Finding Nemo Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡴⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡞⢸⠏⠠⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡿⠀⠀⢠⠁⠐⠀⠀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠆⡰⢁⠂⡼⠀⠈⠗⠒⠛⠛⢻⡆⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⠾⠶⠷⣾⣴⣇⣀⡜⡀⠀⠀⠀⢸⡇⣰⠋⡠⠋⠉⣻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠁⠀⠈⠉⠙⠓⠶⣤⣙⠻⢿⡳⢦⣀⠀⡼⢠⠇⠀⠀⢀⠜⠁⠀⢙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⡄⠉⠳⣦⡉⠳⣌⠻⢤⠎⠀⠀⠀⠀⠀⡠⠞⠉⠘⣿⣷⡀
⠀⠀⠀⠀⠀⣠⣞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠁⠀⠀⠀⠀⠀⠀⣀⠴⠚⢻⣿⡇
⠀⠀⠀⠀⣰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠀⠐⠢⣀⠀⠀⠀⠹⣆⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣿⡇
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⣠⣤⠄⡀⠈⢢⡀⠀⠀⠈⢧⡀⠳⡀⠀⠀⠀⠀⠀⣀⣀⣸⣿⠃
⠀⠀⢰⠇⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⣿⣿⣧⣠⣾⣆⠀⢇⠀⠀⠀⠀⢳⡀⢳⡀⢠⠤⢄⣀⣀⣀⡾⠋
⠀⢀⠞⠉⠁⠀⠀⠀⠉⠒⢄⠀⠀⠀⢰⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⡼⠀⠀⠀⠀⠀⢳⠀⣇⠸⠤⠀⠒⠚⠓⠒⠒⠒⢦⣄
⢀⡏⠀⠀⢀⣴⣾⡿⠓⢤⠀⢣⠀⠀⠈⢆⠀⠀⠀⠙⠻⠿⠿⠋⢀⡴⠁⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣿⡇
⢸⠀⠀⠀⢸⣿⣿⣷⣶⣾⡇⠀⠄⠀⠀⠀⠑⠦⢄⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣸⠀⡏⠀⠀⠀⠀⠐⠠⠤⣀⣀⣰⣿⠇
⠸⡆⠀⠀⠘⣿⣿⣿⣿⡿⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠁⠀⠀⠀⠀⢄⡀⠀⠀⢉⣿⡟
⠀⠙⢄⡀⠀⠀⠉⠉⢉⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠀⢀⡾⢠⣷⠦⡀⠀⠀⡀⠀⠈⠙⢲⣾⡿⠁
⠀⠀⠈⢿⡙⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⠐⡆⠀⠀⠀⠀⢠⠞⣱⠟⠁⠀⠙⣆⠀⠀⠓⢤⣠⣾⡿⠁
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠊⠁⢰⠅⣠⠃⠀⠀⣀⣴⣯⠞⠁⠀⠀⠀⠀⠈⠳⣤⣤⣾⣿⠟
⠀⠀⡠⠄⠂⠉⠷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠆⠀⠲⠚⠋⠁⣀⣤⡾⠿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠸⠄⠀⠐⠧⠀⢨⠛⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⢟⡛⠁⠀⢀⠀⠈⢱⣦
⠀⠀⠀⠰⣤⣀⣀⡼⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠰⣄⡀⠈⣏⠢⢤⣤⣥⠶⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⣿⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣠⡞⠁⠀⠀⠘⠉⠀⠀⣤⣯⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠿⠄⠀⠀⠀⠀⠀⠈⠉⠻⣝⠳⢶⣋⢀⣠⠤⠖⠂⠀⠀⠈⠉⠛⢿⣿⣦
⠀⠀⠀⣠⠴⠖⠲⠯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⠻⣦⡙⠻⣄⣠⠤⠶⠒⠚⠉⠉⠁⠀⢻⣿⠇
⠀⢠⠎⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⣀⠤⠴⠤⠤⣀⠀⠈⠀⠘⣷⡄⠙⢧⣤⠤⠶⠶⠒⠒⠒⣶⠿⠋
⠀⡏⠀⠀⠀⣴⣿⡏⣲⡀⣷⠀⣠⠎⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠸⡼⡄⠈⢷⡄⠀⠀⠀⣠⠞⠁
⠀⢧⠀⠀⠘⣿⣿⣿⣿⢇⡟⢀⡏⠀⠀⣠⣶⡶⢦⡀⠀⢹⠀⠀⠀⣧⢳⠀⠸⣿⡏⠉⠉⢿
⠀⣸⠓⢤⣀⣈⣛⣛⡽⠋⠀⠈⣇⠀⠰⣿⣿⣷⣾⡧⠀⢸⠀⠀⠀⣿⢸⡄⠀⢿⣷⡀⠀⠀⠳⣄⡀
⠀⣿⢀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢦⡀⠻⠿⠿⠟⠁⣠⠏⠀⠀⠀⣿⢸⡇⠀⢸⢸⣧⣠⡤⠄⠈⢿⣦
⢀⡿⠋⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠓⠒⠒⠒⠋⠁⠀⠀⠀⢰⡏⣸⠀⠀⣸⠀⣿⣆⣀⡀⠀⠀⣿⡇
⡟⠦⠈⢲⡄⠀⠀⠀⠒⠶⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡏⢀⣴⠏⠀⣿⢿⠀⣀⣠⣴⠟
⢻⣌⣂⣾⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢡⡞⢠⣿⠋⠀⢰⡇⠈⣯⡉⠉
⠀⠈⠙⠛⠛⢶⣄⡀⠀⠀⣾⡿⠉⠉⠓⠶⣤⣀⡀⠀⣠⡾⠋⣠⠟⠀⣼⡏⠀⢀⣿⠁⢠⡏⢹⡦⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣿⡗⠚⠒⠒⠀⠀⠀⠉⠉⠙⠛⠋⠁⠀⢠⡿⠀⢀⡾⠃⢀⡾⠁⢸⡇⠀⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡤⠤⠶⠖⠒⠂⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⠟⠁⣠⡾⠁⢠⡿⠁⠀⠀⢀⣀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⢀⣠⠤⠂⠀⠀⡀⠀⣠⣋⡴⠚⠁⣀⡴⠋⢀⣴⡿⠁⠀⠀⠤⣀⠀⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡉⠀⠀⣠⠔⠋⣠⠔⠉⠙⠳⢦⡞⢋⣠⣴⠿⠋⠀⠀⠀⠢⣄⠀⠉⠲⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠿⠷⠞⠋⠁⠀⠀⠀⠀⠀⠻⣏⠉⠀⠀⠀⠀⠀⠢⡀⠀⠙⢦⣀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢰⡀⠀⢆⠀⠘⢦⣀⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣧⡀⣈⣦⣤⣾⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⠤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢩⣤⠟⠒⠒⢄⠈⡆⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢻⡃⠀⣴⣧⠄⡖⠁⠉⠒⢄⠀⠈⢯⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠣⣄⣈⣉⠜⠀⠀⠀⠀⠀⢣⠀⠀⢧⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠘⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢳⢸⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⠠⠠⠂⠀⠀⠀⢸⡄⡇⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⠃⠀⠀⡰⠁⡀⠀⠀⠀⠀⣀⡼⠖⢟⣛⣒⣭⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⢀⣀⣠⠴⠋⡴⠃⠀⠀⢠⠃⡌⠀⢰⡤⠒⠉⢀⣀⣬⡴⠾⠿⠃
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⡠⠊⠀⠀⠀⠀⢸⠀⡧⠔⢁⡤⠒⠈⠁⢸⢀⡇
⠀⠈⢧⣉⣑⠢⢄⢠⠒⠦⠤⠤⠴⠚⠉⠀⠀⠀⢀⠀⠀⡸⢊⠤⠊⠀⡇⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠉⠉⠓⠦⢌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡀⠔⣇⠀⠑⠤⠁⠀⠀⢠⠃⡎⠀⠀⠀⡴⡫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⣀⠜⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡸⠋⠁⠀⣠⠎⣊⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠀⢀⣀⣘⠦⠴⠊⠁⠬⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣒⣤⣤⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⢤⣀⣀⣀⣀⣀⣀⡠⢤⠒⠫⣀⡏⠀⠀⠈⠑⢦⡈⡑⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠮⠭⣭⣭⣤⠤⠬⠖⠊⠁⠀⠀⠀⠀⠀⠀⠱⡌⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠈⠉⠛⠶⠶⢤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⠀⠄⠀⢀⣡⣤⡦⡀⠀⠀⠀⠉⠀⠂⠀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠌⠛⠉⠉⠉⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠈⠉⠛⠁⠠⠁⠀⠂⠀⠠⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠉⠀⠈⠉⠛⢿⣴⣯⠆⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡇⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠑⠢⣄⡀⡀⢀⣀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢒⣠⣦⣤⡀⢀⡀⠀⠠⣄⠀⠀⠘⠿⠈⣻⠛⡩⠛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣿⣿⣿⣿⣿⣿⣶⡈⠳⣤⡀⠈⠀⠀⠒⠛⠁⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠻⠓⠈⠈⠉⣂⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣸⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⢬⠤⣀⠀⠈⡴⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠊⠀⠠⠀⣽⡆⠙⣤⣾⠃⠆
⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠷⠾⣻⠀⠐⣆⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢄⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⠿⢿⣿⡇⠀⠀⠀⠁⠐⠤⠄⠐⠁⠀⠀⠀⠀⠀⠄⠂⠒⠀⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⢶⣶⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠈⠁⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠐⢤⡀
⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣦⣀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠻⣿⣶⣤⣤⣄⣀⠀⠀⠈
⠀⢇⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⣠⡶⣱⠛⠀⠈⠛⠿⣿⣷⣶⣴⣾⣿⡿⠀⠀⠀⠀⢀⡬⡿⣿⣿⠀⠈⡆⠀⠈
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⣴⠟⠉⢰⡏⠀⠀⠀⠀⠑⠦⣬⠉⢻⡟⠋⠀⠀⢀⠔⠈⠀⠀⠀⠈⠛⢁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢠⠟⠀⠀⠀⠀⠀⠀⣠⠞⡁⠛⠀⠀⡱⠄⡨⠆⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣘⠃⠀⠀⠀⠀⠀⢠⡏⠰⠁⠀⢀⠈⢠⠂⠀⠀⢀⠠⠄⠐⠚⣀⣤⡀⠸⣯⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⢸⠀⡆⠀⢀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡈⠻⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠁⠀⡌⠀⠀⡸⢀⠂⠄⠀⠀⢀⡀⠀⡀⠀⠀⢀⠙⣄⠀⠙⢦⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠄⠀⠀⠀⠰⠃⢨⡀⢠⠀⢠⠔⠁⡆⠆⠀⠀⢰⠁⣤⣶⣤⠀⢀⣥⣤⡗⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⣜⢠⠃⠀⠀⢰⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠿⢋⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢂⣀⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣈⠅⠀⠀⠀⠀⠀⠀⠈⠁⣤⢸⣇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⢠⢥⠆⠙⠢⠀⠀⠉⠳⣦⣤⣤⡤⠤⠖⠋⢬⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⣿⣒⣏
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠁⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣔⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠔⢦⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠂⠀⢀⣴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠁⠈⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⣶⠵⠞⠛⠛⠳⣦⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡿⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⠇⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡜⢰⡿⠀⣾⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⡰⢃⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡼⠁⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⣧⡀⠀⢊⠀⣼⡏⢠⣿⠿⡛⢿⠛⣻⡿⣿⡿⠷⠀⡜⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⣿⣷⡀⠨⢰⣿⠁⣼⠃⠄⠘⠻⠛⠁⠘⢾⣶⡧⢼⡀⠠⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢜⣀⣿⡟⢠⣿⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢹⠀⡠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣹⣿⡇⢸⣿⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⢤⣤⡖⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⠢⣽⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠍⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣱⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠁⢸⣿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⣿⡄⠙⣿⣿⡄⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⢻⣇⠀⣿⣿⣷⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢸⣿⣿⣧⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⢿⣿⣿⣷⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠘⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⣿⡟⡏⠻⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠟⣸⠁⠀⠘⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡈⠭⠉⠁⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⠔⠀⠀⠀⠀⠀⡈⡚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠈⠀⢣⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢃
⠀⢠⡀⠀⠀⠀⠀⠀⠰⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠚⠄
⠀⠀⢻⣄⠀⠀⠀⢻⢦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠈⠢⣄⠀⡀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣷⠄⢀⣾⣷⡀⠀⠀⠀⣴⡇
⠀⡀⠀⠀⠀⠀⡉⠅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠂⠈⠙⠛⠃⠁⢀⠔⢹⡇
⠀⡇⠀⠀⠀⢀⠀⠄⢸⡇⠐⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠀⣸⡗
⠀⠁⠀⣀⣀⡌⣦⣀⣼⣿⠀⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡷⠈⠀⣀⡴⠋
