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