ㅤㅤㅤ ⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⢿⣷⠒⠲⣾⣾⣿⣿ ⠀⠀⠀⠀⣴⣿⠟⠁⠀⢿⣿⠁⣿⣿⣿⠻⣿⣄⠀⠀⠀⠀ ⠀⠀⣠⡾⠟⠁⠀⠀⠀⢸⣿⣸⣿⣿⣿⣆⠙⢿⣷⡀⠀⠀ ⣰⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠉⠻⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣆⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠟⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣤⣤⡄⠀⠀⣴⣶⣦⡀⣶⣿⣷⡀⠀⢿⣿⣿⣆⠀⠀⠘⢿⣿⣷⣤⠘⢿⣿⣿⣾⢹⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡯⣽ ⣿⡆⠀⢼⣿⣿⣿⠆⠰⣿⣿⣿⡀⠀⠀⢿⣿⣿⣄⠀⠻⣿⣿⣧⡌⢿⣿⣿⣦⠈⠙⣿⣿⣿⠀⠀⡘⣿⣿⣿⡇⠘⢿⣿⡿⠋⡛⡿⢟⢧⢻⠟⡿⡍⡟⣻⣿⡿⢏⠻⡔⠣⡜⡱⢧ ⣿⣿⣦⡈⠿⣿⣷⣆⠀⠙⣿⣿⣷⡀⠀⠈⠹⣿⣿⣷⠀⡘⠿⠿⣿⠀⢿⣿⣿⠆⠀⠻⠿⠿⠁⠰⠄⡌⠋⢉⠀⡄⢢⡐⢤⠓⡼⡑⡎⠦⡍⢞⡰⠱⣨⠡⢏⠞⡈⠱⣈⠱⠠⣙⠮ ⠘⣿⣿⡇⠀⢹⣿⣿⠂⠀⠘⠿⠿⠇⠀⡀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⡀⢆⠱⡈⠔⣁⠊⡔⢨⠣⢜⢢⡙⠴⡑⠬⡑⡘⢄⠣⢑⠠⠑⣈⠂⠡⠁⠄⢂⠡⢈⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀⠀⠀⠌⠠⢁⠜⡀⠎⡠⠑⡈⢄⠊⡔⢡⠚⢌⠢⡘⠤⠑⢢⠑⢨⠐⠄⡃⠄⠃⠠⠈⠄⢁⠈⡀⠐⠠⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠂⠄⠂⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠻⣿⣷⡀⠀⠁⢂⠐⡈⠤⠑⡈⠔⡈⠜⣀⠣⠘⠤⢁⠢⠁⠎⠠⠘⠠⢈⠐⠠⠈⠄⡁⠂⠠⠀⢀⠀⠀⠐⠂ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡴⠒⠚⠛⣿⣿⣶⣿⠟⠈⢻⣆⠀⠀⢀⠂⡐⠠⠡⠈⠔⠨⠐⣀⠂⣉⠐⢂⠄⢃⠈⠄⡁⠂⠄⡈⠄⠁⡐⠀⠄⠁⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠈⠀⠠⠀⠀⠀⠈⢀⡠⠞⠛⠛⢀⡀⠀⠀⣤⣽⡌⠀⠀⠂⠄⠁⢂⠉⠄⢃⠡⢀⠂⠄⡈⠌⠀⠂⢈⠀⠄⢁⠠⠀⢀⠂⠀⠄⠀⠀⠂⠀⠀⠀⠈⢹ ⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠐⠀⠠⠀⠀⠀⠀⢐⡞⠁⠀⠀⠀⠘⣷⣤⣴⣿⣟⢷⠀⠀⣀⣤⣄⡈⠀⡐⠈⠠⠈⠄⠠⠁⠀⡐⠠⠈⠀⢀⠈⠀⠀⠈⠀⠐⠀⠀⡀⠀⠀⠀⠀⠐⢸ ⠀⠀⣶⣶⣦⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠠⠀⠈⣧⢀⣠⠴⡞⠀⠙⠿⢀⣈⡉⢼⡆⠀⢿⣿⣿⠇⠀⡀⠡⢀⠁⠠⢀⣤⣄⣀⡀⠄⠈⠀⣴⣶⣶⣦⡀⠀⠀⠐⠀⣶⣾⣶⠀⠀⢠ ⠀⠀⢿⣿⡿⠁⠀⡀⠄⠀⠀⢀⣠⣤⣤⡀⠀⠐⠘⡏⠁⠀⠁⠀⠀⠀⠉⠉⠈⠊⢵⠀⠀⢼⡷⠂⠐⠀⠁⢂⠈⠀⠻⠿⠿⡿⠃⠄⠠⠈⠙⠛⠛⠛⠀⠀⠠⠀⠐⠈⠉⠁⠀⠀⣜ ⠀⠀⢈⠿⠃⠀⠀⠀⠀⡀⠀⠙⠟⠻⠛⠃⠀⠀⡀⠸⡄⠀⠀⠀⠀⠀⠀⣠⢖⣻⣿⣷⣄⡀⣀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠁⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⣿⣿⠃⠃⠘⠉⠑⠒⠠⠤⢄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⡀⠀⠀⠀⠈⠲⣽⠋⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⡑⠄⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠁⠋⠙⠉⠰⢣⢴⡘