⠀⡴⠋⠀⠀⠀⠀⠉⠈⢿⡀⠀⠘⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⡥⠶⠋⠁⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢤⠘⡄⠙⢦⡀⢰⡀⠀⠀⠀⠀⠈⠳⣄⡀⣀⡜⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡄⠀⠙⢦⣷⡀⠀⠀⠈⣄⠀⠈⠉⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡰⡄⠀⠀⠙⢧⡀⠀⠀⠈⠂⡀⠀⠀⠀⢀⡄⠴⠋⠙⠛⠛⠛⠃⠰⠆⠀⢠⣀⡞⠳⠞⠛⠛⢷⠀⠀⠈⠉⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣦⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡴⠋⠀⠀⠄⠀⠀⠈⠘⡣⡀⠀⠀⠀⠟⠉⠙⠖⠢⠄⠘⠋⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣤⣤⠴⠊⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⡄⠀⠀⠀⠀⠀⠘⡄⠐⢆⠀⢢⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠘⢄⠀⠀⠀⠀⠀⠠⡀⠘⡀⠀⠆⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣆⣤⣤⡀⠀⠀⠀⠀⠀⠘⡌⡀⢡⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⡦⠈⠻⣿⡷⠀⠀⠀⢀⠀⠀⠰⠀⠈⢧⠀⠀⠀⠆⠀⡇⠀⣄⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠁⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⠞⠀⠀⠣⣀⡤⠟⢉⡇⠀⠀⠉⠒⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠠⣤⡤⡤⠤⠤⠶⠶⠛⠁⠀⠀⠀⠀⠀⢠⠞⠀⠰⢯⣤⡴⠞⠁
⠀⠀⠀⢀⡀⠀⡴⠒⠆⣴⡏⠀⢸⣷⣆⠀⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⢠⠋⠀⢸⡄⠀⠈⠃⠀⠀⠀⠉⠉⠀⠀⠠⠂⢱⠀⠀⠀⠀⠀⠀⢤⡶⣌⣁⣤⣤⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⠀⠀⢸⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠈⠦⠠⠼⢥⣌⡀⠀⠑⢤⡀⡀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⡤⠖⠋⠀⠀⠀⠸⢷⣄⣠⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⠙⠛⠓⠶⡶⠟⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠠⠤⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠂⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢠⠔⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⡀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⢤⠤⠀⠀⠘⠦⣀⢀⠔⠀⠀⠀⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠢⣄⣀⣀⣀⣀⣀⠤⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⢦⠀⠀⠀⠀⠘⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡾⡀⠀⠀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣠⣴⣶⠷⠋⠀⠀⠀⠀⠀⢰⣿⠁⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠿⣤⡴⠋
⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢸⡇⠀⠀⠀⢠⡄⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⣿⢠⠀⢠⠈⣷⢰⡆⠀⣿⠀⠀⠏⢷⣄⣿⠀⡐⠀⠀⠀⠀⣿⡟⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢿⣄⣙⡅⢀⡧⢸⡇⢠⣿⣀⣾⣤⠟⠁⠘⠛⠀⠀⠀⠀⠀⠻⣷⣄⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣸⡧⠈⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣼⠁⣀⡤⠖⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣇⣀⠼⢁⡾⠋⠀⠀⠈⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⣴⠟⠋⠉⠙⢧
⠀⢀⡴⠶⠖⠛⠒⠒⠶⠦⣾⠥⢤⣄⣀⣠⣤⠟⠁⠀⠀⠀⠀⠀⣀⡀⣄⠀⠘⠇⣼⠃⠀⠀⠀⢀⡴
⠀⣎⠀⠀⠀⠀⢰⡄⠀⢀⡇⠀⠀⠀⠀⢀⣀⡀⢀⡴⢦⠀⣇⠞⠙⣷⠀⠀⢰⡼⠁⠀⠘⠷⠶⠟⠁
⠀⠈⠓⠶⠶⠶⠛⠁⠀⢸⡇⢀⠴⣦⢰⡏⣸⡇⣾⢀⠞⢀⣿⢀⣰⡏⠰⣨⠟⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡌⡰⠃⢸⣇⢉⡰⠿⣦⡤⠊⣿⠈⠁⠈⠁⠀⠀⠀⠉⡞⡂⠀⠀⠀⠀⠀⢀⡴⢤
⠀⠀⠀⠀⣠⠴⠶⣄⠀⠀⣿⠀⠻⠶⠈⠉⠉⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⡰⢋⡟⢀⡿⠀⣾
⠀⠀⡠⠊⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠇⠀⠀⠀⠀⣈⡁⠀⣀⠒⣷⡠⢺⡆⢸⡇⠀⣿⠃⢸⡇⠸⣧⡠⢿⡀⠀⠀⠀⠀⢀⡀⠤⡤⢄
⠀⠜⣠⠞⣀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣈⠁⢠⡄⠴⣆⡐⢩⡇⢸⣿⠀⣿⠁⣾⢀⢼⣇⡔⠛⠀⠘⠋⠀⠀⠀⢸⡇⠀⠀⣠⠖⠉⠀⠀⠈⣯
⠀⣼⠇⠀⣟⠀⡿⢀⡀⠀⡄⠀⣿⢀⡟⠀⢸⡏⠀⣿⠀⣾⣁⠼⠇⠀⠛⠀⠙⠋⠀⠉⠀⠀⣤⠶⠚⠛⠒⠒⢾⡷⠤⣴⣥⣤⣤⣤⣴⡶⠛
⢠⣿⣄⠀⠙⠊⠁⣾⠁⢸⡇⠀⣿⠸⣇⠀⠿⠇⠀⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣼⠁⡰⠇
⠀⠈⠙⠛⠶⣦⡀⢿⣀⡜⠷⠴⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣠⡤⠴⠛⠁⢠⠁⡆
⠀⠀⣶⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠐⠲⡄⠀⠀⠀⠀⠀⠀⡎⠀⠱⣤⠄
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠊⠀⠀⠀⠀⠀⠀⣸⠁⡶⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢠⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⠾⠋⠀⠋
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⣦⠤⠤⢄⡀⢧⠀⠀⠀⠀⢠⠖⠉
⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠘⢣⣶⠄⢱⠈⣳⣄⠀⠀⡏⠙⠒⠲⢤⡀⠀⠀⢀⡤⠒⠒⠢⠤⠴⠊⣹
⠀⠀⠀⠀⣜⠁⠁⠀⠀⠀⠀⢠⡉⠉⠘⢿⠁⢼⡆⢰⡃⡄⠀⠧⠄⣈⡷⠖⠉⢀⠀⠄⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠹⡤⣤⠀⠀⢀⢠⠞⡃⠀⢀⠾⣤⠀⡇⠀⠀⡌⠀⢄⠀⡉⣀⡀⠀⠂⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⢶⠀⢾⡷⡈⠀⠈⠀⡠⠶⢤⠄⡀⠤⠄⠈⠀⠀⠂⠀⠉⣼⠏⠒⣚⠛⠊⠉
⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⣀⡠⠊⠀⠀⣸⠃⣣⠀⠀⠀⠛⠀⢀⣰⠞⠁⠀⠀⠘⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢏⡉⠙⠛⠂⠉⠁⠈⠳⠤⣄⣀⣀⣀⣀⡠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣀⣀⠀⠈⠑⠒⠒⢂⡸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⣶⠵⠞⠛⠛⠳⣦⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡿⠀⣼⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⠇⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡜⢰⡿⠀⣾⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⡰⢃⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡼⠁⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⣧⡀⠀⢊⠀⣼⡏⢠⣿⠿⡛⢿⠛⣻⡿⣿⡿⠷⠀⡜⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡜⣿⣷⡀⠨⢰⣿⠁⣼⠃⠄⠘⠻⠛⠁⠘⢾⣶⡧⢼⡀⠠⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢜⣀⣿⡟⢠⣿⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢹⠀⡠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⣹⣿⡇⢸⣿⠀⠀⠀⠈⠒⠤⠤⠤⠤⠤⢤⣤⡖⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⠢⣽⣿⣧⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠍⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣱⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠁⢸⣿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⣿⡄⠙⣿⣿⡄⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⢻⣇⠀⣿⣿⣷⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢸⣿⣿⣧⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⢿⣿⣿⣷⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠘⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⣿⡟⡏⠻⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠟⣸⠁⠀⠘⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⠃⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠌⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⠃⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠀⠀⠀⡎⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠈⡄⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⠀⠀⠀⢡⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠡⡀⠀⠈⣆⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠄⠋⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢈⣄⠠⠼⠆⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢐⠃⠀⠀⠀⠀⠀⢀⠃⡀⠄⠂⠉⠁⠀⠀⠀⠀⠀⠁⠤⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡘⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⢳⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⡰⢣⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⡇⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⢃⠀⡁⠀⠀⠀⠀⠀⠀⡇⡰⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠀⠀⠈⢆⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢄⡰⠚⠁⠁⠀⠀⠀⠀⠀⠀⢳⠃⠇⠀⠀⠀⠀⣶⣿⣦⡀⠀⢘⣿⣷⡀⠀⠀⢄⡄⠀⠀⠀⠀⠸
⠀⠀⠀⡘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠏⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠈⡼⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠘⠻⠿⠁⠂⠀⠈⡁⠀⠀⠀⢀⠃
⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡿⠀⠆⠁⠀⠀⠀⠀⣀⣄⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡌
⠀⠀⠀⡇⠀⠀⠀⢢⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⢸⣿⣿⠇⠀⠻⠿⠁⢀⢀⡀⠀⠐⠒⠐⠀⠐⠒⠒⠠⠤⠤⠴⠶⠒⠛⠋⠁⠀⠀⡜
⠀⠀⠀⢡⠀⠀⠀⠘⣆⠀⠀⠀⠀⠸⠀⠀⠸⡄⠀⠀⠄⡈⠙⠛⠀⠀⠀⠀⠀⡌⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⣀⠘⠀⠀⢀⡞
⠀⠀⠀⠘⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠀⣀⠞⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉⡌⠀⠀⢠⠎
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⡤⠤⠒⠚⠁⠤⠴⠋⠀⠀⠀⠸⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⣰⠀⣠⠃
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠔⠀⠶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡔⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠁⢳⣄⣀⣀⣠⣤⡶⠟⢡⠞⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠈⠳⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠈⡀⠀⠀⠀⠀⠀⠀⡆⠠⠉⠉⠙⠋⠁⢀⠄⠁⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⠁⠁⠀⢠⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠳⡄⠀⠀⠀⠀⡀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠎⠀⢰⠆⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠘⡄⠀⠀⠀⠀⠂⠀⠀⢠⠀⠀⠀⠀⠀⡜⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠰⠀⠀⠀⠀⠀⠱⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠐⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠆⠀⠀⠀⠀⠀⢡⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊

⠀⠀⠀⠀⠀⠁⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠤⠔⠁⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠙⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣀⣠⠴⠶⠒⠚⠓⠦⢼⣦⡀
⠀⠀⠀⠀⠀⡀⠤⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡴⠟⠉⠀⠀⠀⠀⣀⣀⣀⣀⡩⠙⢦⡀
⠀⠀⠀⠀⠘⠀⠀⢈⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣠⠶⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠳⣄⠙⣦⣀
⠀⠀⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⡼⣿⡇⠀⠀⠀⠀⠀⠀⣠⠟⢡⡾⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⣬⠿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢻⣿⡀⠀⠀⠀⢀⡾⠋⡰⠋⠀⠀⣠⠖⠒⠒⢤⠟⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠛⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣧⠀⠀⢠⡞⢁⡾⠁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠛⠳⣦⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣿⠸⣇⢠⠋⢀⠞⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣠⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡄⢻⡇⣠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠈⢳⡀
⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⢸⣇⠀⣸⣿⠣⠈⢷⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⠀⢸⣷⣶⣄⠀⠀⢡⠀⠀⢀⢠
⠀⠀⠿⣿⣦⡀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠘⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⢿⣿⣿⣿⣿⣿⠇⠀⠀⢀⠄⠀⢸⣿⣿⣿⠀⠀⢨⠀⢠⠎⣤
⠀⣾⠀⠈⠻⣿⣄⠀⠀⠀⠀⢸⡿⠻⠃⠡⠀⠂⢻⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠛⠿⠿⠟⠁⠀⢀⡠⠃⠀⠀⢸⡿⠿⠋⠀⠀⠌⢠⡟⢠⡇
⢰⡇⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⢹⡄⠈⡀⠀⠘⡈⣧⠀⠀⠀⠀⠘⡀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠲⠂⠐⠶⠈⠁⠀⠀⠀⠠⢸⡇⢀⡀⠆⠁⢀⡾⠀⡼⠁
⣾⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⡏⢻⡄⠰⠀⢂⠁⠸⣆⠐⠀⢂⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣾⠃⢠⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣸⢿⡄⠀⡈⡀⢀⢻⡀⠀⠸⠂⠇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠤⣸⠇⠀⠀⢀⣾⠃⠀⣼⠃
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠳⣄⠻⣆⠰⠀⠂⡼⣇⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⣿⠀⠀⣰⣿⣿⠀⣰⠏
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⣆⠁⠈⡠⢻⡄⢠⡄⠀⠀⠀⢸⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠟⠁⢿⣿⣿⠋
