⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣲⣶⣿⠿⣶⣲⣳⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣯⢓⣛⣛⢳⡞⣭⣿⣾⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⣾⣻⣿⣾⣯⣟⣾⠿⠻⣿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⡟⢋⠉⠉⠉⢉⠀⠀⠐⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⢀⣰⣆⡀⠀⢀⢀⣶⣶⣆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣭⡵⢾⣿⠇⠀⣿⡶⢴⡦⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣝⠀⠀⠀⠑⠚⠁⠡⠀⠈⡉⠋⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠲⡀⠀⡀⠀⠀⠰⡵⡗⡾⠀⠀⠀⣾⣧⣘⢉⢻⡌⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⠀⢀⠂⣡⣤⡴⣭⠦⣴⡂⣼⣿⣿⡿⣣⠿⣩⣾⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣃⣽⣟⣍⡅⠂⡔⠠⡀⠖⠲⠒⢄⣽⣿⢿⢿⡖⡏⣽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⢻⣿⣿⠫⣷⠀⠤⢣⣴⣤⡶⣖⣻⣹⣾⢋⠾⣳⠣⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⣿⣹⢟⠰⢞⣿⡇⠀⡱⢞⢻⢛⣯⣷⡿⣡⢋⡜⣟⣱⣳⣞⣋⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢞⣽⣌⡤⢳⢯⣿⣿⢀⠰⣈⣾⢾⣟⣿⡇⣧⣟⡸⢦⣧⠿⠚⠁⠀⠄⣀⠆⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣋⣋⠿⣷⢫⢻⣿⣿⣶⣾⡿⣫⣿⣟⠧⢾⢮⣭⠗⣞⣁⣠⡐⠈⢐⣰⡹⢠⠄⠂⡁⢀⠀⠀⠀ ⠀⣀⡄⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⡾⣻⣿⣿⣯⠚⣿⣯⡷⡿⣽⣟⣿⠏⢶⡷⣣⡝⣼⣿⠯⠖⣧⢿⣽⢣⢝⣢⢹⣰⡱⢷⣀⡀⠀ ⠀⠸⠁⠀⢈⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡷⡏⢾⢉⣿⢿⡹⣇⣿⣿⣹⣏⣿⣿⠏⣰⡿⢰⣸⢀⢾⡉⣉⠉⣆⢇⡏⡾⣆⣇⣿⣶⡏⢇⡇⠰⡀ ⠀⠀⡀⠀⢂⣴⣿⢻⠺⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⢢⢡⠃⢾⣿⣦⣱⢳⣾⡿⢿⣮⢟⡷⣫⡺⣃⣗⡖⣻⣷⡱⣌⡳⣜⠾⣽⣷⡿⣽⡞⠧⡜⢣⡜⢦⠀ ⠸⣀⡁⠈⠀⠙⡿⠏⡖⣎⠩⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡔⡧⢯⡜⣾⣿⠍⢫⡱⣾⠉⣹⣷⣿⠓⣄⡏⢙⡘⢨⢿⣷⣿⣽⣳⣭⣿⣿⠛⠫⣊⡮⡱⣍⣷⣞⠧⣉ ⠀⢡⣤⣀⡤⢂⡟⡠⣿⣋⣞⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠌⡟⡏⢸⣿⡆⡘⢦⡿⣿⠄⣿⣿⢧⠯⡹⢱⢟⣼⢸⣾⢏⡳⡍⠿⣽⣿⡃⢠⠀⠱⣾⡽⢿⡙⡌⡓⣉ ⡠⣟⠘⠋⢠⣾⡿⣦⣿⣍⠙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣴⡹⢁⣼⣿⣿⣹⢾⣽⡟⣹⣮⡟⢸⣵⡇⡏⢾⢡⣿⣿⣿⢶⣿⣿⣷⣿⣿⣳⠃⣽⢫⠛⡴⣘⠴⣱⢣ ⢖⢫⣡⢩⠿⠝⢿⣾⣾⡾⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢫⠀⣷⣼⡿⢁⠹⣮⣿⡇⢸⣷⣴⡟⡭⢲⠇⡟⠬⣾⣿⣯⣿⣾⣿⣟⣷⣿⣯⣰⡗⣭⣿⢷⣫⣿⣽⣿ ⢈⣧⡱⡡⢉⢺⣟⠯⢕⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡞⢴⢋⣿⣵⢊⡽⣾⣿⣴⡾⠹⡿⢹⢁⣧⢽⢱⣻⣿⣟⡻⣋⡿⣭⠟⣯⢻⣿⣿⣾⣏⢟⠻⡛⢭⠛⡜ ⣒⣉⣣⠭⡵⢸⠳⠣⢤⡙⢷⡦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣏⠸⡎⣭⣿⣿⣧⣿⣿⠯⢁⣠⣼⠏⡮⢻⠤⡏⢺⡙⢰⣦⡇⠿⠇⣽⢰⢻⡹⣿⣿⡯⣝⣎⡳⣙⣦⡽⢶ ⣟⣻⣝⣏⣟⣫⢳⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⢇⡜⣡⣟⣯⠇⣴⣿⣿⣿⡎⣿⠃⡞⢱⢇⡾⢚⣼⣿⡸⣿⣱⣾⣿⣿⣾⣧⣿⢿⣿⢿⣿⣾⣿⣿⣿⢿⡿ ⢾⣱⢎⡿⣎⣧⣹⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡾⢶⢩⡝⣸⣯⣽⢿⣿⣿⣿⢠⡝⢢⠧⣸⢸⡇⡾⣻⣿⡟⣿⣭⣿⠸⣕⢲⣷⣫⣟⡾⣿⣿⣿⢷⡿⣞⠳⣝ ⣷⡹⣞⣿⢯⡴⣏⣿⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⡃⣧⢊⣰⡏⣾⣿⣽⣿⣿⣿⣗⢣⣷⢋⡼⢫⣎⠇⣵⣿⣯⣟⣿⣷⢾⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣼ ⣿⢱⣹⡾⢷⣹⢷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠇⣀⣾⡿⡇⣇⠏⣰⣿⣶⣹⣿⣿⣿⣸⡿⣸⢸⡇⡹⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⡹⡎⣾⣿⠿⣿⠿⣿⡿⣹⠿⠿⣿ ⣞⣣⣟⣹⣓⡮⣿⣷⣿⠇⠀⠒⠒⠂⠀⠀⠀⠀⣠⣾⣾⡿⣿⣾⡇⢃⣽⢈⡞⣿⣳⣿⣿⣿⣧⢷⢳⢣⡮⣣⢿⠘⡏⣿⣿⣿⢻⢽⣻⢶⣻⣼⣭⢿⡲⢿⣿⣿⣿⣱⣎⢷⣛⠿⣼ ⣿⠾⡌⠷⠭⣞⣻⣿⣿⢀⡀⡀⠀⠐⠀⠐⡀⢐⠟⠋⡉⠹⣿⣿⢜⡹⢋⣴⣷⣿⣿⣿⣿⣿⣼⡧⣯⠋⢰⠟⢁⣴⣹⣿⡹⢎⣟⢯⣟⣿⣳⣿⣿⣯⢟⣿⣿⣿⣷⣶⣾⣯⣿⣟⣷ ⣾⣽⢽⡛⣛⢟⣟⠫⠋⠀⠀⠁⠢⢀⢠⠞⡌⡞⠀⢤⣗⠆⢿⡟⣨⣇⢸⣎⢸⣿⣿⣿⣿⣯⣼⠎⣿⡝⡸⢆⡿⢊⣿⡶⣿⠿⣾⢻⡻⣟⠿⡽⣿⢾⣿⣽⣿⠷⣯⢯⡝⣟⢿⡻⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠇⡄⡧⠍⢾⡏⣀⠾⣏⡟⡡⣾⠟⢸⣿⣿⣿⣿⣧⣼⠘⣇⣹⢋⣰⢻⢸⡯⣝⡬⣛⢬⢣⡳⢮⣟⢷⣯⣿⣿⣿⣿⣿⡿⣿⣯⠻⢿⣻⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣍⣞⡐⢯⡜⢸⢶⣽⢇⣸⡇⢷⡁⢰⣹⣿⣿⣿⣿⡉⡧⢃⡯⡹⢸⠟⢁⣿⡱⢮⡕⣛⢺⣷⣯⣷⣾⣛⣾⣿⣿⣳⣟⣾⡽⣿⣶⣽⣵⣯⠹