⠀⠀⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡆⠀⠀⢀⣾⡟⠋⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣤⣶⠿⠛⠋⠉⣿⣷⡶⢿⣿⠏⠀⠀⠀⠘⣿⣶⣶⣶⣤⣀⠀⢀⣠⡶⠛⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡏⠳⣿⣿⠿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠻⠿⠛⢷⡾⠛⣷⡶⠿⠷⢶⣾⠏⠀⠀⠀⠀⠀⢻⡇⠀⠀⠉⠛⢿⣿⣅⠀⠀⠀⠀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣄⣩⣿⢦⡹⣿⢶⣦⡄⠀⣠⣾⠟⣁⢀⣴⣄⣶⣾⢷⡴⠟⢹⣧⢤⣄⣼⡿⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠻⠿⣿⣿⣷⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡁⠀⢻⣿⣄⠘⣿⣴⣿⣣⡾⣿⣾⣿⣿⣿⣿⢸⣅⡀⠀⠀⠀⠉⣿⡇⠀⢀⣴⣷⣦⡀⠀⣿⠀⠀⠀⠀⠀⣙⣿⣿⣯⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⣤⣤⣽⣷⣾⣻⡿⠉⢷⣿⡏⠻⣿⣆⠉⣹⣏⡉⠛⡆⣠⠖⣿⢀⡀⠀⠀⣿⡇⠀⢸⡏⢨⡿⣷⠀⣿⣷⡔⢤⡼⠚⠁⠘⢿⣿⣿⣦⣀⣠⡴⠟⠉⠀⠀⠈⢻⡄⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣧⣀⠀⠀⠀⠈⣿⡃⠀⢸⣿⢥⣄⠈⣿⡿⣿⣿⡳⣦⣽⢃⡾⣿⣸⣇⣿⢰⣿⣿⡀⢸⣧⠈⠁⢻⡇⣿⠘⢿⣦⠀⠀⠀⠀⢈⠻⣷⣶⠛⠉⠀⠀⠀⠀⠀⠀⣼⠇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢀⣀⡹⣷⣤⣾⠏⠀⠈⢳⣼⡇⠀⠙⣿⡼⢿⣿⢻⣿⠋⠛⠻⢾⣿⠹⣿⡄⢿⣆⣀⣾⠇⢿⠇⢀⡻⣷⡄⠀⠀⠘⣷⠿⢿⣷⣄⠀⠀⠀⣀⣴⠞⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⢿⣄⣀⣀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣜⠻⣿⠿⣾⣿⣄⠀⣤⣴⣿⡟⠳⣄⢹⡇⠀⠸⠿⠉⠀⠀⠀⠸⣿⠀⡞⠀⠀⠀⠀⠉⠀⠀⠀⠈⠹⣟⢿⣦⠀⣠⣹⡆⠀⠙⠿⣷⣶⠟⢻⡟⢷⣆⠀⠀⠘⠿⣿⣿⣿⠟⠋⠀⠀⠀⣀⣤⣾⣿⣽⣿⣿⣷⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡈⠳⣼⡏⢻⣷⠿⣧⠞⠛⠀⠸⣾⡇⠀⢀⠀⠀⠀⠀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⠻⣷⡻⣟⠃⠀⠀⠀⠈⠻⣿⣧⡀⢀⣿⠄⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⣿⣿⣿⣿⣿⣿⣧⣀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣿⠃⠘⢿⣧⣉⠀⠀⣀⣼⡿⠀⠀⠸⣾⡀⡀⠀⠸⢿⣿⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢹⣿⠛⠀⠀⠀⠀⠀⣴⣮⣿⣿⣾⠟⠀⠀⠀⢀⣠⣴⣿⡿⠟⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠉⠛⠛⠛⠛⠋⠀⠀⢀⠀⡈⣿⠙⣆⢧⣛⠙⠀⣈⣙⣿⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⡇⣴⣷⡄⠀⠀⡅⠹⣿⣏⠙⠀⢀⣤⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣠⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣀⣀⣤⣀⣀⠀⣀⣠⣤⡠⡆⠘⠆⠁⠉⠀⣍⡈⢿⣿⡛⠛⠋⠉⠐⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠛⢠⡀⣤⢧⠀⠈⢿⣷⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣠⣿⠿⠛⠁⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⢨⡍⠀⠹⣿⠈⣋⠀⠈⠁⠀⠀⢀⢀⣠⣤⣻⡿⠾⠻⣿⣤⣒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡠⡾⠋⠻⠟⠋⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⣾⡿⢿⡄⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣧⣶⣴⣿⣆⣿⣇⡶⢦⣴⠶⢿⢻⣷⣈⠉⢁⣠⡴⠒⠙⠻⠿⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⣼⡟⠹⣷⡀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⢀⣠⣾⠟⠁⠀⢨⣧⠶⠛⠁⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢸⣏⠘⠻⣿⣿⡉⠉⠁⠐⡪⢷⣻⢷⢿⡟⠿⣶⣶⣴⣶⠶⠿⠟⠋⢉⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠙⣿⣶⠿⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⣴⡿⠛⠁⠀⣀⣤⠟⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢠⣿⠹⣷⣔⠲⣶⣍⠈⠉⠀⠘⣿⣿⣿⣿⣿⣷⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⣾⠟⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⡿⠋⠀⣀⣴⢾⡋⢁⣠⠶⠛⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⡀⠈⡛⠿⣾⣧⣤⣀⣀⣀⣼⣿⣿⣿⣿⣿⡇⠀⢀⡀⠀⠀⣶⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣴⠏⢀⣴⣿⠋⣠⣴⠟⠋⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠻⣷⣄⢰⣆⠀⠈⣩⣿⢿⣿⣿⣭⣿⣿⣿⣿⣿⠀⠺⣷⣤⣴⡿⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⣴⡿⠛⢿⣿⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣷⡟⣿⣿⠟⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⡀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠉⢀⣼⣿⠟⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣁⣀⣿⣿⡿⠶⣶⣶⣿⣿⠿⠶⠆⣠⣴⣾⣿⣿⡃⠀⠀⠀⣀⣴⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⠋⠁⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⣠⠖⠈⠙⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢋⣼⡟⠁⠛⠙⣿⣆⢀⣀⣤⣀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠁⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣾⠟⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣟⠋⠉⠀⣀⢠⡄⣬⣿⣿⣅⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣾⣿⣵⡶⠶⠿⠛⠛⠛⠉⠉⠉⣿⠛⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⣿⠀⠀⣰⣿⣾⣿⣿⡇⠙⠿⣷⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⣾⡿⠛⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣿⣣⡤⠤⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣼⡿⣿⣿⣿⡿⢿⣶⣶⣯⣿⣿⣭⠉⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⣠⡶⠛⠉⠉⠛⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⢀⣠⡶⠛⠙⣿⡄⠀⠀⠀⢠⡾⠁⢀⣴⡿⢻⣏⠀⠀⢀⣀⣸⠻⣤⣀⣠⡶⣿⣷⣆⣠⡇⣼⡟⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⡿⠿⠁⣿⣇⣴⡾⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠋⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⢻⣧⠀⠀⢰⠟⠀⣾⠟⠉⠀⠈⢿⣦⡞⠻⠿⢿⣰⡖⠛⠁⠀⠈⠉⠀⣁⣴⡿⠁⡀⣠⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⢻⡏⠉⠀⠀⠀⠀⠀⠀⢀⣸⠿⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⡀⠟⠀⠀⣀⣀⣠⣤⣴⡾⠿⢷⣦⣄⣈⣿⣠⣤⣤⣤⣶⡶⠿⠛⠉⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠈⠙⠻⠿⠿⠟⢛⣻⡿⠛⠁⠀⠀⢨⣿⡍⠉⠉⣿⣉⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠘⣿⡄⢀⣤⡶⣿⡇⠀⠀⠀⠀⠀⣀⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⠀⢀⣤⠶⠋⣿⣷⡀⠀⢸⡍⠙⠻⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡄⠒⢦⡄⠀⠸⣿⣦⡀⠀⢻⣿⣯⡵⠞⠋⠀⠀⠀⣠⡴⠟⠋⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⣀⣴⠾⣯⣁⣀⣀⣀⡴⠞⠋⠁⠀⠀⣘⣿⣷⡀⠀⢷⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠹⣆⠀⣿⡿⢿⣶⣤⣿⣿⡀⠀⢀⣠⡶⠛⠉⠀⠀⠀⢀⣤⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣠⡴⠞⠉⠀⢻⣧⠀⠈⣧⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⢳⠀⠀⠀⠀⢻⡄⠸⣿⡀⢿⡉⠙⢛⣿⡾⠛⠁⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