Grandma Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⣉⣁⣀⣀⣀⣀⡀⠉⠙⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣾⣿⠿⠿⠟⠻⠿⠿⢿⣿⣶⣦⣄⡈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠙⢿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⡀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⠏⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠘⣿⣷⣴⣷⡄
⠀⠀⠀⠀⠀⠀⣼⣏⠉⠉⠁⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠒⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣿⣿⣤⣤⣶⡾⠿⠿⠿⠿⠿⣶⣦⡀⠀⠀⠀⣠⣶⠿⠿⠿⠿⠿⠿⣶⣤⣤⣿⣿⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⡀⣀⣴⣿⠋⠙⣿⠃⠀⠀⢰⣾⠿⠷⣆⠹⣿⣶⣶⣾⡟⢠⡾⠿⢷⣦⠀⠀⠈⣿⡏⠙⢿⣧⣀⢀⣀⣤⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣿⠁⠀⠀⢻⣦⠀⠀⠈⠁⠀⠀⠈⢠⣿⠁⠀⢿⣇⠈⠀⠀⠀⠉⠀⠀⢠⣿⠁⠀⠀⣹⣿⠿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠻⣷⡀⠀⠀⠹⢷⣦⣤⣤⣤⣤⣶⠟⠁⠀⠀⠈⠻⢷⣤⣤⣤⣤⣤⣾⠿⠃⠀⠀⣴⡿⠁⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣜⢿⣦⠀⠀⠀⠀⠉⠉⠉⢀⠠⣆⠀⠀⠀⠀⢀⡶⣄⠉⠉⠉⠁⠀⡄⠀⣠⣾⣏⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣤⣿⣷⡐⢧⣀⣀⣀⡴⠋⠀⠙⠷⠶⠶⠶⠛⠁⠈⠳⣄⣀⣀⣴⠇⣴⣿⣧⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣹⡇⠀⠉⠉⠁⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⣠⠀⠀⠉⠉⠀⢸⣿⠀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣸⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠛⠘⢷⣄⣀⠀⠀⢀⣀⣴⠟⠈⠉⠉⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣉⣉⣉⣉⣉⣀⠀⠀⣀⣈⣉⣉⣉⣉⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣦⣴⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡰⠈⠉⠱⠀⠀⠀⠀⠀⣀⠤⠔⠊⠉⠉⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣠⠂⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠊⠁⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠐⠀⠀⠘⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠁⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠠⠔⠒⠂⠀⠀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠶⠥⠤⡄⢠⠤⠬⠶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⣀⠔⠀⠀⡕⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡗⢺⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢀⡀⣀⣼⠀⠀⠀⠀⠀⠁⡇⢸⠈⠀⠀⠀⠀⠀⣧⡀⢀⠀⠀⠀⢀⡼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣎⡠⠋⠹⣤⢤⣤⡤⢤⣠⣇⣸⣤⡤⣤⣤⣤⣤⠇⠙⢌⣱⠀⢀⡜⠀⡄⠀⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠞⠁⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⠈⠳⡔⠋⠀⠀⠈⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⣀⢀⡀⡠⢄⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠠⣄⠀⠀⠀⠀⠑⠢⠤⠤⠤⠤⠔⠊⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡠⣄⢀⡀⡀
⢀⠤⢧⡀⢸⠁⠀⡅⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠈⠉⠒⠠⠄⣀⢀⡎⠑⠊⢱⡀⣀⠠⠄⠒⠉⠁⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⣈⠀⠈⡇⢀⡼⠤
⢰⡄⠀⡘⠈⠀⠀⠨⣄⣀⠀⠀⡞⠁⢣⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⡜⠀⢳⠀⠀⣀⣠⠅⠀⠀⠇⢃⡀⢠
⢧⣀⣀⣁⠀⢀⣀⡀⠀⠈⠙⠐⢧⣀⣈⢦⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⢀⡼⣁⣀⡼⠃⠋⠁⠀⢀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠈⠁⠉⠀⠉⠓⠦⣤⣀⡰⠉⡝⠀⠙⢦⣄⡀⠀⠀⠑⠦⣄⣀⠀⠀⢀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣠⠴⠋⠀⠫⠉⢆⣀⣤⠶⠚⠉⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠘⠦⣀⡠⡎⠉⠛⠲⢦⠤⣤⣤⣭⣭⣭⣭⣭⣭⣤⡤⠤⡴⠖⠛⠉⢱⢄⣄⠴⠃⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠙⠦⣀⠤⠻⡄⠀⠀⡰⡄⠀⠀⣠⢆⠀⠀⢠⠟⠤⡀⠴⠋⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠄⠞
⢀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠛⢛⣛⠒⠒⠒⠒⠒⠒⠒⠒⠒⣒⠛⢛⡛⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢋⣉⣉⣉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣰⠞⢋⣩⣭⣍⠛⢦⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣧⡤⠷⠶⠞⠓⠒⠚⠒⠶⠶⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⢉⣡⠶⠁⣠⡴⠂⢀⡾⢤⣀⠙⠶⣤⡈⠻⣯⣝⡳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣁⣤⡶⠛⣁⡴⠞⠉⢀⣴⠟⣠⢤⡉⠛⢦⣄⠉⠓⠦⣍⡛⠷⢮⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠚⠛⣉⣡⠴⠚⠉⠀⣠⣴⠟⣡⡞⠁⠀⠙⠷⣤⣈⠛⠦⣄⡀⠉⠛⠲⠶⠤⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠰⠶⠚⠛⠉⢀⣀⣤⡶⠟⣩⡴⠟⠁⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣉⠛⠶⠦⣤⣤⣀⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⣤⣤⠶⠶⠞⢛⣩⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠛⠶⢦⣤⣄⣉⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⣠⣤⣤⠶⠶⠛⠋⢁⣀⣤⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠉⠉⢹⣥⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠓⠦⢠⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣸⡆⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⡀⠀⠀⠀⠀⠀⢀⡿⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠉⠁⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡛⠳⠶⢚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣤⣤⣄⣀⣀⣀⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⡀⣨⠑⠒⠀⠁⠀⠀⠀⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣡⠶⠚⣿⠋⢁⢘⣧⡀⠀⠀⠀⠂⠀⠀⠰⣾⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡵⠃⠀⠀⠈⠙⠶⢾⠿⠛⠛⣶⣆⣀⠐⢉⠲⣄⠋⢿⠀⠀⠙⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡉⠀⠀⠺⣿⣷⣾⣿⡏⠀⠀⠀⢂⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠿⠛⠛⠿⠻⣿⣿⣯⣭⡒⠀⠀⠀⠀⣿⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠘⣷⡀⠀⢄⠀⠀⠀⢂⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢶⡄⣠⠏⡙⢿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡐⣿⣿⣦⣀⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢷⡙⠂⠑⠄⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⢰⣿⣿⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⢆⠘⢠⠏⢸⣿⠏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠘⠂⠁⠀⢺⡇⢠⣰⣶⣾⠷⢶⣶⣤⣄⣠⠀⠰⢀⣤⢴⣶⠶⠾⢶⣶⣄⠘⣷⡀⢈⠼⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡑⠄⠀⠀⢀⣿⣵⡟⠁⢀⣀⣷⣶⣅⡄⢼⣷⠶⠶⣿⢥⣄⣡⣾⣇⣀⠀⠉⣷⣼⣷⢀⢲⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣀⣠⡴⢿⡟⣿⠿⠛⢯⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⣨⠿⠻⢿⡿⣹⠿⣼⣸⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢥⣨⣿⣿⡇⠙⠦⣄⣀⣀⣀⣤⠶⠛⠀⠀⠀⠈⠳⢦⣄⣀⣀⣀⡤⠞⠃⣿⣶⣾⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⢷⡌⠀⠀⠉⠉⠀⢠⣾⣃⣀⣀⣀⣀⡱⣆⠀⠀⠉⠉⠀⠐⣰⡿⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢿⡶⠀⣀⢤⣤⠀⠀⠁⠈⠉⠉⠉⠀⠈⠠⣄⣀⣐⢢⣶⡟⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣇⢼⠉⠀⠈⠒⠲⠶⠶⠶⠶⠶⠶⠒⠀⠘⠛⢸⠂⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⣠⡀⠀⠀⠀⠀⢐⡀⢥⠴⢛⢽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡎⢻⣿⣷⡉⠉⠙⠿⢶⣶⡖⠊⠉⠀⠀⠀⠀⣼⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠒⠉⠁⢠⠀⢻⣧⣌⠲⡅⠀⠀⠀⠀⠐⠂⠀⠀⣠⢞⡟⢸⡇⣟⡗⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠋⣉⠀⠀⢠⡄⠀⠀⠈⡄⠀⢣⡙⢧⡀⠀⠀⠀⠀⠀⠀⣠⠞⣁⠟⠀⡟⠀⠈⠺⠻⢳⢉⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⠀⠀⠀⣠⣾⠵⠛⠉⢳⣤⠃⠀⠀⠀⠀⠁⠈⠜⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⢀⡀⠀⠀⠁⠀⢠⠄⠀⠉⠳⣄⣾⠟⠁⠀⠠⠄⠀⠉⠀⠐⠛⠀⠀⠲⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠃⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠲⠀⠀⠘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠆⠀⠀⠉⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠛⠋⠉⠉⠉⠙⠛⢿⣿⣷⣶⣶⣶⣶⣤⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠻⢿⣿⣿⠿⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠰⣿⣇⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣼⠃⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣷⣦
⣸⣿⡿⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣦⣿⣿⣦⣀⠀⣀⣠⣤⣾⣷⣾⣿⠟⠁⠀⠀⠀⣀⣀⣤⡶⠃⠀⠀⠈⠻⣿⣷
⣿⣿⡇⠀⠀⠰⣇⠀⠀⠀⠻⣦⣄⣀⣀⣀⣀⣠⣤⠆⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠙⠛⠛⢿⣿⣯⣉⣁⣀⠀⠀⢸⡆⠀⢹⣿
⣿⣿⡇⠀⠀⠀⠙⢿⣶⣶⣶⣾⣿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣉⡉⠉⢀⣠⣿⠃⠀⢸⣿
⠸⣿⣿⣄⠀⠀⠀⠀⠀⠉⢁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠿⠛⠁⠀⢀⣼⣿
⠀⢻⣿⡟⠃⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡙⠳⠄⠀⠀⠴⢿⣿⣿
⠀⢸⣿⣧⠀⠀⠀⠀⠉⢹⣿⠁⠀⠀⣠⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⢿⣦⡄⠀⠀⢿⡏⠁⠀⠀⠀⠀⣸⣿⡟
⠀⠈⢿⣿⣧⡀⣿⣶⣤⣼⣷⣶⣶⣾⣿⠿⠶⢶⠶⠿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢷⣶⠶⠶⢾⣿⣶⣶⣾⣧⣠⣴⣿⠀⣴⣿⣿⠃
⠀⠀⠀⠻⣿⣿⣾⣿⣿⣿⣿⣿⠟⠉⠀⣰⡾⢿⣿⣿⣦⡙⢻⣷⣤⣤⣤⣤⣴⡿⢋⣵⣾⣿⣿⠿⣶⡀⠈⠙⢿⣿⣿⣿⣿⣿⣾⣿⡿⠁
⠀⠀⠀⠀⠸⣿⣿⡝⠻⢿⣿⡟⠀⠀⠈⠁⠀⢿⣧⣿⠿⣿⡆⢿⣿⡿⢿⣿⣿⠁⣾⡟⢿⣼⣿⠆⠀⠉⠀⠀⢸⣿⣿⠟⢩⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⡄⠈⣿⣧⠀⠀⠀⠀⢦⣀⣉⣠⠄⠀⠀⣸⣿⠁⠀⢹⣿⠀⠉⠀⢨⣍⣀⣠⠆⠀⠀⠀⢸⣿⡇⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⢹⣿⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣿⠃⠀⠀⠀⢿⣇⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣿⡿⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠃⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣀⣼⣯⠛⠿⠷⢶⣶⣶⠾⠟⠋⠰⢾⣶⣤⣠⣴⣾⠷⠈⠛⠿⠶⣶⣶⡶⠿⠟⣻⣧⣀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣆⠠⣤⣤⣤⣤⣶⠏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢷⣦⣤⣤⣤⠴⢠⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠉⠉⠉⠀⠒⠶⣤⣤⣤⣤⣤⣤⣴⣤⡶⠖⠂⠈⠉⠉⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠟⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣷⣦⣤⣀⣀⣠⣤⣾⣿⠃⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⠀⠀⠈⢿⡏⠉⠛⠛⠋⠉⣿⠃⠀⠀⠘⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀
⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢇⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠿⠛⢛⣉⣉⠉⠉⠙⠛⠉⣁⣤⣤⣤⣤⣤⣄⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠉⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣤⠈⠻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣀⣤⣤⣾⣿⣇⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⣾⡿⠋⠉⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠁⠈⠹⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⢀⣿⡇
⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⣀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣿⣷⡀
⣼⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠿⣶⣤⣀⣀⣤⣴⡾⠟⠋⠉⠀⠀⠀⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿
⣿⣇⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠹⣿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⢀⣴⣿
⢀⣿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣧
⢸⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢹⣿
⠸⣿⣆⠀⠀⠀⠀⢀⣤⣤⣴⣶⠶⠾⠿⠿⣛⣿⡿⢷⣶⣤⠀⠀⠀⢠⣴⡾⠿⣿⣿⣿⠿⠿⠿⢶⣶⣤⣤⣄⠀⠀⠀⠀⠀⣼⣿
⠀⠙⣿⣷⣄⠀⠀⠸⣿⣾⣿⠁⠀⠀⡴⢿⣿⣿⣷⡀⠈⢻⣷⣦⣤⣿⠋⠀⣼⣿⣿⣿⡷⡄⠀⠀⠘⣿⣾⣿⠇⠀⢀⣤⣾⡿⠃
⠀⠀⠘⢿⣿⣧⡀⠀⠀⠸⣿⠀⠀⠂⠀⠘⠿⠿⢮⡇⠀⣸⡏⠉⠉⣿⡀⠀⠣⠾⠿⠿⠃⢨⡄⠀⢠⣿⠁⠀⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠈⣿⣿⡁⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠈⠻⣿⣶⡆⠀⠀⠻⢷⣤⣄⣀⣀⣤⣴⡾⠋⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⣀⣠⣴⡾⠋⠀⠀⣴⣶⣿⠟
⠀⠀⠀⠀⠀⠀⣨⣿⣧⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⣿⣿⣀
⠀⠀⠀⠀⠀⣾⣿⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠲⣤⣀⣀⣀⣀⣤⠞⠉⠢⡀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢻⣿⡆
⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⢃⠶⠀⠀⠀⠀⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⣿⡄⠀⠀⠀⠀⠃⠙⠢⠄⢀⡀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠈⠀⠀⠀⠀⣸⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣷⡀⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣿⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠶⢶⣦⣶⠶⠞⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⡠⠔⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⠢⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠿⠿⢿⣶⣦⣄⣤⣴⣾⡿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣿⣇⠀⣀⣤⣶⣾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣤⣀⠀⠀⣸⣿⣧⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠉⠉⠛⠛⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⡿⠿⠛⠛⠉⠉⠛⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⢻⡏⠀⠀⣠⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⡶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹
⢸⣷⢀⣼⠃⠀⠀⠀⠀⢀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠸⣦⡀⣿
⠘⣿⣿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿
⢰⣿⠏⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⡶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⢹⣿
⣼⡿⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⢠⣾⣿⣁⣀⣀⣀⣀⣴⣾⠿⠛⣛⡛⠛⢛⡛⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⣛⣛⣛⣛⠛⠿⣷⣦⣀⣀⣀⣀⣀⣹⣿⣦⡀⠀⠀⠀⣿
⢻⣷⠀⢀⠀⠈⠛⢿⣿⣟⠻⢿⣿⡟⠁⠐⠋⢁⣾⣿⣷⡌⠑⠈⢿⣧⣀⣤⣴⣶⣦⣤⡀⢰⣿⠋⠈⣰⣿⣿⣦⠈⠙⠂⠈⢻⣿⡿⠟⢻⣿⡿⠟⠋⠀⢠⠀⢀⣿
⠈⣿⣆⣸⡄⠀⠀⠀⢹⣿⡄⠀⣿⡇⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢸⣿⡿⠋⠁⠀⠉⠙⢿⣿⡏⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⢸⣿⠁⠀⣿⡟⠀⠀⠀⠀⣼⣇⣼⡿
⠀⠘⢿⣿⣧⠀⠀⠀⢸⡟⠀⠀⢻⣷⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣾⡟⠀⠀⢻⣿⠀⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠈⠻⣿⣧⡀⠀⠈⢷⡀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⣀⣤⣾⠟⢻⣧⣀⣀⠀⢀⣀⣠⣿⠻⣷⣤⣀⠀⠀⠀⠀⢀⣠⣾⡟⠁⠀⢀⡼⠃⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠁⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠈⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣄⡀⠀⠀⠀⠀⣀⣀⣠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋⠛⠛⠿⠿⠿⠛⠛⠛⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⢿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⠿⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣦⠀⠀⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠒⠂⠈⠁⠀⠒⠓⢄⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⣠⠛⡄⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⡴⠃⠀⠈⢆⠀⠄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡷⠀⢄⡾⠋⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⡇
