⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠫⠝⡏⣏⠗⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣾⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⣾⡿⣽⣻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣸⣟⠋⠉⠳⢿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡻⣡⠾⠁⠀⠀⠰⠭⢛⠻⢻⣿⣿⡿⠂⠤⣄⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡵ ⠀⠀⠀⠂⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠏⣱⣿⠃⠀⠀⠀⠀⠀⠁⠜⣫⢿⠟⠉⠐⢼⣿⢿⣶⣴⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢰⠋⠀⠀⢠⠊⠀⠙⢾⠏⢳⣻⣆⠀⠀⠈⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⣹⠲⣍ ⠀⠀⠀⠀⠀⠀⠀⡐⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⣿⣿⠀⢀⠠⢀⠀⠀⢀⠔⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠹⣾⣄⠀⢀⠎⣄⡴⠦⡤⢀⠀⢢⠀⣠⡔⢯⡼⣡⢛⡬ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⢂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⣿⣼⠁⠀⠀⡧⠔⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⡎⢳⢏⢠⣾⣿⣦⠹⣄⢿⢧⣛⡼⢲⢥⢫⣜ ⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠰⡡⠀⠀⠀⣄⠻⣟⡌⠂⠐⠁⢀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠟⡙⡡⠘⣾⣸⣿⣿⣿⠃⢸⡈⠻⡼⣜⣣⢎⡷⣜ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣄⠀⠀⠀⠘⡕⡖⠒⠢⣸⡄⠈⠙⠿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠏⠀⠈⠊⡔⡙⡀⠿⣸⣿⣿⣿⣧⠀⡇⢂⠘⢦⡝⣮⢳⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡙⠛⠿⣿⣷⣄⣀⢠⣟⡅⠀⡐⢹⠃⠀⠀⠀⣿⣿⡻⠾⠃⢀⣀⣠⣤⣶⣿⡿⠛⠉⠀⠰⣦⠚⠈⠌⠰⠱⡰⡂⢿⣿⣿⣿⠂⡇⠀⠂⠈⣾⣽⠟⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢄⠀⡀⠌⡋⠀⠁⠀⠀⣀⣴⣿⣷⡆⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢤⠀⣀⠔⠊⠈⠓⠀⠐⢡⢚⡄⣗⣢⣿⡿⢃⢰⠇⠀⠀⠀⣟⡵⡻⠁ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⣿⣿⣿⣷⣾⣷⠖⣲⣾⣭⣽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠊⣏⠀⠀⠀⠀⠀⠀⡀⢢⡛⡤⢿⣿⠟⠁⢢⡿⠀⢀⢀⣸⢾⠝⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠏⠀⡨⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠃⠁⠈⠀⢸⡇⣀⣾⡟⡁⣤⣶⣿⡻⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣿⣿⣿⣿⣿⣿⡷⠟⢁⡠⠊⠄⢸⣿⣿⣅⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠒⠛⡭⣿⡟⠀⠀⠀⠀⢾⡿⠟⠋⢠⣿⣿⡿⠊⠀⠀⣀⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣿⣿⣿⣿⣄⣤⣶⡍⠀⡐⠠⠁⠛⠿⠻⠷⠀⠙⡋⠀⠀⢀⣀⡤⠞⠉⠁⠀⠱⡄⢀⢈⡞⡢⠀⠀⠀⠀⣾⠀⠀⣠⣿⡿⠋⣀⡤⣖⠾⡱⢍⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣷⣱⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