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

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