⠸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢈⡷⠘⢧⡀⠀⢞⣷⠎⠀⡇⠀⠀⢸⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠀⠀⠀⣨⠟⠁
⠀⣤⣴⣶⣶⡾⠿⠟⠛⠛⠛⠻⢿⠟⠓⠈⠀⠀⠈⠳⣥⠈⢿⣆⡸⠀⠀⠀⢸⡇⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠔⠊⠁
⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠙⠲⠤⣀⣀⣀⣙⣧⡘⢻⡅⠀⠀⠀⠘⣧⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⡇⠀⠀⠀⠀⠉⠀⠉⠈⠳⡌⢷⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡆⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣮⣙⣒⣤⣤⣄⣤⣤⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠶⠶⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠓⠂⠠⠤
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠛⠛⠉
⠀⠀⠈⠐⠦⢤⣤⣀⣀⢀⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠶⠶⠖⠒⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡼⠋⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠏⢸⠟⢀⠀⠀⠄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡏⠀⠉⠀⠂⢀⠄⠀⠀⡼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠀⠀⠀⡜⢀⠆⢀⠆⣸⠁⠹⣦⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠂⣸⠁⡌⢀⠆⢰⠃⠀⢀⠎⠀⠀⠀⠀⠘⣿⠀⢠⡶⠿⣿⠿⣶⣶⣄⡀⠁⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣶⣶⣿⣛⣛⣛⠛⠿⢷⣾⣤⣄⣞⡠⠀⡠⠂⠀⢀⡿⢠⡟⠀⡴⠁⠀⢠⠟⢻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣤⡉⠻⢯⣟⠶⣤⡐⠀⣼⠁⡾⠀⠈⠀⠀⡴⠃⠀⠀⢙⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣄⠈⠙⠷⣤⡈⠳⣦⡙⠻⣅⡼⠃⠀⠀⠀⠈⠀⢀⣠⠞⠋⠈⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⣦⡀⠙⢦⡈⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⠾⣿⣿⡀
⠀⠀⠀⠀⠀⢀⣾⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠤⠤⣀⠀⠀⠀⠀⠈⠻⣦⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣿⣿⡇
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢷⡄⠘⢧⡀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⣿⣿⠇
⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⣠⣴⣶⠖⠠⣀⠀⠙⡄⠀⠀⠀⠀⠹⣆⠈⢳⡀⠀⠀⠀⠀⠀⠀⠤⠤⠤⣿⡿
⠀⠀⠀⣾⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⣿⣿⣿⣄⣠⣿⣆⠀⠸⡀⠀⠀⠀⠀⠘⣆⠀⢷⠀⢰⠤⠤⣄⣀⣀⣀⣼⠟⠁
⠀⠀⢰⠟⠊⠁⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⢠⠃⠀⠀⠀⠀⠀⠘⣆⠘⡇⠀⣇⡀⠤⠤⠽⠿⠶⠶⠶⠤⣤⣀
⠀⣰⠃⠀⠀⠀⢀⣤⣤⡤⢄⡀⠈⢣⡀⠀⠀⠘⡄⠀⠀⠀⠈⠿⣿⣿⣿⣿⠟⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢈⣿⣧
⢀⡇⠀⠀⠀⢰⣿⣿⣿⣀⢀⣽⡆⠀⠃⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠉⠉⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣿⡿
⢸⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⡘⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠃⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⣤⣼⣿⡇
⠀⣇⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡼⠀⠀⠀⠀⠀⠐⠤⣄⡀⠀⠀⢠⣿⡿
⠀⠈⢧⣀⠀⠀⠀⠈⠉⠉⢁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⣷⠧⡀⠀⠀⠀⡀⠀⠀⠉⠛⢶⣿⣿⠁
⠀⠀⠀⠹⣏⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣀⠼⡄⠀⠀⠀⠀⠀⢀⡼⢃⣼⠟⠁⠀⠙⣆⠀⠀⠈⠢⣄⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⡜⠁⢀⠇⠀⠀⠀⠀⣴⢟⣵⠟⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⣨⣿⣿⠟⠁
⠀⠀⠀⠀⢀⡈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢌⡉⠁⠀⠀⠀⠀⣧⡤⠊⠀⠀⣀⣴⣿⡿⠛⠁⠀⠀⠀⠠⠀⠂⠀⠀⠘⠻⣿⣿⠟⠋
⠀⠀⡴⠊⠁⠀⡠⠊⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢀⣠⣴⣾⠿⠛⠁⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⠷⠀⢀⠘⠳⠀⠀⡌⠉⠛⠻⢶⣦⣤⣤⣤⣀⣤⣤⣤⣤⣴⣶⡶⠟⠛⡻⣍⠀⡐⠈⣀⠐⠀⢨⣿⠆
⠀⠀⠀⠀⢶⣄⣀⣀⣠⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠐⣆⡀⠀⠀⡏⠓⠤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠚⣢⣎⣅⣀⠈⠙⡏⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣾⡗⠁⠀⣀⡀⠱⡀⡿⠤⢄⡀⠀⠈⠻⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠊⠸⡅⠀⠸⣿⣾⢀⡟⠁⠀⠀⠉⢢⡀⠀⠘⣯⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠙⢤⣀⣈⡠⠊⠀⠀⠀⠀⠀⠀⢹⡀⠀⠘⣧⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣧⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢻⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⡠⠊⠉⠉⠀⠀⠀⠀⠀⢸⣃⣿⠤⣖⣒⣲⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠞⠀⠀⠀⡰⠁⡠⠀⡄⠀⠀⣀⡤⠶⢟⣃⠬⢭⣒⣒⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣀⣠⡴⠞⠉⡰⠋⠀⠀⠀⢠⠇⢰⠁⠀⣸⠔⠊⠁⢀⣈⣴⠶⡿⠛⠛⠋
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠞⠀⠀⠀⠀⠀⢸⠀⢸⡠⠊⢁⡠⠔⠊⠁⠀⣟⢀⡇
⠀⠈⢣⡈⡓⠒⠤⣀⠀⡴⠤⢄⣀⣀⣤⠴⠖⠋⠀⠀⠀⠀⢰⠀⠀⢸⡔⢋⡤⠊⠁⡇⠀⠀⠀⠀⡏⢸⠃⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠙⠺⠿⢦⣌⠑⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡠⣢⣔⠁⠘⢄⠀⠇⠀⠀⠀⢸⠇⡼⠀⠀⠀⠀⣠⠔⣫⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⠊⠁⠸⡄⠀⠀⠉⠀⠀⠀⠀⣾⠤⠇⠀⠀⢀⢜⠕⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠟⡡⠔⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣦⡠⠤⠀⠀⠬⠗⠚⠁⠤⠐⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣓⣲⣤⣄⡀⠀⠀⠀⠩⢉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⢤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⢊⠁⡞⠁⠀⠀⠉⠑⢤⡠⡑⠢⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢭⣉⣛⡛⠛⠛⢉⠁⣀⣣⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠹⣌⠢⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⣿⠀⣀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠴⠓⠋⠉⠉⢉⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠖⠚⠛⠛⠛⠋⠛⠛⠿⢿⣾⢿⣤⣀⠀⣠⠤⠀⠀⠀⠀⠐⡛⠛⠛⠻⠿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠳⢮⡙⠻⣦⣀⣠⠴⠖⠋⠉⠀⠀⠀⢀⣀⣀⠈⠛⢿⣿⣷⡀
⠀⠀⠀⠀⣠⠴⠖⠒⠚⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡌⠻⣦⡀⠙⢷⣄⣠⡤⠶⠒⠛⠉⠉⠉⠉⠀⠀⠈⣿⣿⠇
⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠈⠛⣆⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠘⣟⣆⠀⠹⣧⣀⣀⣠⣤⣴⠶⠶⠶⠶⢶⣾⡿⠃
⠀⣸⠃⠀⠀⠀⢀⣠⣶⡶⢄⡀⠸⡆⠀⠀⣠⠞⠋⠁⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠘⡎⢧⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⣰⠟⠉
⠀⣿⠀⠀⠀⠀⣾⣿⣿⣦⣼⣷⠀⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢻⡘⡆⠀⠘⣿⣆⣠⣤⣤⢤⡞⠁
⠀⠸⣆⠀⠀⠀⢻⣿⣿⣿⣿⡟⣼⠃⠀⡏⠀⠀⠀⣴⣿⣿⠋⢳⡄⠀⠀⢻⠀⠀⠀⢸⡇⢻⠀⠀⢻⢿⡄⠀⠀⠀⢧⡀
⠀⢠⡟⠳⣤⣀⣀⠙⣛⣛⡭⠞⠁⠀⠀⣧⠀⠀⢸⣿⣿⣿⣷⣿⣿⠀⠀⣾⠀⠀⠀⢸⡇⢸⡇⠀⠘⡏⣿⡀⠀⠀⠀⠻⣦⡀
⠀⢸⡇⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣦⡀⠈⢻⣿⣿⣿⡿⠋⠀⣰⠇⠀⠀⠀⢸⡇⢸⡇⠀⠀⣷⢹⣷⠀⠀⢀⠀⠈⢻⣦⡀
⠀⢸⣷⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣌⣉⣁⣤⡴⠞⠁⠀⠀⠀⠀⣸⡇⢸⠇⠀⠀⣿⠈⣿⡏⠉⠉⠀⠀⠀⠹⣿⡆
⣠⠿⠁⢰⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣿⠀⠀⣠⡿⠀⣿⢿⡶⠶⠤⠀⠀⢠⣿⠇
⣿⢱⠂⠀⢹⡆⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣸⠇⢀⣴⡿⠁⠀⣿⠘⣇⣀⣀⣤⣴⠿⠋
⢻⣤⣑⣀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣰⠏⢠⣿⡟⠁⠀⢰⣿⠀⢹⣏⠉⠉
⠀⠉⠛⠿⠽⠿⣦⣄⠀⠀⠀⠀⢀⣴⣿⠟⠛⠳⢦⣤⣀⠀⠀⠀⠀⠀⢀⣴⠟⢀⣼⠏⠀⣼⣿⠀⠀⠀⣾⠇⠀⢸⠏⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⢸⣿⣇⣠⣄⣀⣀⡈⠉⠛⠳⠶⠤⣾⣿⣥⡤⠞⠁⠀⢠⣿⠇⠀⠀⣼⡟⠀⢀⣿⠀⢸⡏⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣾⠏⠀⢀⣾⠃⠀⣼⡇⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡶⠶⠖⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⣰⠟⠁⠀⣠⡿⠃⠀⣰⡿⠁⠀⠀⠀⠤⣄⣀⠀⢹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⢀⣀⡤⠒⠀⠀⠀⠀⠀⢀⡜⢁⡴⠞⠁⠀⣠⣾⠟⠀⢀⣾⡿⠁⠀⠀⠀⣀⡀⠀⠉⠙⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡶⠚⠉⠀⠀⠀⣀⠴⠋⠀⣠⠞⠻⠿⣤⣀⣤⠾⠋⠁⣠⣶⡿⠋⠀⠀⠀⢄⡀⠀⠉⠓⠦⣄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⣠⡴⢚⣁⣤⠶⠋⠁⠀⠀⠀⠈⠹⣧⣤⣶⠿⠛⠉⠀⠀⠀⠐⣄⠀⠉⠳⣤⡀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⢀⠀⠈⢢⡀⠀⠀⠙⢶⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣆⠀⠈⢧⠀⠀⠙⢦⣀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⢹⡄⠀⠈⣧⣀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣾⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠖⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⡤⠴⠒⠒⠓⠾⣧⡀
⠀⠀⠀⠐⠈⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣠⠊⡠⠚⠁⠀⠀⡠⠔⠒⠒⠢⣌⠣⣀
⠀⠀⠀⠀⠄⠀⠀⠀⢀⢿⡆⠀⠀⠀⠀⣠⠞⡡⠋⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠳⠉⡵⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣿⡀⠀⠀⡴⢃⠞⠀⢀⠔⠉⠁⠜⠀⠀⣀⣤⣤⣤⣄⡀⠉⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⣿⢷⢀⠞⢠⠋⠀⠀⠇⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠙⢆⠀⢀⣀⣬⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣿⠘⡟⡰⠃⠀⠀⢰⠀⠀⠀⠀⢠⠁⠀⢀⣤⣤⡀⠀⠀⠈⡀⠈⠁⠀⠉⢢
⠀⢸⣦⡀⠀⠀⠀⠘⣧⣴⣿⠀⢹⡃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠃⠸⣿⣷⡀⠀⠂⢀⡄
⠀⡆⠙⢷⣄⠀⠀⠀⢻⠿⠏⠀⠀⢧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⢀⠌⠀⢀⣿⠟⠁⠀⢁⡞⣸
⣸⠀⠀⠀⠙⢷⣄⠀⠈⣧⠀⠀⠀⠘⡆⠀⠀⠈⡀⠀⠀⡠⠀⠀⠀⠁⠒⠀⠒⠈⠀⠀⠀⢸⡇⠤⠂⠀⡼⢀⡏
⡇⠀⠀⠀⠀⠀⠙⠦⡘⠘⣧⠀⠀⠀⢹⠈⠈⡄⠇⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⢸⡇⠀⠀⣴⠃⣸⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⢧⡀⠠⠠⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⣾⡇⢠⠏
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢳⡀⠀⣻⣄⠆⡀⠀⢸⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠁⢻⡿⠋
⠈⣀⣤⣤⣤⠶⠶⠶⢶⣤⠄⠊⠀⠙⣄⠐⣯⣠⠁⠀⢸⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠤⠊
⠀⠛⠉⠀⠀⠀⠀⠀⣀⡃⠑⠢⢄⣀⣈⢷⡘⡇⠀⠀⠀⣇⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢏⢹⠀⠀⠀⠀⠀⠀⠙⠼⡀⠀⠀⢹⡀⠀⠀⠀⠙⠳⣦⢤⣤⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣇⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⢳⡀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡢⣄⡀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⠶⠶⠤⠦⠤
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠒⠂⠉⠉⠉
⠀⠀⠈⠁⠒⠢⠤⠤⠤⠤⠤⠤⠒⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⢀⡤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠑⡒⢶⣶⠶⠶⠗⠛⠛⠿⠿⠷⠂⠀⠀⠰⢶⡿⠑⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠐⠛⠭⣽⣠⣤⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁
⠀⠀⠀⠀⡀⠀⣀⠀⣀⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣴⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⣠⢾⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠈⠒⢤⡀⣀⠀⣀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣤⣦⣤⡀⢀⠀⠀⠤⣀⠀⠛⠃⣹⡛⠭⠛⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣾⣿⣿⣿⣿⣿⣦⡙⢶⣄⡀⠀⢈⡉⠁⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣰⣿⣿⣿⣿⣿⣿⠿⠿⠷⠄⠙⠁⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⠋⠒⣄⠸⡅⢐⣄⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠄⠀⠀⣤⣿⠇⠈⡛⠁⡴
⠀⠀⠀⠀⢈⠒⢤⣀⠀⠀⠀⠀⠀⡀⢠⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠐⠠⢀⠉⠑⠃⠀⠈⠁⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣷⣿⣿⣿⡿⠛⠉⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡋⠀⠀⠀⠀⠀⠀⣿⣇⠀⠐⢦⣀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠿⣷⣤⣀⡀⠀⠀⢀⣿⣿⠀⠀⠀⠙⣿⣶⣦⡤⣤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⣠⠾⣳⠋⠀⠈⠛⠻⢿⣷⣶⣿⣿⠃⠀⠀⢀⠠⠾⠻⢿⣧⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁⢠⠃⠀⠀⠀⠀⠉⢲⣄⣹⠉⠀⠀⠀⠞⠁⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⣏⠀⠀⠀⠀⠀⢰⠋⡄⠉⠀⡀⠈⠐⠁⠀⠀⠀⢀⡀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠚⠳⠀⠙⢦⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡇⡀⠀⡐⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠀⠀⡴⠁⡀⢠⠁⢀⠔⢡⠠⠀⠀⢠⠊⣠⣤⡄⠀⣊⣄⡇⠀⠀⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢠⠃⠀⠀⡆⠀⠀⠀⠀⠈⠛⠁⠀⠹⢛⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢻⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⡄⠀⠀⢄⡀⠀⠀⠀⠀⠀⣀⢆⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠈⠃⠀⠀⠙⢿⣲⣖⣢⠋⠁⠒⠋
