⠀⣷⣳⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠁⠀⢄⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠃⠀⠀⠀⢰⠋⠁⠈⢣⠀⠈⠉ ⠀⠇⠹⡀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡿⠀⢰⠝⣄⢀⣠⣟⡍⡉⠁⠀⠀⠀⠀⠀⠀⣀⣠⢟⡭⣆⢶⣧⣤⣤⣤⣼⠈⡯⣷⢸⣀⣀⣀ ⡛⠁⠀⢣⣶⣿⣿⣿⣿⣿⣿⢿⢟⣛⣿⣿⣷⣌⢾⣋⣑⡋⡿⠿⠦⠤⠐⠒⠂⠒⠒⠚⠻⣿⣳⠶⢺⢦⣻⡆⠀⠴⣮⣲⠲⣶⣾⠀⠀⠒ ⠛⡟⢀⣽⣯⣿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣆⠁⠉⠈⢡⠈⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡯⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⠀ ⠀⠃⣼⣿⣿⣿⣭⡿⡿⣻⣯⣿⣿⣭⡿⣿⣿⣿⣿⡄⠀⠰⡽⠤⠪⢟⠟⠑⠒⠒⠒⠒⠒⠒⣳⠄⠀⠀⠁⠀⠀⠀⠨⡁⠀⣀⠼⠀⠀⠀ ⠄⠺⣿⣿⣿⡻⣟⠯⡽⠋⠹⡿⢿⡏⣠⣿⣿⣿⣿⡷⠖⠒⠛⠛⠛⠛⠛⠭⣉⣩⠭⠛⠛⠛⠛⠲⠶⣒⠩⣍⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⡿⣖⠉⠀⠀⠀⢸⣤⣿⠹⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢔⠰⠒⣿⣥⠀⠀⠀⠀⠀ ⡆⠀⠘⢿⣿⣿⣾⠓⢀⣶⢂⠀⣿⣿⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣀⣀⣀⣀⣀⠀⠀ ⠙⡟⣓⡒⠚⢻⣿⣧⠤⠋⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠉⠉⠉⠉⠀ ⠀⠘⠡⡍⠉⠉⢻⡃⠀⠀⠀⠈⡺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀ ⠤⠒⠂⠐⠶⡆⢞⡅⢆⠀⡠⠐⡇⠘⢄⠀⠀⠀⠀⠀⠀⠀⣇⣷⢯⣀⠔⠀⡼⢙⣆⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠉⢢⡀⠀⠀ ⠀⠀⠀⠀⠀⡯⠭⢵⣈⡞⡄⠀⠚⠒⠠⠭⣖⡲⡴⠒⠂⠁⠛⠋⠈⢀⣴⠞⣴⣦⠈⢗⠻⠁⠀⠀⠀⠀⠑⠲⢖⡲⠭⠔⢊⡡⠀⡇⠀⠀ ⢦⣴⠆⠶⡶⣳⠔⢒⣷⣧⠇⠀⠉⠉⣉⣉⣉⡑⢆⡀⠀⠀⠀⢀⣴⡟⠁⢸⣿⠟⡇⠀⣷⡄⠀⠀⠀⠀⢀⣔⣊⣉⡉⠉⠁⠤⢰⡁⠀⠀ ⠖⢖⣶⠖⢶⡇⡜⡕⠁⠻⣦⠀⠤⠤⠤⠤⠔⣒⡾⠛⠀⠀⠀⠈⠳⣣⡀⡸⡧⠀⢀⣠⡟⠉⠀⠀⠀⠀⠛⣤⡒⠒⠤⠄⠀⠒⣱⠃⠤⣀ ⢲⡶⢿⢲⢶⡷⡇⣳⣄⣀⣻⡗⡖⡖⠒⢺⠋⠙⠻⠦⣀⠀⠀⠀⠀⢹⢻⠻⣷⣸⣯⠏⠀⠀⠀⠀⠀⠀⠔⠂⠉⠉⠲⡖⠒⡟⣇⡏⠑⠢ ⠀⡶⠶⠶⠂⡧⠤⠤⠤⠀⣀⣹⡛⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠪⡗⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⢏⠟⠉⠉⠉ ⠀⠼⠲⠶⠶⡝⠀⠀⠀⠀⠀⢀⣹⣱⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠹⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣔⣲⠶⠍⠛⢛⣹⢽⣳⠄⢳⣄⠀⠀⠀⠀⠀⠀⠀⡇⠁⣤⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⣴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡗⠁⠀⠀⠀⢀⣁⣨⢿⢯⡿⡐⠀⠑⠦⡀⠀⠀⠀⢰⠀⠀⣿⣾⡼⡀⠀⠀⠀⢠⣠⣤⣄⣴⡿⣶⣾⣅⢠⢀⣤⣠⢀⣀⣠ ⣀⣀⣀⣊⣭⣕⣒⣲⣭⡭⠥⠴⠶⠚⢏⠉⠮⠺⣤⡀⠈⠑⠤⣀⠇⠀⡸⢸⡻⡗⣧⠀⠀⠀⣘⠽⣾⣽⡾⣾⣿⣿⣟⡻⣟⡓⡛⣫⠾⠿ ⡀⠀⠈⠑⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠢⣤⠀⠀⠀⣰⢡⣇⢿⡦⢇⡿⡦⠔⠋⠀⣼⠫⣾⣷⣿⣿⣿⠊⠿⠝⠟⠯⠛⠀⠀ ⠀⠸⠾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⢼⣧⠌⡳⠖⠒⠉⠉⠉⠙⢾⣼⣯⢺⣷⢻⠆⣕⣦⠴⠒⠽⠿⢿⡮⠽⠩⠟⠿⠽⠿⠍⠨⠻⠜⠀ ⠀⠰⡻⠿⡠⠤⠤⠄⠀⠀⢀⣀⣀⣀⣉⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⣹⣯⣾⣧⠈⡗⢹⠁⠀⠀⠀⠀⠀⡼⢳⢟⣖⢽⠿⣿⢾⠀⠀⠀⠀ ⠀⠈⠘⠟⡗⠒⠒⠒⠒⠒⠒⠚⢛⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⠔⣺⣻⣏⣼⣿⣆⡵⡈⠧⣀⠀⠀⠀⡴⣢⣲⣾⣿⣝⢖⣿⢉⢁⣀⣀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡤⠊⠁⠀⠀⢀⠀⠀⠀⠀⠀⣔⣉⡭⠵⠿⠯⠭⠭⠽⢿⣯⣖⣀⣑⠢⢄⡉⠈⠈⠁⠁⠉⠢⣀⠉⠁⠀⠀⠀

⠀⠀⠀⠁⠉⣀⠢⠉⠁⠁⠈⠈⡉⢄⠢⣑⣀⣖⣯⢿⠽⠭⠭⠯⠿⠵⡭⣉⣔⠀⠀⠀⠀⠀⢀⠀⠀⠁⠊⡤⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⣀⣀⢁⢉⣿⢖⣝⣿⣾⣲⣢⡴⠀⠀⠀⣀⠧⡈⡵⣆⣿⣼⣏⣻⣺⠔⣠⢀⠀⠀⠀⠀⠀⠀⠁⠟⢛⠚⠒⠒⠒⠒⠒⠒⡗⠟⠘⠈⠀ ⠀⠀⠀⠀⢾⣿⠿⢽⣖⢟⢳⡼⠀⠀⠀⠀⠀⠁⢹⡗⠈⣧⣾⣯⣹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠜⣉⣀⣀⣀⢀⠀⠀⠄⠤⠤⡠⠿⡻⠰⠀ ⠀⠜⠻⠨⠍⠿⠽⠿⠟⠩⠽⡮⢿⠿⠽⠒⠴⣦⣕⠆⢻⣷⢺⣯⣼⢾⠙⠉⠉⠉⠒⠖⡳⠌⣧⢼⡠⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⠾⠸⠀ ⠀⠀⠛⠯⠟⠝⠿⠊⣿⣿⣿⣷⣾⠫⣼⠀⠋⠔⡦⡿⢇⡦⢿⣇⢡⣰⠀⠀⠀⣤⠢⠈⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⠈⠀⡀ ⠿⠾⣫⡛⡓⣟⡻⣟⣿⣿⣾⡾⣽⣾⠽⣘⠀⠀⠀⣧⡗⡻⢸⡸⠀⠇⣀⠤⠑⠈⡀⣤⠺⠮⠉⢏⠚⠶⠴⠥⡭⣭⣲⣒⣕⣭⣊⣀⣀⣀ ⣠⣀⢀⣠⣤⢀⢠⣅⣾⣶⡿⣴⣄⣤⣠⢠⠀⠀⠀⡀⡼⣾⣿⠀⠀⢰⠀⠀⠀⡀⠦⠑⠀⡐⡿⢯⢿⣨⣁⢀⠀⠀⠀⠁⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⣴⢀⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⣤⠁⡇⠀⠀⠀⠀⠀⠀⠀⣄⢳⠄⣳⢽⣹⢛⠛⠍⠶⣲⣔⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠎⢠⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⠹⡾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣱⣹⢀⠀⠀⠀⠀⠀⡝⠶⠶⠲⠼⠀ ⠉⠉⠉⠟⢏⢀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣹⡗⠪⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡛⣹⣀⠀⠤⠤⠤⡧⠂⠶⠶⡶⠀ ⠢⠑⡏⣇⡟⠒⡖⠲⠉⠉⠂⠔⠀⠀⠀⠀⠀⠀⠏⣯⣸⣷⠻⢻⢹⠀⠀⠀⠀⣀⠦⠻⠙⠋⢺⠒⡖⡖⡗⣻⣀⣄⣳⡇⡷⢶⢲⢿⡶⢲ ⣀⠤⠃⣱⠒⠀⠄⠤⠒⡒⣤⠛⠀⠀⠀⠀⠉⡟⣠⢀⠀⡧⡸⡀⣣⠳⠈⠀⠀⠀⠛⡾⣒⠔⠤⠤⠤⠤⠀⣦⠻⠁⡕⡜⡇⢶⠖⣶⢖⠖ ⠀⠀⡁⢰⠤⠁⠉⡉⣉⣊⣔⢀⠀⠀⠀⠀⡄⣷⠀⡇⠟⣿⢸⠁⡟⣴⢀⠀⠀⠀⡀⢆⡑⣉⣉⣉⠉⠉⠀⠇⣧⣷⢒⠔⣳⡶⠶⠆⣴⢦ ⠀⠀⡇⠀⡡⢊⠔⠭⡲⢖⠲⠑⠀⠀⠀⠀⠁⠻⢗⠈⣦⣴⠞⣴⢀⠈⠋⠛⠁⠂⠒⡴⡲⣖⠭⠠⠒⠚⠀⡄⡞⣈⢵⠭⡯⠀⠀⠀⠀⠀ ⠀⠀⡀⢢⠉⢠⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣆⢙⡼⠀⠔⣀⢯⣷⣇⠀⠀⠀⠀⠀⠀⠀⢄⠘⡇⠐⡠⠀⢆⡅⢞⡆⠶⠐⠂⠒⠤ ⠀⠀⠀⠀⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡺⠈⠀⠀⠀⡃⢻⠉⠉⡍⠡⠘⠀ ⠀⠉⠉⠉⠉⡌⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠉⠋⠤⣧⣿⢻⠚⡒⣓⡟⠙ ⠀⠀⣀⣀⣀⣀⣀⢮⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⣿⣿⠀⢂⣶⢀⠓⣾⣿⣿⢿⠘⠀⡆ ⠀⠀⠀⠀⠀⣥⣿⠒⠰⢔⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⡎⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⠹⣿⣤⢸⠀⠀⠀⠉⣖⡿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⡉⠈⠀⠀⠀⣍⠩⣒⠶⠲⠛⠛⠛⠛⠭⣩⣉⠭⠛⠛⠛⠛⠛⠒⠖⡷⣿⣿⣿⣿⣠⡏⢿⡿⠹⠋⡽⠯⣟⡻⣿⣿⣿⠺⠄ ⠀⠀⠀⠼⣀⠀⡁⠨⠀⠀⠀⠁⠀⠀⠄⣳⠒⠒⠒⠒⠒⠒⠑⠟⢟⠪⠤⡽⠰⠀⡄⣿⣿⣿⣿⡿⣭⣿⣿⣯⣻⡿⡿⣭⣿⣿⣿⣼⠃⠀ ⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⡯⠘⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⡄⢀⠀⠈⢡⠈⠉⠁⣆⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣯⣽⢀⡟⠛ ⠒⠀⠀⣾⣶⠲⣲⣮⠴⠀⡆⣻⢦⢺⠶⣳⣿⠻⠚⠒⠒⠂⠒⠐⠤⠦⠿⡿⡋⣑⣋⢾⣌⣷⣿⣿⣛⢟⢿⣿⣿⣿⣿⣿⣿⣶⢣⠀⠁⡛ ⣀⣀⣀⢸⣷⡯⠈⣼⣤⣤⣤⣧⢶⣆⡭⢟⣠⣀⠀⠀⠀⠀⠀⠀⠁⡉⡍⣟⣠⢀⣄⠝⢰⠀⡿⣤⣶⣿⣿⣿⣿⣾⣴⣠⢀⠀⡀⠹⠇⠀ ⠉⠈⠀⢣⠈⠁⠋⢰⠀⠀⠀⠃⠈⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⢄⠀⠁⣸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣳⣷⠀