⠀⠀⠀⠀⣠⢧⠆⠀⠀⠰⠆⠀⡄⠀⠀⠐⡶⠀⠀⠈⢦⠥⡀
⠀⠀⠀⠀⣄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡅⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠱⣄⠀⠀⠠⠂⠀⠀⠀⠂⠀⠀⢀⠜⠉⠁⠀⠀⠀⠀⠀⢈⠷⠓⠂⠈⠉⠙⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢑⡤⣤⡀⢀⣀⡀⡀⠤⡞⠑⠠⣀⠀⠀⠀⠀⠀⡰⢃⡠⠲⡄⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⡠⢶⠁⠀⠘⡦⣀⠀⢀⡠⢺⠇⠀⠀⠀⠑⣄⠀⢀⣰⠕⠁⠀⠀⠱⡄⠀⣄⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⡠⠊⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⡸⠀⠱⣏⠀⠀⠀⣴⡆⠀⠈⠓⠟⢄⠀⠀⠀⠀⢸
⠀⠀⠀⡜⠁⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⢄⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡌⠣⣄⠀⠀⡜
⠀⠀⡜⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠈⢃⠀⠀⠀⢳⡀⠀⠀⠂⠀⡀⠀⠙⠁⠀⠀⡝⡜
⠀⠀⡇⠀⠀⠰⠏⡇⠀⠀⠀⡆⠀⠀⠤⠀⠸⡆⠀⠀⠀⢈⡄⠀⠀⢘⡙⢦⡀⠑⠀⠀⠀⠀⠀⢀⡀⢙⠆
⠀⠀⠱⣠⡴⠾⡄⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⠃⠀⠀⡞⠙⣁⠈⢙⡒⠂⠀⠐⠒⠉⠉⠁
⠀⠀⠀⠹⣄⣀⡼⠣⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⣈⠀⢀⡸⠁⠀⠀⠉⠈⠙⡄
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢰⡁⢣⡀⠀⠀⢀⡔⠊⢹
⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡶⠻⢄⠈⠑⠂⠉⠀⢀⠎
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠉⠐⠳⠄⠒⡏
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣧⣤⣑⣢⣄⣀⢀⡇
⠀⠀⠀⠀⠀⣿⠀⠇⠀⠀⠀⠀⠢⣀⠀⠀⠄⢀⠀⣀⠠⠴⢇⠀⠀⠉⢉⡉⠉⠉⡇
⠀⠀⠀⠀⠀⣿⠀⢰⠤⠤⠤⠤⠤⠤⠭⠒⠒⠊⠉⣀⠤⢾⢸⠀⠀⠀⢰⡇⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠘⡖⠤⠤⠤⢤⠤⠤⠄⠒⡖⠉⠀⠀⡘⢸⠀⠀⠀⡘⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⢡⠀⠀⠀⢸⠀⠀⠀⠀⢱⠀⠀⠀⠇⢸⠀⠀⠀⡇⠘⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠈⣆⠀⠀⢘⠀⠀⠀⠀⠀⠱⢤⣀⡣⠘⣀⡤⢤⡁⠈⠲⠾⠛
⠀⠀⠀⠀⠸⠇⠀⠀⠸⡉⠑⢢⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠟⠁⠀⠀⠉⠙⠉⠁⠀⠀⠙⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣧
⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣤⡀
⠀⠀⠀⠀⣼⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⡄
⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀
⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣙⣢⣴⣤⣀⠀⠀⠀⢀⣀⣾⣖⣚⣁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⢦⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⣼⣿⣇⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢠⣿⣿⡄
⠀⣼⣿⠃⠙⢧⣤⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣠⡴⠟⠀⢻⣿⡀
⠀⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⢀⣠⣴⣶⣶⣦⠀⠀⠀⠀⠀⢴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⡇
⠀⠹⣿⡆⠀⠀⠀⠀⠀⢠⡾⠛⠋⣉⣭⣿⣷⣄⠀⠀⠀⣠⣶⣿⣯⣉⡉⠛⢷⣆⠀⠀⠀⠀⠀⢀⣾⡟
⠀⣼⣿⠋⠀⠀⢴⡲⣶⣿⠀⠠⠚⠿⢿⠿⠈⠘⡿⠻⢻⡏⢀⣿⡿⠿⠟⠦⠀⢻⣷⠖⣲⠄⠀⠈⢿⣿⡄
⠀⠹⣿⣦⣤⣤⣮⣽⣿⠈⢦⠀⠀⠠⠴⠆⢀⡼⠃⠀⠈⢧⡀⠀⠶⠶⠀⠀⡠⠃⣿⣿⣥⣤⣤⣤⣾⡿⠁
⠀⠀⠘⠿⣿⣿⣿⣿⣿⡄⠀⠑⠂⠀⠀⠔⡋⠀⠀⠀⠀⠀⠙⡒⠄⠀⠴⠊⠀⠀⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣧⠀⠀⠀⠀⣠⠜⠓⢦⣄⣀⣀⡴⠖⠱⢤⡀⠀⠀⠀⢠⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢸⣏⣉⣿⡄⠀⠘⠋⢁⠀⢀⣀⣀⣉⣁⣀⣀⠀⢀⠙⠛⠂⠀⣾⣏⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣧⠀⠀⠀⠘⠀⠈⠉⠉⠛⠋⠉⠁⠀⠸⠀⠀⠀⢰⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⢸⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⠙⣿⣶⣄⡀
⠀⠀⠀⣀⣤⣤⣤⣶⣿⡿⠋⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠻⣿⣷⣶⣤⣤⣄⡀
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣾⣿⣿⣿⣀⣿⣿⣿⣷⣤⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⠂⠀⠒⠒⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⣀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠋⠁⠀⠀⠈⠇⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⣼⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠠⠖⠒⠀⠀⠀⠀⣤⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠐⠏⠉⢀⠀⠀⣠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠦⣤⣿⠄⡀⠀⠀⠀⠀⠀⠀⣈⡛⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢮⡳⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡼⠛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠙⣎⠑⢢⡤⠤⠤⠤⠶⠲⡖⢻⠔⣲⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢘⡆⠀⢳⡀⠀⢀⡔⠒⢿⣡⣾⠁⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠞⢩⣽⣿⡲⢇⣰⠉⠁⠀⠀⠁⢸⡙⡒⠒⠲⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣇⠀⠘⢿⡋⢀⣈⣦⣀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⢳⡀⠈⠙⢯⣀⢠⠛⣿⠙⣖⠛⢁⣄⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠉⢹⣄⣠⡬⠽⢶⣉⡇⠈⢉⣻⠀⠃⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠣⣀⡄⠀⡠⠚⠉⠉⠀⠠⠶⠟⡿⠉⠉⠉⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⣄⣘⣣⣀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠲⣬⣉⠁⢈⣑⡶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⣿⠛⠒⠒⠒⣶⠛⠛⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣿⡀⠀⠀⢠⡟⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣰⢃⡇⠀⠀⣎⢣⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡀⢀⡴⢋⢸⠀⠀⠀⢸⡀⡑⢤⣀⠀⠍⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢉⣩⠜⠉⠋⠀⠀⠀⠀⠉⠉⠳⠤⣄⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⢀⡀⡀⡉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠉⡁⠈⠉⠉⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⢀⡴⠳⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡀⠀⠀⠀⣠⠞⠁⠀⠱⣌⠢⣄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⣎⠜⠀⢠⣔⡼⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡏⠉⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠙⡆⢸
⠀⠀⠀⠀⠀⠀⡠⣷⠏⠀⠀⠐⢰⠆⠀⢀⡇⠀⠀⠀⠲⡶⠀⠀⠀⠱⣼⠤⡀
⠀⠀⠀⠀⠀⢸⡁⠸⡀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠶⢧⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⡼⠶⠚⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⣉⠤⠀⠀⠀⠀⠀⢉⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠠⠊⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠗⢲⣤⠤⠶⠶⠦⠤⠒⢺⡇⠈⠙⠲⢄⠀⠀⠀⠀⠀⠀⡼⢁⣠⠤⠒⠒⠉⠉⡸⠃⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡏⠀⠀⠈⡷⠤⣀⣀⣀⡠⠔⠻⠁⠀⠀⠀⠀⠙⣦⡀⠀⣴⠋⠋⠁⠀⢀⣤⠀⠀⠰⢇⡴⢻⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡰⠁⠙⣆⠹⣤⠀⠀⠀⠸⠟⠀⠀⠸⠏⠀⠈⣆⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠃⠀⠀⠈⣷⢰⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣴⡻⢆⠸⠀⠀⠀⡞
⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⠇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠸⡆⣧⡀⠀⠀⠠⣄⡀⠀⠀⠀⠋⠁⠈⢣⡀⢀⡾⠁
⠀⠀⠀⣼⠀⠀⠀⠠⣀⣼⠀⠀⠀⠀⢠⣇⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣼⠇⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⣿⠀⠀⠀⠰⠏⢸⠀⠀⠀⠀⣸⠀⠀⠒⠒⠂⠀⠸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⢽⠶⣶⠚⠉⠒⣤⣄⣀⣀⣀⣀⢤⡖⠒⠶⠋
⠀⠀⠀⠱⣄⣠⣴⢾⡄⢸⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢨⠛⠀⠀⠀⡼⡄⢩⠳⠤⠄⠵⢄⠀⠀⠀⠀⢰⠀⠀⡜
⠀⠀⠀⠀⠹⣟⠁⠀⢈⣾⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣠⡎⡃⠀⣀⣼⠁⣦⠘⡗⠐⢢⠀⠈⣧⠀⠀⠀⡎⢀⡴⠁
⠀⠀⠀⠀⠀⠈⠛⢳⡏⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢸⡇⠰⣄⢸⡆⠱⣤⡾⠊⠉⢹⠀⠀⠀⠓⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠉⢹⣷⣄⠈⠉⠛⠶⡏⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⡶⠋⡇⠈⠑⠲⠤⢼⣹⣀⣤⡎
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣀⠀⠀⠀⠀⠈⠑⢄⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠋⠭⠭⣐⣛⡒⠢⠤⠄⢹⡆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣞⠒⠦⠤⠤⣀⣉⣉⡉⠓⠒⣿⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠈⠑⠢⠄⠈⠁⠒⣠⣤⣤⠴⠒⢻⠀⣿⠐⠒⠲⠤⠤⣄⣈⣉⣉⠁⣿⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡗⠒⠀⠀⠀⠀⠐⠀⠒⠚⠋⠉⠉⢀⣀⡤⠖⢻⠀⠈⢹⠋⠓⠐⠶⠒⠦⢠⠌⠉⢿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢳⠶⠦⠤⢀⣀⣄⡀⠤⠤⠶⠒⡟⠉⠁⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠈⣦⣀⡼
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⠇⠀⠀⢸⠆⠀⣠⠃⠀⠀⠸⣇⡼⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢳⡄⠀⠀⠀⢼⠀⠀⠀⠀⠀⠘⢆⡀⠀⢸⡀⠀⠀⢸⣀⡀⠻⢄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠦⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠃⠀⠀⠘⠧⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠱⣄⣀⣙⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣤⣴⣶⣾⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠉⠀⠉⠉⠛⢿⡿⠛⠉⠉⠀⠉⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠛⣠⣴⣶⣿⣿⡿⠿⠟⠛⠛⠛⠋⠙⠛⠛⠛⠿⠿⣿⣿⣷⣦⣙⠻⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⣠⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡈⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⡿⢁⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠈⢿⣿⣆
⠀⠀⠀⠀⢠⣿⣿⢡⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⡿⠿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄
⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⢰⣿⣿⡷⠀⠀⠀⠀⠲⣶⣾⣿⠿⠛⠁⠠⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⢶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠙⠿⣿⣷⣶⠶⠀⠀⠀⠀⢾⣿⣿
⣿⣿⠋⠀⠀⠀⠀⢠⣤⣀⠀⢀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣷⣶⣶⣶⣤⣀⡀⠀⣀⣤⡄⠀⠀⠀⠀⠙⣿
⢿⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠁⠀⣠⣶⣶⣶⣄⠀⠈⢻⣧⣀⣀⣀⣀⣾⠟⠁⢀⣴⣶⣶⣦⡀⠀⠀⠙⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣿
⠘⢿⣿⣶⣤⣄⠀⠀⣴⣿⡿⣿⡇⠀⠀⠀⠙⣿⣿⣏⣹⠀⠀⠀⣿⡿⠛⠛⢿⣿⠀⠀⢸⣿⣿⣉⡿⠋⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⣠⣤⣾⣿⡿
⠀⠀⢹⣿⣿⠋⢀⣾⣿⠋⠀⢻⣧⠀⠀⠀⠀⠸⠿⠿⠟⠀⠀⢀⣿⠁⠀⠀⠘⣿⡀⠀⠈⠿⠿⠿⠃⠀⠀⠀⠀⣸⡿⠀⠙⢿⣷⡄⠙⣿⣿⡏
⠀⠀⢸⣿⡏⠀⢸⣿⣇⣀⡀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⢀⣀⣸⣿⡇⠀⢹⣿⡇
⠀⠀⠸⣿⣿⡀⠈⢻⣿⠿⠋⠀⠀⠛⠿⣶⣤⣤⣤⣴⣶⠿⠟⢁⡀⠀⠀⠀⠀⠀⣈⠛⠿⣶⣤⣤⣤⣴⣶⠿⠋⠀⠀⠘⠿⣿⡟⠁⢀⣿⣿⠃
⠀⠀⠀⠙⢿⣿⣶⣾⣷⡀⠀⠀⡀⠀⠀⠀⢈⠛⠉⠁⢀⠀⠀⠹⢷⣄⣀⣀⣠⣾⠏⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⢀⠀⠀⢀⣿⣷⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣶⣶⣷⠀⠀⠀⠊⠀⡠⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣾⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⠃⠀⠀⠤⣤⣤⣤⣤⣤⣤⠤⠄⠀⠉⢆⠀⠀⠀⠀⠀⣼⣟⣽⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠈⠁⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⠻⢶⣤⣀⡀⠀⠀⠀⠀⢀⣠⣤⡶⠛⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⡀⠀⠀⠉⠛⠛⠿⠛⠛⠛⠉⠀⠀⢀⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⢻⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣾⣿⠟⠻⣷⣦⣄⣀⡀⠀⣀⣠⣴⣾⡟⠛⣿⣶⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡏⢙⣿⣿⠿⣿⣟⠉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢚⠛⠛⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⢀⣄⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠶⠄⠐⠁⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⠀⠈⣀⡠⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠗⢄⣀⣀⠔⠉⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣾⣿⣿⣦⡄⠀⠘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⠀⠘⣿⣿⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡠⠒⠠⠤⢾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⢿⠛⠟⠁⠀⡿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠻⠿⠿⡇⢈⣤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣾⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢹⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢇⠀⠀⠀⠀⠀⠀⡠⢴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡂⠒⠈⡇⠀⠈⣄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢿⣷⣤⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣼⡇⠀⠀⠀⠙⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⠤⣤⣿⠗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠈⡷⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⠠⠀⠀⣀⢼⣟⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣾⡻⢤⣀⡀⠊⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠠⠤⠌⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⢳⣎⢀⠑⠂⢈⢱⡞⣢⠀⠀⠀⠀⠀⠀⠤⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢏⡷⣭⢣⡜⢀⡄⠀⣮⣿⣼⢣⡄⠀⠀⠀⠀⠀⠀⠀⣀⠠⡦⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⣰⢎⡳⣭⢿⡹⢣⡍⠁⡄⠥⠙⠾⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠈⠀⠈⠁⠉⠉⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢳⢎⡹⣵⠮⣽⠷⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠛⣮⡽⣯⣛⢶⣴⠐⢶⡽⣇⠀⠀⠐⢖⣶⣤⣤⡖⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⣠⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡝⢱⠾⣡⠟⡶⢱⡟⣷⢤⣀⠀⠈⠿⠟⠁⠀⠀⠰⢿⡷⠾⠟⢀⣠⣾⣏⣸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣜⢃⡤⠀⠛⠁⠀⠀⠀⠀⠋⠛⠳⠶⢄⣤⣤⣤⣤⠴⠶⠖⠚⠛⢹⣁⣥⢼⡧⠘⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢿⢙⣇⣥⢴⡦⢼⣶⠄⣀⣤⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢮⣷⣄⣀⡀⠀⠀⣀⠀⠀⢄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠃⣸⡤⣷⠤⣷⠄⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣟⡿⠿⠛⣹⡄⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠖⣿⠋⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢰⡆⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠛⠋⠈⠁⠀⠀⠀⠀⠊⣾⣿⢦⣤⠖⠐⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⠈⠙⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢸⠱⠶⠆⠀⠀⠀⠀⠀⠸⠿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠉⠐⠂⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠐⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⡤
⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢐⣿⣾⣷
⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠣⣽⣿⣿⣷⠀⠀⠀⠀⠰⣄⣀
⠀⠀⠀⠠⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠗⣿⣿⡛⠓⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣿⣿⠛⠂⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠐⠀⠰⢿⣿⣿⣿⣿⣼⣂⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣠⣏⣿⠌⠙⠃⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⣷⡁⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠻⣿⣿⣿⡿⠶⢀⠀⠀⠈⠋⠙⢿⣿⣦⣶⣦⣄⣾⣿⠏⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⠟⢡⣌⠹⠙⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡤⠄⣤
