Spaghetti Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠶⠒⠒⠒⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢲⠀⠸⡇⠈⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠸⠁⠀⠈⠄⠀⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠃⠀⠀⣳⠀⢀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠠⠢⡉⠀⠈⠁⠉⠀⠀⠀⠂⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⡇⠀⢀⡀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⡐⡄⠀⠙⣁⠈⠅⠼⠟⠒⠢⣀⢬⠔⢂⡀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⠄⠄⠸⠄⠤⠲⠀⣵⠁⡬⢀⠀⡌⡶⢦⣄⠐⠀⠐⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠁⠀⠀⢰⢀⢁⠀⠚⡛⠒⡠⠞⠹⠁⠔⠉⢠⣆⠀⡀⡀⠜⡏⠓⠊⢀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠈⣬⢈⠄⢀⠀⠘⡺⠦⠠⣤⠤⠊⠁⠀⢰⠆⠀⣐⠀⣠⠴⠀⢀⠀⠀⠀⡘
⠀⠀⠀⠀⠸⡄⠀⠐⠈⠛⠈⠁⡰⠠⠄⠔⠂⠈⣛⠲⠧⢴⠾⣂⠀⠀⠀⠆⠀⠀⠁⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠂⢤⠂⡀⠀⠀⠤⠂⠈⠁⠀⠰⠔⠓⠂⠔⢶⠂⣠⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠁⠠⢄⠐⠀⡐⠂⡀⢶⠂⠀⠀⠀⠀⠁⠈⠁⠀⡀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠀⢀⡴⠁⠘⢦⡀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠠⠀⡂⣼⠰⣺⣟⡉⢓⡄⠈⢛⣤⣾⣆⢄⣆⣄⠀⢈⠀⠂⠄⣀
⠀⠀⠀⠀⠀⡀⠂⠀⠠⢂⠔⠂⢚⡟⢻⣿⣬⣢⡭⠄⠀⣥⢋⣿⢿⣿⣿⣿⠁⠄⡨⠄⠀⠀⠀⠀⠤⡀
⠀⠀⠀⢀⠆⠀⠀⠀⠁⠀⠠⠀⣾⡿⣾⣛⠫⠵⠈⠒⠈⠣⢸⠫⣿⣿⣿⡦⡟⠌⡔⢡⠲⡀⠀⠀⠀⢱⡄
⠀⠀⠀⠘⣆⠀⠀⠀⡀⠨⠅⠁⢿⣟⠿⣾⣿⣿⡐⣏⣖⣋⣼⣷⣿⣿⣩⣦⣑⡶⣀⠈⠂⠉⠀⠀⠀⣰⠇
⠀⠀⠀⠀⢻⣦⣄⠀⠀⢠⡄⠐⠀⠀⠻⣿⡿⣿⣶⣴⣭⣽⣻⣿⣿⣽⡽⠋⠀⢠⠀⠀⠃⠀⠀⣠⣼⡟
⠀⠀⠀⠀⠀⠙⠿⣿⣦⣤⣈⠀⠒⠘⠉⠈⠻⠉⣻⣟⣈⠏⣉⢋⡠⢀⠲⣥⠂⠉⠀⢀⣠⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣤⣤⣤⣤⣄⣬⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁⣀⣨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠄⣒⣪⡭⠭⠶⠶⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⣖⣶⠒⠃⠀⢰⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣒⣯⢯⢺⣤⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⢿⣼⢻⡿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣴⣿⢬⣿⡎⠁⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠄⠀⠀⠀⠀⠉⠾⢤⣼⠇⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⣀⣀⣾⠟⣉⠲⣤⣠⠞⠊⠑⠒⢣⣤⣤⣸⡏⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⡒⠶⣾⠗⠚⠙⣛⡊⠣⡗⠈⠁⠙⠁⠀⠈⠐⠀⠠⢿⠣⢷⣰⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣯⣎⣀⣽⣷⠁⠀⠀⠀⠀⢹⣾⠋⠀⠀⠘⢤⣤⣀⠀⠠⢼⡗⠀⠀⢀⡿⡶⢦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠑⠋⠁⠉⢛⡀⠀⠀⠀⠀⣀⣼⣖⣂⡀⢴⠻⠖⠀⢠⠀⠌⢳⣀⣀⠜⠋⠠⠀⠈⠩⠯⡍⠙⡦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣾⠀⠀⠀⠀⠀⠰⢋⣭⢾⣻⢚⣿⠉⠄⠐⣠⣕⠷⣿⣅⠀⠀⠀⢀⡆⠌⠳⡀⠑⢁⡴⠀⠰⣾⠁⠀⠁⡟
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢹⡤⢀⠀⡁⠀⡇⠛⠟⣱⣭⣥⣿⢷⣾⡄⢀⣰⠞⣻⢧⠙⠙⠾⠍⠂⠐⣦⡈⢁⡿⣄⡊⣁⠈⠀⣠⠞
⠀⠀⠀⠀⠀⠈⢆⠠⣄⠀⠘⣆⠈⠐⠬⠭⠽⢛⣿⡿⠟⢿⢷⣷⡿⢟⣦⡌⠈⠀⠁⢪⣴⣿⣿⠮⣶⠞⠛⠞⠀⠀⠚⢁⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠧⣤⣀⠉⠉⠉⠈⠙⠯⣧⣬⣤⣓⠙⠛⢷⣾⣞⣿⣤⡬⠿⢚⠟⠁⠀⠉⠁⠀⠤⠀⣀⣤⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢏⣉⠀⠓⠂⠀⠀⠀⠀⠉⠛⠒⠒⠉⠁⠀⣀⣀⣀⣐⣀⠤⠤⠄⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠐⢰⠀⠀⡀⠁
⠀⠀⠀⢀⣿⢈⣿⣐⣀⠐⣀⣸⣿⣀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣾⠀⠀⡇⡇
⠀⠀⠀⠰⣿⠚⢹⡏⣿⢀⣿⢹⡏⣾⢻⣿⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⢀⠀⠤⣄⢦⠞⠀⠀⠀⠀⠀⢸⠀⠸⠐⡟⠀⠀⠁⠁
⠀⠀⠀⠈⣿⠀⠹⡷⠿⠾⣾⠿⠧⠿⡾⠿⠀⠀⠠⠀⢰⠏⠀⠀⠀⡤⢐⣮⡍⠤⠀⠀⠀⠘⠀⠝⠀⠀⠀⠀⠘⡀⠀⢠⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⢀⡏⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⢸⡇⠀⢸⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠶⣬⣥⡄⠀⠀⠀⠀⢨⢸⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠈⢉⡣⢤⣌⠢⡀⡁⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠐⠠⣆⠁⠀⠀⠀⢠⡘⢃⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠴⠄⣀⠀⢒⡊⠙⠚⠷⢂⣰⡬⠃⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠈⠉⠁⠉⠒⠒⠓⠚⠛⠀⠀⠀⠀⠃⡞⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠠⠐⡨⠴⣂⠀⠁⠲⡩⠦⡀⠈⠁⠀⠀⠀⠀⢠⣀⠆⠃⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡇⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠄⡟⠑⡶⣈⢀⣶⣶⠻⠃⠀⠀⠀⢰⠘⠋⡰⠂⣦⣲⠦⠾⠿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠉⠀⠜⠁⠀⠀⠐⠾⠊⠀⣴⠼⠶⠋⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠐⣁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢋⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠠⣀⠀⢤⡀⠀⠀⠀⠀⠀⠐⠖⠘⠂⠀⢀⠀⣠⡞⠁⠀⠀⠀⣾⠃⠀⠀⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢦⡌⣐⡢⡔⢲⣶⡭⠛⠒⠀⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠊⣀⢶⣞⠉⣁⡬⠑⠂⡩⡏⠀⣇⠶⡺⠟⠑⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠌⣛⠚⢂⣈⣛⡖⠀⠉⠄⠱⢤⡀⠐⠀⣉⡱⠋⡍⠃⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠔⣦⡀⠥⠉⢐⢶⣠⡇⠀⣖⡀⠁⠐⢊⠁⠀⢰⡨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠈⠒⡈⠂⠰⡦⢮⣍⠠⣬⠤⢜⡂⣍⣥⣦⣉⠙⠉⡥⢀⢠⠌⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⢸⠈⣇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠉⠻⠧⢶⣴⡁⡠⣦⠀⣀⠡⠔⢉⠡⣄⠀⡐⢿⠏⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⣀⠀⠀⠈⠁⠉⠉⠉⠉⠛⠛⠙⠩⣯⡿⠿⢂⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠐⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⠀⠀⠀⠀⠸⠈⠋⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⡀⠀⢾⡻⣶⣷⣇⠀⠀⣄⠀⢀⡏⠎⢦⣼⡇⠀⠀⢶⡎⡇⠀⠀⠀⠀⢲⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠃⡙⣿⣿⣷⠀⠇⡀⡞⠁⢠⢀⢿⠙⡆⠀⢛⣿⣸⠀⠀⠀⠀⢸⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠐⡆⠀⠀⢶⡌⠻⣿⡄⠞⢡⢃⠠⠃⠌⠈⣷⠙⡆⢸⣿⣏⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠟⣦⡙⣷⢰⠈⠾⠀⠘⢀⢠⠇⡀⣷⢀⣿⣯⢣⢳⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⣯⣷⣌⢷⡄⠀⠃⢀⠃⠈⣆⢳⢺⣸⣿⢃⣿⣼⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠙⣇⠀⠀⢸⣽⢫⣆⠁⡆⠀⠈⠰⠀⣠⢀⠚⣿⣹⠀⢸⣇⡆⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠈⠀⢹⡀⠀⠈⡷⢸⣹⡧⡨⣦⠀⢠⡆⠁⡾⠰⣾⢿⡆⠰⣿⡇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠰⠡⠙⢷⡟⢎⣳⡄⠐⢀⢡⡄⠁⡈⣷⠀⡟⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢂⠆⠈⠻⣫⡷⣥⣡⡇⢸⢇⠀⡀⣿⡄⣧⡇⠀⠀⠸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠀⠈⠌⡀⠀⠹⣻⡝⢦⠸⣇⡿⠀⠇⡼⣧⢈⣿⡄⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠐⠐⠀⠀⢙⣷⣎⠱⡜⣷⡀⠂⢧⣿⡈⢹⣷⠀⢠⡇⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠀⢸⢺⢫⣷⡘⢮⡻⢷⠀⣿⡇⠌⡜⡇⠈⢷⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢁⠀⠀⠘⠆⠻⢷⣎⡳⡱⡅⣽⢻⣄⠇⢹⠀⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡄⠐⠘⡆⠀⠘⣿⣷⡽⢮⠺⣣⡻⡐⣧⢇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⡘⡀⠀⢁⠀⠀⢻⡷⢳⡎⠱⡙⡷⡇⣿⡼⡇⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠐⡡⠀⠀⡆⠁⡘⣡⢱⣟⢗⠙⣎⠿⢿⣣⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠃⠀⠁⠸⢸⠸⢸⡝⣾⡂⢋⣧⡈⡳⣽⡇⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠘⠀⡀⢠⠀⡇⠀⣿⣏⢻⣿⡀⡟⣔⠜⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠄⠀⠀⠘⡄⢠⠀⣼⡜⢿⣿⣿⣤⣿⢆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡀⠐⡀⣠⠆⢣⡜⡄⠹⣠⠀⡟⡜⢟⢿⠸⠷⢔⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢷⠀⠱⣩⠆⠈⣶⣀⢸⣿⡈⣻⢱⡨⠋⣳⣼⣼⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⡆⠀⠉⣟⢤⢻⣷⢂⣿⡧⠏⡆⣧⣸⡗⠹⣿⠇⠐⢝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡘⠀⠀⠘⡄⢘⢹⡎⣸⣧⢼⣇⠸⣞⢃⠘⣟⢦⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠈⣷⠈⠹⢷⠽⣯⡞⣿⠀⢉⢋⠀⠁⠸⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡆⢸⣴⢻⡄⠘⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠙⡀⡎⠀⠀⢀⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣷⣓⢷⡰⣾⡃⠐⢲⣿⣽⠻⣯⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⢹⡿⣻⣌⢻⡛⣺⣷⣾⣦⣴⣷⣿⣿⣷⣆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢃⠻⢗⣶⡞⣷⠙⣷⣤⣧⣿⣿⣿⣿⢿⣿⢣⡿⡽⢷⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠛⣤⡠⠤⣼⡛⢓⣾⣧⡇⢾⣧⠝⣫⡟⣻⣼⣾⣟⢼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠢⠶⠖⢋⣑⣒⡊⢷⠹⣾⣿⠎⡿⢃⡍⠀⢛⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠞⠳⠀⠛⡃⠸⠇⢀⣀⡀⢒⡋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡞⣶⢿⣦⠤⠤⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⣿⢸⣷⠦⠀⠀⠈⠻⣤⣤⡤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⣿⢸⣷⠦⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⡇⢿⠈⡷⠶⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣴⢿⡘⣧⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡾⢣⡾⣧⢹⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣴⢋⣴⠋⠀⠘⣧⡹⣎⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠈⠳⣬⡳⢮⣝⡓⠶⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣿⣷⣶⣭⣝⣓⠶⢭⣛⠿⣿⣿⣶⣶⣦⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠉⠉⢁⣤⢞⣫⠿⣋⡵⠞⣫⡵⢞⣻⣭⣿⣶⣬⡛⢦⡙⢯⡻⢿⡿⣿⣦⡈⠉⠙⠛⠳⠶⣤⣄⡀
⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⣰⠟⣵⠟⣡⠞⢋⣴⣿⡥⠶⢟⣛⣫⣭⡭⠿⠿⣦⡙⢦⡙⣦⡻⣎⢳⡝⣦⠀⠀⠀⠀⠀⠈⠙⠷⣄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢷⣼⢃⡾⢁⣾⡷⢞⣛⣭⠴⠶⣛⣋⣭⡤⠶⠖⢛⣛⣩⣷⡈⢷⡌⢷⡘⣇⢻⡸⣧⡾⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣾⣯⣽⣶⣞⣻⣭⣵⣶⣖⣛⣛⣭⣭⣴⢾⣧⣈⣷⣸⣧⡿⠾⠛⠉⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠉⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⢶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣬⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣥⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣴⣾⣿⣿⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣟⣿⡽⣷⣿⢿⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⣶⣾⣿⣧⣿⣿⣯⣿⠿⠽⠿⠿⠭⣭⣭⣿⣿⣿⣖⣲⣶⣶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡤⣖⣺⣭⡷⠶⢛⣛⣭⣿⣿⣿⡶⣿⣷⣞⠳⡳⣯⢽⣟⣛⡿⢷⣷⠿⢶⣭⣻⢭⡛⠛⠶⠾⣭⣗⣲⢤⣀⡀
⠀⠀⠀⢀⡤⢞⣭⣶⢟⣋⣭⣴⢶⣿⣿⠿⣿⣛⣛⣿⢮⣾⣿⡏⣷⣧⡿⣟⢿⡿⣛⢯⡻⣯⣝⣓⢿⡵⠼⣶⣿⣷⣶⣭⡛⠻⣾⣽⡳⢤⡀
⠀⢀⡔⣫⣾⠟⣫⣿⣿⣿⣩⣿⢟⡭⣲⣿⣿⣿⣿⣿⣿⡟⡏⡆⣿⢿⡹⣻⢿⢫⢺⡿⣻⢳⣮⢭⣝⡻⣽⢺⣿⣯⣿⣿⣾⡦⣄⠙⠻⣷⣝⢢⡀
⢠⠏⣼⡿⢃⣾⣿⣯⣭⢟⣿⣗⣽⣞⣿⣿⣿⣻⣿⠿⣏⣿⢽⣇⣯⣾⣷⣿⡇⣟⢬⣚⣾⣟⣵⣿⣴⣿⢿⣿⣿⣯⣿⣿⣿⡾⣝⣷⣄⠘⢿⣧⠹
⡿⢸⣿⠳⡫⣯⣽⣿⣕⡻⢿⢟⣯⣾⡿⣿⣿⡸⣿⣿⢿⣯⢺⢸⣴⣿⣾⣷⡏⣿⠵⢿⣯⡻⣿⣿⣿⣷⢷⣻⣿⣯⢞⣟⣿⣿⢟⡼⣼⣷⡜⣿⡇
⣷⢸⣿⡄⠉⠙⣷⣿⣿⣿⣾⢻⣟⣿⢿⣿⣿⣿⡶⣶⢯⣿⣻⣸⣿⣿⢵⣷⣻⣼⣷⣷⣹⢳⢻⠿⣛⣻⣓⣻⣼⣿⣓⣿⣷⣿⣿⣷⣿⢿⢧⣿⡇
⠘⢦⠻⣿⣄⠀⠙⠫⢿⡷⢿⠿⢿⣺⣸⢿⣿⡾⣿⢟⣿⣿⣿⣕⣝⣿⣿⣿⢻⣾⣿⣿⡇⣿⡧⣫⣿⡾⣹⣿⣿⣿⣿⣿⣛⣽⣹⣻⠕⣡⣿⠟⡴
⠀⠈⠳⢌⡻⢷⣤⡀⠐⣿⡿⣟⣛⣦⣿⣻⡿⣽⣿⣾⣿⣿⣿⣿⢛⣟⣛⣻⣿⣿⣿⣿⣽⣿⢷⣾⣯⣶⣿⡿⣿⣛⣻⣿⡿⠟⢁⣤⡾⢛⡡⠞⠁
