Hot chocolate Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡄
⠀⠀⠀⠀⠆⠀⠠⠜⠋⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⣄⣯⣄
⠀⠀⠀⠀⠰⠛⠒⠶⠦⠶⠒⠓⠄⠀⠀⠀⠀⠀⠀⢘⠓⠒⠒⠒⠚⢳⠀⠀⠀⠀⠀⠀⠠⠉⠉⠉⣻⠏⠐
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢰⡏⠂⣤⠀⢀⣀⣼⣶⠖⠀⠀⠀⠘⣀⡇⠀⠀⠉⠀⢠⠀⠄
⠀⠀⠀⠀⣄⣈⣶⣤⣤⣴⣎⣠⠄⠁⢀⡀⠀⣀⠴⣃⢠⡟⠀⠸⡇⠀⣿⠠⠀⠀⠀⠀⣠⣥⣀⣀⣀⣀⠘⠀⠚
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢇⣀⡿⠤⠞⠛⠛⠒⠚⠛⠉⠉

⠀⠀⠀⡀⠀⠀⠀⠀⢰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠋⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⠀⠀⠵⢀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⣀⣀⣀⣀
⠀⠀⠀⠠⠠⡶⠄⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠐⠐⠈⡁⠀⠰⠀⠀⠀⠀⠀⢈⠉⠉⠉⠉⢉⠄⠄
⠀⠀⠀⢹⡄⡀⠀⢀⣤⠀⠀⠃⠀⠀⠀⠀⠐⠂⠀⣁⠀⠀⠀⠄⢤⠉⠠⠀⠀⠀⠀⠀⢰⠙⣄⠀⠀⠀⢸⣐⡄⢠⠄
⠀⠀⠀⠀⠉⢣⣀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⡠⠄⢸⣀⠀⠀⢀⡜⠃⢀⠀⠀⠀⠀⢠⠈⡇⠀⠉⠐⠒⠚⠋⡝⠐⡰
⠀⠀⠀⠀⠀⠼⣯⣭⠉⠉⠋⠀⠛⠀⠀⠀⠐⠷⢤⣥⣙⣓⡒⠋⠤⠄⠂⠀⠀⠀⠀⠴⢦⣌⡦⢤⡄⢀⣤⠦⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠄⠠⢄⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⡆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣷⢦⡴⣄⠒⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡔⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣿⠸⣧⡟⠀⡇⢠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠁⠀⠔⠀⠀⠀⠆⢄⠀⣀⠀⠀⠀⢠⠖⠦⠀⡆⡈⠀⠋⠀⢀⡀⠀⣀⢸⡆⣀⡀⣤⣇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠀⠀⠈⠢⠀⣿⠀⠀⠀⡏⢹⣴⡋⣧⡏⠁⣞⢸⢺⣇⡕⣿⢀⡏⢼⠵⠓
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠠⠀⠒⠀⠀⣀⠠⠚⠀⠀⠀⠀⢀⡃⠘⠶⠖⠀⠃⠸⠀⠛⠁⠙⠋⠈⠉⠈⠉⠓⠋⠘⠃⠈⠓⠋
⠀⠀⠀⠀⠀⠠⠖⠊⠉⠀⠀⠐⠂⠈⠉⠀⠀⠀⠀⠀⢀⠔⠁⢸⠂⢒⡄
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡴⠵⡞⢡⠇⠀⠀⠀⠀⡐⠒⠐⠒⠢⠤⣀
⠀⠀⠀⣠⠐⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠖⠚⢩⠁⠠⠀⠃⣼⠀⢠⢞⠋⠉⠅⠀⣀⡀⠀⠄⠊⠃⠀⠒⠠⢄⡀
⠀⠀⠀⠙⣜⠒⠒⢚⠛⠋⠉⢹⠉⠉⠁⢀⠂⠀⠐⠠⠂⠀⠀⠀⠀⢹⠀⡼⢮⡳⣅⡀⠀⠀⠀⠈⡅⠐⠢⠤⠀⠤⢒⠷⢄⡀
⠀⠀⠀⠀⠈⢦⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠈⠓⠯⣗⣲⠤⢀⣂⣀⣀⠀⠀⠀⢘⣀⡤⣳
⠀⠀⢠⠔⠚⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠲⠿⠿⠿⠟⠓⢛⡗⠒⠢⣄
⠀⢰⠃⣠⠊⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠉⠉⠙⣧
⠀⡏⠀⡇⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡰⢈⡇
⠀⠹⡀⢣⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡠⠚⠀⡼
⠀⠀⠱⣄⠳⣄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠋⠀⣠⠞
⠀⠀⠀⠈⠑⠢⠍⣑⠚⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠉⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢛⠛⠉⠉⠀⠀⣹⠄⠠⠤⠤⡙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠓⠒⠒⠒⠉⠀⠀⠀⠀⢀⡼⠀⠀⠀⠉⠉⠓⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⣩⠷⡴⠒⢲⠳⢇⣠⡤⣄⠃⠒⢋⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠑⢀⢞⠁⠀⠙⣚⡹⠛⠋⢱⠀⢠⠀⣔⠀⢀⡤⢥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣠⢨⠙⠒⠀⡄⢢⣀⠀⠠⠛⢯⣑⣀⡀⠳⢔⠿⠉⠀⠮⡄⠾⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⢸⠀⠀⠀⡹⢤⢉⠃⢀⠐⠒⠒⠋⠁⢧⠰⠀⠠⡐⠛⠛⠂⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⢈⣀⡴⠂⠀⠀⡇⣱⢺⡠⠀⠀⠀⠀⠘⡇⠃⠰⣽⡀⠀⠀⠐⠀⡤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠙⠦⡞⢧⣀⠀⠘⠰⡇⠀⢧⠀⠀⠀⠁⠀⢷⠦⠀⣸⠃⢀⣠⣾⠶⠃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣖⣒⡲⠤⣼⠃⠀⠀⠹⣦⠬⣥⣒⠒⠘⠂⣌⡧⢀⡤⡒⣦⣠⣖⢚⣧⠿⡍⠀⡎⢡⣰⢸
⠀⠀⠀⠀⠀⠀⣠⠟⠟⠋⣷⣛⣛⠺⠭⠀⣼⠀⠀⠀⠀⠀⠀⠀⠘⡟⢶⠖⢦⣀⢠⡎⠉⠁⠀⠘⠋⠀⠀⣿⢶⡇⠀⡇⣼
⠀⠀⠀⠀⠀⢰⠃⢠⠞⠉⠉⠉⠉⠙⢲⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⠀⠘⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠀⣿⢹⡆
⠀⠀⠀⠀⢀⡏⢠⡏⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢧⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⡆⠈⢦⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠴⠛⠖⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠉⠛⠒⠒⠚⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⣀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣀⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠚⠉⠛⠁⠉⠄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠒⠒⢲⠒⡶⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢒⣊⢩⡹⡄⠀⠀⠀⢰⠚⠙⢢⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢣⠰⡀⠀⢈⣧⢱⡀⠀⠀⣼⠂⠉⢹⢠⣇⡀⢀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠡⡙⡭⡰⠶⣆⢿⠉⠉⢿⠂⠉⣻⣿⡡⠤⢤⣇⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠱⡱⣄⠤⣚⡼⣄⣀⡴⠊⡁⠥⣏⠠⠤⡜⠈⠛⢯⠑⠁⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⢣⠱⠰⣉⡠⠚⠉⠉⠱⠌⠀⠀⠐⡤⢤⠧⡀⠀⠈⣧⣤⠶⢶⣤⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡢⣸⠓⠋⡋⠉⢣⠀⣠⠜⢰⠖⠒⠲⡏⠉⠀⢹⡀⣰⣿⠀⠀⠀⡷⢡⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠪⢕⣠⠍⣁⡚⠋⠁⠀⠸⠆⠀⣒⡁⢤⣒⠭⠚⠁⣿⠀⠀⣼⢃⠇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠉⠑⠒⠛⠛⠛⠛⠛⠒⠊⠉⠁⠀⠀⠀⡄⣿⣤⠞⡱⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠈⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠈⢿⡢⢄⡀⠀⢀⣀⡀⠀⠀⠀⠀⣀⠤⣺⠃⠀⠀⠀⠉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠙⠦⣭⣑⣒⣒⣀⣐⣒⣒⣩⡵⠞⠁⠀⠀⠀⠀⢀⣤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠒⠂⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠒⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⢀⣟⢀⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣧⠞⠉⡿⢁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⢠⠏⠀⠀⣧⡞⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢿⠏⠀⠀⠰⣏⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠦⢷⠋⠉⠉⠛⠓⠶⣄⠀⠀⠀⠀⡾⢹⣆⡟⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠉⡙⣷⠴⠶⠞⠒⠲⡄⠀⢀⣥⠼⠶⠶⠶⠾⣅⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⣏⠀⠀⠀⠀⠁⡏⠀⠀⠀⠀⠇⣷⢠⡏⠀⠀⠀⠀⠀⢰⢻⡾⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⣉⠀⠒⠒⢻⣄⣀⣀⣀⣠⣧⠀⠀⠀⠀⠀⣿⢚⡇⠀⠀⣀⠀⣀⣉⣼⡧⠀⣈⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡙⠓⠶⠮⣭⣭⣉⣉⣐⣛⣉⠙⠀⠒⠒⠛⢉⣉⣉⣉⣉⣩⣥⠬⠶⠒⢋⣡⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠓⠶⠶⢤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣥⡤⠴⠶⠚⠛⠉⢹⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠉⠉⠉⠉⢛⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡶⠶⠶⠶⠤⣄⠀⠑⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠘⣿⠞⣹⣞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢉⣳⣿⣾⣡⣴⡧⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠉⣹⢿⠳⣄⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣤⠴⠋⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣇⣼⣄⠸⠻⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠁⢠⠀⡄⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠛⠒⠒⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⢀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠁⡿⠉⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⣇⡼⠛⣶⠏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢈⡟⠀⠀⣏⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣧⡾⠀⠀⠀⣿⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⢉⢳⣀⣤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⠀⡿⠀⠀⠀⠀⠳⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⣀⠀⠈⠃⣏⣀⠀⠀⠀⠈⠍⢳⡄⠀⠀⠀⣼⠃⢿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠉⠀⢠⢸⠟⠛⠋⠉⢉⡹⡆⠀⣠⠶⠛⠛⠛⠛⠛⢳⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠟⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠃⣿⢰⡇⠀⠀⠀⠀⠀⢰⡆⣷⠟⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠦⣅⡀⠒⠃⢹⣦⣀⣀⣀⣤⢼⡄⡀⠀⠀⠀⠀⣿⣛⣇⠀⢀⣀⣀⣀⣤⣠⡿⠄⢀⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⡉⠛⠲⠦⢤⣤⣍⣁⣐⣚⣉⣉⡉⠀⠓⠚⢛⣁⣈⣉⣉⣀⣨⣥⠤⠶⠒⠛⣉⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠳⠶⠶⣤⣤⣬⣭⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣤⣤⡤⠶⠶⠚⠛⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠋⠉⠉⠉⠉⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣄⡀⠀⠱⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠙⣦⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢦⣦⡴⢦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢷⣄⣿⣰⠟⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡶⠶⢾⣿⣟⠛⠻⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣴⠋⣷⠈⢳⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠶⠖⠒⠛⠋⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠶⠿⢦⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣀⣘⣀⣂⣀⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠋⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⢀⠔⠊⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠢⢴⡊⠀⠈⠱⠊⠀⠀⠙⠠⡄⠐⠒⠒⠛⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡰⠁⠀⠀⠀⠈⠲⣤⠁⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢸⠑⣢⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠼⡇⠀⠀⠀⠀⠀⠀⡈⣦⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠘⣄⠀⢠⠆⠀⡴⠁⠀⠀⠀⠀⡠⠈⢀⠎⠀⠀⠀⠀⢸⠀⠀⠀⢀⡨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣤⣤⣬⣆⣇⣠⣞⠀⣀⣼⣶⣤⣴⣤⣴⣯⣄⠀⠀⠤⠄⠚⠒⠂⠉⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠻⣿⡟⠉⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⣧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠉⠉⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠛⠒⠒⠓⠢⢄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠙⢆⠗⡘⠳⠖⡀⠶⠴⠆⡂⢄⢤⡤⢄⣂⠒⠦⠲⡄⠦⠒⠘⠋⣍⠀⢾⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⣦⠈⡖⢃⠒⣠⠾⢴⠴⠬⢥⠀⡎⠒⠚⢁⠰⠌⣀⠃⠀⠒⠐⡤⠄⣁⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠋⠤⢡⡈⢨⠉⡾⢀⡐⠦⣔⠂⠌⠈⢷⡈⠆⠄⠀⠆⡼⠃⡑⠲⢾⡻⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠛⠠⠿⠀⣤⢁⣀⣄⠑⢀⠸⠎⠙⠆⣤⣀⠷⡄⠂⡒⠂⢬⡀⠼⢿⠇⠀⠀⠀⠀⠀⢠⠇⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠀⠉⠘⠓⠈⠁⠉⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⢀⣠⠴⠋⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⠂⠉⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣤⠴⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣧⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣶⣿⣿⣷⣾⣷⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⡀⠊⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⠤⠤⢤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢤⡖⠢⡄⠠⢄⣀⠔⠁⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠚⢄⠀⢀⣇⠴⠦⡀⢀⠟⠻⢍⣠⠚⠁⠀⠀⢠⡀
⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⠲⡀⠀⠀⠖⠐⠺⢄⠀⠠⠒⠼⡀⠀⣸⠋⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣀⣀⣤⣧⣍⣉⣢⠀⠀⣠⣁⣄⠀⢀⠁⡃⠙⠦⣔⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠙⠓⠒⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠒⠉⠁⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡴⠊⠉⠙⢆⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠮⣄⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡴⠧⠝⢡⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡰⠁⢀⠂⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡆⠣⠟⣒⣠⡴⢆⠀⠀⠀⠀⠀⠀⢠⡇⠀⠤⠊⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡜⠉⠉⠁⠈⠦⠃⠈⡀⠀⠀⠀⠀⢠⠯⣀⣀⠀⠤⠈
⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠉⠉⠉⢛⣹⠉⠉⠉⠁⠀⠀⠀⢠⡏⠤⣄⣀⠀⠄⣂⣁⠀⠊⣘⠧⢀⠠⢂⡠
⠀⠀⠀⠐⠚⠊⣦⡀⠆⠀⠠⡸⠂⢀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠶⢀⠬⠂⢀⠌⠑⠀⢉⠍⠘⠛⢌⡉
⠀⠀⠀⠀⠈⠁⠈⠩⠒⠚⡳⠖⢓⡠⠷⠄⣀⠀⠉⡱⠒⠶⢦⡤⠶⠄⢐⠲⠊⠉⡠⠀⠒⠒⠛⠍⠀⠙⠓⢖⠒⠚⠦⠴⠒⠂⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⢄⠀⠄⠀⠤⠖⠛⢂⠈⠉⠙⠓⠄⠉⠉⠓⢆⠃⠲⠶⠂⠌⣀⣀⣀⠠⠄⠒⠀⢀⡠⠀⠀⣀⠤⠒
⠀⠀⠀⢂⣌⣂⣠⣈⡑⠤⢄⡵⠖⠘⢲⡞⠓⠀⡙⠶⠕⠦⢤⣤⣀⠠⡄⠀⠀⠀⠛⠘⠀⠀⠀⠙⡉⣄⠲⡖⠒⢥⠴⠶⢏⠐
⠀⠀⠀⠁⠦⠠⠒⠁⠀⠀⠉⠀⠀⠁⠈⠁⠀⠁⠀⠀⠀⠉⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⠀⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠓⣆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠘⡟⠉⠉⠉⠉⢳⣀⡤⠖⠒⠒⠲⣄
⠀⠀⠀⠀⣀⣠⠤⠖⠒⠚⠋⠉⢙⡄⠀⠀⠀⠀⡇⠀⠀⣠⠔⠚⠛⢳⡀⠀⠀⠀⢸⠓⠒⠲⠶⠤⢤⣤⣄⣀⣀
⠀⠀⡴⣎⣁⣠⠤⠴⢶⠶⠒⣶⠉⠹⢄⣀⡤⠾⢥⣠⣼⠁⠀⠀⠀⠀⢳⣀⣀⣀⣸⢷⡒⠲⠦⠤⢤⣀⣀⠀⣈⣉⣳⡄
⠀⠀⡇⠀⠉⠙⠒⠒⠾⠤⠤⠼⢤⣤⣤⣯⣤⣀⣀⣀⣈⣦⣀⣀⣤⣤⣤⢯⠭⠥⠤⠴⠷⠖⠒⠒⠒⠉⠉⠉⠉⠀⠀⡇⠀⠀⣀⣀⡀
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠉⠁⠀⠉⠙⠲⢄
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⣿⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⠉⠓⢦⡀⠀⠀⠀⠀⢳