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠈⠩⠭⠟⠩⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢦⣾⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠁⠀⠀⠀⠀⠀⠀⠰⠞⠉⠀⠀⢠⠀⠃⡀⢮⢃⡕
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡅⢠⣤⣿⣿⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆⣰⡷⠉⣿⡟⡆
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⣿⣾⣿⣿⡏⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣷⢸⠃⣀⡿⣿⡇
⠀⠀⢰⣼⣿⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣿⡆⠀⢹⣿⣿⡇⠄
⠀⢠⣿⣿⣿⣷⣾⣇⣠⠄⠀⠠⠀⡀⠀⠀⢀⣠⠀⠀⢸⣿⡿⣿⡭⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⣏⡿⢃⣶⢈⣿⡿⡇
⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣤⡤⠷⠛⠋⠁⠀⠀⠹⢻⣟⠻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⢠⡿⣻⣇⠀⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡃⣼⣾⡷⢰⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⡏⠁⠄⠀⠀⠰⣴⣤⡆⠀⠀⠀⠀⠀⠀⣀⠆⢰⡄⣧⠀⣿⣽⣿⣿⠁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡀⢠⣶⣯⣿⡿⠀⠂⠀⠀⠀⠀⣽⠇⡈⣴⠏⢰⣿⣿⡟⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠁⠀⠀⢠⠵⡋⣗⠀⢀⠦⠊⣠⠟⠐⣹⠊⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠂⠀⢀⠀⠀⠁⠻⠴⠛⠒⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢉⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⢀⡉⠀⣤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠣⣀
⠀⠀⠀⠀⠀⠀⠃⠀⣈⡏⠀⠀⣒⡀⠀⠀⠀⠀⠀⠀⠒⢂⣀⠀⠈⢷⡐⠀⠀⠈⢢
⠀⠀⠀⠀⡎⠀⠀⢀⣿⠀⠀⠾⣿⠿⠀⠀⠀⠀⠀⢁⡴⢿⣾⠗⢀⢸⣿⠆⢀⡄⠈⠣
⠀⠀⠀⢰⢇⡄⠀⠘⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⢿⡇⠘⠂⠀⠀⠀⠄
⠀⠀⠀⣾⣋⠀⠀⠀⣿⠀⠒⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⡁⣻⣿⡀⡀⠀⠀⡈⢚⠂
⠀⠀⠀⣿⣿⣿⣤⣤⢸⣾⠁⣦⠀⠀⢰⣿⣿⣿⣿⣿⠆⠀⠀⢰⣴⢸⣯⣿⡏⣿⣧⣼⡏⣾⠟
⠀⠀⠀⢿⣟⣏⣾⡾⢸⡜⠦⠹⡗⠀⠈⠙⠿⡿⠟⠋⠀⠀⢠⠟⠠⢾⠟⢿⡇⣻⣿⠄⡜⡇
⠀⠀⠀⠀⠘⣿⣿⡇⡼⢣⡀⠀⢰⣄⠀⡀⣰⣤⣀⣀⠀⣀⢟⡄⠠⠢⠐⣾⣿⢹⣿⣖⡽
⠀⠀⠀⠀⠀⠈⠿⣿⠛⠋⠀⠰⠌⢻⣿⡟⠉⠙⠛⢙⣿⡕⠉⠀⠀⢀⠀⠐⢽⡎⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠘⣷⣄⣀⣠⡿⠏⠀⠀⠀⠀⢄⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣆⢀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⠀⢈⣦⣼⡿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠙⠋⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⠈⠈⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⢶⣄⣷⣠⣀⣤⣴⠄⠘⠃⠀⠀⠀⠀⠉⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢁⣀⣠⣰⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠈⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣿⡿⠿⠛⠛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡿⠿⠓⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠐⢧⡀⢈⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠅⣀⣓⠁⠀⠀⠀⠀⢀⠀⠀⠀⣬⣷⠟⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡉⠓⠂⠂⠁⠊⠀⠀⠀⢀⠀⢸⣷⡂⠀⠀⠈⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡀⠀⠀⠀⠀⠀⠀⢼⣧⠀⠀⢸⠀⢘⣿⡇⠀⠀⢺⠀⠀⠀⣾⣿⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡏⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣿⢴⡶⢻⡟⠀⠀⠀⠀⠀⢸⣿⠹⢷⢤⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣷⡘⢫⠚⠁⠀⠀⠇⠀⠀⢹⡇⠀⠈⣿⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⣿⠻⠑⠢⣤⣤⣤⣤⣤⣶⣶⣾⡿⠟⢿⣷⡈⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⢐⠙⢳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠿⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣇⠀⢸⣿⣧⡸⡄⠀⠀⣼⠀⠀⠀⣿⠐⣿⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢾⡦⠀⡀⠈⠐⠶⠴⠾⠿⠶⠶⠶⢊⣃⠀⢸⣿⡟⠀⠹⣶⣶⣿⣶⣶⣾⣿⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠰⡶⣶⣶⡶⡶⣶⣿⣿⣿⠀⣾⣿⣷⣤⣔⣿⣿⣿⣿⣿⣿⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡟⠁⠛⠛⠛⣿⠀⢹⣿⡿⣫⣾⢿⣿⣿⣿⣿⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⡏⠀⢸⣿⣷⣿⣿⠈⣿⣿⣿⣿⣿⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣤⠀⢰⣿⣿⡄⠀⠀⠀⣾⠃⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⡄⢸⣿⠘⣧⠀⠀⢸⡿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⣧⠀⣿⡁⣿⡄⠀⢸⡇⠀⠀⢸⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣼⣿⠁⡿⣷⡀⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠉⢿⣿⠀⡇⠁⠀⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠀⢸⣿⡆⡇⠀⠀⢻⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢨⡅⣼⣵⠃⢡⠀⠠⡌⠀⠀⢀⠙⠛⢿⣿⡃⠀⠸⣿⡿⣿⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⠳⠖⠞⠁⠀⠸⠦⠴⠇⠀⠀⠷⠾⠾⠛⠋⠀⠀⠀⣄⣴⣿⠀⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠉⠀⠀⠀⠈⠙⠻⠛⠉⠀⠀⠀⠈⠙⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠇⢀⣠⣴⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣶⣤⣀⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⠋⣡⣶⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣦⡈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⣰⣿⡟⢁⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠙⢿⣷⡄
⠀⠀⠀⠀⣰⣿⠏⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠈⢿⣷⡀
⠀⠀⠀⠀⣿⣿⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠸⣿⣇
⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢀⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⣰⣶⣤⣤⣀⣀⣀⣠⣤⣤⣶⣾⡿⠿⠛⠉⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣦⣄
⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⢸⣿⣧⡀⠀⠀⠀⣀⣀⣠⣴⣿⠋⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠹⣿⣦⣄⣀⣀⠀⠀⠀⣠⣿⣟
⣾⣿⠏⠁⠀⠀⢀⠉⠛⠋⠉⣀⣤⣬⣭⣭⣭⣭⣉⡉⠀⠀⠀⠀⠀⠈⣉⣩⣭⣭⣭⣭⣄⣀⡀⠉⠙⠋⢁⠀⠀⠀⠙⢻⣿
⣿⣿⠀⠀⠀⠀⠘⢿⣷⣶⣿⠟⠉⠉⣩⣭⣯⡉⠉⠻⣦⠀⠀⠀⢠⡿⠋⢉⣭⣯⣍⠉⠉⠙⢻⣷⣶⣾⠟⠀⠀⠀⠀⢸⣿
⠘⣿⣷⣤⣄⠀⢀⣼⣿⣿⡇⠀⠀⠈⢻⣿⣏⣣⠀⠀⣿⡿⠛⠻⣿⠁⠀⢼⣿⣏⡹⠛⠀⠀⠀⣿⣿⣿⣆⠀⢀⣤⣴⣿⡟
⠀⠈⣿⣿⠋⢠⣿⡟⠁⢸⣧⠀⠀⠀⠈⠿⠿⠃⠀⢀⣿⠁⠀⠀⢻⣆⠀⠈⠻⠿⠃⠀⠀⠀⢠⣿⠁⠈⢿⣷⠈⢻⣿⡇
⠀⠀⣿⣿⠀⠸⣿⣤⣤⠀⠻⣷⣄⠀⠀⠀⠀⣀⣤⡾⠃⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⢀⣴⡿⠃⢠⣤⣼⣿⠀⢸⣿⡇
⠀⠀⠹⣿⣦⣀⣸⡏⠁⠀⠀⠈⠙⠛⢿⠿⠟⠛⠉⢰⣆⠀⠀⠀⢀⣶⠈⠙⠛⠻⢿⠟⠛⠉⠀⠀⠀⠉⣿⣁⣤⣿⡿
⠀⠀⠀⠈⠻⠿⣿⣿⣦⣄⣆⠀⠀⠀⠂⠀⠀⠊⠀⠀⠙⠛⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠀⠀⠀⠁⡰⠀⠀⠀⣄⣤⣀⣀⣤⣀⠤⠀⠳⡀⠀⠀⠀⢀⣾⣫⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⣠⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣇⠈⠙⠳⠶⣤⣤⣤⡴⠶⠛⠉⢀⣿⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣿⠛⢷⣦⣄⣀⠀⢀⣀⣠⣶⡟⠻⣷⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⢉⣿⡿⢿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⠒⠒⠒⠒⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣀⣠⡤⣤⣀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠖⠋⡉⠉⠉⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⣠⠞⠉⠈⠀⠀⠀⠈⠳⣤⣀⠀⠀⣀⠔⠀⠹⡄⠀⠀⠀⠀⡾⠁⣠⠶⠛⠋⠉⠀⠀⠀⠛⠓⠶⣌⡳⣄
⠀⠀⠀⠀⠀⡼⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⡁⢀⡠⢺⡁⠀⠀⢀⡼⣡⠞⠁⠀⠀⠀⠀⣠⠶⣄⣀⠀⠀⠈⠳⣌⢳⡀
⠀⠀⠀⠀⠀⠹⣄⢀⡞⠀⠠⠀⠀⢠⠀⠀⠀⠀⢀⠐⠀⠀⢄⠹⣅⣠⠞⠁⠀⣠⠟⢰⠏⠀⠀⠀⢀⡴⠞⠁⠀⠀⠉⠳⣄⠀⠀⢹⡆⢷
⠀⠀⠀⠀⠀⠀⠈⢿⠀⠈⣀⡤⠤⣀⡀⠀⠀⠀⣠⠤⠢⠤⡈⠀⣟⠁⠀⠀⢸⠁⠀⢿⣤⣤⠴⢚⡉⠀⠀⠀⠀⠀⠀⣀⠈⠳⢦⣤⡿⠈⠓⣦
⠀⠀⠀⠀⠀⠀⡤⢼⡇⡜⠁⠤⠄⠀⢹⣄⡤⢼⠁⠐⠲⠄⢸⠂⣿⠓⢦⠀⢈⡇⢀⣠⡇⠀⠀⠉⢀⡀⠀⠀⠀⠀⢀⡈⠑⠀⠀⣿⣲⠚⢠⠏
⠀⠀⠀⠀⠀⠸⡅⠀⡇⠹⢤⣀⣀⡤⠞⡄⠀⢀⠓⠒⠒⠒⠁⠀⢿⢀⡜⠀⣼⠀⣾⠀⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠋⠀⠀⠀⡏⠈⣷⠈⣷
⠀⠀⠀⠀⠀⠀⠙⠶⡇⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⣽⠉⠀⠀⠘⢦⠘⠦⣿⠀⠀⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⣇⡴⠋⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠹⣖⠒⢒⡿⠁⠀⠀⠀⣠⠇⠀⠀⠀⠀⠘⣆⠀⢸⡀⠀⠀⠀⠀⢰⠒⠒⡒⠀⠀⠀⠀⢰⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⡀⠈⠉⠉⠀⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢷⣄⡀⠀⠀⠈⢦⡤⠃⠀⠀⠀⣠⣞⡤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⢹⠉⠉⠉⢹⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢦⢤⣤⢤⠖⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢹⡄⠀⠘⠲⡤⠞⠉⠀⢠⠏⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⠞⠹⣫⠽⢷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠹⣦⣠⠞⠉⠳⣄⣴⠋⠀⠀⠀⠪⣳⡄⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⣿⠀⠀⠀⠚⣹⠂⣷⠈⢳⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢻⣳⡀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠐⢹⣆⠀⠀⠀⢀⡞⠀⠀⠀⢸⣿⠀⠀⠀⡼⠁⠀⣿⠀⠀⠹⡄
⠀⠀⠀⠀⢠⡟⠆⣀⠀⠀⠀⠀⠀⠀⢳⣷⣼⡿⠁⠀⠀⠀⠀⠀⢀⡀⢳⢻⡄⠀⠀⡞⠀⠀⠀⣀⡼⠋⠙⠲⠴⡧⠤⠴⢿⡄⠀⠀⢹⡀
⠀⠀⠀⠀⣿⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢏⣷⠀⢸⠃⠀⢀⡼⠉⠀⠀⠀⠀⢸⠃⠀⠀⠀⠳⡄⠀⠈⡇
⠀⠀⠀⢠⡏⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢹⡀⣾⠀⢠⠏⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢹⡄⠀⡗
⠀⠀⠀⢸⡇⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⣧⠀⡇
⠀⠀⠀⠀⣷⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠀⣇⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡄⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠙⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣴⠃⠀⢹⣄⠀⠀⠀⣀⣤⣾⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⢾⡆
⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⠀⢸⠏⠙⠛⠉⠉⠀⣿⠀⠀⠀⢨⡗⠶⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣤⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⡀⢈⡹⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⣒⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⣀⡤⢤⠾⠟⡀⡠⠲⢭⣱⣤⢄⠀⠈⡓⠚⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠛⠁⠀⠀⠈⠀⠀⠀⠉⠟⠶⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢇⡁⢀⠀⠀⠙⠻⠾⠵⢵⡧⠴⡄⠸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠡⠐⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄
⠀⠀⣼⠃⠀⡄⢸⠁⢠⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠉⠀⠈⡁⠀⠧⠜⣧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⣿⠀⠀⢝⣢⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠒⡴⡿⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⡿⢢⡠⠤⣼⡃⠀⠀⠀⠠⠤⠤⠒⢒⡀⠔⣂⣉⣭⣁⠀⣄⢠⣾⡅⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⡀⠀⠀⠀⡸⡇
⠀⠀⢷⠀⡙⠚⠋⣾⠀⢀⣤⠴⠶⠦⣀⣀⣠⣴⣩⣵⣤⣈⣳⣪⣿⡾⠀⠀⠀⠀⠀⠀⠀⢸⣦⡼⢿⠿⠾⣤⣀⢀⠀⠀⠐⢶⣤⣀⡀⠀⠈⠩⠤⠇
⠀⠀⠘⣧⠙⡶⣭⡇⠀⣿⢀⣶⠿⠗⢺⣿⠀⠿⣀⣉⣉⡨⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠛⢶⡶⠦⡿⠛⣿⠟⠿⢭⣝⡻⣦⡤⠶⠞⢒⣷⡄
⠀⠀⠀⠘⢷⡘⢻⠓⠉⠛⠯⣄⣠⠤⠊⠸⠇⠀⠀⡉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠣⠌⣁⣠⠜⠁⠀⣿⡄⠀⠊⠩⢉⡏⠀⠀⢰⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⢀⢰⡻⢧⠀⡤⠏⠶⣄⡀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣰⠊⠐⠀⠈⠓⠸⡖⠂⠒⠊⠀⠀⠀⢙⠟
⠀⠀⠀⠀⠀⠀⢾⡉⡇⠀⡀⢀⡴⢋⣀⣠⣤⡤⠴⠶⠂⢸⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡾⠃⠀⠙⠰⠾⠓⠃⠻⣄⠀⠀⠀⢠⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠱⣜⢇⠈⠛⠗⣒⣂⣨⠂⠀⡎⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢇⠈⠙⠣⢀⡀⠰⠶⠂⡈⢀⠔⡰⡞
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡗⢤⡈⠑⢄⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣇⢸⠀⠀⠐⠒⠂⠐⠁⢀⣃⡞⣰⣹⣿⣆
⠀⠀⠀⠀⢀⣠⡞⠹⣿⠄⠀⠈⠓⠊⠳⢤⣀⣀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠋⠨⠀⠀⠀⠀⠀⠀⢀⣼⣛⣵⣿⣿⡿⠟⠛⠂
⠀⠀⠀⠀⠈⠉⠀⠀⣿⣇⡀⣀⢀⠀⣀⣀⡀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠉⠙⢫⣀⢦⣌⡉⠲⠦⣤⣴⣾⠿⢛⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣉⣙⣶⣰⢷⡓⠚⠉⠉⠛⠛⠓⢲⢲⡦⠀⣠⠴⠎⣀⡴⣉⡈⠙⣶⣻⠀⠈⢿⣀⣀⣤⡀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⡠⢋⠉⠉⠉⠉⠻⣿⣦⡣⡀⠀⡠⢒⣬⡿⠟⠛⠁⠀⡟⠀⠠⠀⣠⣄⡈⠑⠸⣿⢀⠀⠀⢀⡠⠄⣸⣆⣹⡄
⠀⠀⠀⠀⠀⣞⠕⠉⠉⠙⠓⡍⠉⠛⠻⣷⣄⣭⡾⠛⠁⠀⠀⠀⠀⣸⠁⠀⠀⢀⣸⣀⡈⠑⢤⣈⣦⣭⣿⠷⠾⠛⠉⠉⠉
⠀⠀⠀⠀⢴⠻⠋⢀⠙⠛⡶⡙⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣤⣤⣄⣉⣓⣶⠚⠉⠁
⠀⠀⠀⠀⠈⢧⠘⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⡎⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⡶⠶⠶⠶⡶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⢀⣀⣀⣰⢞⡽⢶⣝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣄⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⢀⣀⣼⣿⢷⣄⠀⠀⢠⣿⢭⣍⢻⣿⣀⣶⢹⣿⡷⢿⡛⣦⡀
⠀⠀⠀⠀⠀⠀⣸⠿⣿⡉⠙⠓⠶⢦⡴⠞⠛⣦⡛⠙⢳⡶⠛⠉⠁⣸⣿⡼⠃⠀⠀⣸⡇⠶⢏⣾⠷⣬⣵⢿⡙⣟⠲⠛⣸⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠘⢷⣿⡇⠀⠈⢳⡀⠻⢦⡤⠟⠙⠦⠘⢃⠙⠀⢠⣿⠋⠁⠀⣾⠿⣿⡷⠒⠛⠁⠀⠀⠀⠀⠙⠛⠛⠛⠛⣿⡖⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠳⢄⣀⠀⠀⠀⣀⡰⠋⠀⣠⡾⠏⠀⠀⣼⢟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣶⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⠿⢶⣤⣀⣀⣉⠉⣉⣀⣤⣴⡾⢿⣷⣄⠀⠀⣿⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠃⢰⠇⠀⣾⠉⠉⢿⣏⣹⡏⠉⢹⣿⠀⠈⣿⠙⠷⣼⣏⣸⡏⠉⠛⠶⣄⣀⠀⠀⠀⠤⠄⢀⣀⠀⠀⠀⣀⣠⣿⣯⡟⠁
⠀⠀⠀⠀⢀⡾⠃⠀⠀⣾⠀⠀⠹⣶⣶⣾⢋⠉⠛⠲⣿⠁⠀⠀⢻⡇⠀⠈⠻⣿⡇⠀⠀⢀⣀⠉⢻⡛⠙⢷⣴⡋⢹⡷⠾⠛⠉⠀⣿⢉⣷
⠀⠀⠀⣰⡟⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⢻⣇⠀⠀⣼⠏⠀⠀⠀⠘⣿⠀⠀⠀⢸⣿⡀⠀⠈⢣⡀⠀⠙⠒⠋⠈⠛⠋⠁⢸⠋⠀⢠⡿⠛⠁
⠀⠀⣴⡟⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢻⡄⢠⡟⠀⠀⠀⠀⠀⢹⡇⠀⢀⡼⠛⣿⣦⡀⠀⠙⠦⣀⣀⠀⢀⣀⡠⠔⠁⢀⣴⡿⠁
⠀⠀⠻⣧⣀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣷⣼⠃⠀⠀⠀⠀⠀⠈⣿⣾⠋⢀⣾⠏⣿⠛⠳⠶⣤⣤⣌⣉⣉⣀⣠⣤⣴⣿⠛⢷⡄
⠀⠀⠀⢸⡿⠛⠶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⠃⢠⣿⠀⠀⠀⠀⠹⢟⣫⠿⠋⠁⠀⠀⢹⣇⠈⢿⣄
⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⣆
⠀⠀⠀⣾⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢻⣆
⠀⠀⠀⣿⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢸⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢀⣿⡇
⠀⠀⠀⣿⠀⠀⢈⣿⡷⣤⣄⣀⣀⣀⡀⠀⠀⢸⣿⠀⡀⢀⣀⣠⣤⡶⠞⠋⣿⣷⣄⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠟⢿⡄
⠀⠀⠀⣿⠀⠀⠈⡇⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⣿⡾⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠘⣿⡀
⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢻⡇
⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡇
⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⠀⢸⡇
⠀⠀⠀⠀⢿⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣤⣠⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣤⣴⣶⠿⢋⠻⣿⠀⣾⠃