⠀⠀⠀⠀⠙⠲⢭⣛⠷⣦⣭⣑⡓⠚⠓⠻⢿⣾⣾⣭⣟⣻⣿⣿⡷⡯⢋⣿⣻⣿⣿⡿⡿⣿⢟⣽⣿⢿⣽⡿⠟⢉⣉⣥⣴⠾⣛⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠬⣝⣛⡿⠶⢶⣤⣬⣛⣻⣿⡿⠛⠋⠑⠚⠛⠚⠯⠽⠛⠓⢛⣛⣛⣛⣯⣥⡶⠶⠿⣛⣫⠥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠮⠭⠭⣭⣭⣿⣛⣛⣛⣛⣛⣛⣛⣛⣿⣭⣭⠭⠭⠵⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡆⠀⠀⠘⢌⡁⡖⢲⠘⡀⡶⠢⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠚⣉⡖⢰⢸⢊⠇⠀⠀⢠⠐⠉⠁⠀⠘⠁⠁⠂⠀⢠⠰⠒⠑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢐⠋⠈⢄⠳⣘⠾⠾⠞⠂⣩⡠⣌⠰⢤⠠⠔⢢⡤⢐⣃⠠⢊⡁⣀⣀⠨⠍⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡀⢇⠠⠌⣠⡆⣑⠋⠽⠙⣃⡐⠠⠅⡈⠘⠐⠄⣤⠤⠂⠘⡒⠢⠀⠃⠘⠅⠀⠡⡘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⢆⠉⠛⠋⠭⠔⣒⠲⠒⠎⠐⠖⠖⢠⠳⠄⡰⠁⣎⠀⣀⡴⠁⠪⠄⠴⠦⢂⡠⠄⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⠦⠈⣀⠒⠂⡰⢒⣬⠐⢆⠣⢢⡘⠿⠷⡈⠀⢀⠀⢈⠡⠖⠁⣨⠏⠀⢲⠲⢐⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡋⠰⠂⠀⠥⠤⢒⠃⠞⣉⠄⠊⠑⠤⠭⠭⢥⣈⠥⡴⢞⣩⠔⢂⡋⠆⠰⠃⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠹⢄⠀⠲⠜⠏⡀⠸⠡⡆⡲⢘⠃⡡⠖⡹⣮⣜⣊⠁⠖⣂⣀⡒⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠑⠤⠍⠂⢀⣀⣠⣔⣣⡑⠤⠭⠤⠶⢋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡿⠁⣸⡇⠀⠀⠀⠀⠀⢀⣴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠓⢛⣿⢋⣿⢋⢾⣽⢃⣽⢋⣽⢋⣽⢏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⠀⠘⠿⠛⠿⠛⠧⠿⠋⠻⠚⠿⠊⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠓⠐⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣛⡳⢛⣻⠟⠉⢉⣯⣧⡖⠈⢀⣠⢾⣦⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡾⠋⠉⠩⠿⠉⠃⠂⢀⡊⠒⡬⠉⠉⣿⡐⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣤⠼⣄⠘⠆⠘⠖⠀⣈⠀⠒⢆⣿⡿⣵⠃⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣧⣌⣙⠓⠺⠿⠷⠓⠂⠒⠛⢛⡛⠉⠈⠋⠘⣰⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⢷⣶⣶⣶⠶⠶⠉⠩⠥⢀⠄⢠⣶⡗⠁⠠⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠈⠉⠚⢛⡛⢻⣿⣿⣦⣤⣄⣁⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⠑⠞⠒⡶⠞⠒⠓⠁⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡨

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⡐⠠⠁⠈⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠅⠨⣄⠪⠔⣑⠂⠒⢦⡊⠤⠂⠴⢆⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠄⢐⡩⠥⣜⣛⠡⣤⠉⢢⠙⡏⢘⠓⠂⠌⠐⢷⠄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⠴⠡⠊⠴⠽⣑⡈⠷⣬⠡⡲⢠⡃⣟⣚⠐⢄⠘⣎⠃⠃⢉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠞⣤⡞⡝⠙⠝⡱⢮⡙⣛⣂⠝⣀⣉⡓⢇⠬⢧⣀⠂⡿⠀⠀⠀⢧⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠘⢽⠁⠀⠀⠈⣼⣹⢱⡌⢾⠈⣹⠀⠹⡄⣧⠀⡌⠆⡇⠀⠀⠨⢢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄⢠⠀⢃⠹⣈⡀⣟⣆⠳⢤⠬⣸⢃⡷⣇⣃⢹⠀⡸⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠰⠤⠀⢰⡷⡀⠀⡐⢅⡂⠵⠌⢪⡑⣠⡤⢒⣿⣅⢺⡄⢪⠔⠠⡑⢰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠄⣈⠆⣰⠂⠐⢢⠈⣭⣁⣒⡠⠊⢠⢃⡼⠸⠬⠔⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⢌⡸⠲⠶⢄⡺⢠⠃⢸⢸⣂⡤⠛⠩⠄⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠌⠰⢭⠀⠉⠡⠖⠉⠳⠁⠞⠒⢈⠑⢀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡓⠠⠄⠀⣒⡩⢔⡁⠀⠂⡐⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠐⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⡀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣡⣤⣤⣠⡶⣤⢀⡴⣤⢴⡿⣧⢠⣴⣤⡾⢷⡿⣤⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡿⣿⣵⠿⣿⠾⡧⢿⢼⡯⡿⢸⡷⢿⡭⠾⠷⠿⠼⠯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠐⠃⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢷⠀⠀⠀⢠⣇⣀⣀⠀⠀⢀⡀⠀⠀⣀⣼⠀⢀⡿⢀⡞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣇⠀⠀⣸⣏⡤⠙⣇⣴⣏⣹⢀⡾⢹⡏⠀⣼⠇⢸⡏⢁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢹⡆⠀⡟⢹⠛⣹⠇⣿⣸⠟⠹⣧⠇⣧⡼⡿⠀⠀⢉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢿⣸⡇⠈⠛⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⣛⣀⣤⠤⠤⠤⠶⠶⠶⠶⠤⠤⢤⡤⢤⢤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠐⠂⠉⠁⣀⣀⠈⡠⡄⠢⢷⢄⠙⢄⠀⠀⠈⠣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⢠⠋⢉⠙⠒⢢⣮⠭⣼⠋⢣⡳⡕⢌⠳⡕⡌⢧⠀⢀⠀⠈⣍⠳⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣀⣠⢤⣧⡀⢀⣀⡠⠾⢶⢶⡟⡄⢧⡑⢌⠢⡱⣜⣜⢎⠒⠁⢑⣚⡠⠳⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⡾⠀⠁⠀⢾⠁⢀⣠⠟⢙⡭⠒⣒⣚⡡⠤⠼⣜⢆⠳⣀⣱⡝⣄⠈⢆⠣⡀⠙⠦⡄⠀⠘⡄⠀⠙⢦
⠀⠀⠀⠀⠀⢸⡇⡠⠴⣒⣚⣚⣕⣋⡭⢗⣲⣊⡥⢖⣋⡉⠭⢹⡜⡄⠸⣉⠉⠪⡳⣜⢏⠺⡑⢄⠳⢄⠴⡻⢰⡀⠈⢧
⠀⠀⠀⠀⠀⠘⣿⢖⠭⠤⢜⣫⠥⢴⡊⠁⣠⠔⡪⢕⣲⠬⢖⡪⢳⡸⡀⠀⠧⠠⠼⣜⠮⣓⣊⣿⠴⠶⠮⠤⣈⠇⡀⢸⡆
⠀⠀⠀⠀⠀⠀⣿⣖⢉⡽⠋⠀⠀⠀⠘⢦⡃⢮⡀⠻⠤⣄⣑⢄⣻⠱⣌⣓⢒⣒⡨⡽⢋⡟⣹⠁⠀⠀⠀⠀⠈⣇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡹⣾⠀⡰⠛⠳⡄⠀⠘⡗⠤⣌⣉⠓⢦⠀⠱⡹⡗⠚⢉⣍⡤⢬⣐⣪⠴⠓⠓⠒⢦⡀⠀⣠⡏⢀⡾
⠀⠀⠀⠀⠀⠀⠈⣇⠈⠻⣧⡀⠀⣿⠀⠀⣟⠀⣭⣌⡽⣦⣍⣉⣉⡻⢦⡪⢊⠜⣉⣀⡍⠀⠀⢠⡄⠈⢷⠞⠋⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠙⠶⣯⣀⢰⠇⣰⣮⣭⣥⣲⣥⠾⡮⠽⠦⢴⡞⠉⠁⠀⢲⡄⠀⠀⠀⠀⣰⡴⠞⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣐⣊⡕⠊⠀⠀⠀⡼⠀⠀⠈⠀⣀⣧⣠⡤⠶⠛⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠶⠶⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠙⢛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣍⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⡿⣹⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣳⢏⡟⡷⣝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⡽⣣⣿⣼⣁⢈⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⢫⢞⡽⣡⠞⢛⣿⣷⣮⡳⣞⡛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠲⣌⡓⠎⢿⢸⡸⢥⣷⢳⡼⢪⣷⠿⢯⣚⢫⠷⢂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣿⣯⣬⣷⣭⣻⣿⣟⣵⣏⣽⣿⣶⣼⣷⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣄⣉⣉⣉⠉⠉⠛⠛⠋⠉⣉⣉⣉⣁⣤⣤⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⡄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⢁⠈⠋⠁⠸⢄⣀⢤⢄⢠⣐⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⠄⠊⠃⠈⠈⢨⠐⡰⠤⣔⠀⠀⠀⠀⠐⠁⢡⠐⠂⠳⠤⡤⠤⠄⣀⡀⣀
⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠛⠉⠁⠀⡀⠐⡱⠋⠉⠓⠄⠀⡔⠁⡀⢀⠀⢈⡠⠒⠒⠠⡠⠂⠉⠁⠆⣀⠉⠉⠢⡄⢀⡀⠈⠉⠒⠲⠤⢀⡀
⠀⠀⠀⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠤⠁⠀⠧⢀⡀⡀⠀⠹⢄⣐⠀⠁⠀⡅⢄⡁⠀⡘⠀⡀⠀⢀⡀⡀⢓⠑⠄⢬⣄⠽⠆⣀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⢫⡀⠀⠀⠀⠀⠀⠀⠄⢐⠄⢀⣀⡅⡀⠐⢄⠀⡤⠊⠀⠈⢉⠎⠀⠀⠈⠲⢅⡤⠐⠉⠀⠀⠀⢠⠀⠀⠄⠀⠙⠦⣀⠈⠂⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠑⠦⣄⠀⠀⢀⠰⠊⠀⠨⠁⠀⠒⠀⠁⠢⢏⡀⠠⠄⠂⣜⣀⠀⠀⡜⠈⠣⢄⠀⠀⠀⢂⠌⠁⠈⠀⠈⢰⠀⠀⠀⠁⠢⢄⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠾⢦⣄⣀⡐⣀⠀⠀⠀⠀⠀⠀⠈⠁⡲⠞⠀⠈⠑⠊⠠⠄⠈⠊⠑⠂⠠⡂⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣟⡛⠓⠶⠶⠴⠤⢦⣴⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⡤⠤⠽⠶⠒⢚⣟⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⣀⣰⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⠶⠶⠶⠶⠾⠷⠶⠶⠒⠒⠚⠋⠉

⣿⠿⠿⠿⣿⢟⢿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣟⣻⣻⣿⣿⣟⣟⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⠃⠀⣤⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⣧⠀⠀⠀⠀⣿⣤⠤⣄⠀⠀⢀⣤⡀⠀⢀⣤⣴⡇⠀⢠⣿⠀⣾⣡⡼⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢹⡆⠀⠀⢸⣿⣡⠆⠘⣧⣴⣿⡀⡿⢀⡾⢡⣿⠁⢀⣾⠇⠀⣿⠁⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⣾⠉⣟⠛⢻⡏⢾⣀⡿⠛⢹⣇⡞⢸⣀⡞⣿⠀⠀⠈⠛⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠘⣷⢀⡿⠀⠻⠶⠛⠀⠈⠋⠁⠀⠀⠉⠀⠈⠉⠘⠷⠶⠶⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣿⠇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣀⣤⡤⠶⠒⢛⣋⣩⡍⠉⠉⠉⠍⠉⠉⠉⢩⠗⠋⡭⠛⠛⠛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉⠀⢀⣀⡀⠀⠀⠀⢀⣀⣤⣀⣠⠒⡏⢹⠛⣟⢦⡈⢢⡀⠀⠀⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣰⠋⢉⡉⠉⠓⢲⣯⠔⢶⡞⠉⣦⡑⢌⠲⣌⠳⡙⣄⢹⡀⠀⣀⠀⠀⣧⡙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣀⣤⣅⠀⠀⠀⢀⣠⠾⠾⠤⣾⢣⡘⢇⠙⢌⠳⣌⢣⡹⣌⢦⠳⠞⠉⠓⡚⢁⠛⢄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠐⠃⠀⣰⠋⠉⠀⢘⡾⠳⢖⡫⠭⠤⠴⠊⣉⣉⣧⢳⡈⢣⠀⠙⢎⢧⠉⠙⣆⠳⡀⠀⠯⣀⡁⠀⠈⢣⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣀⣀⣸⣠⠴⣻⠿⠶⣒⣋⣠⠴⠋⣉⡭⠤⠤⠜⣧⢹⠀⢙⡷⠛⠦⡓⢄⠸⣗⢭⡢⢄⠀⢹⠀⠀⢀⢧⢀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠐⣇⡔⣋⡥⠤⠤⣴⡾⠕⢒⣊⡵⠒⠒⢒⣫⠥⢖⡒⠂⢁⣹⡆⢧⠈⠓⢦⠀⠈⢢⡱⡌⢆⠙⣦⡱⡌⠑⢒⡡⠊⠘⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠊⠥⠒⠒⣫⡥⠖⠛⠦⣄⠀⣠⠞⣡⠖⣫⠥⠒⢊⡭⠂⣹⡌⢧⡀⠘⠢⠒⠚⣳⣝⡢⣥⣤⡾⠞⠛⠛⠒⠒⢤⡇⠠⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡩⢤⡟⠁⠀⠀⠀⠀⠈⢳⡏⠐⣅⡀⠓⠤⢤⣈⡳⣄⢣⠘⢦⣉⣓⣒⣈⡭⢶⠎⣩⠋⣼⠀⠀⠀⠄⠀⠀⠀⢳⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠸⡏⢷⣜⠀⣠⠞⠛⢦⡀⠀⠈⣿⠦⣄⣉⡉⠓⢦⡀⠈⢧⠹⡗⠤⠏⢉⢏⣠⠬⠥⢖⣡⠾⠖⠓⠒⢦⡀⠀⠀⢀⡾⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⢦⣇⠀⠀⠘⡇⠀⠀⣿⠈⣀⠒⠙⢳⣄⡑⠒⠚⠒⢿⣄⡰⣫⠏⡴⠚⠉⢹⠁⠀⠀⠀⠀⠀⠙⣆⡠⠚⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠷⣤⣀⡇⠀⠀⣿⠀⣒⠛⠛⠋⣊⠽⢛⢝⡛⢦⣉⠙⣁⣾⠴⠒⠒⠺⡄⠀⠀⠀⠁⠀⠀⢻⢀⣠⠞⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠈⠙⠳⢦⣴⣏⠒⠚⠿⠭⠭⢒⡪⢟⡭⠒⠉⠉⠉⡿⠁⠀⠠⠀⠀⢹⡀⠂⠀⠀⣀⣤⠾⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⣶⣭⣥⣖⣉⣀⣀⠀⠀⢰⡃⢀⣀⣀⣀⣀⣨⣧⡴⠞⠛⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠠⠄⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠉⠁⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣺⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠕⠊⠁⣀⠤⠒⠉⣀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠭⠒⢉⡠⠤⠒⣉⠤⠔⣂⠥⠄⠺⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⡪⠕⢊⡠⠄⣂⠥⢔⣂⠥⠐⣊⣁⣤⣴⠦⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠝⠊⣁⣴⠮⢙⡂⠥⠒⠈⣁⡀⠤⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠮⢛⣩⡴⣞⠫⠕⠂⢉⡡⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⣺⣿⣽⢿⠅⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣏⣿⢧⣿⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⡽⣟⢯⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣳⢯⣟⡾⡽⢤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠛⠉⠉⣉⣉⣤⣤⣤⣤⣤⣤⣧⣏⣿⣾⣽⠁⢀⣀⣀⣀⣀⣀⣀⠉⠉⠉⠉⠛⠓⢲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣉⣠⡴⣞⣿⢽⣷⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡦⢤⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠂⠭⣙⡛⠛⠾⠿⠿⠶⠶⣿⣿⣷⣶⣿⣭⣟⣶⣝⣳⣽⣿⣿⣿⣿⣿⠭⠿⠷⠾⠟⠛⣛⡋⠥⢐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠬⠅⠀⠀⠉⠉⠐⠒⠒⠂⠠⠶⠤⠤⠤⠤⠀⠀⠠⠆⠀⠀⠠⠆⠀⠀⠐⠒⠒⠈⠉⠁⠀⠀⠨⢽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡒⠒⣂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠔⢉⠄⠒⡒⡀⠉⠪⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡬⠐⠈⠀⡜⠁⠈⢣⠁⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⡀⣼⣀⠈⠁⠀⡤⢀⠌⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⠢⢈⣉⣀⡉⠄⡪⠊⠀⠀⠀⠀⠀⠀⢀⡀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡒⠤⠤⣀⣀⣀⠀⠀⠀⠉⠒⠂⠐⠒⠉⠀⠀⣀⣀⠀⠤⠄⢀⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⢭⣭⣭⣭⣭⣭⣭⣭⡥⠤⠤⠶⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⡿⡿⠿⡟⢛⣋⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣤⣤⣴⣶⣶⣤⣤⣴⣶⣾⠿⠿⠛⣛⣋⣩⣭⣤⣴⣶⣿⡿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⠿⣿⢿⢛⡏⡟⡇⣿⣿⣿⣿⣶⣶⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⡏⢹⢸⠀⡇⢸⢰⡇⡏⡇⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⡿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⢾⢸⠀⡇⢸⠸⡆⡇⡇⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣾⢸⠀⡇⢸⢸⠀⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡏⢸⠀⡇⢸⠸⣤⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⢸⠀⡇⢸⢸⣿⡅⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⢸⠀⡇⣼⢸⢻⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣾⢸⡇⡟⢸⠀⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⡇⣿⢸⡇⡇⢸⠀⡇⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣨⣿⡇⣇⣿⣸⣇⣧⣸⣀⣇⡇⣿⣧⣤⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣋⠭⢭⣉⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣯⣤⠤⠬⣝⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣾⣷⣾⣿⣿⣿⣥⣴⠚⣉⣉⣭⣉⣍⣉⣙⠒⠢⢬⡙⠿⣷⣶⣬⣷⣼⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⣋⡭⠥⠒⠒⠒⠒⠢⠤⢍⣉⠛⢿⣷⣤⠤⠤⠤⠤⢬⣉⡓⢦⣬⣷⡿⢛⣉⣉⣉⣛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⢠⣿⠟⣵⠚⣡⠖⣊⣉⠭⠭⠭⣉⡓⠒⠤⣉⠲⣌⢻⣷⡖⠒⠒⠒⠦⣍⣾⡟⣡⠞⣩⠤⠴⠤⢬⡙⢦⡙⣿⣆
