⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⢿⢶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⡏⠀⠉⢿⣝⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣸⡇⠀⠀⠀⠹⢿⣶⡙⢷⣤⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⣧⣀⡀⠀⠰⣌⣿⣽⣾⡹⣟⢿⣯⡓⠤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠿⣻⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⠈⠩⣝⠲⣬⣻⣿⣇⠛⣿⣦⠘⠙⠻⢤⣤⣄⢩⣍⢉⠉⠛⠓⠲⠶⢤⣤⣀⣀⠀⢀⣠⣄⣠⡾⠁⣀⣠⣴⡚⣉⣭⣶⠓⠛⠛⠛⣿⣷⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣛⣛⣓⣚⣷⣤⡷⢻⡿⢁⠹⣾⣆⠀⠀⢈⡿⣿⣼⠋⣿⠀⠐⠠⠐⠲⡄⢶⣾⡍⠛⡽⢻⣯⣿⣶⢚⠋⡽⠄⠛⠛⠁⠀⠀⠀⠀⠀⠸⣷⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡉⠁⢈⠉⠀⡉⢁⡼⢙⡻⢦⣿⣻⣦⣼⣾⣿⡗⠀⠸⣿⣰⡇⠀⠡⠚⠀⢿⣺⡗⠀⣡⣼⢿⠟⠃⠈⠐⠀⠀⠀⢀⣀⣤⣤⣤⣽⠀⢐⣯⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣷⠀⠾⠀⠈⠀⢰⠇⠀⠙⣧⡟⣧⣿⠙⢻⠿⠀⠀⠀⣿⣿⣃⠀⠀⠁⡀⢿⣾⡏⣰⣿⡵⠋⢤⡀⠀⠀⣤⠶⠛⠋⠉⠛⠰⠤⡀⠀⢾⣱⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⡟⠃⣀⡀⠀⠤⡺⣜⢤⠀⠛⢿⣾⠏⠀⠀⠀⠀⠀⠀⠘⣿⣷⡏⢐⠀⢀⡿⣿⣶⣯⠟⢀⣠⡼⠷⠤⣄⡀⠀⠛⠾⠿⣽⣓⠒⠃⠀⠘⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠪⠍⣜⠁⢤⣌⢣⣌⣐⡢⣌⣷⢿⣶⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⣡⠊⣀⢸⣷⡿⣷⡿⢞⡭⠗⠛⠁⠀⠀⠈⠀⠀⠀⠐⢦⣙⠻⣄⣰⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠠⠶⠀⠛⣠⣴⣿⣿⣿⣿⣿⠷⣾⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠴⣿⣺⣿⣿⣿⡾⠉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠐⢂⠾⣟⡗⣾⠾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡇⠉⠲⠄⠛⠚⣿⣿⡿⠟⣿⣿⣿⣿⣶⣿⣿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠾⣛⣽⣯⡾⢟⣅⣀⠁⠀⠈⠀⠀⠁⠀⣀⠈⠀⠀⠒⠲⠿⢽⣼⣧⣤⣶⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢿⡟⠙⣅⡉⠀⡄⢰⡏⣿⣧⣴⣿⣿⣿⣿⣿⣷⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣿⣯⡭⡝⠧⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠈⠉⢉⠛⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⢟⣾⢤⡾⢮⡳⢦⡁⢾⣇⢻⣷⣿⣿⣿⣟⣿⣿⣿⣸⠃⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠈⠉⣓⠦⡈⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠠⣿⠲⠦⣟⣳⠦⣹⣲⣍⠻⣿⣌⢻⣿⣿⣿⣿⢿⠿⠛⠋⠀⠀⠀⠈⣩⣽⣿⡀⠀⠀⠀⢿⡿⠫⠿⠿⠿⠷⣤⣴⣈⠝⠻⢶⣤⣤⡀⠀⠀⠀⣠⠔⣠⠔⠀⠀⠈⠙⢦⡈⢷⡀⠀⠀⠀⠀⠀ ⠀⢀⡞⠠⠄⡈⢁⣽⠿⣇⠈⠟⠀⠉⠁⠈⢀⠀⠁⠀⠀⠀⠀⠰⣏⠓⠚⢛⡷⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡩⠷⠆⠀⠀⢀⣠⠤⢈⣩⠴⠋⠀⠀⠀⠠⠀⠀⢷⠉⢘⣿⠀⠀⠀⠀⠀ ⢀⣞⣤⣟⡻⠍⠙⠛⡆⠙⠳⣄⡀⢀⣀⣸⡋⢳⠦⢤⡀⠀⠀⠀⠈⢓⡖⠋⠀⣀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢀⠑⠂⠉⠁⠒⠈⠁⠀⠀⢀⡀⠂⠀⠀⠀⠀⣌⢿⡂⢹⡇⠀⠀⠀⠀ ⢈⣿⠋⣥⢀⣰⣿⣠⠿⣤⣴⣾⣿⠉⠈⣁⡍⠛⢾⡋⠀⠀⠀⠀⢀⣸⣦⣀⡔⠉⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⠒⠲⠤⠤⣀⠀⠀⠀⠀⠀⠀⢘⡀⠀⡀⠈⠳⡝⢦⣿⠀⠀⠀⠀ ⠸⣿⣿⣿⢾⣽⣿⣻⣶⠋⣹⣀⠉⠙⠒⣾⠅⠀⣌⣳⡄⠈⠓⠒⠉⠻⠛⠋⠓⠶⠿⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡔⠒⠒⠂⠤⢀⣀⠀⢤⣀⠀⣾⣧⣧⡿⠀⠻⣿⡄⠀⠀⠀ ⠀⠙⢿⡡⢿⣛⣿⠏⠋⠀⠛⠿⠃⠀⠀⠀⣤⣤⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠉⠒⠢⢍⡓⢿⣯⠇⠀⣀⣿⡄⠀⠀⠀ ⠀⠀⠈⣧⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢌⡛⢦⣄⣀⠀⡄⣀⢽⠳⠁⢀⣀⣽⠉⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡀⠉⠓⢶⢤⡀⠀⠀⢀⣠⣤⣀⣀⣠⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠹⣷⡽⣏⢉⠳⠹⠉⢠⡶⠋⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⡀⠸⡄⠈⠉⠋⠉⣭⠗⢀⡏⢡⣧⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠆⠀⠀⣴⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⡷⣷⣼⡷⣤⠞⠉⣷⠞⠛⠻⢦⡄⠀⠈⠑⠦⣀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠒⠒⠒⠦⠄⣀⠀⠀⢀⣀⠀⢰⠟⣆⢠⠇⠀⠀⠀⠀⠢⠀⢱⡀⠀⠀ ⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⡀⣿⠹⣦⡼⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠓⢿⣯⣰⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠲⠀⠀⠀⠀⠀⠀⠙⢦⣼⠈⢣⣼⠀⢺⡏⠀⠀⠀⠀⠀⠀⠁⠀⢳⡀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠉⠉⠙⢻⣿⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠦⣈⢻⠖⣤⣄⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠈⣟⢠⡞⣧⣀⣀⣠⠤⠴⠒⠒⠦⣸⡇⠀ ⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣿⠻⢀⣤⣶⣀⣠⡤⢿⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⣽⡀⠙⣄⣧⡿⠳⠦⠤⠤⠤⠤⠶⠞⢉⡿⠃ ⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⣀⡤⢖⣿⠟⠻⡏⠉⠁⠻⡄⠀⠀⠀⠀⠀⢀⣼⠛⠀⠀ ⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⣠⣧⣘⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⢧⠀⠀⡠⠖⠋⣁⣰⠞⠃⠀⠀⣧⠀⠀⠀⠙⢦⡀⠀⣀⣴⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⡤⠤⡤⠴⠖⠛⠻⠛⠁⠈⢣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⠶⡷⠷⠛⠁⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠀⢉⣻⠿⠟⠻⠿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠥⣆⣀⣀⠀⡀⣀⣀⣠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