Marx ASCII Art

⣿⣻⣟⣯⣟⣿⢿⡻⣟⣿⣽⣻⣟⡿⣻⣽⣻⢟⣻⡟⣿⡻⣟⡿⣽⣻⢿⣽⡻⣟⣿⣻⢟⣿⣻⢿⣽⣻⣽⣻⠿⣽⣻⣟⣿⣻⣟⣿⣻⡽⣯⢿⡽⣯⠿⣽⣻⣽⣻⢯⣟⣿⣻⣟⣿⣻⢯⣟⡿⣽⣻⢟⣿⡻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣯⣟⣯⢿⡽⣯⠿⣽⢯⠿⣽⢯⡿⣽⣻⣽⣻⣽⣻⣽⣻⡽⣯⢿⡽⣯⠿⣽⢯⠿⣽⢯⠿⣽⣫⣟ ⣞⡷⢯⣟⣿⣻⣿⣿⡿⣶⢯⣗⣯⣽⣳⢯⣟⣯⢷⣻⢷⣻⣽⣻⢷⣯⣟⡾⣽⣻⢶⣯⣟⣾⣳⣟⣮⢷⣳⢯⣟⡷⣻⡼⣞⣷⢻⣞⣷⣻⡽⣯⢷⣯⣟⡷⣯⢶⣯⣟⣾⣳⡽⣞⣳⢯⣟⡾⣽⣳⢯⣟⡾⣽⣻⢶⣻⣞⣳⣟⣾⣳⣟⣾⣳⣟⡾⣯⣟⣷⣻⡽⣞⡿⣽⠾⣝⡷⢯⣶⢻⣶⣛⡶⣯⠷⣏⡿⣞⣽⣻⢽⡞⣿⣹⡞⣟⣧⠿⣼ ⡾⣽⣛⡾⣽⣏⡿⣿⡽⣿⡿⣾⣷⣳⣯⣟⡾⣭⡿⣽⢯⡷⣯⢯⡷⣯⢾⣽⣳⢯⣟⡾⣽⣞⣳⢾⡽⣫⢯⣟⡾⣽⣳⢿⣹⣞⡿⣞⣳⢯⡷⣯⣟⡶⣯⢿⣽⣻⣞⣾⣳⣽⣻⡽⢯⣟⡾⣽⣳⢯⣟⡾⣽⣳⢯⣟⣧⣟⣷⡻⣶⣻⡞⣷⣻⢾⣽⣳⢯⣞⣷⣻⡽⣽⣫⢿⣽⡻⣟⣾⣛⡶⣯⢟⣞⡿⣹⢷⣛⣮⠷⣏⣟⣳⣭⢿⣹⣞⣻⣳ ⣽⡳⢯⣳⢟⣮⢷⣻⢯⡓⠿⣽⣻⣟⡷⣿⡽⣯⢿⡽⣯⢿⡽⣯⢿⣽⣻⢾⣽⣻⢾⣽⣳⢯⣟⣯⣾⣽⣻⢾⣽⣳⢯⣞⡷⣯⡽⣯⣟⣯⢿⡵⣾⡽⣯⢷⣻⣞⡽⣞⣷⣛⡾⣽⣻⢾⣽⣳⢯⣟⡾⣽⣳⢯⣟⢾⣣⣟⡾⣽⣳⢯⣽⣳⢯⣟⡶⣯⣟⣾⣵⣯⣽⣷⣽⣿⣶⣿⣽⣮⣿⣽⣳⣟⢾⣹⢟⡾⣝⡾⣻⢽⣺⣳⢯⢯⡷⣞⣳⡽ ⢾⡽⣯⡽⢾⣹⠾⠙⠛⣿⣦⠈⠳⣯⣟⣷⣻⡽⣯⢿⣽⣻⢿⣽⣻⣞⣯⢿⡾⣽⢯⡷⣟⣯⢿⣞⡷⣯⣟⡿⣾⣽⣻⢾⣽⢷⣻⢷⣻⣞⣯⣟⣷⣻⣽⣯⣷⣯⢿⡽⣞⡽⣽⣳⢯⣟⡾⣽⣛⡾⠽⠷⠯⠟⠾⠯⢷⣯⣽⣷⣯⣟⡾⣽⣿⣾⣿⣿⡿⢿⡿⣿⢿⣿⣿⡿⠛⢋⣉⣹⣯⣿⣿⣿⣿⣿⣾⡽⡽⣞⣽⡳⣏⡷⢯⣛⡾⣝⣧⣟ ⣻⣼⣳⣿⠋⠁⠈⠀⢾⣯⢟⣷⠀⠸⣿⣼⣳⢿⣽⣻⢾⣽⣻⣞⣷⣻⣞⣯⠿⣽⠯⠿⢛⠛⠛⠚⠛⠳⠯⠿⣳⢯⣟⠿⣞⣿⣽⣿⣵⣶⣶⢀⣀⣀⣀⣀⡀⠈⠉⠙⠛⠻⠷⢯⡿⠞⠛⠉⠀⠀⠀⠀⠀⠘⠠⠉⠞⣿⣶⣷⣾⣻⡿⢹⡿⢫⠟⢰⢈⣿⣎⣵⡞⣼⣏⣠⣴⢾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣶⡻⣭⣟⢯⣯⡽⢯⡶⢯ ⣯⢯⣻⢿⣆⢀⣤⣀⠈⠻⣾⡽⡆⠀⣿⣽⣻⢾⣽⣻⢾⡽⣯⢿⣽⠯⣛⣯⡴⠋⠀⢀⠜⡤⢀⠤⠒⠀⠐⠀⠙⠺⢽⣶⣻⣿⣿⣿⣿⣿⣿⣾⣟⣯⠉⠙⡓⠲⠤⠄⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⢿⣿⣿⣿⠁⡾⢁⡎⠀⢸⣬⣿⣿⣽⡡⣿⣿⡟⠙⠌⠋⢉⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⢯⡽⣾⣭⢷⣞⣳⣞ ⣿⢯⡷⣯⢿⡿⣿⣯⣷⣄⠈⠛⠇⠀⣿⢾⣽⣻⢾⡽⣯⢿⣽⠟⢫⠴⠋⠀⣀⠀⣠⢊⣉⣴⣦⠔⠁⡠⠚⡠⠄⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⠿⠿⠾⠿⠿⣷⣶⣧⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠋⠐⢸⣿⡁⣸⣿⣿⣿⣿⣿⡿⣿⡯⠓⢌⡀⢤⣀⡌⠭⣩⢟⡽⣿⣿⣿⣿⣿⣿⣿⣯⣟⡶⣯⣟⢾⣳⡽ ⣿⣻⢿⠋⠉⢠⣤⡈⠓⠛⠓⠀⠀⠐⢿⣯⡾⣽⢯⡿⣽⠏⠃⣠⣤⠶⠛⠘⠛⠐⠈⠙⠉⠉⠉⠙⠲⠷⠊⠁⠀⠀⡤⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣤⢙⣯⢻⣿⠟⠛⠋⠉⠉⠉⠁⠀⠀⠀⠘⢻⣤⣀⠀⣂⣡⡾⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⣞⣯⢷⣻ ⣿⡽⣿⣧⣶⢿⣽⣻⢶⣶⣶⢿⣳⣄⠀⣹⡽⣯⣟⣿⣉⣴⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠟⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣞⡾⡽⣞ ⣿⣽⣳⣟⣿⡽⣶⢯⣟⡾⣽⣻⣷⣟⡿⣯⢟⣷⠟⠉⠉⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣿⣻⣽⢬⣓⣮⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⢷⣻⢽ ⡷⣯⡷⣟⣾⢿⣽⣛⡾⣽⣳⢟⡾⣽⣻⣭⡿⠃⢀⣰⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⡀⣤⣌⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣛⡾⣽ ⣟⣷⣻⢯⣟⣯⣿⣿⣽⣳⢯⣿⣹⣗⡿⠊⢀⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣜⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣏⡷⢯ ⣿⢾⡽⣯⣟⣾⣳⢿⣻⣽⣻⢮⡷⣾⠀⠀⠀⢙⠶⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢠⣠⣤⣤⣶⣶⣶⣦⣤⣀⠀⠀⠹⣷⣤⣄⡀⠀⢠⣀⣠⣶⣿⡿⠟⠛⠉⠙⠛⢦⣄⣀⠴⠾⡟⠻⢶⡆⠀⠰⠶⣿⣿⠛⢛⣉⠛⠿⣿⣦⠀⠀⠀⠀⠀⠺⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢞⡽⣯ ⣿⢯⣟⡾⣵⢯⣿⣻⣽⣟⣯⡿⣽⡏⢩⢒⡴⠋⠀⢰⣿⣶⣤⡀⡀⢀⢀⣠⣤⣶⣾⡿⠗⠲⢤⣀⠀⠀⠸⡿⢋⣻⣿⡗⠂⠈⠻⣿⣿⣿⣭⣁⡀⠀⠉⠳⣄⠀⢙⢄⣹⣿⠆⠀⠈⣹⣿⣿⣶⣶⣤⣬⣁⣺⣿⣓⢯⣉⠴⢷⣶⣾⠇⠔⠁⠀⢀⣿⣶⣶⡿⢿⣶⣌⣙⡷⠀⠀⠀⠀⠀⢺⡹⣿⣿⡟⠛⢻⠟⣉⣤⣙⣿⣿⣿⣟⣧⢿⡽⣞ ⣿⣻⢾⣽⣻⣞⣳⢿⣿⡾⣽⣻⢷⢣⡞⢉⠟⣤⠤⠿⣿⣍⣭⣿⣿⠚⠛⠻⢿⣿⣷⣦⣤⣤⣀⣩⣳⣄⠀⠱⣿⣿⣿⡇⠀⢀⡾⠛⢿⣿⣟⠿⠙⠳⣦⣶⢽⡁⠈⠿⢿⡟⠀⠀⠀⠙⢿⡀⢿⡯⠭⠀⠈⢉⠿⠋⠉⠁⣀⣈⡿⠇⠀⠀⠀⠀⠀⢙⠿⣿⣐⡀⠀⠠⠛⠉⠁⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⣴⠛⡇⠘⣯⣿⣿⣻⣞⣯⡽⣞ ⣿⣽⣻⣞⡷⣯⣻⠾⣽⢿⣿⡽⣿⣶⠉⣤⠂⠀⠀⠀⢘⣿⣛⣓⡟⠀⠀⠀⠀⠙⢻⣭⣍⡈⠉⠙⠯⠝⠀⢠⠟⢩⡟⠀⢀⠞⠀⠀⠘⣯⣁⠀⠀⠀⠀⠀⠉⠀⢀⡇⡘⠀⠀⠐⠀⠀⠀⠀⠈⠁⠁⠈⠉⠁⠀⠀⢠⡾⣉⢼⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢰⣿⣷⣿⡄⣿⣿⣟⣷⣻⢾⡽⣯ ⣿⣞⡷⣯⣟⡷⣯⢿⡽⡾⣽⣻⣿⣿⣼⣿⡇⣀⠤⣶⣇⡘⢋⡹⠀⠀⠀⠀⠀⠀⠀⠛⢌⠀⠀⠀⠀⠀⠀⣏⠀⡰⠁⠀⠀⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡵⠁⠀⢲⣀⠤⠄⢦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢣⣴⠃⢠⠂⠀⣤⣶⠍⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣼⢢⢉⣿⠇⣷⣿⣿⢾⡽⣯⣟⣷ ⢿⡽⣷⣻⣽⢷⣻⠾⣵⣳⢯⣟⣿⣿⣿⣿⣷⡉⢀⣽⡍⠁⠊⠁⠀⠀⠀⡠⠄⢦⠀⠀⠈⠀⠀⠀⡀⠀⠀⢹⡄⢇⠀⠀⠀⡑⠉⠉⣦⡀⠀⠀⠀⠀⠀⠀⠠⣿⢨⣇⡀⠀⢸⣟⣀⠀⢨⡆⠀⠀⠀⠀⠀⠀⠰⣿⡟⣎⢿⡀⣾⢀⣐⣉⣉⣀⣰⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢾⣯⠬⠸⢋⣶⣿⣿⣟⣾⣳⢯⡿⣽ ⢯⣟⡷⣿⡽⣯⣟⣿⣳⢯⣟⣞⣳⢿⣿⣷⢻⣷⡟⣿⡄⢠⠖⢦⣄⣤⣾⣤⣤⠄⠓⢌⠀⠀⠀⠊⠀⠀⠀⣎⣇⣨⣿⣿⣾⣿⣟⠒⠉⠻⣄⠀⠀⠀⠀⠀⠀⠘⠤⠳⡈⢛⣿⣿⣿⣯⡋⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣜⠦⡟⢛⣿⣿⣿⣇⣀⣀⠀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠐⣶⡀⣹⣾⣿⣟⣾⣳⣟⣯⢿⣽ ⣻⠾⣽⣳⡿⣽⣾⣳⣯⣟⡾⣝⣯⣟⡾⣿⠋⠉⠀⣟⣥⣴⣾⣿⣻⣿⣿⣟⣹⡋⠀⠀⢳⣄⠀⠀⠀⢀⣼⣾⢟⡭⢉⢡⡿⠟⠉⠙⢆⢠⡀⢁⠀⠀⠀⠀⠀⠀⠐⠀⣸⠋⢼⣿⡯⠺⣽⡷⢶⣶⣶⣆⠀⠀⠀⣽⠁⣹⡧⣿⡏⢹⣿⠙⢻⣿⣿⣇⡲⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠈⣼⣷⣄⣸⠷⢫⣿⣟⣾⣳⣟⡾⣽⣻⢾ ⣽⣛⡷⣯⣟⡷⣯⡷⣿⣻⡾⣽⣺⣳⢿⢟⡀⣒⣾⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣷⡣⢘⡄⣿⠳⣄⢠⣿⣿⣿⣿⣥⢇⣼⢈⣄⠀⠀⠀⢡⣷⠘⡄⠀⠀⢀⡀⠈⠀⠐⣿⣿⠿⠛⠛⠛⠒⠺⠯⠿⢿⣿⠀⠀⢘⡇⠀⣾⠳⣿⢀⣾⣿⣷⣾⣷⣿⣹⣷⣹⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠣⡑⢮⣹⡏⠁⢀⠲⣿⣞⣧⣟⡾⣽⣳⢯⣟ ⣾⣭⢷⣛⡾⣽⣷⣟⡷⣟⣿⣳⢷⣻⡏⠼⠟⢿⣿⣿⣿⣿⣿⣿⣷⡶⣶⣟⡿⣿⣿⣷⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣾⣿⣾⣎⣧⠀⠀⠀⢻⡈⠀⢰⡆⠀⠶⠁⠤⠂⠈⠹⡆⣶⣶⣶⠖⠁⠀⠀⠀⢧⣠⠞⠉⠃⣸⠟⡡⢛⢿⣿⢠⡴⣤⠬⣉⡙⠛⠛⢿⡟⠛⠀⠀⠀⠀⠀⠀⠀⢠⠘⢢⠱⡉⢦⠟⠀⠈⠄⢛⣿⣞⡷⣾⣽⣳⢯⣟⡾ ⣷⣻⠾⣽⡽⣳⢯⣿⣽⣯⢷⣟⣯⢿⠁⢀⡤⣽⣿⣿⡿⠭⠉⠙⠙⣻⡶⠯⠿⠿⢿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⡀⠀⠀⣠⣿⣷⢶⠄⢀⠀⠀⠀⢀⠟⢩⡿⠟⠉⠉⠀⠀⠀⠀⠠⠀⠀⢀⢡⠚⡤⢃⠌⠙⡆⠛⠛⠋⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢠⠉⠦⢡⠝⠁⠀⠀⠀⠀⣸⣿⣯⣟⡷⣾⣽⣻⢾⡽ ⣯⢷⣻⢷⣻⡽⢯⣞⡿⣞⡿⣾⣭⢿⠏⢹⡿⠋⠁⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⠪⣄⠀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⢿⣀⠀⠙⠏⠷⣾⠴⠯⡀⠀⢠⣿⣴⣿⣷⣾⡢⠀⠀⣠⡴⢊⣠⠴⡸⢌⠣⡙⡐⣹⢂⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠘⡄⢉⠂⠁⠀⠀⠀⠀⠀⣰⣿⣿⣻⣿⣽⣳⢯⣟⣯⢿ ⡿⣯⣟⣯⢷⣻⣛⡾⣽⢯⣟⡷⣯⠏⠀⡔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⠷⠾⠛⠻⡿⠟⠃⢸⣿⣿⡌⠙⠃⠀⠀⠀⠁⢀⠈⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⢯⢣⠋⠴⡉⢂⠅⡐⠃⢸⠆⣣⡀⡆⠀⠀⠀⠀⢀⣠⣀⠦⣄⡀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣷⣿⣻⢿⣿⣿⣾⣭⣟ ⣿⣳⣟⡾⣯⢷⢯⣟⡾⣛⣾⡽⠃⠀⢼⡓⠀⠀⠀⠀⢀⠀⠎⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⣡⠆⠀⠀⠀⠀⠘⢿⣿⣿⣆⣀⠘⠀⢠⠀⠈⠀⠰⠁⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⢏⡇⠣⠘⠄⡁⢂⠐⠀⠀⠈⡶⠖⠉⢉⣷⣶⣿⣟⢯⣛⠌⡒⢈⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣯⣿⣞⣷⡿⣿⣿⣿⣟⣿⣻ ⣟⡷⣯⢿⡽⣯⣟⡾⣽⣻⣾⡇⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⣿⣿⡿⣿⠋⠀⠀⠀⢀⠜⠁⠀⠈⠫⢛⠛⠻⣷⡏⠓⠀⡀⡔⠀⢈⠀⠀⢀⣼⣿⣿⠛⠋⠉⠉⠙⠲⢬⣁⡌⠐⣀⣢⠴⠚⠁⠂⠀⢠⣴⣿⣿⡿⣾⣹⢷⣮⣧⡈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣽⣟⣾⣽⢾⣿⢯⣿⣿⣿⣽⣻ ⣿⡽⣯⢿⣽⣳⣾⣽⣷⣿⣿⣇⢹⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⡳⢌⣲⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠀⠁⡈⠐⣠⣶⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣷⣦⣀⣴⣾⣿⣿⡿⣯⣿⢷⣯⣟⣞⡷⢿⣛⠦⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢷⣻⣟⣾⣽⢾⣻⣽⣿⣿⣿⣟⣾⢿ ⣯⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⢸⠃⠈⠑⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣽⣿⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢠⣅⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠦⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣽⣟⣿⣻⣾⡽⣾⣽⢫⣟⡷⣌⡀⠀⠀⠀⢀⣠⣾⣿⢿⣽⣻⣽⣾⣻⢾⣻⣽⣳⣿⣿⡿⣯⣟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡀⢀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣯⣿⡏⡄⢠⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣯⣷⢿⣻⣿⣿⣟⡿⣽⣟⣯⣷⢯⣟⡾⣽⣳⡻⣷⢦⣀⣠⣾⣿⢿⣻⣾⣽⣻⡽⣯⢿⣞⣯⣟⣿⣿⣿⡷⣿⣻⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢾⣷⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⢋⢿⣿⣿⣿⣹⣳⣯⢗⣾⣧⣓⣠⣤⣴⣠⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣼⣿⢿⣯⣟⣿⢾⣽⢿⣻⣿⣿⣾⣽⣻⢾⣟⣾⣻⢾⣽⣳⢷⣻⣾⣿⣿⣿⣿⣽⣻⣟⡾⣷⢯⣿⡽⣯⣟⣾⣽⣿⣿⣿⣽⢿⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠷⢮⡐⢦⣷⡀⠀⠀⠀⠀⠀⠀⠀⣩⢾⣿⣿⣳⣯⣷⢿⣻⢾⣯⡽⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⡿⣟⣯⣿⣞⣿⢾⣟⣯⣿⣻⢿⣿⣷⣯⣟⡿⣾⡽⣯⣟⡾⣽⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣻⣽⢿⣞⡿⣽⡾⣽⣾⣿⣿⢷⣻⣯⢿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢡⢻⣼⣻⡽⢤⠄⡀⠀⠀⠠⢊⢳⣻⣿⣿⣿⣽⡿⣯⣟⡿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣷⢿⣻⣽⣾⣻⡾⣟⣯⡿⣞⣿⣻⣿⣿⣷⣯⣟⣷⣟⡷⣯⣟⣿⣿⣿⣻⣾⢿⣯⣿⢿⣿⣿⣿⣽⣟⡾⣿⣽⣻⢿⣿⣿⣿⣻⣯⠟⢯⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣼⣤⣤⢶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⢿⣻⣽⣟⣯⣷⣟⣷⢿⣻⣽⣻⢯⣷⡿⣽⣿⣿⣾⡽⣾⣽⣻⢷⣿⣿⣻⡷⣿⡽⣟⣯⣿⣟⣿⡿⣿⣿⣿⣿⣳⣯⣟⣿⣿⡿⣷⡿⣽⡆⠀⢹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣯⣿⣯⣷⣿⣽⣾⣻⣾⣿⣽⣾⣯⣿⣳⣿⣟⣿⣿⣿⣿⣽⣾⣿⣿⣿⣯⣿⣽⣷⣿⣟⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣻⣏⣛⣉⣓⢊⣸

