⠀⠀⠀⠀⠀⠀⠀⠀⡦⠾⠧⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠷⠴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⠿⠉⠀⠀⠉⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠘⠻⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⡾⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠒⣦⡀⠀⠀⠀ ⠀⠀⢠⣭⢋⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⣀⠄⠀⠘⢯⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⡍⠀⠀⠀⠀⣭⠀⠘⡅⠀⠀⠀⠀⠀⠀⣉⣀⡀⠀ ⠀⢐⠛⠁⠈⠉⠉⡳⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠈⠙⠓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠛⠉⠁⠀⠀⠀⠀⠀⠁⠛⠙⠁⠀⠀⠀⠀⠀⢛⠙⠛⣃⡀ ⢸⡿⢦⡄⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠶⢮⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⣤⠶⣴⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣾⡿⡏ ⠘⢻⣆⣛⢦⣤⡀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢠⡦⠀⢶⡷⡟⣳⣶⣶⣶⣦⣶⣶⣶⣿⢷⣶⣧⡶⠛⢻⠄⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡴⢟⣀⡶⠃ ⠀⠀⠈⠭⣤⣈⣥⣄⡀⠀⠀⠀⡌⠉⢡⡄⣀⡀⢈⣥⣄⣬⡁⠀⠉⠬⡍⣄⠀⠀⠈⢉⡥⢬⠉⡁⠀⣠⣨⡤⠭⠀⠀⠀⠀⢠⣤⣤⣄⢀⣠⡼⡍⣀⡬⠍⠁⠀ ⠀⠀⠀⠀⠈⠙⢛⣋⣙⢐⣀⣈⠙⠒⠊⠁⠀⠉⠙⠛⠋⢉⣉⣁⣀⣸⡛⠋⠀⣒⠒⠒⡃⠈⠙⠛⠂⠉⠉⠀⠀⠀⠀⠀⠀⠙⣉⣁⣛⣛⣙⡓⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⠿⠛⠛⠲⠧⠶⠶⠤⠤⡤⠾⠾⠿⠟⠻⠿⢳⠦⠴⢿⠴⡟⠀⠉⠰⠦⠒⠀⠤⣤⠤⠤⠖⠒⠒⠚⠛⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡴⠿⣿⠀⠀⠀⠀⣀⣀⡤⡴⠶⠆⠀⣠⣶⣿⣾⠿⣰⢾⡇⠀⠀⠹⡏⢀⠹⠆⣦⣄⠀⠈⠿⣷⣶⣶⣆⡀⠀⠀⠀⠀⠘⠻⢦⣤⡀⠀⠀⠀⠀ ⠀⠀⣠⣤⣾⠻⣆⡀⡦⢀⢠⣤⡶⠾⠀⠁⢧⣤⣴⣶⣷⣷⣾⣧⣴⢶⣰⠄⠀⠀⠀⡆⠷⣤⣄⠀⣤⣦⣀⡴⠒⢗⠀⠗⠶⣤⣀⠀⠀⠶⠠⢦⡕⠶⢶⣄⡀⠀ ⢀⣼⡙⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣨⡟⡋⢽⢙⣠⣏⡄⣈⡇⠀⠀⠀⠀⢀⣀⠀⠘⣄⠀⠘⢉⣇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠀⠀⠘⣅⣀ ⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠉⣰⠾⠿⠷⠆⣿⠁⠀⠀⠀⠀⠀⠙⠀⠀⡈⠶⠀⠈⠙⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹ ⠘⠻⣶⣯⠀⣩⠀⠀⠀⠀⠀⣤⠀⢠⠀⠉⠀⢀⣴⡿⠋⠀⠀⠀⢸⠍⠀⠀⠀⠀⠀⠀⠉⢿⡌⠁⣤⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢫⡟⠋ ⠀⠀⠀⣶⣶⠂⠀⠀⠀⠀⠰⣦⣰⣶⡆⡀⣴⡶⠂⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣄⡶⠀⠀⠀⠤⢀⡀⠀⠀⣠⠄⢀⡀⠀⠀⠀⠀⠀⣰⠖⠂⠀ ⠀⠀⠀⠀⠻⢥⡀⠀⠀⠀⠀⠀⢍⢁⣠⡍⠁⠀⠀⠀⢩⡀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠀⠀⠀⠀⠀⠀⠀⠉⢤⣤⣇⣀⠨⠅⠀⠀⣀⣤⠏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⣖⣀⣀⣲⠛⢙⠃⠀⠀⠀⠀⠀⠈⠉⠉⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠘⣋⠙⠛⣀⣀⣐⡚⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉⠰⠞⠰⡆⠓⢤⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠀⠀⠀⠀⠀⠛⠀⢣⡿⡦⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠆⠸⠇⡴⠚⠀⠀⠀⢀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⠀⠀⠀⢀⣤⣷⢾⠇⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⡀⣠⣴⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡆⢀⣠⡴⠆⠁⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⢀⠀⠙⠛⢙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠈⠙⠙⠃⡀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠾⠿⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢾⣿⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠿⠁⢼⣄⣶⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠒⠶⢤⣿⠊⠷⡆⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣠⡖⠂⠀⢰⣦⡒⠒⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⢴⢶⣶⡆⠀⠀⠰⣖⠴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⣿⡏⠀⠀⠀⠀⢨⣥⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢠⡅⠀⠀⠀⠀⠉⣷⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠋⠀⠀⠀⠀⠀⠀⠛⣇⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⡛⠁⠀⠀⠀⠀⠀⠙⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⣾⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