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠙⠻⠞⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢔⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠦⠀⠀⢀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠉⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⠆⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣴⣧⠀⣾⣿⠄⠀⠀⠀⠀⠀⢀⡏⡀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⠀⠉⠀⠀⡄⠀⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡐⠠⠀⠀⠀⠀⢀⠃⠀⠀⠠⠀⢸⡇⡠⠤⢄⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠀⠂⠄⡀⠀⠀⠉⠓⡂⠀⢀⡴⠁⠀⠀⢀⠍⣀⠞⡄⠀⠀⠀⠈⠃
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠚⠉⠀⠀⠀⢀⣮⠞⠁⠈⡐
⠀⠀⠀⣴⠋⠁⠀⠢⡜⠉⣉⡍⠧⠐⠒⠈⠉⠛⠁⠉⠓⢦⡀⠀⢄⠀⠀⠀⠞⠁⠀⣔⠎
⠀⠀⣸⠃⠀⠀⠀⠀⢀⠀⡈⠀⠀⠀⠀⡴⠁⠀⠀⠁⠀⠀⠐⡄⠀⠓⠤⣀⣠⠴⠞⠁
⠀⠀⣿⠀⠀⠀⠘⠀⡄⠰⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠀⢹⡄⠀⠀⢀⠀⡆⡇⠀⠀⡌⠀⠀⠀⠀⠀⠀⣾⠟⢁⣴⠞⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠒⠊⠀⠀⣏⠓⢤⡊⢀⠀⠀⠀⠑⢄⣀⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠘⣄⠀⠀⠀⠀⡈⠉⠉⠉⠉⠉⠀⠀⠀⣴⡄⣠⡄⠘⣆⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠙⠒⠦⠤⠤⠥⠶⠀⠀⠀⠀⠀⠐⠉⠀⠉⠁⠀⠘⠁⠈⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⣀⣠⠀⠀⠰⢄⣀⣀⣠⠆⠀⠀⠀⠀⠀⡀⠀⠀⠂⣀⠈⠂⣤⡃⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⢿⠔⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠀⡀⡠⠆⠀⢄⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠠⠤⠤⡁⠀⠀⠀⠀⠀⢉⡄⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⣞⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠋⠛⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠄⠈⣢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠈⠐⠢⢀⡜⣁⡤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⡸⠁⡠⠋⠉⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⡉⠲⢄⢺⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠊⠀⡨⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠀⠈⡆⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢋⡠⠐⠉⡀⠔⢿
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢲⠃⡇⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣴⡇⠀⠀⠀⠀⠀⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡍⠉⠸⠀⡇⡇⠀⠀⣾⣿⣧⣷⠀⠀⠀⠀⠀⠙⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠞⠁⠀⠤⣇⢹⠀⠀⠻⢿⡿⠟
⠀⠀⢀⣠⠀⠀⠀⠘⠳⡄⢴⠀⢻⢸⡈⣇⠀⠀⠀⠀⠀⠠
⠀⢰⣿⠓⠂⠀⠀⢸⠀⡇⢸⡀⢸⠀⢳⠘⡄
⠀⢾⣿⠀⠀⠀⠀⠘⣆⢳⡀⢣⠸⡀⠀⠳⣌⠲⢤⣀⡀
⠀⢸⣿⡏⢀⠀⠀⠀⠘⢆⠱⢄⠑⠷⣄⠀⠀⠉⠑⠒⠛⠋⠀⣀⡀
⠀⠀⢻⣿⣅⠀⠀⠀⠀⠀⠀⠈⢱⡀⠁⠀⠀⠀⠀⢀⠀⠉⠀⠙⠅⡄
⠀⠀⠀⠙⠿⣶⣮⡄⠀⠀⠀⠀⠀⠙⠶⠶⠒⠀⠀⠈⠛⠛⠁⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠀⠀⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢁⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠠⠀⠈⢄⠀⠀⠀⠱⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠀⠀⠄⠄⠓⠀⠉⠀⠠⡀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⡰⠀⢸⠀⠀⠀⠀⠀⠗⠈⢀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⢆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢅⠀⡈⠀⠀⠀⠀⠐⠀⠠⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣈⡄⠄⠀⠀⠀⠀⠀⣠⠱⠀⠀⠀⢀⣀⡀⠀⢰⣤⡀⠀⠣⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢃⠄⠀⠀⠀⢹⣿⣿⠀⠰⢿⡗⠀⠀⠱⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣮⠀⠙⠀⠀⠀⢀⣀⠀⣠⣷⡄⠈⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⣿⣿⠂⠘⠟⠀⡄⢄⠀⠐⠂⠀⠐⠒⠒⠠⠒⠖⠒⠉⠋⠀⢀⠌
⠀⠀⠰⠀⠀⠀⢱⡀⠀⠀⠈⠀⠀⠓⠀⠀⠀⠀⠡⠀⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠀⢀⠎
⠀⠀⠀⢣⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⡀⠤⠊⣀⡴⠋⠀⠀⡤⠤⠴⠒⠒⠋⠁⠀⢈⠀⡠⠃
⠀⠀⠀⠀⢣⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠰⠔⠀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡐⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⣤⣤⣤⠶⠟⠋⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠙⢆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠳⡀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠀⠀⢠⠇⠀⢀⠂⠀⡄⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠘⡄⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠞⠀⠀⡀⠀⠈⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠐⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⠁⢠⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⡉⠛⠇⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠉⠀⠀⠀⠀⠀⡀⠀⠱⣄⣀⣤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠄⣀⡀⠈⠓⢄⣈⣶⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⣤⡀⠀⠀⣠⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⠉⠓⢤⡜⣹⣯⣤⣤⡀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⢆⣰⠏⢀⡜⠁⢉⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡙⠳⣤⡿⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠼⢷⡀⠊⢀⡴⠋⠀⣨⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠘⣶⣿⠁⢸⠁⢀⣠⠤⠤⢄⡀⠀⠀⠀⠀⣰⠋⣀⠀⠀⠀⠈⢲⡋⣀⠴⠊⢁⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠂⢤⣿⣿⠀⣾⡴⠋⠀⠀⠀⠀⠈⢦⠀⠀⠀⣷⣿⣿⣿⣷⠀⠀⠀⡏⠀⠐⠊⢁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⡶⢶⣿⡇⣇⠀⣿⠀⠀⣠⣤⣤⡀⠀⠀⡇⠀⠀⢿⣷⣼⣿⣿⠁⠀⡰⢷⠄⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣧⡄⣙⣧⣿⠀⢻⡀⣾⣿⠛⣿⣿⠀⢠⠇⠀⠀⠀⠙⠻⠿⠷⠶⠛⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⢃⣀⣠⣽⢿⡄⠈⣿⠻⢿⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⣠⣶⠚⠒⠒⢺⡏⢻⠉⣿⠀⢹⡏⢧⠀⠸⣆⠀⠀⠀⠀⠹⣅⣢⡄⠤⢐⡟⠀⠀⠀⠀⠀⢀⡾
⠀⣾⣿⡏⠁⠀⠀⠀⣇⢸⡇⢹⡆⢸⡇⠈⢳⡀⠙⣦⠀⠀⠀⠀⠈⠒⠬⠖⠋⠀⠀⠀⠀⠀⣠⠞
⠀⣿⣿⡉⠁⠀⠀⠀⢻⡌⢷⡀⢳⡸⡇⠀⠀⠙⠦⣌⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⢻⣿⡏⠁⡀⠀⠀⠀⠻⣌⠳⡄⠙⢿⣦⡀⠀⠀⠈⠛⠶⢭⣽⣒⣶⣦⡤⠴⠒⠋⠁
⠀⠘⣿⣿⡏⣀⠀⠀⠀⢀⡬⠗⠛⢻⡛⠛⡻⠛⠟⠙⠛⠉⠹⢟⢿⣿⣿⢣
⠀⠀⠈⠻⣿⣧⣤⣂⡴⠋⠀⠀⠀⠈⠻⣦⣤⣤⠔⠀⠀⠛⠶⠶⠞⠀⠶⠛
⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⢰⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⣽⣄⠀⠙⠣⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠈⠢⢄⡀⠈⠲⣀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠉⠒⠤⣄⡀⠀⠉⢢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠤⣄⠀⠀⠀⣰⠏⠉⢉⡿⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⠀⠀⠉⠒⡔⠏⣠⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠏⠀⢠⠎⠀⠀⣠⠾⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢄⡉⠙⢦⡄⡜⡜⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠁⠀⣠⠞⠁⠀⢀⡼⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢦⠀⢰⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⡠⠔⠋⠀⢈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⢨⠃⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠀⡀⠀⠀⠀⠀⠠⠒⠁⢀⡠⠔⠚⠉⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⢱⡏⢠⡇⢸⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣴⣿⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠛⠛⠲⢲⡇⢸⡇⢸⠀⠀⠀⢠⣾⣿⣿⡁⣱⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠀⠀⠀⠀⠙⠆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢉⣓⣀⡀⠈⠃⠘⡇⢸⡆⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠺⠁⠈⠁⠢⠄⣷⠈⣧⠀⠀⠀⠙⠿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⡁⠀⣄⠀⠰⣧⢸⡆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⢸⡀⠐⡇⠀⣿⠀⠀⣿⠀⢷⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⣿⡏⠉⠉⠀⠀⠀⠸⡇⠀⣧⠀⢹⡄⠀⣿⠀⠘⢧⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⣿⣿⡗⠂⠀⠀⠀⠀⠀⢿⡀⢻⡄⠀⢷⡀⢿⠀⠀⠈⢧⡀⠑⢦⣀
⠀⠀⣿⣿⣧⠤⠐⠀⠀⠀⠀⠈⢷⡀⠻⡄⠈⠳⡘⣇⠀⠀⠀⠉⠓⠦⣬⣉⣓⣒⣲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢹⣿⣿⡀⣀⠄⠂⠀⠀⠀⠀⠙⢄⠙⠦⡀⠈⠪⡳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⢿⣿⣿⡀⢀⡠⠀⠀⠀⠀⠀⠀⠃⠀⠉⣧⠀⠊⢀⠎⠀⡄⠀⠀⠀⠀⢀⠈⡡⠠⠂⠯⡅⢠
⠀⠀⠀⠀⠻⣿⣿⣇⣀⡠⠊⢀⠄⠀⠀⠀⠀⠀⠙⢷⣤⣁⣀⣈⡠⠂⠀⠀⠳⢦⣤⡥⠖⠀⢰⡴⠋
⠀⠀⠀⠀⠀⠈⠙⠿⠿⠷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠙⢦⠀⠀⠀⠀⠘⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⢟⠀⠀⠀⠀⠀⠀⣴⡶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡿⠤⠶⠿⠞⠋⠀⠀⠀⠀⠀⢸⡏⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠲⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠈⠳⠶⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠅⠀⠀⢿⡀⠀⠀⢠⡆⠀⢸⣅⠀⣾⠁⠀⠀⠀⠀⠀⣰⣿⠛⠉⢻⡆
⠀⠀⠀⠀⠀⢰⡇⢢⣀⠆⢸⡇⣿⠀⢸⡇⢀⡃⣸⡧⢿⣆⡄⠀⠀⠀⠀⣿⡇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠻⣦⠴⠂⢸⠃⣿⣀⠺⣧⠜⠓⠋⠁⠀⠉⠀⠀⠀⠀⠀⠙⠷⣦⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⣿⠃⠈⠁
⠀⠀⠀⠀⠀⠀⣰⠋⠀⣰⠇⣠⠞⠋⠉⢭⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣤
⠀⠀⢀⣀⣀⣀⣙⣒⣊⠁⣼⠃⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠜⠛⢷⠀⣰⠟⠁⠀⠀⠈⡇
⠀⡴⠋⠉⠉⠀⡈⠉⠉⢹⡏⠋⠓⠒⠒⠛⠋⠀⠀⣀⠀⣤⣠⠶⣆⠓⠀⠘⣰⠏⠀⢤⣀⣠⡴⠁
⠀⠳⣄⣀⣀⣠⡼⠀⠀⣼⠀⢀⣀⡀⣠⠖⣦⢠⡏⢹⠇⣿⠉⢀⡿⢀⢀⡼⠃⠀⠀⠀⠉⠉
⠀⠀⠀⠈⠉⠁⠀⠀⠀⢻⢀⠎⡽⠁⣿⠴⠋⣼⣇⢁⡰⣿⠐⠚⠓⠂⠋⠀⠐⠆⡤⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣀⠀⠀⢸⡎⢸⣇⡈⠻⠶⠊⠀⠙⠉⢀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⢶⡄⢠⡞⢩⡇
⠀⠀⢀⠔⠋⠁⠈⠃⠀⠈⠁⠀⠈⠀⣠⣤⠀⠀⠀⠀⠘⠞⠁⠀⢠⣤⢀⣤⡀⣸⠃⢀⣿⠃⣾⠀⣾⠁⣸⡇⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠠⢁⡔⠈⠳⡄⠀⠀⠀⠀⠀⠀⠈⠓⠀⡀⢠⣄⠀⠚⡷⢰⣿⠀⣿⠃⣾⠁⣿⠀⡸⠿⠀⠿⠖⠉⠋⠀⣧⠀⠀⠀⣠⠖⠃⠀⠉⣟
⠀⣱⠏⢠⡇⠀⡟⠀⠀⢀⡀⢰⡆⣸⠃⠠⣿⠀⣿⠇⢸⡇⣸⡏⠀⠿⠀⠻⠎⠈⠋⠀⠀⣠⡤⠴⠦⠤⢠⣿⣄⣀⣜⣁⣀⣀⣀⣤⡿
⢀⣿⡀⠈⠳⠘⠀⣿⠀⣼⠁⢸⡇⣿⠀⢸⡏⠀⠟⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢠⡟⠀⡿⠉⠉⠉⠉⠉⠁
⠀⠉⠻⠶⢦⣄⠀⣧⣀⠿⣄⠜⠁⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣠⡴⠋⠀⡈⢠
⠀⠀⣄⠀⣀⡝⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠚⠛⠛⠉⠙⠛⠛⠓⠲⢤⠀⠀⠀⠀⠀⠀⢰⠁⠘⣄⡀
⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠖⠊⠀⠀⠀⠀⠀⢠⡏⢰⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠟⠁⠘⠁
⠀⠀⠀⠀⠀⠀⣀⠔⠒⠐⡦⠤⠤⣄⠱⡄⠀⠀⠀⢀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠾⠋⠉⠀⠀⠙⢴⣦⠈⡆⢙⢦⠀⠀⣮⠙⠓⠓⢤⣄⠀⠀⢀⠴⠒⠓⠤⠤⠞⠉⡇
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢤⠉⠀⠙⡇⠒⡧⠰⡇⢆⠀⠹⠄⣬⡷⠚⠁⠤⠐⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠱⠔⠤⣀⠀⡀⠔⡩⠀⠀⠜⠳⠄⠣⠀⢀⡄⠁⠠⠀⣁⢤⣀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⢇⠀⠿⠣⠀⠁⠀⡠⠚⠳⣖⡀⠒⠂⠀⢀⠀⠂⠀⢀⡾⠃⠙⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠑⠒⠒⠢⠤⠊⠀⠀⣠⠋⢰⣄⣀⣀⠈⣁⡀⢼⡋⠀⠀⠀⠈⠦⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠐⢄⠈⠉⠁⠀⠀⠀⠉⠛⠦⠤⠤⠤⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣄⡀⠀⠀⠀⠳⢄⣀⣀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⢄⣀⣀⠤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠁⢌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⡄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢀⣴⡀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠂⠀⠘⠋⠁⠘⠛⠁⠀⡀⠀⠀⠀⠀⢸⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠑⢄⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⢸⣇⠃⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⡀⠀⠀⠀⠉⠒⠤⡇⠀⠀⠀⣠⠃⠀⠀⠀⡎⠀⡸⢋⠋⠉⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠐⢤⡤⠞⠁⠈⠀⠀⡐⡠⠚⠠⠃⠆
