⠀⠀⠛⠛⣯⡙⠫⠭⡍⠉⢉⠝⠋⠉⡫⠋⢩⣯⠉⠙⠉⣉⢏⡡⣺⢿⠍⠻⠙⣋⣩⣭⢯⢉⣭⣽⠉⠻⡉⠉⣩⠋⠙⢭⠙⠙⠫⡩⠫⠤⠟⠉⢹⠏⠉⠉⢉⣙⡟⠉⣩⠌⣷ ⠀⠀⢂⣈⠙⣦⡐⢄⠓⡆⠈⠒⠀⣦⠀⢰⡙⢁⠀⢡⡾⢕⡨⣖⠉⠘⢳⣆⣢⢞⠊⠤⡪⠄⠙⠛⢳⡄⣀⡀⣈⠆⠀⣀⣀⣘⣾⠻⣀⠀⢀⡠⠯⣤⠀⠀⢨⡟⠐⠃⠄⠠⣿ ⠀⢰⣄⢉⣄⢱⡿⠂⢀⡜⠒⠖⢳⡔⡋⠈⠿⣟⡾⠝⡞⣉⡸⠈⡦⠖⡶⣿⣮⡁⢢⠾⢢⡤⠀⣶⣚⢛⢓⠞⢀⢀⣐⣒⠢⢤⣽⢀⢀⣇⣯⡏⡔⠁⣀⣗⣿⠉⢀⡠⣪⡖⣿ ⢀⠀⢈⣸⣯⣀⡈⣐⣀⠉⢁⣤⣘⣔⣾⠗⠀⢾⣕⢊⠀⢐⡔⠋⠁⠈⣥⣄⡈⠁⠀⠗⠈⢘⡶⢟⡀⠄⠀⠀⣮⣀⠇⢹⠃⢀⠩⠏⠉⡉⠩⠳⢍⣱⠟⠍⡴⣽⣤⡀⣧⣄⣿ ⠀⢛⣩⢻⡃⢀⠀⣹⣈⣓⣚⠉⠉⢓⡲⠖⣢⣈⣳⠒⠶⠒⢑⠀⣀⣠⠼⢄⡏⢁⠥⠨⡀⠈⢙⠆⠀⠓⣄⠒⠋⠈⠓⠤⣋⣉⣷⢾⠤⠙⢆⣄⠐⢗⣒⣭⠂⠈⣿⠊⣁⡍⣿ ⠀⠀⠘⠊⠁⠉⠉⠀⠀⠀⠀⠁⠀⠈⠉⠉⠓⠊⠁⠀⠀⠀⠀⠉⠀⠀⠀⢸⡚⡠⠀⠀⠃⢸⠃⠒⢒⠠⠤⠧⣀⠀⠀⠀⠀⢇⠀⠀⠐⢧⣈⣈⠀⠤⣃⠻⠀⠳⢧⡔⠁⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠿⠁⠈⢁⠐⠀⣥⠠⠚⠥⢤⡀⠀⠈⠉⠉⡩⣼⢰⠀⣸⠛⠉⠉⠲⠦⢼⡃⣣⠠⠀⢠⡇⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠲⡤⠒⡚⠉⠉⠒⡿⢶⠶⡇⢀⣶⣦⠺⡘⡄⣅⣰⠇⠀⠀⠀⡞⠀⠈⠀⠉⢻⡀⠀⡠⠀⠉⡀⣨⣻⣠⣶⡾⢳⠆⣿ ⠀⠐⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⣀⣸⠀⠄⢳⠒⣶⠂⢼⢣⠀⠉⢩⣋⠁⠀⣈⢹⡭⢤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢜⢄⠀⠂⡠⢁⢀⡉⡾⠀⡀⢲⣿ ⠀⢸⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⡥⠧⣾⠀⠐⠼⣖⡀⢈⠝⠂⡇⠀⠀⠘⠦⡄⢸⠁⠠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣕⡄⠀⠙⠳⠦⢌⠇⣸⡃⣿ ⠀⠀⠳⡝⢦⣀⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠛⠁⠀⠀⠈⢉⠉⠩⠔⢆⢹⠀⠀⠀⠀⠈⠙⣤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢹⡍⡹⠰⠲⠬⣓⣶⡄⣿ ⠀⠀⠀⠈⡆⡝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⠀⠉⠉⠀⠀⠀⠀⠀⠨⣒⠈⠉⠉⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠚⠠⠈⣱⠔⢰⡟⢌⠃⣿ ⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡐⠘⠀⠀⠀⠀⠀⠀⠀⠋⢱⠀⡀⡀⡀⠀⣦⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡽⡁⠀⠀⢿⠀⠀⣿ ⠀⠀⠀⠀⠹⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⡄⠀⠀⠀⠀⠀⠀⠂⢁⡇⡇⡃⠄⠀⡏⢰⠀⢠⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠏⠈⠈⠐⡈⠃⠀⠀⣿ ⠀⠀⠀⠀⢸⣮⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡅⠠⡲⡙⡄⠀⠀⠀⠀⠀⠀⢨⣷⢧⣇⣧⢀⠁⡆⡄⡆⡜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠀⣠⠃⠀⠀⠀⣿ ⠀⠀⠀⠀⠘⡯⠜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡾⡁⡱⡑⣱⡘⡄⠀⠀⠀⠀⠀⠈⢿⣤⠀⠈⣯⠔⣳⣷⣰⢡⠃⡴⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢿⣸⢾⠇⠀⠀⠀⠀⠀⠀⠀⡠⢌⣞⣴⣙⣽⣾⣾⣿⡄⠀⠀⠀⠀⠀⠛⣿⣷⣦⣿⣾⣤⠁⠈⢻⠐⣵⣟⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢸⣽⣳⡅⠀⠀⠀⠀⠀⠀⢠⢡⢀⠫⣻⣿⣿⣿⣿⡿⠸⠀⠀⠀⠀⠀⠠⡸⡻⣿⣿⣿⣿⣷⣆⣾⣾⣿⣾⡎⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢸⢕⣝⡇⠀⠀⠀⠀⠀⠀⢸⢘⢕⢵⣿⣿⣿⣿⣿⠃⠀⠅⠀⠀⠀⠀⠁⠱⣆⠈⠛⢿⣿⣿⣿⣿⣿⣿⣟⡔⡙