Steam Profile Dot Art

⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡿⠋⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⢣⣶⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣸⠃⠀⠈⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⢿⠀⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡌⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣷⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⣿⣿⣷⡘⢿⣤⠀⠀⠀⠠⣖⠚⠛⠛⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠙⠻⣷⣄⠙⢷⣤⡀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⣸⣿⠀⠀⠀⠈⠁⠀⠉⠻⠶⢦⣤⡾⠃⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠈⠙⠿⢿⣿⣷⣄ ⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠉⣿⣿ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⡿ ⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⣷⡄⠀⢸⣿⡇⠀⠀⢀⣿⣿⠃ ⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⠀⠀⢀⣠⣶⣶⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠹⣿⣿⡄⠸⣿⡇⠀⢀⣾⣿⠁⠀ ⠀⠀⠈⣿⣿⣆⣀⣀⣀⣀⣀⠀⠠⠤⠶⠶⣶⣶⣤⣀⠀⠀⠀⢠⣾⡟⠉⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⢀⣠⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⢰⣿⣇⣠⣿⠟⠁⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠙⠓⠂⠀⢸⣿⠀⠀⠰⣦⠀⠀⠀⠹⣿⡆⠀⠀⢸⣿⡄⠀⠈⠙⣿⡄⠀⠀⠀⠀⠀⠀⠿⠋⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⣰⣿⡿⠋⠉⠀⠀⠀⠙⢿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠸⣿⣄⠀⠀⢿⣆⠀⠀⠀⠙⣿⡄⠀⠀⠹⣿⣦⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠛⠻⠿⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⠘⢿⣄⠀⠀⠀⠙⢷⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠉⠻⠿⣾⣿⣷⣤⣠⣤⣼⣿⡿⢿⣏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⣤⣾⣿⣥⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠘⣿⣦⣤⣤⡶⠟⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠘⢲⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠐⢾⣿⣭⡀⠀⠀⢀⣠⣼⣷⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾⡿⠟⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣆⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⢿⣯⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠙⠛⠻⠿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣶⣶⣶⡶⠾⠛⠻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⣀⡀⠀⢀⣀⣠⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠀⠀⠀⠃⠀⠰⠲⡀⠈⠑⠉⠁⠀⢀⠴⠬⠙⠂⠀⠤⠠⡤⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⡹⠁⠐⢟⢷⢕⡀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢀⡤⠏⡀⣠⠖⠂⠀ ⠀⠀⡀⠀⠀⢸⠑⣺⠉⠈⢀⣡⠙⠚⠒⠒⠒⠒⠈⠤⣚⠂⣀⢤⠖⠟⡖⠀⠀⢁ ⠀⠀⠁⠒⢒⡏⠐⡓⡔⠈⠀⡠⢢⡎⠀⠀⠀⠀⠀⠀⠄⠉⢰⠁⠀⠀⢉⠝⠀⠈ ⠀⠀⠀⠀⢹⡣⢊⠜⠁⡠⡐⠡⡇⠀⠀⠀⠀⠀⠀⢡⢂⠀⠀⠉⢤⠀⠈⡇⠀⠀ ⠀⠀⠀⢀⠜⣡⢊⠂⢰⠀⡰⠁⠀⠀⠀⠀⠀⠀⡠⠋⢸⠀⠀⢸⡀⠱⠰⡇⠀⠀ ⠀⠀⣠⢁⠖⠇⡌⠠⢹⢠⢁⣠⠄⠀⠀⠀⠀⡼⠡⢄⣼⡄⠸⠈⣇⠀⠀⠘⠀⠀ ⠀⢼⢫⠏⢸⣰⢀⠇⠚⠯⠁⠀⣣⠀⠀⢀⡰⠀⢀⠀⢷⢡⡀⡆⢾⠀⠀⠀⠀⠀ ⠘⠃⢸⠀⢸⢃⡌⠀⣀⣀⣀⣀⡀⠓⢄⡜⠇⠠⢀⢀⠘⠏⠆⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⢀⡌⣾⢻⠁⠀⠀⠉⠁⠀⠀⠀⠀⠚⠫⡛⣓⣮⣾⢇⠘⠀⠀⠀⠀⠀ ⠀⢀⠃⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠚⠽⢻⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⢰⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡰⠀⠀⠄⠀⠀ ⠀⡀⠀⢸⡏⠀⠀⠀⠀⠀⢠⠎⣥⣬⣅⡢⡀⠀⠀⠀⠀⢀⠞⡐⠀⠀⠀⠀⠀⢰ ⢸⡇⠠⡾⡟⢇⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⠆⠀⠀⠀⢠⢊⢎⢀⠀⠀⠀⡀⠀⠀ ⡄⢷⠀⡿⢿⠈⣆⢰⠈⢉⠈⣟⠁⠀⣀⡝⠀⠀⢀⠔⠅⠀⠀⡐⢂⡢⠊⠀⡀⠀ ⠃⠘⣷⢡⢸⡐⠛⠣⡈⠁⠀⠀⠉⠋⠁⠀⢀⠀⣣⣎⠠⡤⠀⢀⢞⠄⠀⣸⡇⢀ ⠀⠀⠺⣼⡮⣁⠀⢀⣸⣦⢀⠀⠀⢸⣠⡴⢅⡊⡼⠁⢸⠃⢀⣾⡏⢠⡼⡇⠨⡄ ⠀⠀⠀⠙⠃⠀⠙⢻⣿⣿⣧⣑⣂⣀⣌⣁⣀⡀⠁⠀⠘⣡⣾⡟⢠⠿⠇⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⢀⡠⢴⡶⠖⠒⠻⠯⣉⡭⠶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢋⡤⠖⠋⣩⠽⠋⠛⠀⠀⢀⣀⡀⠤⠤⠬⠳⢤⡀⠀⠀⠉⢻⡖⣤⣄⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠟⠒⠻⢄⡴⠛⠉⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠈⠁⠈⢯⣧⠀⠀⠀⠀⠀⠀⢻⡵⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠁⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣽⣦⡀⠀⠀⠀⠀⠀⢻⡽⡀⠀⠀ ⠀⠀⠀⠀⢰⠏⢧⡤⠊⠉⠀⢀⡀⠀⠀⠀⢐⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠈⠁⠈⠳⡄⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⢸⠷⢶⠃⠀⠀⠀⢸⠉⠹⣳⠄⠧⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠘⠦⣾⠄⠀⠀⠀⠘⣎⣷⣼⣁⠀⠀⠀⠀⠙⣦⡔⠒⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣆⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣈⣆⠀⠀⠀⠀⠀⠀⠀⠻⠙⢦⡉⢦⣍⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢬⣿⠀⠀⠀⠀⠀⢼⡇⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠠⣶⠶⢤⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣯⣙⠲⣄⡀⠀⠀⢿⣆⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠈⣧⠀ ⠀⠀⠀⢀⠞⣠⠖⠀⢠⡇⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠉⢻⣷⡤⡙⣳⣤⣀⡹⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀ ⠀⢀⡴⢃⠔⡝⣴⢀⠟⠁⣰⣏⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣞⢉⠛⣷⠀⠈⠓⢝⣯⣻⣻⡛⢲⡀⠀⠈⡇⠀⠀⠀⠀⠀⣇ ⠰⠋⠊⠁⢰⢷⠇⡎⠀⣼⠋⣯⠇⠀⢀⡙⢦⡀⠀⠀⠀⠀⠀⢧⠀⠀⢿⠘⠃⣸⣇⣀⡀⠀⣻⡽⢿⣷⡀⢷⢄⣰⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⢸⢰⠁⣼⠁⠈⡿⡄⠀⢸⠋⢙⣷⡀⠀⠀⢀⣠⣼⣶⠖⠚⠛⠉⣽⠉⢉⣿⠛⠉⡇⢸⣻⡇⡎⣸⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣼⣼⣸⢹⠀⠀⠹⣷⡄⢘⣧⣜⣸⣧⠀⢀⢻⡅⠀⠈⠳⠤⠤⢞⣃⣤⠾⠋⠀⠀⣸⠘⣻⣰⣧⠏⠀⠉⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠈⠹⡇⠸⡀⠀⡤⠾⠻⣯⡁⠉⢹⠙⢷⣠⣀⣻⠴⣤⣤⡴⠾⠋⡵⠀⠀⠀⠀⠀⠘⡛⠉⢩⡄⠀⠀⠀⠀⠀⠀⢠⡏⡆ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣰⢷⡀⠀⠀⠉⢛⣡⡴⠊⠇⠀⠡⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠰⡿⢿⣼⡁⠀⠀⠀⠀⠀⠀⡼⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡾⠛⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⣼⢇⠀⢻⠱⡄⠀⠀⠀⠀⢰⢡⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡼⠀⠈⠓⠹⡄⠀⠀⢠⠇⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠁⣼⢻⠃⠀⠀⠀⠀⠹⡀⢀⡞⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⠠⡾⡟⢿⡄⠀⠀⠀⠀⠀⢳⣸⡥⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣶⣖⣲⣶⣶⣛⣿⠟⠁⠀⠀⣼⠙⠀⢸⢳⡄⠀⠀⠀⡔⠚⣿⠀⠨⢇⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠩⣿⣹⣷⠋⠁⢠⡶⡗⠀⠀⢀⡼⠛⠲⣄⠈⡷⠤⠃⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠿⠁⠀⠀⠘⠃⠁⠀⢠⡽⠃⠀⠀⠀⠹⡿⠲⣄⢀⡤⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠃⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⡿⠟⢛⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣩⠉⠉⢿⠀⢞⠉⠈⠳⠌⢿⣿⣿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢠⠋⢀⣤⢤⣄⠀⡞⠛⢶⡀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⢀⣿⣿⣿⡇⠀⢰⠏⠀⠀⢹⣾⡇⠀⠀⢷⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠸⣇⢠⣦⣤⡇⢷⣿⣷⣺⡇⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⠙⢯⣿⣿⣿⣼⣿⡿⠿⢧⣄⠋⠉⠉⠻⢿⣆⠀⠀⢀⡞⠉⠙⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠛⠻⡄⢠⡜⠋⢰⣿⣿⣿⣿⡇⠀⣬⣥⣤⣤⠀⠀⢹⡆⠀⣸⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⢀⡴⠋⠀⠀⢻⣿⣿⣿⣿⠇⠀⢠⠞⠀⠀⠀⢀⡾⠁⠀⡏⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠰⠟⠷⣤⣀⠀⠀⠈⠉⠉⣀⣠⣴⠋⠀⠀⣀⡴⠋⠀⠀⠀⢹⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠉⠻⣿⣻⣿⣭⣭⣴⠏⣠⡴⠟⠁⣠⠴⢶⡟⠉⠹⣇⠀⢸⡗⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡬⣽⠛⢛⣷⠦⣌⣙⣛⣛⣋⣥⠞⢯⠀⢀⡞⢡⣤⠀⠹⠆⢠⠋⠀⠀⠁⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠉⢁⣠⣾⣃⣰⡿⠁⠀⠀⠀⠀⣹⡟⠀⠀⠈⢷⡾⣷⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡴⢋⣄⠉⠉⠉⠉⠓⠲⢤⣀⣼⠟⠀⠀⠀⠀⠈⢿⡞⠁⠀⠀⠀⢰⠄⢰⠀⡄⢠⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠎⣠⣾⣿⡇⠀⣠⣾⣿⡄⠀⠈⠙⢦⣸⠻⣆⠀⠀⡾⢷⡀⠀⠀⠠⣾⣠⢏⡼⣡⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⣿⣿⣿⠃⢰⣿⣿⣿⣿⠀⠀⠀⠀⠙⡆⢹⡀⠐⣧⠀⠙⢷⣤⡀⢀⣃⣯⠶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠁⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⣹⠀⢧⠀⠈⠳⢦⣤⠼⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠈⠳⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣴⣋⣀⣀⣀⣀⣀⠀⠀⣀⣀⣠⣀⣀⣘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣈⠉⠉⠙⣟⠉⠀⠀⠀⡇⠉⠉⠉⠑⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⣇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⡄⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⡇⠀⠀⣷⡀⠀⢀⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⢤⣤⣄⡀⠀⢀⣶⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣷⣀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡠⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠛⠉⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⡌⣻ ⠂⠀⠀⠀⠀⣠⡿⢀⣶⣧⣄⡀⢲⣄⣀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠟⠋ ⡅⠀⠀⠀⢠⡿⠁⣾⣷⣾⣿⣿⣦⡘⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀ ⡇⠀⠀⢀⣾⠃⣼⣿⣿⣿⣿⣧⣿⣿⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸ ⡇⠀⣴⣿⣿⡄⢸⡟⣿⣿⣿⣽⣷⣹⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⢸ ⡇⠀⠿⠃⠸⣷⡈⢿⣿⣿⡿⣿⣿⣿⣹⠀⣾⠁⠀⠀⠀⠀⠀⠀⠘⢿⣄⡟⠹⠶⡶⠶⢦⣀⣠⣶⣶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠘⢿⣮⣹⣿⣿⣿⣿⠿⢃⣾⠟⠒⠶⢤⣤⣀⡀⠀⠀⠀⠈⠙⠓⠒⢛⣶⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠉⠛⣶⣄⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣠⣴⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠉⠉⠁⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣿⣆⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢲⣿⡄⢰⡏⠀⣴⠀⢤⠀⣸⡷⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣋⣉⡡⠴⠚⠛⠛⠻⢮⣿⣿⣭⣤⣾⡾⠋⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠀⠀⠀⠀⢰⡆⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⣇⣀⡀⠹⠧⠤⠤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠶⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠒⠲⢦⣌⡉⠛⠷⣦⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⠳⣄⠀⠈⣿⣀⣠⡿⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣽⣤⠤⠤⠼⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠘

⠀⢀⣠⣤⣤⣤⣤⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡥⢤⡀⠀⠀⠀⠉⠻⡟⠛⠛⠛⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠈⠳⣄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣳⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⣽⢷⡱⣄⠀⠪⡉⠓⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀ ⠀⣿⠀⠀⠀⠉⠒⠁⠀⣾⠿⠛⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠷⣦⡀ ⠀⣿⡀⠀⠀⠀⠠⣀⣀⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⢸⡇⠀⢸⡇ ⠀⢸⣇⠀⠀⠀⠀⣀⡈⠙⠂⢀⡴⠶⢦⣄⠀⠀⠀⠀⠀⠋⠉⠙⣷⢘⡇⣠⠟⠀ ⠀⢀⣿⠿⠛⢷⣄⣈⡉⠑⠂⢾⠀⢠⠀⠹⡆⠐⢯⣉⡷⠀⠀⠀⠋⢸⡟⠋⠀⠀ ⢀⡿⠁⠀⠀⠈⣿⠉⠛⠷⣄⠈⠳⢬⣦⣀⣙⣤⣿⠁⠀⡄⠀⠀⢀⣾⡁⠀⠀⠀ ⢸⡇⠀⠀⢀⡼⠋⠀⠀⠀⠈⢷⡀⠀⠀⠈⠉⠀⠙⠒⠊⠀⠀⣤⣾⠁⠀⠀⠀⠀ ⠸⣇⠀⠀⠙⠷⣶⡶⠇⠀⠀⠀⠳⠤⢀⣀⣀⣀⣀⣀⣠⠼⢾⡉⠈⠃⠀⠀⠀⠀ ⠀⠹⣦⡀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠓⠒⠒⠚⠻⣦⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⠤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢴⣲⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠋⢓⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⢢⡀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⠕⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⡀⠈⠢⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠘⡆⡀⠀⠀⠈⣧⡛⠀⠀⠀⠀⠀⠑⠀⠀⠈⠢⣄⠀⠙⢦⡀⠀⠀⠀⠀⢠⠈⢷⠀⠀⠀⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠸⣆⠀⠀⢷⠈⠀⠀⠀⠏⣷⣄⠀⠀⠀⠀⠀⣄⠀⠀⠀⢻⡑⠦⣄⠙⢦⡀⠀⠀⠀⠱⡌⣷⡀⠀⠀⠹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠹⡄⠀⠘⢦⠀⠀⠁⠀⠘⡎⠳⣄⡀⠀⣀⣈⣳⣄⠀⠀⠱⡄⠈⠙⠦⢍⡲⣄⠀⠀⠙⠘⣟⢦⠀⠀⠸⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠹⣄⠀⠈⢷⡀⠀⠀⠀⠸⡄⠈⠙⠷⣄⡀⠀⠈⠳⢧⡀⠹⡄⠀⠀⠀⠀⠀⠡⡀⠀⠀⢹⡀⠱⡄⠀⠹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⠁⠀⣀⡤⠤⠽⢦⠀⠀⠻⣆⡀⠀⠀⠙⡄⠀⠀⠀⠉⠓⠤⣄⣀⠙⠢⣝⡄⠀⠀⠀⠀⠀⢳⠀⠀⠀⢧⠀⠘⢦⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣧⠴⠋⠁⠀⠀⠀⠈⠳⣄⠀⠘⢷⣄⠀⠀⠙⣄⠀⠀⢀⡤⢀⣤⣽⣽⣶⣾⡟⠲⢤⡀⠀⠀⠈⣷⠀⠀⠸⡆⠀⠈⢷⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠻⣷⣄⠀⠈⢦⣨⣴⣾⠟⠛⠋⠉⠉⠃⢸⠀⠀⠉⢃⠀⠀⠙⡆⠀⠀⢳⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⢸⠁⠀⠀⣠⣴⣶⣶⠤⢄⡀⠀⠈⠓⢦⡈⠂⠙⠦⣀⣻⡟⠛⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⣆⠀⠀⢿⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⠀⠀⣾⢀⣠⣶⣿⠿⠿⠿⢿⣿⡟⠁⠀⠀⠀⠙⠲⢴⣀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡄⠀⢸⣇⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⡇⢀⠀⢺⡀⠀⣿⠹⠿⠋⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⣧⠀⢸⣿⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⢀⡀⣸⠃⡇⢸⠀⢸⣧⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⡿⡄⠈⡟⡄⠀⢸⠀⠀⠀⠀ ⠀⠀⣸⢠⠇⢠⠁⢸⠀⠀⣯⡆⣿⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡇⠀⠀⠀⡇⢷⠀⡇⡇⠀⢸⡇⠀⠀⠀ ⠀⠀⣧⡎⠀⢸⠀⣿⡀⠀⠘⡾⣿⡣⣄⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡇⠀⠀⠀⡇⠘⡀⡇⡇⠀⢸⡇⠀⠀⠀ ⠀⣼⠏⠀⠀⡼⢸⠁⣧⠀⠀⢻⡼⠙⠺⡟⠲⠬⣝⣢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⣰⠟⢠⣿⠀⠀⠀⡇⠀⠇⠀⢸⠀⢸⡇⠀⠀⠀ ⠐⠃⠀⠀⢰⢇⡇⠀⢹⡄⠀⠀⣷⡄⠀⠙⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣤⠶⠒⠒⠚⣉⡽⠏⠀⠀⠀⡠⠞⠁⣠⠋⢸⠀⠀⠀⡇⠀⢰⠀⢸⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⡞⡜⠀⠀⠀⢣⠀⠀⠹⡹⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⣠⡞⠁⣠⢸⠀⠀⢰⠃⠀⢸⡆⢸⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠀⠀⠀⠈⣆⠀⠀⢧⠘⢦⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢏⠀⢀⡇⢸⠀⠀⣼⠀⠀⢸⡇⢸⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⣇⠈⢳⡀⠀⠘⡄⠉⢻⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⣾⠀⠀⣸⠀⢸⠀⢀⡏⠀⠀⢸⡇⣟⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠘⡄⠀⠙⣄⠀⢹⠀⠀⣟⣾⡏⠛⠷⢤⣤⣄⣀⣠⣴⡿⠻⠁⠀⢸⠀⢠⠇⠘⢸⠀⣸⠀⠀⠀⣼⢡⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⠀⠘⣆⠀⠈⢦⠈⣧⠀⢸⠹⡇⠀⠀⠀⠀⠉⠉⠉⠁⠈⠀⠀⠀⠘⡆⡈⢰⠁⡈⢠⠇⠀⠀⢀⣧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠈⢦⡀⠀⠑⣿⠀⡼⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣸⠀⣧⡟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠽⢦⡀⢿⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⢾⣹⠾⠋⠉⠙⠶⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠤⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡞⠛⠓⠦⢄⣀⠀⠀⠈⠛⢭⡉⣻⡿⠛⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡫⠤⣄⡀⠀⠀⠈⠛⠲⢤⣄⣀⣙⣧⡀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣷⣞⠛⠿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣋⣭⣿⣯⣶⣿⣿⣿⣿⣿⣛⣫⣯⣬⣿⠻⠿⣿⠟⢷⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⣠⣶⣽⠂⢨⡇⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣀⣴⣟⣠⣿⢟⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣉⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣛⣿⣿⣿⣿⣬⣟⣸⣿⣼⣛⡉⠀⠀⠀⠀⠀⠿⢿⣿⡟⢛⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠁⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⡂⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⡟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠶⠂⠉⣁⣠⡴⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣿⢟⡟⠀⠀⠀⠀⣠⣤⠖⠒⠛⠛⠛⢠⡞⢋⣁⢀⣠⣤⠴⢚⣋⣥⠆⠀⣀⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⣽⣿⣿⣿⣏⡁⠀⠀⠀⠘⠿⠁⠀⣠⠾⠛⠛⠉⠉⢛⣙⣥⠤⠴⠾⠛⠉⠀⢀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⢠⡞⠁⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠛⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣭⣶⡄⠀⠀⠀⠀⠀⠀⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣇⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⢊⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣻⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⡼⣿⣾⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⢀⣠⣴⣿⣶⡿⠄⠀⠀⠀⠀⠈⣿⡃⣤⡬⠿⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡴⣫⡿⠋⢷⡿⣿⡦⢰⣾⡇⠀⠀⠘⣷⣆⠐⠋⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⡿⣻⣏⡉⠛⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣤⣤⠾⠛⣿⡄⠀⠙⠃⠀⠀⠀⠘⢿⣧⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣶⢿⠀⠹⣷⣤⣀⠀⠉⠹⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣧⡀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠉⢛⡿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡷⢾⡆⠀⣿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠄⠀⠀⠀⠀⢀⣿⠃⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⣌⢿⡄⢻⣄⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣿⣧⣴⡶⣖⣦⣶⡾⠁⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠ ⠀⠀⠀⠀⠙⢿⣟⣷⣄⠘⠟⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⡟⠀⠀⠀⠀⠀⠀⠛⢻⡏⠀⢀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠹⢿⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢲⣴⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣧⡀⠀⣐⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣿⡼⣿⡇⣶⣤⣄⣀⣀⣠⣤⡶⠿⠿⠿⠟⠻⣿⣿⠷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠉⣧⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠻⠜⠇⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⣀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣭⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣶⣤⣀⣀⠀⠀⠀⣀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠔⣸⠸⠠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢓⠀⠀⠀⠀ ⠀⠀⡠⠊⡰⢻⢠⡆⢣⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠰⡂⠀⠆⠀⠀⠀ ⢀⡼⠔⠊⢳⠀⠈⢸⢄⠡⡀⠑⢄⠀⠀⠀⠀⠀⠐⢄⠀⠐⠤⠒⠉⠢⢾⡀⠀⠀ ⠉⠀⠀⢀⠜⢰⡰⣃⠄⢢⢌⠢⣄⡀⠀⠀⠀⠀⠀⠱⣦⡀⠑⠨⣦⢴⡈⢇⠀⠀ ⠀⠀⠸⡁⠀⠈⣇⢫⣮⣏⠀⠈⠐⠟⠲⣦⣐⣄⠀⠀⠙⠪⣑⣢⠄⠘⢍⠉⡄⠀ ⢄⠀⣠⠖⠊⣈⣈⣮⣞⢟⣕⠄⠀⠸⣶⢌⣁⣶⣽⡒⢄⠀⢝⣟⠫⢁⢒⠸⣿⠀ ⠀⡏⠀⡴⠚⠉⣩⡍⠛⠐⢝⢕⠳⣤⢽⡏⣉⣮⡉⠻⡕⠳⠎⠮⢏⠀⠈⠆⢹⠄ ⠀⢃⠰⠁⠀⣿⠿⠿⠀⠀⠀⠀⠁⠒⠁⢾⠿⢿⠇⠀⠡⢠⡤⠜⡘⠀⠀⢸⠀⠂ ⠀⢘⡀⢄⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣄⣖⡝⠂⡌⢧⡆⠀⠀⡇⠀ ⣄⠚⢷⠟⠁⠀⠀⠀⠀⠀⣀⠤⠠⣄⠀⠀⠀⠄⠚⠉⢪⠿⡓⣥⠃⡆⠀⠀⡇⠀ ⠰⡍⠚⢆⠀⠀⠀⠀⠀⣔⡩⠿⠃⠠⠵⡀⠀⠀⢀⢀⢾⡁⠀⢻⢇⡇⠀⠀⠇⠀ ⢠⣌⠛⢶⣦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⢀⣴⡁⢸⠇⠀⢸⠈⠏⠀⣸⡄⠀ ⡀⠲⢮⣵⡏⠘⡗⠢⣀⠈⢢⢤⡠⡠⣊⡤⠒⡻⠁⢻⡮⣀⢀⣿⣿⠆⣴⠟⢀⠂ ⡉⠣⠀⢹⠀⠀⠈⠢⢈⣾⢏⠤⢝⠙⢿⠦⠊⠀⠀⠀⡄⠀⠙⠻⠮⡉⠈⢖⢦⡀ ⠀⠀⠀⢸⠀⠀⠀⢀⢼⡷⣁⠔⠊⡌⢲⢵⡆⠀⠀⠀⡇⠀⠀⠀⠀⠈⣦⠀⠁⠂ ⠀⠀⠀⠸⠀⠀⠀⣼⠀⠈⠀⢰⣉⠛⠉⠁⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⣀⡄⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⣠⡞⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡼⠋⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⣤⠶⠶⠤⢤⣀⣀⠀⠀⣠⡾⠋⠀⠀⢀⣀⣀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠎⠀⣠⠟⠀⠀⠀⠀⠀⣴⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠘⣇⠀⠀⡇⠀⠀⠀⠀⠀⠉⠳⡞⠉⠙⠛⠦⣖⣛⣭⣥⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⣠⣾⠏⠀⠀⠀⠀⠀⣴⡟⣾⢀⣆⡀⠀⠀⠀⠀⠀⠀⣰⠀⠻⣦⣜⣧⡀⣧⠀⢀⣠⢴⣾⣻⠯⠷⢶⡄⠀⠀⠙⢧⡤⠴⠶⠾⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡞⣹⠃⠀⠀⠀⠀⠀⢸⣿⠀⡇⢸⢯⠙⠦⠀⠀⠀⠀⢠⡏⠀⢠⡏⠈⡟⠉⢿⣖⣿⠞⣩⡵⠖⠊⠉⢻⣽⠀⠀⠀⠈⢧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⣼⠃⠀⠀⠀⠀⠀⢠⣿⢿⣷⣧⡀⠸⡆⠀⠀⠀⠀⠀⢸⠀⣠⠟⠠⠤⢽⣄⠘⣯⡞⠋⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠀⠘⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⠹⣴⠃⠀⠀⠀⠀⡀⠀⢸⠁⣸⣿⣿⣷⣶⠿⣆⠀⠀⠀⠀⣸⠞⠁⠀⠀⠀⢸⣏⡉⠺⠷⣄⡀⠀⠀⢀⡴⠃⢻⠀⠀⠀⠀⠀⢹⡉⠉⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣧⠀⢸⡀⡿⢻⣯⣿⡟⠀⠙⢧⡀⠀⠀⢸⡖⣲⣤⣤⣤⡞⢻⣷⠀⠀⠈⠳⣦⠴⠋⠀⠀⢸⡀⠀⠀⠀⠀⠈⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⢰⠆⠀⠀⠀⠘⣇⣸⠁⠻⠄⠉⠸⠁⠀⠀⠀⠉⠳⢦⣘⣯⡁⣰⣿⣿⣿⣷⣿⣇⠀⠀⠀⢿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⡏⢷⡀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⣿⡀⠀⠀⠀⠀⠘⡟⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡿⢿⣿⣿⣯⣳⡄⠀⠘⡆⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⡀⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⢿⢣⡀⠀⠀⣆⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⠛⣿⣿⡏⠀⠙⠂⠀⠻⡄⠀⠀⢰⠇⢻⡀⠀⠀⠀⣿⡝⣶⣤⣝⣷⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠈⠻⣏⠳⣄⠀⠘⢆⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣤⣈⡉⢹⠇⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⢷⡀⠀⠀⣿⠹⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢣⠈⣿⠒⠬⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠀⢠⠀⢣⡀⠀⠸⡀⠙⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣱⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⠀⡿⠀⠀⢳⡀⠀⣧⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁⠀⠀⠀⡸⠁⠹⡄⠀⠀⠀⠈⠉⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣿⠀⡇⠀⠀⠀⠻⡄⠘⣦⣄⠀⠈⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⡀⠀⠀⡼⠃⠀⠀⠻⣄⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⡿⡄⠈⢿⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠋⠀⢠⡞⠁⠀⡾⠁⠀⠀⠀⠀⢹⣶⣶⣤⣤⣤⣤⣤⣤⡴⠶⠶⠚⣩⠟⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⠀⠀⢹⠀⡇⠀⠀⠀⢸⠃⢹⡀⠀⠙⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⢀⠞⠁⠀⠀⠀⠀⢀⣿⣿⣿⣶⣾⣿⣿⣿⣧⠀⠀⣀⣴⠋⠀⢠⠀⠀⠀⠀⠀⢀⡾⠀⣿⠀⠀⢸⡄⢿⠀⠀⣰⡟⠀⢸⣧⠀⠀⠀⠈⢳⠀⠀ ⠀⠀⠀⢀⡶⠋⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠞⠉⠁⠀⠀⣸⠀⠀⠀⠀⠀⣼⠁⠀⠘⣇⠀⠀⢻⡈⢷⣰⡿⠁⠀⣿⣿⠀⠀⠀⠀⠀⠑⡀ ⠀⡠⠚⠁⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠔⠒⠀⠀⢠⡇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠹⡄⠀⠀⠙⣦⣽⡗⠀⣼⢃⠇⠀⠀⠀⠀⠀⠀⠁ ⠈⠀⠀⠀⠀⠀⣴⠃⢀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡼⠙⣇⠀⠀⠀⠀⠹⣦⠀⢀⣿⣿⢁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠃⢀⡞⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣴⢿⣀⠀⠸⣆⠀⠀⠀⠀⠈⠓⣼⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⢀⡏⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⠾⠛⠋⠉⠉⠉⠛⢳⡴⠟⠁⠀⠈⠳⣄⠹⡄⠀⠀⢀⣀⡰⠟⠁⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⣄⠘⢦⢸⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠛⠒⠒⠒⠶⢦⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣷⠀⠀⠈⠉⣹⣶⣶⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⣹⣄⠀⢸⣿⣄⠀⠀⠀⠀⢿⣿⣿⡙⢿⣿⣿⠙⠳⣤⡀⠀⠀⠀⠀⠙⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⣴⣿⠿⣆⠈⢻⣿⣶⣤⣀⣀⣀⣙⣿⣿⣯⣿⢿⡇⠀⠈⠻⣶⣄⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⣿⣿⣷⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⣿⣷ ⠀⠀⡼⣹⣿⠀⢻⣷⣤⣙⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⠀⢻⡄⠀⠀⠈⠻⣷⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢹⣿⣿⣿⣷⣄⠀⠀⣧⠀⠀⠀⠀⠀⣿⣿ ⠀⢸⠇⣿⡟⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⢁⡿⢃⡏⠀⠀⠻⠤⣄⣀⣤⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢿⣿⣿⣿⣿⣷⠄⠸⡇⠀⠀⠀⠀⣿⣿ ⠀⢸⠀⣿⣷⠀⠀⠘⣿⣯⠛⢿⣿⣿⡿⠁⣾⠃⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣶⠀⠈⢻⣦⠀⠈⢿⣿⣿⣿⣿⣧⠀⡇⠀⠀⠀⢰⣿⣿ ⠀⠈⠀⠘⣿⣦⠀⠀⢻⣿⡄⠀⠙⣿⡇⣰⣿⠀⢸⡇⠀⠀⠀⣸⡟⢧⡀⠀⠀⠰⢲⠀⠀⠀⠀⠀⠀⠘⢧⣤⠟⠀⠀⢀⣿⣿⣦⣤⣉⣻⣿⣿⣿⣆⡇⠀⠀⣠⣿⣿⡿

⠀⠠⠀⢂⢪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣰⢍⢳⡎⢆⠀⠀ ⠀⣠⠊⣾⡕⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢠⠎⠀⠀⣧⠁⠙⢌⡄⠀ ⣜⠼⣴⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠀⢀⣴⡟⣧⡀⠂⠿⡀ ⢀⣎⡿⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢱⠄⠐⠄⡀⠁⢆⢀⢠⢾⣹⣷⡍⡟⣦⡀⠱ ⣷⢻⠁⠆⠀⠀⢀⠀⡟⡀⠀⠀⡆⠈⡎⠢⡀⢸⢢⠈⡄⠁⠀⢻⣿⣷⣿⡘⣷⡀ ⡇⡌⡘⢀⡄⢀⢸⠀⡅⣡⠀⠆⢰⠀⢨⠉⠑⡌⣆⣱⣴⠀⠀⡆⢃⠘⡳⣳⠑⣿ ⣡⣱⢁⡆⠀⢸⡄⠆⡄⠀⢣⠰⠈⣄⠈⣖⡵⠟⢿⠙⣿⡄⢀⢱⢌⠄⠐⡱⡡⠀ ⢩⠸⡘⡇⠠⢼⡟⢻⠛⢯⣔⡱⣴⠏⢂⠻⡉⠝⣼⠀⠉⡃⠈⢦⣂⠙⠒⠓⠊⠪ ⠗⢤⠇⡇⠄⢸⢷⡈⢧⡢⠽⠀⡏⠲⠀⠁⠉⠋⠁⠀⠀⡇⣦⢸⣉⣭⠷⢦⣄⠀ ⡄⠀⣴⣟⣽⢸⣈⡆⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠴⣰⡇⣿⣾⣿⣿⣿⡇⢩⡓ ⢠⡼⡏⢏⣿⡿⣿⠹⡀⠀⠀⢀⣀⡀⠠⡤⢒⠄⢀⣴⠻⡸⠫⢺⠛⡛⠭⠤⠂⠊ ⠍⠃⢱⠀⠹⣅⢸⠆⢸⢤⠤⣀⣁⠈⠁⠈⢘⡴⠋⢸⠀⢧⢃⢸⢣⠁⠀⠀⠀⠀ ⢈⠓⠴⣤⣀⣹⣍⠀⢸⢸⢰⡔⡻⣿⢶⣾⣿⣏⠢⣼⡄⢘⡌⢆⠆⠀⡀⠀⠀⠀

⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠰⠶⢶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⠴⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⠛⣿⣶⣿⣟⡋⠉⠋⠁⠀⠀⠀⢉⣷⡚⠉⣍⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗ ⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⠿⠛⠻⠋⠉⠋⠛⠛⠿⢿⣿⣿⡉⠁⠀⠀⠀⢀⡾⠀⠀⠀⠀⣿⣿⣿⠿⠟⠋⠉⠋⠙⠙⠟⢿⡏⠉⠁⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣤⣤⣿⣿⢻⣶⠦⡄⠀⠀⠀⠀⠐⠂⣾⣿⡟⠃⠀⠀⠀⢀⣾⡧⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢀⣤⣤⠈⣧⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⠿⠶⠏⠀⠀⠀⣀⠀⠒⢾⣿⣷⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⣿⣷⣿⣁⠀⠀⠀⠀⠘⠷⠿⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠟⢻⣿⣿⣿⣯⣧⣀⡄⠀⢠⣄⠈⣇⣠⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠹⣿⣿⣷⣄⠒⠀⢀⣀⣠⣶⣿⡷⣦⡄⠀⠀⠀⠀⠀⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⢛⣵⠃⠀⠀⠀⠀⢠⣿⣿⣧⢀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣿⣿⣿⣿⡏⢀⠈⠓⠀⠀⠀⠀⢰⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠏⠀⣀⣠⡤⠀⠀⣠⣿⣿⣿⣿⣀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣟⣿⣿⠗⠉⠀⠀⠀⠀⠀⠀⣼⠏ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣶⣿⢟⡿⠛⠁⢀⡀⣼⣿⡛⢡⣶⣾⣿⣿⣿⣿⣿⣭⣭⣽⣥⣶⣿⠋⠉⠛⠟⠛⠉⠁⠀⢀⣀⣄⣀⠀⠀⠀⣿⠀ ⡇⠀⠀⠀⠀⢠⣶⠾⠛⠉⠋⠛⠛⠒⠦⠀⠀⠀⠀⠀⠀⠉⠻⠤⠌⠉⠀⣠⣴⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⠋⣦⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠻⡄⠀⣿⠀ ⣿⡀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣍⣳⣌⣢⣠⣿⣿⣾⣿⣿⣿⣷⣴⣤⣀⣀⣀⣀⠀⠀⠀⢀⡇⣼⣿⠀ ⢹⣷⠀⠀⣿⠀⠀⠀⠀⠀⣀⣄⣠⣶⣾⣟⣿⣿⣯⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠿⠷⠦⠶⠤⢤⡬⢭⢭⣤⣤⣤⣤⠤⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣤⡌⢸⣿⡇⠀ ⠀⢿⣧⡀⢿⠀⠀⠀⠀⣾⣿⣿⣾⣿⡯⠕⠚⠛⠋⠉⠉⠁⠈⠉⠉⠛⠿⢿⣿⣿⣿⣦⣴⣴⣦⣶⣷⣤⣴⣶⣶⣶⣤⣤⣤⣤⣶⣾⣿⡿⠿⠋⠉⠉⠁⠙⠻⣿⣷⢿⣷⢸⣿⠃⠀

⡿⠃⠀⠀⠸⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⡳⢿⣦⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⣸⡇⠀⠀⠠⢤⠀⢻⡄ ⠁⠀⠀⠀⠀⠱⡄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣦⣘⣷⡀⠀⠀⠀⠨⣝⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢄⣴⣶⣦⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⣄⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠹⢷⣍⣿⠿⢿⣦⡀⠀⠀⠘⣷⢦⡀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠉⠛⠿⢧⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠘⢦⠀⠀⠀⠀⠀⢀⡩⣿⡓⠒⠒⠀⢈⣀⣐⡚⠿⡆⠀⠀⠹⣷⣮⡀⠀⠀⠈⢿⣷⣤⠴⠮⢍⣙⣳⣶⣚⣫ ⠀⠀⠀⠀⢰⠀⠀⢧⠈⠙⢦⡢⣕⠂⠀⢰⣮⠝⢌⠀⠙⠦⡀⠀⠀⠀⣌⠉⠉⠹⡀⠀⢠⡈⠁⠈⠂⠀⠀⠀⠙⢿⠀⣠⡾⣿⣦⡀⢻⡀ ⠀⠀⠀⠀⠘⡆⠀⠸⡀⠀⠀⠈⢓⣿⣿⡓⠢⠤⢄⣑⣤⡠⠬⢐⣤⣞⣁⣀⣀⡤⠂⠀⠈⡿⢶⣄⠀⠀⠀⠀⠀⠀⠹⡉⠓⠤⣀⠙⡆⢙ ⠀⠀⠀⠀⠀⢹⡄⠀⢇⠀⠀⠀⠋⣽⠃⠀⢀⣠⠖⢻⣼⣿⣿⣿⣿⣿⣿⠉⢹⣏⠀⠀⢀⡇⠀⠈⢓⢄⡀⠀⠀⢰⣌⠘⢦⠀⠈⣆⡇⢀ ⡀⠀⢀⡀⠀⠀⠹⣄⠘⡄⠀⣰⣿⣷⣦⣀⣼⠛⣻⣿⠟⠛⠿⠿⠟⠀⣾⢠⣿⠵⠂⠀⠀⠀⠀⠀⠘⣆⢱⣆⠀⠸⡈⠓⢄⣧⠀⢸⢀⣿ ⡇⠀⢸⣧⢀⣄⠀⠈⠦⣙⡄⠻⣿⣟⠉⠉⡏⢹⣽⠁⠸⡆⠀⠀⣠⣞⣽⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢱⢳⣀⡇⢠⣄⠙⣇⢸⡌⣿ ⣷⠀⠈⢿⣿⢻⣷⣄⠙⢎⠣⡀⠈⠉⠀⠀⠰⢻⠃⠀⢀⡨⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⣽⢇⠸⠿⠋⠁⢳⠁⢸ ⣿⣇⠀⢸⣿⣷⣿⣿⣿⣶⣵⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⢀⡜⠀⠈ ⠛⠞⢯⣧⢻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢀⠖⠒⢺⡟⠀⡤⠀ ⡆⠀⠀⠻⠈⣿⣿⠹⣫⡟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣾⠎⠀ ⡏⠀⠀⠀⠀⠘⢿⣦⣈⠛⣲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀ ⣿⠀⢆⠀⠀⠀⠠⣝⠫⣽⣋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢳ ⠘⣧⠈⢣⡀⣀⠀⠀⠙⠳⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧ ⠀⠈⠢⣈⡿⣍⡳⣤⣄⠀⠈⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠈⡇⣿⣿⣾⠷⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠇⣿⣿⣿⣷⡖⢦⠀⠀⠀⠀⠀⢯⣥⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠀⠀⠀⠀⡆⢿⣿⣿⢹⣿⠘⣷⣤⡀⠀⠀⠈⠁⠀⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⡼⠀⠘⢳⡹⠋⢿⡀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣼ ⠀⠀⡜⠁⠀⠀⠀⠳⣼⣷⡗⠘⢿⣿⣿⣿⣦⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠁⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⠁⠀⠀⠀⠀⠀⠈⠿⣿⡶⠴⠛⠛⣩⣵⣾⣍⡉⣉⡛⠶⢄⡀⠠⣠⣴⣾⣿⣍⡙⠛⢿⣿⣶⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⠀⠀⠀⣿⡀⠀⠀⠀⠘⣿⡿⣿⣟⣻⣿⣿⣿⡿⠷⣮⣍⡉⠑⢀⠈⢿⣿⣿⣿⣿⣷⡀⢀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠁⠀ ⠀⠈⠀⠀⠀⠻⣿⣦⡠⣶⣄⣈⣙⢷⠌⠉⠉⠁⠀⠈⠑⠀⠈⢛⢷⣦⡆⠘⢿⣷⣮⣿⣿⣿⣿⣿⣯⣿⣿⣿⣥⣤⣤⣤⣤⣀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠦⠤⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡏⠉⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣡⢢ ⠀⠀⡼⣰⣳⣦⡑⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⣸⠁⣿⣿⣿⣿⡎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀ ⠾⠛⣆⢿⣿⣿⣿⣿⢸⠆⠀⠀⠀⠐⣟⡒⢤⡤⢄⣀⣤⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠘⠧⣿⣿⣟⣫⠞⠑⠒⠢⢄⡀⠀⠉⠁⡽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡤⠴⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡄⠀⠀⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⡧⠀⠀⢹⡄⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡄⣒⡪⠽⠿⣼⣦⣇⣴⠜⠃⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⢲⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠚⠀⠀⠀⠈⠉⠒⠒⡒⠯⣍⠓⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⢤⣀⣀⣀⣀⣀⣀⣰⣀⣈⠦⠜⠒⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢋⠉⠉⠀⠀⣀⠀⠤⠤⠉⠁⠉⠑⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⠉⠀⠀⠉⠹⢍⣉⠭⠍⠒⠉⢠⣤⣴⡆⠀⠀⠀⠳⡀⠀⠀⠀⠀ ⠀⢀⡤⠚⠁⠀⠀⠀⢰⣲⣶⣤⠀⠀⢰⠂⣱⢗⣤⡍⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀ ⡴⠋⠐⠉⠀⠀⠀⠀⠀⠈⠙⠀⠀⠋⠛⠛⠛⠛⠁⠀⠀⠀⢠⠧⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠋⠁⠀⠀⠀⢸⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢄⣀⣄⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠺⡴⠁⡜⢡⢞⡆⠱ ⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⣀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠀⠎⢠⢊⣼⠇⠀ ⢇⠀⠀⠀⠀⠀⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠒⠉⠁⠀⠀⠀ ⠸⡀⠀⠀⠙⡀⠀⠀⠹⡀⣠⠤⠤⠤⣀⣀⣀⡠⠤⠤⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⡀⠀⠀⢡⠀⠀⠀⢻⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠈⢧⠀⠀⠘⢄⠀⠀⠀⢣⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⠄⠊⠀ ⠀⠀⠘⣆⠀⠀⠀⠁⠀⠒⡾⠒⠂⠀⠈⠉⠀⠀⠀⠀⡠⠚⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀

⠀⢡⣿⣿⣿⡿⣣⣾⣿⣿⡟⣼⣿⣧⣿⣿⣿⣿⣿⣿⣿⣮⢻⣿⡟⣧⠸⡇⠀⠀ ⠀⢸⣿⡿⡿⢱⢿⡿⢻⣿⠁⠟⠹⣾⣹⣿⢹⣿⣿⣿⡹⠙⣇⠡⠀⠈⢻⠁⠀⠀ ⠄⡟⠛⢸⢡⠁⠈⠀⢣⣿⡀⠀⡑⣀⠈⡏⠘⠸⡽⠃⡃⣧⢀⠲⠀⠀⡜⠀⠀⠀ ⡇⡐⡤⢇⣇⡔⡇⣠⡼⣿⣧⣰⣽⣿⡴⣡⠀⠀⠀⢀⣧⡿⣿⡆⡆⣶⡇⠀⠀⠀ ⡇⢿⠁⣼⣿⣿⣿⣿⢳⣿⣿⣿⣿⡇⣧⣿⣿⣿⢁⣾⢿⡇⢿⣿⣧⣿⡇⠀⠀⠀ ⢀⢸⡀⢹⣿⣿⣿⣏⠈⢻⠘⣿⠿⢄⣿⣿⣿⣿⣾⣟⣸⠧⢺⣿⣿⣿⡇⠀⠀⠀ ⣾⣼⣎⣰⢿⣿⣿⣷⣳⣾⣦⣬⢆⣀⡏⣿⣿⣿⡟⢄⣒⡤⢼⣿⣿⡟⡇⠀⠀⠀ ⣿⣿⡿⢧⢞⣿⣿⣧⠹⢍⣁⣐⠀⢀⠸⠛⠉⠨⡾⠋⡓⣠⠎⣿⡿⣁⣧⠀⠀⠀ ⠛⠉⠀⠀⢻⡯⡟⠿⣷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣼⣿⡿⠧⠻⡀⠀⠀ ⠀⠀⠀⠀⠈⡅⠹⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣹⡿⡏⢀⠁⠀⢧⠀⠀ ⠑⢄⠀⠀⠀⢃⠀⠑⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡇⣧⢸⠘⢦⠘⡆⠀ ⠀⠈⢆⠀⠀⠈⡄⠀⡈⢿⠳⣄⡀⠀⢀⢲⣌⡠⠒⠁⠀⢻⣿⣾⢸⡷⣼⡇⠘⡄ ⠀⠀⠈⢆⠀⠀⢡⣀⠐⡀⠜⠁⠙⣶⡞⡡⠛⢇⠀⠀⠀⠀⣿⣽⣿⡇⠘⣆⡀⠘ ⠀⠀⠀⠘⡄⠀⠈⡌⠙⠓⠠⠤⠽⡟⠌⠠⠡⠈⠳⡀⢀⢮⢺⣿⣿⣿⠀⠙⡅⠂ ⠀⠀⠀⠀⢡⡀⠀⠘⠄⠀⠀⠠⡙⡘⢀⠇⡔⠐⢠⣿⡕⢁⣾⣿⣹⡟⠀⠀⢹⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⠚⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⣀⣤⠤⢤⣤⣤⠖⠊⠽⠛⠉⠀⠀⠈⠉⠳⢶⡋⠉⠛⠛⠓⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⣤⠞⠋⠁⣠⡴⠛⠁⠙⠁⠀⠀⠀⣀⣤⡤⠤⠤⠤⠀⠙⢶⣤⡀⠀⠀⠀⠈⢹⡟⢓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠷⠶⠿⠅⣀⡴⠟⠋⠁⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈⠁⠈⠻⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⡇⠀⢀⡴⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢠⡟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⢿⡜⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠁⠷⣶⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⣬⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠈⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⠷⢤⠇⠀⠀⠀⠀⠀⡏⠉⢙⡗⠦⢸⣥⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣀⣾⡀⠀⠀⠀⠀⠀⢷⡰⢦⡙⠷⠀⠀⠀⠀⠀⠈⠻⣆⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⡅⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢙⡟⠃⠀⠀⠀⠀⠀⠈⢧⡛⠛⠛⠒⠀⠀⠀⠀⠀⠀⢸⡿⣅⠀⠲⣍⠓⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⡬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠈⠳⣄⡈⣿⣦⣀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠰⣶⠶⣦⣬⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣯⡉⠻⢦⣄⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⣠⠟⢁⡤⠀⠀⢰⡇⠀⠀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⠿⢿⣷⣄⡈⠻⢦⣄⡀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⠀⠀⠀⢀⡴⠃⡰⣿⢀⠀⢠⣾⠇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣠⣴⣾⣿⡍⠃⠐⢿⡻⣶⣶⣽⣿⣷⣦⣀⡀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⣤⢟⣡⠞⢹⠏⡾⢀⡞⠁⢀⣼⢿⣤⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⣀⡄⠹⣿⡀⠀⠀⠈⠳⣟⢮⣿⣽⣆⠉⢷⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠰⠞⠙⠉⠀⠀⡾⣸⠁⡾⠀⢀⣾⠏⣾⣽⠃⠀⠀⡈⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢿⡈⠛⢀⣿⣇⣀⣀⡀⠀⢘⣿⠻⣿⣿⣆⠀⣷⣄⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⡇⣿⢠⠃⢀⡾⠃⠀⣿⣿⡀⠀⢠⡿⠛⢾⣿⡄⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⡾⠿⠟⠛⣿⠟⠛⣻⣿⣾⠛⢹⡇⢸⣿⣽⠀⡟⢸⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⡾⣥⠀⠀⠻⣼⡇⠀⠘⣷⠀⢾⡽⣿⠀⠀⠀⣰⡶⠟⠛⠙⣧⡀⠀⠀⢀⣴⠟⠀⢀⣿⠟⠀⠀⠈⡇⢸⣷⠟⣰⠃⣸⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣾⣼⠃⣿⠀⠀⠀⠙⢿⣆⣠⣼⣷⣶⣶⣿⣦⠀⠀⠌⢷⡄⠀⠀⠈⠉⠒⠒⢛⣡⣴⠶⠛⠁⠀⠀⠀⢠⡇⠀⢨⣵⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠀⢸⡀⠀⣠⠶⠿⠛⢯⣄⠀⠀⢸⡇⠸⣷⣠⣄⡈⡷⠼⣤⣤⣤⡶⠾⠛⠉⡞⠁⠀⠀⠀⠀⠀⠀⠹⠋⠉⠉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣇⢀⣿⣆⠀⠀⠀⠉⠛⠶⠋⢀⣠⡟⣯⠉⠉⣁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⣿⣦⣀⣀⣠⣤⠴⠞⠛⠁⠀⠈⠀⠀⠈⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⠏⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢡⠀⠀⣿⠘⣇⠀⠀⠀⠀⠀⢀⡏⢠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⡇⡼⠀⠀⠙⠓⠘⢧⠀⠀⠀⠀⡼⢁⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠋⢀⡿⣿⠃⠀⠀⠀⠀⠀⠸⣧⠀⠀⣼⠃⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⢀⣠⣿⣱⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡏⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣛⡍⠀⠀⠀⢊⡿⡟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⣼⠻⠛⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣷⣒⣲⣶⣿⣿⣛⣻⡿⠉⠁⠀⠀⢀⡾⠑⠁⠀⡿⢹⣦⠀⠀⠀⠀⡴⠋⠙⣿⠀⠀⠸⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⣭⡟⢩⣿⡾⠛⠂⠀⣠⣾⡿⠂⠀⠀⠀⣼⠟⠲⣤⡀⠐⢷⣤⣴⠏⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⢹⣿⡟⠃⠀⠀⢈⡿⠹⠁⠀⠀⠠⣿⡇⠀⠀⠈⠙⢶⣿⢧⣀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠲⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠈⢿⣓⣩⣷⡄⠚⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠁⠀⠀⠀⠀⠀⠀

⣾⠟⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡿⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣧⡀⣿⡇⠀⠀⠀⢠⣤⠀⠻⣷⡄ ⠋⠀⠀⠀⠀⠀⠸⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣬⡉⠙⣷⡄⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡁⠀⢀⣤⣤⡈⡆⠀⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢿⣶⣮⣿⣦⡀⠀⠀⠀⠀⠳⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠿⣿⣿⣿⣷⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣀⠀⠀⠀⠻⢿⣴⣞⡛⠿⢿⣿⣦⡀⠀⠀⠀⢹⣿⠳⣤⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⡀⠈⠙⠛⠿⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣽⠷⠶⠶⠒⠀⠈⣁⡀⠰⠶⠿⣽⡀⠀⠀⠀⢿⣷⣮⣁⠀⠀⠀⠀⠙⣿⣷⣦⣤⣶⣊⣉⣉⣛⣶⣶⣶⠿⣍ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠉⠻⢦⣀⣀⠙⢦⡀⠀⠀⣀⡤⢖⡏⠀⠙⠳⣄⠀⠀⠀⠀⠉⠙⠛⠓⠒⠾⣧⠀⠀⠀⠀⠙⠊⠙⢷⡄⠀⠀⠀⠈⠻⣿⡟⠀⠀⣨⣿⣿⣍⠉⢿⡟⠉ ⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠉⠳⣝⡲⢤⣤⣠⣞⠛⠁⠈⠣⣀⠀⠈⠙⢦⡀⠀⠀⣰⠗⠂⠀⠀⠈⠃⠀⠀⢹⣦⣀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢷⣠⢾⣇⡙⠛⠻⢷⡄⠻⣆ ⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣇⠀⠀⠀⠀⠀⣽⣿⣾⣿⠉⠑⠒⠲⢦⣌⣶⣤⠶⠂⢈⣰⣾⣁⣠⣀⣤⣴⡖⠁⠀⠀⢸⡟⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠈⠓⠶⣄⠀⣿⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢹⡄⠀⠀⠀⠘⠁⣸⡏⠀⠀⠀⢀⡤⠚⢻⣤⣿⣯⣿⣿⣽⣾⣿⣿⡏⠉⣿⢉⠀⠀⠀⢸⡇⠀⠀⠉⠓⢆⠀⠀⠀⠀⠰⣦⡉⠘⢦⡀⠀⠈⣷⣿⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢣⠀⠀⠀⣠⣾⣯⣁⠀⠀⣼⡿⣳⣶⣿⣿⡿⠿⣿⣿⣿⡟⠁⣽⠇⣸⡿⣋⡀⠀⠀⠈⠁⠀⠀⠀⠸⣆⠻⣄⠀⠀⠀⣯⠙⢦⡀⢳⡀⠀⢸⡌⢀⣾ ⡇⠀⠀⢰⡆⠀⠀⠀⠀⠻⣆⠘⣇⠀⢰⣿⣿⣿⣿⡷⢾⣿⠧⣴⣿⠛⢁⡄⠈⠉⠉⠁⠀⣠⡿⣰⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⡗⡄⠀⢹⠀⠀⠙⢾⣷⡀⠀⡇⢾⣿ ⡇⠀⠀⢸⣿⣀⣸⣄⠀⠀⣙⢷⣜⠦⠈⠻⣿⣯⡀⠀⠨⠃⢀⣿⠇⠀⠘⢿⣀⣀⣀⣠⣾⣵⡾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠹⡾⡆⣸⠀⠈⣦⣀⣙⣷⡰⣷⠈⣿ ⣿⡀⠀⠈⣿⣿⡟⢿⣷⣄⠈⢳⣌⠷⣄⠀⠈⠉⠁⠀⠀⠰⢿⡟⠀⠀⠀⣀⣽⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢳⡄⡟⡆⢰⣿⠟⠉⠀⠹⡏⠀⢸ ⣿⣷⠀⠀⢿⣿⣷⣌⣿⣿⣿⣦⣜⣷⣈⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠁⠀⠀⠀⠀⠀⣰⠃⠀⠘ ⣿⡝⣧⢠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠀⢀⣀⣀⣤⣴⠋⠀⠀⠀ ⠁⠙⠙⢷⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⢠⠏⠉⠁⡇⣿⠀⣼⣃⡀ ⡆⠀⠀⠀⠻⠀⢹⣿⣿⠉⢏⣹⠟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣾⡷⠋⠀ ⡟⠄⠀⠀⠀⠀⠀⢻⣿⣄⠈⠛⠷⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀ ⣧⠀⢀⠀⠀⠀⠀⠀⠘⠻⣿⠦⢴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡹⣆ ⢿⡄⠈⢦⡀⠀⠀⠀⠘⢶⣍⣁⡾⢤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸ ⠈⢻⡄⠀⢳⣄⢀⡀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧ ⠀⠀⠻⠀⠈⣿⣮⡻⢦⣀⡀⠀⠀⠈⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⠀⠀⠀⠀⠻⣿⢸⣿⣦⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿ ⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣛⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⢠⣤⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⢻⣿⡟⢧⡀⠀⠀⠀⠀⠀⠘⣯⣥⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⡜⣿⡇⠀⣿⣦⡀⠀⠀⠀⠀⠈⠋⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢠⡇⠈⢿⣟⢿⣷⣻⣷⠀⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢠⡞⠀⠀⠀⠸⣄⠁⢀⣿⣄⠸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠙⢶⣿⣷⣝⠀⠻⢿⣿⣿⣿⣿⣷⣤⣤⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⡼⠿⠛⠛⢉⣦⡶⣿⡉⡉⠉⠛⠶⣤⣄⠀⠀⣀⢀⣠⣴⣿⣿⣝⠛⠛⠿⣿⣿⣦⡤⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡇⠀⠀⠀⢰⣤⠀⠀⠀⠀⠈⠻⣿⣤⣤⣤⣤⣶⣿⣿⣿⣿⣾⣿⣭⣒⠦⠬⠿⠷⣀⠈⠻⣿⣿⣿⣿⣿⣷⣦⡀⠈⠉⠉⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛ ⠀⠀⡇⠀⠀⠀⢸⣿⣤⠀⠀⠀⠀⠀⠻⣿⡟⡿⠿⣤⣿⣿⣿⠟⠻⣯⣙⠛⠻⣶⣤⣄⠀⢄⠀⠘⣿⣿⡿⠿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣟⣿⣷⣄⠰⣷⣄⣀⣀⣙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢙⠿⡿⣾⡇⠀⢹⣭⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣧⣤⣶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀

⣀⣀⣠⣴⣶⣿⣿⠿⠟⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣶⣿⣷⣄⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⢹⡏⠀⡀⢈⣉⣿⡿⠿⠷⢾⣭⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄ ⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠚⠋⠉⠉⠙⢛⣾⠭⠤⠄⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠛⠛⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⣀⣤⠄⠒⠂⣀⠀⠀⠈⠙⠛⠒⠪⢤⣭⡙⠓⠶⣤⣄⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⢀⡀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣠⣤⡤⠤⠔⠒⠠⡶⠞⠁⠀⠀⠀⠀⠈⠉⠓⠢⣄⠀⠀⠀⠀⠀⠉⠙⠦⣤⡈⠉⠛⢷⣶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠃⢄⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⢀⡠⠴⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⢿⡟⠛⠒⠶⣌⣑⢦⡀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡠⠖⠉⠀⢀⣀⣴⠶⠖⠓⠀⣀⠀⣀⡀⠀⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⢳⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠸⠙ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⠁⠀⢀⣴⡿⠋⠀⠀⢀⣠⠞⡟⠀⡇⢱⡀⠀⠀⢹⡝⣦⠀⠀⠀⠀⠀⠀⠲⢄⡹⣆⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⠀⣴⠋⠀⠀⠀⣰⡿⠋⠀⠀⢀⡴⠋⠀⠀⡇⠀⢸⠘⡇⠀⠀⠀⢷⢊⣷⠀⠀⠀⠀⠀⠀⠀⠑⢼⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⣆⠀⠠⠂⠀⠀ ⠀⠀⣠⡴⠋⠀⣠⠚⠀⠀⠀⠀⡰⣿⠃⠀⡀⣠⠋⠀⠀⠀⠀⣇⠀⢸⡆⡇⠀⠀⠀⠈⢿⢪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣷⡔⠀⠀⠀ ⠹⢿⠟⠁⠀⣴⠃⠀⠀⠀⠀⣰⢳⠇⠀⢰⡿⠁⠀⠀⠀⠀⠀⣽⠀⠈⡇⡇⠀⠀⠀⠀⠀⡇⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣄⠘⣇⠀⠀⠀ ⢀⠎⠀⢀⡾⠀⠀⠀⠀⠀⢰⣇⡎⠀⠀⣼⠁⠀⠀⠀⠀⠀⣰⢿⠀⠀⠇⡇⠀⠀⠀⠀⠀⡇⠀⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡄⢹⡄⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠞⢸⠇⠀⢸⠇⠀⠀⠀⠀⠀⣴⠃⢸⡆⠀⢀⡇⠀⠀⠀⠀⢰⠃⠀⢿⠄⠙⠷⣄⠀⠀⠀⠀⠀⠀⢻⣧⢸⡾⣆⠀⠀⠀⠀⠀⠀⠀⠘⣦⢻⠀⢣⠀⢀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡎⠀⠀⠀⠀⠀⡴⠁⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⢸⡄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣿⣦⢇⠘⣆⠀⠀⠀⠀⠀⠀⠀⣿⡆⢧⠘⣧⠊ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⣼⡇⠀⢾⠀⠀⠀⠀⠀⢺⠀⠀⣸⠛⢦⡀⠀⠀⠈⠣⠀⠀⠀⠀⠙⢿⣾⠀⠸⡆⠀⠀⠀⠀⠀⠀⢹⢹⢸⡆⢹⣧ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣰⠃⠀⠀⣼⠏⡇⠀⣞⠀⠀⠀⠀⣸⣿⠀⠀⣿⡄⠐⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠐⢻⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇⠀⢱⠸⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡟⠀⠀⠀⢠⠏⠀⠀⣴⠋⠀⢸⢠⣿⠀⠀⠀⢠⠟⡟⠀⢴⡟⠁⠀⠀⠀⠀⠙⢶⣤⠀⠀⠀⣄⠀⠈⣷⡄⠀⢿⡄⠀⠀⠀⠀⠀⣧⢰⠈⡇⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡇⠀⠀⠀⡾⠀⠀⡼⠛⠁⢀⣸⡟⣿⠀⠀⠀⠈⠀⡧⢼⣿⣲⠤⣤⣄⣀⣀⣀⣀⣀⣹⣦⣄⡈⢳⡀⢸⣧⠀⠸⣿⡀⠀⠀⠀⠀⢿⠘⡆⢸⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⠀⣸⠁⠀⣼⠗⠀⣴⠿⢻⣇⣿⡇⠀⠀⠀⢀⡧⠀⡟⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣿⣿⡄⠀⢹⡇⠀⠀⠀⠀⢸⠀⡇⠈⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⢠⡏⢀⡼⠁⣀⠶⠁⠀⠈⣇⡿⡇⠀⠀⠀⣼⣿⣼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣿⡇⠀⠘⣿⠀⠀⠀⠀⠸⠀⣷⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⢀⣴⡟⢀⣾⠶⠚⠉⠀⠀⠀⠀⣿⡇⡇⠀⠀⢀⡟⡿⡟⠀⠀⠈⠁⠀⠀⣠⣀⡴⣶⣶⣶⠿⣶⣶⣶⣦⣹⣾⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣟⣽⢷⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⠁⢱⠀⠀⣸⠁⣿⠁⠀⠀⠀⠀⠀⢸⠟⣡⡾⢋⣁⣀⣀⠀⠀⠉⠛⢿⣿⣇⣀⢸⡇⠀⠀⠀⠀⠀⠈⡆⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢇⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡀⢠⡿⠀⣿⠀⠀⠀⠀⠀⠀⢋⣼⡟⠁⡿⠛⢉⠛⣷⠀⠀⠀⠘⣿⡇⠉⢸⢿⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠟⠀⠀⠀⠀⠀⠀⠤⠤⢴⣶⡀⠀⠸⡇⣾⠇⠀⣿⠀⠀⠀⠀⠀⠰⠛⣸⡇⠘⡇⣾⣿⣿⣿⣧⠀⠀⠀⠙⢷⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⢀⣠⣾⠟⠛⠛⠛⠻⢿⣶⣬⣗⠀⣧⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢿⡛⠉⡤⠀⣿⠀⣠⣤⣶⢾⡀⢈⠈⠀⠀⠀⠀⢨⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣰⣿⠟⠀⠀⣴⡿⠿⢦⣄⠈⠳⢤⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⣞⣡⠼⠟⣫⠤⠿⡇⢸⠀⠀⠀⠀⠀⢸⢸⡇⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠃⠀⠀⠀⣿⣀⣠⣴⣿⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⡂⠃⠀ ⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢿⣿⡟⠛⡁⢹⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⡄⠀⠀⠀⢹⣻⡟⢦⣀⠀⠀⠈⠳⣍⣉⡱⠎⢀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⠀⠀⠀⠀⠀⣀⡇⠀⠀ ⠀⢸⣧⡀⠀⠀⣿⢳⢳⠀⠀⠀⢸⠃⢧⠀⢨⠷⣾⣿⣦⣤⣤⢀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠀⠀⠀⠀⠀⡿⠁⠐⠀ ⠀⠀⢯⣇⠀⠀⣿⣯⣿⠀⠀⠀⠘⡇⢸⣧⠀⠀⠀⠔⢋⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣸⢹⡇⠀⠀⠀⢸⠈⠁⠀⠀ ⠀⢠⣾⡿⡄⠀⢸⢹⣎⣇⠀⠀⠀⡇⠘⣯⣧⡀⠀⣰⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢖⣛⣻⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢁⣿⡇⠀⠀⠀⣿⠀⢂⠀⢠ ⡀⢸⠇⢻⣻⠀⠀⠇⣿⣿⡀⠀⠀⢠⠀⢻⣿⢿⣆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⣿⠀⠈⡇⠈ ⡇⢸⠀⠀⣷⢤⠀⠀⢹⡼⣧⠀⠀⠀⠀⠸⣿⣆⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠛⠋⠋⠻⣄⠀⠀⠀⠀⠀⠀⢀⣼⡇⣿⡇⠀⠀⡿⣿⠀⠀⠘⢆ ⡳⠿⣄⠀⠘⣯⠀⠀⠀⣷⣿⣧⠀⠀⠀⠀⢿⣏⠳⣄⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⣾⠛⡇⢻⣇⠀⢰⠛⢿⠀⠀⡰⠛ ⠉⠲⣎⡳⣄⠘⣆⠀⠀⢹⣇⠹⣇⠀⠀⠀⠈⣿⣳⡾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⣿⣧⠀⢠⠐⢿⠀⣾⠀⢘⢠⣾⣷⣦ ⠀⠀⠈⠃⠙⣆⠘⣧⠀⠀⢿⡄⢹⣆⠀⠀⠀⠘⣧⡇⠈⣿⣦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⣠⣿⡿⡿⣿⠀⢸⡀⢾⡀⣿⡇⠼⢻⣿⣿⡿ ⠀⠀⠀⠈⢣⠙⡄⠈⣷⡀⠸⣿⣦⣿⣆⠀⠀⠀⠹⡇⠀⠋⠈⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡤⠤⠖⠚⠛⠉⠁⠀⠀⣠⣼⣿⣿⣧⣻⢽⡆⠘⣇⠘⣇⣿⡟⠀⣾⡛⠋⠐ ⠀⠀⠀⠀⠀⠀⢻⡀⠈⣷⡄⢻⡄⠘⠻⣦⠀⠀⠀⢿⠀⢱⠀⠀⠀⠘⡏⠻⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣟⠈⠉⠛⠻⢦⣿⣄⣻⡛⡄⠀⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⡟⢞⢷⠀⠀⠈⠣⣀⠀⠘⣆⢸⡀⠀⠀⠀⠀⢀⣻⣿⣿⣿⡿⠿⣿⣷⣶⣶⣤⣄⣀⣀⣤⣾⣿⣿⣿⢿⠃⢹⣷⡄⠀⠀⠀⠈⠙⢯⣇⠹⡄⢻⣿⣿⡗ ⠀⠀⠀⠈⠀⠀⠀⠙⡄⠀⢹⡜⢯⣧⠀⠀⠀⠉⠶⣀⣹⣾⣧⠀⠀⡼⠞⠉⠉⠀⢀⡄⣻⡄⠀⠉⠙⢿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠙⢧⡙⡄⢹⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣶⡟⣻⣿⣿⣿⣿⡬⡝⢿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢁⣤⡧⠈⡏⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡟⣿⣿⣿⣿⣿⣿⣛⣫⣤⣾⣴⣟⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⣿⣿⠻⡟⣿⢿⣿⠟⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠥⠒⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠈⠻⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⢏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣴⣯⣤⠀⠀⠀⠀⠀⣀⣠⣤⡄⢠⡤⠖⠒⠉⢁⡤⠖⡂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣟⣺⣿⣿⣿⡋⠀⠀⠀⡾⠉⢀⣤⠤⠖⠓⢶⣖⣒⣩⠵⠖⠋⢁⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⣠⠋⢀⣀⣀⣀⣈⡀⣀⠀⠀⠀⠀⣈⠛⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⢛⣽⣿⣾⡗⠀⠀⠀⠀⠀⠁⣴⣿⡿⠿⠿⠿⠿⠗⠀⠀⠀⢰⣿⣶⣶⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣿⣥⣯⣾⣿⣿⠟⠂⠀⠀⠀⠀⣼⡿⠋⠀⠀⣀⣤⣴⣆⠀⠀⠀⠘⣿⢉⣙⡯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠉⠁⢀⠴⡿⠋⢷⢿⡦⢰⣾⡄⠀⠹⣦⡐⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣽⠧⣍⠙⠛⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⠟⠓⠒⣛⣽⠗⠀⠉⠁⠀⠀⠘⢿⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠉⠀⠹⠿⣶⡄⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠚⠻⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡷⢶⠀⣾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠆⠀⠀⠀⢠⡿⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣜⣇⠙⢮⣛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⠛⠒⢻⣽⣶⠋⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴ ⠀⠀⠀⠀⠻⣾⣳⣜⠉⠉⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢤⣠⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠋⣠⠆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠈⠛⢾⡅⠀⣰⡇⠀⠀⠀⠀⠀⠱⡄⠀⠘⣟⢿⡏⣦⣄⣀⣀⣤⡴⠶⠶⠞⠻⣶⡷⠶⠶⣶⣶⣶⣶⣿⣿⣷⣷⣶⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢸⣄⠀⠀⠀⠀⠀⠹⣆⠀⠉⠃⠃⠀⠀⠀⠘⠿⠧⢀⣠⣴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠶⠦⠤⠤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣸⡀⢿⠐⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⣿⠃⠸⡄⠸⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡴⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⡰⣿⡟⠀⡄⣇⠀⢳⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠠⣀⡴⠋⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⢀⣼⠟⠁⡇⠀⣧⢸⡀⠀⠱⡄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⢀⣠⣿⣯⡀⠀⡇⠀⢻⠘⣷⡀⠀⠹⣄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⣀⣽⠤⣄⡀⣆⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣧⠴⠊⠉⠀⠀⠈⢻⠀⡇⠀⠈⡇⢻⠳⡄⠀⠘⢦⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢦⡉⠲⣞⠉⠁⠀⠀⠈⢳⡘⢆⣷⠀⠀⠀⠀⠀⠀ ⢠⠾⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⡇⠀⡄⢳⠘⡆⠙⢦⡀⠀⠳⣄⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡝⢦⠀⠀⠀⠙⢦⡈⠳⢄⡀⠀⠀⠀⡇⠘⣞⡆⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⡇⡀⢳⠘⡇⠹⡄⠀⠱⢦⡀⠈⠳⣄⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣑⣄⠀⠀⠀⠙⠲⣤⣍⠲⢤⣴⠃⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢷⣣⠈⣿⡹⡀⠹⡄⣠⠏⠉⠳⠦⣈⡉⠺⣷⣦⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⡝⠳⢤⡀⠀⠀⠀⠙⠿⡓⠮⣝⣓⣶⢼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠘⣿⡄⠸⣧⣹⣦⡿⣇⠀⠀⠀⠀⠀⠉⠓⣶⠽⢻⢯⣳⣤⣀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠙⣝⢦⡀⣉⠓⠦⢄⣀⠀⠈⠳⢶⡄⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣤⠖⢀⣹⣿⡐⢻⡍⢻⡷⣜⢦⡀⠀⠀⠀⠀⠀⢨⣷⡀⠀⠈⢿⢯⣍⠓⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀⠹⣮⡳⣯⣦⣬⣄⣀⠀⠀⠙⠒⠤⣄⣷⡀⠀⠀ ⢀⠀⠀⠀⠀⠀⣠⣧⠾⠛⠊⠉⠀⠀⠘⢷⣄⢳⡄⢿⡞⣷⡙⢦⡀⠀⠀⠀⠈⢷⢻⡶⣄⠀⠀⠉⠙⣝⣶⣘⢾⡓⠦⣄⡀⠀⠀⢢⡈⢿⣿⡳⢦⣌⡉⠉⠱⡖⠒⢚⠻⣽⡇⠀⠀ ⠀⠑⣤⣀⣤⠾⠋⠀⠀⠐⣚⣛⣭⣷⣲⣤⠿⣷⣿⣄⠹⣌⣻⣦⡙⠦⡀⠀⠀⠈⢷⣷⡈⠳⣦⣤⣦⣴⣻⣿⣽⡻⢦⣀⠻⣄⡀⠀⠹⣗⠿⣧⣈⡒⠉⠲⠤⣽⡄⠈⠳⣿⣟⠀⠀ ⠀⠀⣷⡏⠀⠀⠀⣠⣴⡿⠛⠉⠁⢤⡉⠙⠛⠻⣖⠙⠣⣄⠙⢧⡙⠳⣝⣦⣄⡀⠀⢹⣿⠟⠉⠈⠓⢤⡀⠈⠙⠿⣦⣌⡛⢮⡻⣦⣄⣈⠳⣌⣧⠈⠉⠀⠀⠀⢻⡀⠀⢻⡿⡄⠀ ⠀⠀⢹⡇⠀⠀⣠⡿⠋⠀⠀⠀⢀⣴⣿⣿⣆⠀⠈⠀⠀⠈⠳⢶⡍⢦⡀⠉⠺⢯⣟⠻⠽⣦⣀⣴⣶⣷⣾⣧⠀⠀⠈⢿⡄⠀⠉⢸⠂⠈⢻⡉⠙⡦⠄⠀⠀⠀⠀⢣⠀⠘⣧⠈⠀ ⠀⠀⢸⡇⠀⢀⣿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⠶⠤⠈⠙⠲⣾⠿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣏⠀⠀⣸⠀⣀⡀⢳⡀⢿⠀⠀⠀⠀⠀⠸⡇⠀⠈⣦⢀ ⠀⠀⠀⣷⠀⠀⣿⠀⠀⠀⠼⣯⣿⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠛⠉⠙⣿⠟⠀⠀⠀⠀⠘⠃⢰⣿⡴⠋⠳⡌⢇⠈⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⡀ ⠀⠀⠀⢿⡀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣦⠞⢩⣟⣤⠬⠀⠹⡾⡄⢃⠀⠀⠀⠀⠀⢳⣇⠀⠀⠱ ⠀⠀⠀⢈⣧⡠⠖⠉⣉⡴⢂⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠖⠩⢞⡭⢞⣁⣴⠏⠹⠀⠈⡳⠀⢹⢻⢸⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⢀⢀⡼⣿⡄⣀⠿⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⣠⣖⡿⠛⣡⣶⢿⡷⣶⢦⣠⠟⢀⡸⠈⣾⡄⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⣧⣈⠉⠙⠛⣿⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠒⠒⠲⣦⡀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⢈⡟⠛⠛⢉⣠⡴⣞⠁⠀⢇⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀ ⡙⣌⠓⢤⣄⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣿⣿⣿⢛⠛⠉⠋⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⠴⠋⠁⠀⣧⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠿⣦⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⠐⣢⠤⠿⠛⠓⠚⠳⠶⢝⣧⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡾⠳⠆⡄⠀⠀⠀⠹⣸⡿⡀⢸⡇⠀⠀⠀⠀⢀⢿⠂⠀⠀ ⠀⠀⠈⠳⣄⣤⣀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠫⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠐⠋⣠⠞⠀⠀⣧⡇⠀⠀⠀⠀⣿⡇⢻⣸⣷⠀⠀⠀⠀⣾⢀⠀⠀⠀ ⣒⣲⣶⠖⠚⠛⠺⢿⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⢀⣿⣧⠀⠀⠀⢠⣿⠇⠀⣟⡟⠀⠀⠀⢰⡏⣾⠀⠀⡀ ⠀⠹⡾⠿⠶⢶⣶⠶⠛⣿⡿⠙⣶⣄⡀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢀⣴⣾⡿⠙⢿⣄⠀⢸⠃⣿⠀⠀⠀⣸⣿⣦⣴⢃⡇⠀⠀⣼⣞⣧⠃⠀⢀⠇ ⠀⠈⠛⠶⣿⣏⣥⣤⠾⡟⠀⠀⢹⣷⠙⠳⢤⣀⠀⠀⠀⠙⠦⢄⣀⣀⣀⣀⣀⣠⠴⠁⢀⣠⡤⠚⢫⢋⡝⠁⠀⠘⣿⣿⣯⡀⢹⠀⠀⢠⡿⡿⣿⣫⡾⠁⢀⣼⣟⡼⠁⠀⢀⡞⠀ ⣦⣠⣀⠀⠉⠙⢒⣶⣿⠓⠂⠀⠀⠹⣄⠀⠀⠘⢻⣖⢤⣄⡴⣋⡵⠺⣯⡉⢙⣧⣴⣚⡿⠑⠀⢀⡴⠋⠀⠀⠀⠀⠸⡿⠃⠉⠳⢦⣤⣞⣾⣽⡟⣿⢃⣤⣺⢯⡞⠀⠀⠀⠋⠀⠀ ⠈⠉⠻⢯⡉⠉⠉⢁⡇⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠙⢶⣏⡴⠉⢀⣀⣴⠟⠉⠳⣝⣿⣛⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠻⠛⣿⣼⡋⠉⠀⠁⠀⣍⠻⢗⣦⣀⠀⠀ ⠓⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡿⠋⣠⠞⠉⠀⠙⣲⡤⣄⠀⢙⢿⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠙⠦⡉⠻⣟⡆ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣧⡶⠃⠀⢀⡼⠞⠉⡀⠈⠳⣼⣮⢳⣼⡄⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠈⠓⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⠋⢾⠶⢯⣤⡤⠞⠉⠀⠀⣀⣷⣄⠀⢸⣎⢻⠙⣷⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠐⠋⠀⠀⠀⣴⠚⠉⣻⢮⠉⠓⠛⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣳⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡟⠷⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡋⡼⠀⠀⠀⠀⠀

⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣸⣏⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠉⣹⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣏⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠈⢃⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣩⡭⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⠛⠉⠚⠛⠛⠒⠲⠶⠤⠤⠤⠤⠛⠓⠒⠛⢁⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠿⠛⠉⠉⠙⠲⢭⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⠟⠉⠁⢀⡤⠖⠲⣄⠀⣠⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠹⡟⣄⣙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⣀⣴⡾⠟⠧⠴⠋⠀⠀⠀⠙⢦⡀⢀⣼⡞⠋⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⡿⢷⢿⣤⡙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢠⣿⢿⣿⣿⣿⢷⣦⡀⠀⠀⠀⣀⣤⢿⣋⣠⣇⡤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⠟⠛⠻⣿⡿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⡇⢠⡿⠁⣨⡶⠿⣾⡿⠟⣷⣤⡴⠟⠋⠀⠈⣠⡾⠋⣰⡿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⢸⡇⠀⠀⠀⠘⣷⢹⣿⡿⣦⡀⠀⠀⠀⠀⠀ ⡇⣼⡇⣸⡏⠀⠀⠈⣿⡄⣸⡇⠀⠀⢀⣠⡾⠋⠀⣼⣏⣴⡾⣿⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⣿⠉⠛⠻⢶⣦⣤⣤⣤⣤⣴⣶⣿⣿⡈⣿⣄⠀⠀⣰⣿⢸⣿⣧⣹⣷⣦⣄⠀⠀⠀ ⡇⣿⡀⢿⣇⠀⠀⢀⣿⢡⡿⠁⢀⣴⣾⠁⠀⠀⣼⡟⠛⢿⣄⢿⣆⣠⡾⢽⠻⢷⣦⣤⣤⣤⣿⣤⣤⣄⣀⠀⠀⠉⣽⢟⡄⢹⣯⣹⣷⣬⣟⠛⠛⠛⠁⠈⣿⡹⣧⣿⠈⢻⣧⣤⡀ ⣇⣿⣷⠈⠻⠷⠶⠿⣣⡿⢁⣴⠟⢹⢸⣀⣀⣼⡟⠀⠀⠀⢻⡎⢉⢙⣿⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠛⢿⡿⠋⡆⣼⠟⠛⣿⡉⠻⣷⣄⠀⠀⠀⢸⡇⢹⣿⠀⢠⡇⠈⢿ ⣿⣿⣿⠀⠀⠀⢠⣾⠏⠀⢸⡇⣠⣾⠿⠋⠙⡿⠁⠀⠀⠀⣸⡧⣿⡾⡟⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠘⣷⠀⠃⢻⣦⣄⡙⣷⡀⠈⣿⡄⠀⠀⠈⣿⡀⣿⣦⡿⢃⡴⣾ ⣿⣼⡏⠀⠀⢠⡿⠁⠀⢀⣼⠿⢿⣦⣄⣠⣾⣷⡄⠀⢀⣴⡿⢠⡿⠁⠘⠢⡀⠀⠉⠉⠛⠛⠶⣤⣀⠀⢠⠎⠀⢀⡿⠁⠀⢀⣷⠉⢿⣜⣿⡄⠈⢿⣆⡀⣀⣿⠇⣸⡇⠀⢫⣾⠟ ⣿⣿⠁⠀⢀⣿⠃⣠⡾⠿⣥⣤⠆⠈⠉⠉⠁⠙⣻⡶⢿⡛⠀⠘⣷⡀⠀⠀⠙⠢⣄⠀⠀⠀⠀⣼⠟⣶⣾⣀⣤⣿⠃⠀⣰⠟⠁⣴⡾⠛⠛⢿⣦⡈⠙⠛⠛⠁⣠⡿⢁⣴⣟⠁⠀ ⡇⣿⣷⣶⣿⣿⠿⢿⣦⣤⣄⣀⠀⠀⠀⢀⣠⣾⢿⡇⠈⢠⡘⣦⠘⣿⠀⢠⡤⠤⠼⠗⠚⢁⣼⠃⠀⣀⣿⢹⡇⣿⡀⠀⠀⠀⡀⢿⡰⠞⠋⠉⠉⠻⠷⣶⣶⠾⣋⣴⡿⠋⠘⢧⣴ ⣧⡿⠀⠀⣤⣀⠀⠀⠀⠈⠉⢙⠛⠛⠛⠛⠋⣠⡿⠡⠞⢸⡇⠘⠃⣿⣇⣀⣀⣤⣤⠶⠶⠻⣷⠛⠋⠉⠁⠀⠻⣿⣧⢸⡀⢸⡁⠘⣷⣄⣀⣀⣤⣤⣶⢶⡿⠟⠋⠁⠀⣀⣴⠿⠁ ⡿⣷⡀⠀⠙⠛⢷⣦⣀⠀⠰⠃⠀⠀⠀⣀⣴⣿⣷⠀⠀⢸⡇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣟⣛⡟⠛⠷⣤⣿⡆⢇⠀⠳⠼⣮⠉⠉⠹⣷⡀⠀⠀⠻⡀⢀⣠⡾⠟⢁⡼⠀ ⣿⢻⣿⣶⣄⡀⠀⠈⢛⠻⠶⠶⠶⠶⠛⠛⣽⠏⠹⣇⠀⢸⡇⢀⣿⠁⠀⠀⠀⣀⡤⠤⠒⠚⠉⢉⣉⣹⣏⣙⠒⣮⡿⠁⢸⡇⠀⠀⢿⡀⠀⠀⢸⡻⢷⣦⠶⠾⢟⠉⠀⠀⠀⢉⣽ ⡇⢸⣯⠀⠙⠻⣶⣤⣼⣀⣀⣀⣀⣤⣴⡾⠋⡆⠀⣿⡄⣸⠇⣸⡇⢠⠤⠒⠋⣉⣤⠤⣒⣶⣭⡽⠿⢾⣯⣍⣿⠟⠀⢀⣼⠇⠀⠀⢸⡇⠀⠀⠀⢣⡈⢻⣦⡀⠈⠓⢀⣤⡾⠟⠁ ⣷⠈⠿⣦⣴⡶⠟⠉⣩⡍⠉⠉⠉⠉⠀⢠⠟⣧⢀⣿⠁⠻⠀⣿⠃⠠⢶⣚⣽⠷⠟⠋⠉⠀⠀⠀⢸⠀⠀⢹⡇⠰⠶⠋⠁⠀⠀⢀⡾⠁⠀⠀⠀⠈⣇⠀⠙⢿⡿⠟⠋⠉⠀⠀⠀ ⡿⣧⠀⠀⣆⠀⢀⣼⠟⠀⠀⣀⣴⠷⣰⢏⡼⢁⡜⠋⠀⠀⣸⠟⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⣸⡃⠀⠀⠀⠀⠀⠘⢦⣀⠈⢿⡄⠀⠀⠀⠀⠀ ⡇⢻⡇⠀⢻⣆⣛⣡⣤⡶⣿⡛⠡⠞⢁⡞⣤⡿⠃⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡟⠀⣀⣴⠟⠃⣀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠈⢣⡘⢿⡶⣶⣤⡀⠀ ⡇⢸⣧⣤⠀⠉⠛⣩⠟⠋⠉⠀⠀⢠⢞⣿⠏⠀⣀⣤⡾⣿⠃⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀⠀⠀⠉⠀⣠⡿⠁⣀⣉⣀⠀⢠⡟⢷⡄⠀⠀⠈⠻⣦⡀⠀⢠⠀⢱⠀⠀⠀⠙⣷⡄ ⡇⠀⢻⣮⡃⠀⠀⠙⠒⠒⠦⠤⠖⢠⣿⠃⠀⠊⢉⡞⠁⣿⠀⠀⢰⡞⠛⠋⠉⠉⠉⠀⠀⠉⢷⡄⢀⣴⣿⠑⠋⠉⢩⠏⣰⡟⠀⠀⠻⣦⡀⠀⠀⠈⠙⠓⠘⡆⠈⣷⠀⠀⠀⢸⣷ ⡇⠀⠀⠉⠻⢷⣦⣄⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⡶⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⠉⢻⣦⡀⠀⡇⣴⠟⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢱⡀⠘⡆⠀⢀⣾⠿ ⡇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠶⠶⠾⣿⠀⠀⠀⠧⠇⢸⡿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡀⠀⠙⣷⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⡀⠈⢁⣀⠸⡄⢸⣿⠀ ⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣿⠃⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢸⣇⠀⠀⢹⡇⠀⠙⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⣸⡉⢣⡀⠘⣿⠀