⠀⠀⠀⠀⣠⣼⣿⣴⣧⣾⣵⣾⣷⣶⣶⣶⣶⣶⣿⣷⣶⣿⣷⣾⣷⣿⣿⣿⣿⣿⣶⣾⣿⣶⣿⣼⣧⣶⣿⣿⣦⣽⣤⣷⣼⣿⣄⡀
⠀⠀⠀⠀⣿⣟⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠈⣿⡆⠛⠃⠀⠛⠛⠀⠘⠛⠀⠛⠛⠀⠘⠛⠀⠛⠃⠀⠘⠛⠃⠘⠛⠃⠀⠛⠛⠀⠘⠛⠀⠘⠛⠃⠘⠛⠃⠛⢃⣿⡇
⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣾⡿⠋
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠛⠛⠛⠿⠿⠿⠿⠿⢿⣶⣾⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⣿⡇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠃
⠀⢰
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⢍⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠶⠒⠒⠒⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢺⠀⠻⠇⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠐⠀⠀⠀⠃⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠘⡓⠀⣀⢚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠠⠁⡅⠀⠈⠈⠀⠀⠈⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⡆⠀⢀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣠⠐⡄⠀⠃⠀⠐⠀⠞⡏⠀⠣⡀⠠⠛⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡌⠀⠀⠀⠀⡠⠀⢀⠘⠂⠂⣂⡀⡻⠠⡅⠐⠠⠌⠶⡦⣄⣀⠀⢁⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠉⠉⠉⣔⠋⠊⠔⡂⢀⡸⠄⠠⠀⠀⠈⠉⠉⠠⠤⠄⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⢆⠡⠂⣤⠀⠩⠜⠢⠠⣤⡒⠉⠀⠀⣺⠀⠀⠄⠄⠴⠚⠀⡄⠀⠀⢀⠇
⠀⠀⠀⠀⠘⡄⠀⠘⠈⠉⠈⠀⠔⠐⠀⠂⠁⢈⡍⠓⠒⢾⠳⠄⠀⠀⠀⠀⠀⠈⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠶⡁⠀⡀⠠⠐⠀⠀⠀⡀⠐⠊⠉⠁⢂⠟⢀⡦⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠐⠄⠀⠠⠈⠡⠈⠷⠂⠀⠀⠀⠁⠀⠀⠀⣠⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠀⠀⢀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠰⠐⠒⠒⠒⠚⠈⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣛⣘⠠⡄⣅⣉⣉⣉⠉⠅⠠⠀⠠⠀⠤⠤⠤⠤⠤⠤⠤⠤⠠⠤⠦⠦⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠁⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡡⢭⣝⠀⠘⠒⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡏⠛⠀⠠⠭⠀⢔⣍⡐⠠⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⣌⠄⡘⡇⠐⢤⡤⡀⢴⡤⠈⡦⠄⡈⡴⡂⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣝⣀⡘⡉⠀⠄⠓⠞⠁⠗⢄⠻⢋⠤⠫⡄⠀⣀⣱⠘⢓⣤⡉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢠⠭⢄⠁⠂⡀⠉⣀⡆⣮⠤⠶⠟⢀⣀⡀⠇⠉⢉⣈⠄⢍⡺⢿⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡐⠏⡫⡁⠬⣧⡀⢀⣀⡈⠋⢀⠁⣀⡢⠈⠬⠒⠛⠴⡄⡈⢀⠂⣇⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢍⠛⠶⣾⣤⣃⣀⣚⠂⠊⠀⠀⡐⠴⡄⢾⢗⣀⣀⣄⣠⣬⣥⠶⠞⢛⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣬⣉⣉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⢉⣉⣠⡤⠴⠚⠉⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢈⠉⢉⠙⠛⠛⠛⠟⠛⠛⠛⢉⠩⠉⠉⠈⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣔⠡⡀⠀⠈⠅⢒⣤⣀⢤⠀⢐⡖⠖⣦⢀⠀⠠⠀⠄⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣊⢐⠀⢀⠀⢸⡷⡿⡿⣻⢯⢫⢣⠍⠹⡅⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢸⡇⣼⡳⣻⣾⣺⣿⠿⠧⠆⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⢀⠠⠩⠄⠍⠈⠡⠓⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠶⠶⠶⠶⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠠⠤⡀
⠀⠀⠀⢠⢤⣠⡄⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠉⠞⢱⠻⡽⠷⠯⠷⠯⠧⠧⠿⠵⠽⠆
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡤⠀⣀⣠⠖⠁⠀⣠⣤⣤⣄⣀⢀⣁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣊⡐⠫⠲⢄⠙⠇⣠⠞⠋⠀⠀⢰⣶⣤⠄⠉⠙⠳⢬⡑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣤⣴⣯⣝⡙⠻⢹⡃⡀⠸⠀⣼⣟⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢉⡤⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠩⠄⠘⣿⠈⠸⠇⠃⣈⠁⣥⡀⣻⣿⡟⢳⠅⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠗⠄⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠙⡄⠀⡀⠀⣿⣧⡄⢠⣁⠻⠧⣻⢵⡈⣿⡿⣥⣄⢠⡁⣠⡶⣿⣶⣄⠀⠀⠀⣰⠆⠂⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⢿⣀⠀⠀⠙⠿⠙⢧⣙⣄⣩⣭⣥⣄⢼⣽⣿⣿⣽⢈⣿⢾⣿⣤⣻⣿⣟⣠⡧⠞⢸⡗⢠⣄⠰⣘⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠻⡏⠁⣀⣽⡆⢠⣬⠟⢩⡿⣿⣿⣴⣿⡏⠈⢻⣿⣿⣿⣿⠟⠋⠉⠉⢉⣀⠔⣾⡅⠀⠛⠶⣡⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣤⠞⠛⣡⣂⡼⢉⣼⣯⢟⠟⣹⡾⠏⢁⡴⣫⣿⣼⣿⢿⡀⡤⠚⠋⠹⡇⣾⢿⣧⣰⢎⠀⠤⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⢲⠉⣿⢁⡼⣵⢿⠏⣾⠟⠁⡰⢋⣽⢏⣼⣷⡟⣼⡟⠐⠀⠀⠀⠳⠽⢁⠋⢀⣨⣄⠓⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣅⠖⠾⢷⣿⢸⣷⣿⣹⢰⣿⠀⢰⣧⣽⠋⣼⢻⡏⣰⣿⣧⡀⠀⠀⠀⢀⡴⠛⣢⡤⠥⠠⠅⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣧⡧⠀⠀⣙⣷⢸⣾⣿⢿⠘⣿⠀⣾⠻⣿⢠⣧⣼⢳⣿⢓⣽⢻⠞⠓⠶⠞⠅⡈⠁⣀⡤⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣶⣿⣿⣦⣟⣻⣾⡄⣿⡀⣷⣴⣇⣺⢷⡏⣸⣏⢸⣁⡴⢶⣭⡀⣤⣴⡷⠛⠛⠠⣄⡀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⣏⣿⡿⢿⠿⠿⠷⣽⣇⡜⣼⣿⣿⣻⣇⣿⣿⣴⣿⡇⠀⠙⡟⢯⡙⢍⠛⠲⢄⠀⠙⠃⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⡧⠈⡛⠉⠀⠀⠀⠀⠍⠉⠙⠻⢿⢼⡿⠛⠉⠍⠁⢀⣾⡀⠀⢹⣾⣹⡛⢳⡤⢠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡘⢰⢴⣾⢰⣶⣿⡍⢸⠇⠀⢾⠏⠁⠀⠨⠁⠀⢹⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠿⠿⣷⣦⢤⡀⣰⢿⠶⡈⠻⢄⢶⡎⢀⡿⣀⢂⡞⠀⠀⠀⠀⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⠻⠻⠋⠻⣷⣯⣦⠴⠃⡀⠀⣀⡉⣉⣭⡵⠞⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠋⠒⠒⠀⠐⠚⠛⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣀⣀⠀⠀⠀⠀⢀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣠⣤⣴⣶⣶⢄⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⣩⠟⠛⠉⠓⢦⠤⢄⣀⡰⠋⣀⣀⡀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⢧⠀⣰⢃⡞⡱⠚⠙⠲⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣄⣀⠀⡼⠀⣠⠔⠒⠒⢦⡀⠈⡶⢃⡜⡼⢁⡤⠤⣄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⢁⣀⣤⣤⣈⣙⡇⢠⡇⠀⡖⠀⠀⢳⠀⣷⠞⡴⢃⡞⠀⠀⠈⡇⢸⢿⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡤⠛⠛⠛⠛⠛⠋⢁⡴⢋⡠⠤⠤⢄⡙⡇⠈⢧⡀⠉⠀⣠⠏⠀⡷⠊⡴⠋⡤⢄⠀⣠⠇⡼⡼⢳
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠏⢀⠔⠊⠉⠉⠛⠋⠁⣠⠎⣠⠤⠤⠤⣈⠙⣄⠀⠉⠉⠉⠁⢀⠼⡃⢠⠛⢚⢥⣀⣉⡀⣿⡱⠁⢸⠄
⠀⠀⠀⠀⠀⠀⠀⡟⢦⡞⢠⠏⢀⠔⠋⠉⣉⠉⠉⣀⠼⣉⠑⠦⣄⣀⣱⣤⣉⣉⠉⢹⣞⡓⣄⢑⡴⡓⢯⡎⠞⢳⢵⢀⠽⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠑⢾⣀⠏⣠⠞⢉⣩⠭⣉⡉⠲⡌⠓⠤⢄⠤⠤⠤⢄⡈⠙⢿⡀⠙⣼⣾⣋⠉⣶⠯⣒⡯⣊⣘⣦⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⠓⠧⣴⣋⡤⠦⢤⡙⢦⡈⠒⠶⠖⠒⠲⢤⡀⠈⢢⡀⠱⡴⣿⠕⢮⡆⠛⠉⢢⣼⠗⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠦⣀⠀⠀⠀⠈⠙⠒⠦⠽⢤⣉⣙⣛⠉⠑⠲⣄⠉⢦⠀⢳⣀⣱⣹⣤⠤⠷⠒⠊⠁⠀⠀⢀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠉⠉⠓⠒⠦⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠋⠉⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣍⡒⠒⠶⠦⠤⠤⠤⠤⠶⠶⠒⠒⣩⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⠤⠤⠤⠲⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡠⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢓⡂⠉⢐⣒⣛⢛⣉⢉⢉⡉⣁⢀⢀⠀⠀⠀⠄⠄⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⢊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡖⢦⡈⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠲⠉⢘⠇⠀⣖⠀⣈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⣌⠐⠻⠀⢤⡤⡀⣾⠉⡆⠀⠳⠖⢤⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠡⡄⢦⡉⢀⡈⠁⢡⠃⣌⡋⠆⢳⡄⣠⠴⠈⠵⣦⠙⢢⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣔⣴⠂⠠⡆⠐⠛⠙⡍⠩⠐⠂⠨⣤⣠⢖⡃⢰⠙⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢓⠾⣬⣖⡑⠀⠽⢐⠺⢃⢀⣀⠰⡦⠀⢁⣁⣘⣃⣤⠶⢚⡍
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢭⣉⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⡉⠁⠶⠚⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠠⠨⠉⠉⠙⠛⠋⠙⠉⠉⠉⡉⠑⠅⠉⡀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⢀⣟⣶⣷⣤⡿⡭⡷⡤⠀⠀⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⡿⣹⣯⣯⣯⣾⣷⣮⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢙⠉⠙⠉⠉⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⢠⠁⠀⠀⠀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⣀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣀⡀⣶⠒⢠⡄⠠⡿⠒⡟⠉⡽⠤⣼⠶⠚⠁
⠀⠀⠀⠀⠀⠘⠋⣹⡥⠚⠁⠀⣿⠄⣸⢹⡀⡇⠀⡇⠸⣇⣠⠋⠀⠀⠀⠀⠀⢀⡴⢀⡄
⠀⠀⠀⠀⠀⠴⠾⣿⠒⣒⡿⠃⣇⣀⡟⠀⢿⡇⠀⠃⠀⣀⣀⡼⣀⢀⡆⠀⢠⢞⠔⡩
⠀⠀⠀⠀⠀⠀⣀⣿⠚⠁⠀⠀⠉⠁⢠⡆⡀⢸⣤⣴⢧⡿⡵⠿⠙⠋⠀⠀⠋⠁⠋⠀⠀⣀⢀⣀⣀⣄
⠀⠀⠀⠀⠀⠊⠁⠋⠀⠀⠀⡀⣤⣱⣿⣷⣧⣼⣨⠌⠈⠃⠀⠀⢀⣀⣤⠤⠄⠒⠢⢄⡰⠛⠋⠋⠉
⠀⠀⠀⠀⠀⠀⢸⣤⣼⣖⠿⠻⡟⡇⠸⠇⠁⠈⢀⠤⠂⠑⢎⣹⡋⢱⡌⢳⣉⠙⢦⠀⠈⠲⢄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡴⢸⠋⢹⠁⠀⠀⠃⢀⣀⣤⠖⢊⠏⠀⠀⠀⠈⠻⡫⣳⣄⡼⡌⡇⢸⢗⡒⢄⠀⠙⠦⣀
⠀⠀⠀⠀⠘⠦⠎⠀⠀⢀⣠⠔⠊⢹⠟⢛⢦⡄⠀⡠⠀⠒⠐⢆⠝⠀⠀⠑⢶⣃⣾⡄⡷⢸⡠⢒⢄⢌⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢀⠨⠅⠌⠰⠌⠒⢦⣶⣆⠀⠌⠀⠀⠀⡀⠀⢏⡲⠷⢧⣟⠄⡼⢁⢮⡀⠤⡉⠲⡀
⠀⠀⠀⠀⠀⢠⡏⠴⢦⠀⠢⣈⠪⠑⠈⠀⠄⠸⠠⠄⠈⠙⢾⡀⠀⠁⠀⠀⢡⠊⠀⠀⠀⠙⢾⡡⡢⢊⡤⡪⢈⡦⢷
⠀⠀⠀⠀⠀⢸⠣⣀⠈⡇⠒⢂⠀⡀⡤⠠⡈⢢⡁⠂⣴⡶⢷⡌⣑⣾⣶⢀⠃⢠⠒⠒⠀⢢⠈⡟⣢⡭⠖⠋⠁⠀⡼
