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