⠒⠒⠦⣄⠀⠀⠀⠉⠻⣞⣧⢷⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⢦⡈⢳⡀⠀⠀⠀⠹⣿⣿⠀⠀⣀⡴⢻⡿⠁⣰⡟⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢳⣆⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⢲⡀⠹⡄⣹⣄⠀⠀⠀⣿⣿⣤⠞⢋⣰⢿⠃⣴⢻⠇⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣾⣤⢾⠿⣷⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠆⠀⠀⣹⢟⣿⠀⠀⣠⣿⣿⣤⣔⣿⠃⢸⣼⠃⣸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠙⠞⠉⠻⢼⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠿⣿⣶⣿⣿⡿⢛⣿⣿⣩⠞⠉⣿⠁⢀⣾⣷⢀⡏⠀⠀⠀⠀⣿⣀⣤⡤⠶⠒⠚⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠛⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡥⠞⠁⢸⠿⠏⠀⠊⣡⠟⠁⠀⡼⠙⣇⡾⢁⡟⢸⡇⣀⣤⠶⠚⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠋⢹⡇⠒⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣶⡆⠀⠀⣸⠁⢀⣿⠁⣼⣡⢾⡟⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠘⣇⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀ ⠶⢶⣶⠚⢛⣿⣿⣿⠇⠀⠰⣇⣠⣾⣧⡶⠿⠥⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⢀⡴⡆⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⣾⣿⣿⣿⣾⣿⣿⣿⠀⢠⡾⠛⠀⠙⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⢀⣴⠟⢀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢠⡟⠀⢀⣠⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⡞⠁⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⢸⠁⣠⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀ ⣿⣿⣿⣿⣿⣿⣿⡇⣾⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄ ⣿⣿⣿⡿⠛⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⢛⣁⣠⡴⠒⣀⡀⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠰⡋⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠁⢀⡷⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⣀⣀⠴⠋⠀⣿⡿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣾⠃⠀⠀⣸⠇⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠁⠀⠀ ⠉⠀⠀⠀⠀⠘⣿⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠸⣧⠀⠀⣠⡾⠃⠀⠀⣴⠏⠀⠀⠀⠀⢾⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⡿⠉⠙⢻⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡀⠀⠻⠶⠞⠋⠀⠀⣠⡾⠉⠀⠀⠀⠐⣦⣞⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠉⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡞⣿⠀⠀⠀⠀⠀⠐⣻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⣧⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢸⡇⠸⣧⡀⠀⣶⣖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣸⡇⠀⠈⠻⠷⣶⣶⢦⣤⣀⠀⣄⠀⠀⠈⠉⠙⣿⢋⣹⣿⣫⢽⣸⣷⠺⣧⡀⠈⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⣀⠀⠀⠘⣷⡀⠁⣹⣿⠛⠀⠀⠀⠀⢠⣿⠉⢘⡟⠈⢁⡼⠃⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠌⠿⠾⣟⣥⣤⣄⡀⠀⠀⢸⡏⢀⣞⣤⣾⡿⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣀⣴⢶⢿⣍⣀⡀⠈⠙⢶⣶⠚⠛⠉⠉⣾⠋⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢰⠟⠉⠀⠀⠀⠀⠈⠙⢶⠀⠀⠉⠳⣦⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⠻⣦⢹⣆⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