⣿⡻⣟⢿⣽⣻⢿⣻⣟⡿⣽⣫⢟⡽⣫⣟⡿⣏⣿⣻⣟⣿⣻⣽⠯⠝⠛⠛⠩⠯⢽⣫⣟⡽⣫⡝⣮⢯⡝⣯⢻⣝⡯⢯⡽⢭⢯⡝⡭⢯⡝⣯⢻⡽⡭⢯⡹⣭⣏⣽⣍⢯⡽⣩⢯⡽⢭⣏⢳⢭⣛⣼⡭⠯⠷⠭⠳⠙⠚⠓⠯⠽⣭⣋⡷⣩⢯⡝⣯⢻⡭⢯⡝⣭⣋⢷⣩⠯⡽⣭⢻⡝⣯⣟⡽⣫⢯⡽⣭⢯⡽⢭⢯⠽⣭⢻⡝⣯⡝⣞ ⣷⢻⡽⣞⡷⣯⣟⣷⣻⡞⣷⡹⢾⣝⡷⣫⡽⣞⣧⡿⠞⠓⠉⣠⣴⣶⣶⣶⣤⣤⣤⣀⠀⠉⠑⠛⠚⠚⠉⠉⠀⠀⠀⠉⠉⠛⠮⢽⣙⡮⣝⣾⠽⠚⠋⠉⢁⣀⣀⣀⣀⠈⠉⠑⠓⠛⠺⠞⠋⢉⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⣄⡈⠓⢏⣾⡹⢧⣛⢧⣛⢦⡝⣦⡳⠯⠷⠯⠓⠛⠓⠾⠷⢭⣷⣹⢞⡾⣜⢯⡺⡝⣮⢳⡽⣺⡝⣞ ⣯⢿⣹⢯⣟⣷⣻⣞⡷⣽⣣⡟⣯⢾⣝⡷⠛⠉⣁⣠⣤⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡉⠑⠉⣀⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠻⠿⠷⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠻⣝⣮⡳⠞⠃⣉⣀⣤⣶⣶⣿⣿⣿⣶⣶⣶⣤⣄⣉⠛⠾⢝⣶⣹⢳⢭⡳⣏⢷⡹⣎ ⣯⢿⣽⣻⣞⣷⣻⢾⡽⣳⣭⢟⣵⡻⠊⢠⣶⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠁⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡑⢯⣏⢾⡱⣏⢾⡱⣏ ⣿⣻⣞⣷⣻⢾⣽⣳⡟⣧⡟⣾⠝⠁⣰⣿⣿⣿⣿⡿⠿⢻⠿⠻⠛⠙⠋⠉⠋⢻⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠿⠿⠿⠿⢟⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣞⣳⠽⣎⠷⣭ ⣟⣷⣻⢾⣽⣻⣞⣷⢻⣧⠟⢃⣤⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠳⠿⠚⠛⠛⠋⠉⠁⠹⣷⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢧⡻⣭⢻⡼ ⣿⢾⣽⣻⣞⣷⣻⡾⠛⣡⣼⣿⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣜⢧⣻ ⣿⣛⡾⣧⣟⣾⠏⣠⡾⢻⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣞⡵ ⣯⢿⣽⣳⣞⡏⢰⣿⣧⣻⣿⠿⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⣀⠘⣩⣀⣄⣀⡀⠀⠀⠀⠀⠀⣰⣿⠿⠁⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠘⣶⣿⡿⠋⠀⣀⣾⣿⣷⣦⣷⣆⣀⠀⠀⠀⢰⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⡼ ⣟⣯⢶⣟⡾⡇⢸⡾⣿⠿⣿⠓⣻⣿⣇⣘⣶⢠⣶⣤⣤⣴⣾⣶⣦⣤⣀⣴⣿⣁⠀⠀⣶⣤⣶⣶⣶⣿⣿⣶⣦⣄⠀⣴⣿⣶⣿⣷⣽⣿⣿⣿⡿⢛⣛⣿⣿⣶⣦⢠⣾⣿⣿⣧⣤⣾⣿⣿⣿⢿⠿⠿⢿⣿⡄⠀⠀⠀⠈⣻⣷⣿⠚⣿⣿⣟⣉⠉⠈⠻⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣽ ⣿⣞⡿⣾⢽⣇⠈⣷⣤⣼⣏⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡙⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣦⣌⣹⣿⣷⣌⣿⣿⠇⠀⣹⣿⣿⢿⣿⣷⣯⣿⣿⣿⣯⠞⣿⣹⣿⣿⠉⠛⠻⣿⣿⣭⡿⣶⣄⣿⣿⡆⠀⠀⢰⣿⣻⣿⠀⢿⣿⣿⣽⣷⣦⣤⣀⡀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣟ ⣷⢯⣟⣾⢻⡾⡄⠹⣿⣿⣿⣷⡾⣻⣿⣿⡿⠁⣿⡿⠹⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⠃⠀⠸⢿⢻⣿⣿⠿⠟⠿⠿⠟⢋⡿⠋⠀⠈⠉⠛⠃⠸⣿⣿⠟⠴⠛⠝⠀⠀⢸⡿⠛⠀⠀⠀⠚⢻⣿⣯⠽⠙⣿⠿⣿⠀⠀⠀⣿⡿⠛⠁⠀⠀⣿⣥⣤⣌⠙⠛⠛⠁⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣯ ⣿⣛⡾⣽⢯⡿⣽⡀⠹⣿⣿⣍⠙⣿⣿⡿⠁⢠⣯⡄⠀⠘⠻⢿⡆⠀⠀⣾⢿⡿⠃⠀⣶⠄⠀⠀⠙⠿⠶⠆⠀⠀⢠⡟⠀⢀⢀⣤⠄⣆⠀⠀⠉⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⡀⠀⠀⣀⡀⠙⠿⠷⠆⠈⠉⠀⠀⢠⡶⠋⠀⡀⠀⡀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣷ ⣯⢿⡽⣯⢿⣽⣳⢷⡀⠹⣿⣿⣾⣉⣏⠀⢠⣿⡋⢸⣶⣄⠀⠀⠳⣦⠀⣇⡞⠀⠀⠐⠷⠛⣷⣦⡀⠀⠙⢦⣄⡀⠘⣷⣶⣿⣾⣶⣂⣽⡆⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣀⡈⠛⠻⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⠈⠙⠀⢻⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⢿⣛⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣳ ⣿⢯⡿⣽⣻⢮⣟⣯⡇⢠⣿⣿⣿⡏⠻⣿⣿⣿⣿⣞⡉⠻⣧⠀⢀⡀⠀⠻⢻⣶⣶⣿⣿⢷⠞⠻⢿⣆⠀⣀⠉⣙⠀⣼⣿⣿⣿⣯⣽⡋⠀⢶⡄⠀⠀⠀⠀⠀⠈⢻⢿⣿⣿⡟⢷⠼⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣦⣤⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⣼⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⢀⡿⣽ ⣿⢯⣽⣳⢯⣟⣾⡝⢀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⣧⣶⣴⣿⣦⣿⣷⣿⣼⣿⣿⡿⣛⣾⣿⣿⣶⣶⣭⡀⠀⢀⠀⠀⠀⣸⣶⣿⣿⣿⣶⣾⣶⣄⠙⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠛⠋⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣷⡍⣿⡿⢽⣿⣿⣿⣿⣿⣿⡟⢁⡾⣽⣳ ⣿⣻⢾⣽⣻⣞⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡿⠋⣽⢟⠽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⡿⠿⣿⣿⡇⠀⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣥⣄⡀⢀⡀⢹⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢿⣵⣿⡟⣳⡿⢁⣿⣿⣿⣿⣿⡿⠋⣰⣏⠷⣏⡷ ⣿⣹⢿⡾⣷⠇⣸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣇⣾⠀⣿⣿⣿⣿⣿⡆⣿⣸⣿⣿⣿⣿⣇⠀⠈⠹⠁⠀⣿⠀⠀⢿⣿⣿⡿⠿⠿⠿⣿⣿⣏⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠈⠉⢉⣿⡿⣷⣿⣿⣿⣿⣿⡿⠁⣸⢷⣎⢿⣹⣹ ⣿⡽⣯⣟⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⡷⢿⣿⡏⣿⣿⡏⣸⣷⣿⣿⡟⠻⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣿⣷⣶⣶⡆⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣺⣯⣿⣿⣿⣿⣿⣿⣿⡿⢁⡼⣯⢷⡺⣯⡗⣯ ⣯⢷⣻⢾⠃⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⢏⣿⡏⠉⠙⣿⣾⠛⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣻⣴⣿⠟⣴⣿⣿⣿⣿⣿⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⢀⡾⣽⢳⡯⣽⢧⣟⣳ ⡿⣯⣟⡟⣠⣿⣿⣿⣿⣿⣿⡿⢿⢷⠃⠛⠛⠋⠀⠀⠀⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣯⠼⠇⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⡄⠀⠀⠀⠀⡀⠀⢸⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⣻⣿⣭⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠏⠀⣿⣿⣿⡟⢠⣯⠷⣭⢷⣫⢷⣫⢾⣳ ⣿⣳⣯⢃⣻⣿⣿⣿⠙⢹⣷⣡⣾⣿⠟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣿⢟⡿⢻⢿⣿⣿⣿⣿⢿⣿⣦⣬⣭⠁⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡟⠛⠃⠘⢿⣷⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠖⠀⢿⣿⣷⣄⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢁⣀⣤⣴⣾⡿⠛⠟⠋⠁⠀⣀⣿⣿⣿⡄⣟⣮⢟⣭⢷⣫⢗⣯⢟⡷ ⣷⡟⣵⣿⣿⣿⣿⡟⢂⣼⣯⣿⡿⢧⣤⣶⠶⠀⠀⣠⣾⣿⣿⣿⣿⣯⡶⠋⠀⢀⡼⠸⠏⠉⠈⠐⣿⣿⣿⣯⣷⣤⡄⠀⣀⣀⠈⠻⣿⣿⣿⣷⣦⣄⣀⠈⠉⠁⠀⠀⠀⠉⣿⣿⢿⣿⣿⣿⠿⠛⠛⠻⠿⠟⠒⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣱⣦⣤⣼⣿⣿⣿⣯⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⢹⢮⣟⢮⢷⣫⣟⣮⢟⡽ ⣿⡄⢿⣿⣿⣿⣿⣤⣿⣿⢿⣿⣿⠿⠿⢿⣧⡤⠀⣸⣿⣿⣿⣿⣿⣟⣡⣖⡵⠛⠁⠀⠀⢀⠀⢸⣿⣿⣿⣫⣾⣿⣦⡶⣻⣏⠀⠀⣿⣿⣿⣿⣿⣻⣿⣦⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣻⡜⣯⢷⣹⢾⣹⠾⣽ ⣷⣧⠈⢿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣧⣄⣠⣶⣴⣿⣿⣿⣿⣿⣿⣯⣟⣽⣶⡶⠂⠀⣰⡏⡄⣰⣾⠟⢥⡟⣿⢟⣻⡶⣿⠷⠀⣠⣿⣿⣿⣿⣿⡷⡍⠳⢀⣠⡴⠂⢀⣤⣾⣯⣿⣿⣯⣛⣀⣀⣀⣤⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣯⣿⣟⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣷⡻⣵⣫⢾⣹⢯⣟⡵ ⣟⡾⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡏⢼⣿⣿⢿⣿⣿⣿⣿⣿⢟⣿⢯⣴⣦⣼⣿⠛⡄⣼⠇⢀⣬⣽⣿⣿⡽⠟⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⠷⠟⠛⠉⢀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣍⠧⣿⣿⣿⢿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣯⢷⣏⠷⣯⢯⣟⠾⣽ ⣯⢿⡽⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣏⡯⢸⣷⣿⣠⣼⣿⣿⢿⣾⣿⣿⣿⣿⡿⣣⣿⣿⣿⣯⠀⠀⠀⠀⣠⣴⣿⣿⣿⢻⣿⣿⣿⢸⣿⣯⣼⣿⣿⣿⣿⣟⣿⡿⣽⢻⣿⣿⣿⣿⡿⣟⡻⣛⡭⣟⣳⢿⣱⢫⣜⡳⢼⣿⠏⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⢞⣾⣻⡭⣟⣾⣻⣽ ⣯⢿⡽⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣼⣿⡿⣳⢟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣳⣾⣿⣿⣿⡿⣱⣿⣿⣿⣿⢸⣿⠿⣟⣻⢻⡝⣭⣻⣿⡟⣧⣿⣿⣿⣿⣿⢳⣣⠷⣙⢾⣹⢯⡷⣫⢳⡬⣓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣷⣟⢮⡷⣯ ⡿⡿⠰⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⢁⣠⣿⣿⣿⣿⡿⢿⣿⣶⣿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⢸⣯⢳⣎⣵⣫⣾⣴⣿⢟⣼⣿⣿⣿⣿⣿⣿⣣⢏⡞⡭⢾⣹⢯⣷⣹⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣾⣜⣯⢿⣼⣳ ⣿⣻⡄⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⡿⣜⣫⣜⣳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠟⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⢳⡿⣞⡿⡼⢯ ⡷⢯⣟⣦⠈⠻⢿⠿⠛⠋⠉⣁⠀⠉⠛⢿⣿⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠝⠛⠛⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⣀⡴⣾⢻⡜⣯⣟⣯⣷⣛⡿ ⣟⡿⣞⣭⢷⣤⣤⣤⡶⣟⣿⣻⣟⡿⣶⣤⣤⣤⣤⣤⣄⣀⣀⢀⠈⢁⡀⣀⣀⡤⣤⢤⣤⣀⣀⢀⡀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠟⠻⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠛⠉⠀⣀⣤⣖⠿⣽⡝⣞⡯⣝⡶⣻⣟⡶⣏⢿ ⣟⡾⡽⣞⣻⢾⡵⣏⣷⣻⣼⢳⣯⢟⣷⣛⣾⣽⣻⢾⡽⣯⣻⢏⣟⣣⢟⡼⣣⢟⡽⣺⣵⢫⣎⢷⡹⣏⢿⡳⣶⢦⣤⣄⣀⣀⢤⡤⣤⢤⡤⣤⡤⣖⠶⣲⣛⢷⡲⢦⣄⠀⠙⠿⣿⠿⠿⠛⠛⠛⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠋⠁⠀⣀⣤⢶⣻⢧⣳⡞⣟⣳⢯⣝⢾⣹⢞⣿⣞⡿⣹⣞ ⡿⣽⣽⣫⡽⣾⢽⣻⡼⣳⡞⣿⣼⣻⢾⡽⣞⡷⣯⢿⣽⣳⢯⡿⣜⣎⢾⡱⣏⣞⣳⣳⣭⠷⣎⢷⡳⣭⢿⣱⢯⣞⡳⣞⢴⢫⣎⠷⣝⡮⡵⣏⠷⣭⠳⣵⢫⢶⡹⣳⢎⢷⡢⣄⣀⣀⣠⠤⡤⢤⠤⣤⣀⠀⠀⠙⠛⠿⠿⠛⠉⠉⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣀⣤⢶⣻⢏⡾⣏⣷⢫⢷⡹⣽⣫⣟⡮⢯⡗⣯⢾⣯⣽⣳⢯ ⣿⣳⣽⣳⣟⢾⡯⣷⢻⣵⢫⢷⣳⢯⡿⣽⢯⡿⣽⣻⣞⣳⠿⣜⡳⣎⢷⡹⣞⡼⣣⠿⣜⡻⣜⢧⡻⡼⢧⡟⡾⣜⡳⣝⢮⣓⢮⢻⣜⡳⣽⢺⡝⣎⠿⣴⡛⣮⢵⢫⣞⣣⡝⢶⡙⡮⣕⣫⢝⣣⣛⢦⡝⣞⣲⣢⢤⣠⢤⡤⣖⣺⡝⣯⢳⡝⣮⢟⣿⢻⡻⣝⢯⡻⡝⢯⣙⡳⢮⡻⣵⢯⣛⡷⣏⣟⢮⡽⢶⣻⢮⣝⡳⣝⣾⣻⢷⡾⣭⢿

