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