡀⠀⠀⠉⠛⠶⣄⠀⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡴⠛⠉⠀⠀⠐⢦⡀⠀⠈⠁⢐⣛⢿⣤⡴⠆⡶⠀⠀⠀⠀⣼⠄⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⡄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⢿⣷⠇⠀⠶⡶⢤⣤⣤⣠⡷⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡟⠃⠀⠀⠀⠘⠃⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢠⣖⣒⡛⠡⣤⣀⠀⠀⠀⠀⢀⣠⠆⢀⠞⠀⠀⠀⠈⢿⣯⣤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⣤⣤⠙⠳⣄⢀⣴⠿⣧⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⢦⣤⣤⠘⢧⡀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⢿⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢰⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠸⠶⠃⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⠛⢻⡿⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⣤⣤⠀⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣷⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠀⠙⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠛⠛⠛⣿⣷⠀⠀⣠⠖⡉⠉⠑⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣶⣦⣶⡄⠀⣿⣿⡿⣫⣷⣶⣾⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⢛⡛⣠⣚⠽⣻⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣶⢶⡾⡫⣖⡥⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠫⣔⣭⡾⠟⠒⠒⠐⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣧⡚⠕⢫⣣⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠯⣻⢗⡤⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢝⣢⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣭⣬⣭⣽⣼⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣿⣯⣭⣭⣭⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠁⢀⠂⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠄⠀⢰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠤⠤⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⠈⡁⠞⢻⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣨⣄⣾⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠂⡂⢄⣐⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠓⠐⡀⠁⠄⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⡈⢃⡈⠤⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠤⠐⢂⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠉⠉⠓⠒⢤⡀⠀⠀⠀⠀⣠⠴⠒⠒⠛⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡈⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⢉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⣠⠀⠰⣿⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠋⠰⠂⠀⠀⠀⠀⠀⡄⠀⠐⣿⣿⣷⡟⣧⣶⣿⣿⡇⢀⣠⢄⡴⠀⡀⠀⠀⠀⠀⠀⠲⠈⠃
⠀⠀⠀⠀⠀⠀⢰⡀⣈⠀⠀⠰⠁⠂⠘⠿⣟⢝⢰⣲⣵⡻⡻⣿⣽⠟⠛⠱⠀⠀⢈⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣟⣷⡆⠈⣓⡑⣱⣏⢑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣴⣮⣴⡞⣄⡭⣄⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠼⡿⠻⡏⠁⢉⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