⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⡿⣿⣿⣿⣿⡯⠻⣿⣇⢱⡄⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠸⢸⣃⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⢸⣿⣿⣿⣏⢿⣷⣾⣿⡜⣷⢳⡄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⣇⠃⢿⢰⠸⢠⣿⣿⣿⡟⣿⣿⣿⣿⣿⡇⢸⢸⢸⣿⣿⣿⣿⡘⢷⣿⢻⣧⢯⡟⣿⡀⠈⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣡⡷⣲⡎⣼⢣⣷⣿⣱⡾⠸⣿⣿⣿⣿⣿⢃⠔⢸⢸⡟⣿⣿⣿⠇⡎⡻⢇⠛⡮⣇⣿⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣱⣿⢱⠛⢸⣿⣿⢻⢃⢇⣿⣿⣿⣿⡇⣾⠈⢼⢸⡷⢹⣿⣿⣦⠉⣽⡸⣷⢁⠟⣿⣾⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡇⣿⣿⣹⢸⣼⣿⣿⠘⡌⣼⢿⣿⣿⣿⣵⣿⠀⣠⡀⡇⡜⣿⣿⣿⡦⣿⢇⢻⣦⡀⣿⢻⣿⡀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⢸⣿⡟⡇⢾⣟⣿⣿⠀⣼⣿⢸⣿⣿⣿⢹⣿⡀⢼⣇⣧⢱⡹⣿⣿⢷⣿⢺⣧⡏⡇⢸⣹⣽⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⡟⣼⣿⢹⡇⣼⡋⠿⠏⠁⠛⠛⠘⠛⢛⡋⣺⣿⡇⢸⡿⣿⢸⣧⣻⣿⠠⡞⢻⡇⠇⡞⡽⣿⢻⠁⠀⡇⢀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣿⡇⣿⢇⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣛⣿⡇⢸⡿⢘⣃⠀⠃⠀⠸⢿⣸⠇⡻⡘⡇⣿⠸⡀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣿⡇⣿⠆⢠⡃⡃⣤⣔⠀⠀⠀⠀⠀⠀⣂⡇⣿⣿⣷⠀⡇⣇⢷⠀⠀⠀⠀⠀⠈⠀⡃⣿⡁⣿⣆⡇⢸⡜⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣼⣿⡇⣿⡟⣾⣧⢷⡹⡇⡆⠀⠀⠀⠀⢰⣿⣧⣿⣿⣿⣦⠁⣿⢾⠂⠀⠀⠀⢀⠈⣴⣿⢙⡀⢹⣼⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢾⣿⡇⣿⠃⣿⣿⢸⣧⠱⡇⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠁⠀⠈⢸⣿⡟⡈⡇⢰⣿⠀⡏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⣽⣿⡇⣿⠀⣿⣿⢰⡋⠐⢝⡆⢠⠀⢀⣻⡘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⠀⢠⢸⡯⢁⢃⡙⢤⠻⢸⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⣘⡻⠿⠍⠂⢋⣭⡘⡁⢮⠲⢌⠻⣧⣾⣿⣷⡙⠿⠿⣿⣿⣿⡿⢗⣁⡤⡁⠀⠞⣩⢠⣿⢸⢃⠾⡀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⢀⠀⣽⢉⡃⠇⢁⠌⠲⣅⠪⠝⠻⠛⠿⠾⠟⠛⠭⠵⠞⠋⠁⠊⡁⡀⢁⣛⢨⡕⢨⣼⠃⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡛⢛⡈⠐⠢⠭⠰⡆⢀⡀⠈⠀⠘⠃⠀⠰⠠⠈⠋⠀⠤⠀⠄⡐⠀⠀⠚⠋⢈⡁⢨⡇⢘⣉⣥⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⢉⡀⣃⠘⠩⠥⠄⠠⠄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠬⠠⢰⡇⣘⢐⣈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⡒⠀⠠⠠⠀⠠⠦⠌⢀⣀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⣤⣬⢀⣐⣀⣙⠘⢣⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⢐⣿⡥⣴⡆⠀⠠⠖⠄⠖⠉⠀⠘⠃⠀⠀⠀⡀⠁⡀⢀⡀⠀⠀⠀⠂⠈⠀⠀⠀⠈⠙⠉⠿⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⣩⠀⠅⠀⠀⠀⠤⠀⠈⠀⠀⣀⣄⣶⡶⠂⠀⣠⡄⠀⠐⠀⢤⡉⢁⣀⠀⠀⠂⠀⡘⠀⡖⡁⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡒⢣⡄⠀⠀⠀⠀⠀⠀⠀⡤⠆⡘⠁⠀⢀⣶⠘⠀⠀⠀⠐⣀⣀⡄⡉⢀⠐⠶⠙⣂⣥⣭⣥⡆⠰⠍⠐⢂⡁⣈⡁⢤⠡⡀⠰⢂⡬⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠗⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢀⢒⠀⢀⠀⠨⠈⠙⡀⠠⠀⠐⣘⣛⣻⣥⣤⣶⣤⢀⣟⣓⣀⠛⠀⠰⡖⡀⠰⠀⡃⢘⠃⠑⡃⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⡁⠀⢒⠀⠀⠀⠀⢀⡂⠄⠀⡀⠀⠀⠄⠂⠙⠀⡄⡀⡌⠅⣀⠆⣾⢠⠁⣿⣿⣿⣿⣿⣿⠃⢢⡿⠁⡿⡔⠀⠂⡴⢂⡆⠰⡀⢰⠀⣤⠃⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣨⡄⠀⠟⠀⠀⠀⠀⢁⠄⠀⠀⠀⢀⣤⡆⠰⢁⣼⡇⠇⣿⠀⡏⢠⡙⠸⢣⢘⢻⣿⣿⠿⣡⣾⣾⢅⣚⢱⢁⣶⢈⢅⣾⢁⠱⠃⣼⡆⢋⢸⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡇⠀⡄⠀⠀⠀⢠⡄⠀⢠⡇⠀⣾⣿⠀⢠⣿⡏⣦⢰⣿⣿⡅⣿⣼⢰⠘⣷⢱⣦⣶⣾⣿⣿⣿⣿⠁⠂⢸⡌⢠⣿⠋⠀⢰⣧⣿⡇⢠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠋⠀⡀⠀⢀⣾⡟⠁⠀⢸⠃⡀⢹⠃⠀⣼⣿⢹⣷⠸⣿⣿⢗⣧⡍⠎⣿⣿⣷⡝⢿⣿⣿⣿⣿⡏⡼⠀⡌⢡⢸⡟⣼⢠⠻⡼⢻⡇⣌⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣖⣸⠃⢀⣾⠟⠛⠓⢶⣟⣸⢃⠂⢠⢃⢹⣿⢸⣗⣾⣿⣿⣼⡇⣣⢡⢈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⣶⠈⡎⣼⡇⡿⠐⡅⢸⣇⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣌⠿⣴⡿⠃⠀⠀⠀⣴⣿⢳⣞⠄⠻⢸⢸⡇⣾⣿⣻⣿⣿⣿⣷⡇⣼⣿⣷⡙⣿⣿⢿⣿⣯⠃⠆⡀⡇⢣⠄⣼⣿⡇⣷⠹⠀⣾⢸⡇⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣧⡙⠀⠀⠀⠀⢠⣿⡇⣸⡟⣰⡀⣿⡇⠇⣿⡿⣿⣿⣿⣿⣷⠁⣿⣿⣿⣿⡜⢿⣷⣬⠛⠌⢠⢱⡇⢋⣾⣿⣿⡇⣡⢓⡄⠇⣆⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡟⠀⠀⠀⠀⠀⠈⣿⣻⡿⠃⣽⠁⢰⣀⢀⠌⡏⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⡌⢿⣿⠑⠀⡀⢞⡁⣿⣿⠹⣿⣿⡿⠚⢿⡇⢿⢘⢿⡇⡑⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀ ⣧⠻⠁⠀⠀⠀⠀⠀⠀⣿⡿⡅⢰⡟⡘⡌⢸⢨⠀⡇⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⡿⣊⠃⠰⠸⣷⡄⢍⠻⠏⣆⢻⣿⡄⠀⢼⢰⡀⢸⡎⠇⣃⠀⠀⠀⠁⠹⢦⣄⠀⠀⠀⢠⣾ ⡸⣷⠀⠀⠀⠀⠀⠀⡐⣿⡶⢃⣿⡇⣿⡟⠸⠈⢂⣇⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣧⠋⢀⠇⣿⣷⣶⢈⢂⡢⢝⠊⢿⣿⢹⡏⣌⡇⣸⢇⠂⢼⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣾⠟ ⡄⢻⠀⠀⠀⠀⠀⣴⣿⣆⠸⢸⣿⡇⢿⣇⢠⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⡻⠈⠿⠿⣿⣇⢁⠹⣿⣶⡌⣙⠻⠇⡏⡁⣿⣾⠀⢸⡏⡀⠀⠀⠀⠀⠀⢀⣀⡿⢧⣼