⠀⠀⠀⠀⠀⢸⠀⠈⠳⣇⡈⠈⠱⡈⣆⣧⣌⣀⠤⠖⠳⢄⡔⠉⠀⠉⢎⠛⠤⣸⢰⣰⡦⠼⠒⠉⠡⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⠢⣔⡙⠊⠉⡹⠁⢀⣀⠀⡜⢠⠊⠉⣆⣸⡤⠤⠚⠋⠁⠀⠀⠀⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠙⠲⢤⣇⣠⣃⣀⣦⡥⠷⠒⠊⢉⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠤⠄⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⢀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⠲⠤⣤⡤⠤⠖⠚⠉⠁⠀⠀⠀⣰⣆⡜⣧⢻⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠔⢫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠟⠋⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠐⠉⡀⠄⠒⣉⠤⠐⡂⢽⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡒⠕⢊⡁⠄⣊⠩⢐⡊⠥⠒⢉⣡⣤⠨⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠮⢒⣁⡤⠦⣁⠢⠅⠒⢉⣀⠤⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢛⣨⣴⣞⠯⠓⢂⣉⠤⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢵⢾⣿⣽⡻⠐⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣿⣟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣯⣷⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠶⠖⠒⠒⠒⠒⢺⣽⣽⣻⢷⠛⠒⠒⠒⠒⠒⠲⠶⠤⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠅⢀⣠⡤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣤⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⡈⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣛⡻⠿⠿⣯⣿⣺⣿⣿⣿⣿⣿⣿⣻⡿⣝⡻⣟⣿⣟⣿⣿⣿⣻⣿⣿⣿⡿⠿⠾⢛⣋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢐⠈⠉⠐⠒⠰⠄⠠⠤⠭⠭⠭⠉⠩⠉⠉⠩⠍⠉⠉⠭⠉⠉⠠⠀⠖⠐⠒⠈⠉⢐⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣒⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡱⢊⠄⠒⣂⡀⢑⠕⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢨⠀⣎⠀⠈⠂⢺⣼⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢎⢆⠺⢤⣀⠀⡠⠂⡔⡜⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡠⣀⠀⠀⠀⠀⠀⠀⠑⠵⣂⡄⣀⡐⠭⠊⠀⠀⠀⠀⠀⠀⠤⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢥⣀⣒⣒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠄⢐⣒⣂⣀⠥⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣄⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢘⣦⠀⠀⢙⠿⣤⣤⣬⣍⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⢧⡶⠿⠟⠻⢷⣤⣥⡀⠋⠉⠉⠓⢮⣿⣶⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣟⠓⠒⠶⠶⠦⢾⣿⡿⢶⣾⡶⠾⠿⠛⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡀⠀⠀⠀⠐⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠲⠀⡀⠀⠠⢾⣧⣴⠛⠋⠐⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣷⡀⢂⣾⣄⡀⠀⠑⠖⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡡⠐⠒⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⠆⣀⣳⣇⡠⠀⠈⠒⠈⠀⠀⠀⠒⠟⢿⣿⣳⣤⣄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢤⣀⠠⡿⢀⠈⠐⠃⢄⡀⠀⠀⠀⠀⠙⠓⢾⡟⠛⠉⡦⡌
⠀⠀⠀⠀⢀⡄⠀⢀⣠⠔⢟⠀⡇⠀⠈⠉⠀⠁⠀⠀⠸⠀⣀⠀⠀⠈⣧⣤⣀⡶
⠀⠀⠀⠀⠀⠄⠰⢂⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣼⣧⣀⡠⢯⠿⠟⠀⠂⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠠⠰⠖⠶⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⢟⠉⠀⠀⡀⠉⠁⠈⠀⢂⠾⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣀⠀⣸⡇⠀⠈⠀⠆⠀⠉⢣⠿⡤⠓⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⣾⡽⠀⠀⠁⠀⠀⠀⠀⠀⠠⠦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠿⠟⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡤⣦⣂⠤⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢖⠐⠢⣀⠀⠀⠀⠀⠁⠀⠈⠙⠿⣽⡻⠶⣭⣑⡲⠤⣀
⠀⠀⠀⠀⠈⠳⣅⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣝⠻⣷⢦⣍⣒⠤⣄
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠓⢦⣀⣤⠤⣤⣠⣶⣶⡦⠽⡻⡶⣭⣚⠿⣷⡦⣭⣑⠲⢤⣤⣤⢄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣼⣦⠀⠀⡤⠸⠿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣭⣒⠭⣛⡲⢤⣍⡛⠶⢬⡯⢲⣦⣤⣀
⠀⠀⠀⠀⢀⢔⡿⠋⠀⠀⡇⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⣉⠛⢶⣭⣑⠪⢝⡓⠶⣬⣁⠒⠭⢙⣿⣦⡀
⠀⠀⠀⠀⣾⠘⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠯⡿⣿⣿⣟⡩⢋⡹⣼⣽⣭⡭⣻⢻⣻⣯⣻⣻⢶⣭⣑⠢⢍⡛⠷⣦⠬⣉⠓⠠⢄⡀
⠀⠀⠀⠀⠟⢾⣦⣀⣠⣔⣣⣀⣻⣀⣀⣀⡀⣼⡳⡆⠎⣷⣶⠿⣿⡽⣟⣡⣷⣿⢿⣿⢯⣽⣿⣶⣾⣿⣿⣶⡬⡉⠒⢭⣶⣬⣕⡢⠬⣉⠒⠢⠤⣀
⠀⠀⠀⠀⢸⠀⠉⠛⠿⣽⣻⡽⠧⢭⣯⣇⡋⣾⢨⠣⣘⢮⡳⣎⢕⡭⣶⣇⢣⢣⢮⢟⢾⡿⣿⣷⢹⣻⣿⣿⠿⢲⣭⡲⠤⣉⠓⠬⣕⡒⠭⢒⡢⠠⢉⠰⡆
⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠀⠉⠉⠐⠒⠚⠹⠭⠤⠿⢾⣚⣿⣿⣿⣷⣿⣾⣿⣾⣞⣻⣛⣒⣋⡩⠭⠔⠒⠊⠉⠁⠀⢈⣱⡦⢉⡲⠤⣈⡑⠢⣄⡉⠛⠈⠁
⠀⠀⠀⠀⠀⠸⡄⠉⠓⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢴⣺⣥⡼⠀⠀⠈⠑⠢⣍⢳⡔⣻
⠀⠀⠀⠀⠀⠀⠹⣾⣛⡛⢷⢤⡈⠉⠙⢓⣲⣶⣦⠠⠤⠤⠤⠤⠤⠤⣤⡤⠤⠤⠤⠤⠤⠤⣴⠶⡿⣍⡉⢁⡴⡿⣫⣴⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠙⣶⠬⡳⣕⢌⣑⣊⢕⡪⠍⢭⠳⡂⠤⠤⣤⢶⣺⣙⠿⡒⢤⣀⣀⢔⡯⢚⠭⠭⢝⣮⣉⠞⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠮⣺⣗⠾⣲⠷⠊⢩⣐⢽⣯⣶⣦⢕⡩⢄⡠⢽⣯⣖⠀⣒⡩⢖⣥⣮⣽⣿⣿⣿⣟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡦⠤⠴⠯⠭⣍⠢⢍⣛⣛⣋⣱⠾⣓⣒⣻⣿⡯⠍⡿⣿⠿⢓⡭⠒⠒⠛⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣤⣄⣀⡀⠉⠒⠒⠀⠒⠂⠉⠀⠀⠈⠉⠙⠒⠒⢒⢉⣁⡀⣤⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣭⣉⣉⡙⠛⠛⠛⠛⠛⠛⠛⠛⠉⢉⣉⠩⠤⣒⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠦⠭⠭⠭⠭⠭⠭⠭⠭⠽⠶⠒⠂⠉⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣶⣽⣤⣦⣭⣵⣥⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣿⣹⣆⣀⢀⣰⣦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡆
⠀⠀⢸⣿⢻⣏⣿⣾⣽⣷⡟⣿⠀⠀⠀⢀⡤⠊⠀⠀⢀⠀⠀⠀⠴⡖⢀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠈⠛⠈⠋⠉⠙⠋⠋⠋⠉⠀⠀⠀⡎⠀⠀⠐⡀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢊⣁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠤⠀⠀⠀⠀⠏⠀⠀⠀⡆
⠀⠀⠀⠀⢀⣀⠐⠐⠪⠿⢮⡄⠀⡶⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⠬⠌⠧⠄⠀⠀⠆⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠤⡁⠀⠐⠢⠀⠈⠉⠁⠀⠀⡀⠆⠋⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠛⠘⠣⡠⠒⠊⠀⠀⠀⡰⠀⠀⢀⡤⠒⠚⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠄⡀⠀⠀⠀⠀⠀⠙⠀⠀⣀⣠⠊⠀⠀⢰⡇⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⡲⠀⠑⠆⡺⠷⣋⣀⣐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠺⠿⠂⢰⡀⠠⠊⢄⡈⠈⠉⠤⠜⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⠈⠋⠀⢂⠄⠠⡄⠀⢐⡋⠀⢠⠇⠁⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠈⠥⣡⡘⡒⠤⢐⠖⠈⡕⡱⠶⠄⠉⣥⡄⠂⠀⢀⠌⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠚⠁⠒⠾⠴⠦⣶⣶⠍⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠲⠙⠂⡤⠤⡑⠀⣤⡄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⣂⠈⡕⠦⢻⡀⠀⠀⠀⠈⠂⠃⠐⠣⠇⠋⠠⠀⠀⠠⡁⠤⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡼⠡⠚⢳⡀⣥⣆⣂⡠⠀⠤⠈⠂⢀⠀⠀⠁⡀⢀⠠⠤⠈⢃⠔⠀⠀⠀⠠⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠐⠀⠄⣅⢦⣱⠦⡤⣤⠂⣀⠛⡏⠓⢠⢉⡈⠁⠐⢛⠁⣢⣀⠁⢘⠎⣶⠂⠉⠅⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢢⡑⠤⣥⣦⠯⠔⣂⣈⣁⣐⠶⢀⣈⡁⠆⣅⠀⠀⠙⠁⠀⠀⠀⠠⢁⡄⠀⠀⠁⡀⠈⢃⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⣄⠑⠤⡀⠒⣀⠋⡔⠐⠈⢘⠀⡈⡀⣀⣵⡌⢁⠌⠀⠙⠄⠤⠖⣣⢀⢏⣈⢁⡉⠐⠚⠁⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⡋⡡⠤⢤⠍⣠⠉⠑⣢⠘⣢⡁⠵⢌⡙⠩⢦⣀⣐⠀⠤⠄⢉⣠⠤⠚⣂⡀⠻⠉⡠⢐⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠣⣄⣘⠁⠖⠒⢐⡉⡍⠘⢡⠔⠊⠁⢈⡒⠒⠒⣲⣢⡔⡺⣛⠤⠊⡉⠔⠈⠃⠘⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠌⠙⠆⠑⣀⠀⠁⡘⠈⠕⠨⠁⠄⡚⢐⢿⣦⣭⠄⢘⡉⢤⡬⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠑⠦⠭⠀⠀⠀⠤⠮⠵⢌⠒⠠⠴⠒⠛⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠟⠈⣻⠆⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠴⢖⣿⢖⣶⠆⣴⣲⠆⣲⡟⢢⡶⢓⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢾⣧⢾⣯⢾⡌⣿⠖⣿⡵⣿⡥⢿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠉⠉⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠞⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⣿⣤⣤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠤⣽⣿⡤⠤⢤⣀⠀⠀⠀⢰⡟⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⠉⠀⠀⠀⠈⢿⠉⠉⢹⣇⣀⣀⡏⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⢉⣡⣤⣤⣤⣤⣤⠀⢠⣼⣇⡀
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⡤⠾⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠷⣤
⠀⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⡴⠋⠀⠀⠀⠳⢦⡶⢶⣋⣽⣙⣷⣲⣶⣶⣖⣛⣓⣶⢶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣉⣈⣁⣈⣉⣀⣉⣩⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⡀⡠⠖⠒⠠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣽⠖⠋⠑⠫⣍⣆⣸⣤⡠⣌⣣⡀⠀⣀⣀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠒⠉⠉⠀⣀⣀⣀⠀⠈⠀⠀⠀⠘⠉⠀⠀⠁⠀⠈⠐⠄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠐⠁⡔⡞⠀⡄⠠⠀⠁⢀⣀⠀⠈⠢⠀⠀⠀⢀⠔⠉⠀⠀⠈⠐⢄⠀⠀⠆
⠀⠀⠀⠀⡠⢂⡁⠳⠀⠑⢆⣸⢤⠁⠀⡴⣿⡟⠛⣆⠀⢳⠀⢠⠃⠀⡴⣻⡿⠷⡀⠀⠆⠀⢈⣁⣈⠑⠄
⠀⠀⠀⢠⠀⡁⠇⢀⠗⠠⡴⢃⢸⠀⠀⣿⣿⣷⣶⣿⠀⢸⠀⢸⠀⢰⣿⣿⣷⣴⡇⠀⢸⠸⣮⣍⠙⢆⡘
⠀⠀⠀⠀⢄⠈⢆⠈⠫⣹⠀⡏⠸⣆⠀⠙⢿⣿⡿⠏⢀⠞⠀⠘⣆⠈⢿⣿⣿⠟⠀⢠⠇⠀⣉⠂⠡⢘
⠀⠀⠀⠀⡠⠛⣉⡡⠌⠙⣦⣡⡀⠫⢗⠤⠤⡤⠤⠖⢋⡀⠀⢀⠈⠓⠤⢤⡤⠤⠖⠁⠈⠻⢳⡖⢁⠮⠄⡈⠑⡀
⠀⠀⠀⡰⠀⠠⠁⡠⠄⢄⠈⡖⠻⢒⡀⣙⡀⠀⢶⣄⡈⠟⠛⡛⠀⠀⢀⢀⠤⡴⠀⣧⠀⢶⣄⠈⢿⢊⣩⣭⣉⠓⢤
⠀⠀⡠⠁⣠⣇⣰⠋⣅⠙⠋⡟⢉⣀⠈⢣⡈⡛⡟⠀⡏⠻⠬⠜⣩⣆⠘⠓⠚⢁⠔⢰⠀⢸⡇⣧⠈⠃⠀⠀⠈⢳⣀⡀
⠀⠙⠒⠂⢹⠀⠙⠲⢿⣇⣨⣱⠁⡴⡇⠀⠻⣿⣄⡼⢹⣖⡖⠈⠁⠨⣿⣷⡛⢉⣠⠟⠀⡼⠀⣘⡤⠖⢛⡇⡆⠀⣆⠡
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠉⠙⠚⠓⠾⠦⠤⠤⣥⣤⣞⣉⣉⣀⣩⡖⠤⡉⠉⠉⠉⠳⠚⠛⠉⠁⠀⠄⢸⠏⡁⢴⢳⠀⡆
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢨⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⠀⠐⢤⠉⠰
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠸⠠⠔⠁⠀⠀⠀⠀⠀⠀⣸⠁⠘⠂⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠘⣆⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠄⠊⠀⡠⠃⢀⠀⠀⠉⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠽⣒⣒⣒⣒⣒⣒⣒⣒⣪⠭⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⢚⣛⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣤⡤⠶⠚⣛⣉⣭⡴⠶⠚⠛⠉⠉⣀⣀⣤⣴⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢛⣋⣩⣤⠴⠖⠛⠉⣁⣠⣤⣤⣶⡾⠿⣟⣛⣭⡭⠷⠖⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⣱⢞⣫⣭⢹⡶⣦⣤⡤⠶⢚⣛⣩⣥⠶⠖⠛⣉⣉⣤⣴⣶⠾⢿⣛⣛⣭⡭⠷⠖⠛⠋⠉⠁⠀⠀⠀⢀⣀⣀⡀
⠀⠀⡀⠀⣀⣤⣾⠿⢿⣷⣿⣼⣿⣿⣾⠿⣯⣶⠞⠛⣉⣉⣤⣤⣶⠾⢟⣛⣭⡭⠶⠚⠛⠉⠉⠁⠀⠀⣀⣀⣠⣤⡤⠶⠖⠛⠛⠉⠉⠉
⠀⠈⣠⢞⣥⣾⣿⣿⣟⣿⣿⡿⣯⡻⣎⢳⡙⣏⢿⣿⣻⣿⠿⠿⠛⠛⠉⠉⠀⣀⣀⣤⣤⠴⠶⠒⠛⠋⠉⠉
⠀⣼⣿⣿⡿⠟⢛⣋⣩⣿⣝⣿⣎⣷⢹⡄⣿⣿⢈⣏⣁⣀⣠⣤⡤⠶⠞⠛⠛⢉⠁
⢀⣿⣿⣴⣶⣿⣿⣿⡭⠷⣿⣿⡟⣿⢸⣷⣇⡟⣼⣿⡉⠉
⣸⢿⣿⣿⣋⣉⣤⣴⣶⣾⣿⡿⣱⢇⣾⣽⣿⣷⡟⢿⣻⡄
⣿⣾⠈⠉⠉⠹⣟⣿⣿⣿⣿⣳⢫⣿⡿⣿⢿⣟⣧⠈⠳⠛
⠈⠁⠀⠀⠀⠀⣿⣿⢸⣹⡇⡏⣾⢸⣿⣼⣻⣿⣾⡷⢦⡀
⠀⠀⠀⠀⠀⢠⢟⡿⣯⣿⣧⢷⣿⡿⣿⡏⣿⠉⣿⣿⣷⢻
⠀⠀⠀⠀⠀⢻⣸⣷⣿⣿⢹⣧⡻⣷⣧⢻⡘⣿⠵⠋⡟⣿
⠀⠀⠀⠀⢠⣞⣽⣾⣿⡿⣿⣏⣷⣜⣿⣿⣳⣼⢷⡄⢿⣻⣄⡀
⠀⠀⠀⠀⢸⣽⡇⠈⢻⣿⣿⣿⣿⣽⣞⣿⣿⢿⣷⣻⠀⠙⢾⣝⢶
⠀⠀⠀⠀⣸⣿⠃⠀⠸⣷⣿⣿⡻⣯⣹⣿⡿⣿⣿⣿⠀⠀⠀⠿⠾
⠀⠀⢀⠀⣿⢿⡀⠀⠀⣿⣿⡏⣿⣶⢿⣿⡟⠋⢿⣿⡀
⠀⠀⠘⠆⠘⢯⣷⡀⠀⡟⣿⡇⣿⣷⠞⣼⠃⠀⠈⢻⣝⣦
⠀⠀⠀⠀⠀⢸⣿⡇⠀⢷⡻⣷⣿⢣⡟⠁⠀⠀⠀⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠀⢠⣿⣿⢫⣷⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⢣⢿⣿⣿⣿⣯⣴⣞⢲⡄
⠀⠀⠀⠀⠀⣾⣫⣷⣶⠖⠋⠀⢻⣷⡌⠉⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠛⠁⣿⣿⠀⠀⠀⠀⢻⡿⣦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠙⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠣⡄⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠟⠀⡸⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡐⠀⠀⠀⡀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠆
⠀⠀⠀⠀⠀⠀⢰⡏⠠⣐⡈⠀⠀⠀⢂⠠⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡴⠒⢦⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⡿⢀⠭⢒⡂⠀⠀⠀⠐⠌⠁⠀⠀⠀⠈⠙⢶⣄⠀⠀⢀⣠⡇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣾⠁⠀⢊⣁⣤⡤⠶⠖⠒⠛⢛⣛⣉⣉⣍⣉⠉⢹⡇⠀⠸⣄⡄⠀⣀⠀⢶⠁⢀⣀⣀⡤⠖⠒⠲⢤⡀
⠀⠀⠀⠀⣼⣧⡴⠞⣋⣡⡤⠤⠶⠒⠺⠛⠛⠋⠁⠀⠀⢹⠞⠋⠀⠀⢠⠟⠀⣴⠇⠠⠊⡴⠋⠉⠙⠂⠀⠀⠀⠀⢹⠤⣄