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⢸⡀⠀⠙⢦⣸⣠⠋⠀⠀⠀⡇⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠘⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠢⣈⡇⠀⠀⠀⢹⠁⠀⠀⠀⠀⣇⡴⠋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢳
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠓⠛⠳⣄⠀⠀⢸⠀⠀⠀⣠⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠈⠳⣄⢸⠀⡠⠞⠁⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠤⠤⢽⡦⠤⠶⠶⠶⠾⣿⣿⠤⠤⠤⠤⠤⠤⣴⣯⣄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠋⠀⠀⠀⠀⡴⠋⢸⠈⠳⣄⠀⠀⠀⠀⠈⠢⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣼
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣀⣠⠊⠀⠀⢸⠀⠀⠈⠣⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⠤⠤⠒⠋⠀⠀⠀⠀⠀⣰⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠞⣿⠀⠀⠀⣸⠀⠀⠀⠀⢹⢶⡒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⢿⠀⢀⡴⣿⢦⠀⠀⠀⢸⠀⢱⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠋⢀⣇⠀⠳⡄⠀⠘⠂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠉⠛⠛⠛⠋⠉
⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣟
⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⣄⠀⢂⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⡅
⠀⠀⠀⠀⠀⠀⢸⣧⣀⡔⠁⠛⢫⡿⢋⡀⢰⢶⡗⠀⠀⠀⠀⣄⢹⡄⢻⣶⠶⠦⠤⠀⠀⢰⡆
⠀⠀⠀⠀⢀⣀⢀⠉⠉⠣⢀⣤⣴⠠⢾⣿⠃⢨⡆⠀⠀⠀⠀⣿⡿⢿⣮⣁⠀⠀⠀⢀⣰⣾⠃⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠄
⠀⠀⠀⣼⠋⠀⠈⡇⠀⠀⠀⠉⠛⠁⠀⠀⠀⢹⠇⠀⠀⠀⠀⢿⠉⠀⠈⠉⠁⠁⠉⠉⠉⠹⠆⠀⠀⠀⠀⠀⠀⠀⢠⠦⡁⠀⠌⠲⢄⣀⣀⡄
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣧⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠄⠀⠉⠁⠈⠋
⠀⠀⠀⠘⢧⣀⣀⣀⣄⠀⢀⠐⠀⠀⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⠐⢾⣀⠀⠀⠀⣠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠁⠙⠶⢶⣶⡀⣠⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣽⣀⣄⣀⠀⠀⠀⠀⠀⠀⠄⠈⠤⠰⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣴⡄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣠⡴⣻⠷⣬⠁⠀⠀⠀⠀⠀⢴⡆⢤⡀⢄⣀⡁⣶⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡀⠉⠛⠤⠴⢃⣰⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠏⠀⠉⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠨⠛⠲⠤⠶⠷⡶⣭⠶⠾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⠄⢀⠀⠀⣉⣠⣶⡿⠃⢰⡆⠀⠀⠀⠀⠀⠿⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⢛⣿⢸⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠐⢸
⠀⠀⠀⠀⠀⢠⡆⠀⠰⢡⡇⠀⢀⡔⠀⠈⣱⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣘⡎⢸⣿⠀⠀⢀⠇⠀⠀⠀⠀⠀⣀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢨⣯⡉⢲⣄⠌⠉⣣⣀⣀⢲⣿⡖⢀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⢤⡇⢸⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⡼
⠀⠀⠀⠀⠀⠀⢻⡗⠋⠉⠀⠈⠀⢰⡾⢛⡿⢹⠀⠀⠀⠀⠀⠀⠸⣿⡆⢀⡫⠴⣧⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⡀⠀⠀⢀⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠈⣠⠾⠷⠾⠁⠀⠀⠀⠀⠀⠀⠈⠛⣿⣛⣻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣈⣁⣀⣀⣈⡍⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠂⠀⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢧⢭⣽⡏
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠧⠺⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠈⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠤⠄⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⢤⠤⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⢀⠀⠈⠀⠀⠀⢀⠀⠰⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠢⡀⠀⠀⠀⡀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠁⠀⠀⠀⢈⠆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡔⠁⠀⠀⢀⠔⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡠⠄⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠲⠉⠀⠀⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠀⠀⣸⡒⠂⣠⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡩⠀⢀⠤⠀⠀⠙⠐⠠⠀⠀⠀⢀⣀⡄⢆⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⡆⠈⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⠀⠳⢤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠢⠀⢰⠀⠀⠀⠀⠀⢀⣀⡧⠔⠁⠀⠘⡀
⠀⠀⣀⠔⠊⠁⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⠀⠂⠀⠀⠠⠤⠀⠀⠐⠀⠚⠒⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠁
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⡘⠀⠀⠀⠀⢀⡔⠊⠁⠑⠒⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⢰⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⢧⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⡇⠀⢀⠔⠀⠀⢂⢄⠔⢀⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠳⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⡇⠀⢆⢘⡜⠁⣨⠀⠠⢆⠀⢀⠠⠤⡀⠠⠃⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠈⠑⠦⣄⡇⠀⢠⣋⠀⢀⡄⠀⡔⠊⡐⠁⡶⠀⠈⡆⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⢀⠇⡁⠣⠌⡀⠊⢠⠀⠑⡊⢅⠀⠙⡠⠩⠄⠀⢃⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡼⠱⠉⠉⠭⠁⠀⠨⠭⠉⣥⡬⡍⠉⠡⠀⠍⠩⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⠔⡡⠂⠅⠨⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡄⢄⠀⢀⠄⡂⠄⡲⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡰⠁⠜⢇⢈⠔⡡⢂⡝⠈⢂⠔⡵⡆⠴⢊⡾⠁⢌⠔⠠⢢⠃⣐⣀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢠⠁⠨⡀⠀⢀⠔⠀⣘⠀⢶⡀⠀⠄⢔⡁⠸⣜⠬⢥⣀⣩⢦⣠⣝⡁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⡀⠀⢀⣢⣄⠠⠤⠮⠵⠤⠖⢃⣐⣓⠒⠛⠥⠽⠍⠁⠀⠒⠓⠂⠀⠀⣈⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠦⠤⠬⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠶⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣵⠞⠛⠛⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡟⠁⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⢣⡀⠀⣀⣼⡷⠚⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢷⡀⠈⠉⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣮⠻⣦⡀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣬⣻⣆⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⠻⣿⣷⡄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠀⠉⠀⠙⢷⡌⢻⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠸⣇⢀⡙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣝⣷⣶⣤⣀⣀⡀⠹⠀⢻⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⢉⡴⠶⠶⢶⣌⣿⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠛⢳⣿⢸⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠳⠿⣀⠀⠀⠀⣿⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠀⠀⠀⢠⡟⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣶⣶⠤⠀⢸⠁⠀⡀⠤⠶⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠁⠀⠉⠀⠈⠀⠀⠠⠚⠛⠛⠷⣦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⡶⠟⠛⠻⠶⢤⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⠟⠃⠀⠿⣦⣁⠀⠀⠀⣆⡀⠀⠀⠀⠈⢻⡆⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡟⣾⠁⠀⠀⠀⣷⠸⣟⡻⠶⣦⣌⣛⡛⠫⠥⠶⠟⠃⠀⣀⡿⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣧⡀⠀⠀⢹⡀⠀⠉⠛⠶⢶⣭⣭⣓⡲⠄⠀⠀⢞⣥⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡷⣦⡸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣄⠠⠋⠁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⣰⠇⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⡥⠂⠁⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠠⢤⣈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⢸⡁⢰⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣷⠘⣷
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠻⣦⣀⠀⠀⠀⠘⢦⣀⠙⠻⢶⣶⣤⣤⣴⡶⠟⠋⢀⡼⠀⠀⠀⣼⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣙⡻⠶⣦⣤⣄⣉⠛⠶⢶⣤⣤⣤⣤⣤⡶⠶⠋⠁⠀⢀⣼⢏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⢿⣿⣿⣷⡶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⢟⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣷⣦⡀⠀⠀⡼⣱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠸⠁

⠀⠀⠀⠀⠀⠀⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠓⠤⠤⠽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢯⢉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⣲⠋⡧⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣰⠗⣺⣃⣀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠚⠙⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⡎⢱⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣙⣦⣧⣔⡁⠀⠀⠀⠀⡏⠁⢸⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⢉⠜⡟⢯⡉⠁⠀⠀⠀⡗⠚⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⢀⠔⠊⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡸⠓⠲⢤⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠻⡀⠀⠀⠈⠙⠒⠒⠒⠒⠶⠴⠖⠒⠒⠒⠚⠁⠀⠐⢀⠇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⠑⠒⠦⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠉⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⣀⣄⣀⣀⠙⠒⠠⠄⠉⠉⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠾⢏⣉⣉⠤⢠⣤⣓⠶⣤⣉⠙⠛⠉⠓⠀⠀⢀⣠⠴⠚⠫⢑⣈⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢯⣝⣳⠦⣤⣉⠉⠛⠻⠾⣍⣁⠈⢉⣀⡠⠤⠖⠒⠋⣉⣤⡤⠖⣋⣩⡤⡖⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠠⠝⡹⡟⠓⢮⣙⣓⠲⠤⣌⣉⢉⡏⣀⣁⡤⠶⣚⡋⠭⠀⢶⢺⠁⠁⠀⣀⡤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣢⣤⣃⡐⠂⠳⠉⣿⠓⠦⣬⣍⡉⣉⠭⡖⢉⠋⢠⠀⠀⢈⣨⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠁⠂⠬⢭⣛⡳⢦⣌⡀⠀⠘⠇⢻⠀⠒⠁⣀⣠⣤⠶⢏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢥⣌⣓⠦⣄⣀⠀⠀⠉⠓⠲⢭⣓⡲⠦⠼⠴⠾⣟⣛⣭⠭⠶⡚⠋⢳⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⡘⠀⣌⠙⢦⣍⣙⠓⠶⣤⣀⠐⠤⠉⠳⡖⡊⠉⠉⢀⣀⣤⠤⣖⣿⢿⡶⠒⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠞⠉⠻⣦⣄⡈⠀⠙⠉⠙⡓⢾⢿⣗⠢⠤⠥⠴⣒⣺⣋⣥⢶⠟⠋⡉⡜⠙⠋⣀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⡜⢆⠀⠠⡉⡛⠿⢶⣤⣒⡀⠈⠛⠉⠙⢲⡞⠛⠉⠁⠟⠀⣊⣀⣠⠤⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠧⡳⡀⠘⣎⠂⠒⣀⣈⣉⣛⡦⣄⣀⣸⢀⣀⣤⠶⠞⢋⣉⣸⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠣⡤⢱⡝⢆⠊⠟⠛⠉⠉⢁⣀⣀⣠⠭⠿⠛⢛⣓⣻⣭⡭⢥⡶⠖⠚⢻⡀⠀⠀⠀⠀⠀⡠⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠉⠷⣀⠀⠀⢳⡈⠙⣎⢑⣒⣒⣚⣯⡭⠽⠖⠞⠻⠋⠹⠩⠃⠀⠀⠀⠊⢀⣠⣴⠾⠓⠀⠀⠀⠀⠎⠀⠀⣠⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠸⠦⣹⠂⠀⠀⠙⢆⢸⠙⠃⠘⢁⣊⣀⣭⣤⣤⣤⣶⠶⢾⣿⠿⠽⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠙⠟⢳⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠋⠀⠀⠀⠀⠈⠿⠾⠿⠟⠛⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⣉⣳⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣖⣩⣏⣙⣦⠀⠀⠪⢨⣛⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉⠉⠉⣿⠹⠟⠃⢰⣧⠀⠘⠉⣴⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣰⢀⣤⠀⠀⣧⠀⠀⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⡿⠚⢠⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠟⠷⠀⣿⢸⡷⠃⠀⣿⠘⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠿⠿⠿⣿⠶⠿⠿⢻⡟⠗⠻⠒⣟⠀⠀⠀⠀⠀⠀⢸⡗⠿⠿⠷⢿⠾⠶⠾⠖⡔⠲⠶⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡀⣷⡀⢸⡷⠋⠐⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠊⠋⠀⢸⡇⠄⠀⠀⣇⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣯⢤⣶⣤⣼⣥⣤⣤⠀⠓⠐⠄⠀⠀⠀⠀⢸⣧⣤⣤⣤⢘⣀⣠⣤⣄⢃⣠⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠀⠀⠈⠁⠀⠂⠠⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⣀⠀⣾⢠⠄⠀⠈⣷⢦⠄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡔⠀⠀⠀⠀⠀⠈⢛⢸⡇⠐⠋⠀⢿⠈⠠⠴⠀⡟⠁⠨⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠎⠀⠀⠀⠀⠀⢀⠔⠁⠘⣿⣯⣉⠉⣮⢙⣛⠛⢱⡎⢛⠛⠓⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠈⠀⠀⠀⣠⠄⠈⠀⠀⠀⠀⡟⣿⣿⠀⢻⣼⣿⠃⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠘⣻⣤⣾⣿⣿⣿⣯⣶⡶⠟⠉⡇⠀⠀⠀⠀⠀⠀⡷⡶⠶⠶⡸⠶⠶⠶⢮⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⠘⠒⠠⠂⠀⣀⣤⣶⣾⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⣿⠀⡠⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⠀⣀
⠀⢀⣹⣷⡤⠶⠚⠋⢹⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⣧⣤⣤⣤⣨⣬⣥⣤⣈⣧⣠⣤⣀⡇⠀⠀⠐⠻⢿⣦⣀⣴⡶⠟⡻⠿
⠀⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣙⠀⡀⡀⣈⣇⣀⣀⣀⡇⠀⠀⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⢷⣀⣀⣀⣙⣿⣤⣶⠶⠖⠶⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠔⢚⣷⣶⣤⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢶⣟⠁⣀⢀⡀⠀⠀⠀⠀⠀⢿⣿⢋⣉⠁⠀⠈⠻⣶⢒⣀⣀⣤⣤
