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

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