⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣩⡙⢿⣉⣮⡅⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⡿⢠⡙⢻⣿⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣳⣷⣦⠌⣧⣸⡷⠤⠶⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⢿⣃⡤⠼⠏⠀⠀⠀⠀⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠉⠉⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣝⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠉⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣠⠄⠀⠀⢀⣀⣤⣺⠃⠀⡆⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡞⠉⠀⠀⠀⣀⢼⣢⠞⠁⠀⢀⡿⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣀⠳⣜⣷⣢⡄⠀⠀⢠⡀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀⠤⠤⣒⣯⠖⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠸⡆⠈⠛⢿⣄⠀⠀⠀⠙⢦⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣷⠶⠞⠋⠉⠀⢀⡀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠓⢦⣄⡠⠋⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡿⠛⢉⣁⣀⣀⣀⡤⠴⠚⠋⠀⣠⠞⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⢿⠿⢿⣧⣀⣿⡀⠀⠀⠙⣆⠀⠀⠀⠀⠐⠈⠙⠺⢤⡀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣀⣴⡛⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠋⠀⢠⠎⣀⡀⠙⠿⣿⣷⣤⡀⠀⠈⠓⠀⠀⠀⠀⠀⠐⠀⠀⠹⣆⠀ ⠀⠀⠀⣸⡿⣻⢿⠁⠀⠐⢮⡝⠿⠿⢿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⣿⠿⠋⡠⠖⢊⢽⡳⠋⡀⣌⠉⠒⣢⡸⠻⢷⣄⠀⠀⢀⡴⠒⣶⢚⣿⢹⡓⢦⣹⡄ ⠀⠀⠀⠋⡼⠁⠈⢧⡀⠀⠀⠋⠉⠙⠮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⣥⡒⠺⠶⠒⠲⡾⠴⠶⠧⢬⡟⠉⠀⠀⠀⠀⣾⡟⠾⠋⠀⠀⠹⠞⢁⡞⡇⠀⢹⡇ ⠀⠀⠀⢰⠃⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⢠⣋⣉⡉⠉⠉⠙⣯⡽⠓⠀⠀⠈⠉⠙⠲⣤⣀⣿⡀⠀⢀⣨⣧⣤⣤⣀⡀⠀⢻⣿⣦⡀⠀⠀⠀⣠⠞⣰⡇⠀⠈⠁ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⣠⠼⠛⠋⠉⠉⠁⠀⠀⠉⢙⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠞⠉⠀⠀⠀⠀⠀⠉⠑⠾⣿⠧⢽⣓⣶⣴⣷⣾⠟⠁⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠙⢿⡟⠁⠀⠀⠀⠀⠀ ⢀⡞⠑⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⢸⣧⣶⡴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⡾⣆⠀⠀⠀⠀ ⠘⣿⡏⠀⠀⠈⣷⣤⣄⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⣶⣿⣿⠇⢸⠀⠀⠀⠀ ⠀⠉⣇⠀⠀⠀⠀⠀⠀⢈⡽⠋⠛⠛⠻⠿⣿⣿⣿⣶⣄⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣻⠟⣿⠁⢀⣼⠃⠀⠀⠀ ⠀⠀⠘⣧⣠⡆⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢝⡻⢿⣿⣤⡀⠉⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠈⣧⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣦⡀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡻⢿⣷⣶⣶⣶⣶⣿⣿⣿⠟⠛⢿⣿⣿⣷⣶⣦⣤⣴⣶⣾⣿⠟⠉⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠿⣐⣒⠢⠀⠀⠀⠀⠀⠀⠀⣆⣶⠀⠉⠓⠮⣍⠛⠛⡻⣏⠉⠀⠀⠀⣠⠏⠛⠻⡿⠿⢿⣟⡿⡟⠁⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠒⠚⠉⢻⠀⠀⠀⠀⡠⠟⠉⠁⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⢯⠁⠀⠰⡧⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡜⠁⠀⠀⢠⠎⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⣇⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡸⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠘⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠚⠁⠀⡰⠁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠘⢦⡀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠥⠄⠀⠤⠠⠾⠥⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠭⠷⠦⠤⠤⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠈⠙⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⣿⣿⡿⢷⣶⣶⣤⣄⡀ ⠀⠀⠀⢀⣀⣸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠎⠀⣤⣴⡋⣁⣀⣼⣦⣄⠀⢻⣿⡇ ⠀⢀⣶⡿⠟⢿⣿⣿⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣀⣛⣉⣭⣿⣿⣿⣿⣧⢽⣿⣿⠇ ⠀⣼⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀ ⢰⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣷⠀⢀⣈⣿⣷⣤⡄⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣷⣾⡿⠛⠋⠉⠉⠁⠀⣰⣾⠟⠛⠛⠻⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⠃⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢸⣿⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡇⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣦⣀⡀⠀⠸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣶⣤⠈⠛⠿⣷⣶⣶⣶⣦⣤⣄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠈⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⠉⠉⢿⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣿⣆⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠘⢿⣷⣄⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣤⣶⡿⠋⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