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