⣿⡻⣟⢿⣽⣻⢿⣻⣟⡿⣽⣫⢟⡽⣫⣟⡿⣏⣿⣻⣟⣿⣻⣽⠯⠝⠛⠛⠩⠯⢽⣫⣟⡽⣫⡝⣮⢯⡝⣯⢻⣝⡯⢯⡽⢭⢯⡝⡭⢯⡝⣯⢻⡽⡭⢯⡹⣭⣏⣽⣍⢯⡽⣩⢯⡽⢭⣏⢳⢭⣛⣼⡭⠯⠷⠭⠳⠙⠚⠓⠯⠽⣭⣋⡷⣩⢯⡝⣯⢻⡭⢯⡝⣭⣋⢷⣩⠯⡽⣭⢻⡝⣯⣟⡽⣫⢯⡽⣭⢯⡽⢭⢯⠽⣭⢻⡝⣯⡝⣞ ⣷⢻⡽⣞⡷⣯⣟⣷⣻⡞⣷⡹⢾⣝⡷⣫⡽⣞⣧⡿⠞⠓⠉⣠⣴⣶⣶⣶⣤⣤⣤⣀⠀⠉⠑⠛⠚⠚⠉⠉⠀⠀⠀⠉⠉⠛⠮⢽⣙⡮⣝⣾⠽⠚⠋⠉⢁⣀⣀⣀⣀⠈⠉⠑⠓⠛⠺⠞⠋⢉⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣤⣤⣄⡈⠓⢏⣾⡹⢧⣛⢧⣛⢦⡝⣦⡳⠯⠷⠯⠓⠛⠓⠾⠷⢭⣷⣹⢞⡾⣜⢯⡺⡝⣮⢳⡽⣺⡝⣞ ⣯⢿⣹⢯⣟⣷⣻⣞⡷⣽⣣⡟⣯⢾⣝⡷⠛⠉⣁⣠⣤⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡉⠑⠉⣀⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠻⠿⠷⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠻⣝⣮⡳⠞⠃⣉⣀⣤⣶⣶⣿⣿⣿⣶⣶⣶⣤⣄⣉⠛⠾⢝⣶⣹⢳⢭⡳⣏⢷⡹⣎ ⣯⢿⣽⣻⣞⣷⣻⢾⡽⣳⣭⢟⣵⡻⠊⢠⣶⣿⣿⣿⣿⣿⣿⣿⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠁⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡑⢯⣏⢾⡱⣏⢾⡱⣏ ⣿⣻⣞⣷⣻⢾⣽⣳⡟⣧⡟⣾⠝⠁⣰⣿⣿⣿⣿⡿⠿⢻⠿⠻⠛⠙⠋⠉⠋⢻⣿⣿⣿⣿⣿⡿⣿⣿⠿⠿⠿⠿⠿⠿⢟⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣻⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣞⣳⠽⣎⠷⣭ ⣟⣷⣻⢾⣽⣻⣞⣷⢻⣧⠟⢃⣤⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠳⠿⠚⠛⠛⠋⠉⠁⠹⣷⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢧⡻⣭⢻⡼ ⣿⢾⣽⣻⣞⣷⣻⡾⠛⣡⣼⣿⡿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠻⣜⢧⣻ ⣿⣛⡾⣧⣟⣾⠏⣠⡾⢻⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣞⡵ ⣯⢿⣽⣳⣞⡏⢰⣿⣧⣻⣿⠿⢿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⣀⠘⣩⣀⣄⣀⡀⠀⠀⠀⠀⠀⣰⣿⠿⠁⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠘⣶⣿⡿⠋⠀⣀⣾⣿⣷⣦⣷⣆⣀⠀⠀⠀⢰⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⡼ ⣟⣯⢶⣟⡾⡇⢸⡾⣿⠿⣿⠓⣻⣿⣇⣘⣶⢠⣶⣤⣤⣴⣾⣶⣦⣤⣀⣴⣿⣁⠀⠀⣶⣤⣶⣶⣶⣿⣿⣶⣦⣄⠀⣴⣿⣶⣿⣷⣽⣿⣿⣿⡿⢛⣛⣿⣿⣶⣦⢠⣾⣿⣿⣧⣤⣾⣿⣿⣿⢿⠿⠿⢿⣿⡄⠀⠀⠀⠈⣻⣷⣿⠚⣿⣿⣟⣉⠉⠈⠻⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣽ ⣿⣞⡿⣾⢽⣇⠈⣷⣤⣼⣏⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡙⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣷⣦⣌⣹⣿⣷⣌⣿⣿⠇⠀⣹⣿⣿⢿⣿⣷⣯⣿⣿⣿⣯⠞⣿⣹⣿⣿⠉⠛⠻⣿⣿⣭⡿⣶⣄⣿⣿⡆⠀⠀⢰⣿⣻⣿⠀⢿⣿⣿⣽⣷⣦⣤⣀⣀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣟ ⣷⢯⣟⣾⢻⡾⡄⠹⣿⣿⣿⣷⡾⣻⣿⣿⡿⠁⣿⡿⠹⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⠃⠀⠸⢿⢻⣿⣿⠿⠟⠿⠿⠟⢋⡿⠋⠀⠈⠉⠛⠃⠸⣿⣿⠟⠴⠛⠝⠀⠀⢸⡿⠛⠀⠀⠀⠚⢻⣿⣯⠽⠙⣿⠿⣿⠀⠀⠀⣿⡿⠛⠁⠀⠀⣿⣥⣤⣌⠙⠛⠛⠉⡄⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣯ ⣿⣛⡾⣽⢯⡿⣽⡀⠹⣿⣿⣍⠙⣿⣿⡿⠁⢠⣯⡄⠀⠘⠻⢿⡆⠀⠀⣾⢿⡿⠃⠀⣶⠄⠀⠀⠙⠿⠶⠆⠀⠀⢠⡟⠀⢀⢀⣤⠄⣆⠀⠀⠉⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⡀⠀⠀⣀⡀⠙⠿⠷⠆⠈⠉⠀⠀⢠⡶⠋⠀⡀⠀⡀⠀⠙⠛⠋⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣷ ⣯⢿⡽⣯⢿⣽⣳⢷⡀⠹⣿⣿⣾⣉⣏⠀⢠⣿⡋⢸⣶⣄⠀⠀⠳⣦⠀⣇⡞⠀⠀⠐⠷⠛⣷⣦⡀⠀⠙⢦⣄⡀⠘⣷⣶⣿⣾⣶⣂⣽⡆⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣀⡈⠛⠻⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⠈⠙⠀⢻⣄⡄⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⢿⣛⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣳ ⣿⢯⡿⣽⣻⢮⣟⣯⡇⢠⣿⣿⣿⡏⠻⣿⣿⣿⣿⣞⡉⠻⣧⠀⢀⡀⠀⠻⢻⣶⣶⣿⣿⢷⠞⠻⢿⣆⠀⣀⠉⣙⠀⣼⣿⣿⣿⣯⣽⡋⠀⢶⡄⠀⠀⠀⠀⠀⠈⢻⢿⣿⣿⡟⢷⠼⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣦⣤⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⣼⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⢀⡿⣽ ⣿⢯⣽⣳⢯⣟⣾⡝⢀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⣧⣶⣴⣿⣦⣿⣷⣿⣼⣿⣿⡿⣛⣾⣿⣿⣶⣶⣭⡀⠀⢀⠀⠀⠀⣸⣶⣿⣿⣿⣶⣾⣶⣄⠙⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠛⠋⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣷⡍⣿⡿⢽⣿⣿⣿⣿⣿⣿⡟⢁⡾⣽⣳ ⣿⣻⢾⣽⣻⣞⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⡿⠋⣽⢟⠽⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⡿⠿⣿⣿⡇⠀⣿⡇⠀⣰⣿⣿⣿⣿⣿⣿⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⣥⣄⡀⢀⡀⢹⣿⣿⡧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⢿⣵⣿⡟⣳⡿⢁⣿⣿⣿⣿⣿⡿⠋⣰⣏⠷⣏⡷ ⣿⣹⢿⡾⣷⠇⣸⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣇⣾⠀⣿⣿⣿⣿⣿⡆⣿⣸⣿⣿⣿⣿⣇⠀⠈⠹⠁⠀⣿⠀⠀⢿⣿⣿⡿⠿⠿⠿⣿⣿⣏⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⡎⠈⠉⢉⣿⡿⣷⣿⣿⣿⣿⣿⡿⠁⣸⢷⣎⢿⣹⣹ ⣿⡽⣯⣟⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣟⡷⢿⣿⡏⣿⣿⡏⣸⣷⣿⣿⡟⠻⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣿⣷⣶⣶⡆⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣷⣌⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣺⣯⣿⣿⣿⣿⣿⣿⣿⡿⢁⡼⣯⢷⡺⣯⡗⣯ ⣯⢷⣻⢾⠃⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⢏⣿⡏⠉⠙⣿⣾⠛⣻⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣻⣴⣿⠟⣴⣿⣿⣿⣿⣿⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⢀⡾⣽⢳⡯⣽⢧⣟⣳ ⡿⣯⣟⡟⣠⣿⣿⣿⣿⣿⣿⡿⢿⢷⠃⠛⠛⠋⠀⠀⠀⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣯⠼⠇⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⡄⠀⠀⠀⠀⡀⠀⢸⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⣻⣿⣭⣀⠀⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠏⠀⣿⣿⣿⡟⢠⣯⠷⣭⢷⣫⢷⣫⢾⣳ ⣿⣳⣯⢃⣻⣿⣿⣿⠙⢹⣷⣡⣾⣿⠟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣿⢟⡿⢻⢿⣿⣿⣿⣿⢿⣿⣦⣬⣭⠁⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡟⠛⠃⠘⢿⣷⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠖⠀⢿⣿⣷⣄⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢁⣀⣤⣴⣾⡿⠛⠟⠋⠁⠀⣀⣿⣿⣿⡄⣟⣮⢟⣭⢷⣫⢗⣯⢟⡷ ⣷⡟⣵⣿⣿⣿⣿⡟⢂⣼⣯⣿⡿⢧⣤⣶⠶⠀⠀⣠⣾⣿⣿⣿⣿⣯⡶⠋⠀⢀⡼⠸⠏⠉⠈⠐⣿⣿⣿⣯⣷⣤⡄⠀⣀⣀⠈⠻⣿⣿⣿⣷⣦⣄⣀⠈⠉⠁⠀⠀⠀⠉⣿⣿⢿⣿⣿⣿⠿⠛⠛⠻⠿⠟⠒⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣱⣦⣤⣼⣿⣿⣿⣯⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⢹⢮⣟⢮⢷⣫⣟⣮⢟⡽ ⣿⡄⢿⣿⣿⣿⣿⣤⣿⣿⢿⣿⣿⠿⠿⢿⣧⡤⠀⣸⣿⣿⣿⣿⣿⣟⣡⣖⡵⠛⠁⠀⠀⢀⠀⢸⣿⣿⣿⣫⣾⣿⣦⡶⣻⣏⠀⠀⣿⣿⣿⣿⣿⣻⣿⣦⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣻⡜⣯⢷⣹⢾⣹⠾⣽ ⣷⣧⠈⢿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣧⣄⣠⣶⣴⣿⣿⣿⣿⣿⣿⣯⣟⣽⣶⡶⠂⠀⣰⡏⡄⣰⣾⠟⢥⡟⣿⢟⣻⡶⣿⠷⠀⣠⣿⣿⣿⣿⣿⡷⡍⠳⢀⣠⡴⠂⢀⣤⣾⣯⣿⣿⣯⣛⣀⣀⣀⣤⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣯⣿⣟⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣷⡻⣵⣫⢾⣹⢯⣟⡵ ⣟⡾⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡏⢼⣿⣿⢿⣿⣿⣿⣿⣿⢟⣿⢯⣴⣦⣼⣿⠛⡄⣼⠇⢀⣬⣽⣿⣿⡽⠟⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⠷⠟⠛⠉⢀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⣍⠧⣿⣿⣿⢿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣯⢷⣏⠷⣯⢯⣟⠾⣽ ⣯⢿⡽⡇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣏⡯⢸⣷⣿⣠⣼⣿⣿⢿⣾⣿⣿⣿⣿⡿⣣⣿⣿⣿⣯⠀⠀⠀⠀⣠⣴⣿⣿⣿⢻⣿⣿⣿⢸⣿⣯⣼⣿⣿⣿⣿⣟⣿⡿⣽⢻⣿⣿⣿⣿⡿⣟⡻⣛⡭⣟⣳⢿⣱⢫⣜⡳⢼⣿⠏⢊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⢞⣾⣻⡭⣟⣾⣻⣽ ⣯⢿⡽⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣼⣿⡿⣳⢟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣳⣾⣿⣿⣿⡿⣱⣿⣿⣿⣿⢸⣿⠿⣟⣻⢻⡝⣭⣻⣿⡟⣧⣿⣿⣿⣿⣿⢳⣣⠷⣙⢾⣹⢯⣿⣫⢳⡬⣓⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣷⣟⢮⡷⣯ ⡿⡿⠰⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⢁⣠⣿⣿⣿⣿⡿⢿⣿⣶⣿⣿⣟⣿⣿⣷⣿⣿⣿⣿⣿⢸⣯⢳⣎⣵⣫⣾⣴⣿⢟⣼⣿⣿⣿⣿⣿⣿⣣⢏⡞⡭⢾⣹⢯⣷⣹⣧⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣾⣜⣯⢿⣼⣳ ⣿⣻⡄⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⡿⣜⣫⣜⣳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠟⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⢳⡿⣞⡿⡼⢯ ⡷⢯⣟⣦⠈⠻⢿⠿⠛⠋⠉⣁⠀⠉⠛⢿⣿⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠝⠛⠛⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⣀⡴⣾⢻⡜⣯⣟⣯⣷⣛⡿ ⣟⡿⣞⣭⢷⣤⣤⣤⡶⣟⣿⣻⣟⡿⣶⣤⣤⣤⣤⣤⣄⣀⣀⢀⠈⢁⡀⣀⣀⡤⣤⢤⣤⣀⣀⢀⡀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠟⠻⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⢿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠿⠛⠉⠀⣀⣤⣖⠿⣽⡝⣞⡯⣝⡶⣻⣟⡶⣏⢿ ⣟⡾⡽⣞⣻⢾⡵⣏⣷⣻⣼⢳⣯⢟⣷⣛⣾⣽⣻⢾⡽⣯⣻⢏⣟⣣⢟⡼⣣⢟⡽⣺⣵⢫⣎⢷⡹⣏⢿⡳⣶⢦⣤⣄⣀⣀⢤⡤⣤⢤⡤⣤⡤⣖⠶⣲⣛⢷⡲⢦⣄⠀⠙⠿⣿⠿⠿⠛⠛⠛⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠋⠁⠀⣀⣤⢶⣻⢧⣳⡞⣟⣳⢯⣝⢾⣹⢞⣿⣞⡿⣹⣞ ⡿⣽⣽⣫⡽⣾⢽⣻⡼⣳⡞⣿⣼⣻⢾⡽⣞⡷⣯⢿⣽⣳⢯⡿⣜⣎⢾⡱⣏⣞⣳⣳⣭⠷⣎⢷⡳⣭⢿⣱⢯⣞⡳⣞⢴⢫⣎⠷⣝⡮⡵⣏⠷⣭⠳⣵⢫⢶⡹⣳⢎⢷⡢⣄⣀⣀⣠⠤⡤⢤⠤⣤⣀⠀⠀⠙⠛⠿⠿⠛⠉⠉⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣀⣤⢶⣻⢏⡾⣏⣷⢫⢷⡹⣽⣫⣟⡮⢯⡗⣯⢾⣯⣽⣳⢯ ⣿⣳⣽⣳⣟⢾⡯⣷⢻⣵⢫⢷⣳⢯⡿⣽⢯⡿⣽⣻⣞⣳⠿⣜⡳⣎⢷⡹⣞⡼⣣⠿⣜⡻⣜⢧⡻⡼⢧⡟⡾⣜⡳⣝⢮⣓⢮⢻⣜⡳⣽⢺⡝⣎⠿⣴⡛⣮⢵⢫⣞⣣⡝⢶⡙⡮⣕⣫⢝⣣⣛⢦⡝⣞⣲⣢⢤⣠⢤⡤⣖⣺⡝⣯⢳⡝⣮⢟⣿⢻⡻⣝⢯⡻⡝⢯⣙⡳⢮⡻⣵⢯⣛⡷⣏⣟⢮⡽⢶⣻⢮⣝⡳⣝⣾⣻⢷⡾⣭⢿

⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠛⠿⠷⠶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡀⠹⣧⠀⠀ ⠀⠀⢰⡿⠋⠀⠀⣀⣠⣄⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣿⣆⡀ ⠀⠀⠈⣿⣦⠀⣿⣟⡉⠉⠛⠗⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⢀⣤⡾⠛⠁⠈⠙⠋⠛⠻⠿⠃⠀⠈⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡿ ⠸⣯⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⢁⣴⠶⢨⣿⣿⣿⣿⡇ ⠀⣼⣿⣤⣈⠉⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⣼⣿⣿⣿⣿⠁ ⠀⠹⣿⠉⣙⣿⣷⣿⡇⠀⠀⠀⠀⠀⢀⣠⡘⠉⣠⣾⠿⣿⣿⡿⠁⠀ ⢀⣾⠟⣀⡉⠉⠀⣈⠁⠀⠀⠀⠀⣰⡿⠛⠛⠟⠋⠁⠀⢻⡿⠁⠀⠀ ⣿⠃⠀⠿⠁⣤⠀⠙⢷⣤⣤⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀ ⠻⢶⣶⣶⣾⣿⣤⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣦⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠄⣷⠙⠀⠀⠀⠀⠀⠁⠟⢴⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠿⣭⣭⣭⣤⣶⣿⠿⣙⣮⠳⠉⠋⡶⣩⠟⡿⣾⣴⣡⣉⣉⣭⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠾⣶⣤⣭⣥⣿⣾⣴⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠄⡤⣦⣿⣽⣥⣭⣬⣶⠳⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⢟⡿⣿⣿⢣⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⣯⣿⣾⢿⡿⠉⠀⠀⠀⠀ ⠀⠀⠋⡾⣴⣋⢑⣿⢶⣠⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡈⢦⣷⢻⡷⣙⣦⢿⠈⠀⠀ ⠀⠂⣩⠟⣿⣼⡇⣸⠀⠀⡄⣦⣿⢿⠛⠿⠿⠿⠿⠻⠛⠉⠀⠀⠀⠀⠋⣿⣾⢠⠀⡀⣷⡈⣿⣿⠻⢯⠀⠀ ⠀⠟⣾⣨⡿⢺⣰⠀⠀⠀⠀⠁⡟⣿⣿⣿⣼⣤⣤⣤⣦⣶⣿⠿⠙⡿⣼⢀⠀⠀⠀⠀⡀⢠⣿⢸⣌⣷⠹⠀ ⡏⣰⠟⢸⣇⢰⠀⠀⠀⠀⠀⡿⣿⣿⣠⣦⣿⠻⠈⠀⠀⠀⠀⡀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⣧⢰⣿⡻⣧⠘ ⢱⡿⣾⣿⡞⠀⠀⠀⠀⠀⠇⣿⣿⣸⠀⠀⡀⣦⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡏⣼⣷⢿⢰ ⡇⣾⠛⣧⢹⠀⠀⠀⠀⠀⡄⣿⣿⢸⠀⠀⠀⠀⡀⣦⣿⠻⠈⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢣⡘⣿⠘ ⡇⢡⣿⢻⣯⠀⠀⠀⠀⠀⠀⣧⣿⢻⠀⠀⠀⠀⠀⠀⡀⣦⣿⡿⣿⣿⢴⠀⠀⠀⠀⠀⠀⠀⠆⢻⣿⢿⡇⢰ ⡄⡟⢸⣮⣿⠘⠀⠀⠀⠀⠀⠀⣦⣿⢻⠈⠀⠀⠀⠀⠋⡿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⢸⣿⡜⠀ ⠀⡇⢸⣇⡿⣯⠈⠀⠀⠀⠀⠀⠀⡄⣦⢿⠙⠀⠀⠀⣀⣀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣫⡿⢸⣿⢀⠀ ⠀⡀⢳⡏⣽⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⣽⣟⢹⣰⠀⠀ ⠀⠀⡀⣄⣷⣧⣿⢿⠀⠀⠀⠀⠀⠀⠷⠙⠀⠀⠀⡀⠀⠀⠀⠋⠟⠀⠀⠀⠀⠀⠀⠀⣫⡿⢻⣼⢀⠀⠀⠀ ⠀⠀⠀⠀⡀⢄⣤⣷⠹⠀⠀⠀⠀⠀⡀⣿⣶⠻⠉⠀⠁⠟⡶⣿⢰⠀⠀⠀⠀⠀⠁⠟⣶⣠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⣇⢹⡀⣤⣶⣴⢀⠃⣼⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠰⠀⠀⠀⠀⣷⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡶⣠⢀⠀⠀⠀⠀⠀⠀⣄⣦⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣤⣤⣤⣤⣷⠸⠀⠃⣾⣤⣤⣶⣴⣶⢶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣾⠏⠀⠀⠹⣷⣶⣶⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⠀⠀⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⣃⣠⣴⣶⣄⣀⢹⣧⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⢠⣿⠟⠋⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠹⣿⣷⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⢻⡿⣫⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⢿⣿⣧⣷⣄⡀⠀⠀ ⠀⠀⣰⢹⣟⣽⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣽⡏⢳⡀⠀ ⠀⢀⣿⢸⡿⣫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠙⢿⣦⡄⠀⠀⠀⠀⠀⠀⠈⣯⡿⣇⢸⡇⠀ ⠀⡜⣿⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠘⣿⣮⢸⡟⡄ ⢰⡇⢿⣿⢻⠆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⣯⢻⣿⢡⡇ ⠘⣿⡘⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⢹⣧⠛⣾⡇ ⢰⢿⣷⣼⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⡞⣿⣾⡿⢱ ⠘⣧⡻⣿⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠈⠻⣿⣦⣠⣿⣿⡿⠀⠀⠀⠀⠀⢰⣇⢸⠟⣰⡏ ⠀⠹⣷⣌⢸⣿⢠⡀⠀⠀⠀⠀⢀⣼⡿⠙⠿⣿⣶⣦⣤⣤⣤⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⣰⢺⡿⣨⣾⠟⠀ ⠀⠀⢯⠻⣿⣿⡈⣷⡀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⢿⣿⣦⡄⠀⠀⣸⡇⣼⣿⠟⣩⠂⠀ ⠀⠀⠈⢿⣦⣙⡷⢻⣷⢦⡈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣠⢶⣿⢑⣋⣴⡾⠋⠀⠀ ⠀⠀⠀⠀⠉⡿⢿⣾⣿⣯⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢣⣿⣿⡿⢟⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣶⣬⣭⣥⣽⣿⣦⡤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⣴⣾⣿⣥⣭⣤⣶⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣉⣉⣡⣴⣾⡿⠟⣩⡶⠋⠉⠳⣮⣙⠿⣿⣶⣤⣭⣭⣭⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢴⠟⠁⠀⠀⠀⠀⠀⠙⣷⠄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⢿ ⣿⣞⡿⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣯⢿ ⣿⣞⣿⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⢿⣯⣍⡙⠺⣿⢯⣷⣟⡿⣽⣾⣻⢷⣻⣿ ⣿⣞⡿⣞⣯⡿⣞⣿⣳⡿⣽⣻⣾⣯⢿⣞⣿⣽⣦⡀⠉⠛⣾⢿⣽⣞⣿⣻⣽⣾ ⣿⣞⣿⣻⣽⣻⢯⣷⡿⠙⠁⠀⠀⢨⣽⣟⣾⣽⢾⡿⣦⡀⠀⠙⣿⣾⣳⢿⣳⣿ ⣿⣾⣹⣷⢿⣹⣿⠏⠀⠀⠀⢀⣾⣿⢿⣾⣹⣾⣿⣹⣿⣷⠀ ⠀⠈⣷⣿⢿⣹⣾ ⣿⣞⣷⣟⡿⣝⠁⠀⠀⢀⣄⠀⠙⠯⣿⣞⣯⣷⢯⣷⣟⣾⣷⠀⠀ ⠘⣯⣿⢯⣿ ⣿⣞⡿⣞⣿⣻⣷⣦⣶⣿⡿⣷⣆⡀⠈⠻⣷⣯⢿⣳⣯⡷⣿⠀⠀ ⠀⣹⣯⣿⢾ ⣿⣞⡿⣯⣷⣟⣷⣻⣽⣾⣻⣽⣻⣷⣄⠀⠈⠙⢿⣽⣳⣿⣻⠀⠀⠀ ⢼⣟⣾⢿ ⣿⣞⣿⣽⡾⣽⡾⣯⢷⣯⡷⣟⣷⢯⣿⣷⣤⡀⠈⠙⢷⣯⠏⠀⠀⠀⣾⡿⣽⣻ ⣿⢾⣽⣞⣿⣝⠛⠃⣄⠉⠙⠻⢽⢿⣞⣷⣻⢿⣦⡀⠀⠁⠀⠀⠀ ⣼⣿⣻⣽⢿ ⣿⢯⣷⡿⠚⠉⢰⣤⡿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⡿⣷⣻⡽⣿ ⣿⢯⡇⠁⠀⣸⣿⢯⣿⡽⣯⡿⣿⢷⣶⣤⣤⣤⣤⣤⣶⣾⣦⣀⠀⠀⢽⣿⡽⣿ ⣿⣻⢷⣶⣾⣟⣯⣿⣞⣿⣳⡿⣯⡿⣽⢯⡿⣽⣻⣽⣻⢾⡽⣿⣳⣶⡿⣯⢿⣽ ⣿⡽⣟⣾⣳⣯⣟⣾⣽⢾⣯⣟⣷⢿⣻⣯⢿⣻⡽⣷⣻⣟⣿⣳⣿⣳⢿⣻⣯⢿ ⣿⡽⣿⣽⣳⣯⢿⡾⠽⣟⣾⣽⠾⢟⡿⣞⡿⠯⣿⡽⠷⠻⣾⣻⣾⡽⣟⣷⣻⢿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠟⠓⠶⢦⣄⡀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣀⣀⡀⠀⠀⢀⣠⡼⠗⠀⠀⠀⣀⣀⣀⣀⠀⠈⢙⣦⠴⠾⠧⢄⡙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡏⠀⠀⠀⠉⠛⢶⠶⠋⠀⠀⠀⢀⡴⠋⠁⠀⣀⣈⣙⣶⣏⣠⠤⠤⠤⠤⠽⢦⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠚⠋⠉⣭⠉⠉⠉⠉⣧⠀⠀⠘⠃⠀⠀⠘⡆⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⢤⣤⣤⣤⣤⣼⣧⣤⣷⣤⣤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀ ⠈⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠓⠦⠤⠤⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣆⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⠸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠈⢳⣤⣀⡤⢤⣀⡾⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⣼⠁⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠸⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠴⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠞⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡶⠤⠤⠾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠹⣆⠀⢠⠶⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⣸⠙⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠀⠈⠙⢦⣄⡀⠀⠀⠀⡇⠉⢳⡄⠀⠀⣠⠞⠀⠙⣶⣤⠇⢠⣿⣿⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠴⠇⠀⠀⠙⣦⠔⠃⠀⠀⢰⣿⣏⣀⣿⣿⠇⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⣼⡄⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠁⢹⡄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⣼⣿⡿⣿⡇⠀⠀⠀⢷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⣼⣿⡿⠁⣸⠃⠀⠀⠀⢸⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣼⣿⡿⠁⢠⠏⠀⠀⠀⠀⠘⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣤⠏⠀⠀⠀⠀⠀⠀⡇⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⢩⡿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡷⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⣴⣿⣷⠋⠙⡧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣾⣿⡿⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣄⣀⣠⠞⠁⠀⠀⢀⡞⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣤⣴⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⡾⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠉⢻⣄⠀⣀⣴⡏⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣰⡧⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⢟⣥⣶⣶⣶⣄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿ ⣿⡟⣵⣿⣿⣿⣷⣿⣿⣷⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⡿⣸⣿⣿⣿⣿⠏⣿⣿⣿⡶⠶⢶⣤⡤⡤⢽⣿⣿ ⡇⣿⣿⣿⣟⠁⣼⣿⣿⠿⠳⠏⠹⠻⣿⣎⠻⣿⣿ ⡇⢻⣿⠭⡭⣳⣿⣿⣿⣷⣄⠀⠀⠀⢷⡿⢗⢿⣿ ⣿⣄⠳⡂⠿⠯⢿⣿⣿⣿⣿⣷⣀⣶⣿⠿⠾⣸⣿ ⣿⣿⣦⢸⣷⣶⣴⡙⢿⣿⣿⣿⣿⡛⠿⠃⠈⠻⣿ ⣿⣿⣿⡈⣿⣿⣿⣿⣶⣬⣭⣛⣻⠿⣿⣦⣀⠀⣿ ⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠟⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡉⠓⡆⢰⠦⠤⠤⢤⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠧⠤⣷⣶⣧⣾⡀⠰⠆⠀⡇⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠔⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⢸⠀⣀⡀⠤⠤⡤⢤⣄⣀⣀⠈⠛⢛⠋⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⣘⡀⢸⠀⠀⢈⣉⣉⣉⣣⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠉⠙⢍⡑⠲⢤⣀⣀⡤⠏⢀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢀⣴⣿⣿⣶⣤⣤⡤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⣠⠒⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⢀⠔⠁⠉⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢆⠀⠀ ⠁⣠⠀⠀⢣⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡠⢊⡭⠙⠛⠓⠤ ⡷⠃⠀⠀⠀⠱⢼⡦⢄⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⢀⡤⡪⠚⠁⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⣀⠤⣀⣁⡀⠉⠒⠚⠋⠉⠉⠉⠉⠽⠓⣊⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣶⣿⣿⣶⣤⣤⣤⣶⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠟⠛⠛⠛⢧⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠹⣿⠛⠻⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣍⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠐⠟⣧⡀⠀⠀⠀ ⣰⡟⣛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⣄⡀ ⢿⡀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⠶⢯⣝⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡉⣷ ⠘⢷⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣤⣤⣄⣀⣀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣙⣧⡀⠀⠀⠀⠀⠀⠀⣀⠋⣠⡿ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠉⠛⠙⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⣯⣤⠶⠶⠾⠿⠛⠉⠹⣷⠀⠀⠀⠀⢀⣼⠛⠛⠋⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⡟⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠸⣏⠉⠛⠛⠛⠛⠛⠛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠈⢻⣟⠛⠋⠉⠉⠉⣉⡿⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠙⠷⣤⣀⣀⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠙⠳⠶⣶⡶⠾⠋⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠛⢻⡿⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⡤⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣴⣶⣿⡿⢷⣶⣦⣤⣤⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⣾⣟⣛⡉⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠸⠛⠉⠙⠛⠿⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⣽⣶⣶⣦⣌⡉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢋⣵⠟⠉⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣀⣴⠿⠋⠀⣼⠇⠀⠀⠀⢀⣀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠿⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⢻⣍⠛⠁⠀⠀⠀⣿⠛⠛⠛⠛⠻⠿⢦⣤⣀⠈⣿⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠛⠷⢦⣄⠘⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣾⡏⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠉⣿⠏⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠹⣷⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⣀⣀⣀⣤⠞⠃⠀⠀⠀⣀⡀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⡀⠀⣠⡄⠀⠀⠀⢸⡇⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠐⢾⣭⣀⣀⣀⣀⣀⣠⣤⡄⠀⠀⠀⢻⡏⠉⠉⠉⠛⠛⠷⢤⣄⡀⢸⡇⠀⠀⠈⠙⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⣉⣉⣡⡿⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠃⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⢤⣄⣀⣈⡽⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣠⣤⡾⠟⠁⠀⠀⠀⠀⠀⠒⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣀⣀⣾⠏ ⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠙⠛⠋⠁⠀ ⠀⣤⣴⠶⠿⠇⠸⣷⣤⣤⣤⣄⣀⣙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀ ⣸⡿⠟⠛⠀⢀⣠⣿⠏⠉⠉⠉⠉⠛⠛⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⣠⣤⣄⠀⠀⠀⠀ ⣿⡿⠟⠓⠀⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢻⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣏⣥⣤⣤⣴⣾⠟⢉⣿⠇⠀⠀⠀ ⠛⠿⠿⠿⠷⠶⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⣼⡟⢠⣿⣿⣿⣿⡏⠙⠛⠿⠿⣿⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⠶⠿⠟⠛⠉⠉⠉⠉⠉⠉⣽⡿⠀⠀⠀⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣦⣤⣴⣿⢡⡿⠛⢿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠛⢦⠀⢨⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣇⣿⣷⣤⣾⣿⣧⣄⣀⠀⠀⢠⣾⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⣤⣤⣍⣹⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⠶⠶⠿⠿⠻⣷⣦⣭⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠘⢿⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠈⠙⠻⠿⠿⠿⠿⠿⣿⡇⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠋⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠉⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣶⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡔⠒⠖⣩⠿⢽⢿⠕⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⢂⠡⠼⠊⠁⠈⠉⠉⠁⠐⢢⡀⠀ ⠀⠀⠘⡤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠟⠀ ⠀⠀⠀⡔⠤⡀⠀⠀⠰⣶⠖⢰⠂⠀⠉⠀⠀⠀ ⠀⠀⡰⠉⠐⠠⠌⠉⠁⠠⡕⠺⡄⠀⠀⠀⠀⠀ ⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⠼⠀⢸⠀⠀⠀⠀⠀ ⠀⠘⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀ ⠀⠘⡦⠔⠤⠃⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀ ⢠⣔⣉⠆⠀⠀⠀⠀⢄⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⠀⢸⠆⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⠀⠀⠀⢀⠈⡢⠀⠀⢀⢕⠀⠀⠀⠀ ⠀⠀⠀⠑⠢⠄⣀⣀⣱⠸⠂⠀⠚⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⢶⣶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀ ⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⠛⠁⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄ ⠀⠀⣿⣧⡶⠟⠛⠛⠿⠶⠶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡿ ⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧ ⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢠⡇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣸⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷⠶⠶⠶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏ ⢻⡇⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢰⣿⠁ ⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⣀⣤⣼⣧⠀ ⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠉⠉⠉⠛⠛⠷⠶⡶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⡀⠈⣿⡇ ⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣿⠇ ⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤⡶⠶⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡏⠀ ⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠥⠤⠶⠶⠶⠚⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⠶⠶⠒⠚⠛⠛⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣀⣀⣀⣀⣠⣤⣼⡇⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡶⠶⠶⠶⠶⠖⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⣉⠉⠉⢁⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣄⣀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠛⢛⣩⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠙⠿⣧⣀⡀⠀⠀⣠⣤⣤⡴⠟⠉⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⡿⠿⠿⠶⠶⠶⢤⣤⣄⣀⣴⠟⠉⠉⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢰⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢠⢺⠏⢻⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠃⠈⠒⠊⠁⠚⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⣠⠤⢄⡀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣆⠀⠀⠀⠀⠀ ⡞⢀⣰⣶⠿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀ ⢳⡿⠋⣠⣴⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠀⠀⠀⠀⠈⢻⠟⠃⣠⣶⡉⠒⡄ ⠀⠉⠉⠙⡿⡟⠢⠀⠀⡀⠄⡀⠀⠳⣀⢹⠿⠿⢶⠒⠒⠊⢁⣀⢀⣧⡈⢿⡆⡼ ⠀⠀⠀⠀⢻⡝⢳⡑⠚⠋⠉⢂⠀⠀⠀⠩⢭⣭⢽⣀⣀⡴⡿⢼⢽⠟⠓⠘⠛⠁ ⠀⠀⠀⠀⠀⠱⣌⠿⠄⠀⠀⡸⠀⠀⠀⠀⠀⠀⢣⢏⢴⠿⠃⣠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⡐⠒⠪⠕⠃⠀⠀⠀⠀⠀⠀⠻⣢⡒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠊⠉⠑⢢⠀⠀⠀⠀⠀⠀⢨⣾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣿⣀⣀⠀⠤⠄⢺⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡁⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠧⣤⡤⠞⠀⠀⠳⠤⣀⣀⣆⠾⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⣶⣦⣄⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⢿⠟⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣹⣿⣿⣿⣿⣫⠝⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠶⠾⣤⡀⠀⠀⠀⢠⣤⠶⠶⠶⣤⡀⢀⣸⣿⣿⣿⠇⠛⢠⡏⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠈⢻⣆⣀⣴⠏⠀⠀⠀⠀⠈⢻⡏⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠆⠀⠀⠀⠀⢀⡏⠉⣿⡶⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢳⣄⢀⡤⠞⠛⠛⠓⠀⠘⣦⡀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠶⠾⠟⠋⠁⠀⠀⠀⣀⣴⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠓⠲⠶⠶⠶⠶⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⠶⠶⠿⠿⠿⣿⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣷⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⢀⡴⠋⠁⢹⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀ ⠀⠀⣠⠞⠁⠀⠀⠈⠿⠀⠀⠀⠀⠀⠙⢧⣀⡀⠀⢀⣠⣿⣄⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇ ⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠀⠙⠻⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣤⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣶⣄⢹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⠶⠶⠶⠶⠤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⠤⠤⣤⣤⣄⣀⣀⠀⠀⠀⠈⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⠀⠐⠊⣉⣉⣉⡉⠓⠀⠈⣧⠀⠀⠀⣰⠇⠀⠀⠀⠀⠒⣛⡛⠒⠶⢤⣈⠉⠙⠳⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀ ⠀⠀⠀⠀⢸⠁⠉⠻⣇⣴⠛⠉⠀⠀⠉⠓⢦⠀⣿⠀⠀⠀⣿⠀⠀⢀⡴⠟⠋⠉⠉⠙⠳⣄⠀⠀⠀⠀⢻⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀ ⠀⠀⠀⠀⢸⡀⢠⣀⣹⣁⣀⣀⣀⣀⠀⠀⠈⣧⡿⠉⠉⢻⡇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣼⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⢸⡇⠀⢨⣿⠛⠀⠀⠈⠉⠉⠉⠉⣹⠇⠀⠀⠸⡇⠀⢸⡿⠋⠉⠉⠉⠙⠓⠒⠶⢾⣧⣶⠄⣿⠀⠀⢠⣾⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠀⠀⠸⡇⣰⠃⠘⢧⡀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣿⣀⡈⢷⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣿⣀⣠⣼⣿⠃⢀⣠⠤⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⡀⠀⠀⠉⠓⠲⠴⠖⣾⠋⠀⠀⠀⠀⠀⠀⡀⠹⡆⠛⠦⣄⣀⣀⣠⠴⠛⠀⠀⠀⢰⡟⠛⠛⠛⠁⢀⣿⣥⣄⠀⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡉⠉⠉⠓⠒⠒⠒⠒⢛⠳⣤⣤⣤⠶⠞⠉⠉⠛⠓⠦⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣼⠇⠀⠀⠀⠀⣿⠁⠀⠈⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣴⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠸⣍⣉⣛⠲⠶⠖⠚⠛⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢿⣿⠛⠿⠿⠿⠿⠒⠒⠚⠿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣵⡄⠀⠀⠀⠀⠈⠻⣧⣄⣀⣀⣀⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⣿⢿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠿⠋⢹⠹⣄⠀⠀⠀⠀⢀⡆⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣼⠋⠛⠶⢦⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⠁⠀⠀⢻⠀⠈⢦⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡿⠃⠀⠀⠀⠀⠘⣆⠀⠀⠙⢄⣀⠀⠙⠳⣤⣤⣤⣤⡤⠀⠀⠀⠀⣠⣄⣀⣠⣤⠶⠋⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠈⣻⣷⠶⢤⣤⣄⠀⣀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀ ⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⡴⠛⠁⠈⠁⠀⠰⠾⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠙⠻⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⢀⠔⠉⠉⠉⢢⠀⠀⠀⡠⠐⠒⠠⣠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⢘⠊⠉⠉⠉⠉⡇⠀⠘⠒⠒⠒⠒⠚⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢩⢿⡿⠀⠘⢤⠤⢒⣲⡔⠀⠀⡰⡤⠤⠤⠦⣰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠤⠀⠀⠱⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⣍⠀⠱⡀⠀⠀⠀⠢⡀⠀⠀⠘⢄⠀⠀⠀⠀⠙⢄⠀⠀ ⠀⠀⢰⠁⠀⠀⠀⠀⢀⣿⣦⡀⠘⢤⡀⠀⠀⠈⠒⠤⣀⠀⠑⡄⠀⠀⠀⠈⢆⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣀⠈⠑⠢⠤⢀⣀⣀⡈⠩⡁⠀⠀⠀⠀⠈⡆ ⠀⠐⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣶⣤⠤⠤⠤⠏⠁⠀⠀⠀⠀⠀⠀⢱ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⢫⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠣⡀⠹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆ ⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡱⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀ ⠀⠀⠀⠀⠀⢨⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠢⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀ ⠀⠀⢀⣠⣶⣿⣿⡇⠉⠒⠤⢄⡠⡤⠤⢖⠂⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀ ⣠⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣼⡇⠀⠀⠈⠓⠂⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣾⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠋⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣉⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠈⠉⠙⠛⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀ ⠀⠀⡰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡄⠀⠀⠀⠀⠉⠳⣄⠀ ⠀⣾⣡⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠊⠁⢳⠀⠀⠀⠀⠀⠀⢈⣧ ⢰⡟⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⢳ ⢸⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸ ⡆⠁⠀⠀⠀⠀⠀⡷⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣸ ⢧⠀⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠳⣄⠀⠀⢀⡇ ⠘⣆⠀⠀⠀⣠⠒⠉⠑⠒⠲⠔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠉⣧ ⠀⠈⢣⡀⠀⠹⡀⠀⠀⠀⠀⠀⠊⢀⠤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇ ⠀⠀⠀⢙⡶⠖⠚⠓⢦⠀⠀⠀⢰⡏⠉⠉⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀ ⠀⠀⠀⠘⣅⣀⣀⣠⣼⠃⠀⠀⠘⢦⠤⠤⠤⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠈⢲⡖⣒⠅⠀⠀⠀⠀⠀⠩⣒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⢰⡎⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⠀⠀⠀⠀⢀⡴⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠈⠙⠤⢤⣶⣖⣁⣀⣀⡸⠟⠿⢦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣒⠉⠉⠑⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠤⠴⢯⠔⢀⡠⠔⠓⠊⠉⠉⠉⠉⠒⠊⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢋⠀⠀⠠⠃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⢀⠴⠓⡆⠀⡠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠡⠊⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠐⠁⠀⠈⢀⠀⢸⠀⠀⠀ ⠀⡿⠖⡇⢠⠃⠀⠀⠀⠀⠀⢀⡴⠊⢀⠤⠒⠒⢄⠀⠀⠀⢀⠤⠘⠦⣸⠀⠀⠀ ⡼⠀⠀⠇⢸⠀⠀⠀⠀⠀⢀⠎⠀⠐⡏⠉⣉⠉⠉⢣⠀⠠⠓⠉⡉⠉⠙⡟⠀⠀ ⢇⣠⡆⠀⢸⠀⠀⠀⠀⠀⡌⠀⠀⠀⢃⡀⠀⠀⢀⠎⠀⠀⠱⡀⠀⠀⠠⡇⠀⠀ ⢸⠁⢣⠀⠸⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠘⠖⠈⠁⠈⠆⠀ ⢠⠀⡀⠁⢀⠧⣤⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⡆ ⠈⡆⢇⠀⢎⠀⠌⢄⡀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢹ ⠀⡇⠈⠢⠈⠢⢤⠀⠈⠐⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸ ⠀⠱⡀⠀⢄⠀⠀⢆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡜ ⠀⠀⠈⠳⡈⠒⠤⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠁ ⠀⠀⠀⠀⠈⠂⠤⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠲⡶⠥⣈⣩⠭⠃⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢁⣢⣄⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⡠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢑⡄⠀⠀⠀⠀⢀⠔⠲⢍⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡇⠉⠒⠒⠀⡀⡜⠈⠀⠀⠈⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠊⠐⢄⡀⠘⠅⠂⠤⠤⠁⠡⠜⡄⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣌⠔⠒⠢⡀⠉⢢⠈⢆⠀⠀⠀⠀⠀⠘⡠⢻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡄⠀⠑⠌⠆⠀⠀⠀⠀⠀⠇⢸⠸⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⣠⡾⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢠⡾⠋⠀⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠙⠻⣧⡀⠀⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⢨⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⣿⣀⣀⣀⣀⣀⣰⣶⣆⠀⢀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⣿⣿⣷⣶⣿⣿⣇⣹⣏⠉⠉⠉⠉⠙⠛⢻⣶⡾⠏⠀⠀⢸⣧⣤⣤⣤⣤⣤⣼⣿⣿⡀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⡿⠛⠉⢉⣹⡿⠟⠛⠋⠉⠛⠛⠷⣦⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⢻⣅⠀⠀⠀⠀⠈⠉⠉⠛⣷⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡏⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣶⠶⠶⠿⠿⠷⠶⠾⢿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⡃⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⡶⠶⠦⣴⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⢿⣿⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠙⢿⣿⣷⡀ ⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⢀⣤⣶⡟⠛⠛⠃⠀⠀⢹⣿⣧ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠉⣩⡅⠀⠀⠀⠀⢀⣭⡉⠉⠛⠛⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⠟⠉⠉⠻⡆⠀⠀⠀⠀⢈⣿⣿ ⠀⢹⣿⡇⠀⠀⠀⢀⣴⡾⣻⣇⠀⠀⠀⣼⠟⣿⡀⠀⠀⠀⣾⢿⡇⠀⠀⠀⠀⣴⡌⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏ ⠀⢸⣿⣷⡾⠀⢠⡾⠁⣰⡟⣿⠀⠀⣸⡏⠀⠸⣇⠀⢀⣾⠃⠈⣿⠀⠀⠀⣼⢿⣧⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁ ⠀⢀⣿⣿⠃⢠⣿⡇⢀⣿⠀⢹⣇⢀⡿⠀⠀⠀⣿⣠⡾⠁⠀⠀⢻⡆⢀⣾⠋⠀⣿⠀⠀⠀⢀⣼⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⠀⣀⣀⣤⣶⣿⡿⠋⠀⠀ ⠀⢸⣿⣿⠀⢸⡏⢿⣼⡏⠀⠀⠹⣾⡇⠀⠀⠀⠸⠟⠀⠀⠀⠀⢸⣷⠟⠁⠀⠀⣿⠀⠀⣰⠿⢻⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀ ⠀⠈⣿⣿⡀⠀⢻⣌⣻⡇⢀⣀⣀⣬⣤⣴⡶⠶⠶⠶⠶⠶⢶⣤⣬⣁⠀⠀⠀⠀⣿⣤⠞⠁⠀⢸⡇⠸⡇⠀⠀⡆⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣷⣄⠀⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢦⣄⡉⠁⠀⠀⠀⢸⡇⣸⡇⠀⢸⡇⠀⣀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⢿⣶⣶⣦⣴⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣤⣿⡿⠋⠀⢀⣾⣷⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣶⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠦⠀⠀⠀⣀⠤⣀⡄⠤⡀ ⢠⠂⠁⠀⠀⢀⣡⠒⠒⢢⠂⠐⠴⠉⠙⡒⠛⡏⠀⡏⢆⠀⠈⢀⠔⠁ ⠈⡇⠀⠀⠏⠫⡸⠀⠀⠀⠆⠀⡀⠀⠀⠇⠀⢠⠀⠰⠈⣇⠀⠸⠀⠀ ⠀⢧⠀⠀⠠⠒⡇⠀⣴⡀⣸⣀⡟⢻⡀⠤⠤⢼⣀⡠⠤⣟⠒⠚⠀⠀ ⠀⠘⣆⡀⠼⠀⠉⠉⠁⡩⠐⠂⠐⢒⠊⡇⡆⠉⡇⠑⠞⠀⠨⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣴⡶⢾⠀⠈⠁⠀⡴⡄⠀⢰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠈⠙⠁⢈⠦⠤⠤⠊⠀⢧⡠⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⣤⣤⣴⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⣄⣀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣶⣶⣶⡆⢠⣶⣿⣿⣿⣄⠀⢀⣿⣿⣿⣿⣇⠈⠒⠒⠚⠋⢠⣤⣤⣶⣶⡆⠀⢰⣶⣿⣿⣿⣷⡀⢀⣴⣿⣿⣿⣿⠆ ⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⢰⣾⣿⣿⣷⡎⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠋⠀ ⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣹⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡏⠹⣿⠏⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⣶⡆⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡟⠋⢹⣿⣿⣿⣷⢻⣿⣿⡇⠀⠉⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠸⠿⢿⣿⡇⠀⠀⠿⠟⠋⠀⠉⠉⠙⠃⠀⠀⠀⠘⠛⠛⠋⠁⠉⠉⠉⠉⠉⢾⣿⡿⠿⠿⠿⠿⠟⠃⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⠘⣿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⢠⣶⣶⣾⠀⠀⠀⢰⣶⣶⣶⡎⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣷⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠙⣸⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⣶⣶⣶⣶⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣀⣉⣹⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠿⢿⣿⡿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠷⣶⣾⣿⣿⣿⠿⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡥⠢⢄⡀⠉⠉⠁⢀⣀⠤⡀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣀⡀⣀⠉⡇⢠⠋⠉⠀⠀⠘⡄⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢛⡻⠿⠚⠢⣤⠭⠛⠁⠘⣖⠒⢚⠛⣤⢃⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⠋⠀⠀⠀⠀⠁⠢⠤⠄⠤⠋⠉⠉⠉⠉⠙⠻⣿⣿⡿⠷⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣀⠤⣴⠖⠲⡦⠤⢄⡀⠀⠀⠀⠀⠀⠈⣏⠴⢖⠂⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠸⣧⠀⡔⡹⡄⢰⠹⡀⡰⢹⠀⡰⡏⠑⢄⠀⠀⠀⠀⢸⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⢸⢣⡇⠱⠇⣀⣛⣁⠘⠖⠁⡇⡠⢺⢣⠀⠀⠀⣸⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⠋⠉⠻⣿⣿⣿⣿⡄⠀⠀⠹⢦⣙⣋⣉⠉⠁⠀⠀⠉⠑⠢⢭⣀⣸⡜⢠⣧⣴⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⢈⣩⣿⣦⠀⠀⠀⠀⠀⠀⣲⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⡿⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠉⠩⡉⠛⠛⠛⠶⠶⢦⣤⣀⠀ ⠀⠀⠙⠛⠛⠁⠀⠀⢸⣿⣿⣿⣿⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡏⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣟⠀⠠⡠⠀⠀⣰⠠⢀⣀⠀⠀⠀⠀⠙⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣄⠀⠣⣀⣔⠁⠀⠀⣿⠛⠷⠶⠶⠾⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣼⡅⠈⠉⠂⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⣶⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠉⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⢫⠖⢁⠔⠂⢀⡻⠋⠛⠻⠟⠻⠻⣷⣦⣤⣀⣀⣀⣀⣤⡶⠛⠉⠉⠙⠉⠉⢁⡈⠉⢝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⣇⣠⡣⠔⢚⡡⠀⢀⠀⠀⠀⠀⠀⠈⠻⢿⡏⠉⠀⠀⠉⠉⠉⠉⠙⠓⢦⡀⠀⠈⢢⠀⠳⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡠⠒⢉⠔⠊⠁⠀⣠⠶⠒⠶⣄⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣇⣀⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠶⢾⣤⡤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠒⣒⣿⡛⠛⠛⠓⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⢠⣶⣿⡿⠋⠁⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠈⠓⠲⠤⠤⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢠⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠤⠤⠤⠤⢤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⡟⢻⠋⠉⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡔⠁⠀⠀⢀⣠⠴⠖⠛⠉⠁⠀⠀⠤⠶⠶⠶⣇⠀⠀⠀⠀⠀⠃⢰⡄⠀⠀⠀⠀⠀⠚⣿⣦⡀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⠋⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣸⠃⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣰⠃⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣤⣤⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣟⠁⣿⣿⣿⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣴⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⢀⣴⣶⣿⣷⡀⣼⠉⢻⢼⣻⣿⣿⣿⣷ ⣇⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢸⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⣼⣿⣿⣿⠛⠛⠉⠀⣠⠖⠒⠂⠀⠀⠀⢿⣿⣿⣿⡟⠀⠹⣄⣸⣸⡿⢻⣿⣿⣿ ⢸⡄⠀⠀⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢸⠀⠀⢸⣿⡿⠀⠀⠀⣀⣸⣿⣿⣿⠇⣀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣠⠀⠀⣭⣿⡀⠈⣿⣿⣿ ⠀⢿⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⢧⣄⣼⣿⣄⣀⣼⣿⣿⣿⣿⣿⠋⢾⣿⡿⠀⠀⠘⣢⠄⠀⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⣹⡧⡟⣦⣿⣿⡏ ⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⡆⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⢰⣿⡇⠀⠀⢰⡇⠀⠀⢠⡤⣄⢀⡏⠉⠉⣧⠙⠤⢴⣋⣇⣿⣿⣿⡿⠁ ⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢳⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⡀⠀⠙⡿⠁⠀⠀⠀⠳⢤⠤⠏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠏⠀⠀ ⠀⣀⣴⣿⣿⣿⣿⣄⠀⣀⠀⠀⠀⠈⠻⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣴⣿⡟⠀⠘⠃⠀⠀⠀⢀⣀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⠀⣀⣴⣿⣿⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣠⣄⠉⠀⠀⣾⠀⠀⢀⣤⠀⢀⣾⣿⣷⣾⣿⡟⠀⠀⢀⣤⣤⣤⣶⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⣉⡉⠓⠈⣿⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣄⣀⣼⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢉⣩⣁⡀⠀⣽⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠦⣂⣀⣀⠀⠀⢸⣿⣄⣠⣾⡟⠛⠛⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⠿⣿⣿⣷⣾⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣍⣹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠙⠿⣿⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠒⠒⠞⠛⠒⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡴⡺⠟⠓⠲⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⠶⠋⢸⠥⠤⣤⣀⠈⡆⠀⠀⢀⠀⠀⠀⠀⠀⣀⠬⢍⡛⢢⣄⠀⠀⠀⠀ ⠀⠘⡏⠀⠀⠘⢆⠀⠀⢀⡽⠁⠀⠰⡁⠀⠀⠀⢀⡎⠀⠀⠀⠈⢆⠙⣆⠀⠀⠀ ⠀⠀⢷⠀⠀⠀⠀⠉⠉⠉⠀⠀⢺⠤⠤⠤⡆⠀⠸⡍⠉⠙⠓⢤⡜⠀⠉⢷⠀⠀ ⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠟⠢⠬⠋⠀⠀⠀⠈⠢⠤⠤⠚⠁⠀⠀⠚⣧⠀ ⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦ ⠀⠀⢀⡀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣭⠟ ⢠⣴⠟⢱⡤⠤⢝⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀ ⣿⣒⣀⣟⠀⠀⠀⠀⢨⢹⣶⣦⣤⣀⣀⠀⠀⠀⠀⢀⣀⣠⡴⠾⢭⡤⠞⣹⠀⠀ ⠀⠀⠈⠉⠛⠲⠤⢤⣯⡞⣿⡃⠀⠈⣹⣿⡟⠉⠉⠉⠀⠀⠀⠀⢸⠑⠄⠽⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣶⣏⣿⠁⠀⣀⣠⡤⠤⠤⠴⠾⠷⢮⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠙⠻⠿⠿⢿⡏⠛⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⠦⠤⠴⠖⠛⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⣠⣀⣤⣄⣤⣀⣤⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠼⠟⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠒⠶⠿⢟⡻⠍⠉⢉⡶⡦⠴⢲⣀⣀⣁⠒⢄⠀⠐⠿⠀⣀⠀⠀⠀⢀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⣾⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⢀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⡀⠃⠘⣶⠆⠛⠁⠀⠀⠁⠀⠀⠀⠀⢯⠀⠀⠀⠀ ⡤⠤⢬⣷⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠶⠖⠛⠛⠙⠋⠁⠀⠀⠈⠓⠾⠦⠶⢤⡀⠀⡐⡾⠦⠀⠀⠀⠀⠀⠀⠀⠩⢉⠀⠀⠀⢸⠀⠀⠀⠀ ⣤⣀⠀⠀⠉⡟⠙⢆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠙⠢⡀⠀⠀⠀⣠⠴⠒⠒⠤⣄⠈⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀ ⣀⣉⣛⠲⣄⢳⣄⠀⠓⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠀⢳⠀⠀⡞⠁⠀⢀⠀⠀⠈⢳⡀⠀⠀⠀⠀⣀⣀⡠⠏⠉⠁⠑⠈⠉⠐⠚⢃⠀⠀⠀⠀ ⣍⡉⠉⠙⢻⡟⠀⣠⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⣠⠞⠁⢸⠀⠀⠀⠛⠃⠀⠀⠀⡇⠀⠀⢀⡤⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠈⠉⠛⠲⣄⠀⠀⢻⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣲⠶⠋⠁⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠓⡄⢀⣤⡀⠀⠀⠀⠀⠀⢀⣤⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⢦⡀⠀⠑⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠈⣲⡀⠑⢦⠤⠤⠴⠊⠁⠀⠀⠀⠀⠓⠃⠄⣸⠀⠀⢀⣄⡔⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢠⠞⠉⠁⠳⡀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⢚⡡⠾⠿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡀⠀⠀⠳⣶⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠙⢦⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⣼⠁⠑⢄⠀⠀⠀⣿⠀⠀⠀⠀⢠⡇⠀⢀⠀⠀⣀⣀⣈⣩⣿⣿⣿⡇⠀⠀⢰⠀⠀⣇⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠹⣄⣴⠃⠀⠀⠀⠑⢦⡀⠘⠷⣤⣤⡴⠞⠙⠓⠚⠛⡶⣏⣉⢉⣿⡟⣹⠋⠀⠀⠀⡜⠇⠀⢹⡄⠀⢹⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⣹⡦⠤⠤⢤⣀⡀⡖⣦⠀⣸⣿⣿⣿⣿⣿⠴⠁⠀⠀⠀⢰⠁⠀⠀⠀⣷⠀⢸⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠸⠛⠳⡿⠿⠷⣿⠟⠛⠉⠁⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⡟⠀⠈⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠈⠦⣄⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⠶⠶⠖⠚⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠁⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠙⠉⠉⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡩⠝⠲⢖⠀⣀⣐⠒⠤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⣀⠀⢠⠋⠀⠀⠙⡄⠀⠉⠉⠙⢆⠀ ⠀⠀⠀⢀⠔⠂⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠒⠂⠹⡀⠐⠂⢀⠇⠀⠀⠀⠀⠈⡆ ⠀⠀⣰⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁⠀⡀⠀⠀⠀⠀⢁ ⢠⠞⣡⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸ ⡾⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠔⠁ ⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠒⠂⠠⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⢈⡋⠛⠛⠻⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠉⠙⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⢶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣤⣤⣤⣤⠤⠴⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⣼⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣀⣀⣀⣀⡉⠳⡄⠀⡰⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡇⢠⡀⢀⡴⠋⣁⣀⣀⣉⣻⣦⡀⠀⠀⠀⠀⣸⠛⠉⠉⠉⠉⠉⠉⠉⠉⢻⡿⠵⠊⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠲⢽⡿⠚⠉⠉⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠸⡇⠀⠀⠀⠀⣿⠆⠀⠀⢸⠇⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⡏⠀⠀⢀⡼⠁⠙⠲⢤⣤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀ ⢸⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⢸⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⡟⠀⢰⠇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⢿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁ ⢸⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⠞⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀ ⠀⢧⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⠃⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀ ⠀⠘⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠘⣆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡀⠀⢀⣠⠴⠒⠲⢤⣤⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣉⠉⠉⠀⠀⣀⣀⡤⠴⢪⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣉⠉⠉⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣌⡙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠬⣭⣛⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠂⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⣧⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⢰⠓⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡞⠀⠀⢸⡄⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡇⢀⡠⠤⣷⣀⣔⣁⣀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣧⠊⠀⠀⡼⠋⠁⠀⠈⢳⡄⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⣧⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⠾⣤⡴⠚⣻⣿⣛⣲⣾⣟⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⣾⠛⣭⠉⣧⡘⠏⣇⣳⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⠀⠈⡆⠘⢤⡽⠾⠃⠈⠉⠉⠉⠀⠀⠀⠉⠉⠙⠢⣄⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀ ⠀⠀⠀⠀⠈⡟⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡈⠓⠤⣀⠀⠀⠀⠀⠻⠿⠟⢋⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠋⠙⠢⣄⡀⠈⠉⠚⠛⠒⠒⠊⣁⠤⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠈⣹⢇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⢰⠂⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⠯⠔⠻⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢶⣋⣀⡤⢷⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠐⠧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣆⠀⠀⠀⢀⠀⣌⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠲⡀⠱⣼⠀⠀⠀⠀⣧⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣀⣀⣀⡵⠴⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

