Muscle Bunny ASCII Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⣣⠞⠁⣀⣤⡤⠤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⣵⠏⠁⡴⡪⣙⣌⣋⣀⣸⠇ ⠀⡀⠀⠀⠀⠀⣠⡿⠾⠒⠺⢧⡽⠋⠁⠀⠀⠀⠀ ⢠⡜⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⣀⢸⡆⠀⠀⢦⡀ ⠀⠀⣄⠀⡇⠀⠀⠀⠛⠁⢠⣈⠀⢸⠇⠀⠘⠲⠃ ⠀⠀⠉⠀⠹⣄⠀⠀⠀⠀⠁⠀⣠⣏⣀⠀⠀⣶⠀ ⣠⠖⠒⠒⠚⢚⡿⠒⠶⠶⠒⠋⠙⣧⣭⠙⡆⠀⠀ ⠉⠓⠓⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⣿⣉⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⣸⢧⡀⠀⠀⣀⣠⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠋⠻⣍⠉⠙⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣳⢤⣀⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⣤⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⡾⣸⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣾⢠⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣞⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣄⡀⣰⠟⠉⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠀⠿⠙⠉⠉⠉⠙⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠋⠁⠄⠙⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣾⣄⡸⣧⠀⠀⠀⠀⣼⡟⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⣉⡉⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠿⣷⣬⣙⠆⠀⣰⡟⠀⠈⠉⠓⢤⡀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⢷⣼⡟⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣴⠖⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⣸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣧⠀⠀⠀⠀⠀⢸⡁⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠛⠛⠋⠀⢀⣠⣴⠶⠟⠛⠛⠛⢷⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⠀⠀⠀⠀⠈⠳⠤⠤⠞⠁⠀⠀⠀⣠⣤⣤⣄⠀⣸⠏⠀⠀⠀⠀⢸⡟⠁⡄⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⢶⣖⠒⠒⠒⠶⢿⣍⡉⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⣦⣤⡀⠉⠀⠀⠉⣴⠏⠀⠀⠀⠀⠀⢸⣇⡞⠁⠀⢀⡀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠞⠋⢡⡤⠤⢤⣄⠉⠉⠑⠲⣤⣐⠀⠉⠛⠻⣷⣶⣶⣀⡀⠀⠀⢻⡶⣷⠭⠇⠀⠀⣠⣾⣯⣤⣄⣀⡀⠀⠀⠀⠙⢻⣦⣀⣨⣿⠀⠀⠀⠀⠀⢹⣆⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⠻⠶⠶⠶⠛⣀⣀⣤⠶⠦⣍⡳⣆⠀⠀⠈⠻⣟⢛⣿⢶⣶⠸⠷⣧⣠⣶⢶⢻⠟⠉⠁⠀⠉⠉⠻⣷⣄⣀⣀⣀⣹⣋⣹⡿⠀⠀⠀⠀⠀⠀⢿⡄⠀ ⠀⠀⠀⠀⠀⣴⡿⢷⣤⡆⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠹⣏⢳⡀⠀⠀⠈⡋⠛⠦⢬⣓⠚⢛⣟⣁⠴⠛⢷⣤⡀⠀⠀⠀⠀⢈⡿⠛⠉⠀⠈⠙⠻⣇⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⢠⣾⠏⠀⣰⠏⠀⣠⠞⠛⣶⠀⠀⣈⣛⠓⠲⠴⠇⠀⢳⠀⠀⠀⣧⠀⠀⠀⠈⠻⡏⢸⠁⠀⠀⠴⠃⠳⣄⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⠀⢀⣾⠃⠀⢠⡏⠀⢸⡇⠀⢀⡟⢀⡞⠉⠉⠳⣆⣀⣀⡀⢸⣧⠀⠀⢸⣧⣀⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠘⢧⣸⢣⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢦⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⣼⡇⠀⠀⢸⡇⠀⠘⣧⣢⠞⢀⡏⠀⠀⠀⠀⠸⡍⠈⠙⢿⢿⡀⠀⣸⠁⠉⠓⠄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⢧⠈⢷⡀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⣇ ⠀⠀⣿⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢰⠇⠀⠀⢸⡇⢇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠸⣇⢀⣳⣤⣀⣀⣀⡠⢶⣋⣙⢦⣀⣀⡀⠀⠀⠀⢻ ⠀⠀⢹⣇⠀⠀⠀⠘⠷⢤⣀⣤⠼⠋⢧⣄⣀⣀⣴⣏⣀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣁⣀⡤⠴⠋ ⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⢻⣿⣿⣷⡀⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⢠⣿⣀⣀⣀⣀⣀⣀⣠⣤⡶⠾⠛⠋⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠅⠉⠉⠿⣮⣄⡀⠀⠀⠀⠀⠀⠀⢠⣴⠗⠛⠷⣤⡤⠴⣿⡇⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣾⢿⡿⣦⣠⡀⠀⠀⠈⠉⠑⠶⠶⠒⣲⠋⠉⠁⠀⣶⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣤⣼⠶⠶⣿⣟⠉⠀⠙⢿⣄⡙⠿⡄⠀⠀⢀⡠⠴⠖⠋⠁⠀⠀⠀⢀⡏⠀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠙⢻⣀⠁⢠⠔⠃⠀⣀⠀⠀⠀⠀⠀⣠⣞⣀⡤⢼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠻⠀⠀⠀⠀⠰⢯⠀⠀⠀⠈⠉⠁⠀⠀⡴⠁⠈⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⠖⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠉⣠⡾⠉⠉⠳⣄⡀⠀⠀⠀⠀⠈⠢⠶⠶⠖⠂⢠⠗⠒⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⣰⡏⠀⠀⠀⠀⠀⠙⠳⠦⢤⣀⣀⣀⡀⠀⠀⠠⢋⣀⡤⠴⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠛⠛⠓⠒⠆⢀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢁⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠀⠀⠰⡏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣾⠀⠀⡆⡄⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠒⠉⠉⠉⠁⠐⢄⠈⢺⡄⡰⢳⣠⡰⠇⢓⣾⠃⠄⠂⠈⠉⠉⠀⠢⡀⠀ ⡔⢩⡂⠐⢄⠀⣀⠀⢀⡠⠧⡀⣿⠃⠋⠀⠈⠁⠙⢟⡌⠤⠤⠠⣤⠤⠄⠀⠈⠀ ⢣⢈⢇⠀⠈⠉⠐⢶⠋⠉⠢⣴⡇⠀⢀⠤⠐⠙⣖⣺⡀⢀⣠⠊⠉⠉⢹⠂⠀⠰ ⢸⣿⠘⢦⣀⡀⠀⢘⡀⠀⢀⡏⢿⢲⠀⢩⢄⡀⢈⣥⢸⠁⢸⠀⠀⢠⠞⠲⠐⡂ ⢸⢿⡀⠀⠀⠙⠫⡉⠳⡄⢎⠈⠻⣧⢷⣄⠁⠤⠠⡾⣳⡖⠉⢱⠤⣧⠊⠀⢠⡇ ⠀⢿⣶⣄⠀⠀⠀⠈⣶⡒⢼⠄⠀⠉⠙⠛⠿⡷⣿⠟⠁⠀⠀⣼⣾⡞⣀⣴⠟⠀ ⠀⠀⠙⠛⢧⣴⣶⠾⠛⠻⣍⡇⠀⠀⠀⠀⠀⠈⢕⡔⠀⠀⠀⠹⡛⠛⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⢻⡀⠀⠀⢻⡿⣄⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠳⡬⣷⣄⡀⠀⠀⣠⣼⣄⣠⣴⡛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⡀⠙⠻⣙⡭⣒⠾⠛⠒⡍⢲⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠖⠳⢬⡳⡄⠀⠤⢳⢚⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⣹⢷⣤⣤⢯⣣⡤⠤⢚⣉⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠛⠢⢬⣙⣭⣕⢻⣿⢄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣆⡀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⢇⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠃⡄⠑⠒⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⢠⢈⣉⡁⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⠖⠉⠩⠉⠉⠉⠘⠒⢤⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⠀⢠⠋⠉⠉⠀⠒⠄⠒⠀⠈⠈⢂⠀⠉⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⢀⡠⣇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣧⡀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠜⠉⠀⢹⠑⢂⠀⣐⠪⠨⢒⠀⠄⠰⠹⠀⠁⢳⠀⠀⠀⠀⠀ ⠠⡖⣿⢷⠴⠚⢄⡠⠜⡧⠀⠈⣅⣀⡁⢀⡍⠀⢠⠣⢀⡠⠛⠤⡔⢶⢲⡀ ⢠⠗⡩⢂⣀⣠⣔⠠⠔⠛⠲⢌⡤⠤⣀⠤⢦⡤⠼⠦⢈⣂⣀⣄⡙⢏⠺⡄ ⠈⠉⠓⠁⢠⠋⢄⠀⡀⠀⠀⠀⢲⣄⠈⠈⠁⠀⠀⠀⠀⠀⠀⠙⡏⠚⠉⠁ ⠀⠀⠀⠀⠸⣀⣀⠂⠀⠁⠀⠀⢀⣀⣵⣦⣄⡐⠀⡀⠂⠁⠠⣣⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠒⠀⠒⠒⠉⠉⡀⠉⢁⠀⠉⠑⠒⠛⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢸⣿⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣽⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢹⠀⠀⢠⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡈⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢻⡆⠘⣧⠀⠈⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢣⡀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⣄⠀⠈⣧⠀⠘⣆⠀⠸⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡀⠘⢦⡀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡀⠀⠸⣧⠀⠘⣦⡄⠁⡇⢀⣀⡤⢤⡤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣄⠀⢙⢢⡀⠀⠀⠙⠲⣤⡀⢀⣠⣤⣤⣤⣼⣷⣤⣤⣼⣧⠀⠘⡇⣼⣿⡋⠹⠳⣬⡙⢿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⢢⡉⠳⢆⡀⢀⣬⠛⢉⢧⢀⣀⡞⢋⣱⣽⠚⣿⣿⢿⣿⢿⡁⣸⠃⠀⠀⠈⠳⡜⠻⡍⠓⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠢⢄⣉⡿⣿⢄⢸⠘⣨⠟⢳⡄⣿⣿⣿⣽⣭⣿⣿⡇⢹⣿⡂⠒⣴⡀⠀⢳⡄⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣽⠀⢸⣾⣾⣿⣿⠀⢠⢻⡿⠻⣿⡿⠀⣧⡏⣧⢀⣿⣷⡄⢠⢇⠀⠘⢷⠀⠻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢤⣀⣿⣿⣿⠓⣐⣾⠛⠳⢀⡞⠁⠸⣿⣷⣿⣿⢻⣷⡆⠈⡾⣆⠄⢸⣷⠀⢱⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⣰⣿⣼⣿⣗⣼⣿⡃⣀⢀⡾⠁⣴⣿⣿⣶⣽⣿⢿⡏⢰⢠⠁⣿⠀⢸⠃⢳⡜⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⢰⡟⠋⠹⣿⣿⠋⠿⣿⣿⠋⠀⠀⠁⠙⠛⠃⣸⠋⣸⠇⠘⣼⡼⣿⢇⣾⠀⠀⢳⣽⠀⠀ ⠀⠀⠀⠀⢀⣠⣦⣄⡀⠀⠀⠀⠸⣿⠀⣇⠀⢻⣿⠷⣄⠈⢙⠀⠀⠀⠀⠀⠒⠀⢹⣤⣿⠀⠈⣿⢃⡟⣸⣸⠀⠀⠀⠙⠀⠀ ⠀⢀⣤⣾⡿⢚⠀⢸⡷⣤⡀⠀⠀⠀⠀⢹⡆⠀⢿⣆⣼⡿⠿⠖⠀⠀⢰⡆⠀⢠⣼⣷⡇⠀⠀⢻⡾⠀⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⢿⣅⣴⣿⠿⣿⠀⠙⢦⡉⣷⠀⠀⠀⠀⠹⡆⠘⡛⠷⣝⣷⣶⣤⠖⢉⣠⠴⠋⣿⣿⡀⠀⣰⣾⠷⣤⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⣫⡶⠊⠁⠀⠀⠀⢧⡿⠀⠀⠀⠀⠀⠀⢀⣧⡜⣾⣯⡉⢻⢿⣿⡿⠀⠀⣸⣿⣿⡿⠋⠁⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣷⢿⣿⠇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢰⠟⠻⣼⠃⣠⡿⠿⠿⠁⠴⠚⢻⣿⢳⠿⠃⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⢾⣍⡀⠀⣠⣤⣴⠋⠀⠀⠀⠀⢀⡏⢀⡴⣻⣾⠋⠁⠀⠀⠀⣠⠀⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⢯⣤⢿⠀⠀⠀⠀⠀⣼⣧⠼⠖⣿⠃⠀⣠⡴⣢⠞⠁⢰⠟⡏⠀⠀⢷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣼⣇⠀⢀⡴⠚⠉⠁⠀⠀⠉⢠⡞⠙⠊⠁⠀⠀⠈⡆⣤⠀⠀⣸⣷⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣜⣿⢿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⣤⣤⡿⢹⣇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢦⠀⣿⢃⣾⠃⠀⢿⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢿⠃⠀⠀⠀⠘⣆⠀⠂⠀⠀⢱⣀⣧⣯⠇⠈⢲⣿⣿⠃⠀⠀⠀⢻⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠉⢶⡀⠀⠀⠈⠏⠉⠀⣀⣶⠟⣹⠏⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⠀⠉⣹⣿⡟⠛⠉⠉⠛⠛⠛⠛⠋⠉⠀⣴⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠟⢀⡾⠋⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢀⣴⠛⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⡇⠀⠀⠀⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣧⠤⢤⣴⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣤⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⣧⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠟⠛⠛⠛⢻⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠹⠀⢿⡿⠶⢤⣀⣀⠀⠀⠀⠀⠀⡀⢀⡾⠉⠀⠀⠀⠀⠀⠘⠁⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢡⣼⠀⠀⣿⡜⠓⠮⣽⣿⣒⠠⠤⣤⣷⣿⣥⣴⡾⠆⠀⠀⠀⢸⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠸⡿⡇⢠⢃⠙⢦⣀⠀⠀⠉⠙⠳⠦⣄⣀⡀⠠⣏⠀⠀⠀⠀⣸⣧⠀⠘⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠓⠦⣇⣻⢸⢿⣰⠀⠙⢦⡀⣀⠀⢠⢠⠀⠀⠁⠀⣿⠀⡄⠰⡔⢦⠈⣧⣸⣾⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠉⠷⣌⡙⡇⡄⠀⡿⣿⡄⣸⡟⠀⠀⠀⣆⣿⡆⢻⠀⢹⠿⣇⡟⠉⠈⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣇⠀⡇⣿⡆⠁⢹⡀⢀⣾⣿⠿⡇⢸⣰⠃⠀⠙⠃⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣇⢿⡇⠀⠸⡇⠟⠋⠀⠀⠹⣼⡇⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠇⡏⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⢸⡟⡄⠀⠀⢸⠀⡇⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠠⢄⡀⠀⠀⠈⣟⣧⠀⠀⠀⣼⢡⠁⠀⠀⣸⡄⢿⣀⣰⣿⠏⠀⢀⡀⠤⠄⠒⠒⠢⠤⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠈⢾⣦⠀⣼⠃⣾⠤⣟⡽⢛⡏⢉⣽⣿⠏⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⢀⡴⢊⡵⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠨⣿⣷⠃⢸⡇⠀⠀⠉⠉⠉⠛⢿⣿⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⠀⠀ ⣿⠀⣿⣷⠀⠀⠈⢳⣄⣠⡴⢒⠀⣀⣲⣖⣋⠉⠣⡀⣿⠟⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢻⡾⠚⠉⠉⠉⠉⢉⣽⣏⣉⣁⡀⠀⠀⠀⠀⠀ ⢸⡆⣷⠸⣇⠀⠀⠈⠁⠀⠉⠺⣷⠟⠁⠀⠈⠱⣤⣿⣿⠀⠀⠀⢀⡤⠔⢾⠋⠙⣗⠐⢺⡇⠀⠀⢀⣠⡖⠉⠀⠀⠀⠈⡗⠀⠀⠀⠀⡔ ⠀⣿⣿⠀⢻⣄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢹⢿⣿⣄⣠⠀⠉⠴⠖⠒⠒⠀⠛⠿⠟⠉⢷⠞⠛⢻⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⢠⡇ ⠀⣿⣿⠀⠀⠻⢦⣀⣀⣀⠀⠀⠀⣇⠀⠀⠀⠀⣼⡀⢻⣧⢹⡀⠀⠀⣖⠲⣄⣀⣀⣤⣾⠇⡸⠀⠀⢸⡆⠀⠀⠀⢠⡟⢁⠜⠛⠉⢩⡇ ⠀⣿⣿⡇⠀⠀⠀⠈⠉⠻⢍⠉⠙⠻⣦⣀⣠⡞⠁⠙⢾⣿⣇⣿⣄⠀⠘⢦⡀⠀⠀⢠⣾⡴⢷⣤⠖⠉⠙⣆⢀⣰⣟⡴⠃⠀⠀⠀⣾⠃ ⠀⢿⣿⡷⡄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢻⠀⢱⡀⠀⠀⠘⣿⣟⢿⣷⣦⣄⣈⠉⣉⣽⣿⣤⡿⠇⠀⠀⠀⢻⠋⣽⢿⠇⠀⠀⠀⣼⡟⠀ ⠀⠈⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢹⣗⠚⢷⣄⡧⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢤⣼⣿⣯⡞⠀⢀⣤⣾⠟⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⡀⠀⣠⣀⣀⣴⣿⣿⣿⡖⠚⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢞⠁⢀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣼⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⢿⣿⣷⣿⡿⠿⠋⠉⠉⢿⣦⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣽⡏⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣟⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠈⢿⡍⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠘⢿⣄⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣀⣀⣀⣀⣼⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⠀⠀⠀⠈⢻⣄⣿⢿⣿⢿⣦⣀⣀⣲⣿⣿⣁⡽⢭⣉⣩⣟⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⡀⠀⠀⠙⣦⣉⣷⢦⣤⠴⠛⠉⠀⠀⢳⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⣤⣿⣆⠈⠳⣧⡀⠀⠀⠀⢀⣼⡦⠴⢿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠀⠀⠈⠙⢳⣬⣿⠛⠛⠋⠉⠀⣱⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⡿⣿⣶⣄⣠⡼⢧⡙⣶⡤⡤⠴⠞⢻⣄⣸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⠉⠛⣿⣇⡀⠙⠻⠷⣦⠤⠶⢛⣯⣟⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡄⠈⠉⠙⠻⣷⣦⣭⣓⣿⣏⠉⣿⣷⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡏⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣕⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢷⠀⢠⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣆⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⠀⠈⡇⠈⣆⠀⢱⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠐⢄⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⢫⣂⠀⠹⡀⠘⣄⡘⢹⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢣⠀⢑⢄⠀⠈⠓⢦⣀⣀⣤⣤⣤⣷⣦⣤⣽⡄⠘⣇⣾⡒⠙⠢⡑⢺⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣌⠢⡉⠢⢄⣴⠋⢰⡆⣤⣎⢩⣾⣭⣿⢟⣿⡻⣤⡃⡀⠀⠘⣎⠹⡍⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⣌⠑⣾⠙⣰⣸⣴⠃⢘⣼⣿⣿⡟⢳⡟⡇⢻⣯⠉⢳⠀⢸⡄⠹⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠳⣄⣿⣿⡿⢀⣼⢻⡄⡽⠁⢾⣷⣿⡞⣿⡅⢣⣧⡀⣿⡄⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣾⣽⣿⣢⣿⣃⣀⡴⠁⡶⣿⣿⣿⡗⣿⢸⡌⢸⡀⣾⠘⡌⣇⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⡼⢩⠈⣯⣯⠸⠻⡏⠀⠀⠀⢉⠁⢾⢠⠃⠨⣿⢹⢣⣿⠀⠘⢾⠀ ⠀⢀⣤⣾⠟⠙⣦⡀⠀⠈⠃⠸⡄⠘⣏⣑⣤⣖⠄⠀⣠⠀⢀⣸⣿⠀⠀⣧⡎⣾⡏⠀⠀⠀⠀ ⠀⣏⣠⡾⢿⠀⠳⣍⢳⠀⠀⠀⠱⡄⢛⠷⣕⣦⣤⠔⣋⡠⠞⣿⣇⠀⣠⡾⢤⣝⠀⠀⠀⠀⠀ ⠀⠸⡵⣖⣉⠀⠀⠘⣾⠀⠀⠀⠀⠀⣸⠖⡿⢮⣙⣻⠿⠃⣀⣼⢿⣿⠉⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⢿⣽⠏⠀⠀⠀⣸⠀⠀⠀⠀⡜⢀⡼⣥⠾⠉⠁⠀⠁⣼⣟⡟⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠈⠑⠶⣞⣹⡇⠀⠀⠀⢸⣇⡮⢾⠏⠀⣠⢆⠔⠁⡿⡏⠀⢰⡀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣧⣷⠀⣠⠖⠉⠁⠀⠈⢠⠊⠓⠁⠀⡀⣆⣤⠀⢠⣷⠀⠈⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠽⢟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣼⢒⡿⠘⡄⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠘⣦⠄⠀⠀⢰⠀⠠⠀⠀⡀⢄⣰⠈⢤⣿⡾⠁⠀⠱⡄⠀⠀⠀⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠦⣄⡀⠀⠳⣀⣀⠀⠙⠉⢁⣠⠾⣻⠃⠀⠀⢀⡕⠂⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡿⢈⣽⢿⡋⠉⠉⠉⠉⠉⠉⠁⠴⡇⠀⠀⠀⢸⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢁⠞⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⢸⠀⠀⠀⡸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠃⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⣀⣀⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡤⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣷⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⢻⡦⣄⡀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠀⠀⠀⠿⠻⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣰⠀⢻⡐⠯⢽⣒⣦⠤⣀⣷⣞⣠⡶⠀⠀⠀⣴⠀⢱⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣃⠘⡿⡀⡜⠘⢢⡀⠀⠈⠙⠲⠤⢀⠀⣯⠀⠀⠀⠼⣆⢈⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠙⠲⢧⡃⢾⠀⠙⣦⡆⠀⣴⠀⠀⣀⣿⠸⡄⢯⣣⢸⠼⠻⡅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠲⣝⠀⡇⣿⠙⢳⠀⢠⣿⡿⠀⣇⠎⠈⠿⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠱⣧⣿⠀⠘⡇⠛⠁⠀⢣⣟⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠀⠀⢳⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣴⣾⠻⣾⡀⠀⣀⣤⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢤⣀⡠⢄⡲⠋⢈⣹⣦⣽⣿⡿⠃⠀⢢⡙⡵⡀⠀⠀⠀ ⠀⠀⠀⢴⠗⣩⣤⣬⣭⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⢡⣣⠀⠀⠀ ⠀⠀⠘⠛⢁⣀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⡷⣀⠀⠀⠀⢣⢆⠀⠀ ⠀⣠⢪⡡⡔⡌⡧⡀⠀⠀⢻⣿⣿⠋⠁⠻⣿⣧⢈⢧⠀⠀⠀⡾⡀⠀ ⢀⠛⣦⣑⡡⠝⠋⠀⠀⠀⠈⢿⡗⢦⣄⠀⢹⣿⣿⣾⣷⢦⡀⢱⠘⡄ ⡜⠘⠛⠱⡀⠀⠀⡀⢀⢔⡭⠿⠿⢿⡶⢴⣿⠿⠋⠻⢾⡗⠳⡄⠀⢸ ⠁⠁⢰⠀⢁⡼⠁⠐⠚⢻⡇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠇⡀⠈⠀⣸ ⡆⠀⠈⡐⢹⡀⠀⠀⢀⠈⣿⡄⠀⠀⢠⠀⠀⠀⡄⠀⠀⠁⢐⢄⣠⢻ ⢳⠀⣞⠸⠂⡏⡆⠀⢺⢰⡿⠳⢦⣔⢺⣂⠐⠂⠴⢂⢰⠒⠸⣜⠁⠁ ⠀⠑⠒⠋⠁⠓⠓⠛⠈⠁⠀⠀⠀⡹⠰⠻⠀⠃⠐⠚⠉⠺⠀⢸⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⣅⣀⡀⠀⠀⠀⠀⠀⣇⢆⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡃⠀⠑⠀⠀⠀⠀⢠⡫⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠉⢲⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⠁⠀⠀⠀⠀⣠⠚⠉⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⢊⠜⣦⡀⠀⢨⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡁⠀⢀⣔⠏⠐⠉⠍⠱⣤⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠋⡎⠀⠀⠀⠀⠈⢆⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡃⠀⠀⠀⡃⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠉⢆⡀⢱⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡐⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡉⡝⠀⠀⡇⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠈⠳⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠪⣄⡜⠀⠁⠢⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠑⠀⡇⠀⠀⡖⠉⡆⠀⠀⠀⢀⠗⠶⢀⣀⠤⠴⢤⡀⠀⠀ ⠀⠀⠀⠀⣀⠤⠤⣄⡠⠴⢳⡀⠀⠈⢈⠠⢄⠂⢐⡜⠀⠀⢸⡔⢀⡀⠀⠱⠀⠀ ⠀⠀⠀⣏⠐⠉⠓⢠⠬⠵⣄⠈⠻⢲⢤⣳⡽⢶⡛⠉⠐⢦⡠⠼⣾⠃⠀⠀⢣⠀ ⠀⠀⡜⢁⠋⠔⠲⢀⠵⡒⠃⢃⠀⡆⠈⠰⠍⠀⠊⠢⢠⠊⠀⠀⠀⢦⠀⠀⠈⡄ ⠀⢸⠀⢸⠀⠒⢣⠁⠀⢸⠈⢻⣀⠃⠑⠀⠈⠆⠀⠀⢡⠡⣀⠀⡀⠦⡀⠀⠀⡇ ⠀⠘⣆⠀⠑⠒⠊⠒⠐⠓⣤⣼⣁⠀⠀⠀⠀⢸⡀⠀⢠⣁⣀⣀⣀⠤⠖⠐⠂⠁ ⠀⠀⠈⠳⣄⠀⢀⠀⣀⣴⡧⣀⠙⠒⠠⣤⠐⠊⡍⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠳⣄⠙⠪⢢⠂⠉⠀⠀⠴⠤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⣤⢟⡀⠀⠘⢄⣀⡀⡌⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠰⠥⠤⠬⠐⠂⠠⠤⠤⠔⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡫⠿⡶⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡻⠋⣀⢼⣡⣶⠿⠋⠀⠀⠀⣀⣠⣤⣤⣴⣶⣦⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡝⢁⣼⣿⡿⠟⠁⠀⠀⣠⣴⡿⢟⣛⠭⠽⢵⡄⠀⠉⠻⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢷⢡⣾⣿⠏⠀⠀⠀⣴⣿⠟⣩⠖⢋⣥⠴⠚⠉⠀⠀⠀⢀⣽⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢸⡜⣾⠏⠀⠀⢀⣾⡟⢡⢞⡥⣺⣵⣶⠿⠿⠿⠿⠿⠿⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣼⣾⣿⣶⠶⣶⣾⣿⣤⣀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠛⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⡾⠉⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣿⠀⠀⠀⠀⠀⢸⢿⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣤⣴⠶⠤⠀⠀⠀⠈⠻⠋⠉⠀⢸⣿⠀⠀⠀⠀⣴⣇⣀⣠⡟ ⠀⠀⠀⠀⢰⣆⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⢰⣷⠀⣀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠉⠘⠿⠁ ⠀⠀⠀⠀⢻⣬⠇⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠛⠛⠛⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⢀⡟⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠿⠿⣷⣦⣄⠀⠀⠀⠿⠛⠀ ⢀⣴⣶⠿⠿⠿⠿⠿⠟⠛⠛⠛⢛⣿⣿⠿⠿⢷⣶⣶⣶⡾⠿⠟⠛⠉⠈⠻⣷⣄⣀⡀⠈⠻⣿⡄⠀⠀⠀⠀ ⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣿⠀⠀⢸⣷⠀⠀⠀⠀ ⠈⠻⠿⠷⠿⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠋⠀⢀⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢻⣷⣄⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣽⣿⣿⣶⣶⣶⣶⡿⠟⠻⣿⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢻⣷⣤⣄⡀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⣿⠏⠙⠛⠿⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡽⣿⡆⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⠟⠋⠉⠀⠀⠉⠉⢳⠏⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠶⢤⠾⠀⣀⠀⠳⣤⣬⠏⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⣀⣯⣤⠄⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⠖⢠⣀⣈⡀⢀⡀⢀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢿⢾⠓⠛⠛⠟⠓⠚⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠒⢲⠟⠁⠀⠈⠈⠆⠀⠀⠀⠀⠀⠘⠈⠙⢶⠦⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⣸⠋⠉⠉⠁⠒⠒⠢⢄⡀⣀⠤⠄⠒⠒⠁⠈⢣⡀⠀⠈⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣴⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢆⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠾⠋⠁⠻⡷⣄⣀⠀⠀⠀⠀⣀⡼⠹⢄⡀⠀⠀⠀⠀⢀⡴⣿⠉⠛⠦⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣷⠀⠊⢍⠉⠉⣩⠥⠂⠀⠒⢬⡉⠉⠛⠉⡩⠊⡏⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⡴⣶⣾⣶⣀⣠⡼⢦⡀⠀⠀⣰⡟⣧⡀⠀⠁⢻⠑⠀⠀⠂⠀⠀⢚⠑⡄⠈⠀⣼⣅⠀⠀⠀⣰⠷⣄⠀⣴⣶⣶⢦⣄⠀ ⠀⣿⠀⢻⣏⠙⠋⠁⠀⠀⠙⡶⠋⠀⢠⣟⠁⠐⠂⣰⠓⠒⠠⠤⠀⠀⠚⡄⠀⠀⢾⡇⠈⠙⡲⠋⠀⠀⠈⠻⣅⣈⣿⠀⣿⠀ ⢠⡽⠋⣀⡙⠢⣀⣄⠀⣀⠔⢁⣀⠴⠿⠿⠿⠷⣶⠤⣤⣀⣀⣀⣀⡠⣴⣁⣤⣤⣾⣷⢄⣀⠈⠂⠀⢀⣠⡀⠼⢟⡁⠚⢯⡀ ⠹⠷⠺⣟⣠⠞⠉⠉⣹⠿⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣁⠀⠀⠙⣯⠤⠴⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣿⠦⣄⣻⡶⠴⠇ ⠀⠀⠀⠈⠁⠀⠀⣾⠃⠐⢤⡀⠀⢄⡀⠀⠀⠀⠀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢳⠀⠀⠉⠑⠒⠂⠀⠀⠀⠀⠈⢙⣦⣄⡀⠀⠀⢤⡀⠀⠀⠤⠊⠀⠀⢀⠎⣸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠷⢴⣶⠒⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⣿⣿⣿⠿⠶⢦⣄⡉⠲⠤⣀⣀⣀⣀⣎⣴⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠖⠒⠚⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠛⠛⠳⠖⠆⠠⣄⣠⣤⠔⠉⠉⠙⠉⠑⠓⠒⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⣿⣥⣶⠟⣿⣽⣿⠏ ⠀⣀⡄⠀⠀⢀⡠⠔⠛⠉⠉⠉⠉⢉⣩⡷⠟⡗⠀⠀⣀⣤⡴⠖⠛⠉⠀⠀⠀⠀⢀⠈⠀⠀⠀⠂⠀⠦⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⣤⣤⣤⡄⣗⣛⣻⣿⣿⣆⣿⡄⣿⣦ ⠊⠉⢀⣠⠚⢉⣀⣀⣤⣴⣶⡶⠿⠟⠉⢀⣰⡷⠞⢋⣉⣠⣶⠀⠀⠀⠀⠀⠆⡤⢀⡠⠂⠀⠀⣰⢆⡰⢴⣦⡹⣆⠀⠀⠀⠀⢀⣴⢏⣀⣀⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠘⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⣀⣤⡴⠟⣉⣀⣤⡾⠻⠽⡇⠀⠀⠀⠀⢀⡼⡱⠋⠀⠀⠀⣼⠃⠈⠇⠀⣠⡼⠟⢿⡷⣄⣠⡞⠁⠀⠉⠉⠛⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣠⣾⠟⣋⣉⣵⣀⠀⠁⣤⠀⠀⠀⡾⠁⠀⣀⡔⠀⢐⣻⣤⣀⣀⣀⣿⣇⠀⠀⢿⡘⢻⡄⠀⠀⠀⠀⡀⠀⠉⠉⠉⠉⠉⠉⠛⣛⣛⣻⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⡏⠀⠉⠉⢉⣩⣭⠿⠟⢀⠀⠀⡇⡆⢸⠉⠕⠀⢿⣿⡿⠛⣽⣍⡙⣿⡆⢠⡀⠙⢧⠻⣆⠀⠀⠀⠐⠂⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡿⠉⢷⠶⠞⠛⠉⠁⠀⠀⣠⠏⠋⢰⣷⣶⣿⠲⠶⠦⠄⠁⠀⠀⠈⢛⢿⣿⣿⡈⣿⠀⠈⠳⣞⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠏⣨⣷⠚⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣜⠟⣠⠄⠀⠚⣉⠁⠀⠀⠀⠀⠀⠀⠩⣟⣷⡌⢷⡀⠀⠈⠑⠘⣷⣤⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢇⠁⠀⠀⠈⣿⢧⡠⠀⠠⣍⠀⠀⢀⡀⠀⠀⠀⠈⠛⠛⣿⡿⢿⣦⣀⣀⣼⣿⣇⣤⢀⡄⢉⡀⢀⣀⠘⢿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠻⠀⠐⠀⠀⠈⠃⠙⠲⠤⢤⣀⠀⣀⠈⡁⠀⠀⠀⣀⡴⠛⠳⣤⡉⠙⠛⠛⠋⠉⣽⠋⣼⣿⣵⣿⠟⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣤⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⣴⡾⠋⠀⠀⠀⠈⠻⣦⠀⠀⠀⠴⠀⠸⣿⠋⠈⠁⠀⣼⣿⣿⡏⣿⣷ ⠀⠀⠀⠀⣀⣴⣿⣟⠁⠀⠀⠀⣀⣤⠞⠛⠉⢙⡻⠆⠴⠒⠀⠀⠉⢿⣶⣷⣷⣶⣶⣶⣶⣶⣶⣾⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⠶⣤⣀⠈⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿ ⠀⣀⣤⣾⣿⠟⠙⣿⣷⣤⡶⠛⠋⠀⠀⠀⠀⡨⠖⠃⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⠀⠀⠀⠉⠻⣦⡀⠀⢸⡿⢋⣵⣿⣿⣿ ⣾⣿⠿⠿⠿⠿⠿⣿⣿⡟⠀⠀⠀⠀⡄⠀⠘⢦⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⢀⠀⠀⠀⢻⣷⡀⠈⢠⣾⣿⣿⣿⣿ ⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⡆⠀⢰⠃⠀⠀⠀⣨⡟⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠒⠂⠀⠀⠈⡧⠀⢀⣸⣿⣧⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⢷⠀⢸⣷⣆⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠲⣾⣯⣿⣾⠉⢠⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣴⠞⠉⠈⢻⣦⣸⣦⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣄⡿⣫⣸⣿⠏⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠐⠿⣿⣿⠀⠀⠀⠀⠉⢻⠙⢉⠿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⢿⡿⠿⡽⡿⠟⠁⠀⠀⠙⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢹⡿⠀⡀⠀⠀⠀⢈⣷⠋⠀⠀⢈⣿⣿⣷⣆⡀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣼⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠀⠀⠁⠀⠀⠀⠀⠀⢀⠸⡀⣿⡏⠉⠉⠛ ⣆⠀⠀⠀⣼⣃⣼⠃⠀⠀⠀⣾⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠛⠁⠀⠉⠛⠿⣿⣶⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⢸⡆⠀⣿⣿⣄⠀⠀ ⡏⡀⠀⣰⣟⡟⠁⢦⠀⠀⡾⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⢀⢀⣀⠀⠀⢀⣀⠈⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠁⠀⠀⣸⠃⢀⣿⣿⣿⣷⣔ ⠁⣴⡾⣿⡿⢰⠀⢨⣶⣿⣁⠀⢀⣴⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⠿⣶⣶⣶⡟⠉⠻⠿⠶⠛⠿⠿⠿⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⢀⠀⣀⣤⣆⣰⠋⠀⠘⣿⡟⢿⣿⡿ ⣿⠉⢸⣿⠀⣻⠀⠾⣻⣿⣯⣶⣿⣿⡿⠁⠀⠀⢠⣿⣿⣿⢻⣷⢠⣤⣀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣤⡶⢛⡿⢫⣽⣿⣿⠟⠉⢿⣿⣿⣿⣿⣶⣾⡿⠇⠀⢸⠀⠻⣧⠀⠹⣿ ⣿⠀⣼⣿⠀⣿⠀⠀⠁⣿⣿⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣾⠿⠿⠿⠿⠿⠷⠶⠶⠿⠿⠟⠛⠛⠋⢀⣫⣶⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⡃⠲⠀⢈⡇⢠⣿⣇⡀⠈ ⣿⣶⣸⠟⡇⠘⡆⠀⠀⠘⣿⣿⡅⠀⠀⠀⠀⠀⢸⣿⢿⣿⣦⣿⡿⣶⣤⣀⠀⣀⣀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⣋⡴⠟⠁⣿⠀⠀⠀⠀⢈⣿⣿⣿⡿⢃⠀⠀⢸⣆⣿⣿⣿⣿⣶ ⣿⢿⣿⠀⢹⣄⡁⠀⢠⠀⢘⣿⡀⡀⠀⠀⠀⠀⢸⣿⢞⠏⠙⣿⣿⣦⣍⠙⠿⢶⣯⣍⣤⣶⣾⣿⠿⠿⠛⣡⠟⠉⠀⢀⣾⣿⠀⠀⢀⣴⣿⡿⣿⣿⠃⢸⠀⠠⡿⠋⡿⣿⡎⢙⣿ ⠋⢸⣯⠀⠈⣿⡅⠀⡼⠀⢢⣿⣧⠃⠀⠀⠀⠀⢠⣿⣯⣷⠀⠈⢿⠙⠿⠿⠋⠉⠀⠶⠶⠆⠀⠀⠀⢀⣾⠋⠀⣀⣤⣾⣿⣿⣤⣶⣿⠟⠁⠀⣿⡏⠀⠘⠀⠀⣴⣦⢀⣿⣿⠈⣡ ⠀⢸⣿⠀⠀⠈⠓⠚⠃⢠⣿⢽⣿⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣤⣸⣦⣄⠠⣀⣀⣐⣂⣒⣦⣀⣤⣤⠾⢿⡶⠟⠛⠛⠛⣻⣿⣿⣿⠁⠀⠀⢸⣿⢧⠀⠀⢠⣴⣿⠇⠀⣿⣿⣾⣿ ⡆⠀⣿⣷⡄⣿⠀⠀⢠⣯⣿⡟⠁⠀⢠⣾⣿⡿⢻⣿⣿⣿⣟⠛⠛⠛⠛⠛⠉⣽⣋⠉⠁⠀⠀⠀⠹⣶⣿⣳⣦⣄⣠⣾⣿⣿⣿⣿⠀⠀⠀⠈⣿⣎⢧⡀⠀⠈⠁⠄⠰⣿⣿⣿⣿ ⣿⣦⣼⣿⣇⠛⢳⡄⣼⡿⢿⡁⢠⡄⣿⣿⣿⠇⣼⣿⣿⣿⣯⣄⣀⡐⠐⠂⠰⢾⣻⣅⣤⣄⣤⣄⣴⣿⣿⠿⣛⣻⣍⣽⡏⢛⣿⡏⠀⠀⠀⠀⢸⣇⣸⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿ ⠈⠉⠛⣿⣛⣧⣴⣿⡿⢷⣾⣯⣿⡇⣿⣿⡟⢸⣿⣎⣉⡙⠛⠛⠽⠿⠿⣿⣷⣿⣿⣶⣦⣶⣶⣿⣾⣿⣿⠟⠿⠛⢛⣁⣠⣤⣿⣇⣠⣴⣶⣾⣿⣿⢟⡱⡄⡠⠀⢰⣿⣿⣿⡟⠻ ⠀⠀⠀⢻⡏⣿⣿⡷⠾⠿⣿⣿⣿⠇⣿⣿⣯⣿⣿⣿⣟⣛⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⡟⣛⡛⠭⠾⠁⢸⣿⠿⠟⠛⠉⠹⣷⣾⡷⢿⣥⣜⣙⡛⠙⣿⡇⠀ ⠀⠀⠀⠈⣷⣻⡿⢧⠀⠀⠈⠉⠙⠻⢿⣿⢛⠌⡯⠌⠛⠯⢟⡿⠿⣼⣿⣳⣶⠿⣿⣿⠀⢉⣿⠿⢿⡗⠾⢏⠁⠀⠀⠀⠀⠀⠀⣻⡀⠀⣀⣀⣼⣿⡿⠷⢶⣿⡟⢨⣧⠀⢻⣿⡄