⠀⠀⠀⠀⠈⠻⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⠉⠀⠉⣉⠉⠙⠙⠛⠛⠋⣉⠉⠁⠀⠘⡆⠛⠂⢻⣴⡿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⠀⣠⡖⠙⠶⡄⠀⠀⣠⡌⠉⠶⢄⠀⠀⠘⠎⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸⡇⠸⡄⠻⠟⢰⠇⠀⠀⣅⠸⣭⠆⠼⠂⠀⣀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠈⠣⠴⠓⠊⠀⠀⠀⠨⣀⡴⠒⠂⡠⠴⠉⠶⡄⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⡠⠶⣤⠴⢄⠀⠀⠀⢈⠆⠸⣽⠂⠜⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⢈⡃⡴⠒⡄⠺⡀⠀⠀⠀⠂⠔⠒⠔⠂⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢺⣅⡙⠛⢁⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⠷⣤⣄⣀⣈⣑⣦⣶⣀⣀⣠⣤⣤⣤⣶⣶⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣯⠉⠉⠉⠉⠉⣻⡏⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⣀⣀⣀⣠⣾⠇⠀⠀⠀⠀⣿⣄⣀⡀⠀⠀⢿⡇⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠶⠶⠶⠶⠶⢶⣶⣶⡾⠿⣿⠶⠚⠛⠛⠋⠉⠉⠉⠻⣦⠀⠀⢀⣴⣿⡋⠉⣙⣷⣆⣸⣇⣠⣶⣛⣋⣩⠟⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡿⠁⠀⠉⠉⠉⠀⠸⣿⡿⠁⠀⠉⠉⠁⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⢸⣷⣶⣦⣤⣤⣤⣴⠶⣿⡷⢤⣤⡤⣤⡤⠴⠶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠶⠦⠤⠤⠤⠤⠴⠞⠛⢛⣿⣉⠙⠛⠛⢛⣛⣓⣒⣛⣉⣹⡷⠸⢧⣀⣠⣤⣤⠤⠤⠤⠿⠧⠤⠤⠤⠤⠴⠶⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠚

⠀⠀⠀⣀⡤⠤⠀⠤⢤⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠶⣄
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠊⠀⠉⠈⢦⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⣠⠵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠁⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡡⠤⠠⠤⠒⠒⠁⠀⠀⢀⡤⠦⢤⡀⠾⢤⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠰⠆⢈⡤⠤⢤⡀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣳⠀⠀⠑⠶⠤⠤⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⡤⠞⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⣇⠀⠀⠀⠀⠀⣘⡲⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠋⠙⣦⣄⠀⠀⠀⠀⠀⣼⠙⠲⠴⠚⢹⣆⣀⣠⠴⢻⠋⠉⢉⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠓⠾⣄⠙⠒⠒⠛⣋⣧⡤⠀⠀⠀⢸⣿⠉⠀⢀⡏⠀⢠⠏⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢿⠉⠓⠋⠉⢹⡇⠀⠀⠀⠀⡼⠸⡆⢀⣸⣡⠴⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⢿⡀⠀⠀⢰⠛⠛⣏⠉⡟⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠹⡦⠀⠏⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣀⣀⣀⣼⡇⠀⠀⠘⢦⣀⣀⣀⣀⣤⠤⠟⠀⢙⡏⠉⠉⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠉⠁⣹⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢸⣇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⣿⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⣼⠇⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠓⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣾⣻⡅⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣭⠻⡟⠗⠒⡛⠋⠉⠈⠻⠑⠃⠈⢧⣀⠀⣄⡠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡶⠞⢱⣬⢅⡙⠗⢋⣬⡳⢄⣇⠀⢳⡟⠐⣒⣺⢷⡌⠧⡈⠛⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠃⠴⠋⠍⠢⠙⠛⢻⢉⡠⠔⠚⠉⠉⠉⠉⠓⠤⣬⡿⢐⡖⣂⣇⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢴⡯⠀⠀⠀⡆⢀⣾⠟⠁⣠⡔⠒⢞⢃⠉⢋⢱⠴⢄⡙⣧⡤⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣱⠀⠀⡤⠀⣹⢇⡞⣡⡶⠙⠀⢉⡄⠤⠈⣁⠀⠈⠣⡘⡇⣽⢿⡖⠆⣸⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⣁⠀⡳⢸⣱⠟⡌⣷⠶⠒⠛⠋⠀⠀⠀⠀⠀⠉⠀⢆⣀⠘⢘⢰⠂⢍⢛⡆⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠝⠀⠓⣤⠖⠋⣏⠀⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢯⣗⢄⣙⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠄⡧⢀⡿⠈⡟⡃⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⣿⢾⠶⠟⠚⢁⣰⣞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⡃⠛⠈⣾⣷⡟⠀⡄⠀⠀⠀⠙⠿⠦⡌⠳⠀⠀⠀⠀⠀⣸⡄⣈⠄⡇⣈⡥⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡡⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡼⠩⢥⢃⣐⣱⡯⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣘⣀⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠋⠙⢶⠁⢸⣤⣿⡆⢠⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠫⠒⠢⢤⡀⣀⣈⣁⠸⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠶⡞⠋⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠑⢄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡀⠀⢀⠄⠀⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠢⣀⣀⠤⢰⠖⠉⠀⠀⠀⠀⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⣐⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡰⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢠⠔⠁⠀⠀⠀⠀⢀⡄⠒⠊⠁⢀⢀⣀⣀⡀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⠀⡀⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠂⠐⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠐⠈⠂⡁⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢂⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⡀⠀⠀⠀⠀⠂⢀⣂⠀⡀⠀⠀⠈⡒⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡌⠀⢀⠊⠴⠂⠀⠀⠊⠀⠀⠀⢀⠀⠁⠀⢀⠠⠠⠌⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢨⠀⠠⠀⡠⠆⠀⠀⠀⠀⠀⠀⣈⡈⠀⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢈⣤⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⡀⠀⠀⡐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡁⠀⠨⠛⠒⠂⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⡗⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢱⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⠁⠔⠱⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢈⠃⡀⠒⠡⠒⠆⠀⠐⠊⢉⠀⠐⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢄⠀⠀⠄⠀⢠⠂⠔⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠈⠖⢃⡀⠠⣌⠙⠀⠀⠀⠀⠀⠑⠤⠀⠀⢀⠄⠦⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠔⠈⣄⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠫⡢⣀⡀⠀⠀⠀⡀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡰⠁⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠁⠀⠘⠃⡤⠊⠑⠠⢀⣀⣀⡀⠠⠤⠀⠀⠤⠤⠐⠋⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠴⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠉⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡰⢁⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠤⠒⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠃⠙⡤⠂⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠐⠒⠈⢁⡄⠀⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠃⠀⠀⠑⠒⠢⡤⠀⠤⢀⣠⣄⣀⣀⠤⣤⠄⠴⠒⠒⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⡇⠀⠀⠀⠀⠀⠸⠤⠐⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⠿⠿⠿⠿⣿⠿⠟⠛⣛⣛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⣩⣴⠶⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⢶⣤⡈⠻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠙⢿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⣠⣤⣼⣿⣇⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⡀
⠀⠀⢰⣿⠟⠉⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠉⢻⣷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⣸⣿
⢀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣦
⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠈⠛⠿⠶⠶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻
⢿⣷⡀⠀⠀⠀⠀⠙⠶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠆⠀⠀⠀⠀⢀⣾
⢈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⢸⣿⠉⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣿
⠸⣿⣄⠀⠀⠀⢀⣤⣤⣶⡶⠾⠿⢛⣿⣿⠿⢶⣦⡄⠀⠀⣤⣶⠾⢿⣿⣿⠿⠿⠷⢶⣦⣤⣤⡀⠀⠀⠀⣸⣿
⠀⠙⣿⣶⡄⠀⠘⠿⣿⡏⠀⠀⡴⢿⣿⣿⣷⠀⢹⣿⣶⣶⣿⠁⢠⢿⣿⣿⡷⡄⠀⠀⣿⡷⠿⠃⠀⣠⣾⡿⠃
⠀⠀⠘⢿⣿⡆⠀⠀⢸⣧⠀⠘⠀⠈⠛⠛⠚⠁⢸⡏⠀⠀⣿⡀⠈⠚⠛⠋⠁⠸⠀⠀⣿⠇⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠘⢿⣦⣀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⢀⣼⠏⠀⢀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠈⠛⠿⠷⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠾⠿⠛⠁⠀⠀⣾⣿⠋
⠀⠀⠀⠀⢠⣾⡟⢻⣦⠀⠀⠀⠀⠀⠀⠀⠜⠢⣄⠀⠀⠀⠀⣠⠞⢢⡀⠀⠀⠀⠀⠀⠀⣾⠟⢿⣷
⠀⠀⠀⠀⠸⣿⣷⣾⣿⡄⠀⠀⢀⠠⠐⠈⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠈⠒⡤⠀⠀⠀⢸⣿⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢹⣷⠀⠀⠀⠀⠉⠓⠠⠀⡀⣀⢀⣀⠀⠀⣀⠤⠒⠈⠀⠀⠀⢀⣿⠇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣦
⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣎⠲⣤⣀⣀⣀⣀⡤⠖⣰⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⢀⠴⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠉⠉⠉⠁⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓⠦⡀
⠀⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠢⠐⠂⠐⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡁⠀⡀⠀⠀⡀⠀⣃⠁⠀⠀⠀⠀⠀⢀⠄⠀⠐⠒⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠁⢀⠀⠀⠀⡇⡁⠀⠀⠀⠀⠀⠆⠠⠀⠠⡀⠀⠀⠡
⠀⠀⠀⠜⣏⢂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠡⠐⠰⠒⠲⠑⠠⠁⠀⠀⠀⠀⠀⡈⠀⡄⠀⠀⠐⠴⡄⠀⠡⡀
⠀⠀⠀⠉⠪⡃⠙⢠⠀⠀⠀⠀⠀⠀⢀⣰⣷⡒⠂⢒⣺⣷⣀⠀⠀⠀⠀⢰⠀⢴⠦⢒⢤⡔⠓⠜⣖⠂⡀
⠀⠀⠀⠀⠡⡀⠃⠀⡀⠀⠀⣠⠔⠈⠀⠹⣿⣿⣦⣿⣿⣿⣅⡨⠐⢄⠀⠀⠱⡈⢄⠘⠢⠴⠀⠠⣁⠏
⠀⠀⠀⠀⠀⠀⣶⣾⣿⡄⢠⣿⡀⠀⠀⠀⠈⠻⣿⡿⠛⡝⠅⡁⠂⣼⣷⠀⠀⠀⣁⣓⠂⠂⢻⣉
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣼⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠈⠢⣀⡴⣿⣿⢀⣴⣿⣟⠂⠭⠯⠐⢺⣽⣶⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠽⢾⠷⠿⠇⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠊⠉⠉⠲⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣊⣁⠀⢀⣉⣒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠀⠀⢸⡧⣿⠀⠀⠈⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⠞⣩⠛⡇⠀⠀⠀⠀⠀⢘⡇⣟⠀⠀⠀⠀⠀⠀⡟⢫⡙⢦⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣘⠖⠁⠀⠉⠉⠉⢉⡩⠙⠛⠃⠛⠛⠩⣉⠉⠉⠉⠁⠀⠑⢎⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢤⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⣰⠄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠀⠀⠈⠩⢉⠩⠉⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠸⡄⠀⠀⡼⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⢤
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⡇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡗⠒⠦⣄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠘⡦⢤⡜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣤⠤⡞⠀⠀⠀⠈⠳⣄
⡠⠖⠉⠉⠁⠀⠠⡖⠉⠉⡟⠀⢰⡀⠀⠉⢳⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠋⠁⠀⣰⠀⠹⡏⠉⠑⡦⠀⠈⠉⠉⠑⠦
⠣⣤⠖⡻⠇⠀⣠⠇⠀⣰⠁⠀⠀⠙⠲⠖⢻⡀⠈⠉⢙⡟⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠚⣟⠉⠉⠀⣸⠓⠶⠚⠁⠀⠀⢱⡀⠀⢧⡀⠀⠿⡓⢦⡤
⠀⠈⠊⠀⠳⣄⡼⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠙⠂⠔⠊⠱⢄⣀⡠⠛⢄⣀⣀⠜⠣⣀⣀⠴⠉⠒⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠸⣀⡴⠃⠈⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⡶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⣶⣶⣿⣿⣿⣿⣿⠇
⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⢡⠄⠀⢨⠄⠈⢀⡄⡀
⠀⠠⢔⠀⠀⠈⠁⠀⠨⣄⣠⠞⡅⠈⠀⡀
⠀⠈⠑⠀⠤⢔⣮⠽⠀⠈⠁⢸⡇⠀⢀⣽⠛⣶⡀⣤⣤⣤⣀⣀⣠⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠐⠒⠂⠀⠈⢠⡀⠀⢾⠅⠀⠞⠁⢰⣿⡇⠈⣿⡿⠓⢤⡥⡴⢶⠦⠤⠀⠉⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⢀⠌⣿⠇⠀⠹⠀⠀⠟⠁⠈⠀⠀⠀⠀⡰⠃⠀⠑⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠁⠀⠀⠀⠀⣄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠸⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠸⢦⣄⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⣝⠀⠀⠜⡗⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠇⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⣿⣦⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣿⣷⣄⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⡏⠘⠄⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠁⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠐⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⡤⠋⠠⡤⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣑⡾⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠓

⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠠⠤
⠀⠀⠀⢀⣮⣴⡿⠷⠶⣤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣁⡤⠤⠤⠄⡀⠀⠡
⠀⠀⠀⢸⡥⠤⠀⠠⢖⠮⢻⣤⣷⢄⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⡄⠀⠤⣀⠄⢀⡀
⠀⠀⠀⠈⣇⢸⠀⠰⡀⡁⠸⠿⣿⣈⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⢤⠁⠸⠀⠀⠀⠉⢰⡄
⠀⠀⠀⠀⡇⠁⡈⢀⡈⠀⢠⣾⡯⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡠⡊⠬⣧⠀⠀⠀⠠⡝
⠀⠀⠀⠀⠙⠲⢭⣉⣤⣶⠞⣿⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⣀⣀⠤⠴⠃⡀⠀⢸⠀⠀⢠⡓
⠀⠀⠀⠠⣖⣶⣶⣭⣿⡴⠄⣸⠦⢼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠒⠈⣩⡄⠀⠀⡡⠠⡌⠀⠀⡮⠁
⠀⠀⠀⠀⠿⣿⣿⣿⣿⡤⠞⢋⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢵⡠⠕⣴⣁⠤⠊⢀⡠⢁⣀⣠⡉
⠀⠀⣠⠞⠉⠁⠀⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠧⠤⠐⣊⡉⠠⣤⠀⢚⡃
⠀⢰⠁⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢠⠥⢽⣩⠀⡀⠊⠀⠕⣺⠇
⠀⡻⣤⣄⣀⣤⣿⣿⡿⠿⠛⠛⠋⠉⢻⣿⣷⡀⣀⠀⠀⠀⠀⢘⢤⡀⠀⠀⠀⣿⠿⠭⠁⠐⠒⠀⠙⡀⠏⢆
⠘⠦⠷⡾⣭⣿⣿⣿⣶⣦⣤⣤⣶⣶⡿⠟⢻⣿⣿⠀⠀⠀⠀⠣⠤⠶⠍⣹⣉⠝⡔⠂⠀⠀⠀⠒⢈⠠⠒⣀⡩⠇
⠀⠀⠀⠳⢾⣿⣿⣯⣭⣙⣛⣋⣩⣥⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠐⠶⡙⠅⠰⠭⠀⠐⠂⠈⠩⠤⠐⠈⡠⠊
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠤⠤⠤⠤⠄⠒⠉
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠎⠀⠈⠀⠀⠀⠉⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⢀⠈⡡⠆⠤⠒⠙⡆⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⢰⢋⡏⢀⢄⡤⡤⣶⢷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⡄⠀⠀⢀⡼⠉⠉⠢⠤⡀⠘⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⠀⠐⢯⣀⠀⠀⠀⠊⠥⠌⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣄⠀⠀⠘⠒⠶⣺⠃⠁⠀⣤⣀⣉⡔⠁⢀⡴⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣒⠉⠀⠀⠈⠣⡤⢤⠖⠊⠳⣄⣠⡾⠃⠂⢄⡀⡠⠊⠀⠀⠈⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠈⠢⢕⡤⠤⠴⣏⠒⠤⢔⡪⠋⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠉⠒⠛⠊⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠦⢄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠛⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣨⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⣿⣿⣶⣤⡄⠀⠀⣀⠀⣤⣤⣴⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⢿⣿⣿⡿⠋⠀⢀⣼⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⣀⣤⣴⣦⣤⣤⡙⣄⣮⢦⠤⠚⢉⡱⢄⡈⠑⢏⣤⡶⠋
