Black and white animal Emojis & Symbols

⠀⣀⠀⠀⠀⠀⠤
⠀⠿⢿⡮⠀⠀⠀⠀⢰⡿⣿⡇⢤⣄⣀⠠⠀⠀⠤⠀⡀⣄⣤⣄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⠀⡀
⠀⠀⠘⡆⠀⠀⠐⠓⠌⣿⠏⡀⠀⠈⠉⠀⠀⠀⠀⠈⠋⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠙⠋⠁⠈⠙⠛⠿⣦⣄
⠀⠀⡀⠄⠀⠀⠀⣀⣇⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣷
⠀⠀⢿⣿⣥⣤⣶⣿⣿⡽⣿⣿⣿⣷⡟⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⢄⠿⣧⡤⣾⠀⢿
⠀⠀⠀⠀⠀⠀⠙⠛⢿⡄⠙⢿⣿⣿⠅⣤⣾⠀⠙⢷⣿⣦⣀⣶⣆⣧⣄⣾⡆⣴⡀⣠⣾⣿⣿⡑⠀⠉⠋⠉⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠘⠻⢿⣻⣿⣿⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⣤⣠⢈⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⢸⣿⣿⣿⣄⣹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣀⣈⣛⣿⣿⣿⣿⣿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣢⣤⢿⣷⣽⣿⣿⡤⠮⣿⣿⣿⣿⣿⣿⣿⣟⡀⠠⠍⠉⢹⣿⣧⣿⠻⣿⠙⢻⣶⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣶⣿⣿⣿⡟⠎⠀⠀⠀⠀⠈⠉⠉⢻⠟⠉⠀⠀⠀⠀⠈⣿⣿⣿⠄⠈⢶⣿⡟⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣧⠾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⢻⣷⣄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠇⠀⠀⠀⠀⢿⡇⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠾⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠨⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠃⠀⠀⠀⠀⠀⠠⣖⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠈⠻⠿⣿⣦⡀⠀⠀⠀⠀⣀⠼⠅⢡⣄⣀⠀⢀⡀⠀⣼⡋⠉⢹⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠠⠆⠈⣿⣏⠁⢦⣀⠘⠅⠀⡄⠀⠀⠀⠀⠀⠀⠀⢻⣷⣥⣿⠃⠀⠀⠀⢠⡀⢀⡀
⠀⠀⠀⠀⠀⠘⠿⠶⠋⠀⠀⠀⠀⡈⠀⠐⣶⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠋⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢽⡆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⡤⠀⡠⡏⠀⢻⢄
⠀⠀⠔⠀⠀⠀⠲⠀⠤⠂⢸⡇⠀⠀⠀⠀⠠⠂⣠⡋⠀⣀⠀⠀⠀⠀⠐⠛⠉⢻⣿⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣷⡀⠀⠀⣇⡄⠀⢀⡇⠀⠘⣿⡏⠀⠀⠀⢀⢀⣾⠟⠁⠀⠀⠤⠀⠄
⠀⠐⠀⠀⢠⠀⠖⠒⠀⠀⠘⢽⢿⣷⡄⠈⠀⠀⠈⠓⠀⠀⠘⠃⠐⠀⠀⠈⠹⠁⢀⠠⠤⣀⡀⠠⡄
⠀⠸⣿⣤⣼⣷⢶⣧⠀⠀⠈⠃⠘⠏⠀⠄⠠⣤⣠⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠁
⠀⠀⠙⠋⠁⠙⠛⠁⠀⠀⠤⠠⠀⠂⠄⠀⠠⠔⠋⠉⢹⣿⣿⡿⢿⣿⠿⠷⢤⠀⠠⠈⠃⢲⠆⠉⠉⠁
⠀⠀⠀⠀⠀⡴⠀⠀⢰⢹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⢠⣏⡀⠀⠈⠈⢡⣤⠐⠠⡀⣀⠐⢛⣇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣶⣤⣤
⠀⠀⠀⣠⣾⡏⢧⠀⠀⢠⡀⠁⢰⢄⠀⠁⠐⡯⢙⢷⣦⠀⠂⠀⢤⣀⠀⢀⢀⡀⠀⠆⠀⠈⠻⣿⡟⠁
⠀⢀⣴⢿⣿⣿⡋⠀⠘⢈⠁⢠⠃⡎⠀⠀⠀⠇⠈⢏⠿⠀⠀⠀⠀⡟⠀⠈⣿⠁⣸
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢶⡂⠐⠠⠀⡠⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⡀⠀⠀⠀⠐⠒⡶⣴⣶⠾⣿⣧⡀⠇⠀⢠⡆⢀⡐⠋⢉⣻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⣀⣀⣤⠴⠞⠉⢰⣿⣇⣾⣿⣿⣗⣀⣸⣿⠀⢘⣷⣶⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⣾⣿⡟⠁⠀⠀⣼⡿⠛⠿⣿⣿⡟⠉⡉⠉⠩⡿⢿⣿⣿⣿⢷⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡏⠀⠀⠀⢸⣿⠁⠀⢠⣿⣭⣿⣶⣬⣶⣿⣷⡈⡿⢿⣿⣯⣿⠽⣿⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢰⣿⠃⠀⠀⠀⣼⣿⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢸⣿⠀⠀⠀⣴⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣤⣶⣿⡿⣿⣿⠀⠀⠀⠉⠙⣿⠿⠿⣿⠿⠊⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠐⣿⣿⡀⣀⣤⣴⣶⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠉⢳⣤⣤⠄⢀⣈⡛⠳⢤⡀⠀⠀⠀⢠⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣉⠎⣱⠿⣿⣿⣇⠈⠋⠀⠹⠒⠋⠛⠛⣶⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠏⢀⠏⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣾⢢⡀⢸⣽⣿⣷⠀⠀⠀⠀⠀⠀⡘⢻⣿⡇⠀⠉⠻⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⣿⣿⡇⢘⠁⠟⢻⡄⠀⠀⠀⠀⢠⡷⠞⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣧⣸⠀⠀⠀⢷⠀⠀⠀⢠⠎⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡆⠸⣿⣿⣿⣧⡀⠀⠀⠠⡆⠀⠀⠃⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⡙⢿⣿⣿⣇⠀⠀⠀⠀⠀⡀⠀⠀⡠⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣾⣭⣙⢷⣄⠄⠀⠀⠉⠀⣆⣳⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⢿⣿⣷⣄⣄⣴⣾⡷⠈⢛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⠃⠀⠒⠤⣙⢿⣿⣿⣿⣿⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠸⠿⠣⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣀⣀
⠀⠀⠀⠀⠀⠈⠂⠠⠒⠃⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠂⠙⠋

⠀⠀⠀⠀⠀⣄⠀⠈⣠⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁⣴⡄⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠐⠒⠋⠁⠉⠁⠈⡁⠘⠓⠂⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠂⠀⠀⠀⠁⠂⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠄⠂⠠
⠀⠀⠀⠀⡀⢢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠁⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡈⠀⠀⠀⠈⠀⠃⢈⠣⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⢸⡖⠀⠀⠀⠀⠰⣶⠁
⠀⠀⠀⠀⠁⢰⣾⡆⠀⢠⣶⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⡀⠀⣠⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠱⠶⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⠡⠤⠙⠃
⠀⠀⠀⠀⠀⠈⡐⠒⠒⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠒
⠀⠀⠀⢀⡄⢢⡀⠠⡀⠄⢰⠬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢥⠁⠉⠀⡀⢡⢄⡄
⠀⠀⠀⠀⠁⠀⠃⠒⠓⠂⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠐⠓⠂⠃⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⢳⡀⠀⠀⢠⠎⠁⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣰⠃⠀⠀⠸⡄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠓⠒⠚⢣⠀⠀⠀⠀⡜⠓⠒⠊⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⢣⠀⠀⡜⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⢀⡠⠤⠔⠒⠒⠤⢤⣀⠀⠈⢢⡀⠀⠀⠈⡆⢸⠁⠀⠀⢀⡔⠁⠀⣀⡤⠴⠒⠒⠢⠤⢄⡀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⢀⠎⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠱⡄⠀⠀⣇⣈⠀⠀⢠⠎⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠱⡀
⠀⠀⠀⡞⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡸⠊⠉⠀⠀⠉⠓⢏⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢣
⠀⠀⢀⠃⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠘⡀
⠀⠀⠈⡄⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢏⡷⠈⠋⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⠁
⠀⠀⠀⢣⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡜
⠀⠀⠀⠈⢇⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠒⠢⠤⠤⠤⠤⠔⠒⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠳⢄⠀⠀⠈⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⢤⠤⠚⠁⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠒⡲⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠸⠉⠑⠒⠒⠒⠒⠒⠒⠊⢉⠃⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠙⠛⠛⠋⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣇⡀⠀⠀⠀⠀⣀⣰⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡴⠻⡈⠉⠉⠉⠉⢁⠟⢦⠀⠙⠦⣀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠑⠒⠒⠒⠉⠀⠀⡠⠊⠀⠀⢳⣀⣀⣀⣀⡞⠀⠀⠑⢄⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⢀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠣⡀⢀⠜⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠂⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠀⠠⡿⠁⠀⢀⢀⠱⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⢀⠀⠁⠀⢠⣦⠁⠀⠀⣩⣭⡀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣤⣄⠠⠀⢹⣦⡁⠀⠀⠀⠹⡀
⠀⠀⠀⠀⢠⠁⠀⠀⠀⣨⣟⠀⡀⠐⣿⣿⠇⠈⠀⠀⠀⠀⠀⢠⡔⢿⣷⡿⠃⢀⢸⣿⡧⠀⢰⠀⠀⠙⠄
⠀⠀⠀⠀⣸⠃⣤⠀⠀⢻⣧⠀⠁⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠰⠀⢻⣿⠀⠺⠀⠀⠀⠀⢠
⠀⠀⠀⢀⣷⠛⠁⠀⠀⠸⣿⠀⢬⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢼⣿⡇⠀⠀⠀⠀⠀⠲⠷⡀
⠀⠀⠀⢸⣿⣷⣤⢀⢀⠀⣿⢰⠆⡀⡀⠀⠀⢠⢶⣶⣶⣶⣿⣦⡀⢀⠀⠀⢀⢈⠑⣶⢻⣿⢸⣷⣄⠀⣶⠦⣴⣦
⠀⠀⠀⢸⣾⣿⣿⢛⣞⡇⣿⢼⠈⢸⣄⢀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠂⢀⣼⠿⢰⣿⣺⣿⡄⣿⣿⠿⠛⣴⠟⠁
⠀⠀⠀⠀⠿⣵⣧⣿⣿⠇⣾⡆⠑⠈⢳⠁⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⡞⠁⠐⠻⠏⠙⣿⡇⣿⣿⠗⢼⠹
⠀⠀⠀⠀⠀⠘⣿⣿⣷⢂⡟⢣⡀⠀⠘⣦⡀⠀⣀⣰⣶⣬⣀⣀⠀⢀⡼⣥⠄⠰⠒⠀⢱⣿⣧⢹⣷⣷⣡⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣟⡾⠾⠋⠀⠰⣦⠙⣿⣿⡟⠉⠉⠟⠛⠻⣿⣫⠞⠁⠀⠀⠀⠀⠈⠢⢻⡌⠓⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠈⠹⣷⡀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⡈⠀⠀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⢠⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠐⣤⠀⠹⣄⢀⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠈⢷⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠿⠿⠟⠋⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠘⢷⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣍⠀⠤⠀⠀⠀⢀⡀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠻⢿⣦⣹⡅⣤⣀⣦⣴⡦⠀⠛⠁⠀⠀⠀⠀⠀⠉⠀⢌⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⢸⣽⣶⣿⣿⣿⣾⣽⠀⠀⠀⠀⠀⢀⣤⡴⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠹⢀⠇⢀⣀
⠀⠀⣾⣿⣿⠏⡭⢹⣿⣿⠇⠀⠀⠀⢠⣿⣷⡦⢰⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠈⠉⠑⠆⠈⡅⠈⠉
⠀⠀⢛⣽⣿⠀⠀⢸⣿⣿⡛⠀⠀⠀⢸⠉⠉⠁⠂⠉⠉⣻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠈⠐⣿⣂⣀⣘⣿⠈⠁⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡄⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠉⠉⠛⠛⣛⠀⠀⠀⡀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣭⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠈⠉⠛⠋⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠉
⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⢀⡀⠴⠆⠀⠀⠐⣆⣼⠀⣼⡆⣶⣴⢸⡆⢰⢰⣦⡆⣸⡆⣶⠀⣶⢠⣷⢰⣦⡆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠽⣿⢖⠂⠀⠈⠉⠁⠀⠀⠀⠀⠉⠈⠀⠈⠃⠉⠉⠈⠁⠈⠈⠉⠁⢀⠃⠈⠀⠁⠀⠉⠈⠉⠁⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠛⠘⠚⠓⠚⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠙⣱⣄⣀⣠⣞⠃
⠀⠀⠀⠺⡆⢰⣶⠄⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣶⣂⣷⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⣸⣿⠀⠀⠀⣄⡙⡟⠋⢀⠈⠹⡟⢁⡀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠉⢸⣿
⠀⠀⠀⠐⡛⠒⠠⠴⠾⠀⠀⠀⠘⣿⡀⠀⠀⠀⣿⠃⠀⠀⠀⣛⣻⠇⠀⠈⠠⠀⢹⣟⡃⠀⠀⠀⠀⠀⠛⢻⣽⡄⠀⠀⠀⠀⠀⠘⣿⡇⠀⢸⣿
⠀⠀⠀⠠⣤⣤⣤⣽⣿⠀⠀⠀⠀⠘⠁⢀⡀⠀⠋⠀⠀⠀⠀⠿⠟⣧⣀⣀⣀⣠⣞⠿⠇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⣇⠀⣸⠋
⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢹⡿⣿⠹⡿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⡀⣀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣭⠀⠀⠀⠀⠀⠰⠿⠟⠁⢀⣴⣶⣦⠀⠘⠻⠿⠃⠀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⢠⡄⠠⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠻⠷⢀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠐⣀⡄⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⡀⠀⠐⢫⣦⠀⠀⠠⡄⠀⠰⠆⠀⠜⠇⠀⠀⠀⢠⣠⠀⠀⢣⡶⠚⡿⢧⣤⡀⠠
⠀⠀⠀⠀⠀⢀⡄⠀⠋⠀⢤⣝⠲⠘⠦⣗⢦⠄⠀⠿⠟⠀⠀⠀⠘⢣⣰⠆⠸⠊⠀⠀⠀⠀⠸⠋⠀⠀⠘⠁⠀⠛⠰⠃⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠳⢮⣙⠮⠛⠦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠂⠈⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠄⢀⠀⠐⠐⠄⠸⠀⠀⠀⠀⠀⠀⠀⢯⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⢥⡄⠀⠰⡶⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡆⡈⠀⢈⡈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠨⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡅⠀⠀⠀⢤⠘⠂⡙⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡽⠀⠛⠀⡇⠀⠀⠀⠀⢁⠀⡀⠄⠐⠂⠀⠀⠀⠀⠀⠀⢀⡀⣴⠂⠀⠀⠈⠁⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠒⣀⠆⠀⡛⠀⠂⡆⠀⠀⠀⠀⢸⠆⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠛⠀⠤⢀⡔⢀⡡⠄⡀⠅⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣀⣸⠁⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠇⡲⠇⠀⢂⠀⠀⢈⣁⠀⢁⣼⠀⠀⠀⠀⢸⡄⠀⢤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠈⠉⢴⡷⠘⠂⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠆⢠⡆⠀⠿⠀⠀⠀⠀⠀⠀⠐⠊⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⣀⠀⠀⡠⠄⠀⢠⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡐⢠⡄⠀⠀⠀⠀⠁⠀⠀⠹⠀⠇