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢰⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠘⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡤⠿⠆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⠀⢀⠀⠀⣤⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢹⡀⠐⢻⠃⠀⠙⢁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⡇⠀⢠⣄⣀⣠⣾⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⡀⠀⠙⠛⠛⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢋⣿⠟⠿⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢽⣦⣀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢽⣻⣯⠴⣶⠛⠉⠙⢦⡤⠖⠒⠶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡤⠶⠒⠋⣩⠾⢋⣡⠟⠉⢰⣧⠴⠛⠉⠉⠀⣴⠶⢶⠋⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⢾⣉⠀⣀⡴⠶⠚⢛⣠⡟⠉⢻⠂⠀⠀⢠⢤⣀⣏⠙⢿⡇⠈⢷⢺⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢯⡆⣼⠞⢿⡤⠤⠴⠚⢿⠀⠀⢸⠀⣖⠲⢾⢠⡈⢿⣧⣬⣷⣤⣿⠿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠛⢦⠀⢧⠀⠀⠀⠘⢧⣲⣾⣧⣙⣦⡈⢻⣷⣼⣿⣿⡽⠛⣦⠀⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡈⢣⠈⣆⠀⠀⠀⢨⡟⢳⡟⠛⠯⣟⠻⢿⡋⠛⣇⠀⠋⠈⢧⡟⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢾⣇⣸⠶⢤⣀⣸⣋⣻⡛⠶⠾⠋⣦⠈⠻⠇⣸⢧⣷⢀⡾⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⣤⣴⡾⠟ ⠀⠀⠀⠀⠀⠀⠈⢳⡋⠀⣼⣮⣿⣌⣿⠳⠤⠤⠄⣼⠀⠀⡼⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠋⣹⣿⣾⣍⡳⠤⠖⠀⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⠀⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⢈⡇⣿⣿⣯⣿⣿⡟⠉⠉⠉⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣶⡦⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⢀⡴⠋⠓⡼⠿⣿⣿⢸⠁⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣉⣉⣿⣦⣤⣦⠀ ⠀⠀⡸⠃⠀⠀⣠⠞⠁⣠⠞⠁⠀⠈⢻⡰⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⣿⡧⠁⠀ ⠀⣼⣣⣤⠴⠞⠃⣠⠞⠁⠀⠀⠀⠀⠀⢻⠡⠀⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠉⠁⠀⠀ ⢰⡏⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⣦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⡀⠀⠀⠀⠀ ⠈⠻⡄⠀⢸⡏⠙⢦⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⠀⠘⡆⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀ ⠀⠀⠈⢦⡀⠳⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠸⡽⡆⠀⠛⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡄⠹⣆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠹⣞⢤⣀⠀⠘⠲⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣌⠘⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⡉⠳⣄⠐⢦⣀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠶⣤⣈⠙⠒⠂⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡏⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢴⣶⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣠⠤⠞⠋⠁⠳⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⣄⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠛⠛⠛⠋⠉⢉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⢒⣒⢛⣉⣠⡬⣿⣸⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⢿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣶⠛⠉⠉⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⡼⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⠀⠀⠀⠀⢸⡏⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢹⢧⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠙⠄⠀⠀⠘⡟⠲⢤⣤⡀⠀⠀⠀⠀⢠⡶⠛⠉⠈⠀⠀⠀⠀⠈⠉⠛⠶⡶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠙⢷⡀⠀⣴⠟⠁⢀⡤⠤⢤⡀⠀⠀⠀⠀⠀⡼⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢻⣼⡏⢀⣀⠈⠙⠒⠲⠇⡀⠀⢀⡤⠤⣷⣄⣀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣀⣴⠚⢻⣿⠿⣿⣧⡀⠰⣀⣀⡛⠃⣀⠙⠦⣄⡇⠀⢸⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠷⣤⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣼⡇⠀⠀⠉⠛⠦⣀⠀⠈⠒⠋⠀⠀⠀⠀⠀⢸⡇⠀⢈⣹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⣄⠀⠀⠀⠀⢸⠓⠒⠒⠲⠤⣿⣿⠷⣤⣿⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣶⣄⠀⠀⣿⠀⢠⠀⠀⣧⠀⠀⠀⠀⣶⣿⡀⠻⣷⣤⣀⣰⠏⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠮⣳⣄⠻⣦⣸⣆⡀⠈⢳⣄⠀⠀⢸⣿⣿⣦⣈⠙⠾⣍⡛⠒⠒⠂⠀⠒⠒⠚⠉⠀⠹⡄⠀⠈⠙⠻⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠰⣦⣄⡈⠘⠓⠀⣿⠛⣏⠙⠛⠉⠳⢾⡿⠿⣿⣿⣿⡳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠙⢷⡄⠀⠀ ⠀⠀⠀⠀⠈⡙⠛⠷⢄⠀⣿⠸⡌⠳⢤⣀⣀⣀⣀⣀⣈⣻⣯⣿⣦⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠶⠄⠐⣿⡀⠈⢳⠀⣰⠦⠀⠀⠀⠀⠈⠉⠝⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠓⠦⠄⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠲⡄⢷⡇⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠙⢦⣄⠀⠀⠀⡴⠋⠹⣧⣤⣾⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠘⢈⠳⢄⣀⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣸⣇⠀⠀⠹⠿⣧⣀⣀⠤⠴⠶⢤⡀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠈⢦⠀⠀⠀⠈⠁⠒⠂⣸⠛⠉⠉⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠈⠣⣼⡆ ⠀⠀⠀⠀⠀⠠⠴⠞⢒⠀⠀⣸⡄⠀⠈⣇⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡆ ⠀⠀⠀⠀⣀⡤⣶⠶⠋⠀⢀⡏⠙⢆⢀⠎⠑⠒⠒⠒⠂⠤⠀⠀⠀⠐⠒⠲⡇⠀⣩⢿⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣀⡠⠄⢠⡇ ⠀⠀⠀⠾⠗⢋⣡⣴⠞⠁⣸⠇⠀⠈⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡸⠁⠈⠻⣆⠀⠀⠀⣀⡴⠛⠉⠉⠉⠀⣀⣴⠟⠀ ⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⣿⠀⠀⠀⠀⡿⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠈⠙⣟⠛⠛⠛⠒⠶⠦⠴⠾⠋⠁⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣦⣄⣀⡀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⣀⣀⡤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠆⠀⠀⠀⠀⠀⠀ ⠙⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢁⠠⣴⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⢍⠂⢄⠀⠀⠀⠘⣆⠘⡄⢂⠘⠀⣀⣀⡀⠀⠀ ⠀⠀⠈⢆⢑⠄⣈⡰⢒⣒⢞⣶⣾⣦⢟⡇⠁⢊⢗⠤⠀ ⠀⠀⠀⠀⠑⠅⡎⢹⣿⡎⣽⠻⡏⣟⣌⣯⠱⡀⢆⢃⠀ ⠀⠀⠀⠀⠀⢰⢁⣿⣿⢾⣁⠍⠴⣿⡿⡟⣔⣁⡘⢊⡆ ⠀⢀⣤⢦⡀⠀⠏⠆⢻⣢⣩⠀⠀⠀⣡⠇⢹⢧⡇⠀⠁ ⠘⣷⡻⠊⠪⡂⠀⠈⠈⣙⣷⢶⣥⠊⣿⣤⠞⠺⡇⠀⠀ ⠀⠸⣟⠀⣀⡇⠀⠀⡌⣽⡼⠙⢁⢸⡿⠁⠀⠀⢠⠀⠀ ⠀⠀⠀⢉⣿⡇⠀⠔⠋⠙⠀⠞⠁⢈⡃⢰⡄⠀⠘⡀⠀ ⠀⠀⠀⢸⠙⢛⡁⠀⠀⠀⠀⠀⠀⠈⣧⠏⢁⠀⠀⢃⠀ ⠀⠀⠀⠸⡀⠈⠢⢀⣀⠄⢀⣋⠁⠜⡏⠀⢀⠇⠀⢸⠀ ⠀⠀⠀⠀⢱⡀⢀⠎⠱⡀⠀⠀⠀⠈⠢⡀⢸⠀⠀⠎⠀ ⠀⠀⠀⠀⠀⠉⠁⠀⢀⠇⠀⠀⠀⠀⠀⠈⢺⢒⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⢀⡸⠾⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⡀⠫⡶⠦⣤⠀⢶⢡⡄⠀⠀⠰⡀ ⠀⠀⠀⠀⠀⠀⡞⠢⢧⣠⠉⢂⡀⢉⠀⢈⡦⢠⣎⣦⢇ ⠀⠀⠀⠀⠀⠰⠁⠀⠀⠉⠺⣸⣿⠹⣀⠾⢃⡗⠉⠃⢸ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠏⠀⠃⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠌⠀⠀⠘⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠋⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⣡⣞⣴⡿⠋⠀⠀⢀⣀⣠⣤⣤⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⢃⣾⡿⠛⠁⠀⣠⡶⢟⡫⠽⢛⡷⠀⠈⠻⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⣿⡟⠀⠀⢠⡾⢋⠔⣩⣔⣪⣥⣤⣤⣤⣴⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣧⣿⣧⣤⣴⣿⣁⢉⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠁⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⣤⠇⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⣿⡆⠀⠀⠀⡸⠷⣄ ⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠰⠾⠛⠂⠀⣀⠈⠃⠀⠀⣿⠃⠀⠀⠘⠷⢤⡾ ⠀⠀⠀⢸⣛⡆⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠶⠆⠀⢰⡟⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠉⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢀⡷⡆ ⠀⠀⣀⣀⣤⣤⣤⣤⣬⣿⣷⣦⣤⣀⣀⣀⣀⣠⣤⣴⠿⢿⣟⠛⠛⠷⣦⡀⠀⠋⠁ ⢠⣿⠋⠉⠉⠉⠁⠀⠀⢀⣿⠏⠉⠉⠛⠛⠛⠉⠁⠀⠀⠈⢿⡷⣶⠄⠘⣷⠀⠀⠀ ⠈⠛⠷⠶⠶⠶⣤⣤⡴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠀⣠⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠶⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣽⣿⣶⣶⡶⠶⠿⠻⣯⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠹⣷⣄⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣦⡀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠟⠛⠷⣶⣼⠇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣖⡛⠛⠛⠒⠂⣠⣤⠤⠂⠉⠉⠉⠀⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣶⠛⣿⢿⡏ ⠠⠆⠀⠠⠔⠈⢁⣀⣀⣤⡴⠟⠉⣧⡤⠴⢒⣉⠁⠀⠀⢀⠀⠀⢀⠀⠀⢀⠈⣀⡘⣆⠀⠀⠀⠀⢀⡔⠀⢺⣿⣿⣼⣿⣿⣿⣿⣿⣾⣷ ⠀⠐⠾⠒⠒⠛⠛⠉⠉⢁⣀⡴⢛⣁⣤⣽⣿⠇⠀⠀⠀⢀⣮⠞⠁⠀⣰⠋⠃⠈⢩⡿⢶⣦⣀⣴⠋⠘⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣴⡟⢩⣽⣄⣀⣠⡄⠀⢀⠏⠀⣠⠂⢀⣿⣤⣤⣤⣿⡄⠀⠳⣙⣧⠀⠀⠀⠀⠀⠈⠉⣉⣉⣉⣻⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣀⣠⡤⠴⠚⠋⢡⠄⢨⣛⣸⣀⣁⠘⠿⠋⠹⢷⣼⣿⡐⣦⠈⢿⣷⣄⠀⠀⠐⠒⠟⠿⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⢛⡧⠊⠉⠀⠀⠀⠀⢠⠃⠀⡸⢟⡉⠀⢞⡃⠀⠀⠀⠀⠙⢻⣷⡙⣄⠀⠙⠋⢷⣄⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⠋⣠⠟⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠙⣿⣄⠀⠨⠁⠀⠀⠀⠀⠀⠘⠛⣿⡟⢧⣤⣤⣾⣧⣄⡀⣉⡀⣠⡀⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⢡⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⢀⣤⠞⠉⠙⢦⡈⠉⠁⢀⠋⣰⡿⠻⠟⢀⣿⣿⣿⣿ ⠀⠀⠀⢀⣴⣾⠋⠀⠀⠀⣠⠴⠖⠲⡯⢠⠤⠈⠙⢿⣵⣤⣤⣤⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⠀⠀⠹⠦⠶⢤⣀⠘⠃⠀⠀⣼⣿⣿⣾⣿ ⢀⣠⣶⣿⠋⢻⣷⣤⠖⠋⠁⠀⠀⡼⠛⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠈⠙⢦⡀⠀⡿⢋⣽⣿⣿ ⠿⠛⠛⠛⠛⠛⣿⠇⢀⠀⢠⠀⠀⠓⢤⣄⡠⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠘⣿⡀⣠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣾⡆⢹⠀⢸⣤⢠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⣶⣤⠃⣠⣺⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⡴⠋⠉⢿⣌⣧⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣴⢿⣽⡿⠛⢿⣿⣿⣿⣿ ⠀⠀⠙⢿⡇⠀⠀⠀⠈⢏⡸⠛⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠟⠛⠛⠋⠀⠀⡈⣿⡿⠿⣿ ⡄⠀⠀⣸⠃⡖⠀⠀⢠⡟⠀⠀⢰⣿⣿⣿⣶⣦⣤⣴⣶⣤⣴⠾⠋⠙⠿⣶⣤⣤⣤⣄⣠⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣦⠁⣿⣇⠀⠀ ⡇⠀⣠⣿⠏⢠⡀⢠⠎⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⢁⡀⣀⢀⠀⣀⣉⣙⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡟⠀⣿⣿⣷⣤ ⣠⠾⣿⠏⡆⢀⣿⣿⡄⣠⣾⡿⠋⠙⢿⣿⣿⣿⡟⠻⠷⠚⠁⠙⠛⠉⠙⠛⠛⠛⢉⣻⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣦⡜⠁⠀⣿⡟⢿⣿ ⣇⢀⣿⠀⡇⠈⠙⣿⣿⣿⠟⠁⠀⠀⣸⣿⣿⣿⣿⣿⣶⣤⣶⣦⣤⣤⣴⡶⠶⠞⠋⣟⣴⣿⣿⡏⠀⠙⣿⣿⣿⣿⣿⠁⠀⣇⢈⣧⠀⠙ ⣿⣾⡿⡆⠳⠀⠀⠻⣿⡇⠀⠀⠀⠀⣽⣿⣿⣮⣿⢷⣄⡀⢀⣀⡀⠀⠀⣀⣤⣶⣾⢟⡽⠟⢹⡇⠀⠀⠈⣿⣿⣿⠟⠀⢀⣧⣾⣿⣿⣦ ⡿⣿⠇⢹⣤⠀⢠⠀⢽⣇⠀⠀⠀⠀⢻⣏⡏⠙⣿⣷⣭⣙⣿⠿⣵⠶⠿⠟⠛⢋⡽⠋⠀⣠⣿⡇⢀⣴⣾⠿⣿⡏⠀⠀⠘⠋⠛⣿⡈⠿ ⠀⣿⡀⠀⠻⠤⠎⢠⣞⣿⠀⠀⢀⣀⣼⣿⣷⣄⠘⣄⠉⠁⠀⠀⠉⣁⠀⢀⣰⣿⣤⣴⠾⠿⣿⣿⣿⠋⠀⢠⣿⡅⠀⢀⣰⡿⠀⣿⣧⣾ ⡄⢸⣧⡀⡆⠀⢠⣿⣿⠋⠀⣰⣿⣿⣿⣿⣿⡟⠛⠻⠷⠛⢻⡛⠉⠉⠉⠙⣷⣾⣶⣀⣀⣴⣿⣿⣿⠀⠀⠈⣿⡷⡀⠈⠉⠁⠀⣿⣿⣿ ⠿⣶⣿⣧⠛⢦⣼⣟⣧⣠⡔⣿⣿⢃⡿⠿⣿⣷⣤⣄⣀⣀⣺⣿⠤⠤⠤⣤⣿⣿⣿⣿⣯⡿⠋⢻⡇⠀⠀⢀⣸⣧⣧⠀⠀⠀⣼⣿⣿⣿ ⠀⠀⢹⡾⣷⣿⣫⣿⣿⣿⡷⣿⣏⣼⣿⣶⣦⣤⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣥⣤⣶⡾⠻⣷⣾⡿⠿⢿⣛⣿⣷⣃⡤⡿⢿⡏⠈ ⠀⠀⠈⣧⣿⠿⠀⠈⠉⠛⠾⣿⠟⠛⡏⠛⢿⡻⠿⣽⣿⣿⠿⣿⣿⠙⣿⠿⣿⠻⠟⠁⠁⠀⠀⠀⣿⠀⢀⣀⣾⣿⠷⣼⣿⠋⣧⠈⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠈⠁⠉⠉⠳⢖⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⡫⠊⠀⠀⠀⠀⠀⠀⠀⠻⡧⠀⠈⢓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠔⠀⠀⡠⠒⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠆⢂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⠀⠀⡘⠀⣠⣦⠀⡇⠀⠀⡐⠈⠉⠐⡄⠈⡈⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⠀⠀⠀⡇⠀⣿⡿⢠⠁⠀⠀⣧⣶⡆⠀⢰⠀⢃⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⡱⠀⠀⠀⠀⠈⠒⠂⠄⠃⣀⣀⠀⢿⡿⠃⠀⡸⠀⠘⡌⡄⠀⠀⠀⠀ ⠀⠀⠀⢇⡬⢼⠀⠀⠀⠀⠑⠄⢀⡱⡀⠁⢈⠑⠒⠊⠁⠀⠀⣰⢧⠀⠀⠀⠀ ⠀⠀⡶⢿⡖⢸⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⡀⠀⠀⠀ ⠀⢸⡿⢶⡗⡄⣀⣿⢒⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⠹⠁⠀⢃⠀⠀⠀ ⠀⢀⡏⠉⠢⡁⠀⠀⠀⠀⡀⠄⠒⠛⠋⢍⠉⠙⠣⡀⠟⡀⠀⠇⠀⠘⡄⠀⠀ ⠀⣌⣸⣣⡜⠉⢲⡆⡄⡘⠀⠀⠀⠀⠀⠀⢡⢠⠀⢸⢸⣇⠀⠘⡀⠀⢡⠀⠀ ⢠⠋⣽⢻⡇⢀⣧⡡⠁⠃⠀⠀⠀⠀⠀⠀⠀⠃⠳⡊⠀⡾⡀⠀⢃⠀⠈⡄⠀ ⡜⠀⢹⠗⠽⡙⡿⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠱⠀⠸⣣⠀⠈⡄⠀⢡⠀ ⡇⠀⡌⠀⡰⡙⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠆⠀⢰⠀⠀⠹⣇⠀⠸⡀⠈⡀ ⠣⣀⣓⡪⠟⠀⠘⢄⡀⠀⠐⠄⣀⣀⣀⠤⠊⠀⣠⠎⠀⠀⠀⠱⡦⠴⢃⠴⠀ ⠀⠀⣀⠠⠤⠤⠐⠒⠉⠀⠀⠁⢹⠀⡃⠉⠀⠉⠈⠉⠒⠠⠄⢀⡀⠉⠁⠀⠀ ⠀⢸⠀⢰⠁⢰⠊⠀⠀⢀⡠⠂⠁⠀⠁⠂⢄⡀⠀⠀⢰⠀⢰⠀⣸⠀⠀⠀⠀ ⠀⠀⠈⠉⠒⠚⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠒⠈⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⢉⡠⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⠔⡹⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⠞⢁⠔⢁⡼⠋⣉⡉⠉⠓⠲⠤⢤⣤⣤⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢠⣃⣴⡡⣶⣿⣊⡁⠀⠠⠭⠥⠒⣁⡠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢘⣴⠟⠒⠛⢿⣉⣉⡙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣦⠊⠈⣉⣻⣷⣄⢩⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡴⠛⠁⠀⠸⣉⡷⢹⠉⠸⣿⢂⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢀⣀⠀⡠⠙⠻⣿⣶⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⣟⡄⠀⠀⠀⡰⣡⠾⠟⠫⣄⠀⠀⠉⡛⠉⡆⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⢧⠀⠀⠀⠇⠛⠁⠍⠁⠚⠛⠶⢲⠳⡞⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣟⠢⣑⠦⣀⠀⠀⠀⠀⠀⠂⠤⢤⣄⣴⣷⡏⠋⠀⠀⠀⠀⣠⣀⡀⠀⠀ ⠀⢀⡞⠁⠀⠈⠓⠬⣉⠒⡖⠒⠒⠒⡖⠚⡟⠉⠁⢻⠀⣀⣤⠶⣛⢁⠬⠝⣷⠀ ⢀⡟⠀⠀⣀⣀⡀⠀⢀⣉⣳⠀⢀⡠⠧⠤⢞⢶⡶⠾⣾⠁⢝⠒⢁⠜⠀⠀⠛⡆ ⢸⠇⡠⠚⠀⠀⢈⠳⠀⡀⠀⠹⣧⢀⠀⠀⠀⠉⠻⣄⢹⠀⠀⠀⡠⠀⠀⠀⠐⡧ ⢸⣾⠁⠀⠀⠀⠈⠂⠣⠈⠄⠀⡻⢾⢆⣀⠀⠀⠀⠘⣎⠳⣄⡰⠂⠀⠀⠀⢀⡇ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⠆⢠⠋⠲⢄⠊⡑⢆⠀⡄⡟⢀⣸⠧⠂⠀⠀⠀⢸⠀ ⠀⢻⣤⣀⠀⠀⠀⠀⢀⡨⢄⠁⠀⠀⣀⠱⣼⡠⠟⠚⠟⠉⢁⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⢻⠟⢷⣒⡒⠊⠋⠀⠀⠑⡀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠈⢷⣄⣱⡀⠀⢄⠀⠀⠑⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⠀⠀⠀⠈⠳⣌⣙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⢹⣶⣶⣉⣳⣦⣤⣄⣀⣀⣤⣀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣂⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠏⠀⣼⣿⠀⣀⣤⣶⣶⡾⢿⡋⠁⣴⣿⣿⡇⠀⠀⢀⣠⣤⣶⣾⣿⠿⠛⢋⣭⣶⣶⣀⣀⣀⢀⣀⣠⣤⣤⡤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠟⢋⡾⠋⠀⣸⣿⣿⠿⣿⡿⢻⣿⡄⠀⢧⣼⣿⣣⠟⢳⣤⣾⣿⡿⢿⣿⠏⣀⣤⣴⢟⣿⠟⢩⣼⣿⢿⣿⡿⠛⠉⠁⣠⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⢻⣇⣴⠟⠀⠀⣰⣿⢿⣿⡀⠈⢧⢸⡏⣳⣀⣾⣿⠟⠁⣠⡟⠋⠈⠁⢠⣿⠟⠉⣡⡾⢋⣾⣯⠴⠛⠋⢁⣾⠏⠀⠀⣠⣾⣿⣿⠏⠀⣀⣤⣶⣶⣶⣾⣿⠿⢿⣄⣤ ⠀⠘⠉⢀⣾⣟⣿⣧⡀⣰⣿⣧⠟⣿⡧⠀⣈⣿⡟⠉⣿⣿⠃⡀⣰⠏⠀⠀⠠⠚⣹⠇⠀⣴⣿⠾⣻⠟⠀⠀⠀⠀⣼⠏⠀⣠⣾⠟⣽⡿⠃⠀⠀⢛⠋⣩⣿⠟⠀⠀⣠⡾⣿⠇ ⠀⠀⠰⣿⣿⡏⠀⣿⣿⣹⠏⠣⠀⢸⠙⠒⠻⣾⣷⡾⣹⠃⣸⣽⠟⠀⠀⠀⠀⢠⣿⠖⠚⠿⢤⣰⠏⠀⠀⠀⠀⢰⠏⢀⣾⠟⢛⣻⣿⡥⠖⠚⠉⠉⢿⣿⠋⠀⣠⣾⣫⣾⠃⠀ ⠀⠀⠸⢣⣿⣇⡞⠁⢹⣿⡀⠀⠀⢸⠀⠀⣸⣿⠟⣡⡏⠠⠟⠛⠉⠙⠛⠲⢦⣼⢋⢧⡀⠀⠀⠙⣆⠀⠀⠀⢀⡟⣴⣿⣵⡾⢛⡿⠁⠀⠀⢀⡄⢀⡿⢿⣧⣾⠟⠉⣼⠇⠀⠀ ⠀⠀⠀⠞⣸⡏⠀⠀⡾⠉⠳⡀⠀⠈⣴⡾⠋⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠛⠳⣤⣀⣸⢀⣠⣴⣾⡟⠛⠉⠀⠀⠞⠀⠀⠀⢰⠛⠇⠸⢀⣼⣿⡇⠀⡼⠃⠀⠀⠀ ⠀⠀⠀⢠⢻⠀⠀⠈⠁⠀⠀⠙⣠⣾⠟⠀⠀⡾⠁⠀⠀⢀⣀⣦⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⣬⠴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠧⠤⢶⣿⡷⠾⠓⠘⠁⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⣰⠆⠀⣠⣾⠋⡿⠁⠀⠀⢸⡇⠀⠀⠀⣿⡁⠈⣟⠂⠁⢠⡾⡛⡆⠀⠸⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡼⢧⡀⠀⠀⢀⣀⣫⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠃⢀⡼⠛⠁⠀⠀⣀⡴⠖⠻⡇⠀⠀⠀⠈⠙⠫⡅⠀⠂⠀⠳⠶⠃⠀⢀⡇⠀⠀⠀⠀⠀⠰⢾⠿⠛⠛⠛⠒⠒⠾⢿⣿⣟⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⢠⠏⠀⣠⡶⠖⠺⠥⢤⡀⠀⢷⡀⠀⠀⠀⠀⠀⣽⢯⣹⠏⠀⠀⠀⠀⣾⣄⣀⣀⡀⠀⠝⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⣠⠾⠋⠀⠀⠀⠀⠀⠈⠳⣌⠻⣦⡀⠀⠀⢰⠇⠀⢸⠀⠀⢠⣀⠾⠓⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠀⠀⠉⡿⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⣦⡈⠛⢶⣤⣾⣳⣒⣿⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠀⠀⢠⣇⣤⣿⣒⣲⠤⠄⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⣉⣳⣮⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⠿⠆⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡜⠀⠈⠉⠉⠙⠛⠒⠀⠀ ⠀⠀⠀⠀⠸⣾⡆⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠉⠉⠙⢻⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⠲⣄⣀⣀⣰⣧⣄⣀⣀⣇⣀⣰⠃⠀⠀⢀⣠⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣦⠈⠻⢦⣀⡆⢀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⢀⡀⠀⠀⠀⢳⠀⠀⠀⠀⢉⡓⠪⢷⣲⡤⡄⠹⣄⠀⠀⠀⠀⠀⠈⠉⠉⠈⢙⣇⣴⣟⡀⠀⠀⠀⢸⡙⠁⠀⠀⢀⠀ ⢰⡆⠀⠀⢻⠀⠓⢤⣈⠉⠓⠛⠷⠶⢶⠯⠄⠀⠀⡀⠀⠀⠳⡄⠀⠀⠈⣇⠀⠀⠀⡸⠁⠀⠀⠀⠈⠙⠒⠈⠳⣤⡀⠀⣀⣀⣤⠤⠖⠛⠉⠀⠈⠻⣶⡄⠀⠀⠳⢤⣄⢐⡉⠀ ⢰⡇⠀⠀⠈⠃⠀⠈⢻⡉⠓⠢⠤⣄⣰⣀⠀⠀⠀⠳⣄⠀⠀⠹⣄⠀⣀⣼⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠉⠡⠤⣀⣠⡒⠲⢦⡄⠀⠀⠙⠿⠵⢶⣤⣤⡾⠉⠀⠀ ⢻⣇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⡈⠙⠻⣦⡀⠀⠀⠈⢦⣀⡴⠏⠉⣡⡟⠀⢩⢿⣤⣠⣤⣤⣴⠶⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠷⠶⢤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠈⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠛⠻⠷⣮⠻⢦⣀⣀⡴⢷⡤⠶⠛⠁⠀⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢹⡇⠀⠀⠀⠀ ⠀⠈⠘⣦⡀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢦⠀⠘⣧⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢳⡀⠀⢷⠦⣤⣀⣀⡀⠀⠀⠀⠀⢠⠀⠀⡀⠀⢹⡄⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⣾⠀⠀⠀⠀⠰⡄⠀⠀⠈⢧⠀⠘⣇⠙⠓⠲⠤⣤⣄⣀⣀⣤⠀⠀⠀⡀⠀⠀⠈⢧⠀⠀⠀⢳⠀⢸⡆⠀⠈⠉⠙⠻⣶⠀⠀⡞⠀⠀⢰⠀⢸⡁⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⢲⡄⠀⠀⠹⡄⠀⠀⠘⣇⣠⡾⠆⠀⠲⣤⣀⠀⠈⠉⠙⠳⢦⣠⡿⣄⠀⠀⠘⡆⢀⣠⠼⢗⣿⠃⠀⠀⠀⠀⠀⢹⣀⣀⣛⣒⣲⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⢦⡀⠀⣸⡤⠒⠋⣉⣨⡧⠀⠀⠀⠉⠚⠭⣕⣒⡢⠤⣄⣈⡛⠿⢦⠤⠤⣿⣉⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡛⢛⢙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠺⠥⣤⣤⣄⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⡀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣤⣶⣍⣤⣀⡀⠀⠀⠙⠶⠖⠒⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⣟⣟⣭⣿⠬⢷⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⣿⠟⠉⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⡅⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠉⠁⠀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⣄⠀⣄⡀⢰⡦⡆⣶⢀⡇⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠦⣤⣀⡀⠀⠀⠀ ⠀⠀⢿⡀⣿⡀⣿⣿⣿⠇⣷⢿⣸⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⣸⠀⠀⠀⠀⣈⠑⡄⠀⢀⡰ ⠀⠀⠘⣿⠙⣧⣿⠻⣿⡄⣷⢸⣿⡇⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⢀⢀⣴⠃⠀⢈⡩⠃⢈⠇⠙⠒⠋⠀ ⠀⠀⠀⠘⣇⠙⠛⠀⠈⠁⠀⠀⢉⡀⠀⠀⠀⠙⢦⡀⠀⠀⢠⠿⣻⣷⣧⣠⣤⣤⢤⣇⣸⡾⠃⠴⠒⣉⡤⠖⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⣀⡀⣀⣴⠾⡟⠲⣤⡤⠀⠩⠿⢿⣵⣽⣿⣿⠟⡿⢷⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠋⠉⠀⠈⢹⣟⡉⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⡠⠟⠁⠀⠁⢀⣹⠟⠛⠛⠛⠛⠳⢶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⣀⡔⠀⠈⠉⠒⠦⢄⣀⠀⡇⢀⣠⠤⠚⠒⠒⠚⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣸⡦⠟⠋⠀⠀⠀⠀⠀⠀⣀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⢀⣴⠟⠉⠉⠉⠙⠲⣄⣰⠃⠀⠀⢀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢻ ⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⡿⠒⠲⠚⠉⠳⢄⠀⣰⠃⠀⢀⣤⠔⠚⠓⠦⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⣼ ⣼⠁⠀⠀⠀⠀⠀⠀⠀⣸⣷⠂⢀⡀⠐⠒⠚⠛⠋⠉⠉⠉⠉⠉⠙⠲⢤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣰⡟ ⣿⠀⠀⠀⢀⠤⠒⠋⠉⠉⠛⢧⣀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣰⡟⠀ ⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢳⡀⠈⠑⠒⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣷⠤⠤⠴⠖⠒⠒⠲⠤⠄⠀⠀⣰⡟⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀ ⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠷⢶⣶⠒⠒⠒⠺⠛⠛⠛⠉⠹⡇⠀⠀⠀⠉⠉⠉⠛⠶⠦⠤⢤⣄⣴⡿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠘⠄⠀⠀⠀⠀⠙⠂⠀⢤⣤⡤⠤⠤⠎⠀⠀⠀⠀⠒⠒⠘⢿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⡄⠀⠀⠀⢀⣠⣤⠤⢠⣾⡆⠀⠀⠀⠀⢀⣀⣠⣀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡾⢿⠟⠀⣾⣧⣤⣾⣿⡿⠋⡇⣰⡿⣿⣅⢀⣤⣶⣾⡿⠛⢋⣡⣶⡿⢗⣤⣦⣤⣶⠶⠖⢁⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⢿⣋⡴⠋⠀⣼⢿⣯⠘⢣⢸⣿⣀⣸⣿⠏⢁⡾⠛⠛⢉⡿⠇⢊⡿⣫⣿⡤⠞⠋⣽⠏⠀⢀⣴⣿⡟⠁⣀⣤⣤⣤⣤⣤⣤⣀ ⠀⠋⢁⣾⣿⣷⣀⣼⣿⠞⢿⠆⢀⣿⠋⣹⡿⢁⣠⠎⠀⠀⠐⣹⠁⣠⡿⢺⡟⠁⠀⠀⣸⠃⢀⣴⣟⣿⠏⢀⣀⣛⣩⡿⠋⢀⣠⢾⡟ ⠀⠀⣿⣿⠃⡼⢿⡿⠉⠀⠈⠉⢉⣿⡿⢻⢃⣾⣟⣀⣀⣀⢀⡿⡉⠙⠲⢞⠀⠀⠀⢠⠇⣴⢟⣩⣿⠟⠚⠉⠀⢸⣿⡅⣠⡾⢿⡟⠀ ⠀⠀⠸⢿⠏⠀⣸⠻⡄⠀⠀⣠⡾⠋⡵⠋⠀⠀⠀⠀⠀⠈⠙⢶⡷⢤⣀⢈⡆⢀⣠⣾⠾⠛⠋⠠⠋⠀⠀⡴⡇⠜⢨⣿⠋⢠⠟⠀⠀ ⠀⠀⢠⢻⠀⠀⠁⠀⠘⣠⡾⠋⠀⡞⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠱⡀⢈⡭⠿⠛⠋⠁⠀⠀⠀⠀⡀⠀⠀⠣⠤⣴⣿⠽⠃⠋⠀⠀⠀ ⠀⠀⠀⠀⢀⠆⢀⣴⠏⠟⠁⠀⣸⡇⠀⠀⠸⣀⡼⠁⠀⢸⣋⡇⠀⡇⠀⠀⠀⠀⠀⣀⣀⣤⣤⣒⢳⣄⣤⣤⡬⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠃⣠⠊⢀⣄⣤⣖⠉⠈⣇⠀⠀⠀⠀⢰⡤⢤⠄⠉⠀⢀⡇⠀⠀⠀⢠⠬⠋⠁⠀⠀⠀⠉⠙⠳⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢁⠴⠋⠁⠀⠀⠉⠢⣜⢦⡀⠀⠀⡜⠉⡟⠀⢀⣀⠞⠛⠊⠁⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠙⢳⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣱⠁⠀⠀⠀⠀⠀⠀⠀⢙⣦⣉⡲⢶⣿⣿⡧⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⡆⠀⠀⠸⠀⠀⡿⠼⣿⣶⣖⠀⠀ ⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠻⠿⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⣏⠁⠀⠀⡇⠀⠀⡀⠀⡸⠀⠀⠀⠀⠈⠁⠀ ⠀⠀⠀⢌⠻⢄⡀⡀⠀⠀⠀⠀⡴⠊⠀⠀⢀⠀⠀⠈⣇⠀⠀⠀⠂⠤⢤⣤⡀⠸⡀⠀⠈⠑⠚⠛⠛⠛⣿⣩⣟⠁⠀⠀⣾⠃⠀⠀⠀ ⢰⠀⠀⢫⠀⠢⣌⡙⠛⠓⠒⠾⠁⠀⢀⠀⠀⠳⡀⠀⠸⡄⠀⠀⡎⠀⠀⠈⠉⠒⠉⠢⣄⣀⣀⠤⠤⠒⠋⠁⠈⢳⣆⠀⠘⠢⢄⣀⠁ ⣿⠀⠀⠀⠀⠀⠑⣌⠉⠒⠢⣶⣄⠀⠈⠣⡀⠀⢱⠤⠴⡇⠠⣾⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠒⠰⢏⣓⣆⠀⠀⠙⠛⠓⠒⠋⠀⠀ ⠹⣆⠀⠀⠀⠀⠀⠈⠛⠶⠶⢤⣝⢦⣀⠀⣸⣞⣡⠴⠚⠡⠾⠿⠟⠛⠋⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⣆⠀⠀⠀ ⠀⠉⢦⡀⡰⠁⠀⠀⠀⠀⠀⣄⠘⣆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⡀⠱⡤⢄⣀⣀⠀⠀⠀⢀⠀⢀⠀⢰⠀⢹⠀⠀⠀ ⠀⠀⠀⠙⢧⢀⠀⠀⢢⠀⠀⠘⡄⠘⣎⠉⠒⠒⠤⠤⢤⣦⡀⠀⡀⠀⠀⢃⠀⠀⢳⣀⡇⠀⠀⠉⠛⡇⠀⢘⣀⣀⡄⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢾⣧⡀⠀⢳⣀⡤⠖⢺⡉⠀⠈⠷⣦⡤⢄⣀⠙⠺⢿⣄⠀⣨⡆⢒⣩⠽⠃⠀⠀⠀⠀⠐⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠓⠒⠚⠉⠁⠀⠀⠀⠀⠈⠉⠒⠋⠱⠶⣭⣉⣈⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣰⠋⠀⠀⡠⠚⠉⠀⠀⣠⠔⠀⠀⣀⡤⠤⠤⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⠀⠀⠀⠉⠁⢰⡃⠀⠀⣼⠥⠤⠤⣴⣭⣁⣠⠖⠋⠀⠀⠀⠀⠈⣷⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⣠⢬⡀⠀⠀⠀⢀⣴⣞⡡⠤⠤⠴⠒⠒⠒⠶⠤⢌⣁⡀⠀⣴⠚⠋⠉⠉⠁⠀⢠⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⡰⠁⠀⠁⠀⠀⡴⠋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠘⠀⢠⠃⢠⠞⠣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⢰⠃⠀⠀⠀⠀⣼⣡⠼⠖⠒⡺⣏⠉⠉⠉⠉⢉⡽⠑⠒⠲⠤⣀⠀⠀⢿⡇⠀⢀⠇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⡎⠀⠀⠀⣀⣤⣿⠁⢠⡊⠉⠉⡷⠀⠀⠀⠸⡟⠉⠉⢳⠀⠀⠀⠉⠓⢶⣿⢤⣼⡀⣸⣤⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⢠⠁⣠⣴⠞⠛⡿⡏⠀⠀⠉⠀⠉⠁⢤⡤⠀⠀⠑⠲⠒⠋⠀⠀⠀⢀⠀⣼⡇⠀⡟⢦⡇⠀⠈⠙⠿⣶⣀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⢸⢰⠟⢃⣀⠴⠤⣼⣀⠀⠀⠀⢠⣀⡼⢆⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⢸⠀⢸⠀⠀⠀⠀⠀⠘⡌⠙⢦⡀⠀⠀ ⠀⢸⠀⢠⣿⡏⠀⠉⠀⠀⠀⠈⢧⢂⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣇⣤⡾⠁⠀⡌⠀⡼⠈⠐⠒⠢⣀⠀⢱⠀⠀⠻⣦⠀ ⠀⢸⣴⠛⣷⡟⠀⠀⠀⠀⠀⠀⠀⠳⢄⡃⠘⠀⢰⠀⢦⠀⢄⠰⢦⣲⣌⣑⣶⠏⠀⠀⢠⠇⡀⡇⠀⠀⠀⠀⠀⠁⣸⠂⠀⡀⠈⣱ ⠀⣸⠃⢀⠇⢧⡀⠀⠀⠀⠀⠀⠀⠈⠢⢌⣓⠶⣤⣥⣬⣤⣬⣥⣴⣾⠿⠋⠘⣀⡠⠔⢹⠋⢀⠇⠀⠀⠀⠀⢀⣴⠟⠀⢠⠇⢀⠇ ⢀⣿⡄⡎⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡴⠀⠈⠉⠒⠯⣝⠛⠻⠟⣫⠥⠒⠚⠉⠁⠀⠀⠈⢣⣸⠀⠀⠀⣀⠔⠋⠀⢀⣴⢃⡠⠊⠀ ⣼⠇⠛⣇⠀⠀⠀⠀⠈⠓⠶⣤⣤⠎⠀⠀⠀⠀⠀⠀⠈⠓⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣴⣾⠷⡶⢶⣾⠛⠛⠉⠀⠀⠀ ⠹⣦⡀⠘⠦⣄⣀⠀⠀⣀⣴⣿⠛⣦⣀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢃⡜⠀⠀⠻⣇⠀⠀⠀⠀⠀ ⠀⢻⣿⡄⠀⠀⠀⢉⠙⣏⠀⠈⣧⠀⠙⠷⣦⣤⣄⣀⣀⣀⣠⣷⣄⣀⣀⣀⣀⣀⣀⣤⣤⢾⣿⣿⡷⡋⡇⠀⠀⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠙⢿⣆⠀⠀⢸⢁⡘⣆⠀⢹⠀⠀⠀⢸⡟⠷⠤⢀⣀⣀⣹⣦⣍⣩⡭⢹⠉⠛⢻⣾⣿⡾⠏⢰⣿⣧⢀⠀⠀⠈⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⠦⣞⡁⠀⠈⢦⣸⠀⠀⠀⡞⡇⠀⡇⠀⠙⠻⣏⡈⠻⢻⣿⢿⣟⠛⢻⢿⣼⣇⠀⣸⣿⣁⡾⠇⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⣜⣿⢢⣄⣀⣽⣧⡀⠀⡇⡇⠀⡇⠀⢀⠀⠀⠉⠑⠚⠟⢞⡛⠂⠏⠀⠀⠉⠹⣧⣄⠉⠀⠀⢰⠀⣻⡇⠀⠀⠀ ⠀⠀⠸⠀⣤⡾⠋⠀⡤⢀⣈⣠⣾⣯⣷⣼⠁⢧⠀⡇⠀⢸⡆⢠⡀⠀⠀⠀⣠⢽⡷⢶⣖⠒⠂⢠⣿⠶⢿⠦⠤⠽⠓⢿⡇⠀⠀⠀ ⠀⠀⠀⢰⣇⡟⠀⢀⡾⠋⠀⢠⡆⠈⠀⣿⠀⠈⠀⣣⡴⠆⢣⡌⣧⡤⠤⠴⣇⣼⠀⣸⠀⠀⣤⢸⣿⣀⣏⠀⣚⠀⢀⣾⠁⠀⠀⠀ ⠀⠀⠀⠈⠛⠳⠤⣿⠀⠀⠀⣿⣶⡤⠼⠛⡇⣀⣤⡿⣤⠀⢸⡇⢸⠀⠀⠀⠀⠈⢉⣉⣉⣉⣿⡿⡇⠤⠬⠹⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠶⣿⣤⣤⡴⠿⠟⠋⠙⠛⠛⠛⠛⠛⠿⠘⠚⠛⠛⠒⠖⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢻⠋⠲⡀⠱⡄⠀⠀⠀⠀⠀⠀⢠⠏⣠⠟⠓⠦⡤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢦⠘⣆⠀⠀⠀⠀⠀⠘⠀⡏⠀⠀⢠⢧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠈⣧⢹⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⣦⡀⠀⠀⢸⡜⣦⣖⡖⠫⠵⣁⠘⠧⣀⠜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⠃⠉⠻⣦⣄⡸⠗⣁⢼⠁⠀⡀⠈⠳⡀⠈⠒⡪⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠟⠀⢠⡾⠁⠀⡰⠾⢅⠀⠀⠀⠈⠢⡀⠘⣄⠀⠈⢢⡈⠺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⢠⡿⠀⣠⡞⠀⠀⠀⠀⢤⡀⠀⠀⠙⠄⠘⡖⡄⠀⠙⢄⠀⠈⢉⣉⣩⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⢀⣿⠁⢰⠟⠀⠀⠀⠀⢸⠻⣾⣦⠀⠀⠀⠀⣹⡈⢦⠀⠈⢯⠉⠥⣄⠠⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠖⠁⠀⠀⠀⣼⢇⡰⠋⠀⡀⠀⡾⠀⣾⢐⣻⣩⢷⣦⠀⠀⠹⡇⠈⣆⡇⠈⣇⠀⠈⠉⠒⠒⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⢊⡴⠋⢠⡆⠀⡇⢠⡇⠀⣿⠉⠀⠀⠈⢻⣧⡀⠀⣿⠶⣾⣷⡤⢸⡍⢒⣴⢖⡚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠨⠥⠴⢯⠖⢊⣽⠀⠀⡇⠸⡇⢀⣿⠀⢀⡠⠔⠋⢻⣧⣠⣼⣿⣿⣿⣿⣮⣇⠀⠢⣉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠋⠀⡼⠃⠀⡠⣯⡄⣧⢸⣿⣯⣭⣤⣤⣄⠀⣿⣿⣿⡟⠉⠋⣿⣯⣿⡖⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠋⠀⢀⡔⢁⡠⡖⠁⣿⣧⠙⠘⣿⠟⠛⠉⠁⠀⠀⢹⡏⢿⠃⠀⠀⣿⣿⣜⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⣻⡷⠂⡇⢠⣿⣿⣧⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣿⡏⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣙⡭⡒⣧⢱⡀⠀ ⠀⠀⠀⠀⢰⡿⣿⠁⡟⣧⢸⠘⣿⣿⣷⣪⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠷⣌⠻⠌⢧⣷⠀ ⠀⠀⠀⠀⠘⡇⠻⢠⡇⠘⣿⠀⠘⣿⣇⢿⢿⣯⢷⡲⠤⢤⣀⣀⣠⢿⠿⣿⡃⣿⠟⣍⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠙⢌⠑⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠁⠀⣸⣡⠞⢹⡆⡴⠙⣟⠞⡆⢹⣦⠉⠑⠲⠤⠭⠽⠏⣠⠻⣇⣿⠀⠈⠣⡀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⠥⠒⠻⡆⢹⡄⢷⠀⠀⠀⢀⠤⣼⣿⣿⣁⣈⣿⢖⠀⠀⠈⠢⡀⢸⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠳⠤⠤⠤⢿⡀⢷⢸⡧⣄⡀⠙⢤⣴⣿⠍⠀⠉⠁⠀⠙⠦⣀⠀⠈⠪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⢸⡷⡄⠸⡇⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠙⡄⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠹⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠹⡄⠀⢠⠞⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⣀⡈⣷⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠒⠚⢣⣷⣜⠁⠀⠀⠉⢒⡞⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠣⣄⡀⠀⠀⢀⣼⠃⠙⢺⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡖⠢⣷⠈⠳⣄⠀⠀⡼⠁⠀⠈ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠉⠉⣹⡿⣿⠀⠀⢻⠀⠀⢸⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠇⠀⢸⡇⠀⠻⡳⣞⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⢀⡾⠁⠸⡆⠀⡿⠀⠀⢈⡷⠃⠈⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢸⠁⣸⠀⠀⡾⢳⡀⠀⠙⣎⠳⡄⠀⠀ ⠀⠀⠀⡼⠀⠳⣄⡀⣀⣰⡟⠀⠀⠀⠹⣄⡇⢀⠀⠈⡇⡠⠒⠢⢄⠀⠀⠙⠢⣄⠀⠀⠀⢠⡏⠀⡏⠀⣴⡇⠀⢱⣤⠀⠈⣧⢹⡄⠀ ⠀⠀⣼⠁⠈⠉⠉⠉⠙⠾⣄⠀⠀⠀⠀⢸⠧⣼⡆⢔⢿⠀⠀⠀⠀⠙⠢⣄⠀⠀⠙⠢⢤⠞⠀⣸⡥⠴⣿⣇⡴⠋⢹⣄⠀⠸⡆⡇⠀ ⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢸⠀⢹⠱⡘⠞⣇⠀⠀⢀⠀⢀⣠⠽⠲⢤⣀⠀⢀⡰⠃⠀⢰⣿⡇⠀⠀⢸⠹⡄⠀⢸⡇⠀ ⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢸⠀⠸⡆⠣⠀⠹⡍⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⣿⡇⠀⠀⣸⠀⣧⠀⢸⠁⠀ ⠀⠀⠀⠻⣅⡀⠀⠀⠀⠀⢀⠔⠉⠀⠉⠻⣧⠀⢷⠀⠀⠀⠙⢆⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠳⡀⢠⣇⡴⢻⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠒⠢⣤⠾⠀⠀⢀⣀⡠⣧⠑⢌⢧⡀⠀⠀⠈⠳⡄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠛⠯⣀⡀⠸⠚⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣴⣶⠗⠛⢻⡀⠘⡆⠈⢦⠱⣄⡀⠀⠀⠈⢲⣄⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⠈⣕⢦⣀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢾⣏⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠙⠻⢯⡙⠛⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠄⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠃⠀⠀⠀⠘⣎⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠁⠀⠀⠀⢀⡤⠖⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣀⣤⠤⣄⠀⠀⠀⢹⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣸⠃⠀⢠⣾⣷⣆⠀⢸⠇⠀⠀⠀⢠⡞⠁⠀⠀⠈⠙⣆⠀⠀⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢀⡏⠀⠀⣿⣿⣿⣿⠀⡿⠀⠀⠀⠀⢸⢁⣤⣤⡀⠀⠀⢸⡆⠀⢸⡄⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⡁⠀⠀⠀⠀⠀⠀⢷⡀⠀⠻⣿⡿⠋⣸⠃⠀⠀⠀⠀⣾⣾⣿⣿⣷⠀⠀⠀⣧⠀⠀⣷⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣻⠃⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⢤⠴⠃⠀⡀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⢠⡿⠀⠀⠸⡆⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⡴⠲⡄⠀⠀⠀⠀⠀⠀⠤⣆⠀⠀⠀⠯⣉⣉⣳⡆⠈⠳⣍⣁⠀⠀⣠⠟⠁⠀⠀⠀⢻⡘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣴⠓⠲⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣤⠼⣅⡀⠀⢀⣠⡄⠉⠉⠉⠁⠀⠀⠀⠀⠀⣴⣷⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⢿⡯⠤⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⣛⠛⣿⠀⢸⡏⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡟⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣷⡿⣿⣿⠲⣼⣀⠀⢸⢻⠛⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⢻⡁⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⠈⣻⡶⠿⣏⢀⡇⠈⠙⠛⠛⠛⠋⠉⠉⠉⠙⢛⣒⣲⣶⣶⠶⠶⠶⠶⢶⣶⠒⠚⠋⣿⣧⠀⠀⠘⣇⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⢰⢿⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠉⠉⠉⠳⣄⠀⠀⠈⠙⢦⡀⢹⣹⡀⠀⠀⢹⡀⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⢀⡟⠈⡿⢷⠀⡼⠉⠓⢶⣤⣤⣄⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢤⡀⠀⠀⢻⠸⡟⡇⠀⠀⠈⣧⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⣾⣻⢿⡇⣾⣿⠀⠀⠀⡿⣾⠀⡟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⡄⢀⡾⠀⢷⢻⡀⠀⠀⢸⡆⠀⠀⠈⣧⠀⠀ ⠀⢠⡟⠀⣼⣷⢻⣿⠃⠀⣸⣳⡇⣼⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠹⣏⠀⠀⠸⡟⣇⠀⠀⠀⢷⠀⠀⠀⢹⡄⠀ ⠀⣸⠁⠀⠛⣿⣦⡻⣷⢦⣟⣿⡞⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣆⠀⠀⢻⣿⡄⠀⠀⠘⣇⠀⠀⠈⣧⠀ ⠀⡟⠀⠀⢀⡿⠉⠙⠛⡾⣹⡿⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⡆⠀⠈⢷⣷⡀⠀⠀⠹⡄⠀⠀⢹⡄ ⢸⡇⠀⠀⣼⠁⠀⠀⣼⢳⢿⡇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢸⠇⠀⠀⠈⢯⣷⡀⠀⠀⢻⡄⠀⠈⡇ ⢸⡇⠀⠀⣏⠀⣀⡼⣣⠏⠀⢷⡀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⡾⠀⠀⠀⠀⠈⢯⢷⡀⠀⢈⡇⠀⠀⡿ ⠀⠻⣆⣀⣈⣋⣥⠞⠁⠀⠀⠀⠳⣄⡀⠀⠀⠀⠙⠲⢄⣀⣀⣀⣀⡠⠖⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢳⡳⠶⠞⠁⣠⠾⠁ ⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣀⣀⣤⠤⠿⠓⠶⠶⠶⠒⠉⢻⡍⢉⡟⠙⠒⠲⠖⠒⠛⠙⠓⠲⢤⣄⣀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀ ⠀⠀⠀⣠⠴⠖⠚⢛⠋⠉⠉⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⣰⠋⠀⠀⡾⠉⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⡄⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠳⠶⠿⣤⣀⣀⣧⣀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣿⣀⣠⠼⠷⠶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡀⠀⠀⢹⡀⠀⠀⠀⢀⠴⠋⢉⡉⠱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡜⠀⠀⠀⣸⠁⠀⠀⢠⠃⣠⠞⠁⣠⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⣰⠃⠀⠀⢠⡇⢰⠁⠀⠀⣁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⠀⣠⡇⠀⣀⡠⠼⠦⣦⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢳⣿⠗⠉⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠁⠀⠀⣠⡀⠀⠀⢐⣦⠀⠈⣧⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠘⠋⢀⣤⣤⠀⣀⣀⣼⡀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠉⢻⡀⢾⢿⡿⠀⠘⠛⠛⠀⠘⠻⣿⠃⣀⠤⠠⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⣠⠴⠒⠒⠒⠚⠉⠙⢷⣦⣤⣀⣀⣀⠀⣀⣠⢾⡟⢠⠃⠀⠀⠘⠄⢹⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡼⠁⠀⠰⡄⠀⠀⠀⠀⠀⠈⠙⠺⣿⡟⠉⡽⣵⠏⠀⣼⠃⠀⠀⠀⠀⠈⡆⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢰⠃⠀⠀⠀⠹⠀⠤⠤⢄⡀⠀⠀⠀⠈⢧⠐⡀⠀⠀⠀⢻⠙⠒⠤⠤⠴⠀⠃⠀⠀⢀⣀⣀⡙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠋⠰⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠈⡏⣷⠂⠀⠀⣸⣁⠂⠀⠀⠀⢠⡴⢚⣩⠤⣀⣀⡈⠉⠲⡄⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⢹⡀⠰⡄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡇⣼⠲⡄⣠⡟⠚⠓⢦⣀⡀⡾⡴⠋⠀⠀⡀⠉⠉⠣⣄⠸⡄ ⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢙⣧⡄⠘⢦⡀⠀⠀⠀⠀⠈⡆⠀⣰⣧⠘⣟⣛⡟⣀⣤⠞⠉⠙⠿⠷⠷⣦⠀⣸⠁⠀⢀⠀⠀⠿⣇ ⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⢸⠀⡇⠰⡀⠑⢄⠀⠀⠀⢀⠁⠀⡘⠹⣤⣞⣋⣸⣹⠃⠰⠆⠀⢀⣀⠀⠸⢶⡇⠀⠀⡼⠀⠀⡄⢻ ⠀⠀⠀⠀⢀⡿⠞⠃⠀⠀⠀⠀⡌⠁⢇⠀⢳⡀⠀⠙⠛⠋⠁⠀⠸⠁⠀⡇⠀⠀⠀⠉⠉⠓⠆⠀⠀⠉⠀⠀⠀⠙⣧⡞⠁⢀⡜⢀⠞ ⠀⢰⡴⠋⠛⠳⣄⠀⢀⠀⠀⠀⢧⡀⠸⡄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⡏⠓⠒⠚⠛⠁⠀ ⡠⠿⢤⣄⣄⠀⠘⢉⣓⣦⣤⣀⣰⣭⣉⣹⣄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⣋⠀⠀⢀⣔⣢⠴⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⡿⠉⠉⠁⠀⠀⠸⡄⠀⠀⠀⠈⠑⢦⡀⠙⢦⡀⠀⠀⠀⢰⠅⠀⠀⠀⣀⡤⠊⠁⢀⡼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠉⠳⢄⠉⠢⢄⡀⠈⠠⠚⠉⠉⠀⢀⣠⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⠤⠤⠖⠒⠒⠒⠋⠉⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠉⡹⠃⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠔⠒⠉⣀⡤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡏⠢⡐⠄⠀⠀⠀⠘⡰⠉⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡇⠀⠈⡼⠀⢀⣀⡀⡇⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠙⢦⣀⠧⡋⠋⠉⠂⡉⠪⠅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠃⣰⠋⡠⠊⠀⠀⠀⠀⡈⢄⠈⢈⠑⠦⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠁⢠⠇⡸⠁⠀⠀⢚⡧⡀⠀⢰⠐⠀⠱⠈⠭⣕⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠠⡪⢊⠄⡆⡀⢸⠒⠉⠹⣆⠀⡧⣵⣤⢓⠠⣄⠐⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠊⡵⠀⡇⢁⢸⣤⣔⡈⠹⣦⣾⠿⢿⢿⡀⠢⠍⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⢀⣔⡤⡎⣼⡌⢸⡛⠋⠁⠀⠋⠋⠀⡸⣧⣱⠀⠀⠀⠀⠀⠀⡄⣳⠄⠀ ⠀⠀⠀⢸⠿⠱⠃⠙⣿⣎⣧⡀⠀⠀⠀⠀⣰⡇⣿⠈⠀⠀⠀⠀⠀⣽⢜⠪⠮⡄ ⠀⠀⠀⠘⠀⣆⡸⡄⡹⣏⡟⣟⠣⢒⣂⣮⢋⡇⡏⠡⡈⠑⡄⠀⠀⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⢀⡿⠐⢱⠰⢸⠀⠀⡄⢾⡿⠬⠗⢀⠈⠢⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⠀⠉⠉⡦⠙⡍⠐⠚⠋⠁⠀⠀⠀⠁⠢⡈⠆⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⡀⠃⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⢊⣆⠔⠐⠤⡤⠀ ⠀⠀⠀⢀⠋⠢⠄⢀⣴⠉⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠒⢇⠑⣄⡰⠁⠀ ⠀⠀⢀⢌⠀⠀⢀⡜⠘⡀⡈⠀⢸⠊⠀⠢⢄⠀⠀⠀⠀⡘⠸⠀⡜⡀⠑⠕⠄⠀ ⠀⠀⡌⠀⠓⠰⣞⠀⠀⠐⡇⡄⠸⠈⠉⠂⢄⠈⠂⠄⡠⠁⣇⣼⣅⠼⡇⠈⡜⠀ ⠀⠀⡆⠀⠀⠀⠀⠑⡀⠀⠀⡗⠔⢣⠄⠀⠤⠘⠐⠠⠤⠈⠀⣾⠃⠀⡟⡄⢰⠀ ⠀⠀⠙⠅⡀⠀⠀⠔⠈⠐⡧⠰⡀⠀⠢⡀⠄⠀⠀⠀⠀⠀⠀⢋⢂⣠⠠⠃⠀⠀ ⠀⠀⠀⠀⠀⠈⣏⣤⠴⢖⠱⠐⠕⣄⠀⠐⢄⡑⡄⠀⠀⠀⠀⠀⠁⣁⠂⡤⡀⠀

⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠉⠉⢂⣾⡏⠀⣿⡄⠀⠀⠀⠀⠀⢀⠠⢐⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠈⢧⠸⡟⣁⣀⡀⠀⠀⣰⡿⠚⠀⠀⡠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⡈⠁⠀⠀⠠⢂⠽⣷⣘⣒⡒⠤⣑⡾⢚⡡⢴⠲⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⠔⡰⠋⠀⠰⠁⠀⢹⠛⠮⠹⡫⠁⠀⡔⡫⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣝⣛⢻⡟⠠⣸⢠⡆⠀⠀⠨⢠⣪⣵⡇⢃⣀⢴⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢛⠭⠀⠭⣿⡕⣶⣿⣿⡇⢀⣤⣧⡾⣻⡿⠁⠀⠀⠀⠈⡰⠀⠀ ⠀⠀⠀⠀⠀⠡⡇⠀⠀⠀⠸⣷⣿⠈⠉⠣⠾⠯⣵⡷⠋⢀⠧⠇⡀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⢹⣿⣇⠀⡀⠀⢀⣺⣢⣾⣿⠓⠾⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢌⠄⠀⠀⢀⠠⣎⡽⣝⣆⡴⡶⢋⠵⠛⠉⠀⠈⠑⢹⣿⡠⠂⠀⠀ ⠀⠀⢀⠔⡱⢥⠒⠓⠋⠁⠈⠀⠉⠉⠷⡞⡔⠁⢀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀ ⠀⡐⣡⠎⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠫⡑⡴⠁⠀⠀⠀⡠⠚⡀⠀⠀⠀⠀⠀ ⠎⢄⠏⡄⠀⠀⠀⠈⠄⠀⡠⠈⠀⣀⣀⡀⠈⢪⠢⢀⣠⢻⠀⠠⠐⡄⠀⠀⠀⠀ ⠈⡜⡄⠈⠢⢄⡀⠀⠘⠮⠐⠈⠀⠀⠀⠈⠢⠀⡇⠱⡃⡌⡄⠀⠡⡈⠂⠀⠀⠀ ⢰⢠⡟⠢⣀⣀⠀⢉⣹⠀⡀⠀⠀⠀⣀⠀⠀⠁⡆⢠⠁⠃⠰⠀⠀⠐⢄⠑⢄⠀ ⠘⡇⢳⠀⡇⠂⠒⡏⠙⣦⡀⠁⠁⠁⠄⠁⠐⣺⡇⣸⡇⠁⠀⠡⠀⠀⠀⠹⡀⢢ ⠀⡏⢸⡄⢡⠠⠀⠑⠊⠈⠛⠔⢦⠤⠄⠒⡹⡙⢐⠟⠁⡀⠀⡆⢣⠀⠀⠀⢑⠀ ⡄⠀⡄⡇⠘⡄⠀⠀⠀⠀⢀⠊⠁⠀⠀⢠⡱⠕⠁⠀⣠⠁⢠⣇⠀⡇⠀⠀⠸⠀ ⠠⠇⠐⠘⡰⠱⠇⠀⠀⠀⢾⠀⣶⡶⠿⠛⢇⠀⢀⢴⠇⡠⢣⠰⢀⠃⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠁⠉⡄⠀⢀⠔⣂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡰⠀⠀⠆⠌⠀⣂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠡⣰⡣⠄⠚⠚⠰⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠋⠀⢠⡀⠀⠆⠈⡦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠘⡆⣴⣦⠠⠿⠂⠶⡷⢀⣀⡱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠔⢂⠉⠉⠈⠳⠖⣤⣤⢤⡾⠃⡇⠀⠑⢹⠐⠂⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⡘⠀⠀⠃⠠⠤⡀⠀⠈⢇⡄⠁⠘⡗⠠⠤⠀⢀⡀⠀⠘⡄⠀⠀ ⠀⠀⠀⢰⠁⠀⠀⢢⠀⡀⠀⠀⠈⢂⠀⢸⠸⠅⣰⠵⢄⡀⣘⡕⠊⡒⠒⢌⢣⠀ ⠀⠀⠀⡌⠀⠀⠀⢩⠂⠐⢄⠀⠀⠈⠀⡾⡘⡭⡣⡖⣉⠙⠛⠳⣠⠁⢀⠀⡛⡄ ⠀⠀⣀⠗⠂⠀⠀⡌⢠⠘⡀⠑⠒⠈⠀⠁⡏⠉⠉⠐⠢⠀⠉⠀⠉⣦⠊⣠⡡⠃ ⡠⣋⣀⠙⠂⢄⣀⣰⣊⣂⠐⢄⠀⠀⠀⠀⡌⠀⠀⠀⢴⠀⢀⢄⡩⠃⠈⠀⠀⠀ ⠀⠀⠈⠋⠁⠀⠀⡇⠀⠀⠑⠢⡑⠄⡀⠀⢃⠤⠄⠒⢁⠔⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠑⠬⠥⢀⣀⡒⠊⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠄⢂⣀⠤⠐⠂⠉⠀⠎⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⡴⢠⡄⣀⣠⢴⢒⣼⠇⠀⣀⣤⠤⢄⣤⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀ ⠀⡴⣟⡕⢀⣿⡟⢋⣟⣨⡾⢋⠗⠛⡿⢁⣞⣿⠵⢛⡟⢁⣴⡟⢀⣤⣤⠤⢄⡀ ⠈⣰⡟⠳⡿⠁⠃⢸⣧⡟⣱⠊⠀⠈⡆⠚⡝⠁⠀⡎⣰⣻⡿⠄⠘⣾⣁⣴⡟⠁ ⠀⢙⡇⠀⠃⠀⣠⠞⠝⠁⠀⠀⠀⠁⠚⠂⣰⡤⠼⠋⠉⠘⠀⢰⣂⣽⡏⠜⠀⠀ ⠀⠈⢀⠀⠴⠋⢁⢸⠀⠀⠭⡇⠁⡖⠄⠀⠀⠀⢠⡤⠤⠞⣤⡤⠜⠋⠀⠀⠀⠀ ⠀⠀⢂⢊⠔⠈⠒⢌⢤⠀⠀⡟⠉⠀⠠⠆⠀⠈⠁⡀⠀⠀⠀⠉⠓⢦⡄⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⠑⢩⣲⡿⠓⠈⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠑⠛⠧⠄⠀ ⠀⠀⡙⠄⢀⡀⠀⡤⠊⠀⡀⠈⠆⠀⠀⠤⢤⠸⡀⠁⠒⠚⠒⣞⣆⠀⢐⠂⠀⠀ ⡆⠀⠁⠑⠀⠉⢩⡀⠐⠄⠐⡄⣼⢠⡆⠀⠀⠀⠈⠀⠐⠀⠤⣄⠈⠓⠀⠰⠀⠀ ⠹⡄⠀⠀⠀⠙⠓⢊⠂⠄⠓⠂⠁⠛⠋⠉⠀⢀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⠀⠈⠻⣀⠀⠀⠈⠄⣣⠀⡒⠀⠤⢄⡀⠀⠂⠀⡆⡇⠈⠉⠂⠀⢀⠀⠀⠁⠀⠀ ⠀⠀⠀⠙⠦⠴⠦⠅⠃⠀⠈⠚⠠⠦⠙⣒⣚⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠘⣄⣷⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠁⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢷⠀⢠⡄⠐⡶⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⡦⠀ ⠀⠀⠀⠀⠀⠀⠹⡘⡆⠀⣀⣀⣠⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣧⡀⠉⠛⠉⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡿⠻⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⣤⣀⣠⠼⣅⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀ ⠀⠀⠀⢀⣀⠤⠴⢒⡽⢉⡿⠛⣽⣡⠴⠒⠋⢠⣤⡝⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢮⢉⣠⠔⠒⢫⣴⠋⢱⠀⠉⢠⠤⣸⡉⢻⡆⢹⣾⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⢻⢰⡋⠹⡒⠒⠉⢻⣀⣸⡀⣏⠻⣦⡈⣿⣶⣿⣾⠛⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠳⡘⢆⢳⠀⠀⠈⣻⢿⡿⢿⣷⢾⣿⠿⣏⠁⠊⢦⡇⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢾⣌⡷⢤⣀⣟⣻⡓⠴⠛⡆⠘⠓⣸⢶⣄⡼⠁⠀⠀⠀⠈⢿⣦⣤⣤⠾⠇ ⠀⠀⠀⠀⠈⠻⣄⣾⣿⣷⣿⡑⢒⡂⡌⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠾⠀⣿⣿⣷⣮⣍⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠁⢀⡇⣿⣿⣿⣿⠛⠉⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣤⠄⠀⠀ ⠀⢀⠎⠁⠀⡰⠋⣹⠞⠻⣿⠚⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣬⣿⡶⠶⠀ ⢀⣏⣀⡠⠞⢡⠞⠁⠀⠀⠘⣦⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠈⠛⠀⠀ ⡎⠉⠀⣠⡔⠁⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠀⠀ ⠙⢆⠀⢏⠉⢦⠀⠀⠀⠀⠀⠘⣆⡄⠸⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀ ⠀⠀⢳⡈⢢⠀⢇⠀⠀⠀⠀⠀⠹⣷⡀⠀⠘⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⣄⠁⠸⡄⠀⠀⠀⠀⠀⠘⢏⠓⢄⠀⢄⡈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⡀⢱⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣌⡉⡀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠼⢣⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣄⠈⠳⡀⠀⠀⠀⠀⠀ ⠀⠛⠛⠓⠒⠒⠚⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣔⣒⣉⣸⣆⣧⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡰⠉⢠⠒⠁⣠⠔⢀⠤⠄⢤⡀⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠉⣑⠀⠀⢀⣠⣃⠀⠣⠤⠬⢒⡚⠁⡠⠄⠀⠃⢠⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⡜⠀⠁⢠⢊⣀⢀⠤⠤⠤⢤⢀⣀⠈⠘⣦⠈⢠⠃⠎⠃⠀⠀⠀⠀⠀ ⠀⠀⠃⢰⠀⢀⣠⡼⠡⡂⢑⠅⠀⠰⠛⢐⡄⠈⠐⢸⠦⡤⡼⠴⣀⠀⠀⠀⠀⠀ ⠀⢸⠀⡄⡖⣋⡘⣁⠀⠀⢀⣈⡃⠠⠈⠁⠀⠀⠀⠸⢠⠈⠇⠀⠈⢻⠢⡄⠀⠀ ⠀⢸⡠⣻⠄⠁⠀⠈⢆⠢⢀⢀⢀⢀⢀⡀⡨⣊⡶⠁⠘⢰⠀⠀⠀⠄⣇⡈⠢⡀ ⠀⣸⢁⠹⡀⠀⠀⠀⠈⠪⢒⡤⣤⣤⣥⣼⠞⣙⠠⠔⡗⠘⠀⠀⢀⠴⠃⡘⢠⠁ ⢀⠟⢆⠀⠈⠐⠤⣀⡠⠃⠀⠀⠑⠨⠩⠊⠁⠀⠀⠀⠈⠢⣠⡴⣥⣤⠾⠒⠁⠀ ⠀⢷⡈⠒⠤⠤⡴⠫⡱⢄⡀⠀⠀⠀⣃⠀⠀⠀⠀⠀⣀⣾⣟⢼⠀⠙⡄⠀⠀⠀ ⠀⠈⠳⣄⠀⡗⠡⡀⡇⠀⢹⠛⠭⢍⣙⢭⣩⣽⣙⣻⡿⡿⢹⣾⢄⠀⠙⡄⠀⠀ ⠀⠀⠀⠈⢫⣦⢄⢑⣧⠀⡇⠀⡇⢀⠑⠂⠼⢿⠯⠙⠙⠓⣞⡓⠉⠀⢰⠁⠀⠀ ⠀⠀⠃⢶⠍⢐⡄⢐⠻⢳⡇⠆⣇⡘⠀⡄⠀⡐⡟⠳⠈⡀⡿⢺⢒⠚⢹⠂⠀⠀ ⠀⠀⠀⠛⠤⡇⠀⣾⣤⣜⣇⣤⣯⢀⣇⡋⠀⠈⠁⠊⠴⠷⠏⠍⠚⠒⠉⠀⠀⠀ ⠀⠀⠀⠀⠉⠑⠊⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣧⣼⣿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⣿⠿⢿⠻⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠿⠢⠄⠁⠀⣬⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢀⠠⠧⠄⠈⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⠀⣀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠉⠠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠑⠀⠲⣤⠤⠘⠉⡁⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡀⠀⠀⠀⠰⠀⠀⠀⢹⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢲⢧⣠⣀⣀⠴⢄⣀⣤⣆⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠎⡾⣄⣀⣀⣴⠒⢄⣀⣿⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⣷⣖⠁⠁⢈⡀⠣⣾⢻⣄⡜⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢳⢉⡏⠃⠠⡀⠀⡏⠉⣼⠸⠙⡀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢰⠟⣄⢰⠈⢹⠉⢰⣿⣆⡆⠱⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⡔⠊⠉⡱⢆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡞⠀⠈⠳⡶⢼⠤⡿⠁⠘⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀ ⢀⡔⢺⠁⠀⡇⠀⠀⢷⠈⢣⠀⠀⠀⠀⠀⢀⣼⢦⣼⣁⣀⠤⠤⠷⠤⠼⠥⠤⢤⣻⣟⣻⡀⠀⠀⠀⠀⠀⡴⠋⠀⢸⠈⠹⠒⢄⡀⠀⠀ ⢻⠀⢸⠀⠀⢧⠀⠀⠸⣷⡞⢧⢀⡠⠤⠒⠛⣿⡓⣛⣧⣤⠒⡶⢶⣲⡶⠒⠶⣶⠏⠨⣹⣗⠒⠢⠤⣀⡎⠀⠀⠀⡘⠀⢠⠀⠈⡏⢳⡄ ⢸⠀⠀⡆⠀⠸⡄⠀⠀⢣⣤⠊⢁⡠⠤⠒⠉⠻⢿⡿⠋⠋⠐⡅⠀⣿⠀⠀⠰⠉⠚⣿⠋⠀⠉⠑⠢⡤⣉⣲⠀⢠⠃⠀⡜⠀⢠⠀⠸⢸ ⠀⡆⠀⢹⡀⠀⢳⠀⠀⠈⢏⠋⢳⠀⠀⠀⠀⠀⠸⣇⢄⡖⠀⢸⢸⢿⠰⠀⠀⡟⢰⠇⠀⠀⠀⠀⣸⠀⠀⠀⣰⠏⠀⣰⠃⢀⡎⢀⠇⡸ ⡀⠹⡄⠀⢷⠀⠀⢧⠀⠀⠈⡆⠀⡇⠀⠀⠀⠀⠀⢹⡟⠑⢤⣾⠋⠀⢳⣀⠘⠙⠇⠀⠀⠀⠀⠀⡟⠀⢀⣼⠋⠀⡰⠃⠀⡜⠀⡜⢀⠃ ⢣⡀⢹⣆⡀⢳⣀⠀⠳⣄⡀⠘⢦⡕⠀⠀⠀⠀⠀⢸⡇⠀⠀⢳⠀⠀⣼⠉⠀⢸⡆⠀⠀⠀⠀⠀⠺⣶⡚⠁⣠⠖⠁⣠⠎⢀⡜⣠⠊⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠿⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⢠⡒⢛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢠⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠪⠤⡈⠵⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠀⠀⡀⠀⣸⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢲⢍⠉⡄⠉⣹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⢺⠋⡀⢰⢰⡟⢚⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⢘⠀⡜⠢⣎⡉⣸⢣⡎⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⢴⠉⡇⠀⡍⢄⠀⠀⠀⡸⣤⣃⠠⠽⠭⠧⠤⣳⣢⠀⠀⠀⡠⠊⢩⠲⠠⡀⠀ ⠇⢸⠀⢃⠀⢙⡋⠄⢂⠩⢿⣭⠷⢈⠙⡝⠉⡽⢡⡾⠩⠔⡒⢄⠀⡄⢠⠀⠇⣷ ⢰⠀⠆⠘⡀⠀⠗⢩⠀⠀⠀⢣⣰⠀⣧⢇⠀⣰⡜⠀⠀⢀⠃⢉⡔⢀⠆⠰⢠⠸ ⢄⢣⡈⢄⠐⣄⠈⢄⠄⠀⠀⠈⡇⠹⡅⢀⡖⢠⡀⠀⠀⠸⣤⠎⣠⠊⡠⢁⢂⠂

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