🚩☭✊

☭⭐🟥

📕✊🔴

👴🚩☭

🤡☄️⭐

✍️🧔‍♂️🏭

🧔‍♂️☭🏛️

🛠️⚔️💰➡️📈

”🧔‍♂️📕”

👴📕✊

📕✊➡️🌍🛠️

👨‍🦲🧔☭️

💬🧔‍♂️☭

☭️📕🧱⛓️

👨‍🦲⭐☭

🇩🇪🧔‍♂️🏭➡️✊

☭🚩✊

🇷🇺🚂💥🚩

📜✊🌍⛓️‍💥

💰🏭⬆️🏛️⚖️🧠

👨‍🏫📖☭

📖🧐💰📉

👨‍🦲☭🇷🇺

💰🎩🆚🔨✊

☭🚩👤

🧔‍♂️📕☭

🧔‍♂️🏠🇩🇪

👴🚩⭐

🧔‍♂️📖☭️

🧔🏻🖋️📖

☭📖💰

📖☭

📖🧔‍♂️☭

☭📕

📖⛓️💰

☭⭐🏙️

🧔🏻‍♂️🤝🧔🏼‍♂️📖

🚩📖✊

☭️

✨📰🇷🇺

🏙️🕺🛠️📖

✊⛓️🏭

📰🔥

⭐️🧔‍♂️🎸📉

📖✊🏭

☭🇷🇺

🎶💰🤔📕

👷🛠️>💵=📈

🇷🇺☭🚩

🕺✨📖✊

☭🟥⭐️

🎩🎤🧔‍♂️☭

🧔‍♂️☭

☭🧔‍♂️📖

🧔📖

🧔‍♂️📕⭐🚩

🧐⛓️‍💥🧑‍🏭

📄✊🌍

📕✊☭️

📖💰🚫

📕☭

🧔‍♂️📖🇩🇪

☭️🚩✊

🧔📖☭️