⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢣⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢤⣀⣀⣀⣀⠸⡄⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⡄⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⢄⣀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠳⡀⠀⢀⡴⢚⡭⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣧⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠑⢄⠀⠀⠀⠀⠀⠀⢸⠋⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠈⠑⢦⣀⣸⠀⠀⠀⠀⢠⠞⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢒⣋⣩⡤⠤⠴⢬⣧⡀⢀⣠⠔⠛⢯⢷⣄⡀⠈⡳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⡰⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠰⣄⠀⠀⠀⠀⠉⠻⡄⠐⠂⠀⠀⠘⣍⠻⣄⠙⢦⡑⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⣀⣀⡤⢄⣠⠀⠀⢰⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⣆⠀⢹⡄⠀⠀⠀⠀⠘⣆⠈⢧⠀⠙⣶⣽⣦⣄ ⢆⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠯⠤⠖⠒⠒⢉⡟⢉⡥⠔⣋⠁⣾⠀⠀⠈⡇⢲⡀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠹⣎⢷⡀⠀⠘⣇⠸⣷⡀⠀⠀⠀⠀⠸⡄⠈⢧⠀⠈⣧⠈⠝ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⠞⠁⠀⢀⣿⠀⣿⠀⠀⠀⢹⣄⢳⡄⠶⠒⠛⢿⣗⠒⠦⢤⣀⠀⠈⢳⣷⡀⠀⠸⡄⢻⣿⡀⠀⠀⠀⢰⠃⠀⠈⣷⡀⠈⡇⠀ ⠀⠀⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣀⢀⡶⠋⢠⢾⠀⠀⣠⣿⢽⡆⢹⠀⠀⠀⢸⠛⢦⡙⣦⠀⠀⠈⢯⠳⣄⠀⠈⠁⠀⠀⠙⣷⠀⠀⢷⠸⣿⠉⠻⣶⢶⡋⠀⠀⠀⢸⡝⣄⢸⠀ ⠀⠀⠈⡂⠀⠀⣰⠃⢀⠏⢠⠖⠋⡇⢸⠃⠀⢸⢸⡴⠋⢹⡝⠀⢹⡘⡇⠀⠀⢸⡄⠀⠙⢮⣷⣄⠀⠘⣇⠈⠳⣄⡀⠀⠀⠀⠘⣧⠀⢸⡆⣿⠀⠀⠈⢧⡙⣦⠀⠀⠀⢇⠘⣎⠃ ⢀⠀⣰⢣⢀⡼⢁⡴⡟⢠⠏⠀⠀⣰⡏⠀⠀⣽⣿⡁⠀⣿⡇⠀⠀⠳⣷⠀⠀⠈⡇⠀⠀⠀⠈⢛⣷⣤⣼⣦⣀⡀⠙⠶⣄⡀⠀⠘⣧⠀⣟⣿⠀⠀⠀⠀⢳⡙⢧⠀⠀⢸⡀⠘⠃ ⡎⢠⢇⣾⡯⠞⠉⢠⢇⡎⠀⠀⣰⢯⠀⠀⠀⣿⣿⣇⠀⣿⡇⠀⠀⠀⠹⡇⠀⠀⡇⠀⠀⠀⠐⠿⠟⣽⣿⣿⡿⠻⣷⣦⡀⠙⠶⣄⣹⣧⢿⣿⣤⡀⠀⠀⠀⣿⣎⢷⠀⠘⡇⠀⠀ ⡅⡼⠋⣿⠀⠀⠀⣸⣸⠁⠀⢰⠇⢸⠀⠀⠀⣿⠈⢻⣴⣧⣧⣶⣶⣦⠀⢹⣦⡀⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⠈⢿⣷⡀⠀⡏⠻⣿⣳⢿⣽⣷⡄⠀⠀⢹⡿⣄⠀⠀⡇⠀⠀ ⡇⠀⠀⡽⣆⠀⢰⡏⠏⠀⢀⣿⠀⠘⡇⠀⢠⡟⠀⣰⣿⣿⣿⣿⠟⠃⠀⠀⠁⠙⠺⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⡆⠈⢿⡇⢸⡇⠀⣿⠁⢸⢿⣧⠉⠀⠀⠀⢿⣿⣆⠀⡇⠀⠀ ⡇⢀⣼⠋⢸⠟⣿⡇⠀⠀⣼⡟⠀⣸⣧⠀⢸⠁⣰⡟⠀⣿⣿⣿⣶⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣨⣵⣼⠃⠀⠈⠀⢸⠇⠀⣿⢣⢾⡛⣏⢳⡀⠀⠀⢸⡹⡟⣇⡇⠀⠀ ⡄⣼⣸⠀⠟⢰⣿⡇⢀⡼⠋⡇⢀⣿⣿⡄⣿⠀⣿⠁⠀⢿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⠀⢸⣷⠏⠀⠻⣿⡀⠙⢦⡀⠈⡇⢻⠸⡇⠀⠀ ⡷⣿⣿⠀⢀⡟⣿⡇⡾⠛⢠⡇⢸⢹⡇⢿⣿⡄⢻⡆⠀⠈⠏⣰⣶⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠏⠳⠒⠒⢾⡿⣄⠀⠙⢾⣿⠘⠆⠁⠀⠀ ⠀⠈⢹⠀⣼⠀⢿⣿⠁⠀⣿⣷⡟⠸⣷⡈⢿⣿⡄⠈⠂⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡅⣸⣴⣀⣀⡀⠀⢳⠈⠙⠂⠀⠈⠃⠀⠀⠀⠀ ⠀⠀⠘⣶⢿⠀⢸⡟⠀⣰⣿⠻⠃⠀⠘⢧⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⢀⣤⠶⠚⠋⠹⣇⣯⡅⠀⠈⡇⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠘⡄⠈⣷⢸⣿⠃⠀⠀⠀⡤⠼⣆⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠈⠁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣿⠃⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⢾⠀⣿⠏⠁⠀⠀⣠⠞⠃⠀⣸⣆⢻⡟⠛⠛⠒⠒⠒⠶⠦⢤⣄⣀⠀⠀⠀⣀⣀⣀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠟⢀⣠⣴⣾⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⡇⠀⢰⡟⠁⠾⣯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠋⠁⠀⠀⠈⣿⣴⠞⠀⠀⠁⢀⡠⠀⠀⠀⠈⠉⠉⠻⣇⠀⠀⢙⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣰⠋⠀⠸⡇⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⣀⠒⠶⢾⣇⠀⠀⠀⠀⢸⣇⡀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠞⠛⠓⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢧⠀⠀⠀⠹⡄⠀⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⣦⠄⠀⣠⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣆⠀⠀⠀⠙⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠖⠛⠛⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⠤⢤⡀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠸⣄⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣇⠀⠀⠀⠀⣻⡏⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠹⡆⠀⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⡜⠉⢿⣺⣩⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢿⡇⠙⢀⠀⠀⢰⡏⢻⣆⠀⠘⢿⣶⣦⣤⣄⣀⡀⢀⣰⠇⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⢸⡇⠀⡎⠀⠙⠶⣷⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠁⢸⠃⠀⠀⠀⠀⣾⠆⠀⢻⡆⠀⠀⠈⠉⢛⣿⣿⠛⠛⠉⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡼⠂⢰⠃⠀⠀⠀⢸⡄⠀⠀⢀⣤⣶⢿⣿⣿⣁⠀⠀⣾⠀⠀⠀⠀⢠⡞⠀⠀⠀⠹⣆⠀⣴⡋⠉⠋⠉⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢠⠏⠀⠈⠳⡄⠀⠀⠀⠳⠦⠟⠋⠀⠈⠉⠉⠀⠙⠲⢾⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡞⠉⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⡾⠃⠀⠀⠀⠉⠷⣄⣠⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⢀⡞⠸⠁⠀⠀⠀⠘⡷⠂⠀⠀⠀⢀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