⠀⠀⠀⢀⡀⠀⢰⠀⠀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣶⣿⣟⢡⣀⠙⠻⣷⣦⣄⡘⢷⡀⠀⠀⠀⠀⠀ ⠉⠉⠉⠱⡇⠀⣸⠀⡼⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢰⣿⣿⣄⣿⡷⣤⠈⢿⣿⡉⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⡴⠁⣼⣧⠏⣠⠖⠁⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⣷⠟⢹⠀⠀⠉⢷⡌⠳⠄⠙⢿⡄⠘⣧⠀⠀⠀⠀ ⠀⠀⢀⣴⡟⠉⢩⣿⣏⣼⠋⢀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠘⡾⠁⠀⢸⠀⠀⠀⢸⣷⡀⠀⠀⠀⠹⣆⠹⣇⠀⠀⠀ ⠀⣰⠟⢸⡇⠀⣸⣿⡿⣡⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠃⠀⠀⠚⠀⠀⣠⡟⣿⣷⡀⠀⠀⠀⠈⢷⣻⡄⠀⠀ ⠾⢓⣲⡾⢶⣶⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣼⡟⣧⠸⣿⣷⣄⠀⠈⠑⠦⣻⣷⠀⠀ ⠚⠉⠁⣰⢟⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠈⢷⡀⠀⠀⠀⢀⠀⠀⠀⠀⢄⢀⠹⡄⠀⠀⣿⠀⠀⠀⣠⣾⢿⡇⢿⡆⢻⣿⣿⣷⣄⠀⠀⠀⠘⢧⠀ ⠀⠀⣴⡏⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⣡⠀⠀⠀⢿⣆⠀⠀⠀⠳⡄⠀⡀⠀⠈⢣⠹⡀⠀⢿⠀⠀⣾⣿⣿⢸⡇⢸⣿⣘⡏⣿⡝⣮⣳⡄⠀⠀⠀⢷ ⢀⡾⢃⣷⣼⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢳⠂⠀⠀⣼⡎⠳⣄⠀⠀⠙⠀⢻⣆⠀⠀⠀⢻⡀⠈⢇⣼⠃⠈⢻⣾⣷⣼⣿⣿⠀⣿⣧⠘⢿⣟⢧⠀⠀⠈ ⢿⣾⡟⢺⡟⠀⢠⠇⠀⠀⢠⠀⠀⠀⢠⡄⠀⢠⠉⡇⠀⠀⠀⠀⠀⠈⣟⠀⠀⠘⢷⠀⠙⢦⡀⠀⠀⠈⣏⢷⣄⠀⠀⢣⠀⠈⠁⠀⠀⠀⢻⣿⢿⣿⣽⣄⣿⣿⣇⠘⢿⣾⣆⠀⠀ ⢸⡿⠁⢸⠇⠀⡼⠀⠀⠀⡎⠀⠀⠀⣼⠁⠀⢸⠀⢻⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠸⣆⡀⠀⠱⣄⡤⣄⣸⡀⠻⣦⡀⠈⡆⠀⠀⠀⠀⠀⠀⢷⣾⠻⢿⣿⣿⡝⣿⡄⠈⡿⣿⣷⣀ ⣿⠇⠀⡟⠀⢰⠇⠀⠠⣸⠀⠀⠀⠀⣿⠀⠀⢸⠀⡌⣧⠀⠀⠀⣄⠀⠀⡇⠀⠀⠀⣏⠉⠉⠉⠙⣦⡀⠸⡇⠀⠘⢷⡄⢹⡀⠀⠀⠀⠀⡄⠈⣧⠀⠀⢻⡙⢷⡙⣿⡄⠳⢾⣸⣾ ⡟⠀⢸⠃⢀⡞⠀⢀⡇⡇⠀⠀⢸⠀⣿⡆⠀⣾⠲⠦⠼⣇⠀⠀⢻⡀⠀⢹⠀⠀⠀⢸⡄⠀⠀⠀⡈⢷⡄⣿⣴⣶⣿⣿⣜⡇⠀⠀⠀⠀⣷⠀⠘⣇⠀⠀⠱⡀⢳⡨⠟⢆⣘⣿⠿ ⡇⢀⡟⢀⡾⠀⢰⡾⠘⠀⠀⠀⢸⢰⠇⣧⠀⢸⠀⠀⠀⠘⣆⠀⠀⡇⠀⢸⣄⠀⠀⠈⣧⣠⠴⢋⣴⣾⣿⣿⡻⠍⠛⣿⣿⣿⠀⠀⢀⠀⢹⣆⠀⠘⣆⠀⠀⢱⡀⢷⡐⠛⢌⠈⢨ ⢡⡾⣡⢾⡇⠀⡞⡇⠀⠀⠀⠀⢸⣾⣀⢸⣆⢸⠀⠀⠀⠀⠘⣦⠀⢱⠀⢸⡟⣆⠀⠀⣿⢁⣴⣿⠿⠛⢉⠻⣷⡀⠀⢹⣿⣿⡆⠀⢻⡄⠈⣯⠳⣄⠹⡄⠀⠀⢣⠀⢳⣮⠚⢀⠀ ⡿⢚⡏⢸⡇⢰⠃⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣭⣙⠲⠦⡌⢧⡘⡆⢸⣿⠘⣇⠀⢸⣿⡟⢻⡒⢊⡽⠃⣿⡇⠀⠸⠿⠻⡇⠀⠈⢷⡀⠘⣆⠈⠛⢿⣦⣀⡀⣇⢀⠽⢧⡈⠓ ⡁⣸⠁⠘⣇⡼⠀⡇⠀⠐⠲⠶⢸⣿⠋⠙⣿⡟⠉⠛⠻⣿⣦⣄⡀⢻⣇⣾⠸⡆⠈⢧⣼⠈⣿⣄⠙⠚⠂⣴⣿⠁⠀⠀⠀⠀⣷⠀⢰⠀⢻⣦⣙⢧⡀⠀⠈⠉⠉⠉⠁⠀⠀⠙⢦ ⣧⡇⠀⠀⣿⡇⠀⡇⠀⢀⠀⠀⣼⣿⣆⠀⠘⣷⡠⡀⠞⢩⠛⣿⠁⠀⢹⣿⣄⢧⠀⠈⢿⡀⠈⠻⠷⣶⣿⠿⠁⠀⠀⠀⠀⢰⣿⠀⣼⠀⠈⣿⠻⠿⢿⢶⣢⣤⣀⡀⠀⠀⠀⠀⠈ ⡿⠉⠓⢤⣿⠁⢸⠃⢀⣾⠀⠀⡏⢿⡻⡆⠀⠙⣷⣍⠓⠾⢾⡟⠀⠀⣼⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡟⢀⡿⡆⠀⣏⠄⠠⠤⠤⠼⠯⠿⣿⡷⣄⡄⠀⠀ ⠁⠀⠀⠘⡏⠀⣸⣤⣾⣼⡇⢰⣇⠀⢳⡌⠀⠀⠀⠙⠻⠖⠋⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢸⠶⢿⡀⣿⣿⣿⣿⣿⣶⣶⣶⣦⠹⣾⣷⣄⠀ ⣄⠀⠀⠀⢱⣼⠟⣿⢡⣾⡇⢸⣿⡄⡈⣷⡀⠀⠀⠤⠤⠤⢖⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠁⢠⡏⣿⢸⡤⣿⣷⣹⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡄⠉⠛ ⡟⠀⣀⣠⣾⣿⠟⣷⢸⣿⡇⣸⣿⣷⣇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⣿⡇⢻⣼⣄⣽⢻⣯⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⡙⠲⢤ ⠾⢭⣩⣽⡿⡇⠀⣷⠸⣿⣷⣿⣿⣿⣿⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⣹⠇⠀⠀⢠⣾⡟⡿⣧⠘⡿⢷⡘⠷⣶⢿⡿⠿⡿⣯⣭⣤⣤⣴⠞⠈⠑⢦ ⣀⣞⢹⡏⢰⣣⠀⠹⢦⣿⣿⣭⠤⠖⢻⠀⡿⠻⣦⡀⠀⠁⠀⠀⠺⣷⢷⠒⠒⠚⢉⣭⠵⠚⣀⣤⢶⠋⠀⢀⣴⠟⣿⠀⣿⢹⡆⢱⡀⠑⠀⢸⣼⠃⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣨⠭⠇⠈⠻⡄⠀⠀⠘⣦⢸⡄⠀⢸⢰⡇⠀⢨⢯⣢⣄⡀⠀⠀⠀⠉⠉⠛⠋⠙⠒⠒⠋⠁⠀⡾⣠⣶⠟⠁⠀⣿⠀⣿⠈⣷⠀⢷⠀⠀⣸⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢀⠀⠀⠀⡟⠀⠀⠀⠹⣷⣷⡀⢸⡟⠀⠀⢸⠀⢹⣿⠉⢻⠷⠦⢤⣤⣀⡀⠀⠀⠀⠀⢀⣠⣼⣿⠋⠀⠀⠀⣿⠀⣿⠀⢹⡇⠘⣇⠀⡿⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠯⣧⣀⡀⡇⠀⠀⠀⠀⢹⣧⡑⠋⠀⠀⠀⢸⠀⢸⣿⠀⣼⢀⣾⢷⣏⣾⣿⣿⣶⠰⣾⣿⣿⣿⡟⠳⣦⣀⠀⣿⠀⡏⠀⠈⣿⠀⢸⡼⠁⣸⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀ ⠒⣄⢤⠀⠈⠓⣿⣷⣶⣤⣄⣬⣿⣷⣄⠀⠀⠀⢸⠀⢸⣿⠀⣿⡟⢁⣤⡜⢿⣾⣏⠳⣾⣿⣿⣿⢿⣦⣤⠀⠙⠻⡿⣺⠁⠀⢀⣼⣆⠀⢳⣀⠇⠀⠀⠀⣀⠔⠁⠀⣠⠄⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠔⡈⠆⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⣁⠚⠀⣠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢦⠀⠀⠀⠀ ⠀⠀⢀⢊⠔⠁⠀⣰⠃⠀⠀⠀⠐⠌⢆⢸⠈⢉⣐⣖⠓⠠⠶⢭⡆⠀⠀⠀ ⠀⠀⡞⠏⠀⠀⣰⣁⡸⡑⠀⠀⡄⡘⢹⠹⣞⠏⠓⠙⡇⠀⠹⡀⢸⠀⠀⠀ ⠀⠈⡏⠀⠀⡀⡇⢿⣷⠳⡀⠀⣏⣀⣨⢯⠛⠤⡠⠊⢃⠀⠀⢏⠹⠀⠀⠀ ⠀⠀⣠⠀⠀⠱⠧⠁⠀⠀⠈⠑⠓⡾⣿⣿⣧⠀⡄⠀⢸⡀⠀⢪⠢⡀⠀⠀ ⠀⠀⠙⡧⢀⢢⡇⠀⠀⠀⠀⠀⣠⣦⣌⣛⠇⠀⠘⠀⠈⠱⠀⢸⢽⠈⠁⠀ ⠀⠀⠀⢈⠎⠉⠱⠀⠀⠀⡀⠀⠈⠉⠙⡛⠀⠀⢠⠀⡆⠆⠑⡈⡌⠢⠀⠀ ⠀⠀⠠⢂⠀⡔⠀⠱⣀⡀⠋⠀⣀⡀⡔⠀⠀⠀⣸⠀⠇⡇⠀⡵⡘⢆⠀⠀ ⠀⢀⠔⠁⠜⠀⠀⣰⣿⣿⣿⣿⡠⠌⢀⠀⠀⢠⠁⡄⠰⢣⣰⠁⠇⠀⠐⠀ ⠀⠁⢀⠊⠀⠀⢠⣿⣿⣿⡿⠟⠂⠀⡌⠀⠠⢇⠀⠘⡄⢹⣟⠜⠂⠀⠀⠀ ⠀⠀⡎⡘⠀⠀⣾⣿⣿⣿⡦⠔⠒⠚⢠⠜⠑⢌⡄⠀⣀⠟⣁⠄⠀⠀⠀⠀ ⠀⢀⡆⢻⣀⠀⠻⣿⣿⡟⠢⡀⠉⠓⡎⠀⠀⠀⠳⠀⢰⣿⡄⠀⠀⠀⠀⣀ ⢠⢿⠈⣦⣽⣿⣿⢟⢿⠘⣄⠈⣣⠜⠁⠀⠀⠀⠀⢇⠈⣿⣷⣄⢡⠀⠀⣿ ⠀⢸⡀⢸⡏⠻⡟⡞⢸⠀⢀⢇⠀⠀⠀⠀⠀⢌⡀⠈⣦⣘⣿⣿⣼⠀⣠⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠤⢄⠀⠀⠀⠀⡠⢄⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⢸⠹⠄⠜⣀⣀⣀⣘⢄⣨⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠴⠚⡉⡁⢛⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡤⢶⡲⣞⡀⠀⠀⠀⠀ ⡀⣠⣶⣭⣌⠀⢈⣢⣺⣡⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⡇⣾⠿⢷⣽⡄⠀⠀⠀ ⣵⢱⠋⢹⣍⠎⢁⡴⢊⣎⢴⠦⣄⡀⠀⢸⠓⠦⠤⣀⣤⣿⡹⣄⣠⢿⣯⡦⣀⠀ ⣼⡞⠢⣾⠞⡔⣿⣤⡞⠈⢻⣙⣯⡚⠉⠉⠉⠑⠖⣞⠡⡟⢟⠳⡄⠀⣏⣇⣸⢱ ⣿⠁⢰⢃⣤⠛⠥⠼⢆⣠⠏⡏⠐⢌⠁⠒⣤⣠⢃⡜⢀⠍⣻⢧⡹⢤⠼⡸⣡⠟ ⣽⢒⡛⠛⠢⠤⠤⠴⡻⡈⡔⢽⣐⣒⣁⢴⠥⠜⠻⣇⡄⡜⣆⢉⣉⣒⡾⠟⢁⡶ ⡿⣤⡉⠓⡤⠥⠤⣺⢳⠀⡇⡜⠀⣀⠠⠌⣛⣹⡱⡾⢠⠁⢇⠉⠣⣤⠦⡖⠁⣣ ⡇⢧⠼⢓⠒⠒⠊⣵⣀⠇⢱⠃⣭⠶⠚⠋⠉⠉⣞⠤⠊⠀⡜⠀⠘⡈⢢⠔⠊⠁ ⢻⡈⠶⢯⡴⠊⢋⡧⠂⢀⡏⠉⠀⠀⠀⠀⠠⠀⡼⠠⠔⣀⠀⠢⡀⠈⠢⠳⠤⡀ ⡆⠫⣄⡑⠒⠐⢼⠁⢨⢹⠀⢰⠂⠉⠉⠑⣆⢼⡀⠩⡱⠁⠱⣄⠈⠃⢃⢃⠀⣹ ⠃⠀⠀⠉⠑⠒⢻⠀⢐⡸⠀⣇⠀⠀⠀⠀⡉⡄⢱⠘⠀⠀⠀⠈⠑⠂⠈⡤⡂⡇