⠀⠀⠀⢰⣟⣇⣰⣟⠩⠔⣂⠨⠀⠀⠀⠥⠐⠀⠀⠀⠀⣸⠀⠤⡀⢰⠋⢠⠎⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠼⢄⡀
⠀⠀⠀⠀⠉⠉⠉⢿⡄⠀⢂⠩⠄⠀⠀⠀⠁⠀⠀⠀⠀⣿⠀⠀⠐⠃⢠⠀⠀⠀⠀⣀⠷⠒⠁⣀⣠⠤⠖⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠂⠀⠀⢻⠀⠀⠒⣈⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⠁⠀⠄⣀⡤⠒⢋⡠⠴⠒⠉⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢷⠀⠤⢐⡂⠀⠀⠀⣠⢞⣩⡤⣹⢀⣠⠴⠚⠉⠅⠒⠉⠀⠠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⣧⠊⡡⠄⠀⢀⡞⣱⣿⡿⠗⠛⠉⠀⠖⠒⣚⣉⣀⣤⡤⠤⠶⠖⢲⠒⠀⠀⠀⠀⠀⢀⠀⣸⠏
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⠨⠀⣼⢰⣩⣤⣤⠴⠖⠒⠚⠉⠉⠉⠀⢠⠂⠀⠀⡤⠒⠲⡟⠲⣧⣀⣀⣠⠟⠉⠁
⠀⠀⢀⠑⠀⠀⠀⠀⠀⠀⠀⢿⡀⡊⠁⣿⢸⣿⣿⣮⠟⣶⡄⠀⠀⠀⠀⣄⣀⣈⣉⡉⠉⠁⠀⠀⠀⣸⠉⠁⠀⠀⠀⠀⢀
⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡀⠘⠓⠒⠒⠛⠋⢹⡇⠀⠀⠀⠀⠀⠐⢁⠉⣽⠋⠛⠃⠀⠈⣧⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠠⠃⠹⠦⠴⠛⠦⠖⠃⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠈⠁
⠀⢀⡤⠴⠶⡒⠂⠀⠀⢀⠤⠤⡀⢹⣦⡤⢄⠀⡀⠤⠤⠼⡇⠀⢀⣀⣠⡄⠀⠀⣀⡠⠤⠤⡄⠀⢀⣀⣀⠠⡄⠹⡆⠀⣠⠔⠐
⠀⢫⡇⠀⢸⢠⠀⠤⠀⢹⠀⠀⡇⢸⣽⠀⢸⡏⡇⠀⠀⠀⠸⡰⣿⠀⠀⡟⢠⡞⠁⠀⣀⣀⡼⢰⡇⠀⢸⢸⡇⠀⡅⠀⣾
⢸⢾⠀⠀⢸⠀⠀⠀⣼⢠⡇⠀⡇⢨⣿⠀⢸⡇⡄⠀⢰⡀⠀⣷⣻⠀⠀⣴⣽⠀⠀⡾⠓⠊⠀⢸⡇⠀⢸⣿⡇⠀⠇⠀⡯
⢸⡞⠀⠀⡇⠀⠀⠀⢸⢸⠀⠀⡗⢻⣿⠀⢸⡇⡗⠀⢸⣇⠀⢸⡿⠀⠀⣿⢸⠀⠀⡇⠀⠀⠀⢘⡇⠀⠈⠉⠁⠀⢠⠀⣿⡇
⡆⡇⠀⢠⠇⠀⠀⠀⢸⢸⠀⠀⡇⣸⡏⠀⢸⠧⢺⠀⢸⣿⡄⠀⠁⠀⠀⣟⢸⡀⠀⠳⣀⣀⣄⡐⡇⠀⢠⡟⡇⠀⢸⠀⣿⢷⣲
⡧⡇⠀⠈⠉⠉⠉⠉⢹⠘⡆⠀⠉⠉⠀⣠⠇⢸⢸⠀⠸⣧⢧⠀⠀⠀⢠⠙⡈⢧⡀⠀⠀⠀⠈⡇⡇⠀⠀⣧⡇⠀⢸⠀⢀⡔
⢯⠓⡖⠒⠶⠖⠲⠶⠞⠑⢝⡦⣤⡴⠞⠁⠀⢸⡾⢴⠶⠉⠿⠛⠻⠟⠟⠀⠈⠒⠬⠽⠿⠿⠟⠻⠟⠶⠾⠻⠟⠒⠞⠀⠺⠷⠤
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠉⠉⠒⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣊⠭⠥⠤⣀⡠⠔⠒⠈⠉⠒⠲⠤⣀⠀⠈⠑⠒⠒⠒⠦⣀
⠀⠀⠀⠀⣠⠔⠒⠋⠀⡞⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠀⠀⠀⠀⠉⠈⠉⠑⠲⢄⠀⠀⠉⠒⠢⢄
⠀⠀⢀⡜⠁⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢱⡀
⠀⡴⢻⠀⠀⠀⠀⠀⠀⠀⢉⠗⠒⠒⠈⠉⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣗⠒⠒⠦⡀⢱⢄
⡞⠀⢈⡇⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⢀⡠⢤⡀⠀⠀⢸⠀⠀⠘⡶⠴⠀⠀⠀⠀⠉⠀⠀⠙⠂⠀⠈⢏⠀⠙⡄
⣧⠚⠉⠘⠦⠤⠞⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡇⠀⠀⡈⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇
⡇⠀⠀⡤⡔⠋⠉⠉⠉⠓⠚⠉⣠⠚⠉⢳⠀⠑⠤⠴⠃⠀⠀⠀⠀⠉⠲⠤⣀⠴⠊⠉⢱⣀⡤⠃⠀⠀⢣⡀⠈⠢⡀
⠘⠦⣀⠀⠸⢠⠖⠒⡶⠒⠒⠊⣡⠴⠒⠁⢀⣀⡀⠤⠤⠀⢀⣀⣀⠠⠤⠚⠁⠀⠀⢀⠞⠀⠀⠀⠀⠀⡄⠘⢆⠀⡇
⠀⠀⠈⢢⡀⠇⠀⠀⠁⠀⡰⠋⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠚⠁⠀⠀⢲⠀⠀⠀⠁⠀⠘⡄⡇
⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠓⠒⢴⠁⠀⢀⠤⠀⠠⠤⠤⠤⠤⠤⠒⢆⠀⠀⠀⡌⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⢠⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠁⠀⢠⠃⠀⠀⠀⠀⣰⠁⠈⢳⠔⠊⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠢⠤⠼⠤⢄⣀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠁⠀⠀⠸⠁⠀⢠⠃⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣀⣀⣀⠀⠀⠀⡱⠀⠀⠀⣠⠔⠒⠉⠓⣖⠒⠒⠉⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠉⠓⠯⣀⡀⢀⡜⠁⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠈⠉⠉⠑⠒⠤⣀⠀⠀⠈⠢⢄⣀⡠⠄⢀⡼⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠑⠒⠤⣀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⡖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢹⠦⣀⣀⣠⠤⠤⠤⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢥⡰⣬⣩⠐⠂⢄⣀⣤⣤⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣄⡨⣏⣊⡴⠯⠷⠓⠚⠓⠿⠗⠛⠁⠒⠾⢯⡭⢄⣙⢎⢲⣲⡤⡀
⠀⠀⠀⠀⠀⠀⣄⠶⣢⢦⡭⠟⠂⠁⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⠛⠾⣶⣯⣄⡰⠤⠦⣄⢄
⠀⠀⠀⢀⡞⡽⡽⢪⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠂⠀⠀⠀⠘⣷⠝⢿⣿⡎⣁
⠀⠀⡀⠶⠕⠟⣿⡾⣷⠀⠀⠀⢄⠀⠦⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⢤⡐⣻⡆⣠⡀
⠀⠺⣴⠖⣓⣃⣒⢕⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢳⠟⠚⠻⣟⣯
⠀⣨⠷⢉⣫⢵⣩⣬⣓⢤⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⣯⣞⡜⢈⢝⢣⠘⣽
⠀⣯⡤⢬⡽⣦⣺⣻⣭⣤⣽⣆⠀⠀⠨⢇⣀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⡴⡿⠟⣝⡆⣸⠟⢀⢇⠈
⠀⠙⢗⡿⢖⡢⣍⣛⣋⡭⢡⡞⢳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡠⢋⢜⣗⣞⡛⢅⣿⠴⠫⡪⠂
⠀⠐⢶⠈⠝⣓⠭⠷⣮⠿⢊⡾⣶⢫⢺⠭⠍⠰⠶⢖⢀⣤⡀⠀⠀⠀⣠⠾⣫⢲⡴⢻⡶⢫⢵⡾⡐⡷⠞⢉⣢⠔⠈
⠀⠀⠀⠀⠺⠿⢸⡐⣲⢯⣝⣾⢡⣿⢸⠹⠵⡥⣣⠶⢶⢆⠯⡛⢦⡛⣹⢟⡌⣰⣖⡚⢠⡏⡬⠵⢝⡺⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠳⠾⠭⣝⣛⠭⢶⣃⠫⠶⠽⢷⢎⣬⠽⢳⢛⡔⢁⣫⢞⣉⡙⠑⡫⠞⠂⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠙⠋⠉⠵⢂⣊⢏⡚⠯⠊⠉⠣⠍⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠀⠀⠾⠒⢒⣂⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠉⢀⠀⠀⠘⡉⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣶⡻⣿⣷⣾⣢⠀⠠
⠀⠀⠒⠠⣾⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣠⠀⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣮⣿⣿⣿⣿⣿⡀
⠀⠀⡆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠿⢷⣶⣆⠀⡀⠀⡀⠀⠀⠀⠀⠀⢷⣿⣽⣿⣿⣿⣿⣿⣿⡷⠀⠈
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣿⡾⠇⠀⠀⢀⠂⣻⣷⣿⢟⣻⣾⣿⣿⣿⠃
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡄⠀⠀⠀⠣⠃⠉⠻⠿⠵⠛⠛⠉⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣩⠯⣑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠠⠆⠀⠀⠀⠀⠀⠁
⠀⢀⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣟⣛⠿⣦⣼⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀
⠀⠸⠉⠙⣿⠀⠀⠀⢨⠀⢀⠀⠀⠀⠐⡖⡮⣻⢿⢷⡞⢫⣼⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣻⣿⣿⣷⡆⠀⠀⠠
⠀⢘⣀⣶⣿⠀⠀⠀⢰⠀⠀⠑⠤⣀⡀⠘⠙⠎⠻⠛⠿⠟⠿⠿⢿⠿⠓⠀⡠⠔⠀⠀⠀⠀⠀⠈⠀⡀⠀⠿⢿⢿⣿⡿⣿⣿⣿⠄⠀⡠⠄
⠀⠘⠸⠪⠿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠴⠶⠴⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠲⠶⠶⠒⠒⠋⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢴⠆⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⢘⠀⠀⠈⠁⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠀⠉⠈⠁⠠⡀⠀⠀⠀⠀⠠⠀⠈⠈⠁⠐⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣑⡀⠀⠀⢀⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⡤⠶⣾⡿⠿⠛⠋⠀⠀⠀⠈⠙⠻⠿⣿⡶⠦⣤⣄⣀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⣶⡯⠿⠟⢓⣈⠥⠔⠒⠚⠛⠛⠛⠛⠛⠋⠒⠒⠤⢬⣀⠛⠻⠿⣿⣶⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡤⠚⠉⠀⢀⡀⠀⢀⠣⡀⠐⠀⠲⢀⠂⡕⢀⡀⠈⠙⠲⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⠔⠁⣀⠂⠠⠂⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⢠⠂⠠⠙⢦⡀⢀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡴⠃⠀⠀⠀⠁⠀⠀⠀⠰⠆⠀⠀⠀⢈⡃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢧⠄⠙⢆⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠁⠀⠤⠁⠠⠀⠐⠿⠂⠀⠀⠀⠀⠀⠀⢧⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡾⠁⠀⠀⣶⠋⣭⡔⢄⢠⠄⢀⡀⢀⢰⠆⠀⠐⠀⠀⣰⠖⢢⠀⠀⢰⠀⣄⡤⢄⠀⠀⠈⢧⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠠⠀⢰⠃⠀⢠⡄⢻⡀⠒⠃⡌⢸⡀⠥⠟⡠⢸⡆⠀⢠⠀⢠⡏⠼⠇⢃⠀⣾⠀⠋⡐⢁⡀⠀⠀⠘⡆⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡜⢀⠀⠀⠀⢸⡇⠚⣳⡌⠺⡇⠺⡌⠀⢸⡅⠈⠀⢀⡾⢀⠀⢻⡀⢀⡏⢰⢦⠑⡈⠁⠀⠀⠀⢃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⢸⠀⠀⠀⠀⠷⠈⢩⠐⠁⠓⠠⣩⡌⠈⠩⢩⡄⠄⢠⡤⠄⢠⠄⠀⠉⡅⠈⠉⠀⠀⠀⠀⠁⢸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⢃⠈⠀⠐⢅⡐⣀⡀⠘⠂⣦⠀⠈⠁⢹⡆⠀⢸⡇⣀⠛⣠⠀⣾⠀⠁⠀⠀⠀⠰⡦⠀⠀⠀⠀⡆⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠸⡀⠀⠀⠀⠔⡦⢙⠆⠀⢿⠰⠀⠀⣸⡇⠀⢸⡇⠻⠒⣿⠀⣿⠀⠂⢁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⠀⠀⠀⠑⠒⠋⠀⠀⠸⠀⠀⠀⠃⠀⠒⠈⠓⠀⠀⠛⠂⠛⠒⠂⠀⠀⠄⠑⠀⠀⠀⢀⠷⠀⠒⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠄⠒⠀⢉⣁⡉⣉⢀⡀⠐⠀⠠⢀⡀⠀⠀⠸⠇⠀⠀⠀⠀⢘⠡⠇⠰⠀⠀⠀⢠⣾⣤⣤⡀⠐⠃⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠑⠀⡀⠀⠀⠘⠛⠒⠒⠀⠀⠖⠖⣢⠄⣤⠈⠀⠀⠂⠠⠄⢀⣀⠈⠑⠒⢁⣀⡠⠴⠿⠛⠉⠀⢳⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢯⣠⣤⣶⣶⣾⣉⠉⠉⠉⠉⠐⠂⠀⠀⠉⢉⠀⠊⠽⠂⠀⠢⣀⡄⠀⣀⠀⡀⢠⠀⠀⠁⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⣀⠀⠈⠛⠿⢿⣿⣿⡇⠙⠢⢤⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠄⣀⣈⢓⠀⠒⠘⠁⢈⣀⠠⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠉⢀⠀⠐⠀⠀⠀⠁⣠⡀⠀⣤⠈⠉⠓⠒⠢⠤⠤⠤⠤⠤⠤⠔⠒⠊⠉⠁⣬⠅⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠩⠤⠤⠤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠄⠤⠤⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠉⠉⠉⢉⠉⣉⣉⡉⠉⠀⡉⢀⢁⠈⡀⢁⠈⣉⠈⡁⣈⢉⢈⡁⡁⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⣀⣀⡀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠀⠁⠁⠈⠀⠁⠁⠀⠀⠀⠀⠔⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠄⠀⣐⣂⣀⣀⣀⣠⣤⠤⠤⠤⠤⠶⠶⠒⠒⠒⠚⠚⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣛⣚⠀⡄⣇⣩⣉⣩⠩⠅⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠶⠧⠦⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡡⢭⣍⠂⠘⠒⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢰⡇⠛⠀⠠⠥⠀⢄⣍⡐⡠⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⣄⠄⠘⡇⠀⢤⡤⡄⢴⡄⠈⡆⠄⡈⡴⡂⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣍⢀⡘⡙⠀⠄⠓⠟⠁⠓⢄⠻⢋⠤⠣⡀⠀⣀⣱⠈⢑⣤⡉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢀⠭⢄⠁⠂⡀⠉⣐⡂⣮⠤⠶⠞⣠⣀⡀⠃⠉⢉⣀⡄⢍⡸⢼⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡐⠏⡣⡁⠬⢧⡀⠀⣀⡀⠋⢐⠁⣈⡢⠊⠬⠂⠛⠶⡄⡘⢂⠂⣇⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡛⢷⣾⣤⣃⣀⣚⠂⠊⠀⠀⡀⠴⡄⢾⢗⣀⣀⣄⣠⣬⣥⡶⠾⢛⣭⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠳⢦⣭⣉⣙⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣉⣥⡤⠶⠛⠉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⢉⠉⠉⠛⣿⠟⣿⡿⠟⠿⣿⠿⠿⢿⣬⠻⣷⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠿⣛⣛⣛⠿⣾⣯⣼⢯⣼⢟⡟⠖⣾⠿⣶⣽⣧⣽⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢛⣉⣙⠻⢾⡷⡿⡿⣻⢿⢻⢣⠇⠹⣟⣉⣉⡙⢷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣉⣙⢿⡬⡇⣼⡳⣛⣾⣺⣿⡿⣧⡞⣉⣉⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⢸⣧⣹⣟⢿⣮⣻⡷⠿⢃⣿⢰⡟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡿⣮⣝⣧⣿⢏⣴⠞⣛⣡⡾⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⠿⠿⠾⠿⠾⠟⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠁⠀⠀⣀⣤⣴⠶⠾⠟⠛⠛⠛⠶⠶⢦⣤⣀⡀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠛⠷⣤⡀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⢀⡴⠛⠁⠀⢀⣠⡴⠞⠛⠉⠉⠉⠉⠉⠉⠛⠒⠶⣄⡀⠀⠈⠙⢦⣀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣴⠋⠀⠀⣠⡶⠋⠁⠀⠀⣀⣀⣠⣤⢤⣤⣤⣀⠀⠀⠀⠙⠷⣄⠀⠀⠙⢦⡀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⣼⠃⠀⢀⡾⠁⣠⣴⣾⣯⣀⠀⣠⡶⣿⡏⣼⡟⠁⡠⠀⠀⠉⠙⠲⣤⠖⣤⢬⣷⡄⢀⣈⣳⡀⠀⠘⣷
⠀⠀⠀⠀⢰⡏⠀⠀⣾⠁⢸⣿⣿⣿⣿⣿⣿⡁⢡⡈⣷⠜⠓⠚⢳⣾⣿⣷⡀⠀⢸⠀⠃⣜⣹⣿⣿⣿⣿⣷⡀⠀⠘⣧
⠀⠀⠀⠀⣿⠀⠀⣸⠇⢀⣀⣿⡅⠀⢰⠏⠉⠃⣰⡏⠓⢄⠀⠀⣿⠿⠛⠉⠙⣦⣞⡲⣤⣟⢸⣿⢿⡟⠋⠈⣧⠀⠀⢻⡀
⠀⠀⠀⢰⡇⠀⢀⣿⠚⣩⣼⣷⣶⣶⡏⠀⠀⣼⣫⠀⠀⠈⢣⠀⠁⠀⣠⠖⠛⠷⠶⣮⣵⡼⠟⠁⣈⡧⣀⠀⢻⠀⠀⠸⡇
⠀⠀⠀⢸⡇⠀⠀⡏⣼⣿⣿⣿⠋⢸⣧⣴⠖⣾⠃⠀⣄⢢⣠⠇⠄⠴⣁⡀⢰⡆⠀⣠⠙⠇⡆⠘⣇⠀⣸⣄⣼⠁⠀⢐⡇
⠀⠀⠀⢸⡇⠀⠀⣷⠹⣿⣿⠃⠔⠁⡿⠃⢀⠇⠀⠀⣿⠏⠀⠀⠀⠀⠀⠹⡄⠁⠀⠙⠘⠛⠧⠤⠞⠀⣏⣤⢘⠇⣴⠿⠋
⠀⠀⠀⠈⣷⠀⠀⢻⣀⡤⠘⠧⢤⣀⠿⠒⢺⡀⠀⡰⣿⠀⠀⠀⠀⠀⠠⢂⡇⠀⢀⣾⡋⠂⠀⣀⣤⠜⠸⢃⡜⢠⠞⣉⠙⢇⢀
⠀⠀⠀⢀⣽⡊⣠⠜⢿⠀⠀⠀⣰⠃⠀⠀⣾⡷⠛⠛⠻⡶⠛⠓⢄⠀⠀⣸⣥⡀⣼⠀⠻⠉⢭⠀⣸⣄⣠⡍⠙⠃⠾⠋⣠⠇⢸
