⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣟⣙⢻⡿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣴⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣠⣶⣿⡿⠿⠟⠛⠳⢶⣾⣭⣛⣿⣶⣽⣷⡄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣼⣽⢳⣗⡟⣿⣿⢹⣿⣇⡏⣿⡿⣸⢿⣧⡟⠉⣭⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢿⣆⠀⢀⣴⡿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣮⣻⣿⣿⡌⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⣰⣧⣏⣿⣘⣼⣧⣿⣿⣿⣿⣽⣿⣏⣷⣿⣼⣿⠿⠃⢸⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠟⠁⠀⠀⢻⣦⣿⣿⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣷⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠁⠀⠀⠿⠿⠀⠈⢁⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠯⠵⠶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣇⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣀⣉⣬⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⢸⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣿⡟⠀⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⠛⠳⣤⠀⠀⠀⠀⠀⠀⠿⠟⠛⠿⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠉⣿⣷⣄⠸⣿⣄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⡀⠀⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠋⠉⠀⠀⠀⠈⠙⢿⣧⣿⡏⠳⢦⣀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⣄⣀⠀⠈⠛⠶⣄⣀⣸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⣿⡀⣀⡀⠐⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠐⠲⢶⣤⣤⣄⣀⠙⣿⡇⠀⠀⠙⠳⣄⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠳⢦⣀⡀⢸⡟⠻⡏⠉⠛⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⣴⣾⣿⣤⣄⠀⠀⢀⣤⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⢸⣿⡀⠀⠉⠉⣿⡿⢦⣄⡀⠀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⢸⣇⠀⢻⡿⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢃⣴⠫⢼⡏⠀⣀⡙⣻⠖⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠉⠘⢷⡀⣀⣀⣿⡇⠀⠈⠙⢳⣿⡻⡝⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠲⢦⣄⠀⢻⣆⠀⠻⣦⣿⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⢿⡄⣨⣿⡿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠈⠻⣿⣿⡟⠶⣄⡀⠀⣿⠛⠿⣷⡌⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠶⣽⣷⣦⣤⣀⣠⣴⡶⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣽⠋⠀⣀⣴⠾⢓⣼⡿⢋⣽⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣀⡀⠀⠀⠙⢿⣦⡈⠛⣾⣿⣄⠀⠈⠻⣦⡹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠋⠉⢻⣯⠀⠀⠀⠀⠀⢀⡴⠟⠁⣠⠞⠁⠀⣴⠟⠁⡾⣫⣠⣶⠿⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢿⡟⢻⠟⠁⠀⠛⢿⣿⣿⣄⠀⠈⠻⣯⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⢐⡶⠋⠋⢀⣴⠻⣦⣄⣾⡏⠀⢀⣴⡿⠋⢀⣠⣾⣙⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠋⠀⠀⠀⠀⠈⠻