⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠠⣖⡤⣻⢻⣽⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠹⣕⡾⠔⠛⠂⠀⠀⢍⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢀⢀⡴⢋⣀⠤⣤⠤⠤⣀⡤⠓⠙⠓⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⡵⣯⣶⣿⣿⣿⣷⣶⣦⡏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⣵⣿⣿⠟⠉⠀⠀⣘⡻⠉⠀⢱⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡞⠉⠉⠙⡿⣖⣉⣁⣴⣿⣿⣿⣿⢿⠖⠶⣂⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⢋⢱⠀⣠⣊⣰⣿⡿⢻⠛⠿⡝⠀⠀⣯⣄⣴⠷⠥⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣷⣀⢽⣹⣩⣟⡻⡻⢺⠋⠉⢹⣶⣶⣿⣿⣿⣿⣄⢇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣸⣿⣿⡀⣸⠏⠀⠈⢿⣧⣴⣾⣿⣿⣿⡿⠿⠿⠿⠿⣧⡘⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⢉⠁⠀⠀⢀⣀⣿⣿⡟⠀⠀⠀⠘⣿⣿⡿⠭⠤⠤⠒⠒⠒⠆⠉⠉⠃⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢤⡀⠀⠉⠉⠁⠀⠀⠁⠙⡄⠀⠀⠀⠀⠈⠫⢄⣀⣀⣀⠀⠤⠤⠤⠐⠒⠒⢀⡭⠁⠙⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⡤⠴⠒⠒⠒⠢⠽⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠫⡉⠉⠑⢦⡀⠉⠀⠒⠲⢖⡤⠄⠒⢊⡼⣻⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⣸⠾⠿⣦⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈⠹⣿⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡇⠀⠀⢈⢿⠉⠁⠀⠐⠒⠒⠒⠒⠒⠒⠉⠙⣝⢎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠀⠀⠀⠀⠀⢀⡤⠊⠙⢯⣒⣲⠭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⣿⣧⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠙⠢⡈⠳⡀⣸⠀⠀⣀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣹⠋⠈⣷⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⣀⡀⠀⢀⡀⠘⣆⣵⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢀⡜⠀⠀⠉⠳⢦⡀⠀⠀ ⠀⢀⡧⠒⠉⠁⠀⠀⣀⣀⡀⠑⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠙⣦⠀ ⣰⠋⠀⡠⠔⠂⠀⠀⠀⠀⠀⠙⠺⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠐⡄⠀⠀⢰⢀⡔⠀⢸⡆ ⢹⢠⠊⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡏⠒⡇⠀⠀⢸⠀⠈⠀⢨⡇ ⠀⣿⢸⣤⣿⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠘⡄⢤⠊⡒⠀⠐⣾⠀ ⠀⡟⣿⠝⠇⠀⢀⠀⠀⠀⠀⢠⠒⢦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⢿⡘⠀⠉⢀⣰⠟⠁⠀ ⠀⣿⠛⠀⣀⠀⠈⠳⣄⠀⠀⠀⠀⠘⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠛⠒⠋⠀⠀⠀⠀ ⠀⢹⠰⣄⠈⠳⣄⠀⠈⠳⡤⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢣⡘⢷⣄⠘⠗⣆⣤⠵⠞⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠻⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⠀⠰⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠲⠥⠟⠋⠉⠀⠀⠀⠀⢿⣿⣿⣿⢿⡿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣀⠀⢀⡀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠉⠉⠙⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