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⠉⠀⠀⠀⡜⠁⠀⠀⢀⣵⡟⠛⠛⠫⡑⢊⡁⠒⠀⠀⠈⠈⠀⠀⢀⣚⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢺⣲⣿⠿⣿⣽⣻⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠦⡹⢷⣾⣿⣿⣿⣿⣇⡇⡀⠀⠀⢹⣻⢈⢷⡀⠀⠐⢄⠡⠆⡑⠠⠀⠀ ⠀⠀⢺⡅⠀⠀⠀⢀⣿⣋⠤⠀⠀⠳⠞⠀⠀⠀⠁⠀⠀⣀⣠⣶⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠛⠉⠙⣿⣿⣿⠄⠈⢿⣾⢂⣽⡿⢟⢋⣁⣀⣀⠰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣜⣳⣷⣿⣿⣿⣿⣿⣿⣼⣿⣏⠀⠢⠘⣷⡌⡚⠿⣆⡈⠆⣊⠀⠈⠀⠀⠀ ⠒⠠⡏⠀⢄⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡉⢭⠖⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡠⠴⢊⣽⣧⣿⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢀⠔⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠠⣁⢻⣥⡙⢦⢩⡇⠸⣀⠀⠄⠀⠀⠀ ⠞⠲⠛⢲⣤⣠⡟⠁⠀⠀⠀⠀⠀⠀⣠⠶⠴⢚⡩⢐⠡⣊⡿⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣏⣠⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣤⢸⠃⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⠤⠤⣄⣠⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢏⠴⣩⣹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⡆⣼⣿⡉⢖⠣⡍⠱⢀⠠⠀⠀⠀⠀ ⣀⠀⠂⠉⠀⠁⠀⠀⠀⠀⠀⡀⣠⠖⡨⣣⢭⡦⠤⢧⣕⡩⣀⣀⡄⠀⠀⠔⠆⠀⠀⠀⣠⠞⡵⠋⢁⣾⣿⡿⡏⠿⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠘⠦⣀⡤⣀⠀⢠⠊⠀⠈⡧⡐⣬⢵⣀⢚⡶⢹⡟⢠⢈⡙⣒⡲⠤⠤⠤⠤⠴⠒⡒⠒⣈⢋⠛⡛⠶⣽⣹⣾⣿⢟⣋⣿⣿⣿⣿⣿⢻⣿⣷⣹⣾⡿⡘⢬⠓⡌⢁⠂⠀⠀⠀⠀⠀ ⣀⠤⡄⠀⠀⠀⠀⢀⡤⣲⠟⡩⢁⡴⣋⣁⠀⠀⠀⠐⢋⣥⣻⠋⣠⣠⠆⢲⠇⠀⠀⣴⣳⠞⠁⠀⣾⡿⠃⢈⡡⣾⣾⢋⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣶⡟⣆⠸⡀⠀⡴⢹⠐⣛⣺⣤⣟⣴⡿⡼⡐⠢⢔⡙⠻⠭⢿⣚⡳⢸⠦⢵⡌⡀⠆⡡⠘⠖⡛⡋⢭⡙⢮⣼⣿⠞⣿⢏⣽⣿⣿⢟⢷⢋⡱⡘⢆⡳⠨⡄⠂⠀⠀⠀⠀⠀ ⣄⡂⡔⠀⠀⠀⡴⣫⠚⡄⡮⡴⠿⢭⣒⡉⠝⢈⣴⢞⡩⡐⠿⢻⡧⣆⠀⠀⠀⠀⣼⠗⠁⠀⢀⣼⣟⠠⠒⠉⠚⠡⠑⠊⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⡹⡏⠀⢡⢸⣿⣿⣻⣟⣽⡾⣿⣷⣾⣷⣟⡿⣶⣭⢣⡝⢢⢒⡐⠩⢉⠋⣄⡐⠡⣂⢉⠒⡰⠁⠆⣉⠦⢼⡏⢻⠏⢢⢍⢣⠻⣾⢻⡆⡱⣉⠦⡱⢱⠐⠀⠀⠀⠀⠀⠀ ⡻⣷⠀⠀⢀⣮⠏⡤⢃⡼⠋⡵⠋⠁⠀⠀⠀⣸⠡⢆⡱⢨⢐⣿⢱⡽⡄⠀⠀⢸⡏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣀⠔⠉⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⣇⠀⠎⢈⣻⣿⣿⣻⣽⣿⣿⣿⣿⣟⣾⡝⣧⣎⠱⡈⢇⢊⣄⣓⣈⡒⣌⣹⠷⣈⣍⣛⣖⣶⠶⠤⣎⣘⣉⠆⡘⢄⢊⠤⢣⣿⡯⢇⠳⣌⠲⣡⠃⠌⠀⠀⠀⠀⠀⠀ ⡁⠇⠀⠀⠸⡁⢎⣰⠟⡤⣸⠁⠀⠀⠀⣠⠞⣡⠚⡄⣃⣶⡿⠀⢨⠴⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠰⠥⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠿⣣⣤⣴⣃⣪⢍⢫⣍⠙⡛⠻⣿⣿⣿⣿⣷⣾⣷⡾⣶⢶⣚⢯⡭⢷⢟⣚⣟⣫⣭⣭⢭⡍⣛⠷⣾⣥⡅⢦⠱⢌⠢⢎⢟⣿⡇⢎⡱⢌⠣⠆⡍⡀⠀⠀⠀⠀⠀⠀ ⡥⠠⣀⠅⣢⠵⠞⠁⡼⢱⡇⠀⢀⡴⠏⡱⠨⣐⠣⢰⡟⠉⣀⡰⢋⠰⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠻⠿⣿⠯⠷⢛⣛⡛⣛⢿⠶⠚⠀⠀⠀⠈⠉⡛⠻⢿⣯⣿⣟⣿⣟⣿⢾⣽⣻⢾⣽⣾⣻⢷⣻⢯⣿⢿⣾⣍⢿⢻⢆⠣⢎⠘⢢⠚⣿⠿⣳⠶⣊⠥⢋⠐⠀⠀⠀⠀⠀⠀⠀ ⡯⠑⡄⠊⠉⠀⠀⢀⠟⡼⠀⣰⡿⠛⣷⠠⢃⢠⠱⢸⢣⠏⡡⠒⠭⡐⣿⠋⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢼⣿⡿⠯⠤⣀⡀⠀⠀⠀⠀⠈⠒⠤⢀⡈⠙⠻⢟⠛⠛⠚⢣⠿⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⠾⣛⠬⡓⡌⠌⡁⢾⣿⠟⣡⡷⣈⢎⢡⠎⠀⠀⠀⠀⠀⠀⠀ ⡜⡱⢈⠁⠀⠀⠀⡼⡰⠃⠚⠃⠀⠀⣼⠣⣉⠦⢨⡟⡼⠖⢳⡉⠖⣡⢻⣸⢒⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠁⠀⣿⣿⣿⣿⣿⣿⣿⡿⣟⡬⠓⣌⠒⡡⠘⢠⠰⣾⣵⣞⡿⢰⢡⢊⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠗⠀⠀⠀⠀⠀⣠⡟⠁⡇⠀⠀⡠⠉⢸⢰⠡⢊⡟⣏⠡⡎⣹⠰⠩⠄⡟⡗⣾⣠⢗⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⣸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⡽⣿⣿⢿⣻⠵⣨⠓⡬⠑⡄⠃⠆⣰⢿⡷⣫⠘⡥⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⣰⠟⠀⠀⠁⠀⡴⠁⠀⣸⠌⡜⣉⠻⠯⣰⡇⡏⡜⢡⠭⡇⢃⡽⢯⠞⣳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡗⠀⠀⠀⠀⠀⣠⡺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣽⣻⣿⣿⣏⢷⣡⢋⡴⢩⡐⡩⣸⣿⣯⢞⣵⡿⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⡼⠁⠀⣰⠋⡜⡰⢄⢃⠣⢼⠁⡇⣎⠡⢊⣥⣦⡜⡍⢢⡼⣠⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⠤⢀⣠⣦⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⣿⣿⣟⣷⣟⣿⣿⣿⡞⡴⣋⠴⣃⠶⣵⢿⣿⣽⡿⢋⢆⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢠⠀⠀⠈⠀⠀⡎⠀⣼⠁⠀⠰⣅⠪⡔⢡⠊⡔⢃⢾⡀⣗⢠⣙⣴⢿⠛⠛⠓⠻⢲⠛⠒⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣪⣽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣸⣿⣟⡾⣽⡾⣯⣟⣿⣿⣷⣭⣳⣝⣾⣿⣿⡿⣫⡌⢃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣋⠐⠀⠀⠀⠀⡼⠀⠘⡇⠀⣀⣀⣏⠰⣡⠊⣰⢣⠌⢼⣷⢸⢢⡞⣼⢼⢲⠲⠷⢶⣿⣶⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣿⣻⢙⣿⣽⢷⣻⢾⡽⣟⣿⣿⣿⣿⣿⣟⡼⢣⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⢰⠁⠀⢈⡔⠋⠀⡼⠹⢷⢀⡞⡿⢠⠋⡄⣿⣸⠺⡇⣿⡎⠀⠀⠀⠀⠻⡿⢿⣯⢿⠀⠀⠐⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠭⣦⣾⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡿⡑⡎⡔⣿⣯⣟⣯⢿⣽⣞⣿⣿⣿⣿⣯⢜⡡⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⣠⢤⣀⠉⠀⠀⠀⣇⢸⣯⠏⣸⠁⢦⡑⣸⢽⡞⡉⢧⡽⣧⣄⡁⠀⠀⠀⠙⣹⣁⣼⡷⠀⢈⣿⣿⣿⣶⢤⣀⣀⣀⣀⣤⣰⡶⢉⣴⡿⣫⠆⠀⡄⠉⢻⢸⠀⢿⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡱⢜⡰⢻⣟⣾⣽⣻⢾⣽⢾⣿⣿⣿⢏⠆⣑⡾⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢊⡐⠆⡌⢣⢀⠐⠀⠈⡟⠁⠀⢯⠘⣼⠋⡇⡾⢁⠜⡈⢷⣆⡉⠛⠶⠶⠶⠛⠋⣉⣁⣀⡴⠞⠋⡉⢁⠀⠌⡐⠲⡤⠶⠖⢧⣾⠋⠵⠛⠁⠤⢁⠐⠈⡜⢸⡀⢸⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣣⢑⠮⡔⢣⢿⣷⣿⣿⣿⣯⣿⣿⣿⣻⡞⡜⢹⡡⠖⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⠀⢀⠰⡃⣌⠲⡘⡼⣠⠐⢠⡟⠀⡠⠀⡖⣷⠇⡼⢸⠁⡎⢒⠡⣬⠼⠛⠷⢒⢒⡋⠍⠭⠙⣿⣿⣤⣤⠴⢀⣂⡬⠤⠴⠒⠛⠒⠒⠋⠀⠸⢦⣈⡐⠠⢂⠈⢼⡃⢸⢁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⢎⢲⣉⠦⢻⣿⣿⣿⣿⣿⣿⣿⡿⡓⣥⣼⠋⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡈⢆⠣⡑⠤⢓⣸⢣⠃⠀⡞⣴⡞⢣⠞⣽⠏⡔⡇⣇⠣⡜⢡⣞⣡⠮⢚⢺⠏⡒⢌⣺⡴⣣⣬⡙⠲⣮⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠦⠬⠧⣾⡙⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⠚⣤⢃⢎⣿⣿⣿⣿⣿⣿⣿⣿⢣⣟⣿⠵⠋⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣍⢢⠱⣁⠚⢄⡞⡎⠀⣸⣱⡟⡄⢣⠸⢇⠸⡄⡙⡟⡇⢘⡨⢡⠒⣌⡵⢋⠦⢛⣼⢋⡼⣩⢼⡟⠶⣽⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢢⡙⢤⢋⢲⣿⣿⣿⣿⣿⣿⣿⢷⡿⢟⡥⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠉⢿⣆⠡⢉⡞⡞⠀⣰⢳⣟⠰⣈⠥⡃⢌⡒⡌⢡⢧⡳⢈⡔⢡⣪⠏⡰⣁⣮⣯⡕⢮⠰⣱⣎⣷⡶⢱⢬⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡜⢢⣋⢼⣿⣿⣿⣿⣿⣿⣯⢏⣿⣷⢏⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣾⠇⠊⡕⢀⠀⣠⢣⠿⢆⠱⡈⠖⣉⣾⡞⣐⠣⡐⠤⣣⡼⠛⣹⢇⣱⣯⣾⣟⣿⠟⣷⣿⣿⣿⣿⡨⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣍⠣⡜⣾⣿⣿⣿⣿⣿⡟⣴⣻⡿⠃⡏⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠃⠈⢨⠔⠒⠚⢁⡾⠘⢤⠣⢍⣲⢋⡏⠴⣁⢒⡡⣾⠏⠀⣴⠿⠋⣽⠟⠋⠉⣀⣾⣿⡟⣿⠻⣇⠠⢤⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠵⠀⠀⠀⠀⠀⠀⠀⠨⣾⣿⡇⠀⠌⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⡓⢬⣿⣿⣿⣿⣿⣿⡟⣡⠏⣤⢟⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⣅⠪⡑⣤⠞⡡⢍⠢⡑⢂⣵⣾⢟⣰⠾⢛⡷⠋⠀⠘⠃⣠⡞⢀⠂⣁⣲⡿⠭⠛⢿⣯⡶⠿⣆⡘⢤⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⣿⣽⡟⠀⢂⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢒⡍⣺⣯⣿⣿⣿⣿⣿⡾⢑⣞⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠦⢙⣠⠷⣛⢡⠚⡰⠌⢒⣵⠟⣱⡿⠋⠀⠀⠀⠀⠀⣠⠶⢋⡁⠐⢰⡏⠉⠀⠀⠀⠀⠀⠉⠙⠢⡈⠑⠦⡁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢾⣿⣿⠇⠐⠠⢈⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡣⠜⣿⣿⣿⣿⣿⣿⡟⣴⣻⡼⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⠊⡍⠥⣃⠜⡀⠎⢆⠱⢈⢬⡧⠈⠁⠀⠀⠀⠀⢀⡴⠾⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡸⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⢀⡇⢻⣿⠠⢈⠡⠂⠄⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⣿⣿⣿⣿⣿⡿⣱⢟⠰⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⡜⠰⡁⢎⣰⣉⣆⠃⣬⡾⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠁⣾⡿⢀⠂⠔⢀⣢⡟⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣿⣿⣿⣿⣿⣿⣳⠏⠏⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢃⡼⠛⠋⠉⣉⣴⡯⠾⠋⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡀⠀⠀⠀⢾⢸⣿⡇⠠⠈⡀⢶⡟⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⢳⠁⣪⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⡟⣟⢻⡛⠶⢦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⢳⠀⠀⠀⡏⢸⣿⣯⡁⢂⣵⡟⠄⡃⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⡾⣴⢋⡞⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⠶⡹⣌⠳⣜⡹⢎⠶⣬⢹⠻⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⢰⣦⡀⢰⠃⣸⣿⡿⠱⡟⠉⡄⢢⠀⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡽⣡⢾⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣋⢎⡳⡱⢎⡳⣌⠳⢎⡳⣌⢧⣛⡴⣡⢏⡛⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣘⣌⢷⣌⡌⢺⡿⠁⠀⢸⠃⡀⡍⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢳⢏⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⢌⢧⢳⠹⣌⠳⣌⢿⡬⣵⣮⣾⣵⣫⣷⣯⣟⡷⣯⣟⣿⣗⡦⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⡤⠦⢽⣋⣼⣧⠀⢠⠏⡴⢤⡁⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣏⠞⡾⡈⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣻⠹⣍⠞⣢⠏⡵⣊⢗⡻⢿⣷⣶⣖⡲⣌⠧⢭⡹⣙⠿⢷⣿⣾⣽⣿⣶⣆⡉⠭⠭⠖⣒⡲⠤⠤⣀⡀⠀⠀⠀⠀⠀⡺⠟⠉⠀⠒⠦⠤⣀⣿⠿⢃⡼⠚⠁⢸⠁⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡏⣾⣷⠁⠆⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⢿⢫⡜⡥⡛⣬⣞⡱⢎⡵⣩⢎⡵⢣⢎⡻⢿⣿⣶⣙⢦⡓⣭⢚⡥⢫⡝⡻⣿⣻⣿⣿⣷⠄⠀⠀⠀⠀⠉⠒⠪⢝⣣⡔⠥⠊⠀⠀⠀⠀⠀⠀⠀⢹⣿⠠⠞⠀⠀⠀⡼⢰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣥⣿⢈⠰⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⢀⣾⣿⡟⣬⢳⡸⢱⣹⢏⡖⣭⢚⡔⣣⠞⣘⠧⢎⡵⢻⣿⣿⣿⡦⡹⢤⢫⢜⡣⢞⡱⢎⡵⣘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⡇⠀⠀⠀⢠⢃⣾⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣼⢼⠂⡜⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣙⢦⢣⣵⣿⡷⣎⡜⢦⢋⡜⢦⢛⢬⡛⡼⣰⢻⣿⣿⣿⣷⡙⢮⡱⢎⡵⢋⡜⣣⠜⣥⢺⣿⣿⣯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣤⢀⡟⢡⠃⠀⠀⢀⡟⣾⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⣾⢁⠎⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡟⣜⢢⣿⣿⣿⠿⣢⠝⡬⢳⣘⢣⠏⡦⢳⡱⢣⢎⢿⣿⣿⣿⢜⡣⡝⣎⠶⡹⡜⣥⢛⡴⣃⢿⣿⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢿⡀⣿⠀⠀⠀⢜⣽⡛⢦⣹⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⡆⡘⢄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣾⣿⣿⡿⢏⡳⢥⡛⢬⡓⣬⢣⡛⡴⢣⡝⣣⠞⡼⢿⣿⣿⢌⡳⢍⠶⣩⢓⣭⣶⣏⠶⣩⣿⣿⣿⣿⣿⣿⢹⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⢀⣼⢏⢧⡙⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⡧⡗⣺⠠⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⣙⠮⣱⠣⢞⡡⢞⡔⣣⠝⣒⠧⣚⠵⣪⠵⣩⢿⡿⢢⢝⣪⠳⣥⢫⠼⣿⣿⣗⣿⣿⣿⣿⡟⣿⣏⢮⡱⣋⠿⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡤⣨⣷⢻⣋⠞⣦⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⡗⢯⢼⠐⡡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⡟⡲⣍⢞⡡⢏⡎⠵⣋⠼⣡⢛⡬⢓⡍⡞⠴⣋⠖⡮⢜⣣⢚⡴⢋⠶⣩⠞⣿⣿⣿⣿⣿⣿⣿⡿⣉⡖⢮⡱⣍⠞⣥⢲⡡⢏⣛⢳⠲⣦⢤⣤⣶⡞⠿⣌⣣⣜⢾⣿⣿⢿⣋⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡧⢿⣞⠸⣽⡀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⢏⡼⣑⢎⡎⡵⢪⡜⣣⠝⣎⠵⢣⡚⡵⢚⡜⣣⠝⢮⡱⣋⠴⣃⠞⣭⢳⡡⢏⣿⣿⣿⣿⣿⣿⣿⡱⡱⢎⡣⢖⡬⢛⡴⢣⡙⢮⡜⣡⢛⣤⡿⡟⣭⠚⣵⣾⣿⣋⠮⡝⣭⢲⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣧⠘⡖⣈⡇⠈⡇⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⣘⠖⡭⠲⡜⣥⠳⡜⣥⢚⡜⣎⠧⣓⠭⣳⠸⣥⢚⡥⢳⣌⠳⣍⠞⡴⢣⡝⢮⡜⣼⣿⣿⣿⣿⡯⣱⡙⢮⡱⣋⡜⣣⠞⣥⢛⡲⣜⣥⣿⢏⡳⣹⢰⣿⣿⠻⡴⣩⠞⣱⣾⣿⣿⡿⣋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⢌⠣⠄⣷⠈⠱⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⡷⢩⠞⣱⠹⡜⡴⣋⡜⢦⣋⠶⣌⠳⣌⠳⣆⢻⡰⣍⠺⣅⢎⡳⣌⢻⡘⢧⡚⡵⣚⢼⣿⣿⣿⡟⣱⣾⡿⢢⣓⣱⠎⡵⣚⣤⣏⣶⣿⢟⡱⢎⣵⣷⡿⡻⣌⠷⣱⣣⣾⣿⡿⠟⢫⢴⣱⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡜⢎⡱⢨⠸⢀⡈⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⡏⢧⡛⡴⢋⡼⢱⡜⠼⣡⠞⡜⣬⠳⣬⠳⣬⠳⡜⣬⠳⣜⠪⡕⣎⢥⡛⢦⡙⢶⡩⢾⣿⣻⣿⣼⣿⣿⢍⣇⣾⡿⣹⣾⣿⣿⣿⢻⣱⣮⣷⣿⠿⡹⢼⡱⣮⣿⣿⣿⠟⠉⢀⠀⣞⢫⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡎⡎⠴⡁⠎⡄⢀⠠⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣽⣿⣿⣿⣿⡏⢶⡙⡼⡑⣎⢳⡘⢧⢣⡛⡜⢦⡛⡴⣋⠶⡹⡜⢦⢛⡔⣫⠜⡜⢦⣙⢮⡙⢦⣙⣾⣶⠟⣽⣿⣿⣳⣾⣿⣿⣿⣿⣿⢿⣫⣼⣷⡿⣟⡹⢬⢳⣹⣶⣿⣿⣿⠋⠀⠀⠀⠎⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡧⡙⢦⠉⡆⢃⠠⠀⢀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠈⠀⠀ ⣼⣿⣿⣿⣿⣿⡏⠶⣙⠴⡹⣌⢧⡙⣎⢧⡹⢜⡣⡜⣵⣮⣿⢳⡙⣎⢣⠞⣡⢛⡜⣣⠞⢦⡙⢧⣾⣿⣯⣽⣿⣿⣳⣿⣿⣿⣿⣿⣻⣽⣿⡿⢻⡙⢶⣡⣿⣾⣿⣿⠿⢛⡟⡎⠀⠀⠀⠀⢠⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠝⡢⢕⡘⡌⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⣿⣿⣿⣻⣿⣿⣏⠳⣍⢞⡱⢎⠶⣙⠲⣌⣣⣧⣷⣿⣿⡟⡥⢧⡙⢦⣋⠞⣥⢫⡜⡱⢎⢧⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣏⠳⣜⣣⣽⣾⣿⡿⠛⠉⠀⢄⣿⢱⠁⠀⠀⠠⣙⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⡑⣎⠲⣍⠆⢁⠀⠁⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⣿⡿⠳⣜⢻⢻⡷⡹⣜⢪⡕⣫⢚⣥⣿⣿⣿⣿⣿⡿⢗⡹⡜⣣⠝⣦⡙⡞⡴⢣⡚⣍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⢯⡑⢮⣱⣾⣿⣿⠿⠛⠋⠁⠀⠀⠠⢨⣾⠇⠃⠀⠠⢀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡣⢜⡤⢳⢸⠠⠸⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⡱⢫⡜⣥⠳⣜⡱⢎⡱⢮⣥⣿⣿⣿⢏⣿⣟⢣⡝⡎⡵⢪⢥⣋⢦⡹⢜⡱⣣⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣥⣯⣶⣽⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⡄⣡⡿⡍⢀⠐⣬⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣗⠪⣔⠣⡎⡗⠀⠃⠀⢃⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⣛⠿⡧⣜⠢⢏⠲⣍⢮⣱⢳⡿⣛⢳⣋⡜⢲⡌⣳⢸⣱⣭⣳⣶⣭⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⡛⢛⣛⠯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⣴⡿⣱⣣⠴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠸⣄⠳⡙⠽⣤⣁⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣻⢯⣟⢿⡻⣟⣻⡟⣿⣛⡿⢯⣟⢿⣛⣯⣟⢿⣛⣿⢻⣻⢟⣻⡟⣿⡽⣻⡟⣿⣻⢟⣿⣻⣟⣿⢻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣟⡿⣟⡿⣿⣻⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣽⣿⣽⣿⣽⣾⣿⣽⣿⣽⣯⣷⣿⣻⣾⣟⣷⣿⣳⣿⢾⡷⣟⣿⣽⡾⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡿⣽⣻⠾⣽⣻⢟⣿⣻⢿⣿⣿⣿⣿⣿⢿⣻⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣟⡾⣝⣳⡻⢮⡟⣽⡭⣗⣻⢵⣫⡽⣛⣮⢟⡽⣖⢯⢯⡽⣚⣯⢳⢯⣳⢻⡵⣛⡷⣛⣧⢟⣻⢮⢷⠾⣭⣟⠾⣵⣻⣼⢳⣛⣾⢳⣛⣾⢳⣟⢾⣳⣟⡾⣽⢯⡿⣽⣻⢷⣻⢯⡿⣽⢯⡿⣽⢯⣟⣯⣿⣻⢷⣿⣻⢾⣟⣷⢿⡾⣷⢿⡾⣟⣾⣯⣷⡿⣯⣿⣽⡿⣽⣿ ⣿⣿⣾⢿⣯⣿⣾⣟⣿⣾⢿⣾⢿⣽⢿⡾⣟⣷⢿⣻⣞⣯⣟⣯⢿⣻⣽⢾⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⡟⣯⡽⡶⣏⡿⣳⣭⣟⡾⣽⢯⣿⣟⣯⣷⣿⣿⣿⣯⣿⢿⣷⣿⣻⣾⢿⣿⣻⣿⣻⢾⣻⢾⡹⣞⡽⣲⣛⢧⣛⢶⡹⣎⢷⣫⠶⣝⢧⣛⢮⡳⣝⢮⡻⡼⣝⢮⣏⠷⣭⡳⣽⡹⣞⡽⣎⢯⣳⣛⡞⣯⢳⣞⡻⣵⢳⡞⣯⢽⣚⣯⢽⣚⣯⢞⡯⢷⢾⣹⣏⣯⣽⡳⣯⢟⡽⣯⠿⣽⢯⡿⣽⣻⢾⡽⣾⣽⣻⢾⡽⣟⡾⣯⣟⡿⣽⣻⣟⡿⣽⡷⣟⣿⢿⣽⣯⣿⢿⣻ ⣿⣯⣿⢿⣯⣷⢿⣯⢿⡾⣟⣯⡿⣯⣟⡿⣯⣟⣯⢿⡾⣽⣞⣯⣟⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⢿⣿⣿⡿⣟⣷⣻⡽⢮⣝⣧⢿⣽⣯⣷⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⢿⣽⡿⣯⣿⢷⣟⣯⠳⣭⠳⣭⠖⣧⢛⡮⡝⢮⣳⢹⡚⣖⢻⡜⢧⣛⢮⢳⡝⢮⡳⡝⣮⠳⣎⠟⣶⠹⡶⣙⢮⡵⢫⡞⡵⣋⢾⡱⣏⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⡹⣎⠿⣼⢫⣗⡳⢾⣱⢾⡹⢧⡿⣹⣞⡻⡽⣞⡽⣳⢯⢯⣟⣳⣭⡟⣯⢿⣽⡻⣷⢯⡿⣽⣳⢯⡿⣽⣻⡽⣯⡿⣾⣳⣿⣻⢿ ⣿⣟⣾⢿⣽⡾⣿⣽⣻⣽⢿⣽⣻⢷⣯⣟⣷⣻⣞⣯⣟⢷⣻⣞⣭⢿⣽⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⢯⣷⣿⣻⣞⣷⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⢾⡱⣛⠴⣛⠴⣛⢬⠳⡜⣭⠳⣌⢧⡹⡜⣣⠞⣣⠞⣬⢓⡎⢧⢳⡙⢦⡛⣬⢛⡴⢫⡕⣫⠞⣜⡣⢽⡱⣋⢮⠵⣋⢶⡹⢎⢧⠻⡜⣧⢛⡼⢣⡟⡼⣛⡼⢳⢮⡝⣧⣛⢮⣝⡳⣝⡳⢮⣝⡳⣝⢾⡹⣞⢯⡞⣧⢟⡾⣝⣳⠾⣝⡷⢯⣻⠷⣯⢿⣽⣳⢯⣟⣷⣻⢷⣻⢾⣽⣻ ⣿⣻⢾⣯⢷⣟⡷⣯⢷⣯⣟⡾⣽⣻⢮⣷⣫⢷⣽⣚⣾⣫⢷⣻⣾⣿⣷⣿⣾⣿⣷⣿⣟⣿⣿⣻⣿⣽⣷⡿⣟⣷⡿⣯⣿⢿⣻⣷⣿⡿⣟⣯⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣻⢷⣷⣭⣾⣌⠳⡜⢪⡕⡓⢦⣙⠲⢬⡑⣎⡱⢎⡱⢚⡴⣉⢎⠇⡧⣙⠦⣙⠦⢭⣘⢣⡜⢥⠛⡴⡙⢦⡓⢭⢎⠳⣍⠶⣙⢎⢮⡹⡱⢎⡽⣘⠳⣜⢣⡝⣜⢫⠶⣙⠶⣙⢮⢞⡱⣏⠽⣓⢮⡝⣮⢳⡝⣮⢳⡝⣮⢻⡼⣭⢳⡻⣝⡞⣯⡳⢿⣹⡞⣧⣟⡻⣞⣳⢯⡿⣽⣻⢾⡽ ⣿⣽⣻⣞⡿⣾⡽⣯⣟⡾⣞⣽⣳⣯⣿⣶⣟⣿⣾⣽⣾⣽⣿⣿⣿⣿⣿⡿⣿⣟⣿⣯⣿⣟⣾⣿⣽⢿⣾⢿⣟⣯⣿⢿⣻⣿⢿⣿⣻⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⣻⣮⣷⣘⠧⣜⣡⠳⣌⢣⠓⡜⡤⢓⢎⡱⢃⡖⡩⢎⣚⠱⣌⢣⠣⢞⡡⢎⠖⡬⢃⣏⠲⡙⢦⡙⣒⢎⠳⡸⠜⣬⠚⣔⠣⣝⡘⢦⢍⡳⣌⠳⡜⣬⢣⢛⡬⢛⡜⣎⠮⡕⣎⢯⡙⢮⣙⠶⣋⠾⡱⣏⠾⣱⢏⢾⡱⣏⢷⡹⣞⡵⣻⡝⣶⢻⡵⢾⣹⡭⣟⣞⣳⢟⡼⣯⣻ ⣿⣞⣷⣯⣿⣷⣿⣷⣯⣿⣽⣾⢿⣽⣿⣿⣿⣿⡿⣿⣿⢿⣿⣟⣿⣯⣷⣿⣟⡿⣽⣻⣞⣯⢿⣞⣿⣻⡽⣟⣯⢿⣽⣻⢯⣟⣯⣟⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣭⢻⢿⣿⣶⣣⣗⢬⠒⣍⠲⣡⢋⠦⡱⣉⠖⡱⢊⡴⣉⢆⢣⡙⢦⡑⢎⡜⢲⡉⠦⣍⠱⢆⢣⡱⢊⡕⢣⠝⡤⢋⢦⡙⣤⠙⡦⢎⡱⢌⡳⠜⣤⢣⢋⡴⢋⡼⢌⡣⣝⠸⢦⡙⢧⢎⡳⣍⢳⡹⣌⠳⣭⢚⠧⡝⣎⡳⡝⡮⢵⣣⢟⡼⣣⠟⣧⢳⡝⡾⣼⡹⢾⣹⢧⣻ ⣟⣾⣯⣿⢿⣾⢿⣾⣟⣿⣽⣿⣻⣯⣿⣾⣟⣷⣿⣟⣯⣿⣻⣞⣯⢷⣻⠾⣝⠿⣽⣳⢯⣟⡿⣞⢷⢯⠿⣽⡞⣟⡾⣝⢿⣚⡷⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣎⣟⣿⣽⣻⣷⢫⠔⣣⠲⣭⢶⣱⢊⡜⣡⢣⠒⡥⢊⠦⡙⢤⡙⢦⡘⢥⢊⠵⣈⠳⣌⠣⡜⡡⢎⡱⢊⠴⡋⢦⡑⢦⡙⡔⢣⠜⣡⠎⡵⢂⢧⣉⠖⣩⢒⠥⡓⣌⠳⣊⠵⣊⠶⡱⣌⠳⡜⢬⠳⣌⠏⣞⡱⢣⡝⡼⣩⢓⠮⣞⡱⣭⠻⣜⢧⡻⢵⣣⢟⣧⣛⢮⣳ ⣿⣯⢿⡾⣟⣯⣿⣳⢿⣯⡿⣟⣿⣽⣳⣛⠾⣝⢾⡹⢞⡵⢫⢞⡱⢯⡜⡹⢎⡽⢲⢭⡳⣞⡳⣏⡟⣞⢯⡳⣽⡹⢞⡽⢎⡷⡹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣹⣷⣫⢞⣣⢛⡴⣻⡜⢧⠻⣜⡲⣕⣎⡳⣌⠣⡜⡱⢢⠜⡢⢜⠢⣍⠲⣡⠓⡬⡱⣌⡱⢊⠴⣉⠖⡩⢆⡍⢲⡘⣌⠣⢎⡱⢊⡔⣋⠦⣘⠬⡑⢎⡱⡑⢎⡱⢥⠚⡔⡣⠵⣈⢳⠸⣡⠳⢬⠹⢤⢋⡵⢪⢕⢣⣋⠷⣌⠳⣌⠷⣩⠶⣙⠧⣝⡺⡴⢫⡞⡵ ⣿⣽⢿⣻⣯⣟⣾⡽⣟⣾⢿⣿⣻⡷⣧⢏⡞⣭⢲⡙⢮⡜⣫⢎⡵⢣⢞⡱⢫⠜⣣⠎⡵⢪⠵⣩⠞⣭⠲⡝⢦⡝⣣⠞⣭⢲⡙⢖⡬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⢿⣷⡎⠶⣩⢖⡱⢮⣍⢳⢣⡝⡼⣌⢳⣌⠳⣜⡱⢣⢞⡱⢎⡳⣌⠳⣥⢛⡴⢳⣌⠳⣍⠞⡼⣸⠱⣎⠼⣡⢚⡤⢋⢦⡑⡣⡜⡤⢓⡬⢲⡙⡬⢒⡍⢎⡔⢣⡙⠴⣉⢖⡩⣒⠭⡒⢭⠒⣭⢊⢎⡴⢋⡜⢆⡣⠞⣌⠳⣌⠳⡥⣛⢬⡛⡴⣍⠳⣏⡼⢳ ⡿⣞⣿⡽⣾⡽⣾⡽⣯⣟⡿⣾⣽⣻⡽⣎⡳⣌⠧⣙⢦⡝⣦⢯⣼⢳⣎⡵⢣⡙⢤⢋⠴⣋⠞⣥⢛⡴⢋⡜⣣⠜⡱⣚⢤⠳⡌⡇⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⢛⣋⠳⡡⢎⡱⠲⣌⠣⢇⠮⣑⢎⡣⢎⡳⣌⠳⣍⢺⡘⢇⡳⣌⠳⣌⠳⡜⢣⠜⠳⣌⢋⠖⣡⠛⣌⢣⠣⣍⠲⣍⠲⡱⡱⢣⠝⣣⠚⡥⢋⡴⠣⢜⢢⡜⣣⢞⡱⣭⢶⣱⢣⣛⡬⢣⡙⡤⢋⠖⣌⢣⠜⣪⠱⠭⣌⠳⣌⢳⡑⣎⢖⡹⢴⣩⠳⡜⣜⢣ ⡿⣽⢾⣽⣳⣟⣷⡻⣗⣯⡽⣞⣳⢯⣷⢯⡷⣎⢷⡹⣮⢟⣭⡟⣾⣻⢾⣽⢣⡝⢦⡍⢶⣉⠞⡤⣋⠔⡫⢔⡡⢚⠱⡈⢆⠓⡘⢸⣽⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠃⠰⠁⠜⠱⢈⠓⡌⠓⡌⠦⢙⠢⠱⢌⠓⡌⠦⡙⢌⠒⡌⠣⢌⠱⡈⢅⢊⠱⡀⢎⡘⢄⠣⢌⠢⡑⠤⢃⠬⡑⢡⢃⠣⢎⢡⠋⡔⢣⠒⣍⢎⠶⣭⢳⢯⡽⣞⢧⡟⣯⣳⡝⣧⣚⡥⣏⡞⣤⠓⡎⢥⢋⢞⡰⢋⡖⣣⠝⡜⣮⢱⢧⣎⢷⡹⣬⣓ ⣷⣻⢾⡽⣯⢟⣭⢷⡻⣝⡷⣻⣟⡾⣽⣾⣳⢿⡼⣳⢏⡾⣝⡳⣏⡿⣞⡽⢮⡵⢮⡵⣮⣝⡲⣥⣛⡴⢣⡜⣡⠎⣄⠣⡘⢄⠣⡌⣿⣿⣿⣿⣿⣿⠟⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣻⣷⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠈⠀⠂⠈⠐⠡⠠⠑⠈⠆⠁⠆⠘⡀⠣⠘⢈⠂⠱⠈⡑⢈⠂⠌⢂⠱⠀⠎⠄⠣⠌⡘⠤⠘⠌⠢⠑⢌⢲⡹⣜⢶⡹⣞⡼⣣⢟⣼⢳⣏⡯⢷⣹⣏⡷⣽⢳⡭⢶⡱⣎⠞⡌⠃⠎⡱⣍⢶⣳⣝⡾⣼⣻⡼⣧⢯⣟ ⣳⢯⡟⣾⢱⣋⠞⣦⢻⣭⣟⠷⣯⡻⣗⢯⡽⣞⡳⣽⢺⡵⣫⢷⡹⢾⡽⣞⡷⣹⠯⣝⠶⣭⢳⢣⡟⣼⡳⣽⣣⢞⡤⢣⣽⢾⣛⣼⣿⣿⣿⣿⠟⠁⣧⠀⠀⣸⣿⣿⣿⣿⣿⠻⢿⠛⡿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣙⢮⡳⡝⢦⠳⣑⢎⡎⠷⢮⡝⣯⢳⡞⣽⠺⣭⣛⢯⡗⣯⢻⡔⣩⢔⣱⢮⡟⣵⠾⣽⡳⣏⢿⡽⣻⢞ ⡽⣳⣛⠦⣃⢌⠻⡜⣯⢶⣫⢟⡵⣻⢼⣣⢟⡼⡳⣭⢳⡳⡝⣶⣛⢯⡽⣝⢾⣱⣛⢬⡛⡴⣋⠷⣸⡱⢏⡷⡹⢞⡜⡳⢎⡳⣌⣿⣿⣿⣿⢟⡾⠛⣿⡇⠀⣿⣿⣿⡿⣯⣦⢿⣐⣯⣔⣿⣦⣶⣡⣋⡝⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠭⡒⠱⡙⢌⠳⡘⢎⠼⣩⠓⢮⠱⢫⢜⠲⣙⠦⡙⢮⡙⢎⡳⢍⠧⣛⠼⣣⠟⣜⡛⢶⡹⢎⢧⠹⡱⣋ ⡽⢣⢏⡳⢔⠨⠑⡘⠤⢣⡙⢮⠱⣏⠞⣥⠻⡜⡵⣩⠶⡹⣜⡱⢎⡳⡜⣜⢲⡱⢎⢧⡙⠖⡩⠚⢥⡙⢎⠶⣩⠳⡜⣱⢋⠖⡥⢿⣿⣿⡿⡎⠁⣿⣿⠇⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡈⢉⡛⠛⠿⣿⣿⣿⣾⣴⣣⣝⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠈⠀⠁⠂⠈⠀⠁⠂⠁⠂⠈⠀⠐⠈⠐⠀⠁⠐⠈⠀⠉⠄⠑⠈⠂⠡⠑⠠ ⠅⢋⠰⢁⠊⠄⠁⠀⠐⠠⠘⡀⠓⠌⡙⠤⠋⡜⠡⢃⠣⠓⠬⡘⠡⠓⡘⢌⠣⠜⡘⠢⠉⠄⠁⠈⠀⠐⠈⠐⠁⠣⠘⠄⠉⠘⠠⠙⢿⣿⣟⣧⠀⣹⠏⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⣸⡏⠀⠀⠉⠉⠙⠓⠺⢿⣟⡻⢿⣿⣿⣿⣿⠬⣙⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠌⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣽⣿⣧⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢶⣍⠙⠿⣿⣡⢿⣻⣷⣾⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠰⡌⢎⡱⡍⢦⡙⣌⠳⡘⠥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⡀⠀⣿⡧⠀⡎⠀⠀⠀⠀⢀⣾⣿⣿⣷⣾⠏⠀⠀⢠⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣊⢆⠳⣉⠮⡱⢌⠣⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡐⢤⠒⣤⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⣿⣷⠀⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⡞⠀⣾⣿⣿⣻⣿⣿⣿⣟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⡄⢢⠑⡌⢎⡱⢅⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠁⡀⠀⠀⠀⠀⠀⡀⢢⡑⢎⡱⢎⡹⢤⣋⠜⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⡇⣸⠄⠀⠀⠀⠀⠀⠀⠀⠈⠱⠈⢻⣿⡄⠀⠀⠀⠀⠠⣿⣿⣿⣿⠏⠀⠀⠀⢰⡇⢰⣿⣿⣿⠿⠿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡀⠀⠀⠀⠀⠀⠀⠒⡌⠜⣡⠚⡜⢢⡑⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠄⢀⠠⡘⢤⣁⠒⣌⢣⢞⡡⢏⡎⠵⢣⡜⡸⠄⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢸⡟⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⡀⠀⢀⣈⡽⠟⠁⠀⠀⠀⠆⢸⠁⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢄⠠⡀⢄⡘⠰⡈⢆⠡⠚⡌⡡⢌⡱⢌⡒⠤⣀⠄⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⡀⢄ ⢈⠔⣌⠲⣍⠶⣩⢛⡬⣓⢮⠱⣋⠜⣩⠒⣌⠱⡈⠔⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⡎⠀⢀⢠⣿⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢢⠑⠢⢌⠱⣈⠦⡙⢢⠑⡴⢡⠒⡥⢊⠵⣈⠞⢤⠣⡜⢢⠒⠤⡀⢄⡠⢄⡰⢠⢒⢤⡙⠦⣜⡡⠞⡌⢆ ⢈⠒⢌⠳⣌⠳⣥⢋⡶⣩⢎⡳⣌⠞⣤⢫⡔⣣⢝⡸⠰⡁⠀⠀⣀⢀⢠⢀⡄⣀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⢷⡇⠀⠈⣿⠇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠘⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⡉⠆⢡⠊⠔⠢⣁⠣⢑⠢⢡⠓⡌⡑⠪⠔⡩⢆⠳⢌⠣⡙⠦⡙⢢⠑⢎⠲⢍⡚⠦⣉⠳⣌⠱⣋⠜⡣ ⠜⡬⢆⠳⣌⠻⡔⡫⢖⡱⠎⡵⢊⡝⢢⠳⡘⠱⢊⡑⠃⠄⠡⠚⠄⠋⠆⠣⠘⠌⠢⠙⠢⠉⠎⠁⠂⠌⠐⠁⠊⠐⢻⡆⠀⠙⢄⠀⢸⡀⠀⠀⠐⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⣠⠇⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⢁⡏⠙⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⠐⠈⠀⠄⠂⠌⠠⢁⠂⠄⠡⢁⠊⠐⠈⠐⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⠈⠐⠀⠁⠀⠁⠀⠘⠀ ⠉⠄⠉⠐⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣿⠦⠄⠀⠣⠀⢳⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢉⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⡼⠁⠀⠈⢷⡹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢂⠠⢐⠠⡈⢄⠂⠄⠂⠌⡐⢀⠐⠠⠁⠄⠂⠄⢂⠄⡐⡀⠆⡐⢠⢂⡐⠠⢄⢂⣄⢢⣔⣢⣵ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣄⣀⣀⢀⣀⣀⣀⣀⣤⠴⠒⠉⠁⡀⠸⣆⡀⠠⢄⠁⠈⢿⡀⠀⠀⠹⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⠒⠚⠤⢄⡀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡞⠁⢀⣀⣀⠀⠻⣜⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣓⣬⢶⣫⣶⡽⣎⡾⣬⣱⢢⡔⢢⣌⣣⠭⣌⡱⡈⠆⣌⠰⣁⠎⡴⣡⢆⣼⣳⣾⣿⣾⣿⣿⣿⣿ ⣿⣜⣦⣳⣌⣖⢦⣱⣎⢶⡹⣎⢷⡭⣞⣵⡹⢦⡹⣄⢣⡜⢤⣃⠞⡼⣎⡷⡽⣎⡷⢮⣻⡼⣶⠟⠋⣀⠤⠒⠁⠀⠀⠀⠘⢷⣀⡈⠐⠀⠘⢻⣄⠀⠀⠙⣿⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣄⡀⠈⠻⡄⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⣞⣯⢷⣯⢿⣽⣻⢷⣯⢷⣻⢯⣞⣷⣻⢷⣳⣽⣺⣴⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣟⣿⣿⡿⣿⣻⣿⢿⣽⣻⣾⡽⣾⡽⣯⡷⣯⣳⣞⡳⣎⣟⡳⣽⢺⡵⢯⣝⢯⣷⠟⢁⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠙⠦⣀⠈⠻⣦⠀⠀⠈⠳⣝⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠛⠓⠂⣵⣾⢯⡗⡶⣤⢤⣄⣄⣠⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⡿⠁⠉⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣻⣞⡿⣼⣻⢮⣷⣻⣞⣯⢯⣟⣾⣳⣯⢿⣳⣿⣷⡿⣿⣻⣿⣟⣿⣿⣻⣿⣟⣯⣿⣿⣾⣟⣿ ⣿⣟⣿⡿⣿⣽⣿⢿⣟⣿⣿⣻⡿⣷⣿⣟⣿⣿⣽⣷⡿⣾⣽⣳⢮⡽⣎⣷⣹⣳⣞⡿⠃⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠳⠄⢻⣷⠀⠀⠀⠈⠳⢯⣛⢶⣄⡀⠀⠀⠀⠀⠀⠀⡤⠂⣠⣾⢿⡹⢮⣝⡳⣽⢺⣼⣾⣷⣻⢿⣟⣿⣟⣿⣽⣯⣷⡿⣷⣿⢿⣳⣿⢿⣿⣿⣿⣿⣿⣿⠃⠀⢠⡇⡎⡆⠀⣾⣿⣿⣿⣯⣽⠛⠓⠦⢬⣭⠭⠿⠿⢿⣿⣿⣿⣿⡿⠟⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⣯⣿⢷⣯⣿⣞⣷⣻⣾⣻⣾⢷⣿⣽⡿⣟⣿⡾⣿⣟⣿⡷⣿⣻⣾⣟⣷⣿⣻⣽⣾⢯⣿⣻ ⣿⣻⣽⢿⣻⣽⣾⢿⣻⣽⣾⣟⣿⣟⣷⣿⣻⣾⣟⣾⢿⣻⡷⣿⢯⣿⣽⢾⣳⣿⡾⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠙⣮⢜⣻⣷⣦⣤⣄⣀⣠⣤⣾⢻⡜⣧⣛⠷⣮⣟⣾⣻⢯⣷⣟⣿⣻⣯⢿⡾⣿⣽⣾⣻⣽⢿⡾⣟⣿⣽⣿⣿⣿⣿⣿⡿⠋⠀⠀⣼⢡⢰⠃⢠⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⠑⠒⢼⡿⣿⣿⣿⠁⣰⠾⣯⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣻⡾⣟⣿⢾⣻⣽⣟⣷⢿⣯⣿⣳⣯⢿⡿⣽⣻⣽⡾⣯⢿⣻⣽⢷⣻⣟⣾⢿⣽⣯⡿⣯⢿ ⣿⢯⣟⡿⣯⡷⣟⡿⣯⡷⣟⣾⣻⢾⣽⣞⡿⣾⡽⣯⢿⣯⢿⡽⣟⣷⣻⣟⡿⣾⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠻⣄⠀⠀⠀⠀⣸⢮⡟⠙⣿⣯⣟⡿⣽⣳⣭⢷⣻⢶⣯⢿⣳⣟⡾⣯⢿⣳⡿⣞⣷⣻⣯⢿⣳⣟⣾⡽⣯⢿⣽⣻⢷⣯⣿⣿⣿⣿⡏⠀⠀⠀⣾⠃⠈⠎⠀⠈⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇⢰⣏⠿⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⡷⣯⢷⣻⡽⣟⡾⣿⣽⣳⢿⣞⡿⣞⡷⣯⣟⣯⢿⡽⣯⢷⣟⣯⣟⡿⣞⣿⣻⣞⣯⢿⣞⣷⣻⢯⣿ ⣿⢯⡿⣽⣳⣟⣯⣟⣷⣻⢯⣷⡻⣟⡾⣽⡻⢷⣻⣽⡻⣞⣯⠿⣽⡞⣷⢯⣿⠇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠣⡌⠳⣄⡀⢠⣿⡟⠀⠀⢹⡷⢫⡟⢷⡛⠾⣏⢟⡻⢞⠯⡟⠾⡽⢫⢟⡳⢟⡽⢳⡛⠾⣏⠟⣞⢳⠻⣝⠻⡞⡽⣛⢞⣿⢿⣿⣿⣧⣄⣤⠿⣁⡤⢶⠀⠀⠀⠸⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡾⣓⣿⣿⡇⢸⣿⣮⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡽⢯⢷⣻⢽⣛⡷⣏⢿⣛⡾⡽⢯⣟⢷⣻⢞⣯⠿⣽⡻⣞⡷⢯⡿⣽⡞⣷⣻⣞⢿⣞⡷⣯⣟⡾ ⣯⢻⣼⢳⡝⣞⢶⡹⠶⣭⢳⢎⠷⣙⡞⣱⢋⡟⢦⢳⡙⢮⡜⡹⢦⠹⡜⣊⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⢢⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⠳⣼⣽⡃⠀⠀⢸⡁⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡀⠈⠠⣏⣀⡀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠀⠀⢀⣐⣴⠋⢻⣼⣿⣿⣧⠀⠙⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠱⡙⢎⠳⡌⢧⢹⡘⢭⠎⡵⡩⡝⠳⣎⠳⣍⠾⣱⢫⠳⣝⣣⠟⣽⠺⣵⢫⣗⡳⣞⢯⡞⣵⡻⣼⢻ ⣯⠷⣞⣧⣻⡜⣧⢻⣝⡲⢏⡮⣝⣲⡙⢦⢫⡜⣣⠧⣙⠶⡸⣑⢎⡱⡘⢤⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢫⢎⠂⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠋⢹⡄⠀⢠⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⡇⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⢳⡶⠶⡶⠞⢿⣉⠘⠁⢸⡇⣿⣿⣿⣶⢎⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡙⢬⠱⡘⢆⢣⢚⠥⡚⠴⡱⣘⠳⣌⠳⣎⠳⣥⣋⠷⣱⠮⣝⢮⡝⣮⢳⣎⢷⡽⢮⣽⢳⣽⢳⣯ ⣯⢿⣹⢶⢧⡿⣼⢳⢮⣝⢯⡖⣧⢧⣛⡭⢶⣙⢦⡛⣬⢳⡱⣍⠶⣡⢝⣸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⡆⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣀⠇⠀⢼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⠀⠀⣤⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⠀⠀⢸⣇⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢢⡙⡆⢧⡙⡬⢎⡣⢞⣡⠳⢥⣋⠷⣘⡗⣎⡟⡴⣭⢻⣜⡻⣜⡧⣟⡞⣧⡟⣾⣹⠿⣼⣻⣞⡿⣼ ⣿⢯⣟⣯⣟⣾⢳⣯⢟⣮⣗⣻⡜⣧⢻⡜⣧⢏⡶⣹⠦⣇⡳⣬⢳⡱⢎⣽⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣇⠀⠘⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⠷⣩⢖⡹⡜⣥⢛⡜⢦⣛⠶⣩⢞⡵⣺⢵⡺⣵⢫⣗⢾⣹⢧⣟⡾⣽⣳⣻⢷⣯⣟⣷⣻⢾⣽⣳ ⣿⣟⣾⣳⣟⣾⣻⣞⡿⣞⣾⣳⣻⣽⣫⡽⡾⣝⡾⣵⢻⣜⡳⣥⡳⣝⢮⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢠⠀⡄⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡩⢞⡱⣎⡵⣙⢦⡻⣜⢧⣛⢾⡱⣏⡾⣵⣫⢷⡽⣫⣞⣯⣟⡾⣽⣞⡷⣯⣟⡿⣾⣽⢾⣯⣿⡾⣽ ⣿⣿⢿⣻⣽⣿⣯⢿⣳⡿⣽⢯⡿⣭⣟⣷⣳⣟⣧⣟⡾⣽⡳⣭⢷⡹⣎⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢹⡆⢌⠠⡁⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠠⢀⣠⠔⠚⠁⠹⠂⠢⡀⠀⠀⠀⠀⠀⠀⡀⢽⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡞⣧⡝⣧⢻⡜⣧⣻⡜⡿⣼⣳⣻⢧⣟⣯⣞⡷⣯⡿⣽⣻⢷⣯⣟⣷⡿⣽⣷⣯⣿⣾⣟⣯⣷⢿ ⣿⣿⣿⣿⣿⣷⣿⡿⣿⣽⣯⣿⡽⣷⣻⣞⣷⣻⣞⡾⣽⣳⢿⡽⣾⡽⣽⡿⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡯⣌⠳⣌⡱⣡⢎⠰⡀⢆⠠⡀⢀⠀⡀⡐⣰⠏⠀⢀⣀⠀⢰⡠⣷⠀⠀⠀⡀⣄⠣⡜⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠿⠛⠉⠙⣷⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡷⢧⣻⡼⣯⣽⣳⣳⢿⣽⣳⢯⣷⣻⣞⡷⣯⢿⣳⣿⣻⣽⡿⣞⣿⣽⣿⣟⣷⣿⣯⣷⣿⣿⣿⣻ ⣿⣿⣿⣿⣽⣿⣷⣿⣿⣻⣾⣯⣿⢿⣽⣿⣾⣷⡿⣿⣻⣽⣿⣻⣷⡿⣷⡏⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⣿⣌⡳⣌⢳⡒⢮⡱⣉⢦⢣⣕⣧⣞⡴⠵⣿⠉⠳⡈⠿⠃⣈⣰⠏⣀⠂⡁⠒⡌⠳⡌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣟⣯⢷⣻⢷⣯⢷⣯⣟⣾⡽⣟⣾⣷⣻⣿⣽⣿⣻⣷⣿⣯⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣽ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣮⢳⣭⢳⡝⣧⢳⡭⢶⡟⠁⣀⣥⡀⣠⠮⢷⣄⠉⠒⢂⣠⣏⠖⡤⢒⠠⡑⢬⡱⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣯⣿⣟⣿⣾⣿⣷⣿⣿⢿⣿⣿⣾⣿⣽⣾⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⣯⢿⣼⣛⡾⣽⣳⣟⣯⢿⣄⠈⣽⡻⠃⢀⣨⣿⣿⡿⠿⣧⣏⣾⣰⣋⢶⡹⢶⣹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣾⣽⣻⢷⣻⣾⣽⠿⠿⣦⣠⣍⣸⣿⣿⢿⡏⠁⠀⡜⡁⠙⢳⣿⢯⣟⣯⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⠏⠙⢀⡤⣀⣿⠏⠹⢣⠀⠠⡇⠰⣦⠀⠀⣀⢤⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣍⡁⢀⣼⣇⠀⠀⣿⣷⡀⣹⣄⣀⢉⢅⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠄⠈⠉⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣠⡀⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⣠⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣧⠀⢀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠮⠷⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡉⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⣁⣤⠽⡙⠳⣄⠸⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠴⣣⣱⡿⣴⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣛⢛⡛⠟⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣶⣳⣭⣱⢸⣳⡌⢲⡜⣋⢳⣛⡿⢳⣱⢮⣍⠲⢏⠢⣜⡧⠿⣛ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⢃⠀⠃⠀⡗⡎⠣⣔⠪⣗⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠖⣬⠐⢀⡍⡿⣡⡄⠀⠀⠀⠀⠀⠀⠉⠛⠟⡿⣿⣶⣽⣶⣯⣥⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣣⡱⢜⡹⢦⣋⢥⢪⡵⡎⡝⢣⣟⣿⢏⣿⣿⣿⣥⢮⡱⢎⡱⣜⠳⣥⡜⢫⡱⣿ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠸⠠⢸⢳⡤⢜⡣⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⢀⠠⠀⠃⠇⣾⢨⠠⠀⠀⠁⠋⠛⠿⣿⣿⣾⣱⢮⡑⢯⡛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣍⡚⢣⡴⡞⡙⣦⠝⣣⡜⡹⢗⡿⣿⣿⣿⣿⣿⣥⢚⣫⡕⢪⣜⡹⡷⢻⢻⣜⠳⡿⣿ ⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠁⠀⢁⠆⣍⠲⣎⡑⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠝⣙⠠⠀⠀⠁⢱⣿⢄⠀⠉⠛⡿⣿⣾⣽⣣⣜⠳⣏⡟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣹⢧⢎⡱⡜⢫⣥⠞⣋⢦⡙⢧⡥⡟⣿⣿⣷⣧⣣⣌⠲⣙⠶⢎⡱⢞⣍⠳⣏⣿⣿⣻⣿⣿⣿ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡌⡘⢕⡢⠝⣧⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢠⠀⠀⠀⠀⡎⡟⢛⠿⣿⣿⣾⣿⣡⢶⡙⢻⡿⣿⣽⣻⣿⣿⣿⣿⣿⣳⣿⣿⣽⣯⣿⣾⢧⡙⢦⠞⣣⡜⢛⣡⠞⢣⣎⡙⢳⣿⣮⣵⡜⡣⢜⡹⢧⣎⡙⢧⣌⡹⠴⣙⠶⡏⣿⣿⣿⣿⣿⣼ ⠀⠀⠈⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⢀⠀⠠⢃⡆⠉⢦⡙⡧⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠎⠀⠀⠀⠋⣿⣿⣿⣶⣹⢳⢬⡹⣟⡿⣷⣼⣫⢿⣿⣿⣿⣿⣿⣾⣳⣿⣿⣽⠟⣶⣾⣙⢦⡙⢮⣙⢦⡜⠜⣫⡔⢛⢦⡜⡹⠶⣋⡴⡛⢦⡜⡛⢣⢧⡘⢳⣎⡑⡼⡙⢶⡏⣿⣿⣿⣿⣽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠠⢀⡄⠎⡁⠴⡎⡎⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⢫⣞⠀⢀⠉⠟⣿⣿⣿⣮⡱⢼⡹⠿⣿⣷⣮⣱⢻⣿⣿⣿⣾⣹⡿⣾⣇⢍⣿⣿⣼⣿⣻⣿⢾⡩⢶⡙⢦⡛⢥⣎⡕⠪⣜⠳⣬⡜⠳⣬⠳⣬⠳⣬⡜⠞⣡⠼⡜⢱⡼⢋⡴⡛⢧⡏⣿⣿⣿⣿⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⡈⢀⠸⢨⡱⢎⡜⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣱⢴⢫⠟⡿⣿⣾⣣⣱⠷⣌⡻⡿⣷⣵⢎⡱⢟⣿⣶⣏⣤⣚⡵⠎⣱⣓⢢⡿⣾⣱⡟⣿⣿⣿⢼⣚⡵⡚⢧⡘⢻⣌⡳⢎⣅⠺⣍⡰⢻⣆⠳⣌⠳⣌⠶⣋⢦⡜⣋⡴⡜⠹⣱⠞⢩⡷⣿⣿⣿⣿⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠱⠈⣷⠄⠣⢌⣸⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣋⡿⣿⣿⣾⣱⠞⣩⡴⠻⣿⣿⢰⣹⡳⢏⣿⣥⣜⡲⢛⣥⠞⣣⡜⣋⡱⢮⡙⣱⡯⣿⣿⣿⣿⣼⡜⢮⡝⢣⡴⠞⣍⠳⣌⢳⡥⢚⣥⠸⣳⠭⣓⠧⣎⡜⢚⣥⡜⠳⣥⡜⠲⡭⠖⣘⡿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⡇⠈⡇⣈⡖⠘⣧⣇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⢲⣭⡝⠮⣋⣿⣾⣵⠚⣭⡟⡿⣤⢛⣡⡜⢮⡙⢣⡴⢛⡬⢖⡣⢎⡱⡱⣿⣿⣿⣿⣿⣿⣿⢏⡡⢳⣭⠞⣃⠴⣋⡱⢮⠝⣣⡜⢚⡵⡚⢣⠵⣎⠝⣣⡜⢪⡵⡎⢎⣑⡼⢏⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⡀⣽⠸⣞⢿⡧⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣾⣋⢿⣿⣿⢾⣜⣣⣌⠿⡞⣶⣤⢤⣦⠲⢳⣛⢏⡡⢲⣥⠞⣍⡱⢮⡖⣉⡿⣿⣿⣿⣿⣿⣿⣿⠞⣩⠶⢋⡴⢚⣣⢜⡮⠖⣋⠴⡞⡍⢓⡬⢛⣡⠼⣋⠵⡎⢏⡡⢞⣍⡲⡟⣿⣿⣿⣿⣿⣿⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡡⠐⢼⢯⡗⣏⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡿⣿⣿⣿⣿⣿⣿⣿⣦⠞⣋⢻⣷⣨⡤⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢦⠿⣋⡱⢮⣏⣿⡟⣿⣿⣿⣿⣗⣿⣿⠼⢫⣥⠳⣪⢝⢢⡿⢿⣩⠵⣪⠵⣚⠧⣒⠝⣣⡔⢞⡡⢞⠣⣱⠮⣙⡿⣿⣿⣿⣿⣿⣿⣿⢀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠚⠠⣺⡗⡧⡇⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡙⢧⢏⣼⢀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢳⢹⣿⣿⣿⣿⣿⣿⣩⠶⣏⣶⣭⢓⣩⠶⢍⡳⢌⣿⣿⢿⡼⠞⣣⡝⢣⡴⡛⢣⣬⡓⢬⡛⢥⡳⢏⡿⣿⣿⣾⣿⣿⣿⣿⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢄⡘⡆⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣹⢦⡛⣽⢜⠀⠀⠀⣿⡀⢿⠚⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣾⣿⣿⣿⢿⣃⡴⢛⣥⡜⡹⠶⣎⡝⡣⢜⣿⣿⣿⢿⢎⢣⡱⢳⡦⠏⢣⣘⢳⡬⠝⣢⠿⣿⣿⣿⢢⣜⡟⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡁⠎⢁⣾⡇⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⢿⣾⡟⢀⠀⠀⠃⢡⡟⢀⣤⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⣯⣿⣿⢺⣥⠜⣣⡜⢋⡵⢎⡱⢮⡙⣷⣿⣿⣿⢻⣰⡼⡛⢬⢛⢦⡜⢋⢦⡜⣎⡷⣿⣵⢣⢦⣙⣿⣿⣿⢠⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡜⠂⢼⣼⡟⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣿⣿⣿⣿⣾⢃⢠⠀⠀⠀⡇⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣘⡵⢎⡱⢞⡣⢜⢫⢤⡹⡦⣿⣿⣿⢻⡵⢎⠧⣘⠞⣣⡔⢚⣭⡖⢏⣹⢱⡸⢳⣬⡟⣿⣾⢀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠰⢈⣿⣥⡟⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⢰⡼⠀⠀⠀⠞⠠⣿⢹⠀⠀⠀⠀⠀⠀⠀⠊⠥⡔⣣⢝⠪⠒⠉⠀⠀⠀⠀⠄⣷⣿⣿⣻⣿⡻⡝⢫⡥⢚⣭⡓⢦⣙⣶⣿⢿⡻⢎⢣⡵⢎⣩⡵⢎⡱⣞⣬⡛⡥⡜⢫⢿⣿⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠆⠁⣷⣾⡏⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣾⠁⢸⠁⠚⡼⢃⠿⣿⣀⠤⠦⠒⠀⠉⠟⡺⠀⠀⠀⠀⠀⡀⣀⠤⠤⡲⣒⠖⠭⠭⡉⣆⣶⣿⣽⣾⣿⢷⠿⣙⡹⢭⠧⣌⡲⣖⣶⣷⢿⡻⢗⣊⡵⠏⣢⠞⣍⠹⣻⡿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡈⡾⠞⣏⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⡁⢤⡴⠏⢠⠀⣧⣼⣋⢽⠦⡤⣀⣞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣠⡦⣗⣿⣟⣯⡷⣟⣯⣷⣫⣵⣾⣮⣵⡬⢿⣌⠳⣌⠹⢳⢧⢌⣷⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢏⢳⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⠀⡍⡀⠃⢸⠀⠁⡿⢺⡌⣌⢷⣌⣘⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⡶⡛⢏⣡⡴⣛⢧⣌⡳⢎⠳⣌⡳⢎⡱⡳⢎⣋⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⢾⣡⡽⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⠀⢢⡄⠉⡟⠱⡿⣿⣸⠃⢰⡀⣦⢰⣏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠻⢹⣬⠶⢎⡹⣜⠳⣌⡹⠶⢏⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡞⢋⣴⡾⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⡃⠄⡟⣵⢂⡁⣯⣿⢸⡏⠀⠀⠀⢳⣡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⢦⠶⡛⢻⣟⡟⡿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠟⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣪⠁⢳⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠐⡟⢶⡀⠈⠠⡇⣿⢸⢾⠀⠀⠀⡀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠀⠀⠀⠋⠾⡯⣴⣉⠉⠋⠛⡼⢃⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠏⠏⣳⣿⣿⣿⣿⣿⣿⣿⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⡟⣢⢀⠔⠂⢀⡿⣾⠁⢸⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠋⡴⢀⠀⠀⠀⠀⠁⡾⣬⠃⣆⣉⣰⢎⡁⠰⡜⠃⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠰⢟⣱⡿⣿⣿⣿⣿⣿⣿⢻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣹⠄⠂⠡⢈⠠⣿⢻⡇⢀⠀⠀⠀⠀⣧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣌⡸⠤⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠛⠾⡴⢀⠀⠀⠀⠀⠁⠈⡧⢬⢈⠱⢆⠎⡀⠜⣃⠥⡍⠊⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢫⡼⣻⣴⡟⣿⣿⣿⣿⣿⣿⠜⡣⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⠘⢈⠠⠐⠇⣿⣿⢾⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡁⠦⠑⡈⠢⠙⠉⠀⠀⠀⠀⠀⠉⡏⢰⠐⡁⢋⠶⣠⠀⠀⠀⠀⠀⠋⡿⣱⠟⣵⢒⠌⡰⠚⢡⣛⠷⣠⢙⠦⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⢑⡾⣿⣿⣿⣿⣿⣯⣺⡍⢒⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢻⠀⢂⠀⡟⣽⣿⢰⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⢤⡘⣆⠿⡶⣯⢿⠛⠭⡿⣲⣁⠂⢀⡞⣠⠃⠘⠀⠋⡷⢛⠾⣰⢟⣾⣵⢂⡑⠢⢍⡡⠞⣤⡑⠪⣅⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