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