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⢸⢮⢮⡇⠀⠀⠀⠀⠀⠀⢀⠧⠓⢿⣿⣿⣿⣿⠃⠐⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣝⣶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠘⣼⢷⡇⠀⠀⠀⠀⠀⠀⡄⡄⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⣟⡠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢹⡱⡇⠀⠀⠀⠀⠀⠀⢱⣘⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡵⢯⡈⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⣼⡿⡇⠀⠀⠀⠀⠀⢠⠃⠀⣹⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢠⡬⠁⠀⣼⣜⡄⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢀⡠⢿⣹⡓⢦⡀⠀⠀⢰⡇⡀⢰⣿⡈⠠⢽⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡩⠔⠊⠁⠆⠀⢰⠿⣿⣿⣆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⢀⠜⠁⠀⠘⣿⢧⠀⢻⡀⠀⢰⣷⠒⢴⣿⡇⡀⠘⡄⠉⠀⠐⡧⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⣠⣧⠀⠈⠻⢿⣂⣌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠎⠀⠀⢀⡴⠷⠖⠒⠚⢒⣒⠂⣷⡕⣄⠙⣠⡱⣄⣰⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡩⣺⠄⠀⠀⠀⠹⡜⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠘⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣺⣃⠿⡿⠁⠑⣟⠃⢸⠈⠑⠠⠀⡀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠔⢩⠠⠁⠀⣀⠜⠈⠺⣀⣧⣀⠀⠃⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⢸⣉⣀⡠⠤⠄⠐⠂⠉⠇⠀⠑⢿⠀⣌⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⡀⣿ ⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠘⠐⠁⢸⢸⣟⢦⡀⠈⠒⠖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠐⠉⢲⢀⠔⡢⡀⠀⡀⣿ ⠀⠀⠣⡄⣤⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸⠘⣿⠀⠙⠲⣦⡤⢤⣤⣁⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⢷⡶⠒⢶⡇⢠⡇⠸⠀⢱⠃⠈⠆⣿ ⠀⠀⠀⠙⢿⣉⣽⡟⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⡸⠀⡛⡇⠀⠀⠈⠣⣊⣟⣬⣽⡩⡿⡷⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⡏⠀⠓⠤⠤⣵⡿⢆⡇⣤⠇⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠙⠊⣿⢁⠀⠀⠀⠐⠁⢀⣤⠖⠉⢣⠀⠀⡇⠀⠀⠀⠀⠀⠙⠺⣷⣛⣻⠈⣳⡟⠛⡞⢿⣶⠠⢤⣄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡱⠋⠀⠀⡐⢀⣿ ⠀⠀⠀⠀⠀⠀⢐⣇⡈⠀⠉⠁⢀⠀⠸⠙⠀⠀⣸⡀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣙⣦⣀⣁⣀⣈⣀⣈⣉⣀⣐⣒⣒⣀⣀⣠⣄⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣘⣴⣀⣿