Cursed Kaomojis

(;´༎ຶД༎ຶ`)

⠄⠀⠄⠀⠀⠀⠄⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⡉⢋⣿⠀⡇⢙⠀⠀⠀⠀⠀⢀⣀⠀⣄⣶⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀ ⠄⠀⠄⠁⠄⠁⡏⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡾⣿⣛⡿⣶⣤⣧⠘⠉⣌⠳⠉⠋⠛⠙⠉⠛⠛⠉⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⠙⠄⠁⠄⡁⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⠟⠶⡤⣤⣉⢟⡴⣠⢀⠀⠀⠀⡟⣸⠀⠀⡠⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢯⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠿⠉⠆⣿⣿⣿⢠⠀⠀⠁⠉⠉⠛⠟⠿⡿⣿⣿⣿⢿⠿⠿⣿⣴⣠⢀⠀⠀⠀⠀⠀⡏⣴⠀⠀⠀⠀⠀⣳⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠈⣆⣻⠏⣿⣿⣸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠁⠞⣤⢀⠀⠀⠉⠀⠀⠀⡄⠹⠀⡀⣄⣶⣿⣿⣿⡿⣴⠀⠏⣿⣿⣿⣿⢿⠻⠙⠈⠀⠀⠀⠀ ⣦⣿⠻⣌⣷⣿⡾⠀⣿⣿⣿⣿⣿⣽⣀⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠟⣶⠳⣼⠀⠀⠀⠀⠀⣯⢠⠀⠀⠀⣷⠀⠀⠀⠀⡀⣤⣷⣿⠀⠀⣿⣽⣄⣶⣶⣶⣷⣶⣿⢿⠛⠙⠈ ⠀⡀⣦⢱⡾⣿⢣⠈⣶⣷⣹⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡄⠻⡼⠉⠎⠀⠀⠀⠀⡟⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣄⢦⠓⡏⣻⣿⡿⣿⣿⣿⣿⡾⣠⠀⡁⣿ ⠀⠀⠀⡀⣿⣤⠀⣿⠈⡇⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⢈⢀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣟⣿⣶⣶⣿⣿⣿⣠⠀⠀⠁⣿⣥ ⢳⠀⠀⠀⣇⠀⠀⡇⣿⡿⣿⣿⣿⣾⣠⠀⠀⠆⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠁⡿⢻⠀⠀⠀⡇⣿⠹⠀⠀⠀⠀⠀⡄⣣⢛⠙⠀⣀⣆⠻⡙⣀⢦⠓⠈⠀⡇⣿⣠ ⡀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡿⢿⠈⠀⠀⠉⠟⣿⣿⣿⠻⠈⠋⡿⣿⣿⠹⠀⠀⠀⠀⠀⡄⠾⣄⠀⠀⠀⣄⣿⣿⠻⠀⣀⣤⡿⣿⠀ ⠀⠄⠀⠀⡆⠀⠀⠀⣿⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⣿⡻⢷⠈⠀⡀⣷⠈ ⠀⠀⠇⠀⡀⠀⠀⠀⣧⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⣾⣠⣄⣶⠀⠀⠀⠀⠀⡄⣤⢤⠿⠙⠈⣇⣿⣻⢿⠀⠀⡀⣿ ⠀⠁⠐⠁⠀⠀⠀⠀⡇⠀⢿⠰⠀⠀⠀⠉⠋⠛⠖⠰⠀⠀⠀⠀⠀⡿⣿⣶⣶⣷⢉⣌⣦⣶⣶⣤⣤⣠⣁⠋⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠁⡞⢠⡌⣶⠿⣟⣿⣿⢹⠀⠀⡇ ⢿⡸⠀⡀⠸⠀⠀⠀⡇⠡⣸⠁⠋⠵⣿⣴⣀⠀⠀⠀⠀⠀⠀⠁⡾⣠⠀⠀⠀⠀⠀⣀⣤⢤⠲⠴⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡽⢈⠃⡼⠃⡽⠀⠆⣧⣿⣷⣿⣿⠀⠀⡄ ⣿⢸⠀⠀⢀⠀⠀⠀⡇⡿⢾⣠⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣫⡴⠟⣰⠋⣿⣵⡼⠀⡄⣿⡹⢰⣿⠀⠀⠀ ⡜⢻⠀⠀⠀⠀⠀⠀⡏⣰⠀⠏⣠⠀⠀⠟⠷⠐⠀⠀⠁⠞⣠⠤⠁⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡴⢞⣡⡾⢥⡿⣤⢣⡾⢤⠩⠀⡇⣿⠸⣧⠘⠀⠀ ⣆⣇⠸⠀⡃⠀⠀⠀⡇⠀⡇⣰⠀⠀⠀⢰⡿⠡⠊⠛⣱⠘⠀⠞⣠⠀⠐⠁⠚⠀⠈⡋⠑⠜⢀⠀⠀⠀⠀⠂⠈⠀⠀⡤⢏⣠⡔⢞⣠⠃⡽⣉⠟⣿⢩⡯⢛⠀⡀⡆⢻⡀⢸⠀⠀ ⠀⣧⢿⠀⡇⠀⠀⠀⡄⠀⣼⢿⠈⠀⠋⡱⢞⣣⡼⢋⡰⠋⡴⢉⠀⠃⠞⣠⠋⡿⡵⢞⣠⠀⠀⠀⠀⠀⠀⠀⣆⠙⠋⡴⢀⠄⡤⢤⠤⣤⣤⣠⣀⠀⡀⣥⣿⢻⠘⠀⣿⠘⢰⠀⠀ ⠀⠀⡇⢻⡏⠀⠀⠀⠀⡇⢠⡇⢿⠏⣾⣡⠞⣯⣴⢋⡴⢂⡠⢃⠟⣠⢟⡶⣷⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢘⠀⠀⠀⠋⠶⠴⠷⠙⠀⠀⠀⠀⡅⣿⣿⣿⡿⣿⢰⠀⠀⠀ ⠀⠀⠀⣇⣿⢸⠀⠀⠀⡟⠀⡇⣟⣴⢸⡳⡘⢋⡵⢋⠟⠛⠟⠻⠖⣷⡿⣶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣟⠿⠿⠻⡛⢿⠉⠉⠟⣿⣿⣷⣿⣿⣿⠈⠀⠀⠉ ⠀⠀⠀⠀⣷⣿⠀⠀⠀⣻⠀⡀⣿⠀⢸⠀⣁⠞⣠⢄⠤⠤⠤⣤⣀⣀⠁⠘⠈⠀⠀⠟⠸⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⡄⢷⣿⣯⣶⣶⣶⣷⣿⣿⣾⣴⢀⠀⢿⣧⣶⠶⠶⡴⣄ ⠀⠀⠀⠀⡆⣿⠘⠀⠀⣤⠀⠀⢸⠀⢸⠁⡿⢠⠀⠀⠀⠀⠀⠀⠃⡴⣀⣀⣄⢷⡿⣾⢩⠀⠀⠀⠀⠀⠀⠀⡇⢻⠈⠀⠀⠀⣧⣴⣤⣤⣤⣤⣈⠀⠀⠀⠀⡀⣿⡆⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢹⠀⠀⠀⠀⡇⢀⠀⣿⡟⣿⠹⠀⠀⠀⠀⠀⠀⣼⠁⠟⡿⣿⣿⣴⢏⣹⠉⠀⠀⠀⠀⠋⠙⡀⣆⢿⠀⠀⠀⡀⢿⠉⠉⠉⠋⣷⠻⠉⠀⠁⠛⡿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠘⠀⠀⠀⡄⠀⠀⣿⠀⣴⣶⣿⠿⠻⠛⠛⠛⣿⣿⣿⣶⣤⢋⡿⣴⣠⣆⣤⣤⠤⣤⢡⡌⢷⠛⣯⠘⠀⠀⠀⡇⡘⣀⣀⠀⡀⣸⣷⢷⣴⣠⡇⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠃⠈⠀⡇⢸⠀⠀⠀⣀⣀⣄⣭⣬⣈⣁⠛⠿⡿⣲⢶⠠⠛⠉⠉⠉⠋⠞⣴⢿⡀⣿⢮⣿⠂⠗⠿⡿⢸⠀⠀⠀⠀⢧⡀⣽⢷⠻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠈⠀⠀⡇⢻⠇⠈⣷⠈⠀⠀⠀⠀⠁⡼⣻⣽⣀⣰⣀⠀⠀⠀⠁⡏⣿⣿⣀⣀⠀⠀⡆⣿⣿⢀⣦⠹⠀⠀⡀⢻⠀⠀⠀⠀⡇⠸⡇⡸⣿⣼⠀⠀⠀⠀⠀⠀ ⠴⢠⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⣿⡜⢿⡝⢹⠇⠷⠀⠀⡿⢀⣷⡘⣿⠳⠛⠛⠟⡿⣿⣾⣷⣄⠀⠀⠀⠀⠀⣿⣼⢸⠀⣇⠸⠀⠀⣿⠀⠀⠀⠀⡇⢸⠀⢷⣟⢰⠀⠀⠀⠀⠀⠀ ⠀⡀⠸⠀⠀⠀⠀⠀⣇⠸⠀⠀⡆⣾⣿⡀⣄⣠⡄⣿⠶⣼⠀⡄⣿⣿⠀⠀⠀⠀⠀⡄⢻⡇⢹⠀⠀⠀⠀⠀⣇⢸⢻⠀⠀⣧⠹⠀⣼⠀⠀⠀⠀⡇⢠⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠙⠀⠀⠀⠀⠀⣧⠈⠀⠀⢧⣎⢹⠀⠀⠀⣧⠸⢸⠀⠀⢿⣷⢹⠀⠀⠀⠀⠀⣧⡟⣿⠀⠀⠀⠀⠀⡄⢹⡇⠀⠀⡄⣿⢿⢠⠀⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢷⠈⠀⡀⢿⣆⠹⠀⠀⠀⣇⢻⠀⠀⣼⢻⣧⠸⠀⠀⠀⠀⡀⣿⡆⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⢳⠈⠀⡀⢳⠀⠀⠀⠀⠀⣦⠐⠀⣇⡄⢹⣄⠀⠀⠀⠀⠀⣆⠘⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣇⣿⠀⠀⠀⠀⠃⢰⠀⠉⡟⠉⠉⠋⠂⠒⠒⠄⠤ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⢷⠘⠀⡄⢻⠉⠀⠀⠀⠀⠀⠀⡄⢱⣆⠹⠈⠀⠀⠀⠀⠀⣀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢹⠉⠛⠛⠶⠶⠤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⣿⠀⣳⠈⠀⠀⠀⠀⠀⡀⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠶⡭⣾⣴⣤⣀⣇⠸⠠⣇⠿⠿⠿⠿⠿⠻⠛⠉⢎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠻⠈⠂⡿⣿⢰⠀⠀⠀⠉⠉⠛⠛⠿⡿⣿⣛⠛⠞⡴⣀⠀⠀⠀⠁⡾⠀⠀⠀⡆⣾⣷⣿⣿⣿⣿⣿⣿⣾⣶⠻⠙⠀⠀⠀⠀⠀⠀⠀ ⠉⡈⣷⠏⣿⣼⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠁⠔⣠⠀⠁⠈⠀⠀⢇⠀⣀⣦⣷⣿⣿⣾⠀⠏⣿⣿⣿⠿⠙⠈⠀⠀⠀ ⣄⣷⡸⣧⣿⢠⣿⣿⣿⣿⣻⡟⣿⣿⣾⣴⢀⠀⠀⠀⠀⣽⣧⣰⠁⠀⠀⡀⣸⠀⠀⡄⠀⠀⠀⠀⣀⣦⢹⠀⣷⢹⣭⣽⣭⣽⣿⢾⠶⠛ ⠀⠀⢄⣻⣰⠧⣀⣧⡿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⡄⣿⠴⢠⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣠⠀⠃⣾ ⠹⠀⠀⣧⠀⡄⢿⡿⣿⣿⣾⣠⠀⠂⠓⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⡿⠈⠀⠀⡿⠹⠀⠀⠀⠀⠆⣩⣉⣀⣤⣻⣉⣤⢳⠈⠀⣿⢼ ⡀⠀⠀⡆⠀⠀⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠸⠀⠉⠛⡿⣿⢻⠙⠏⣿⣿⠹⠀⠀⠀⠀⢦⡀⠀⠀⡀⣷⢿⠘⣀⢦⣿⠀ ⠀⠀⠀⠀⠀⠀⣧⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⢻⠈⠀⠀⡀⠀⠉⠉⠀⡄⣿⣿⠹⠀⡄⠹ ⠀⠀⠀⠀⠀⠀⡇⡆⢸⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⡏⣿⣿⣿⣬⣶⣷⣾⣶⣶⣤⣩⠞⣠⠀⠀⠀⠀⠀⠁⠐⠀⡞⣄⠻⣟⣿⣿⠘⠀⣇ ⢻⠰⠀⠘⠀⠀⡇⠏⢰⠋⠗⡾⣠⢀⠀⠀⠀⠀⠏⣰⢀⠀⠀⣀⣄⠤⠒⠔⠤⣠⣀⠀⠀⠀⠀⠀⠀⠋⡡⠃⡴⠏⢠⠆⣷⣿⣿⢸⠀⡀ ⣷⠘⠀⠀⠀⠀⡇⣾⣠⠏⣠⠀⠈⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⢏⣩⠟⣼⡝⠀⡆⢿⣌⢻⠀⠀ ⡵⢹⠀⠀⠀⠀⡇⠀⠟⢠⠀⡇⣇⢘⠀⠋⡰⠀⠋⠠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⡳⣹⡼⢃⣶⢋⡾⢃⠼⠀⣦⢹⣇⠀⠀ ⡀⣿⠈⡇⠀⠀⡄⠃⢷⠘⠀⠋⣫⡿⣽⢎⢋⡴⢀⠁⠞⡡⠛⠟⣾⠠⠀⠀⠀⠀⠀⠱⠁⠞⢀⠆⣲⠖⣶⡴⣤⢀⡦⣿⠙⠀⣿⡌⠀⠀ ⠀⡀⢷⡏⠀⠀⠀⡏⡄⢿⡟⣴⢞⣯⣣⡴⢆⡠⠒⣱⠟⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠃⠶⠤⠳⠈⠀⠀⠁⣿⣿⢿⣿⢠⠀⠀ ⠀⠀⡄⣿⠸⠀⠀⢸⠀⣿⣧⡄⠷⠕⢛⡷⠿⠿⠿⣶⣴⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⣿⣿⠿⣿⠛⠿⣿⣴⣧⣷⣿⠈⠁⠛ ⠀⠀⠀⣇⢹⠀⠀⢰⠀⣼⡇⠀⠇⣸⠀⠀⠀⠀⠀⠊⡤⠦⠳⠟⣿⠀⠀⠀⠀⠀⠀⡿⠈⠀⡀⣦⣾⣶⣶⣶⣤⣠⢀⠀⡇⣿⣘⣀⣀⠀ ⠀⠀⠀⠀⣷⠈⠀⠀⠀⢸⡇⠻⣿⠹⠀⠀⠀⠀⠇⢁⠟⠿⡿⣴⢟⢉⠀⠀⠀⠁⠈⣄⢿⠀⠀⠀⠻⠉⠉⠋⢿⠙⠀⠁⡛⢸⢸⠀⠀⠀ ⠀⠀⠀⠀⡄⢹⠀⠀⠀⢀⠀⢹⡤⣦⣶⠿⠿⠛⡿⣾⣶⣥⣛⡿⣤⣀⣠⣠⣠⢉⡜⢷⡟⠹⠀⠀⡇⡘⢀⠀⡆⣼⣿⣼⣀⢸⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠆⠹⠁⣧⠈⠀⠀⠀⡀⠿⠚⠖⡾⣴⣤⣀⡄⠻⠿⠶⡴⣀⢧⡟⣸⣷⡀⣤⣦⢸⠀⠀⠀⢸⣇⣿⣿⢸⠀⠀⠀⠀ ⠒⠰⠀⠀⠀⠀⢹⠀⠀⣷⡿⡙⢹⠃⠙⠀⡏⣀⣽⠻⠙⠉⠋⠟⡿⣿⣬⠀⠀⠀⡆⣿⢸⡀⢳⠀⠀⢸⠀⠀⠀⠇⠀⢿⣾⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⠀⡆⠘⠀⡄⣿⣸⣄⣠⣇⠾⢸⠀⣧⣿⠀⣀⣀⠀⣇⡏⢹⠀⠀⠀⠀⣿⢷⠀⡄⢻⠈⢸⠀⠀⠀⡀⠀⡇⢀⠀⠀⠀⠀⠀ ⠀⠀⢠⠀⠘⠀⠀⢧⠈⠀⣇⣿⠘⠀⠀⢣⢸⠀⡇⣾⢹⠀⠀⠀⡀⣿⣿⠀⠀⠀⠀⣆⡇⠸⠀⣇⣿⢀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⢳⣄⠀⠀⡀⢷⠀⡆⣧⣌⠰⠀⠀⠀⡆⣸⢸⠀⠀⠀⠀⡀⢸⠀⡇⣿⠀⠀⠀⠃⢰⠀⡏⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠈⡀⢳⠈⠀⠀⠀⠀⠀⢰⢦⠈⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⢸⠀⡇⣹⠉⠛⠚⠶⠴⣤⣠⢀⣀⠀⠀⠀⠀