⠀⠀⠀⠀⣤⠖⠂⢀⠀⡤⠤⢤⠧⡀⢀⣀⠠⠤⣤⠤⠱⣄⡀⠀⠀⠀⢀⠈⠀⠀⡴⠋⠁⢀⢢⠎
⠀⠀⢀⡾⠁⠀⠀⠀⠙⠀⠔⡖⠂⠩⠀⠀⢀⠄⠀⠀⠄⠀⠈⠲⡀⠀⢠⡀⠀⠀⠀⢀⣠⠕⠁
⠀⠀⢸⠇⠀⠀⠀⡀⠀⠌⡐⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠉⠒⠒⠒⠋⠁
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⢠⠀⠜⠀⠀⠀⠀⢀⣄⣰⠀⠀⡆
⠀⠀⠘⣇⠀⢀⡀⠄⢸⢘⠃⠀⡠⠁⠀⠀⠠⡀⠀⠀⠿⠟⠁⣾⠟⡁⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠉⠁⠀⠀⠸⣌⡑⢶⠁⢸⠀⠀⠀⠈⠢⢤⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⣦⡀⠀⠀⠀⠄⠀⠀⠁⠉⠉⠀⠀⠀⢠⣷⠂⣴⡆⠈⢧⡠⠠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠉⠙⠒⠦⠤⠤⠴⠂⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⢘⠁⠀⠏⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣴⠀⠀⠐⢤⣀⣀⣠⠞⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⡠⠊⠒⢤⣇⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡺⢿⠖⠒⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠂⠀⠀⠀⠉⠉⠁
⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈
⠀⠀⠀⠀⠀⠠⠆⠈⠀⠀⠁⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠒⠁⢀⡠⠉⠉⠁
⠀⠀⠀⠀⠈⠑⠠⠄⣠⣀⣤⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣀⣾⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣬⣿⡉⠉⠛⠇⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⠈⢳⡄⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠲⢤⡀⠀⠑⢦⣀⣠⠿⠛⠋⠉⠉⠉⠉⠉⠉⠛⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠒⠢⢤⣀⠀⠀⠉⠲⣤⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣳⣤⡀⠀⠀⣰⣿⠿⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠈⠙⠲⣤⡾⢉⣿⣥⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠳⡄⢠⡟⠀⠀⡼⠋⠀⠈⣻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠛⠶⣦⡀⣰⡿⠁⣾⠿⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⡀⢀⠞⠀⠀⣠⠞⠋⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠳⣄⠈⣹⣿⠁⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠓⢦⣀⣠⠞⠁⠀⣀⡴⠟⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠘⣿⣿⡇⠀⢸⠇⠀⣠⡤⠖⠒⠒⠶⣤⡀⠀⠀⠀⠀⠀⢰⠏⣀⣀⣀⡀⠀⠀⠀⠀⢻⡄⣀⠴⠚⠋⢀⣀⡴⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠢⢤⣴⡿⣿⠁⠀⣿⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⢁⠠⠔⠚⠉⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣤⣤⣄⣰⣿⡇⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣿⣿⡏⢉⣿⣿⣿⡇⠀⠀⢀⣿⣀⣀⣀⠤⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠉⠙⢿⣿⡇⣿⠀⠀⣿⠀⠀⣠⣾⣿⣿⣷⣦⠀⠀⠀⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⢀⣠⠞⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣻⡶⠦⢄⡙⣧⣿⡆⠀⢹⡆⢰⣿⣿⡉⢹⣿⣿⡇⠀⣰⠏⠀⠀⠀⠀⠀⠉⠛⠻⠿⠾⠛⠋⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⡽⠁⠀⠀⣈⣿⣿⣇⠀⠈⣿⠾⣿⣿⣿⣿⣿⣿⣥⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⣤⡿⢷⣶⠶⣾⡟⠉⣿⡏⣿⡄⠀⠘⣧⠀⠈⠉⠉⠉⠉⠻⡷⠤⣀⡀⠀⠀⢀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⣠⣾⣿⣅⡀⠀⠀⠀⢸⡇⠀⣿⠀⢻⡇⠀⢹⡇⠘⢧⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢶⡶⠯⣉⠉⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠸⣧⠀⣿⡀⠸⣧⠀⢸⡇⠀⠈⠳⣄⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠙⠲⠼⠓⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⢸⣿⣿⡟⠉⠁⠀⠀⠀⠀⢿⡄⢹⣧⠀⠹⣆⢸⣇⠀⠀⠀⠘⢷⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⢸⣿⣿⣧⠶⠂⠀⠀⠀⠀⠈⢿⡄⠻⣆⠀⠹⣦⣿⣄⠀⠀⠀⠀⠉⠳⢦⣄⡙⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣤⡴⠛⠉
⠀⠈⣿⣿⣿⣀⣠⠔⠀⠀⠀⠀⠀⠙⢦⠘⢷⣄⠈⢛⣿⣦⣄⡀⠀⡀⠀⠀⢉⣛⣳⣶⣶⣯⣽⣿⣿⠟⠛⠉⠉
⠀⠀⠹⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⢀⡤⠷⠚⠛⢻⡏⠛⠋⡹⠛⢹⠏⠉⠟⠉⠉⢹⡿⣻⢿⣿⣿⣿⢳⡀
⠀⠀⠀⠙⢿⣿⣿⣏⠀⣠⠊⢀⡴⠋⠀⠀⠀⠀⠘⢿⣦⣀⠁⠀⢀⡠⠊⠀⠐⢷⣬⣤⣥⡴⠃⢩⣭⡾⠃
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠐⠁⠀⠀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠠⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀
⠀⢠⡀⠀⠀⣤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢀⡀
⠀⠀⠑⢄⠀⠈⣏⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⣰⣄⠀⠀⢀⡞
⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠉⠛⠀⠠⠊⡇
⠀⠀⠀⢀⣄⠀⣿⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⠀⠀⡰⠏
⠀⠞⠉⠁⠈⠁⠹⡆⠀⠂⠀⠀⠀⠣⡀⠀⠀⢀⡧⠖⠋⠀⠀⠀⠀⠀⠤⢤⣀
⠀⠀⠀⠀⠀⠂⠁⠈⠲⣌⡄⠀⠀⠀⠈⠲⠤⠎⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠢⡡⡀⠈⠻⡄⠀⠈⠂⡀⠀⠀⢀⠠⠖⠰⠦⠔⠀⠄⠀⣀⡴⠤⠶⠶⡄⠀⠒⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⡀⠀⠀⠀⡠⠂⠀⠔⠋⠀⠀⠀⠀⠈⠄⠀⠀⠘⠁⠑⠒⠀⠋⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠈⠄⠐⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠰⣠⣤⡀⠀⠀⠀⠐⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⠆⠈⠻⠃⠀⢀⠄⠀⠀⠀⠣⡀⠀⡁⢴⠀⠂⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠠⠀⠀⠀⠀⢁⣀⣀⣀⣠⠤⠖⠀⠀⠀⠀⡰⠀⢵⣊⣠⠞
⠀⠀⠀⠀⡰⠐⣰⠏⠀⢶⡆⠸⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡴⠇⠀⠀⠁⡀
⠀⢠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠛⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⡷
⠀⠈⠄⠀⢧⣀⠀⠀⣄⢀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠲⠤⣤⠤⠂⠀⠀⠸⣄⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠑⠉⠉⠺⠛⠭⠁
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠊⠀⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣈⠁⠀⠀⠀⠀⠀⠁⡄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠄⠴⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠀⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠉⠁⠀⠀⠀⠀⠀⣈⣉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⠦⣈⠛⢦⠀⠀⢀⠴⣶⠶⢤⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠁⡎⣸⣿⣿⣆⠙⣿⣞⡾⣥⣿⣍⣉⣙⣒⠲⢤⣤⣄⢂⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡆⢫⠙⣿⣟⠛⢋⢿⣝⢿⣿⣶⣌⠙⢷⣶⣖⠚⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⣹⢿⣿⣷⠘⢧⡀⠛⠃⣸⡼⣯⡼⡟⢻⣿⣿⣦⣮⡻⣿⣃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣱⣾⣃⣏⣻⣿⣇⢀⣹⣧⠀⢡⠄⡏⠃⣿⠇⠟⢉⣿⣿⣿⣮⡻⣤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠴⠶⠶⠦⢬⡻⠿⢿⣶⡶⠚⡈⠀⣼⣿⡿⠄⠀⠉⢹⣿⣷⣽⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣤⣒⠢⡀⢀⡀⢄⠒⠤⠄⡴⢺⣿⠟⠋⠀⢀⣴⢻⡿⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣌⡑⠛⠦⠕⠒⠊⠀⠀⠈⠓⠂⠒⢫⡍⣨⢁⣾⢻⣿⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⡏⣼⢿⣿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡞⢆⠰⣤⣄⣀⠀⠀⠀⠀⠀⣉⣾⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢧⡀⠳⣜⠿⣮⠙⢶⣄⠀⠀⢈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠋⣻⣷⣦⡈⣆⣼⣿⣷⣬⡛⠿⣄⢼⣿⣷⡄⠈⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠿⢿⣿⣿⢿⣿⣿⣿⣾⡿⡟⠿⣹⣷⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⡀⢀⡀⠀⠀⠛⣦⣹⣿⣷⠻⣿⣿⡈⠁⠉⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⣷⠀⠀⣿⣿⣿⣿⣯⠈⢉⣟⣿⡶⠒⢹⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⢀⣮⣿⠀⣷⣿⣿⣿⢿⡟⢰⠿⣫⣟⣡⣤⣼⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⠏⣼⣿⢇⣿⡟⣼⡠⠴⣺⢿⣻⣿⣿⣿⠻⣿⣟⠀⠙⠆
⠀⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠶⠀⠀⠀⣠⣴⣶⣿⣿⡿⠋⣰⡿⢋⣾⠟⡼⠉⠀⢘⣵⢿⣿⣿⠿⠏⠙⠈⠛⣿⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⢂⣼⡿⣛⣽⣾⣿⠁⡈⠉⣴⡿⠃⠈⠀⠀⣰⠟⣵⠿⠟⠉⠀⠀⠀⠀⠘⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠫⣾⣿⠿⠋⠛⠛⠁⠸⠋⠀⠀⠀⠀⠈⠁⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣻⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣾⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣾⣿⣿⡿⠿⠿⢃⣀⣀⣀⣀⣤⠴⠶⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⢟⣩⣴⣶⣶⣾⣿⡿⣻⣿⡟⠡⡜⢿⣼⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣀⠸⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⢷⢹⢸⡿⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣮⡉⣸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⠀⡟⠀⡟⡾⡇⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣇⢹⣿⡇⣿⣿⣧⣈⣉⡙⢿⣷⣶⣤⣀⡀⠀⢙⣦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣻⣽⡔⢮⣅⣈⣛⣛⣫⣥⣾⣷⣮⣝⠻⢿⣿⡿⠿⠛⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠿⡿⣦⣝⡛⠿⠟⠛⢋⣛⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⠉⠉⢉⣴⠟⠉⠉⠀⠙⠃⠀⠀⠀⠐⠳⣶⣶⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣼⡿⠿⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡤⣤⣤⢀⣤⣤⣤⣤⢠⣤⡄⣤⣤⡤⣤⣤⢠⣤⣄⢠⣤⡄⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡌⠁⢸⣿⠘⢿⣷⣬⣉⠀⣿⣦⣼⣿⠀⣿⡇⢸⣿⣿⣦⣿⠀⣿⡏⢈⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⣾⣿⠼⡿⢶⣿⠿⢰⣿⡆⢼⣿⠤⣿⣧⢼⣿⠌⠿⣿⠀⠻⣿⡶⢿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢒⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⢤⡀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢼⣆⣀⠀⣀⣤⣶⣿⣟⣛⣿⣿⣿⣿⣿⡟⢿⣷⣶⡅⠀⠀⠀⠀⢀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣼⣷⡘⢷⣽⡿⠿⠿⣛⡋⡉⠛⠛⠻⣾⣿⠏⣴⣿⣶⣄⠀⠀⠓⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣞⠉⠀⣴⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⠀⠈⣉⣉⣉⣡⣄⣜⣷⣿⣿⣿⣷⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡁⢈⣧⣾⣷⣾⣿⡯⣄⡀⠀⠀⣠⠴⡒⡋⠉⠉⠀⠈⠠⠀⠀⣉⣻⣿⠿⢿⡿⢿⡿⣿⡿⢟⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢍⣉⣿⣿⡿⠋⠀⠀⠉⣽⠟⠉⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠞⠐⣛⠛⠈⢀⡼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⢠⠀⣱⠟⠇⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠠⣄⡈⣿⣦⣾⣥⣇⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢫⠀⣒⠿⡈⠠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣛⠶⣄⠈⠁⠉⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢦⣄⡠⠀⠀⠀⣤⠀⠀⣰⡦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢖⣛⣿⡦⠖⢻⣿⣿⣿⠦⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡿⠉⣹⠃⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⡀⢰⢖⡓⢲⠶⠚⠁⠀⢰⠇⣰⠏⢇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣷⣀⠀⡀⡠⠚⠙⡟⡇⡿⠀⠀⠀⠀⢸⢞⣅⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢻⣿⣿⣿⣷⣾⣄⡜⡇⢀⣿⠇⠠⣀⠀⣀⡄⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⡱⢄⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣆⠀⢹⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡐⠀⡄⡌⠙⢻⣶⣯⣿⠿⢿⣿⡿⠿⠿⣿⣿⣿⠿⠛⡿⠲⠁⠀⡠⡀⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢳⠮⠥⡘⠃⠀⠀⠀⠙⢿⣷⣆⠈⠚⢿⣿⣿⣿⡿⠁⠀⡰⠃⠀⠀⠀⠈⠛⣀⠭⢶⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⣤⠀⠀⠀⠀⠙⢻⡄⠀⠈⠹⣿⣿⠀⠐⡏⠀⠀⠀⠀⢀⡔⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣥⠀⠀⠀⠀⠀⠀⠿⠒⠦⣤⣿⢟⠁⠀⣧⠀⠀⠀⠀⢤⡁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠻⣄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢛⠽⢻⣶⣄⠀⠀⠀⠀⣀⣤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠀⠁⠀⠉⠈⡟⠓⠀⡤⠾⣽⣶⣿⣿⣿⡷
⠀⠀⠀⠀⠀⣺⣦⡀⠑⡄⠀⠀⣀⣀⡀⠀⢸⠇⠀⢸⠇⠀⠀⠈⠙⡿⠛⠁
⠀⠀⢄⡀⠀⠙⠉⡇⠀⣸⠴⣾⣿⣿⣷⡄⠟⠀⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⣴⡶⢶⣾⣿⠷⣆
⠀⠀⠁⢁⣈⣁⡼⠁⡰⢃⠀⣹⣿⣿⡶⣿⠀⠀⠀⢸⠁⠀⠀⠀⣏⠀⠀⢸⣇⣀⣼⣿⣷⣄⢿⣄
