⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠳⡀⠀⢀⣀⡀⠀⠀⣸⡇⠀⠀⠀⣸⡟⠁⣀⣀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠈⢳⣿⠛⣿⠀⢠⡿⠁⠀⠀⠀⡿⢀⣾⠟⢹⣧⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣼⡇⣰⡿⣠⡿⠁⠀⠀⠀⠀⣧⠸⣿⠀⢸⡿⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠸⣷⣿⣽⣿⣷⣶⣶⣦⣤⣄⣿⡄⠻⣧⣿⠃⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⡷⢿⣿⣭⣡⡾⠟⠛⣿⣆⣬⣭⣝⠳⡴⠟⠛⠿⢶⣾⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⣋⠥⠚⠋⠀⢀⣿⢻⠁⢀⡴⠋⠀⠉⠉⢻⣦⣙⡀⠀⠀⠀⠈⠻⣦⡉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⣿⠟⠉⠰⠀⠀⢠⡿⠁⠈⣇⡟⠀⠀⠀⠀⠀⠀⢻⣟⠛⢷⣦⡀⠀⠀⠈⠻⣆⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣥⡾⠋⠀⠀⠀⠐⠂⢠⣿⠁⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⠀⠈⠻⣦⠀⠀⠀⠙⣷⢀⣀⡀⠙⣷⡀⢀⡀⣠⣴⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢟⣛⣿⣾⠟⠀⠀⠠⠤⡀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡀⠹⣧⠀⢠⣶⣿⣿⠟⢿⣆⠈⢿⡟⢿⣏⣤⣾⣟⣙⠻⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠋⣹⣿⢻⣦⠀⠀⠀⠀⠹⡀⠏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⡀⠀⠀⠀⣇⠙⢿⣆⢻⡆⢿⣿⠀⠹⣧⠘⣿⡶⣾⣿⣄⠉⠉⠙⣿⠉⢻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠁⣀⡜⣵⡇⣼⠷⣦⣦⣤⠶⣶⣠⢊⣻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡈⡆⠀⢸⣿⡀⠀⢻⣾⣇⠈⢿⣧⡀⣿⡆⣿⣧⣄⡉⠻⣷⡀⠀⣿⢃⣀⠈⠙⣷⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣾⡏⣼⣿⠀⣠⡶⠶⠾⣿⣠⣿⠃⠉⣼⡇⠀⠀⠷⡀⠀⠀⠀⢸⡇⠀⢸⡇⢀⣿⢻⣧⠀⠀⢿⣿⠀⠀⣿⡗⠈⠁⢉⣻⣷⣈⣳⣼⣇⠠⢿⣜⠻⢿⣦⣻⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⢹⡄⣿⠛⣿⡏⠀⠀⠀⠈⣿⡟⠀⣼⡿⣷⠀⠀⡅⢳⡀⠀⠀⢸⣷⠀⢸⢃⣾⠏⠀⠻⣇⠀⠘⣿⡄⠀⢸⡇⠸⠇⠼⠁⣿⣿⣛⠛⣿⠀⢀⣿⡠⢤⣙⣿⣆⠀⠀ ⠀⠀⠀⣸⡇⣯⢨⣷⡈⢠⠇⢳⠀⠀⠀⢰⡿⢀⣼⣟⣠⣿⣆⠀⡇⢤⣷⡄⠀⠀⢿⡄⣸⣿⣧⣤⣤⣀⡙⣧⡀⣿⡇⠀⠸⣿⣦⣀⣀⣠⣿⣿⠟⢀⡿⣴⡟⠛⣿⣄⠈⠛⣿⡀⠀ ⠀⠀⠀⡟⣶⣷⡿⠁⣷⢸⢀⣈⢧⠀⠀⢸⣧⣾⣏⣭⣤⣤⣿⣆⢧⢸⣿⣟⠦⡀⠘⣿⡟⣩⣤⣤⣤⣌⣑⠦⠙⢺⡇⠀⠀⠈⠛⢿⡭⠟⠋⠁⢰⣿⠁⠈⣷⠀⠈⢿⣦⢀⣹⣷⠀ ⠀⠀⠀⢷⣿⡟⠠⠀⣿⣟⢸⣿⠈⢧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⡘⣿⠙⢷⣌⠓⠾⣿⣿⣿⣿⣭⣽⣿⣿⣦⣼⣧⡤⠀⠀⠀⢿⠃⠀⣰⡇⠈⣿⣤⣼⠏⠀⢀⡟⢻⣿⣧⣿⠀ ⠀⠀⠀⠀⣿⢳⢠⠀⢻⣇⢸⣿⣧⠀⠱⣌⣿⠏⠁⠀⣏⢉⣉⣿⠏⠻⢿⣷⡄⠙⠻⢾⣯⣿⣿⡟⠉⣿⠛⣿⣿⣿⠋⠀⠀⠀⠀⢸⢀⣴⣿⠀⢀⣿⠋⠁⢀⣠⡾⠃⠀⢻⡿⠃⠀ ⠀⠀⠀⣼⢋⡈⢯⠀⠈⢿⣌⣿⡘⢷⣄⡈⠘⣧⡀⠀⢻⣇⣸⣟⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⢸⣾⠛⠳⣤⣟⣽⡿⠀⣠⠄⠀⠀⢸⣿⣿⡏⢀⣾⣏⠀⢀⠴⠋⠀⢀⠴⡸⣧⠀⠀ ⠀⠀⢰⡇⣾⣧⠈⠳⣄⠈⢻⣿⣷⣾⠋⢻⡿⠾⠿⠓⣶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣿⣶⣿⣿⢟⣿⠃⣜⡏⠀⠀⡄⢸⣿⠟⢠⣾⠏⢻⣷⡑⣢⠤⠖⠁⢸⣳⠹⣧⠀ ⠀⠀⠈⢷⣝⡿⠧⠀⠀⠉⣿⠁⢸⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠋⢀⣾⠏⣰⠟⠀⠀⢀⣿⢸⢉⣴⠟⠁⠀⠀⢻⣇⠀⠱⡀⢠⣿⣿⠇⣿⠀ ⠀⠀⠀⠀⠙⢿⡗⢶⣦⡀⢿⡄⣾⡇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣾⠿⠛⠁⠀⠀⠀⣸⣿⢸⡿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠓⣛⣛⣥⡾⠋⠀ ⠀⠀⠀⠀⠀⠈⣿⠈⣿⠻⣾⣿⣿⡇⠀⣷⠙⣷⣄⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⢙⣿⠷⣶⣾⠇⠀⠀⢠⠿⣡⣿⠃⠀⠀⠀⠀⣘⣰⡟⣠⣾⡿⢛⣿⠏⠀⠀⠀ ⠀⠀⣀⡀⠀⣠⣿⣲⣿⡀⢨⣿⣿⣿⡀⣿⣧⡈⠛⢷⣄⡀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣣⡾⠟⠁⠀⠀⢀⣴⣾⢹⡟⠀⠀⠀⣠⣾⣿⣿⡿⢋⣿⠁⣾⠇⠀⠀⠀⠀ ⣰⡿⠿⢿⣿⠿⠟⠋⠀⣷⠉⠉⠹⣿⣷⣹⣿⣿⣦⣀⡙⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠿⠟⠋⠀⠀⠀⣀⣴⠟⢛⣿⣾⡇⠀⣴⡿⠋⢩⡿⠋⠀⣮⢿⣧⣿⣆⣀⠀⣀⣀ ⠙⠁⠀⢀⣿⠆⠀⢀⡴⠃⠀⠀⢠⡿⠈⠙⢛⡿⡞⠯⣿⣿⠿⢟⡿⢶⣤⣴⣶⣶⣿⠿⠋⠙⠻⢷⣶⣶⣶⣶⠾⣻⠟⠀⢈⢀⢹⣧⠔⠁⠀⢠⣿⠁⠀⠀⢿⡀⠙⠛⠿⢿⣿⠿⠿ ⠀⠀⠀⣾⠃⣠⣖⣋⣀⣀⣀⣴⠟⠁⠀⣠⣾⡽⠁⠀⡟⢻⡆⣸⠇⠀⣿⠿⠛⠋⠁⠀⠀⢀⡴⢸⡇⠀⠀⠀⣾⠏⠀⣴⣿⢸⢀⢿⡀⠀⠀⢸⣿⠀⠀⠀⠘⢧⡀⠀⠀⣾⡃⠀⠀ ⠀⠀⢸⣧⣾⠟⢹⡟⠻⠿⣿⣷⣤⠶⣾⡿⠊⠀⠀⣰⠇⣼⡿⠏⠀⠀⣿⠀⠀⠀⠀⣀⠔⠋⠀⢸⣧⠀⠀⠀⣿⡄⣼⠟⣿⠈⠣⣊⣻⣄⠀⠀⠻⣷⣄⠀⠀⣀⣙⢦⣀⠘⣷⡀⠀ ⠀⠀⢸⠟⠁⠀⢸⡷⠒⢂⣿⠋⠉⣩⣀⠀⠀⣤⡾⠋⠀⠁⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣀⠀⠈⠻⣿⣆⢻⣄⠀⠈⢻⣿⣷⡦⣤⣬⣿⣿⡿⠿⢿⡟⢿⣧⣸⣧⠀ ⠀⠀⣼⣀⣀⣤⣾⠇⢀⣾⣃⣠⣾⠟⢿⣷⣤⡸⣷⣠⣤⣶⣦⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠿⣶⣦⣤⣌⣿⣦⣄⣠⣧⣽⣿⣧⣬⣻⣧⣄⠀⢸⡇⠀⠙⢿⣿⠀ ⠀⠀⢻⣿⣭⣿⣋⣴⠟⠛⢛⣽⡿⢿⣿⠿⠛⠛⣿⣿⠁⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡏⠉⠉⠉⣉⠭⠗⣀⣴⣾⠿⢻⣿⡄⠙⢿⣇⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⠉⠉⠉⠁⢀⣴⡿⡋⠀⠀⢹⣿⣦⣼⡿⢹⡆⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢸⣷⠐⢒⣉⣤⣶⠿⣿⣯⠔⠁⠀⠹⣿⣆⡈⢿⣿⢶⣶⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡈⠑⣶⡿⠋⠉⠙⡷⢾⣧⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣠⣼⣿⡟⠛⠉⠁⣀⠴⠛⡿⡄⢀⣤⣶⡿⣿⡟⠾⠿⠿⠚⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⢿⣾⣞⠉⠓⠤⣀⢇⢈⣿⡆⠀⠀⢿⣿⣤⣤⡄⠀⠀⠀⣀⣤⣤⣤⣴⠶⠿⠛⠋⠉⠀⠹⣧⡤⠔⠋⠀⢀⣠⣿⣿⠿⠛⠉⠀⣹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠛⢿⣦⣄⡈⠉⣼⡜⢿⡄⠀⠈⣿⡄⣿⡏⠉⠉⠉⠉⠉⠁⠹⣹⠀⠀⣀⣀⠤⠔⠊⢛⣆⣠⣴⣾⠿⠛⠉⠳⠤⠠⠤⠊⢸⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣀⠀⠀⠈⠙⠻⢷⣷⣧⣘⣷⡀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⠀⢀⣀⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⠊⠀⢑⣤⡀⠀⠀⠀⠀⡍⠙⠻⣷⡄⠀⠘⣿⣧⣀⣀⣀⣀⣀⣀⣠⣿⣷⡶⠾⣟⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡿⠐⡜⣶⣄⠼⣧⠃⠀⠀⠐⠼⠀⠀⠀⠘⣷⣄⣠⣌⢿⡍⡟⣟⠛⠋⠉⠉⠁⠀⠀⢰⡃⠀⢹⠀⠀⠀⠀⠀⠀⣀⣤⠲⡄⠀⠀⢰⠀⢸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠃⠭⡅⠈⢧⠀⢘⠀⠀⠀⠀⠀⠐⠉⠉⠀⠘⠿⡇⢉⣿⠻⠍⠁⡳⡀⠀⢀⣠⣀⠀⠀⢳⣤⣿⠀⠀⠀⣀⣴⠾⠋⢡⡾⠃⠀⠀⠀⠣⢸⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⠛⢛⠂⠇⠀⣿⡗⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⠿⠻⠶⣶⣿⣷⣾⡟⠋⠻⣷⠀⠘⡌⡟⠀⢀⣾⠟⠁⠀⠀⣾⠃⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠃⠀⠈⠀⠀⢸⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠘⢿⣿⣿⣿⣦⣴⡿⠀⢠⣷⠃⠀⡿⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠈⢻⣿⣿⡿⠿⡅⢠⣿⠃⠀⠀⣧⡀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠁⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⡀⠀⠙⢿⣄⣰⢀⣮⠇⠀⠀⠀⠙⠿⣿⠽⠋⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠃⡏⠙⢶⡄⠀⢧⣇⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣹⣷⡄⢀⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⠘⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡀⠃⠀⠈⢿⣄⠸⣼⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣫⣶⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⠟⠁⠀⠀⠀⠀⠈⢿⡆⠄⠀⠀⠀