⠀⠀⠀⠀⠀⢀⡴⠋⠨⡑⠲⠃⠀⠀⠙⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠃⠀⠈⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠲⠶⣦⣄⠉⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⣴⢦⠶⡶⡴⠶⠦⠤⠄⢀⡀⠀⠀⠀⠀⠀⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠉⠉⠉⠈⠙⠁⠈⠁⣈⠀⠀⠘⠛⠷⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀⡀⠀⢀⣰⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠥⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣤⠂⢹⠻⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠙⢆⡀⠐⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣏⡤⠀⡴⡋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⢀⠀⠀⢸⠣⣀⠆⢠⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠹⣿⣿⣿⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠈⣷⠀⠀⣤⡟⢀⣿⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁⣿⡀⠀⠀⡠⠋⠁⠀⠀⠀⢀⠀⢀⠀⢀⡄⠈
⠀⠀⠀⠀⠀⠸⡇⠀⢋⠀⡾⠏⠀⠀⠀⠀⠀⠀⠘⠟⢻⠦⠄⠀⢠⡄⢿⣷⣷⡞⠀⠀⠀⠀⠀⠀⠘⠀⠘⠐⠸⡇
⠀⠀⠀⠀⡀⢀⠛⣦⡀⢿⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⢡
⠀⠀⠀⠀⢱⡞⠀⠟⣧⠘⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠃⠘⠀⠛⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡴⠒⠛⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠋⠉⠙⠉⠈⠁⠀⠀⠀⠈⠉⢈⠀⠁⠀⠀⠀⠀⡗⠈
⠀⠀⠀⠀⠀⢴⣀⠀⢀⢀⣿⢷⡎⢻⠀⠀⠀⠀⠀⡀⣠⡀⠀⢰⡀⠀⢀⡄⢀⣠⠀⠀⠀⢠⡇⠀⣾⣄⠀⠀⠴
⠀⠀⠀⡔⢀⡾⠈⠁⠀⠀⠀⠀⣣⠘⣼⠁⠀⠀⣸⡴⠋⠅⠀⠀⠀⠀⠀⠀⠜⠇⠀⠀⠀⠘⢁⡎⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢰⣠⡎⣇⢠⡀⠀⠀⠀⠀⠘⣼⡏⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠐⠟⠂⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠳⢧⡀⠀⠀⠀⠀⢖⠖⡒⠀⡀⠐⠒⢊⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣇⠀⠂⠑⢄⠀⠀⠀⠀⡀⠁⠰⡶⠈⠁⠐⠶⠒⢶⠆⢤⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢧⡈⢧⡀⢀⣼⣳⠀⠀⠀⠱⢄⣈⣁⠀⠀⡶⠀⠖⢀⣄⠈⠁⣬⠙⢆
⠀⠀⠀⠀⢀⡠⢤⡖⢲⡖⢺⡏⠻⣄⠙⢦⡟⠻⠿⠟⠀⠀⠀⠀⠀⡟⠀⠷⢀⡀⠰⠆⢠⡄⠘⠋⢀⡀⢛⠒⠤⢀⣀⣀⡀
⠀⠀⠀⣴⠛⡄⠈⣇⠀⢧⠀⠳⡄⠘⢦⡀⢋⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⢢⢈⠗⠒⠒⠒⠂⢾⠂⡜⡃⢾⠈⠐⠒⠛⠋
⠀⠀⡼⢹⣄⡙⣆⠘⣆⠈⣣⡀⠙⢦⣤⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⢸⣼⠀⠀⠀⠀⠀⠀⣧⡅⢰⡌
⠀⠀⠀⢴⣸⢹⣘⡏⠉⠀⠀⠈⢧⣸⠀⡷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣉⢀⣤⡠⣄⣄⡤⣌⢤⡀⡡⢒⠦⡀
⠀⠀⠀⢸⡿⠸⣽⠀⠀⠀⠀⠀⢸⣽⠀⢷⡆⠀⠀⢀⣤⣴⠲⠴⠏⠛⠛⠓⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⢉⣉⣉⣑⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣀⡀⢞⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣒⣓⣚⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠉⠉⠲⡀⡖⣄⡜⠉⠉⠉⠉⠉⠉⢧⡸⢳⣰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠪⡒⣈⠉⠉⢉⡒⡶⠈⡇⠀⠀⠀⡀⢀⠀⠀⠉⠁⠉⠀⢠⡲⠤⠤⠤⢄⣀⣁⡈⠁
⠀⠀⢀⡤⠖⠒⠛⠛⣯⠀⠀⡀⠀⠲⡞⠀⠀⡇⠀⡇⠀⢀⡠⠟⠺⡄⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠉⢣⣇⣀
⠀⡴⡏⠀⠀⠀⠀⠀⠘⢆⡀⠑⠤⠀⠀⠤⠊⢀⡴⠁⠰⣭⣄⠀⠀⢻⣧⠀⢠⢊⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠐⢤⣀⣀
⠼⠄⡇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⡤⠖⠋⠀⠀⠀⠀⠈⢷⠛⠈⣿⡆⠸⡀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊
⠀⠀⡇⡘⡇⣰⠒⠒⠒⠒⠒⢦⠀⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠺⢯⣿⠀⠙⠲⠤⡤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢧⠇⢆⡏⠀⠀⠀⠀⠀⢸⡸⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⢸⣾⡆⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⣀⣀⠀⢀⣀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⡯⣵⠀⠀⠀⣇⠀⡘⡆⠀⡏⠀⠀⠀⡇⠀⣿⠀⢰
⠀⠀⡔⠁⠀⡼⠋⠁⠀⠈⠱⣏⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⢹⣺⣆⠀⠀⠈⠉⠁⠑⠒⠁⠀⠀⠀⠉⠉⠈⠑⠉
⠀⠰⡇⠀⢸⣀⠀⠀⢀⣀⠀⢹⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠻⠿⠋⢩⣭⡍⠉⠉⠉⠹⠿⠟⠲⢦
⠀⠀⠳⢄⣸⡈⠀⠀⠀⠈⠀⠙⠲⠤⠤⠞⠉⠉⠓⠦⡀⠀⠀⠀⠀⢻⠛⠀⢠⣶⡄⠈⣉⡁⠰⠿⠂⢀⠀⣿⡇⠈⡇
⠀⠀⡴⢤⣀⡷⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠘⡇⣀⠈⣭⣄⠀⠻⢏⣀⣀⣀⣿⡃⢠⡀⡞⢱
⠀⠀⠘⠢⢌⣀⣀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⣇⡏⡇⠏⠉⠉⠉⠀⠀⠀⠀⠀⡇⡟⡇⠀⠼⠄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢸⡇⢷⢸⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⡇⠀⠀⠀⠈⠇⠀⣻⠀⢸⠀⠀⠀⠘⣼⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠈
⠀⠀⠀⠀⠀⠀⠀⣇⢀⠛⡆⢠⠁⠀⠀⠀⠀⢰⠀⡿⡀⣸⠀⠀⠀⠀⣿⠀⠈⣆⡇⠀⠀⠀⠀⠀⠀⠘⣸⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⢉⠀⠀⡀⠀⢀⠈⠉⠀⢉⠁⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠋
⠀⠀⠀⣀⣤⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⣴⣶⣴⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⠀⠘⠄
⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⣀⣤⣾⣿⣿⠏⣿⣄⠀⢢⡀
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣧⠶⢒⣤⣿⣿⠿⣿⣿⠟⠀⣽⠉⠀⠀⠓⣄⣀
⣿⣿⣿⣿⣿⠟⠀⠀⢀⠀⠀⠀⣀⡤⠿⣟⣫⣭⡶⢟⠕⣫⣿⡟⣰⡿⢩⡆⡆⠘⣦⠀⠀⠀⠀⠙⠷⡶⢶⠀⡀
⣿⣿⡿⠋⠁⠀⠀⢰⣏⡙⢟⣋⡥⠖⠠⠾⠛⠉⢚⣠⣾⠛⠟⠀⠉⢡⣿⣇⠘⡀⠁⠘⢆⣀⠀⠀⢤⡙⠦⠀⠈⠳⢦⣄⡀⣶⢀
⠟⠉⠀⠀⠀⢀⣴⣿⣿⣷⡈⠁⢠⠞⠃⢀⣤⠴⣿⣿⢃⡆⠀⣠⣴⣿⠿⣿⡄⠱⢤⡀⠀⠿⡄⠄⠈⠓⠐⢤⡀⠀⢰⢬⡉⣿⣼⠇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⠶⣫⣤⠶⠟⢁⣰⣿⣿⠋⣿⠁⡼⠿⠋⢀⣰⠋⢿⡄⠀⠀⡰⣤⠙⡀⡀⠀⣼⠀⠁⣶⣾⢰⣁⣏⣹⣆
⠀⠀⠀⠀⢠⣿⣿⣿⡛⠉⠘⢋⣥⣶⠶⠿⣿⠿⠁⠞⢡⠾⠃⠺⠄⠸⡁⠀⢈⠹⠀⠀⠀⠸⠀⠀⣿⠀⢿⢀⣐⣿⣿⣾⣿⣿⣿⣿⡄
⠀⠀⠀⣠⣿⣻⠟⠀⠀⢀⣂⡍⠉⣠⣔⠉⠁⠀⠀⣴⡟⠀⢰⡌⠀⢰⡇⣴⠘⠀⡈⠂⢀⣇⠀⣦⣁⣴⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠙⠻⠶⠾⠟⠛⠻⠻⠶⠟⠛⠿⣧⡈⢠⠐⠉⠘⠀⣿⣿⠀⣿⡇⡟⣀⢸⣇⣠⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⣼⠀⣆⠀⢘⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⡀⢀⡀⡷⢸⣀⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢿⢸⢘⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⢸⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⡇⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂

⢠⠆
⢸⠆
⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣰⣿⣿⣷
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⠀⣀⠼⣿⣿⣧⣿⡄
⢸⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠁⡠⠚⢉⠀⠀⡈⠻⠿⠛⣧
⢸⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠛⣿⣿⣶⣾⣿⣷⣾⣿⣾⣿⣹⢶⡀⠙⡀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶
⢸⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣟⣿⣿⡿⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⢿⠿⠍⠀⠰⣾⣿⣿⣿⣿⣿⡿⢛⣿⠟⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠛⣄⡶⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠡⠔⠈⢿⣿⣿⣿⣿⢆⠼⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣶⣋⡁⠀⢰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⣿⣧⣤⣴⣶⣿⠛⠿⠷⠏⠂⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡋⠈⡀⣿⣿⠁⠸⣿⣿⢿⡇⣀⣨⣿⣿⣿⣿⠟⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠙⠋⠘⡇⠀⠲⣿⡏⠀⡀⠀⠀⢾⣿⣿⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡟⠁⠀⠀⠀⠁⣠⣶⣿⡀⢠⠀⠀⠀⠀⠉⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⣄⠰⠀⠘⢿⡿⠟⠃⠈⠀⣰⡄⠀⠐
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡘⠹⠇⠀⠀⠈⠷⠀⠀⠀⢠⠉⠀⢀⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⢀⣀⣀⣀⢀⣖⣀⡀⠀⣴⣦⢸⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⠏⠛⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⠿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠻⠟⠇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣤⣠⣾⣿⣿⣿⣿⣿⣾⡿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠸⠿⠷⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⡄⢀⡀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣼⡟⠀⢈⠈⠁⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣠⣤⣼⣿⣿⣿⣿⠁⣀⡀⢡⡉⢃
⠀⢀⣠⣤⣤⣤⣴⣶⣶⣚⣛⣉⣭⡍⠉⠉⠻⣿⣿⣷⣖⠒⠒⠲⢦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢿⣻⡄⠇⢀
⢠⣿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠙⢿⣿⣶⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠈⠛⠀⠐⡏
⣾⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⡄⠀⠀⢀⣼⣿⣿⡀⠀⠀⣠⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡇
⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⡏⠁⠀⢀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⢀⣙
⠀⢻⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢾⣿⣿⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⠶⠔⠛
⠀⠈⣧⢻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⢹⣥⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⣿⠘⣿⣷⣌⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠋
⠀⢀⡟⠀⢿⣿⣿⡀⠙⣿⣿⣿⣿⣆⠀⠀⢀⡤⠀⠀⡿⠁⠀⠀⠀⠀⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⢀⡾⠁
⢀⣿⡇⠀⢸⣿⡟⠁⠀⠋⠹⣿⣿⣿⡇⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢠⠀⢻⣿⣿⡿⠛⠉⠀⠀⡼⠁
⢸⣿⠁⠀⠀⣿⡷⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⠲⠤⠤⠤⠤⠤⠤⠄⠒⠒⠒⠛⢧⠸⡿⠋⣴⡃⠀⠀⡰⠁
⠈⣿⠀⠀⣰⣿⣄⠀⡄⠀⠀⠀⣿⣿⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠉⢹⠒⠚⠁
⠀⡿⠀⠀⣿⡿⠉⣸⠀⠀⠀⠀⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇⠀⠸⡇
⠀⠁⠀⠀⢻⠀⢠⠇⠀⠀⠀⠀⢻⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢿⡀⠀⡇
⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠈⢇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⢠⠃⣸⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⡟⢀⡏
⠀⠀⠀⠀⢸⠀⠸⡆⠀⠀⠀⠀⠀⠀⠓⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢷⡼
⠀⠀⠀⠀⣼⡄⠀⠁⠀⠀⠀⠀⠀⠀⢸⣄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠘⡇
⠀⠀⠀⠀⠀⢹⣶⣶⣦⠀⠀⠀⠀⠀⠀⠘⣷⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⠆

⠀⣀⣀⠀⢀⠋⢆⠀⢀⡀⠸⠳⡀⣸⣿⢆
⠀⣿⣮⣑⡾⠤⠞⠁⠀⢿⣷⣤⣿⣿⡏⢸⠄
⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⢉⠻⢿⣿⠀⡼⠀⢀⣀⣤⣤⣴⣶⣶⣶⠒⠒⠒⠒⠒⠠⣤⣤⣄⣀⡀
⠀⠀⢹⠟⡡⣂⠐⠖⠉⣉⢳⡀⠀⠉⡞⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄
⠀⠀⠸⣀⣄⡽⢁⡠⠤⠬⢴⣃⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁⠀⠙⢆
⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⠀⠀⢀⠀⢡
⠀⠀⡇⠀⣶⡄⠀⠀⠀⠰⣿⠆⠀⢸⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠈⢱⡄⢣
⠀⠀⠱⡀⠉⠁⠀⠀⠀⠀⠀⢶⠂⡜⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠋⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠋⠀⠀⠀⢰⢻⢸⡆
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⣠⣋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⢆⡇
⠀⠀⠀⠀⠀⠉⠓⠒⡲⠚⠙⡇⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠰⡄⠀⠀⠀⠀⡀⠀⡜⠀⢠⣾⢿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⢀⣸⠀⠀⠀⠀⠀⢀⠁⠒⠤⢤⣶⣾⣿⣿⣿⣤⠤⠖⠋⠙⢦⡄⠀⢸⡥⠊⠀⠀⡏⠃⢸⠸⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢠⡄⠀⠰⡀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠘⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⠉⠒⡇⠀⠀⠀⢷⠂⠤⠄⢀⡤⢇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⢸⠀⠘⢴⠛⠚⠉⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣴⠀⠀⠈⣧⣄⣀⣼⠀⠀⠀⠘⣦⣴⣾⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⡄⡀⠀⠈⠀⢠⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⣶⣿⡇
⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢠⣿⠆⠀⠀⡀⠈⢀⣄⠐⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⡀⠆⠀⠀⠈⠙⡀⠠⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⡔⠀⠠⢠⠂⠀⠀⠀⠐⠪⠋⠀⠀⢀⣀⠀⢀⣀⠀⠀⢠⡄⠀⣰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⢻⠊⠀⠀⠀⠄⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⡜⠓⠀⠀⠀⠀⠈⣹⠁⠐⠀⠀⠄
⣀⠀⠀⠀⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠸⠀⠀⡄⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⡋⠀⠠⠄⠉⠉⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠐⢀⡀⣠
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⣀⠀⠀⠐⠀⣀⡀⠀⠈⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠈⠙⠀⠀⠈⢸⣷⡀⠀⠀⠈⠁⢀⡀⠄⣧⢀
⣀⣤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠠⠀⠀⠀⠘⠁⠀⣿⣿
⢈⠙⠂⠀⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠋
⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⠀⠀⠀⠀⣿⠠
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⢱⡇⣀
⠆⠀⠀⠀⣀⡳⠀⢠⠄⠀⠀⠀⠀⠈⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣾⠁⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐⠄⠀⠀⠁⠀⠙⠋⠀⠀⠀⠹⠟⠃⠀⢀⠀⢀⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠐⠋
⡀⠀⠰⠆⠀⢠⡇⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡤⠃⠀⠀⠰⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⣤⡄⠉
⠁⢀⠀⠀⠀⢹⡇⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈
⠀⠀⠄⠀⠀⠘⠇⠉⠀⠄⠀⠀⠐⠐⠀⠓⠀⢀⡀⢰⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⡆⠀⠀⠀⠀⠀⠈⠂⠀⠄⠐⠀⠀⠀⢀⡌⠀⣼⣿⣾⣇⢀⡀⠀⠠⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠈⠁⠉⠉⠙⠉⠀⠀⠂⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⠛⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠂⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠆⠒⠐⣶⣶⣤⣤⣤⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢤⡤⣰⢆⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⢶⣿⣿⣿⣿⣿⣽⡄⠸⠐⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣴⡏⠀⠀⣻⣭⣦⡝⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠇⠀⠀⣽⣿⠿⣿⣿⣿⠟⠀⠀⠀⠻⠏⠉⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⡀⠀⣿⣿⣿⣿⠎⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⠁⣀⠔⠀⠀⠀⠀⣿⠏⠉⠀⡎⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣦⣴⣻⣿⣿⣿⠉⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⢀⡞⢉⡙⠶⢦⣤⣄⣀⣠⣤⣴⣇⠀⠀⣠⠀⢶⣿⣿⣿⣷⣄⡄⠀⠀⠀⠀⠀⢿⠿⣿⡻⣿⡧⢛⣥⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⢡⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠆⠀⠛⠳⠶⠨⣅⢈⣿⣩⠡⠀⠀⠀⠀⠀⠀⠲⣀⡇⠉⢀⡘⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⠤⠻⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠠⣤⠀⠀⣿⡀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⢲⡔⣄⢠⣤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠈⢘⢁
⠀⢀⣤⣶⣶⣶⠲⠶⠦⣤⣄⣀⣀⣀⣠⣤⡤⠤⠠⣤⣄⣀⣀⣀⣀⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡜⠛⠶⠞⠋
⠀⢸⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⢰⣾⣿⣿⣿⣿⣿⠿⣟⡧⠀⠀⠀⠀⠀⠀⢦⡠⠠⠢⡔⣀
⠀⢸⣿⠛⣿⢱⡆⠀⠀⣼⣿⣿⣿⣿⣿⠿⠛⠁⠈⠁⢘⣿⣿⣿⣀⣄⡻⢿⣆⡄⠀⠀⠘⠷⢿⡄⠃⢠⣿⣿⣿⣦⠐⠢⣶⣤⣤⣶⣶⣶⣶⣶⣿⢉⡙⢿⣷⣶⡄
⢀⣾⡟⠁⠀⢈⡴⠁⠘⠿⠁⠀⠻⠿⠋⢀⡀⠀⠠⡆⠈⠉⡹⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⢀⣿⣿⣿⣿⣧⣀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣧⡸⠧⠸⢿⣿⣿
⣸⣧⡿⢂⡞⠋⠛⢦⣄⣀⣀⣀⣠⣴⠶⠿⣧⠀⢸⣀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣭⣿⣿⣿⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉⢀⠀⠀⢾⣿⣿
⠀⢹⢃⡾⠙⣤⠤⠚⠁⠉⠉⠉⠁⠀⠀⠀⠘⡇⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠆⣴⣶⠐⡌⠉⠉⠁⠉⠁⠀⠀⠘⢣⠀⠀⠘⡇
⠀⢰⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡉⠀⠉⣻⢇⣷⣄⣀⣀⣠⣤⡶⠺⠏⣈⡱⠀⠀⣧
⠀⠘⠶⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠀⢠⠎⠀⠈⠉⠉⠉⠁⠀⠀⠃⢨⡆⢃⠈⡿
⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⢤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡈⠀⠀⡀⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢄⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡐⠀⠀⠀⣇⡇
⠀⠀⠀⠀⢹⣿⣿⣿⡛⢛⡃⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠸⣿⣿⣟⠁⠘⠁⠀⣸⣿⣿⣿⣿⡟⠿⣿⠃⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠐⣦⣀
⠀⠀⠀⠀⠀⣿⢻⣯⠀⠀⣼⠀⠈⠛⠉⠙⠿⢰⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠏⢀⠤⣿⣭⣽⣲⡶⠒⢀⣶⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢸⣷⣿⠈⠁⢀⡞⠻⠷⢦⣤⣤⡤⠴⠿⡆⠀⣶⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⢠⣤⣾⠟⣡⣿⣿⡿⠛⠀⢻⣿⣿⣿⣿⣿⣿⣿⠛⠀⠿⢲⣤⣀
⠀⠀⠀⠀⠏⡇⢿⠀⡜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⣼⡿⣏⠰⢈⡟⠛⠋⠁⠀⠀⠀⠈⠓⠀⠈⠹⣿⡟⠷⠀⣶⣿⡿⠿⢿⣿⣿⠍⠀⠀⡄⠀⠻⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠈⢂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢶⡀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣋⡴⠖⠀⠀⠀⢡⣂⡀⠙⠋⠀⠀⠰⡇⢰⡿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠱⠶⠈⢷⡷⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⠀⠻⠿⠘⢧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢦⣄⣠⠀⢸⡿⠿⠿⠿⢿⣷⣦⠘⣁⠀⠠⠟⠛⡟⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠤⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣤⣠⠡⠤⠀⠀⠠⠐⠁
⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⠿⠋⠀⠀⠀⠻⠿⠟⢿⣿⣿⣿⣿⣶⣾⣄⡙⢍⠀⠈⠁⠈⠛⠉⠗
⠀⠀⡔⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⢾⣝⠻⠿⠿⢿⣿⣿⣿⡟⠀⠛⠀⠀⢨
⠀⠀⢱⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⠿⠛⠃⠀⠀⠀⣀⠀⢂
⠀⠀⠀⡸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣿⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡱⠂⠀⢁⣄⡸⠃
⠀⠀⠀⠀⢻⣧⠀⠀⠀⣠⡀⢢⣸⣿⣿⣿⣿⣿⣿⣩⡄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡜⣿⡀⠀⠀⣿⡷⠀⠈⠻⢿⣿⣿⣿⣿⣿⣧⣬⡉⠀⡊⠀⠀⠀⠰⠁⠀⠠
⠀⠀⠀⢸⡇⣿⠇⠀⠸⣿⠁⣠⠈⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠈⡡⠀⠀⢀⠃⠁
⠀⠀⠀⣾⢱⣿⠀⢀⣼⠗⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡀⠀⠈
⠀⠀⠀⠋⢸⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡐
⠀⠀⢐⣢⡿
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠋⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠃⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢸⣣⣼⣦⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⡿⢿⠟⠿⠆
⠀⠀⠀⠀⠀⢠⣶⣿⠞⢹⢻⣿⡦⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠
⡀⠀⠀⠀⢀⣟⠛⠀⠀⢰⠀⠋⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢂
⢿⠀⠀⠀⠾⣿⡆⠂⣄⣸⠀⠈⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓
⣿⡆⠀⠀⢸⣿⣃⠀⠙⠛⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣡⣴⠀⠀⠀⠀⠀⣼⣾⣷⣆⢠
⢿⠃⠀⠀⠀⠼⢿⣶⣶⣖⣦⣼⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⠟
⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⣶⣶⢰⣶⣶⠎
⠀⠀⣀⡀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⢻⡟⠀⠀⠀⠀⠀⠀⠠⣄⠠⣶⠖⣀⠂
⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠈⢣⣶⣦
⠀⠀⠀⠀⠠⠶⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠠⣽⢹⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣿⡮⣭
⠀⠀⠀⠀⢀⠀⡀⠀⠄⠇⠀⠀⠀⠀⣀⣀⠔⠒⣒⠒⠠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢏⢀⠀⢐⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢰⣿⡷⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣿⣷⣾⡧
⠀⠀⠀⠶⢤⣤⡤⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⠛⠛⣿⣷⣿⠆
⠀⠀⠀⠀⠸⢿⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡏⠀⠀⠀⣿⣿⣧⠄
⠀⠀⠀⡖⢢⣤⣴⠐⡇⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉⠖⠚⠀⠀⠀⠀⠀⢨⣿⣿⡇⠀⣶⠄⢿⣿⣷⡄

⠀⠀⠀⠀⠠⠦⡀⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⡿⡿⢦⠤⣾⢱⣏
⠀⠀⠀⠀⠀⡦⠁⣤⠀⠉⠋⢹
⠀⠀⠀⠀⠈⠇⣄⢋⡿⠷⡀⢈⣆
⠀⠀⠀⠀⠸⣇⣿⣧⠀⠀⠄⢸⣧⣆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠈⠀⣽⣿⠶⠤⢶⠖⠒⠒⠀⠐⠒⠒⠦⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣴⣿⣿⣦⣄⠀⠐⡀⠀⠀⠀⠂⠂⢄⠁⠾⣿⣿⣿⠿⠷⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢚⣿⣼⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⡷⢾⣿⣿⣗⣙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⣬⣹⣉⣧⡀⠀⠀⠀⣀⣀⢔⠀⠀⠀⠀⠘⠟⢿⣽⣿⠏⠾⢣⢴⣬⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣤⣵⣾⣌⣿⣿⣿⣿⠿⠿⣯⣿⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⢿⣝⠀⡰⣍⠂⠉⣭⠿⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠈⣿⣿⡟⠀⠀⠀⠀⠀⠙⣧⣷⣦⢁⣀⡈⠀⠀⠀⠀⠀⠈⠳⣧⣀⠾⣿⢋⠒⣹⣿⣿⣻⡖⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⠻⣿⡳⡄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣈⠛⣿⡀⠉⣿⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠶⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⣀⣼⡏⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠾⠿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠚⠛⠃






⣿⢿⠿⠿⣿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢸⡦⠠⢄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠒⠓⢀⠠⣿⣿⡥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡧⠀⢶⣟⣵⣯⣶⣶⣶⣦⣤⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠙⢷⣷⠿⠿⣿⡿⠻⢿⣿⣿⣿⣿⠁⠀⢙⣯⣉⣿⣿⣿⣿⠎⠁⢼⣷⠀⠘⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠤⠄⠠⠤⡀⠀⣀⣀⡀⠀⠙⠻⠛⠁⠀⢠⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⣿⣿⣶⣦⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⢴⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢹⣿⣿⣿⡂⠀⠀⠀⠀⠙⣿⣿⡿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⠛⠙⢿⡆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣴⡇⠀⠀⠀⠘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣵⠀⠀⣸⣷⡆⠤⠴⠆⠀⠀⠀⠀⠨⢔⠀⠀⠀⠀⢘⣦⡀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⢺⣿⠟⢆⠈⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡏⠀⠀⠀⠀⠰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠄⠀⠀⣀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣸⣿⣢⠀⢀⣄⠀⠀⢀⣴⡜⡉⣀⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⠿⠛⢉⣻⠘⣻⣇⣻⣾⣯⣼⣻⠷⣠⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⡟⠃⠈⡅⡀⢀⣼⣮⣹⠗⢈⣼⠦⢉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡤⣐⠠⠸⣿⡟⣾⢸⠠⠋⠚⠟⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡟⠉⠵⣬⣷⣍⢿⠀⠀⢷⡏⣴⠶⣹⢻⠿⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⠀⠈⠽⣿⣾⡇⠀⢻⣿⣯⣿⣿⣿⣁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠀⠀⠐⠋⠙⠣⣤⣾⢿⣿⣎⠛⠫⢶⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠄⠀⠀⠀⠀⣭⡀⠀⠈⠉⣹⣿⣿⣯⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⡀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠊⠀⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⢿⣽⣿⡿⢻⣿⣷⣿⡟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠞⣶⣢⠀⠀⠀⠀⠀⢰⣢⠔⠒⠒⠒⠒⠒⠲⢖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠀⠠⠌⠳⣄⠀⠀⠀⠀⢸⠀⠛⢠⣌⡆⠘⠀⠣⣤⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠈⢧⡀⠀⠀⣨⣦⡀⠀⠀⠈⢆⠀⠠⠛⠄⠀⠀⣀⠀⣤⠀⠉⠀⠾⠇⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣶⣿⣿⡉⠳⣄⠹⣦⣴⣿⣾⠇⠀⠀⠀⠀⠙⣶⡖⢒⣌⠀⠉⢀⡀⠀⠛⠃⢠⣄⠛⠃⢸⣦⡀
⠀⠀⠀⠀⢀⣤⠚⠹⡇⠀⢿⠀⠹⡆⠈⠳⡄⠈⠳⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⢩⡀⣈⠉⢠⡄⠈⢃⡀⠿⠂⣀⡀⢰⡶⠀⡦⣍⣒⠒⣶⣶⡦
⠀⠀⠀⣰⡏⠸⣆⠀⢻⡀⠘⣧⠀⠹⣆⠀⠙⢦⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠉⡷⢠⠊⠉⠉⠉⠉⠑⢻⡁⡎⢑⠸⠃⠀⠀⠈⠉
⠀⠀⢰⠃⡿⣄⡙⢦⡀⢷⡀⠈⣧⣀⠈⠷⣤⢄⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⢰⣼⠀⠀⠀⠀⠀⠀⠀⣷⡇⠸⣶
⠀⠀⠀⢰⣆⢹⢹⡈⡟⠉⠁⠀⠀⠈⢷⡀⡇⠸⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⣀⣄⣀⣀⡤⣈⣤⡀⢉⡴⠶⢄⡀
⠀⠀⠀⠀⡟⡿⢨⣹⠇⠀⠀⠀⠀⠀⢨⣙⠇⢸⣤⡇⠀⠀⠀⢀⣀⣤⣤⣲⣶⠶⠭⠿⠽⠷⠚⠓⠛⠚⠓⠛⠀⠉⠀⠉⠉⠀⠀⠀⠉⠉⠑⠒⠒⠒⣤
⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⣉⣀⣀⠉⠀⠀⡤⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣋⣹⣉⢭⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠁⠉⠉⠓⢦⡉⠙⠒⠒⠒⠒⠒⠢⠤⣄⡀⠀⣀⠀⢀⠤⠤⠤⠤⠤⠤⠤⣄⠀⣤⡀⢠⠴⠖⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⢀⣀⣀⠀⣀⣀⡀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠉⢦⠏⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠣⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢳⠁⢤⢀⠒⠀⣤⠈⡟⠁⢻⠀⠀⠀⢀⡄⢀⡄⠀⠀⠀⠀⠀⠀⠠⡋⠑⠒⠒⠒⠲⢤⡤⢤
⠀⠀⠀⣠⠔⠚⠋⠉⠉⢹⡄⠀⠸⡀⠀⠘⣿⠃⠀⢠⠃⠀⣸⠀⠀⣀⠴⢛⠛⣆⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀⠨⣴⣁⣀⣀
⠀⣰⢿⠁⠀⠀⠀⠀⠀⠀⠳⣀⠀⠑⠦⢄⣀⡡⠴⠋⠀⡰⠃⠀⣞⣉⡀⠀⠀⢸⡿⡄⠀⢠⢊⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠑⠢⣄⢀⡀
⣰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠙⣦⠶⠀⣿⣧⠀⢲⠈⠁⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠏
⠀⠀⢸⢀⡶⡄⢠⡤⠤⠤⠤⠤⠤⣄⠀⠴⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⣿⠾⡆⠈⠳⢄⣀⡀⣀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⢸⠀⡇⡿⠀⠀⠀⠀⠀⠀⢹⢸⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣟⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠞⠀⠳⠃⠀⠀⠀⠀⠀⠀⠘⠞⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⠽⡄⠀⠀⠀⢸⠀⠀⣠⡀⠀⢠⠖⠒⠒⠲⡄⠀⢠⡀⠀⢸
⠀⠀⠀⢀⡤⠤⢤⣀⣠⣤⣄⣀⡀⣠⠴⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣴⡼⡗⢶⠀⠀⠀⠸⡀⣀⡇⡇⠀⣸⠀⠀⠀⠀⣇⣀⡾⡇⠀⡸
⠀⠀⣰⠃⠀⢀⠞⠁⠀⠀⠀⠀⠹⡅⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢯⣹⣄⣀⣀⣀⡀⣀⣀⣉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⡇⠀⠀⣜⡀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠿⠿⠁⢉⣴⣤⠀⠀⠉⠉⠉⢿⠿⠋⠲⢤
⠀⠀⠹⣄⡀⢫⠁⠀⠀⠈⠉⠁⠀⠘⠤⣀⣀⡠⠎⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⢸⡿⠃⠀⢠⣤⡀⠈⠛⠋⠀⢰⣿⠆⠀⠀⢰⣿⡆⠈⣇
⠀⠀⢀⣀⠉⠙⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠈⣇⠀⠀⠙⠛⠃⠀⢸⣿⠆⠀⠀⠀⢾⡷⠀⠉⠀⡴⢻
⠀⠀⠘⢌⠙⠒⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣿⢸⢳⠰⡿⠳⠶⠖⠒⠒⠒⠒⠛⠉⢳⢠⢿⢠⠇⢸⡀
⠀⠀⠀⠀⠉⠓⠒⠒⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⡇⢸⠘⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⢸⢸⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⡤⠤⠤⠤⠤⢤⡀⠀⢀⠀⠀⣿⠀⠀⠀⠀⡇⣾⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢻⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⣿⠀⠀⠀⠀⣇⡿⠀⢸⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡸⢸⡀⢀⠇⠀⠀⠀⠀⠀⢇⠀⡼⡇⠀⡟⠀⠀⠀⠀⢿⡇⠀⠘⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢇⡾⢸⣸

