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