⠞⠀⠼⠓⢚⣆⣀⠀⠀⠀⠈⢷⣻⣆⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⣤⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⣀⣰⡟⠀⠀⠀⠀⠈⠉⠉⢳⣀⡀⠀⠈⢿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⢯⠛⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀ ⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠛⠉⢻⣆⠀⠘⡏⢿⣿⣆⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⡇⠀⠀⠀⠈⠻⢦⡀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠘⢷⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⣼⠇⠈⠃⣿⠷⣤⡀⠀⠀⠀⠈⣇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠻⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠙⢦⣄⣀⣸⡇⠀⠀⠀⠀⠈⣷⠏⠀⠀⠀⣿⠀⠀⠙⠳⣄⠀⠀⢹⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡿⣍⡈⠛⠶⣤⣤⣤⠞⠃⠀⠀⠀⣴⡏⠀⠀⠀⠀⠈⠳⣄⢸⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⠤⠶⠛⠁⠸⣿⡓⠒⠒⠂⣀⣀⢀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⢉⣁⣤⣴⣶⣾⣾⣾⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠂⠈⠉⠉⠉⠉⠉⠁⠒⠒⠢⠤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣽⣳⣦⣄ ⢀⣀⣀⣀⣀⣀⡔⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⣭⣭⡥⠶⢶⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀ ⠎⣾⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⢀⣾⣯⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠿⠿⣿⣿⣯⣭⣑⢦⣀⠀ ⠸⣿⡇⠀⡼⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣈⠙⠿⣿⠟⠚⠓ ⠀⢻⣿⣰⣏⣿⣿⣿⣿⣿⡿⣫⣵⣶⣬⣙⢿⣿⣿⣿⣷⣆⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣦⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣾⡟⠋⠁⠉⠹⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠧⣀⠀⠀⠀⠀ ⠀⠀⢈⡿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠳⡀⠀⠀ ⠀⠀⣮⡿⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡴⢂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢱⡀⠀ ⠀⠀⠘⢷⠀⢻⢿⣿⢿⠁⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀ ⠀⠀⠀⠘⡄⠈⡾⢟⡎⠀⠀⠀⠀⠀⢸⡏⢀⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⢏⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡄⢸⣻⠀⠀⠀⢀⡠⠔⠋⡭⢍⢹⡿⠾⠟⠛⠋⢉⠙⠓⢦⣄⠀⠀⠀⠀⠀⠀⣀⠀⣒⠦⢄⠀⠙⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠷⠿⢿⣟⣀⣈⣠⣀⣒⣙⡲⠬⠞⠁⠀⠀⠀⣰⠶⢲⡄⠀⢹⣒⣒⠦⣄⡀⠥⠒⠉⢀⠔⢪⣵⣀⣸⣶⠶⠍⢑⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣉⠉⠉⠉⢉⠭⠶⡒⠒⠒⠒⢺⠁⠙⠛⠧⠶⠼⠟⠛⢃⡸⠀⠀⠀⠀⠘⡲⠂⠤⡀⠀⠀⠠⠊⢉⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣀⣀⡀⠀⢈⣀⡠⠆⠀⠀⣠⣔⡙⠓⠦⠀⠀⠀⠀⠰⠥⢈⠆⠀⠀⠀⠀⠑⡦⠤⠤⠤⠄⠰⠾⣅⠀⠀ ⠀⠀⠀⣀⣤⣤⣾⣥⣀⠀⠀⣈⡻⢿⣿⣻⣧⠀⡴⡝⣝⣿⣷⣶⠄⠤⠤⠤⠐⠲⢾⣿⣣⠀⠀⠀⢀⣎⣧⣶⡿⣿⢿⣶⣦⣧⢱⠀ ⠀⣔⣫⣭⡒⠫⢗⢿⣻⣷⡥⢒⠒⠆⣿⣷⠿⣇⠘⠷⣜⠿⠇⢃⣀⣤⣤⣤⣀⠀⢠⠃⣸⡇⠀⠀⠸⣸⣿⣳⡿⠿⣻⠾⣽⣿⢾⠀ ⠀⠙⠻⠵⢟⣧⣄⣑⠯⠿⠧⠈⢭⣧⠗⠬⠍⠊⠀⠀⠀⠉⣶⣿⡟⢯⢟⣷⡿⣷⣦⠀⡇⠁⠀⠀⠀⢣⠟⠕⣊⢥⣤⣬⣑⠒⡻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⢖⡩⣭⣉⠐⠿⣻⠿⣄⣼⠃⠀⠀⠀⠀⠁⠚⠛⠋⠈⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠭⠭⠷⠦⠤⠭⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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