⠀⠀⠀⠊⠀⡟⠁⠀⣨⠟⠚⠉⠉⠉⢙⣿⡈⣇⠀⠀⠀⠘⣧⡄⡼⠛⢱⡋⠀⠉⠋⠑⠲⣶⡞⢁⡀⠀⠙⡄⠶⠀⡴⠊⠁⠆
⠀⠀⠀⠀⠀⠁⡀⣸⠁⠀⣴⣶⡿⠿⠟⣛⠛⠉⠑⠠⢀⣀⠈⢿⣧⣤⣤⣃⠀⠀⠀⢰⡆⣽⣧⡘⠓⠀⣰⡇⠀⡰⠃
⠀⠀⠀⠀⡠⢸⠀⡏⠀⠀⣿⠁⠘⠓⠀⠉⢸⡆⠀⠈⠀⠉⠑⢄⠐⠀⠀⠈⢳⠤⣄⡈⠀⠙⢿⣿⡦⠚⠛⠶⣞⡥⠖⠲⡶⣄
⠀⠀⠀⠀⠱⠈⠀⣧⡀⠀⢻⡄⠀⢠⣤⣶⣾⣇⠰⠦⠀⠟⢀⢸⡆⠀⢀⠀⡄⠀⠀⣧⣀⣶⣞⡙⢿⠀⣠⡀⠉⠀⣸⣇⣼⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠾⢁⣄⡈⠧⣤⣶⣿⣤⣐⣲⣿⣡⡼⢇⠀⣸⢀⡇⢰⢀⣿⠟⠉⣍⡙⢮⠁⢉⣵⣏⠹⠿⠛⡉
⠀⠀⠀⠀⠀⢀⠀⢀⣼⣇⣀⣀⣠⡿⣳⣿⣿⣿⣿⣿⠛⣍⠁⢠⠘⡇⣿⣼⢁⡇⣼⣷⠛⡆⠙⠛⢸⡤⠋⠀⠈⣧⣿⠀⠇
⠀⠀⠀⠀⢀⡏⣰⣿⣿⣿⡟⠉⠀⠙⣾⠟⣿⡏⣤⡜⣧⠗⢒⠢⡄⣿⣿⣿⡿⣿⣿⣇⣰⣷⣦⣤⣼⠦⠈⠀⣠⠟⠁
⠀⠀⠀⠀⠈⠇⢿⣟⣻⠏⣰⣾⠡⣯⣉⣇⠉⠐⣦⣤⠿⠀⠈⠑⣇⠛⢉⣩⡿⢯⠠⠀⣿⣿⣿⣿⣿⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢨⠇⣼⣿⣿⠀⠻⡀⠉⠉⢻⠁⠀⣠⡀⠀⢀⡈⣻⢷⣎⠳⡖⣶⠀⡟⠉⠉⢠⣿⣿⠃⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠻⡿⠏⠀⠀⠙⣄⠀⢸⡀⠀⣿⢇⠀⢠⠋⠁⢀⣿⢀⡇⣯⡼⠃⠀⡰⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣛⠓⢦⣑⠶⠃⠘⠶⠋⠀⠀⡞⡞⢸⠀⢀⣠⡴⢾⣷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠐⣧⣀⠀⠈⠙⠓⠲⠤⠤⠤⠼⣇⠣⣌⣻⠿⠛⣉⣩⣍⢹⣜⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣭⣉⣒⣒⠲⠤⠤⠄⠀⠀⠈⠙⠚⢛⣋⣉⣡⣤⠽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⣤⡀⣀⡀⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣪⣗⠓⠚⡏⠤⢔⣍⣀⡛⠿⠳⡶⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣆⢀⡤⠼⢩⣡⠀⠀⠀⠀⢤⠿⣭⡁⠀⠀⠈⣷⡜⠉⠑⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣐⣽⣧⠙⡉⠀⠀⣄⠉⣔⣦⠀⠀⡘⣇⣸⣷⣤⣎⣠⡟⣶⣞⠲⣯⡁⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣌⢰⡏⢹⠀⠀⠀⠀⢹⣧⣼⠿⠦⠤⣡⣿⡿⠉⠀⠀⠙⣿⣟⠿⣭⡽⣿⣶⡿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠴⣿⠻⣿⣄⡀⠉⣱⣿⠋⠀⠀⠠⣴⡎⠓⡀⡄⠔⠀⠈⢨⣿⡇⠖⢠⣿⣿⣿⢿⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣔⠂⣈⡀⠬⢿⣾⡋⠃⠣⡄⠀⠀⠄⠹⡙⣿⡇⢐⡀⢀⣼⣞⣿⣟⣠⣾⡟⢇⣀⢉⡴⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡎⣩⡔⠔⡨⠿⢛⣾⠷⣄⠀⣀⡠⢮⣛⣵⡓⠾⡟⣿⣯⣾⣿⣿⠿⡧⢨⠻⠑⠅⠘⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠁⠸⣧⠀⠁⠀⠉⠚⣏⣽⡛⠻⠟⠟⣩⣾⠿⠿⠿⠩⠽⠶⡳⢶⣶⡞⢊⢄⣄⣴⠴⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⣀⣐⣤⢰⠇⠀⢠⡄⣤⠞⠦⢤⠍⣙⠦⣴⡽⢂⣀⣠⡉⣉⠤⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠄⠋⢩⠭⠐⠢⠘⠻⠖⡊⠩⠅⠪⢊⠁⠁⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠤⠤⠀⠒⠒⣒⣂⣉⣉⣡⡤⠤⠤⠤⠔⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣲⠖⣶⣖⣋⣉⣉⡉⠁⠀⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢺⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⣄⡀⠁⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠈⠩⠠⠤⠀⠀⠠⠦⣠⡀⢄⠀⠀⠤⡠⡀⠉⠑⠒⠢⠤⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀⠀⣀⠀⠐⠠⡔⠛⠠⢜⢲⡨⣭⠅⡍⠦⠀⠀⠄⡀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠗⠤⢄⡀⠈⠐⠂⢠⡱⠂⠂⠓⢬⣩⠷⡒⠂⡓⠭⢲⠤⢉⠉⢁⣈⡡⠖⡏
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠁⠒⠚⠒⠐⠰⠮⠲⠽⠴⠠⠔⠲⠀⠂⠓⠊⠉⠁⠈⠁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡈⠉⠙⠐⠒⠒⠒⠂⠉⠉⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁



⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠶⣤⡀
⠀⠀⠀⠀⡤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡠⠬⢍⣔⠵⢀⠊⢴⡈⠅⠠⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠂⠀⠘⠄⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣀⢠⣀⠜⠫⠛⠁⠀⣨⡗⠁⡙⡉⠒⠤⣶⡍⠓⣀⡀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢀⠒⢀⡤⠧⠦⣮⠁⢉⡏⢀⣀⣋⢄⢈⠢⣑⠶⡼⢀⠋⢩⠀⣀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠰⡀⠀⠀⠀⢸⠃⠀⠀⡠⣮⠀⡞⢋⠓⣄⡌⠀⢸⣌⢲⡂⢒⡡⠂⡎⠀⠀⣅⡫⠂⠈⠠⠊⠑⣀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣿⠀⠀⡜⠀⠀⣸⠁⢰⠂⡉⠀⠀⡁⠀⠉⡋⣱⠄⠀⣩⡀⠀⣀⣀⢠⣶⠊⠔⠃⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢢⠀⠀⢹⣄⠨⡇⣰⠛⠉⢆⢂⠠⠐⠢⠰⢆⠖⡉⢹⢹⡜⡲⢧⣀⡀⢉⠔⠊⢐⠈⣿⡶⠿⠩⠢⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢣⠀⠘⣿⣨⣵⣏⠀⢠⡟⢹⠛⠲⡤⠀⡇⢀⠞⢣⢸⢄⠀⢸⣭⣉⣊⣀⡀⠴⠀⠈⢸⠑⡂⢄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏⣙⣲⣬⢥⣄⠑⠀⠰⢄⣼⣾⢂⠨⠘⣃⣀⠠⠨⢈⣛⡞⣐⡨⠀⠀⠖⠄⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠆⠀⠈⢷⣆⡎⠈⣄⠁⠬⣡⣄⣠⠉⠈⠳⣄⣦⡦⠛⠉⠍⢉⢘⠀⠉⡔⠣⣀⢈⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠆⠀⠈⢋⠻⣶⣄⢙⠖⠋⣀⣈⡄⠔⠀⣥⠦⢤⣄⡐⢆⠲⠆⢂⠜⡀⢀⣴⠟⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠱⡄⠙⠻⢶⣬⣁⣩⢀⠁⢊⠲⠇⠀⢒⡑⣠⣋⣩⣥⡶⠟⡋⢐⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠸⡀⠀⠀⠈⢦⡀⠀⠀⠉⠙⠛⠻⠿⠿⠷⠿⠿⠿⠛⠛⠉⡑⠂⠅⣪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠉⠀⠈⠂⠀⠀⠀⠀⣂⡤⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⠀⠀⠀⠀⣟⡳⠦⣤⣄⣀⣀⣤⣀⣀⣤⡴⢞⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⢳⠀⡄⠀⠀⠀⠻⣿⣷⣶⣬⣭⣭⣭⣭⣴⣶⣾⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡜⡆⢻⠹⡄⠀⠀⠀⠈⠑⠪⠭⣭⣭⣭⣭⡭⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⡄⢧⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣈⣿⣿⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠟⢉⣄⡙⢿⣿⣿⣿⠿⠟⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠏⣰⣿⣿⣷⡄⢻⣿⡇⢰⣷⠀⣿⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⡿⢀⣿⣿⣿⣿⣷⠈⣿⡇⢸⣿⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⣴⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢹⡇⢸⣿⢀⣿⡇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿⣿⠟⢀⣿⣷⡈⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⡇⣴⣿⣿⣿⣿⡆⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣿⣿⣿⣿⠏⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⡇⢸⣿⡇⣿⣿⠟⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⡇⢸⣿⡇⠙⠁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠛⠛⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠤⠄⠐⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠀⣒⣒⣒⣀⡩⠥⠤⠤⠤⠄⠒⠒⠒⠒⠚⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢭⠋⠻⠉⠀⠀⠀⠀⠀⠀⠒⠒⠐⠒⠒⠒⠒⠂⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠄⠒⠒⠀⠒⠂⠀⡖⠂⠀⠂⠠⠤⠄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⠀⠀⠂⠀⢀⣭⠘⢢⠐⠨⠡⢄⢄⠂⠀⠀⠈⠉⠐⢤
⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠐⡒⠐⢤⡀⠈⣧⡀⠨⣕⣈⡈⣓⠤⣅⠁⠄⠈⠒⠂⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠆⠉⠐⠒⠤⠄⣠⣏⣀⣒⣒⣍⢻⣉⡀⣀⣀⣀⡺⣍⠷⠤⠖⠒⠉⡘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠉⠐⠒⠂⠠⠀⠄⠐⠒⠊⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⢌⠒⢄⡀
⠀⠀⠀⠀⠀⠜⠮⣙⠦⢭⡓⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠍⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠒⠢⢄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠷⣄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠀⠀⠙⠢⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠒⢲⣤⠤⢄⣠⠒⠲⣤⢀⡠⠔⠒⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡒⡫⢎⠥⠂⠁⠀⢸⣿⠆⢌⣙⢯⣋⣍⢀⣤⠶⢿⠿⡧⠦⠤⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⡬⠴⠐⠆⠐⣛⡻⠿⠋⠉⢆⣀⣀⠈⠭⣙⠲⠤⣄⣀⠀⠀⠩⠭⢅⡘⠻⢿⣦⡀
⠀⠀⠀⠀⠀⣠⠴⠖⡻⠟⡫⢕⣠⡴⢀⠴⢋⠥⠒⠂⠉⣁⡤⢤⣤⡤⡤⣤⣬⡱⢶⡩⢓⢦⣤⣀⠀⢙⡳⣦⠻⣜⢿⣛⠲⢦⣄
⠀⠀⠀⠀⡾⣅⠐⠏⠐⠠⠖⠡⠋⠀⠂⠀⠁⠀⠂⠁⠈⠐⠈⠝⠓⠀⣈⠄⣱⠘⡆⡩⢑⠢⠭⣙⠻⠶⣤⣬⠁⢀⣼⠏⠀⢀⣸⡇
⠀⠀⠀⠀⠘⢎⡉⠓⠲⢦⡤⢤⣤⣤⣀⣉⣉⣁⣐⣒⣒⣊⣁⣀⣐⣈⣁⣈⣀⣀⣘⣁⣀⣈⣒⣒⣚⣋⣠⣤⣤⣤⡶⠒⠚⣩⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠑⠴⣤⣀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⣤⣼⡿⠿⠋⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡗⠛⠻⣿⠷⠶⠶⠦⠤⠤⠤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠤⠴⡶⣿⡷⠟⠓⠚⣻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣈⠛⠷⢄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣶⢾⠟⢃⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠭⢽⣶⣤⣤⣤⣀⣄⣂⣽⣭⣭⠭⠵⠾⠓⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⣈⣁⣤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣀⡭⠴⠖⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠂⡡⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡣⢿⢢⣉⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣫⡵⡃⠈⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠘⠘⠃⢿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⠂⠀⠀⠀⠀⠀⠀⠀⠉⠤⢸⠊⠠⢾⡿⡟⣇
⠀⢀⡠⠐⠀⠀⠀⠀⠀⠄⠀⣤⢞⣽⠿⠛⠉⣳⡌⣛⡛⡦⣤⣤⡀⡰⢽⠄⠃⢹⡀⠀⢠⠄
⠀⡆⠀⠀⡄⠛⠀⠀⢠⠶⢀⣻⣻⠷⠞⠉⣉⢿⣶⣞⣛⣷⣿⣿⣶⡧⠀⠁⠾⠀⠀⠟
⠀⠡⡀⠠⡀⠀⢀⣀⠧⡽⠛⢻⣻⣿⡓⢻⢛⡐⢒⢼⣛⢿⢾⠿⣿⠿⠿⢾⢳⡀⠈⠅⣂⠀⡀
⠀⠀⠀⠠⠌⠁⠐⢷⣽⢿⣁⣡⡻⣮⠕⣓⣿⣤⠟⠞⣩⣾⣋⠳⢅⠁⠈⠉⠉⢷⣠⡀⠀⠈⠒⢕⠠⡀
⠀⠀⠀⠀⠀⠈⠒⠠⣈⠙⠻⡜⣚⠿⣦⣌⣉⣉⣉⣤⠭⠭⠵⠌⠂⠁⣩⣉⣉⣍⣭⡇⠀⠈⠀⠀⠡⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠅⢒⠠⠁⢈⠓⠿⠅⣂⣤⠿⠶⠶⣒⡴⢾⣩⠟⠣⠀⠁⠨⠯⠂⠀⠀⠔⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠢⠭⢀⢀⡀⠉⠠⠄⠀⠀⡛⠁⠁⠀⠀⣀⣀⠀⡀⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠒⠒⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⣿⡏⡟⢻⢻⠛⣿⡷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⡇⢸⢸⡇⣿⡇⠈⠻⣷⣦⣤⣤⣶⣶⣶⣶⠶⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣿⡇⣿⢸⢸⡇⣿⡇⠀⠀⣀⣤⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⢸⠸⡇⣿⣧⣤⣾⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⢸⢸⠀⡇⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢸⠀⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢸⠀⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣸⣧⣸⣸⣀⡇⢸⣇⣠⣤⣶⡶⠿⠿⠿⢶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⢛⣻⣿⡿⠟⢛⣛⣛⣛⣛⣛⠻⠿⣿⣿⣡⠖⢒⣛⣉⣛⡒⠲⢬⣙⣿⣶⣶⡶⠿⠿⠿⠿⠿⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣾⡟⣡⢖⣿⡿⢋⡥⠖⣋⣩⠭⠤⠤⠤⠬⢭⣓⠢⣝⠻⣾⣉⡤⠤⠤⣍⣓⣶⡿⢋⡡⠴⢒⣒⣋⣉⣙⣓⣒⠢⢭⡛⢷⣦⡀
⠀⠀⠀⠀⠀⣸⣟⣰⣃⣿⣏⣴⣋⣔⣋⣥⣖⣚⣛⣛⣛⣓⣶⣌⣹⣎⣷⣽⣿⣴⣶⣶⣤⣿⣏⣴⣋⣴⣋⣡⣴⣒⣒⣒⡲⠬⣙⠲⣍⢢⡙⣿⡄
⠀⠀⠀⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢶⣶⡄
⠀⠀⠀⠘⢿⣦⡘⠛⠀⠚⠛⠃⠀⠒⠒⠀⠐⠶⠖⠀⠰⠶⠖⠀⠛⠛⠃⠀⠛⠛⠃⠀⠛⠛⠃⠘⠛⠃⠀⠛⠛⠀⠲⠶⠂⠀⠶⠶⠂⠴⠶⠆⣠⣾⠟
⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠾⠿⢿⣿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣋⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠶⠶⠶⣶⡶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⢶⣶⣶⡾⠿⠿⣦⣶⠿⠻⢿⣶⡿⠻⢿⣭⣭⣉⣉⣩⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡅⠀⠀⣿⠃⠀⠀⢰⣿⠀⠀⣾⣏⣉⣉⣉⣉⠁
⠀⠀⠀⠀⠀⠠⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣻⣇⠀⠀⢿⡇⠀⠀⣸⡇⠀⢠⣿⣋⣉⣉⣉⣹⣷