⠀⠀⠀⠀⠈⠛⠦⢞⡵⠋⠻⣿⣿⣿⠾⠁⣶⠀⠀⣿⠀⠀⠀⠀⣿⡀⠀⠚⠿⠿⢿⣿⣿⣟⣓⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣤⣤⣤⣬⣽⠿⠆⠀⢿⣶⣶⣿⣿⣿⣿⣶⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⣿⠀⠀⠀⠀⠈⠛⢿⣿⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⢡⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠎⡐⢁⠞⡠⣊⢔⡁⢒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣰⣘⣃⣃⣊⣐⣡⣊⣊⠕⡰⠲⠕⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣲⠟⢹⣿⡿⡪⠋⠛⣽⣽⡝⡟⠹⣷⣷⣯⣀⣠⡾⠪⣂⢐⢌⢂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⢀⣤⠔⠛⠿⠱⠑⡀⡢⠙⣿⡇⡄⠜⣾⣿⣟⣄⣜⣿⣿⣻⡟⠊⠻⣿⣷⡶⢵⣯⡇⠀⠀⠀⠀⠀⠀⣠⣶⣫⡂
⢀⣠⠖⣁⠣⠖⠇⠀⠀⠀⠀⠍⠉⠎⢅⢄⠌⢜⣿⣞⢀⠈⠜⣿⣽⡟⠔⠴⣽⣽⣟⣔⢜⣿⣿⢁⣦⣿⣷⣘⡮⣿⣥⠂⢀
⠫⣁⠑⢬⡁⣧⢠⠆⠀⠂⡙⠂⠃⣀⢂⡎⠊⠊⠻⠏⠔⠐⡠⣻⣿⠏⡊⡀⣾⡿⣫⠎⠨⠛⠋⠉⣉⢉⢩⣉⡡⣿⣆⠡
⢀⠈⣢⢤⠳⡈⠜⣠⠤⠈⠀⡠⢠⡾⠛⠇⠀⠀⡐⠄⡸⡈⢀⡿⠋⠈⢁⠁⠙⠈⢄⢠⣢⣥⢾⣉⠀⠀⠀⠀⠙⠯⣍⠒⡠
⠀⠀⠈⠁⠉⠐⠲⠤⢤⡄⠀⠐⠰⡋⠅⠲⡀⠄⡠⢑⠀⠀⠎⡈⣖⣱⣕⡤⠴⠚⠻⠛⠈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢺⣷⠖⣚⣒⠛⠒⠓⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣲⡽⡟⢌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣀⠈⢁⠘⠋⢹⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠞⠁⡠⠊⠀⡠⠊⠁⢈⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⣴⣁⣀⣜⠀⢀⠔⠁⠀⡐⠁⠀⣨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣚⡋⠉⠉⠉⠉⠉⠉⠙⠓⠶⢮⣀⡠⠊⢀⠼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠈⠳⣎⣀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠒⠒⠲⠤⠤⠤⠤⢄⣀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠘⡷⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠤⣄⠀⠀⠀⠀⢀⣀⣀⠀⠈⠑⢤⠀⠀⠙⡄⠀⠀⠀⠀⡧⠙⣧⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠱⡀⠀⠸⡀⠀⠀⠀⠀⠀⠸⣇⢈⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢇⠀⠀⠀⡗⠀⠀⢹⡅⢈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⣉⢱⠀⠀⠀⠀⠀⢀⣤⠶⠾⠶⢶⣄⠀⠀⠀⠱⡀⠸⡀⠀⠀⡇⠀⠀⠀⢻⡄⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⡼⢠⠋⣠⣹⠇⠀⠀⠀⢠⠟⠁⠀⡀⠤⣀⠈⠻⣄⠀⠀⢣⠀⢡⠀⠀⡇⠀⠀⠀⠀⣿⠿⣿⠟⠒⠒⠒⠛⠛⠛⠉⠉⠉⠉⠀⢀⣿⣿⣿
⢀⣀⣀⣀⡀⠀⠀⣇⡌⢸⣿⣿⠀⠀⠀⠀⡞⠀⢠⠊⣴⣶⣌⢳⠀⢹⡄⠀⠈⡆⠘⡀⠀⢧⠀⢀⡴⠊⠁⣀⠻⢿⣿⠆⠒⠀⠀⠈⠉⠉⠉⠁⠀⠀⣽⣿⡁
⠸⣿⡟⠉⠉⠛⢲⣿⠸⣌⣹⠃⠀⠀⠀⠀⢹⡀⠘⣄⠻⠿⠋⡼⠀⡼⠀⠀⠀⢧⠀⡇⠀⣈⡶⠋⢀⣤⣊⣀⠠⠴⣿⡶⠖⠤⠤⠄⣀⣀⠀⠐⠒⠚⣿⣿⠃
⢀⣿⡿⠂⠤⠄⣼⠈⢣⠜⠁⠀⠀⠀⠀⠀⠀⠑⢤⣈⣑⣒⣋⡤⠞⠁⠀⠀⠀⢸⠀⡇⠀⢼⣒⠉⠁⠀⠀⣀⣤⣴⡿⠃⡒⠒⠂⠤⠤⢀⣈⠉⠁⠐⢿⣿⡄
⣸⣿⠦⠤⠤⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⠉⠀⠀⠀⠀⠀⠀⠀⡼⢰⠀⠀⠀⢸⠙⠲⣄⣠⣿⠏⠉⡐⠂⠄⡁⠒⠢⢄⡀⠀⠉⠒⠠⣾⣿⡇
⣿⣯⠀⢀⡠⠔⢻⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⡩⠚⢸⡆⠀⠀⠀⠀⠀⠀⢀⠇⡎⠀⠀⠀⢸⠀⠠⠀⡍⢹⠁⠒⠤⡁⠢⢄⠉⠂⠄⡀⠁⠂⢀⣠⣿⣿⡇
⢸⣿⠋⠁⡠⠔⠉⣧⡀⠈⠙⢟⡛⠩⠍⠒⡖⠉⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡎⡼⠀⠀⠀⠀⡎⢠⠃⢰⣀⣸⢁⠢⢀⠀⠑⠤⡁⠢⡀⠈⠑⢤⣴⣿⡿⠟⠁
⢸⣿⣤⠞⠀⠀⠔⠀⠳⣤⡀⠀⠙⠲⠤⣰⣄⣠⠤⠚⠁⠀⠀⠀⠀⠀⣠⢎⡜⠀⠀⠀⢀⠜⣠⣦⠶⢋⠙⣿⢦⡑⠄⠑⠢⡀⠈⠢⡀⠀⢀⣠⣿⣿
⠘⢿⣇⠀⢀⠎⠀⠰⠀⢨⠙⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢞⡥⠊⢀⣀⣤⣴⣿⣫⣁⡄⠀⠀⠐⣿⡇⠹⣆⠀⢀⠈⠢⡀⢈⣦⣼⣿⣿⠁
⠀⠈⢿⣿⣏⠀⠀⠃⠀⠀⠀⡇⠀⢈⠉⢛⣶⣶⠶⠴⠮⠥⠤⠶⠾⣷⠚⣏⢻⡁⡙⢦⣉⠉⠛⢷⣶⣬⣶⡿⠁⠀⠈⠻⣶⣿⣶⣿⣿⡿⠛⠛⠁
⠀⠀⠀⠙⠿⢷⣾⣤⣤⣶⣄⣤⠀⢀⣦⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠷⣷⡌⡂⡈⢹⣦⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣤⣾⡟⠾⣦⣴⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣦⠀⠀⠀⠀⠀⢠⠃⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⣒⣺⠇⣠⠶⢷⠀⡌⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠶⠿⣿⣿⣿⡟⣦⣼⠚⡇⢠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣉⠉⠛⣇⠀⠈⣿⠟⠀⢸⡟⣆⠹⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⠷⣆⠘⣧⣰⡏⠀⣠⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢻⠁⡠⠬⣿⣷⡘⣿⣇⣼⡏⠀⠈⢿
⠀⠀⠀⣀⡀⠀⢀⣀⣻⣿⣧⣴⣿⣿⣿⣿⣿⣿⠎⠸⣷⡀⣀⣿⣷⢸⣿⣿⣷⠊⠀⣸
⠀⠀⣾⣿⣿⣷⣾⣿⣿⣶⢟⣽⠿⣿⣿⠿⠿⣧⣀⡀⣈⣩⣿⣭⣿⣼⢻⣿⣟⠉⣡⠏
⠀⠀⢿⣿⣿⣿⣿⢿⣾⣧⣿⣟⣢⡘⢿⣷⠀⠙⠻⣿⡿⠿⡿⠿⡿⢿⣿⠉⠙⠛⠁
⠀⠀⠀⠙⠛⠉⠀⢶⣽⣿⣿⡿⣧⣃⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠻⠿⠿⠯⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣀⣀⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠠⡀⠀⠑⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠉⣶⣄⣻⣯⣿⠿⢟⣻⡦⠀⠀⠰⡆⠀⠄⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⠀⢿⣿⣿⣏⠀⢸⣽⣽⠇⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡰⣿⣿⣦⣀⣬⣙⣛⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⣻⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⠟⠛⠋⣀⣤⠞⠋⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⣤⠤⠴⢶⣯⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣿⣿⣿⣷⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⣿⣿⣿⣿⣿⡟⣻⠷⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣿⣿⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢁⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠙⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⡌⠀⠹⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠐⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣆⣶⣶⣶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣧⠺⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣆⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⠿⣿⡿⠿⠿⢯⣭⣿⣿⣾⣿⣮⣜⡿⣆⠀⢉⣦⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣒⠚⠓⠈⢀⣀⣀⡼⢥⣿⣿⠼⠋⠛⠻⢿⣼⡄⠀⢀⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢠⣾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠒⠒⠢⣤⣤⠰⢿⣿⡦⠌⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣤⣤⣤⡾⠙⠏⢀⣼⠅⠀⠀⠒⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣀⡔⢿⣿⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡎⢠⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠀⠀⠀⠀⢀⠀⠀⠐⠀⣀⠤⠀⠀⢀⠀⠀⠀⠘⠄⠀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠉⠠⠀⠘⠓⠁⠀⠀⡐⠂⠾⡐⢄⡀⠀⢠⡘⠀⠄⢼⣷⡤⠅⢷
⠀⠀⠀⠀⠀⠠⠄⢰⡀⠀⠂⠠⠀⠀⠀⠀⣰⡿⣣⣾⣧⣁⣈⠀⣇⠉⠀⠀⠀⡀⠱⡄⠈
⠀⠀⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⠀⠈⠆⠠⠄
⠀⠀⢳⡀⠀⠈⠛⠿⠿⠷⠾⠲⠶⠶⠶⢶⣶⣒⣛⣛⣛⣛⣛⣉⠉⣿⠀⡸⠃⠀⠀⠀⠀⠂
⠙⠛⣉⣉⣐⣛⣛⣛⣋⣁⠀⠀⠈⠛⠿⠯⠭⢥⣤⠀⠀⠀⠀⠀⠀⢹⡗⠰⠀⠀⠀⢱⠀⠀⠁⠀⠀⣠⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣦⣬⣭⠉⠁⠀⡀⢠⠀⠀⠀⠬⣤⣴⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⡉⠀⡀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠀⣿⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⢰⡀⠀⠀⠛⠁⠀⠀⢰⡀⠐⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼⠁⠠⠄⠀⠀⠀⠀⠀⠀⠁⠐⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡓⠀⠀⠀⠄⠈⠛⠉⠓⠄⠀⠠⠀⠀⠐⠊⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠽⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣀⣀⣤⣤⣶⣦⣀⣀⣀⣓⣠⣤⣤⣤⡀⠀⠀⠶⠿⠿⠛⠛⠉⣉⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠉⠉⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⢐⠉⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠻⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢠⡾⠿⠟⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⡼⠋⠉⠉⠛⢿⡆⠀⠀⢀⡎⠀⠀⠀⠀⠊⠈⠻⣿⣦⡀
⠀⠀⠀⢀⠄⠈⠉⠉⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢀⠂⢀⣀⠀⣀⣾⠡⢤⣮⣤⣤⠤⠤⠤⠾⣥⣀⢴⣍⠀⠀⠀⠀⠀⠀⠀⠄⠚⢿⣷⡀
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠠⠶⠐⠋⠁⠉⠉⠁⢸⡇⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠙⢦⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠈⠒⠀⠀⠐⠀⠀⠀⠀⠀⣀⣤⠒⠉⠛⠓⠲⠦⣤⣀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠁⠲⣤⡀⠀⠀⠀⢻⡀⠹⡆⠀⠀⠀⠀⠀⠈⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠘⠛⠒⠲⠦⢤⣀⡈⠙⠳⢤⡀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠘⡇⢠⡇⠀⠀⠀⠀⠠⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠑⠶⣤⡉⠳⣤⡈⠙⠶⣤⣀⠀⠀⠀⠀⠘⣇⠀⢀⣧⠼⠖⠂⠠⢤⣀⣠⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢂⠠⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⠙⢆⠀⠀⠈⠙⢦⡀⠀⠀⣿⣴⠟⠳⣦⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⡀⠈⢳⡈⢣⡀⠀⡁⠀⠀⠉⠉⠛⠧⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠈⠰⠀⠀⠀⠀⢿⠀⠀⢱⠈⣷⠀⢡⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⣠⣾⡿⠷⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣴⣿⣷⡇⠀⠀⢀⠈⠀⠀⠀⡆⢸⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⣿⡟⠁⠀⠀⠈⠓⠢⢿⡄⢠⠋⠀⠀⣀⣡⣀⠀⠀⢿⣿⠟⠀⠀⠀⡼⠀⠀⠀⠀⡇⠀⣷⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⣼⡷
⠀⠘⣿⡧⠄⠀⠀⠀⠀⠀⠀⢧⠈⢄⠀⠰⣿⣿⠃⠉⠙⠋⠁⠀⠀⣠⡾⠃⢠⠀⠀⠀⡇⢠⡿⢋⠁⠀⠀⠀⠀⠀⠀⢂⣰⣿⠃
⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠑⠂⠉⠁⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠆⠀⠀⢸⣠⠞⠁⢼⣦⣄⣀⣀⣀⣀⣴⣿⠟⠁
⠀⠀⠀⢻⣿⣅⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⢀⠎⠀⢀⣤⠟⠁⠀⠀⠈⠙⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠙⢿⣷⣆⡀⡀⠀⠀⣠⠻⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⢀⠔⢁⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⠉⠐⠤⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠢⡀⠀⠸⡇⠀⠀⠀⠀⡀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠑⠆⠀⡇⠀⠀⠀⠐⠁⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠑⠄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⡌⠀⠀⢃⠀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠉⠁⠑⢢⡄⠀⠀⠀⠀⠀⡄⣀⣤⠨⠿⠀⠉⠁⠠⠀⠀⠒⠓⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⡀⠾⡀⠀⡀⠤⠀⠤⠤⠘⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢙⡿⠄⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⢀⣉⣣⡐⠀⠂
⠀⠀⠀⠀⠀⡴⠀⠀⠙⡎⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡏⠀⣰⣾⣿⡏⠠⢠⣿⣿⠃⠙⠤
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡀⢀⣠⣤⡌⠙⢶⠄⣠⡿⠀⠀⠻⠿⠟⠁⠀⠀⠠⢀⡀⠄⠀⠐
⠢⢄⡀⠀⠀⢷⠀⠀⠀⠀⠉⠲⣤⣀⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠙⠦⣰⠆⡿⢘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠗⢹⡆
⠀⠀⠈⠀⠒⠘⠃⠠⠤⢀⣀⠀⡆⠩⠏⠛⠶⢤⣀⠀⠈⣦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠁⠃⡜⢀⠀⠀⠀⠀⠀⠠⠒⠒⡈⠀⠀⢀⣼⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⠀⠀⠀⠈⠙⢦⡈⢧⡀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢠⠙⢄⠳⣄⡀⠀⠀⠀⠀⢀⣀⣤⣲⠟⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠉⢢⡙⢦⡀⠀⠀⠀⠹⣷⡀⠀⠀⢀⣴⠙⣄⠀⠑⠦⠍⣉⣉⣀⣉⢿⣽⠞⠡⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⠀⠀⠀⠀⠜⠀⠘⢆⠈⠲⣄⡀⠀⠈⠛⠿⠒⠉⠙⢷⣤⣙⢶⣤⣤⣤⠴⠲⣇⠠⡥⠦⠰⠧⠄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⠄⠓⠉⠀⠀⠀⠀⠀⠀⠈⠢⡾
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣦⠀⠀⠀⠘⠃⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠈⢄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢠⠇⠀⡠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠀⠀⠀⠀⠀⠘⣦⡀⢀⡎⠀⠰⠁⠀⠀⠀⢀⣠⠖⠀⠄⢀⡀⠈⠳⡀⠀⠘⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠁
⠀⠀⠀⠀⢠⠎⠀⠐⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠉⠛⠤⠴⠆⠀⠤⠄⠚⠉⡌⠀⠀⠀⠀⠀⠒⠠⢧⡀⢶⡀⠀⢀⣠⠴⠋⠁⠀⠀⠜⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢌⡉⠉⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠞⠁⠐⠔⠀⠀⠀⠀⠙⢧⡤⠄⠃⠁⠀⠀⠀⠀⠀⠀⡰⠃

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣦⣠⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⢀⣀⣤⣾⣿⣷⡚⠓⠂⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⡤⠊⠁⢈⠂⠀⠀⠙⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⡧
