⢀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣴⣶⣄⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣤⣤⣀⣤⣤⡀⠀⣀⡀⢀⣀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣴⣶⠋⠉⢻⣿⣿⠟⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁⠀⢿⣿⣿⠟⣀⣀⣀⠙⠏⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢏⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠈⠁⠀⠙⠿⠋⣀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣀⣀⠀⠀⠀⠹⣏⠙⠛⠷⠶⣄⣀⣀⣀⣀⣀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣶⣤⣶⣄⠀⠀⣠⠞⠁⠀⠉⠙⠛⠛⠶⠶⠾⠃⠀⠀⠀⠈⠉⠉⠉⠉⠙⣦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⢿⣿⡿⠋⠀⢸⡇⢀⣶⣶⣶⣤⣴⣾⣿⣷⣆⠀⢀⣴⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠉⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⢷⣄⠀⠀⠀⠙⢦⡀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠎⣼⠃⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⡶⢶⣦⡀⠀⠀⣀⣴⡏⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⠀⠀⠈⣁⣤⡾⠛⠛⢧⣄⣀⠀⠀⠀⠻⣥⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣷⣀⡀⠀⠈⠙⠛⠶⢦⣀⣀⣙⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠶⢶⣦⣤⣤⣭⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⠃⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣀⣤⠜⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠳⣄⠈⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠙⢿⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠘⠛⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⢰⡏⠀⠀⠀⠀⣾⠉⠉⠿⠿⠿⣏⠉⠉⠉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⣿⣷⣤⣤⣼⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠛
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣴⣶⣄⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣤⣤⣀⣤⣤⡀⠀⣀⡀⢀⣀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣴⣶⠋⠉⢻⣿⣿⠟⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁⠀⢿⣿⣿⠟⣀⣀⣀⠙⠏⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢏⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠈⠁⠀⠙⠿⠋⣀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣀⣀⠀⠀⠀⠹⣏⠙⠛⠷⠶⣄⣀⣀⣀⣀⣀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣶⣤⣶⣄⠀⠀⣠⠞⠁⠀⠉⠙⠛⠛⠶⠶⠾⠃⠀⠀⠀⠈⠉⠉⠉⠉⠙⣦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⢿⣿⡿⠋⠀⢸⡇⢀⣶⣶⣶⣤⣴⣾⣿⣷⣆⠀⢀⣴⣿⣿⣿⣶⣿⣿⣿⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠉⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⢷⣄⠀⠀⠀⠙⢦⡀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠎⣼⠃⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⡶⢶⣦⡀⠀⠀⣀⣴⡏⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⠀⠀⠈⣁⣤⡾⠛⠛⢧⣄⣀⠀⠀⠀⠻⣥⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣷⣀⡀⠀⠈⠙⠛⠶⢦⣀⣀⣙⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⠶⢶⣦⣤⣤⣭⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⠃⠻⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣀⣤⠜⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠳⣄⠈⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠙⢿⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠘⠛⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⢰⡏⠀⠀⠀⠀⣾⠉⠉⠿⠿⠿⣏⠉⠉⠉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⣿⣷⣤⣤⣼⣇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠛
