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