⠀⠀⠀⠀⢀⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣤⣤⣄⡀
⠀⠀⠀⣀⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⢠⠂⠀⠒⡀⠀⠀⣈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⣿⠇⣄⠀⠀⣤⠻⡿⠛⢿⣦
⠀⠀⠀⠀⢈⣻⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠳⡀⠀⠀⢀⡵⠴⠂⠀⠀⠀⣠⣶⣿⣿⣷⣦⡀⠀⠀⣼⡏⠀⠀⠀⠀⠈⠃⠈⠁⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠻⢿⣿⣿⡿⠄⠤⠐⠋⠀⠀⠀⠀⠘⢄⣀⠊⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⢻⣇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡿
⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣦⡄⠀⢀⣀⣴⣀⡀⠙⠦⠀⠀⠀⠘⣆⢀⠇⠀⠀⠠⠊⠁
⠀⠀⡇⠀⠀⡄⠀⠀⢐⠀⠀⠀⠀⠠⣾⣾⡟⠂⠀⠀⠀⢀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣦⡀⡽⣿⣿⡀⢀⣤⣶⣶⣦⣄⠈⠀⠀⠀⠀⣀⢀
⠀⠀⡇⠀⢸⡇⠀⠀⠘⠁⠀⠀⠀⠀⠋⠉⠀⣦⣄⠀⠸⣿⣟⣀⣤⢴⣿⣿⢻⣧⣀⣉⣤⣤⡘⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣰⣮⠟⠁
⠀⠀⠹⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⣿⣿⣯⣀⣾⣿⣿⢿⣏⣿⣿⣭⣍⡓⠀⠀⠘⠻⢿⡿⠿⠋⠀⠀⢀⡿⣿⠂
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⠿⡴⠃⠉⠀⠀⠙⠇⠢⠀⠀⠀⠀⠀⠀⢄⢀⡆⠀⠻⣿⣆
⠀⠀⠀⠀⠀⣇⠀⠀⠘⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠳⠞⠀⠀⠐⠀⠀⠀⠀⠀⠐⠢⠀⠘⠿⣦⣀⣈⣙⣳⣀⠀⠉⠙⠓
⠀⠀⣠⣤⠀⣿⠀⠀⢠⢣⠀⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⣿⠀⠀⡰⠿⠿⠗⠿⠿⢷⡀⢀⠁⠄⠀⠀⠈⠉⠉⠉⠉⠙⣳⡄
⠀⠀⠙⠛⠀⠈⠀⠀⠈⠳⠥⠴⠚⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠹⠇⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠿⠀⣠⡶⠀⠀⠀⣹⣡⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⣄⣴⣶⣯⣦⡜⣧⠀⠀⠈⠉⠀⢀⡀⠀⠀⠐⠀⢀⠀⣾⣿⣿⠆⠀⣿⠀⠀⠀⠀⠾⠿⠟⠉⣀
⠀⠀⢠⣤⣤⣤⣴⣾⣿⣿⣇⡀⠀⠀⠀⢿⣿⠻⠿⠿⠟⠃⠉⢁⡾⠁⠀⠁⠀⠀⠀⠤⠀⠀⠀⢰⣿⣿⠉⠁⠀⠙⠷⣤
⠀⠀⠀⠉⠉⠉⠉⠹⡿⠿⠉⣿⠀⠀⠀⠀⠙⠻⠶⣤⡀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠛⠛⠀⢠⠄⣀⣀⡼⠃⠀⠀⠘⠃⣀
⠀⠙⠃⠀⢀⣤⠀⠀⠀⠀⠀⣩⣶⣶⣶⣶⣦⣤⣤⣿⠇⠀⠀⠀⠀⠀⢠⣤⣄⡀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠸⠜⠧⠀⣀⣀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠈⠉⠉⠉⠀⠀⢠⣴⠶⡶⣄⠸⢿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⢠⣴⡶⠾⠋⠛⠉⠀⠀⣀⠀⠀⠶
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠻⣿⣶⣤⣤⣤⣤⣤⣤⡀⢸⡌⠀⢃⣿⠀⠀⢿⣿⣿⣿⡅⠀⠠⡀⣠⡎⢸⡯⠀⠀⠀⠀⣮⡇⠀⠉
⠀⠀⠀⠀⠀⠰⡿⠤⠀⠐⠀⠂⡀⢉⡉⠉⠉⠉⠉⢻⡿⢨⣧⣀⣸⡏⠀⠀⠈⣿⣾⣿⠃⢄⠢⣹⣿⡽⠀⢀
⠀⠀⠀⠀⠿⠀⠁⠀⠀⠀⠀⠁⠚⡠⢡⣶⣾⡆⢠⣿⠃⣼⣿⣿⣿⡇⠀⠀⠀⠸⡟⠽⠀⠈⠳⣽⡿⠁⠀⣿⡇⠀⠀⠀⠀⠀⣀⡄⡀⣀
⠀⠀⠀⠀⢠⣧⡠⠀⠀⣬⣬⣥⡋⠀⠀⢉⢿⡇⡀⠙⠆⢸⣿⣿⣿⣿⣦⣀⡀⠐⢀⠀⡀⠀⠀⠈⠁⠀⢀⣸⣷⠀⠀⠀⢀⣼⠟⠁⠙⠋⣴
⠀⠀⠀⠐⢒⣀⠀⠀⢀⣬⣍⣤⣤⣶⣾⣹⡎⣷⣯⣄⣀⠈⠉⠉⠉⣋⡉⠉⠁⠀⢈⣷⡏⠀⠀⢀⣀⠸⠟⠻⣿⡀⠀⢠⣟⡁⠀⠀⠻⠄⢡
⠀⠀⠀⠀⠘⠋⢘⣇⢾⣿⣿⣿⡟⣿⣿⡖⠛⠘⠋⠟⣿⣷⣄⠀⠀⠀⣠⣄⠀⠀⠈⠁⠉⠀⠀⣨⣿⣅⠀⠀⠈⣛⣰⣿⣿⡿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣿⣿⠀⣿⠿⣿⡤⠀⠀⠀⣿⣿⣿⠇⠀⠀⠈⡁⠀⠀⠀⠀⠀⠈⠔⣿⣿⣿⠂⠁⠀⠈⢿⠿⡿⠁⠀⠀⢢

⢀⡤⢤⡀⠀⠀⡀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄
⠈⠳⠞⠁⠀⠀⠀⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣿⡤⡆
⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠇⠀⣀⠀⢸⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠙⠃⠀⡿⡿⣿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡼⢿⣿⠀⣰⠂⢰⢶⡄⠀⢀⡄⠀⠀⠀⠀⠀⠀⣮⣆⣀⠤⡀⠐⠒⠂⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠃⠀⠈⠙⠉⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠄⢰⢶⢤⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠒⠐⠐⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣧⣀⠀⠿⠋
⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⡄⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⢻⣄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠖⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠻⠇⠀⠀⣀⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡷⠀⢠⣬⣿⣿⣿⣿⣿⣿⣿⠁⡴⠁⠉⠉⠁⠙⠐⠚⠁
⠀⠀⠀⢸⡏⣿⣿⡿⠉⠛⢤⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⠟⠃⠜
⠀⠀⠀⠀⠀⠹⢻⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠋⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠟⠃⠀⠈⠁⠀⠀⣸⣿⣿⠏⣸⡿
⠀⠀⠀⠀⠀⠀⡃⠇⠀⠀⢠⠊⠉⠉⠢⡄⠀⠀⠀⠀⡀⠀⣀⢀⣀⣂⣤⣅⠿⠀⠀⣃⡄
⠀⠀⠀⠀⠀⣰⠅⠀⣠⠞⠁⠀⠀⠀⠔⠛⠛⠿⠆⠚⠨⠬⠋⠉⠉⠉⣿⣿⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠋⠀⠀⢹⣧⣤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠷⢀⡆⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠲⠆
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⢠⣤⣄⢀⣀⡀⣀⠀⢀⠀⡀⢀⠀⣄⠀⠀⣀⡀
⠀⠀⠀⠙⠓⠀⠺⠟⠙⠛⠛⠒⠛⠋⠱⠛⠫⠽⠖⠙⠒⠛⠚⠛⠛⠛⠛⠛⠛⠲⠾⠓⠒⠚⠓⠐⠒⠒⠂

⠀⠀⠀⠀⠀⢘⣳⣷⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣶⡆⢀⠀⠀⠖
⠀⠀⠀⠀⢰⣿⠎⢹⡇⠀⠀⠀⠀⠀⠠⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢿⣯⡠⣿⡍⠉⢹⣿⣿⣷⣤⣾⣿⡀
⠀⠀⠀⠀⣾⣿⣷⣼⠀⠀⠀⠐⠽⠇⠀⠀⠉⠉⠹⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⡟⠀⠀⠀⠘⣿⡇⠛⠿⠿⠾⢿⣾⠟⠉⠋⠉⠃
⠀⠀⠀⢠⣿⣛⣟⠵⡶⠃⢀⡀⠀⠈⠀⠀⠀⠀⠀⢹⣿⣿⣿⠉⠉⢹⣿⣿⣿⣿⠃⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⢸⠃
⠀⠐⠘⠋⠈⠉⠁⠀⠀⠀⠰⢇⠀⠀⠀⠀⠀⠀⢀⣸⡟⢙⡿⠀⠀⣸⡟⠀⢙⣿⠆⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠛⠄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡤⠃⠀⠀⠀⠀⠀⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠞⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⢞⡜⠃⠀⠀⠀⠀⠀⣄⠀⠑⠄⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⡩
⠀⠀⠀⠀⣀⣤⣴⡿⣿⣷⢉⡆⠀⠀⠀⠀⠀⠀⣿⠀⠤⠈⢶⡄⠀⢰⣿⣿⠶⠂⠀⠀⠀⠀⣤⠏⠐⢤⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⣾⣿⢿⢻⡞⢛⣷⡌⣥⠀⠀⠀⣴⣦⣀⡏⠀⠀⠦⠈⠀⠀⢸⣿⣩⡴⠖⠀⠀⠀⠀⠳⠶⠶⠟⣫⠷⠉⠉⠁⠀⠉⠚
⠀⠀⠀⢻⡇⠀⠸⡇⢀⢹⠃⠀⠀⠀⢠⣅⣿⣿⣇⠀⠀⠀⠀⠀⠠⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦
⠀⠀⢀⣄⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡝⡛⢫⡭⠿⠀⠀⠀⠀⣠⣶⣾⣶⣶⣶⣶⣦⣶⡗⠀⠀⠀⠀⠀⣤⡀⣠⣾⣿⣿⠏
⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠿⠿⠿⣿⣿⠋⠀⠀⠀⠀⠁⠀⠈⣰⣿⣿⣿⣿⡟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠘⠹⡋⠁⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠱⠄⠀⠀⠀⠚⠀⠰⠄⠀⠀⠀⢀⣿⣿⣻⣿⣿⣿⣿⠇
⠀⠀⠐⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣟⣿⣿⣿⠏
⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠰⠟⠛⠉⢷⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣶⣆⠀⠀⠀⠀⠀⠋⠈⢿⡿⠟⠒⢶⠛⡿⠶⣦⣀⡐⠿⠻⠿⠟⠟⠁
⠀⠀⢿⣿⣿⣿⡟⢿⣿⣿⣿⣸⣿⣿⣿⣿⠿⢿⠿⢷⣄⠀⠀⠀⢠⣴⣿⣦⣀⡀⣠⣧⣀⠀⣾⠁⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢸⣿⣿⡿⠇⠠⠿⠿⠿⣿⢿⡟⠉⠉⠑⠘⠦⠼⠟⠀⠀⠀⢠⡟⠁⠉⠉⠉⠉⠀⠁⠹⡏⠀⠿⠀⠀⢠⣤⣾⣟⣿⣿⣿⣷⡀
⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢃⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢰⢷⠀⠀⠀⠀⠀⠁⣿⠿⠿⠿⠿⢿⡋
⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠠⠂⠀⠉⠉⠉⠉⠉⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡉⠁⠀⠀⠀⠓⠀⠀⢀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢰⠀⠘⠛⡁⠀⠀⠈⠻⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡆⠀⠀⠸⡀⢀⡀⠀⠀⠀⠀⢀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢷⡘⢄⠀⣈⢌⣀⣀⡤⠞⢀⣼⢦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⣌⠾⠀⠀⠀⡥⢊⠔⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠈⡇⠀⠀⠀⠗⠁⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢇⠀⠀⢇⠀⠀⡠⠁⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢹⠀⠈⢆⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡇⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⡾⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠱⡀⠀⠀⢡⠀⠀⠀⣇⠀⠀⠀⠀⢀⠎⠱⡀⠀⠀⠸⡄
⠀⣠⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡜⠀⠁⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⣴⠁⠀⠀⠱⡀⠀⠀⢇
⡎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠇⠀⠀⠘⡄⠀⡜⢹⠀⠀⠀⠀⠙⡄⠀⠸
⡇⢰⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⢧⠈⠀⡼⠀⠀⠀⠀⠀⠘⡄⠀⢇
⠳⡀⠳⢄⡀⠀⠀⣀⡇⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠘⣖⣋⣄⡀⠀⠀⠀⠀⠀⠱⡀⠸⡄
⠀⠙⠢⣄⣈⠉⠉⠀⣘⡦⠀⡀⠐⠺⣄⣀⣀⣀⣀⣀⣀⣀⣧⠀⠀⠹⣄⡀⢨⡣⠀⠀⠀⠀⠀⠘⡄⠈⠒⠢⣄
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠑⠲⠷⠤⠦⠃⠀⠀⠀⠀⠀⠀⠀⠹⣀⣰⠀⢈⣹⠉⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣇⢈
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣆⣂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⡛⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡷⣄⣠⠀⠀⠀⠀⠀⠀⠂⠈⠻⠶⠄⠀⠀⠠⣀⡀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⣷⡿⢥⣔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠝⢧⣄⣀⠀⠀⢠⠀⠀⠀⠀⠐⠇⢲⣴⠙⡉⠀⠆⠘⠀⢰⠀⢡⠄⠀⠀⢬⣿⣀⣗⡉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣴⣆⡫⠛⢦⣄⠀⠀⠂⠀⠀⠸⠇⠉⠳⢼⣦⡀⠀⠀⠘⠀⠈⠰⠀⠰⣶⣾⣏⣉⣛⡩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⣱⣤⣀⢻⣵⣾⠟⣿⣿⣦⠀⠉⢁⠳⢤⣦⣄⠓⠂⠀⠈⠂⠀⠙⠢⢰⡇⠀⠀⠀⠀⢰⣦⣿⣽⠛⢛⣻⠖⠀⠀⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣯⠀⣼⣿⣯⣦⣤⣄⠀⠀⠈⠙⠿⣷⣶⣶⣦⠤⣤⣤⣼⣷⣀⣠⣄⠐⣮⣛⣛⣻⡏⢉⣽⣛⣠⠀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡃⢤⠹⠿⠿⠿⠿⠿⠟⠛⠒⠐⠶⠚⠛⠓⠖⠀⠀⢠⠿⡿⠐⠒⠀⢰⣿⣯⣿⣿⣿⣻⣿⣿⣷⣶⣿⣗
⠀⠀⠀⠀⠀⣀⢶⠠⡀⡠⡳⠰⣤⣴⣿⠗⠤⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡤⠤⠀⢼⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠳⠬⣷⣷⣶⣷⡾⠷⠿⠿⢿⡤⠞⢿⠟⢻⠟⠂⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣦⡀⠰⠶⠶⠶⠶⠶⠾⣿⣿⡿⠿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠄⢠⠀⠀⠀⠀⠀⢨⣇⠀⣄⠀⠀⠀⠀⠀⠀⠠⣭⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⢾⠊⢿⣿⢆⠀⠀⠠⣆
⠀⠀⠀⠀⢀⣀⣀⣤⣶⣤⠀⠀⠀⠀⣰⣤⣰⠶⠀⠀⠀⠀⠀⢸⣷⢠⣿⡄⣀⣀⣠⣴⣶⠖⢊⠀⢀⠀⠀⠀⠀⢀⠀⠀⢠⡄⢀⢼⣿⣿⣷⣄⣴⣶⠇
⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⢦⣀⣴⣬⣛⣿⣬⣥⣶⢛⣛⣁⣿⡋⠉⠉⠀⠀⠀⢀⣼⠿⣶⣄⣴⣿⡄⠀⠀⢀⡾⢀⣤⣺⢀⣤⣤⣼⣿⣿⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠋⠛⣉⡁⠀⠀⠁⠀⠁⠀⠈⢹⣷⢶⢤⠀⠀⠀⢀⡠⢀⣼⣿⡿⠋⠀⠀⠀⠾⠗⠉⠟⣠⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠐⠚⠋⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠭⠑⡄
⠀⡘⠩⠛⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠰⠌⠈⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠈⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⢀⣄⡀⣷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣠⣤⠐⠂⠀⢀⣄⣀⣄
⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⡤⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠐⠃⠉⠀⠀⠀⠀⠀⠀⠔⣒⠠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⠤⣀⠢⠙⠆⠀⠀⠀⠀⣀⠀⡎⣿⠿⠀⢀⡀
⠀⠀⠘⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⡄⠻⠿⠁⠀⡌⠀⠀⠀⠰⠁⠀⠀⠈⠀⣶⡋
⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠄⢰⠍⠂⠀⠀⠀⠙⠢⠤⠈⠀⠀⢂⠀⠀⠀⠀⢀⣾⢠⠀⡀⠉⠂
⠀⠀⠀⣦⣥⣧⡄⠀⠀⠀⠀⠰⠄⠂⠐⠄⠀⠀⠀⠀⠉⠠⠜⠅⠉⠀⠀⠀⠀⠶⠀⠅⠇⠈⠉⠀⠀⠀⠀⠹⠈⠑⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢤⢄
⠀⠀⠐⡋⠟⠤⠀⠀⠀⠀⠐⢀⡉⠀⠀⠀⠀⠀⠀⠀⢀⣩⣍⢃⠀⠀⠀⠀⠀⠒⠂⢊⡆⠀⠀⠀⠀⢀⠄⠠⠂
⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡈⢀⠀⠀⠀⠀⠀⠠⠠⡷⠀⢀⠀⠀⠉⠀⠀⠀⣀⠘⠂
⠀⠀⠀⠀⠛⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡐⡀⢂⢔⡄⠀⠀⠀⠀⠁⠐⡀⠐⠀⠀⠀⠀⣞⠉
⠀⠀⠀⠐⠁⠰⠁⠀⠀⠀⠈⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡦⡤⠀⠀⠀⠀⠀⠀⠐⣢⠢
⠀⠀⠀⠁⠿⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢰⡞⠀⠠⣼⣿⣿⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠄⠀⠈⠀⠀⢀⣹⣿⣿⣿⣷⠀⠰⣼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠠⣄⣿⣿⣇⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⣶⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣦⡶⠆⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⣹⣶⣄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣿⡄⢀⣿
⣾⠀⠀⢰⠀⠀⠀⠀⠈⠉⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠀⠀⠀⣰⣿⣿⣿⣶⣤⣈⠉⠉⠉⠉⠙⢿⣿⡿⣿⣿⣿⣿⠷⣾⣿⡇⢸⣿
⣿⡅⠀⣿⡆⠀⡆⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣼⣿⡅⠀⢀⣻⣿⣟⣽⣿
⣿⣧⠰⣿⡷⢸⣇⠀⠀⢘⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠛⠻⠿⠛⠛⠀⠀⠀⠀⠐⣿⣿⣗⠀⢠⣽⣿⣯⣾⣿
⣿⣿⣺⣿⣿⣿⣿⠀⠀⣬⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣯⣁⣤⣿⣿⣿⣿⣿
⣿⣿⣽⣿⣿⣿⣿⡂⢠⣼⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠀⠀⢠
⢰⣜⣧⡄⢠⢸⡆⢀⣇⠀⠀⠀⠀⠀⠊
⠘⢿⣿⡇⢼⣿⡇⣺⣿⢠⡀⣠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣤⣠⡀
⠀⠀⠈⠹⠛⠻⠧⠿⢿⣼⣇⣿⣸⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠛⠙⠿⠇⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢃⠀⠀⠅⠀⠂
⢠⢁⡀⢀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣉⡂⠀⡞⡃⡤⠔
⢈⡋⣠⡅⠔⠋⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢆⡆⠠⡄⠈⢺⢔⣰⢿⠩⠐