⢟⣤⠏⣡⡟⣿⣿⣿⣿⣿⣿⢬⡓⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⢻⠌⠀⡇⣿⣾⠨⠀⠀⠀⠀⠀⠀⠀⠵⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⢤⠠⣇⠻⣿⡟⣿⣾⣀⠉⠋⠟⣽⠋⠿⣴⠀⠏⣾⡡⢒⣁⠴⡏⢋⣲⢍⠣⢤⠘⡾⢁⠚⠒⠔⢨⠈⠃⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⡏⠃⡿⣻⣴⡟⣿⣿⣿⣿⣿⣾⡜⠣⣍⡧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⢆⢞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡨⣿⣿⣿⣿⣷⠟⣿⣟⣾⣯⣱⢇⣹⠛⡼⣣⠤⡐⠣⣐⡞⣾⣉⠖⡈⠱⢆⠿⢣⣠⠀⢀⡕⠊⠇⣾⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡤⢀⠀⢏⣷⣿⢏⣯⣿⣿⣿⣿⣿⣿⢼⣋⢢⡜⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡱⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⢱⡶⣷⣎⣱⠰⢮⡕⣯⣮⣁⡰⠏⣪⢡⡔⢈⡳⢧⢡⡌⡒⢌⡃⠥⣈⠰⣟⢳⣰⠀⡞⡞⢉⠡⣆⢿⠉⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡠⡥⢟⡿⢷⣿⣿⣿⣿⣿⣿⣿⢲⢋⢤⡙⢢⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣽⠶⡟⢼⣩⡼⢋⣼⢛⠦⢋⡵⣌⠒⢡⡨⢘⡇⡟⡙⡄⠸⢇⠸⢣⡄⡟⣱⣸⠀⡎⡞⢄⠚⣁⠱⢢⣍⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⣀⠋⠵⣿⣟⢣⣿⣿⣿⣿⣿⣿⣿⣿⢎⢃⣤⠚⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡆⡙⣾⠧⠬⠦⠒⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣮⠲⡙⣬⣣⡴⣺⢌⡒⠏⢺⢚⠮⣡⣞⢡⡜⠣⣇⡇⡔⠏⣽⠞⢣⡞⣴⡞⠀⠃⢣⣸⢓⠤⡑⠣⢆⡈⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⣠⠋⣼⣥⡓⡿⣿⣿⣿⣿⣿⣿⣿⢻⠦⣉⢲⢎⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⢁⢸⡃⢼⠈⢂⠠⡐⣈⢦⠸⠀⠋⠒⠒⠛⠒⠴⠤⡬⣂⢀⠴⣤⣤⣿⣿⠙⠭⠍⡋⢒⢒⠷⠛⠼⣬⠡⢒⡎⠁⢸⡼⠇⣷⡖⠀⡠⠀⡟⢠⠐⣠⡼⡘⠲⣌⡃⠰⢀⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠖⡡⢹⡜⡞⣻⣿⣿⣿⣯⣿⣿⣿⣷⢿⢣⡔⠮⢑⣣⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣷⣿⣿⣿⣿⣿⢸⡀⢸⡜⠈⠐⢁⠤⠁⠛⠵⠋⣾⢧⠖⠶⡤⠲⡐⠌⠀⢁⡉⠋⠞⡴⣀⣁⣉⠋⠛⠶⠶⠶⠛⡉⣆⢷⡈⠜⢁⡾⡇⠋⣼⠘⢯⠀⠁⡟⠈⠀⠐⢀⢣⡌⠆⡐⢊⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⡾⣑⠆⢏⣿⣿⣿⢾⣽⢾⣻⣽⣾⣟⢻⡰⢜⡱⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⢿⠀⢸⢻⠉⡄⠀⠆⣫⡿⣴⢉⡶⣰⣤⣀⣀⣀⣀⢤⣶⣿⣿⣿⢈⠀⡷⣼⣁⣹⠙⠀⠀⠀⡁⣄⣧⡽⢧⡉⡞⢽⣸⡑⢦⠁⣸⠏⣯⢸⣇⠀⠀⠀⠉⣀⢤⣠⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡡⢜⣯⣿⣿⣿⣿⣞⣽⢿⣯⣟⣯⣿⡔⡎⡑⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣼⣾⣦⠭⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⠐⠀⠀⢿⣯⢿⡿⠻⠀⠀⠀⠀⡎⣿⡇⠺⣸⣿⡄⠋⢠⡿⡞⢀⢷⠹⡼⠀⠋⡔⢈⠀⠁⢰⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢣⡼⣟⣿⣿⣿⣿⣿⣟⡽⢾⣻⢷⣽⣿⢙⣻⣿⣹⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣠⢾⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣒⣶⣿⢶⠷⠲⢲⢼⣼⡞⢢⢸⣷⢼⠌⢣⣰⠊⣡⠰⣏⣀⣀⠀⡇⠘⠀⡼⠀⠀⠀⠀⠐⣋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⢃⡌⣫⡿⣿⣿⣾⣝⣳⣭⣷⣿⣿⣟⣯⡾⣽⡾⣟⣿⣸⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣽⣪⣸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠛⢲⠻⠓⠛⠛⢿⣴⣙⢠⣗⡀⢾⢃⡔⠊⢡⡔⠪⣅⠰⠀⠁⣼⠀⡎⠀⠀⠈⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⢆⢋⡿⣽⣿⢿⣵⠶⣃⠴⣋⡴⡞⣿⣿⣿⣟⣷⣟⣿⣿⠹⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣦⣠⢀⠤⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢷⣠⡼⢢⡍⡜⣦⣥⢊⠡⣎⡇⠁⢼⠣⢃⢄⡰⡜⠋⣰⠀⠁⡼⠀⠀⠀⠀⠏⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢁⡿⣵⢞⣯⣿⣸⡩⡐⢩⡴⢋⣡⢷⣏⣿⣿⣻⣽⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡺⣠⠀⠀⠀⠀⠀⡗⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣳⠞⢯⡽⢃⡇⠭⢡⡜⡏⡇⣰⠯⠻⣉⡜⠌⣸⠀⠁⡴⠀⠁⠀⠀⠟⣰⠀⠀⠀⠀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢂⡥⠘⣫⡷⢿⣰⠆⠃⡄⠑⡬⠓⣨⠵⣻⢿⣿⣿⡽⣿⣿⣿⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣸⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⢗⣠⣾⡗⡟⠄⠩⠰⣹⡎⠡⣏⡟⢊⠡⢰⢸⠉⡠⠀⠀⡇⠁⡟⣠⠀⠀⠀⠀⠀⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⢊⢡⢰⡿⣞⣵⣾⠰⢠⠘⡡⠒⣌⠓⡬⣟⡿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠒⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠁⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⣀⣁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⢒⣸⢻⣡⠖⡉⢳⠖⡼⡟⢨⠦⣉⠣⣼⠀⠀⠃⠚⠃⡰⡼⠀⠀⠀⠁⢈⡱⡜ ⠀⠀⠀⠀⠀⠀⠀⠎⢡⢎⣈⡷⣡⠟⣿⢾⡁⠌⡌⡓⠬⣛⠾⣿⣷⣿⣿⣿⣿⣿⣿⣿⢾⠿⢣⠚⠛⠛⢟⠻⠙⡈⢀⠤⠒⠈⠀⠀⠀⠀⡀⣀⠤⠯⡿⣿⢼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠋⣿⡐⠭⠒⡡⠏⢣⢸⠱⢠⢃⠠⣷⠛⡿⣰⠀⡼⠟⢀⠀⠀⠉⠊⡄⠑⡯ ⠀⠀⠀⠀⠀⠀⠀⠐⢋⠥⣊⠶⣳⠿⣿⠚⢢⠘⢎⠣⢆⢻⢿⣍⣾⢿⣿⢯⣻⢷⣻⣾⣽⢾⣻⣽⢾⣿⣟⣿⣟⣿⣯⢿⠻⡛⠉⠈⠀⠀⠀⠚⠶⢿⣛⡛⣛⢛⠷⠯⣿⠿⠻⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡇⠰⢋⡰⣀⠉⡟⢰⠣⣐⠨⡱⠏⡴⢀⠀⡇⢱⡼⠁⠞⠵⣢⠅⣀⠠⡥ ⠀⠀⠀⠀⠀⠀⡀⡍⠆⠣⢌⡱⢎⡇⣿⢟⢎⠢⢌⠱⢦⡅⣥⣾⠷⣛⡍⢭⣭⣭⣫⣟⣚⢟⢷⡭⢯⣚⢶⣶⡾⣷⣾⣷⣿⣿⣿⣿⠻⡛⠙⣍⢫⢍⣪⣃⣴⣤⣣⠿⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠥⠰⠄⠤⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡇⠴⢨⠀⡿⣶⣃⡄⠚⣡⠞⣠⠀⠀⠀⠁⣸⡤⠟⣰⢎⡁⠸⠀⠀⠇⡁ ⠀⠀⠀⠀⠀⠀⠌⠃⣡⠲⣌⠳⢇⡯⣿⢣⠤⢊⢄⡘⠆⣉⣘⣎⠤⠶⣶⣖⣛⣍⣈⠷⣹⣌⡒⣈⣓⣄⢊⢇⡈⠱⣎⣧⡝⣾⣟⣿⣿⣿⣿⣽⣻⣿⣿⣻⢈⠎⠀⣇⡗⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠉⠔⣀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⡏⢸⠀⠀⡄⡽⢱⣿⢐⢨⡱⢆⠡⣸⠀⠀⠀⠁⠋⡵⠋⡼⢃⡤⠏⣮⢀⠀⠀⣷⡻ ⠀⠀⠀⠀⠀⠀⠐⢱⡱⠦⣉⡱⡆⢻⣾⠻⢣⢍⢢⠏⢻⡏⢼⠦⣉⠆⠁⡰⠒⢉⣂⠡⡐⣄⠋⢉⠩⡐⢒⢢⡝⢣⣭⣶⡿⣟⣷⣾⣷⣿⡾⣽⣟⣻⣿⣿⢸⢡⠀⡏⡹⣡⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⠊⠑⠡⠚⠉⠒⠠⣟⣼⢀⠀⠁⠗⣼⠀⠀⠀⠀⣆⡧⢻⠿⡐⡩⢞⣴⢈⠝⡉⣒⢭⠿⡴⡮⡄⠚⣫⡴⠀⠀⠀⡔⡂⣄ ⠀⠀⠀⠀⠀⠂⡄⠨⡳⢆⡘⡱⢋⢷⢟⣿⣿⣽⢏⣿⠞⣿⣼⢮⡙⢭⡋⡛⠖⠘⡡⠆⡀⡌⢵⠦⢸⡳⣚⢿⠭⠻⡙⢔⠢⡐⡼⡿⣴⣟⣤⣺⣛⠐⢹⡴⠀⡀⠸⣆⡟⣶⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⢋⣾⣾⡡⢈⠃⡿⣾⠀⠁⠞⣳⣴⠀⠀⠇⢲⠆⣠⣠⠋⣻⣥⢋⠐⠀⠀⠀⣁⣋⡴⢁⡩⠟⣲⡤⢀⠀⠀⠀⠀⡄⠤⣀ ⠀⠀⠀⠀⠀⠂⢁⡌⠓⢬⡘⡿⣾⣹⣷⣿⢻⣿⣿⣿⣿⣿⣋⢟⣿⣾⣹⣽⠶⡛⠛⢋⣈⠒⡒⠒⠴⠤⠤⠤⠤⡲⣒⡙⢈⢠⡟⢹⡶⢚⣀⢵⣬⡐⡧⠈⠀⠊⢠⠀⣀⡤⣀⠦⠘⠁⡎⢀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠿⡏⡿⣿⣾⢁⠋⡵⠞⣠⠀⠀⠀⠆⠔⠀⠀⡄⣀⣀⡩⣕⢧⠤⡦⢭⣣⡨⠖⣠⡀⠀⠀⠀⠀⠀⠁⠀⠉⠂⠀⣀ ⠀⠀⠀⠀⠠⢀⠱⡍⠣⢖⡉⣿⣼⡆⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣹⣩⠴⢏⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢤⠤⣠⣄⠤⠤⣤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠃⢸⣤⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⡴⣠⣏⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠝⡿⣊⠡⢐⡩⢚⠴⠶⣠⠀⠀⠀⠀⠀⠀⠁⡟⣠⣤⢲⠛⠲⠞ ⠀⠀⠀⠄⠀⣀⠸⡇⢩⢦⡙⣥⢻⣁⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠔⢀⠀⠀⠁⠉⠉⠉⠈⠀⠀⡀⣿⣧⣽⢊⠴⡠⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠖⢭⡉⡶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⢠⠀⢄⠀⡏⠠⠒ ⠀⠀⠀⠈⠀⣊⠆⡈⣆⠿⡚⡌⣷⠘⠢⠀⣏⣿⣼⣿⣿⣿⣿⣿⣿⣷⣳⣜⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠰⣀⣀⣁⢋⢟⡿⣽⢂⣾⢿⠈⠄⣿⣿⣿⠙⠉⠛⠅⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣶⣠⣀⠀⠀⠁⠀⠀⠀⠞⠳⠀⠀⠤⣋⣿⢀⠀⠀⠀⡅⢺⠀⠀ ⠀⠀⠠⡑⠆⠡⢄⠐⠀⡀⢷⢈⣻⢹⠀⠀⡀⡇⣇⣿⣿⣿⣿⣾⢷⡹⠦⣏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⣿⣿⣿⣻⣽⣿⠿⣿⣲⢺⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠷⣚⢀⠀⠀⠈⠈⠀⠀⠒⡁⢊⡑⠫⠛⠛⡟⣵⢀⠀⠀⠁⡜⠀⠀⠀⠉ ⠀⠠⡔⡈⠰⢀⠀⠀⠀⠀⡀⢧⣄⣿⠀⠀⠀⡇⡄⡧⣿⣿⣿⠜⢩⡻⢝⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⣿⣿⣿⣿⣿⣿⢷⣯⡽⣿⣷⣿⠷⣾⣿⣯⠷⠾⠿⠛⠛⠛⠙⠛⠛⠔⠶⠶⠶⣶⠶⠐⠀⠀⠄⠤⠲⢒⠒⡐⡁⠟⡿⢶⠭⡿⣴⠨⠑⢀⠋⡶⠗⠿⣭⣄⠉ ⠀⡐⠢⢀⠈⠀⠀⠀⠀⠀⠀⡟⢣⣿⠀⠀⠀⡆⡩⢌⡱⣿⣿⡿⣿⣼⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⠿⣿⣿⣿⣿⣷⣿⣷⣾⣟⡷⣯⣞⡿⣟⣯⡽⣻⣽⢿⣯⣳⣽⢿⣯⡿⣴⡇⢹⡂⣌⠢⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⡶⣴⣐⠢⢐⡠⠟⣶⢤⠶⠛⣛⣜⣀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⢴⡏⣸⠀⠀⠀⠀⢸⡍⠣⣾⣾⣿⣿⡓⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣽⣿⣷⣾⣟⣻⣷⣯⣞⣻⣿⢯⣿⣞⡽⢾⣻⢷⣯⡾⣟⣯⡷⢯⣿⣼⠋⣫⢸⡀⢾⠙⠈⠃⠙⠈⢀⠀⠀⠀⢦⠽⠤⠤⣤⣤⣤⢴⣤⣤⡤⢤⣤⣤⣤⢤⣤⣤⣠⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣼⡟⣾⠀⠀⠀⠀⠀⠄⡏⠺⢌⢱⣿⣿⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣳⢾⣽⣻⣷⣟⢯⣻⣷⢯⣽⢾⣽⣾⡿⣿⣾⣶⣶⣶⢿⣿⢿⣿⣶⣵⣫⡟⣶⣤⢀⠀⠀⡀⣤⠑⡀⣼⠦⠒⠛⠛⠉⡉⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠇⢸⠀⠀⠀⠀⠀⠀⠠⡃⢻⣑⡧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡿⣿⣿⣽⣿⣿⣞⣻⣷⣞⣽⡾⣽⡾⢿⣯⣳⣽⡾⣽⣻⣷⣟⢯⣷⣯⣟⣯⡷⢿⠿⠾⣴⣠⣀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠀⠀⠀⠀⠀⠀⡆⢿⡡⡾⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⣿⣿⣿⣿⣿⣿⣯⣽⡾⣟⣻⣷⣯⣟⣯⣟⣯⢷⣽⣻⣷⣟⣯⡽⣾⡿⣞⣻⢷⣻⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣳⣾⢏⣿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣷⣿⣿⣿⣯⡽⢾⣻⣽⢿⣳⣾⣟⡷⣞⡿⣟⣯⡷⣟⣯⡽⢿⣯⣞⢿⣯⣟⣿⣾⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⢸⠀⠀⠠⠀⠀⠀⠀⠀⡄⢻⣿⣿⠧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣻⣷⣿⣿⣿⢾⣻⣽⢿⣯⡽⣾⣟⣳⣿⣞⢿⣯⣟⣯⡽⢿⣯⡽⢿⣯⢿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣽⢾⣻⣿⣿⣿⣾⣟⢷⣯⡽⢿⣯⣟⣯⣻⢷⣯⢷⣽⡿⢯⣽⡿⢯⣽⡿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠌⣹⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣟⣻⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣾⣻⣷⣟⣿⣿⣿⣟⣳⣾⣟⡽⣻⢷⣻⢷⣻⣽⣻⣽⡾⢿⣳⣽⡿⢯⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠇⠘⣿⠀⠀⢀⠀⠀⠀⠀⠀⣿⣽⣿⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣾⣻⣷⣟⣿⣿⣿⣿⣿⣻⣷⣟⢯⣷⡽⣾⡽⣾⡿⣟⡷⣟⣯⣟⣯⡽⢿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⡘⣿⠀⠀⠠⠀⠀⠀⠃⡟⢣⣟⢰⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣾⣻⣷⣟⣿⣿⣿⣿⣿⣿⣿⣽⣾⡿⣟⣯⡷⣯⣟⣷⣞⡽⣾⡽⢾⣻⢿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠤⡘⢧⡇⢹⠀⠐⠂⠀⠣⣜⡷⡙⡧⣸⡇⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠏⣽⣻⣷⣟⣯⣳⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⢾⣻⣽⣾⣟⡽⣻⣾⣟⣯⣟⣿⣿⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡑⢢⡙⢣⣼⠂⠀⠠⠁⠀⠀⣦⡙⡬⣷⢿⣉⣿⢸⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣟⣯⡽⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⣟⣯⢾⣻⣷⢯⣻⢿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠢⢍⡰⡟⢂⢀⠀⢀⠀⠈⡀⠀⣄⡳⢌⣯⣟⣿⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣯⡽⢿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣽⣻⣽⡾⢿⣯⣟⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⠱⢢⡜⡏⢹⠀⠀⠄⠀⢀⠀⠐⠀⠂⡄⢷⡌⣿⣟⠸⠀⠀⠀⠀⠀⠏⣿⣿⣳⣽⡿⣿⣿⣿⣯⡷⣞⣽⣻⣾⣟⣳⢿⣳⣽⢿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⠀⠀⡁⢲⢦⡕⣧⢹⠀⠀⠀⠈⢀⠀⠁⠀⠀⠠⢛⣇⢻⣇⠘⠀⠀⠀⡟⣿⣿⣞⣽⡿⣿⣿⣾⡿⣞⣻⣽⣻⢾⣽⣻⣾⡽⣾⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⡀⣣⣷⢿⠀⠀⠐⠀⠠⠀⠀⠀⡇⢹⡧⢻⢡⢶⠙⠟⡿⣿⣿⣻⣾⣟⣿⣿⣯⣟⢯⣷⢯⣷⢯⣽⣻⢾⣽⣻⣽⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠠⠀⠀⠠⠀⠀⠀⢠⣷⢸⠈⠀⠂⠀⠈⠂⠐⡆⢻⣴⢮⡳⢍⣢⣯⣿⣿⣿⡾⣟⣿⣿⣽⢾⣻⣽⣻⣽⣾⣟⡷⢯⣽⣻⢷⣯⡿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠁⠀⠀⠠⠀⠀⡀⢳⠀⠀⠈⠀⠀⠀⠀⠀⡈⢧⢼⣊⢷⢭⡘⡧⣷⣿⣿⣿⣿⣿⣟⣯⢷⣯⡷⣟⣯⣳⣾⣟⡷⣞⣻⢷⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠄⠀⠀⠠⠀⠐⣾⢇⡌⣯⡜⠱⣫⣧⣿⣿⣿⢾⣻⣽⣾⣟⣯⡽⣻⣾⣟⣳⣾⣟⣳⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⢁⢦⡘⣿⠰⣳⢄⣿⣿⣿⣿⢷⣻⣽⢾⣻⣽⡿⣞⣻⣷⣞⣻⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠐⠀⠂⠄⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡘⢧⡌⡜⣻⡑⢦⡘⣿⣿⣿⣯⡽⣻⣽⢿⣯⡷⣞⣻⣷⣯⣟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡜⡙⣧⡚⢌⠳⣆⣿⣿⢿⣿⡿⣟⡿⣟⣻⣿⣟⣻⢿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
my dad’s dick was hard today and i looked at it, he saw me lookign at it and he told me to meet him in his room in 5 minutes. i thought he was going to tell me a surpise like buying me something but no… i went into his room and keep in mind my mom is in another country. but when i went into his room he was naked and uh he raped me . //mia
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