⠀⠀⠀⢀⠀⠉⠘⠒⠤⠀⡤⠀⡀⠴⠦⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠈⠳⡄⠀⣀⡴⠋⠀⠀⠀⢀⠀⠀⠘⢛⣟⠃⠟⠙⠛⠛⢻⣿⣦⣄⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠷⠶⠶⠶⠓⠚⠉⠀⠀⠀⠀⠚⠰⣦⠀⠀⢹⡶⣤⣀⣀⢢⣄⣮⣵⣿⣷⠶⠶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣀⣀⣠⣀⣾⣿⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣯⡉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣇⢁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⢻⢠⣏⠂⡴⢐⢸⡇⣴⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠋⠀⠙⠊⠋⠉⠉⣇⠘⢺⡗⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡾⠋⠡⠊⡀⠀⢸⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠘⢷⣶⣆⡘⠁⠀⠸⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣤⣴⣿⣾⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣰⡄⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠶⠚⠙
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⢻⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣀
⠑⠃⠀⡰⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⡞⠋⠁⡢
⠀⠀⣸⡇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⢰⡞⠂
⠀⠀⢿⡇⠀⡞⠀⢀⡔⠀⠀⢠⡄⠀⢡⠀⣧⠀⢠⠰⡟⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠁⠀⣻⡇⢠⡇⢀⡿⠁⠀⠀⠀⠀⠘⡉⣇⣻⠀⡆⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠄⠀⣿⣇⡼⠁⣼⠇⠀⠀⠀⠀⠀⠀⢹⣿⡟⣸⣏⣴⣿⢃⡀⠀⠀⣀⣀⡤⠘⢿⣼⣸⠟⠶⣶⣶⣦⣤⣀⠐
⠀⢠⣿⡟⢁⣼⠇⠀⠄⠀⠀⠒⠀⠀⠀⠙⠷⠟⠿⠿⠛⠚⣠⣴⣾⣷⣶⣶⣆⣀⣿⡗⠇⢤⣼⡾⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣤⣀
⠀⣸⠟⡴⠟⢁⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡏⢀⣹⣧⡷⣀⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣰⠟⣭⣷⣦⣽⣧
⢰⣿⣫⠔⠚⠋⠉⠀⠈⠉⠙⢶⡀⠀⡀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠒⣶⣿⣶⣿⡿⠙⢿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⡖⠔⡄⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⣾⣿⣿⠟⠫⠁⠈⠲⡟⢿⣿⣷⡄⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠋⠈⠉⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠀⠀⢀⣀⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣛⣋⣭⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠙⠻⣭⠭⠿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠳⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⢱⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⡀
⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠁
⠀⠀⠀⠀⣿⠃⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⢀⣄⠀⢁⣤⣄⡀⠀⣤⡀⢠⣄⠀⣤⡀⢠⣄⠈⢩⡍⠁⢀⣤⣀⡀
⠀⠀⠀⢰⡟⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠋⠀⣿⠀⣿⠀⠘⠇⠀⣿⠀⢸⡇⠀⣿⠁⠸⣿⡄⢸⡅⢠⡟⠀⠘⠇
⠀⠀⠀⠸⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣴⠀⠀⣿⠀⢿⣦⣀⠀⠀⣿⣀⣸⡇⠀⣿⠀⢀⡻⣇⢸⠇⣾⡷⣆⣀⣀
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠛⠀⠀⣿⠀⠈⠙⢻⣷⠘⣿⠉⢹⡇⠀⣿⠀⠰⡆⢻⣼⡅⢿⡇⠀⢸⡏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣆⠀⠀⣿⠀⣿⠀⢸⡇⠀⣿⠀⢰⡇⠘⣿⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣃⡀⠀⢐⣟⣀⠛⣳⣖⠁⢀⣿⣆⢸⣷⡀⣿⣇⣸⣧⡀⢹⡀⠀⠙⣳⣞⢿
⣿⣿⡿⠿⣿⡿⠿⠿⡿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠐⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⡂⣄⠀⠀⣸⠀⡈⠁⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠀⠀⣀⠀⠀⠀⢀⡶⠀⠀⡄
⣀⡄⠈⣿⠀⠀⠀⠀⠀⠀⠤⠀⡰⣄⠀⠸⠇⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠈⠐⢶⠗⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠰
⠶⠦⠛⠉⠹⣋⢛⣴⣦⣤⡆⠄⣐⠀⢣⠰⠛⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⠔⠊⢁⠀⠀⡀⠀⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠙⠂⠘⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠮⠡⡀⠀⠀⠈⠉⠉⠻⠂⠀⢠⣄
⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⠄⣀⣀⡄⠔⠂⠈⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣀⢀⣀⡀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠉⠑⠖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠰⠿⡓⠡⠆⠂⠤⣥⣖⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⠦⡖⠀⠀⠀⠀⠀⠀⠀⠃⠐⢠⡼⠉⢝⠲⠀⢀⣶⠠⠔⠀⠁⠀⠀⠆⠈⠁
⠀⠀⢠⢤⡤⣶⢏⡌⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠙⢤⠤⣶⢺⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⢄⠚⣶⡄⠀⠀⠀⣆⡁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠙⢤⡆⡀
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⠌⠠⠋⠀⠉⠀⠀⣰⢃⡃⠀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠠⠀⠀⠀⠘
⣤⣤⣦⣜⣀⡛⠀⠈⠈⠀⠐⢀⠊⠀⠀⠀⢰⡾⠞⠁⠎⠀⠀⠐⠀⠀⠀⡆⠐⠀⠈⠐⠁⠒⠀⠉⠀⢀⣠⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤
⠈⠁⡉⠀⠐⠃⡤⠀⠤⠠⠞⠁⠀⠀⠀⠀⠛⠁⠈⠂⠀⠀⠀⠀⠀⠀⠍⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣀
⠠⠐⢀⠄⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⣠⡀⢄⠀⠠⠁⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢰⡆⡀⠀⠘⠿⠃⠂⠀⢈
⠟⠀⢁⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠈⠀⠀⠀⠀⠈⡴⠀⢀⡀⠀⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⢀⡀⠢⠠⠈⠓⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡄⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⢄⠀⠀⠀⠀⠀⠀⡂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠆⠀⠀⠀⠀⠀⠘⡂⠀⠀⠠⢾⡿⠈
⠀⠀⠀⠀⡨⠣⠄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢣⠹⠌⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠁⠈⠀⠀⣠
⠀⠀⠀⠘⠀⠀⠂⠀⠄⠀⠀⠀⢀⣰⠆⠀⠀⠀⣀⠀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠄⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⣀⡔⠁
⠈⠀⠀⠀⠀⠄⠤⠊⠈⠀⢣⡀⠠⠁⡆⣀⠖⠉⠀⠁⠀⠈⢋⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠔⠈⠀⢀
⠀⠈⠐⣄⠀⠀⠀⠀⠀⢈⠄⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢰⡵⠂⠉
⠺⠃⠀⠁⠐⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠠⠀⠉⠊⠉⢳⠂⠀⢄⡰⢾⠀⠀⠚
⢂⠒⠀⠀⠀⠀⠀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈⠺⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⢦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣄⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣟⣷⣼⣿⣿⣿⡿⢟⣯⣽⡟⠟⡴⢋⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⢷⣶⣿⣿⣿⣿⡿⠋⠑⢋⡽⢛⡅⣠⢿⠟⡉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠻⠿⣿⡘⣿⡇⡄⠀⠀⠀⢉⡞⠟⢸⣴⣷⣦⣿⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⠀⣘⣶⣶⣝⠻⡧⢳⣄⣀⢀⣼⣤⡄⣨⡭⠭⣂⣀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠽⣿⣿⠀⢷⣆⠛⠛⠛⢛⡭⠀⢰⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣷⣤⠙⠿⠶⣟⣫⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠩⢭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⣠⠴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣣⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⡏⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢿⣿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⠈⢻⣷⣄⠀⠀⠰⠿⣧⣀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡇⠀⠀⠀⢿⣿⣷⣦⡀⠀⠀⠉⢿⣿⡟⠋⣉⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇⠀⣦⡄⠈⠿⠟⠙⠻⣷⣤⣤⣾⣟⠳⣌⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⢻⡝⢳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠰⢦⣄⣀⣛⣙⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣭⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣟⡽⠚⠋⠉⠀⠈⠁⠀⠀⠀⠠⣄⠀⠰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣶⣶⣾⣷⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⢋⡄⠀⠀⠀⠀⢲⡴⠋⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⢃⠀⠿⢿⣿⣿⣦⡾⠁⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⡥⢾⠀⢠⣶⡇
⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠈⠳⠀⠘⠟⠁⣿⠇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠙⠻⢿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣷
⠀⠀⠀⠀⣰⠿⠁⠀⠈⠉⠀⠀⠀⠀⠈⠈⠓⢀⡀⠤⠤⠄⠻⠀⠀⠀⠸⠹⡤⠀⠀⡐⠀⠔⠈⡇⠀⠀⠀⠀⠀⠲⠈⠀⢀⣀⡀⢻⡆
⠀⠀⠀⢠⠏⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢰⡆⢛⠶⠄⠀⠀⠀⠀⢀⠑⠀⠀⣶⣄⠀⠁⡠⠂⠀⠀⠀⠀⠀⠀⠠⣍⠡⣦⡁⣀
⠀⠀⠂⠈⢢⡈⠛⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠰⠋⣠⡎⠀⠀⠀⠘⢿⡀⡠⠖⣁⡠⣴⠊⠀⠀⠀⠀⠀⠀⠙⢶⣾⣿⣶⣶⠟
⠀⠀⠐⠗⠤⣅⣀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣯⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⢀⣤⠖⠚⠉⠉⠁⠒⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⣻⣿⡿⠛⢻⣿⣿⣦⡀⠀⢸⣿⣷⢹⡄⠂⠀⠀⠀⠀⢀⣤⣾⣿⠋
⠀⠀⡠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⣿⣿⣿⣿⡀⠀⢿⣿⠇⠁⢀⠁⠀⠀⣾⣿⣿⡿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃⠀⠀⣿⣿⣿⣿⡇⡠⠊⠀⠀⠀⢿⡆⠀⠀⣿⣿⣿⡇⠐
⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠠⠐⠈⠀⠀⠀⢀⣿⣿⣿⣿⣸⣧⣀⣠⣴⣿⠘⣿⠀⠀⢿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠋⠁⠁⣿⣿⣿⢸⡿⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⡏⣼⠁⠀⠀⠀⠛⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⢀⣴⣿⣿⣿⣿⠁⠀⠀⢰⢸⣿⣿⣇⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢛⣿⣿⣿⣿⡇⠀⠀⠀⠘⢸⣿⣿⣿⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿⣦⠉⠃⢄⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠘⣿⠀⠀⠀⠈⠀⠀⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⣿⣼⣿⣻⣟⣩⣿⣾⣀⢴⡿⣿⠯⢀⣩⡐⢺⠦⣿⠙⣽⣾⢻⣟⣹⡯⣿⢻⠤⠦⢀⣶⣂⠤⣤⣤⣄⠀⠃⣶⣴⡄
⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠉⠉⠀⠀⣩⣿⣿⡿⠻⠙⢷⣄⡙⠀⣇⣼⡞⣯⣿⣷⣿⣨⣧⡏⠈⠁⠝⡘⣯⡿⢹⠋⢰⢞⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⢋⣠⣤⣦⣿⣿⣿⣀⠈⠭⠵⠯⠌⠸⠟⠟⠇⢤⡤⠙⣿⣿⠇⠀⣴⣗⠼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⠀⢸⡧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣯⣿⣻⣿⣿⢟⣻⣿⣿⣷⣯⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⡇
⠀⠀⠀⠀⢀⡀⣴⢿⣿⣿⣿⣿⣿⣿⡛⠩⡽⠎⠈⠓⠊⠁⠉⠙⢼⡽⠃⢘⣿⡯⣵⠉⢻⣿⣷⣄⡀⠀⠀⠀⠀⠉⠛⣻⡷⠇
⠀⠀⢰⡾⣏⡿⢋⣿⣿⡟⣿⣿⣿⠁⠂⠀⠀⢀⣀⠀⠀⠀⠀⢠⡶⠁⠀⠈⠉⠁⠀⠀⠈⠴⠬⠻⣧⡀⠀⠀⠘⠳⠾⠙⠇
⠀⢠⢤⣷⡽⣤⣿⣿⣿⣴⣿⡿⠉⠀⠀⠀⣀⠜⢿⣦⠙⢷⣤⣸⣿⠳⠤⠀⠀⠀⣀⡔⠀⣀⣤⠴⠒⣬⣶
⠀⢹⡄⢿⣷⣿⣿⣿⣿⡿⣿⡇⠀⠀⠘⠋⣁⡈⠀⠙⠃⠘⠻⠿⠌⠳⣄⠈⠶⠬⠄⡁⠈⠙⢁⣴⢋⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⣿⣷⠙⣿⣻⣿⣿⣿⣿⣷⣤⠶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣽⣿⣦⣤⣤⣬⣷⣤⣥⣈⣙⣳⢦⡆⠀⠀⠀⣿⣿⠋
⠀⢀⣿⣿⠀⠛⢿⣿⠻⣿⣿⣾⣧⢀⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣿⠿⣻⣯⣥⣼⡿⣿⣦⢈⠉⢭⡿⠎⠀⠀⠀⠀⠈⠉
⠀⠈⣽⣿⣧⢀⣠⠙⣷⡌⠛⠚⢿⣿⣿⡇⣾⣿⣿⠷⠾⣫⣾⣿⣿⣿⣿⠿⠋⢉⣿⣿⠇⠀⠀⠀⠄
⠀⠀⠸⣻⣿⣦⡈⢁⣙⠻⣦⣀⠈⠉⢻⡇⢸⣿⣯⡿⠟⣵⣿⡿⢃⣴⣶⣶⠏⢉⠛⠉
⠀⠀⠀⠹⣿⠿⠿⢦⣝⣄⠀⠉⠳⣀⣠⣇⢸⣿⠏⢀⣠⣷⣻⠿⠋⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠸⠟⠙⠋⢂⠰⡶⠾⣿⡧⢿⡇⠀⣰⣶⣦⣤⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠵⣮⠓⠉⠁⢾⡇⠀⠀⠀⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⡤⢚⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣾⣾⣿⣿⣿⣶⣤⣤⣾⣍⣴⠋⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱
⠀⠀⢀⣠⣤⣶⡾⢿⣿⢿⣿⠿⠿⣿⡿⡿⢿⢿⡟⣻⣿⡿⣿⢿⢿⡿⣿⣿⣷⣤⣄⣀⣀⠀⠀⠀⣰⠋⣰⠁
⠰⢾⠋⠩⣽⣿⠃⠀⠉⢷⣶⣶⠶⠾⠿⠷⠚⠳⢶⣷⡌⠀⠁⠉⠚⠁⠉⠁⠋⠙⠛⠛⢛⣿⣾⣾⣿⣿⠃
⠲⢦⣧⡶⠈⠁⠀⢀⡄⣾⣸⣄⣀⠄⠒⠒⠒⣈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠋⠉⠉⠙⣿⠿⢇
⠀⠀⠈⠉⠛⠲⢦⣼⣿⣟⣻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣶⣶⣶⣾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠿⡿⠛⠛⠛⠛⠋⠉⠉⠉⠙⠯⣉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡈⠙⠻⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠉⠻⢿⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⢿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡿⠿⢿⣶⣦⣄
