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