⠀⠀⢀⣠⣴⣀⣀⣿⣿⡟⣛⣓⣲⣿⣿⣿⣦⣀⡄⠀⠀⣀⡀⠀⣤⡶⢎⠀⠈⠓⣦⣠⢤⠶⠏⠹⢿⡃⠄⢀⣀⡀⠀⠀⠀⢿⢧⣾⣿⡿⣟⣛⡤⠭⠹⠿⠖⠁⠃
⠀⡀⠘⢿⣿⣿⣯⣽⣷⣶⣤⡤⣼⣛⠋⠉⠙⢛⣳⠖⢚⣫⡵⣀⠙⢿⣦⣖⠋⠉⠀⠙⢳⣄⣠⣤⠖⠋⠛⢭⡛⠀⢀⣀⡀⠘⠋⠉⠉
⠀⠀⠀⠀⠉⠻⢿⣿⣿⡛⠛⢳⣿⣿⣿⣳⣞⣩⡤⠚⠉⢉⣩⠥⠆⠀⠙⣿⣷⣴⡲⢿⠋⠀⠙⢶⣌⣢⡤⢴⣉⣾⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣈⠉⠉⠙⠿⠛⠛⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡦⢤⣶⣾⣿⣶⣶⣾⡯⠽⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠿⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⢳⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡁⠀⠈⠑⠂⠄⠀⠀⠀⠀⣀⡤⠤⠒⠉⠁⠀⠀⠀⢀⣀⠼⠇⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⢍⡓⠢⢄⡀⠀⠀⠀⢠⠉⠁⠀⠀⠀⠀⠀⠀⢂⣉⢥⡴⠾⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡍⠙⠖⠦⡁⠀⠀⢼⣤⠴⠖⢈⣁⣀⡤⠊⠉⠃⠘⠀⠁⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠲⣤⣄⡀⠈⠀⠀⢸⡇⢠⡤⠖⠚⠋⠁⡼⠁⢀⣴⣊⣤⣴⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢿⠿⣶⣄⡀⠐⠀⢸⠀⠀⠀⣠⡿⠤⠚⠛⠉⠉⠀⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠸⣆⠈⢮⡙⠓⡤⣼⠶⠖⠋⠁⠀⠀⠀⢀⡀⠠⠤⠤⠶⢛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡄⠀⢹⡄⣿⠓⣄⠀⠸⠄⠀⣀⡀⣀⣀⣀⣤⡤⡴⠶⠒⠊⣹⠏⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠙⣇⠀⠈⠷⢶⠒⠛⠉⠹⠉⠁⠀⢸⡞⢁⠤⠂⠰⠃⠐⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣞⣻⠖⠋⢳⢀⠈⢦⡀⠇⢸⠀⢀⠀⠀⠀⠀⣠⣏⡴⠿⠥⠴⠓⠒⠒⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣱⡦⡀⠀⢀⠛⠀⠰⢏⡀⢹⢦⠙⠦⠼⠴⠖⠒⠒⠘⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠃⠀⠞⠀⠀⠀⠈⠳⣇⡏⠀⠀⠀⠀⠀⠀⣀⣈⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡴⠀⠀⠀⢀⡀⠀⠀⠀⢰
⠀⠀⠀⠆⡀⠈⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣤⣀⠼⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⡙⠷⠂⠀⠈
⠀⠀⠀⣤⡉⠂⢄⠒⠠⠱⠲⠤⠤⠞⠤⢄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠉⢻⠃⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊
⠀⠀⠀⠀⡐⠠⢄⠀⠀⠂⠈⠙⠢⣮⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡼⠁⠀⠀⠀⢿⠎⠀⢀⡤⠄⡂⢀
⠀⠀⠀⠀⣍⠒⠠⢤⢀⠀⠀⠀⠀⠄⠀⡈⠀⠛⠢⠀⠀⠠⠈⠒⠹⢲⠎⣅⣀⡀⢀⠎⠎⠀⠀⠈⠀⡀⠐⡌⡆⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠉⠛⢿⠌⠀⠀⠀⠳⢄⣰⣀⠤⠃⠀⠀⠀⢄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⡀⠀⢀⣀⠀⠀⢀⡾⠀⠀⠀⠀⢠⡟⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣿⣁⡀⠀⠀⢀⡎⠀⠠⣪⢟⡭⣿⣿⣆⠀⠀⠀⠀⡀⠘⠐⠊
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⡟⠀⢀⣄⠁⠊⠀⠀⠛⢉⣄⠀⠀⠀⢇⡀⡀⠀⠀⠄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠃⠂⠀⠉⠀⠀⠀⣤⠀⠈⠉⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠰⣄⢀⣄⣀⠼⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣾⢁⣀
⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠒⠒⠀⠀⠀⠠⠀⠀⠀⡀⢀⠄⢀⡽⢞⣫⠝⢛⣡⣷⣀⠀⠀⠀⠰⣿⣦⣀⠈⠙⠯⣌⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⣋⣷⡦⣻⣽⣾⡯⣭⣭⣹⠿⠀⠀⠀⠈⠻⣝⠿⠁⠀⠈⠉⠒⠠⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠤⠐⠀⠀⠀⠀⠀⠉⠛⠓⠉⠉⠉⠁⠉⠙⠊⠁⠁⠂⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⢆⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡀⠀⢏⡉⠁⣀⠜⠁
⠀⠀⠐⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⡂⠀⠀⠀⠰⠀⢀⡉⠓⠀⠀⠀⠀⠀⠐⠒⠢
⠀⠀⠀⠀⠠⠇⠀⡀⠀⠀⠇⡀⠀⠈⠂⠚⠀⠀⠀⠀⠀⢯⠀⢀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢷⣄⠡⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⣐⢁⠀⠀⠀⠙⣣⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⡆
⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠛⠯⠉⠑⠂⢊⠕⠉⠢⣄⠑⡔⣀⠀⠚⠁⠀⠐⠂⠈⠀⢀⡀⠁⢀⣴⣁⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠻⠿⠉⠀⠀⠀⠀⠈⠒⠀⠄⠈⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢝⡳⠶⠬⠤⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡽⠲⣶⢶⣬⣛⡿⣿⣭⠉⠀⠲⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠈⡹⢦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢹⣟⣶⣎⣉⠟⠻⢿⣿⣻⣦⣄⡀⠀⠉⠒⠽⠒
⠀⠀⠀⠀⢠⠔⠀⠀⠀⠈⠻⢦⣄⠠⠖⠁⠀⠀⠈⠛⢦⣄⣀⣠⣴⠞⠀⠀⠀⠀⢸⣿⣟⣟⣧⡜⠛⢲⣶⡉⢉⠻⢿⣝⢿⣷⡦⢤⡐⠂⠀⠈⢠⡀
⠀⠀⠀⣤⡻⣶⣄⠀⠀⢀⠠⠊⠛⠳⣦⡀⠀⠀⠀⢀⢠⣽⠟⠋⠁⠀⠀⠀⠀⠀⠀⢻⣿⣎⢿⣳⣴⠁⢨⠟⠳⣤⠖⠙⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⣠
⠀⠀⠀⠘⠻⣮⣹⢷⣆⡉⠀⠀⠀⠀⠀⠙⢷⣤⣾⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣝⢿⣷⣧⣠⡄⠉⡳⢯⣀⡼⢿⣿⣿⣟⣻⡭⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠹⠶⢿⣿⣶⣀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣬⣉⠛⠿⢿⣧⣴⡛⢳⣔⢿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⢶⣮⣍⣹⣩⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡆⢢⡦⣭⣞⣋⣻⣷⢎⡶⣶⡀⡤⠄
⠀⠀⠀⠀⠀⠀⠘⣤⡉⠛⠙⠷⠿⠥⠿⠿⠾⠏⢿⣶⡟⠴⠛⠋⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠈⢣⣄⣐⢀⣀⣲⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣤⠞⠉⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠉⠉⠛⠛⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⣧⣴⣿⣟⢳⣇⣦⡀⠀⠀⠀⠀⠀⡀⠳⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠐⣂⢴⣮⠔
⠀⠀⠀⠀⠀⠀⢈⠄⠒⠀⠤⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⣾⣿⣿⣿⢿⣿⣿⣿⣴⣾⠷⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠛⠒⠲⠖⠲⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⣟⢿⠟⣩⠧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠽⠋⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⣀⣄⣄⢀⡀⠀⠀⣲⡀⠀⠀⠀⠲⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠉⠀⠀⢠⣄⠀⠙⠂⢀⠈⠀⠁⣉⠋⣷⡆⠀⠀⣬⠖⠠⣇⠀⠈⡲⠄⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣄⠀⠀⣀⠀⠀⠄⣆⢬⡼⠓⠀⢠⣰⡧⣀⣀⣻⣇⡀⠀⠀⠀⢀⠉⢀⠙⣄⠈⠉⡒⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⠀⣧⡄⡈⣥⢾⣜⡓⢉⣁⡀⠀⡀⠈⠁⠀⠀⠀⠈⢛⣁⠐⠤⠤⢀⡉⠁⠳⢽⡄⠀⡇⠀⠀⣷⣼
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⣶⣿⣦⣿⠿⢋⠁⡠⢈⣨⠍⣁⠐⠦⠀⠀⠀⠀⠀⠈⢥⡆⢀⠀⠨⡇⠢⣀⠀⣿⠢⣅⠀⠀⠹⣿⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠎⠀⣠⣿⡏⢱⢋⣴⠥⠐⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⡆⣷⢀⠈⠀⢹⠆⢺⣷⡀⢣⢹⣦⠞⢹⡆
⠀⠀⠀⢸⡄⠀⡄⠀⣸⠿⣸⠷⣿⠁⣀⢂⡂⣔⣬⣰⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⠓⠾⢬⣤⡈⢧⡑⣼⢠⣿⣦⣿⠁
⠀⠀⠈⡀⢧⣠⠓⣤⣿⢟⡟⣸⡿⠬⠋⠣⠑⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⠌⢳⣄⠸⡋⠙⢫⣷⣼⠁⢸⣿⠁⢰
⠀⢢⠀⢧⠸⣧⠑⣾⢧⡾⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠙⣿⡗⢾⣿⣊⣋⠄
⠀⠈⣧⢨⠃⠸⣿⣣⡾⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⣄⣿⣧⠸⣿⠈⣯⠆
⠀⠀⠘⣷⣀⠀⢻⣿⡡⣺⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⢻⣿⠀⣿⣇⡳⠂
⢦⡀⢰⡛⣿⣦⣾⣯⣠⣿⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠹⣿⠳⣿⣧⣟⠁
⠈⢷⡌⡾⠰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣱⣿⣧⣿⣿⠃
⠀⠈⢷⡸⡇⢸⣿⣿⠁⣀⡀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⣿⠇
⠀⠀⠘⣿⠷⣸⣿⣿⠘⡿⠛⡸⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⠀⠈⠣⣼⣿⣿⣿⣆
⠠⣼⡇⣹⣯⢸⣿⣿⡏⠀⠐⣮⣿⢅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢷⣫⣴⣶⣼⣿⣿⡇⢸
⠀⢨⣟⡵⢻⣿⣿⣿⣇⠀⢐⡫⢷⢝⡂⠀⢄⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣷⡋⠡⣼⣿⣿⡇⢸
⠀⠀⢻⣫⠌⢻⣿⣿⣿⡆⠀⢩⠽⣝⣃⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⡂⢀⣿⣿⣿⡃⣾⠀⢸⠁
⠀⠀⠈⠧⣞⢄⢹⣿⣿⣿⣄⠈⠬⣯⢲⣵⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢽⣿⠒⣾⣿⣿⣿⣶⠃⠀⠅
⠀⠀⠀⠀⠻⢎⢔⣿⣿⣿⣿⣦⠨⣧⣾⣿⢓⣂⣤⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣯⣄⠀⡄⠀⢀⣦⣄⢺⣿⣃⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢏⣿⣿⣿⣿⣿⣷⣾⣿⠻⠛⢻⣟⣿⣿⣤⣤⠀⠀⠀⢀⠀⠀⠐⡩⣻⣽⠇⡇⣇⡼⣻⠏⡽⢷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣿⣿⣷⣬⣧⣼⣽⣽⣿⣿⣀⠀⣈⣄⣄⣀⣈⡴⠖⠓⣚⡛⠛⣿⣾⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣤⣀⡀⢹⣿⣟⠁⠀⠀⠀⡀⢀⠌⠋⠙⠻⣧⡊⠁⢀⣅⠚⢻⣛⣠⣿⣿⣿⣿⣿⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⢿⣯⣭⣭⠾⢿⣤⣀⢀⠠⠊⢀⣱⡤⢶⣿⠖⡛⠛⠋⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣿⣿⣧⣼⣾⣾⠾⠷⣦⠾⡉⠐⢣⡏⠀⠀⠀⣈⡥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣙⣇⣀⣜⣁⣀⣈⣠⣎⣈⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣤⣀⣤⣤⣤⣄⣀⣀
⠀⢀⣀⣤⣤⣤⣤⠶⠶⠶⠶⢶⣶⡶⠿⠛⠛⠋⠉⠛⢻⣿⣿⠿⣿⣿⣋⣉⣉⣹⣿⣭⡿⠟⢋⣩⠿⣷⣶⢾⣿⣿⣿⣷⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⣿⣿⣿⣟⠿⠿⢷⣤⣤⣤⣾⣯⣀⣀⣀⣀⣀⣤⡴⣾⣧⣤⣶⣿⣿⣿⣭⣭⠷⣾⣿⣶⠾⠉⠁⢀⣸⣷⠿⠛⠉⢸⣿⣶⠟⢻⡿⠁⠀⠀⠀⠉⢻⣷⣦⣄
⠀⣿⡟⣉⠛⠿⣾⣷⣌⣁⣽⣿⡏⠉⠉⠉⠉⠉⠀⠀⠈⣿⠁⠀⢀⣀⠉⠉⢀⣲⠄⣹⣿⣶⡶⠾⠛⠋⠁⠀⠀⠀⢸⣿⡁⠀⠘⣧⠘⠀⠀⠀⢠⡾⠃⠀⠈⠳⣄
⠀⣿⠠⠉⠀⠀⠀⠀⠉⠉⠙⠛⠻⠷⠶⣶⣶⣶⣤⣤⣼⣷⣤⣤⣬⣵⠶⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢵⢀⣠⣿⣷⣤⣄⣤⡟⠁⠀⠀⠀⠀⢹
⢰⣿⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣤⠔⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⠀⢸⣿⡷⠛⠉⠀⠀⠀⠈⢻⡁⣄
⢸⡏⠈⠀⣴⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠞⠁⠀⠀⠀⣤⣄⡀⠀⢄⠀⡈⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠟⠛⠒⠚⠻
⢸⡇⠀⠀⠋⠈⠁⠀⠀⠐⣿⡅⠀⠀⠀⢀⠏⢁⣤⣾⣿⠀⣿⣿⠚⣦⠐⣿⣷⢤⣀⣤⠀⠈⠉⠛⢪⣿⣦⡂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣹⡐⠁⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⢷⡀⡜⠀⣿⢁⣸⣿⠀⢻⡏⠻⠟⠁⣿⡇⢸⡇⢸⠀⠀⠀⠀⢡⠉⢿⠉⠿⣧⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀⡀⢀⣾
⢸⡇⠀⢀⣀⡀⠀⠀⠰⠆⠀⡿⠇⠈⠿⠇⠀⠉⠉⣹⣿⠀⠿⠿⠀⠀⠀⠿⠧⠘⠃⠘⠀⠀⠀⠠⢧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠗⠎⠉⠙⠻⣿⠇
⢸⡇⣰⡿⠋⢻⡄⠀⠀⡀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢠⡎⠉⢳⠄⣿⡇⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢠⠟
⢸⡇⠘⠳⠶⠟⠀⠘⣿⡇⠀⠀⢨⡋⠻⠛⠀⣴⣶⣀⠀⣼⣿⠧⠀⢀⣴⢦⠄⠀⣾⣧⠴⢶⡄⠀⠀⠘⠷⠖⠋⠀⣿⠁⠀⠀⠀⠀⠀⣰⠿⣦⡀⠀⠀⣰⠏
⢸⡇⣤⠀⠀⠀⠀⠀⢻⣧⢀⡄⢸⠀⣿⡟⠀⣾⡿⢹⠇⣿⣇⡴⡄⣾⡟⠉⢠⠀⣿⡏⣶⡤⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⠏⠀⠀⠙⢷⣴⠏
⣸⡇⠀⠀⠀⠀⠀⠀⠈⣿⡏⠹⣾⡀⣿⡏⠀⣹⡟⢸⡀⢿⣇⣃⠇⠸⠿⠾⠃⠀⣿⡇⠀⠀⠀⠀⠐⣶⣧⠄⠀⠀⣿⠀⠀⠀⣠⣾⠡⠀⠀⠀⢀⣼⠏
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠀⠙⠉⠈⠃⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⢀⣠⣀⠀⠀⠀⠹⠄⠀⠀⣿⠀⢀⡼⠋⠙⠷⣤⣀⣠⠞⠁
⣿⡇⠀⠀⢠⣄⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⣠⠀⣶⠄⣴⠞⠙⢳⣴⡶⢀⣴⠻⡆⣼⡏⢠⣽⠇⠀⠀⠀⠀⠀⠀⣿⣴⡟⠀⠀⠀⠀⢨⡿⠃
⢻⡇⠀⠀⠠⣤⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⡏⢠⣤⡄⣿⣆⠓⠋⢹⡇⢸⣿⠞⡁⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣌⠀⠀⢀⣴⠋
⢸⡇⠀⠀⠀⠈⣃⠀⠀⠀⠀⠈⣿⣀⢿⡅⢸⠀⠀⣿⠀⠈⢿⣧⠀⣿⣧⣄⠛⠛⣁⡀⢹⣿⠀⡀⠀⠀⠀⠀⠀⢸⣿⠀⠉⣷⣤⠞⠁
⢸⡇⠀⠀⠀⢠⣴⣞⠀⠠⣤⣤⣿⡏⠀⢻⣧⠀⢀⣿⡌⢿⣤⡿⠀⣿⡇⠈⡇⠀⠹⠶⠾⠃⡀⠀⠀⠀⠀⠀⠀⢸⣯⠀⣠⡾⠋
⢸⡇⢤⢿⠒⠃⠉⢻⡧⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠛⠋⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋
⢸⣷⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⢀⡶⠛⠛⢆⠀⠀⠀⠀⠀⠀⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⣿⡄⠂⠀⠀⠀⠀⠟⢉⡀⠀⠀⠀⠸⣧⣤⣴⠏⠀⠀⠀⠀⠀⠀⠙⠁⠄⠀⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⢀⣼⣿⠁
⠀⠙⣿⣄⡋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠞⣁⣴⣾⣿⠃
⠀⠀⠈⠻⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠻⢿⡿
⠀⠀⠀⠀⠈⢻⣯⡟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣉⣉⣅⢀⣀⣀⣸⣵⣿⠇
⠀⠀⠀⠀⠀⠘⠻⠿⠿⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠶⠾⠶⠿⠟⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠄⡠⣤⣤⠀⠀⠀⠀⠀⠀⠄⠶⠶⠛⠛⠉⠉⡉⢉⡽⢣⣤⠒⢆⠀⢀⡖⢢⣄
⠀⠀⠀⠀⠀⠰⡈⠐⢄⣀⠀⢁⡤⠒⠀⢉⡟⠁⡀⠀⢀⣀⠁⠤⠄⠠⢤⣄⣲⣦⡵⠞⠋⣠⠟⣈⠆⠐⡄⡔⠀⢎⡘⢷⡀
⠀⠀⠀⠀⠀⡆⠈⠑⠂⠂⠤⠉⠀⢀⡴⠋⠀⠀⢡⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢠⡟⠂⠀⢋⠖⠁⠑⢎⠊⠀⠚⣧
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠚⠓⢮⠀⢈⠖⠛⠂⠀⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠊⠉⠀⠀⠀⠈⠉⠂⠀⠘⡇
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡆⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡆⣇
⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠀⣉⢒⠂⠀⠀⠐⠒⠒⠛⠛⠉⠉⢿⡁⠀⠀⠀⢸⠀⢸⠀⠀⠀⠐⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣠⡤⣶⣯⣶⢿⡷⢿⣿⢿⣺⠟⢋⡩⠭⠝⢛⣓⣢⠉⠛⠒⠂⠘⠀⠘⠂⠒⠒⠋⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠞⣫⠾⣭⢴⡭⢖⢭⣺⣧⣴⠋⢉⣠⡏⢳⡀⠀⢠⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡟⢸⠁⢰⠁⣰⢁⠎⠀⠀⠀⢉⠉⠀⢀⠔⠉⠉⢧⢳⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠃⡾⢀⡇⠀⢀⡏⢰⠀⠎⢰⡆⠠⣸⡿⢸⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⢷
⠀⡼⠁⠀⠀⠀⠠⠤⠄⠒⠁⣀⠔⠁⡿⣇⡀⠀⠀⠀⠀⣧⡼⠀⠀⢸⠀⡇⠀⠀⠘⡇⢀⡜⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠀⠔⢈⣀⠀⠀⠀⠈⠉⠉⠀⣂⠜⠁⠈⠙⠓⠒⠒⠒⠒⠒⠒⠒⠶⠶⠤⠤⠴⠶⠗⠋⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘
⣼⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠴⠤⠴⢖⣒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠
⣿⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⠀⡐⣳⣤⠗⠚⠛⠓⠚⢭⣲⢞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠐
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠜⠀⠀⢰⡯⠗⠚⠉⠚⠿⠭⣙⠢⡀⠑⡙⡆
