⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠉⠉⠛⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠋⠉⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⢶⣦⣄⣀⠀⠀⠀⢀⣴⠟⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣦⣴⡟⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⡷⠦⣄⡀⠀⠀⠀⠀⢻⣷⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠻⢦⣰⠏⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠹⣄⠈⠙⠂⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠙⣦⡀⡴⠋⠀⣰⠏⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⣠⠞⠁⠀⠀⠀⠀⢴⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⣤⣴⠾⠛⠁⢀⣷⡀⠀⠀⠀⠀⠀⠀⠙⣶⡟⠁⠀⢠⠖⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⢠⡿⠙⡛⠒⠲⣶⣶⡶⠀ ⠀⠀⠉⠛⠻⢷⣶⠟⠈⢳⡀⠀⠀⠀⠀⢀⣰⠟⠀⠀⢰⠏⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⠀⠀⢠⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣔⠃⠀⠀⠈⣧⠀⠀⠀⠀⠀⣾⠁⠀⠻⣶⡟⠛⠉⠀⠀ ⠀⠀⠀⠀⢠⡿⠃⠰⣄⠀⢳⡄⠀⢀⡴⢻⡏⠀⠀⢠⠏⠀⠀⠀⢀⡏⠀⣀⠀⠀⠀⣴⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣷⡀⠀⠁⠀⢸⣆⠀⠀⠀⢸⡀⠀⠀⠀⠸⡗⠂⠉⢳⡀⣿⠀⠀⢀⠹⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠅⠀⠙⠮⡴⠁⡇⢠⠟⠁⣿⠀⠀⠀⡟⠀⠀⠀⠀⢸⠃⠀⠛⠷⣤⡾⢻⠃⠀⣼⢻⠀⠀⠀⠀⠀⢰⢿⡇⠀⣸⠋⣷⠀⣀⡤⠞⣿⣆⠀⠀⠘⡇⠀⢀⠀⠀⢿⡀⠀⢰⢳⡇⢀⡴⠃⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⣼⠏⠀⣴⠀⢰⠃⡼⣧⠘⠀⢸⠇⠀⠀⢸⠁⠀⡀⠀⠀⣼⠀⠀⠀⠀⡼⢙⡿⣄⣸⠃⢸⡇⠀⠀⠀⠀⡾⢸⠇⣰⣃⣤⠼⣿⠁⠀⠀⢹⢻⡄⠀⠀⢿⢀⡿⠀⠀⠸⣇⠀⢯⡿⣆⢣⠀⠀⠀⠈⣿⡀⠀⠀ ⠀⢀⣼⢏⣠⣾⠃⢀⣇⡼⢁⡸⣆⠀⡿⠀⠀⠀⠏⠀⠠⡿⡀⣼⣿⠀⠀⠀⡼⠁⣾⣡⣼⠋⠓⢸⡇⠀⠀⠀⣸⠃⢸⣰⠏⠡⠤⣄⣹⡆⠀⠀⢸⡇⢿⡀⠀⢸⣄⡇⠀⠀⠀⢻⣴⠟⢄⠘⢿⡇⠀⠀⠠⣾⣷⡀⠀ ⢠⣾⡿⠟⣻⡇⠀⣠⡞⢡⠎⠀⠘⢿⠇⢀⡄⠀⠀⠀⠀⡇⣱⠇⣿⠀⠀⢠⣣⣼⣷⣾⠷⠄⠀⠘⡇⠀⠀⣰⠇⠀⣼⠏⠀⢰⣿⣶⣦⣷⡀⠀⠘⡇⠈⣧⠀⠈⣿⠇⠀⠀⠀⠸⡇⠀⠈⢳⡈⢻⡄⠀⠀⢿⣿⣷⣄ ⠈⠁⠀⠀⣿⠀⢴⣏⣀⣃⣀⠀⠀⢸⠆⢸⠇⠀⠀⠀⠀⣧⠏⠀⣿⠀⣴⣿⢟⣽⡞⠻⡆⠀⠀⠀⡇⠀⣰⠏⠀⠀⠀⠀⠀⠀⣴⣿⡿⡝⢿⣶⡀⡇⠀⠸⣆⠀⣿⠀⠀⠀⠀⠀⣷⠀⠀⠀⠹⡄⢙⣦⡀⢸⡏⠙⠛ ⠀⠀⠀⠀⣿⠀⢠⠆⠀⠉⠉⠉⠛⢿⠀⣼⠀⠀⠀⠀⠀⢿⠀⠀⢸⣾⡟⠁⠞⠁⣿⡀⢹⠀⠀⠀⡇⣰⠏⠀⠀⠀⠀⠀⠀⠰⠏⢈⡇⠹⣆⠹⣿⡇⠀⠀⢻⣄⡇⠀⠀⠀⢀⡼⢻⣤⣤⠶⠒⠋⢻⠁⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⣿⣆⠈⠀⠀⠀⠀⠀⠀⢸⢸⢿⡟⣄⣳⠀⠀⢸⡆⠀⣸⡟⠀⢀⣆⣠⠏⠃⢸⠀⠀⠀⡷⠃⠀⠀⠀⠀⠀⠀⠀⢸⣦⣼⠃⠀⢹⠀⢹⣷⠀⠀⠈⣿⠃⠀⠀⣠⠞⣤⠈⡏⠀⠀⠀⠀⠸⢠⠀⢸⡟⠀⠀ ⠀⠀⠀⠀⣿⠸⣴⡀⠀⠀⠀⠀⠀⢸⡟⢸⡇⠈⣹⡄⠀⠈⣧⠀⣿⠀⠀⢸⠟⣿⣤⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⣿⣠⣿⢶⡇⠀⣿⠀⠀⢀⡟⠀⣠⣾⠁⢠⡿⣆⣷⠀⠀⠀⠀⠀⣿⠀⣾⠇⠀⠀ ⠀⠀⠀⠀⢹⡇⠀⣿⡄⠀⠀⠀⠀⢸⠁⠀⣿⠀⣟⣷⠑⢦⣿⡀⠀⢄⠀⢸⡀⠈⠉⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠛⠁⣠⠇⠀⠀⠀⠀⣸⠇⠊⣽⢻⡇⣼⠃⠘⢿⡆⠀⠀⠀⣸⣿⣼⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡄⣿⣷⠀⠀⠀⠀⠘⠀⠀⢸⡆⣿⢸⣧⠀⢸⡇⠀⠈⠳⢄⣛⣶⡶⠛⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠛⢶⣶⣾⠋⠀⠀⠀⠀⠀⡿⠀⣼⣿⣼⢠⡟⠀⠀⠈⠛⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⡿⣿⡈⢳⣿⣆⠘⣇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠈⠉⠳⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠇⣼⣷⠛⢁⡟⠀⠀⠀⠀⠀⢀⣴⠟⠙⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⣬⣿⡟⣷⠀⠀⢀⣠⣾⡟⠀⠘⣷⣾⠛⣿⣆⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣾⠿⣿⠀⣾⣇⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⣤⣾⠿⠋⠀⢹⠀⠀⠸⣿⠀⠈⢻⣾⣿⠙⠻⢿⣶⣦⣤⣄⣀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣀⣠⣤⣴⣶⡿⠉⢠⣾⠋⠀⣿⣿⡟⢿⣧⡀⢠⡿⠋⠉⠉⠉⠁⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⠇⠀⠀⠀⡀⢻⠋⠁⠀⠀⠀⣸⠀⠀⠀⠉⠀⠀⠀⠙⢿⣤⣶⠟⠉⢷⣮⠙⠻⢿⣿⡿⢷⣶⣤⣤⡤⠴⣶⡾⢿⣿⡟⠛⠉⣹⠟⠻⡇⣴⡿⠃⠀⠀⣿⠏⠀⠈⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠑⠀⠒⠂⠀⠛⠁⠈⣉⣩⠭⠥⣄⠀⠀⠀⠀⠀⣴⣴⡿⠋⠀⠀⣀⣀⠙⣆⢠⣿⣿⢥⣀⣭⣿⡏⢻⣿⣍⣠⣤⣻⣿⣧⢞⣁⡀⠠⠿⠻⣧⣀⡀⠀⠀⠀⠀⠀⣈⣉⣙⡒⠒⠒⠀⠀⠀⠀⠀⠐⠃⠀⠀ ⠀⠀⠀⠀⣀⣀⡀⠐⠒⠒⠚⠉⠁⠀⠀⠀⠸⡄⠀⠀⠀⣼⡏⠈⢷⡀⣰⡿⠷⣌⣷⣸⡏⠉⣡⣤⣭⣀⣬⣷⣿⣥⣉⣥⡄⠛⢹⣿⣭⠵⢿⣦⡾⡇⣽⠋⣿⡆⠀⠀⠀⣸⠁⠀⠐⠫⢽⣒⡦⠤⠤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠷⠀⠀⢸⣟⠛⠀⣹⣿⠋⣠⠞⠉⢉⣿⣶⠛⢋⡿⢶⠁⠀⣇⣸⠀⢸⡴⡏⣻⠿⡏⠈⢳⡄⢹⡲⣿⣇⠐⠿⣷⡀⠀⠀⣇⣠⢄⣀⠀⠀⠀⠀⠀⠉⠒⠈⠉⣿⠀⠀ ⠀⠀⠀⠀⢳⠀⢀⠀⠀⠠⣐⡤⠔⠚⣉⠴⠓⢦⡀⠀⠘⠿⣶⣾⡁⢹⣞⠑⠲⣴⠏⠀⣿⢤⣈⡷⢾⠀⠀⣯⣹⠀⢸⢤⣿⢻⠀⣹⡤⠖⠙⣾⠇⠀⠈⣧⣶⡿⠁⠀⠀⡤⠭⣍⠛⠯⣗⡲⢤⣀⠀⠀⠀⢀⠇⠀⠀ ⠀⠀⠀⠀⠀⠳⣤⠤⠖⠋⠁⣀⣴⣾⠅⠀⠀⠀⢹⠀⠀⢠⣾⣿⡋⠀⠙⠳⣤⣀⡀⣋⡽⠀⣿⣧⣸⠀⠀⡇⢹⠀⢸⣀⣽⣌⣞⣁⣀⣤⣾⠇⠀⠰⣾⣿⡃⠀⠀⢠⠮⠔⠐⠺⣕⢦⣀⠈⠙⠺⢝⣂⣠⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⡿⠟⠉⠀⠀⣠⢞⡵⠋⠀⠀⣿⠃⠈⢿⡅⠀⠀⣙⠛⠛⠋⢱⠛⢻⡉⣽⠀⢠⡧⣼⠀⢸⢈⣻⡀⢀⡈⠉⠉⢡⣀⣀⡴⠏⢸⡿⣦⣄⡘⢦⡲⢄⠀⠀⠉⠻⢿⣢⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣏⠈⠁⠀⠀⠀⢀⣺⣷⡋⠀⢀⣴⡾⠟⣧⠀⠀⣙⡶⠚⢙⣦⣀⣠⡼⠶⠒⠿⣿⠀⢸⠷⢿⠀⢸⡼⠷⠿⢭⣳⣤⡴⠿⣟⡉⠀⣀⡜⠀⠀⠉⠻⣶⣜⠦⣴⠟⢿⡆⠀⠈⠓⠉⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⣦⠀⣰⣿⠏⠹⣿⣶⣿⡋⠀⠀⠈⠉⡟⠉⠀⠀⠀⠈⡛⠁⠀⠀⠀⠀⢸⣦⣼⣇⣼⣴⠏⠀⠀⠀⠀⠉⢁⡀⠀⠈⠉⠋⠹⡆⠀⠀⠀⣀⣨⠿⣿⡏⡀⣼⣧⣀⢴⣾⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡏⠀⠀⠻⣧⣌⣉⠛⠓⠒⠶⢷⡀⠀⢀⣠⠾⣿⡀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣸⡿⣦⡀⠀⢀⡴⠷⠒⠚⢋⣉⣤⣶⠿⠶⡇⠈⢉⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠶⠀⠘⠚⢿⣍⠉⠛⠓⠚⠛⢿⡟⠋⣿⠀⡟⢷⣄⢀⣠⠾⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⡾⠋⢷⣻⡙⠛⢋⡿⠶⠚⠋⣩⠟⠉⠀⢀⡰⠃⣤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⣀⣀⣀⠀⢻⠙⠦⢤⣀⠀⠀⠙⢿⡟⣦⢷⣤⡽⠇⠀⠀⢀⣤⠴⠒⠒⠦⣄⣈⠉⠙⣏⣤⠴⢺⠟⣷⠞⠉⠀⢀⣤⣺⠵⢢⠴⣞⣽⣧⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⢠⡿⠁⠀⠀⠙⣷⡄⠀⢀⣀⣴⣿⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢀⠀⣿⡄⣀⣀⣸⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⡘⠻⢦⡀⠀⣿⠀⠀⠹⣇⠀⠀⠀⠀ ⠀⠀⣾⠇⠀⠀⠀⠀⢈⣿⠀⡈⢉⣽⠃⠀⠀⠀⠀⣿⠀⠀⢀⣤⡾⠋⠉⣹⠛⠁⠀⠀⢰⡟⢰⡟⣷⠀⠀⠀⣿⣿⠳⢦⣸⡇⠀⠀⡄⠀⠀⠀⣘⢧⡀⠈⡇⠀⣿⠀⠀⠀⣹⣧⠀⠀⠀ ⠀⠀⡿⣀⠀⠀⢀⣾⠛⣿⣆⣸⣿⠇⣶⠃⠀⠀⠀⣿⣦⠞⠁⢸⡇⠀⣼⢿⠀⠀⠀⣰⣿⠀⡸⠀⠘⣧⠀⠀⢸⣿⣆⠀⠘⣿⢆⢀⡇⠀⠀⠀⣽⡜⢿⣴⣶⣴⠏⠀⠀⠀⣷⣜⢳⣄⠀ ⢠⢱⣷⣿⠀⠀⣾⢁⣼⠁⣿⡿⡋⢸⡏⠀⠀⢠⠀⢸⡇⠀⠀⣿⠃⢸⠃⢸⠀⠀⣴⠋⡸⣰⠇⠀⠀⠈⢧⡀⠀⡇⠹⣆⠀⣿⡎⣀⡃⠀⠀⠀⡿⣿⢶⣿⣿⡿⡄⠀⠀⠀⢸⡏⠙⠛⠓ ⢠⣿⣿⡇⠀⣼⢃⡾⢃⣾⣿⣧⣵⣿⠁⠀⠀⠈⣇⢸⡇⠀⢸⢻⣦⡇⠀⢸⠀⣴⠃⢀⣷⠟⠀⠀⠀⠀⠀⠳⣄⢹⠀⢹⡄⡧⢷⣽⠃⠀⣀⠀⢾⣿⣾⣿⣋⠀⠹⣆⠀⢆⢸⡇⠀⠀⠀ ⠈⠉⣿⡇⢸⣏⣼⣅⣼⣿⣟⣩⣾⣿⠀⠀⠀⠀⣿⣾⢷⣀⡿⢸⡿⠀⠀⣧⣼⠃⠀⣸⠏⠀⠀⠀⠀⢠⡤⢄⣙⢿⣇⠀⣿⠁⢸⡿⠀⢀⡟⢀⡾⠿⠿⣿⣿⣆⢀⡙⣦⡌⢸⠃⠀⠀⠀ ⠀⠀⢿⡇⣸⡇⠉⠉⢉⠉⠁⢭⣿⣿⡀⠀⡇⠀⢹⡏⠘⣿⡇⠈⠁⣀⣰⣿⣄⡀⠘⠁⠀⠀⠀⠀⠀⢀⣿⠿⠶⠶⣽⣄⡈⠀⢸⡇⠀⣼⣇⣾⡅⠀⠀⠟⠛⠛⣿⣿⣿⢿⡟⠀⠀⠀⠀ ⠀⠀⠈⣿⣻⣷⢠⠉⠁⠉⠻⠟⠁⠈⢹⣶⣿⡄⢸⣇⠀⠹⣿⠞⠉⠉⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢻⣦⢸⠃⢀⣿⣿⣿⣷⡀⠀⠀⢀⣠⣿⣿⣿⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣾⣧⡀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⢿⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⣿⣿⣿⣿⡟⠋⠉⣩⣩⡿⠃⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣏⢿⣏⡻⠲⢤⣄⣴⣿⣿⣿⣧⣿⣧⡸⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠛⠛⠛⠉⠙⢷⡀⠀⠀⠀⠀⠀⢘⣿⣶⣿⣿⣿⣿⣿⣷⡀⠰⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠻⣷⣠⣤⣿⣿⢿⡟⢿⣿⡿⠿⣿⣿⣄⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⢀⣠⡴⣿⣻⣿⢿⣿⠃⠘⣿⢻⣄⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣿⣿⣟⠀⣀⣿⣇⠀⠙⣿⣏⣽⣷⣶⣤⣤⣄⣸⣇⣀⡀⠀⠀⠀⣀⣀⣠⣼⡷⠞⠻⢯⣾⣄⢹⣿⠃⠛⢃⡴⢾⡟⣮⡿⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⣦⣀⠙⣿⠈⢿⠿⡿⠉⢹⣦⣴⣟⣙⣿⠀⠻⠂⡀⠈⠹⢿⣿⣭⠉⢻⣿⣿⠟⣿⣽⡇⠀⠀⠘⠙⠛⠛⢛⡷⣶⡾⠁⠀⠀⠘⣷⣤⠶⠚⣽⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⣉⣿⡿⠀⠘⢦⣄⠀⠀⠉⠹⡍⠉⠉⠱⡄⠠⡇⠀⠀⠛⠛⠓⠂⠘⠿⠟⠁⠉⠛⢷⡞⢇⠀⠀⠀⠀⢀⠁⠀⠀⢀⡴⠀⠀⠉⠁⢠⣾⣇⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡤⠼⠟⠋⠀⠀⠀⠀⢈⣙⣿⠗⠒⠃⠀⣀⡼⢃⣀⣠⣴⣷⠦⣶⠛⡗⠲⡖⠀⢻⢸⡷⣾⣧⣈⠓⠲⢤⣄⣼⣧⡴⣿⣉⣀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠳⣶⠶⠀⣀⣤⣶⣶⠿⠋⠀⠀⢀⣴⠿⠿⣶⣶⡿⠾⢿⡟⠀⣀⣀⠀⢰⣷⠀⢸⢨⣙⠉⣿⠳⠤⠞⠛⠋⠀⣽⠃⠀⠀⠻⠿⠶⢦⣤⣤⣈⣻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⡶⠟⠛⠻⣶⢶⣤⣀⣤⣿⡉⠀⠀⢀⡾⠟⢷⣄⣼⠁⢀⡁⣹⠀⢸⣿⠀⢸⢀⣼⣄⣿⡆⢀⣤⣄⡀⠀⠈⢹⣿⡗⠀⣠⣤⣀⡟⠁⢻⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⡿⠛⠉⠙⠓⠲⣤⣇⠀⠀⠀⠀⠘⣷⣀⣶⠏⠀⢀⡈⠛⠟⠉⠉⠻⣿⠀⢸⢿⠀⢸⣿⠀⠈⠙⣿⠉⠀⠀⠙⣆⣠⡟⠀⠙⠋⠁⠀⠀⠀⣰⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⣼⡿⣿⣷⣾⣿⣇⠀⠀⠀⠀⣰⡟⠓⠛⠛⠲⢾⡃⠀⠀⠀⠈⣶⣤⣤⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⢧⡾⠋⠀⠸⠷⠾⣿⣏⣻⣦⡤⠴⠋⠀⠀⠀⠀⠀⠀⢷⣵⣤⠶⣾⠿⣿⣿⣿⠏⠻⣦⣀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⢸⣇⣀⣠⠾⢿⡿⠿⢶⣶⣶⣶⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⢤⣽⣤⣼⣯⣥⣤⣤⣾⣿⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠙⢿⡻⠇⠀⠛⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⣠⣴⣿⣿⣦⡀⠀⠀⠀⣼⣿⠛⠛⠛⠛⠋⠛⠋⠁⠀⠛⣤⡇⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠈⠙⠻⣇⠀⢀⣆⠐⠲⠶⣤⣹⣿⣷⣶⡿⠟⠋⠁⠙⢿⣿⣶⣤⣾⡿⠋⠀⠀⠀⠀⢰⣄⢀⣸⡿⠋⠉⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠈⠉⠙⢿⣤⣄⠀⠀⠈⡈⠛⠛⠓⠒⠒⢠⠒⠲⠾⡿⠿⠟⠉⠉⠀⣠⣤⣤⠾⠋⠉⠉⠀⠀⠀⠀⣀⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣀⣈⣿⡳⣶⠟⠛⠛⠦⣤⣀⣀⣼⣦⣄⡤⠷⠤⠄⠤⢴⣾⠋⠀⠀⠀⠀⠀⣀⣀⣤⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⡆⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⢸⡏⢀⣀⣠⡤⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢸⣿⣾⡀⠀⠀⠀⠀⢀⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