⠀⠤⠀⠀⠀⠀⢀⣀⣤⢤⣤⣤⣶⣶⣶⡾⠿⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠻⠙⠈⠀⠛⠲⣤⣤⣘⡉⠽⠛⠉
⣠⣤⣤⣶⣾⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠿⠟⠛⠉⠁




⣀⣀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡀⠀⠙⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢱⠀⠹⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠄⢠⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡈⢻⣦
⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⢿⡄
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠐⠉⠀⠈⠉⠉⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣸⣷
⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣓⣶⣤⣀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⢿⣧⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⢻⡆
⠀⠀⠀⠀⠀⠙⢿⣦⣧⡐⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣌⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⣰⡿⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣽⣿⣿⣿⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣨⣵⣿⣿⣿⣿⣿⢟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⠿⠛⢁⣴⣾⣿⠛⠋⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠀⠐⡜⠝⢸⠇⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⢳⡀⠀⠀⠀⠑⠀⠀⢀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢳⡀⠀⠀⠀⠀⠀⠀⠱⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠠⢂⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠜⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⣠⡀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣀
⠀⠀⠀⢠⣶⣿⡍⠀⠀⠀⠀⠀⢀⣽⣥⣤⣼⣧⡀⠀⠀⠀⠀⠀⣈⣿⣆⠀⠀⠀⠀⠀⠀⠈⣹⣿⣦⡀⠀⠀⠀⠀⣾⣧⠀⣠⣾⡟⠁
⠀⠀⠀⣿⣿⡇⠹⠄⠀⠀⠀⠀⢾⣿⣿⠆⣿⡿⠙⠀⠀⠀⠀⠘⢉⣿⣿⣴⠀⠀⠀⠀⠀⠰⠇⢹⣿⡇⠀⠀⠀⢸⣿⡏⢻⣿⡏⠳
⠀⠀⠀⢻⣿⢃⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⣿⡇⠀⠀⠀⠀⠀⠀⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⠛⡇⢸⣿⠁
⠀⠀⠀⠈⠈⠈⠀⠀⠁⠀⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠁⠁⠁⠀⠀⠀⠈⠀⠁⠈⠉
⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⣦⠀⢠⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⣾⣯⣄⠀⠀⠀⠀⢀⣾⣧⡀⣠⣶⣟⠁⠀⠀⠀⠀⢀⣾⣷⣄⠀⠀⠀⠀⠀⣠⣿⡤⢶⣿⣦⡀⠀⠀⠀⢛⣷⣦⣀⣼⣷⡀
⠀⠀⠀⣼⣿⣷⡘⠁⠀⠀⠀⢸⣿⡏⢹⣿⣏⠹⠆⠀⠀⠀⠐⠋⣿⣿⠈⠃⠀⠀⠀⠘⣿⣿⡟⢾⣿⡧⠙⠀⠀⠀⠞⠙⣿⡏⢹⣿⡧
⠀⠀⠀⣿⣿⡏⣷⠀⡀⠀⠀⢸⠁⡇⠘⣿⡏⠀⠀⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⣿⠃⢸⣿⡇⠀⠀⠀⡀⠀⠀⣿⡇⢸⠃⣇

⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢠⣦⠀⠀⠀⠀⢰⡦⠀⠀⢠⣄⡀
⠀⠀⠀⢀⣾⣿⢯⠀⠀⠀⠀⠀⠀⢀⣺⠇⢀⣼⣿⡄⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⣠⣾⣷⣄⢀⣾⣷⣄⠀⠀⢀⣾⣷⣀⣴⣿⡏
⠀⠀⠀⢸⣿⡇⠈⠃⠀⠀⠀⠀⣺⠽⠿⡗⠉⢘⡿⡇⠀⠀⠀⠋⣼⣿⡇⠉⠀⠀⠘⠁⣿⣿⠈⠉⣿⣿⡌⠃⠀⢸⣿⡇⣽⣿⡇⠹
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠾⠣⠀⡀⠀⠀⢸⡇⡧⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⣿⣿⠀⠀⢹⣿⠁⠀⠀⢸⠘⡇⢹⣿⠃

⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢶⡆⠀⠀⠀⠀⠀⢴⣞⡀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⢴⡆
⠀⠀⠀⣴⣿⡶⣄⡀⠀⠀⠀⠀⣠⣾⣶⠚⣿⣷⣄⠀⠀⠀⠀⢠⠿⣿⣦⡀⠀⠀⠀⣿⣷⣄⡐⣿⣄⡀⠀⠀⢀⣴⣿⣷⣄⣠⣾⣷⣄
⠀⠀⠀⠟⠉⠑⣮⡁⠀⠀⠀⠀⠋⣿⡏⠛⣿⡿⠈⠁⠀⠀⠀⠚⠀⣿⣿⡇⠀⠀⠐⡿⣿⠀⠈⡿⠛⢭⣅⠀⠈⠀⣿⡇⠈⢁⣿⣿⠈⠁
⠀⠀⠀⠠⠀⠠⠎⠿⠆⠀⠀⠀⠀⠿⠇⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⢹⢿⠀⠀⠀⠀⠇⢹⠀⠀⠀⠀⠴⠻⠂⠀⠀⠿⡇⠀⠀⠿⠯

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⣦⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⡾⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⠔⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡏⠀⢀⣄⢤⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠉⠀⣼⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣿⠹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡴⢚⣛⣛⣦⡀⢠⠇⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣠⠤⠶⠤⣀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠹⢶⣶⣎⣉⣤⣤⣶⠖⠊⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⡀⠀⠀⠀⠈⠉⠛⠛⠛⠉⢀⣠⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣦⣀⣠⣄⣀⣤⣴⣿⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢻⡆⠀⠀⢀⡴⠛⣉⡉⠙⢷⣄⣠⡾⠋⠉⠉⠛⢶⡀⠀⠀⢰⡟⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⠁⣼⠋⠁⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⠀⠀⣿⡀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣼⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⠀⠀⠘⢷⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣼⡛⢷⣄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡾⢛⣧⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⣷⡀⠙⢷⣄⠀⠈⠻⢦⣄⣠⡴⠟⠁⠀⣠⡾⠋⢀⣾⠃⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠈⢷⡄⠀⠙⢷⡄⠀⠀⠉⠉⠀⠀⢠⡾⠋⠀⢠⡾⠁⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠻⣦⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⡀⢀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠛⠉⠉⠉⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⠁⠀⠀⠀⣀⣠⣤⣤⣴⣾⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⣀⣴⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣦⣄⡀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡉⠛⢿⣦⡀⠀⠉⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⠿⣿⣿⣶⡀⠙⠧⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⣰⣿⡟⠁⠀⠀⠀⠀⠈⠙⠿⡄⠀⠀⠀⢤⣀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠠⣤⣤⣴⣶⡿⠟⠋⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣄⠙⢷⡄⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⣀⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠘⣿⡄⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠙⣿⡿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠘⣷⡀⠀⢹⣿
⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠰⢶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠀⠀⠘⣿⣧⠈⠿⠆⢸⣿
⠀⠀⠀⢠⣿⡟⠀⠀⠀⣀⣀⣀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⡀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⢹⣿⣷⣄⡀⠈⢿⣷⡀
⠀⠀⠀⢸⣿⠁⠀⠀⠀⣿⡟⠛⢻⡿⠻⣦⣀⠀⠀⠀⠶⠶⣷⣶⣤⡀⠀⢻⣷⠀⠀⢸⡏⠀⣠⣶⣶⡤⠀⠀⠘⣿⡉⢻⡇⠀⠀⣿⣷
⠀⠀⠀⢹⣿⡀⠀⠀⠀⢸⣿⣄⣿⠇⠀⠀⠙⢷⣦⣀⣤⠤⠿⠿⠿⠷⠦⣼⣿⣀⣀⣸⣀⣨⡭⠿⠿⠷⠶⠶⢤⣿⣧⣼⡇⠀⠀⣼⣿
⠀⠀⠀⠘⣿⣧⡀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠹⣏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠁⠀⣰⣿⡟
⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠦⢶⣶⡶⠚⢋⠀⠀⠀⠘⣿⠲⠶⠶⠴⠶⠶⠚⢻⡿⢀⣴⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠛⠻⠷⡶⠿⠛⢿⣷⡀⠀⠀⠀⠀⠀⣾⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠙⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⣠⣴⣶⣶⣶⣦⣤⠀⢻⣧⠀⠀⠀⠀⣼⡟⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣦⡀⠀⠀⠀⠀⠸⣿⠀⠀⣴⣿⣋⣉⣉⣉⣹⡟⠀⢸⠏⠀⠀⢀⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷⣄⠀⠀⠀⠀⠙⠂⠀⠹⣿⣍⣉⣉⣉⣻⣇⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠋⠀⢀⣀⣼⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⠉⠀⢻⣿⣿⣷⣦⣴⣤⠀⠀⠀⠐⠶⠶⠶⠂⠀⣠⣾⡿⢻⣿⠇⠀⢹⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠘⣿⡇⠉⠛⠻⢿⣷⣤⣀⣀⣀⣀⣀⣤⣾⡿⠋⠀⣼⡿⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡟⣿⣷⡀⠀⠀⠙⣿⣦⡀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠁⠀⢀⣼⡿⠃⠀⠀⣼⡇⠸⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⣿⣷⡀⠀⠀⠈⠻⢿⣶⣤⣀⣀⠀⠀⠀⢀⣀⣀⣤⣶⡿⠛⠀⠀⠀⢠⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢼⣿⣷⡀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⣿⠿⠟⠛⠁⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⢀⣿⣿⣷⣄⠀⠀⢀⣠⣴⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⣀⣀⣀⣉⣉⡛⠛⢛⠛⡛⠛⠛⣀⣀⣀⣀⣀⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣁⣀⣀⣀⣀⣀⡛⠛⢛⣛⣋⣉⣁⣀⣀⣀
⣿⣿⡿⠿⢿⡿⠿⠿⢿⢿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣾⣷⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⣝⣿⣿
⣿⣿⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣄⣀⡀
⠀⢸⣭⣙⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣷⣦⡁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⠛⣿⣿⣷⣤⣘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⡇
⠀⠀⠹⣿⡿⠀⠸⣿⣿⡿⢿⣷⣌⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠋⠉⠘⣏⣡⣴⣾⣿⣿⣿⣿⣃⣀⣀⣉⠉⠉⠉⠁
⠀⢠⡀⠹⠇⠀⠀⢹⣿⠃⠘⣿⣿⣷⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢟⣡⣶⣿⣷⣿⠟⣫⣿⣿⠿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⢸⣦⠀⣠⣾⡄⠀⡟⢀⠀⣿⣿⣿⣿⣧⡙⢆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣿⣿⣿⣟⣁⣤⣯⣭⣶⣶⣾⡿⢻⡾⢟⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣾⣿⣿⣧⠀⢀⣾⡀⣻⡏⢸⣿⣿⣧⠈⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣠⣾⣿⡇⢛⣀⢸⣿⣿⣿⣧⢰⠀⠀⠀⠘⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣴⣿⣸⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠙⠛⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⡿⠟⣻⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⣼⣷⣶⣶⡶⠶⠦⣤⣀⡀⠀⠀⠉⠋⢸⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣶⡷⡿⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡟⠀⠀⠀⠀⠀⣽⣿⣿⣷⣿⣿⣿⣶⣮⣽⣓⠄⠀⠀⠀⠙⠿⡿⢡⣿⣿⣿⣶⣿⣿⣿⣧⣼⡆
⠀⢸⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⡟⢠⣿⠁⠀⠀⠀⢀⣾⣿⣿⣟⠉⠹⣯⣽⣿⠟⢿⣿⣷⣦⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣯⣽⣽⣿⣁⡸⢿⣿⣿⣿⣿⡗⢀⡿⠃⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣶⣼⣦⣤⣤⣤⣿⣿⣯⠃⠀⠀⢀⣸⣿⣿⣿⣿⣭⣭⣭⣭⣽⣛⡁
⠀⠀⠀⠀⠈⠉⠙⡛⣻⣷⣦⣏⠐⢹⠧⠟⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠉⠹⠟⠛⢛⠠⠤⠅⣈⠉⠉⠛⠻⠇
⠀⠀⣀⠤⢐⡒⣚⣓⡛⠟⠉⠉⠳⠎⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠙⡇⠀⠀⠞⠁⠸⣯⣽⣶⠖⠈⡀
⠀⠐⡥⠀⠘⣧⣿⣿⠏⠀⠠⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣲⠁⠀⠀⠀⢄⡐⠛⠛⠀⠀⠀⠐
⠀⠀⠒⠠⠀⠀⠉⣢⠤⠌⠒⠀⠘⣆⠀⠐⠀⠀⠈⠙⠻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢢⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠐⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⢈⡿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⠤⠔⠊⠀⠀⠀⠀⠀⢀⡀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⢣⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠙⡆⠀⠀⠀⠀⠀⢠⡄⠄⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣤⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠠⠴⠤⠥⠆⠠⠤⠀⣒⡂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⢉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣯⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣯⣽⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⣭⡍⠉⠛⠛⠿⢿⣿⣿⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⠟⠀⠀⣠⣤⣶⣟⣷⣦⡀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⡀⠀⣿⣿⣿⢹⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡷⠀⠈⠙⢻⣾⠛⠋⠀⠀⢀⣤⣾⣿⣿⠏
⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⣿⠿⠛⢁⣤⣶⣾⠏⣻⣶⣄⠀⣴⣿⣿⡿⠛⠁
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠀⢸⣿⣿⡿⢀⣿⣿⠟⠀⣿⣿⡟
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠋⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⢀⡀⠀⢰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⠄⠒⠢⠄⠠⡀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠉⣀⡤⢴⣶⡦⢄⡘⠦⣄⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡤⠊⠁⠠⠊⠀⠙⠀⠙⢆⠀⢳⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠞⠀⣠⡶⠶⠂⠤⢤⣤⣀⠀⢳⡈⢧⡀⠀⠀⠀⢻⡀⠀⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⢿⣠⠚⠙⣶⢄⠀⡴⠋⠉⡙⢷⠀⢳⠀⢳⠀⠀⠀⠸⡇⢠⡵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⣾⣏⣿⣶⢾⢰⣿⣭⡜⡇⠈⡇⢻⡀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⡙⢿⡿⠁⢻⣈⣛⡿⠣⡛⠀⣻⠀⢳⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠞⠦⠀⢈⠻⠶⠤⠞⠁⠀⢹⡄⢢⡀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⡲⠚⠃⠀⠀⠀⣠⠴⠛⡇⠀⣷⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣤⡤⠴⠲⡋⠀⠀⠸⣇⣰⠃⢠
⡀⠀⠈⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠊⢀⠄⠀⠀⢈⡶⢢⡀⠀⠉⠀⠐
⠑⠤⠐⢀⡤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠹⠶⠶⠚⠉⠄⠀⣇⠀⠀⠀⡀
⢠⠒⡀⠚⠀⠀⢀⠴⡀⠀⠀⠀⠀⣠⠔⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢁
⠀⠀⠄⠒⠢⠤⢺⠀⢘⠂⠒⣒⣩⠴⠊⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⡀⢂
⠀⠀⠀⠀⠀⠀⠈⠚⠋⠀⠀⠉⠀⢀⣀⡾⠙⠳⢤⠀⠀⠀⠀⢠⠀⢸⠃⠠⢢⠀⠱⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⡼⢄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⢀⠃⢠⣧⣄⠻⢼⠓⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢸⠀⢻⡀⠀⠱⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠦⢠⠎⠀⠀⢳⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣄⣀⣇⠀⠀⠀⠱⡄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠫⡠⠆⠀⠀⠙⡄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠀⠀⢀⡁⠂⠀⠀⠀⠘⣆⠀⠀⠈⢧
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡄⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠂⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠒⠉⠉⠉⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⣤⣉⠉⠉⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠒⠉⠉⣂
⠀⠀⠀⠀⠀⠀⠀⠀⡲⠦⡈⠉⠛⠲⠶⠦⠤⠤⠤⠤⠤⠴⠶⠶⠶⠒⠒⠒⠒⠒⠚⢛⣋⣉⣁⠴⠦⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠰⢁⣀⠤⠤⠞⠋⠐⠀⠀⠒⠒⠂⠠⠐⠶⡋⠛⣲⠞⠉⠉⠉⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣾⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣴⣿⣿⣿⡿⢿⣿⣿⣿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⢿⣿⣿⣿⡿⠁⠀⠀⢿⣿⠃⠀⠀⠀⠀⠸⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠛⠉⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄
⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄
⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣤⣤⣤⣿⠿⠿⡶⡶⠶⠛⠁⠀⠀⠀⠀⣠⠎⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣤⡾⠛⠉⠀⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠀⢀⣠⣴⠞⠛⠲⣶⣿⡷⠋⠀⠀⠀⠀⠈⠛⢷⣦⣄⣿⣿⣿⡇
⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠁
⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣠⣴⣿⡟⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠈⣿⣿⠃⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⣹⣿⣿⡟⠀⠀⠀⠀⢈⣉⣉⣛⣿⣿⣿⡿⠟⠛⠛⠿⢿⣿⣦⣀⣀⣠⣄⣀⣠⣶⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣋⣉⣈⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⢠⣾⣿⣿⡟⠁⠀⠀⢰⣾⣿⣿⣿⣿⣿⡿⠁⠀⣠⡴⠶⢦⣄⠙⢿⣿⣿⣿⣿⣿⣿⡿⢋⣠⡴⠶⢦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣷⡄⠀⠐⣶⣶⣶⣿⣿⣿⡿⠋
⠀⠀⠻⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠈⣱⢚⣿⣷⡌⠃⠈⣿⣿⠛⠻⣿⣿⠁⠞⣱⣿⣯⠳⡌⠂⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⢈⣿⣿⣿⡟⠉
⣀⣀⣤⣾⣿⣿⡟⠁⠀⠀⠀⠉⠙⢿⣿⣿⡀⠐⠀⠉⠈⠻⠟⠃⠀⢠⣿⡿⠀⠀⣿⣿⡄⠀⠙⠿⠛⠀⠁⠀⠀⢠⣿⣿⡟⠉⠉⠐⣶⣶⣶⣿⣿⣿⠟
⠙⢿⣿⣿⣿⣿⣤⣤⣴⡆⠀⠀⠠⢾⣿⣿⣷⣄⠀⠀⠀⠀⠘⢉⣠⣿⡿⠃⠀⠀⠘⣿⣿⣄⡙⠒⠀⠀⠀⢀⣠⣿⣿⣿⡷⠆⠀⠀⢿⣿⣿⣿⣛⠁
⠀⠀⠉⠛⠿⢿⣿⣿⣿⣧⣀⠀⠰⠛⢻⡟⠿⣿⣿⣶⣶⣶⣾⣿⡿⣟⠁⠀⠀⠀⠀⢈⡛⢿⣿⣷⣶⣶⣾⣿⡿⠟⣿⢋⠛⠂⠀⠀⣠⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⢧⠀⠀⠉⠉⠉⠉⠉⠁⡰⠧⣄⡀⠀⠀⣀⣠⠽⣆⠈⠉⠙⠉⠉⠁⠀⢀⡟⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣇⠸⡇⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠈⠑⠋⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⣾⠀⣿⣿⣿⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⣷⠀⠀⠀⠀⢻⡏⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢻⡗⠀⠀⠀⠀⡟⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠀⠀⢸⠀⠀⠈⠉⠉⠉⠙⠉⠉⠉⠉⠁⠀⠸⠁⠀⠀⠀⣸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⠤⣀⣀⣀⣠⠤⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣴⣶⣶⣤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⡵⠚⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣤⠤⣴⠧⠤⠶⠚⠀⠀⠀⠀⠀⠀⢀⢠⠚⡀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠉⠛⠛⠉⠉⠑⣷
⠀⢠⢠⡀⠈⠛⠶⢾⠴⠀⣠⢄⡀⢀⣤⣄⣠⡀⢈⠹⣠⠀⡀⠀⣀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢠⡏⣽⠅⠀⠀⠀⠈⡆⠸⣅⣨⣇⢸⡅⢸⡀⣿⣸⣀⣿⣀⣿⣀⣿⣠⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠁⠀⠀⠀⠳⠤⠞⠀⠀⠈⠁⠈⠈⠀⠈⠀⠈⠀⠀⠀⠁⠀⡡⠛⡇⠀⠀⢳⡄⣀⡔⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠢⠀⠀⠒⠶⣄⠀⠀⠀⠀⠀⠣⠤⠇⠀⠀⠘⢿⣷⣶⠟⠀⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠶⠋⠉⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣁⣤⡶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣀⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⢠⡾⠋⠀⠀⠀⣠⣴⣶⣾⣗⠦⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢠⠏⠀⠀⠀⠀⠜⠋⠉⠉⠉⠙⢷⡔⠀⠀⠀⠀⠀⢀⠞⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⢠⠏⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢸⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢠⠋⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠳⣽⡦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⡌⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠛⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡿⠁⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠾⠛⠻⢦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠾⠿⠶⢶⣤⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣨⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢰⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⣤⣴⠾⢃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠛⠛⠒⠶⠶⠛⠀⠀⠈⢷⣭⣭⣤⠤⠶⠖⠒⠒⠒⠒⠶⠶⢶⣾⣿⣯⣭⣭⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠦⠬⠉⠉⠁⠐⠂⠤⡀
⠀⠀⠀⠀⠀⠀⢠⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⠟⠸⠙⠻⢖⡒⠀⠀⠀⠻⡒⠠⠄⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⢄⡀
⠀⠀⠀⠀⠀⢸⢀⠆⠀⠀⠀⠀⠉⠐⠒⠀⠘⠂⠀⠀⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣀⠀⠀⢀⡈⣆
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⢸⡅⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⢠⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⢀⣸⠀⢀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠎⠀⠀⠀⢀⡼⠁⠣⡀⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠐⠁⢸⠀⠀⠀⠹⠿⠀⠀⠀⠀⠀⠨⠿⠀⠀⠀⠀⠀⢱⠀⠀⢘⠀⠀⠀⡴⠋⠀⠀⠀⠙⢆⡁⠀⠀⠀⠈⡄
⠀⠀⠀⠈⢄⠀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠴⢀⠌⠀⠀⡏⢁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⡀⠀⡇
⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⡆⠈⠉⠀⠰⠀⠀⠀⠀⢀⠋⠁⠀⠀⠀⠇⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠀⣠⡂⠀⠀⠀⠀⡔⠻⠁⠀⠀⠙⠁⠀⠔⠀⠀⠀⠙⠁⠀⠀⢙⠓⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢶⠤⠤⠤⠀⠀⠤⠄⠐⣾⡻⠉⠒⢄⠀⠀⠣⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡬⠤⠞
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠘⡄⠀⠀⠘⠀⠀⠀⡪⡷⠁⠀⠀⣠⠓⢄⠀⠀⠈⠢⣀⠀⠀⠁⠀⠈⠀⠀⠀⢀⣠⠊
⠀⠀⠀⠀⠀⠀⡔⢠⠀⠈⠜⣄⠀⠀⠀⢀⣴⠟⠀⠀⠀⢀⠁⠀⠀⠣⡀⠀⠀⡠⠟⢲⡦⠄⠲⠆⢐⢖⡛⠀⠉⠢⢄
⠀⠀⠀⠀⠀⡰⠀⠘⠀⠀⠈⠢⡙⠒⠫⠑⠁⠀⠀⠀⠀⠸⠃⠀⠀⠀⢱⡔⢛⠀⠀⠀⡗⠩⠀⠨⠔⠊⡇⠀⠀⠀⠀⡱⢄
⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢥⢸⠆⠀⠀⢁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠀⠀⠣
⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠒⣦⣂⠀⠐⡈⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠑⡇⠀⠀⠀⠇
⠀⠀⠀⢀⠜⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠝⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠈⡀⠀⠀⠀⠰⠀⠀⠀⢸⠄
⠀⠀⢀⡏⠒⢢⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠂⠒⠤⣠⠃⠀⠀⠀⠀⡜⠈⠉⠁⠀⠀⢃⠀⠀⡀⣀⣇⡀⠀⢠
⠀⠀⠮⢤⡂⡎⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠀⠉⡷⠖⠁⠀⡁⠀⠀⡔⠀⠀⠀⠀⠀⠀⠈⢢⣾⠄⠈⢻⡄⠀⡜
⠀⠀⠀⠀⠉⠁⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢶⡃⠀⠀⠀⣴⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢽⡟⢹
⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠁⣿
⠀⠀⠀⠀⠀⠘⢰⢸⠂⠤⠤⠀⠉⣉⣉⣙⣉⡉⠉⠁⠤⠤⠀⠚⡇⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡴⠟
⠀⠀⠀⠀⠀⠀⡎⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹
⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⢀⠄⠺⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠇⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡁⠘⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠂⠤⣆⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢈⢻⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠃
⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠄⠀⢤⠀⠀⠀⠀⢲⠈⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠄⠀⠀⠀⠈⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣇⡠⠤⠤⣁⠀⡆⠀⠀⠀⠀⠀⢶⠚⠛⠓⢶⠄⠀⠀⠀⠈⣇⠀⠀⠈⡁⠀⠀⠀⠀⠑⢤⣤⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣈⣉⣈⣉⡻⠇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠰⡉⠑⢦⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠲⢤⣀⡀⠀⢀⣇⣠⣀⠊⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⡤⠛⠉⠀⠀⠀⠀⠑⢄⢀⡴⠋⠉⠁⠈⠉⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢀⣰⠁⠀⠀⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠈⠋⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⡇⠀⡀⠀⢴⣹⠗⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣅⣀⠀⠇⠀⡿⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠈⠁⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⡠⠚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠎⠀⠀⡏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢸⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠶⣦⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣼⠇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣤⠾⠋⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠻⣅⠘⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡤⢤⡀⠀⠀⠹⠀⠀⠈⠉⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⡤⠤⢴⡀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠚⠠⣤⣀⣈⢷⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠀⠀⠁⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢱⠀⠀⠀⠀⠀⣠⠀⠀⠀⣸⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⠟⠻⠅⠀⠀⠀⠀⠀⣿⣇⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⣔⣽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣠⣞⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡿⣣⣾⣯⣿⣹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣷⣚⡿⢶⣿⣩⣿⣽⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣽⣟⣿⡿⣟⣽⠋⠀⡠⠞⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣻⡿⣾⡿⢡⠞⠁⣰⣶⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣩⣿⣛⣿⠁⡋⠀⢰⡿⠋⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣿⡇⠆⠁⠀⣿⡗⠂⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣾⡯⣿⠃⢠⠀⠀⣿⣧⣇⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠿⢿⣶⣦⣤⣤⣴⣾⣿⠿⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣼⣿⣇⠀⣀⣤⣶⣾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣶⣤⣀⠀⠀⣸⣿⣧⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠉⠉⠛⠛⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡿⠿⠛⠛⠉⠉⠛⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⢀⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⡏⠀⠀⣠⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⣹
⢸⣿⢀⣼⠃⠀⠀⠀⠀⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠸⣦⡀⣿
⠸⣿⣿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠹⣿⣿
⢰⣿⠏⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢠⣤⣤⣶⣶⣶⡶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⢹⣿
⣾⣿⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⢠⣾⣿⣁⣀⣀⣀⣀⣴⣾⠿⢛⣛⣛⠛⡛⣛⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⣛⣛⣛⣛⠻⠿⣷⣦⣄⣀⣀⣀⣀⣙⣿⣦⡀⠀⠀⠀⣿
⢻⣿⠀⢀⠀⠈⠛⢿⣿⣟⠻⢿⣿⡟⠁⠐⠋⢁⣾⣿⣷⡌⠑⠈⢿⣷⣀⣤⣴⣶⣦⣤⡀⢰⣿⠋⠈⣰⣿⣿⣦⠈⠙⠂⠈⢻⣿⡿⠟⢻⣿⡿⠟⠋⠀⢠⠀⢀⣿
⠈⣿⣆⣸⡆⠀⠀⠀⢹⣿⡄⠀⣿⡇⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⢸⣿⡿⠋⠉⠀⠉⠙⢿⣿⡏⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⢸⣿⠁⠀⣿⡿⠁⠀⠀⠀⣸⣇⣼⡿
⠀⠘⢿⣿⣧⠀⠀⠀⢼⡟⠀⠀⢻⣷⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣾⡟⠀⠀⢻⣿⠀⠀⠀⢠⣿⣿⡟⠁
⠀⠀⠈⠻⣿⣧⡀⠀⠈⢷⡀⠀⠈⢻⣷⣄⡀⠀⠀⠀⠀⣀⣤⣾⠟⢻⣧⣀⣀⠀⢀⣀⣠⣿⠻⣷⣤⣀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠀⢀⡼⠃⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠁⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠈⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣄⡀⠀⠀⠀⠀⣀⣀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠛⠛⠛⠿⠿⠿⠟⠛⠛⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⢿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⠿⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣄⣴⣦⠀⠀⣷⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠺⢥⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡀⠒⠢⠔⢛⡧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣔⣍⣦⡀⠀⠀⣠⡿⠀⠀⠀⠀⣂⢀⡄⢸⡇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⣿⠟⠟⠛⠿⣯⡀⠂⠀⠀⠀⢀⣈⣉⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⣦⠀⠀⠀⠈⠻⣶⣿⣿⠿⢿⣵⣿⠯⠽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣴⣾⣦⣀⡆⠀⠀⠀⠀⠀⣿⠉⣀⠞⠹⣇⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠈⠻⣇⣆⡀⢻⠀⠀⠉⠊⠀⣩⠿⣙⠀⢀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡙⢿⡄⠀⠀⠹⣿⣷⠸⡆⠀⠀⢰⠞⠥⠤⣼⡗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠙⣿⣄⠻⡆⠀⠀⠘⢿⣷⡝⣌⣠⠈⠀⠀⠈⢻⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠻⣝⢷⡝⠄⠀⠀⠀⠻⣞⢷⣭⣷⣶⣶⣿⣿⡀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠘⠈⢻⣎⢆⠀⠀⣠⠟⢿⡘⣿⠛⣿⣿⣿⣯⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢰⡆⠀⠻⣯⣧⡾⠛⠲⣄⡙⢿⠀⢸⣿⣿⣿⠀⣿⡞⣇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣆⠀⢻⡀⠀⢹⣯⠀⠀⠀⠀⠉⠻⣧⠀⢿⣿⣿⡆⢹⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠹⣦⠘⣧⠀⠀⢻⣦⠀⠀⠀⠀⣤⣹⡄⢸⣿⣿⡇⢸⣧⣿⣆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⢿⡆⢹⡇⠀⢸⣿⠁⠀⠀⠈⠻⢻⡇⠀⣿⣿⣿⠀⣿⣿⠾⠖⠒⠒⣄⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⢿⣸⡇⠀⠸⣿⠃⠀⠀⠀⠀⠀⣧⠀⢿⣿⡿⠖⠉⠀⢀⣨⣦⣴⣿⣿⡟⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣦⡀⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⢠⡾⠋⠀⢀⡴⠾⠛⠛⠉⠉⠀⢈⣿⣎⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠶⣿⣇⠀⢾⣿⣀⣰⠟⣷⠦⣤⣿⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠛⢫⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡤⣽⢷⣾⣿⣿⡏⠀⠸⡇⢨⠅⠀⠀⡄⠐⢄⠘⠋⠁⣀⡤⢴⣾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠉

⣶⢶⢶⢶⠷⠷⣶⠶⢶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⢶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⡶⠤⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣶⡼⣿⠷⡇⣤⢴⣷⢀⡄⠄⣾⣿⠓⠂⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡟⣋⡉⢠⡯⢇⠀⠿⣴⢼⣿⡿⠸⡯⠿⢫⣼⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠍⠃⠀⠆⢠⠁⣄⣾⣷⢭⡟⠀⣴⡿⢂⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣑⠢⠄⢳⣿⡟⢾⢹⡆⠝⡑⠚⠟⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⠛⠛⣥⣌⣷⣉⣹⡆⠀⢸⢡⡏⣠⠴⠖⡶⢶⠿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⠉⣻⣿⣤⣷⠀⠀⢾⣷⣟⣷⣾⣿⣟⠂⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⢀⣽⠯⢿⠀⣀⣽⣿⣿⣟⠻⣿⣋⣙⣯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣤⠀⠀⠀⠀⠀⠉⡿⠛⠙⠙⣿⠶⣤⣭⣽⣿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⡀⠀⠀⠀⠐⠶⠄⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⡷⢦⣄⣀⡀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣦⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠀⢰⠋⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢻⠟⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣺⣿⢻⣿⣾⣿⣿⣟⢿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⡿⢾⢿⣏⣹⣿⢿⠿⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠋⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠀⠉⠻⠒⢴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⠚⠉⣀⣤⣤⣀⡀⠹⢄⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⣠⠖⠋⢁⠿⠛⢧⠈⠳⣄⠉⢳⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠞⠁⢀⣄⣁⠀⠀⠈⠆⠀⠘⢦⡀⢷⠀⠀⠀⠀⠀⣷⠀⠀⠸⢠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣰⠏⢀⣴⣿⡋⠁⠀⢉⣹⠿⣷⣄⠈⢧⠈⢳⡄⠀⠀⠀⢸⡆⠀⢀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣴⠋⠐⣘⣟⡆⣀⣿⢄⣤⣦⠹⣇⠈⣧⠀⡟⠀⠀⠀⠀⣧⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⣿⣼⣿⠗⣿⢸⣿⣶⣷⢻⡀⢸⡄⢳⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠤⠙⣿⠟⠀⢿⣤⠭⠿⡃⣮⠁⢈⡇⠀⣷⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠛⠆⠀⢄⡙⠒⠒⠚⠁⠀⠠⣿⠀⢧⡀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢄⠐⢒⡴⠊⠃⠀⠀⠀⣀⡤⠞⢻⠀⠀⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⣀⣠⡤⠶⣟⠉⠀⠀⢾⡀⣸⠃⠠