⠈⠓⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠊⠀⢀⠤⠒⠒⠦⣌⠑⣜⣆⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠳⡜⡜⡖⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⢳⡦⠙⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠆⠘⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣇⠀⠀⣿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣀⣠⣦⡀⠀⢀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠙⢉⡟⠁⠀⠀⠀⠀⢤⠀⠀⠀⣷⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⢰⣤⣠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡄⠀⢰⣿⡇⠀⠀⢠⠀⠀⠀⣀⣂
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢰⠛⡚⣅⠀⠀⠀⠀⢸⣿⡯⠀⠀⡞⠃⠀⠀⣿⣧⠀⠀⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠻⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⢶⣀⠀⠀⠀⠀⠹⡿⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠄⠈⢆⡀⠀⠀⠐⢍⣣⡀⠀⠻⠿⠿⢷⣿⣽⠄⠀⠘⠀⠶⠀⠀⠀⠄⡠⠀⠀⠢⣄⣠⡆⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠁⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠖⠛⠇⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠀⢈⣴⠛⣹⣤⠀⠀⠀⣠⠖⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡩⠘⠁
⠀⠀⢠⠀⠀⠀⠀⠀⢼⣦⡄⠀⠀⠀⠀⠈⢹⡿⣿⡇⠀⠀⢀⣒⣀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠀⠀⢰⠶⠶⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠶⠦⠄⠀⠀⠀⣅
⠀⠀⠀⠀⠰⣛⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠛⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠳⢤⣀⣀⣠⣴⢿⣀⢀⣰⣤⣤⠴⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢄⡀⠀⠈⠉⠁⠀⢢⣭⠟⠁⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠛⢶⣀⠀⢀⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⠙⣷⣟⡁⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠞⠁⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡍⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⣶⣄⢄⠀⠀⡀⢀⣵⡿⠃⠀⠀⠀⠀⠀⡙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⡾⠷⣶⠟⠒⠳⣦⡀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠙⢿⣦⣀⣵⡿⠋⠱⠀⠀⠀⠀⠀⢀⣼⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢉⣁⣀⠀⠤⢤⡄⠀⣎⠛⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⡿⢿⣷⡀⠀⠀⠀⠐⠀⣸⡾⢣⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⡛⠋⠉⠉⢛⣦⠤⠲⠄⡼⠃⠈⣿⠿⢷⡄⠀⠀⠀⠀⠐⣤⢾⠓⠀⠀⠙⠳⣼⡆⠀⢀⣾⣏⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⡆⠀⠀⠀⠀⠀⣻⢧⣤⡴⠞⠻⡳⣼⣀⠀⢻⢷⠶⢤⣤⣾⣝⠅⠀⡐⠄⠀⠀⠘⠟⣶⣟⣿⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⣏⠀⠉⠀⠈⠄⢸⠛⠿⣏⣀⣀⣙⡆⠀⠀⠙⠶⠶⣶⡄⠀⠀⣠⣾⣝⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡞⠀⠀⢸⡄⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠙⣿⠀⠋⢠⠶⠆⠀⠘⢷⣌⣼⣿⣷⠟⠁
⠀⠀⠀⠀⠀⣠⡞⠁⠀⢠⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣾⠃⣴⢶⡄⠀⣠⣄⠀⠀⠻⢟⣿⢿⡄
⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠞⠁⠈⠳⡌⠁⠈⣀⡀⠀⣀⡀⠈⠻⣆
⢀⣠⡾⠋⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⣾⣿⣷⣿⠘⡉⠋⠀⢹⣷⣤⣼⠃
⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣿⡏⠀⠰⣿⡉⢸⣿⠿⠁
⠙⢷⡄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣠⡾⠉⠄⢠⡼⠛⣧⣀⣴⠿⢷⠾⠁
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣠⠾⡃⠀⢀⣴⠟⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⡄⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣴⠋⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠀⠀⠀⠀⠀⠀⠀⠑⣠⡞⠑⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣠⡾⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠠⠁⣀⣠⣂⠀⡤⠃⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⢀⠈⢸⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠃⠄⠀⠁⠀⠁⠏⠀⠀⡤⠂⣠⠾⠅⠀⠀⠊⠭⠋⠀⣈⠉⠛⢤⡀⣧⡀⠀⠘⣿⢃
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡟⠀⢁⠞⠁⠀⣢⠎⠀⣂⣴⡤⠊⠁⠀⠈⠈⠁⠀⠀⠀⣸⣿⣿⡧⠀⠙⢿⡄⠑⢀⣿⡈⣞
⠀⠀⠀⠀⠀⠀⡰⠃⡿⠀⢸⠃⣠⡶⢋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡄⠘⠀⠉⣷⣾⣿⣧⡿⡄
⠀⠀⠀⠀⠀⣰⠁⢰⡇⠀⣿⣟⠁⣰⣿⠡⠄⠀⠀⠀⠀⠀⠀⠒⠠⠤⣭⡽⠦⠤⡿⣿⣿⣿⣧⠀⠀⠀⣌⣿⣿⣿⡇⠘⡄⠀⡀
⠀⠀⠀⠀⢠⣿⠀⢸⣧⣰⡿⠈⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢦⡀⠀⠀⣿⣿⣿⡇⠀⢸⣠⠃
⠀⠀⠀⠀⠘⣿⠀⠀⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⣼⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⠃⠀⡊⣉⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣧⠀⢀⠀⠀⠀⠀⠀⢈⣽⡇⠀⣿⠀⠀⣄⡟⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠻⠿⡿⠶⡷⠶⠶⣤⣬⣾⣿⣸⣿⣶⡶⠿⡿⣿⠟⠋⠉⢙⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣧⣤⣤⣴⣷⣤⣧⣦⣀⠠⠬⣿⣿⠛⡲⣗⡂⢠⢠⣿⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣨⣿⣾⣿⠁⠀⠀⠴⠿⠿⢭⣭⡭⠀⠼⠿⠷⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠶⠒⠾⠖⠛

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢟⡻⡿⢿⣿⢿⣻⣿⡿⠿⣻⠿⣟⢿⢟⡻⢿⣿⡿⣿⡿⡿⢛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣠⣙⣣⣿⣿⣿⣜⣻⣏⣇⣜⣛⣤⣛⣻⣜⣣⣞⣿⣩⣼⣇⣿⣘⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡯⣿⣟⡩⣟⡯⣫⣿⢻⣿⡟⢿⠛⡿⢻⣟⢻⢻⣛⣿⠛⢻⠟⣿⢻⡿⣿⣿⡟⣟⠛⣿⣿⢛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⣵⣦⣧⣼⣧⣽⣼⣤⣶⣦⣵⣦⣧⣿⣽⣧⣭⣾⣤⣦⣿⣧⣿⣿⣿⣿⣧⣿⣿⣯⣿⣿⣿
⢸⣿⣿⣛⣩⣭⣶⠀⠀⠐⠒⠒⣶⡶⢭⣭⣛⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛⠛⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠈⠛⠛⠋⠉⠛⠛⠓⠚⠓⠒⠖⠛⠛⠛⠋⠉⡟⠛⡛⠛⠛⠃⠀⠀⠙⠛⠛⠛⢛⡛⠋⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀⠠⠀⠀⠀⠀⢀⠇⠀⠯⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡻⢿⠿⠛⠁
⠀⠀⠀⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠲⠶⠚⠛⠛⡋
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠶⠂⢀⣶⡶⠀⠡⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⢀⠐⠄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠿⠤⠼⠿⠖⠘⠋⠁⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠈
⠀⠀⠀⠀⣠⡄⢶⠀⠀⢁⣀⣸⠿⠛⠀⡄⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠀⣀⠌⠀⣤⠀⣀⡀
⠀⠀⠀⠀⠉⠙⠛⠁⠈⠉⠁⠀⠀⠀⠀⢻⠀⣀⣤⢔⣐⣶⣤⠉⠙⢯⣭⣭⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠛⠉⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠃⠀⠀⢠⣪⣵⣦⣀⣤⣀⣹⣿⣶⣶⣾⣿⣿⠿⠀⠀⠀⣀⠀⠀⠀⠀⢀⠸⣧⠁⠀⠈⠹⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠄⠀⠖⢀⣀⡿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣁⣀⣴⠀⠀⠈⠁⠀⠢⠀⠀⠘⠓⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡀⠀⣾⣿⠟⢷⣤⣤⣤⣤⣴⣶⣶⣶⣿⠿⠟⠋⢉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣧⠀⠁⠉⠉⠉⠉⠉⣉⣁⣀⣠⣤⣴⡆⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠿⠿⠿⠿⠿⠿⠿⠛⠛⢉⡁⣴⠀⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣤⣤⣶⣶⣶⣶⣿⣿⠿⠇⠛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⢋⣉⣉⣉⣉⣁⣤⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠁

⣿⣿⡿⠿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠿⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠈⠙⠋⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠁⠀⠀⣤⣦⠰⣦⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢺⣷⡿⠛⠛⢦⣌⣛⣾⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠛⠉⠁⠀⠀⠀⠀⣛⣛⠛⠛⠒⢺⡷⠶⠶⠦⠤⠤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠉⠉⠉⠉⠛⢻⡟⠓⠒⠲⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⠟⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣾⣿⣿⣷⣶⣦⣾⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠆
⣿⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠉⠛⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣶⣦⡀⣠⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⣀⡀
⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡌⠉⡀⠙⣶⣂⠀⠀⢠⣄⣀⣰⡿⠃⢦⣄⣀⣘⣿⠆
⠀⠀⠀⢻⡇⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⢸⠀⣿⡏⡆⠀⠀⠉⠉⠁⠀⣤⣤⡈⠉⠉⠀⠐⢲⡄
⠀⠀⠀⠘⢷⣤⠐⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⢸⠇⠀⠀⢸⠀⣿⣿⠀⠀⠀⠰⢥⣄⣴⡾⠟⠁⠀⡀⢀⣴⡿⠁
⠀⠀⠀⠀⠈⢻⣧⣌⠐⢀⠀⢂⠄⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⢹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢻⣿⡦⡀⢪⠄⠐⡄⠀⠀⢀⠀⡄⠀⠀⠀⡇⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣜⠦⠀⠀⠀⠀⣆⣷⣆⠀⢸⣷⣿⡿⠀⠀⠀⠀⢀⡀⣹⠟⢻⣿⠷⠴⣾⡅⠄⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠦⠥⠀⠀⢻⣼⣿⡦⣸⣿⡿⠃⠀⠀⠲⣦⣀⠽⠃⢐⣿⡿⢶⣶⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⠄⢤⣤⣤⠄⢠⣤⢤⢍⠛⠿⠿⠛⠀⠀⠙⠲⢾⣿⣟⣶⣛⣻⣿⣷⣿⣿⡿⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡰⠶⠂⣿⠠⠴⠆⢸⡅⠶⠦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡿⠀⠀⠀⢸⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⠛⠓⠉⣻⡙⠛⢂⣼⡇⠀⠀⠀⠀⠄⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⠿⣄⡄⣠⣿⣧⣤⣤⢽⢷⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣬⡇⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠀⡤⠂⠀⠀⠀⠀⠠⠤⢦⣤⡔⠲⣶⠖⠚⠃⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣒⣶⣶⣶⣼⣥⣶⣿⠅⣀⡀⡛⠓⠶⣄⣲⣶⠶⠶⠤⣤⣄⣈⣡⣿⣿⣆⠀⣀⣤⡄
⠀⠀⣹⢦⡠⣄⣀⣾⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢙⠞⢿⡒⢦⣄⣈⡁⠐⠂⠚⠋⠁⠀⢀⣠⣼⣿⣿⣿⠃
⠀⠄⣠⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠀⠉⢺⣍⠉⠉⣛⣳⣶⣤⣀⠀⣽⣿⣿⣿⣿⣿⣿⠄
⠀⠘⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠌⣱⣿⣿⣿⡿⠿⠿⠷⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠀⢀⡄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢮⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⢀⠀⠈⠁⠠⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⣀⡴⡼⠁⠀⡠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⢀⠊⢹⣷⠻⡆⠸⣴⠏⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⡄⠰⠏⠀⠀⡀⠀⠀⠀⢀⠀⠀⣿⢷⣿⣿⣱⢿⣾⢷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠆⠀⠀⠀⠂⠀⠀⠁⠀⠀⢀⠈⠀⠀⡹⣾⣿⡿⠁⣾⢃⠌⣰⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⢀⡀
⠀⢸⣀⡆⠀⡀⠀⠀⠀⢀⠤⡀⠀⠑⠀⠀⠁⢿⣿⡇⢠⠛⡏⣴⠿⠒⠀⣴⠁⠀⠄⢠⠈⠀⠀⠈⠙
⠀⠐⠀⠀⠈⠇⠀⢀⠔⣋⡀⠄⠁⠷⠛⢷⡉⠷⣼⣷⡶⢻⣠⡿⣢⠴⠆⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠖⠈⣩⠖⠈⠀⠀⠀⠀⠀⠀⠚⠳⣦⣴⡬⠛⠛⠿⣵⠄⠀⠀⠛⠓⠚⣁⡴⠆⠰⢤⠤⠄
⠀⠰⡄⢰⠀⡔⠁⠀⠐⣦⡠⡄⠀⠀⠀⠀⠐⠉⣙⡕⠊⠉⠑⣖⠓⣞⡤⡶⠐⣊⠁
⠀⠀⠄⡌⡀⠀⠀⠀⠀⠈⠻⣶⣃⡀⠀⠀⠀⠀⡿⠀⠴⠀⠛⠹⡆⣉⢷⡄⢀⢈⠙⠢⣀⠀⠀⠀⣠⠄⠶⠀⡄⠀⠀⠀⠄
⠀⠰⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⢀⡝⠳⡄⠰⠟⠀⢿⣸⠎⠷⠆⢘⣋⡄⢹⠗⠂⠉⠐⠖⠒⠈⠀⢠⠾⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠀⠉⠒⣰⣷⡶⠟⠊⣠⣔⣻⣧⢈⣁⣙⣧⠳⣄⢦⣄⠠⠀⠉⣸⢇⣀⡀
⠀⢰⠆⡄⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⣼⠆⣠⣤⡀⢠⠞⢢⣴⢇⣼⠿⠿⡄⣉⡻⣹⡆⠈⠴⣉⣦⡰⠞⠁⠀⠈⢉⠆
⠀⢨⡂⡇⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⡧⠴⠇⠀⠳⢶⣢⣶⣶⣿⣷⠄⣀⠿⢿⠙⢦⣛⡶⡘⠗⣤⠸⣄⠀⠰⠆⠈
⠀⢠⠍⠀⠀⠈⠷⢀⠀⠀⠀⠀⠀⠈⢉⠅⡲⣓⢛⠶⠹⠃⠌⢹⡄⣀⠙⠶⡫⠄⠰⢇⠠⡏⢳⠚⣤⠀⠙⢿⡓⠳⣄
⠀⢠⠀⣆⠐⠀⣄⠀⠙⠙⠢⠄⣠⣖⣁⡴⢉⠋⡽⢛⢄⣼⢳⣷⡾⠙⠥⠀⡿⣤⡚⠁⠀⠿⠀⠃⢻⡉⠩⣈⠣⢤⣁
⠀⠈⠀⠉⠠⡀⠈⠀⠀⢀⠀⠉⠉⣠⠞⣴⠋⣼⠳⠟⣘⡣⠙⠁⢀⡐⠂⠤⠭⢙⣡⡴⠂⠀⠀⠙⢮⣹⠶⠺⢿⠂⣉⠓⡀
⠀⠀⢀⠀⠰⠁⠀⠀⠴⣿⠀⠀⠀⠀⠘⠀⠢⠙⠒⠎⠁⠴⠣⠾⣦⡀⠀⠀⠀⠈⠳⠶⢞⡉⣤⡄⡀⠈⢷⡒⠦⠀⢉⡜
⠀⠀⠈⠂⠀⠀⠀⠀⢠⣄⠙⠆⣰⡆⠀⠂⠀⠀⠈⠀⠀⠀⢰⡞⢻⣿⡧⠀⠀⠀⠀⠀⠈⡡⠟⠐⣻⣿⡀⠘⢦⠁⠈⠓
⠀⠈⠀⢀⠄⢰⡆⠀⠰⣿⠀⠘⠉⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠⡿⢇⣈⣿⣀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠏⠿⣄⠈⠼
⠀⠀⠀⠈⢀⣈⠹⠀⡀⠁⣾⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⢷⣄⣤⠙⣟⠻⡶⣦⣤⣄⣰⡁⠀⢸⣿⣿⠛⡇⢠⠀⠀⠀⡀
⠀⠀⡄⠀⠈⠟⠀⢠⡁⠢⠘⠄⠀⠀⠐⣦⠠⡀⠀⢀⠀⠀⠀⠀⢠⡁⣘⣇⠠⡏⡹⢏⡿⢻⢦⡏⠀⠀⠀⡀
⠀⠀⠁⢀⡈⠀⣀⣾⠑⠊⠀⠀⠀⠀⠈⠈⡠⡏⠀⠘⠀⠀⠀⠀⠀⣉⣹⠟⢻⡷⠇⠈⠱⡟⢬⣿⣶⠟⣿⣀
⠀⠀⠀⠸⠓⠁⠙⢉⠀⠀⠠⢦⠀⢠⡀⠄⠡⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⣼⢁⢦⡀⠆⢻⡆⣿⠻⣿⣽⣯⣶⡖⠀⠠
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⣇⠄⠻⢠⠀⢈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠤⠜⣡⡜⠀⠈⠀⡌⢛⣦⡁⠈⠉⢻⡎⣠⠀⠇
⠀⠀⠀⠀⢳⡤⠤⣄⡈⠀⠀⠈⠀⡀⣦⠈⢀⣊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠁⠻⡄⠀⠀⠸⡇⠙⠻⣦⣡⣤⢹⡗⠀⡀
⠀⠠⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠞⠉⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠙⠄⠀⠀⣷⢀⡀⠟⣀⠀⠀⠀⠀⠁
⠀⢰⣤⠐⠒⣋⠟⣚⣡⡾⠲⣟⣵⠞⣍⣓⣶⣤⣼⡵⠦⠠⠀⢠⠀⠠⠄⠠⠤⠆⠤⠤⠔⠉⣉⣠⣾⠷⢦⠟⠷⣦⡄
⠀⢸⡟⠛⠛⠟⠛⠉⠏⠑⠛⠋⠉⠀⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠙⠋⠴⠁
⠀⠸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀⡀⢘⡀⢀⠐⠀⡀
⠀⢠⡀⡀⢀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠁⠁⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⡄⠅⠈⢡⠈⢢
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠄⠀⠀⠀⠝⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠴⠂⠀⠼
⠀⠀⠀⡰⠳⠀⡀⠀⠀⠀⠀⢀⠞⢩⠺⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⠉⠁⠀⠀⠀⠀⠋⠘⠀⠀⣿⣿⢮⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈
⠀⠀⠈⠀⠀⢄⠀⠀⠀⠀⡀⠀⢻⠋⠀⠀⠀⠑⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡄
⠀⠀⠀⠃⠀⠀⠑⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠆⠀⠐⢄⣀⣀⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡘⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠔⣁⠴⠋
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡉⣤⡤⣬⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠐⡊⢉⡀⠇⢂⡀⣀⢀⠤⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠴⠁⠀⠉⠁⠸⠈⢀⡀⠂⡠⠁
⠀⠀⠀⠑⠒⠀⠢⠤⠤⠀⣤⣄⣠⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⠀⠀⣀⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠
⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠐⠀⠠⠤⠤⠄⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠠⠐⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣿⢿⡿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡏⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣀⡼⡴⢃⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣛⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⣠⠏⠀⣏⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡤⠤⢤⣤⡼⠛⢩⣏⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣶⣶⣶⣶⣶⣖⣒⣒⣒⣖⣾⣵⣾⣿⣶⣶⣬⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠁⠈⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⣀⠀⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠉⢳⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠦⣀⣿⣠⠔⠃⠀⠀⠀⠀⠀⡗⠋⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⠶⠒⣺⣿⣗⠒⠶⠀⠀⠀⠀⠀⣇⣀⡤⠏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡜⠁⣿⠈⠧⠀⠀⠀⠀⠀⠀⣇⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⡤⠖⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠦⣤⣈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠁⣴⠋⠀⠀⠀⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⣠⠏⠀⠀⡈⠙⡆⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠙⢄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⣡⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠉⠓⠲⠦⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠊⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⡤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣬⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣋⣴⣿⣿⣿⣿⣿⢟⣿⣯⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣽⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣒⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣟⠋⡽⠋⠉⢻⣿⡿⠿⣿⡿⠛⣿⣿⣿⣿⣿⡟⣭⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣓⣽⣿⣿⣿⣿⣇⠀⠀⣼⡿⠁⠀⢈⡇⢀⣼⡷⠿⢿⣿⣿⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠋⠈⠙⣿⣷⣾⣿⣷⣿⣿⠿⠿⠿⠋⢀⡴⢊⣽⣿⣿⡿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⣠⠴⠚⠙⠻⣿⣿⣿⣿⣿⣷⣶⡶⠋⠉⠉⠁⢿⣿⣿⣆⣣⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠁⠀⣰⠏⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣍⣀⣉⣉⣉⠙⠛⠒⠒⢐
⠀⠀⠀⠀⠀⣠⣾⣄⣀⣐⣀⣀⡟⢠⠍⠉⣳⣆⡤⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⠁⠀⠉⠉⠉⠳⢀⠉
⠀⠀⠀⠀⠀⢧⣦⣤⣬⣭⣍⣉⣉⣿⡷⠟⣋⠡⠒⠁⠀⠀⠀⠀⠞⠛⠻⠛⠛⠛⠛⠓⠒⠂⠒⠛⡁
⠀⠀⠀⠀⣠⣸⣻⣯⣛⢦⡴⠟⢋⣡⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠷⢿⠿⢿⡻⠿⠛⠛⠛⢉⠉⠟⠁
⠀⠀⠀⠀⠓⠮⢭⣛⡛⠿⢷⠞⡉⠋⠰⠦⠶⠀⠀⠀⠀⠀⠀⠀⠈⢂⣰⠁⣀⠤⠐⡀⢅⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠂⠐⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠤⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⠀⠀⠀⠀⠈⣦⣄⣀⡀⡀
⠀⠀⠀⠀⢀⣠⡤⣼⣿⣶⣷⣄⡀⠀⠤⠄⠙⠓⠀⠀⠀⠀⠀⠀⠀⠆⠛⠻⠗⢀⣀⣤⠤⠤⠀⢰⠃
⠀⠀⠀⠀⠻⣷⣾⣦⠙⠛⢿⢿⣿⡆⢀⣠⠤⠶⣦⠀⠀⠀⠀⠀⠀⠰⣦⠤⣤⣀⣀⣀⣀⠀⠀⠀⣹⠆⠄
⠀⠀⠀⠀⠀⣈⡙⠿⣿⣷⣢⡑⠎⠉⠉⢐⡚⠉⠈⠐⡂⠀⠀⠀⢠⡀⢻⣷⣝⢿⡂⠘⠉⠛⠉⠈⢉
⠀⠀⠀⠀⠀⠉⣅⣀⠈⠛⠻⢿⣷⠂⠁⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⣄⠀⠩⡟⠈⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠈⠁⢀⠀⠀⠀⠀⢀⢤⠀⡆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣉⣉⡤⢬⣉⡉⠉⢉⣡⣈⡷⠁⠀⠀⠈⠒⠒⠦⠤⠦⠀⢶⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡀⠀⢀⣠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠙⣿⣁⢄⣒⢐⡄⠐⠊⠀⠀⠀⠀⠠⠄⠈⠑⣀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠉⣭⢄⣀⡀⠀⠀⠀⠀⢠⡄⢠⣅⡬⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⢠⡉⢩⠀⠠⠀⠄⢉⡐⡀⠀⠀⠀⠙⡜⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠈⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠘⣬⣆⠀⠔⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡠⠂⠊⡀⠀⠰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣴⡺⠟
⠀⠀⠀⠀⠀⠀⠀⡅⠒⢢⣀⠙⢁⠀⠐⠺⣶⢤⠚⠗⠁⠀⠀⠀⠤⠄⣪⠀⠐⢒⡩⠂⠀⠀⠀⠀⠀⠀⠠⡤⠄⢀⠐⡀⠠⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠷⠤⠴⠛⠚⠛⠒⠚⠀⠀⠀⠀⠀⠀⢰⠡⣤⣴⠒⣭⠄⠲⠖⢤⠀⠀⠀⠀⠀⠇⡀⠀⠈⠙⠖⠲⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢢⣖⣀⡠⠴⠃⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⣁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠃⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢃⠀⠀⠀⠀⠰⠈⡀⢄⡀⠤⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⡐⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⡄⠀⣀⡠⠠⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠰⠆⠀⠀⠀⢀⢠⣤⡀⠉⠰⠂⣀⠀⢂⣰⠄⠀⠀⠀⠀⢀⡓⢀⡠⠴⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠀⠀⠀⡀⠀⠀⠈⢃⠀⢈⢉⠰⠶⠤⠄⠊⠛⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⣀⡌⠗⠀⠀⠀⠨⠀⢠⣤⠠⠀⠴⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠔⠂⠲⡌⠉⠉⢀⠙⠆⣀⣀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⡄⠉⠀⠀⠱⣄⣀⣤⣤⠴⣴⠖⠛⠛⠙⢧⡀⠠⠀⢐⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⢰⡀⠀⠀⠀⢠⡖⠠⠀⢤⢀⡀⠀⠀⠀⠀⠀⠙⡆⣀⣠⣤⠽⡶⠖⠛⠋⠛⠉⠀⠄⠀⢙⡄⢀⡠⠴⠌⠓⠒⠛⠉⢉⡄
⠀⠀⠀⠀⠐⡈⠑⠒⢀⡌⢀⡃⠀⠀⠀⠀⢀⢠⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⡜⡅⠀⠀⠀⠰⡀⢀⣠⠤⠴⠄⠐⠚⠋⣉⢀⣤⠆⠠⠴⠚⠐⠂⠈
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡽⡙⠚⠲⢿⠆⠉⠀⠀⠀⠀⠀⠹⣠⠔⠒⠛⠉⣉⣀⢠⡦⠤⠠⠖⠂⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⡂⠁⠀⠀⠀⠀⠀⠀⠙⠤⠐⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡟⠁⠢⠤⣀⢀⡒⠀⢤⡀⠀⢸⣿⠀⢀⡎⣰⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⡇⠀⠀⠀⠀⡀⠁⠐⠃⠀⢠⣿⡿⠁⣾⠀⣿⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣇⠀⠀⠀⠀⡇⢰⣂⠴⠀⠀⠈⠸⠆⢹⡄⢿⡀⠀⢠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⠀⠀⠀⢀⡳⡀⠀⠀⠀⠠⠃⠀⠀⠘⡇⢸⡇⠀⣾⣿⡿
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠓⠒⠈⠉⠦⣼⡄⢀⠤⠓⢤⣄⡀⠀⣷⠸⡇⢰⣿⣿⡇
⠀⠀⠀⡆⣿⢰⢶⣄⠀⠀⠀⠀⡄⠲⣤⠤⠼⠄⡀⢴⡀⠀⠀⡤⠀⢠⡴⠇⠈⠁⢠⠀⠀⠀⠉⠓⢿⢀⡇⣾⣿⣿
⠀⠀⠀⣷⣿⣼⡀⣿⠀⣀⡀⠀⠻⠀⠹⡆⠀⠠⡁⢀⠇⠀⡸⢀⣴⠏⠀⢀⡤⠀⠐⣶⢤⣄⡀⠀⣸⣸⢣⣿⣿⡏
⠀⠀⠀⣿⣿⡇⣃⣿⣎⠳⣄⠉⠙⠒⠒⠒⠒⠰⠤⠠⠴⠒⠂⠈⢠⡀⠀⠾⠀⠀⠀⠟⣀⣠⣭⣼⡏⠁⣼⣿⣿⠃
⢀⠀⠀⠉⠉⠁⠻⠿⠛⠁⠘⠧⢤⡄⠶⢤⣀⣀⣠⣄⠀⠀⠀⢠⡎⢠⠂⣤⣶⠷⠿⠛⠋⠉⠁⠀⠀⠀⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠒⠒⠒⠂⠀⢲⡀⠉⠉⠉⠓⠒⢺⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠳⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠸⠃⠙⠓⠒⠒⠂⠘⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⡇⡎⠀⢘⠰⠀⠈⡔⠋⠈⠉⢍⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁
⠀⢠⠠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡆⢧⠠⣀⣀⣀⡀⠀⠀⠀⢿⢸⡇⠀⠀⠀⢀⣀⣀⣠⡤⠴⠶⠚⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠉⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠰⠂⠑⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠂⠠⠤⡀⠀⢘⠀⢸⠀⡐⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠃⠠⠇⠀⠀⢀⠀⠀⠈⠀⠈⠀⠈⢠⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⣄⡀⣀⠀⠈⠆⠀⣸⠏⣔⠀⢀⣸⠆⢠⠁⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣜⢋⠁⡀⠂⠁⠈⢲⡁⠄⠤⢍⠐⠍⡆⠈⠼⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⡉⠀⠀⠹⠦⠀⢤⠀⢨⡀⠀⠀⠁⠀⠱⠾⢦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠄⠐⠐⠆⢊⡀⡔⢁⡘⠀⠀⢨⠒⣄⡴⠂⠸⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⢀⠀⡄⢀⠀⠀⠠⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠠⠈⠀⠂⠠⢂⠄⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⠁⠱⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡊⠴⠂⡅⠀⠒⢌⡒⢀⠀⠁⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠆⠂⠀⠀⠀⠇⠍⠀⠀⠀⠂⠋⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡑⣤⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣀⠈⢛⢳⣿⣶⣿⣾⡾⣾⣷⣴
⣿⣿⡿⣠⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠐⢯⣑⣸⣧⣽⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣵⣿⡫⢈⣠⣂⠤⠀⣀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿
⣿⣿⣿⣿⣿⣿⣿⡷⢺⣿⣿⣿⣿⣿⣿⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠩⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⠃⠘⠀⠀⢀⣾⣭⡙⠻⣿⣷⣶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠢⡀⠹⢿⣿⣎⢦⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠝⠉⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡻⡧⠀⠀⠀⠂⠀⠙⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠘⠀⠀⡤⠚⠋⠉⠉⠉⠹⡿⠹⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻
⠈⠈⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠄⡀⠀⠀⣠⠄⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⠘⠁⣼⣿⣇⠀⠛⡴⠽⠂⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠋⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⣿⠂⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⣤⠴⠶⠖⠒⢂⠀⠀⠀⠀⠤⠀⠛⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⣀⣀⣀⠌⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣯⠷⠿⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠠⠄⠐⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀⠀⠴⠖⣒⣺⠃
⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠉⠀⢐⡀⠈⣭⣤⣿⣉⣄⣀
⠀⠀⠀⠀⠀⡀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠿⠿⢿⡄⠘⠟⠿⠟⠋⠁⠀⠘⢁⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠠⠀⠀⠀⡀⠀⡀⣈⠂⠛⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢦⣤⠿⡿⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠈⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠙⡏
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⡄⠀⢂⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢱⡁
⠀⠀⠀⠀⠀⠀⢼⣧⣀⠈⠁⠛⢯⠿⢁⡀⡰⢾⠇⠀⠀⠀⠀⡄⣻⡀⢷⣶⠒⠢⠄⠀⠀⢰⡄⢀
⠀⠀⠀⠀⢀⡀⢀⠉⠉⠣⢐⣠⣔⠠⢾⣿⠅⣰⡆⠀⠀⠀⠸⣯⡻⢷⣎⡀⠀⠀⠀⣀⢐⠿⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠢
⠀⠀⠀⣼⠁⠀⠈⡄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠔⢠⡀⠀⠈⠢⣀⣀⡴
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡖⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠈⠧⣄⣀⣀⣆⠀⠀⠀⠀⠀⣀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢶⡀⢤⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡄⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⣬⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⣶⠀⠀⠀⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⢠⡖⣿⠲⣄⠀⠀⠀⠀⠀⠀⣴⠃⠠⠀⠄⠀⠀⠠⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠉⠁⠤⠊⢠⠞⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡈⠙⠒⠲⠿⠿⠶⠶⠚⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠤⠀⢀⢀⣀⡤⢴⣾⠋⠀⢻⡀⠀⠀⠀⠀⠈⠋⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠈⡇⣸⡏⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⣇⡀⠘⠰⢄⣀⡠⠂⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⠁⠀⠀⠀⠀⠀⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣅⡌⣱⣤⠀⢀⠥⠀⣔⣻⣿⡃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡀⢰⡆⢸⣷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⢈⠍⠁⠀⠀⠀⠀⠰⠛⢹⡏⢈⡀⠀⠀⠀⠀⠀⠹⣿⣂⣀⣑⣐⣧⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠄⡀⠀⠀⠀⢸⣰
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡴⠟⠓⠋⠀⠀⠀⠀⠀⠀⠀⠈⢙⠿⠭⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⢀⣀⣠⡤⠈
⠀⠀⠀⠀⠠⡀⠀⣀⡀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠓⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡆⠶⣟
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠘⠓⠛⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠖⠒⠂⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢠⣾⡟⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⡇⠀⠀⢹⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢿⣷⣶⣾⠟⠀⠀⠀⢸⣿⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠛⠛⠿⣿⣦⡀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠹⣿⡄⠀⢸⣿⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢀⣼⣿⠃⠀⣸⣿⠃
