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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠋⠷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⣠⡰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠏⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⢉⣟⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣹⠉⠀⠈⣿⣌⡏⠀⢈⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡥⢤⣆⣀⣵⣄⣑⣦⢬⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣁⣬⣽⣶⠿⢋⡬⣍⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⠟⠛⠉⢉⣅⠀⠀⢸⣢⣸⠇⠀⠈⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡩⡓⠁⠀⠈⣯⣈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠟⣀⣠⠀⢉⡀⠁⢀⠀⠀⡀⠀⢠⣀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡿⠹⠷⠒⡿⠤⡖⠋⠓⠦⠽⠗⠺⠏⢻⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⢾⢷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⡾⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢆⠅⠀⢀⣉⣉⠓⠛⠛⠛⠓⠒⡏⠉⠉⠀⠀⠀⠰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⡴⠞⠕⠁⠀⠀⢺⣿⣿⠆⠀⠀⠀⠐⡞⡙⡖⠀⠀⠀⠀⠀⠈⠛⠦⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢛⣶⠞⢀⡀⠀⢀⠉⠁⠀⠀⠀⢀⠀⠋⠉⠃⠀⡀⠀⠀⣀⠘⢶⡞⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡿⠻⠿⠒⠚⠿⠴⠖⣯⠤⠔⠋⠳⣤⣼⡖⠦⠽⠓⠒⠾⠿⠻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡀⠀⠀⣠⠾⢧⠀⠀⠈⠙⢓⣶⠀⠀⠀⠀ ⢠⡴⠶⠚⠋⠋⠁⠀⠀⠀⠀⠀⣴⠛⣦⠄⠀⠀⠀⣀⣀⠀⢻⣧⠀⠀⠻⣤⡼⠁⠀⠀⠀⠀⠉⠛⠲⢶⣤ ⠀⠙⠓⢷⡶⠂⠀⠀⠀⠀⠀⠀⠸⠒⠗⠀⠀⠀⢸⡁⢈⡇⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣖⠖⠛⠁ ⠀⠀⠀⠾⠷⣶⣏⣀⣀⣤⠆⠀⡀⠀⠀⠀⢠⠀⢀⣩⡉⠀⣄⠀⠻⣷⣄⡀⠀⢦⣄⣀⣘⣷⣶⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⣿⣥⣤⠴⠾⠿⢾⡿⢿⣿⣷⠾⠗⢶⢬⣿⣿⠛⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠙⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⢦⡀⠀⠀⣀⡘⣧⠙⠚⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢧⣀⣴⠃⠀⠘⢯⣭⠉⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢲⣸⠄⢧⡼⣫⠇⢀⡼⠉⢉⣛⣒⣶⣫⠾⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣄⣀⣀⣠⢮⣙⣒⣾⠴⠊⠉⠉⣈⠉⣷⢞⡽⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⢀⣠⣤⣤⣧⣀⡴⠚⠉⠉⠉⠃⣾⡤⠞⠁⠀⠀⢰⣲⣶⣵⣄⠀ ⠀⠀⠀⠀⠀⠈⠻⣍⣙⣒⣮⡍⠀⠀⡀⢀⣀⠀⠈⢧⡀⠀⠀⠀⣞⣿⡏⡿⡷⠁ ⢠⡤⣴⣶⠀⠀⠀⠀⠈⠉⢹⠀⠀⠘⠿⠘⠋⠀⠀⠀⢳⡀⠀⠀⠀⠹⠝⠊⠊⠀ ⢰⡕⡊⣻⣿⠃⠀⠀⠀⠀⢸⠀⢀⡤⠖⡺⢯⠉⠉⠓⢆⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠷⠛⠛⠀⠀⠀⠀⠀⢸⢰⠏⠀⠀⠓⠋⠀⡀⠀⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣧⣄⣈⣒⣒⣩⠴⢚⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣏⣳⠻⠿⡷⠲⠛⣋⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣰⠃⠉⠉⢙⡿⡟⠋⣭⠍⢇⢳⡀⢀⣀⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠀⢻⠉⡏⠀⠀⠀⣏⡼⢉⣠⡗⠒⢹⠈⡏⢉⡏⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⣾⠀⡇⠀⠀⠀⣏⠓⠦⢞⣯⣩⠜⠀⡇⠸⡇⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠧⠖⢳⡖⠋⠉⢹⡶⠶⣾⠉⠉⠓⢶⠓⠦⠗⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠘⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣴⠶⣦⡀⠀⠀⢰⠶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⣶⠀⠀⠀⣠⡶⣶⡄ ⠘⢷⣄⠈⠻⣦⡀⢸⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⣠⡾⠋⢐⣾⠏ ⠀⠀⠙⢷⣀⠈⠳⣾⣤⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿⡾⠋⢀⣴⠟⠁⠀ ⠀⠀⠀⠀⠙⣶⣤⠞⠁⠀⢻⣆⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⢠⣿⠁⠀⠛⠀⣴⡟⠁⠀⠀⠀ ⠀⢠⡖⠚⠛⠉⠁⠀⠀⠀⠀⠹⣶⡟⠈⢻⡆⠀⠀⠀⠀⠀⠀⣿⡉⠙⣷⠞⠁⠀⠀⡀⠈⠉⠙⠓⠲⣶⠀ ⠀⠀⣷⣤⠶⠶⠟⠋⠻⣦⡀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠋⠛⠲⠶⢦⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠂⠀⠀⠀⢿⣤⠴⠶⠶⠶⠶⢦⣼⠃⠀⠀⠀⠺⠷⣬⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⠛⠛⠛⠛⠳⢦⣽⣆⣀⣤⡴⢶⡄⠈⠻⠀⠀⠀⠀⠀⠸⠇⢀⣰⠶⣤⣄⣠⡿⣠⡶⠛⠛⠛⠛⠳⣶ ⠀⢿⡄⠀⠀⠀⠀⠀⠙⢯⣽⠏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠻⣯⡿⠁⠀⠀⠀⠀⠀⣰⡇ ⠀⠈⢳⣄⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⠀⠈⠙⠓⠶⠶⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠶⠶⠚⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⣿⡦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠉⠉⠉⠀⢀⣀⣀⡀⠀⠉⠉⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢰⣟⢩⡉⣿⡆⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⡁⠙⠿⠾⠋⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠹⢄⡼⢦⣠⠇⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠋⠉⠛⠒⠲⠶⠶⠖⠒⠛⠉⠙⢷⡄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣆⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣴⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣴⠞⠉⠉⠳⣆⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⣿⠀⠀⠀⠀⣿⡄⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠤⠾⠋⠀⠀⠀⠀⠘⠷⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀ ⢸⣆⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⣠⣤⣿⠀⢹⡆⠀⢠⣤⣄⠀⠀⠀⠀⣀⣀⠀⠀⢰⡏⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⢿⡀⠀⢀⣀⣙⠛⠋⠀⠹⣄⠀⠀⣼⠋⠹⣧⡴⠟⠀⠘⠓⢲⡄⠀⠀⠀⠀⠀⠀ ⠈⠙⠛⠋⣉⣩⣿⣶⡴⠞⠛⠛⠿⣧⡀⣠⡴⠖⠒⢶⣤⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⣠⠴⠚⠋⠁⠀⣼⠋⠀⠀⠀⠀⠀⠀⠹⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢄⡀⠀⠀⢸⡇⢀⣔⡆⠀⠀⢀⣀⠀⢹⠀⠀⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⠒⣿⠀⠘⠟⠁⠀⠀⢸⡾⠀⡼⠀⠀⠀⣀⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣄⠀⠀⢠⠚⠑⡦⠀⢸⡟⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡏⠻⠶⣄⣉⣋⣥⢶⣋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠲⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠛⠻⢯⡄⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⣻⣿⠀⠀⢸⣀⣀⣀⣀⣠⣷⡀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⡿⠀⠀⣾⠉⠉⠉⢻⡍⠀⢿⢦⡀⠀⠀⠳⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢰⡇⠀⠀⡇⠀⠀⠀⠀⣷⠀⠈⢢⠙⠳⣄⠀⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠘⣧⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣾⠀⠀⠀⠀⢀⡇⠀⠀⡟⠀⠀⠀⣿⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠇⠀⠀⠀⢀⡾⠀⠀⣼⠃⠀⠀⢀⡟⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠀⠀⠀⠀⠈⠛⠛⠛⠡⠬⠥⠽⠾⣥⣀⣀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⢷⣦⠸⣿⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠹⠿⠟⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠆⠀⠀⠀⣴⡿⠿⠶⠾⠃⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠈⠿⣦⣤⣴⣟⠀⠀⠀⠀⠙⠷⢶⣶⠃⢰⣶⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣶⣄⢸⣇⠈⣿⢀⣴⡿⢻⣧⠀⠀⢀⣿⠋⠙⠛⠷⠶⢶⣤⣄⣼⠏⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣿⠀⠻⠿⠟⠀⠙⠛⠋⣤⣾⠃⠀⣠⡿⠃⢀⣠⣤⣤⣶⢶⣮⣿⣿⡾⠋⣀⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⣀⣴⣤⣈⡛⠛⣿⣿⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⢹⣷⡾⢋⣽⠟⠁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠈⠙⠛⠛⢻⡿⠁⠀⠀⣠⣤⡶⠾⠿⠿⠶⣾⡟⢠⡿⠁⣀⣾⠏⠀⠀⠀⠀⠀⢀⡀⣀⣠⠶⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⠶⣾⣿⣄⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠁⢿⣷⠾⠛⠁⠀⠀⠀⠀⠀⠐⣯⣽⢷⣽⣿⣟⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⡛⠛⠷⢶⣤⣌⣙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠙⢿⣽⣷⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣤⣿⡟⠀⠀⠀⠀⣤⢦⢀⣿⣷⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠛⠻⣿⣟⣸⠯⣽⢿⡀ ⠀⣠⠤⣴⠶⣯⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢿⡿⠀⠛⠟⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠹⠥⠟⠛⠉⠋⠀ ⠀⣹⢒⣉⣿⣯⣿⣾⣲⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡶⠶⠶⣶⣤⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣛⡇⣩⠄⣐⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⡾⠛⢋⡽⠶⢶⡆⠀⠀⠀⠈⠻⣦⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠳⡿⢶⣽⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⡟⠁⠀⠀⠈⠳⠶⠛⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⠀⣀⠀⠀⠀⢀⣠⠎⠀⢀⣼⢟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣜⢿⣤⣀⠀⠈⠙⠛⠛⣋⣁⣤⡾⠛⣡⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠻⣷⣯⣝⣻⣿⡟⡛⣛⣋⣉⣥⣴⡾⠋⢹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⣽⠉⢹⡟⠛⡟⠉⢹⡁⢀⣿⣤⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠙⠛⠛⠿⣿⣶⣿⣿⣟⣛⣋⣉⣿⡄⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⢶⣦⣤⣤⣾⠃⠀⠀⠀⠀⢀⣾⠋⣹⣇⡀⢀⣿⠋⠀⢈⣷⠈⣿⣦⣤⣴⣶⡾⢷⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷⠀⢸⡟⠀⠀⠀⠀⠀⢸⡇⣴⣏⡀⠉⢹⣿⠓⠉⠁⢹⡄⢸⡇⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⣧⡀⠈⢉⣿⣿⠤⠴⠒⣻⠇⠈⡇⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⡏⠀⢸⡇⠀⠀⠀⠀⣀⣸⣇⠈⠉⠛⠛⢹⣿⣦⣴⠞⠋⠀⢰⡇⠀⢸⣇⠀⣸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⣿⣅⣤⡾⣿⣤⡶⠟⠛⠛⠛⢿⣦⣤⣤⣤⣾⠛⠛⠛⠻⢷⣤⣾⠷⣤⣄⣿⡶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⡀⠀⠀⠀⢀⣼⡏⠀⠀⠸⣷⡀⠀⠀⠀⢀⣹⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠾⠛⠋⠀⠀⠀⠀⠈⠛⠷⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⢠⣶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠸⣆⢹⡄⠀⢸⠙⡇⠀⠀⠀⠀⠀⠀⠀⢀⡖⣶⠀⠀⢀⣾⣿⠇⠀ ⣀⣤⠤⢼⡈⠛⠲⠾⠇⣇⠀⢀⣀⣠⡄⠀⢀⡼⠛⢷⣶⣶⣋⣁⠛⢲⣦ ⠛⠓⠒⠋⣉⣉⣉⠓⢦⣘⣦⠤⠿⠛⠿⣶⣏⣴⣾⣿⡿⢥⡀⠉⠉⠉⠁ ⠀⠀⠀⠸⣇⣻⣟⡻⣶⠟⠁⠀⠀⠀⠀⠀⣿⡿⢛⣹⣷⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⢻⠏⢸⡆⠀⠀⠀⣾⡶⠘⢿⠟⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣃⡤⠔⠒⠒⠢⢄⠈⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠉⢯⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠈⠳⣄⡤⠔⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠙⣏⠀⢸⠀⠀⠀⠐⡶⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣈⠳⠼⣦⣀⢤⠞⢁⣤⠞⠓⠖⠒⠉⠉⠉⠳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⢾⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡄⠀⠀⠀⠀⢰⡀⢠⣏⣳⡦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⠀⢷⣒⣲⣿⡇⢸⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠀⢸⣽⢸⢹⠃⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸⡆⠈⡇⠀⢸⠀⠸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣿⠃⠀⢸⣀⣿⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡙⠒⣻⢻⠶⠖⠚⣿⣿⠶⠚⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠛⠁⠈⠦⠤⣼⠋⠈⢓⠚⢋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣿⣀⣀⣿⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⣶⡀⠀⢀⣄⠀⠀⣀⣀⠀⠀⣠⡀⠀⢀⣶⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⣿⠻⣶⠟⠙⢷⡾⠋⠙⢷⡾⠋⠻⣶⠟⣿⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⣾⠃⠀⠀⢰⣿⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⣿⡆⠀⠀⠘⣷⠀⠀ ⠀⢰⡟⠀⠀⠀⣼⣿⢷⣤⠞⠛⢦⣴⠟⠻⣦⡴⠛⠳⣤⡾⣿⣧⠀⠀⠀⢻⡄⠀ ⠀⣼⠇⠀⠀⢀⣿⣿⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⣿⣿⡀⠀⠀⠸⣧⠀ ⢀⣿⠀⠀⠀⣸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⣿⡀ ⠈⣻⡶⠶⣶⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣶⠶⢶⣟⠁ ⠀⠿⠷⠾⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠷⠾⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⠀⠀⡀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⠃⠘⠟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⢀⠘⣧⡀⠐⠢⠔⠂⢀⣼⠃⢀⣀⣀⣀⣀⡀⠀ ⢠⡿⠉⢈⡟⠉⠛⠛⠻⠿⠂⠀⠀⠐⠿⠟⠛⠛⠉⢻⡁⠉⢿⡄ ⠘⢷⣄⣾⡃⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⢘⣷⣠⡾⠃ ⠀⠀⠈⠉⠙⠛⠿⣶⡀⠀⠀⠈⠁⠀⠀⢀⣶⠿⠛⠋⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢾⡷⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⣄⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢠⡟⢻⡄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣧⣤⣀⢠⡿⠀⠀⢿⡄⣀⣤⣼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⠉⢉⣿⠁⠀⠀⠈⣿⡉⠉⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⠀⠀⠀⠀⠈⠓⠶⠞⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠑⢦⠀⠀⠀⠀⠀⠀⠀⠠⡾⠉⠀⠉⠲⡀⢠⠖⠉⢙⡦⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣀⠀⠀⠀⠀⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⡀⠈⠁⡴⠒⠉⠀⠀⠀⣰⠞⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⠈⠳⡀⠀⠀⠸⡄⠀⠀⢸⠀⠀⣠⠤⣄⠀⠀⠀⠀⣀⣀⠈⡇⠀⠙⠋⢹⡇⠀⣼⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⠀⠀⠹⡄⠀⠀⠙⣆⠀⠈⡇⠀⡇⠀⠀⠱⡀⠀⠸⡁⠈⠉⠁⠀⢰⠊⠁⠀⢠⠇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠈⠢⡀⠀⠈⢆⠀⢇⠀⠹⡄⠀⠀⢧⠀⠀⠈⠳⠤⣀⣀⣈⣙⡶⠶⠚⠓⠲⠦⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠓⠒⠛⠀⠈⠦⡴⠃⠀⠀⠘⢆⡀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⣋⡿⠷⠚⠃⠀⠀⠀⠀⣠⣤⢤⡀⠀⠀⠉⠛⢻⠟⠉⠉⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠶⠒⠒⠉⠁⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠮⠽⠀⠀⠀⠀⠸⡀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠓⣺⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⣄⣀⣀⡤⠴⣞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⣄⣿⠲⣄⣀⢀⣀⣠⠴⠖⢚⡟⠶⠴⠶⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠛⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠀⢸⠀⠀⠈⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡦⠚⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⣠⣼⣿⠤⣿⡁⠀⠀⠀⠀⠀⠀⠀⢰⡗⠣⠤⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠻⠏⠉⠀⣿⡁⣀⠀⠀⠀⠀⠀⠰⡾⠇⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣠⡤⢼⣇⠀⠀⢠⡤⡄⠉⠹⣄⢀⡀⢠⣄⣼⠃⠀⢀⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡈⠛⠃⠀⠀⠈⠉⢉⡁⠀⠀⠀⠀⣏⣹⠠⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡀⠀⠀⠀⢯⡽⠃⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣆⣀⣀⡀⠀⠀⣀⣀⣀⢠⠞⠉⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠶⠋⠀⡼⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠗⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢯⡀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⣏⠉⠉⠉⠉⠛⠛⢻⡇⠀⠀⠀⠀⢧⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⣠⠜⢹⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⢧⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢧⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠸⡄⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢷⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⢦⣀⣀⠤⠔⠋⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠧⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⢳⡀⢹⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠘⡈⡇⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄⠀⠀⢸⠘⡆⠀⡇⢻⢠⠇⢸⡇⠀⡠⢲⠄⣤⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⢇⠘⡇⠀⡸⠀⣧⣴⠃⠘⢿⡄⢸⡦⠞⢱⡏⡜⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣆⣸⠀⠿⠦⡇⠀⣿⣠⡤⢶⣾⠃⠈⠳⠶⠬⠟⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⢣⠀⢻⣏⢀⣠⢶⡇⠀⠈⠙⠒⠉⠀⣀⣀⣀⣀⡀⠘⠿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡧⠤⠤⠧⡄⠉⠛⠛⠉⢀⣀⣀⣤⡤⠶⠛⠋⠁⠀⠀⠉⠓⠦⣈⠳⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⢹⠀⠀⣰⠞⠉⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⣏⣀⢀⣿⠤⠔⠉⠁⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠟⠉⣠⣄⠀⠈⠁⠀⠀⢀⣀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠖⠛⠁⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠘⢯⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣏⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢶⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠓⢛⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⠶⠚⠉⠉⠳⡄⠀⠀⠀⠀⢀⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠈⠁⢲⠤⠤⠄⠀⠠⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⡀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀ ⠀⠀⠀⠀⡰⠃⠀⠀⠀⢠⠃⢠⣖⠅⠀⠀⠀⠀⠀⢀⣠⠄⠀⠈⠱⡀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⢀⠋⡀⠖⠁⠀⠀⠀⡀⢀⡴⠁⠀⠑⢄⠀⠀⠈⢆ ⠀⠀⢸⠀⠀⠀⠀⢠⡧⠊⠀⠀⠀⠀⣸⣀⡷⡟⠁⠀⠀⠀⠈⢂⠀⠀⢈ ⠀⠀⢸⠀⠀⠀⢀⡾⠀⠀⠀⠀⢀⡟⠁⠟⢽⢧⠀⠀⠀⠀⠀⢸⠀⠀⠞ ⠀⠀⠀⡄⠀⠀⡜⠀⠀⠀⠀⠀⡜⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⡜⠀⠀⡜ ⠀⠀⠀⡇⠀⢰⠁⠀⠀⣀⠴⡊⢢⡀⠀⠀⣶⣿⡇⠀⠀⠀⡐⢁⠤⠊⠀ ⠀⢀⡠⠗⠒⠼⣄⠀⠀⡃⠳⢕⣼⣷⠀⠀⢹⡿⠷⠀⠠⡾⠊⠁⠀⠀⠀ ⢠⠋⠀⠀⠀⠀⣸⢆⣀⠁⠀⢀⠟⠋⢴⣶⢶⡤⠄⠀⢀⡇⠀⠀⠀⠀⠀ ⠘⢿⡀⠀⠀⢀⡟⠀⠉⠉⠂⠉⠢⠤⠤⣬⠁⡠⠒⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠄⠣⠎⠀⠀⠀⠀⢀⡤⠲⣠⡾⡋⢈⡈⡦⢊⣱⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠚⠉⠑⢸⠁⠃⠀⠉⠀⡹⡖⠒⠂⠤⠤⣀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⢉⡐⢶⡤⢀⣸⠀⠀⠀⠣⡾⠖⠁⠀⢀⠔⢨⠃⠀ ⠀⠀⠀⢀⡀⠤⠇⠀⢸⣦⡀⠞⡆⠈⠁⠢⠄⣀⠇⠀⡠⣶⠥⠴⡅⠀⠀ ⠀⠀⠀⠉⠀⠐⡆⠀⠀⢹⠙⠀⠇⠀⠀⠀⠀⠈⢱⠊⡐⡽⣷⠶⠃⠀⠀ ⠀⠀⠀⠓⠒⠒⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⠸⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⠀⣀⡄⠀⢠⠀⠀⠀⠀⠀⠎⠀⣃⠗⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠼⣀⠀⠀⠀⡘⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣠⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡶⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⠳⡸⣄⣀⡇⡇⠀⠀⠀⠀⠀⢠⣯⣇⣀⡴⢻⣏⡀ ⠾⠭⠽⠒⠒⠪⣅⢣⣀⣳⠾⣦⣔⣫⣼⣿⣛⠒⠒⠚⠃ ⠀⠀⠀⢏⣿⣳⣮⠏⠁⠀⠀⠀⢹⡿⣛⣷⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢩⠇⠺⠂⠀⠠⠿⠋⢻⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢧⠒⠉⠉⠉⢲⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠈⠣⣀⣠⠔⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡌⢺⡀⢁⠀⠀⢐⡆⠀⣰⠃⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⢝⣚⠦⢐⣊⡤⠚⠙⠋⠉⠀⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢀⠀⢰⢧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⣦⢤⣸⡄⡏⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⢹⠇⣯⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⡇⠘⡄⣿⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⡾⣄⡠⢷⣿⣠⠼⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⠚⠀⠧⢠⡞⠙⠶⠞⡃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⢶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⣻⡟⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠠⠟⠁⣸⡏⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⣤⡤⢤⡤⣤⣄⣀⣀⣸⣿⣿⣿⣄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⢀⡄⣿⣇⣤⡿⠛⠛⠛⠛⠉⠈⠋⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⣿⣦⣤⣽⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣘⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠉⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣀⣼⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢰⢲⣶⡖⠒⠒⠒⠊⠓⠒⣦⣄⣀⣤⡀⠀⠀⠀⠀⠀⣧⠴⠋⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡇⡏⢣⠤⡟⢹⡏⣧⠀⠀⠀⠀⣀⣸⠁⡇⢹⠟⣏⠙⢶⣤⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠋⠀⠸⠟⠑⡄⠸⡆⠀⠀⣀⡤⠖⡎⠉⢸⡀⠀⣿⣇⣸⣤⣇⡈⠀⣸⡞⡇⠀⢠⣧⣇⣀⣧⣟⣀⣸⡀⣸⠀⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⣹⠀⠹⡤⠞⠁⠀⠀⡇⠀⠀⢳⣆⣿⡏⣽⣿⣿⣿⣿⠛⠻⢷⢀⡾⠟⣿⣿⣿⣿⣿⢻⣧⡇⠐⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⢀⡟⠀⠀⢷⠀⠀⠀⠀⡃⠀⠀⠀⠹⣿⠀⢛⣻⣿⣿⣿⠀⠀⢸⠟⠀⠀⣿⣿⡿⣿⠀⡟⡿⠁⢸⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⣄⣤⠖⠋⠀⠀⠀⣸⢰⠀⠀⠀⢱⠀⠀⠀⠠⣿⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⢸⡇⡇⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡀⠀⠀⠘⡆⠀⠀⡆⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⡇⠀⠀⠀⢿⠀⠀⢸⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡿⢀⢢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⢦⠀⠀⠈⣇⠀⠘⣧⣷⣄⣀⠀⠀⢿⠛⠲⡦⠀⣀⣠⡤⢾⠟⠀⢰⠇⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡀⠀⠠⠈⠷⡄⠸⣿⣞⠙⠛⢿⣗⡒⢲⣾⢿⣍⡀⠀⣿⡀⠀⡏⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⣿⡀⣠⣶⣷⣿⣶⣿⣿⣦⡀⠀⠈⣿⣼⣷⡀⢹⣿⣶⣿⣧⣾⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣰⡏⢳⠀⢳⣿⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡋⠳⡀⠀⠀⠀⠀⠀⣠⣿⠿⠿⠃⠈⢿⣿⣿⣿⡟⢪⠻⣧⣼⣆⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⠖⠛⠛⠛⠛⡇⠀⠹⢦⣴⣤⡀⢰⣿⣧⣀⣀⣀⣀⣀⢿⣿⢿⣿⣿⣟⣛⣻⣿⣷⢸⣿⣿⣿⡟⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣉⣉⠀⠀⠀⠃⠀⠀⣰⣿⣿⣿⣾⣏⠈⠛⠛⠛⠉⠉⢸⣿⣿⣛⣛⣿⣿⢟⣩⣽⠿⣿⣭⢿⣧⠈⣿⡆⠀⠀⣀⣤⣤⣠⠤⠤⢤⢤⡀⠀⠀ ⠻⣭⢤⡄⠠⠖⠀⠀⣰⣿⣿⣿⣿⡿⠛⢷⣄⠀⠀⠀⠀⢸⣿⡋⣩⣽⣿⣻⡽⠟⠁⠀⠸⣿⡀⣿⡀⡟⣿⡶⠿⣿⣿⣿⣿⣦⠀⢘⢯⡁⠀⠀ ⠀⠹⠭⠴⠶⣦⣴⠾⣿⠛⣾⣿⡿⠁⠀⠈⢻⣷⣄⠀⠀⣿⣿⣶⣿⣿⡏⠉⠀⠀⠀⠀⠀⣿⡇⣸⡇⠁⢹⣿⡀⠹⣿⣿⣿⣿⣷⡀⡰⠿⣦⠀ ⠀⠀⠀⠀⠰⣿⣿⠆⢁⣴⣿⡟⠁⠀⠀⠀⠀⢿⣿⣷⣿⣿⠿⠋⣡⣿⣿⣠⣤⣤⣤⣤⣶⡿⣧⢿⡇⠀⢸⣿⡇⠠⠌⣿⣿⣽⣿⠧⣽⣦⣼⠇ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⢻⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠈⡇⠀⢸⣇⠀⣾⢻⣿⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣴⣄⠀⠀⢀⣼⠋⢹⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡁⠘⣿⣅⠋⠉⣽⣷⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣴⠟⠁⠀⣸⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⣿⣀⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣯⡁⠀⢀⣀⣿⢿⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠈⠻⢦⣬⠉⣿⡿⠷⢶⣤⣄⣀⣠⣼⣿⡋⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⠶⠶⠶⠶⠶⠷⠿⠿⠷⠶⠦⠴⠾⠿⠿⠿⠿⠶⢶⢿⢿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠖⠀⢠⠀⠀⠀⠀⣠⠀⣠⡄⠀ ⠦⠑⣚⢩⣆⠰⠆⣔⣽⠟⠒⠛⠂ ⠀⠈⠙⡻⡇⠀⢤⠸⠟⠁⠀⠀⠀ ⠀⠀⠜⠂⠉⠉⠂⠀⠂⠀⠀⠀⠀ ⠀⠀⡔⠆⡅⠀⠔⢀⠁⡀⣀⠀⠀ ⠀⠀⠀⠈⠁⠘⣀⠁⠀⠀⢀⢆⠀ ⠀⠀⠀⠀⠀⠀⠸⢃⢶⢲⢈⠉⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠸⢸⠘⡀⠀ ⠀⠀⠀⠀⠀⠸⠤⠛⣀⠟⠦⠇⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢶⡞⡏⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠇⠈⣴⡧⠖⠒⠊⠒⠉⠉⠉⠒⠛⠻⢦⠤⠀⠀⠀ ⠀⠀⠀⣰⣇⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀ ⠀⠀⣰⣿⠇⠀⠀⠀⡀⢤⢖⡰⡶⠀⠀⢰⠆⣤⠤⡀⠰⠊⠀⠀ ⠐⠁⠈⢡⠠⡠⠂⡅⠱⣸⢺⣷⣴⢿⠰⢷⣶⡶⣶⢨⡅⠀⠀⠀ ⠐⠄⠤⠊⠀⣇⠀⠂⠀⢸⠘⠛⠃⠈⠁⠘⠛⢱⡇⠸⠑⠀⠀⠀ ⠀⠀⠀⠀⠰⠙⠀⠘⡀⢛⡁⠀⢀⡀⠀⠀⣠⢜⠁⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠀⣑⣜⣿⠐⠲⣺⢪⣅⣇⣬⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠀⠀⠈⣿⠿⢿⣿⡷⢼⣁⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣆⡉⠉⠀⢱⣶⣼⠃⠤⠒⣻⣿⣿⣟⡿⣿⣟⢻⠀⣀⣀⠀⣀⠀ ⠘⠧⢤⡤⢿⣿⠋⠱⣤⣀⣿⣾⣟⠉⠀⢹⣸⠈⣏⠻⣿⣧⢨⢄ ⠀⠀⠈⠓⢾⡇⠀⠀⢹⣿⠃⠸⣯⠉⠉⢹⢹⡠⢻⣀⣿⠿⠉⠉ ⠀⠀⠀⠀⠀⠈⠣⠔⠁⣼⠀⠀⣿⠀⠀⢸⠀⢣⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣈⣳⣿⣟⣒⠦⣾⣏⣨⡆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⡠⠤⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠤⡀⠀⠰⠀⠈⡄⠀⠀⠀⠈⠃⠤⢌⠊⣄⣊⠀⢠⠔⠉⡇⠀⠀⠀⠀⠀ ⠀⢸⠀⠘⢄⠀⠣⠀⢠⢠⠋⠒⡀⠠⡒⠒⠀⡠⠘⠀⠇⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⢣⠀⠈⠢⢀⣱⠘⡀⡃⠀⢡⠀⠉⠒⠀⣨⠖⠊⠀⠒⠮⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠀⠀⠀⠑⠒⠒⡺⠁⠀⠀⠀⠀⠀⠑⣄⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠠⠄⠂⡡⠒⠉⠉⠀⠀⠰⢿⣢⠀⠀⢸⠁⠀⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠁⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣽⡦⣀⣀⡠⠄⣳⠤⠤⠜⠀⠀ ⠀⠀⠀⢠⠋⢘⠀⠀⠀⠀⠀⠀⠀⢠⡠⠎⠀⢠⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠰⠇⢠⣾⠇⡏⠀⠀⠀⠀⢠⡒⠠⣆⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠈⠒⠤⢀⣀⣀⡀⠸⡄⠀⣠⡑⠲⣀⣀⣄⠟⠀⡀⢸⡀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣌⠀⠀⠀⣤⡄⠀⠘⠚⣸⠁⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠦⠤⣀⡠⢤⢄⠂⠙⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢎⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠙⢆⠀⠀⠀⠀ ⠀⡔⠁⠀⠀⠀⢀⡞⠀⠀⢹⠉⠁⠐⠒⡆⠀⠀⢫⠀⠈⢆⠀⠀⠈⢣⠀⠀⠀ ⢸⠀⠀⠀⢀⠔⠁⢡⠀⠀⠈⡄⠀⠀⠀⢇⠀⠀⠀⢣⠀⠈⠆⠀⠀⢈⡄⠀⠀ ⢸⠀⠀⠀⣇⠀⠀⠀⢆⠀⠀⣸⠀⠀⠀⠘⡀⠀⠀⠀⠑⢄⠸⠤⠔⠊⠀⠀⠀ ⠀⡄⠀⠀⢈⠆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⠀⠉⠉⠉⠀⠒⠤⡀⠀⢤⠈⢢⠀⠀ ⠀⠀⠀⠀⡠⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣼⠀⢸⠀⠀ ⠀⠀⠠⡀⢃⢝⠍⠉⠭⡐⠶⠤⣄⡀⠀⠀⠀⠈⢆⡘⠀⠀ ⠀⡤⢄⣇⡿⡸⣀⠰⣿⡇⣾⣥⠈⠙⣱⢦⡀⠀⡜⣇⡀⠀ ⢸⠀⣾⣻⠁⠨⡒⠚⠚⠘⢝⡫⠤⣰⠼⠦⢽⢦⣏⠀⠈⡆ ⠀⢣⠈⢻⢠⡀⠘⠔⣂⣀⠤⠔⠂⠀⠀⠀⡜⠀⠙⣯⠉⠀ ⠀⠀⣱⡈⠙⠁⠅⡒⠠⠤⠀⠀⡀⠤⠄⢰⠁⠀⠀⢰⢡⠀ ⠀⠀⢧⠁⠀⠰⣰⣭⡆⡹⠀⠀⡸⠓⠚⠯⣢⠀⠰⠂⠀⡆ ⠀⠀⣘⣆⠀⠀⢱⠒⠊⠀⠀⢰⠵⢧⡦⠷⡡⠇⠀⠀⢀⠇ ⠀⠀⠡⣉⢿⡲⠼⢤⢀⣀⣀⣈⡢⠔⠁⠀⠀⢀⣀⣠⠎⠀ ⠀⠀⠀⠈⠈⠀⠀⠀⠧⠤⠽⠕⠣⠀⣀⣀⠠⠤⠊⠁⠀⠀

⢰⡏⠛⢦⡀⢸⠏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⡇⠀⣠⠞⢙⡦ ⠀⠙⢦⡀⠻⣼⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣧⠞⢁⡴⠟⠁ ⠀⠀⠀⣙⣦⠞⠁⠀⢷⡀⣰⢤⡀⠀⠀⠀⠀⠀⣠⢦⡀⣼⠃⠀⠉⣰⣏⡀⠀⠀ ⠀⢻⡉⣀⣀⡤⣤⡀⠀⠻⠃⢠⠏⠀⠀⠀⠀⠘⣧⠀⠛⠁⠀⣠⣤⣄⣀⡉⣽⠀ ⠀⠈⠉⠁⠀⠀⣈⡽⠆⠀⠀⠸⣆⣤⠤⠤⠤⣤⡟⠀⠀⠀⢾⣽⠀⠀⠈⠉⠁⠀ ⢰⡖⠒⠀⠒⠲⣽⣄⣤⡴⢦⡀⠙⠀⠀⠀⠀⠻⠀⣰⠶⣤⣤⣟⡴⠒⠚⠁⠒⣶ ⠀⢷⡀⠀⠀⠀⠈⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢻⡏⠀⠀⠀⠀⣠⠇ ⠀⠀⠙⠲⠤⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠰⢿⠿⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡖⡒⢦⡄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡈⠛⡟⠛⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠙⠒⠓⠒⠁⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⠛⠶⠤⣤⣤⡤⠤⠖⠻⣏⠱⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡴⠛⠉⠙⡆⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣠⠇⠀⠀⠀⢿⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠤⠾⠧⠤⠤⠼⠷⠤⣄⡀⠀⠀⠀ ⠀⠀⣴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣦⠀⠀ ⠀⢸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀ ⢀⡟⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢻⡀ ⣼⠁⢀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠈⣧ ⣿⠀⢸⡇⣿⣦⡴⠷⣤⣤⠾⢦⣴⣿⢸⡇⠀⣿ ⣿⣀⣸⡇⣿⣈⣀⣀⣈⣁⣀⣀⣁⣿⢸⣇⣀⣿ ⣿⣭⣽⠇⣿⣭⣭⣭⣭⣭⣭⣭⣭⣿⠸⣯⣭⣿

⢀⢄⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⣠⣄ ⠈⠢⡑⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⢊⡴⠋ ⠠⡐⣚⣁⡀⠳⠊⡆⠀⠀⠰⡛⠞⠁⣀⣚⠒⡄ ⢀⡁⢀⣠⡛⢀⡀⢧⠒⠒⢲⢁⣀⠚⣇⡀⠈⣀ ⠸⣄⠀⠈⡻⠁⠈⠀⠀⠀⠀⠈⠈⢻⠁⠀⢀⠜ ⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀ ⠀⠀⠀⠀⡇⠀⠘⠛⣀⣀⡘⠋⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⠀⠀⡓⡗⡁⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠼⡲⠄⣈⣈⡠⠴⡚⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠃⡜⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠀⠀ ⠀⠀⢀⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀ ⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠆⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠀⠀⠖⠑⡆⠀⢀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⢚⠀⠀⠘⣒⠁⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠙⠲⣄⠀⠀⠀⣠⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠈⠳⣤⠾⠁⢀⣀⡴⠏⠀⠀⠀⠀⣀⣤⠶⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠶⣤⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⢤⣀⠀⠀⣾⣉⣁⣀⠀⠀⠀⢀⣾⠏⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠹⣆⠀⠀⠀⠀⢳⡀⠀⠀⠀⣷⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠀⣀⣀⠀⢹⠄⠀⠉⠉⠉⣹⡇⠀⠀⣾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⢳⡀⠀⠀⢹⠀⠀⣿⠀⠀⠀⠙⣆⠀⠀⠀⣟⠉⠉⠛⠛⠀⠀⢀⡴⠛⠁⠀⠀⣸⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠻⣄⠀⠸⡄⠀⠙⣆⠀⠀⠀⠹⡄⠀⠀⠙⠶⣄⡀⠀⠀⠀⠘⢧⣄⣀⣠⣠⣿⣀⣀⣀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠈⠳⣄⡀⠀⢹⠀⠀⢳⡀⠀⢹⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⣶⠾⠋⠉⠀⠀⠀⠉⠉⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠻⠶⠟⠀⠀⠀⠀⠈⠷⣀⡀⠀⠀⠀⠀⣀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⢶⣾⣤⠤⠶⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠛⠶⠶⣶⠖⠚⠓⢶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢄⣀⣀⣀⣀⣀⢀⣀⣀⣀⠴⠖⠉⠁⢀⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⣀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣀⣀⣀⣀⣀⣀⡤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡀⣹⣷⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠼⣿⣦⣀⣀⣀⣠⡼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠤⠶⠿⠾⣧⠙⠻⠶⠦⠶⠶⠞⠋⠉⠀⢰⡟⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⠶⠛⠁⠀⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠈⠀⢀⣰⣾⣶⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⣞⣿⠷⠏⠀⣽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠈⠉⠹⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠉⠉⠀⠀⠀⠛⢷⡴⣶⠀⠀⠀⠀⠀⡀⠀⣹⡏⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⣤⣀⣀⣀⣤⠤⠴⠶⠖⣿⣄⠀⠀⠀⣶⣶⣆⠀⠀⠹⣦⣀⣤⣀⣠⣶⡤⠟⠁⠀⢀⣀⡀⠀⠸⣧⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⡀⠙⠟⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⣉⣽⠠⢰⡾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢶⣀⠀⠀⠀⠀⠀⠀⢴⣟⣿⡆⠀⠀⠀⠀⠈⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠶⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⠾⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠶⠶⢦⣀⠀⣀⡴⠶⣶⢦⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠿⠃⠀⢠⡟⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠁⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⠶⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠘⣇⠀⠈⠉⠉⠉⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢻⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠘⣧⣀⣀⣀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⣀⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣆⠀⠀⠀⢀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠤⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⠶⠞⠳⠶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠃⢀⡀⢀⡀⠘⣷⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣿⡀⢈⡁⢈⡁⢀⣿⣀⣀⣀⡀⠀ ⢠⡟⠉⠉⠙⠛⠓⠈⠙⠋⠁⠚⠛⠋⠉⠉⢻⡄ ⠈⠿⢦⣤⣀⣀⠀⠀⢠⡄⠀⠀⣀⣀⣤⡴⠿⠁ ⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠘⠃⠀⠀⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⡞⠁⠀⢀⡾⢷⡀⠀⠀⢻⣄⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⣠⡟⠁⠈⢻⣄⠀⠀⢹⡆⠀⠀ ⠀⠀⠘⠷⣤⠶⠋⠀⠀⠀⠀⠙⠷⠶⠾⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠁⠠⡦⠀⠀⢴⠄⠈⣿⡇⠀⠀⠀⠀⠀ ⠀⣀⣤⣤⣄⣘⣿⣆⠀⣠⣀⣀⣄⠀⢰⣿⣃⣀⣤⣤⣀⠀ ⣼⡏⠁⠈⠉⠙⠛⠿⠂⠈⠛⠛⠁⠐⠿⠟⠛⠉⠁⠈⢹⣧ ⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟ ⠀⠉⠙⠛⠿⢷⣶⡆⠀⠀⠘⠃⠀⠀⢰⣶⡾⠿⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡄⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠁⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠁⠀⠀⢀⣴⣶⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⣠⣾⠋⠙⣷⣆⠀⠀⠀⠹⣷⡀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⣼⡟⠁⠀⠀⠈⠻⣧⡀⠀⠀⣸⡇⠀⠀ ⠀⠀⠈⠻⠷⣶⠾⠋⠀⠀⠀⠀⠀⠀⠙⠿⠶⠾⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠻⣿⣿⠇ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⠿⠀⠀⣹⣿⣷⡄⠀⠀⢠⣾⣿⣏⠀⠀⠿⣿⣷⣦⡀⠀⠀ ⠀⣰⣿⡟⠋⠀⠀⠀⠀⠻⠿⠛⠃⣀⣀⠘⠛⠿⠟⠀⠀⠀⠀⠙⢻⣿⣆⠀ ⢠⣿⡟⠀⠀⠀⣾⣶⡀⠀⠀⠀⠺⢿⡿⠗⠀⠀⠀⢀⣶⣶⠀⠀⠀⢻⣿⡄ ⢸⣿⣷⣶⡆⠀⠘⢿⣿⣶⣤⣄⡀⠀⠀⢀⣠⣤⣶⣿⡿⠃⠀⢰⣶⣾⣿⡇ ⠈⠉⠙⣿⣧⣀⣤⡀⠈⠙⠛⠿⣿⣷⣾⣿⠿⠛⠋⠁⢀⣤⣀⣼⣿⠋⠉⠁ ⠀⠀⠀⠙⢿⠿⠿⣿⣶⣤⣀⠀⠀⠙⠋⠀⠀⣀⣤⣶⣿⠿⠿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⣿⠛⠛⠛⠛⣿⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⡾⢿⣿⣿⣇⣿⣦⣤⣤⣴⣿⣸⣿⣿⡿⢷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⠛⠉⠀⠀⠈⢻⣿⣿⣷⣤⣀⣀⣤⣾⣿⣿⡟⠁⠀⠀⠉⠛⣶⠀⠀⠀ ⠀⠀⢸⡏⢰⣆⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣰⡆⢹⡇⠀⠀ ⠀⠀⣼⠇⠀⣿⡀⢠⣄⡤⠀⠀⠀⠈⣭⣭⠁⠀⠀⠀⢤⣠⡄⢀⣿⠀⠸⣧⠀⠀ ⠀⠀⣿⠀⠀⢸⡇⠰⠛⠗⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠺⠛⠆⢸⡇⠀⠀⣿⠀⠀ ⠀⢸⡏⠀⠀⢸⡇⢀⣾⣦⡀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⣷⡀⢸⡇⠀⠀⢹⡇⠀ ⠀⣼⡇⠀⠀⣾⢧⣾⣿⣿⣷⡀⠀⢸⣿⣿⡇⠀⢀⣾⣿⣿⣷⡼⣷⠀⠀⢸⣧⠀ ⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⢀⣿⣿⣿⣿⡀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀ ⢸⡟⠀⠀⠀⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⣿⣿⣿⠀⠀⠀⢻⡇ ⣼⠇⠀⠀⠀⣿⣿⠃⠀⠀⠹⣿⣿⣿⠏⠹⣿⣿⣿⠏⠀⠀⠘⣿⣿⠀⠀⠀⠸⣧ ⠻⣶⣤⣤⣴⣿⠃⠀⠀⠀⠀⠹⣿⡟⠀⠀⢻⣿⠏⠀⠀⠀⠀⠘⣿⣦⣤⣤⣶⠟ ⠀⣿⣿⣿⣿⡇⠀⢘⣷⣏⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣹⣾⡃⠀⢸⣿⣿⣿⣿⠀ ⠀⠈⠉⠉⠉⠛⣿⠿⣷⣷⣶⢶⣶⣶⡶⢶⣶⣶⡶⣶⣾⣾⠿⣿⠛⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⣿⣼⣿⣿⣧⣼⣿⣿⣧⣿⣿⣿⣤⡿⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦ ⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠙⠛ ⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀ ⠀⣠⡾⠟⠀⣿⣷⠀⠀⣾⣿⠀⠻⢷⣄⠀ ⣾⠏⠀⣤⡄⠉⠁⣶⣶⠈⠉⢠⣤⠀⠹⣷ ⠿⣶⡆⠈⠻⢶⣦⣄⣠⣴⡶⠟⠁⢰⣶⠿ ⠀⠘⠟⠻⣶⣤⣀⣙⣋⣀⣤⣶⠟⠻⠃⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣄⠀⢰⣿⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠈⢻⣷⣈⣿⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠙⠛⠋⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡿⠿⢷⣶⣾⠟⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⢀⣠⣾⠏⠀⠀⠀⠀⠀⢻⣧⣤⣤⣤⡆⠀⣤⣤⣤⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣿⠛⢻⣷⠀⠀⢀⣤⣤⣤⡀⠀⠈⠙⠛⣿⡿⠿⣶⣤⣄⣀⣀⡀⠀⠈⠉⣹⡿⠀⣰⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡿⢿⣧⠀⣿⡆⢸⣿⣄⣰⣿⠏⠁⣿⡇⠀⠀⠀⣴⡿⠁⠀⠀⠉⠉⠛⠛⠿⢷⣶⣾⠟⢁⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡁⠈⠻⠿⠿⠃⠀⠙⠛⠛⢁⣤⣾⠟⠁⠀⢀⣾⠟⠁⠀⣀⣤⣴⣶⣶⡶⣶⣶⣿⣿⣿⠟⠋⢀⣠⣴⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠙⠻⠿⣷⣶⣿⢏⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦⣶⡿⢋⣵⡿⠟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣦⣤⣤⣤⣴⡾⠟⠛⠿⠿⣶⣦⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀⣸⡿⠃⣠⣿⠏⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣀⣴⣾⠿⠟⠛⠉⠉⠉⠙⠻⢿⠁⣴⡿⠁⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⣆⡶⢶⣏⣙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠾⠷⠶⣾⣿⣧⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣝⢷⣦⡝⣟⣉⣷⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣟⠛⠻⠿⣷⣶⣤⣤⣀⠙⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣭⣿⣿⠝⢻⣛⣻⣯⡤⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⣀⣉⣛⣛⣿⡟⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⣿⢻⣶⠆⡤⡟⢾⣯⠟⠀ ⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠟⢻⣿⠁⠀⠀⠀⠀⢰⣿⣉⡇⢸⣷⣼⡇⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⠷⢶⣝⣹⣿⣉⡷⠀ ⠀⢰⠖⠲⣾⠛⢿⣦⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠈⠉⠀⠁⠀⠀ ⠀⢨⠿⢒⣉⢿⣧⣽⣿⣾⠞⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⡀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⢷⠝⢚⣓⠈⢩⣶⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⣴⡾⠿⢛⣫⣭⣥⣄⠀⠀⠀⠀⠈⠛⢿⣦⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠳⢾⡁⣿⣋⢸⣷⣿⡿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⡿⠏⠉⠀⠀⣿⣉⣀⣠⡿⠁⠀⠀⠀⠀⠀⠈⢿⡆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣟⢹⡷⠷⠟⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⡟⠁⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⢀⡀⠀⠀⢀⣼⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⣿⣇⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⢠⣾⠟⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡘⣿⣆⡀⠀⠀⠈⠙⠲⠶⠾⠟⠛⢁⣀⣴⣾⠟⢁⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣬⣛⠿⢷⣶⣤⣤⣤⣴⣶⣶⠾⠿⠛⠉⣀⣴⡿⢿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⣟⠻⢿⣶⣾⣭⣭⣭⣭⣥⣤⣴⣶⣾⠿⢻⡏⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣤⣀⣧⡀⠈⣿⠉⠉⣏⠁⠀⢹⡀⢀⣸⣷⣴⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠉⠙⠛⠿⠿⠿⠿⢿⣶⣿⣾⣿⠟⢛⡛⠉⢉⣿⡇⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣀⣀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⣀⣶⠿⢻⡿⠉⠉⠉⣿⡟⠚⠉⠘⣷⠀⠹⣿⣀⠀⢀⣀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠻⣿⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⡾⠛⠦⠤⢤⣿⣇⣀⣤⡴⢿⡆⠀⣿⣿⠛⠛⠋⣿⠟⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⣿⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢸⡏⣠⣿⣥⣀⠀⠀⣼⣿⠃⠀⠀⠀⢸⣷⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣿⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣄⠀⠈⠉⢩⣿⣿⠤⠤⠶⠞⢹⡿⠀⠀⣿⠀⠀⢸⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⣿⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⠙⠿⠶⠶⠿⢻⣿⣄⣀⣀⣴⡿⠃⠀⢀⣿⠀⠀⢸⣿⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣼⡿⠀⠀⢸⣿⡄⠀⢀⣤⣤⣴⣶⣾⣿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣭⣭⣥⣄⡀⠀⣼⣿⠀⠀⠘⣿⡄⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⣴⡶⠟⢻⣧⣾⠟⠋⠉⠀⠀⠀⠙⣿⣿⣶⣶⣾⣿⡟⠉⠀⠀⠀⠉⠛⢿⣦⣿⠛⠿⣶⣤⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢶⣶⣶⣶⡾⠿⠉⠀⠀⠀⠀⠈⠻⠿⣶⣶⣶⣶⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠓⣆⠀⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠘⡆⢹⡄⠀⢳⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢷⡀⠀⢱⠘⣇⠀⣸⠁⢹⡄⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠳⣦⠀⠀⠀⡇⢸⡇⠀⣼⠀⢿⣀⡏⠀⣼⠇⠀⣠⠎⣽⠇⡴⣻⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⢻⠀⢹⡆⠀⢸⠃⢸⣿⣴⠏⠀⠈⠻⣧⠀⢿⡷⠾⠃⣾⡇⡜⢀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣷⡄⢸⡆⠘⢷⡤⣼⠀⠘⣿⣁⣤⡤⢶⣾⡟⠀⠘⠿⣶⣤⡼⠟⢁⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