⡀⠀⢐⠣⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡴⠊⢀⡀⠀⠀⠈⣣⡤⣄⠀⠉⠉
⠣⢀⠀⠄⢁⡠⢃⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⠛⠁⢿⣤⣤⡴⠞⠫⠀⢸⡀⠀⠀⠐
⠀⠠⠙⢠⠋⠀⠈⢀⡄⠀⠀⠀⠀⠀⠀⣀⠔⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠂
⠈⠀⠐⡤⣄⣀⣀⡏⠈⢦⣀⣀⣠⠴⢚⣡⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⠘⡄
⠀⠀⠉⠀⠀⠉⠁⢇⣠⡵⠤⠤⠶⠚⠋⠀⢀⡿⣦⣀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⢆⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣾⠁⠈⠉⠛⠀⠀⠀⠀⠀⠁⠀⣏⠀⣆⠁⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⢀⠀⣸⠋⢤⡿⣦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⡤⢠⡆⠀⡷⢶⡌⠛⢫⡁⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⢀⡇⠈⣧⠀⠀⠙⢦⡢
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⠤⡞⠀⠀⠘⢧⡀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣤⣀⢻⡀⠀⠀⠈⢳⡀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠻⣁⠠⠄⠀⠀⠱⡄⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣴⠀⠀⠀⠉⠐⠀⠀⠀⠀⠹⡄⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⡘⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠉⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠑⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡾⠀⠁⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠖⠒⠓⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠂⠀⠠⠤⠤⠤⠤⠄⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⢴⢾⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡷
⠀⠀⠶⠤⠄⠀⠈⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠉⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠈⠉⢉⡝⠢⠤⠄⢉⡙⠓⠒⠲⠶⠶⠦⠶⠒⠒⠒⠒⠛⠛⠛⠉⢉⣉⠉⢉⣉⣉⣀⣀⠴⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠾⢠⠤⠤⠴⠒⠉⠑⠂⠀⠐⠒⠒⠂⠀⠐⠺⣍⠉⢉⡾⠋⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠇⣿⣿⣿⢇⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣋⣀⣈⠋⢱⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⠈⠛⣛⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⣠⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⢀⣠⣀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣦⢠⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠈⠛⠛⣽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⠏⠸⣿⡿⣯⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣆⠘⠛⣛⣁⡀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣦⣄⠀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠀⣾⣿⣿⡷⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆⢀⣭⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⠀⠙⠛⠉⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠺⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⣶⣆⢠⣾⣿⣧⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⣿⣿⡏⢺⣿⣿⢟⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣉⣡⣤⣤⡉⠁⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡄⢈⣩⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⢺⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐
⠀⠀⠀⠀⠠⠀⠈⠁⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠂⠀⠀⡀⠀⠀⠐⠤⠄⠀⠀⣦⡔⠀⠄⠀⠀⠄⠀⢤⡾
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠿⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠆⠀⠀⠐
⠀⠀⠀⠀⠈⠠⠠⠈⢠⠠⠘⠊⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠂⠀⢀⠀⠀⠀⠀⠈⠧⠀⠀⠂⡐⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠁⠒⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠁⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠄⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠂⠄⠀⠄⠂
⠀⠀⢀⠰⣀⠌⠀⠀⠀⠀⣀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠈
⠀⠀⠀⠀⡁⠤⠀⣀⡀⠤⠀⠀⠀⠀⠀⠠⣀⠁⠐⠀⠀⠐⠂⠀⣀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡄⠈⣛⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠩⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠬⠉⠧⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠀⣀⠀⠐⠁⠀⠀⠀⠀⠐⢄⠀⠂⠑⠀⡀⠀⠀⠀⠀⣇⡀⠀⣀⣀⣀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠣⠦⡉⠀⢉⢴⠜⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠈⡀⣀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠔⠀⠀⠁⠀⠁⡀⠢⡀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⡄⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠲⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠈⠀⠉⢀⠘⡟⢀⠈⠀⠊⠀⠀⠀⠀⠀⢀⠄⠉⣄⠉⢠⠀⠀⠀⠀⠀⢀⠀⢠⠀⠰⠆⠀⡄⠀⡀⠀⠀⠀⢷⠀⠁⣀⠈⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠟⠒⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠃⠀⠈⠀⠀⠀⠀⠀⣧⡀⢘⠀⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠤⠄⠀⠀⠂⠀⠀⠀⠀⢈⠀⠀⠀⡈⠀⠠
⠀⠀⠀⠀⠀⢠⡀⠀⢠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠺⠆⠀⠠⠟⠂
⠀⠀⠆⡀⢀⡀⠀⣛⡀⢀⡀⢀⠰⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢴⠀⠐⡄
⠀⠀⠀⠀⠀⠁⠂⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⡈⠀⠄⠀⠀⠀⠀⠀⠀⠑⠄⠈⠅⠀⠐⠀⠀⠀⠀⠀⠸⠤⣀⡘⣀⣤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠶⠂⠀⠀⠈⠁⠂⢄
⠀⠀⠀⠀⠀⢠⢂⣄⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⡌⡜⠀⠈⠙⠡⠄⣀⠀⢡⡈⠑⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠙⠒⠢
⠀⠀⠀⠀⠀⡠⠁⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⢰⠀⠀⠀⠀⠀⢀⠤⠚⠈⢁⠉⠀⠁⠓⠠⡀
⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣎⠀⠀⠀⠀⡔⠁⠀⠀⢀⠎⢡⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠐⠉⡇⠈⠀⢘⡧⠀⠀⠀⠀⠀⡷⠀⠀⠀⠉⠁⡄⠀⢐⠀⠀⢀⡴⠋⠀⠀⠑⢌⠂⠀⠀⠀⢃
⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠇⡠⠁⠀⡏⢁⠔⠉⠀⠀⠀⠀⠀⠀⠑⠢⢀⡀⢸
⠀⠀⠀⠀⠈⠙⡀⠀⠀⠀⡄⠈⣀⠀⠆⠀⠀⠀⡘⠉⠀⠀⠀⢃⠂⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢃⢸
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⠀⠀⠀⡎⠹⠀⠀⠀⠉⠀⠜⠀⠀⠀⠉⠀⠀⠀⡏⢱
⠀⠀⠀⠀⠀⠀⠀⡔⢻⠂⠒⠒⡐⠒⠒⢈⣿⠇⠀⠑⢤⡀⠈⠒⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠈
⠀⠀⠀⠀⠀⢀⠺⠀⠸⣇⠀⠀⠈⠀⢀⡼⠋⠀⠀⠰⠁⠑⢄⠀⠀⠑⠢⣄⣀⠀⣀⣀⢀⣠⡔⠫⢄
⠀⠀⠀⠀⠀⡌⠸⠀⠀⠡⡁⠤⠤⡒⠝⠁⠀⠀⠀⢰⠀⠀⠈⢂⡠⢖⠁⠀⢻⢕⡀⢐⡂⢴⠁⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⡇⢰⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠈⢄
⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⣦⣀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠈⠆
⠀⠀⠀⡠⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠘⠀⠀⣰⡇⠀⠀⠀⠀⠀⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣸⠍⠒⣬⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⢀⡐⠢⡤⠁⡇⠀⠀⠸⠁⠉⠁⠀⠈⡄⠀⡀⠀⣴⡀⠀⢸
⠀⠘⠒⠮⣼⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣹⠋⠀⠀⡇⢀⠰⠁⠀⠀⠀⠀⠀⠈⠺⣇⣀⣸⣇⣠⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠇
⠀⠀⠀⠀⠀⠇⠸⡀⠀⠀⠀⠄⠦⠤⠷⠦⠤⠀⠀⠀⣀⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢸⢠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠉
⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⡀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠘⠈⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠠⢴⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⡒⠒⠀⠠⡄⠐⠒⠀⠏
⠀⠀⠀⠀⠀⠀⣞⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢀⣀⣀⣀⡁⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⠀⠸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⢳⠪⠍⠡⠦⣤⠀⠀⠀⠀⠈⠛⠠⠬⠙⠃⠀⠀⠀⢨⠦⣀⠀⡇⠀⠀⠀⠀⠈⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠬⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⢶⣤⡀⠀⣠⣴⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠈⢻⡾⠋⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⢸⡏⠈⢻⡆⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢰⡟⠀⢹⡇
⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠈⣿⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣦⣀⣴⠿⢶⣄⠀⠀⠀⠀⠙⠷⠾⠛⠁⠀⠀⠀⣠⡶⠿⣦⣀⣴⠟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠈⠛⢿⣦⡀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣴⡿⠋⠁⠀⢀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠉⠻⣦⡀⠈⠛⣷⠀⠀⠀⠀⣾⠛⠁⢀⣴⠟⠉⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠿⠷⠷⠶⣶⣾⡾⠿⣷⠀⠀⣾⠿⢷⣶⣶⠶⠶⠾⠿⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠿⢿⡇⠀⣿⠀⠀⣿⠀⢸⡿⠿⠃⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠀⠀⠿⠶⠾⠷⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠉⠉⠉⠐⠒⣤⢀⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠤⣤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡦⡇⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⣄⠰⠆⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠩⡒⠝⠜⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡜⠉⠑⠂⠬⠭⠥⡍⠛⠛⡀⠀⢸⠀⠀⠀⠃⠀⠀⡔⠒⠂⠠⠤⠤⠤⠐⠒⠂⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⡄⢸⠀⠀⠚⠁⠀⠀⠈⠙⠀⠀⡇⢠⠼⡀⠀⠀⣣⣀⢠⠁⠀⠰⠛⠀⠀⠀⠛⠂⠀⢰⣀⡸⡀
⢀⡴⣞⡶⠀⠀⠀⠀⢸⠀⢦⠆⠀⠀⠀⠒⢀⣀⠒⠂⠀⠀⠰⣔⠀⡇⠀⠀⡁⢨⡝⠁⠒⢲⠉⢱⠒⡎⠉⡖⠂⠉⢅⠃⠰⠀⠀⠀⠀⠀⣴⣲⢦
⢿⡾⢁⠔⠣⢄⣀⡤⢄⠑⡆⠀⠀⠠⠢⣀⣁⣀⣀⠔⠂⠀⠀⠰⠊⠀⠀⠀⠑⢼⠀⠀⠀⠄⢉⡉⠉⢉⡑⠤⠀⠀⢸⠔⠛⣄⡀⠀⣀⠼⠀⠙⢯
⠀⠈⠉⠲⢄⢀⠏⠀⠜⠑⠰⡄⠀⠀⠀⠈⠒⠂⠁⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⣜⡀⠐⠛⠈⠙⢄⣀⠔⠊⠉
⠀⠀⠀⠀⠀⢏⢀⠎⠀⠀⡠⠊⡳⠤⢤⢄⣈⣀⣠⣤⠤⡚⡍⠲⡒⠒⠒⣖⠴⠒⡞⠒⢄⣀⣀⠀⠀⢀⣀⣠⠤⠚⣅⠀⠀⠀⠀⡄⡸
⠀⠀⠀⠀⠀⠀⠉⠒⠄⣠⠁⠀⠇⡆⡆⠀⣿⣻⠆⢈⠀⠇⡁⠀⢱⡔⡟⠁⠀⡌⠀⠀⢰⠀⠣⡉⠉⢁⠜⠁⡇⠀⠈⡆⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠁⠈⠉⠡⠆⠉⠉⠀⠰⢠⠀⠀⡀⡀⠀⠰⠀⠀⠀⠀⠓⠀⠚⣿⠓⠤⠐⠁⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⢸⠀⠀⠀⠠⠆⠀⠀⠀⢀⢸⠀⠀⡟⠾⠃⢹⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⠀⠀⠀⠠⠆⠀⠀⠀⠈⢸⠀⢰⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠈⡀⠀⠀⠠⠆⠀⠀⠀⠰⠘⠀⡆⠀⠀⠀⠀⢇⠈⠉⠉⠀⠉⠉⠀⠈⠉⠀⠈⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡇⣇⠀⠀⠀⠀⠀⠀⢀⡆⣥⠴⠀⠀⠀⠀⠀⠆⠈⠉⠈⠁⠐⠒⠒⠒⠂⠈⠁⠉⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠈⠉⠉⠉⠉⠉⠈⠁⠙⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⠤⢠⢧⠤⠤⢎⡀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⣤⠤⠾⠰⠦⠤⣤⡼⠄⠀⠀⠀⠀⠀⠀⠀⠈⢲⣳⣞⣶⣾⠴⣷⣶⣁⢶⡏⠉
⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⡄⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠹⣿⣿⣿⡿⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⣿⠈⢿⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⣛⣳⣶⣶⣦⣤⡀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠘⠀⢠⣿⡟⠀⠀⠀⢀⣀⣤⣤⣤⠶⠶⠂
⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢻⣿⣧⠀⠀⠀⣰⣿⡟⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⡇⠀⢰⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠥⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠉⠙⢢⠀⠀⠀⠀⠘⠲⠛⠂⠠⠰⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡰⠯⠗⠒⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢀⠄⠁⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⡴⠁⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⡞⠀⠀⠀⠀⡶⣤⠀⠌⣁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢃⣸⣆⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀⠀⠀⠀⠀⠈⣿⠈⣀⠿⠄⠀⢁⠅⠀⢀⡖⠀⠀⠀⠠⡀⠈⢿⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⠁⣀⢀⣀⠀⠤⠄⠹⠊⣧⠀⢄⡠⡎⠀⠀⠞⠀⠀⠀⠀⠀⢈⠀⠘⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠠⠀⠀⠀⢠⡇⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠲⣿⡀⢠⡇⢀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⠀⠀⡧⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠸⠃⠀⢀⡠⠤⠀⠀⠐⠛⠛⠛⠋⠁⠀⡓⢲⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠰⡇⠀⠀⠀⠀⠀⠠⠶⢦⣤⠉⡀⠀⠂⠀⠀⠀⠀⠀⠉⠉⠉⠩⠉⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⡩⢋⡆⡇⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠤⠀⠐⠊⠀⠋⠇⠂⠀⠀⠀⣐⠃⠈⢿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠰⣆⠁⠒⠂⠀⠉⠀⠀⠀⣴⠂⠀⠃⠐⠄⠁⠀⢸⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⡀⠈⠃⠀⠀⢀⡔⠀⠀⣴⠇⣤⠘⣄⠠⠶⠂⣠⢸⣧⠀⣠⡆⡼⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣿⣿⠁⠀⣵⠆⠀⠀⠀⠊⠀⠀⢀⠟⢸⣿⠀⠈⠁⠀⢀⣍⠈⠀⠈⠉⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠀⠐⠏⠀⠀⠀⣦⠀⠀⠀⠉⣰⠿⡿⠀⠀⠀⠀⠘⡏⢘⡩⠤⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠾⠿⠷⢦⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣿⠀⠐⢰⣾⠁⠀⠀⠀⠀⡄⠠⠀⠀⢀⡀⢸⠋⠀⠀⡀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠈⡏⠀⠀⠀⠀⠀⠀⠄⡈⣠⣏⠀⠻⠾⠂⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⣄⣤⣀⣵⣦⣀⡀⠀⠀⠄⠀⠷⣿⠃⢆⠀⠀⠚⠁⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⠿⠿⠟⠛⠁⠀⠀⢘⣩⣿⣧⠀⢨⣛⣻⣿⠿⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠲⠀⠀⠐⠐⠀⠐⠀⠀⠐⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣷⣶⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⣃⣠⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣫⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣄⡀⢸⣿⣿⣿⡿⢣⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⠙⢿⣿⣿⣿⣿⣿⣏⣿⣿⡿⢱⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣜⢿⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡹⢿⣿⣿⣿⣿⣿⣧⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⡏⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣻⣿⣿⡟⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⡿⢈⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⢟⣣⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠉⠁

⠍⠉⠁⠀⠉⠩⢭⠀⢈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡖⢀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡤⠀⠀⣴⣤⣴⡲⣶⣄⠠⡟
⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⡔⠀⠀⣀⣼⣾⣡⣶⣿⣗⣀⣜⣾⡷⣿⣿⣿⣯⢈⣿⢄⡀⠠⣚⢀⠄⠀⠀⠀⠃
⠉⠉⠁⠀⠀⠀⠀⠰⣫⣴⣆⣰⣾⣿⣿⣿⣻⣿⡿⢏⡿⣿⠹⢈⣿⢿⣿⣽⣿⢿⣾⡇⠀⢸⡃⠄
⡶⠀⠀⠀⠀⠠⣤⣼⣷⣿⣿⣿⣿⣿⣿⣿⠯⢵⣿⣿⡞⢻⢚⣯⡴⣾⣥⣤⣿⣿⠹⣷⠀⠀⢸⡧
⠇⠀⠀⢠⡴⠒⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣻⡞⡛⢔⠸⣬⣿⠔⢿⣹⣿⣿⣿⣿⣿⠶⣯⣽⡍
⠀⠀⠀⡖⡐⠊⢉⣿⣿⣿⣿⣿⣿⣿⣿⣟⣣⣧⠿⣬⡿⣏⠿⢘⠋⠹⠁⠘⢯⣽⣿⣿⣿⡿⢀⣴⡆⠀⠀⠀⠂
⠀⠀⢾⡔⢀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠳⢻⣉⡛⠗⡛⠀⠰⡄⢁⡀⠀⢀⣤⣼⣟⣷⠾⣿⣿⡿⢛⡇⠀⠀⠀⠂
⠀⠀⠈⠣⣭⣿⣿⣿⣿⣿⣿⣿⢿⡏⣁⣞⣯⣽⡿⡟⠚⠀⠀⣾⢤⣐⣟⣛⡛⣻⣿⠿⣿⣿⣟⣯⣏⡤
⠐⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⢁⡟⣅⣠⡞⠙⣧⠑⠊⠀⠀⠋⠀⡆⢯⡝⣭⠳⣾⢻⣿⣿⣽⣿⣿⣦⡄⠀⢀
⢀⠀⠀⢲⣍⣿⣿⣿⣿⣿⣿⣿⣄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⠠⠛⣦⠀⣹⣿⣿⣷⡷⡟⠂
⠆⠀⠀⠉⠹⢿⣿⢿⣿⣿⣿⡅⢩⠀⠀⠀⠂⠄⠀⠀⠀⢀⣄⡀⠀⠀⠠⠒⡛⠛⠛⠁⣁⣙⣿⣿⠛⣰⠄⢰
⡀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠰⠶⣋⣭⣭⡀⠀⢀⡴⣠⣖⣳⣎⠋⠙⣿⣿⣻⠟⠁⠀⠈⠆
⠧⠀⠀⠀⢿⡷⣿⣿⣿⣿⣿⡿⣤⡀⠀⠐⡦⡄⠀⣾⣿⣿⣷⣽⡄⢸⣸⣿⣿⣿⣿⡦⠀⠙⠛⡃⠀⠀⠀⠀⠃
⠀⠡⡀⠀⢸⣿⡛⣿⣿⣿⣿⣷⣉⣆⠜⠏⡀⠉⢿⣽⣿⣿⣿⡾⢃⠀⠘⠿⣿⣿⡯⠀⠀⢀⣾⣧
⠀⠀⢠⠀⠀⢈⠉⠋⢳⡾⢻⣿⣿⠛⠙⠦⠳⣦⣄⢈⡽⠟⢩⠀⣀⠀⢀⢹⡌⠻⡏⠀⢀⣾⣿⠉
⠀⠀⠈⠀⠀⠀⠀⡀⠀⠹⢬⣿⣿⠃⢴⡊⣶⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⠏⢧⠀⠉⠀⢸⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠋⠁⢸⣇⢸⡆⠀⢄⣀⣰⣟⣁⣀⣽⣿⣤⣬⡇⠀⣄⣿⡿⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠳⢶⣤⠀⠉⠉⠙⠛⠿⠿⠿⠋⠃⣼⣿⢿⢀⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠘⣿⣿⣇⢹⣧⡀⣧⣷⡄⠀⠀⠀⠀⣰⣿⡏⣾⠀⠉⠛⠲⠦⠴⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠈⣿⣿⣆⢻⣏⠉⠉⢷⣤⣤⣤⡶⢿⡟⣼⣿⣦⣀
⠀⠀⠀⠀⢀⡀⠤⠒⠂⠀⠈⠀⠉⠁⠀⣠⣾⣿⣿⣋⡃⣿⠂⠐⠀⠀⠀⠀⢀⣼⣇⢿⡟⢿⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠐⠐⠃⢀⣀⡠⠤⠖⠚⢋⣿⣿⡿⠸⣿⣿⣷⣿⣦⡀⠀⠀⠀⠀⣼⣿⢣⣾⠄⣾⣷⣿⣿⠉⠉⠙⠲
⠀⠀⠀⠈⠀⡠⠞⠉⠁⠀⠀⠀⠀⣼⣿⣿⣧⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⣰⣿⣥⠿⠋⣼⠏⢀⢠⣿⠄
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⡛⠳⡀⠻⣷⣿⣀⢀⡀⣀⣠⣿⠟⢁⣠⡞⠱⢀⠺⣼⡟
⠀⠀⣰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣡⡑⡀⢸⣷⣬⡙⠻⠿⠻⠿⠟⣁⠴⣿⠃⠂⢁⣎⣗⣿⠃
⠀⡴⣣⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡙⣤⣿⢡⢻⢟⣿⣿⠟⡻⢿⠻⠶⣭⣴⣴⣿⣿⣿⠃
⡼⠃⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢻⣿⢹⢫⣸⡞⠹⡛⠀⡇⠈⠀⣄⣿⣟⣿⣿⠟⠁
⢁⡘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣱⣇⣄⣇⢓⡏⣸⢹⢰⣟⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠄⠠⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠀⠀⠀⠀⠀⠀⠀⡀⠖⠛⠃⠀⠀⠀⠉⠛⠠⠄⡀⠀⢀⠔⠁⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉⠉⠉⠝⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣆⠐⠉⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠓⠀⠈⠦⣀⠀⠀⠠⠤⠤⠄⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⡆⠈⠉⠀⠦⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠐⢤⡄⠀⣿⣀⠀⠀⠀⠘⢦⡀⠰⠒⠒⢀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠠⠊⣠⠏⠘⠉⠀⠀⠀⠀⠀⠈⠁⠀⢠⡌⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢆⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⣲⢄⡀⠀⠀⠀⣀⣀⠀⣀⣤⠞⡀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡇⢀⠼⡑⠛⠁⠀⠈⣋⠞⠁⢀⠰⢄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡳⠁⠀⣝⠄⠢⣄⢠⠋⠀⡐⠃⠀⠈⠳⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡗⠁⢠⠎⡌⠀⠀⠈⠇⢀⠂⠀⠀⠀⠀⠀⠙⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠀⡰⠁⢠⠁⠀⠀⠸⠀⢃⡀⢀⡀⠀⠀⠀⠀⠈⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡰⠁⢀⠎⠀⠀⠀⠀⠀⠘⠀⠀⠈⠢⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡰⢁⡤⠟⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠁⡸⠀⡤⠐⠈⠀⠀⠺⠀⠇⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡴⠛⠛⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠣⡈⢆⠀⠀⠀⠀⢀⣠⡄⠊⠁⠀⠀⠀⠀⢀⠔⠁⣀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⠀⠈⣠⠷⣤⢤⠞⠁⠈⠻⠂⠀⠀⠀⠤⠞⠉⠺⡄⠈⠳⣆⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠦⢦⣻⠀⠀⠋⣴⡶⣤⡴⣤⠀⠤⠀⠀⣦⠀⠀⠀⠘⡦⠀⠈⠓⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠀⠀⠀⠀⠀⡃⡄⡇⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⡟⠀⣷⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡈⠀⠀⠀⠀⠀⡬⠁⠀⡇⠰⣀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⠀⢀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠆⠀⠀⠀⡇⠈⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⡰⠁⢸⠁⠀⠐⠦⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠈⠇
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡇⠀⠀⠀⡇⡇⠀⠀⡔⠁⠀⠸⡄⠤⠄⣄⣀⣀⣀⣀⣀⣀⡀⢀⣠⡤⠤⠀⠒⢇
⠀⠀⠀⠀⠀⢠⡄⠃⠀⠀⠀⢰⠀⠀⠀⠀⡇⠇⠀⡜⠀⠀⠀⠀⡇⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⡀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢧⠀⠀⢐⠒⠺⣄⠀⠀⠠⡇⣁⡜⠀⠀⠀⠀⠀⡧⠄⣀⡈⠐⢄⠀⠀⠀⠀⢀⡀⠀⠰⠑⢄⠀⢀⡸⣄
⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠙⠢⢄⠁⠢⢤⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠀⠑⢆⣀⣀⣀⣀⠀⠀⢃⠀⢟⠁⠀⠘⢆
⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠧⠇⠀⠀⠐⢌⡁⠉⠀⠀⡈⠁⠀⠀⠰⠧⠤⠤⠬⠭⠭⠭⠙⢀⡠⠵⠄⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡀⢀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠿⠷⠆⠈⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣏⣀⢀⠀⠀⠀⠻⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣿⠴⠖⠀⠀⣶⡄⢀⣷⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣾⣿⣿⣿⣿⣿⣧⣤⣴⣦⡄⠁⣰⣿⣟⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣤⣤⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠾⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣤⠌⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⣠⣾⣿⠇⣀⠀⡟⢀⢛⣥⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⣼⣿⣿⣿⣦⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣹⣷⡀
⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠁⠉⠙⠿⣿⣿⣿⣷⠈⠙⠻⣿⣭⣿⣿⣿⣿⣿⣿⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠉
⣀⣀⣀⣠⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣄⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠓⡄
⠀⠀⠀⠀⡠⠖⠚⠒⢦⠀⠀⠀⣀⡀⠀⣠⠤⠒⠴⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⣄⡴⠋⢹⡄⠀⠀⠀⠀⠀⠱⡸⡄
⠀⠀⠀⢸⢧⡷⠨⠤⠔⠀⠀⠘⣄⠈⠳⠁⡀⡄⠠⠇⠚⢹⡆⠀⠀⢀⡤⢤⡤⠤⠤⠬⠶⠿⣼⣹⠓⠜⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⢱⢸⡀⠀⠀⠀⠀⠀⠀⠀⢙⡖⠒⠈⠁⠀⢮⡽⡀⣻⠀⠀⠘⢦⠴⠃⠀⠀⠀⠲⠖⠀⠀⠉⠓⠒⠒⡖⠒⠋⡩⠟⢀⠇
⠀⠀⠀⠈⢣⡳⢄⠤⢴⠒⢻⠉⡏⠉⠱⡆⠀⠀⠐⠤⠞⣡⠇⠀⠀⠀⠸⡀⠀⠀⠀⠀⡗⠀⣠⠞⡦⢄⠀⠀⠓⠤⠖⠁⢠⢾
⠀⠀⠀⠀⠀⠈⡇⠀⠘⠀⠀⠀⠀⠀⠀⡞⠓⠦⠤⠖⠊⠁⠀⠀⠀⠀⠀⠈⠲⠤⠤⠾⠓⠋⠀⠀⢸⢷⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⣠⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⡷⠤⠤⠔⡶⣿⠁
⠀⠀⠀⠀⠀⠀⡇⢻⡟⡟⠒⠋⡝⢸⡔⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠚⡸⢹⢻⠀⠀⠀⡅⣟⡄
⠀⠀⠀⠀⠀⠀⢧⣈⠧⣉⠆⠀⣇⠈⢓⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠹⡥⠞⠀⠀⣖⣻⠿⠭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠋⡇⠀⠀⠀⠀⠀⠀⣏⠛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⡴⠦⠶⣤⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠈⠁⠀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠙⢦⡴⠋⠁⠶⠂⠠⢌⡑⣄⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠠⠤⣤⠤⢤⡌⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣯⠿⠴⠶⠶⠶⠦⢄⣙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⡾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢇⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⠀⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⣧⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⣷⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠠⠤⠿⠦⠼⠟⠀⠉⠉⠙⠛⠒⠒⠒⠶⠶⠶⠶⠶⠶⠖⠒⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⡖⢲⡤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠤⠤⣴⠒
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢨⠁⢐⠉⢲⢰⠈⡏⠁⡐⡀⢾⢱⠀⠀⠀⡎⠁⠀⢎⡁⠈⠋⢰⢁⠆⡆⠑⡆⣦⠖⢰⠁
⣠⣀⣀⣄⣀⣀⣀⣤⣤⣬⣤⣌⣸⣄⣧⣼⣁⣥⣵⣤⣠⣤⣤⣤⣤⣠⣤⣥⣠⣄⣼⣨⣦⣧⣤⣁⣧⣱⣼⣤⣄⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡨⠀⠁⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇
⠀⠀⡠⠄⠀⡀⠀⠀⠲⢄⠐⣿⠉⢳⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢫⢧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⡂
⠀⠀⠬⠁⢐⣦⡀⢦⣤⠀⠨⢿⡆⠈⢷⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⣌⢇⡀⠀⠀⢀⣠⡤⠔⡦⣶⠂⠉
⠀⠀⠈⡁⠀⠀⠽⣤⡉⠳⣶⣤⣤⠈⠚⢧⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢹⡈⡆⠀⣰⢿⡏⣠⡏⢥⠇⠀⠀⢀
⠀⠀⠀⠒⣀⠀⠠⢙⣿⣮⣤⡼⡏⣷⡄⠀⠑⢬⠇⠀⠀⠄⡀⠀⠀⠀⠀⠸⣄⠻⠄⠟⣠⣾⢃⡟⢵⣒⡾⠃
⠀⠀⠀⠀⠐⢂⠈⣐⢠⠼⠫⡪⣫⠈⣧⣶⡀⠀⠀⠀⢀⠊⠀⠀⠀⢠⠀⠀⠈⠃⣤⡾⠋⣳⢏⣞⣭⠾⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢞⢷⣶⠎⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣷⣽⠿⡿⠓⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢴⢶⠃⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠯⣀⣤⠤⠾⣿⣽⡷⠚⠫⠏⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠼⢿⡶⠊⠟⠆⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠻⢤⣀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠐⢤⣄⡀⡄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢰⠄⠐⠰⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡊⠉⠛⢢⡀⠀⠀⠀⠁⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣⣤⡊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡴⠛⢥⠀⠀⢩⣿⡄⠀⠀⠆⡀⠘⠋⢀⢚⠃⠀⠀⠀⣤⡆⠀⠘⣰⠋⢹⠛⣶⣦⠠⠂
⠀⠀⠀⠀⠀⠤⠂⠀⢁⣐⠦⣍⡂⣙⠪⠗⠆⠀⠚⠛⠁⠀⠀⠈⠱⠴⠂⠘⠁⠀⠀⠀⠀⠌⠀⠀⠀⠉⠀⢈⠁⡋⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣛⠦⣝⠊⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠂⠀⠀⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠶⠂⠀⠛⠃⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⡄⠀⠠⠆⠸⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠄⠃⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠈⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢤⡄⠒⠀⠀⠀⠙⠄⠀⠂⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢐⡒⢊⠙⢡⠀⡀⠃⠀⠀⠀⠀⢰⡀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠘⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡥⠀⠐⠊⡀⠐⠀⠀⠁⠀⠀⠀⠀⠸⢡⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⡴⠂⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⣠⣚⣰⠀⢈⡁⠛⠀⠶⠉⠰⠸⠀⠀⠀⠀⢰⡈⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠃⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠰⠆⠀⠀⠚⠂⠀⠛⠀⠀⠀⠀⢸⣇⠀⠙⠿⣣⡄⢠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡄⢀⡉⠡⡖⠈⠀⠀⠀⠰⢲⣤⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡋⠀⠙⠁⢠⡓⠀⠀⠀⠀⠐⠋⠁⠐⠆⠻
⠀⠀⠀⠀⠀⠀⡠⠂⡒⠤⡴⠋⠈⠑⠶⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠤⠱⠆⠀⠐⠃⠙⠀⠀⠀⢸⠒⠀⠀⠀⠑⠻⣦⣤⡀⠒⠢
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠟⠛⠛⠛⠉⠑⠋⠘⠃⠙⠀⠀⠰⠶⡶⠶⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠉⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠠⢄⠀⠈⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡀⠀⠀⠀⠀⠀⠐⠄⠀⠀⡱⣤⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠈⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⡄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠒⠤⠤⠤⠒⠁⠀⠀⡰⠁⠀⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠠⣠⠴⠚⠉⠉⠉⠀⢄⠀⠁⣤⠤⣀⣀⣀⣀⢀⠔⠊⠀⢀⡀⠀⠀⢠⡠⠀⠀⠁
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢀⠀⠠⠊⡿⡔⠊⠒⢊⡇⠌⠀⢁⡀⠀⠈⠀⠢⡄⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡌⠠⠃⠈⠉⠛⠉⠸⡄⠀⠉⠀⠀⠀⠀⠀⠘⢄⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣁⠎⠁⠀⠀⠈⠀⠀⠀⢀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⡽⠠⠀⠀⠁⠀⠀⠴⠀⠀⠀⢀⠓⢌⠀⠀⠠⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⡀⡆⠀⠀⠒⠀⢀⠀⠐⠀⠈⢰⠄⠘⢀⠀⢠⠀⠉⠀⢨⡀
⠀⠀⠀⠀⠂⠀⠀⠉⠐⣀⠀⠀⠠⠖⠭⠀⠐⠀⢄⠀⠤⠤⠔⠲⠇⠀⠂⠀⠀⢰⠀⠀⠀⠙⠧
⠀⠀⠀⠠⠒⡄⠀⡀⠀⠀⠀⠀⣄⣠⠃⠀⠀⠀⠋⠈⡀⡀⡀⠔⠊⢠⠓⠒⠤⠔⠂⣀⠀⠀⠀⠀⠐⠠⠆
⠀⠀⠐⠤⠀⠁⣰⠐⠈⠈⠉⠉⠀⢈⠀⠀⠀⠀⠁⠀⠀⢀⠄⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢀⣀⠤⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠉⠰⠈⠀⠁⠀⠈⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠉⠈⠑⡊⠀⠀⠋⠐⠀⠀⠀⠃⠂⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⢶⣤⣀⠀⠀⢀⣤⣴⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠈⠙⢷⣶⠟⠁⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⣾⠛⢻⣆⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢰⡟⠛⣷⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⣿⠁⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⡆⠀⢸⣇⠀⠀⣀⣄⡀⠀⠀⠀⠈⠻⢶⣄⣀⣴⠟⠋⠀⠀⠀⢀⣠⣀⠀⠀⣸⡏⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⢷⣼⣏⠉⠻⢶⣄⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⣠⣶⠟⠉⣹⣧⡾⠋⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠻⣷⣄⠀⠙⠷⣦⡀⠀⠀⠀⠀⢀⣴⡾⠋⠀⣠⣾⠟⠉⠀⠀⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⠷⠀⠀⠈⣿⠀⠀⠀⠀⣿⡇⠀⠀⠾⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣇⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⢻⣿⣿⡟⠛⣿⠀⠀⣿⠛⢻⣿⣿⡟⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⢻⡇⠀⣿⠀⠀⣿⠀⢸⡟⠛⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠾⠷⠶⠿⠀⠀⠿⠶⠾⠷⠶⠶⠶⠶⠶⠶⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠼⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡿⠿⠛⠃⠀⠀⠈⠻⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣶⣶⣦⢻⣿⣿⡿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣤⡈⠻⠿⢋⣼⡿⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⢻⡟⠛⣻⠋⢠⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⣸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣿⡇⠻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠐⣷⡄⣴⣿⣿⠇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠁⢻⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣂⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠁⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⢹⡄⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠉⠉⢸⣶⣤⣴⣶⣤⣤⣤⣴⣶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