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⡿⠟⠁⠀⣴⣿⠏
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⠁⠀⠀⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡦⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠋
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠘⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⠏
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲
⠀⠀⠀⠀⢠⠀⠠⢤⣴⡦⠀⣀⡀⠀⠀⠀⡄⢇⡀
⠀⠀⠀⡀⠙⠓⠆⣀⡉⢴⠶⢹⠁⠀⠀⣶⢿⣜⠁⠀⠀⢠⡇⠰⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡎⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠄⠀⠀⠄⠴
⠀⠀⠱⣄⣀⣀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠹⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠓⠒⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡆⠦⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠀⠰⢂⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠜⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣀⡙⠢⠤⠶⠤⠬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠀⠠⢤⠴⡿⠁⢸⠀⠀⠀⢈⠁⢰⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⡄⠀⢀⡀⡠⠀⢰⠀⠀⠀⠀⠀⣇⠀⠀⠈⠘⡇⠀⢸⠀⠀⠀⢀⡀⢘⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠐⢦⠹⠆⠀⠃⣰⣽⠇⠀⠀⠀⠀⣧⡀⠀⢰⢀⡿⠂⠀⠀⠀⠀⠀⠀⣬⡀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠐⢄⠀⠀⠀⣡⠾⠔⠀⠀⠀⠀⠈⢳⡿⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⣀⡙
⠀⠀⠀⠀⠤⠄⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠠⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠀⣴⣶⣶⣶⡄⠉⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣰⡀⠻⠿⠿⠟⠃⠸⠂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠘⢿⠟⠀⠀⠀⠰⠆⠀⠀⠘⠁⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⣿⠟⠀⠃⠀⠈⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠻⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⢰⠄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠺⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡟⠀⠀⠀⠀⣠⡀⠘⠋⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠺⣿⠗⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣥⣤⣶⠾⠃⠀⠀⠀⠈⠻⠿⠋⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⡀⣠⡀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⡶⠿⠿⠿⢿⣿⣯⣽⣶⣿⣭⠔⠻⡟⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠻⠯⣼⣗⣦⣶⢆⣠⡼⠓
⠀⢀⡤⠶⠚⠓⠒⢒⣾⣾⡿⢟⣍⣻⢯⡞⠁⠀⡘⢀⡠⠔⠒⠈⠛⠁⠒⠢⢤⡀⠀⠀⠀⢰⣆⠀⠀⠈⡻⠉⣧⠙⣒⡦⠄
⠰⠋⠀⠀⠀⣠⡾⠛⠋⠁⢠⣬⣳⠁⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠳⡄⠀⠎⣿⢗⠄⠚⠒⠉⠈⠉⠁⠀⠘⠛⠃
⠀⠀⠈⠀⠈⠁⠀⠀⣠⠀⠛⠃⠁⠀⠀⠀⣰⠃⠀⠀⠰⠆⢀⠁⡄⠈⡄⠐⠂⠀⠀⠘⢆⠀⠀⠘⣷⣄
⠀⠀⠀⠀⢰⣷⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⢩⡄⠡⣀⣣⣧⣼⣀⠌⣤⠋⠀⠀⠘⡄⠐⠰⢻⡙⠃
⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⢠⣤⠀⢸⠀⠀⣈⠀⠈⣐⣾⡷⣾⢎⣷⡊⡠⠄⡉⠀⠀⡇⢀⠆⠀⣿⣄⠁
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠈⡄⠀⠀⢀⠛⡐⠛⡿⢲⢫⠉⢂⠘⣃⠀⠀⢠⠃⢎⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⠄⠀⠱⡀⠀⠀⠀⠄⠐⡁⠐⢀⠁⠠⠄⠀⠀⠀⠌⠀⠈⠀⢠⢿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣌⠓⠀⠀⠘⠄⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠿⡠⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡿⠸⣿⡟⠷⢦⣄⡀⠀⠀⡶⠀⠀⢀⣀⠀⠠⡤⠐⠀⠀⠀⠀⢀⡀⡀⠃⠀⠑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃⠀⢻⠀⢨⡦⡈⠙⢆⠀⠃⠀⠀⠀⡋⠀⠀⡅⠀⠀⠀⠀⠰⡸⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣆⠈⠁⣨⡅⠘⠀⢰⠄⢲⡀⠀⢨⡇⠀⠀⠀⠃⠀⠀⠀⠀⡘⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠓⢀⠀⣰⠀⠈⠁⠀⠸⡻⣦⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡃⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀⠀⠸⠀⠁⡑⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢃⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣭⠔⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠛⠩⡐⠢⢄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠈⡄⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠋⠁⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢀⡀⠴⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠤⠄⠠⠤⠄⡙⠢⠤⠤⠄⠠⣀⠀⠀⠓⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡑⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣀⠀⣤⡤⠔⠊⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣺⠅⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠆⠛⢉⡴⢋⣁⠤⠄⠚⠛⠁⠀⠀⠙⣛⠛⠛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠊⠉⠀⠀⠀⠀⢠⡾⠂⠁⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⣀⣀⣤⡔⠒⠉
⠀⠀⠀⠀⠀⣀⡠⠤⠄⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠴⠶⠶⠶⠦⠤⠄⢀⣀⣀⡉⠛⠂⠤⠤⣀⡀
⠀⢀⡴⠊⢉⣠⠴⠂⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠦⢤⡈⠁⠢⣄
⡔⠁⠀⡴⠉⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠱
⡇⠀⠀⢦⡀⠀⠀⢀⣀⠠⠤⠤⠙⠓⠤⢄⣀⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠓⠂⠠⠤⠤⢀⣀⠀⠀⠀⣠⠋⠀⠀⡀
⡇⠀⠀⠀⠉⠐⠟⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠙⠗⠉⠀⠀⠀⠀⠿⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠂⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠑⠒⣄
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⢳
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠳⣄
⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⡆
⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇
⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⠁
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⠃⠀⠀⣸
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠀⢀⡤⠃⠀⠀⡰⠃
⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠀⠘⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⣠⠤⠊⠁
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠄⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢐⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠉⠐⠒⠒⠲⠖⠒⠒⠒⠈⠉⣁⡠⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣶⣶⣶⣶⣶⣶⣶⣶⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠙⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⡥⠒⠉⠀⢀⡤⢲⠎⢀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣟⠀⠀⠙⣆⠠⡇⡇⢀⡔⠁
⠀⠀⠀⠀⡀⠀⣸⠃⢀⠀⢰⠁⢀⣀⣰⣋⣠⣤⡴⠧⠒⠀⠀⢀⡠⠤⠒⣀⠀⠀⠐⠂⢀⡂⠄⠀⡀⠀⠀⣿⠀⠀⠀⠘⣿⣷⢷⣞⡀⠀⢀
⠀⢘⡐⢰⠃⡰⠃⢀⠈⡠⠃⠀⠘⠁⡝⠁⠀⢀⣄⠤⠀⢀⡴⣋⠀⠀⠀⠰⠋⣩⠟⠉⠉⠉⠉⠛⠧⣄⠀⢸⡇⠀⠀⠀⠸⣿⡾⡁⠀⣠⠋
⠀⢸⡇⣿⠞⠁⠶⢉⡼⠀⠀⣈⠀⡼⠁⣄⠐⣠⠃⣀⡶⠫⠤⠅⡦⠤⠖⢊⡉⠀⠀⠀⣰⣷⣶⣶⡊⠈⠳⣌⣇⠓⠠⣄⠈⣿⡇⢧⡴⠁
⢠⡞⣸⡏⠀⣀⡰⠋⠀⠀⣀⡵⠊⠁⣀⣭⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠃⠀⠀⡈⠻⣦⣀⠉⢠⣿⣧⠘⡇
⠏⢰⡿⠀⠀⣽⠁⢀⣴⠟⢉⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠈⠉⠐⠀⣹⣷⣿⣿⣿⣆⡿⣄
⠀⢸⡇⠀⢰⣿⡾⠋⠀⣰⣿⢋⣤⡁⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣉⣉⣉⣙⣳⣤⣀⣘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡈⢹⣿⣿⣿⣿⠇⠙⣆
⠀⢸⡇⠀⣼⣿⠱⠆⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣤⠤⠤⠤⠞⠋⠉⠁⠈⠉⠉⠛⠻⣿⣿⣿⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⠀⠀⠸
⠀⢸⣿⣰⣿⡏⢀⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠙⢶⣄⠀⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣿⣿⣿⡆⠀⣸
⠀⢸⣿⣿⣿⣿⡏⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⣰⡟
⠀⠈⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⢷⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠍⢸⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣃⡤⠾⡟⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧⠀⢰⣯⠄⠀⠀⡞⣼⠃⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⣤⣦⣤⣀⣀⠀⢀⢒⣻⣷⡒⣶⣻⣧⣤⣤⣿⣿⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⠟⠉⢹⣿⡏⣿⣿⡃⠀⠈⠉⠉⡿⡉⠉⡏⢹⠛⠛⠻⠷⠭⣽⣯⣷⣿⠿⣿⠟⠛⠛⡛⢻⡿⠁⠀⠀⠀⣠⣿⣿⠿⠛⠛⠛⠻⠿⠿
⠛⠉⠀⠀⠀⠀⢿⣷⣜⢿⣷⣦⣤⣤⣴⣷⣷⣶⣷⣾⣤⣀⠀⠶⠶⣿⣿⡛⢛⡛⣟⣋⡁⢰⡇⣼⣇⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣿⣷⣾⣿⡏⠀⠈⠉⣉⣽⣿⣿⣝⣋⣛⣏⡁⢀⣼⣷⢿⣿⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠛⠒⣶⠄⠀⠐⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠉⢀⠞⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠁⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⠼⢦⣄⠀⠀⠀⠰⠋⠀⠀⢀⣀⣨⡤⠤⠴⠶⠶⢦⡀⣼⡇
⠀⠀⠀⠀⠀⣾⠙⣍⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢈⡤⢒⣛⠫⣄⠀⠀⠀⠀⠀⠀⠀⢹⢸⠁
⠀⠀⠀⠀⠀⠸⠀⠹⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⡐⠁⠀⢱⠘⣆⠀⠀⠀⠀⣀⡤⠎⢸
⠀⠀⠀⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⠂⢀⣿⠤⠐⠊⠉⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⡇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠡⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠂⣴⡀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣯⡒⠢⣤⠤⣀⠀⠀⠀⠀⠴⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠙⠷⠊⡬⣹⠲⡁⠀⠀⠀⢠⢀⡇⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣌⡉⠒⠂⠤⠁⠁⠀⠀⠀⡌⡼⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠀⠁⠀⠪⠚⠀⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠊⠙⠿⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠯⡀⠀⠀⠀⠀⠀⠀⠙⠟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠐⠊⠉⠀⠀⠁⠀⡈⠒⢄⠀⠠⠔⡈⠄⣂⠤⠌⡙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠈⠢⡀⠀⠀⠀⠀⢀⠠⢓⠀⠁⠒⢹⠀⠀⠀⠀⠀⠀⠀⠄⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⡏⠀⠀⠀⠀⠀⠀⠂⢀⠑⠄⠐⣨⡔⠂⠅⠒⠀⠂⠀⠑⠤⡀⠀⠀⢀⠠⠀⣈⣀⡼⠿⠃
⠀⠀⠀⠀⢀⡤⠦⠖⠛⠈⠐⠀⠈⠢⢀⠀⠀⢀⠠⠒⠈⠀⢀⠈⠀⢇⠀⠀⠀⠀⠀⠀⠁⣢⠈⠀⢈⣵⠾⠟⠋⢁⣠⠴⠂
⠀⠀⡏⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⣰⠄⠁⠠⠔⡾⠁⠂⠁⠀⠀⠀⢀⠁⠢⡀⠀⠠⢒⡠⣤⡤⠖⠋⢀⣀⣴⠟⠋⠁
⠀⠀⠳⣄⠈⠠⢌⠐⢄⠀⠤⢐⡡⢄⡢⠤⠄⡀⠑⢄⠀⠀⠀⠀⠀⡀⠜⠂⠀⣑⣾⣿⠟⢉⣀⣶⠶⠛⠁
⠀⠀⠀⠈⠻⢦⡀⠑⠠⡀⠂⢹⠀⠀⠀⠀⠀⠀⠐⠀⡈⠂⢀⢒⡩⢔⣪⠶⠟⠋⣉⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠐⢄⠑⠤⡀⠀⠀⣀⠄⠂⡉⠀⣠⡵⠚⠋⣀⣤⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠉⠢⣌⠀⠨⠔⣊⡤⠒⠋⡀⣠⡶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠑⠔⠋⢁⣢⡾⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣼⠞⠋⠉





⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠖⠀⠤⢄⣀⣠⣤⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⡀⠒⠀⠀⠀⠀⠀⠀⠬⠽⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡟⠁⠀⠐⠁⢀⠀⡀⣄⠀⠀⠀⠀⣀⣀⣀⡈⢻⠇⢀
⠀⠀⠀⠀⠀⠀⣸⣷⡀⡀⢀⣼⠿⢋⣡⡴⢚⣀⣠⡴⠞⠛⠋⢀⣠⣴⣾⠿⠋⠉⠉⠻⢿⣶⡾
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣾⣿⡴⢛⣭⠶⠛⠉⠀⣀⣤⣶⣿⠿⠿⠓⠒⠲⠶⢦⣤⣀⣀⠙⠁
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣾⠟⠀⢠⣴⣿⣿⡿⠟⢉⣁⣠⣴⠞⠛⠒⠒⠲⠶⢶⣽⣦
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠋⣄⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡃⠀⠀⢀⢠⣤⡤⢾⣿⣦
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣍⠛⠋⢉⣻⣿⣿⣿⣿⣿⣵⣶⣤⣶⣿⢿⣾⣯⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⠟⡋⠁⠀⣴⣿⣿⣿⣿⣿⣁⣘⣤⢾⣿⣿⣷⣴⣦⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⡿⠿⡿⡿⠟⠋⢻⠿⠷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠁⣝⣛⣽⠏⠀⠀⠀⠘⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡮⠉⠀⣴⣀⣀⣠⣤⣬⡻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡻⢟⣿⣿⣿⣿⡿⠿⡃⣀⣠⣾⠙⠿⡿⢿⣿⣿⣷⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣦⣀⣠⣤⣭⡟⠁⢀⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡉⠻⣿⣿⣯⣽⠏⢀⣴⠏⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢾⣧⡄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⣿⣿⠋⠀⣸⠏⢠⡾⠋⣸⠟⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣁⣀⠀⠀⠀⠀⠀⢸⡟⢠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠖⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣤⡈⠁⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠻⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⣦⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⣿⣿⡭⠭⢽⡿
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⠉⠙⠛⠚⠳⣮⣽⣿⣯⣭⣿⡭⠽⢭⣭⣉⣉⣙⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠒⠂⠀⠀⠠⠀⠀⠠⡄⡀⠈⠉⡙⠉⢠⠊⠈⠀⠨⠻⣿⡟
⣤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⣈⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣷⣬⣿⣭⢡⣆⣀⣈⣄⣠⣄⣴⣶⣶
⣾⠓⠤⣄⣀⣀⣂⡈⣀⠀⠀⠑⠒⠖⠘⠉⠉⠉⠉⠉⠉⠉⠤⡤⠤⣤⡭⣽⣟⣄⣬⣤⣧⣏⣈⣈⣹⣿⣿
⡉⠉⡒⠀⠐⣦⢤⣬⣾⣿⠟⢻⠇⠚⢛⡟⠛⠛⠙⠉⠉⣽⣿⣿⢻⡉⠻⠉⣯⣌⣁⣉⣘⣩⣭⣿⣿⣿⣿