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡄⠀⢸⣷⠀⠀⣿⡇⠀⢸⣿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢸⡿⠀⠀⣿⡇⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣾⡇⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⡇⠀⢰⣿⡀⠀⠀⣼⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠉⠁⠀⠀⣿⡇⠀⢸⣿⠻⣷⣴⡿⠁⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣿⡿⠁⠀⠀⣠⣴⡾⠟⠻⣷⡀⠀⢿⡆⠈⢻⣧⠀⠀⣰⡿⠁⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢰⡿⠁⠀⢠⣾⠟⠁⠀⣠⣴⣿⡇⠀⠸⣷⠀⠀⢻⣇⣴⣿⡿⠿⠛⠛⠛⠛⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣠⣾⡇⠀⠀⣿⠃⠀⢀⣾⠏⠁⣼⡇⠀⢀⣿⠀⠀⢸⣿⠋⠁⢀⣀⣤⣤⣤⣀⡀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢰⡿⢿⡇⠀⠀⣿⠀⠀⠸⣿⠀⣰⡿⠀⠀⣼⡟⠀⠀⣼⣧⣴⠿⠛⠋⠉⠉⠉⠙⠻⢷⣄⠀⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠸⣿⡀⠀⠻⣷⣄⣠⣿⡿⠋⠀⢀⣼⠟⠀⠀⣰⡿⠋⠁⣀⣤⣶⠾⠿⣷⡄⠀⢸⣿⠀⠀⠀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠶⠶⠿⠷⠶⠿⠿⠶⠶⠾⠿⠿⠿⠶⠶⠶⠿⠿⠶⠶⠾⠿⠷⠶⠾⠿⠿⠶⠶⠶⠿⠷⠶⠿⠿⠶⠶⠶⠶⠾⠿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠆⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠛⠉⠉⠉⠉⠁⠉⠉⠉⠙⠛⠛⠷⠶⣤⣀
⠀⠀⠀⠀⢀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⠶⠚⡡⣚⠒⠤⣒⠲⠄⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⢃⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⣀⡴⢾⡄⠉⠚⢪⡡⠺⢔⠿⣋⠀⠈⠤⡄⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⡀⠖⠐⡾⠠⢂⠅⠆⢤⡔⠚⢀⡐⠒⢬⡀⣍⡛⠓⡀⢰⠤⠄⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⡄⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡴⠁⢴⣯⣙⠕⠻⠆⢠⠛⡔⠂⠀⢒⠆⡐⢹⠖⡙⡖⣡⡆⠀⠀⠄⠠⡀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠸⡄⠀⠀⠀⢸⡇⠀⠀⡀⠚⢃⢘⠎⠀⠈⣢⠐⠀⠀⠒⢌⣯⢇⠠⠊⠠⣃⠀⠀⠦⠔⠀⠀⠀⡋⢂⠉⠄⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⡸⠁⠀⣠⣏⠀⠸⠀⠄⢀⠀⠴⠀⠀⣨⡀⣳⢀⠠⡴⠄⠀⢶⡌⠔⡦⠏⣐⠃⠩⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠱⡀⠀⢸⣇⡬⢂⢀⡞⠁⠘⢦⣀⠐⠌⠑⠘⢒⡔⡨⠀⠀⣹⠈⠙⢷⣄⣀⠈⡒⠁⠀⠇⠨⡻⡟⠋⠪⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢣⠀⠀⢿⣇⢴⣾⡆⠀⣠⠏⠹⠛⠷⠖⠒⡎⠀⡰⠉⡀⢻⠀⠀⠨⣤⣍⠘⡀⣠⠴⢂⠂⢀⠯⠉⡓⢄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢿⡜⢉⠚⣢⡌⢠⣄⠑⠀⠐⠄⢈⣶⡑⠐⠄⠚⢄⠀⠂⠠⢈⣛⡒⢁⢊⠅⠀⠸⠸⡌⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢆⠀⠀⢻⣦⡰⠇⢌⡌⠀⠌⣡⣄⣂⠍⠁⠙⢮⣐⣐⡢⠛⠫⠋⠉⠑⡃⠁⢁⠚⢄⡀⢁⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢆⠀⠀⠹⡻⢶⣔⡀⠐⡶⢊⠀⣀⣥⠀⠀⢠⣠⣠⢠⡀⠭⡄⢢⡭⠔⠠⠃⠀⢩⣵⠟⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠙⠻⢾⣤⣔⠋⠙⠃⠒⠡⠪⣤⠀⠉⠭⡣⠈⠒⠒⣈⣤⣽⠾⡋⢕⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⡄⠀⠀⠀⠳⡄⠀⡈⠉⠛⠿⠶⢷⣾⣶⣶⣴⣶⣾⣶⡷⠿⠟⠛⠉⢐⠠⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⠀⠀⠀⠀⠈⠳⣀⠀⠁⠀⠀⠀⠀⢀⣂⣀⡀⠀⠄⠀⠀⠀⠀⠌⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠱⡀⠀⠀⠀⠀⠀⣿⣶⣭⣙⡛⠶⠶⠾⠿⠶⠞⣛⣫⣥⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢆⢳⢀⣆⠀⠀⠀⠈⠻⣟⡻⠿⠿⢿⣿⡿⠿⠿⠿⣛⡯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡝⣆⢣⠸⣆⠀⠀⠀⠀⠀⠉⠛⠒⠒⠶⠶⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⡆⢇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠿⠿⡿⢿⣟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣛⣻⣿⣻⣻⣟⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠐⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⣀⣤⣤⠤⠴⢤⣀⣀⣀⣸⠦⢤⠤⠤⠐⠒⠒⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠠⣤⡤⠤⠤⠤⠒⠒⡞⢛⣻⣧⣈⡏⠛⠿⣿⡛⣯⡄⠤⠀⠀⠠⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠐⠀⠀⠀⠀⠒⠒⢻⠓⢃⡻⠿⢄⡀⠀⠈⠒⠾⣿⠏⠉⠉⠉⠫⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠀⠀⡀⠀⠂⠀⣀⣀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣶⡎⠀⣀⢐⣨⠀⡀⢧⡑⠰⠂⢜⡿⣣⠴⣦⡀⠀⠗⠒⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢰⢻⣶⠷⡸⠿⡏⣀⠀⠉⣃⢠⠛⠻⡙⠺⣿⣃⠛⢤⠞⠁⣎⣴⣴⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⣤⣤⣢⣥⣀⣦⠤⢋⣠⣀⣴⡈⣰⣾⣿⣿⣷⣤⣤⣬⣭⣀⣶⣭⣷⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠉⠉⣉⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠠⣤⣶⣶⢶⣶⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⣤⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡶⠿⢿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠤⠽⠿⠿⠿⠿⠿⠛⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢤⣴⣾⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣛⣿⡽⣷⣿⢿⣻⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣶⣾⣿⣧⣿⣿⣯⣿⠽⠿⠽⠯⠭⣭⣭⣽⣿⣿⣖⣲⣶⣶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡤⣖⣺⣭⡷⠶⢛⣛⣭⣿⣿⣿⡶⣿⣷⣞⠳⡳⣭⠽⣟⣛⡿⢿⣾⠿⢗⣭⣻⢭⡛⠛⠷⢾⣭⣗⣲⢤⣀⡀
⠀⠀⠀⢀⡤⢞⣭⣷⣟⣋⣭⣴⢶⣿⣿⠿⣿⣛⣛⣿⢮⣾⣿⣇⣷⣧⡿⣟⣾⡿⡚⢯⡻⣯⣝⣓⢿⡵⠼⣶⣿⣷⣶⣭⡙⠻⣾⣭⡳⢤⡀
⠀⢀⡖⣩⣾⠟⣫⣿⣿⣿⣩⣿⢟⡭⣲⣿⣿⣿⣿⣿⣿⡽⡏⡆⣿⢿⡹⣻⢿⣪⢺⡿⣻⢳⣮⢭⣝⡻⣽⢺⣯⣯⣿⣿⣜⡦⣄⠙⠻⣷⣝⢲⡀
⢠⠏⣼⡿⢃⣾⣿⣯⣭⢟⡿⣗⣽⣞⣿⣿⣿⣛⣿⠿⣏⣿⢽⣇⣏⣾⢷⣿⣇⣟⢬⣚⣾⠿⠵⠿⢾⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣄⠘⣿⣷⣻
⡿⢸⣿⠳⡋⣯⣽⣿⣕⡻⣿⢟⣏⣾⡿⣿⣿⡸⣿⣿⢿⣯⢺⢸⣴⣿⣯⣷⡏⣿⠵⢿⣯⠲⠷⠷⡿⠷⠳⡛⠿⠟⠟⠟⢿⣿⢿⣿⣿⣿⣼⣿⡇
⣷⢸⣿⡄⠉⠙⣷⣿⣿⣿⣮⢻⣟⣿⢿⣿⣿⣿⡶⣶⢯⣿⣻⣸⣿⣟⢵⣿⣻⣽⣿⣷⣹⢻⢻⠿⣛⣛⣛⣻⣽⣿⣛⣿⣿⣿⣽⣿⣿⢿⢿⣿⡇
⠘⢦⠻⣿⣄⠀⠙⠫⢿⡶⢿⡿⢿⣾⣸⢿⣿⡾⣿⢟⣿⣿⣿⣕⣝⣿⣿⣿⢳⣾⣿⣿⡇⣿⡧⣫⣿⡾⣹⣿⣿⣿⣿⣿⣛⣽⣸⣻⠕⣣⣿⠟⡴
⠀⠈⠳⢌⡛⢷⣤⡀⠐⣿⡿⣟⣛⣦⣿⣻⡿⣽⣿⣾⣿⣿⣿⣿⢛⣟⣛⣻⣿⣿⣿⣟⣽⣿⢷⣾⣯⣶⣿⡿⣿⣛⣻⣿⡿⠟⢁⣤⡾⢛⡡⠞⠁
⠀⠀⠀⠀⠙⠲⢭⣛⠷⣦⣍⣙⡒⠒⠓⠻⢿⣮⣾⣭⣟⣻⣿⣿⡷⡯⢋⣿⣛⣿⣿⡿⡿⣻⢟⣿⣿⢿⣿⣿⠟⢉⣉⣥⣴⠾⣛⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠬⣝⣛⡿⠶⢶⣤⣬⣛⣻⣿⡿⠛⠋⠑⠚⠛⠚⠯⠽⠛⠓⢛⣛⣛⣛⣯⣥⡶⠶⠿⣛⣫⠥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠮⠭⠭⣭⣭⣽⣛⣛⣛⣛⣛⣛⣛⣛⣿⣭⣭⠭⠭⠵⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⠀⠀⠈⠢⡠⠊⠀⠀⠀⢀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠂⠉⠉⠁⠒⠐⠒⠊⠉⠒⠂⠐⠂⠁⠈⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣬⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢊⡏⡯⠐⡒⠂⠐⠒⠈⠉⢉⣉⣁⡆⠐⢒⣀⣤⠒⣈⠩⠠⣂⣭⡢⡿⢓⢄⠑⠢
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠸⡑⢌⠢⢤⣄⠉⠛⡉⠩⠤⠀⠒⠒⠈⠍⠒⡨⢁⣂⣍⣉⣘⣓⠶⠔⢃⢩⠦⢤⠡
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⡬⣖⣨⢄⡐⣉⠭⠁⠀⠐⠤⠬⠅⣀⣒⣴⣋⣥⣂⣀⠶⠟⣒⢶⡫⢒⠝⣩⠎⢀
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠢⠵⡬⠍⣊⣷⢦⡤⡤⢝⠋⠍⡁⡰⢂⠭⠄⠀⠒⡒⡂⠩⠗⠓⠦⢔⣡⡾⠋⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢆⣮⢅⡖⠒⠒⠬⣐⠂⠁⠉⠓⠛⠴⢺⠤⠤⠀⣤⢤⡨⢒⡬⠖⠋⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠈⠉⠉⠉⠉⠛⠋⠉⠀⠙⠒⠒⠋⠉⠀⠈⠁⠈⠁⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢸⣃⠠⠤⡀⣬⣠⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠐⠼⠃⡀⠊⢰⣷⡌⡰⠀⢀⡀
⢀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠶⠟⠉⠁⠁⢰⢈⠆⡴⠓⡆⢜⠩⠀⠁⠀⣆⠠⡀
⠀⠀⠀⡈⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠐⠁⠄⠎⠀⠚⢣⣨⠀⠄⠀⢰⣀⡰⢄
⠶⠞⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢤⣀⠀⣀⣦⠀⠃⠃⠞⡀⠄⠺⢃⠔⢤⡓⠄⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⡮⢊⠀⠔⠂⠄⢀⡌⡀⠀⠦⠀⠀⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣀⢤⡞⠁⢀⠀⠁⠀⠁⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⠇⠸⠀⡴⠁⠀⠀⠀⣴⣦⢚⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢃⠀⠀⠀⠀⢡⠀⠀⠀⠀⠘⠋⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢁⠃⠀⠀⠀⠂⠳⠀⠰⠃⢈⣆⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡆⠘⢯⠀⡁⠀⠀⠀⡇⠠⢀⠀⢠⠳⡷⣄⠈⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠉⠁⠠⡇⢀⠆⡼⠀⠀⠀⢈⠆⠔⠉⠂⠈⡟⣀⠀⠆⠰⠈⡛⠻⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⠐⠚⢩⠂⠀⠐⢱⠛⠚⡁⠊⡐⠁⠀⡂⠰⡇⠂⢠⢄⠤⢯⡠⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⡸⠃⠀⢀⠼⡄⡄⠀⡃⠀⠁⠀⡖⠡⢦⠘⠀⠀⠏⠎⡇⠉⠐⠄⣘⡁⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⡀⠀⣁⠆⠐⠉⠀⠍⢀⡐⢧⠰⡀⠀⠀⠘⠺⠀⠀⡜⠠⡄⠈⢶⡄⠸⠑⠐⠡⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢳⢰⣏⡼⣨⢂⠀⠀⠀⣱⡈⡇⠡⠀⠀⡠⠘⡐⠞⡁⢠⠹⡀⢰⢥⠘⢠⠐⠀⡋⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣾⠤⠊⠐⡉⠄⠀⠀⠈⠽⡇⡃⠅⠀⠈⠀⣆⠉⡞⠀⣠⣜⣀⣎⡤⠗⡄⢚⢸⠄⠈⠂⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠐⡄⢠⣡⡤⣤⠂⠀⢢⠀⠀⠀⡴⠡⠁⠐⠠⠠⢀⡿⠃⣷⢀⣐⡀⠀⡀⡠⠊⠀⠲⣄⣯⡰⠜⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⠘⢄⢲⠰⡇⠀⢀⢰⠆⠐⠀⠤⠀⢀⡋⠉⢁⡈⠀⠠⠟⢧⡞⠁⠁⣡⣛⠃⠀⠄⠨⣟⠏⣆⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⢈⠓⡹⠀⠚⠦⣀⡴⡲⠶⡒⢇⠚⠛⠂⢶⣈⠣⠀⠀⣀⡴⠊⠁⠩⠀⠀⠀⠓⢤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⡳⢬⣀⡠⠶⢦⡈⠀⢀⣘⠃⠄⣀⡤⢈⠀⠈⠁⠀⠀⠀⠇⠀⠀⢈⣃⣠⣴⠾⢛⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠉⠛⠿⠶⣶⣤⣌⣁⣀⡀⡀⣇⢀⢀⢁⣐⣦⣤⣌⣤⣴⡶⠿⠛⠋⢑⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡠⢐⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠐⢂⠨⠀⠈⣂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣈⡑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠴⠊⠁
⣿⢿⢿⠿⣿⢟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣟⣟⣿⣿⣿⣟⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣉⢉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠶⠒⠒⠒⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢲⠀⠻⡇⠁⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠙⠀⠐⢠⠀⠀⠇⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠁⠀⠐⡧⠀⣀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠂⠠⠣⡃⠀⠉⠈⠀⠀⠀⠐⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⣆⠀⢀⠀⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣠⠐⡀⠀⠃⡁⠨⠀⡾⡛⠒⢧⡠⠥⠖⡂⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⡌⠀⠀⠀⠀⢨⠀⠄⠽⠄⠠⠆⠨⣺⢀⡧⡐⠠⣙⡴⣤⣀⡀⠀⠂⠄⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠁⠀⠀⡰⡀⠀⡠⠚⠛⠂⡠⠏⠕⡡⡔⠀⡰⡀⢀⣀⠀⠙⠟⠓⠩⢤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⡆⠀⠀⠀⡄⢈⠄⣀⠀⠐⡸⠤⢀⣤⠴⠊⠁⠈⢲⠀⠀⡄⠔⡠⠾⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡀⠀⠸⠈⠚⠘⢁⠔⠤⠠⠔⠃⠈⡛⠶⠠⡴⠿⡈⠀⠀⠀⠂⠀⠘⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠠⢴⠃⡀⢀⠀⠄⠀⠈⠁⠀⠰⠔⠓⠂⠖⡶⢂⣄⠂⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠑⠰⣅⠀⢀⠐⢀⠐⣳⠄⠀⠀⠀⠊⠀⠈⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠈⠁⠂

⢀⣤⣤⣶⣶⣶⣶⡶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⣶⣶⣶⣶⣤⣤⣄
⣿⡏⣥⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡍⣿
⣿⡇⠈⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⢨⣿⠛⠿⠿⠿⢶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⡶⠿⠿⠟⠛⣿
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⢰⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⡆⠀⢸
⣿⡇⠀⢸⣿⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⣻⣿⣿⠿⠿⠿⢿⣿⣟⡛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⡽⢳⣶⣾⢻⣿⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠛⣷⣿⣧⣶⢀⣩⠶⣦⣔⣿⣿⡟⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⣿⡇⠀⢸
⣿⡇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸
⣿⡇⠀⠀⠙⠿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡾⠿⠋⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠷⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠾⠿⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠈⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠉⠙⠛⠿⠷⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⠾⠿⠛⠋⠉

⠀⠀⠀⠀⢀⠄⠒⢀⢀⠔⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣆⠀⠀⠀⠀⢀⠖⢀⣀⣀⠒⢰⣤