⠀⠀⠀⠀⠈⢿⣧⠉⠛⠻⢿⣶⣄⡀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠈⠙⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠉⠻⢿⣦⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⢀⣠⣴⡿⠟⠛⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⢀⣿⣟⣠⣴⣾⡿⠟⠋⠀⠀⠀⠀⠈⠙⠿⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⢾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⣀⣤⣾⡿⠛⠛⠛⠿⠿⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉

⠠⠱⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⡶⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠋⠃⠀⠠
⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧
⠀⠀⠀⠀⠀⢣⣥⡆⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠀⠈⠀⠲⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠘⡃⡔⠀⠀⢸⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠄⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠢⢞⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠘⠁⢐⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢁⡀⢀⠀⠀⠀⡀⠀⠐⠋⠘⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠈⠃⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠖⢰⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⠀⢀⡂⠀⠀⠀⣀⣀⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣅⠉⠀⢀⠛⡔⠀⠁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣶⣌⣠⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠘⠃⢋⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠂⠀⠀⢠⢷⡾⠋⠁⠄⠸⡷⠆⠀⠐⠃⠀⠰⠆⠈⠁⠀⣄⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠸⢼⠇⠀⠀⠀⠀⢠⣶⣦⡀⠀⢰⠀⠀⠁⠀⠀⠀⢘⣈⠁⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠧⠀⠀⠀⢸⡇⠈⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹
⠀⠀⢠⠀⠀⠀⠀⠀⠚⡀⠁⠀⢠⡥⢿⣄⠀⢻⣶⡄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⢸⡀⠀⠀⠀⠀⠠⠁⡄⠀⠈⠀⠈⠙⣧⢸⡆⠀⠤⣀⢒⣾⣿⣀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⢀⣀⣀
⡿⠋⠉⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣈⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⢀⣿⡥⣾⡿
⠃⠀⠀⣸⠏⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣧⠀⢀⡀⠀⠀⠰⣶⣦⣼⡄⠀⠀⠀⠀⠈⢧⠀⠈⢿⡇⠀⠃
⠀⠀⠀⢫⠾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡏⠁⠐⠂⠀⠀⠀⠀⠈⠐⠀⠀⠀⡀⠈⢇⠀⠀⠈⢀
⠀⡠⠀⠀⠀⠀⠉⠀⣀⣀⣤⣶⠛⠛⡐⠂⠀⠀⢤⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡼⠶⣶⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠽⠏⠉⢛⡷⣾⣛⠉⠉⠀⠀⠀⠈⠈
⠀⠀⢤⡀⢀⠠⠖⠉⠀⢀⠈⠉⠀⠀⡠⠀⢤⡀⠀⠀⠀⠁⠀⠀⠱⡍⠢⢭⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠐⠓⠀⠀⠐⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⡶⣧⡇⠀⠀⠀⠉⠉⠛⠛⢷⡴⠞⠁⠀⠀⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⡀⠀⠀⠸⠇⠀⠀⠀⣀⡘
⢙⣀⢀⠀⠀⠀⢀⡦⠀⠀⠀⢀⣀⣀⡦⠀⠀⢀⠀⠀⠀⠀⢀⠎⠲⣀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠐⣾⠐⠉⠳⠒
⠋⡏⣸⠧⠤⠖⠋⢀⣶⢟⡺⢯⣍⣭⡄⠀⠀⠠⠀⠀⠀⢠⡟⣗⠀⠈⠑⠂⠀⠀⠀⢻⠀⡔⠻⠆⡠⠚⠐⠟
⢀⡁⠀⠀⠀⠀⠀⢸⡟⢸⣋⣐⡤⠄⠀⠀⠀⠀⠳⡀⠀⠈⡤⠚⣀⠀⠀⠀⠀⠀⠀⢈⣾⣱⡁⢀⡷⠤⣴⠋⢰
⠘⠀⠀⠀⠀⠀⠀⣠⡿⢛⠿⡿⣿⢯⣧⣠⡀⣰⠀⡗⠀⠀⣹⡉⠱⠆⠀⠀⠀⠀⠀⢸⣬⡉⠙⣿⡀⠠⣟⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠏⠐⣾⠚⠇⠈⣷⡦⣤⣴⡇⠘⠀⠀⠀⢹⡖⠆⢛⠀⠀⠀⢀⡜⡀⠠⠿⣤⣯⣤⣟⣁⣠⣀
⢶⡄⠀⠀⠀⢀⡀⠀⠀⢩⠀⠀⠀⣿⣼⠛⢿⡸⡆⠀⠀⠀⠘⣷⠬⠋⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠉⠈⠉⠉⠉
⠉⠀⢀⡴⡞⢯⠉⠳⠄⠈⠀⠀⢀⣿⡇⠀⠰⣇⠁⠀⠀⠀⠀⠿⡂⠴⣢
⠀⠀⢸⠀⠀⠀⠀⣄⡗⠀⠀⠠⠞⡿⠁⠠⠴⠋⠀⠀⠀⠀⠀⠈⠣⠿⠟⠀⠀⠀⠀⠀⢀⡔⠛⠛⠐⠒⢠⡀
⣀⣀⣰⣛⣆⣀⣂⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣐⣒⣄⣀⣀⣀⣀⣄⣀⣀⣀⣀⣸⣀⣘⣛⣀⣀⣀⣘⣄
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⡀⠀⠀⣀⠘⠻⢛⠛⠋⠉⠉⠉⠉⠁⠐⣒⡄⠀⢄⣀⡀
⠀⠀⠀⠀⠸⣷⡴⠾⠳⠦⠾⠛⠉⠉⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠀⠑⠿⢿⡯⠝⣚⣩⢠⠄
⠀⠀⠀⢀⡀⢽⡇⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠃⣀⣉⡴⢀⣤
⠀⠀⠀⠸⠟⠛⠋⠀⠀⣠⣌⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠠⢐⠁⠀⠈
⠀⠀⠀⠀⠀⠐⢠⠤⢿⠀⢦⠀⠀⠀⠠⣲⡦⠤⠄⠀⠀⠀⠀⣰⡠⠟⠓⠁⣰⠄⡿⠤⡄⠂
⠀⠀⠀⠀⡠⠒⠁⠀⠸⠖⠉⠁⠀⠀⠲⠀⢀⡀⠀⠀⠀⢀⡀⠀⠔⠂⠀⠈⠉⠲⠇⠀⠈⠐⠄⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠷⣦⡄⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠇⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠘⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡧⢤⡀⠀⠀⠘⣧⡀⠀⠀⣠⢤⣿⡀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⠀⠂
⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠈⢳⡄⢳⠀⠀⠀⠘⣧⠀⢸⠃⠈⠀⠄⠀⢸⠈⠀⠀⠀⠀⢠⣶⡖
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢳⡄⠀⠀⠸⣆⠸⡄⠀⢀⡀⠀⢸⢸⠀⠀⠀⠀⠀⠉
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⡆⠀⠀⢻⡄⠀⠀⢀⡇⠀⠈⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠛⠀⠀⠸⣷⠀⠀⣼⠁⠀⠀⠸⡰⠀⠀⠀⠀⠀⠀⠐⠶⠶⣶⠶⠾⠋
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⣤⣀⣀⣸⠏⠀⠀⠁⠀⠀⢀⡄⠱⢤
⠀⠈⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠦⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠈⠙⠛⠛⠛⠁

⠀⠀⠀⢀⢠⠄⠐⠶⠀⠈⢈⡠⠊⠁⠀⠐⠃⠸⠃⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢟⠏⠉⠀⠈
⠀⠀⢰⢁⡾⠀⠀⠀⣀⡼⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠂⡔
⠀⠀⠈⠠⢤⣀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢠⠄⠁⠀⠶⠘⢲⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⡤⠀⠀⠀⠶⠁⢀⡴⡁⠈⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢶⣶⢶⢲⠒⡆
⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠐⡷⣮⡏⠿⠘⢰⠃⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢤⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣤⣴⡖⡖⡆⠀⠀⠀⠚⠳⠧⠆⠎
⠀⠀⠀⠾⠀⢠⠆⠀⠀⠰⣄⠀⢸⣴⡇⠀⠀⠀⠀⠤⠔⠀⠀⠀⢲⣾⡏⡇⠀⡇
⠀⠀⡀⠀⠰⠈⠀⠀⠀⠐⢂⢼⣿⣷⠯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⣰⡾⣠⠀⠀⠀⠀⡤⣡⠻⡟⠻⡕⠀⠀⠀⠀⢠⢿⣷⠀⣠⡤⣶⣶⡶⠀⠀⠀⣄⠒⣄⠀⢠⠀⠀⡆⠂
⢠⠀⠀⢐⣿⠁⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠩⠬⠱⡰⠉⠁⠀⠀⠀⠀⠈⠁⠘⢀
⢸⡄⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡽⣆⠁⠀⠀⠀⠑⣃⠀⠀⠀⠀⠀⠀⣀⡝⠀⠄⠀⣤
⠀⢳⡄⢰⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢸⣿⠁⠝⠀⠠⠄⠀⠄⡑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠃
⠇⣺⡄⣾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⡄⠚⠃⠀⠈⠠⠢⠁⡀⠒⠬⣆⠀⠄⠀⠀⠀⠶⠄⠀⠁⠈
⣇⣟⣼⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠸⠾⠛⠋⠈⠙⠀⣆⠀⠀⠀⠀⠀⡀
⠘⠋⠁⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⡇⠀⠀⠈⠢
⣤⠶⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠈⣆⠘⡇⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⡀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠨⡇⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡯⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢆⣰⡂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⢀⠀⢀⠄⠀⠀⢸⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠂⠀⠰⠆⢠⣩⣅⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠄⣀⣀⠀⠁⠀⠀⠀⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣿⠋⢀⣴⡄⠠⣀⡀⣀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠏⠒⠛⠉⠀⠀⠀⠀⣉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣠⣾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢿⡄⠀⠀⠐⣦⣿⣧⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⠻⣦⡀⠀⠀⠈⠛⠋⠓⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠹⣿⣿⠀⠀⠀⢀⣠⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⡀⠀⠉⠁⠀⠀⠀⠈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠁⠙⠷⣦⣄⣀⡀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⣀⠀⠀⠀⣠⣤⠀⠀⣠⡄⢀⣠⡀⠀⠀⡤⠠⠄⠀⠠⠀⢀⣠⣄⣀⡀⠀⠀⣀⣀⣀⡀
⠀⠸⠀⠉⡜⠀⠀⠙⠿⠃⠐⠿⠀⠐⠛⢋⣤⣤⣤⣶⣶⣤⣤⣄⣈⠙⠉⠉⠁⠀⠻⢿⣿⣿⡿⠂
⠀⢠⠠⠊⠀⠴⢶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠁⣀⣀⠀⠀⠀⠀⡀⠄⠀⢸⢰⢺⡇
⠀⡄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠘⠿⣿⣿⣿⣿⣿⡿⡛⠛⠛⠛⠛⢻⣿⠛⠁⠀⢤⢠⣿⠇⠀⠀⠈⠈⠈⠁
⠀⠈⠑⠀⠀⣾⣖⠀⠀⢠⣤⠀⠀⠉⠉⠀⠀⠀⢡⠄⠀⣀⠀⠀⢠⣶⣆⠀⠈⠻⠀⠀⠀⠈⠛⠀⠀⠀⠀⣶⢠⡄⡆
⠀⢰⣿⣷⡄⠙⠇⠀⠀⠘⠋⢠⠀⠀⢠⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠉⠁⢠⣴⡶⠿⡇⠀⠀⠀⠀⣍⡀⠀⠛⠘⠃⠃
⠀⠘⣿⠀⠀⠀⠀⠘⠃⠀⡀⢸⡇⠀⠈⠉⠡⢠⢀⣤⢠⠉⠉⠀⡤⠀⢀⠘⠻⢷⣦⡇⠀⠀⠀⢸⣿⠄⠀⢠⢀⣀⡄
⠀⠀⣿⠀⠀⠀⠀⢸⣦⠀⣿⢸⣷⠀⠑⠀⠀⠀⠄⠀⠀⠀⢀⠠⠈⠀⠈⣀⣀⠀⠀⠀⠀⠀⢠⠀⠋⠀⠀⢸⠸⠯⡇
⠀⠂⠻⠤⢝⣤⡄⠀⣿⣆⣿⣿⡿⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⢿⡇⠀⠐⠄⠀⠀⢰⡀
⠀⠘⢷⣲⣼⡽⠀⠀⠈⠿⣿⠟⢁⣀⡈⠉⠀⠀⡆⢰⢶⡶⠂⠀⠀⡄⠈⠀⠀⠀⣰⣿⣿⣿⣦⠀⣳⠀⠀⢸⣶⣴⡇
⠀⠀⠀⠉⣿⣇⠀⠐⠀⢀⣴⣾⣿⡟⠓⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠰⣿⡄⠀⠈⠈⠉⠁
⠀⠠⡀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⠃⠀⠀⢰⣿⣷⡄⠐⠐⠄⠀⠄⠀⠀⠀⠀⣀⣸⣿⣿⣿⣥⣄⢼⠃⠀⢀⢤⣤⡆
⠀⠀⠀⠀⠘⣿⠿⡿⢛⡉⠿⠛⠁⠀⠄⠀⠀⠉⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⢿⠿⣿⢻⡆⢀⠀⠰⠛⠹⠇
⠀⠀⠀⣶⣤⠈⠓⠁⠋⡀⠀⠀⣴⠀⠘⡶⠀⠸⠏⢹⡏⠀⠀⣿⠘⣿⡄⠙⢛⣱⢇⡇⣿⢸⣇⡀⠛⠋

⠀⠀⠀⠀⠀⠀⠸⠿⠛⠿⠂⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⣻⣶⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠀⠀⠀⠀⠀⠀⠑⠓⠀⠀⠀⠀⢸
⠛⡻⠀⠀⠀⠀⣀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣵⣠⣶⣶⡶⢶⣖⠒⠀⠀⠀⠀⠀⠐⠛⠀⠺⠿⠿⠀⠀⠀⠀⠀⡏⡀⠀⠠⣧⣷⣾⣷⣾⢿⠇
⠀⠀⠰⠶⡀⠳⣿⣜⢿⣛⠛⢛⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⣼⣿⠿⣟⡆
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣳⠫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣤⣄⡀⠀⠀⠀⠀⠘⣯⣾⡿⠁
⡀⠀⠀⠀⠀⠀⠣⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣠⡴⠾⠟⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⣀⣸⣾⠆⠀⠀⠀⢰⣶⣶
⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⣠⠀⣄⠄⠄⠀⠀⠀⡟⠉⠀⠀⠘⠃⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠠⢤⣀⣄⣠⠎⣽⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠑⢤⣀⢹⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⣀⣀⣀⣺⠩⠁⣀⣬⣤⣤⣒⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠛⢷⣿⡟⠢⠀⠀⠀⡀⢀⣿⣿⣶⡎⣀⠀⢈⣀⣠⣤⣴⡿⣽⣿⢾⡷⣷⡷⠟⢿⣿⣿⣿⣿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⡀⠀⠀⢀⣤⣾⣿⣿⣷⣿⣶⣿⣿⣛⣿⢿⣟⠿⣯⡭⠾⠃⠀⠀⠈⠙⢻⡿⠟⠉
⣤⣄⣤⣴⣆⠀⠀⠀⠀⠀⠰⠝⠿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠐⠀⣠⠬⠟⠚⡻⠟⠀⠀⠀⢀⡠⠔⠋⠁⠀⢀⣀
⠉⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⣽⣿⣀⡀⡠⠄⠒⠀⠠⠽⠖⣚⣋⣉⠠⠄⠀⠶⠿⡿⠿⠂⠀⠀⠀⠛⠛⠃
⠀⠹⣿⠏⠀⠀⠰⠶⠶⠀⠀⠀⠀⣠⠒⠛⣿⣿⠋⠐⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠬⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠟⠛⡉⠉⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⡿⠂⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣶⣶⣭⣵⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠄
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠟⠯⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⢀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠃⢈⣿⡷⠂
⠿⠟⠛⠒⠤⠀⠀⢸⡁⡠⠄⠀⠀⢠⣶⣴⣤⣷⠄⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢺⠟⠛⠁⠀⢺⠟⠁⠀⠀⢰⠤⠤⠴
⠀⠐⠂⠀⠀⠀⠀⠀⠑⠚⠃⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⡀⢠⣶⣾⣿⣯⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⢀⣠⢄⣀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠁⠀⠿⣷⣷⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣿⣿⣿⠿⢿⣿⡿⠟⠋⠓⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣡⣾⣿⡿⠋⠁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠈⠀⠘⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⣀⣒⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⠀⠀⠙⠋⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠟⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⡠⠊
⠀⠀⠀⠀⠀⠛⠓⠶⠶⠖⠚⠛⠛⠛⠓⠲⢶⢶⣶⣶⣿⣿⣿⡁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠛⠛⠋⠉