⢿⣇⠀⠸⣇⠀⠀⠹⣆⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠘⡇⠀⠀⠀⠀⢷⠀⢿⣇⠈⠙⠛⠋⠁⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠶⠶⠾⠋⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢻⡀⠀⠀⠹⣦⡀⠀⠀⠀⠛⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⡇⠘⣿⡄⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠾⠋⠁⠈⠻⡆⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⡇⠀⠀⠀⠈⠙⠓⠶⠶⠖⠛⠉⠀⠀⡾⡄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢻⡄⢹⣷⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣿⡏⠻⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⠀⠀⠀⣰⠇⠀⠀⠘⣧⡀⠀⢀⣠⡴⠖⠲⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣯⡁⣩⡥⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⢷⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠘⣿⡆⠀⠀ ⠀⠀⢀⣤⠶⠛⠁⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⢀⣠⡿⠀⠀⠀⠀⢸⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧⠀⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣿⣿⣄⠀⠀⢸⣿⠀⠀ ⠀⣴⠏⠁⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡴⠆⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⣇⠈⢿⣧⠙⠻⢿⣶⣤⣤⣴⣶⣶⡿⣿⣇⣀⣤⣶⡾⠟⠻⡆⠀⠉⠈⢻⣧⣀⣸⡿⠀⠀ ⠀⢿⣄⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⢿⣇⠀⣯⣛⠇⠀⠀⢀⡼⠃⠻⣿⡋⠉⠀⡴⠀⠀⠛⢶⡀⢴⣞⢙⣻⣿⡇⠀⠀ ⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣀⣴⠞⢻⣿⠋⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⣿⣷⣾⠛⠀⠀⢄⣻⠀⠀⢺⣯⠀⠀⠘⣳⠀⠀⠀⢀⣹⡖⠘⢿⣽⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣦⡀⠀⠀⠀⢻⣄⠀⠀⠀⣠⡴⠞⠉⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢿⡿⢷⣦⣜⡁⠀⠀⣴⠞⠃⠀⠀⠈⠙⠒⣲⡄⠿⠵⠞⠳⢿⣿⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠓⠒⠛⠁⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⢿⣄⠉⠛⠻⠿⠿⣿⣦⣄⣀⣠⣤⣀⣀⠏⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⣿⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⠿⠿⠿⠿⠷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉⢸⡟⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣈⣩⣽⣿⣿⣶⣾⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⢀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠇⠀⣿⣿⣿⡿⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣀⡤⠖⠋⠁⠀⢀⣠⣴⣾⣿⣯⣥⣶⣶⣾⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠛⠋⠉⠉⠀⢀⣀⣿⣿⣿⣇⠢⣿⡿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣾⣉⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣧⡤⠶⠖⠚⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⡟⢰⢸⡇⠈⣿⢿⣿⣿⣷⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠚⠛⠋⠙⢿⣿⣿⣿⣦⣤⣤⣼⡃⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⠿⢟⠛⠍⠉⠓⣐⣸⡇⠀⣿⠀⠈⢻⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⠟⠛⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⡏⠉⣐⣂⣠⣤⢤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⢠⢰⡶⠶⠟⠛⠋⠉⠀⢀⣿⠀⠀⢸⣿⣿ ⢠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣰⣿⣿⠏⠀⠀⠀⠀⣼⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠶⣚⠛⢹⣿⣿⡇⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠀⠀⢸⠉⠻⣿⡿⠿⡿⠛⠛⢿⣿⣿⠄⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⠈⢸⡇⠀⣠⠴⠶⠞⠛⠋⠉⠀⠀⢸⣿⣿ ⠈⢿⣿⣿⣿⠛⠛⠉⠉⠁⠈⢿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⣸⠏⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡯⠿⣁⣀⣠⣤⢤⣤⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣶⣥⣤⠶⢾⣿⣿⠄⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⠸⢸⡇⠀⢸⠀⠀⢀⣠⣤⣤⣶⣶⣿⣿⣿ ⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠈⢻⡽⣿⣿⣿⠏⠀⠀⠀⠀⣰⠏⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠀⠀⢸⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠾⠂⠀⣿⣿⣿⡿⢷⣤⣸⣿⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⢠⢸⡇⠀⢸⠀⠀⢸⣿⣿⠿⠿⠛⠛⠋⠉ ⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠹⣞⣿⠏⠀⠀⠀⠀⣰⠏⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⡟⠍⠉⢀⣀⣀⣤⡤⠶⠿⣿⣿⡇⢀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⠈⢸⡇⠀⢸⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣰⠏⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠼⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠗⠚⠛⠉⠉⠁⠀⠀⠀⠀⡇⠙⢿⣎⢸⣿⣿⣿⡇⠀⠀⠀⣀⣀⣼⡇⠀⢸⣿⣿⣿⠸⢸⡇⠀⢸⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣋⠩⠁⢀⣀⣠⣤⡤⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣷⣖⠛⠋⠉⠁⠀⠀⣀⣸⣿⣿⣿⢰⢸⡇⠀⢸⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠷⠒⠛⠋⠉⠉⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⢸⢸⡇⠀⢸⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣀⣀⣠⣤⠴⠶⠖⠛⠋⠉⠉⠀⢀⣀⣀⣤⣤⣴⣾⣿⣿⣿⠐⢹⣟⢿⣿⣿⣿⣿⣿⢟⣛⡛⠛⠏⣀⣀⣸⡇⠀⢸⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⢾⣿⣿⣿⣯⡉⠀⢀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠉⣿⠀⢸⡟⢿⣿⣿⣿⣴⡶⠶⠟⠛⠉⠉⠁⢀⣼⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⡟⢾⣿⣿⠀⢀⣀⣀⣤⡤⠴⠖⠚⠛⠉⠉⠁⠀⢀⣀⣠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⣿⡟⠏⠩⠿⣴⣎⣠⣤⣤⠶⠟⠀⢸⡇⠀⢹⣿⣿⣿⣿⣦⣤⠶⠶⠚⠛⠋⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣭⡉⠀⠀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣉⠉⠠⢄⣘⣠⣤⡶⠶⠶⠛⠛⠋⠉⠉⠀⢀⣀⣠⣤⡼⠇⠀⢸⣿⣿⡿⢿⣿⣿⣷⣄⣀⣤⣤⣴⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣤⣤⠶⠶⠚⠛⠀⠀⣿⣿⣿⡇⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠻⠿⠉⠉⢀⣘⣋⣽⣿⣿⣿⣿⣿⣟⡉⠉⠁⠀⣀⣀⣠⣤⡴⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⣀⣸⣿⣿⡇⠀⠙⠻⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀ 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