⣟⠛⣧⡀⠀⢘⣧⠊⢿⣷⣄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠽⢭⣭⣭⣉⡙⠿⢯⣉⣉⠉⠉⠉⠉⠻⣯⣍⡉⠉⠉⠉⠉⠉⠉⠻⣿⣯⡻⣏⠉⠉⠻⠏⠉⠉⠉⠉⠻⣿⡙⢻⣿⠛⠋⠉⢉⣽⠿⠿⠿⠙⡏⠉⠉⠉⠉⢉⣩⣽⠟⠉⠉⠉⠉⣉⣩⣭⣿⠟⠉⠉⠉⠉⠉⢉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠀⠀⠀⠀⠀⠈⠙⢿⣮⠓⢀⣴⠞⠛⠉⠉⠙⠳⢿⣇⣼⡟⠀⠀⠰⠟⠉⠳⣦⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⢀⣴⠾⠛⠛⠉⠀⠀⠀⠀⠀⠠⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⡄⠀⠀⠀⠀⣿⣇⣾⠁⠀⣾⣧⠀⠀⠀⣸⡿⣿⡇⠀⠀⢀⣴⠏⠀⠈⠀⠀⠀⠀⠘⠁⢀⡤⠀⠘⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣺⡇⠀⣠⣿⣿⠀⠀⢠⣿⣿⣿⠀⠀⠀⣿⣿⡀⠀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠦⢤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠴⠶⠤⢶⠶⠶⢶⣿⡷⠶⠶⢾⣿⣿⡿⠤⠶⢶⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⠁⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⠿⠿⠾⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣶⠶⠿⠀⠀⣤⣤⣤⣤⣴⣿⣷⣿⠇⠀⠀⢾⡧⠀⠀⢠⡶⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡿⠉⢏⡹⠯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠉⢉⣩⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠭⢭⣭⣄⡬⣭⣿⠿⣿⡥⠭⢽⣿⡿⠿⠿⠿⣿⣿⡿⣈⣽⣽⣿⡿⠅⠼⠯⠬⢿⣯⣭⠭⠭⣤⣬⡥⠤⠤⠤⠤⠤⠤⠬⠤⠤⠠⠤⠤⠤⠬⠭⠭⠭⠭⡭⠭⢭⡭⠭⣭⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠉⠉⣁⣈⣿⣶⣿⠁⠀⣠⣶⡆⠀⠀⣰⣿⣿⡞⠉⠉⣹⣧⣤⡶⠒⠒⣶⣦⣈⠉⠉⣉⣉⠉⢉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣠⣌⣁⣀⣉⣡⣀⡉⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠄⢀⣤⣾⣿⡿⢟⣁⣤⣾⣟⣹⣯⣍⣹⣛⣛⣙⣋⣿⣿⣿⣻⣿⣿⣿⣷⣦⣀⠈⠹⠋⠻⣿⡿⣿⣿⣛⣉⣉⣉⣙⣿⣿⣿⡿⠟⠋⣉⣩⣭⣴⣶⣶⣶⣭⣝⡛⠿⠿⠟⠛⠿⢿⣿⣿⣽⣛⣋⣉⣉⣉⣉⣉⣉⣿⢿⣿⣿⣿⠛⣩⣿⣟⣽⣿⣋⣵⣾⢿⣿⠿⠿⢤⡄ ⠀⠀⠀⠀⣀⣒⣛⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣿⣾⣿⣾⣿⣿⣿⣏⣹⣿⣥⣿⣀⣀⣀⣭⣬⣭⣭⣥⣤⣭⣍⣁⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣿⣿⣿⣷⣿⣿⣿⣾⣿⣶⣶⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣶⡖⠛⠛⠁⡄⣶⣠⠄⠀⢀⣀⣬⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣛⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⣹⡟⣸⡿⠀⠀⠀⠀⠙⠀⠀⠀⠘⢿⣅⠀⠀⠀⠙⠳⣤⡀⠀⠀⠠⣟⡻⣿⣄⣀⡀⠀⠐⠲⢤⣤⣈⡛⠛⠃⠠⠀⠲⣶⠠⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠒⠐⠛⠚⠁⠻⢖⢒⡐⠛⠃⠀⠒⠒⠒⠒⠒⠒⠒⠲⣾⣿⣿⢟⣿⡗⠀⠀⠀⠀⠀⠀⠒⠀⢀⣶⠿⠛⠒⠶⠖⠂⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠖⠒⠚⠛⠓⠒⠒⠚⠛⣶⣾⣿⢻⣷⣶⣶⠒⠒⢻⠟⠓⣶⡶⠂⠒⢻⣿⣾⡿⠀⠐⠒⠒⠒⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⢞⡀⠛⢄⠈⣇⠳⣄⠀⢀⠀⠀⠀⠀⠀⣠⣼⡿⢋⠚⠱⠈⣿⣧⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢧⣿⣿⣿⣿⣿⢦⡀⣾⡆⢰⣿⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣜⡇⠡⠀⠄⠈⠳⣽⣾⡝⢧⣸⣦⣠⠀⣿⣿⠟⠁⣠⠖⠁⠀⠀⢻⣿⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣤⣿⣿⣿⡿⠋⣿⠈⢻⣿⣷⡟⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣻⡕⣯⢪⠤⠀⢟⣷⢷⣠⣻⣿⣿⣆⠈⠁⠀⠈⠁⠀⠘⠀⠀⢸⣿⣄⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⣾⣿⣿⣿⠋⠠⡆⠘⢷⣼⣻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⣽⣯⢀⡡⣌⠄⠠⣻⣌⣿⣿⡇⠙⢿⡷⠀⠄⠠⠀⠀⣀⣀⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣓⣿⠁⠂⠁⠀⣡⣾⣿⣿⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⢾⣧⡁⢘⡄⣠⣀⡍⢸⣿⣯⢿⠀⠸⣿⣦⡀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⣹⣿⡟⡉⠉⡀⠀⠄⣸⡟⣿⣿⣿⣥⡀⠉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢞⡿⣫⣝⣿⢣⣵⣯⢾⣼⡿⠘⣿⣇⣀⣿⠿⢿⣟⠙⢷⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠀⣰⠏⠙⠻⣧⡀⠁⣡⣾⣿⣿⣿⡁⠸⡏⠻⢶⣤⣈⣻⣏⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣫⣛⡽⣪⢺⡿⣿⣾⣿⣿⣧⠶⢿⣿⣿⣇⠀⠀⠉⠳⣤⣈⠛⠶⣤⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡟⣽⡾⠛⠉⠀⣰⠏⠀⠀⢤⣤⣷⣾⣿⣿⡿⠿⣿⣿⠿⣧⣀⠀⠈⠙⠻⢿⣧⡁⠈⠙⠻⢶⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣾⡷⠿⠿⠿⠋⢉⡉⠀⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⠉⠛⠶⣤⣈⣉⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣉⣥⠌⣩⡾⣿⣿⠿⠃⠀⠀⠀⣴⠋⠀⠀⣠⣾⣿⢿⣿⡿⠋⢳⣿⠀⣽⣷⡶⡟⠻⢶⣤⣀⠀⠈⠙⠷⣦⣄⠀⠈⠛⢳⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠋⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⣹⡿⣿⣦⣄⡀⠀⠀⠀⠉⠙⢿⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⢁⣴⠞⠉⢠⣿⡟⠀⠀⠀⢠⡾⢡⣴⣿⣿⣿⠛⠁⣾⡋⠀⠀⢸⣿⡀⠈⠹⡿⣦⣄⡀⠌⠙⠳⢦⣄⡀⡴⠋⠛⢶⣤⣈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡙⠻⢿⣷⣦⣤⣀⣀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⣸⣿⡇⠀⢀⣴⣫⣤⣾⣿⣿⠿⢿⣷⣦⣼⣇⠀⠀⣾⣿⣧⣀⠀⡇⠀⠉⠛⠶⣤⣀⠀⠉⡙⠷⣦⣄⢸⣿⢙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣆⠀⠐⠀⣀⡉⠉⠛⠛⠲⠶⠤⠤⠀⠀⠀⠀⣤⣤⣾⠋⠁⠀⠀⠀⠀⠀⣿⣿⣤⠞⣯⡴⣿⣿⣿⣟⠁⠀⠀⠈⠙⢿⣿⡇⡄⢸⡇⣀⠙⢻⣷⣄⠀⠀⠀⠈⠙⣻⣶⡌⠁⠀⠉⠛⠻⣮⣐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⠛⠶⣤⣀⡉⠁⠺⢷⣤⣀⣀⠀⠀⣀⣴⠿⣿⠃⣿⠀⠀⠀⠀⢀⣠⣴⣾⡏⠙⠷⣿⣿⣭⣿⢿⣿⠀⠀⠀⠀⠀⢸⣝⣿⠁⢸⣿⣷⣴⣿⣿⡿⠤⠤⠤⢤⣤⣿⣾⡿⢶⣶⢾⣿⣆⠘⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢩⡟⠛⠲⢦⣤⣈⣩⠿⠟⠉⠀⠠⡿⢼⣯⠀⠀⠐⠋⠉⠁⣿⡟⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⠀⢈⣿⣟⠻⢿⣿⠀⠀⣶⣒⡒⣲⡶⡆⠀⠀⢀⣾⣿⡏⠶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠃⢀⣠⡼⣿⡏⠁⠀⠀⠀⠀⢸⣿⣸⠇⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⢸⠇⠹⣆⠀⣿⠀⠘⣟⣳⣁⣀⣿⡇⠀⠀⣾⠻⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⢀⣠⣷⣾⣿⣧⣤⣽⣧⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⢸⡇⠀⠹⣦⣿⠀⠀⢿⡿⣿⣯⣿⣿⡆⢰⣿⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢘⣇⣷⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢸⡇⢰⣶⣾⣿⠀⠀⠈⢿⡽⣿⣿⣻⣧⣸⡟⡿⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠘⠇⢀⣀⣠⡤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⠟⠁⠙⣿⣶⣦⣶⣾⣥⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⢿⣾⣿⢿⣿⠀⠀⠀⠀⠙⢮⡿⣿⣼⠺⣧⡇⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣠⣤⣴⡾⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠿⣝⡻⢦⣯⣇⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠟⠀⢀⣼⡿⠈⢻⠙⣿⠛⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⠙⠛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣥⣴⣾⡿⠉⠀⠀⢸⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