⠀⠀⡂⠁⠀⠄⣀⡤⡏⡷⣶⣤⣄⣠⣶⣿⠑⠀⠀⠀⢸⢇⠀⠀⠤⠴⡲⢍⣅⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⠏
⠀⠄⠻⣿⠖⣛⠱⣀⣍⡀⠎⠸⠫⠽⠟⢉⠔⠀⠀⣴⠃⡼⠀⠀⠀⠸⠒⠛⢄⢂⠅⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠇⠆
⠀⠀⠀⠈⢉⣺⡉⠁⢐⠎⠀⢒⡁⠄⠒⠁⣀⢔⠟⠁⠊⠂⠀⠀⠀⠀⠢⠠⠊⡀⠀⠀⠂⠀⡆⠀⢀⡠⠀⠀⢘⢀⢠
⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠉⠀⠀⢀⡔⠞⠊⣠⠖⠋⠀⠀⠀⠀⠀⠁⠈⠀⠀⠠⠀⠀⡄⠀⢇⢀⡀⠀⣀⣀⣈⡤⠚
⠀⣄⠅⠀⠂⠀⠨⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣰⠣⠀⠄⠀⠀⢀⠌⠎⡩⢥⡭⠆⠀⠀⠀⢀⣀⣀⡀
⠀⡗⠒⠐⠀⠀⠀⢹⠀⢀⠀⠀⠠⠤⠀⢀⠀⠀⠀⢚⠂⠀⠀⠀⠀⠅⠀⢈⣀⣀⢀⡌⠤⠦⠀⠐⠳⣢⠛⢛⣿⣶⣾
⠀⡿⡦⢀⣀⣀⠠⠺⡄⠀⢱⠔⣒⡩⣿⡭⡥⠀⠀⠡⠀⠀⠀⢀⣀⠂⠀⠘⠀⠀⠀⠐⠃⠀⠀⠈⠀⠻⠶⠟⠙⠋⠁
⠀⡇⡇⠀⠀⠀⢄⠀⡇⠀⠈⠎⢟⡿⣿⢯⡇⢡⠀⠀⠑⠠⠄⠘⠃⠀⠀⠀⠀⣐⠂⠀⠀⠀⠠⢀⡀⠀⠀⠀⢀⣴⠎
⠀⠙⢀⠀⠀⠀⠈⢢⢰⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⠄⠀⠀⠀⡔⡀⠀⢠⡄⣄⠁⠂⠀⡬⠄⡠⠬⠟⡀
⠀⠀⢨⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⢤⣐⣂⣬⠴⠒⡺⠉⠉⢂⠀⢀⡊⠐⠸⠁⠀⠐⠀⠘⠁⠀⠇⢩⠴⠛⠃⠁
⠈⠒⠦⡄⠀⠀⠀⢀⡀⠇⠀⠀⠀⠀⠀⢈⢡⡎⠁⠀⢁⠀⠀⢨⠈⡀⠪⠌⠁⢒⡂⠀⠄⠌⠀⠀⠀⠀⠠⢒⡨⠸⡀
⠀⢀⣀⣀⡀⠄⠀⢀⠀⢀⠔⠀⠀⠠⡀⠀⠈⢷⡀⡐⠁⠀⠀⠀⡄⠡⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠘⠒⠒⠀⠈⠁
⢈⠔⣉⣡⢞⡋⠥⠐⠀⢈⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⡠⠊⢺⠀⢀⠀⢠⡴⠢⠄⠤⡆⠀⣀⣠⣒⠒⢲⣄⣀⣀
⠈⠂⠉⠀⠀⢀⠄⢲⡄⠈⠂⠤⠤⠔⠃⠀⠈⠀⠷⠄⠄⠀⠒⠃⠄⠂⠈⠀⠈⠻⠄⡠⠤⠗⠛⠒⠚⠒⠲⠾⢶⢦⠢
⠀⠀⢀⣴⠆⡖⠀⠀⣰⢒⣶⣤⣴⣖⢄⠀⠀⠀⠀⠁⠀⡠⡄⠤⡤⡀⠀⠀⠀⠠⠀⢀⡓⠀⠠⠌⠀⠀⠠⢧⠔
⢀⠰⣿⢇⣴⣿⣫⣿⡗⠐⡟⠿⣽⢿⢆⠡⡀⠀⡀⠮⠉⢉⠍⠒⠆⠉⠒⣄⠀⢀⠸⣿⣂⠠⢀⢠⠄⠀⠀⠈⠀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠛⠛⠉⠉⠉⠛⠛⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠼⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠂⠀⠈⠀⠈⠀⠀⠁⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠸⠆⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣿⣷⣦⣤⣤⣀⡀⠀⠀⠀⠴⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠁⠀⣠⣴⣾⣿⣿⠟⠛⠋⠉⢹⡏⠉⢁⡿⠋⠙⠛⠿⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠁⠀⠄⠀⠀⢀⣤⣾⡿⣿⠏⠁⢹⠀⠀⠀⠀⠸⠇⠰⠿⠥⠀⠀⠀⠀⠀⠈⣿⠻⣿⣶⣄⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣆
⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠀⠠⠀⠀⢀⣴⣿⡿⠋⠀⢸⡀⠀⣼⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢿⣷⣄⠀⠀⠠⠀⠀⠹⣿⣿⣿⣿⣧
⠀⠀⣸⣿⣿⣿⣿⣿⠁⠀⢤⡄⠀⣠⣾⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢨⡇⠀⠀⠀⠀⣀⣴⣶⠀⠀⠀⠀⠈⢹⣿⣧⡀⠀⢠⡄⠀⠹⣿⣿⣿⣿⣆
⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣸⣿⡿⣿⠁⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠛⠉⢻⣿⡄⠀⠀⠄⠀⠹⣿⣿⣿⣿⡆
⠀⣿⣿⣿⣿⣿⠃⠀⢀⠀⠀⢰⣿⣿⡇⢿⣄⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣻⣿⡀⠀⢀⡀⠀⢻⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣿⡿⠈⠁⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣧⠀⠀⠀⠀⠈⣿⣿⣿⣿
⣼⣿⣿⣿⣿⡇⠀⠀⠁⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠉⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠲⠂⠀⣿⣿⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⠀⠰⠆⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⡄⠀⠠⠀⠀⣿⣿⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣿⡇⠀⠠⠄⠀⢸⣿⣿⣿
⢻⣿⣿⣿⣿⡇⠀⠀⡀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⡀⠀⠀⣾⣿⣿⣿
⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣿⣷⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⡝⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⡆⠀⠈⠀⠀⠘⣿⣿⣧⣤⡟⠀⠀⠀⠀⠀⠀⢰⡿⢋⠜⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⣷⣾⡿⠁⠀⠈⠀⠀⣼⣿⣿⣿⡿
⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⣿⣧⣀⡿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢤⣼⣿⡿⠃⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃
⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠘⠁⠀⠘⢿⣿⣅⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠙⠃⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⠀⠐⠁⠀⠀⠙⢿⣷⣆⡀⠉⢉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣭⡀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⣃⠀⠀⠀⠀⠀⢠⡾⣛⡛⠀⠀⠀⠀⠀⣀⣀⣬⣿⣿⠟⠋⠀⠀⠀⠁⠀⣠⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⡀⠀⠁⠀⠄⠀⠈⠙⠿⢿⣿⣶⣦⣤⣀⣿⣋⣉⣹⣦⣠⣤⣶⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠰⠆⠀⡀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠲⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠶⠶⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠉⠠⠐⡏⣀⠀⠀⠈⠉⠉⠉⠙⢧⣀⡀⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣄⡀⠀⠐⠀⠀⠇⠏⠀⠀⢀⠀⣀⠴⠀⠒⠀⢹⡄⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⣾⣿⣄⣀⡄⠂⠰⠀⠀⢀⡬⠁⡑⠀⠀⠂⠀⠀⠅⠀⠀⢇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣞⠀⠀⠘⢛⡔⡀⠐⡂⣰⠟⢥⡆⠘⠀⠀⠀⡄⠀⢠⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠘⣿⠟⡜⡇⠀⠀⠀⢂⡈⠒⡼⢮⠁⠀⠀⢈⣦⣀⠀⠴⠀⠀⠘⠀⡐
⠀⠀⠀⠀⠀⠀⠀⢿⣏⢞⠝⢦⣦⢲⠿⠿⣩⢿⣟⠀⠀⠀⠈⠟⣝⣹⢔⢧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣦⢮⣇⣇⠀⠀⠈⠁⠻⡇⡀⠀⠀⠀⠈⢻⠖⡇⣡⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢹⡼⢸⡙⣤⣄⡀⠐⡈⣏⢆⢀⡁⡀⠠⢚⠜⢁⠏⣷⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢲⡣⣜⣛⣛⠵⣹⢯⣖⠀⣥⣀⡀⠖⠚⡉⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣭⣤⡠⠬⢿⣚⣭⣖⣒⣬⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠁⠚⠝⡷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⠛⠉⠉⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠉⠒⠫⢝⡳⢦⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠉⠀⠀⣀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⣦⣕⣤⣀⠀⠈⠑⠫⢗⡆
⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⡙⠲⢤⣀⠀⠈⠑⠦⣀
⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠈⠙⠲⠦⣤⣀⣙⣢
⠀⠀⠀⠀⠙⠁⣿⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢠⣷⡠⣕⢮⣷⣦⢄⡀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢸⣿⡟⢾⡿⠟⠁⠀⠈⠂⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⣿⣷⠀⠉⠓⠖⠚⠛⠳⣤⡈⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⣿⣧⠀⠈⢿⣄⠀⠀⠈⠙⢦⣌⠻⢗⡢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⡄
⠀⠀⠀⠘⢿⣧⡀⠀⠙⢷⣄⠀⠀⠀⠙⠳⣤⡉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢠⠎
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠙⠳⣦⣀⠀⠀⠈⠻⢦⣄⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⡀⠀⠉⠛⠷⢦⣤⣀⡙⢷⣄⠀⠙⠳⢦⣄⡀⠤⠤⠶⠖⠚⠉⠁⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⣀⠀⠀⠈⠉⠀⠙⠷⣦⡀⠀⠈⢿⡄⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢷⣶⣶⣤⣤⣤⣬⣝⡳⠶⢛⣤⣴⣶⠶⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⢤⣀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡴⠞⢛⣶⠶⠛⢋⣉⣡⣤⣉⣉⡉⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠛⠛⠛⠿⣥⣴⠚⢉⣁⣤⣤⣤⣌⣉⠛⢦⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣤⠶⠖⠛⠒⠶⣤⡉⠻⢯⣅⡀⠀⠀⠀⠉⣳⣄⣈⣷⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡾⠋⢀⣠⡤⠶⠶⢤⣄⠙⠳⢤⣈⠉⠙⠛⠛⠋⠉⣁⣀⣀⣀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⡟⢀⡴⠋⠁⠀⠀⣀⣀⣈⣛⣦⣄⣉⣙⣛⣓⣛⣛⣉⣉⣉⣉⣉⣙⣦⡀⠈⢷
⠀⠀⠀⠀⠀⠀⢠⣤⠴⠾⠷⠚⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⢲⡆
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠛⠛⠋⠉⠙⠛⠛⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣠⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠐⠀⠀⠓⠀⠐⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠋⢡⡀⠀⠂⠀⠀⠀⠀⠀⠀⣠⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠐⠀⣠⡉⠛⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠛⠁⠐⠀⠀⠁⣀⠀⠀⣀⠀⠀⠀⠈⢹⡇⠛⠀⣸⠇⠀⠀⠀⠀⢀⡀⠀⠁⠀⠐⠀⠙⠻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠃⠀⠀⠀⠘⢻⡇⠘⣿⠀⠀⠀⠀⢸⡇⢠⣼⣋⠀⠀⠀⠀⠀⠛⣗⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠈⠁⠈⢉⠉⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⢿⣿⣿⣿⣿⣷⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠛⠀⠀⠀⠀⢀⠀⡀⢰⠀⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⢻⣿⣿⣿⣿⣷⡀
⠀⢀⣾⣿⣿⣿⣿⣿⠏⠀⠙⠁⠀⢶⡆⣴⠟⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⣸⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⡼⠛⢻⡆⠀⠘⠁⠀⢻⣿⣿⣿⣿⣷⡀
⠀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡇⣯⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⠀⠀⢀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧
⢠⣿⣿⣿⣿⣿⡟⠀⠐⠀⠀⠀⠀⠸⠇⠘⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠾⠿⠶⠆⠀⠀⠀⠐⠀⠘⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠠⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⣠⡀⠀⠸⣏⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⢠⡄⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣈⣛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⣼⠇⠀⢀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠀⢸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⡀⠐⠀⠀⠀⠀⢰⣏⣙⡧⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡣⠃⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⡇⠀⠀⠀⠀⠐⠀⢰⣿⣿⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣧⠀⠠⠀⠀⠀⢸⡛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠸⢯⠜⠁⠀⠘⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣸⡇⠀⠀⠀⠀⠄⢠⣿⣿⣿⣿⣿⡏
⠀⠀⢿⣿⣿⣿⣿⣿⣧⠀⡴⠆⠀⠈⠳⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠰⡄⢠⣾⣿⣿⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠒⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣠⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⣠⠴⠦⠀⠀⠀⠀⠀⠈⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠂⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⣼⡷⠖⢶⡄⠀⠀⠀⠀⠶⣤⡴⠏⠀⠀⠀⠀⠂⢀⣴⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣄⡐⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠘⣀⣴⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠻⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⣤⡀⠀⣸⣿⡆
⠀⠀⠀⠀⠘⢿⣷⠀⠙⣿⠣⣤⣄⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⡀⢀⡀⢀⡀⠀⣀⣀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⣰⠆⠙⣧⠀⣇⠀⠀⠉⢳⣄⠀⠀⡇⠀⠀⣿⠀⢸⡇⣿⢧⢸⡇⣼⠁⠈⠃⣿⣀⣀⡇
⠀⠀⠀⢸⡏⠀⠀⠈⢷⣿⠀⠀⠀⠀⢻⡄⠀⣧⣀⡀⢿⣀⣼⠃⣿⠈⢿⡇⠹⣄⣠⠆⢿⠀⠀⡇
⠀⠀⠀⢺⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⠀⣀⣀⣀⠀⣀⣀⣀⠀⢀⡀⠀⢀⡀⢀⡀
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣧⣤⣽⠀⣿⣀⡽⠀⣯⣤⡄⠀⡼⢻⡄⢸⣧⡏
⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⢀⣀⣴⠟⠁⠀⠀⣧⣤⡼⠂⡿⠈⢷⠀⣧⣤⣤⢰⠟⠛⢧⢸⠏⠻⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