⠸⠃⠿⠗⠶⠿⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣠⡀⢠⣤⣷⣼⢯⣿⣾⣟⣿⠷⠄⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠴⠒⣀⣠⣶⣶⣶⣶⣤⣶⣶⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄⠀⠀⢰⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⣿⣟⡁⠀⢠⣤⡀⠀⢿⣿⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣼⣿⣿⣿⣿⣿⡆⠀⢹⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠋⠘⢿⡿⠁⠀⢸⣿⣷⡄⠀⠻⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⣿⢿⣯⡻⢿⣿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣠⣴⣿⣿⣿⣿⡄⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠛⠿⣿⡇⠙⠇⠀⠀⠀⠈⠻⢿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⢰⡁
⠀⠀⠀⠀⠀⣀⣤⣄⣰⣿⣦⣾⣿⣿⣿⣿⣿⣿⣟⠉⠁⠀⠰⡄⠀⢰⣦⣁⠃⠀⠀⠀⢀⣀⣀⣀⡀⠀⣤⣾⣿⣿⣿⣿⣿⣿⠟⠛⢫⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⣄⠀⠀⠉⠀⢠⣾⠏⠐⠉⠛⠛⠻⠿⠿⣿⣿⣷⣦⣍⣉⡻⢿⡿⠟⠁⠀⠀⠀⠁⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠛⠁⠀⠈⠁⠀⠀⠙⠋⠀⠀⠀⠀⣾⡏⠀⢢⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⣄⣀⣀⠀⠰⠇⠀⠀⠀⣽⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡿⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡀⠀⠀⠱⡀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠐⠃⠀⠀⠀⠀⠀⠀⣠⡀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣎⡀⠺⠀⠀⣠⡁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⣤⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⢀⢀⣾⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠫⠷⠊⣴⡾⢣⡮⠟⣡⣿⡦⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⣶⣷⠊⠀⠁⢰⣼⢃⣤⠂⢈⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣸⢋⣿⣴⣶⡀⢺⡆⣸⠋⣄⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣱⡟⡁⠀⠈⣾⣿⣈⣡⣾⡿⡿⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣥⣶⣿⡾⣷⢀⣐⣁⠙⠿⣟⡙⠇⡀⣇⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣄⣀⣼⣣⡶⣛⣉⡙⢷⡜⣶⣝⠆⢹⣿⡆⣿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⣱⠋⣾⡿⠛⡿⣸⠇⣿⣿⡄⢚⣳⡄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠁⠀⣿⣷⡀⠠⠴⠾⣿⣿⠇⠞⠛⠢⡜⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⣀⣈⠻⢿⣶⣶⣾⣿⣿⣷⣦⡈⢻⡟⣸⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦⣾⣿⣿⠁⠀⢘⣿⠀⠃⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠶⠾⠏⣸⣧⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⡉⣷⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠉⠉⢿⣎⢷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢠⠀⠀⠀⣿⣿⣿⡇⠀⢲⡀⠈⢿⡜⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⢸⡄⠀⢀⣿⣿⣿⣿⣶⣾⣿⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠘⣿⣷⣿⡿⢻⣿⡿⠛⠛⢿⣿⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠹⣷⡀⠀⢸⣿⡇⠀⠀⠈⣿⠇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠙⣿⣦⡈⣿⣇⠀⠀⢀⡿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠈⠻⣷⣾⣿⡄⠀⠘⠁⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠈⠙⠳⢆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣦⡤⣤⣼⡀⠉⠙⢿⣶⣤⡈⢷⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣍⣿⣿⣿⣷⣄⠀⠀⢹⣿⣇⠈⠐⠄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣩⠟⣱⣿⣥⣤⣨⣿⣿⠒⠀⢀⡈⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⠁⠿⢿⣿⣿⣿⠿⠏⠀⠀⠀⠁⣠⠈⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣾⣿⣿⡀⠀⠀⠀⠠⣾⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣿⣿⣿⣿⣿⡟⠻⠿⡮⠀⠒⠂⠐⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠈⣴⣿⣦⣤⣙⣧⠀⠀⠻⠄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢠⣿⣿⣿⠿⣿⣿⣷⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⠁⢀⣾⣿⠛⢿⣴⣾⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣿⠿⠿⣿⣿⣷⣾⢿⠍⠀⠉⠉⠀⠀⢸⣿⠛⠳⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠅⠀⠀⠀⠠⠀⠀⠀⠀⠈⢫⡀⠀⠀⠻⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢁⡒⠁⠀⢀⢠⣤⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠎⠁⡀⠀⠀⠀⣤⣤⢟⠛⠋⠀⠀⣴⣿⣿⠯⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣠⡀⢠⠄⢪⣼⣿⣿⣯⣴⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣟⡛⠴⢾⣾⣿⣿⣿⣿⠟⠋⠁⠀⠀⠰⣶⡌⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠾⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣰⣔⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡤⣴⣿⣿⣯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⣶⣿⣯⣷⣾⣿⢻⡟⣹⡇⡄⠐

⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⣶⣦⣴⠀⠀⠀⠀⠀⠀⣠⡄⠄⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⣶⣶⠿⢦⣤⣦
⢶⣆⠈⠀⠈⢀⣶⠀⠀⠀⠀⠀⠀⣼⠃⠀⠋⠁⢷⡀⠀⠀⠀⠀⠀⠈⣴⡆⢠⣶⡌⠀⠀⠀⠀⠀⣨⣿⠉⠀⠀⠀⠈⢻⣶
⠘⣒⠀⠲⠆⢐⡚⠀⠀⠀⠀⠀⠀⢿⣶⣾⣿⣶⣾⠃⠀⠀⠀⠀⠀⢜⠋⠡⣤⠉⢋⠀⠀⠀⠀⠀⣹⣧⠀⠀⠶⠂⠀⣸⣇
⠶⠈⠆⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⠁⠀⠀⠀⠀⠀⠉⢹⣷⣦⣤⣴⡾⠏
⠸⣼⠁⡄⣤⢸⡀⠀⠀⠀⠀⠀⠀⢠⠯⢭⡭⡭⡄⠀⠀⠀⠀⠀⠀⣠⡀⣴⢰⡆⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⡠⠂
⠈⠛⠠⠇⠧⠘⠛⠀⠀⠀⠀⠀⠀⠾⠭⣭⢩⡍⠷⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠘⠛⠻⡿⡿⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⣦⠀⣶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠉⠀⠉⠙⠟⠁⠀⠀⠀⢀⢤⣤⣀⣤⣀
⡀⠄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣦⠄⠀⠀⠀⢀⣧⣴⠟⠛⠛⠛⢷⣤⣄
⠈⠀⢠⣦⣦⠀⠈⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠙⢻⢿⠟⠋⠀⠀⠀⠀⠘⣷⠯⠀⠀⠀⠀⠈⠷⣟
⠈⠂⡀⠉⢁⡀⠀⠀⠀⠀⠀⢼⣿⣧⣀⠀⠀⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠨⢌⡀⠀⠀⠀⠀⠀⠀⠘⠳⢾⠖⠒⢶⣄⢼⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢨⠡⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⣸⣏⡞⠈
⢔⣅⣀⡀⣀⣀⡲⠀⠀⠀⠀⠀⠀⢸⣟⣡⣿⣿⡆⠀⠀⠀⠀⠀⠀⠐⣃⡅⠦⠦⣻⠁⠀⠀⠀⠀⠀⠻⠿⣷⢶⡿⠿⣿
⠀⠀⠑⠉⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⢸⣿⡿⣾⡛⢰⣿⣯⡛⢿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⢶⣾⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢿⣾⣅⡾⣿⣿⣿⢩⢁⣡⠿⢛⣹⠿⢿⣿⣿⣷⣼⣿⣯⣾⣿⣾⣽⢿⣿⣿⡟⣿⡛⠀⠀⠀⠀⢀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠈⣿⣿⡗⢿⣿⢿⣼⡎⣯⡇⡞⣫⣶⣧⡽⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⠠⠤⠾⠂⠁
⠀⠀⠀⠀⠀⠘⣿⣷⣦⣤⣼⣿⣷⣿⣧⢿⣿⠿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣦⣀⣤⡤⣴⣾⡶⣾⣶⣤
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣭⢛⠿⣹⣧⣾⡝⡡⢽⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠣⠹⣿⠇⠿⠿⣵⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣥⠛⠇⣻⣃⣿⣶⣿⡖⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⢰⣌⣷⡄
⠀⠉⠉⠀⠀⠀⠤⠴⠲⢷⣽⣶⣧⣿⣿⣿⣛⡿⢉⢿⣽⡝⢻⣿⢿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣟⣳⢽⣿

⠀⠀⠀⠀⣀⢤⣄⢠⣤⣾⣶⣄⡀
⠀⠀⠀⢰⣷⢿⣟⣿⣥⣾⣿⣿⣿⣾⣇
⠀⠀⠀⢹⣿⣿⣴⣙⣟⣿⣿⣿⣿⣿⣿⡁⠀⣀⡄
⠀⠀⠀⠀⠙⢻⢹⣿⣽⣻⣿⣿⣿⣿⣿⣋⡏⠛⠛⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠾⠿⠿⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⠀⣀⡀⣀⡀⣀⣀⣠⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠂⠀⠀⠀⠀⠿⠿⠿⠿⠅⠯⠟⠀⢧⠽⠿⠿⡥⠰⠇⠯⠟⠷⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠋⡤
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠰⠀⠀⠀⠸⣦⣿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢸⠁
⠀⠀⠀⠀⣈⠁⠀⠀⠀⠈⠉⢠⡸⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⢀⠀⠀⢄⠙⢸⠇⢸⣤⠀⢠⠀⡀
⠀⠀⠀⠀⢘⡠⣄⡁⠀⣀⣤⣯⠀⠀⠀⠀⠀⢀⢸⡟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠈⢃⡀⣠⣀⢸⣄⢸⣿⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠙⠉⠀⠀⠀⠂⠁⣁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠉⢁⠿⢿⢸⢹⣾⣿⣸⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣾⡘⣿⢁⣇⡾⣰
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⡓⡆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠄⠀⠄⠠⠴⠒⠀⠀⠀⠉⠉⠀⠀⠀⣀⣀⡀⢈⣠⣜⠇⠉⠀⠉⢰⠋⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⠈⠉⠠⠡⠂⠒⠊⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣤⡀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠛⣿⠿⡆⠀⢠⣶⠾⠓⠶⠄
⠀⠀⠀⠀⠀⠀⠉⣿⡿⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⢰⣄⡀⠁⠀⠃⣠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣼⣿⡟⡛⠿⣿⣿⣿⣿⡷⠀⠀⠀⢿⡟⠉⠙⠻⢿⣿⡿⠟⢫⣴⣶⣶⣾⠏⠁⠀⠴⠏⢹⣿⣿⡝⢦
⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠸⣿⣿⠇⡏⠀⣸⡏⠈⢻⡇⠂⣀⡀⠸⣇⠀⠀⢀⡄⢿⡀⠀⣿⣿⣿⠋⢹⠀⠀⠀⠀⢠⣼⣿⣿⠷⣄
⠀⠀⠀⠀⠀⠀⣴⣀⣭⣆⠀⢸⠛⠁⣧⣀⣛⢁⣄⠘⣯⠄⠻⠀⠀⠀⠀⠀⢈⡷⢀⣀⣀⡟⠙⢿⣆⣀⡀⠀⢀⡐⠋⠘⠟⠉⠀⠛
⠀⠀⠀⠀⠀⠀⠉⠻⠋⢉⣥⡴⠁⠀⡟⢿⠇⠘⢿⣿⡷⠀⠈⠰⣦⣤⣶⠔⠊⠁⢠⣴⣶⣤⣤⣤⣤⡀⠀⠰⣿⣿⣿⣶⣄⣠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠰⠒⢺⡿⠋⠀⢀⣠⣴⡶⠀⢀⣨⣭⣁⣀⣀⣀⣼⣿⣧⠀⠀⠀⣿⡿⠿⠿⢿⡟⠛⠿⠀⣼⠟⠻⣿⣿⣿⣿⣿⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣤⣴⣿⠿⠛⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⣿⠛⠉⠁⢹⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠀⠀⠀⠈⣿⣿⡿⢿⣿⣿⣿⣿⡟⠁⠀⠀⢶⣶⣦⠀⢀⣴⣆⣀⣶⣄⠀⠀⠀⢸⠙⠂⠀⠀⢀⢷
⠀⠀⠀⠀⠀⠀⢠⡾⠿⠋⠀⠀⠀⢀⡀⠀⢸⢿⠋⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⢿⣿⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠞⠠⠃⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⣶⠶⢟⠂⠀⠸⠸⠄⠀⠀⠀⠀⠅⠀⠇⠀⣀⢠⣤⠈⠛⠛⢿⣿⣿⣿⣿⢿⣿⣷⠀⢀⣤⣤⣄⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣠⣴⣶⣶⣦⣤⣶⣾⣷⣦⣀⣄⠀⠀⠀⠈⢹⣿⢋⣀⠀⠀⣿⠀⠀⠀⢘⡏⣿⠀⠋⠟⠉⠉⠃⢈⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡠⠀⢲⡚⠛⠿⠃⠀⠀⣷⠆⠀⢠⠜⠁⡏⠀⣶⣶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⢰⡿⠋⠉⢻⣯⡙⠛⣿⢟⣿⠁⠈⠛⠛⠀⠴⠂⠁⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⢠⡿⢋⡛⠋⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣘⠃⠀⠀⠀⠉⠁⠀⠛⠂⠉⢀⣴⣿⡆⠀⠀⢸⣀⡠⠚⠀⠀⠀⢿⣿⣿⣿⣷⣶⣄⢸⠀⠀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⣀⠀⠀⠀⢠⣴⣾⣿⣿⠿⣧⡀⠀⠈⢿⣷⣤⣦⣴⣤⠀⢿⣿⣿⣿⣿⣿⠀⠀⢤⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣆⠀⣻⡿⣿⣽⣿⠀⠹⢿⡄⠀⠈⠙⣿⠛⢿⣿⠀⠈⣿⣿⠉⢿⡟⠀⠋⠀⠉⠈⠻⠯⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⣿⣿⠏⠰⠿⠁⠘⠛⠃⠀⠀⠀⠁⠀⠀⠀⠽⠀⠜⢈⠀⠀⠿⠇⠀⠾⢇⣀⣠⣤⡊⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠘⣿⣴⢀⣴⣶⣶⣶⣶⣾⣿⣶⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣶⣄⡈⠉⠉⠙⠿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠸⡀⠀⠀⢿⠁⠘⠟⢻⣿⣿⣿⡿⢻⡿⣿⡦⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⠧⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⣸⢸⡄⠀⠀⣼⠋⢻⠀⠀⣸⠇⠀⠓⠀⠀⢸⡟⣿⠛⠻⠛⣻⣿⠋⠛⢿⣿⡄⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡉⠀⠃⠚⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠀⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢧⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡄⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠄⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⣸⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠿⣿⡿⣿⠛⣷⠀⠀⣼⠃⠉⠛⡿⢿⠿⢿⡇⠀⢀⣈⢁⣠⣤⡀⠙⣿⠙⠛⠟⠛⠁⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠰⠃⠀⠸⠀⠀⠻⡆⠀⢠⠃⢸⠀⠈⣡⡾⠛⠿⠿⣃⣨⡁⠀⣿⠀⢶⣶⣶⡄⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠋⠀⠈⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢴⣄
⠀⠀⠀⠀⠀⣀⠠⣄⣲⣾⠓⢛⣿⣷⢤⠀⠀⠀⠀⢤⣴⣺⠟⠁⠀⠣⡀⠀⣍⠉⢁⣶⣾⣫⠽⠛⠁⠀⠘⠈⠻⣶⣄⡀
⠀⠘⢿⠀⠀⠀⠀⠩⡍⠉⠀⠙⢻⣟⠀⠈⠀⠄⢀⠛⠛⢧⣤⣀⣀⠀⠙⢄⡇⣠⡾⠝⠋⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣿⡷⡀
⠀⠀⠈⠳⣶⣤⣤⣄⣄⡀⠀⠀⠈⠉⠐⠤⣀⠀⡜⠑⠦⣀⠻⣏⣈⡩⠛⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣀⣠⡤⠟⢳⣽⣄
⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⣄⡀⠀⠀⠀⣽⠷⠶⠤⣌⣑⠨⣿⣁⡼⠃⠀⠀⠀⠀⠀⡀⠄⠠⠀⣺⣋⠉⠀⡁⠄⠊⠁⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣾⡏⠀⠀⠀⠀⠀⠈⠉⠻⣇⡀⠉⠀⠀⠀⠀⠀⠀⠀⣰⢻⡅⠀⢀⠠⠐⠀⠀⠀⠀⠘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠇⠀⠀⠀⠀⠀⠀⠀⢀⠰⡎⠢⣄⠀⠀⠀⠀⠀⢠⠃⣟⡷⠈⠀⠀⠀⠀⠀⢀⠠⠐⣹⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣦⡀⠀⠀⠀⠀⠀⢐⠀⢹⡤⢊⣱⢦⣀⠀⢠⡆⠀⣧⣿⡀⠄⢀⠠⠄⠈⠀⠀⢠⣇⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣵⣄⠀⠀⠀⠀⢴⠀⠀⢡⡄⠈⢉⠙⢳⡟⠓⠶⠿⡿⢶⠚⠁⠂⠀⠀⠀⢠⣿⣿⠿⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣀⠠⠄⠾⣟⣿⡟⠙⠻⢷⡟⢿⡇⠠⣠⠚⠁⠀⠑⣄⠀⠀⠀⢀⣿⠟⠉⢠⣟⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠙⢿⢀⠎⢸⣷⣾⠇⠀⠀⠀⠈⠙⣿⠚⢀⠀⠀⠀⠀⠈⠠⡀⢀⡞⠁⠀⣰⡏⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢰⠎⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠉⠀⠒⠀⠂⣨⠾⣷⣄⣴⣿⣿⣶⣾⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡆⠀⠐⢄⠀⢀⣠⣶⠟⠁⠀⠀⠙⢿⣧⢸⣿⠟⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣀⡟⠉⠓⣿⡟⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠈⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣿⡿⠖⢩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⢀⣹⣀⣀⣼⡟⠀⠀⠀⢀⣀⣀⣤⣴⠿⣿⣦⣰⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣷⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠋⠉⠛⠛⠁⠀⠀⠀⠋⠉⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠐⡇⡾⣫⠾⣧⢤⡄⠀⢠⢞⠿⣷⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠋⠉⠓⢡⣠⠁
