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