⠉⠉⠉⠉⠉⢩⡽⡭⠿⠻⣿⣽⠿⠽⠿⣯⡭⠭⠿⢿⣯⡭⠭⠿⢿⣯⣭⠽⠽⣿⡽⠯⠿⠿⣯⢭⡙⠿⢿⣿⢭⠭⠽⢿⣯⡽⠩⠽⣿⡽⣭⠿⠿⣯⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⢀⠞⠹⣟⣦⠀⠀⠹⢻⣄⠀⠈⠽⣣⠂⠀⠘⢻⣥⠀⠀⠹⣷⣦⠀⠀⠛⢯⣆⠀⠈⠳⣭⡄⠠⠘⢯⣗⡀⠀⠙⢻⣮⠀⠀⠛⣭⣓⠄⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣧⡠⠈⠛⢳⣤⠀⠈⠙⢶⣀⠀⠁⠛⣦⢀⠀⠉⢻⣤⡄⠀⠙⢯⣄⡀⠀⠙⢲⡄⠀⠀⠛⣦⢆⠀⠘⠳⣆⡀⠀⠉⢻⣤⠀⠀⠛⢮⣳⣌⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠙⢷⣆⡀⠈⠙⠳⣄⠀⠀⠙⢲⡄⠀⠈⠉⢦⣀⠀⠙⠯⣄⡀⠀⠙⠳⣄⠀⠀⠉⠧⣄⠀⠈⠩⢣⣀⠀⠉⠻⣄⡀⠀⠘⠻⣄⡀⠈⠛⢦⣟⡈⠓⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⣀⠀⠘⠷⣆⠀⠀⠙⢳⣄⠀⠀⠘⢧⣀⠀⠈⠹⢆⣀⠀⠉⠳⢆⡀⠀⠘⠳⣄⠀⠀⠙⠲⣀⠀⠘⠹⢆⡀⠀⠘⠳⣆⡀⠀⠘⢳⢶⣀⡈⢻⡴⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠸⣿⢧⠀⠀⠘⢿⡀⠀⠀⠸⢧⡀⠀⠄⠸⢧⠀⠀⠘⠻⣄⠀⠀⠘⢧⣀⠀⠀⠛⣿⡀⠀⠀⠛⣧⠄⠀⠘⠻⣄⠀⠀⠣⢿⣀⠀⠀⠸⣟⣣⢇⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠾⣯⣄⠀⠋⢷⣤⠀⠀⠛⣧⡀⠀⠈⠹⢶⡀⠀⠈⠳⢦⡀⠀⠈⠷⣄⡀⠀⠙⣶⡀⠀⠀⠙⣶⣀⠀⠀⢛⣦⡄⠀⠈⠷⣤⠰⠀⠙⢶⣄⠀⠈⠳⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠀⡿⢫⣖⣀⠀⠚⠽⣄⡀⠀⠙⣶⣀⠀⠈⠙⣦⡄⠀⠈⢹⣦⣀⠀⠈⠳⣄⡀⠀⠙⢦⡄⠀⠀⠛⣾⣄⢠⠈⢛⣦⡄⠐⠈⠷⣆⠀⠀⠚⢷⣴⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⣨⠙⠿⢦⣀⢨⠟⠹⣆⡀⠀⠹⢺⡤⠀⠀⠻⣟⣦⠀⡜⠻⣦⣀⠀⠁⠳⣆⠀⠀⠙⣧⣄⡀⠈⠻⣿⣄⡄⠘⢻⢧⣠⠀⠙⠻⣤⡀⠀⠟⣷⢶⡄⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡿⣷⣀⠀⠻⠿⣣⣄⠀⠉⠷⣤⠀⠌⠹⣟⣤⡄⠙⢻⣾⣇⡀⠉⠿⣦⡀⠀⠘⠫⣄⡀⠀⠹⢷⣆⣰⠿⢿⣿⣶⣄⠚⠟⣷⡄⡀⠘⢽⢦⣸⡀⠻⡇⠈⠃⠀⠀⠀⠀⠀⠀ ⠀⠰⠉⠀⣿⡿⣿⣆⠀⠘⡿⢦⣀⠀⠘⢿⣆⠀⣸⣿⣷⣦⠜⢁⣿⣷⡄⡄⠘⠻⢧⡀⠀⠘⢹⢧⡄⢈⣿⠏⠀⠈⢻⡿⢩⣆⣤⠘⢻⡽⣀⠀⠙⢷⣝⣂⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣟⡾⣷⢆⡀⡘⢿⣶⡐⠀⠹⣿⣿⣥⣿⣧⣤⣤⣼⣧⣿⣿⡤⠀⠈⠻⢧⣀⡀⠩⢿⣿⣶⣶⣶⣿⣿⣷⣿⣿⣿⡕⢄⠈⢻⣾⡄⡀⡯⢿⡇⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣹⣿⣯⣔⡀⠘⢻⣿⣴⠟⠀⣴⣿⡇⢸⣿⣫⢻⠿⣜⣻⣶⣤⡀⠉⢻⣾⡣⢀⡍⢩⣿⣿⠀⣿⣽⡋⠉⣼⣻⣿⣳⢌⣿⢿⣿⣿⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠁⡿⠙⣿⠉⢿⢻⣽⣶⡙⣾⣁⠀⠀⢯⣿⡇⣼⣿⣷⠀⠁⠉⢻⢋⢷⣿⣄⠀⡘⡻⠹⠀⠀⢿⣿⣣⣸⣿⠇⠀⡽⣽⣿⣻⣿⣯⣞⣹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠋⠰⡘⢸⡏⢻⣿⡿⠈⠲⣄⠈⠛⠃⠛⠛⠁⡀⠔⠀⠀⠀⠙⠙⢿⠟⠂⠀⠃⠀⠐⠄⡄⣉⢉⠡⠔⠊⠀⢹⣿⣿⣯⣿⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣦⠙⢾⣟⡇⠀⠀⠀⠀⠒⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣿⣟⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣷⣄⣸⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⢹⠯⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣏⡻⡧⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢙⣾⣽⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⣿⢾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⡿⣼⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠪⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⢳⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣎⠑⡌⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⠘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣏⠻⣕⣂⢸⢢⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡿⣯⣺⠀⣯⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣙⣛⢖⠸⢸⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣠⣿⡿⠙⣗⠿⣃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣮⣽⡷⡼⡘⠑⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⣛⣾⣿⣿⣿⣿⣿⣟⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣷⣺⣞⣶⠄⢤⠶⠄⣆⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡿⠟⠣⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠽⠻⢿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