⠀⠀⠀⠀⠀⠀⠀⡠⠊⣸⡄⡇⢠⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣂⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠜⠁⣰⣿⠀⢰⠀⢆⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢁⠔⠙⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⢀⣴⠏⡿⠈⡌⡆⠈⢆⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠹⡁⠀⠀⢱⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⢀⡠⠾⣧⠀⡇⠀⠇⢻⡀⠈⢣⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠈⠳⢄⠀⣀⣀⠷⠤⡀⣄⢧⠀⠀⠀⠀⠀ ⠀⣴⠟⠋⠁⠀⠀⢀⡇⡇⠀⢸⡸⡙⢄⠀⠱⣄⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠘⢦⡙⢅⡀⠀⠀⠘⡌⢞⡆⠀⠀⠀⠀ ⠹⠁⠀⠀⠀⠀⠀⡼⠀⣇⠀⡄⠃⢣⠈⠳⣄⠈⠣⡀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣕⣄⠀⠀⠙⠦⣉⡲⣄⣠⠇⠈⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠔⠋⠀⠀⢸⣇⢸⣷⡀⢣⣠⠎⠑⠢⢌⡙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠓⢤⡀⠀⠈⠙⢿⡻⡷⠶⠼⡇⠀⠀⠀ ⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⢿⡄⣻⣼⣾⡳⡀⠀⠀⠀⠀⠙⣟⠛⠻⢷⣤⢌⣢⣀⠀⠀⠀⠀⠙⠑⢄⣬⡉⡒⠤⠀⠉⠻⣄⡀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⣼⣠⠶⠏⠐⠈⢳⡈⢧⢹⡿⣿⢄⠀⠀⠀⠀⢾⣦⣀⠈⠙⠲⢤⣍⢳⣦⣄⡀⠀⠀⢈⠻⣿⣿⣙⠒⠦⢤⡤⠭⢷⣷⠀⠀ ⠈⢢⣄⡤⠞⠁⠀⢐⣰⣤⣤⣦⣿⣿⣧⡙⢌⣷⣅⠠⡀⠀⠈⢿⣯⠓⣤⣤⣬⣿⣿⣟⠦⣉⠢⡀⠈⠳⡿⢧⣈⡛⠒⠤⣧⠀⠻⣿⡀⠀ ⠀⢸⡏⠀⠀⢠⣶⠟⠉⠀⢠⣌⡉⠛⠗⠙⠦⡙⢮⡑⠮⣦⣄⣀⣻⡟⠁⠈⢳⢄⡈⠙⢷⣮⠙⠿⢷⠦⣝⣦⣧⠀⠀⠀⠈⢆⠀⢻⠣⠀ ⠀⠀⡇⠀⢠⡟⠁⠀⣤⣴⣿⣿⣿⠀⠀⠀⠀⠈⠓⠙⠢⢌⣙⠻⢍⣹⣶⣿⣿⣿⣷⠀⠀⠹⡆⠀⢸⠀⠈⢇⠈⡇⠀⠀⠀⠈⡄⠈⢆⠀ ⠀⠀⢳⠀⢹⠁⠀⠠⣿⣿⠟⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠛⠛⢿⠟⠀⠀⠀⠓⢀⣾⡶⠳⡌⡆⢡⠀⠀⠀⠀⣷⠀⠈⠈ ⠀⠀⠸⡄⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⡶⢉⣿⠤⢃⠘⣾⡈⡀⠀⠀⠀⢹⡆⠀⠰ ⠀⠀⢀⣷⠈⢡⡔⡫⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠛⢉⣨⡿⠗⣲⣯⣈⡀⢸⠀⢹⢣⠀⠀⠀⠀⠈⡇⠀⠀ ⣆⠒⠛⠿⣖⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠤⢄⡀⠀⠀⠀⠀⠠⠖⠉⠉⠀⠈⢡⠿⠿⢋⣡⣴⠃⠸⡇⠀⠀⠀⠀⡇⠀⠀ ⠹⡙⠢⠄⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⣿⣛⠋⡉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠴⠊⠁⢹⢸⣆⠀⡇⠀⠀⠀⠀⡇⠀⠀ ⠀⠻⢆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⢶⠤⠒⠉⠉⠉⠉⠙⠻⡆⠀⠀⠀⠀⢀⠆⣠⠏⢸⣄⠀⠀⠀⣿⠛⡄⣇⠀⠀⠀⣀⠃⠀⠀ ⠀⣤⡤⠽⠿⣶⣼⣦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠁⠀⢸⣿⠀⠀⠀⣿⠀⢹⣿⠀⠀⠀⣟⡀⠀⠀ ⠉⢻⠳⠆⣤⠴⢛⣿⠛⣶⣄⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⣠⣶⡟⠻⣦⡀⡞⢹⠀⠀⢠⣿⣦⡜⡁⠀⢠⣿⡿⠀⠀⡇ ⡀⠈⠙⠿⣷⣖⣻⣇⠀⠘⣿⠉⠓⢤⣀⠀⠈⢓⡤⢦⡤⢤⡴⢊⣠⡴⠚⠉⢨⠟⠀⠀⢹⣿⡧⣼⡀⠀⣾⣟⣿⣿⠃⣠⣿⡝⠁⢀⡜⠀ ⠛⠲⣦⠤⠴⠛⡏⠀⠀⠀⠈⠳⣄⠀⠙⢏⣷⡛⠊⠉⣳⠶⠿⣿⣾⣆⣀⠖⠁⠀⠀⠀⠈⣏⠀⠀⠉⠛⡿⣿⣱⠷⠚⠋⠛⠴⣤⡀⠀⠀ ⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⢰⣾⠏⡠⠊⠉⠙⣤⢄⠈⠻⡏⢳⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⠉⠓⢤⡀⠀⠑⠪⡙⠷⡆ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⣿⣻⠞⠁⣠⠼⠋⢠⠀⠑⡿⣜⣾⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠈⠓⠄ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠙⠙⠶⠋⠀⢀⡤⢾⣷⠤⢼⠎⠁⢳⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣀⡜⠁⠀⠀⠀⠀⢸⠳⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠈⢉⣉⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⡪⠐⣢⠔⠊⠀⡁⠀⠤⠙⠬⡉⠉⠲⢦⣀⠀⠀⠀⠳⡄⠀⠀⠀ ⠀⠀⠀⢠⠋⢁⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢙⣄⠀⠀⠀⢹⡆⠀⠀ ⠀⠀⢰⣙⡖⠁⠀⠤⣀⢠⠓⣄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡈⠈⢢⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⢴⠄⠀⠀⢶⠮⠀⠀⠀⢳⡄⢂⢄⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠸⡀⠀ ⠀⠀⠀⡌⠀⢠⠄⣺⡆⠀⠀⠀⠀⠈⠑⢵⡢⢄⠀⠐⣄⠀⠀⠘⢧⠀⠀⠈⠇⠀ ⠀⢀⢌⡔⠀⠌⣠⠋⠀⠀⠀⠀⠀⢠⠎⢉⠽⣖⠙⢦⣬⣷⣄⡀⠘⡇⠀⠀⢸⠀ ⠐⠃⠁⡟⠌⡰⢻⡏⠉⣲⡀⠀⠀⠈⡄⢘⣗⣸⣆⣀⣹⡿⣧⢱⣄⡇⠀⠀⠀⠇ ⠀⠀⠀⡇⣴⡇⠘⣧⠘⣄⣹⡀⠰⡖⠙⠍⡠⢞⡠⠟⠀⡇⢿⣜⠇⠓⠀⠀⢀⠀ ⠀⠀⠀⠈⠇⢣⢰⠊⠛⠤⠝⣹⡄⠕⠒⠒⠊⡙⠀⠀⠀⣩⣍⡄⠀⠀⠀⠀⢾⠀ ⠀⠀⠀⠀⠀⠀⢻⠓⠒⠒⠉⠀⡀⠀⢀⠤⠊⠀⠀⠀⢀⡼⠈⡗⡀⠀⠀⡘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡤⢫⡷⠀⠈⠘⡀⠰⡙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢀⣀⣀⣀⣀⣤⡖⠁⢰⠟⣷⡀⠀⢀⣱⡗⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠩⢯⡿⠂⢠⠗⠀⣡⠓⠤⣸⡔⠁⠈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁⠀⠀⠀⠀⠉⠀⠀⠘⡛⠂⠁⠀⠀

⠀⠀⠀⠘⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⡄⢸⠀⠀⢢⠀⠉⠻⣧⠀⣿⣿ ⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⠔⠂⢀⠀⠀⠀⠀⢀⠔⠀⠀⠀⡴⡇⠀⠀⠀⢰⠁⡸⠀⠀⠐⣧⠀⠀⠘⢧⣿⣿ ⣷⡀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢠⠎⠀⠀⠀⢀⠔⠁⢀⠔⠁⠀⠀⢀⠴⠃⠀⠀⢀⡞⠀⠁⠀⠀⢠⠃⠀⡇⠘⡆⠀⠙⣧⠀⠀⠀⢻⣿ ⡿⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⡴⠁⠀⠀⢀⠔⠁⠀⡴⠁⠀⢀⣤⠞⠁⠀⠀⢀⡴⠛⠁⢰⠁⠀⢀⠎⠀⣸⠇⠀⢣⠀⠀⠘⡆⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡜⠁⠀⠀⡠⠋⠀⢀⠎⣠⠴⢊⠝⠁⠀⠀⠀⣴⠋⠀⠀⠄⡎⠀⠀⡜⠀⢠⠇⢤⠀⠈⡆⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡔⠁⠀⣰⣿⣿⣤⠔⠁⠀⠀⢀⡴⠊⠉⠛⠉⠁⢰⠀⠀⡰⠁⢀⡞⠀⢸⡀⠀⠸⡀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠞⠀⠀⣼⠋⢹⠟⠁⠀⠀⢀⣴⣏⠀⠀⠀⠀⠀⠀⡎⠀⣰⠁⠀⡜⠀⠛⠙⡇⠀⠀⠃⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠎⢀⠆⠀⢠⠎⠀⠀⡾⣿⠞⠁⠀⠀⢀⣴⣿⣿⣿⡙⢦⡀⠀⠀⠰⠀⡰⠁⠀⡜⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⣠⠎⢠⢦⠃⠀⠀⣼⡔⠁⠀⠀⣠⠞⠉⡏⠹⣙⣿⣿⡍⠻⠀⢠⠃⡰⠁⠀⡰⠁⠀⠀⠀⢀⣘⣇⠀⠀⡇⠀⠀⠀⠀⠀ ⡀⠔⠉⢀⡠⢾⡟⢀⡿⠃⠀⠀⡼⠋⠀⢀⡴⡊⠀⠀⠀⠙⠦⠤⠾⠻⠗⠀⢠⢇⡜⠀⠀⡴⠁⠀⠀⠀⠀⠀⠈⣿⣄⠀⢣⠀⡆⠀⠀⠀ ⡰⠂⠋⠛⠀⢸⢁⠜⠀⢀⡜⣸⢋⣠⣾⣯⡟⠉⠑⠦⢄⣀⡀⠀⡀⠀⠀⢠⠓⠋⠀⢀⡞⠀⠀⠀⢀⡀⠀⠀⠀⠈⢽⣇⢸⣤⠁⠀⠀⠀ ⠁⠊⠀⠀⠀⡾⠊⠀⡠⠊⢠⣷⠋⣿⡏⠁⠑⢶⡄⢀⠲⡀⠉⠑⣟⢄⣰⠃⠀⠀⣰⠟⠀⠀⠀⣀⣀⣉⣉⣒⠢⣀⠀⢣⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢁⡠⠊⠀⠀⡘⠨⠛⠁⠙⢧⠲⡷⣵⣤⡱⣌⢞⠀⡸⡼⠁⠀⣠⣞⠁⠀⡄⠀⠘⡟⡿⢿⣿⣿⣿⣿⣥⠄⣧⡟⠀⠀⠀⠀ ⠖⠶⠏⣴⡞⠉⡇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠋⣱⠋⠀⢀⣼⣿⢻⣦⡄⠻⣆⠀⠹⢿⠿⠟⠁⠀⠹⣿⣶⣿⠃⠀⠀⠀⠀ ⢇⠀⠀⢸⠇⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣠⠾⠟⠹⡴⣵⣝⣿⣷⣿⠳⡀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀ ⠈⣧⡀⢹⠀⢰⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣥⡖⠉⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡘⢶⡤⠤⡤⠞⣹⣿⣿⠇⠀⠀⠀⠠⠀ ⢀⡿⠉⡿⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠴⠟⣻⣅⡀⠈⠓⠢⠤⣀⡀⠀⠀⠀⠀⠙⢝⠿⣿⣦⠙⢶⠂⣰⣿⡿⢻⠀⠀⠀⠀⠀⠀ ⣼⠃⢀⠇⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⠒⠉⠀⠀⢰⣿⣳⢛⠋⠉⠛⠒⣦⣉⠓⣄⠀⠀⠀⠀⠀⠛⢿⣷⡄⠀⣿⡿⠁⡆⠀⠀⠀⠀⠀⠀ ⠋⠀⡼⠀⢠⣿⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣄⣠⡿⡽⠭⠤⠬⢧⣈⣆⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⠃⢰⠁⢠⠀⠀⠀⠀⠀ ⠀⣰⡇⠀⣼⣥⡇⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠀⠉⢻⡿⣏⣑⣺⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⡎⠀⡈⠀⠀⠀⠀⠀ ⠔⠉⠀⢰⠏⠀⢣⠀⠀⣿⣿⣦⡀⠀⠀⣀⡴⠟⠉⢹⡀⠀⠀⢸⠇⠀⠘⣿⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢠⠃⠀⠃⠀⠀⠀⠀⠀ ⠠⠀⢀⠏⠀⠀⢸⠀⠀⡏⠉⠛⠻⣶⡞⠋⠀⠀⠀⠀⡇⠀⠀⠊⠀⠀⢰⡋⢷⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⠃⠀⡼⠀⢀⠀⠀⠀⠀⠀⠀ ⠂⠀⠈⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⣯⣵⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⡣⠠⡀⢆⠀⠀⠀⠀⢀⣴⢟⠇⡌⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⢠⠀⠀⠀⠀⢻⡇⠻⣷⣄⡀⣠⣧⣄⣀⣤⢾⠏⠀⠀⢉⣸⣀⣠⡤⣶⡟⡹⡺⢰⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⠈⢹⣿⣯⣀⣠⣔⣑⡥⠔⠒⠊⠉⠁⠀⢠⠁⢹⡟⢳⡇⡜⠀⠸⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠾⠯⠭⠤⠤⠤⣄⣀⣀⣠⣾⣿⣿⣷⠶⣬⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠞⣿⠿⠿⣶⣀⠀⠀⠀⠀⠀⣸⣿⣯⡿⣟⣿⣿⡌⢿⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⡵⣿⠃⠀⠀⠘⣿⡄⠀⠀⠀⢠⡟⣯⡷⠋⠙⠳⢬⣿⣬⣷⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣴⣿⠞⠁⠀⠀⠀⠀⠸⣷⡀⠀⠀⠼⠀⠿⠁⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⢳⡻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠋⢰⣶⡟⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠖⢻⠷⣦⣄⡻⢿⢦⡀⠳⡘⡇⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⢿⡆⠀⠀⠉⣠⠞⠋⠁⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠁⠀⠀⠀⠈⠻⠿⠛⣷⡄⠀⠀⠀⠹⡿⠋⠈⢳⡀⠀⠀ ⠀⠀⣰⠋⠀⠀⠇⠀⢀⠞⠁⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠁⠀⣇⠈⣧⠀⠀ ⠀⢠⠇⢀⡏⠀⠀⢀⡎⣀⡤⠶⠒⠒⠒⠲⠶⢬⣷⡀⠀⠀⠀⠀⠀⢀⡿⠒⠛⠉⣉⣉⣉⠉⠉⠛⠒⠶⣾⣇⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀ ⠀⣼⠀⢸⠁⠀⠀⣼⠟⠁⠀⠤⠴⠒⠒⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠀⠀⠀⠙⠆⠀⠀⠀⠀⢸⠀⢸⡄⠀ ⢠⡟⠀⡏⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⣀⡀⠀⠀⠀⠀⢀⡤⢀⡠⠆⠀⠀⠀⠀⠀⡞⠀⢸⡇⠀ ⣾⡇⠀⡇⠀⠀⠀⠈⠛⠿⠷⠶⠶⠾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⣄⡇⠀ ⡟⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢸⣼⠀ ⡇⡇⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠈⣿⠀ ⣧⡇⠀⠀⠨⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠟⠛⠛⠓⠦⠀⠀⠀⠀⠀⣿⠀ ⣿⡇⠀⠀⠀⣠⣴⠿⠷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⠶⠞⠛⠉⣹⠏⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⣿⢇⠀⠀⠀⠁⠀⠀⠀⠻⣄⣀⣀⠞⠛⢿⠉⠉⠙⢻⠋⠉⠉⠉⣹⠟⠉⠁⠈⠉⠓⢦⠤⠤⠞⠋⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢻⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠈⡷⠤⡴⠿⢦⣤⡴⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⡌⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡞⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⣇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠸⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠹⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁ ⠀⠀⠀⠸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠀⣧⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⢸⡄⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀

⠀⠀⠀⣸⡟⢿⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⡀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣷⣆⢿⣿⣿⣿ ⠀⠀⠀⣿⠁⠀⢻⡀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠛⢷⡀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣿⣿⣿ ⠀⠀⣸⠁⠀⠀⠀⠻⡀⢹⣷⣄⡀⠀⠀⠀⠀⡀⢹⡆⠀⠀⠉⠛⠶⢄⣠⣤⣀⣀⡀⣀⣀⣀⣀⠈⠛⢿⣶⣄⡀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢿⣿⡿⠏⠁⠀⣹⣿ ⠀⣰⡏⠀⠀⠀⠀⠀⢳⡘⣿⣿⣿⣷⣶⣤⣄⣳⣄⢱⡀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⢳⣤⣄⣀⣀⡀⣮⣿⣦⡀⠀⣤⠻⣄⢀⣴⠏⠁⠈ ⣰⣿⠀⠀⠀⠀⠀⠀⠀⢳⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡀⠀⠀⠀⠀⠀⠀⢤⣀⣈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣾⣻⣇⣡⠔⠂ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⢿⣄⠀⣠ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣽⣻⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢣⣽⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣉⣀⣀⣀⣀⡀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣦⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿ ⣿⡇⠀⠀⣀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠿⠛⠛⠒⠛⠿⠿⢷⣶⣦⡙⠻⣿⣿⢿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻ ⣿⡧⠴⠋⠁⠀⠀⠀⠀⣀⣤⢤⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠒⠋⠁⠀⠀⣠⣶⠿⠓⠛⠶⣤⡀⠀⠙⢿⡳⣿⣿⣷⡙⣿⣿⡆⠻⢿⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⣀⣠⡤⢶⣆⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣻⠁⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⢸⣿⣿⣿⣮⣻⣿⠦⣄⡙⢷⣮⣿⡿⣿⣿⣿ ⣿⡇⠀⠀⣄⣤⣶⣿⡿⠟⠛⠉⠛⠋⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣏⢠⡤⠀⣧⠖⣀⠀⢹⡇⠀⠀⠈⣿⣿⣿⣿⣿⡿⣴⠋⠉⠳⣽⣿⣿⣿⣿⣿ ⣿⣇⢀⣴⡿⠿⠋⣀⠀⡒⠚⢓⢶⣄⠀⠀⠀⠀⠀⠀⠈⠻⣮⡻⢾⣿⣿⢿⣿⣧⡀⠀⠀⠀⠀⢿⠇⠸⠷⣿⡿⠋⡿⠋⠙⠃⠀⠀⠀⣿⡇⠘⣿⣿⢠⡿⣄⠀⠀⠈⣯⢿⣿⣿⣿ ⣿⣿⣿⠋⠀⠀⠘⢻⠄⣁⣤⠤⠄⢻⣧⡀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠙⢿⣄⢹⣿⣷⡄⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠳⢤⠀⠀⠀⠀⠀⡟⠃⠀⠙⣿⡜⡇⠘⡏⠐⠊⠉⠈⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⣼⡿⠠⣯⣠⣞⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠈⠻⣧⡘⣿⣦⠀⠀⠀⢈⣿⣿⣿⣿⣶⡿⠿⢠⠜⢀⡄⢠⣿⠀⠀⠀⢻⡇⠀⠀⣷⠈⠉⢓⠀⣿⣿⣿ ⡿⢻⣷⠀⠀⠀⢻⣿⠀⠘⠛⠛⠁⠅⢀⡀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣴⡏⠉⠳⣄⠀⠀⠀⠀⠀⠞⢠⣞⠞⠁⣿⡇⠀⠀⠈⢳⡀⠀⠘⡆⡠⠏⢠⣟⢿⡻ ⡀⠀⢻⣦⣤⡀⠈⠛⠂⠀⠀⣀⣤⣶⡿⠃⠀⠀⡀⢠⠖⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⡒⠒⠊⠳⣄⠀⠀⠀⢰⢫⠏⠀⢰⡏⣿⡄⠀⠀⠈⢧⠀⠀⢻⡁⢀⣿⣿⣦⡙ ⣿⡀⢻⣿⠘⣟⣆⠀⠀⠚⣿⠟⠋⠁⠀⠀⡠⢏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠘⠀⣿⣿⡀⠀⠀⠘⡇⠀⠈⢷⣾⣿⣿⣿⣿ ⠻⣿⣾⡇⠀⡏⠉⠳⡄⠀⠀⠀⠀⠀⡠⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⣿⠀⠀⢸⡟⣿⣿⣿⣿ ⣇⢹⡙⡇⠀⣇⢠⠁⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠈⢧⡀⠀⢸⣿⠇⢻⠀⠀⠀⠘⡄⠀⠀⣧⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⢻⠀⠀⠘⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠳⢄⣀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠙⢦⣸⠏⠀⠘⡇⠀⠀⠀⢻⡀⠀⢸⣿⣿⣿⣿ ⣿⡿⣿⠀⠀⢸⡄⠀⠀⡇⠉⠙⠳⠶⢤⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣦⣀⣀⠈⠉⠓⠦⣄⠀⠀⠀⢣⡀⠀⠀⠀⠻⣄⠀⣰⣿⠀⠀⠀⠀⢧⠀⠀⢿⣿⣿⣿ ⠟⢁⡏⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠁⢹⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠁⠀⠈⠳⣤⡀⠀⠀⠀⠈⠱⣄⠀⠈⢧⡀⠀⠀⠀⠈⠻⣿⣿⣤⠀⠀⠀⠘⢧⠀⠘⣿⣿⣿ ⠀⣼⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠁⠀⠀⣸⠃⠴⢻⠇⣰⣶⡶⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠓⣄⡈⢳⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⣿⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⡰⠃⠀⢀⡟⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡀⠀⠀⠀⠀⠙⢮⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠻⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⡼⠃⠀⢀⡾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠹⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⣆⠀⣾⠁⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠚⠉⠁⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠃⠀⠀⠀⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⢸⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡿⠛⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠓⠶⢤⣀⣀⣀⣠⡴⢟⣹⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠉⢉⣁⣶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠦⣀⣀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣤⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⡿⢀⣿⣿⠿⣿⣿⠟⠁⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠿⠼⠗⠚⠁⠀⣼⡟⠁⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡁⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢠⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣒⣛⠓⠒⠒⠠⣴⢿⣿⣖⢯⠲⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢋⡾⡞⠀⠘⣧⠀⠀⡸⢿⠟⠛⠭⢮⣆⠀⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⢀⡾⠋⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⣿⣄⠀⠀⠀⠀ ⠀⠀⢠⣞⠃⠺⢋⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⡠⠒⠋⢿⣶⣝⠓⠌⢾⡤⢤⠀⠀ ⠀⠰⢁⠸⠀⡔⠁⠀⠀⠉⢳⠀⠀⠀⠀⢀⣎⣀⣀⣀⣀⡀⠘⡆⠀⠀⠀⡆⠃⠀ ⢀⠇⡎⠀⣰⠖⠉⠩⠭⠉⠙⡇⠀⠀⠀⠘⠁⠀⠐⠒⠠⠄⠉⠛⠀⠀⠀⠀⢸⠀ ⣸⠀⠁⠀⠣⣤⣀⣀⣤⡤⠎⠀⠀⠀⠀⠀⠢⠤⣤⣤⣤⣤⠤⠂⠀⠀⢀⠃⢸⠀ ⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢨⡆ ⣿⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠿⠄⠀⠀⠘⡇ ⣿⠀⠀⠐⠛⢳⠒⠠⡤⡤⠤⢤⠤⠤⢤⡤⠖⠶⢖⠊⣉⠟⠉⢆⠀⠀⠀⠀⠀⡇ ⠏⡆⠀⠀⠀⠀⡹⠋⠀⡱⠠⠜⢤⠔⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢰⢱⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁ ⠀⠀⢸⡈⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀

⠀⠀⠀⣾⣷⣾⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⣾⣿⢃⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣿⡿⣿⣆⠀⣿⣿⠁⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣧⠘⢿⠟⠛⠈⢻⣆⢸⡏⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠟⣿⣿⡿⠀⢸⠛⢹⣟⣿⠇⣸⣿⡇⢿⣿⣿⣿⣿⣿⡇⢻⠉⢿⣇⠈⢇⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⠋⣼⠃⡰⠛⠉⠛⠋⢠⢫⣿⡇⠀⠀⠀⠞⡸⠉⡞⢻⣿⠇⢸⡟⣿⣿⣿⠇⢿⠀⣇⠀⠙⢆⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⡂⠀⡏⡏⠃⢠⠇⣰⠁⠀⠀⠀⠀⠁⢸⣿⡇⡆⠀⠀⡰⢁⣄⡇⠀⡿⠀⠀⡇⠹⠇⠫⠁⢈⠄⣿⣆⢠⠀⢰⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀ ⡇⠀⢀⣄⡀⡼⢀⡇⢀⣄⣼⢠⢀⢀⣿⣿⣇⣇⡀⢠⣇⣾⣿⣇⢰⠃⣀⠀⠀⠀⠀⠀⠀⣸⣆⣿⣿⣮⣧⠈⡆⢰⣤⣼⠁⠀⠀⠀⠀⠀ ⡇⠀⡃⣶⠈⡇⣿⣿⣼⣿⣿⣸⣼⣼⢻⣿⣿⣿⣿⣾⣿⣿⡟⣿⠊⣼⣿⣀⢠⣤⡀⠀⢠⣿⣿⣿⠘⣿⣿⣄⣷⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⡇⠀⣷⠁⢸⣱⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣇⣿⣿⣿⣿⣿⠃⣿⣴⣿⣿⣿⣾⣿⡇⢠⣿⡿⣿⣿⠀⣿⣿⣿⣿⣸⣿⣿⠀⠀⠀⠀⠀⠀ ⠇⠀⢻⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⡏⠹⣿⣿⡇⣿⠀⣿⣿⢻⣿⣿⣿⣿⣣⣿⣿⠃⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⣸⢸⣧⡈⡆⣿⣿⣿⣿⣿⣿⣯⡀⠀⠸⡇⠀⠹⣿⡟⠻⠦⣿⣟⣿⣿⣿⣿⣿⣿⣿⣇⡠⡿⠛⠊⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣼⣿⣾⣧⠙⡆⣼⣿⣿⣿⣿⣿⣷⣾⣶⣦⣥⣄⣂⠻⠧⠀⠀⢸⠏⣿⣿⣿⣿⣿⣿⠟⠀⡠⠥⠔⣒⣸⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣆⢣⢿⣿⣿⣿⣿⡛⢷⣼⣿⣿⡟⠛⠿⠛⠳⣆⠸⢰⣿⣿⣿⠟⣩⠏⣀⣵⣶⡿⠟⠛⢛⣿⣿⣿⣿⡟⢸⡄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠿⡜⣎⢿⣿⣿⣿⣷⡈⠿⢅⠈⠁⣀⠖⠀⣀⣈⣀⡾⠟⠋⠁⠈⢡⣾⠟⠁⠙⡒⠀⣤⡎⢸⣿⣿⡟⣠⣸⡇⠀⠀⠀⠀⠀ ⣿⣿⠟⠋⠁⠀⢱⣹⣮⡻⣿⣿⣿⣷⣄⠀⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠦⣴⠯⠔⠚⠉⢀⣿⣿⣿⣶⡟⣻⣿⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⢻⣿⠙⣿⡙⠻⣿⣿⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⣿⠋⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠘⣷⡀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⣿⣿⣿⡏⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⡝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⣿⡏⢺⡇⠀⡆⢸⠀⠀⠸⣇⠀⠀⠀ ⠈⢳⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⢆⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⢸⣇⠀⣿⠘⠹⣦⠀⢹⡄⠀⠀ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⢦⢻⡳⣤⠀⠀⠀⠀⠀⠀⠀⣐⡒⠒⠂⠀⢀⣤⠞⠉⠀⢿⣿⣿⣌⣿⢠⣿⠀⡀⢿⡆⠀⢻⡀⠀ ⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⡇⠀⠀⢂⠀⠹⣷⡙⢷⣦⣀⠀⠀⠀⢸⠉⣿⣤⢤⡖⠋⠀⠀⠀⠀⠈⣿⣿⢿⣿⢸⣿⡀⢿⣾⣧⠀⠀⢻⡄ ⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢸⡀⠀⠈⢢⠀⠀⣨⠟⠉⠙⣷⣦⣤⣾⠞⣱⣿⣯⡀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣿⣿⣿⡇⠀⢻⣄⠀⠀⠀⠻ ⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⣷⢦⣤⣀⣲⠈⠁⠀⠀⣀⣼⣿⡟⢁⠜⢀⡇⠘⢷⣄⠀⠀⠀⠀⠀⡰⢿⣿⣿⣿⣿⣧⡀⠀⣿⣦⡔⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⡄⠈⠉⠛⠳⠦⢤⣈⣤⡟⡝⢠⠋⠀⡞⠁⡄⠀⠹⣦⠀⠀⢀⡞⣱⢻⣿⣿⡿⣿⡿⡇⠀⡄⢿⡄⠘⠢ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡞⡞⢀⠃⠀⡼⡐⠀⠀⢀⠀⢸⣷⡴⢋⡼⠁⣸⣿⣿⣿⣿⣿⠀⠀⠁⠘⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠜⡰⠁⡜⠀⣰⠇⢠⠎⠀⠀⠀⣾⣿⡵⠋⢀⡴⣿⣿⡿⣸⣿⡟⠀⠀⢀⠀⠘⡆⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠴⠶⠶⠶⠦⠤⠤⠤⠤⢤⣤⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⢤⠄⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠠⠴⠚⣻⠧⠤⠤⠤⠤⠴⠚⢋⣩⠷⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣤⠶⠒⠚⠉⠉⠀⠀⠀⣸⣋⣻⣿⣿⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⣤⡤⣤⣤⣔⣂⠀⠀⠀⠀⣤⢤⠘⠳⣖⢮⣀⡉⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠾⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣿⡿⠿⠿⡇⠀⡄⣠⣙⣂⣀⣺⣣⣴⣷⠏⠧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⣤⠞⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠘⠁⠙⡟⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣄⣀⣤⡴⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⠘⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣴⠟⢻⣴⠟⢻⣆⠈⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠞⠉⣇⡞⠁⢀⡿⠁⢠⠟⢹⡇⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⡞⠀⢀⡞⢠⣿⡆⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⡀⣀⣀⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠏⠀⢠⠋⣀⣾⣼⠃⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀ ⠸⡆⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢻⡄⠀⢀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⣷⢞⣍⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣤⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠈⢿⣀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀ ⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⢀⣠⣤⠶⠒⠒⠒⠒⠒⠒⠒⠒⣶⣶⡶⠤⠤⠴⠖⠒⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⢲⡿⠶⠒⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣇⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣾⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⢿⣷⠀⠸⡄⠀⠀⠀⠀⢀⡞⠀⠀⣾⡟⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡆⠀⠉⠀⠀⠀⠀⠈⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠆⠀ ⠀⠈⠉⠛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⡶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⠤⣴⣴⠾⠿⠧⢤⡙⠟⠙⢧⡀⠀⠀⠀⢠⠞⠀⣿⣿⠿⠿⠿⠶⢖⣒⡛⠋⠀⠀⠀⠀⠀⠀⡀⠀ ⡀⠀⠀⠀⠀⠀⠘⢄⠀⡴⠋⢱⣶⠀⢀⣤⣾⠏⠀⠀⠀⠑⠀⠀⠀⣏⠀⠀⢫⡀⠀⠰⡿⠆⠀⠀⠈⢳⠖⠀⠀⠀⠀⠀⠣⠀ ⠀⠀⠀⡘⠲⣤⠀⠀⢻⢤⣤⡤⠶⠞⢛⣥⠏⢠⠖⠒⠦⠀⠀⠀⠀⢻⡤⢤⡈⢯⡻⢶⣦⡤⠤⠤⠒⡏⠀⣠⠔⡂⠀⠀⠀⠀ ⡄⠀⠀⠙⠂⠈⠁⠀⠨⠤⠤⠤⢴⡺⠟⠁⠀⢸⠀⣠⣤⣦⡀⠀⠀⠘⣧⠀⣷⣀⠙⠶⢄⣉⡉⠉⠁⠀⠘⠁⠚⠁⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⢡⣄⠠⣤⠀⠀⣀⣉⣿⣭⣳⡀⠀⠀⢸⣄⣀⠈⠛⠀⢶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⠄⠀⠈⣀⣤⠶⢾⣟⠉⠁⢹⣿⠿⠶⣦⣤⡿⠛⠻⣶⣤⣤⣀⡀⠙⠒⣶⡄⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⠀⠑⢀⣠⡾⠿⢿⣧⣀⣼⣿⣷⣶⣿⣿⣿⣶⣿⣿⣷⣶⣾⣿⣇⡀⢸⣿⠿⢷⣤⣉⠀⠈⢻⣧⠄⠀⠀ ⠀⠀⠀⠀⣀⡤⠞⠈⣠⡶⠿⢿⣤⣠⣾⡟⠛⢻⣿⣁⣨⣿⣏⣀⣹⣿⣯⣉⣹⣿⡟⠙⢿⣿⢿⣦⡤⢼⣿⣷⡀⠀⠈⣷⠀⠀ ⠀⠀⣶⡶⠉⠀⢠⣾⣿⣀⣠⣿⣟⢉⣽⡷⠖⠛⠛⠉⠉⠉⠀⠀⠀⠈⠈⠉⠉⠉⠙⠛⠛⠷⠼⣿⣧⣴⣿⣿⡇⠀⠀⣸⡆⠀ ⠀⠀⣸⠁⠀⠀⣿⣿⣯⣤⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠀⢀⣠⡿⠀⠀ ⠀⠀⢻⠀⠀⠀⢿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠛⠓⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡄⠀ ⠀⣆⠘⢷⣄⡀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠠⠤⠞⠋⠀⠀ ⠀⠈⠉⠀⠉⠛⠛⠉⠀⢀⣠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠘⠦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⣛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⢇⡘⠷⠀⠀⠀⢀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⣤⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠟⠛⢉⠀⠀⠀⠀⣀⠀⠀⢀⣠⠔⠀ ⠀⠀⠰⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⡤⠴⠒⠚⠁⠀⠀⣀⣀⡭⠔⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⠒⠶⠀⠀⠒⠀⠀⢠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⣠⣾⠿⠿⠛⠛⠛⠿⠿⠿⠿⣶⣦⣄⣀⣤⣤⣤⣦⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⢇⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡏⠉⠉⠉⠙⠛⠛⠻⠿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⠁⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⢿⡀⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡸⣧⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣷⠹⣦⠀⠀⠀⠀⠀⣀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢿⣷⡘⢷⣄⠀⠀⠫⣍⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠈⠙⠂⠙⠳⢤⣀⣨⠆⠀⠀⢀⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣤⡀⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠉⠛⠿⣷⣦⠀ ⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⣿⠀⠀⠀⢈⣿⠇ ⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣷⣆⠀⠈⣿⡆⠀⠀⣼⡟⠀ ⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠀⢀⣤⣶⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⣿⡇⠀⣿⡇⢀⣾⡟⠀⠀ ⠀⠀⠀⢿⣿⣤⣤⣤⣤⣄⠀⠚⠛⠻⠷⢦⣄⠀⢀⣿⠋⠀⠀⠀⠉⢿⣧⠀⠀⢠⡴⠒⠤⢤⡀⠀⠀⠀⠀⠀⣽⡇⠀⣿⣧⡾⠋⠀⠀⠀ ⠀⠀⢀⣾⣿⠟⠋⠉⠛⢿⣷⣤⣤⣀⡀⠀⠀⠀⠘⣿⡀⠀⢻⡄⠀⠀⢻⣇⠀⠈⢻⣆⣠⣴⠟⠀⠀⠀⠀⠀⠉⠀⢰⣿⠋⠀⠀⠀⠀⠀ ⠀⢠⣿⠟⠁⠀⠀⠀⠀⠘⣿⣿⠛⠻⠿⣷⣦⡀⠀⠙⢷⣤⡈⢷⡄⠀⠀⠻⡄⢀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀ ⠀⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠈⠙⢿⣦⡀⠀⠉⠛⠻⠿⠷⣶⣶⡿⠟⢻⡇⠀⠀⣀⡞⠀⠀⠀⠀⢤⣾⡿⠶⠤⠀⠀⠀⠀⠀ ⢰⣿⠁⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⢤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡄⠀⠀⠀⠠⢾⣿⣁⠀⢀⣠⣴⡆⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⠟⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⠀⠀⠀⠀⠈⠙⠻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠈⢿⠒⠤⠤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠾⠛⢿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⢿⣦⣀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠛⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣦⣤⣶⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣀⣀⣀⠀⠀⠀⠐⡆⠸⠀⠀⠀⠀⡜⠀⣴⠀⠀⢀⣀⣀⣤⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⡀⠁⠀⠀⠐⠀⣼⣧⣴⣾⣿⣿⣿⣿⣿⡤⠀ ⠈⠉⠉⢛⣛⣛⣛⣿⣿⢿⡷⡄⠀⠀⢀⡜⣿⣿⣿⣛⣛⡩⠉⠁⠀⠀⠀ ⠀⠀⠀⠢⣠⠚⠭⣀⣤⡟⠀⠈⠂⠀⢌⠀⢯⣀⠰⠀⠉⢰⠀⠀⠀⠐⠀ ⠀⠪⠑⠀⠋⠘⣩⡵⠊⢰⢉⣁⡀⠀⠸⡉⡎⠪⠙⡋⠉⠉⠐⠩⠀⠀⠄ ⠀⠀⠀⠀⠀⢉⠁⠆⢒⣀⡤⠿⣾⣄⣀⣧⣤⣉⡐⠀⢤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠘⣀⡴⠚⣯⣸⣷⢶⣿⢶⣿⣷⣶⣿⣉⣻⡖⢮⣁⠁⢦⡄⠀ ⣠⡔⠊⣡⣞⣉⣷⢺⡯⠼⠗⠚⠓⠒⠛⠒⠚⠳⠼⠏⣿⣹⣿⡆⠀⣧⠀ ⢸⠀⢰⣿⣷⠿⠋⠁⠀⠀⢀⣀⠤⠤⢤⣀⡀⠀⠀⠀⠀⠈⠉⠡⠴⠃⠀ ⣌⢦⣀⣉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠐⠋⠀ ⢀⠀⠀⠀⠀⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⡠⠁⠁⠀⠀⠀⠀ ⢀⠰⠀⠀⠀⠈⠒⠤⠤⣄⣀⣀⣀⣀⣠⡤⠴⠒⢛⡩⠀⠀⠠⢀⡠⠒⠀ ⠀⠁⠒⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡶⠿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣶⣄⡀⠀⠀⣀⣤⡶⠛⢛⠛⠛⢿⣿⣿⠁⢠⠊⡭⠛⠶⣄⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣷⣾⡟⣡⠊⣁⠤⠬⢍⡲⢌⠻⣇⢸⠸⠀⡎⡩⠽⣿⣆⠀⠀⠀ ⠀⠈⣿⣿⣿⣿⣿⡟⠀⠃⡘⢁⡔⠒⠂⢬⡳⡵⡜⢎⣆⢃⢣⢱⢻⣟⢻⢧⡀⠀ ⠀⠀⢹⣿⣿⣿⣿⣇⠀⠀⢃⠘⡄⢰⠉⣵⣿⣜⡜⡎⢿⣎⢢⡱⣕⠠⠴⢸⢳⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⠀⢇⠘⡄⠳⡈⢣⡣⣉⢿⢸⢸⠈⡝⢷⣝⠢⢍⣒⣋⢼⡇ ⠀⠀⢸⣿⣿⣿⣿⣿⣧⠈⢆⠈⢆⠙⢤⡉⠒⠋⡸⢸⠀⠇⠀⠈⢛⣶⣶⣄⠂⣧ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡈⠳⣄⠑⠤⣈⣉⣉⡤⠃⡜⠀⠀⣰⣿⣿⣿⣿⡇⣽ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡉⠒⠠⠤⠄⣲⠜⠀⠀⠀⢻⣿⣿⣿⠿⠁⡇ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠀⣰⠋⠀ ⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⡼⠃⠀⠀ ⠀⠀⠀⠀⠀⠲⠿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠊⣠⠶⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣦⣤⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠿⠿⢿⣿⣿⠋⠁⣠⠶⠶⣤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⡴⠀⠀⠘⡿⠀⠘⣅⡀⠀⠘⠧⠘⣿⣿⣿⡟⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡾⠋⢀⣀⣠⣀⡀⠀⣰⠟⠿⣶⡀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠋⢁⣿⣿⣿⣿⡇⠘⠀⣰⠟⠉⠀⠙⣷⣰⡇⠀⠀⠘⣷⡀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡅⠀⠀⣯⠀⠀⠀⠀⢻⡟⣧⢀⣤⣄⣸⡇⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⢻⣆⢰⣿⣶⣾⡇⠸⣿⣿⣿⣍⡇⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡄⠀⠀⠹⣯⣻⣿⣿⣿⣴⣿⣿⠿⣿⣷⣤⡜⠋⠉⠉⠙⠻⣿⣷⡀⠀⠀⠀⢠⡟⠉⠙⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢿⣿⣄⠀⠀⣸⠿⠋⣹⣿⣿⣿⣿⣷⣆⠈⢉⢛⡂⠀⠀⠀⠀⠀⠙⣷⠀⠀⢠⡿⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⠈⠛⢃⡜⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢻⡟⠛⠇⠀⠀⢀⣿⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠈⢿⣿⣿⣿⣿⡿⠃⠀⢀⣴⠟⠀⠀⠀⠀⢠⣾⠏⠀⠀⢸⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣰⠟⠻⣶⣄⡀⠀⠀⠀⠈⠉⠉⠉⠀⣀⣤⡞⠁⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⢸⣇⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⡶⠶⠶⣶⣟⣛⣁⣽⠃⠀⣠⣴⠿⠋⠀⣀⣀⣤⠾⠿⠿⣿⡄⠀⠀⣿⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢶⣦⣤⣤⣄⡀⠉⠷⣿⣿⣿⣿⣿⠟⢁⣤⡾⠋⠁⢀⣴⠞⠉⠉⠻⣧⠀⠀⠙⡷⠀⠀⠻⠆⠙⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠴⠞⣿⠇⠀⣼⡿⠛⠲⢤⣤⣭⣭⣭⣤⡾⠟⠙⢷⡀⠀⣾⠁⢰⣶⠀⠀⠙⠃⢀⠞⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⠁⣀⣴⣾⣋⣀⣾⡟⠁⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠘⢷⡸⢿⣦⣾⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣠⠞⠋⠘⠛⠛⠛⠛⠳⠶⣤⣄⡀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⢿⣦⡿⠁⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⡼⠋⣠⣾⣦⡀⠀⠀⢀⣠⣤⡀⠈⠙⠻⢿⣏⠀⢠⣤⡀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀⢸⡇⢠⡿⢀⡟⢠⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠀⣼⣿⣿⣿⠇⠀⣠⣿⣿⣿⣿⠀⠀⠀⠈⠙⢷⣿⠈⢳⡄⠀⠀⣾⠉⢻⣄⡀⠀⠀⠐⡿⣥⣟⣴⠟⣰⡞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣿⡟⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣆⠘⣧⠀⠀⣿⡀⠀⠙⢿⣦⣄⡀⠀⣋⣸⣯⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠙⠛⠋⠁⠀⢾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⡆⠸⡆⠀⠈⢿⣦⣄⣀⢈⣽⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠻⣄⣀⣀⣠⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣄⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣧⣤⣤⡤⢤⣤⣤⣤⣄⣀⣤⡶⠶⠾⠷⢶⣦⣤⣽⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣀⠀⠀⠀⠉⢻⡁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠉⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠘⣧⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢻⡇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣀⠀⠀⢠⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠒⠒⠠⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⠊⣩⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡄⠀⢰⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠈⢳⣤⡈⠢⡀⠀⠀⠀⢄⢣⡀⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢳⡀⠈⢆⠀⠀⠀⢹⡢⣄⠀⠀⠈⣢⡀⠀⠳⡈⠓⠬⡲⢄⠀⠀⠋⢻⢆⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠳⡀⠈⢦⡀⠀⠀⢣⠈⠑⠮⣅⡀⠉⠳⣄⠱⡄⠀⠀⠀⠁⠀⠀⠈⡆⠱⡀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⠤⠒⠚⠛⣄⠀⠹⣆⠀⠀⠳⡀⠀⠀⠉⠓⠦⣤⣑⣦⣀⠀⠀⠀⠰⡄⠀⠸⡀⠘⢄⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠳⣄⠘⢷⣄⠀⠱⣄⣀⣶⡾⠿⠛⠻⠛⡄⠉⠢⠀⠀⢳⠀⠀⢃⠀⠈⠂⠀ ⠀⠀⠀⠀⢸⠀⠀⠃⠀⢰⠁⠀⢠⣤⣤⣤⠤⣀⠀⠑⢤⡑⠙⠢⣘⣟⠛⠀⠀⠀⠀⠀⠃⠀⠀⢳⠀⠈⡇⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⣠⠀⢸⢤⣾⠿⠛⠛⠛⠿⠯⠀⠀⠀⠈⠚⠤⠈⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡇⠀⢻⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⢠⢻⠀⡄⢸⡀⢸⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢿⡀⢸⡇⠀⡇⠀⠀⠀ ⠀⠀⣇⠏⢘⢠⡇⠘⣧⣸⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠘⠇⠘⢡⠀⢹⠀⠀⠀ ⠀⣸⠟⠀⡎⡸⡇⠀⢹⣿⣗⣤⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣇⠀⠀⠀⠸⠸⢸⠀⢸⠀⠀⠀ ⠠⠋⠀⢠⢧⠃⢸⠀⠀⢣⡀⠙⣌⠉⠚⠋⠒⠂⠀⠀⢀⣀⡀⠤⠤⢒⡷⠀⠀⢀⡠⠋⡰⢿⠀⠀⡀⠀⡄⠸⠀⡸⠀⠀⠀ ⠀⠀⠀⣼⠏⠀⠀⢇⠀⠸⡷⡀⠈⢣⡀⠀⠀⠀⠀⠀⠘⠓⠄⠒⠚⠉⠀⠀⠀⠀⣠⠞⢀⣸⠀⠀⡇⠀⢡⢀⠀⡇⠀⠀⠀ ⠀⠀⠰⠋⠀⠀⠀⠘⡄⠀⢡⠙⢄⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡇⠀⡎⢸⠀⢰⠁⠀⢸⢸⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇⠈⢢⡀⠰⠀⠸⣏⡷⢦⣄⣀⠀⠀⣀⣴⣾⠋⢻⡇⠰⠃⣀⠀⡜⠀⠀⡗⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⢆⠀⠑⡄⣇⠀⡯⣷⠀⠀⠉⠙⠛⠉⠉⠀⠀⠘⡇⡀⠀⡈⢰⠁⠀⢰⡷⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢿⣠⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢧⣄⣷⣇⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡩⠿⣏⡀⠀⠈⠳⢤⠤⢤⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣥⣄⠀⠈⠑⠢⢤⣀⡙⣺⡁⠀⠀⠀⠀

