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