⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⣷⠀⠀⠀⠀⠀⢀⣇⡔⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⡄⠀⠀⠀⠀⠀⣃⠍⠍⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⣲⠂⠀⠀⠀⠀⠺⡰⠯⠍⠷⠧⣠⠀⠀⠀⡐⡵⣊⠉⢹⢺⣷⡄⠀⠀⠀⠐⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⢩⡇⠀⠀⠀⠀⣰⡟⠁⡀⠀⡀⠁⢽⠀⠀⢀⡟⠀⠨⠄⠨⠄⢣⡛⠀⠀⠀⠀⣻⢣⠀⠀ ⠀⠀⠀⠀⠀⣏⡀⠘⡇⠀⠀⠀⠠⣔⡇⠀⢅⠀⡀⠂⣿⠀⠀⢸⡏⡇⠀⠆⢈⠄⠘⡅⠀⠀⠀⡰⡝⠀⣷⠀ ⠀⠀⠀⠀⠀⠉⠋⠋⠃⠀⠀⠀⣶⡃⠆⠀⠁⡀⠄⡂⢿⠀⠀⣹⠆⢅⠀⠆⠠⠐⣄⡇⠀⠀⠀⡟⠛⠛⠋⠀ ⠀⠀⠀⠀⢀⣤⠴⠶⡶⣦⡀⠀⣿⠀⠔⠀⠁⡀⠄⢐⣻⠀⠀⣾⢅⠄⡀⠔⡠⠀⡸⠇⠀⠀⠀⣀⡀⢀⠀⠀ ⠀⠀⠀⠀⡾⠁⢦⠀⢁⠈⢫⡆⣿⠀⠘⡀⠁⠀⠂⠈⡇⠀⠀⣿⠂⣀⢀⡀⢂⠄⣧⠃⠀⣠⣗⠋⡉⠙⢦⡀ ⠀⠀⢀⣞⡁⠀⠐⡠⠠⠀⢸⡇⣿⠥⣈⠐⠇⠈⢥⢼⠃⠀⠀⣽⡁⠐⠄⢦⠀⣻⡏⠀⡴⡕⠃⠄⡒⠀⠀⢳ ⠀⠀⣐⡃⠸⠠⠀⠄⠠⠂⡎⡆⠱⡘⠏⢀⣔⡼⠋⠋⠀⠀⠀⠹⣇⣀⢃⣄⡶⠃⠀⣸⣙⠀⠀⡁⠐⠁⡀⢸ ⠀⠀⣟⡧⡀⢁⠁⠔⡀⠙⣯⡇⠀⠙⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠓⠛⠃⠃⠀⠀⢀⣿⢎⠂⠀⢀⠁⢁⠈⠪ ⠀⢰⡟⠃⠐⡀⠂⠈⠁⡔⡟⠣⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⠠⠤⢄⠀⠀⠀⠀⠀⡏⣯⠀⠥⠁⠄⡀⠡⠄⢠ ⠀⠘⡯⡂⠀⠁⢎⡀⡔⡟⠀⠀⠀⠀⠀⠀⢤⠂⣍⡿⠷⡛⡛⠒⠲⣿⣵⡀⠀⠀⠀⡿⡄⠀⡂⡘⠆⠈⣡⠏ ⠀⠀⠙⠺⣿⣶⣗⣳⡟⠁⠀⠀⣤⢢⡌⡷⠞⡋⠃⠀⠂⠀⠄⠀⠀⡀⠯⣯⠂⠀⠀⠘⢍⣒⣤⣦⡤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣀⡪⣣⠟⠏⠀⠐⠀⠂⠄⠀⡀⠀⠀⡄⠁⠀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡙⣿⠏⠁⠁⠄⠀⠄⠠⡀⠀⠀⠄⠀⠢⠀⠀⡀⠀⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⣿⠏⠙⡁⠀⠁⠠⠠⠀⡀⠀⠀⠐⠠⠐⠀⠄⠁⡁⠀⠀⠻⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡘⡁⡷⠗⠀⠀⡃⠀⠁⠠⡀⢀⠄⠀⠀⠅⢀⠁⠂⠀⠠⠀⠠⠚⠁⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢵⡟⡃⡂⠅⠀⢡⠐⠀⠀⡆⣴⠀⠀⠘⠀⡄⠂⠀⠠⢁⠈⠀⠄⢇⠈⣟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡁⢇⠠⠈⠄⠀⠏⠀⠀⠁⣠⣠⡠⣄⣀⠁⠀⠀⠇⡀⢅⡅⠃⡀⠂⡿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣧⣄⡫⠆⠐⢄⡂⡠⣰⣇⡕⠒