⠀⠀⠀⠀⠈⣷⡀⠀⢳⡀⠀⣀⢿⡟⠡⡎⠀⡄⡇⠀⢸⡘⠆⠈⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠉⢀⣤⠞⠿⠃
⠀⣀⠄⠂⢀⣿⣿⡆⠉⢷⣶⡏⢉⢧⠀⢻⠓⢣⠇⠀⣾⣿⠆⠀⠀⠀⠀⠀⢰⣀⠀⠀⢀⢁⡀⢹⣄⠠⡟
⠸⡿⠀⠀⡏⠉⠈⢷⠀⠀⠈⠻⡌⣧⢳⣀⡴⠃⠀⣰⡿⢿⠂⠀⢠⣶⣶⣶⠇⠈⠂⠀⣸⠉⠉⢐⠨⢧⣀
⠀⠀⠀⠀⠀⠠⠀⠈⠇⠀⢀⣴⡷⠸⠋⠁⠀⢀⡼⣯⣟⡞⠀⠀⠀⠀⢸⡟⠁⠀⠀⢸⣇⠀⢰⡏⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠁⠀⠀⠀⣔⣭⣿⣮⣛⠁⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠉⠳⠚⠷⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢎⠟⡟⡝⣿⡇⠀⠀⢢⠴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡍⢲⢊⠂⡓⡬⢷⡩⣇⠀⡠⠿⠅⢾⣙⣿⣇⢀⣀⣀⣀⣤⣤⠴⣆⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢇⡍⡦⢚⣣⠋⠠⢽⡇⠘⠿⠋⠁⠿⡿⢻⢳⣋⢟⣿⢴⢫⢗⡭⡛⢒⠏⠑⠢⠴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⢂⡁⣀⡕⠀⠀⡹⠢⠾⡛⣀⠀⠀⠀⠀⠻⠅⢋⡫⣿⢻⣸⠛⠘⣋⣵⡆⠁
⠀⠀⠀⠀⠀⢀⣶⡦⠀⢀⢋⠁⢑⠀⠀⠀⠀⠇⠃⠀⠀⠑⡁⠀⠀⠀⠀⠀⠁⡰⠟⠀⠛⠂⠀⠈⠁⠍⠂
⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠸⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⢀⠠⠀⠀⠀⠀⡀⢀⣧⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠤⠶⠚⢀⡜⢡⣠⣼⣡⣴⡄⣐⣼⣿⣿⣿⠇⠀⠀⢰
⠀⠀⠀⣦⣴⠎⠁⠐⠖⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⣆⡽⢭⠉⠹⠿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⡀⢠⣤⡷⣄
⢰⠀⠀⢸⡿⠀⢀⠀⠀⠐⣧⣆⠀⠀⠐⢰⣷⠀⣦⠹⢄⠨⠀⠀⢠⣿⠿⣿⣿⣿⣦⣤⣴⣿⣿⣧⣿⣿⠇⠘⡇
⠘⣆⠲⣼⠁⠀⢸⣿⣶⣶⣿⣿⣶⣶⣾⣿⣟⣾⢯⡀⠀⠀⠀⢀⠎⣀⡴⠛⢿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣆⠀⠙⠶⠄
⠀⠈⣿⡇⠀⠐⠛⢿⣿⣿⡿⠿⠿⠛⢹⣿⣻⣿⠀⠀⠀⠀⢰⣴⡞⠋⠀⠀⠘⠿⣿⠀⠀⠀⣿⣿⡏⢻⡋
⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣸⣿⣹⣿⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠀⠠⠙⠆⠀⣰⣿⡏⠀⣸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠈⠙⠛⠁⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣦⣀⠠⠞⢿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠉⢀⣴⠚⢉⡀⠠⣈⣈⡙⢋⢭⣆
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠀⠀⠀⠀⠀⠛⣻⣿⣷⣿⣿⣿⣿⣿⣷⣿⣯⣿⣧⡀⠉⡀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡁⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⢯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠀⡀⠙⣿⣿⣿⣿⣿⣿⡿⠓⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⢡⣴⠂⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡖⠈⠐⠂⠀⢻⣿⣿⣿⣿⠞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠷⣌⣉⠁⠀⣾⣿⣿⢻⣿⣿⡿⢿⣿⣿⣿⡿⠿⢿⣿⣤⣴⣶⣾⣿⠛⠛⠿⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁⠈⠀⣿⣿⠁⠸⡿⣿⢿⡇⠀⣀⣼⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠉⠛⠇⠘⡇⠀⢲⣿⡟⠀⢀⠂⠉⠠⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠿⠀⠀⠀⠀⠃⣠⣶⣾⡅⢀⡈⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡀⢰⠀⠸⢿⡿⠟⠷⠀⠇⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠸⢹⠆⠀⠀⠈⠷⠀⠀⠀⠀⡌⠉⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠀⣀⠀⣀⢀⡰⠀⠀⠈⢁⣴⡀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣿⣿⣿⣾⣿⣿⣿⣦⢸⣿⠳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡾⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣿⣿⣿⣿⢷⡽⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⢀⣽⣿⣿⣿⣿⣷⣼⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠠⡄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢧
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⠟⠛⠁⠀⠐⠀⣄
⠀⠀⠀⠀⠐⠈⠀⠀⠉⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣴⡦⠀⢪⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⡆⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠺⢿⣷⠀⠀⠈⠪⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠋⢻⣿⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⢀⢀⠀⣀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢄⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢉⠀⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠀⠠⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠠⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣶⣶⣄
⠀⠀⠀⠀⢀⣠⣴⣶⣤⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡀
⠀⠀⠀⠿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⠿⢿⣿⡿⠛⠻⠟⠀⣤⣤⣤⣀⣤⣶⣿⣿⠉⠇
⠀⠀⠀⠊⠙⠋⢛⣛⠉⢙⣿⣦⠀⠀⠒⠀⠃⠉⠉⠉⠁⠐⠚⠓⠃⠀⠀⠀⢶⣒⡿⢙⠛⠷⠿⠋⠁
⠀⠀⠀⠁⠈⠉⠉⠉⠉⠋⠉⠛⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠄⢈⣟⠟⠀⠉⠈⢿⠆
⠀⠀⠀⠀⠀⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣨⣀⢂⠀⢀⡀⣨⣇
⠀⠀⢠⣴⣶⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠿⣿⣟⠉⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⡀
⠀⠀⠸⠯⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠙⠂⢤⣷⣞⡿⠠
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠀⠀⣠⣶⣿⣿⡿⣉⣾⣿⡿⣿⠁⣼⠁⡀⠀⠸⣁⡼⠁⢧⣠⠇⠀⣠⡀
⠀⠀⠀⢀⣠⠎⢝⢽⣿⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣶⣿⣷⢻⣦⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣥
⠀⠀⠀⡿⢋⡴⢾⠖⠋⠁⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⡿⠈⠻⡇⠀⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠃⠀⠃⠀⠀⠀⠀⠀⣼⡿⣿⡟⠀⠀⠀⠀⠀⣿⢿⠃⠀⠀⠱⣄⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠠⡀⠀⠀⡀⠀⠀⢀⣤⣼⣿⠿⠷⠤⠤⢤⣤⣤⡿⠺⠆⠀⠀⠀⠉⠀⠀⠀⣠⡼⠋⠋⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉
⠀⠀⠀⣿⣥⣴⣾⡿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⡀
⠀⢀⣠⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢿⠛⢻⡿⣿⡆⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠰⠛⠉⠁⠘⠳⣿⣿⣿⣿⣿⠿⣿⣻⣿⠏⠀⠀⠀⠋⠘⠀⠼⠀⠈⠂⢸⠹⣿⠋⠙⠛⠛⢿⣏
⠀⠀⠀⠀⠀⠀⢠⣿⣹⣇⣀⣀⣀⣈⣿⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠆⡏⢀⣀⣀⣀⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣰⣦⡄⠀⣰⣿⣷⣀⣶⣿⣧⣤⣼⣷⣗
⠀⠀⢀⠀⢀⣦⠀⠀⠰⣶⣦⠀⣼⣿⣿⣏⡀⠀⣶⠀⠀⠀⣠⠀⠀⠀⢼⣇⠀⠀⢹⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣶⣯⣤⣿⣿⣷⡄⠨⣽⣿⣟⣿⣿⣿⣿⢡⣾⣿⢷⡀⣀⣿⣆⠀⠀⣺⣿⣤⠀⣺⣿⣧⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣬⣾⣿⣿⣿⣼⣿⣽⣿⠇⣿⣿⣿⡶⢶⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣧⣼⣿⣿⣿⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⡠⡤⢠⡄⠀⠀⠀⢀⡀⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⡤⡄⢀⠁⠀⢠⡄⠀⠀⡂⡀⠀⠀⠀⠀⠀⢀⢡⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⢠⠢⠀⢄⠕⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⢀⠀⠀⠀⡈⣠⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⠄⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠸⠰⢳⣦⠁⠀⠉⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡂⠀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠇⢀⡀
⠀⠐⠐⠀⠉⠛⠒⠆⠀⠀⢠⠀⠀⠀⠀⠈⠀⠘⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠠⠄⠐⠛⠀⠀⠐⠒⢀⡄⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠
⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠎⠄⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢔⠄⠑⠀⠁⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠉⠁⠀⠀⠀⠀⠀⠒⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠠⠄⠂⠀⠐⠠⠀⠀⠠⠤
⠀⠀⠀⠐⠀⢀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠐⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⡂⠀⢠⠅⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠐⠾⠣
⠀⠀⠀⠐⠂⠀⠑⠀⠄⠀⠀⠁⠀⠋⠃⠀⠀⠘⠉⠀⠀⠀⠐⠀⠀⠋⠀⠀⠀⠀⠐⠀⠀⠀⠠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⠄
⠀⠀⣤⡄⠡⠄⠀⠀⠀⠀⠀⠀⠂⠀⠐⡐⠂⠀⠀⠀⠈⠀⠐⠀⠀⠀⠒⠲⠒⠐⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⣤⠄
⠀⠀⠀⠀⡄⣅⡀⠀⠀⠠⠦⠄⠀⠀⠀⠰⠀⠀⠀⠈⠥⠖⠀⠀⣔⠠⠀⠀⠐⠡⢐⠄⠀⠀⠀⠀⠂⠠⠀⠁⠀⠀⠂⠀⠀⠒
⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠒⠀⠀⠐⠂
⠀⠀⠁⠀⠂⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠈⠀⠐⡃⠀⠀⠸⠂⠀⠐⠆⢀⡀⢆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠧⠀⠀⠠⠄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡈⠀⠉⠈⠀⠱⠎⢠⠃⠈⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠰⣄⡀⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘
⠀⠀⠀⠀⠐⠀⠂⠀⠀⠒⠀⠀⠄⠀⠀⠀⠂⠀⠔⠀⠀⠈⠉⠀⠀⠀⠂⠄⠰⠀⠀⠀⠀⠀⠀⢈⠈⠀⠉⡀⠸⠀⠀⠀⠀⠨⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠘⠐⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠈⠘⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣶⣶⣟⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⢒⣶⣶⣦⣤⣤⣤⣤⣴⡶⠒⠚⠛⠛⢻⣿⣿⠛⠋⣿⣿⣿⣿⣿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⡾⠁⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠈⠛⠋⠀⠀⢻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣤⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⢻⣿⣿⣀⠀⠀⣰⣶⣶⣤⣾⠟⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⡀⣠⣿⣿⣁⠀⢈⣹⠶⣤⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠸⣿⡇⢹⣿⠁⠙⠾⣾⡅⠀⠀⠀⠉⠉⠉⠁⣸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠟⠀⢸⣿⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⢻⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠹⢿⣄⡀⠀⠀⠀⠀⣾⡇⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣤⣶⣤⣤
⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⡩⠀⠀⢀⣀⣠⣤⣤⣤⢶⣤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠐
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠚⠛⠛⠛⠯⠙⠋⠉⠙⣇⠀⠀⠀⡄⠀⠀⢠⣤⠀⠀⢠⡄⠀⢀⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠶⠛⠁⠀⠀⠀⢹⠀⠸⡇
⠀⠀⠀⠀⠘⢿⡇⠘⠻⠆⠹⣿⡈⠿⡄⠀⠀⠐⡄⠴⣾⣷⠆⠀⠀⠀⠀⠀⠁⠀⣀⠐⠂⠀⠉⠒⠀⠀⠀⠀⠲⠦⠖⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠋⠀⠘⣿⠁⠀⢀⣴⠻⡿⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⢤⣤⡤
⠀⠀⠀⠀⠜⣿⣿⣿⣿⡿⠻⠟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠁⢀⠀⠀⢀⣠⠄⠀⣠⢦⠟⠉⠁⠛⠈⠁
⠀⠀⢠⡴⠃⠐⠇⠀⠹⠃⠀⠀⠀⠀⠀⠀⣤⣄⢰⡄⣀⢀⡀⡀⠁⠐⠀⠀⠠⠖⠩⠶⠃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠟⢿⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣰⢻⢠⠼⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢾⠅
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠷⠶⢦⠟⠀⠀⠀⠀⣠⡴⠀⡿⢛⡒⠛⠛⢷⣦
⠀⠀⠀⠀⢸⣾⣿⣶⣶⣶⣾⣿⣿⠀⠀⢲⣶⣶⣶⡆⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠼⠵⠷⣦⣴⣿⣿⣷⣶⡸⣿⡇
⠀⠀⠀⠀⠘⣿⣿⠿⠿⣿⡿⠟⠛⠀⠀⠞⠉⠉⢹⠟⠐⠧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⡻⠉⠽⠟⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣀⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠃⠀⠀⠀⠀⣀⣀⣀⣔
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⡷⠀⠀⡞⠉⠉⠙⠁⠀⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⣾⠃⠀⡾⢇
⠀⠀⠀⠀⠀⣶⣿⠷⡶⢿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⢺⡁⠉⢸⣿⣿⡏⠈⠙⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⡶⢿⠇⠸⠀⠀⠧⠀⠀⢹⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠉⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣤⣽⠃
⠀⠀⠀⠀⠀⣀⣀⣀⡀⣠⣤⣠⣶⣤⠀⠀⠀⠙⠀⠀⠀⠁⠀⠀⠠⠶⢾⠷⠶⠂⠀⠀⠀⠀⠰⣤⠖⠀⠀⠐⠛⠀⠀⢈⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣶⣿⣿⣿⠿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣲⣄⠠⢴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⠾⠃⠀⠀⢸⣿⡷⠿⠷⠿⣿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡴⡿⠛⠉⠛⣿⠀⠀⠀⠀⠁⠈⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠂⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⡄⠲⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢹⡗⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡈⣷⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣹⣿⣿⣷⣶⣤⠴⠶⠲⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛⠋⣻⣿⡿⠿⠇⠀⠀⠙⢿⣿⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢀⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣼⣇⡀⣀⡀⠀⠀⠀⣿⣿⣍⠋⠉⠙⠻⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡿⠋⠉⠙⠃⠀⠀⠀⠲⢦⠀⠀⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡏⠀⠀⠀⠘⢷⠔⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣀⣀⢀⣸⣆⠀⢀⢀⠀⣾⣶⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣯⣭⣿⣿⣟⣿⣿⣿⣥⣴⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⢻⣿⠟⢻⡟⠛⠻⠻⠏⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⡄⢶⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡇⠠⠀⠀⠀⠀⠘⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⡆⢀⡀⢠⣴⠤⠀⠈⠀⠀⠀⠀⠀⢰⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢻⣿⣿⣿⣯⣅⣾⠁⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⡄⠀⣸⣿⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣽⣷⣼⣿⣿⣇⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣇⡀⢀⠀⢀⡸⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠻⠤⠦⠄⠐⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⡆⡆⠀⢸⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⢠⢰⣻⣿⠀⠀⠀⠀⠀⢠⡄⢸⠀⡀⠀⠀⣠⣇⣿⣴⣷⣧⣴⢺⡇⣴⣼⣿⡖⣤⣄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣤⣿⠸⡀⣾⣿⣿⣿⡇⠀⠀⢰⣦⣼⣧⣿⣶⡇⠀⠒⠾⢿⡟⠉⠻⣿⣟⣨⢻⣽⣿⣼⢣⠙⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣧⣾⣿⣿⣿⣤⠇⢹⣿⣿⠙⠀⠀⠀⠘⠟⣿⣿⣿⡿⠆⣀⣀⣀⡜⠀⠀⠀⢹⡶⢺⣿⠦⣿⠇⣽⣦⢙⡇
⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⠗⡿⠀⠀⢿⠏⡀⢲⣣⣠⡜⠀⡘⣿⡏⠀⠀⠀⠆⢘⣧⠀⠒⠢⠀⣹⡏⢸⣧⣿⢾⣭⠻⣍⠁
⠀⠀⢠⣿⣿⣿⣾⣿⠿⠯⠻⠾⠃⠀⠀⢺⠀⠀⠸⣯⡿⠁⣀⠀⠻⡿⠧⢴⣶⣴⠃⠀⢀⣀⣄⣀⣸⠿⣾⣽⡟⢂⣿⠦⡇
⠀⠀⠿⠟⠋⣉⠁⠀⢀⣠⡄⠀⠀⠀⠀⠁⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠋⠉⠛⠚⠋⠛⡈⢁⣸⠄⠈
⠀⠀⠀⠀⠀⠋⠀⠀⠤⠤⠧⠀⠴⢶⣄⡄⠀⠤⢤⡤⢤⡄⢠⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠛⠁⠶⠺⠷⠶⠶⠾⠯⠀⢀⣀⣀⣀⡙⢓⣚⣦⠐⠛⣦⣀⣘⡧
⠀⠄⠀⠖⡀⣠⣤⡤⠄⡀⢠⣄⠀⠀⢀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣾⣿⣴⣄⠻⣧⣰⡴⡿⣦⡆⣬⣿⡀⣆⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢷⣿⣿⣿⣿⡿⠟⠻⣿⣷⣿⡇⠀⡀⣆⣄⢀⢸⣿⣷⠐⣼⣧⠀⠀⢀⢧⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠝⢻⣿⠛⠛⠛⢿⡆⠀⠅⡽⢻⣿⣾⣿⣿⡄⣥⣿⠀⠀⢰⢼⣷⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⠄⠉⠀⠀⢸⣭⣭⢍⣻⣿⣭⣤⣤⡖⠃⠺⠿⢿⣉⣉⣱⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠐⠘⠻⠗⠚⠟⠻⠟⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡹⠼⣖⣦⣤⣀⠀⢀⣀⢠⣤⣶⣷⣦⡀⠀⠀⠶⠶⠶⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠭⠈⡀⢶⣿⣿⣿⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⢻⣛⡛⣉⠱⣄⢙⡛⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⠙⠛⠢⡬⠴⣀⣺⣿⡧⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⡰⠋⠁⠀⠀⠉⢀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢻⣿⣿⣿⣯⣶⡖⡁⠀⠀⠀⠀⠀⣈⣷⡶⣫⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⢰⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠓⠦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣷⣦⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠇⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣷⡘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡾⣶⣶⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠀⠉⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠈⠿⠿⠙⠿⠿⠁⣿⣿⣿⣿⣿⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠻⡌⠟⠁⠉⢻⠛⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢿⣿⣿⣿⡿⠀⠀⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡇⠀⠀⠀⣿⢠⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣤⣀⣠⣾⣷⣤⣄⠛⢿⣿⡇⠀⠀⢾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣤⣼⣿⣿⣿⡟⠀⠉⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⡀⠹⣆⠀⠈⠁⠀⠀⠈⠻⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⢸⣧⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⡟⠉⠙⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⠀⠈⢧⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠋⣹⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⣿⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣶⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣯⠐⠀⠀⠀⣾⣷⣾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠓⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠿⠻⣦⡀⠀⠀⡀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠂⠀⣀
⠀⠀⠀⠈⠙⠛⢻⣿⣦⣄⠀⠀⠀⠀⢸⡴⠚⠛⠀⠠⠷⠦⠤⠄⡀⢰⠀⠀⢸⣿⡌⢀⢁⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠶⠀⠘⣿⣿⠀⠈⢢⣤⡄⠘⢤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣾⣿⠃⠀⠀⠀⠀⢀⣄⠀⠀⣠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣴⠟⠀⠀⠀⠀⠀⠀⠑⠀⠀⢤⣴⠀⠀⠀⠀⠀⠀⠈⡿⠛⠻⠁⠀⠀⠀⠀⠀⠸⠃⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⠀⡨⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢲⡇
⠀⠀⠀⠐⠀⠐⠃⠀⠀⠀⠀⢀⠀⠲⢠⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣦⡦⠀⠀⡰⡿⠀⠀⢿⢦
⠀⢀⠀⠠⠀⠀⡀⠀⢰⡀⠀⢀⡀⠀⢾⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠻⣿⣿⣧⠀⠈⠀⡇⠀⠀⢸⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⢰⠈⠁⠀⠘⠻⣆⠀⠈⣧⣤⣤⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢴⠀⠀⠐⠄⠀⠀⠀⢩⣮⢧⣀⠀⠀⢸⣴⠆⠀⠀⢸⠁⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⣀⣀⣾⠿⠋⠀⠀⠀⠀⠐⠂⠐⠒
⠀⠀⠒⠀⠀⠀⡄⠀⠺⠁⠃⠀⠀⠀⠰⣼⣭⡯⣷⡆⠀⠀⠀⠀⠀⠘⠃⠀⠰⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⠤⣄⣀⠀⠀⢤⡀
⠀⠀⢸⣶⡄⠀⣿⣦⣤⣴⡆⠀⠀⠀⠘⠎⠐⢾⡟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠚⠉
⠀⠀⠘⣿⣿⠿⠻⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⢻⣿⡿⢶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⡀⠀⣄⡀⢀⡀⠸⠦⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠃⠀⠆⠈⠀⠂⠀⠀⠰⠚⢁⡀⠀⠸⠿⣿⣿⡿⠟⢿⣿⠛⠛⠛⠳⠄⠀⠘⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⢰⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠸⠟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⢸⡓⠃⠀⠀⠸⠀⠛⢃⢀⡀⢀⠀⠀⠀⠀⢠⠶⢦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣾⡧⣦⠀⠀⠀⠁⢀⠸⠹⠂⡀⢈⠇⢳⠆⢀⣤⣿⣶⡟⠂⠀⢀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⡿⠊
⠀⠀⠀⠀⣠⣿⣿⣇⢲⡄⠀⠀⢀⣦⠇⠀⠀⠷⢐⠀⠀⠀⢸⡟⠠⣉⣿⣷⠀⠈⠀⠀⠀⢾⣄⡀⠀⣀⣀⣄⠀⢀⡇⠀⠀⠀⠙⢟⢿⠃
⠀⠀⠀⣠⣿⣿⣿⣷⡋⠀⠀⠰⠁⠈⠀⢀⠞⠀⠆⠀⠀⠀⠘⡇⠀⠸⣇⢿⡀⠀⠀⠀⠀⠀⣿⠁⠀⠉⣿⠏⠀⢸⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠉⠀⠛⠛⠛⠉⠀⠀⠀⠀⠂⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠋⠒⠊⠀⠉⠀⠁⠉⠀⠀⠀⠀⠀⠑
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣽⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣾⣿⣷⣿⣿

⣀⠀⠀⠀⡇⠀⡸⢧⣀⠀⣀⡴⡋⠀⣶⣾⡆⢸⣟⠁⢰⣿⠏⢀⢸⡇⠀⢸⡿⠀⣸⡷⢀⡛⢣⣤⠉⣾⣿⠀⣿⡇⠀⣿⣇
⠁⠉⠙⡏⢹⠏⠀⠀⠀⢹⠁⠀⠀⢀⣉⠁⠉⠈⣭⠀⣸⡿⠀⣿⠀⡇⠀⣸⡇⢠⢡⣦⡙⢏⣌⡋⠶⣿⣿⠀⣿⣷⠀⢿⣿
⠀⠀⠀⠳⣼⠀⠀⠀⠀⢸⠀⠀⣆⢸⠿⣿⠁⢾⣿⢀⣿⠃⢀⣿⠀⢱⠀⣿⠀⣼⡦⣉⡁⣈⣛⠱⠆⣿⣿⡀⢻⣿⡆⠘⣿
⢧⠀⢀⠴⠟⢦⣤⣤⡤⠼⠓⠜⠁⣀⣶⣦⠀⣄⣁⢸⡿⠀⣸⣿⠀⣾⠀⣿⠀⣿⣚⡛⢣⡌⣩⣤⠺⢸⣿⣇⠈⢻⣿⡀⢹
⠈⡷⠃⠀⠀⠸⡀⠀⢃⠀⠀⠀⠀⠿⠿⠟⠀⣿⡏⢸⠇⢠⣿⠇⢠⣿⠀⡏⠀⡟⠛⠱⡶⢊⣏⠁⢿⠀⢿⣿⣦⠀⠹⣷⣄
⢿⠁⠀⠀⠀⠀⣇⣠⠼⠖⠓⣧⡄⢠⣶⡶⠀⠈⣥⡜⠀⣾⠏⠀⣼⡏⠀⠁⠀⡟⠃⣶⣶⢈⣉⠚⡛⠀⠈⢿⣿⣷⣄⠈⠻
⠛⠳⡄⠀⣤⠒⠉⢧⠀⠀⠀⠻⠀⠀⠋⣡⣴⣄⢹⡇⢸⡇⠀⠀⣿⠀⠀⡀⠀⣿⡶⣬⡥⠘⠿⠪⠿⣧⣀⠀⠛⢿⣿⣷⣤
⡀⠀⠈⡟⠀⠀⢀⡼⢦⠀⠀⠼⣿⣿⠀⡙⣋⠉⢠⡄⠸⠀⡄⢰⡏⠀⢰⠁⠈⢠⡄⢙⣁⠿⢧⣶⠘⠛⠿⣿⣶⣦⠈⢻⣿
⠙⡶⠞⠹⡞⠉⠁⠀⠀⠑⡤⣶⣶⠄⠐⢿⠿⡇⠸⠧⠀⢰⡇⢸⡇⠀⣾⠀⢀⡌⣁⠿⠛⢱⣮⠡⣿⢰⠀⣸⣿⠏⢠⣿⡏
⣠⣟⠀⠀⢠⠀⣠⠤⠀⠚⣇⣥⡍⠀⢠⣦⣤⡀⣀⣾⠀⢸⡇⢸⡇⢠⡟⠀⢈⡘⢛⡀⢿⡆⠁⣶⡦⠙⠀⣿⡟⠀⣿⣿⠃
⠀⠀⢳⣀⣈⡏⠀⠀⠀⠀⠘⣿⣾⡇⠚⠛⠛⠀⠹⠟⠀⣾⡇⢹⡇⠘⣿⠀⡈⢋⣼⡛⣴⣦⢲⣦⠜⢋⠀⣿⡇⠀⣿⡏
⠀⠀⠘⡇⠀⢹⡀⠀⠀⠀⣠⣤⡍⠀⣶⣿⣧⠐⣶⡦⠀⣿⡇⢸⣷⠀⣿⠀⣿⣆⠙⣵⡯⢐⡓⣴⡿⣨⡀⣿⣧⠀⢻⡇
⠀⢤⠴⢧⡴⠋⠙⠒⣤⠞⠉⠿⠇⠀⠉⡙⠉⠀⠿⠇⢸⣿⢀⠘⣿⠀⣿⠀⠎⣙⠃⣭⢈⣛⠁⣶⢆⣭⡇⢻⣿⠀⢸⣿
⠀⠘⡄⡼⠀⠀⠀⠀⡇⠀⢠⣦⣾⠆⠘⣿⠟⠀⠀⣷⣿⠇⣼⢠⣿⡄⣿⠀⡆⣩⣤⢁⠻⠿⢃⣶⡌⣭⣤⢸⣿⠀⢸⣿⠇
⠀⠀⣸⣧⡀⠀⠀⠀⣹⣀⡀⠋⣩⣄⣄⠀⢶⡾⠧⠹⠛⢠⡿⣸⠉⡇⢿⣇⠠⣮⡐⠟⣷⡞⣠⡝⢁⢫⣽⠈⣿⡆⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⡠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢋⢠⣿⣷
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠐⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⣿⣿⣦⡀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣴⣷⣿⣿⣿⡷⠙⣦⠤⢶⣿⡀
⠀⠀⠀⡼⠁⠀⠀⠀⠀⡄⣀⠀⠀⢸⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡛⢻⣿⣿⣿⣷⠀⢈⢾⣿⣿⣷⡀
⠀⠀⣰⠁⠀⠀⠀⠀⠀⡆⢹⠀⡂⡤⣿⣴⣹⣦⡄⠀⠀⠀⠀⢀⡀⣠⣗⢄⣾⣿⣿⣿⡿⠀⠤⣿⣟⢺⣿⣷⡄
⠀⠀⡇⢰⠀⢰⢸⢨⣠⣷⣼⣦⣷⣾⣿⣿⣿⣿⣧⣸⢀⠀⣀⣈⣫⣴⡑⠈⣿⣿⣿⣿⣷⣶⣰⢹⣗⢐⣿⠀⠃
⠀⢸⣷⣸⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣞⠛⡏⠩⠟⢰⣖⣿⣿⣿⣿⣿⣿⣤⣹⣷⣶⣿⠄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠑⠈⠉⠙⠛⠛⠛⠻⠿⢿⣿⣴⣅
⠀⢸⣿⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠻⠿⠟⠉⠛⠉⠩⠉⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠙⣿⣶⣄
⠀⠀⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠂⠀⠀⠀⢀⡀⢀⣠⣼⣷⡾⡛⠻⠌⠙⣹⠟⠈⠛⠛
⠀⠀⢹⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠦⠬⠀⠀⠀⣠⣴⣷⣿⣿⣽⣿⡋⠂⠀⠀⠀⢠⠏
⠀⠀⠀⢣⠀⠀⠀⣠⣿⣶⡆⠀⠀⠀⠄⠐⠲⣤⣅⣨⣟⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠳⡀⣸⣿⢿⠏⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⡿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠙⢄⢏⣪⣿⣦⣄⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡟⣈⣿⡿⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢬⡉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⢿⡇⢳⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣽⣿⢛⣿⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⣿⠳⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣶⣯⡤⠤⣰⣾⣿⣿⣿⡏⢘⡟⠂⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣟⣭⡵⠞⢝⣽⡿⣡⡿⣻⠀⠌⢷⡀⠀⠀⠈⠻⣶⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⢛⣯⠔⢂⠰⠛⠉⣋⣴⡞⠻⠁⠉⣡⣿⡇⢁⠈⠈⠢⣄⠀⠰⣬⠣⠀⠈⠳⢦⣄⣰⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠌⡀⠴⢋⣠⠴⢚⣿⡿⣵⠀⣤⣶⠟⢻⣿⡀⠒⠆⠀⠻⡔⠀⠈⢀⠲⣄⡀⡖⡤⢹⢾⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢋⣵⠟⣋⣡⣴⣿⡟⣠⠇⣼⢫⡁⢠⠞⠈⡿⡀⠀⠚⢶⠀⢠⡀⣸⡇⢠⣿⣇⣵⣾⣾⣧
⠀⠀⠀⠀⠀⢀⣼⣿⠟⠓⠀⠠⠴⠟⢋⡩⠟⠋⠀⣡⡎⠁⡈⠇⢨⡆⡀⠧⠀⢄⠀⡄⠀⡸⢁⣘⣴⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠺⢿⣥⣶⠶⠶⢿⣥⡶⢿⣷⡀⢀⠠⠋⠆⢠⣿⡀⣼⡧⡇⡀⣷⠀⣰⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢸⠀⡄⠀⢺⣿⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⠀⢰⠀⣀⣿⢸⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⡦⣈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠿⣿⣿⣿⣿⣽⣿⣿⣯⡶⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢠⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠀⠘⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠉⠀⠀⣰⣶⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⡄
⠀⢘⣿⡀⣦⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⣽⣷⣐⣧⡀
⠀⣾⣿⣿⣿⣣⣾⣷⣰⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⡀⢰⡀⢐⣷⢠⣆⢈⣲⣗⣾⣿⣧
⠐⢿⣿⣿⣿⠏⣿⣿⣎⠉⠉⠛⠛⠻⠷⠠⠤⠤⠤⣰⣸⣤⣾⣧⠀⣾⣿⣟⣇⢿⡗⡺⣿⢾⣿⡤⣾⣿⣻⣿⣿
⠠⢿⣿⠀⢿⠀⠹⢿⠗⠀⢠⣄⡀⠀⠀⠀⠀⠂⠌⣍⣙⠛⠛⠉⠂⠾⠟⠟⠳⠿⠗⠚⢻⣽⠇⢻⣿⣵⢷⣿⠿
⠀⠰⡷⠜⠋⠐⠋⣁⠀⡀⠥⠉⠉⠈⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⠖⢶⣤⣤⡤⣤⣤⡄⠄⠈⢑⠛⠿⠽⠿⠿⣿
⢀⡀⡀⠤⠒⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⠷⢟⡿⠋⢿⣷⣳⣮
⠈⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠐⠒⠂⠀⠉⠛⠛⠋⠫⠟
⠀⠀⠀⢠⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⣀⣦
⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠅⠀⠀⠀⠶⣜⡦⠥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢷⣝⢦⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠈⠛⠿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣶⣄⠀⠀⠉⠳⠄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⠖⠛⢻⣿⣿⣆⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣶⣄⣀⣀⣤⣾⣿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣖⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢀⣤⣿⣿⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠙⠛⠻⠯⠶⠗⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⡴⠋⣰⣿⣷⣄⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢊⣠⣿⡦⣄⡠⢲⠾⠋⠀⠀⢿⣿⣿⠙⠷⢒⣦⣴⡊⠉⢠⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡥⣾⣿⠷⠚⠋⣡⡤⠴⢺⣦⡀⠘⠛⠂⣠⣿⣿⣷⣭⡂⠈⠻⠉⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢀⡀⠈⠀⠀⠀⠻⠯⠑⠀⠀⠀⠈⠉⠛⢺⣿⢠⣐⠄⠀⢻⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣄⠀⠈⠉⠛⠿⣆⠈⠉
⠀⠀⠀⠀⠀⠀⠤⠐⠶⠶⠶⠖⠒⣛⣿⣷⡶⠷⠷⣷⣾⣿⣧⠤⠴⠾⠿⠷⠶⠾⠿⢶⣶⣖⣲⣶⡿⠿⠷⢤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠭⢓⣚⡿⠷⢦⣀⠀⠀⠀⠐⠒⠒⠒⠒⠤⠤⠤⢍⣉⠉⠒⠂⠉⠉⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⡀⠐⠒⢬⣭⡕⠂⠨⠀⠀⠀⠙⠓⠒⠶⠿⢛⣛⠓⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣺⡟⠛⠿⠇⠉⠸⢿⣿⠿⠃⠺⣤⣤⡶⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠀⠀⢠⣶⣶⣶⣤⣤⡘⠫⡑⠀⢰⣆⠀⠁⢀⣄⠀⠘⡏⢖⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣥⠀⠀⠀⣀⣠⣀⠈⠙⢻⣿⣿⠟⠁⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⠀⠗⠉
⠀⠀⠀⠀⠀⠀⡠⠐⠀⠘⠛⠀⠀⣾⣿⣿⣿⡇⠀⠀⠈⠁⣀⣀⠀⠞⣙⡂⠀⠀⠀⠀⢀⡤⡀⠄
⠀⠀⠀⠀⠀⣠⠔⠒⡀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⠀⠀⣾⣿⣿⡄⠀⠙⠃⠀⠀⠀⠀⠾⠃
⠀⠀⢀⣤⠊⠀⠀⠀⢱⠀⠀⠀⠘⠿⠋⠀⠀⣀⣀⢀⣰⣿⣿⣿⣧⠀⠐⠢⡤⣄⣀⡀⠠⠆
⠀⠀⠊⢉⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠁⡒⠊⠀⢀⡠⠔⠁
