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