⣿⡟⠁⠀⣀⣤⣾⠀⠀⠙⠻⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠈⣧⡀⠘⠿⣦⣾⣯⠽⠋⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠛⠛⠓⠦⣤⡀⠉⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡒⠊⠉⠻⣦⠀⠀⠀⠀⣀⣤⠤⠤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣹⣿⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⣿⠀⠀⠀⣾⠋⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣾⣏⣀⠀⣰⣧⣤⠴⠋⠉⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⢁⣀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠰⠿⠿⠃⠀⠀⠀⠀⠀⠀⠰⣶⡶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡶⢟⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠛⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⡶⠖⠛⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⢀⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣦⠤⠤⠴⠖⠒⠒⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡾⠀⢀⣠⠔⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⢯⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⡼⠃⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡴⠊⠀⠀⠀⠀⠀⠀⠀⣆⠀⢾⣇⣼⡿⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⡵⠋⠀⠀⠀⠀⠀⠀⢀⣄⣴⢻⢰⣼⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⣯⠄⠀⠀⠀⠀⠀⠀⠀⣸⡾⠁⢸⡾⣧⣳⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡼⢹ ⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢸⡟⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⡾⠃ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡴⠻⣤⠀⠀⠀⠀⠀⡇⣰⣯⣹⡧⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣠⠞⠁⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⣎⠙⣇⠀⢨⣧⡀⠀⠀⠀⢿⣿⣿⣿⣯⠀⠀⠀⠀⠀⡴⢁⡤⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠿⠶⠦⠤⣿⡀⠀⠀⠀⢸⠁⠈⢦⡈⢳⣸⣿⣧⠀⠀⠀⠈⢿⣿⣿⡷⠤⠀⠀⣤⣾⠜⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠸⠇⠀⠀⠈⠳⣟⣿⣿⠇⢀⣀⣀⡉⠉⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⢀⠀⠀⠀⠀⠀⠀⢀⣀⡟⢦⡀⣄⠀⠀⠀⠀⣰⠃⠀⠀⠰⢯⣶⠴⣛⡶⠒⠂⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⢿⠀⠀⠀⠀⠀⠀⢀⡟⠇⠈⠛⠿⠓⠲⠖⠚⠻⣄⡀⠀⠀⠀⣙⡉⠁⠀⣀⠤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠹⣆⠀⠀⣀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⣩⢽⠁⡰⠿⡄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⠤⣈⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⠜⠹⣀⣠⢾⠞⡥⠀⢀⠀⠘⣦⠴⣍⣉⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠟⠒⢦⠘⢣⡇⢰⠁⠀⠈⡗⠦⠥⠴⢯⣭⣍⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣒⠋⠉⠉⠀⠀⠀⠀⠀⠉⢹⠃⠈⠁⠀⠀⡇⠀⠀⡴⠋⣼⠀⠀⠀⠉⠉⠓⠲⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠉⠉⠓⣦⠤⣀⡀⠀⠀⢸⠄⠀⠀⠀⠀⢷⣄⣾⢖⡼⠁⠀⠀⠀⠀⣠⠴⠊⡽⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣞⡉⠉⠙⠺⣍⠙⠒⠾⣅⡀⠀⠀⠀⠀⠙⣏⠁⠀⠀⠀⢀⡠⠞⠁⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⣿⠀⠀⠸⣶⣷⣆⢠⡞⠉⡇⠀⠀⠀⠈⠑⠦⣄⡀⣠⠏⠀⠀⣀⠴⣿⠶⠶⠶⠾⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠾⠭⠤⠤⠤⣿⠀⠀⠀⠙⠹⡟⢾⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣤⠞⠁⡼⢉⣿⣠⣤⡁⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⢹⠛⠛⡿⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠒⠒⠶⠶⠶⡿⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⢀⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⠃⣸⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣀⠀⡟⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣰⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⣸⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⢀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⡆⠹⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡠⡀⢘⢱⢰⢸⠐⢸⢀⢔⡄⡶⠀ ⠀⠀⠀⠀⠀⠓⣄⡁⠠⣈⠸⣏⣀⡽⠘⢭⡸⣠⠃⠀ ⠀⠀⠀⢰⣄⣠⡘⠧⠶⠋⠀⢀⣀⠤⠒⠒⠠⣙⢄⡀ ⠀⠀⠀⠀⠑⢢⣸⠀⢰⠊⡉⠁⡀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⢀⡠⠖⣩⠉⠁⠉⢀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀ ⡴⡾⠁⠀⠀⠁⠀⠀⠀⢈⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⣇⠠⢄⡀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡀⠈⠛⠛⠁⢀⣤⣤⡀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿ ⣿⣿⠀⠸⠿⠟⠙⠻⠟⠋⠻⠿⠇⠀⣿⣿ ⣿⣿⠀⢠⣤⣴⣶⣤⣤⣶⣦⣤⡄⠀⣿⣿ ⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉ ⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡟⢻⡟⢻⣿⡆⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠀⠸⣿⣿⣻⣟⣿⣿⠇⠀⠀⣀⣀⠀ ⣾⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣷ ⠘⠛⠁⠿⠿⣿⣿⣿⣇⣸⣿⣿⣿⡿⠿⠈⠛⠃ ⠀⠀⠀⠀⠀⠈⣿⣿⡟⢻⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⠇⠸⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢰⣦⣭⣉⠋⠀⠀⠙⣉⣭⣴⡆⠀⠀⠀ ⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠀⠀⠀⠉⠉⠉⠁⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⢼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀ ⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⠀⢀⣠⣧⠀⠀⠀ ⠀⠀⣀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠈⢢⡟⠿⠹⣶⣤⠀ ⠀⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡏⠁⠀ ⠀⢠⠯⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢀⡆⣾⣏⣢⣄ ⣀⢟⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠉⢰⡋⢹⡿⠟ ⢸⣿⣿⣿⡿⣻⣆⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⢿⣟⣫⠿⣾⢿⣷⡦ ⠀⣸⡿⣿⢧⣴⣿⣽⣾⢇⠀⣆⡀⠰⣄⡀⠀⣵⢀⣶⢾⣽⣿⣾⣿⣿⣭⣀ ⠀⠉⠋⢹⣿⣿⣯⣿⣿⣾⣽⣿⣧⡀⣙⣿⣿⡟⣿⣿⣗⣛⣼⣿⣽⣿⡿⠟ ⠀⠀⠀⢀⣬⣿⣿⣿⡟⣻⠛⠻⣿⣿⣤⣿⣧⣿⡟⠛⣿⣿⣿⣯⡆⠉⠁⠀ ⠀⠀⠀⠀⠉⠻⣿⣤⡛⣳⢦⣼⡿⡁⢈⢻⣧⣼⣷⣿⡟⡷⠻⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⠘⣦⡟⠛⠻⠏⠪⢵⣿⡽⠛⡅⢿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠶⢤⣤⣤⣄⣀⣀⣀⣀⣡⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢷⣿⡿⠟⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠢⢀⡀⠀⠀⠀ ⠀⠀⡤⠒⠟⠻⠛⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀ ⠀⠠⡄⠀⢄⠀⠀⠀⠀⠄⠈⠂⠀⠀⠀⠀⠀⢀⣀⣀⡤⢤⣈⠂⠀⠀ ⠀⠀⣘⣆⠀⢁⡠⠸⢠⠄⠀⠀⠀⠀⠸⣉⠀⠁⠀⢀⡈⠸⣿⢹⣄⠀ ⠒⡎⡸⠠⡦⠞⠀⠀⢯⠀⠘⠋⠀⢀⡰⠿⢦⣀⡀⢈⣡⠔⣿⠀⡛⠃ ⠀⢷⠁⠀⢇⠀⠀⠀⠀⠉⠉⣹⠟⠋⠀⠀⣸⠇⠀⠀⠁⠀⣸⢠⠃⠀ ⠀⠀⣱⡄⠸⡀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣾⠊⠀⠀ ⠀⠀⣿⠈⢱⠀⠀⠀⠀⠘⢇⣀⣀⠔⠋⠀⠀⠀⠀⠀⠀⡸⡙⠀⠀⠀ ⠀⠠⡿⠀⠈⡆⠀⠀⠀⠀⠀⠀⢲⡤⠤⢤⠤⠀⠀⠀⣰⠁⡇⠀⠀⠀ ⠀⠀⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢰⢹⠀⠃⠀⠀⠀ ⠀⢸⠇⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡈⢸⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⡇⢸⠀⠀⠀⠀ ⠀⡬⠀⠀⠀⠀⠀⠀⢀⠗⠢⠤⠀⣄⣠⠊⠁⠀⠀⢰⢰⢸⠀⠀⠀⠀

⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⢀⠏⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠈⣽⡅⠀⠀⠀⠀⠈⢗⠀ ⡜⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣘⠁⠀⠀⠀⠀⠀⠀⠀ ⠓⢖⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠉⠉⠁⠀⠈⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⠀⠀⠀⠀⠀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⢤⡀⠁⠀⠀⠀⠀ ⢀⡀⣠⢞⣴⠟⠉⠀⠀⠀⠀⠀⠀⢀⡠⣴⢶⠭⠍⢺⠢⢄⣀⡈⢸⠁⣹⡅⠀⠀ ⠁⢻⡵⠋⠀⠀⠀⠀⠀⢀⡠⠔⢨⠷⡉⠀⠈⡄⠀⢸⠀⠀⠀⠷⡀⡄⠘⠁⠀⠀ ⢀⡟⠀⠀⠀⠀⢀⣤⠚⠛⢢⢔⡁⠀⠘⢄⡠⢴⠒⢺⠢⢄⡘⠀⣱⡇⠀⠀⠀⠀ ⠀⢳⠀⠀⢠⠖⣩⣿⣴⡶⠾⠉⠙⣲⣴⡉⢆⠈⣄⣸⠀⡰⠙⡴⠉⡇⠀⠀⠀⠀ ⠈⣿⡀⢰⡗⠉⠛⢻⠛⠋⠙⡖⠚⣻⡶⠿⣿⣯⣷⣤⣿⣶⣾⣏⣻⠒⠂⢶⡀⠀ ⠀⠋⣼⡋⠹⡄⠀⢸⠀⣀⠴⢿⡉⠀⢣⡠⠞⢧⣏⣹⡽⢆⢠⠓⡅⠀⠀⠘⠃⠀ ⣠⡾⢻⣷⠀⢳⢀⡼⣏⠀⠀⠀⢳⣠⠞⠑⢄⡘⠀⠀⡇⡨⢆⢘⠃⠀⠀⠀⠀⠀ ⣎⡽⣏⡿⣦⣸⡏⠀⠈⢦⠀⢀⠜⠳⢄⠀⢨⠋⠉⠉⠋⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⣏⣠⠞⣇⢸⣧⠈⢦⠀⠨⣷⡋⠀⠀⠀⢳⡯⠤⠄⢀⣠⠔⠱⠁⠀⢩⡏⠀⠀⠀ ⡟⣿⡀⣿⣏⠙⣷⣄⣳⡀⠁⠙⢦⡀⢀⡞⠀⠀⠀⠀⠀⡠⠃⠀⠀⠘⠃⠀⠀⠀ ⠧⣽⡿⡿⢸⣦⠹⣿⣿⢿⡖⠢⢄⣙⠾⣤⠤⠤⠤⠤⣖⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⡀⠘⣧⡿⣡⠞⣻⠿⠃⠛⠀⠀⠀⠈⠓⠾⠷⣶⠤⠊⠀⠀⢹⡅⠀⠀⠀⠀⠈⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠖⠋⠉⠉⠙⠓⠒⠒⠒⠦⠤⠬⠷⣄⣀⠀ ⠀⢸⠁⢂⠀⠀⡰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻ ⠀⣿⠀⢈⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⣿⢠⠋⠀⠀⠀⠀⢀⣠⠤⠴⠟⢲⠟⠉⠉⠓⠛⢏⡟⠋⠉⠉⠓⠲⡖⠒⢲⡞ ⠀⢿⠸⡀⠀⢀⣠⡞⠉⠉⡆⠀⠀⡇⠀⠀⢰⣾⡖⠈⡇⣶⣷⡆⠀⠀⣽⠀⠀⡇ ⠀⢸⠀⠉⠻⡏⠠⠐⠄⢰⠀⠀⠀⡵⢶⢤⣌⠚⢊⡼⣅⠑⠚⢁⣀⠴⣇⠀⢰⠋ ⠀⢸⠀⠀⠀⣇⠡⣀⠇⠀⡆⠀⠀⠑⢲⢆⠙⠚⠉⠀⠈⠉⢉⡀⠠⠴⠋⠀⣏⠀ ⢠⡞⠓⠒⠳⣿⡆⠀⠀⣀⢠⠀⠀⠀⢸⠀⠉⠐⡶⠲⡖⡖⢲⡟⠂⢀⣀⠀⡟⠀ ⣾⠀⠀⠀⠀⢸⠹⡄⠸⡀⠈⡇⠀⠀⢸⠀⠀⠀⠉⠈⠀⡗⠈⠀⠀⠁⠀⢹⡇⠀ ⠙⢦⣤⣀⣠⠞⠀⡻⢄⠈⠈⡇⡔⠢⡘⢍⡉⠋⠉⠢⣄⠇⠀⠀⠀⠑⠠⢂⡇⠀ ⠀⠀⠀⠈⠁⠀⢰⠃⠈⣇⠀⢃⠣⠠⠃⠐⠬⠭⠝⠫⠥⣜⣀⣀⡩⠜⢀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢳⢶⣿⣽⣿⣭⣿⣿⣿⣿⣷⣶⠾⢿⠭⠼⠬⠽⠿⢻⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⢹⠉⠉⠉⠉⠀⠀⢸⡅⢼⠁⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠊⢟⠲⡼⣤⠤⢤⡤⠤⠤⠤⠿⠿⠴⠶⡶⠶⣶⡾⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣷⠀⡦⠃⠑⢢⠤⠚⠁⠀⠀⠀⠀⢹⠒⠚⠁⠰⣷⡌⡦⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠈⠙⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⣸⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠒⠤⡀⠀⠀⢰⣁⠀⠉⠉⢲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣤⡤⠇⠀⠀⠀⠉⠈⠙⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣶⣶⣶⣤⡄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠊⠁⠉⠉⠛⠻⢿⣻⣶⣿⣿⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡾⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣠⠾⠠⠐⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⢹⣿⠃⠀ ⠀⠀⢀⡤⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⣹⣿⡿⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠛⠐⠢⠦⠄⠀⠀⡀⠀⠀⠈⠣⡴⠋⠉⠁⠐⢄ ⠘⠧⠀⠠⠄⠒⠒⠢⠤⢀⣀⡀⠀⠈⢫⠀⠀⠀⠐⢇⠀⠀⠀⢀⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡁⠀⠀⣀⣠⣄⡀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀

⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣴⠶⠦⠴⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀ ⠀⣸⠋⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠄⠀ ⢠⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀ ⣼⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣄⣤⠶⠾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⢦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣀⣤⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣤⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⠴⠶⠶⣶⣤⡀⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠇⢠⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣒⣛⣋⣩⣽⣦⣀⠀⠀⠀⠀⡏⢹⡟⠉⠉⣿⡏⠀⠀⠀⠀ ⣠⢶⣤⣴⡿⣫⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢚⣋⡵⠛⢹⡍⠉⠁⠀⢸⠀⠉⠙⠒⠶⢼⡁⠀⢳⠀⠐⣿⡇⠀⠀⠀⠀ ⠀⠈⣿⣥⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠉⣽⢿⡍⠀⠀⠀⠀⢷⠀⠀⠀⠸⡆⠀⠀⠀⠀⣸⢧⠀⢸⠀⠀⠙⠁⠀⠀⠀⠀ ⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣋⠁⠀⣠⠞⠁⠀⠙⢦⠀⠀⠀⠘⣇⠀⣀⣠⣇⠀⠀⠀⢠⠇⠈⢧⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠁⠀⠉⠛⡿⢧⣀⠀⠀⠀⠈⢷⣤⠤⠞⢻⠉⠉⢰⠉⠓⠦⢤⡞⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⡄⠀⠀⠀⠀⢠⡴⠋⣹⣿⣇⣤⣤⣶⣾⠟⠒⠺⢷⣦⣄⣴⠏⠻⡄⠀⠸⡄⠀⢸⠀⠀⢀⡼⠻⣄⣰⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣸⡇⠀⠀⢀⡼⢋⣀⣴⣿⣿⣿⣻⣯⣭⣭⡅⠀⠀⣐⣚⡻⠿⣶⣄⡹⣄⣠⡷⠴⢾⢦⣤⡞⠁⢀⣾⣥⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣇⠀⢰⣿⡿⠋⠁⠸⠿⢿⡛⠉⠉⠉⠙⣿⠛⠛⠛⢻⣿⣿⣷⣾⣿⣿⣥⣿⣷⣤⣾⣿⣿⣿⣛⣻⡇⣚⡟⠒⠒⠒⣶⣖⠀⠀⠀ ⠀⠸⣿⠟⣶⣾⡿⢿⡄⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⣤⠴⠖⠛⢿⡄⠀⠀⣹⡿⠛⣿⠿⠿⡟⢿⡛⠉⠛⢿⣟⢻⠃⠀⠀⠀⠺⣿⡆⠀⠀ ⠀⠀⠉⣴⣿⡇⠀⠈⣿⠀⠀⠀⢸⡇⢀⣠⡴⠞⠙⢷⡄⠀⠀⠀⢳⣤⠞⠋⠙⢶⣯⣤⣤⣷⠶⢻⡄⢰⠏⢙⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⣠⣼⣿⣿⣧⡄⠀⢸⣧⠀⠀⣸⣿⠋⠁⠀⠀⠀⠀⣽⡄⠀⣠⠞⠻⢦⡀⠀⡼⠁⠀⠀⢹⠀⠀⣹⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⣿⣟⣁⣿⣿⡇⠀⠀⣿⣠⡾⠋⠙⣧⡀⠀⠀⠀⠀⠀⣷⡞⠁⠀⠀⠀⠹⣾⣧⣤⣤⣀⣸⣶⠞⠉⢹⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢁⣽⣿⡁⣿⣿⣷⡀⢻⣟⠀⠀⠀⠈⢿⡆⠀⠀⢀⡼⠛⠻⢦⡀⠀⠀⢠⡟⠀⠀⠀⠀⠹⡇⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠟⠁⠘⣿⡟⠀⢻⣿⠏⠙⣦⡀⠀⠀⠀⢿⣄⣰⠟⠀⠀⠀⠀⠙⣦⠀⡾⠁⠀⠀⠀⠀⠀⡇⢀⡴⠋⡽⠒⠒⠒⠦⣤⡤⠀⠀⠀⠀⠀ ⣿⣄⣤⠾⠛⣿⡄⢸⣿⣧⡀⠈⢻⣄⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⠧⠶⠶⠶⠤⢤⣤⣷⠋⠀⣰⠃⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀ ⣿⢿⣯⡁⠀⢿⣿⡞⠉⢻⣷⣄⠀⠹⣦⠀⠘⠁⠙⠳⣄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠃⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀ ⡇⠘⣿⣷⣤⣿⡏⢻⡆⠀⣿⣿⣿⣶⣿⣷⡄⠀⠀⠀⠈⠻⣦⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣧⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⣤⣿⣿⢿⣼⡇⠘⣿⡆⠈⢿⣿⣿⣿⡿⢿⡛⠓⢦⣄⠀⠈⣻⣯⡤⠤⠤⠤⠤⠤⣤⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⡈⣿⣤⠞⢋⣿⣦⣼⣿⣿⠋⣾⡿⠀⠀⠀⠈⠙⠻⢷⣤⣉⣳⣄⣀⡀⠀⢀⣰⠛⠛⠒⠒⢶⡶⠒⠂⠀⠀⠀⠀⠀⠀⠐⣷⠀ ⣀⡀⠈⡿⣷⣿⠷⣄⡛⠀⢸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠈⠉⠉⠋⠉⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⡴⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣟⡋⠙⠿⣦⠀⢀⣠⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠿⠟⠀⠀⠀⠰⡘⡟⠿⠿⠙⢷⣶⣶⣦⠀⠀ ⠀⠀⣠⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢃⠀⠀⠀⣸⣿⠿⠟⠀⠀ ⠀⠈⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⡀⠀⢠⣿⡅⠀⠀⠀⠀ ⠀⠀⠀⣨⣉⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢧⠀⣸⣿⡟⠳⠀⠀⠀ ⠀⠀⣼⡏⠉⠙⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⣤⠾⠐⣿⣿⣷⣴⣿⣿⣷ ⠀⣀⣟⢻⣒⣾⣟⣻⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠋⠀⠀⢸⡏⠉⢹⣿⣿⠿⠟ ⠸⣷⣤⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣈⣤⣴⡶⢶⣿⣿⣦⣾⣿⣤⣄⠀ ⠀⣛⣿⣿⣿⣿⣿⡿⢯⣿⣿⣤⣤⡒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠈⠻⣿⣿⣉⣠⠞⠻⣿⣿⢻⣿⣿⡿⠇ ⠀⠉⢙⣿⣿⣿⣿⣶⢀⣴⣿⣟⢿⣷⣾⣧⠀⠀⣠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⣇⠀⢠⣤⣠⣼⣻⣟⢿⣦⣾⣿⣿⣿⣏⠉⠁⠀ ⠀⠐⣿⣿⣀⣹⣯⣻⣿⣿⣿⣏⣿⢳⣿⢿⣇⣠⣿⣿⣦⠀⠈⢿⣿⣤⣤⣠⣼⣿⣆⣾⣿⣏⠻⣿⡿⢶⣿⣻⣿⡿⣷⣿⣿⣶⡆ ⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣏⣿⣿⣿⢧⣄⠀⠀⠛⣿⣿⣿⣿⡿⢿⣿⣿⣿⢻⡿⢳⣼⣿⣿⣮⣿⣿⣿⡿⠿⠏ ⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣷⡞⠉⣻⣿⡜⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠉⠿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠋⣽⡿⠀⠀⠸⣿⣿⣿⣿⣶⣿⣿⣿⣶⣿⣿⠉⠈⢹⣿⣿⣿⣿⣿⣷⣋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠿⢿⣻⣇⣀⣽⠿⢿⣧⣄⢀⣶⣿⣿⠉⠁⠹⣿⣿⠏⢀⣼⣿⣤⣶⣾⢿⣯⣥⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⡷⠀⣸⣋⣻⣿⣯⣽⡍⢦⣤⠄⣸⣿⣿⣿⣽⡿⢿⣿⣿⣤⠇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢷⣤⡭⠙⠋⠉⢿⣿⠙⠳⠶⣾⣿⣿⣭⠙⠉⣇⠘⢿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⢀⡿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣶⣶⣶⣂⣀⣀⣀⣀⣀⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠈⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠖⠒⠂⠀⠀⠀⠒⠒⠦⢄⣀⠀⠀⠀⠀⣄⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠸⡇⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣇⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠤⡤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⠀⢷⣄⣈⣧⠎⡴⠂⠉⠉⠐⠦⡈⠻⠟⠛⢲⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⢧⢠⡇⠀⠀⠀ ⠀⠀⣀⡀⠘⡆⢹⣿⠀⡇⠀⠀⣴⣯⣶⣷⢠⣞⣛⡉⠉⠑⢯⠓⣦⣀⠀⠀⠀⠀⣸⢾⠀⠀⠀⠀ ⢀⡾⠁⠉⣻⣧⣿⠉⢦⡈⠲⠤⢹⡿⡿⣃⢸⣿⣿⡿⠀⠀⠀⡇⣟⡟⢷⣦⠀⢠⣏⡾⠒⠲⣄⠀ ⢸⡇⠀⢿⣷⢛⡏⠀⢀⣍⠓⠒⠒⠒⠉⠉⠣⣙⠻⠤⠤⠤⣊⡴⠿⠥⢄⣸⣷⣾⣏⠀⠀⠀⢈⡇ ⠀⢧⠀⠘⣿⣾⡀⠀⠀⠈⢳⣤⣀⡀⠀⠀⠀⠈⠉⢒⠒⠋⠁⠀⠀⠀⠀⡿⠀⠙⢿⣶⠤⠤⠚⠁ ⠀⠈⢧⡀⠈⢻⡈⣢⣄⠀⠀⠙⠢⠬⣉⣉⠽⠿⠛⠉⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠹⣧⡀⠀⠀ ⠀⠀⠀⢳⣄⡸⠙⣿⠋⠉⠒⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡟⠀⠀⠀⠀⠀⠏⢳⡀⠀ ⠀⠀⠀⢸⠥⡇⠀⠀⠀⠸⠉⣲⣦⠤⢀⣉⠉⠙⠒⠚⣏⢭⠉⠀⣀⣼⡁⠀⠀⠀⠀⡀⡆⠀⢧⠀ ⠀⠀⠀⢸⡞⠀⠀⠀⠀⢧⢸⣿⣽⣿⠀⣠⠃⠀⠀⠀⢹⡿⠟⠛⠲⢇⡙⣧⠀⠀⢸⠟⠁⠀⢸⡄ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⢦⣙⣛⡡⠞⠁⠀⠀⠀⡰⢏⣤⠀⢀⠀⣄⡝⠙⡇⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⢀⣈⣷⣄⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠚⠿⢶⣿⠞⠻⠥⠴⠃⠀⠀⠀⠀⠀⣼⠁ ⠀⠀⠀⠸⡉⠙⢿⣿⠶⣤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠱⠄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀ ⠀⠀⠀⠀⠙⢦⡄⣻⠗⠋⠈⠉⢻⣒⠒⠲⣶⣶⣶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠤⢔⣶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢯⣍⣉⣩⣽⡎⠛⠷⣄⣀⠀⠀⠀⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠒⠖⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢿⡟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠛⠀⣿⠀⣀⣀⣀⣀⡤⣄⣤⠤⠶⠶⠦⣤⣄⣸⣿⣿⣆⠠⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⢠⣾⣿⠾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⠒⠓⢤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡇⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡼⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⢀⡦⣿⡏⠉⠉⠁⠈⡹⡖⢶⣦⠤⣀⠀⠀⡷⠊⠀⠀⠀⠀ ⠀⡠⠒⠘⠿⢋⠁⡄⠀⠀⢀⠠⠔⠚⡁⠀⣿⢸⣹⡁⠃⣸⣶⠀⢀⣶⡁⣇⡜⠈⡆⠸⠙⡶⠁⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⡆⠘⡤⠊⠁⠀⡇⠀⢻⣶⡿⢽⣿⣿⣿⠟⠻⣆⡼⢻⣿⣿⣿⢿⣷⡇⢰⣷⠀⠀⠀⠀⠀⠀ ⠐⢄⠀⠀⢀⡼⠁⠀⢻⠀⠀⠀⡄⠀⠀⢘⡇⠨⣽⡿⠿⠀⠀⠋⠀⠰⢿⡿⠟⢸⠿⠀⢸⠙⠧⠀⠀⠀⠀⠀ ⠀⠀⠉⠋⠁⠀⠀⠀⣾⣇⠀⠀⢰⠀⠀⡌⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡆⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⢸⠀⠀⠈⡇⠀⢡⢧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠇⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⢳⠀⠀⠸⣄⠘⣿⣶⣤⣄⣘⣉⣛⣦⡤⠔⢺⠏⠀⡼⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣦⠀⣠⣬⣦⣼⣿⣄⠈⠙⢢⣼⡍⢻⣦⣼⣇⣰⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⣿⣿⣿⣷⣄⡟⡏⠹⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣘⡍⢣⡀⠀⠀⠀⣼⡟⠛⠁⠈⢿⣿⣿⣯⣈⣷⣿⣼⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠧⠀⠀⠀⠃⠀⢙⣿⣷⣤⡟⠳⠶⠶⠶⠚⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⠙⣯⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀ ⠸⣯⣥⠠⠄⠀⢀⣾⣿⣿⣿⠛⢦⡀⠀⠀⠀⣿⡛⣫⣿⣿⠿⠋⠀⢹⣏⢻⣄⡿⣶⠶⣿⣿⣿⣄⠀⠻⡁⠀ ⠀⠘⠓⠒⣲⣶⠻⠊⣿⣿⠃⠀⠈⢿⣦⣀⣸⣿⣿⢿⣿⡁⠀⠀⠀⢘⣿⣼⡇⠀⣿⡄⠹⢿⣿⣿⣇⢠⠛⣆ ⠀⠀⠀⠀⠛⠿⣤⣾⣿⠁⠀⠀⠀⠈⢻⣿⣿⠋⠀⢺⣿⡛⠛⠛⠛⢻⡟⢹⡇⢀⣿⣧⠈⢸⣿⣿⡏⠙⠛⠋ ⠀⠀⠀⠀⠀⠀⠈⠙⠾⣤⣄⠀⠀⣠⠟⢻⣯⠀⠀⠈⣿⡇⠀⠀⠀⠸⣗⠈⣷⡚⠃⢿⣦⡼⠟⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠞⠁⠀⣼⣇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠹⣧⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠷⣄⡰⢾⣿⣇⣀⡀⠀⠀⣿⡴⠆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⢤⣬⣷⣾⡿⠤⣬⠽⠿⠿⡿⠧⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣼⣶⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⢿⣿⠟⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⡁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⠟⠟⠋⠉⠁⠀⠀⠀⠙⠂⢤⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠤⢾⣿⣿⣿⣿⣿⣿⠿⠛⠿⠟⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀ ⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀ ⠀⠀⢸⣦⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠴⣤⣠⣄⠀⠁⠀⠀⠀ ⠀⠀⠀⠹⣦⠀⠀⠘⢄⠀⠀⠁⠄⠁⠀⢈⠀⠀⠀⠠⠀⠀⠈⢀⠤⠥⠆⣠⠔⠋⠉⠉⠉⠑⠢⣙⣿⣿⢶⣄⠀⠀ ⠀⠀⢀⣠⣼⣧⠀⠀⠐⣴⡴⠀⠘⢢⢖⠋⠀⢀⣀⠀⠀⠀⠀⠈⢳⣤⠎⠁⠀⠀⠀⠀⣤⣤⠀⠈⣿⣷⠀⣿⣧⠀ ⠤⢴⡋⢁⡿⠀⢣⢀⣴⠏⠀⠀⠐⣿⠋⠀⠀⠿⡿⠃⠀⠀⠀⠀⣼⣿⣦⡀⣀⠀⠀⠀⠛⠛⠀⣠⢿⣿⠀⠸⣿⠿ ⠀⢸⠁⡾⠁⠀⣿⡈⠁⠀⠀⠀⠀⠈⠷⣄⣀⣀⣀⣀⣀⣠⡼⠞⠋⠉⠙⢿⡟⠲⠤⠤⠴⣶⠟⠁⠸⣿⠀⠀⣾⠀ ⠀⠸⣾⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣿⠟⠛⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⣼⠃⠀ ⠀⠀⠙⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⢀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⢘⣿⣴⠋⠀⠀ ⠀⠀⠀⢸⣿⡂⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⣼⡇⠉⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⡇⠀⠀⠀⠀ ⠀⠀⢸⣿⠇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠶⠴⠤⢤⣤⡤⠀⠀⠀⠀⠀⢠⣿⠁⣸⠁⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠦⠴⠜⠁⠀⠀⠀⠀⠀⢀⣿⣿⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡇⠀⡏⠀⠀⠀⠀⠀ ⠀⠀⢸⡟⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢸⠃⢠⡇⠀⠀⠀⠀⠀ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⣼⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⢰⢿⡀⢸⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠛⠶⠦⠀⠴⢦⣠⡟⠁⠀⠀⠀⠀⠀⠀⣸⢸⡇⢸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠿⠷⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠉⠉⠉⠛⠛⠛⠿⠶⠶⠶⠶⣦⣤⣄⣀⡀⠙⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢰⣿⠀⢀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠛⠛⠛⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⠷⠶⣦⣀ ⠀⠀⣼⡇⠀⠸⡀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠐⣿⠁⠀⠈⢻⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⣿⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⣿⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⢿⠟⢲⣾⠟⠉⠉⠉⠛⠛⠛⢿⡍⢩⡿⠋⠉⠉⠉⠙⠛⠛⢶⣶⠶⠖⠲⣦⣾⢿ ⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⢧⡀⠉⠉⠁⠀⡾⠁⠀⠀⠀⠀⣀⣀⣀⠀⠻⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣿⠀ ⠀⠀⣿⠀⢸⣆⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⢈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⢱⣷⡆⢳⠀⣿⠀⡯⣾⣶⢹⡆⠀⠀⠀⢠⡇⠀⠀⠀⢸⡇ ⠀⠀⣿⡀⠀⠻⠷⢶⣾⠏⠁⡠⠤⢄⠀⠀⣼⠀⠀⠀⠀⠀⢷⣠⣀⣀⡀⠘⠦⠽⠵⠋⣰⡟⠀⠳⠬⠵⠞⠀⠀⠀⢀⡾⠁⠀⠀⢀⣾⠁ ⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⢸⠀⠀⠘⡄⠀⣇⠀⠀⠀⠀⢰⡟⠙⡧⠍⢝⢷⠀⢀⣠⡾⠋⠙⢦⣀⠀⣀⣠⡤⠶⠚⠉⠙⡇⠀⠀⣼⠃⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⣿⡄⠸⡀⢀⡸⠃⠀⠘⡆⠀⠀⠀⠀⠙⠒⣿⣶⡄⠸⠛⠛⠁⠀⠀⠀⠀⢉⣉⣁⣀⣀⣀⣠⡴⠞⠁⠀⠀⣿⠀⠀ ⠀⠀⣸⣷⣄⣀⣠⣄⣿⣷⡀⠈⠉⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣿⠈⠻⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠻⣤⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⣾⠏⠉⠉⠉⠁⠙⢿⣎⢷⡀⠀⠀⠀⣀⣀⢸⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⢹⠉⠉⣿⠉⡟⠉⠉⣿⠉⠁⠀⢀⣠⣀⡀⢰⡏⠀⠀ ⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⢺⠁⠀⠙⢿⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⠒⠒⠋⠀⢷⠖⠚⠁⠀⠀⢰⠁⠀⠀⠙⣾⡆⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠀⠀⣹⡆⠹⣦⠀⠘⢦⡀⢀⣼⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⠟⣇⠀⠀ ⠈⠻⣦⣄⣄⣀⠀⣀⣼⡏⠀⠀⣿⠶⣄⠀⠈⠁⢸⠀⡤⠚⠒⡄⠹⢧⣀⠈⠙⠂⠀⠉⠳⣤⣠⡟⠀⠀⠀⠀⠀⠀⠙⠤⠤⠋⢸⡏⠀⠀ ⠀⠀⠀⠉⠈⠙⠛⠋⠁⠀⠀⣸⠋⠀⢹⡆⠀⠀⢸⡆⣇⠀⠀⢸⠚⢄⡉⠛⠲⠶⠶⡶⡶⠞⠋⢀⡷⠀⠀⠀⢴⠋⢲⡀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣄⡀⢀⣇⣈⡓⠒⠁⠀⠀⠙⠒⠒⠛⠉⠉⠉⠙⢛⣋⣤⣤⣤⣄⣈⣓⣊⣀⣠⣴⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣶⣶⣿⣿⣙⣻⣻⣉⠛⠿⣿⣛⣛⣛⣿⣻⣷⣶⣶⠾⠟⣿⣉⣀⣨⣇⣈⣭⣿⣭⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠛⠛⠫⠭⣿⠽⠿⠿⠿⠿⠯⠯⠯⠯⠿⠽⣯⣉⡉⣽⡯⠭⠤⠤⠤⠤⠤⠔⠰⢾⡯⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣷⣤⣄⡀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣘⣷⣶⣾⣁⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢻⣌⠙⢿⠻⠷⠖⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⣿⡋⠉⠉⠉⣹⡏⠉⠉⣿⠩⣋⠙⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠀⣦⣼⠇⠈⠳⢦⣤⣤⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⢻⠟⠛⠉⠀⠀⣾⣡⢂⠜⣦⣬⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⡇⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠙⠿⢼⣆⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠾⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠳⠶⢤⣄⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠫⢽⣒⣦⣤⣄⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣶⡶⠞⡁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢿⣦⣼⣿⣿⣿⣿⣿⣿⣟⡲⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠋⠁⠀⠈⠉⠀⠉⠛⠻⢿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣟⢻⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢀⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⢹⣷⣿⣿⠇⠀⠀⠀ ⠀⠀⣠⡿⠏⠁⠀⠀⠀⠀⠀⣾⣿⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⢠⠿⠿⠿⠿⠄⣀⠀⠀ ⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠦⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠓⣲⠋⠀⠀⠀⠀⠀⠀⠹⡄ ⢿⣇⠀⠀⠀⢀⣀⣠⡴⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⢠⣾ ⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠤⣤⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⢀⡀⠀⠀⠴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢻⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠤⠶⠒⠋⠉⠉⠉⠙⠓⠲⠾⡏⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠀⠀⠀⠀⠈⠉⠉⠛⠶⠦⣄⡀⠀⠀⠀⠀⢰⣀⡀⠀⠈⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⢻⡇⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⢸⡇⠐⢒⠖⠒⠒⠒⠒⠲⠶⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⢰⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣦⡀⠈⣷⣴⠃⣴⠞⠉⠉⠉⠙⠢⣄⠈⢷⡼⠟⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢯⠉⢻⣯⡇⢸⡇⠀⠀⠀⣤⣶⣦⣸⣆⠀⣠⡶⠞⠛⠛⠲⢭⡛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀ ⢀⣴⠖⠲⣄⣸⡆⣼⡟⣇⠈⢷⣀⠀⠈⣿⣿⣿⢯⡏⢸⢱⣾⣷⣦⠀⠀⠀⠙⣄⢸⣿⣶⣤⠀⠀⠀⠀⣿⢃⡏⠀⠀⠀⠀⠀ ⣾⠃⠀⠀⣨⡿⣿⣽⠃⠙⢧⣀⠉⠒⠲⠼⠟⢛⣉⣴⠘⣞⣽⣿⡟⠀⠀⠀⢀⡟⣼⢀⠏⠻⣷⣆⠀⢰⣧⡾⠋⠉⠉⠳⣄⠀ ⣿⠀⠀⢿⣿⡖⢋⡇⠀⠀⢀⡉⠙⠓⠒⠒⠚⠉⠁⠈⢳⣌⠛⠶⠤⣤⡤⢶⣋⣴⠿⠿⢤⣄⣠⣿⣧⣾⣿⠀⠀⠀⠀⠀⢹⡄ ⢻⡄⠀⠸⣿⢷⣾⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠶⠛⠋⠀⠀⠀⠀⠀⣸⡇⠙⠳⣿⡧⣀⣀⣀⣠⠟⠀ ⠈⢿⡀⠀⠙⠿⣿⢦⣄⠀⠀⠀⠈⠻⣍⠓⠲⠤⠤⠤⠤⣤⣤⡤⠾⠄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⢻⣦⡉⠉⠀⠀⠀ ⠀⠈⢷⡄⠀⠀⣿⣄⡭⣳⣤⡀⠀⠀⠈⠙⠒⠲⠶⠖⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢻⣳⣄⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⡟⠙⢏⡟⠀⠉⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡟⠀⠀⠀⠀⠀⠀⠀⡇⠻⡆⠀⠀ ⠀⠀⠀⢰⣇⣠⡇⠀⠀⠁⠀⢰⠓⠲⢤⣀⣀⠉⠉⠉⠒⠒⠶⠶⠶⡖⢒⡋⠉⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄⠀ ⠀⠀⠀⢸⡀⡼⠀⠀⠀⠀⠀⣿⢀⣴⠿⠻⣦⡉⠙⢓⡦⠀⠀⠀⠀⢳⣳⣾⣠⣤⣚⣻⡟⢷⣄⠀⠀⠀⠀⡞⣼⠃⠀⠈⣧⠀ ⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⢿⡸⣿⣻⣷⣿⠇⢀⡞⠁⠀⠀⠀⠀⣰⡟⠋⠉⠉⠉⠙⠢⣤⣻⣦⠀⠀⠐⠟⠁⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠈⢳⣌⡉⢉⣡⠔⠋⠀⠀⠀⠀⠀⡴⢿⣠⡇⠀⢀⡄⢰⡄⡿⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⣶⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠓⠮⣝⣷⠤⢾⣥⡾⣿⣁⣠⡾⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀ ⠀⠀⠀⢸⡛⠿⣿⢿⣦⣀⡀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⢹⡿⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀ ⠀⠀⠀⠀⢷⣄⠈⠳⣝⣌⢙⣷⠾⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⣒⢹⡿⠛⠁⠀⠀⠈⢿⣉⠙⠛⢒⣲⣶⣶⣟⠛⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣺⡽⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⣯⣭⣉⣙⣉⣩⣶⠙⠷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠙⠓⠶⠶⠶⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣸⣴⣶⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠿⣟⣅⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠿⠟⠋⠉⠉⠉⠙⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⡿⡿⡿⠟⠽⠋⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣤⠀⠾⠚⢿⣿⣿⣿⡿⢿⠿⢟⠿⠟⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣦⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣗⡀⠀⠀⠘⣄⠀⠀⠀⠀⣄⠀⣄⡀⠉⠲⠄⠀⠀⠈⠑⠀⠁⠀⠠⡄⠀⠀⢤⡀⢀⣀⠀⣠⡴⠦⠤⣭⣭⣉⠛⠶⣿⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠈⠳⣄⠀⠀⠀⠱⡀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣖⡳⠒⠛⢀⡴⠛⠁⠀⠀⠀⠀⠀⠈⠻⢦⣹⣿⡟⠿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣸⣷⡀⠀⠀⠘⢆⣦⡴⠆⠘⠓⣠⠞⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣴⠋⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⢻⣿⣷⠀⣾⣿⣆⠀⠀ ⠀⠀⣀⣀⡴⠟⢁⣿⠀⢳⡄⠀⢠⣾⠏⠀⠀⠀⣴⣯⠞⠀⠀⢰⣿⣿⡧⠀⠀⠀⠀⠀⠀⣙⣿⣧⠀⠀⠀⠀⠀⠀⠀⢽⠿⠿⠄⠀⣸⣿⣿⠀⠉⣟⣿⣶⠄ ⠈⠉⠉⢹⡷⠀⣼⠃⠀⢦⣷⠴⠟⠁⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢄⣴⡿⠟⠿⣿⣦⣓⠄⠀⠀⠀⠀⢀⣀⣤⡞⠉⣿⣿⠀⠀⠈⡿⠈⠀ ⠀⠀⠀⢸⠀⣼⠏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣶⣤⣤⣤⣤⣤⣤⣤⡾⠟⠉⠀⠀⠀⠈⢿⣏⢉⡛⠒⠒⠒⠻⣿⠋⠀⠀⢻⣿⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠸⣶⡏⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣹⣿⠿⠙⠂⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣱⣿⠀⣠⡿⠀⠀⠀ ⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢀⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣔⡀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⣧⡀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⡇⠈⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢀⣤⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⠛⠛⠛⠛⣛⡿⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠷⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⡏⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⢠⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⠁⠀⠀⠀⢸⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣼⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⢠⡟⢸⡆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠁⠘⠛⠛⠓⠖⠀⢚⣿⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠉⢳⣰⠋⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀ ⡀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠙⠷⠋ ⣰⠟⠉⠙⢦⡀⢀⣾⡟⠉⠳⣆ ⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠙⢧⡀⠀⠀⠀ ⠀⢀⡴⠃⠀ ⠀⠀⠀⠙⠶⣄⣀⠴⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⠟⠁⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢼⣿⠀⢿⣿⣿⣿⣿⠀⣾⣷⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣿⡀⠙⠋⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀ ⢀⣀⣀⣀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣾⣿⣷⣦⣤⣴⣿⣿⣿⣿⣤⠤⢤⣤⡄ ⠈⠉⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀ ⠐⠚⠋⠉⢀⣬⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣀⡀⠈⠀⠈⠛ ⠀⠀⠴⠚⠉⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠉⠛⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠇⣷⢶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡝⢚⣷⢿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠁⠉⠈⠀⠀⡀⢦⠉⣄⠑⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣼⣫⠛⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⣭⣯⣹⣉⣉⣤⠤⣖⠻⡈⢦⠘⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠇⣳⠴⢯⡴⢀⠀⠀⡄⠤⠢⠛⠈⠀⠀⠀⠀⡟⠚⠒⡀⣦⣷⠿⠤⣶⣛⢍⠤⠶⢰⠀⣆⠘⠋⣿⣴⠀ ⠀⠀⠀⠀⠀⣧⣸⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠋⠴⣠⢀⠀⠀⠀⠀⠀⡀⢄⠶⠓⠉⣀⠀⠀⠀⠀⣄⢹⡇⢀⠀ ⠀⠀⠀⠀⠀⡏⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⡄⣷⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⡄⢳⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⡀⠹ ⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠑⠀⠀⠀⠃⣾ ⠀⠀⠀⠀⠇⢀⡇⢸⠀⠀⠀⠀⠀⠀⠃⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⣀⣳⣾⠓⣴⠀ ⠀⠀⠀⠀⡟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠁⢸⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⡏⢠⠀⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠁⡿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀ ⠀⠀⠇⢠⠀⠀⠀⠀⡇⣼⠹⠀⠀⠘⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⡇⡾⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠳⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀ ⠀⡇⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⢦⠛⣿⣿⣿⣿⣿⣿⢿⠻⠙⠉⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀ ⠀⡇⢀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢧⠈⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣥⣼⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⢷⠀⡶⣶⡠⣤⢦⡴⡷⣯⡿⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠘⠀⠀⠀⠀⠀⡄⢹⠀⠞⢠⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⡼⢀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠈⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠎⣠⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢼⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⡆⠘⠀⠀⠀⠇⡼⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠋⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢤⠀ ⠀⠏⠀⠀⠀⠈⠳⡄⠀⠀⡠⠚⠁⠀⠀⠀⠘⡄ ⢸⠀⠀⠀⠤⣤⣤⡆⠀⠈⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡀⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⡼⢁⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⣴⠥⠼⠀ ⠀⠀⢠⡾⠉⠀⢠⡆⠀⠀⢸⠃⠀⠈⣿⣆⠀⠀ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⠃⣀⡤⢍⣈⡀⠀ ⠀⠀⠀⠀⠀⠙⠼⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⣓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡵⣆⣰⢦⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡴⣄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣋⣀⠀⣀⡀⠀⣠⣄⣠⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠉⠁⠈⠒⠃⣤⡈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣙⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣓⠏⠧⣔⡉⣇⡴⠒⠢⡏⠉⠉⠠⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡔⠁⠀⠀⠧⠃⠀⠉⠀⠀⠀⠀⠸⣽⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣤⠀⠀⠀⠀⢀⣤⡀⠀⡖⣆⡴⢦⣰⠛⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠁⠓⠉⠉⠉⠃⠀⠉⠉⠀⠀⠀⢠⢄⡀⣇⠀⠀⠀⠀⠀ ⠀⠀⣀⡖⠁⠀⠀⠀⠀⠧⠝⠀⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠉⡆⠀⠀ ⠀⠀⡧⣲⠖⣆⣀⣀⣀⡀⠀⢀⣀⡀⠀⠀⡰⠂⠦⡴⠛⡛⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⣠⠶⡄⠀⠀⠉⠋⠁⠀⠈⠉⠉⠀⢀⣤⠀⠀⢡⡀⠀⠀ ⢀⡤⠇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠀⠀⣹⡆ ⢯⡀⠤⠒⢆⠀⠀⢀⣄⢀⡤⢶⡤⠒⡆⡠⠶⡀⢀⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠋⠀⡏⠀⠀⠀⠀⠀⡇⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠖⢂⣽⣿⣿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟ ⠀⠀⠀⠀⣀⣤⡶⢿⣋⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⢀⣠⣾⠿⠋⠀ ⠀⢀⣴⣿⠟⠉⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⡿⠛⠋⠉⣀⣤⠶⠟⠋⠁⠀⠀⠀ ⢰⣿⡟⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⣿⣿⣟⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣧⣀⡠⠤⢾⣿⣷⠤⠄⠀⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⠇⠨⡦⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⢈⣹⠜⠻⢾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢠⣿⡵⠾⣻⣶⠿⠦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⢀⣠⣮⣦⡶⠻⠛⢶⣄⡀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣽⠏⠁⣠⣂⣦⣈⣝⣦⣄⠀⠈⠁⠀ ⠀⠀⠀⠀⠁⣠⣾⣵⣾⣾⠟⡙⠟⠿⣍⡉⠀⠀⠆⠀⠀ ⠀⠰⠀⠀⠄⣠⣶⣾⣭⡶⠟⠻⣶⡰⣜⣳⣦⣄⠀⡀⠀ ⠀⠀⠀⢀⣠⣴⣿⣋⡴⣪⠎⣄⡙⠻⠿⣯⣉⠉⠀⠀⠀ ⠀⠂⠀⢀⣉⡭⢿⡛⣛⣵⠎⠀⠙⢾⣶⣦⣭⣷⣦⠐⠀ ⠀⠀⢈⣙⣿⡿⠿⠟⣋⢅⡄⡄⡐⣄⢤⣉⠷⢦⣄⣀⠠ ⠐⠾⠿⢽⣷⡶⠶⡿⣓⣭⣾⣿⢷⣬⣓⢿⠿⠿⣯⣉⣁ ⠀⠀⠀⠉⠉⠉⠛⠛⠉⢀⣿⢿⡀⠙⠋⠓⠿⠿⠏⠉⠉ ⠀⠀⠀⠀⠀⠀⠠⠤⠶⠾⢿⡯⠷⠶⠤⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠔⠒⢺⠻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⠀⢀⣴⢳⣖⢁⡴⠂⢹⣉⣳⡀ ⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⣁⣈⣯⣛⡦⡤⠠⠔⠋⣠⠊⡸⠋⡠⢾⣹⡀⠀⢵ ⠀⠀⠀⢸⡟⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡴⠋⣀⣠⡷⠬⣉⡗⠒⢲⣾⣿⠔⢁⠜⢁⠜⠁⠀⠀⠀ ⠀⠀⠀⢸⠁⢀⣾⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⢁⠎⡠⠊⢙⠿⠓⠒⠢⡯⣁⠒⠋⢁⡤⠋⡠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣦⣾⠏⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡎⡸⢰⢁⠔⢁⡤⠒⠉⠉⡗⠢⢍⣉⣁⡠⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⠟⠒⠉⣉⣀⣈⣉⣹⣑⡗⠢⢤⣆⣀⠀⠀⠀⢸⡼⣹⠃⡇⡎⡠⠃⠀⠀⢾⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⠟⢹⡐⠊⢉⣀⠠⠤⠾⠿⠀⣉⣉⢺⠻⢷⢍⣹⣾⢟⡠⠊⣸⢰⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡿⠁⣠⣾⣿⣿⣧⡄⠤⠐⠒⠒⠒⠤⣤⣨⣍⣛⠒⠤⠄⢀⠠⠔⢹⣯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠰⡟⠉⢳⠊⢹⣷⠔⠒⠀⠉⠁⠐⠛⠛⠦⠬⣉⡑⠒⠠⠤⠔⢻⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⡀⠳⢄⢸⡎⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢒⣶⣾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠲⠤⠴⣗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⡻⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⣠⡀⠀⠀⠀⠀⠀⣤⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣻⡏⠀⢀⡤⢲⣒⡤⠨⡿⣃⡀⠀⢀⣀⣶⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⣀⣈⠉⠚⢶⠎⢀⣼⣿⣷⠔⠉⣉⣀⠀⠀⡹⡿⢯⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡉⠘⡳⠛⠋⠉⠉⠙⠛⠳⡉⠀⢰⠃⠀⢠⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠾⣠⡶⠬⡉⠉⡩⠶⣦⡣⠔⠁⠀⢀⡎⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⣸⡽⠇⠀⣿⣽⡇⡇⠀⠀⢀⠞⢀⣄⣠⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⡀⠇⡙⡛⡀⠅⡨⠃⠀⠒⢥⠀⢘⣲⠭⣪⠬⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣤⣮⣽⣤⣪⠀⠀⠀⣰⣩⡿⢳⣎⡏⠧⠷⢄⠀⠀⠀⠀ ⣦⣀⡠⢤⣾⣿⣿⠻⠿⠛⣿⡀⠀⠙⢒⡆⠉⠉⠀⣀⡠⢷⡒⠋⠀⠀⠀ ⠙⠏⢀⣾⣿⣷⠃⠀⠀⠀⢸⣇⡠⠔⠡⢍⡫⡭⢥⢰⢮⣏⣹⣢⢀⡀⠀ ⠀⡆⠺⢿⣿⣾⣄⠀⠀⢀⢆⠃⠉⢲⣄⠀⠀⠑⠪⠜⠚⣚⣩⣔⠉⠀⠀ ⠀⢸⠒⢠⡤⠀⢢⠭⠞⡗⣾⡠⠖⠙⢴⠓⢖⢲⢲⠾⣽⢳⡼⠬⠓⠄⣀ ⠀⢸⢰⠋⠀⠇⢸⠀⠀⢃⠛⠒⠒⠊⠉⠢⠤⣽⣾⣶⠭⠟⠉⠓⠒⠒⠉ ⠀⠀⢷⣇⠀⢸⣼⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡄⠀⠀⠀⠀⠀⣼⠀⠀ ⠀⠀⢀⣷⡀⠀⠀⠴⣶⣿⣶⠦ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⢻⠀⠀ ⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