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠠⢃⠀⠱⡄⠀⠀⠀⠀⠀⢀⠖⣬⡀⠀⠀⣠⡄⠀⣀⠀⠀⠀⡡⢳⠈⡹⢊⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⣶⣶⠄⠀⡀⠀⠀⢀⣦⠀⠚⠴⢁⣴⠾⣉⣴⠞⢉⡀⠀⢀⠃⠇⠀⡑⠂⠀⢀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠈⠐⠂⠀⠀⠀⢹⣿⠀⠀⢈⠛⠄⣼⡏⠀⣉⣴⡟⣣⡴⠋⣡⡴⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⠄⠀⠀⠀⠀⠀⠈⠁⣠⠸⡘⡇⢰⣿⣷⣾⢿⡿⢿⣥⡴⠋⢉⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠄⠀⠀⠀⠀⢀⣠⡋⢟⡂⢁⠀⢸⣿⣿⣿⡿⢏⣉⣩⣤⠞⢉⢠⠀⠀⠀⠀⠀⠀⠀⣀⡄⠁⠀⠀⢆⠱⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣸⡿⠷⠀⠠⠉⢀⣼⣿⢿⣟⣱⢶⣈⠁⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠻⠿⣿⣿⡾⠋⠈⠁⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠄⠁⠀⣔⡀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢈⠓⡀⠀⠀⠀⣠⠞⢁⠀⠀⠛⠉⠀⠀⢀⠈⠀⠁⠀⠀⠀⠀⠀⠠⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⢣⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡆⠀⡿⣉⠣⠀⠀⠉⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠦⠶⠴⢒⡒⠂⠀⣠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠷⢇⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⡀⠄⠀⠀⡀⡄⠀⠀⢸⡧⠁⠀⠣⢉⠀⠀⢐⠀⠈⠢⢄⠀⠀⠀⠀⠀⡀⠀⡀⢠⡤⢠⠐⡄⢎⣁⢀⡴⠟⠉⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠢⣄⠤⠚⣂⠀⠀⠀⠀⠄ ⠀⢈⠀⠀⠀⠐⠠⠀⠀⡘⠡⠀⠀⠘⢁⣀⠉⠀⢠⠴⠃⠀⠂⠀⠀⠀⠀⠀⢀⡆⡌⢁⡤⢾⠸⡇⠸⣎⣀⠤⣾⠀⠁⠀⠀⢀⣴⠃⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⣚⡝⢣⠀⢀⠀⠂ ⠀⠀⠀⠂⠄⡠⢁⠄⡠⢐⠠⢠⠀⠙⣁⠄⠀⣶⠋⠀⠄⠀⠀⠀⠀⠀⠀⠰⠄⠇⠳⠈⠛⠛⠆⠙⠤⠆⠐⠈⠀⠀⣀⣠⡴⠛⠉⠀⠀⠘⡤⣂⡀⠀⠀⠈⢀⠀⠐⢊⠄⢣⡐⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⣠⣀⣀⣀⣀⣀⣤⡶⠿⠛⠉⢠⡞⢀⢾⠀⠀⣱⠡⢳⢄⠀⠀⠀⠁⠀⢁⠂⠀⠱⡀⠂ ⠀⠀⠀⠀⠒⠄⠢⠐⡐⠢⠒⠰⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠉⠉⠛⠚⠈⠉⠁⠀⠀⠀⢀⡴⠏⢠⡟⠀⡂⠀⠀⡙⢢⢉⠦⠀⠀⠒⠀⠄⠀⠠⠀⠡⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠠⠀⠀⠀⠀⢀⣰⡯⠃⢀⡟⢀⡦⠁⢸⠀⠑⠢⠌⠊⠡⠀⠀⠈⠀⠂⠔⠀⣶⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⣠⢿⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⢠⡞⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⢆⠫⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠛⠋⠁⠀⠀⣠⠟⠀⠀⢨⠂⠀⣿⡇⠀⠀⠀⡀⠀⠀⠀⡀⠀⠠⢄⡀⢸⣷