⠀⠀⠡⠌⠀⠀⠀⠀⢴⣿⣷⠆⢄⡀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠙⠛⠉⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠇⠀⡀⢠⠀⡔⢲⠖⠀⠀⠀⠀⢿⣿⠀⢰⠄⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠐⠑⠂⠘⠐⠂⠈⠀⠀⠀⠀⠸⠿⠃⢨⠠⠀⢙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⢠⠀⠀⠀⠀⠠⠀⠒⢄⠀⠀⠀⠀⢆⠀⢄⠀⠯⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⠤⠔⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣖⣿⣿⡿⣿⣿⣿⣿⣻⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣯⣿⣿⣿⣿⡿⣾⡟⣿⡏⢾⡿⣿⣿⣿⡏⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣉⠙⣹⠁⣿⢿⣫⢯⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡜⣿⢸⣿⡼⣿⡏⣿⠀⣿⠀⡟⡾⠀⡾⢀⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⢿⡄⢿⡇⢻⡇⢿⠀⣿⢠⡇⡇⢸⠇⣰
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢿⡿⣏⢷⡈⢧⠘⣧⠘⡇⢸⡆⣿⢰⣵⠀⣾⡴⠃⡆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⢧⡙⢌⠫⣷⠘⣇⢹⣆⢿⣸⣇⣿⣼⣾⣵⣿⡷⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⢦⠑⠈⢳⡈⢧⣸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡅
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠷⠦⣀⠀⠁⣽⣾⣿⣿⣿⣿⣿⠿⢻⠿⢿⡿⣿⣿⣦⣀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⢬⡀⠀⠀⠑⣶⣿⣿⣿⡿⢏⡁⠉⡄⠀⡂⢀⡀⠈⢋⠝⣿⣷⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⡀⠀⠀⠀⢀⣿⣿⣿⣿⢧⣄⣑⣢⣼⣿⣿⣿⣿⣷⣯⠈⠉⢽⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⠈⠭⠀⠀⣬⣽⣿⣿⣷⠦⠭⢽⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠐⠫⣿⣇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣭⣥⠤⠤⠀⠸⣿⠿⠿⠟⠚⠻⠻⣿⡿⠿⠿⣿⠿⣿⣿⣿⢧⣴⣾⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⠒⠂⠀⠀⢿⢂⣷⣷⣵⢄⣴⢋⣿⣿⣍⣽⣾⣿⣿⣿⠯⢷⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶⡊⠁⠀⠐⠀⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡛⠓⠫⣛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣾⡅⢤⣀⡄⣊⡾⢻⣿⣿⣿⢿⢿⣿⣿⡏⠙⢄⠀⠸⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣫⣾⠘⠁⢠⠃⠃⡀⠀⠈⡅⠈⠁⡀⢀⡻⣮⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠆⡀⡾⢀⢀⡇⠀⡄⣸⡴⣤⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣽⣿⣿⣿⣿⣿⡧⣷⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⡄⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣴⣄⢀⠀⢀⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣷⣤⡈⠁⠀⠀⠀⡇⠀⡇⠀⢄⣴⣶⣷⣾⣧⡄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠁⠀⣼⣿⣿⣶⠀⠀⠀⡇⠀⡇⠀⢹⣿⣿⣿⣿⡟⠿⣶⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡘⢿⠁⠻⠀⠀⠀⡇⠀⡇⠀⢼⠑⡯⠿⣸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡃⠀⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣾⣿⠿⢿⣷⠄⠀⠀⡇⠀⡇⠀⠀⠀⠀⣰⢂⣡⠀⠀⠀⢸
⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠐⣿⣿⣻⡘⢁⣿⣷⡄⠀⡇⠀⡇⠀⢀⡠⢘⣿⣻⣟⠐⠀⠀⢸
⠀⣨⡏⠀⠛⢿⠄⠀⠀⠀⢸⠀⠀⢹⣿⡷⣟⣿⣿⠃⠀⠀⡇⠀⡇⠀⠀⠉⠸⡿⠿⠏⠚⠂⠀⢸
⢿⠋⣀⣀⢀⡒⠀⠀⠀⠀⢸⠀⠀⠀⢘⠛⠛⠛⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⢸
⡄⠀⠸⠿⠟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⣠⡇⠀⣧⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠋⠁⠀⣠⣴⣦⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠺⣿⣿⣿⣿⣦⣤⣤⣶⣿⣿⡇⠀⠀⠀⠉⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠻⢿⠿⠻⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣀⠀⠀⠰⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⢀⣶⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠿⢯⣿⣟⣿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡍⢊⢘⡞⣸⢫⡾⣻⡷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠿⢠⠘⣾⡼⢡⠟⣵⢏⡿⢫⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣜⡅⢋⢍⠞⠀⢼⢠⡏⡼⢣⡟⣱⠟⣵⣿⡀
⠀⠀⠀⠀⠀⢀⣿⣌⣩⣾⡧⠷⠚⠻⡞⣰⢣⠟⣸⠇⡼⢃⣴⢟⡴⢠⢄⡄⣀⡀⣀⢀⢀⣀⣀⣤⣴⡶⣶⡶⢤⣄⣀
⠀⠀⠀⠀⠀⠈⠧⠽⠿⠋⠀⠀⠀⠀⠘⢧⡶⢛⣉⣼⢣⣾⠃⣾⢣⡟⣸⢣⡇⣿⣿⢨⡟⣫⡴⣫⡵⢛⣵⣾⠿⠛⠛⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⣫⣵⡾⢁⣼⢣⢟⣴⢫⣿⢃⡿⣾⣾⢰⡟⣼⠋⣴⡿⢉⣤⣶⡿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣡⠴⢛⣵⡿⢛⡅⣾⡏⣸⢧⣧⣇⣿⡟⣡⡾⢋⣴⠟⢋⣥⣤⣶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢡⣾⣫⣄⣄⠿⣘⣿⠁⡿⢸⣿⢸⡏⢰⡟⢠⡿⣡⡾⠛⣋⣁⣤⣴⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⢉⡭⢬⣓⣜⣿⠀⣿⢸⡇⣿⠀⣿⢀⡟⣰⢋⠔⣋⣩⣭⣥⡎⠀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿⡞⢛⣺⣽⣸⢀⡏⢸⡇⣿⠸⡇⢸⠀⡏⠿⣋⠵⠶⢶⢋⣿⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠿⢷⣒⠋⣩⠉⠙⠃⠛⠀⠛⠀⠓⠈⠁⠀⠀⠈⠭⢛⣭⠔⣲⡀⢹⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢤⠎⠩⠭⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡟⠶⣚⣷⠄⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣚⠻⠀⠘⣿⡭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠇⠀⠑⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⠂⠀⠀⢨⠽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡱⠆⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠀⠀⠀⠀⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠁⠀⠀⠀⢠⣇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠄⠀⠀⠀⢀⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡼⠃⠀⠀⠀⣠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⣀⢀⣀⠰⠾⣲⣦⡦⢲⣾⢻⣿⣷⢸⣷⣿⣿⣭⣷⣀⡠⠄⡀⢀
⠀⠀⠀⠀⠀⣀⣭⡍⣩⣠⣿⣿⣿⣷⣵⣿⡿⠋⠥⢨⣰⣿⣿⣾⣿⣿⣿⢿⡂⠉⢟⣢⡀⡀
⠀⠀⠀⠀⠀⣾⣎⣻⣽⢿⣿⣿⡏⣯⣽⣧⣬⣴⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⣼⣿⣀⠧
⠀⠀⠀⠀⢀⡿⣿⢿⣟⠀⣾⡿⡝⣻⣿⣿⣿⣿⡿⢸⣿⡿⣿⣿⡷⣿⣿⣿⡇⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣷⣞⣻⠸⣿⡇⡇⣶⡏⣩⡟⣋⠿⢸⣿⣿⣾⣿⣾⣿⣿⠿⡇⣿⣿⣿⣹⡏⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤
⠀⠀⠀⠀⠀⠘⢿⣧⣝⠙⣋⣿⣟⣿⣇⣷⣾⣿⣭⢸⣽⣿⣿⣿⣿⣿⣿⡿⡇⣿⣿⣿⣿⣿⣄⠀⣀⢀⢀⣤⣭⣭⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⡤⣯⢟⡻⣹⣯⣼⡟⡬⣿⢸⢿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠫⢹⣿⠇⠸⠿⢧⣾⣿⠟
⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⣱⡌⣓⣹⣧⣿⣿⣿⣆⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣻⣐⣦⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣷⣿⣿⣿⣿⣿⣽⣷⡧⢸⣿⣇⣹⣿⣽⣿⣿⣿⡇⣿⣿⣯⡙⢿⣾⣜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠾⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⣰⣿⡿⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣿⣷
⡀⣸⠆⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⣠⣾⡟⠁⢰⣿⡇⠀⠀⣦⠀⠀⠀⢄⡀⠀⠀⢸⣿⠀⠀⢀⣴⡀⢀⡁
⣇⣿⠈⣰⠄⢀⢻⣧⠀⠀⠀⠐⠃⠀⢿⡿⣀⣴⣿⣏⠀⠀⠀⠹⠀⠀⠀⠀⢠⣷⠀⠞⠁⣠⠜⠛⠟⡛⠀⠁
⢮⣿⠒⢿⡐⣗⢀⠹⣷⣆⠀⠀⠀⠀⠘⠛⠿⠟⠿⠟⢿⡦⠀⡀⠀⢀⣴⠀⠀⠀⢀⠀⠈⢀⡆⠀⢠⡇⡄⣼⢴
⣿⣿⡀⣸⣿⣇⢺⠀⠀⢠⢾⣄⢆⠀⠀⠀⠀⢀⣠⣀⠀⢀⠀⠃⠀⣀⣠⣀⣢⣇⣾⣶⣴⣼⠧⣿⣾⣿⣷⣿⢸
⠈⠉⠉⠙⠻⠿⣾⣶⠿⠻⠛⠟⠋⠀⠘⠃⠀⠈⠙⠛⠛⠛⠿⡃⠀⠙⠿⠿⣿⣿⠿⠿⢿⣿⡴⠿⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢉⣀⣲⣖⠂⠀⠀⠀⠀⠀⢀⣀⠀⠂⠠⠠⣄⣀⣤⣤⣤⣀⣀⡀⢀⣀⣈⣁⣠⣴⣶⣦⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⠉⠉⠉⠉⠉⠹⠿⠋⠁⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠒⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⣿⣶⣤⣤⣾⣿⣤⣤⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂
⠀⠀⠀⢠⣼⣷⣤⣿⣿⣿⣿⣿⠏⠙⠻⢿⣿⣿⡉⠩⠤⠀⠤⣤⣶⣤⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒

⠀⠀⠀⠰⣶⣶⠆⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⣀⣤⣄⡀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡦⠀⠀⣀⣀⠀⠀⠀⣠⣄
⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠐⠻⣯⣭⣽⣿⣿⣿⣿⠄⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⣿⡿⠋⠉⠀⣤⣾⠟⠁⠀⠀⠀⠛⢿⣿⣶⣶⣶⣄⡀
⠀⠀⣼⣿⣿⡟⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠉⠀⠀⢀⡤⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⡀⠀⠀⠈⢻⡟⠛⠻⣿⣧⡀
⠀⢾⣿⣿⣿⡇⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣠⡿⠻⣿⣿⡆⠀⠀⡿⠦⠀⠀⠀⠹⠄⠀⠀⢀⣿⣿⠁⠀⠘⠁⠀⠀⠉⠘⠁
⠀⠈⠁⠙⠉⠛⠀⠀⠀⢿⠿⠧⠤⠀⢀⣴⣶⡦⠴⠖⠃⠀⠀⠀⠈⠑⠚⠛⠛⠁⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⢠⡷⠇⠀⢀⣴⣿⠗
⠀⠰⣿⣦⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠿⣶⣶⣾⣶⡶⣄⠀⠀⠘⠲⣾⣿⣧⠀⠀⣤⣿⣿⣿⡇⠀⠀⠀⢻⣦⣀⢼⢿⠏
⠀⠀⢸⣿⣷⣶⣶⣶⣿⠟⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⡀⠀⠀⡴⠋⠹⠀⠹⠟⠈⠁⠀⠐⠛⢫⣿⣧⠀⠀⠙⠛⠁⠋⠃⠀⠀⠀⠤⣼⣟⠀⣁
⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢻⡟⡹⠋⢿⠻⢟⠳⠄⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢰⡕⣿⡟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠹⠾
⠀⠀⠀⠀⠘⡿⠛⠟⠁⠀⠀⠀⡄⠀⠈⠐⠃⠀⠈⠀⠰⠃⠀⠀⠀⠀⣼⣏⠁⠀⠀⣀⠀⠙⠁⠛⠁⠀⠀⠀⠀⠀⠸⠟⢿⣷⣤⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠑⣯⡀⡀⠀⢀⣀⣀⠀⠀⣠⣀⣀⣾⣿⡇⠀⠀⠀⠹⣷⣦⣤⣠⣴⣿⣇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣤⣤⣀⣐⣂⣄⣠⣤⠀⠀⠀⣠⣿⠟⠉⠀⠈⢻⣿⣧⡀⠈⠉⠉⠉⠉⠁⠀⡀⠀⠀⠙⢿⡿⡟⠋⠁⠘⠀⣤⢀⣶⠇⠀⠸⣯⠉⠀⠀⢻⣿⣿
⠀⠀⠛⣫⣛⣛⣿⠛⠁⠀⠀⠘⣿⠁⠀⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⠀⠀⠈⡐⠄⠀⠀⠐⠀⠘⠀⠀⠀⣴⣿⣿⡟⠀⠀⢠⠯⠆⠀⠀⠼⡼⠙⠃
⠀⠀⠀⠁⠛⡛⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⢀⠀⠀⠀⠘⢹⣊⠓⠄⠀⠀⠀⠀⠀⠀⠙⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⣀
⠀⢀⣀⡀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⣿⣷⡀⠀⠀⠀⠈⠳⡄⠟⠀⠀⠀⠀⠀⠔⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣻⠉⠁
⠀⠀⠉⢿⣤⣤⣾⣿⣿⣿⣿⣷⡄⠀⠀⣠⣶⣶⣿⣿⣷⣾⣿⣿⡏⠈⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⣤⣤⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠆
⠀⠀⠀⠀⠉⠉⢹⣿⠛⠋⠁⢿⣇⠀⠺⠟⠛⠉⢻⡟⠛⠿⠿⠿⣧⡀⠀⠀⣤⣴⣦⡄⠀⠀⢀⢤⡘⣯⡀⣹⣷⡏⢿⣀⣀⡀⠀⠀⢰⣿⣿⣿⣿
⠀⢀⠀⠀⠀⠀⠀⠏⠇⠀⠀⢸⠘⠆⠀⢀⠀⠀⠘⡗⠦⠀⠀⠖⠁⠇⠀⢠⠿⢛⣿⣿⠀⠀⠀⠀⢧⣸⠇⣿⢀⣿⠈⠉⠉⠁⠠⠤⢾⡿⣿⡯⣯
⠀⣺⣿⡄⠀⠀⠐⠀⠘⠀⠀⠂⠘⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢤⣾⣶⡀
⠀⠘⢇⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⡿⠁⠀⢀⣠⣤⣤⣶⣶⣄⠀⠀⠀⠈⢿⣿⡿⡇⠀⣾⡲⢄⠀⠀⢀⠴⣺⡆⠈⠉⣿⣿⣶⣶⣶⣶⣶⣤
⠀⠀⠈⠳⠄⠈⠒⠦⢤⠤⠖⠂⠁⡠⠋⠀⠀⠀⠉⠛⣿⢿⣿⣿⣿⠀⠀⢠⢦⠀⣿⠃⠀⠀⠙⣷⠤⠐⡶⠀⢤⡞⠁⠀⠀⠹⣿⡿⠿⠟⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠚⣠⣤⣤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠴⠃⠀⠘⠶⠾⠟⠀⠀⠀⠀⠻⢷⠆⠁⢶⡿⠃⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢹⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠈⡟⠛⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡋⢣⠀⠀⠀⢹⠠⡇⠀⢠⣿⠟⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠣⠤⠒⠚⠀⠙⠢⢾⡏⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣦⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠈⢙⡏⠀⠀⣀⠀⠀⠀⠀⠀⢀⡆⢙⣮⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⠀⠶⠛⡇⣸⣀⣽⣧⠀⠀⠀⠀⠘⣿⣿⣿⠇⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⣿⣿⠏⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⣤⠤⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⢴⡊⠁⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⠤⣀⡀⠀⠀⠀⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⣀⠉⠉⢹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠘⠛⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠠⣾⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡀⠀⠀⣾⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠿⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⢹⣶⣦⠀⠀⠀⢀⡀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠙⢿⠇⠀⠀⠀⠉⠁⠀⠀⠀⠻⠟⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠙⠿⠃⠀⣠⣄⠀⠀⢾⣿⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡰⢡⠿⠿⠀⣀⡀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⢠⣧⣄⠀⠾⣿⡟⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡌⡏⠛⠋⠀⠀⣀⡀⠐⠿⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⣠⡳⠀⡾⠆⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇
⠀⠀⣴⣶⣾⡗⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⢸⡇
⢀⣸⣿⣿⣿⠃⠀⠀⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⡆⢰⡄⠀⠀⠀⢰
⠀⠉⠉⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡌⠀⠀⠀⠀⠸⠀⠀⢣⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠃⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡜⠀⠀⣷⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⢸⠀⠀⢰⠁⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⡅⠀⣼⣤⣤⣼⠀⠀⠀⠜⠀⠀⢠⠁⠀⠀⣿⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⣿⣿⣿⣿⡄⠀⠀⣿⣶⣶⣾⠀⠀⠀⣿⣶⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠈⠀⠈⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣖⣾⣿⣌⡒⠒⢤⣄⣤⣤⣤⣴⣶⣖⣦⣿⣷⣤⣤⣤⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠙⠋⠀⠈⠛⠛⠻⠟⠋⠀⠈⠻⠛⠟⣿⠿⡿⠀⠀⣹⠿⣿⣟⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⣶⣆⣇⠀⠀⣾⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣆⣸⣍⢻⡆⣤⣤⡿⣿⠿⠿⣿⣤⣄⠀⣈⣿⢤⣿⣠⣴⣿⠋
⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠉⠛⠛⢻⣿⣿⣿⣿⠁
⠀⢸⣿⣿⣿⣿⣿⡿⠟⣻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠉⠉⠁⠀⣠⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⣽⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠁