⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣤⣶⣶⣶⣤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣮⣿⠋⢀⠙⡟⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠂⢀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢫⣿⣤⣀⣤⣧⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠐⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡿⣷⡄⠀⢄⠀⠀⠀⠀⠀⠀⠂⢁⣠⣤⣽⢷⣯⣟⣯⣤⣀⡈⠐⠄⠀⠀⠀⠀⠀⡀⠀⡠⣪⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⡀⠀⣠⣾⣿⣳⡿⣽⣻⣦⠀⠀⡀⠀⠀⠀⠀⠀⣇⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠀⠃⠀⠀⠀⢀⠈⢀⢔⣵⣿⣳⣯⣟⣷⣄⠀⢄⠀ ⠘⢄⠈⠫⡻⣞⣷⢿⣻⣷⣻⢷⣄⠈⢀⠀⠀⠠⡀⠙⠿⣾⣷⣿⣾⣿⣟⣿⠾⠋⢀⠅⠀⠀⡀⠁⡠⣫⣾⣟⣷⣯⡷⣿⢾⠝⠀⡠⠃ ⠀⠀⠣⠀⠘⢜⡻⣿⣧⡻⣟⣿⢿⡄⠀⡀⠀⠠⠘⠀⠀⣀⢸⢸⠀⡇⣇⣀⡀⠀⠃⠠⡀⢠⠀⢸⣿⡿⣧⠿⣻⣧⡿⡟⠃⠀⠜⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢎⣻⣽⣮⠛⢻⣧⠀⠋⢀⠄⣶⣩⣛⣲⡽⣼⡼⣧⣯⣕⣒⠧⢒⡤⣀⠈⠀⣾⣟⠙⣡⣾⣟⠷⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⠶⢮⣻⡠⣊⢓⡭⢖⣏⢻⡈⡇⡿⣱⡈⡟⡀⡏⣿⢓⢮⣒⢗⠠⣿⡡⠶⠿⠛⠁⡠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⡀⠀⡠⣋⣪⠾⣝⢾⣎⣻⠾⠗⠛⠋⠉⠉⠛⠛⠶⣍⣊⣿⣿⠷⣝⢕⢆⠀⢆⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣰⠔⣴⡛⢮⣲⡶⠋⠁⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⣙⣿⣥⣼⣸⣷⡫⡢⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⡘⣼⠱⣛⣲⢿⣷⣄⣠⠖⣚⣛⢷⣯⡤⠬⣽⠶⢛⣩⣼⠙⢷⡔⣠⣷⡩⢣⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⣡⢸⢟⣓⢶⠇⠈⠹⢟⣾⡘⠻⠟⣸⣻⡴⠶⡶⠞⣛⣩⡼⠀⠘⣏⣥⡶⢧⢋⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⢔⣚⣓⣿⣬⣩⣾⠀⠀⠀⢮⡹⠹⢓⣉⣥⡶⠶⠶⡶⢛⣩⣤⡶⠇⠀⢹⢒⣒⣻⣚⣒⣒⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠠⠀⠀⠰⠀⡳⠤⠦⣯⠺⢇⣷⠀⠀⠀⠘⣧⠻⢛⣉⣤⡶⠶⠶⠷⠛⣉⣤⠶⠞⡀⢸⡚⠻⢿⠧⠤⢼⠀⠐⠀⠀⠄⠀⠀⠀ ⠀⠀⡈⠀⠡⡀⠈⢄⠈⢹⢋⢻⣿⣿⣻⡀⠀⠀⠀⢉⠚⢛⣩⡴⠶⢛⣛⣳⢟⣩⣴⡾⠟⣓⣼⠽⣉⣻⠹⡍⠉⢀⠜⢀⠈⠀⠇⠀⠀ ⠀⢀⠁⢰⡄⠐⢄⠀⢃⠀⡞⠜⣏⢿⠎⣧⠀⠀⠀⠈⢿⣋⣥⠶⢻⣛⣭⣾⠟⣋⣥⠶⠛⣹⡛⠶⢳⣏⢧⠃⢠⠂⡀⠀⣠⡄⠸⠀⠀ ⠀⢸⠀⣸⡿⣦⡀⠁⠌⡄⠘⡚⡘⣶⣾⡯⠷⣄⠀⠀⠸⢯⠀⠀⠘⣛⣩⡴⠞⠋⠁⢀⡼⢇⡹⣧⣏⢮⠆⢀⠇⠀⢀⣴⣿⡇⠀⡀⠀ ⠀⢸⠀⢽⣿⠘⠿⢦⣄⡈⠀⠈⢞⢌⢿⡱⣱⣿⣷⣤⣀⢂⡆⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⡶⡫⣦⠊⠀⢀⣠⡾⠿⢃⣿⡇⠀⡄⠀ ⠀⠘⠀⢸⣿⣡⡰⣿⡋⠁⣀⣤⠀⠰⣓⢝⠿⣿⣄⣽⣿⡛⣿⢖⢲⣶⢺⠋⡍⣿⣧⣬⡿⡫⢰⠔⠁⣠⣀⠉⢹⣿⢂⣌⣿⠇⢠⠀⠀ ⠀⠀⠃⠀⢿⠋⢷⡘⣷⡀⠘⠁⣠⣞⠕⠙⠭⡪⠝⡻⠿⢥⣿⣚⣴⣿⣼⣷⠵⢿⢫⣕⠸⠃⠫⣳⣄⠈⠃⢠⣿⢃⡾⠹⡟⠀⡈⠀⠀ ⠀⠀⠈⠄⠀⢠⠈⢻⣌⢿⣦⡾⠛⠁⡠⠂⠀⡀⠉⠘⠩⠵⢾⢸⠀⡇⡷⠭⠝⠒⠉⢀⠠⠐⢄⠈⠛⢷⣴⡿⣡⠟⠀⡀⠀⠰⠀⠀⠀ ⠀⠀⠀⠐⢠⠃⠑⠀⢹⣦⠙⣿⣦⠀⠁⠂⢠⠀⠈⠀⠂⡆⠘⣾⣶⡗⠃⢠⠐⠀⠈⠀⡄⠐⠀⠀⣴⣿⢫⣾⡏⠀⡎⠑⡄⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢟⠝⢷⣬⡻⢟⣶⣤⣀⡈⠁⠐⠈⢀⣴⣟⣿⣻⣦⡀⠁⠂⠈⣁⣀⣤⣶⡿⢛⣵⠟⠫⡻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠁⢰⣟⠕⠁⡰⠀⠈⠻⢶⣍⡛⠽⣿⣻⣟⡿⣟⡿⡞⢸⣟⡷⣿⣻⣟⣿⡽⠟⣋⣵⡾⠟⠁⡠⢀⠈⠪⣻⡄⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⣀⠠⠊⠀⠀⠁⠠⠀⠉⠛⠿⣶⢮⣭⣍⣛⡋⠀⢸⣿⣛⣣⣭⣭⢶⣞⠿⠛⠉⡀⠄⠈⠀⠀⠐⠄⣀⡀⠜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠀⡈⠉⠛⠫⣿⣧⢸⣟⣾⠝⠛⠈⢁⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⠻⣿⠏⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