⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡄⢸⢩⠂⢄⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣖⡒⠒⠒⠒⠒⠶⠤⣦⡤⠤⣀⣀⠀⠀⠀⢀⡴⡫⢀⠍⠀⢸⠈⠀⠀⢳⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠚⠛⠓⠂⠠⠀⠀⠀⠈⠁⠠⠀⠉⠑⠲⣤⢏⠈⠀⡌⠀⠀⡆⠀⠀⠀⠀⢻⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⣀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⠁⠀⢠⠃⠀⢰⠇⠀⠀⠀⠀⠀⢳⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⡑⠉⠢⡈⠛⠦⣄⡀⠀⠀⠴⢛⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⠁⠀⠠⠃⠀⢀⡎⠀⢸⡷⡆⠀⠀⠈⣧⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠟⢡⢻⣆⠈⠐⠤⢠⣉⠓⢶⠶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⡎⠀⠀⠰⠁⠀⠀⡜⠀⠀⢸⠁⡇⠀⠀⠀⣸⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⠀⡀⠀⠎⢧⡀⠀⠀⠀⡽⠋⠔⢈⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣴⣿⠁⠀⠀⠔⠁⠀⠀⣜⠁⠀⢀⠆⠸⠋⡃⠀⠀⠈⡇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡇⠀⠈⡄⠙⠣⣀⡼⡁⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⠃⠀⢠⠀⣼⣿⣿⣿⠀⠐⠀⠀⠀⠠⢾⠟⠀⠀⡀⠀⠀⣰⣁⠀⠀⠰⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡇⠀⠀⠈⠄⢄⢸⣃⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡰⠃⠀⣴⣿⣾⠟⠉⡿⠉⠀⠀⠀⠀⠠⠞⣁⣀⣀⣐⡀⠀⠀⠁⢨⠇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢃⠀⠀⠀⠀⠀⠞⢩⠏⠀⠀⠀⠀⠀⠀⠀⣀⠔⢁⣴⡾⢃⣠⣾⡿⠟⡡⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⣀⠀⠀⢀⠎⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠸⣄⠀⠀⠀⠀⠀⡾⢀⣠⠖⠀⣀⣤⣶⣿⣵⣾⣿⣿⣷⡿⠟⢁⡠⠊⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠘⢾⡓⠆⠀⡠⠆⠀⢰⠃⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⢡⠀⠀⠀⠀⠀⣷⣿⠿⢟⡟⣩⠿⠛⠛⠋⣉⣤⣉⣀⠤⠐⠁⠀⣰⣿⣿⣿⣿⣿⠿⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠙⢮⠉⠀⠀⢀⠎⡠⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠈⢳⡀⠀⠀⠀⠘⡄⠀⣼⢉⣷⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⡿⢟⣉⣀⣀⣀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⢀⡜⢈⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⠀⢳⡀⠀⠈⠻⡉⠂⡏⣾⡿⠟⠛⠛⠻⠿⡇⠠⡄⠀⠀⠠⢲⠈⢀⣏⣤⡶⠶⣶⣾⠿⣧⣄⣀⠀⠀⠀⠀⠀⠁⠒⠮⣥⣡⡴⠋⠰⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⡄⠀⠹⣤⠀⠀⢿⠂⡇⠉⠀⣞⣍⣙⣲⡄⠹⡍⠉⠁⠀⠀⠘⡀⠉⡏⣾⢧⣀⣿⣿⡆⢹⠀⡽⠀⠀⠀⠀⠀⠀⠶⣺⣿⡁⠀⠀⢀⣾⣤⠤⠤⠴⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣆⠀⠘⠧⣀⠀⠀⣿⠀⢉⡏⢰⡏⠉⢻⣷⣿⠀⠀⠀⠀⠀⢇⠀⣇⠘⣄⠛⠿⠟⠁⣾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣱⡝⢳⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⡄⣸⠄⠀⣇⠈⣏⠒⢿⡿⢻⡇⠀⠀⠀⠀⠈⡀⢻⡀⣈⡳⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠤⣀⢀⣰⢹⡍⠁⠀⠤⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠀⣰⠁⠀⢀⡙⠶⢬⣳⣤⣤⣾⡧⠤⠤⠀⠀⠀⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣸⡉⣀⠀⠀⠀⠀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⢷⡠⠚⣁⣠⣴⠶⠿⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣿⠀⡇⠉⠐⠐⣂⣀⠀⠀⠀⠙⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣫⡼⢹⡟⣴⠛⠉⠀⠰⣥⣧⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣸⠇⠀⡇⠀⠀⠈⠑⠛⢿⢯⡉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣰⠏⠀⢠⠁⠀⠀⢀⡀⠤⠒⠃⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠖⢋⠠⠊⢰⠁⠙⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣀⠔⠊⣠⠞⢁⠀⡠⠃⠀⣠⣂⠉⢀⣀⡠⠴⠖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⣤⣄⡀⠸⡄⠀⠀⠙⠻⠿⠿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡠⠔⠊⣠⡴⠞⢁⡔⠿⠊⠀⠀⣠⣴⣵⣺⡟⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠻⣄⠀⠀⠀⠀⠀⣸⠤⠤⣤⣄⣀⣀⣀⣀⣠⡤⠖⠋⠀⠀⠀⡠⠐⣡⡤⠖⢋⡝⢀⡔⠃⠀⠀⠀⠤⠮⢼⢉⣵⠟⠀⣀⣀⣠⡤⠞⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠈⠳⢄⣂⠀⡼⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣂⡥⠞⠋⠁⠀⠐⡛⢒⠧⠂⠀⠀⠀⠀⣀⣴⠵⠛⠁⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⡁⡲⠈⠉⠉⠳⣄⠀⠢⠄⠀⠀⠀⠀⠀⠀⠂⣈⠴⠚⠁⠀⠀⠀⢀⠎⠉⢚⡡⠀⠠⠴⠖⠶⠯⠉⠠⠀⡀⠄⠀⠀⠀⠀⠀⠀⢈⣑⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣦⣤⣄⡀⠈⢻⣶⣤⣤⣤⣠⣤⡤⠖⠋⠁⠀⠀⠀⠀⢀⠔⠁⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⢉⠀⠀⠀⠀⠀⠀⠀⠙⠛⢭⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠲⠶⣖⡛⠛⠉⠉⠁⠈⠉⠙⠓⠠⢵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠀⠀⣠⠴⠚⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣂⣄⣀⠀⠀⠀⠀⠀⠩⢷⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠝⢦⡀⣀⣀⠀⢀⠠⠂⠔⠁⠀⣠⠞⠁⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠈⠳⢄ ⠀⠀⠀⠀⠀⠀⠯⢤⣄⠀⠀⠀⠀⠀⠤⠤⢄⣀⡀⠂⠀⠘⢦⣀⠀⠀⠑⢧⡡⠖⠉⠀⠀⠀⡷⠋⠐⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠿⢟⠛⠃⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⣠⠖⠋⡠⠔⠈⠀⠀⠀⢀⡴⢊⡡⢀⠈⠀⢾⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠰⠓⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣛⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠥⢒⠁⠀⠀⠀⠀⠀⠀⠙⠋⢱⡕⠁⠀⠀⠘⠂⡤⢀⡤⠀⠀⠀⠀⠀⡰⡜⠀⢀⣠⠔⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀ ⠀⠀⠰⠃⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠐⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