⠏⠀⠈⠄⠀⡀⠀⠀⠀⠀⠀⠈⢾⣟⠢⡀⠀⠀⠤⡀⠀⠀⠀⠉⠲⠇⢀⣐⡈⢃ ⠀⠀⠀⠈⣆⠐⡀⠀⠀⠀⠤⣀⠈⠯⠽⠿⢦⡀⠈⢶⢄⠀⠀⣀⠀⠀⣈⡛⠧⣀ ⠀⠀⢠⠀⠟⠣⢌⡂⠀⢠⡴⡙⠠⡀⠀⢒⠚⠳⠀⢈⠛⠢⠀⠈⠻⠋⡱⣾⡛⡟ ⠀⠀⠀⠆⠸⠀⠀⠹⡿⠃⠒⣠⣦⣤⣴⣧⡤⡴⠀⢸⠓⠤⡀⠀⠀⠸⡍⠂⣼⠈ ⡀⢀⠀⠘⢄⢂⢀⣾⣧⣠⣟⡾⠛⠻⠟⢹⣣⠯⠀⠈⠀⠀⢎⢦⠀⡏⠨⡆⢨⣸ ⡇⠘⣷⢧⡀⢗⢄⠙⠂⠈⢼⠁⢘⠤⠐⠛⠉⠀⠀⠀⠀⠀⠈⠀⣕⠇⠷⠜⢺⢸ ⢿⣤⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⣀⣠⠎⡀ ⡄⠈⠋⢿⠛⣟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢼⠂ ⡇⠀⠀⠈⣳⢲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷ ⠘⠌⢦⣄⡀⠙⠿⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷ ⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⡀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠈⣿⣿⣿⢱⣄⠀⠈⠚⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠠⠂⠈⢍⣹⡘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠀⠀⠀⢀⣠⣤⣤⣶⣾ ⠀⠃⠀⡀⠀⠹⣷⣘⣛⣩⣿⣩⣐⣢⣄⠠⣴⣾⣏⡛⠿⢆⣤⣾⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⢷⣄⢠⡈⣻⡟⠛⠛⠙⠏⠒⢦⣤⠸⣿⣿⣿⣴⣿⣿⣿⣛⣉⣁⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡴⠒⠲⣄⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡗⠀⢀⡼⠀⠀⠀⠀⠀⠀⢿⠀⠀⠚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡿⣿⣶⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠐⠒⠒⠒⠒⠲⠶⠬⠑⠒⠚⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉⢀⣀⠈⠑⢿⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢾⡟⢷⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⢀⣠⡶⢏⡹⠃⠀⠀⠮⡁⢈⣳⠞⢻⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣼⣿⣶⣞⡙⢷⡀⠀⠀⠀⠀⠀⠀ ⡇⢀⣾⣿⣿⣶⣶⣤⠀⠀⢀⣠⢿⡏⣽⡤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⣿⡟⠛⠻⣿⣾⣷⡀⠀⠀⠀⠀⠀ ⡇⣼⢁⡾⠛⠻⣿⠛⣷⠚⠋⠀⢀⡴⠋⣴⠋⣠⣤⣀⠀⠀⠀⠀⠀⠀⣿⢷⣤⣀⠀⠀⠀⠀⢀⣸⣿⢻⡄⠀⠀⢸⡎⣿⡻⣦⡀⠀⠀⠀ ⡇⡏⢸⡇⠀⠀⣿⢠⡟⠀⣠⡶⠋⠀⣼⠿⣿⡉⣏⢉⣿⣶⣦⣄⣀⣀⣿⣀⣀⠉⠙⠛⢻⣿⡛⣿⣿⣎⣻⠶⠴⠟⠀⣿⣷⣿⠛⢷⣄⡀ ⣥⣿⡌⠻⠶⠾⣷⠟⣠⠞⢹⣇⣤⣼⠏⠀⠈⢿⢉⣙⣷⡖⠚⠉⠉⠉⠀⠉⠉⠙⢟⠳⣿⢋⣦⡟⠛⣯⠙⢷⡄⠀⠀⢸⡎⣿⠀⣸⠉⢻ ⣿⣿⠃⠀⢀⡾⠃⠀⣨⣴⡟⠋⢈⣟⠀⠀⢀⣾⢻⡟⢋⠙⠳⠦⢤⣄⣀⠀⠀⠀⡸⠀⣻⡄⠈⢿⢦⣽⣧⡀⢻⡄⠀⠈⣧⢸⡷⠋⢴⣿ ⣿⡟⠀⢀⡾⢁⣠⣞⣋⡉⠛⠓⠛⠻⣦⣴⡾⠁⢿⡀⠀⠑⢄⡀⠀⠀⠉⣳⣦⣴⠁⣠⡟⠀⣠⠟⢠⡽⠿⢷⡀⠻⠶⠾⠋⣸⠇⣠⡟⠁ ⡍⣿⣴⡾⠷⠿⢧⣤⣀⣀⡀⣀⣠⣴⣿⠀⢁⠰⡌⣷⠀⠤⠤⠙⠒⢂⡼⠃⣀⡿⢻⣿⡇⢀⠁⡀⢿⡐⠚⠋⠙⠳⠶⣴⣾⣯⠾⠋⢲⣤ ⣿⡇⠀⢶⣄⡀⠀⠀⣩⠉⠉⠉⠉⣴⡋⠊⢸⡄⠉⣿⠧⠤⠶⠖⠚⠋⣿⣉⣉⣀⣀⠙⢷⡼⠀⢇⢘⠷⢤⣤⡶⠶⠛⡟⠉⠁⢀⣴⢟⡁ ⣿⣷⣄⡀⠈⠛⠶⣤⣅⣠⣤⠴⢾⡟⣷⠀⢸⠁⢰⠏⠀⠀⠀⢀⣀⠤⠼⠋⠓⡿⠬⢝⣿⠇⢣⠈⠙⣇⠀⠀⢻⣦⣀⣨⣶⠾⠋⠀⠘⣤ ⡇⢸⠉⠙⠷⣤⣜⣀⣀⣀⣤⡴⠛⡄⢸⡇⢸⠀⣿⠀⠤⠒⣉⣡⣤⣴⡶⠿⠿⢯⣹⡾⠁⢀⡼⠀⠀⢹⠀⠀⠘⣄⠻⣆⠀⠑⣀⣤⠾⠋ ⣷⡘⠳⡶⠛⠉⣽⠉⠉⠉⡀⢠⢞⡧⣸⠇⠘⢰⡇⢀⣶⠿⠓⠋⠉⠀⠀⠀⡇⠀⢸⡄⠚⠋⠀⠀⢠⠏⠀⠀⠀⠸⡄⠈⢿⡛⠉⠀⠀⠀ ⡍⣧⠀⣧⠠⠞⣁⣠⡴⠞⡱⢣⢏⣴⠂⠀⢀⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⡇⠀⣀⡤⠀⠚⠀⢠⡀⠀⠀⠈⠢⡈⢷⣄⣀⡀⠀ ⡇⢻⣤⠈⠙⢛⠟⠛⠁⠀⠠⣿⠟⠁⣀⣴⣾⠃⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢠⡾⠀⣈⣉⠀⡼⢦⡀⠀⠙⠶⣄⠀⢀⠘⡌⠁⠉⢻⡄ ⡇⠈⢿⣅⡀⠈⠑⠒⠒⠒⢰⡏⠀⠈⣸⠁⡿⠀⠀⡞⠉⠉⠁⠀⠀⠈⢻⣄⡴⣿⠉⠁⣠⢋⡼⠁⠀⠙⣦⠀⠀⠈⠙⠘⡄⢹⡀⠀⢀⣿ ⡇⠀⠀⠉⠛⠳⠦⣤⣄⣀⣼⡇⠀⠀⣿⠁⡟⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⠋⡇⠘⢷⡄⢻⡘⠁⠀⠀⠀⠈⠳⣤⡀⠀⠀⠁⠀⢣⠀⣼⠋ ⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣼⠃⠀⠸⣄⡀⠀⠀⠀⠀⠀⢸⠀⣷⠀⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡟⢢⠁⢻⠀

⣦⡶⠟⠋⠁⠙⣿⣿⣷⡀⠛⢟⠓⢓⡦⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⢘⠟⠛⠋⠐⠒⠋⣉⠀⠀⣀⠀⠡⠖⣢⠤⢀⠀⢀⡀⠄⠀⢀⠀ ⠀⠀⠀⠀⠠⠈⢁⠄⠀⣊⠉⠀⠈⢀⡠⠶⠒⠤⣢⡀⠀⠈⠂⠌⡃⠀⠀⠀⠀⢰ ⠀⠀⢀⠄⡠⠊⢠⠖⠉⡠⢲⢀⠀⠀⢷⡄⠀⠀⠪⣪⢂⠀⠀⠀⠈⠢⡠⡀⠀⠀ ⣀⠔⢁⠊⠀⢰⠏⣠⠊⠀⠸⠈⣶⠀⠈⣧⠀⠀⠀⠈⢃⢡⠀⠀⠀⠀⠐⡜⡆⠀ ⠈⠠⠁⠀⠀⠛⢀⠃⠀⠀⠜⡀⡯⠀⠀⡇⣗⢄⠀⠀⠀⢣⢳⡀⠀⠀⠈⡶⠱⠀ ⠀⠁⠀⠀⠀⡇⠘⠀⠀⠌⢀⡇⡇⠀⠀⠇⡰⢄⠀⠀⠀⠘⢯⠰⡀⠀⠀⢹⢃⢯ ⠀⠀⠀⠀⠀⠀⡇⠀⡌⢀⠎⢇⡇⠀⣼⠀⠗⠀⠑⠤⡀⠀⠈⣇⢡⠀⠀⢸⠀⣼ ⠀⠀⠀⠀⠀⡄⠁⢰⢀⠎⡴⢪⡇⠀⢸⢸⠛⠒⠀⠀⠈⠑⢕⣾⡀⣇⠀⠀⢈⢸ ⠀⠀⠀⠀⠀⣿⣠⣃⠖⠊⠀⢸⢿⠀⣼⡇⠀⠀⢠⢤⠴⠶⠶⣼⡇⢸⠀⠀⠸⠈ ⠀⠀⠀⠀⠀⢸⣯⠃⠀⠀⣀⡸⢸⢠⠛⠃⠀⠀⢳⢃⢛⣗⡀⠈⣏⠹⡆⠀⠀⡁ ⠀⠀⠀⠀⠀⢸⢃⡴⠚⣩⣚⠻⡀⡟⠀⠁⠀⠀⠈⠀⢏⣉⢇⠴⣺⢀⠁⠀⠀⡇ ⠀⠀⢀⠀⠀⢀⣿⠀⠸⣷⠾⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠇ ⠠⡀⢸⣷⠀⠸⢯⠂⠤⣙⢒⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠆⠀ ⢀⣷⠀⢿⡄⠀⠞⣧⠀⡵⠃⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠂⣸⠀⢠⠀⠀ ⣾⠈⡇⠘⣷⡀⠀⢻⠑⢄⠀⠀⠀⠀⠀⢰⣿⠿⠿⠛⠣⡀⠀⠀⣰⢻⠀⣸⠀⢁ ⠘⠕⡐⡄⢹⢡⠀⠈⣾⢢⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡄⢀⣴⡇⡌⣆⡏⣴⣧ ⠀⠀⠰⡘⣄⠗⢧⡀⠸⠈⠉⠐⢤⣀⡀⠈⠂⠒⠂⠈⢁⣴⣿⠿⢧⣡⣿⡇⣾⡥ ⠀⠀⠀⢡⠙⣺⡄⠑⢄⢣⡄⢀⠤⠛⡻⡟⠳⢶⣤⣴⣿⠟⠉⣧⡀⠈⠙⢔⠹⣷

⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠛⢗⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣦⠐⣴⠀⠀⠀⠀⡜⠀⣀⠤⠐⢒⢾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⠀⢤⡓⠉⠣⡏⠇⠐⠒⠲⠚⠛⠀⡠⣾⡥⠀⠊⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⠘⠉⠀⠀⠀⠸⣰⠀⢰⠣⡠⠀⠂⠈⠈⢽⡦⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⢀⢤⣀⠆⠿⠿⠷⣈⣀⢘⡱⢠⣤⣄⠀⠀⠘⢇⠀⡇⠀⠀⠀ ⠀⠀⡤⠥⠐⡂⠭⠙⣇⣠⠈⠀⢀⠨⣏⠁⠈⠍⣛⠛⠓⠠⠄⠀⠴⣇⠀⠀⠀ ⣀⡏⠀⠀⢀⠄⠊⠁⠈⠀⠉⠁⠀⠀⠀⠑⠠⠬⠷⠬⡽⡋⢄⠀⠀⠀⢧⠄⠀ ⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠢⡑⠈⠂⠄⢺⠁⠀ ⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡆⠀ ⠀⡀⠀⡀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠀⠀⢳⠀ ⠀⢹⣆⣿⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠴⠤⠴⠛⠁⠀⠀⣸⡆ ⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠉⠙⡇

⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣶⣶⣿⣇⠀⠀⣼⣿⠇⠀⠀⢀⣴⣿⠟⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠇⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣿⣷⣄⠀⠉⢻⣿⣿⣷⣶⣿⡇⠀⠀⢠⣿⡟⠁⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠏⠀⣿⣿⣿⠀⢀⣴⣶⡄⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣾⡿⣋⣴⣄⠀⢿⣿⠀⠀⠈⠛⠀⢩⣿⡿⣿⣷⣦⣿⠟⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⠈⠙⠉⠀⢸⣿⣿⡏⠀⣸⣿⡇⠀⠀⠀⠀⠀⢸⣿⠃⣿⣿⡿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⢿⣿⣷⣤⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠘⣿⣧⣈⣉⣠⣼⣿⠟⠀⢀⣴⣾⣿⣷⣦⣄⠀⠀⠉⠉⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⢀⣾⡟⢉⣩⣙⢿⣿⡆⠀⠀⠀⠸⣿⠟⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣄⡀⠀⠀⠀⢀⣤⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⣿⣿⠂⣿⡿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⢉⣡⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣤⣤⡀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠈⠛⢿⣦⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠻⣿⣦⡀⠀⠀⣀⣤⣾⡿⠃⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠉⠻⠿⢿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⣀⣴⡿⠋⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠾⠛⠋⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣦⣄⣀⣠⣤⣤⣶⣶⣿⣿⡿⠀⠀⠀⠉⠻⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠟⠁⠀⠀⣀⣀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣬⣿⣿⣿⣿⣿⣿⡿⠿⠛⢹⣿⡇⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⣀⣤⣶⡄ ⠘⠻⠟⣿⣿⡟⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣷⣾⣿⣿⠛⠁ ⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠉⠉⠉⣿⣿⣿⣶⣶ ⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⢸⣿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⣤⣶⣿⣶⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣄⠀⠀⢸⣿⠋⢙⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣠⣤⣾⣿⣿⠟⠋⠀⠻⣿⣷⣤⣸⣿⣦⣿⡿⠃⢀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⣷⣶⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀

⠀⠸⠙⡀⡄⠀⠀⠘⡶⢄⡀⠀⠀⠀⠙⠲⣄⠀⠈⠢⡀⠀⠠⡀⠉⢻⣿⣷⣽⣿ ⢀⠃⠀⠐⣸⣦⣤⣀⡜⡀⠈⠑⠲⢶⣶⣶⣬⣿⣦⡀⠈⢆⣀⣈⣦⡀⢙⣋⡠⠚ ⣾⠀⠀⠀⠹⣿⣿⣿⣿⣷⡀⠀⠀⠒⠊⠽⠿⣿⣿⣿⣦⣀⠹⣿⣿⣿⣦⡻⣗⢀ ⡇⠀⠀⢀⡤⠚⢿⣿⣿⣿⣷⡀⠀⠀⠀⠤⣀⣀⡉⠚⠿⣿⣷⣜⢿⣿⣿⣿⣞⣿ ⡇⠄⠊⠀⠀⠄⠈⠻⣿⣿⣿⣷⡀⠀⠀⠚⢉⡭⠉⢍⡙⢪⣿⣟⣷⡻⣿⣿⣿⣿ ⡇⠀⣠⡴⠞⠛⠂⠀⠙⢿⣿⣿⣷⡀⠀⠀⣴⢀⢠⣄⣱⠀⢸⣿⣿⢯⠚⢿⣿⣿ ⣷⠞⠁⡢⠠⢌⣣⠀⠀⠀⠙⢝⢏⣻⣄⠀⠡⣈⣉⢠⡀⠀⢸⠀⢻⠎⠆⠘⢹⣿ ⠿⡄⠀⣇⠑⠛⢉⠀⠀⢀⡠⠀⠀⠉⠻⢦⣖⢫⠉⠉⠈⡼⢺⡄⠈⠄⠰⡐⢸⢿ ⣆⡏⠳⡀⠰⠚⠉⡠⠖⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠢⡈⠁⠈⣷⡀⠘⠀⢳⣿⣷ ⣾⡇⠀⠘⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠂⢄⠈⠢⠀⡟⠇⠀⠇⠸⣽⣿ ⡿⠇⢰⠀⡏⠓⠠⢀⢄⠀⠀⠀⠀⢀⠠⠦⠈⠐⠠⡀⠡⠀⠙⢄⣼⠀⠈⡀⢻⣿ ⢰⠀⠈⠀⡇⠀⢀⠆⠺⣰⠖⠂⠉⠁⠀⠀⠉⠢⡀⠈⠠⣡⠀⠀⠉⠁⠀⠀⢸⣿ ⠘⠀⠀⠀⠃⢀⠎⢠⠃⠋⠀⠀⠀⠀⠀⢀⡀⠔⠑⢄⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⢸⡎⠀⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢦⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠈⠁⠀⣷⣦⣀⡀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⡀⠀⠀⠀⠀⠀⠀⡾⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⡍⠒⠠⢔⡪⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⠀⢀ ⠀⠀⠀⠀⠀⠀⢸⣻⣼⣿⣿⢻⡆⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃ ⠀⠀⠀⠀⠀⢀⠛⠋⠁⡞⠁⢸⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀

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