⠙⠛⠻⣟⡄⡠⠊⠀⠁⠀⣮⣤⣞⣷⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠛⠓⠒⠚⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣶⡶⠾⡛⡛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠤⣄⣀⡀⠀⠀⡔⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⣺⠀⠀⡜⢠⠋⠉⣇⠀⠀⡒⢑⠀⠀⢠⠔⢒⠀⠀⢸⠉⠣⠇⠀⠀⠀⠀⠀ ⠀⢀⠀⠒⠒⠃⠒⠀⠀⠀⠑⠂⡉⠑⠊⠀⠘⠒⠊⠈⠁⠀⠁⠀⠓⠀⠈⠀⠘⠀⠀⠸⠔⠁⠇⠀⠀⠀⠀⠀ ⠀⠀⣇⣤⣦⢀⡔⠒⢲⠀⠀⣷⠛⠓⡆⢀⡀⡔⡟⢉⡻⣆⢠⣋⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡗⢁⡼⢸⠉⠉⡉⠀⠑⢺⡖⠀⢰⠋⠙⣿⠉⡉⠁⠀⡏⠉⢁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⠉⠀⠈⠉⠉⠁⡠⠆⠈⠃⠀⣈⡀⠀⠈⠙⠃⠀⠀⢈⠉⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⠮⠤⠜⡀⢰⡋⢀⣟⡰⠊⠁⢁⢿⠀⠀⣼⠀⢀⠞⠛⣆⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⡄⠈⠁⠀⡷⠤⠌⠀⠸⡀⠀⣿⠀⡎⡀⠀⢸⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⢸⠀⡀⡎⠀⣿⠀⡀⠸⠀⠌⠤⡷⠀⠁⠈⡄⠹⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⣆⠛⠞⢀⠀⣼⠀⠀⢿⢁⠁⠊⡰⣟⢀⡋⢰⡀⠜⠤⠮⡴⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠋⠉⢈⠀⠀⠃⠙⠈⠀⡀⣈⠀⠃⠈⠆⡠⠁⠉⠉⠈⠀⠉⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢁⠉⡏⠀⠁⡉⠉⣿⠙⠋⢰⠀⡖⢺⠑⠀⡉⠉⠉⢸⡼⢁⡗⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣉⣋⢠⣆⡻⢉⡟⡔⡀⢀⡆⠓⠛⣷⠀⠀⢲⠒⡔⢀⣦⣤⣇⠀⠀ ⠀⠀⠀⠀⠀⠇⠁⠔⠸⠀⠀⠘⠀⠈⠀⠓⠀⠁⠀⠁⠈⠊⠒⠘⠀⠊⠑⡉⠂⠑⠀⠀⠀⠒⠃⠒⠒⠀⢀⠀ ⠀⠀⠀⠀⠀⠇⠣⠉⢸⠀⠀⢒⠔⢠⠀⠀⢑⡒⠀⠀⣇⠉⠋⢠⡜⠀⠀⣺⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡔⠀⠀⡀⣀⣄⠤⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⡛⡛⠾⡶⣶⣶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠒⠓⠛⠓⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣷⣞⣤⣮⠀⠁⠀⠊⡠⡄⣟⠻⠛⠙⠒⡕⣇⣰⡠⡂⢄⠐⠆⡫⣄⣧⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⡿⠂⡀⠃⡅⢅⡀⠇⠀⠀⠁⣀⣄⡠⣠⣠⠁⠀⠀⠏⠀⠄⠈⠠⢇⡁⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣟⠈⢇⠄⠀⠈⢁⠠⠀⠂⡄⠀⠘⠀⠀⣴⡆⠀⠀⠐⢡⠀⠅⡂⡃⡟⢵⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣇⢿⠁⠚⠠⠀⠠⠀⠂⠁⢀⠅⠀⠀⠄⢀⡀⠠⠁⠀⡃⠀⠀⠗⡷⡁⡘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠻⠀⠀⡁⠁⠄⠀⠐⠠⠐⠀⠀⡀⠀⠠⠠⠁⠀⡁⠙⠏⣿⠚⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠙⠀⡀⠀⠀⠢⠀⠄⠀⠀⡀⠠⠄⠀⠄⠁⠁⠏⣿⡙⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣧⠘⠀⠁⡄⠀⠀⡀⠀⠄⠂⠀⠐⠀⠏⠟⣣⡪⣀⢀⠀⠁⠉⠀⠀⠀⠀⠀⠀ ⠀⠁⠚⡤⣦⣤⣒⢍⠘⠀⠀⠂⣯⠯⡀⠀⠀⠄⠀⠂⠀⠃⡋⠞⡷⡌⢢⣤⠀⠀⠁⡟⣳⣗⣶⣿⠺⠙⠀⠀ ⠏⣡⠈⠆⡘⡂⠀⡄⡿⠀⠀⠀⡀⣵⣿⠲⠒⡛⡛⠷⡿⣍⠂⢤⠀⠀⠀⠀⠀⠀⡟⡔⡀⢎⠁⠀⡂⡯⠘⠀ ⢠⠄⠡⡀⠄⠁⠥⠀⣯⡏⠀⠀⠀⠀⠀⢄⠤⠠⡠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠣⡟⡔⠁⠈⠂⡀⠐⠃⡟⢰⠀ ⠪⠈⢁⠁⢀⠀⠂⢎⣿⢀⠀⠀⠃⠃⠛⠓⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠙⠀⡇⣯⠙⡀⠔⠁⢁⡀⡧⣟⠀⠀ ⢸⡀⠁⠐⡁⠀⠀⣙⣸⠀⠃⡶⣄⢃⣀⣇⠹⠀⠀⠀⠋⠋⡼⣔⢀⠏⡘⠱⡆⡎⠂⠠⠄⠀⠠⠸⡃⣐⠀⠀ ⢳⠀⠀⡒⠄⠃⡕⡴⠀⡏⣻⠀⢦⠄⠐⡁⣽⠀⠀⠃⢼⢥⠈⠇⠐⣈⠥⣿⡇⢸⠀⠠⡠⠐⠀⡁⣞⢀⠀⠀ ⡀⢦⠙⡉⠋⣗⣠⠀⠃⣧⠄⢂⡀⢀⣀⠂⣿⠀⠀⡇⠈⠂⠀⠁⡀⠘⠀⣿⡆⢫⠈⢁⠀⢦⠁⡾⠀⠀⠀⠀ ⠀⠀⢀⡀⣀⠀⠀⠀⠇⡸⠀⡠⠔⡀⠄⢅⣾⠀⠀⣻⢐⠄⡀⠁⠀⠔⠀⣿⠀⡀⣦⡶⠶⠴⣤⢀⠀⠀⠀⠀ ⠀⠋⠛⠛⡟⠀⠀⠀⡇⣄⠐⠠⠆⠀⢅⠆⣹⠀⠀⢿⡂⠄⡀⠁⠀⠆⡃⣶⠀⠀⠀⠃⠋⠋⠉⠀⠀⠀⠀⠀ ⠀⣷⠀⡝⡰⠀⠀⠀⡅⠘⠄⢈⠆⠀⡇⡏⢸⠀⠀⣿⠂⡀⠀⢅⠀⡇⣔⠠⠀⠀⠀⡇⠘⡀⣏⠀⠀⠀⠀⠀ ⠀⠀⢣⣻⠀⠀⠀⠀⡛⢣⠄⠨⠄⠨⠀⡟⢀⠀⠀⢽⠁⡀⠀⡀⠁⡟⣰⠀⠀⠀⠀⡇⢩⠞⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠐⠀⠀⠀⡄⣷⢺⢹⠉⣊⡵⡐⠀⠀⠀⣠⠧⠷⠍⠯⡰⠺⠀⠀⠀⠀⠂⣲⡴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠍⠍⣃⠀⠀⠀⠀⠀⡄⠛⠒⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣳⡔⣇⢀⠀⠀⠀⠀⠀⣷⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