⣷⣦⣶⡶⠶⠀⠀⠈⠁⢹⠷⡄⢀⣶⡄⠀⠀⠀⠉⠹⣶⣿⣿⡇⢸⣿⡀⢿⣛⣅⣀⣀⣈⣹⣿⣿⣿⣿⣿
⣿⣿⡿⠃⠀⠀⠀⠀⠀⣸⠀⠀⠸⡟⠻⢿⣾⣎⣿⣟⣏⣿⣿⣷⣾⣿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠉⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠇⠀⠀⠀⢸⣿⣿⣏⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⣸⣷⡀⡰⣾⣦⣲⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠙⢦⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⠀⠀⠈⡏⠀⠀⠀⣹⣤⡖⠉⠉⠙⢦⣀⣀
⠀⠀⣠⠴⠒⢉⣉⣀⣀⣠⠜⢆⠀⠀⣠⡇⠀⡴⠉⠁⠀⠹⡄⠀⠀⢸⣄⣈⣉⡉⠙⠒⠒⠒⠦⣄
⠀⢸⠉⠓⠻⠥⠤⣏⣀⣸⣀⣈⣹⣋⣀⣉⣉⣣⣀⣀⣀⣀⣱⣒⣒⣉⣹⣤⠤⠬⠭⠛⠒⠒⠚⢙⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠖⠉⠉⠉⠒⠤⡀
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡤⠤⠤⣀⠀⠀⠀⠀⠱⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡄⠘⢦⡘⡇⡰⠃⠀⢠⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⣄⠀⠀⠀⢱
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⡀⡇⠀⠀⠙⡏⠀⠀⠀⢸⣠⠜⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠳⣄⠀⠀⡇⠀⠀⡠⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢹
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠈⠳⣄⣇⡴⠊⠀⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠸⠿⠒⢒⠟⠈⠉⠉⢉⡽⡿⣍⠑⠒⠒⠒⠺⡓⠒⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠎
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⡴⠋⠀⡇⠈⠳⡀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣠⠔⠋⠀⠀⠀⢰
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⡹⢻⠀⠀⢀⡇⠀⠀⠈⣦⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠋
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⢸⠀⣠⢼⠧⡀⠀⠀⡇⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⣀⠤⠊
⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣼⡀⠙⠆⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠉⠉⠉⠉
⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⡾⠛⠻⢿⠿⠛⠻⣿⠟⡿⢿⡿⠟⠛⢿⡿⠛⠻⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣤⣤⡀⢀⣤⣤⡀⣠⡀⣄⠀⣠⣤⣄⢀⣤⣤⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⢷⣯⣁⠿⣿⣶⣤⡀⠀⣇⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣈⠑⠒⠁⡀⠉⠛⠻⣿⣧⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡼⠛⠿⣾⣝⡻⢿⡿⢟⣫⣴⣮⣭⣛⡿⠆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⣤⣄⡉⠳⢤⣀⣀⣠⠴⠛⠛⠲⠦⣬⣹⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣾⣥⣤⣤⣤⣭⣿⣷⣾⣿⣯⣥⣤⣭⣽⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠃⠸⠛⠿⠟⠳⠆⠈⠉⠀⠰⠾⠻⠗⠶⠀⠀⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣶⣿⣷⣦⣀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⠰⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⣿
⠀⠰⢿⣿⣦⣀⠀⢀⣈⣙⣿⣿⣯⣻⣶⣿⣦⣄⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠰⠿⠗⠒⠲⠶⡿⠶⠶⠒⠒⠂⢺⡷⠒⠒⠒⠒⣺⣿⡀
⠀⠀⠈⠻⠟⢿⡟⣛⠋⠉⠉⠀⠈⠛⠿⢿⣿⣻⢿⣶⣄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⣿⣥
⠀⠀⠀⠀⠀⠛⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣨⣿⣿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢿⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⡴⡶⠞⠋⠹⠿⣛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⣀⣀⣀⣀⣠⣇⣤⣠⣤⣤⣤⣼⣠⣤⣤⣤⣀⣼⣿⠟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⠶⠽⣷⣀⠔⠊⠉⠉⠉⠓⠤⢐⡚⠹⠂⠀⠀⠀⠛⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡈⣧⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠤⠔⠊⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⡿⣿⣶⣤⣀⡀⠀⠀⠀⢀⡼⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣾⣿⣿⡷⢾⣽⣿⡷⢶⣰⠏⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡛⠻⢿⣙⡻⠿⣿⣿⣿⣇⠞⠉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣶⣤⣙⡓⣾⣿⠋⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢿⢿⣛⡹⠉⠋⠛⠛⠿⠿⢿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠛⠛
⠀⠀⠀⠀⢸⠁⠃⢸⠁⠈⢻⠘⣧
⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠄⠀⠙⠩⠄⠀⠈⠅⠀⠀⠀⠀⢤⣤⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⢄⡀
⠀⠀⠀⠀⢡⠀⠀⠀⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣉⣦
⠀⠀⠀⠀⠈⣧⣠⠀⢰⡀⢠⣃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠘⠃⠀⢱⠀⢱⠀⠀⠂⠀⠨⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠈⢻⣦⣻⣧⣼⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡁⠘⢠⠐⠄⠰⠀⢁⡼⠀⠀⠀⢀⣠⣤⡤⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⣀⠦⠀⠧⢀⠁⠑⠀⢈⠀⢰⡀⡶⠌⠀⠀⠀⢰⣿⣯⠀⠀⠀⠀⠀⣠⡼⠂⠀⣠⣤⠐⠀⠀⠀⣀⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⢿⣤⡃⡁⢀⣄⣀⠆⡠⠖⠈⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⡾⠿⠋⠀⠀⠀⠻⠿⠿⣶⡶⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠄⠀⠀⢀⣀⣀⣀⡀⠀⠄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⡀⠀⠤⡔⢷⣦⣠⣀⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢠⡍⠉⣁⣬⣆⣻⣿⣿⣷⣯⣏⡛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣠⣶⡿⣿⡏⢉⣉⣁⡸⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⡖⢠⣾⠟⠁⠈⠋⣠⣿⠋⠁⠀⠙⠻⠮⣝⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⡞⢠⡿⢁⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠈⠳⠙⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣾⢡⡟⢀⠀⠀⢀⣼⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⡟⠀⠄⢀⠀⣾⠃⠈⠀⠀⢀⣤⣤⣤⣄⠀⠀⢰⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡿⢰⣾⢡⠇⣸⣿⡇⠀⠀⠰⢃⡀⢈⣿⡞⢿⡀⠸⣯⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠗⠊⣿⠏⣰⣿⣿⠇⠀⠀⠐⠿⠏⠛⠐⠁⠈⢷⡄⠱⣦⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⢸⣦⣿⣟⠗⢶⡄⠿⢿⠿⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⢧⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣠⠿⢿⣿⣯⣽⣿⣿⣆⠸⣷⡀⠀⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⠀⠀⢄⣠⣾⣷⣦⠴⢶⣆⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣴⣟⣭⣅⣠⣤⣿⣿⣄⡈⠑⣶⡀⠀⠀⠈⢤⠘⢷⡄⠀⠀⠀⠀⠀⢀⣼⡇⣠⣶⡆⢻⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⢀⢺⣿⣋⣩⣽⣿⣿⣷⣿⢻⣿⣶⡟⠳⣄⠀⠀⠀⠀⢿⠁⠀⠀⠀⢴⣶⣋⣙⣧⣼⡏⢧⠸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⠿⠖⣉⣛⠉⠹⠏⢻⡛⠛⠛⠋⣿⠃⠀⠉⢓⠤⣀⠀⠘⠀⠀⠀⠀⠀⠀⢛⣡⠟⠋⠀⠀⣠⡿⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⣴⣿⡂⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⢄⣤⣤⣴⡶⠛⠁⠀⠀⢀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠿⠿⢾⡭⠉⢉⣛⠿⡦⠀⠀⠀⠈⢦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣛⣾⠇⣤⣄⣴⡀⠀⡀
⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢄⠀⠈⠳⣤⣀⠂⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣸⠿⣿⡇⠘⣿⣿⡇⢻⠇
⠀⠀⠀⠀⢸⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣀⠂⠀⢹⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⡿⠀⣿⡇⠀⠘⣿⣧⠀⠆
⠀⠀⠀⠀⣸⣿⠀⠀⢰⡁⠀⠀⠀⠂⠀⠀⡀⠀⠘⣿⣷⡀⠉⢻⣷⣄⠀⠀⠀⢰⠋⢸⡿⠀⡇⢺⣿⡇⠀⠀⢹⣧⠀⢠
⠀⠀⠀⢠⡏⣿⡀⠀⠈⠀⠀⠀⠀⠀⣀⣢⠈⠀⠀⠸⣿⣧⠀⡌⣆⠉⠀⢤⡄⠀⠀⢸⡇⢰⠇⠀⣿⡇⠀⠀⢰⣿⡄⢸
⠀⠀⠀⣾⠀⠻⠇⠀⠀⠤⠤⠀⠀⠂⠉⠻⢿⡳⠆⠀⣿⣿⡄⢁⢹⡄⠀⠀⡤⠀⠀⣿⠀⣾⠀⠀⣿⡇⠀⠀⠈⣿⡇⠀⡆
⠀⠀⢰⡏⠀⣠⣴⣶⣶⡶⠶⠶⠶⠦⢤⣤⣀⣁⠀⡀⢹⣿⡇⢸⠈⣷⠀⢸⡇⠀⠀⠘⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣷
⠀⠀⢸⠁⠀⠈⠓⠾⢿⡇⠉⠁⠀⠀⠀⠀⠈⠉⠝⠛⢼⣿⡇⢸⡆⢻⡄⡺⠁⠀⠀⠀⠀⠀⠀⣼⠏⠃⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⣠⠔⠒⠂⠄⠀⠀⠀⡀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠹⠿⠟⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠠⣶⣦⣄⡀⠀⠀⠀⠀⢫⢻⡀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠙⣿⠿⣦⠀⣄⣀⠈⠇⡷⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠹⠀⢟⡇⢻⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⣀⣤⡀⢰⡀
⠀⠀⠀⠀⣀⠄⢀⣨⣿⡐⢄⢠⣠⡖⠀⠀⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠈⢳
⠀⠀⠀⡰⠋⠀⣻⣿⣿⣷⡘⠿⢿⡇⠀⠀⠰⠋⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⢐⣿⣿⡇⢻⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠻⣿⣄⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠁⡜
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠈⠛⠿⢷⡤⡀⠀⠀⠀⠀⠀⠀⠶⠂⢸⠁
⠀⠀⠀⢠⡀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠈⠐⠢⠤⢄⣀⣀⣀⡰⠇
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠟⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⢠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣻⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣶⣦⣤⣤⣤⣶⡟⢻⣧⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡟⢻⣿⣯⣨⣿⣿⣿⣷⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠛⠿⠿⠛⠉⠻⠭⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣄⣠⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣰⠀⢰⠀⠀⠀⢀⠀⠶⢀⡀⠀⠀⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⢰⡀⠀⠀⢠⡀⠀⢠
⠀⠀⡅⠉⡄⠈⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠃⢠⠞⠉⠂⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢉⠀⠠⡐⠋⠘⠃⠈⠀⠏⠀⠈⠒⢀⠀⢨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠾⠒⠲⣄⠈⠳⡀⠀⣠⡄⠀⠀⠀⠀⠀⣄⠀⠀⠉⣤⣀⡂⠐⢤⣄⠀⠀⠘⠋⠁⠘
⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⡾⠃⠀⣤⢀⠁⠀⠀⢿⡆⠘⠀⠀⠀⠀⠠⠒⠉⠀⢠⠻⠋⣉⣹⣶⠀⠙⣷⠀⠀⠋⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠐⣏⠀⠀⠀⢱⠀⠀⠀⠀⠈⢡⠃⠀⠀⠰⠃⣠⠜⠀⠀⠚⠀⠷⠀⢷⡀⠀⢠⠀⠰⠛⢐⠤⠀⠀⠀⠀⠉⠀⢸⣧⠀⢸⡇⠀⠖⢱⣾
⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⡤⠂⡲⣘⠛⣗⣤⠘⠣⠀⠙⠀⢀⣄⠙⠃⠀⠠⡀⠀⣠⡄⣠⡏⠀⣸⠃⠀⢤⡄⣩
⠀⠀⡇⢠⠆⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣀⠀⠘⣠⠂⣠⠟⠁⠈⢁⣈⠁⠐⢀⡆⠀⠀⠛⢁⠑⡶⠀⠀⣿⡛⠿⠿⠋⢀⣰⠏⠀⠀⣀⡸⢿
⠀⠀⡇⠉⡆⠀⠀⠀⠰⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣥⠀⠐⠃⢰⣯⠀⠀⠀⠀⠀⢀⣶⡄⣥⠀⠀⠀⠈⠣⡀⣀⠀⠀⠑⠒⠲⠚⠛⠁⠀⠤⡀⠸⣀⣈
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠦⠀⡄⠀⠀⠀⢀⠀⣀⣾⠇⠀⠛⠇⠀⠐⠿⣿⡇⢸⣇⠀⣿⢆⣠⠀⠉⣀⠴⡂⢀⠂⡄⠀⣷⠀⡜⠋⠛⠉⡸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡖⠁⠀⠀⠀⠀⣰⣧⡟⢰⠄⠀⠀⡀⠄⠠⣿⢠⡇⣿⠀⠑⠈⠉⠂⡀⠋⣤⠈⣸⡇⣧⡜⠀⠐⠶⣠⣶⣾⢷
⠀⠀⡇⠀⠀⣰⠃⠀⠀⠀⠀⢀⡀⠀⠀⢀⡶⠀⠘⠀⠀⢠⡟⠁⢃⣼⡀⠀⠀⠀⠀⣸⣷⡌⢃⠘⡆⢻⣏⣀⣀⡀⠚⠛⣦⠀⣤⡈⠁⣦⣽⣦⠟⢻⡇⢘
⠀⠀⡅⠀⠀⠈⠃⠀⠀⠀⠘⠄⠀⣠⣶⡏⠀⠀⠀⠰⡄⠁⣰⣶⠚⢅⠱⢦⣀⣤⣴⡉⠏⣛⠉⠴⣣⠀⢉⠉⠀⣄⢹⠀⠘⢦⠛⡧⠘⠃⠙⠃⢴⣬⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡶⠀⢻⣿⡌⠛⠂⠀⡀⢾⠀⣀⠀⠘⠋⢼⣿⠀⣉⣤⢷⡆⢸⡍⠛⣀⠙⢆⡀⠁⠀⢿⣥⡄⠀⡀⠀⠇⠘⠀⠀⢀⠾⢋⡀⢸
⠀⠀⣯⠀⠀⠀⠀⢈⡷⠀⡴⠀⠀⣀⣤⠐⠒⠋⢤⡈⠀⡀⠉⠀⠀⠀⢻⡇⠀⣨⡼⣷⣾⠕⠊⡙⠰⠚⠉⢂⡀⠀⠀⠰⣶⡅⡀⠀⠀⠀⠀⠈⢰⡾⠃⢸
⠀⠀⠉⠀⠀⠀⠀⠈⠁⠸⢧⠄⠒⠂⢠⠀⠳⢄⠀⠹⣆⠀⠀⠀⠈⠂⢸⣇⠀⢈⠀⢻⡃⠀⣹⡍⠂⢀⡤⠚⠡⣄⠀⠘⣶⣴⡍⠆⠀⠀⠀⠀⢩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡼⠖⠀⠀⠀⢋⣶⡄⠓⡀⠉⠳⢦⡁⢀⠀⢸⡟⠀⠈⠀⣸⠁⡂⢹⣇⡀⠂⣠⡈⣰⠛⣀⠀⠿⣤⠀⢄⠀⠀⠀⣠⠞⠁⡄⣠
⠀⠀⡄⠀⠀⠀⠀⡾⢠⣾⠃⢲⣶⣟⠀⠈⠁⣿⠀⠀⣠⣤⣄⠙⢦⡀⢨⡗⠂⠔⠸⢷⣈⣱⡞⢋⠀⣤⠼⠈⢉⡴⢇⠀⠂⠀⠀⢸⠁⠀⣐⠁⠀⠈⠓⠹
⠀⠀⡧⠤⠔⠀⠤⢇⣼⠟⠀⣿⢿⣿⠚⣤⠀⠙⣧⡀⢀⠋⠀⠛⠲⠷⣌⡛⠛⠛⠛⠂⡉⢡⡀⣹⣶⠏⠠⢠⡾⡇⠀⢣⡾⠦⣀⠈⣦⠀⡉⠠⠤⠤⠄⣸
⠀⠀⠃⠀⠀⠀⣴⣾⠇⠀⠀⣹⢿⣿⠐⢸⡄⠀⠈⢷⡀⠻⣷⣄⡀⠀⠈⠙⠛⠧⠼⠶⠷⠾⠿⠿⠟⠓⣐⠿⡄⠈⠒⡋⠀⠞⠛⠛⡤⠟⠀⠀⠀⠀⠀⢿
⠀⠀⡆⠀⠀⠈⢻⠋⠀⣤⠀⠇⢸⣿⠀⠈⠀⠀⠀⠈⠳⣄⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠚⠟⣇⠈⡖⠀⠀⣾⠀⠘⣾⠤⠀⠦⠀⠀⠀⠀⣸
⠀⠀⡇⢠⠀⠀⠇⢀⡴⠉⠀⠃⣼⠇⠀⠀⢸⡀⠀⡀⠀⠻⣆⣀⠈⠛⢿⣶⣄⡀⠀⠀⠤⠄⢀⣀⣀⡀⠀⡈⠓⠀⡀⢸⣿⣧⣀⡀⠀⠋⠀⠀⠀⢀⠀⢨
⠀⠀⡁⠘⠆⠀⣀⡌⠁⠀⠁⠀⣿⠀⠀⠄⠀⣷⠀⠹⡀⠀⠙⢾⡦⠀⠈⠻⣿⣿⣷⣤⣤⣤⣴⡾⠋⣡⡞⠃⣠⡾⠃⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⢼
⠀⠀⠟⠃⠘⠃⢸⠀⢀⣿⣠⡄⢩⣷⡄⠀⠀⠘⣧⠀⠀⡀⠀⠈⠷⡼⢆⡀⠈⠙⠷⠾⠟⠉⠁⢀⣼⡟⠀⣠⠁⠘⠃⠸⣿⣿⠏⠠⠖⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠎⠀⠈⠁⠀⠶⠾⢻⣿⢀⡄⢻⣷⠀⠀⠀⢹⣄⠀⠘⠀⠀⠀⠈⠺⢏⠂⡀⠀⠀⠀⡀⠀⢠⡿⠀⡄⢙⡂⠀⠀⠁⠈⢡⣤⡀⢀⠀⠀⠀⠞⠁⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣹⣿⣆⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠈⠀⠉⠀⠈⠀⣈⣡⠏⠱⠀⠀⠀⣠⣌⠟⠻⢮⣧⣆⣰⠇⠀⢀⣿
⠀⠀⠇⠀⠀⠀⠠⠀⠀⣰⠊⠙⢿⣿⣿⡟⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⡏⠀⢠⠀⢠⡎⠁⢈⣅⢠⣼⠋⠙⢿⡎⢉⠉⢻
⠀⠀⠄⠀⠀⢠⠆⣠⠎⡉⠁⠀⠀⠙⢿⡇⠀⢆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠒⠋⣠⣼⠟⠀⢠⡞⠂⠺⣁⠀⠸⢧⣸⣧⡀⢀⠸⢅⣸⣇⣤
⠀⠀⠆⠀⢸⡅⠀⠹⡄⠁⠤⠀⠘⠇⣠⠀⠀⠘⢄⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠠⡾⢂⠀⠛⣷⣤⣤⣠⡄⠀⠀⠀⢤⡄⠀⠆⢸
⠀⠀⠂⠀⠃⠰⣦⡄⠈⢑⣆⣠⣤⡄⢸⠀⠀⠀⠀⢂⠀⠀⠀⠄⡀⠀⠀⠀⠀⠈⠉⠿⠿⠛⠉⠀⠀⣠⠀⣷⠈⡆⠀⠸⠁⢘⡁⢀⠀⠄⠀⠀⠉⡀⠀⢘
⠀⠀⠁⠐⠂⠄⠘⢷⠟⠛⠋⠉⠀⠀⢸⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢱⡄⠀⣦⠎⠁⠐⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⢾⣧⣀⡀⣀⣄⠀⠀⠸⢂⡀⠀⠀⢮⠀⣤⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⢀⡜⠀⠀⢸⠖⢲⠆⠀⠐⠛⠁⠀⠀⠀⣦⡀⠀⡤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠉⠁⠀⢠⡆⠈⠷⠀⠀⠆⠀⡏⠑⣄⣀⢀⠀⠀⠀⠢⠀⠀⠀⣠⡞⠀⠀⠀⡞⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠂⢀⡄⠀⠀⠸⠁⠀⠀⢆⠀⠐⠀⡇⠸⠟⠉⠉⠻⠷⣤⣀⠀⠀⠈⠀⠀⠀⢀⡰⢿⠄⠀⡅⠀⠁⠀⠀⠀⠉⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡄⠀⠀⠀⠐⡀⠀⠀⣀⣴⡄⠀⡇⠀⣿⡟⠳⠦⣤⣤⡾⠛⠙⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⣁⣀⣀⠀⠠⠤⠤⠤⠀⠀⠀⢰⣿⣟⠀⢱⡄⣠⠀⠀⢹⣿⠀⢀⠀⠀⠿⣿⠀⠀⠘⠁⡇⠀⢸⡆⠘⣷⠀⠀⡀⠤⠛⠀⠓⠀⠀⠤⠤⠤⢀⡀⠀⢨