⣁⡶⠉⠀⠈⡀⠀⣀⠰⠎⢿⢀⡎⡎⡱⡀⠀⠀⢀⣏⡰⣾⣿⣹⣶⣿⠹⣎⠹⣎⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣠⠖⠛⡄⠀⠀⡀⠤⠲⡍⠀⠀⠀⡨⠋⠈⣊⡱⢁⠀⠀⣸⣿⣿⢿⣻⡝⡾⣸⠹⡌⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣞⣷⣳⡀⠀⠀⣠⡴⠋⠁⠀⢀⡼⢖⠉⠀⠀⠀⠰⣄⡤⠊⠀⠀⠀⠐⢠⠡⠂⣰⣿⡿⣭⣛⢶⡹⣕⠇⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣻⣾⢷⣷⣤⠎⠃⠀⢢⡠⠚⠁⠀⠈⠂⠀⢀⠀⠔⠁⠀⡀⠀⠀⠀⠠⠡⡲⣵⢿⡻⣽⢷⣯⣯⣟⣾⠄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣍⣻⣿⣿⣿⣿⣿⣿⣿⣽⢮⣄⢀⠔⠀⠑⡀⠀⠀⡠⠄⠃⠁⠀⣠⣴⡾⠁⠀⠀⠀⠀⣴⣿⣯⢷⣹⢎⡿⣜⢯⣟⣷⣦⡈⠐⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠉⠀⢀⣀⣠⣴⣶⣿⡿⠛⠀⠀⠀⠀⣠⣾⣿⣿⣿⣻⡿⣿⢾⡽⣞⡾⣯⠿⠿⣷⣄⡀⠑⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⢳⡄⠙⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⢰⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣽⣯⡿⠻⠽⢿⣼⣀⠀⠀⠉⠙⠲⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣷⠀⠹⣆⠈⢿⣾⡿⡿⣽⣚⣷⣻⣿⣿⣿⣿⣦⣄⣀⢀⡀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣩⣙⣖⡦⣄⠈⠉⠓⠦⢠⡀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣯⣧⡀⠙⣆⠀⢻⣽⣳⢯⡿⡾⣷⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣷⣩⠙⡛⣟⠲⢿⡿⡝⠦⣄⠀⠘⠀⠅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣮⢇⠀⠹⣧⠀⠹⣯⡙⠿⣷⣻⣯⣟⡿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⡿⢿⠿⣤⣯⣾⣻⣦⠽⡧⠜⢦⣇⡟⠀⠈⡙⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠘⢿⣯⢟⡆⠀⢻⣦⠀⠙⣿⡄⠈⠉⠳⠯⣽⢻⡿⣯⡁⠒⠒⠒⠒⠈⠩⠉⢍⣩⣙⣫⣿⠛⣉⣩⠽⣜⣇⡗⠒⡐⠬⡱⢈⠐⣠⣿⢿⡶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢯⡶⠀⠀⢻⣧⠀⠈⢿⣄⠰⡄⠀⠀⠉⠙⠓⠻⠮⣐⠀⠀⠀⠀⠀⠀⠀⠂⡉⢙⠯⣅⠐⠈⠈⠄⠀⠀⠀⠐⢀⠂⣹⣿⡟⣯⢞⣭⢧ ⣶⣲⢦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⡇⠀⠀⢿⡇⠀⠈⠻⣄⠙⣦⡀⠀⠀⠀⠀⠀⠈⠙⠦⣡⠀⠄⡀⢀⠀⠀⢀⠈⠙⢊⣤⡁⠠⠀⠄⢠⠈⣄⣎⣿⡷⣿⣼⣫⢞⡽ ⣷⢯⣟⡿⣮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣽⣛⠀⠀⠘⣿⡄⠀⠀⠈⠂⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢈⡲⢦⣆⣌⡢⢄⠨⢄⡣⣙⣿⣷⣌⢲⣇⢾⣿⣷⣿⢿⣳⣟⡿⣟⢾ ⣿⣻⢾⣽⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣷⣻⠀⠀⠀⢹⣿⠃⠀⠀⠠⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠐⢍⠈⠹⣮⠉⠛⠿⢾⣾⣿⣧⣿⣿⣿⣿⣿⣿⢻⣞⣿⣿⣿⣾⣽⣛⢾ ⣿⣽⣻⠾⠹⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡽⣞⡷⡄⠀⠀⡰⢻⡄⠀⡰⠁⠀⠀⠀⠀⠀⠈⠉⠒⠦⣀⡀⠀⠉⠋⠁⠀⠀⠀⠀⠉⠙⠺⢯⢿⣿⣿⣿⣿⣿⣼⡳⣟⣷⢯⣗⡯⣟ ⣿⣾⠁⠀⠀⠀⠀⠀⠀⠈⢀⣠⣾⣿⣿⢯⣟⣯⢿⣧⠀⠘⠀⠀⡇⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣷⣿⡽⣞⣯⢾⣝⣯ ⣿⣾⠀⠀⠀⠀⡀⠀⠂⣠⣾⣯⢿⣿⣯⡿⣽⡾⣟⣾⡀⠀⠀⠀⠌⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣭⡉⠙⠛⠾⠿⣞⣷