⠀⠀⣙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⠁⠈⠁⠀⠦⠀⠀⠛⠀⠸⠀⠀⠂⣿⠀⠀⠀⠀⢱⠀⢸⡇⠀⢻⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠄⠀⠀⠀⢳⣄⠀⠀⠄⡇⠀⠀⢹⡀⠀⠀⠀⢸⡀⠈⣷⠀⠀⢻⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠒⣰⣤⡀⠀⠀⢸⣿⠟⠉⠀⣷⠀⠰⣿⣧⠀⠀⠀⢸⠃⠀⣹⣦⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠞⠛⠁⠙⠁⠶⠚⠛⠦⠤⠴⠿⠀⠀⠿⠗⠀⠀⠐⠚⠓⠘⠛⠹⠶⢶⡴⠆⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⣠⡶⢶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣉⢶⣷⣶⠂⡉⠑⠄⡀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡎⣠⣤⡤⣅⠀⢹⣿⣷⡁⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢰⣿⠫⣿⣷⠀⢾⡿⠻⢿⠊⠀⢀⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣗⡀⠸⠃⠀⠀⠀⠄⣦⠀⠀⣾⢻⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢹⣿⣿⡷⠋⡰⠊⠙⢱⠀⠱⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢙⣋⢔⡠⠃⠀⠀⡨⠁⠀⢹⢏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⡉⠀⡚⠁⠀⡀⢴⣮⠀⠀⢀⣜⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡤⣤⡾⣅⠈⠉⠳⣄⡺⡗⢤⠌⣢⡤⠞⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠓⢒⡶⣶⢄⠀⢀⡈⠑⠻⠱⠿⠉⠙⠛⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣀⣀⣜⢿⢤⣦⡏⠘⠋⡛⢒⣂⢊⣤⣿⠀⣿⡁⢀⣶⠄
⠀⠀⠀⠀⠀⢀⠤⣒⣁⠤⢐⣋⢁⠼⠀⣙⣧⣛⡛⣿⣈⡟⠀⣉⡵⢖⠜⣰⣿⣃⡀
⠀⠀⣀⠄⠊⠀⢎⢀⠀⠀⢀⣀⠏⢐⠝⠂⠀⠈⣉⣀⣀⡤⢋⣀⠔⣡⡞⢁⣤⣾⠷
⢰⡉⠘⠠⠤⠄⠠⠀⠈⠉⢀⣀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣿⡾⢟⡽⠋
⠀⠀⠀⣩⠝⠃⠐⠐⠒⠀⠄⠤⠀⣀⣀⣀⠀⠉⠉⠁⣁⠴⣒⣿⢟⣭⡾⠋
⠀⠀⠸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⢡⢾⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⢙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠀⠀⠑⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢻⠏⠉⠒⠺⠋⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠱⢄⠀⠀⠀⠈⠰⢌⡀⠀⠀⠀⠀⣠⡞⣩⠖⠁⠀⢀⠄⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢠⡶⢀⠑⢄⡀⠀⠀⠀⠉⠐⠀⠒⢛⣸⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠺⡃⠀⣈⠠⢄⠀⠀⠀⠀⢀⠜⠁⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠶⡥⢀⠂⠟⠢⢠⡴⠁⠀⠀⢀⡔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠑⢄⠚⡇⠐⠖⡀⢃⠀⢀⡴⠃⠈⠢⡁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠃⠂⠤⠀⢑⣤⡰⠆⡀⠈⠛⢩⣦⡀⠀⠆⠈⠑⠄⡐⠠⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡤⠏⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⡀⠈⠳⡀⠛⣀⠚⢁⡝⢦⣀⠀⠀⠀⠀⠐⠠⠀⠀⢀⡴⠊⠀⠀⡴⢊⡀⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠁⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡚⠲⣌⡰⢤⡄⠨⠈⠕⢤⡀⠀⠀⠀⠀⠈⠁⠀⠀⣴⡼⡄⠠⢘⣏⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠞⠛⠿⣳⣞⠤⠰⠷⣀⠈⠒⢄⡀⠀⢰⢀⠄⠚⠃⣤⠂⣹⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠂⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠴⠊⠁⠀⣄⡴⠟⢡⣑⢄⠂⢀⠰⣿⢛⣈⠒⠼⠇⠲⠶⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠉⠁⠉⠓⢲⠒⠤⠒⠋⠀⠀⢀⡠⠖⠻⠐⢿⢈⣡⠞⠛⢦⣜⡋⢸⡄⢀⡘⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⣼⠀⠈⠀⣴⠂⢄⠄⢀⡀⠀⠀⠀⠀⢸⡄⢀⡠⠐⠋⠀⠺⢖⣤⠞⠋⠀⠀⠀⠀⠈⠻⣦⣀⠛⣁⡴⠋
⠀⠀⠀⠀⠀⠀⣿⠠⠻⠴⠉⢠⣤⡀⣼⠃⠨⠈⣒⡐⠾⠛⣉⠉⠰⠖⢋⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠤⠭⢠⣄⡐⠖⠀⢉⢀⢠⠠⠫⡅⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠲⣬⣤⠴⠛⠁

⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢲⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿
⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⣴⣿⣿⣷⣾⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣼⠟⢒⡆⠀⠀⠀⠀⣀⣀⣄⣀⣤⣾⡷⢿⣿⣿⡿⠟⠉⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣄
⡟⠀⣿⣵⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣄⣨⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠿⢿⡿⣷⡀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣟⠛⠛⠛⢙⡃⠀⠀⢁⣿⣿⣿⣶⣶⠶⠆
⠀⢠⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣟⠁
⣴⡾⡗⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀
⣽⠟⢿⣶⡆⠀⠀⠀⠀⠀⠀⢸⣟⣹⣿⣟⠁⠛⣿⡏⠉⠻⣿⣿⣿⣧⣀⡴⢾⣿⣷⣴⣾⢿⡿⣿⣿⣿⡿⠛⠹⢿⣟⢾⣿⣿⡇⠀⠀⠀⠀⠀⢦⡻⠄
⡟⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⣾⣽⣶⣤⣭⣳⣠⣼⠺⣿⡟⣹⣿⡦⣴⣿⣴⠿⠇⣯⣿⣿⣫⣯⣤⠠⣤⣶⣛⡮⣿⡻⠀⠀⠀⠀⠀⠀⢾⣷⡀
⠤⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⢠⣽⣿⣿⡿⣏⣾⡟⢿⣧⣿⣻⣾⡀⢈⣛⢿⣿⣿⣿⣿⠿⢫⣙⢿⣿⡿⢛⣿⣷⣼⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄
⡿⠂⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣟⣺⡿⢧⣌⢁⡀⠀⢿⢿⣿⣿⣶⣾⣿⣿⣟⡍⣤⣴⣿⣿⢛⣅⣀⣿⣧⣆⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠓⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡽⠧⢥⠡⣟⢢⣙⣿⣿⣿⣿⡿⣿⣿⣿⠿⠯⢽⣿⣿⣿⣿⣿⣈⣮⣿⠵⠼⣿⠵⠶⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣌⣸⣶⣠⣿⡶⠿⣿⠿⠛⢛⣉⡉⢰⣿⣿⣿⣿⣿⡷⠀⠀⠙⠻⠿⠷⣷⣿⣾⣮⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⣿⣿⡿⢀⣴⣇⠀⠀⠀⠀⢙⣿⣿⣋⣉⣁⣸⣟⡏⠀⠘⣛⡏⠀⢀⣉⣭⣿⣿⣿⣿⣿⣶⣄⢠⣀⣈⣿⣿⣻⣿⡿⣿⣾⣿⣿⠓
⢸⣿⣿⠇⣾⣿⡿⠀⠀⠀⠀⠀⠉⠛⢿⣟⠻⣿⣷⣶⡶⣶⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡾⠿⠋⠀⣭⡉⠉⠉⢁⣘⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀
⣾⣿⣿⣸⣿⣿⠇⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⢿⣿⣷⣗⣷⣾⣿⣿⣿⣿⣿⡿⠏⠀⠀⢀⣤⣤⣤⣤⣤⡿⣿⣿⠋⠟⣡⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⠀⣿⢿⣯⢹⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⡿⠿⣿⡟⣹⣶⣿⠟⠁⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠀⠰⠆⠀⠀⣿⠀⡙⢾⣿⠟⣿⣿⠁⡘⣿⢿⠋⣼⣯⣴⣷⡟⠩⣿⣿⣿⠀⠐⠋⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢶⡦⠀⠀⣠⠀⣿⠀⣀⣼⣿⣿⣿⣿⣾⡇⢹⠘⡀⣸⣽⣿⣿⣿⡿⠋⢹⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠤⠀⠻⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣱⣿⣿⣿⣿⣿⠄⠀⢸⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⣶⣿⡄⠈⢹⣿⣿⣿⡿⣿⣿⣿⠀⢿⣿⣿⠟⠉⠃⠀⠀⣸⣿⠈⠛⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿
⣿⣿⣿⣿⡇⢀⣴⣦⡀⠀⠀⠀⠀⠀⠃⠀⠀⠻⡿⠃⠀⠘⣿⣿⣿⡇⠘⣿⣿⣶⣾⡿⠁⠀⠀⢀⠀⠀⣻⡿⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟
⣿⣿⣿⣿⣧⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⣿⣿⣿⡇⠀⣿⢿⣿⠏⣹⣷⣷⡞⠁⠀⠀⠿⠁⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⣿⡇⠀⣿⡇⠁⠀⠹⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠉⠉⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⠾⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠁⠀⠀⠀⠔⢂⣈⡭⠥⠤⢤⣀⡐⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡷⠋⠀⠀⣀⣤⠴⠄⠒⠋⠉⠁⠀⠀⡄⠀⠀⢉⠛⠆⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡛⡴⠖⠒⠉⣁⣀⣀⣤⣴⣦⣾⣴⣿⣿⣿⣷⣷⠟⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠯⢱⣤⠐⢠⡉⢹⣿⠟⠉⠉⠀⠉⠉⠋⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⣷⠂⠀⠀⡜⠁⠀⣀⠤⠴⠤⢄⠀⠀⠒⢓⣛⣒⣒⣚⣛⡒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣒⣸⡆⠂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠉⠛⠋⡩⡭⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣨⢿⠞⢫⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠰⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⡿⠀⢀⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⡄⠀⠀⠀⠀⢀⡾⠀⢰⣧⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⡿⠟⠿⠷⠷⠼⢼⠟⠁⠈⢨⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠂⠀⠀⠀⠀⠀⠘⠀⠈⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⢚⢼⠀⠳⠀⢾⠆⣠⣤⣶⣶⣤⣴⣦⣤⣄⡀⠀⢠⠖⠙⠠⠌⠕⢆⠀⣇⠀⠀⠀⠀⢈⡇
⠀⠐⠋⠓⠋⠛⠛⢌⡌⣄⡰⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠱⣌⣂⣁⣐⠤⡎⡔⣡⣤⣭⣭⣥⣤⣑⠆
⠀⠀⢀⠌⢩⠗⠠⠤⢉⣉⠀⢠⠖⢯⠿⢨⣿⣿⣻⣻⣟⢟⣿⠹⠿⣄⠱⣄⣀⣀⡠⠃⠉⢙⣛⣛⡛⠛⠛⠉⢩
⠀⠰⠁⡰⠁⠀⠀⠀⣀⡠⠬⠆⠓⠄⡑⠒⠡⠥⠈⠀⠁⠀⠭⠔⠊⡠⢇⡀⢄⡀⠀⠀⡘⠥⣀⣀⣈⠇⠀⠀⣠
⠀⢸⠀⡁⡔⠂⢉⣁⠠⠄⣒⡗⠀⠀⣂⢌⠉⢑⣒⠒⠒⠒⢂⡉⠁⠀⢯⠀⣀⠗⠒⢄⠫⣛⠲⠶⠶⠶⢖⡫⠇
⠀⠀⡇⡇⢈⠭⠐⣂⣈⠥⢔⣾⠀⣎⡸⠁⡴⠁⠈⠓⠒⢲⡘⢋⠤⠤⠠⠄⣘⠢⠠⠋⠐⣷⡈⠉⠉⠉⢀
⠀⠀⠸⢐⠀⣭⣛⣷⣬⠯⠟⣋⡈⠚⠃⢰⠅⠀⠀⠀⠀⠀⠃⢃⠀⠀⠀⠀⠀⠑⡢⣄⡀⢱⠳⠲⢄⡀⠺⠃
⠀⠀⠀⠙⢓⣈⢉⠀⠀⡴⠫⡑⠈⠳⡀⠸⣀⣀⣀⣀⠠⠔⠁⠈⠢⣄⠆⠀⢰⡾⠋⢻⡇⠀⠀⠐⠑⢌⠢⡀
⠀⢰⢎⠉⠙⣦⣠⡵⣄⢇⠀⠈⠀⢠⠇⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣬⣑⢤⣘⠧⣤⡺⠗⢠⠘⡀⠀⠄⢣⢡
⠀⠀⠣⡻⡋⠉⢳⣄⣬⢦⡑⠒⠛⠁⢰⣿⠶⣭⡰⡀⢶⢆⢸⣁⢻⣼⣿⡆⠈⠉⠀⢀⣠⣤⠣⡈⢆⠀⠀⢺
⠀⠀⣠⡑⣜⢟⠋⠙⣦⣀⡸⡆⠠⡦⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⢀⣠⣴⡾⠟⢋⠭⠰⠈⠒⠷⣤⡞
⠀⠀⠙⠁⠈⠢⣑⡨⠭⠒⠊⠁⠀⢀⡤⠒⢟⠉⢝⠉⢛⠲⣄⠀⡤⣒⠽⠟⠋⠁⠀⠀⠸⣀⠟⠉⠒⢄
⠀⠀⠏⢹⡎⠑⠆⢀⣀⠀⠸⠳⡀⡎⠁⠀⠠⣖⡚⣤⠀⡀⠈⢣⠈⠀⠔⠂⠀⢰⠒⢦⡀⠸⠀⢄⠀⠀⠑⡀
⠀⢀⠃⢸⠃⣸⠀⢀⠂⡇⢰⢠⠃⡧⣀⣀⠠⠈⠙⣛⠄⠀⢠⢺⠀⢠⠒⠒⠒⣺⠒⠒⠛⣲⠑⢄⠀⢠⡤⣁
⠀⢨⡁⢜⠀⡌⠀⠈⠦⠀⠈⠋⠀⠐⢄⠀⠱⢄⡀⠔⠐⢒⡡⠃⡎⠈⠑⢦⣄⡿⠄⠀⠠⣿⠀⣠⡌⢩⡡⠴⠃
⠀⢸⢀⡇⠐⢣⠒⢈⣉⣉⣩⣉⡁⠒⣄⡉⠐⠒⠒⣒⣊⠁⠀⠀⠈⡖⡖⠒⠀⠛⠒⡶⠴⢟⢢⡈⠀⢀⡤⡀
⠀⢸⣰⠂⣸⠈⡄⠀⠀⠀⠀⠀⠀⢠⢳⢹⠀⡴⢍⡂⠈⠫⣲⡄⢰⢠⠁⠀⠀⠀⠀⡇⠀⣨⠤⠇⢰⡁⠀⢳
⠀⠀⠉⢒⡂⠤⠵⡄⠀⠀⠀⠀⢀⣞⠥⢂⠸⡀⠀⠈⠁⠉⢀⡕⡌⠘⡄⠀⠀⢀⡴⠀⠀⠇⡤⠔⡆⠨⣍⣁
⠀⠀⠀⠘⠦⣤⣐⡻⣷⣶⣶⣾⢿⣂⣤⡤⠇⠈⠑⠢⠤⠔⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⣰⠀⠑⠤⠇⡆⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢦⣀⠀⠩⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠁⠀⠀⠐⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢴⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠋⠀⠸⡖⢄⢸⣿⣿⣿⣿⣿⡗⠀⠀⠀⣀⣰⣦⣄⠀⠀⠀⠀⢻⣿⣶⣦
⠰⠖⠀⠀⠀⠀⠈⠛⢠⠀⢀⣠⣦⣤⡀⣠⣿⣿⣶⣶⣿⣿⣧⡀⠀⢸⣿⣿⣿⣿⣷⣶⣣⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣅⣈⠉⠙⠛⠛⠻⢿⣿⠿⠿⠿⠿⠆⠈⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣿⣛⠃⠀⠀⠀⠀⠀⠀⣴⣆⢹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣷⣶⣦⣤⣶⣶⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠠⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠛⠏⠉⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠙⠻⣿⣧⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⠻⠿⠋⠀⠀⠀⠀⠀⠀⠈⠛⢿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠛⠁⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠈⠟⠛⠿⠿⣿⣷⣶⣤⣀⣹⣿⡶⣾⣿⣿⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣴⣾⣷⣶⣮⣽⣿⣿⣿⣿⣧⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣌⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣤⣦⣴⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⡀⠀⣀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢻⣦⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣾⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠙⠻⢿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧
⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡄
⠀⢹⣿⣷⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⠿⣿⡿⣿⣿⣿⡿⠟⠿⢿⣿⣿⣋⣀
⠀⠀⢻⣿⡄⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣿⣿⣆⣿⣿⣿⣇⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠙⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣙⣿⡟⠉⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣋⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⠟⣁⣴⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣵⣾⠟⠉⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡙⣏
⠀⠀⠀⠀⠀⠀⢀⡄⠂⢠⣄⣀⣠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢸⡅
⠀⠀⠀⠀⠀⠀⢽⣧⣄⠀⠈⠙⠾⠃⣤⢀⢿⡿⠀⠀⠀⠀⣦⣸⣄⢻⡶⠒⠒⠂⠀⠀⣶⠄⣀
⠀⠀⠀⢀⣠⠄⢤⠈⠈⠓⣤⣴⡂⠲⠿⠟⢠⡞⠀⠀⠀⠀⣿⡟⠻⢦⣄⠀⠀⣀⠠⣻⠟⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠂
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠐⠋⢀⡀⠀⠑⣂⡤⢴⡆
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠈⢓⣦⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠃
⠀⠀⠀⠈⠓⠤⠤⠼⣆⢀⣀⠁⠀⠠⣤⡶⠁⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠯⠰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣴⠒⠲⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠂⠈⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⠀⢀⠟⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠾⢹⠏⠻⠀⠀⠀⠀⠀⠀⠸⢃⠈⠀⠓⠐⠀⠊⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣀⣀⣍⣩⢐⢋⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠆⢀⣠⡤⠀⣄⠀⠀⠀⠀⠀⢴⡖⢮⠀⠀⠉⠉⠉⠉⠉⠁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠀⠐⠆⢶⡞⢻⡿⠁⠀⢹⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢀⠀⠀⡠⢲⠀⠀⢀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢞⡃⢾⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⢸⡓⠢⡄⠙⠒⠰⡋⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢘⡄⢻⣇⣀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⢿⠥⠛⠃⠀⠊⠁⣹⠡⣿⠗⠔⠀⠀⠀⠀⠀⢸⣷⡀⠀⣆⣸⣇⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣠⣿⣴⠖⠀⠀⠀⠀⠀⠀⠙⠷⣾⠷⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠙⠀⠀⠀⠘⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠄⠠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣬⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣍⣛⣹⠛
⠀⠀⠀⠀⠈⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⣀⠀⠀⠼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⣀⣀⡤⠔

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠻⠿⠛⡻⠿⡿⢛⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