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⠈⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠓⢛⢛⠚⠗⡼⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠒⠋⡛⣛⡛⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⠘⠀⠀⠀⠀⠀⢻⠈⠀⠀⠀⠀⠀⠀⠛⠞⡡⠊⠖⠤⢦⠒⠓⠉⣀⣷⢽⠤⠦⠿⣿⣿⢠⣀⢄⡲⢿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠙⠀⠀⠀⠀⡇⢿⠈⠀⠀⠀⠋⡿⣿⡴⢀⠀⠀⠀⠀⠀⠀⡀⢆⣮⣿⠀⡇⡟⣴⣤⠤⠤⠤⠒⡙⣦⣽⠳⠈⠀⠀⠀⠀⠃⠀⠀⠀ ⣿⣿⣿⠹⠀⠀⠃⡉⣽⣼⠤⠷⡮⣽⣼⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣽⡼⣯⠀⠉⠈⠀⠀⠀⠀⣝⣧⠻⠈⠀⠀⠀⠟⡿⠀⠀⠀ ⣿⣿⣿⣿⢻⠈⠀⢣⡾⢸⠀⡆⢿⡜⡠⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠛⡼⠀⠀⠀⡀⠀⠀⠀⠀⡀⢦⣌⣾⢿⣿⣠⣏⢠⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠘⠀⣄⣷⠳⠉⢧⢸⣆⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣏⡇⡇⠎⢠⠉⠀⠀⠞ ⣿⣿⣾⣴⣱⠀⣄⠑⠀⠀⡀⣦⣿⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡟⡾⢀⡟⣠⠁⡼⠀ ⣤⢀⠀⠀⡀⠳⠀⡀⢣⠈⠀⡀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢁⡞⢠⠃⣰⠀⠀ ⠀⠀⠀⠀⠀⡀⢢⠈⠀⢧⠙⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡾⠀⠁⠛⠼⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⣦⢽⠾⠛⡕⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⢁⠔⣠⢧⣄⠳⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⠉⣀⣤⣶⣾⣖⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣫⠴⢀⠀⠀⡀⢢⠓⣏⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⠒⠉⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠵⣞⣠⢀⠀⠀⠁⠉⠚⠔⡤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢄⠢⠑⠈⠀⠀⣀⠢⡑⣍⡿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⣴⣀⣀⣁⣉⣒⠒⠤⠤⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠤⠤⠢⠛⡴⠉⣇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣊⢁⠚⠴⣠⢀⠀⠀⠀⠋⠽⠦⠿⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠤⠤⠒⠒⣸⠏⢠⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢀⠀⢧⣰⠀⠀⠀⠀⠀⠀⠉⠊⡖⠠⠀⡀⢢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣱⠀⠀⠏⢃⢡⡾⢀⠀⠸⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⢼⠤⠤⠤⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢄⠓⠈⠀⠀⠀⡀⣟⣸⡞⢀⠀⡀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⢶⠖⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠒⠋⣸⢃⢰⠀⠁⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⣿⠻⠙⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⠒⠑⠉⠉⠉⣿⢠⡏⠀⠀⡄⠓⠈⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⣿⠻⣈⣄⠤⠲⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠇⣠⠀⠀⠀⠀⢰⠀⣀⠀⠀⠀⠋⠰⠀⠀⠀⠁⣸⠀⢸⣹⠀⣄⠢⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠲⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⡇⠈⠀⢀⣹⠯⠙⠉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠼⣽⣤⠤⠤⠤⠤⠤⠠⠒⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠦⠗⣸⠈⠀⠀⠓⠓⠚⠙⠚⡋⢻⠀⠋⠱⠋⠻⠀⠉⠉⠉⠀⠀⠆⢠⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠝⠿⢾⢱⠉⠹⣻⡾⠿⣿⣿⣿⣿⠏⣿⣿⣿⡼⣀⠀⠀⠁⣟⠻⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠀⠽⣾⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠋⠘⠀⠀⠀⣀⣆⣿⠻⣇⡏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡟⣠⠉⡏⡇⣇⣿⣿⣷⣿⣿⣿⣞⣿⣿⣿⢸⠀⠁⠉⠂⠿⣿⣿⡾⢷⣹⣄⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⢴⣀⠀⡀⣿⡿⣿⣯⣿⣿⣺⢸⠀⣿⣿⣿⢸⡀⣀⠀⠈⣯⣿⣼⢣⡀⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠀⠀⠀⡞⣿⣿⣼⣿⣿⢿⢀⠃⣾⣿⣾⢿⠸⠒⡟⣿⣿⣿⢹⡀⠱⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⡰⢀⠀⠀⠀⠁⠚⡴⢤⡳⣿⢸⣯⡞⣿⣤⠷⣿⣿⣹⣾⣿⠿⣿⣿⣽⣯⡄⠘⡄⠸⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡤⢀⠀⠀⠀⠀⣄⣷⢿⣿⡿⢿⡀⣷⢿⣍⢿⡦⣾⣿⣽⣿⣸⠀⡄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣷⣿⢿⠟⣼⣷⣖⡖⣭⠛⣾⣴⣠⠀⠀⠉⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣢⣖⣭⣭⢬⡴⣤⣄⢤⠢⠖⠿⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠞⣠⢈⠀⠀⠀⠇⣿⣿⢿⣌⡼⡷⣷⡻⠣⡏⢳⠋⣏⢿⠈⡃⠈⣀⠳⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⣀⠀⠀⣄⠀⠀⠀⡿⣿⣿⣿⣿⡜⡻⣳⣯⢫⣦⡞⢼⣄⣿⣿⠨⢧⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠖⣥⢙⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠻⢯⣎⢞⠝⢿⡏⠘⡇⣿⢿⠘⢽⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⠴⠦⠓⠛⠟⠥⡴⣠⣀⠀⠀⠀⡀⣀⣤⠾⠓⠉⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⢿⣝⡹⣤⡱⣿⣯⠘⣿⣿⣿⡽⠻⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⡼⣋⡾⢠⠂⠐⡀⣱⣉⣉⣍⣭⢭⠯⠒⠒⠓⠉⡉⠉⠈⣀⣤⠢⠙⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠙⣄⣷⣿⡍⣿⣿⣿⣿⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠴⣀⠀⠀⠁⡟⣴⡿⣰⠀⠀⠋⠖⡤⣀⣀⣀⣀⣤⠦⣙⣌⠤⠓⠈⣀⣀⣄⣤⠦⠷⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡙⣾⣤⣦⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠁⠉⠞⡴⣠⠀⠀⠁⠉⠞⣠⣿⡿⣰⠃⡴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠄⢻⣈⠣⠈⠀⠀⠀⠀⣄⠳⣈⣦⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠉⠋⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡤⣀⣉⠉⠚⠶⡤⣠⣀⠀⠀⡟⣿⣰⠀⡆⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣅⡷⢻⠀⠀⠀⠀⠀⠀⣄⠳⡙⣄⠷⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠒⠔⡤⣨⣀⣧⣿⢿⠿⠛⠙⠀⠃⣾⢠⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⡸⡟⣿⠀⠀⠀⠂⠿⠈⠀⡀⣤⢾⡓⣮⣿⣿⣿⣿⣿⣿⣿⣿⣬⣦⣶⣶⣿⣿ ⠄⡀⠀⠀⠀⠀⣆⠹⡀⣿⣿⣿⣿⣿⢿⣼⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠛⠛⠛⠛⠛⡿⢹⢺⣯⣟⠀⠀⠀⠀⣄⢳⠈⠀⠀⡆⡘⣦⡿⣿⣿⣿⣿⣽⣤⣀⣤⠻⠈⠀⡀⣦ ⠀⠀⠀⠀⠀⠀⠀⣧⠹⡇⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠁⠟⣻⣾⣴⣠⣀⣀⣀⣀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢆⠙⠀⠀⠀⢦⡌⣳⣯⣻⣿⣿⠻⠈⠉⣾⣿⠻⠈⡏ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠛⠟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠀⢧⡘⢧⣿⣿⣿⣿⣿⣿⣿⡙⣧⣾⢁ ⠀⠀⠀⠀⠀⠀⠃⣸⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢶⣶⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠀⣄⠱⣇⡿⣿⣬⡿⣻⣌⣦⣷⣼⣿ ⠀⠀⠀⠀⠀⠁⡿⠀⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠞⡤⢁⠮⠒⠓⠙⢦⣦⣿⣿⡼⣷⢷⠙⠘⠒⡗ ⠻⠛⠈⠀⠀⡿⣸⠀⣿⣼⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⣤⣤⢦⡙⣈⢀⠀⠋⣾⢿⠛⣞⣿⣿⡈⢰⣆⢸⠀⠀ ⡀⣦⣿⢿⡟⣿⢸⠀⣿⢠⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⣄⣷⣿⣿⣿⡙⠛⣟⠿⡶ ⠀⠀⡆⣿⣿⣿⣿⡿⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⣿⣿⢠⠀⡄⢿ ⠀⠀⠀⡟⣿⢹⣿⣿⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠊⠀⠉⠀⠀⠀⠋⣿⣿⣿⣿⣿⢻⠀⠀⡇ ⠀⠀⠀⣿⣿⣇⣻⣿⢣⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡼⣠⢀⣷⠉⠟⢻⠉⠛⡿⣿⣿⣿⣼⣤⣿⣿⡹⢻⡄ ⡇⠀⡇⣿⣿⡇⣿⣿⡟⠘⡇⢹⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠈⠀⠀⠈⠀⣄⠦⠳⡟⣹⠈⠏⠿⡙⣉⠛⡿⣿⣿⣾⣥⣟⣿⢸⠀⣯⣿⣿⡿⠸ ⢩⠀⡇⣷⣿⡇⣿⣿⣿⢸⣿⠸⠀⢂⠈⠀⠀⠫⠴⡠⣄⢧⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠈⠀⢸⠀⠀⡀⣁⣯⣶⣷⣿⣾⣶⣶⣶⣤⣧⣿⢿⣠⠇⣿⢾⠠⣇⣿⣿⢿⣿ ⠨⠀⢿⠟⣿⡇⣿⣿⢿⢆⢸⠀⠀⡃⣎⠛⡴⢁⠞⣡⠞⣠⠀⠀⠀⠏⠠⠀⢀⠀⠀⠀⠀⠀⠀⠃⣘⡇⢻⠀⠀⠀⢸⠀⣏⣿⣿⢿⠒⠒⠖⠴⣿⣿⣿⡼⣄⣿⢸⠀⡇⣾⣿⣿⣿ ⢶⠀⣿⣿⣿⡆⣷⣿⣿⡟⢽⠀⠀⠁⣼⢁⠞⣫⡴⢀⠀⠀⠁⠼⠉⣿⢸⠀⠀⠀⠀⠁⠉⠟⡿⣿⢸⡇⣿⠀⢸⠀⢸⠃⣿⣿⣿⣿⠉⠋⠖⡧⣿⣿⣸⢸⠀⣿⢸⠹⡄⣺⣿⣿⣿ ⠛⠀⣿⣿⣿⠦⡿⣿⣿⣿⣿⢋⡀⣟⠈⣭⠞⢠⠀⠀⠁⠞⣠⠒⣧⣿⢁⠸⠀⠁⠟⣿⣿⣿⣿⣿⢹⡇⣿⢹⢱⠀⢸⡿⣿⣿⣿⡟⣹⠀⠿⡇⣿⣿⠀⣇⠘⣿⢿⣿⠀⣿⣇⣿⣿ ⣿⢹⣀⣯⣿⢸⣖⣿⣻⣿⣿⠺⡏⣿⣴⣀⠀⠀⠀⠀⡿⢀⠃⠿⡿⣼⡜⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⣿⣿⣿⣿⣠⡀⣿⠀⣧⡌⣿⢸⠀⡀⢻⣿⣿⣿⠈⣿⡗⣿⣿ ⡇⣿⣿⣿⣿⢿⠀⣧⣾⣷⣿⣻⣀⣿⠀⠀⠀⠀⠀⠇⣿⠀⠃⣿⣾⣾⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣸⠹⣿⣿⣿⣸⠀⠀⣧⢸⡇⢹⣿⢨⠀⠀⡆⡿⣿⣿⢸⣄⡧⣿⣿ ⡇⣿⣿⣿⣿⣿⠛⠀⣷⡿⣿⣇⡞⣿⠘⠀⠀⠀⠀⡇⣿⣿⣿⣴⣏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣏⡿⣿⣿⢀⠀⠀⡄⣿⠀⣿⣿⢸⠀⠀⠀⣷⣿⣿⣿⠈⡄⣿⣿ ⠀⣿⣿⣿⣿⣿⢹⠀⠀⣧⣿⡸⣿⣿⢿⠉⠛⠟⡿⣿⣿⣶⢫⡴⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣧⣿⣿⣥⣿⣿⠘⠀⠀⠀⣇⢻⣧⣿⢿⠀⠀⠀⡆⣿⣿⣿⢻⠀⣿⣿ ⠀⣇⣿⣿⣿⣿⣿⠨⠀⠀⣦⢿⣧⣿⣿⣿⣿⣿⣿⣻⣟⣤⢹⠀⡇⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣼⣠⠈⠃⣠⣿⣿⠹⣧⣿⢻⠀⠀⠀⡛⣿⡿⣿⣿⢿⠈⠀⠗⣇⣿⣿⣿⢹⣇⣿ ⠈⡀⣷⣿⣿⣿⣿⢻⠀⠀⠀⣇⣾⣿⣾⣠⣀⣀⢀⡇⣿⠙⣏⠛⡟⣿⣿⣿⡟⣼⣿⣿⣿⣾⣠⠀⠀⠀⡄⠀⣇⣿⣿⡿⣿⣿⠘⢻⠀⣿⡿⣿⣿⣿⣿⢹⠀⣧⣹⣿⣿⣿⣿⡯⣿ ⢿⠀⡆⣿⣿⣿⣿⣿⠿⠘⠂⡰⠀⣇⣿⠈⠀⠃⠁⣿⣿⣿⡄⢻⡄⣿⣿⣿⢸⢷⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⢹⡇⡟⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣟⣿⣿⣿⣾⣿ ⣧⠹⠀⣆⣿⣿⣿⣿⣾⣷⠈⠀⠀⠀⣷⢻⠉⡗⣸⣿⣿⣿⢸⣷⢈⣿⣿⣿⢿⡎⠘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⢿⣷⣿⣿⣿⣿ ⡀⣷⠸⠀⣧⣿⣿⣿⢿⡿⢻⠘⠈⠁⡈⣿⢻⡀⢻⣇⣿⣿⣿⡈⢻⡇⣿⣿⡇⠸⢀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡜⠈⣆⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡼⣿⣿⣿⣿

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𝒊 𝒎𝒂𝒅𝒆 𝒂 𝒑𝒓𝒐𝒎𝒊𝒔𝒆 🍡 𝒕𝒐 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒎𝒚𝒔𝒆𝒍𝒇 𝜗ৎ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⣟⣟⡻⣝⣫⡝⣯⡝⣯⣛⢿⣻⢿⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⢿⡟⣿⢻⢟⡻⣟⡻⣟⢿⡻⣷⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣻⢶⣝⡾⣼⣳⡽⣶⣻⢶⣛⡶⣽⣎⣧⢻⡜⣭⢟⡿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⢟⡧⣏⣞⡽⣜⣧⢯⢷⣮⢗⣮⢷⣹⢶⣹⢎⡟⡿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⡻⣝⡯⣷⣻⣿⣿⣽⡷⣯⣟⡷⣯⢿⣽⣻⢷⣻⣞⡿⣼⢧⢯⣙⢧⡿⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⣫⢗⣮⢷⣻⢾⣽⣻⣞⣯⣟⣾⣻⣞⣯⣟⡾⣽⢯⣞⡷⣳⢎⡟⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⣏⣷⣻⣽⣻⢷⣻⣞⡿⣿⣿⣷⣯⢿⡽⣟⣾⡽⣯⣷⢯⡿⣽⢾⣯⣟⠾⣜⣳⢮⡭⣿⣿⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣫⣞⣷⣻⣞⣯⣟⡿⣞⣷⣻⡾⣽⣞⣷⣻⡾⣽⣻⣽⣻⢾⡽⣯⣟⣾⡱⣏⡿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⠿⣼⣳⣟⣾⣳⢯⣿⣳⡿⣽⣯⢿⣿⣿⣯⢿⣻⢷⣟⡿⣞⣿⣽⢯⣿⢾⣽⣻⡽⣮⣳⠽⣽⡿⠀⠀⠀⠀⣴⣿⣿⣿⢟⡧⣿⣵⣻⣞⣷⣻⢾⣽⣻⣽⡾⣷⣟⡿⣾⡽⣷⣟⣯⣷⢿⡽⣯⣟⣷⣻⣞⣷⣹⢞⡵⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣹⣟⣳⣟⣾⣳⣟⣯⣷⢿⣽⣷⣻⣯⢿⣽⢯⡿⣯⣿⢾⣟⣿⣳⣯⣿⢾⣟⡾⣷⣻⢷⣯⣿⡿⠀⠀⠀⣠⣾⣿⢿⣻⢼⣻⣞⡷⣯⢷⣻⣞⣯⣿⣳⢿⣳⣿⣳⡿⣽⡷⣿⣻⢾⣽⣾⣻⣽⣷⣻⢾⣳⣟⡾⣽⢾⣹⢧⡿⣿⣄⠀⠀⠀ ⠀⠀⣸⣿⣟⡷⢯⣞⣷⣻⢾⣽⣾⣻⢾⣯⣷⢯⣷⣟⡿⣾⣻⣟⣷⣯⢿⣾⣳⣟⡷⣯⣿⢾⡿⣽⢯⣿⣾⡿⠁⠀⠀⢰⣿⣏⢷⣫⣞⣯⡷⣯⣿⡽⣟⣯⣟⣷⢯⣟⣿⣽⣞⣯⣿⣽⣻⢷⣟⣯⣷⢯⣟⣾⢷⣻⡿⣽⣾⣻⡽⣯⣟⠾⣽⣻⣿⡄⠀⠀ ⠀⢠⣿⡟⣾⣽⢻⡞⣷⢻⣯⣷⣯⡟⣿⣾⣽⢻⣷⣯⣿⣷⢻⣽⣾⣽⡟⣾⣽⣯⣿⣽⣾⢻⣽⡟⣿⣿⣿⠁⠀⠀⢸⣿⣿⡞⣯⣷⢻⣾⣽⣷⣯⡟⣿⣽⣾⣯⣿⢻⡞⣷⣯⡟⣾⣷⢻⣿⡞⣿⣾⢻⣯⡟⣯⣿⣽⡟⣾⣷⢻⣷⣯⡟⣷⡏⣿⣷⠀⠀ ⠀⣿⡿⣽⣳⣯⢿⣽⣻⣯⢿⣽⡾⣟⣷⣯⣟⡿⣾⣽⡾⣽⣟⣯⣷⢿⣽⣟⡷⣯⡿⣽⡾⣟⣯⢿⣳⣿⣿⣦⡀⠀⣿⣿⣿⣽⣟⣾⢿⣽⣳⡿⣞⣿⢷⣻⡷⣯⣟⣯⡿⣯⢿⣽⣷⣻⣟⡾⣟⣷⣯⢿⣾⣻⣟⡷⣿⡽⣟⣾⣟⣾⣽⣻⢷⣻⢽⣿⡆⠀ ⢰⣿⣟⣷⣻⢾⣯⣟⣷⣻⣟⣾⣽⣟⣷⣻⢾⣟⣷⢯⣟⡿⣾⣽⢾⣯⣷⣻⣽⢿⣽⡷⣿⣻⣽⣟⣯⣟⣿⣿⣷⡄⠈⢻⣿⣿⣾⢯⣿⣞⣯⢿⣻⣽⣻⢯⣿⣽⢾⣯⢿⣽⢿⣞⣷⣯⢿⣽⣟⡷⣯⣿⣞⣷⢿⣽⡷⣿⣻⢷⣯⡷⣯⣟⣯⢿⣝⣾⣿⠀ ⢸⣿⢾⣳⣯⢿⡾⣽⣾⣻⢾⣻⡾⣽⣾⣻⣟⣾⢯⡿⣯⢿⣳⣯⣿⣞⡷⣿⣽⣻⣾⡽⣷⣟⡷⣯⣟⣾⢯⣿⣿⣿⣦⠀⠻⣿⣿⣿⡾⣽⣯⢿⣯⢷⣿⣻⢷⣯⡿⣾⣻⣽⢿⣞⡿⣞⣿⣳⣯⢿⣻⡾⣽⡾⣟⡷⣿⣳⣿⣻⣾⡽⣟⣾⣽⣻⣞⣾⣿⡄ ⢸⣿⣟⡷⣯⣟⣿⣽⣞⣿⣻⢷⣟⡿⣞⣷⣯⣟⡿⣽⣟⡿⣽⣳⣟⣾⣟⣷⢯⣷⣯⢿⣳⡿⣽⣻⣽⡾⣟⣷⢯⣿⣿⣷⡖⢿⣿⣿⣿⣷⣻⣟⣾⢿⣞⣯⣿⢾⣽⡷⣿⣽⣻⡾⣟⣯⣷⢿⣽⣻⡷⣟⣯⣿⣻⣽⡷⣟⡷⣟⣾⣽⣟⡷⣯⢷⣻⢞⣿⡇ ⢸⣿⡾⣽⣳⢿⣞⣷⣯⡷⣿⣻⡾⣟⣿⣳⣟⣾⣟⡿⣞⣿⣻⣽⡾⣷⣻⡾⣟⣷⣯⢿⣯⣟⡿⣽⣾⣻⣽⡾⣟⣷⣻⣿⣿⣿⡙⢿⣿⣿⢷⣯⣟⡿⣾⣻⢾⣻⣷⣻⢷⣯⣷⢿⣻⣽⡾⣯⣷⢿⣽⢿⣽⡾⣽⣳⣿⣻⣽⢿⣽⡾⣽⣻⡽⣯⣟⣾⣿⡇ ⢸⣿⡽⣳⢯⡿⣞⣷⢯⣿⣳⡿⣽⣻⢷⣯⢿⡾⣽⣻⢯⣷⣟⡷⣿⡽⣷⣟⣯⡷⣟⣿⢾⣽⣻⣟⣾⣽⣳⡿⣯⣟⣷⣻⣿⠇⠀⢸⣿⣿⡿⣾⣽⣻⢷⣟⡿⣽⣞⣿⣻⡾⣽⣻⣽⣾⣻⢷⣯⡿⣾⢯⣷⢿⣻⣽⡾⣽⣯⢿⡾⣽⣻⢷⣻⢷⡺⣼⣿⠇ ⢸⣿⡽⣏⣿⣽⣻⢾⣟⡷⣿⡽⣿⡽⣟⣾⢿⣽⢿⣽⣻⢷⣯⢿⡷⣟⡿⣞⣯⣿⣻⢾⡿⣽⣳⣯⣟⣾⣽⣻⢷⣯⢿⣿⡏⠀⢀⣿⣿⣿⣟⡷⣯⣟⡿⣾⣻⢯⣟⣾⢷⣟⡿⣽⣳⣯⣟⡿⣾⣽⣟⣯⡿⣯⣟⣾⣽⣷⣻⣯⣟⡿⣽⢯⣟⣳⡝⣾⣿⠀ ⠈⣿⣿⣹⣞⡷⣯⢿⣾⣻⢷⣿⣳⣿⣻⡽⣿⢾⣯⢿⡽⣟⣾⢿⣽⢿⣽⢿⣽⣞⡿⣯⣟⡿⣽⣳⡿⣽⣾⣻⣟⣾⣿⣿⠀⠀⣾⣿⣿⢿⣞⣿⡽⣯⢿⣷⣻⣟⣯⣟⡿⣾⣻⢿⣽⣞⣯⡿⣷⣻⣾⣽⣻⢷⣻⣽⣾⣳⣯⡷⣿⡽⣯⣟⣾⢣⣿⣿⠏⠀ ⠀⠹⣿⡷⢾⡽⣯⢿⣞⣯⣿⢾⣽⣞⣯⣿⡽⣟⣾⣟⡿⣯⣟⡿⣾⢯⣟⡿⣾⣽⣻⣽⡾⣟⣯⡿⣽⡷⣯⣷⣟⣷⣿⠃⠀⣸⣿⣿⣯⢿⣻⣞⣿⡽⣿⢾⣽⣾⣻⢾⣟⣷⢿⣻⣾⣽⣳⣿⡽⣷⣻⣞⣯⡿⣯⣷⢯⣷⢿⡽⣷⣻⢷⣻⢮⡟⣼⡟⠀⠀ ⠀⠀⢹⣿⡯⣽⢯⣟⣾⣻⢾⣯⡷⣿⡽⣞⣿⢯⣷⣻⣽⣟⣾⢿⡽⣟⣯⡿⣷⢯⣟⣷⢿⣻⣽⣻⢷⣟⡿⣾⣽⣿⡏⠀⢠⣿⣿⣟⣾⣟⣯⢿⣞⣿⡽⣯⣷⢯⣟⡿⣾⢯⣟⡿⣞⣷⢿⣞⣿⡽⣷⣻⣽⣻⢷⣯⡿⣯⣟⣿⣳⣯⢿⣭⣷⣹⣿⠃⠀⠀ ⠀⠀⠀⠻⣿⣧⣟⣾⣳⣟⡿⣾⣽⢷⣿⣻⣽⣯⡷⣟⣷⣯⣟⣯⣿⣻⣽⢿⡽⣟⡿⣾⣟⣯⣷⢿⣯⢿⣽⣷⣿⣿⠁⠀⣿⣿⡿⣽⡷⣯⣟⣯⡿⣞⣿⣽⡾⣟⣯⡿⣯⣟⣯⣿⣻⡽⣟⣾⢯⣿⡽⣯⣷⢿⣻⣾⡽⣷⣻⣞⡷⣯⡟⣼⣫⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⡾⣼⣳⢯⣟⣷⢯⣿⢾⣽⣾⣳⢿⣻⢷⣻⣾⣻⢾⣽⢯⣟⣿⣻⣽⣷⣻⣟⣾⢿⣾⣻⣽⣾⣿⠇⠀⣼⣿⣿⣟⣯⣿⣽⢾⣯⣟⡿⣽⣾⣻⣟⡷⣿⢯⣟⣷⢯⣷⢿⣻⣽⢿⣞⣿⣳⣯⣿⣻⢾⣽⣻⢷⣯⡟⣷⣹⣶⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣫⣟⡾⣽⣻⢾⣟⡷⣯⣟⡿⣯⣿⣻⢾⣽⣟⣯⣿⣻⣞⣯⣷⢯⣷⣟⣯⡿⣾⡽⣿⣿⣿⠀⠰⣿⣿⣿⢾⣯⣷⣻⣟⣾⡽⣟⣿⣞⣷⢿⣽⣻⣯⢿⡾⣿⣽⣻⣟⣾⢯⣿⣞⣯⣷⢯⣟⣯⡷⣟⡿⡾⣽⣣⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⣯⢿⣷⣻⣟⡾⣿⣽⢾⣟⣷⢯⣟⣯⣷⢿⣽⡾⣷⣻⣽⡾⣟⣷⢿⣯⣟⣷⢿⣿⣿⣿⡀⠀⢹⣿⣿⣯⡷⣟⣷⢿⣽⣻⣯⣷⣟⣯⣿⡽⣷⣻⣯⢿⡷⣯⣷⢿⣽⣻⣾⣽⣳⣯⢿⣻⢾⡽⣯⣟⡽⣣⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣞⡷⣯⣟⡷⣯⡿⣞⣯⡿⣯⣟⣾⣯⡷⣟⣯⣟⡷⣿⣻⣽⢿⣳⣯⣿⣻⡾⣿⣿⣷⠀⠘⣿⣿⡷⣿⡿⣽⣟⣯⣷⢿⣞⣿⣽⡾⣿⡽⣷⣻⣯⢿⡷⣯⣿⣞⡿⣞⣷⢿⣽⣻⡽⣯⣟⡷⣺⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣳⢯⣟⡷⣟⡿⣽⣻⢷⣻⡷⣯⣟⡿⣽⡾⣿⣽⢯⣟⡿⣯⣷⣟⣷⢿⣻⢿⣿⡇⠀⢹⣿⣿⣿⣻⣯⣿⣽⡾⣟⡿⣾⣳⣿⣽⣻⣽⢷⣻⣯⢿⣽⡾⣽⣻⣟⡾⣟⡾⣽⣻⣳⡽⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⡽⣯⢿⡽⣯⣟⣯⡿⣷⣻⢿⣽⣻⣷⣻⡿⣯⣿⣟⣾⣽⡾⣿⣟⣿⣿⣿⡆⠀⢿⣿⣿⣿⣽⣾⢷⣿⣻⢿⣽⣻⣞⣷⢿⣽⣻⣟⣾⣟⡷⣟⣯⡷⣿⣽⣻⣽⣳⢯⣷⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣽⣯⣟⣷⣻⣽⣻⣽⢯⡿⣯⣷⣟⣷⡿⣟⣾⣽⣾⢷⣿⣻⣽⣟⣿⣿⣿⠀⠘⣿⣿⣿⢾⣻⣯⣷⣿⣻⣽⣷⣻⣽⢿⣞⡿⣞⣷⣻⣟⣯⡷⣟⡷⣯⢷⣫⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⡷⣯⢷⣻⣽⣻⣽⣟⣷⣻⣾⣟⣿⣯⣿⢾⡿⣯⣿⣟⣾⣿⣽⣿⣧⠀⢹⣿⣿⣿⡿⣽⣷⣟⣯⣷⢿⣽⡾⣿⣽⣻⣯⣟⣷⣻⢾⡽⣯⢿⣽⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⣟⡷⣯⣷⢿⣞⣯⣷⣿⣻⣾⣟⣿⣟⣿⣳⣿⣯⣿⣟⣿⣿⣇⠀⢿⣿⣿⣿⢿⣾⣻⣽⡾⣟⣷⢿⣻⣞⣯⡷⣟⣾⡽⣯⢿⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣿⡿⣯⣿⢾⣽⣻⣽⣾⢿⣽⣿⣻⣷⣿⣷⣿⣿⣿⣿⣠⣿⣿⣿⣿⣻⣽⡿⣽⡿⣟⣯⣿⢯⣟⡷⣟⣯⢷⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣯⣿⣿⣿⣽⣾⡿⣯⣿⣿⣽⣾⡿⣷⣿⣿⣿⣹⣿⣿⣿⣿⣻⣯⣿⣟⣿⣟⣿⢾⣟⣯⢿⣯⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣾⣿⣿⣽⣾⣿⣟⣿⣾⣿⣻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣻⣽⣷⡿⣿⡾⣯⣿⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣟⣿⣿⡟⢣⣿⣿⣿⣿⡿⣟⣯⣿⣟⣷⣿⣯⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⢿⣿⣿⣻⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⡿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣼⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠆⠘⡄⠷⠈⠀⠀⠀⢦⠙⠀⠀⠀⡇⠀⠤⠤⢾⠠⠀⠀⠀⡀⣻⢀⢿⠛⠈⡀⣀⢤⠦⠳⠉⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠟⠀⠀⠀ ⠀⡄⠳⠀⣧⠘⠀⠀⠀⡄⠻⠈⠀⡿⠀⠁⡟⢠⠀⠀⠀⠀⠀⡏⠸⠀⠀⣀⣄⣤⠤⠒⠛⠉⡈⣄⢤⠤⣶⠛⠉⠈⠀⡟⢠⠀⠀⠇ ⠀⠀⠀⢦⠙⣇⠘⠀⠀⠀⡀⢻⡿⢰⠁⡾⢠⠀⠀⠀⠀⠀⠏⣲⢷⠈⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⠤⠶⠒⠙⡉⣀⡤⣶⠑⠈⠇⣰ ⠀⠀⠀⠀⡀⢠⢇⠘⠀⠋⡴⢃⣻⠞⣠⠀⠀⠀⠀⠀⠀⠟⢠⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠦⠓⠉⣇⣸⠀ ⠀⠀⠀⠀⠀⠀⡃⣆⠛⢠⠁⡿⣴⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⡀⢶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⣿⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⠷⢻⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢦⠙⠀⡄⠻⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⡄⠻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠇⠸⠀⣇⠸⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠷⠀⡇⢸⠀⠀⢸⠀⠀⡀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⡀⢸⡿⢸⠀⠏⢸⠀⠀⠀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⢸⠀⠀⠇⢿⣿⢀⠇⣴⣿⠀⠁⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⣾⣿⢸⠃⣸⠇⣿⠃⡿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠀⠀⠀⠀⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠁⡿⣿⣼⠏⣿⢰⡿⣿⣼⣏⣿⣿⢀⠀⠀⠀⠀⠃⢸⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⣿⢿⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⢰⠀⡞⢟⣯⠾⢫⣸⠇⣽⣟⡴⣤⣠⣤⣤⣤⠳⠈⠀⡇⢠⠁⡿⢠⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣄⣆⣿⣿⢿⠈⠀⠀⠀ ⠀⠀⠀⡇⠀⡏⣏⣾⣴⠀⣶⠁⡟⣼⢀⠀⠀⠀⠀⠀⠀⠀⣄⠷⡟⠟⣵⢀⠀⠀⠀⠀⡀⣀⣀⠄⠲⠙⠀⠀⠀⣇⣿⣿⣿⠘⠀⠀ ⠀⠀⠀⡇⠁⢸⣠⠀⠀⠁⠟⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣷⣿⣿⢿⠀⠀ ⠀⠀⠀⡇⣽⢀⠀⠋⠟⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⣿⣿⢺⠀⠀ ⠀⠀⠀⡇⣿⠟⡿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⢹⠀⠀ ⠀⠀⠃⡟⣴⢡⠈⠀⣆⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⠸⠀ ⠀⠀⡇⣾⢾⠶⣶⠲⠳⡉⣇⣿⣿⣿⣿⢿⠻⠛⠉⠉⠉⠉⠉⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⣿⣿⣿⣿⣿⣿⣿⢸⠀ ⠀⠀⡟⢤⢻⠈⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠛⠛⠛⠛⠛⠛⠿⡿⣿⣷⣯⣿⣿⣿⣿⢳⣿⣿⢻⠀ ⠀⠀⡇⠈⣧⣫⣬⠶⠓⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⢻⡀⣾⢸⠀⠢⣀⣀⣀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⣆⠹⠆⠀⠀⠀⠁⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣦⣶⣿⣿⣶⣦⣀⣷⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⣆⠘⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠆⡴⣠⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⡇⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⡟⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠈⠀⠀⠁⠉⠉⠋⠿⣿⣿⣿⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⣄⣦⢿⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣀⣀⣀⣧⡙⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣝⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣴⣤⣤⣤⣠⣀⠀⠀⠀⠀⠀⡀⣿⣿⣾⡇⣼⣾⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣘⣷⢸⡇⣸⠇⣿⢛⠿⠿⠘⠁⠀⠁⠟⠀⠀⠀⠀⠀⡇⣿⢰⡟⢀⢾⡸⣀⣀⣀⣀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⡈⢿⣿⢁⢸⣿⣤⣤⣤⢃⡿⠟⣠⡿⠀⠀⠀⠀⠀⡏⣰⠇⣷⠇⢰⢸⠀⠈⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣇⢿⣇⢰⡇⢠⣇⠸⠀⠃⡿⣷⢀⠏⣿⠟⣿⣿⠸⠋⣴⠃⡾⠀⡏⠀⢸⠀⡌⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⣷⣿⠀⡇⠀⡀⣿⠋⣿⣸⠀⠇⣸⣿⣄⣦⣷⣿⣼⠀⡟⢸⠃⢸⠁⢹⠄⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⠀⡇⠀⠀⡇⣽⣾⠀⠃⣸⠃⢹⠉⡟⣯⣰⠁⡾⣏⣽⣸⠀⡏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡈⣿⠀⡇⠀⠁⡿⣿⠀⠁⡼⠀⡏⡿⣡⡞⢀⠃⡴⠁⣿⣴⠀⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⢳⣾⠘⡇⠀⡇⣿⢀⠀⡀⠀⠏⣴⠂⣠⠁⠞⢠⠁⡾⢀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⢻⢧⡏⠘⡇⣼⠀⠀⠁⡞⢀⠀⠁⠞⣠⠀⠋⡴⠀⠀⠏⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣝⠻⣿⢻⡟⢩⠋⠖⣠⠀⠉⠞⣠⠀⠋⡔⣀⠀⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣾⣷⣟⣿⣿⣳⠉⠍⡩⢉⠒⠶⣠⢀⠁⠋⡾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣠⠀⡀⢧⢸⡀⢤⡲⣛⣉⠉⠉⠛⠛⡶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣦⣲⢛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠓⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠄⠿ ⢶⠶⠷⠼⠶⠦⣾⠶⠿⠤⠤⠧⠾⠷⡼⣤⣤⣿⠶⠿⠤⠤⠦⠛⠛⠛⠛⠛⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣤⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞ ⠀⠁⡟⢸⠀⠀⣿⠀⣿⠀⠀⡄⢸⠀⢸⠀⠀⣧⠀⣇⠀⠀⠀⣿⠀⠇⢰⡀⢳⠀⠀⠀⠄⠿⠴⡤⣭⣭⣬⢤⠤⠤⡤⣤⠤⠤⠦⠶⠒⠓⣟⢾⠒⠒⠛⠙⠉⢉⠉⠉⠉⠛⠛⠛⠿ ⠁⣟⣿⢸⠀⠀⣿⠁⡟⠀⠀⡇⢸⠁⢸⠀⠀⡿⠀⡏⠀⠀⠃⣺⠟⣴⠀⠀⡇⠀⠀⠀⠇⢸⠀⠀⠀⠀⡀⣀⠦⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣰⣀⠀⠀⡤⣤⣿⢹⠋⠋⣿⠛⡼⠀⠀⠏⢹⠟⣰⠀⠋⡿⣽⢉⠉⠉⠋⡟⢿⠶⠤⣤⣤⠹⠀⠀⠀⠀⠀⠀⠀⣄⡲⠙⠉⠀⠂⠙⠉⠈⠀⠀⠀⠀⣼⠃⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⠀⠀⠀⠋⠿⣿⣴⣠⠀⡀⣀⣄⢤⠤⡿⣿⣾⣠⡀⣤⣶⣿⡻⣉⣉⣉⠉⣿⢿⠙⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⠷⡛⣧⢸⠀⠁⠈⡅⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠒⡤⣣⣴⢀⠀⠀⠀⠀⠀⠀⠃⠃⣿⣼⢦⠿⠛⣠⠀⠀⡀⣀⣀⣀⣀⣼⣠⣄⠹⠀⠀⠁⠀⠀⣄⠳⠈⠀⠀⠀⠀⠏⣷⣿⡿⣿⡀⢦⣷⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⠀⠀⠖⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠏⣴⣦⡿⢹⡉⣼⠦⠶⠒⠛⠉⠉⡞⠀⠀⠀⡄⠙⠉⠋⢾⠒⠑⠉⣈⠦⠙⠉⠞⣫⣿⣿⣿⢠⠀⠀⠀⣄⣧⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⡟⣻⠈⠀⠀⣀⣄⠦⠲⠓⠙⠉⠉⡟⢰⠀⡀⢄⠦⡷⢀⠀⢸⠀⠀⠀⡀⣧⣠⣄⣶⣻⡿⣾⢠⠀⠀⠀⠀⠀⠀⣧⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⢀⠀⠀⠈⠈⠀⠀⣿⣿⣿⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⣀⣄⠦⠓⠀⠀⠀⠀⠀⡏⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡆⢀⠀⡄⡿⠺⢯⢣⠃⣰⣄⣶⣿⢨⡀⣄⢤⠦⠶⠶⠶⠿⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠟⣤⢸⡇⣾⣤⣠⣀⣄⣿⣾⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣷⣿⡿⠛⠴⢀⠀⣀⣤⣦⠶⠒⠒⠖⡷⣤⢹⠀⠀⠀⠀⠀⠁⢸⡠⠉⠛⡿⣿⡎⠶⠛⡉⢯⠉⠉⠉⠛⠔⡤⣀⣀⣀⣆⠘⢸⡇⠀⠋⠀⠀⣤⡤⢿⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⣼⠀⠀⠀⠁⠛⡿⢟⣿⣿⣿⣿⣿⣿⢿⠻⣛⣝⣩⣀⠒⠈⡙⠦⠙⠀⢧⠋⣷⢻⠞⣧⢫⠐⠀⠀⠀⣇⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⢰⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⡀⡄⠘⡄⢿⡃⢫⣿⢴⠏⣿⢠⠛⠀⠁⡿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⡇⣼⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⢠⠀⡀⣻⣾⢀⠏⢨⣿⣤⣦⠷⡿⠀⣄⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠛⡽⣽⣫⣿⣿⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⢀⠀⣀⢻⣆⠘⠀⡿⢰⠀⠃⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⣁⣋⡴⣠⠃⡿⣿⣻⡛⢉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⢿⠏⣠⠀⠁⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠏⣾⣧⠻⠈⠀⠀⠀⠀⠀⡟⣻⣟⣶⢀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⣇⠀⠀⠀⡀⠰⡄⣼⠀⠁⡿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣿⢼⠀⣷⣿⢿⠻⠛⠖⣤⣀⢀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠙⠈⠀⠀⡀⢻⠈⠀⠀⠀⠃⢰⠋⡿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⣿⣿⣿⢠⠀⠀⠀⠀⠁⠟⣼⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸⠀⡀⣄⠦⠛⠛⡉⣿⠻⠛⠛⡿⣿⣿⣿⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⣿⣿⣼⠀⠀⠁⠟⣿⣿⣟⢟⢠⣌⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢠⠀⠀⠀⠛⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣿⣾⢀⠀⠀⡏⣾⣠⣀⣀⣷⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠉⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⣿⣴⢀⠀⠀⠃⣿⣿⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡴⢀⠋⣿⣰⠂⠀⠀⠋⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⢳⠀⣆⣿⣯⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⣷⠈⠀⠀⠀⡄⡽⢸⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢦⠙⠀⠀⡄⢻⠀⣧⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⡇⣿⡸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡀⢻⠀⠀⠀⠀⡄⣿⠈⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣳⣿⣿ ⠀⡀⢷⠘⠀⡆⠸⡀⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⡇⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡀⢳⠈⠀⠀⠀⡄⢿⠘⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢧⣜⠳⠈⣧⠀⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⡟⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡀⢷⠈⠀⠀⠀⡄⣿⠈⠀⠀⠀⠑⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿ ⠘⠀⠀⣧⡹⢧⡌⣿⣀⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠁⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡀⣦⠙⠀⠀⠀⡀⢷⠘⠀⠀⡀⢦⠈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢳⠀⠀⠀⣧⠹⢧⣿⠈⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⡏⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⣄⠻⠀⠀⠀⠀⣦⠹⠀⠀⠀⡄⠹⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡭⣿⣿ ⡄⠘⠀⠀⡀⣵⠹⣆⢸⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠃⣿⣿⣿⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣽⣠⣀⠀⣦⠻⡈⢧⠘⠀⠀⠀⡀⢧⠈⠀⠀⡀⢷⡈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿ ⠀⢸⠀⠀⠀⡆⡎⠸⣧⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠁⡿⣿⣿⣿⢠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣳⣇⠻⠈⡄⢳⠉⠀⠀⡀⣦⠻⣌⠻⠀⠀⠀⠀⣄⠻⠀⠀⠀⣦⡘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡇⠀⠀⠀⠀⢸⣿⠘⣷⣿⠁⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⡟⣿⣿⣿⣸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡄⢻⣷⣾⠙⠀⣄⠳⠈⠀⠀⡏⣦⡻⢮⠙⠀⠀⠀⡀⢦⠙⠀⠀⣄⠹⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⠈⠀⠀⠀⢸⡿⢷⡄⣿⡏⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠀⡟⣿⣿⣿⣼⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢻⠀⡆⡹⢷⡈⢷⠉⡀⣄⠻⡉⡄⢸⡀⣮⡿⢿⠈⠀⠀⠀⣄⠳⠈⠀⡄⢳⡈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿ ⠀⠀⢸⠀⠀⠀⠇⣿⡄⢹⣇⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⡟⣿⣿⣿⣰⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡄⢻⠀⣆⡹⢷⠀⣄⠳⢈⢓⣿⢿⣟⠀⢻⡀⣦⣝⠹⠀⠀⠀⠀⣦⠙⠀⡀⢧⠘⣄⣿⣌⣷⣿⣿⣿⣿⣷⣿⣿ ⠀⠀⢸⠀⠀⠀⡀⣾⠀⣿⡀⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⡟⣿⣿⣾⢠⠀⡟⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⣀⣤⣶⣿⠛⡌⢻⠀⣆⡿⢳⠁⢀⣆⡻⣇⠈⣄⢷⡟⠘⠈⣄⣿⢿⠘⠀⠀⠀⡄⢳⠈⠀⣆⠹⡀⣷⠘⢆⣜⣧⣿⣽⣿⣿ ⠀⠀⢸⠀⠀⠀⠁⢸⡗⣿⢸⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⡟⣿⣿⣴⢀⠁⡟⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠋⠔⠤⠳⠀⣄⣦⡿⠛⠊⡌⣳⢻⠠⠀⡀⣧⣿⠿⠝⣯⣾⣟⡘⡂⣷⣞⠻⠀⠀⠀⠀⢦⠘⠀⣄⢻⡀⣧⠙⣧⠘⣿⣾⣸⣤ ⠀⠀⢸⠀⠀⠀⡟⢸⡇⣿⢿⣿⣾⢀⠀⠀⠀⠀⠀⠁⡿⣿⣴⢀⠀⠁⡿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠞⢁⠟⡴⣮⠳⠙⠀⠀⣄⣦⢷⡛⣿⢻⠀⠀⡀⣄⡿⣿⣮⢻⡟⣿⠘⡁⣧⡽⢷⠘⠀⠀⠀⣄⠹⠀⡀⢷⠈⣧⠸⢿⣾⣿⣇⠘ ⠀⠃⠀⠀⠀⠇⣟⠀⡿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠃⡿⣴⢀⠀⠀⠃⡿⣿⣼⣠⠀⠀⠀⠀⠀⠀⠀⡄⠟⣴⢀⠀⠀⢀⣄⠻⠈⠀⠀⠀⣀⣤⣶⢿⠈⠀⠀⡀⣷⣿⠚⣦⣿⣷⠛⠌⣆⣻⣯⠙⠀⠀⠀⡄⠹⠀⡀⢷⠈⣧⣞⣾⡯⢸⢷ ⠀⡆⠀⠀⠁⣹⣼⠃⣿⣼⢀⠀⠀⠀⠀⠀⠁⠟⣴⢀⠀⠀⠀⠏⣾⣫⣠⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾⢀⠀⠀⠀⠀⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⡀⣄⢷⠻⠉⠀⣯⣟⡘⡀⢷⡞⣶⠿⣄⢿⣎⠻⠀⠀⠀⡄⠹⠀⡀⢻⠀⣷⣏⣀⢿⡆ ⠀⠀⠀⠀⡞⡏⢡⡟⣠⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⡟⣵⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢷⠻⣯⣿⠘⢁⣯⣽⡹⢧⡝⣿⣌⢻⠀⠀⠀⡄⠹⠀⡄⢹⡄⣻⠸⣷⠸ ⠀⠀⠀⠏⢁⣻⡾⢀⠀⠀⠀⠀⠀⠁⡞⣠⠀⠁⠀⠀⠁⡿⢣⣰⠀⠀⠁⠉⠋⠚⠶⠤⣠⣟⢯⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⢻⢌⠀⣧⡹⢳⣄⣿⢿⡌⢻⠀⠀⠀⡄⠘⠀⣧⠘⣇⢻⡆⢻ ⠀⠀⠂⢡⡟⣠⠀⠀⠀⠀⠀⠀⠋⣴⢀⠀⠏⢠⠀⠃⡾⢇⢪⠕⡻⣽⣾⣠⢀⠀⠀⠁⡿⣷⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⢷⠛⠊⣧⠘⢧⡈⣷⢿⡄⢻⠀⠀⠀⢇⠀⡀⢻⡄⣿⠀⣿ ⠀⠀⠃⡼⢀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠏⣰⠀⠃⣾⢁⡛⡴⣫⡴⣠⠀⠀⠀⠀⠁⡿⣼⡀⠀⠂⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⣀⣮⠻⣯⠘⢧⡌⣿⢻⡱⢷⠈⠀⡆⠈⠀⣇⠈⣿⠀⣿ ⢠⠏⣰⠀⠀⠀⠀⠀⠀⠋⡼⢀⠀⠀⠏⣰⠀⠋⣽⠟⣴⢃⡾⢠⠀⠀⠀⠀⠀⠂⣰⣿⢀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠘⣿⡀⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣅⢷⣿⡘⢷⡄⣿⡸⣳⢷⠈⠀⢀⠀⡆⢸⣧⠀⣇ ⡞⢠⠀⠀⠀⠀⠈⠀⠟⣰⠀⠀⠀⠏⣼⠀⠏⣿⣴⢁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⠀⠀⠀⠀⠀⠃⣵⠠⢁⠀⠀⠀⠋⠮⠇⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⡌⢹⣇⣿⡈⣣⢿⠀⠀⠀⠀⢸⡇⢸⡇ ⢀⠀⠀⠀⠀⠇⢀⡞⢠⠀⠀⠀⠇⣼⠀⠏⣼⢀⠋⣿⢍⠢⠈⠀⠀⠀⠀⠀⠀⡟⣿⢈⠀⠀⠀⠀⠋⣰⠠⠀⠂⢤⠤⡠⢁⠛⣿⣿⣿⣿⣾⣿⠻⠈⠀⠀⠀⠁⠋⠛⠿⠽⠬⣶⣶⣷⣛⣟⢻⢷⣿⡈⣿⢳⠀⣧⠸⠀⠀⠀⢿⡇⢸⡇ ⠀⠀⠀⠀⠃⢡⡾⢀⠀⠀⠀⠃⣾⠀⠟⣠⠁⡟⣢⠈⠀⣅⡵⠳⠀⠀⠀⠀⡟⣿⣿⣴⠒⠒⠒⡦⢀⠀⠁⠁⠛⡽⢋⠟⣿⣿⣿⣿⣿⣿⢸⣆⣿⣿⠹⠀⠴⣠⣀⣀⠀⡀⣀⣄⠦⠳⠙⣀⣤⣷⣿⢹⣇⡞⠘⠀⣷⠈⠀⠀⣇⡄⢸⡇ ⠀⠀⠀⠁⠣⣼⠀⠀⠀⠀⠁⡾⢁⡾⢀⠃⡾⢀⠀⡀⡲⡪⢸⣣⠱⠀⠀⡟⣿⣿⢭⠨⠀⠀⠠⠁⠉⠋⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠳⡈⣧⣿⢿⠈⠀⠀⠀⠀⠀⠀⠄⠤⠤⡒⣗⠻⠈⣦⣿⡜⢸⢣⠀⡀⢻⠀⠀⡆⠀⢸⡇ ⠀⠀⠀⡏⣰⠀⠀⠀⠀⠀⡟⢣⡰⠀⠃⣼⠀⠀⠀⠀⠀⡀⡱⠀⣧⠸⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀⢁⠞⣤⣤⣷⠞⠀⠀⠀⠀⠀⠀⠀⠁⠀⡏⡀⣍⠳⡌⣵⣿⡎⠈⠀⣇⠈⠀⠀⠸⢸⡇ ⠀⠀⠃⣰⠀⠀⠀⠀⠀⠏⢠⢀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠇⣴⣧⡫⠁⡀⣿⣿⣿⣿⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣠⢀⠁⠈⠀⠟⣰⠀⠀⠀⡇⢸⠀⠀⠊⠁⡰⠉⠁⡰⠇⢰⠏⢣⡇⣿⠘⡀⢷⢹⠀⡄⢸⠀⠀⢠⢸⡟ ⠀⠀⡜⠀⠀⠀⠀⠀⠃⣸⠀⠀⠃⣿⢠⠀⠁⠊⠟⠶⣽⣭⡻⠻⢞⣞⠈⣿⣿⣿⢸⠀⠀⣄⣶⣶⣶⣶⣤⣤⣠⣀⢀⠀⠀⠉⠋⡛⢖⠶⡶⢀⠀⠀⠀⠀⡀⠀⠀⠎⢁⡰⠏⢡⡴⠃⣰⠏⢣⢡⡱⣿⣷⢫⡀⣿⠀⠀⢹⠀⠀⡇⢸⣿ ⠀⠇⢀⠀⠀⠀⠀⠀⡾⠀⠀⠁⣿⣹⠖⡡⢋⡖⡵⣾⣩⣚⢶⡤⣣⡮⢫⣷⣿⣿⠀⡅⠻⠞⠶⠴⠤⠶⠶⠶⠶⠶⡶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢃⣰⠎⢁⡰⠏⣠⠞⢯⢣⡵⡱⣿⡏⢸⠀⣇⠸⠀⣿⠀⠀⡇⢸⣿ ⠀⡸⠀⠀⠀⠀⠀⠇⢠⠀⠀⡟⢩⠟⡴⣠⠀⠉⣾⣷⢸⠀⠀⠂⠒⡓⠽⡏⣿⣿⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡞⢋⢠⡞⢋⣠⠞⢡⡾⢞⢯⣻⣿⣻⣷⣾⣿⠀⡇⢹⠀⡇⠀⠀⠀⢻⣸ ⡏⠀⠀⠀⠀⠀⠀⣼⠀⠀⡏⣴⣠⠀⠀⠋⡴⣉⠋⣶⠝⠋⠛⠒⠐⠀⠀⣢⣮⣮⢿⠿⠻⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⢡⠁⡼⠞⢃⡴⠞⢣⡴⢋⣻⡽⣶⣯⣵⣟⣿⣿⢿⣿⠀⠀⣿⠀⡇⠀⠀⠀⣿⢸ ⢰⠀⠀⠀⠀⠀⠇⢠⠋⡴⢋⠀⠀⠋⡾⣥⣛⢿⡿⣻⣖⢿⠶⠷⠺⠓⠀⠀⡀⡤⢞⣀⢦⡛⣌⣦⣷⠯⠑⠈⠀⠀⠀⠀⠀⠊⠠⠊⡠⠎⢡⡜⠎⢣⣡⡱⡴⠎⣣⡴⠞⣣⡵⢟⢿⢻⡾⢾⡶⣿⣻⣉⣧⣿⠀⠀⣿⠀⡇⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⡎⠟⣣⡼⢀⠀⡿⣿⣾⣪⢴⣥⣚⡴⣀⠁⠔⣠⠀⠊⡠⠀⠊⡠⠀⠀⠁⠔⣍⠳⠙⣀⣦⡳⢭⠳⠙⠋⡰⠋⡴⠉⡕⣵⣷⣾⢎⢣⣻⣡⡵⢞⢫⡵⢜⢟⣿⣿⣴⣁⡾⢠⠀⠀⣇⣿⣿⣿⣾⣩⣏⠀⡇⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠀⠀⣟⢯⣼⠀⠀⠏⣾⣠⠀⠋⡴⣉⠉⠛⠟⢒⠒⠛⡰⠀⠋⡰⠎⣠⠁⠞⣡⡴⢋⡱⣷⢻⠈⠀⣀⣦⣷⣿⣷⢿⣯⢗⢯⣩⡏⣽⠟⣼⢞⣫⡽⡿⣶⣟⡯⢶⣥⢟⣶⣭⠈⠀⠞⢟⣿⣿⣿⣿⣼⣀⡇⠀⠀⠀⠀⠃⢸⠀ ⠀⠀⠀⠀⠀⡇⢷⢇⢀⠀⠁⣼⠀⠋⡿⢴⣠⣁⠚⡴⢁⠚⡠⠁⠞⡠⢋⡠⠁⠞⣡⠔⢁⡴⢋⣮⣪⣧⣞⠙⠀⠀⠀⣀⣦⣷⣿⢯⡙⣦⣷⡿⡛⣿⣷⣿⣾⣷⣭⣋⠛⡶⣻⡈⣇⢰⠂⡫⡿⣿⣿⣿⣿⢸⢸⠀⡇⠀⠀⠀⠀⡇⢸⠀ ⠀⠀⠀⠀⠀⣼⠀⡰⠀⠀⡄⢋⡴⣠⠀⠋⠾⣠⠋⠖⣠⠋⠖⣡⠚⡤⠋⡴⢋⡴⢁⠞⢡⡴⣋⣴⠊⣡⣿⡌⠹⠀⠀⠁⠀⠀⣄⢦⡿⢾⠙⣄⣲⣯⣿⣝⣮⣼⣻⠐⡉⢎⡥⢟⣰⠁⠟⣿⣿⣿⣿⣧⣿⢧⢸⠀⡇⠀⠀⠀⠀⡇⢀⠀ ⠀⠀⠀⠀⡇⢸⠀⠀⠀⠃⡼⢀⠀⠁⡟⣿⣻⣷⢫⠖⣡⢋⠴⣫⠖⣡⢚⡴⢁⠟⣫⠵⢋⡽⢞⡡⠟⣫⡱⢿⡀⢳⠀⠀⣀⢤⠓⠈⡀⣄⣷⢿⠘⠀⣄⣷⣿⣿⡿⣾⢶⡤⣩⠛⠿⣿⣿⣿⣿⣉⠋⣿⣼⡿⢸⠀⡾⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⡇⠇⠀⠀⠏⣰⠀⠀⠋⣿⣾⢷⡿⣻⢟⡿⣛⠽⣩⢛⠿⣶⡿⣶⣽⣻⢿⣿⣿⢿⣿⣿⣭⢕⢸⡿⢸⡀⠱⠣⠉⠀⠀⣀⠢⠉⠀⣄⣷⠻⠀⡀⣧⣿⣿⣿⡿⣿⣿⣶⣶⣤⣤⣠⣃⣞⣯⣿⣿⣳⢸⠀⢸⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⡇⡀⠹⠏⣰⠀⠀⠏⣿⣾⢿⠛⠋⣉⣭⣿⣾⣷⣿⣶⣷⣾⣶⣖⣶⣶⣤⣷⣷⣋⣫⣷⣻⡽⠃⣾⣿⠀⠀⠀⣄⢷⠙⠀⠀⡀⢧⠈⡀⣦⢿⠈⠀⣦⣿⣿⣿⣤⣤⣤⠠⠀⠉⠞⣠⠃⣿⣿⣰⡏⢠⠀⢸⠀⠀⠀⡇⣿⠀⠃ ⠀⠀⠀⠀⡇⠈⣅⣰⠀⠀⠏⣷⡏⢻⠿⣾⣴⣀⢀⣄⡶⢚⠛⠛⠛⠛⠛⠛⠛⠖⠾⣶⣇⢰⠁⡿⡼⡳⣮⢹⡇⢸⠀⠀⠀⠀⢆⢿⠘⠀⠀⣄⠹⠀⡀⢷⠘⠀⣆⣿⣾⣿⢾⠶⠶⡴⣥⢤⠠⡿⣇⣱⠉⣾⠀⡇⢠⠀⠀⠀⣼⣼⠀⡞ ⠀⠀⠀⠀⡀⢸⡄⠁⠉⠛⢿⣿⣿⣿⣻⠙⠉⠉⠀⠀⡀⣦⢽⡤⢵⠤⠀⡶⠁⣟⡥⠟⣱⠟⣿⣿⡛⡟⣾⡝⣷⢻⠀⠀⠀⠀⠀⡀⡷⠻⠀⠀⡀⢳⠈⠀⣦⠹⠀⣄⣿⣯⠉⠋⠒⠤⠄⠀⡟⢿⡿⣾⣯⢰⠀⡟⠀⠀⠀⡇⢱⢸⠇⢠ ⠀⠀⠀⠀⠀⠀⡀⣀⣀⣇⣓⣾⣷⣿⣿⣿⣿⡿⣻⢟⠭⠩⡂⢤⣳⣝⣭⣯⢻⠷⣫⢿⣿⣿⣴⣫⡿⣿⢷⣆⠻⣦⠹⠀⠀⠀⠀⠀⠀⣆⢿⠘⠀⡀⢧⠈⠀⣆⠹⠀⡆⣿⣹⠀⡀⠀⠋⡿⣿⣼⠇⢣⣼⠀⠁⢸⠀⠀⠀⡞⡇⢡⢰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⡷⣿⣶⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣾⣴⣩⠟⣺⡿⡿⠇⠀⣰⢿⣌⠻⠀⠀⠀⠀⠀⠀⡀⣷⠹⠀⠀⢧⠈⠀⡆⠹⠀⣧⣿⠀⠋⡿⣿⣼⣟⢀⣼⡾⢀⠀⡏⢀⠀⠀⡏⢠⣾⡘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣹⢦⠈⡀⢦⠛⠿⣾⣶⣿⣿⣿⣾⣶⣤⣠⣀⠀⠀⠫⡿⣴⢏⢻⣼⠀⠀⡇⣿⢧⡈⢳⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⠀⢧⠈⠀⣆⠘⡇⣿⡿⣾⣣⣿⢇⣸⡆⣟⢠⠀⠀⠸⠀⠀⠁⣼⡇⣾⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⢦⠙⠋⡴⣀⢧⠿⣿⣭⣉⠉⠉⠉⠉⠋⠛⠶⣤⣀⠁⠟⣿⣇⢸⠀⠀⡀⣿⠀⢷⡈⢳⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⡀⢻⠀⠀⢅⠟⣿⣸⠃⣿⢱⣾⠀⠏⢠⠀⠀⡏⢀⠀⠃⡏⢡⣿⢀⠀⠁⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⡏⣸⢧⡘⢧⠈⠆⣢⠙⣄⣷⣙⣀⣥⣓⣈⠀⡄⢹⠁⠚⡴⢇⣸⡇⢠⠀⠀⠀⣧⠀⡀⢻⡄⠸⠀⠀⠀⠀⠀⠀⠀⣇⢻⠀⡇⠈⠋⡾⣠⣿⢻⣿⣼⡟⢠⠇⣰⠀⠀⠇⣰⠀⠀⠹⣼⡟⢰⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⢸⢹⠀⣆⠹⣄⡱⢄⡑⣮⠻⣌⢷⠙⠀⣄⠢⠬⣧⣀⠀⠀⡿⢀⡿⠀⠀⠀⠀⡆⠀⠀⡆⢹⣧⠈⠀⠀⠀⠀⠀⠀⠀⣧⠸⠁⣿⣴⠀⠀⣿⣿⣾⢃⣸⠃⣰⠁⠆⢋⣼⠀⠀⡎⡏⢧⣼⠇⢠⠎⠄⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢻⣿⠹⠀⡄⢳⡈⢦⠘⣆⡻⣮⠻⣌⠻⠈⠀⣄⡜⢸⠁⡇⣸⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⢸⠀⠀⠀⠀⠀⠀⠀⡀⢿⣴⣀⠘⠀⠀⣇⣿⢡⡾⠁⡼⠉⡹⢣⣿⢓⢰⠃⢣⣹⣿⢁⣱⡾⢀⠀⠀ ⠙⠈⡄⠢⠉⠀⠀⠀⠀⠀⠀⢸⡀⣿⡄⠹⠀⡀⢧⠘⣍⠻⡛⣿⡿⣿⣿⣿⣿⣿⣿⢿⠻⡿⢫⣷⡎⠀⠘⠀⠀⠀⠀⠀⠀⡆⢹⣧⠀⠀⠀⠀⠀⠀⠋⡴⣄⠘⠀⢠⠀⠀⡏⣸⡟⢣⣼⡁⣼⡸⣯⣬⡜⠀⡰⡾⡟⢰⡝⡾⢀⠀⠀⠀ ⡀⣤⠷⠙⡈⢤⠑⠀⠀⠀⠀⣇⠀⣿⠈⡆⠹⠚⠴⣦⣹⣀⢦⠘⡀⣦⣮⣻⣦⣽⣧⣷⣄⣿⣿⣿⢻⠈⢱⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠀⠀⠀⠀⡴⢀⠀⠀⢃⠀⠀⠂⠀⣿⠇⣸⡠⠃⢧⢀⠇⢰⡞⠀⡄⡎⣏⣼⠄⣞⢀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⠳⠙⢄⠑⠀⠀⡆⠘⣇⢻⡠⣆⠘⠀⠁⡄⢳⠈⡄⠐⠀⣄⡜⢳⡄⣿⣿⢿⣸⣼⢦⣙⣦⡿⠙⠀⠀⠀⠀⠀⠀⡇⡾⢸⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠁⣿⣼⠀⠂⢡⢠⠁⣰⡟⢀⠀⠃⢿⣾⠀⡞⢀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⣄⢷⡙⢦⠙⠀⢸⡅⣻⠀⠀⣧⠘⠁⢦⠈⣦⠙⠀⠀⠀⣆⡘⢧⡟⣸⣿⣿⡇⠀⡀⢧⡙⣤⢷⠈⠀⠈⠀⠀⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣾⢀⠀⠀⡸⠀⡠⠏⢠⠀⠀⡿⣼⠁⡞⢀⠀⠀⠀⠀⠀⠏ ⢧⠘⠀⠀⠀⠀⠀⠀⣄⢷⡘⢣⡏⠀⣧⠌⠈⠀⣧⡘⠱⣆⠙⣄⠻⠈⠀⠀⢇⠈⣷⢸⣿⣇⡀⠀⠀⠀⣄⠻⠀⣦⠻⢇⠀⠀⡀⢸⢸⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠃⢠⡿⢀⠀⠀⡞⠀⠀⠃⢰⠀⠀⡟⣼⠁⡼⢀⠀⠀⠁⠞⢁⡾⢠ ⠹⣄⠹⠀⠀⠀⠀⠀⠀⠀⣄⠻⣄⢀⡆⢹⠆⠀⠀⣧⡌⠘⡄⠱⡀⣷⠮⠻⠀⢳⡇⢸⣿⠆⠠⠀⠀⠀⠀⡀⢷⠈⡀⣷⡾⠀⠀⢸⢸⠀⢸⠠⠀⢠⠅⠀⠀⠃⠀⡇⠃⣸⠀⠀⠏⢠⠀⠃⣸⠀⠀⡏⣼⠃⡼⠀⠀⠀⠊⣠⠏⣵⠟⡴ ⣆⠹⡄⠳⠀⠀⠀⠀⠀⠀⠀⡀⢧⠘⠀⣿⠈⠀⠀⠀⢧⡌⡜⠘⢢⡌⣟⡙⢳⡆⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⢷⠈⠀⢧⡇⢰⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢰⡟⢀⠀⠃⢰⠀⠁⡼⠀⠀⡟⣰⠋⣰⠀⠀⠀⠀⠃⡿⢾⣤⢋⠞ ⠀⣧⠸⡀⢷⢎⠈⠀⠀⠀⠀⠀⠀⣧⠘⡇⢹⠀⠀⠀⡀⢳⡄⡜⠹⣆⡘⡦⡻⠸⢸⢸⣿⠀⠀⠀⠀⠀⠈⠀⠀⡇⢀⠀⡀⢸⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠃⣸⠀⠃⣰⠀⠀⡼⠀⠀⡟⢠⠟⢠⠀⠀⠀⠁⠟⣷⣫⠞⣴⣀⠀ ⠀⠁⣧⠘⠀⢦⢞⠈⠀⠀⠀⠀⠀⠀⣷⠘⣷⠈⠀⠀⠀⡀⢣⡄⡄⠱⡄⠘⡀⣷⣏⢄⣿⠀⠀⠀⠀⠀⢹⠀⠀⡀⢸⠀⠀⢸⢸⣿⢱⠀⠀⠀⠀⠁⠀⠀⡇⢠⠀⡟⢀⠃⣰⠀⠀⡞⠀⠁⡾⢁⡞⢀⠀⠀⠀⠋⣵⢟⡶⣿⠻⠈⠀⠀ ⠦⠨⣀⣷⣘⣀⣷⣧⢽⠾⠛⠉⠀⠀⡀⢿⡆⢻⠈⠀⠀⠀⠀⢣⠀⡀⢣⡀⠀⡀⣳⢹⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⢿⠀⠇⢠⢻⢸⡌⠀⠀⠀⠀⡆⠀⠀⡾⠀⠇⢰⠃⣰⠀⠀⡜⢜⠋⣴⠋⣰⠀⠀⠀⠁⡿⢷⣿⣰⠀⡄⢻⣧⠹⠀ ⠢⢄⠈⡀⢷⠈⡀⢳⢦⣌⢦⣙⣤⠳⠙⣇⢸⣧⢿⠈⠀⠀⠀⠀⢆⠈⠀⢦⠈⠀⡀⣿⣿⠀⠸⠀⠀⠀⡇⠀⠀⠀⡇⠀⡇⠀⣿⢠⢸⠀⠀⠀⠀⠘⠀⠃⢸⠁⣾⠃⣰⠀⠀⡜⡜⠟⣱⡾⢀⠀⠀⠁⠟⣴⢋⡾⢠⠀⠀⠊⣧⠘⣧⠘ ⠛⠋⠀⠀⡅⢿⠈⡀⢳⣆⠘⡀⢦⠻⡈⣦⣿⡝⣿⢯⠈⠀⠀⠀⠀⢄⠘⠀⣄⠙⠀⡇⣿⠈⢸⠀⠀⠀⡄⠀⠀⠀⡇⠀⣿⠁⣾⠇⢰⠀⠀⠀⠇⢠⠀⡞⠀⡟⢎⢀⠀⠁⡱⡽⡽⢞⣠⠀⠀⠀⠋⡾⢋⡿⣴⠀⠀⠃⡰⠀⡇⢸⡀⢻ ⠀⣀⢦⠳⠙⡄⢿⠈⡀⠳⣆⠹⠀⡀⣦⠻⠈⣄⣷⢿⣎⠙⠀⠀⠀⠀⡀⠱⠀⡀⠱⠀⣿⢸⢸⠀⢰⠀⠀⠀⠀⠀⡇⠀⣼⡏⢰⡎⠀⠀⠀⠀⡞⠀⠇⢰⡏⣴⠀⠀⠁⡰⡟⣾⣠⠀⠀⠀⠁⠞⣫⡵⣞⣠⠀⠁⠋⣠⠀⠀⡏⢸⠀⣿ ⣌⠦⠑⠈⣀⢧⡔⢿⠈⡀⢳⣄⠹⠀⠀⡈⣧⠙⠀⣦⢿⡝⢷⠈⠀⠀⠀⠀⢦⠘⠀⢣⣧⢹⢸⠀⡇⠀⠁⠀⠀⠀⡇⠁⢹⣾⠁⢰⠀⠀⠀⠃⢰⠁⣸⠏⣰⠀⠀⠋⢫⡿⣠⠀⠀⠀⠁⠟⣾⣡⢞⣠⠀⠁⠟⣴⢀⠀⠀⠁⣿⠀⠀⣿ ⣦⢶⠻⡙⢌⠢⢻⡄⢷⠈⡀⢳⡌⢳⠈⡆⠙⣄⢻⠈⡀⣷⣿⣽⠦⠙⠀⠀⠀⡄⠳⠈⣇⣿⢙⠀⡇⠀⡁⠀⠀⠀⡼⡇⣿⢰⡜⠀⠀⠀⠀⡼⠁⡼⠟⣰⠀⠀⠏⢷⣴⢀⠀⠀⠁⠟⣴⣋⠾⣠⠀⠁⠟⣼⢀⠀⠀⠀⠀⡏⣸⠁⠁⢸ ⠟⡼⣰⣂⣽⠷⣝⠯⡛⣿⠙⠁⢧⡘⢧⠙⣆⢻⡆⢿⠙⠀⢆⣝⠻⡉⢬⠑⠈⠀⠀⢆⡝⣿⡿⠀⡇⠀⠏⠀⠀⠁⢹⡿⣼⠇⢠⠀⠀⠀⡏⢁⡵⡟⣰⠀⠋⡴⢞⢠⠀⠁⠋⠾⣡⢛⡴⣀⠀⠀⠟⣴⢀⠀⠀⠀⠀⠀⠏⣾⠀⠰⡏⢀

⠀⠚⠛⣿⣿⣿⢿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢻⠼⠀⠌⢀⢃ ⠀⠀⡘⣷⣿⣿⢸⠀⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣿⣿⣿⢹⢇⢠⠘⡇ ⠨⠁⢼⣅⣿⣾⠋⡤⣀⠀⣀⣀⢦⠙⠀⠀⠀⠀⠞⡤⣀⣤⣦⣿⣿⣿⡀⢱⠇⡀ ⠀⡎⠁⠡⣿⢼⢀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠀⠀⣀⠀⠀⠀⡀⣦⣿⢻⡀⠐⢠ ⠀⢀⡡⡶⣿⢀⠀⠏⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣧⣿⢿⠘⠀ ⠁⡔⢀⠃⣸⠀⠀⢆⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡏⣿⣿⣿⠹ ⢀⠀⠏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣾⢠⠀ ⠧⠿⣿⣼⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣤⣀⠀⠀⠀ ⠀⠀⠀⢸⢃⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⢠⠉⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠤⣀⣀⠀⡀⣀⠤⠑⠀⠀⠀⠀⠀⡎⠐⠒⠐⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠈⠁⠔⢀⠀⠀⠀⠀⠀⡀⢦⠈⠀ ⠀⠀⠀⠀⠀⡸⠀⠄⠀⠀⡀⠠⠀⠀⠀⠀⠀⢇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘ ⠀⠀⠀⠀⠁⢸⠀⠄⠑⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀ ⠀⠀⠀⠁⠀⠀⡀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀ ⠀⠀⠀⠀⢣⠈⠀⣀⠀⠄⢠⠒⠈⠀⠁⠜⢀⢂⠀⠀⠀⠀⠀⠀⠉⠒⡠⢸⠀⠀ ⠙⠀⠁⠀⠀⢡⠀⠀⠀⡀⣀⣁⢲⠁⢈⠀⠀⠀⢀⠀⠁⠖⡐⣀⣂⠐⠁⢀⠀⠀ ⡋⠀⠀⣀⠄⠒⢀⡌⣀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣞⣦⣶⡚⠘⠁⠾⢤⢠⠀⠀⠀ ⡄⢑⠀⡀⣀⠀⡤⢖⠙⠶⠤⠢⠋⠞⠴⣤⣀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠣⠝⠀⠄⠤⠭⡯⠀⠀⠁⣲⠈⠐⠇⠐⠉⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠤⡦⠬⢀⠁⠹⢀⠁⢞⢾⣠⢁⣉⠾⢨⢀⡁⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠤⣳⠀⢧⢁⡠⠀⠀⢤⠅⣶⣈⠢⡌⢇⠒⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⢸⠀⠀⠀⠠⠀⠀⠀⠁⢋⠀⢡⡀⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡿⢩⠙⠀⡟⠿⠯⠈⣄⣤⣶⢻⡆⠸⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢣⡇⣾⢿⣇⣶⣠⠀⠀⠀⠀⡇⠀⢻⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⡀⣦⢳⣯⠀⠀⠣⠚⠚⠑⠈⠠⠄⣌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠠⠀⡀⢄⠒⠒⠇⢀⠀⠒⡢⡠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠋⠠⢀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠤⠤⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⣴⣠⣃⣰⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠤⠀⠀⠀⠀ ⡀⠀⣿⣿⣿⠿⠙⠈⠀⠀⠀⠀⠀⠀⢀⠉⠚⠤⢀⠄⣠⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠑⠈⠀⠀⠀ ⠀⠏⣿⣶⣤⣠⣀⣅⢯⠻⠈⠀⠀⠆⡠⢀⣀⣁⠮⡤⣻⣙⣀⢤⡢⣐⢄⠦⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⣾⠃⣏⠀⠀⠀ ⠞⣿⠀⠀⠀⠀⠀⠀⠀⡀⣿⢿⠿⠿⠤⡀⣀⣀⠀⠀⣀⣄⣤⠦⠑⠈⠀⠀⡇⢰⡀⣦⢽⠦⠓⠛⠉⠉⠉⠉⣄⠘⢱⡞⣇⠀⠀⠀ ⢸⡆⠀⠀⠙⠀⠀⠀⠀⠅⣿⣿⢼⣬⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⣤⣷⢿⠻⡼⢦⠙⠀⡀⠣⠈⣆⣿⠻⠉⠀⡀⢄⡛⢾⣠⠀⠀⠀ ⢘⠀⢰⠀⡇⠀⠀⠀⠂⡟⢺⣡⠔⢀⠀⠂⠑⠈⠀⠀⠟⠓⠈⠀⠀⠋⣿⣿⢀⠀⡀⢦⠈⠀⢆⠘⣇⣿⣾⣶⣾⣷⣛⣈⠀⠀⠀⠀ ⢀⠀⠃⠀⡀⠱⠀⠏⠿⣽⢖⣠⠀⠀⠀⠀⠀⣄⠀⠀⢳⣹⣟⠻⡿⣾⢓⢹⠀⠀⠀⠀⡄⠙⠀⣆⠘⡄⢘⠀⠀⠀⠀⣄⢤⠓⠈⠀ ⠀⠀⡀⢢⠈⡀⢦⣹⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⢒⡥⣿⣏⢿⠙⠀⠀⠀⡀⠱⠀⣄⠀⢇⠀⠀⠀⠀⠀⠀⠀⢄⠐ ⠀⠀⠀⠀⣆⠘⢱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⠈⠇⢠⡀⢦⠙⠀⠀⡀⠱⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡁⠙⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⣄⢤⠀⠀⠀⡀⢦⠈⠀⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⡀⢰⠃⣿⣿⢠⠀⠊⠓⠉⠀⠉⠀⠀⠀⠃⡹⠉⠈⠀⠀⠀⠀⠀⠀⠀⡄⠑⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠎⣀⠳⢻⡆⣾⣤⣹⠊⡤⢱⣹⣏⣿⣿⢁⠸⠏⣶⣛⣞⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠃⣯⣤⠤⠤⠤⠒⠒⠐⠀ ⠀⠀⠁⠞⢀⠀⡀⣷⢳⢻⠀⣣⠀⠀⠀⣀⣉⣟⣰⡔⠎⣧⠞⣀⢄⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣏⠈⠁⠉⠉⠊⠐⠀⠀ ⠀⠋⡾⢿⠈⠀⠀⠀⢣⣦⢻⡇⠘⠀⠀⠛⣿⣰⠃⡴⢀⡠⢀⠀⠀⠀⡀⢤⠒⠈⠀⠀⠀⠀⠀⠀⠀⡆⠁⢹⠉⠉⠉⠉⠉⠉⠈⠀ ⡿⣿⢿⡆⣽⠙⠀⠀⠀⢢⡈⡳⣯⢿⣿⣴⢈⠞⢳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣷⣿⠹⣢⣻⢈⠀⠀⠀⢄⠑⣄⣷⣍⣯⣠⠀⠀⠀⣀⠤⠢⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡗⢠⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠉⠀⣀⢦⡑⣬⠑⠀⠀⠀⡀⢀⠀⣄⣓⢬⠲⠉⠀⠀⠀⠀⠀⠀⣀⠤⠠⠀⠀⠀⠀⠀⠞⢀⡃⡴⠀⠀⠀⠋⠙⠈⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⠤⠠⡀⣀⢄⠑⠈⠀⠀⠀⠀⠀⡀⠦⠑⣈⠠⠒⠐⠀⠀⠀⠀⠀⠀⠀⠁⠊⡠⠀⠃⢠⠀⠀⠀⡿⣷⣶⠀⠀⠀⠀⠀⠀ ⠶⠻⠒⠁⠉⠀⠀⠀⠀⠀⣄⠲⠈⠀⠀⠀⠀⠀⠀⡀⢄⠠⠀⠁⠉⠚⠖⠶⠤⡤⢱⠈⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⠙⠐⠀ ⠀⠀⣄⠦⠓⣈⠀⠀⠀⠀⠀⠀⡀⠦⠙⠀⠀⠀⠀⠀⠋⠖⣤⣀⠀⠀⠀⠀⠀⠀⠀⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀ ⠀⠉⠀⠀⠀⡀⢄⠳⠙⠈⠀⠀⠀⠀⠀⠁⠘⠀⠀⣹⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀⠀⠀ ⣈⡄⠘⠀⠤⣤⢤⠤⠂⠒⣒⢉⠍⠀⠀⠀⢸⠀⠀⡀⢲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⡝⣠⢤⢦⠈⠀⠀⠀⡀⢤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡵⣈⠣⠈⠀⡀⠢⠑⠈⠀⠀⠀⠀⣀⢄⠤⠦⠒⠒⠒⠛⡰⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣎⢠⠘⢸⠀⠀⠀⠀⡀⣄⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢆⠏⢡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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🥺😔😟😞😢😧😥😢😭😿😮😨☹️😩🤕😓😕😬😣

⠀⠀⠀⠀⠁⢸⠏⣿⢦⠀⠏⣼⡞⢀⡀⢉⢨⠀⠁⠉⢉⠒⡔⠭⣻⣛⠒⠐⠀⠀⣀⢀⠀⣯⣿⣿⣶⣤⠀⠠⠀⠀⣆⣿⠻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣾⣞⢀⠀⠏⣿⣾⢀⠀⠀⢋⣀⠁⡋⣠⠋⠔⣩⢖⣠⠀⡇⢸⠀⠀⠀⠀⠀⣄⣦⢹⠀⠀⠀⠀⠁⠛⠼⣱⣧⠹⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⢞⢀⠁⡜⣃⣼⠀⠛⠀⡶⣴⡤⣿⣾⡠⠋⡤⢀⠀⠀⠀⡀⣇⠈⠀⠀⠀⠀⠀⠀⡀⢦⠛⠉⠉⠛⣟⠀⡇⡈⣿⠘⠀⠀⠀ ⠀⠀⠀⠇⢾⢀⠀⡁⠟⣿⢧⡾⢀⠀⠀⠀⠋⣰⢋⡴⢀⠀⠀⠀⠁⠞⡰⣤⣤⣦⢳⠈⠀⠎⣠⢄⠳⡀⣷⣾⣀⡆⠘⡅⢼⡦⣿⠈⠀⠘ ⠀⠀⠃⢠⠀⠁⡔⢁⡘⠀⡶⠓⠛⠀⠀⠀⢋⡴⢀⠀⠀⠀⠀⠇⣹⠀⠁⠈⠀⠉⡿⢿⠀⢱⠈⠉⠖⢀⠀⣧⠈⠂⢿⡿⢹⠀⣿⢸⠇⠀ ⠀⠀⢰⠀⠏⣾⡠⣘⠀⡜⣄⣶⣡⠞⢁⠞⢀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⡀⢀⠀⠀⠀⠀⢧⠈⣿⡟⣿⢰⣄⢻⡿⠀ ⠀⠀⠀⡆⢀⠀⡾⠀⡜⠀⠀⠃⡰⠃⣰⠀⠀⠀⠀⠀⠀⠀⣦⣟⣷⣿⣿⣿⣿⣿⣀⣧⢸⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣿⢘⠀⠀⣿⢰⠀ ⠀⠀⠀⡇⠻⠋⢀⡄⠀⠀⠏⢠⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡓⣉⣄⣤⣥⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣿⢠⠀⠁⣾⠀⠀ ⠀⠀⠀⠀⣧⢸⠀⠀⠀⠎⢀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣟⠀⠀⡇⢠⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠎⢀⠀⡼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠆⣾⢃⣰⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⡇⠿⠽⠁⡛⣀⠲⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⡴⢤⣀⢉⠉⠉⠀⠀⡇⢸⡜⠀⠀⠀⢸⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠃⢰⠀⠂⡄⢹⣿⣿⣿⠭⡠⣄⣦⣙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⠤⣍⡽⣤⣦⣈⢯⠻⡏⠄⢀⠀⠀⡇⠀⠀⠁⣸ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⣾⣣⣄⡹⣄⣵⠾⠷⡾⣴⢠⠄⠩⠉⠈⠀⠀⠀⠋⡿⠻⠉⣉⣋⣛⣞⣶⣳⣈⣺⠙⠀⠀⠁⣸⠀⠀⡼⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⢃⡀⠹⡇⠹⠀⠀⣀⢀⠤⠠⠀⣿⡼⡀⢄⠛⠈⡀⢀⣀⣀⣀⡀⣀⢀⠀⡇⣷⢀⣿⠀⠀⡇⢿⠀⡏⣿⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⡇⠀⡆⠘⣿⠘⠀⠀⠄⠀⠀⡏⣿⢠⠀⠀⡀⣧⠺⠒⠐⠀⠓⠙⠀⠀⠀⡸⡁⡾⣇⠀⠀⡏⣰⠏⣿⣠⠀ ⠀⠀⠆⠏⠀⠀⠀⠀⡀⣿⠘⡆⠈⠀⣧⣧⢻⠈⠀⠀⠀⠃⢠⢰⠀⠀⠀⠀⠀⢧⠀⠉⠛⡗⣼⣼⢂⡞⠀⡇⢀⡎⠀⠏⣿⠟⣾⢀⠀⠀ ⠀⠀⠀⣆⢻⠀⠀⠀⠀⣧⢹⠀⢱⠀⡀⣿⣇⡀⢤⠲⠟⣻⠈⠀⠀⠀⠀⠀⠉⡟⣨⣀⠀⡼⠀⢹⠏⢠⠁⢰⠃⢡⠟⣰⠋⡴⠀⠀⠀⠀ ⢄⠀⠀⠀⣆⠙⠉⠈⠀⡀⣿⠐⡄⠀⠀⣇⡾⠈⠁⡟⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠐⡜⠀⠀⣾⢀⠀⡜⠁⡾⣫⢡⠜⢀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠇⣸⢢⢆⠙⠀⡄⢸⠀⠀⠀⡃⠀⢹⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡜⠁⠀⠇⢠⠀⡄⠃⡠⠅⢟⣰⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡆⠘⠀⠀⡀⣦⠘⢄⠀⠀⠀⡄⠃⣠⠀⠊⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠁⡸⠋⢠⠀⠀⠞⢠⠊⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠄⣷⠸⠀⠀⠀⡄⢤⠙⠀⠀⠀⢠⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣰⠃⡰⠀⢀⠀⠂⡪⠛⡠⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠀⠆⡽⢉⠉⠈⠀⠀⠀⠁⡔⠥⠉⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢤⡭⢀⠀⠀⠉⠒⡤⢄⣥⡞⢠⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠸⠀⠀⠀⠁⡟⢋⠟⠫⡿⢲⠤⢀⠀⣀⠤⠲⠒⠑⠁⠀⠁⠉⠛⡽⣭⢉⠉⡀⣵⠠⣀⠀⠀⠁⠟⣠⠉⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠘⠀⠀⣁⣊⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⢢⠈⠳⠚⠄⠤⣤⣁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⠒⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⠻⣟⠙⠉⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈ ⡇⣹⠀⠀⠀⠀⠀⠁⡚⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠐⣿⣿⢸⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣼⠀⣇⣾⠀⠀ ⡀⣳⠀⠀⠀⠀⠀⡇⢹⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⢜⠀⣿⣿⢈⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⠁⠈⡟⢀⠀⠀ ⠀⡇⠹⠀⠀⠀⠀⡇⣿⠸⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⠀⠀⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢠⡟⠿⢠⠀⠀⠀ ⠀⡇⠀⢦⣙⠀⠀⡀⣿⣿⠘⡀⢧⠈⠀⠑⠀⠀⠀⠇⣿⣿⢸⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⡇⣿⣸⡟⣿⣠⠀⠀⠀⠀ ⠀⡏⠀⠀⡀⢦⠙⠀⣯⣤⢸⠀⠀⣧⠀⠀⠀⠀⠀⡇⣿⣿⢸⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣇⣟⢠⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠀⠀⣿⢸⣿⠉⢸⠀⠀⡄⠀⠀⠀⠀⠀⡄⣿⣏⢸⠄⣴⣷⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⢀⠀⠀⠀⠀⠀⠀ ⠃⢸⠀⠀⠀⠃⣿⢸⣿⣿⢸⠀⠀⠁⠟⠀⠦⠛⠉⠀⣿⣿⣿⠀⠀⡆⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⡆⣴⠇⣿⣿⢸⠁⠟⣴⣤⠷⡟⣿⣻⢬⣿⣧⣿⢹⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢸⠀⠀⠀⠀⠀⡿⢠⣿⢃⣼⢀⠀⠀⣁⣾⡀⣶⣷⡟⠈⣿⣿⠈⠀⡆⢸⠀⠀⠀⠉⠈⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠈⠀⠀⠀⠇⢰⡇⣻⠛⠿⣿⣿⣾⣴⢦⠳⠻⠈⣧⢸⡄⣿⢿⠈⠀⢀⠀⠀⠀⣀⣄⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⢤⠤⠤⣾⠀⡏⣿⣿⣾⣤⢀⠃⠾⠰⠀⡀⣄⡶⢹⠀⣇⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢸⠃⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣷⣿⣿⢿⠻⠛⠛⠛⠞⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⣾⢠⡿⢠⡤⢀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⡖⢸⠀⡀⣿⣿⣿⣿⣾⠇⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣾⣶⣶⣷⣿⣿⣾⣷⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⡿⣿⣿⣿⢸⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⢀⠇⠸⠃⣿⣿⢠⠀⣸⠀⣧⣿⣿⠛⠀⡇⣿⢹⠈⣀⣿⣿⣿⣿⣿⢤⡇⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⡏⢸⡇⣿⣸⠀⠈⢀⠈⡇⣿⣿⣉⠀⡇⣿⣿⢸⠅⣿⣿⣸⣿⣿⠈⠣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠉⣌⢠⡇⣿⢸⡇⢸⠇⢸⡄⣿⣼⣤⠀⡇⣿⣿⢰⡇⣿⣿⢺⣿⣿⠿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⣶⣾⣿⣾⣿⣷⣿⣷⣾⣶⣶⣷⣿⣿⣿⢿⠿⡿⣿⣿⢿⡿⣿⢻⢸⣿⣾⢺⡀⣏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⢣⢸⠀⣦⡙⣿⡾⢀⠀⠀⠀⡀⣿⣷⢸⠏⣿⣴⣀⣿⣯⢀⠃⢸⣿⢸⢼⡇⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡇⢸⠀⠀⠀⡇⢸⠀⠀⡇⠀⡀⣷⣦⣹⣿⣼⠀⠀⣿⣼⠀⡇⠀⣷⠀⢀⣿⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡿⢸⠀⠀⠀⡀⢠⠀⠀⡇⠀⠀⡇⠁⣿⣧⢡⠰⡁⣸⢠⠘⠸⠁⡼⠀⠁⣼⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⠇⢸⠀⡄⠀⡇⠀⡄⠀⠀⡄⠀⠀⡃⢯⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢆⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⣷⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠦⠒⠒⠒⠒⠒⠴⠤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠁⡿⣸⠀⠀⠀⠀⠀⠀⡀⣆⣀⣇⣉⣈⣇⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⡄⣿⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⣿⢠⠀⠀⠀⠀⠀⠋⢿⡿⠿⣼⣶⣿⡿⣬⣿⢿⠿⠛⠈⠛⠙⠀⠀⠀⣿⣿⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣿⣿⠀⠀⠁⠟⣿⣿⢾⣐⣉⣿⢸⣄⡦⣿⡀⢦⣿⣒⣍⣯⣿⣬⠿⢻⠙⡇⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⣿⣿⠻⠿⣿⣺⡤⡇⢸⠀⠀⡇⢸⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸⡀⣷⣿⣭⣷⣿⣿⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⣿⣿⣿⣤⣤⣧⠸⠀⡆⣿⠀⠀⡀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠀⢸⠀⡇⣿⡀⣦⣿⣷⢸⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠋⡟⣼⣠⣦⢸⠀⡇⢸⠀⠀⣿⠀⠀⠀⢸⠀⠀⠃⠀⠀⡇⠀⠀⠀⢸⠀⣯⣇⠀⠀⣾⡇⢿⠿⣿⠈⠀⠀ ⠀⠀⠀⡄⣿⣆⣿⠀⠀⢷⠀⡀⣷⠀⠀⣷⠸⠀⠀⠇⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⠀⣿⡆⠀⠃⢰⡏⢸⠁⣿⢀⠀⠀ ⠀⠀⠀⠀⣇⠹⣦⢸⠀⡄⠹⠀⡀⢸⠀⡄⢹⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⣼⠀⠀⡇⠀⢻⠀⡟⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠘⣧⠈⠀⣆⠘⠀⢧⠈⠀⣧⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⡜⠁⣼⠃⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠈⢷⠈⠀⢣⠀⡀⢸⠀⡇⣄⠀⡇⠐⠀⠀⠀⠀⠘⠀⠀⠀⠀⣸⠀⠀⠀⢸⡇⢃⡿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢆⠙⢳⠀⡄⢸⠀⡇⠀⡀⠀⠀⡏⠉⠃⠀⠀⠃⠀⠀⠈⠀⡆⢀⠀⠀⠃⢠⣿⣽⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⡻⢻⠀⡇⠈⡀⠺⠴⣠⣀⣀⠀⠀⣀⣀⣀⠄⠦⢒⠉⠀⠀⠃⠁⣸⠇⣾⡞⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡹⠱⠀⢻⠋⠻⠶⡤⣀⣀⣀⣀⣀⣀⣀⠤⠦⠲⠉⢄⠗⣠⡇⠀⡿⡾⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡷⢿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠣⠏⢱⡿⡴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠛⠛⠙⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⣿⣿⣿⣿⣿⢿⠙⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⣿⣿⣿⣿⣿⣿⣿⣿⠻⠁⡞⢀⠁⠉⠾⠶⠶⠶⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠏⣤⢀⠁⠀⠀⠀⠀⣄⢷⠈⠀⠀⠀⠁⠋⠖⠶⠶⠛⡊⠟⠿⠿⠻⠙⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠎⣠⠀⠀⠀⠀⠀⣄⣦⣿⣿⣿⣿⢿⠘⠀⠀⠀ ⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⣧⣿⣿⣿⣿⣿⠈⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⢸⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡛⣝⢭⠉⠉⠬⠤⣤⣤⣤⣶⢷⠙⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⢿⠀ ⠀⣇⣿⣿⣿⣼⣀⣁⣼⣶⣿⣿⣿⣾⣶⣦⣶⣶⣷⣿⣿⣿⣿⠿⠛⠛⣙⢭⠂⠐⠋⠞⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠ ⠀⠀⣿⣿⣿⢠⠟⡠⠀⠃⣿⣽⣾⣭⢭⠿⠿⡻⣿⣾⣼⣧⣷⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⡇⣿⢿⠙⡋⠿⠘⡀⡏⣿⣿⣿⣿⣿⠿⠛⢛⠉⢍⠬⠔⣆⣄⣭⢭⣿⣿⡿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀ ⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⢿⡿⣾⣰⠀⡗⣈⢀⠀ ⠀⠀⠀⠀⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⡤⢣⠉⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⠉⠒⠰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣤⣀⣉⣟⣠⠋⠟⣶⠓⣿⡼⣦⣿⣿⣿⣿⣿⣿⣿⣿⢠⡀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⣇⣿⡿⢼⡟⢏⢞⡤⣀⠀⠀⠀⡀⢦⠙⡟⣿⣿⣿⣿⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣾⣿⢿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣹⣿⢻⣟⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠟⠟⡧⣿⣿⣶⣰⠀⠞⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣧⣿⣏⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠏⣰⣿⣿⣿⣾⢠⢸⠙⡿⠦⡷⡿⢹⠙⠀⠀⠇⠉⠚⠀⡏⣿⣿⣿⣤⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠎⣿⣿⣿⢸⠂⢃⣿⣹⠀⠀⡒⣐⢠⠋⠿⣿⣭⣾⢿⣿⢰⣇⣸⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⣿⣇⣽⣷⠴⣷⣿⣷⢿⠈⠀⠁⡿⣶⡿⣿⣿⣿⣿⢸⠀⡿⢀⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⠘⣧⡞⢀⡄⣿⡈⣷⣦⠘⡟⣿⣚⣟⢺⣟⣿⣠⠀⠏⢰⠁⣾⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠀⢧⠋⠈⡄⢿⡘⠙⣇⣸⠀⠁⣴⠀⡏⣳⠀⠏⣰⠃⡿⢫⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⢣⢦⠘⡄⡵⡄⢀⠀⢀⡖⠀⠎⢠⠁⠞⣠⠋⣿⢻⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠈⡄⠑⣄⠳⡈⢤⠧⠻⠛⠖⣠⠁⠚⡤⠁⠟⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠈⡀⢦⠙⡀⠤⡥⢘⠒⠤⡤⣀⠋⠗⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠙⠀⣁⣭⣈⣀⠀⠴⡤⣉⠟⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⣤⣤⠤⠤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠁⠉⠉⠉⠚⠒⠓⠛⠛⠒⠙⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠓⠟⠿⣿⣿⣿⣿⣴⠃⡿⣿⠘⢐⢀⠑⢊⡰⡟⣿⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢈⠧⠤⡤⣀⣀⣁⣏⠫⣼⣷⣿⣿⣽⣿⣿⣿⣷⠽⠾⠶⠤⠦⠶⠴⠤⠤⠤⠤⠿⣿⣽⣏⢰⡇⣴⣤⣤⣿⣿⣰⠋⣿⣿⣿⣿⠻⠟⠦⠻⡿⣿⣿⣿⣿⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⠼⣯⣛⡶⣠⠋⡟⣿⣿⣿⣿⣿⣽⣹⠒⠒⠒⠒⠒⠓⠙⠉⠉⠉⠉⣏⢿⣿⣿⠀⣾⠠⠀⠀⣿⣰⠟⣿⣿⣿⣿⣿⣾⢀⠀⡆⣿⣿⣿⣿⣿⢸⠀⠁⠟⣿ ⠀⠀⠀⠀⠀⣄⠱⢳⠉⣞⡟⢰⠀⠟⣿⣶⣭⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⢴⠷⢳⠀⠀⠃⣿⡾⣀⣄⣌⣯⣿⣴⠀⠀⠀⡟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣄⠿⡿⣯⣽⡾⣱⢋⣴⣋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣸⠛⠃⣾⣠⠀⠀⠀⠛⡾⣷⣿⠿⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠃⠞⣠⠀⣀⣦⣽⢏⣼⠀⡞⢠⠀⠀⠀⠀⠀⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣽⣿⣼⠁⠀⠀⠋⡾⣤⢤⠲⡙⣿⣾⣠⢀⠀⣅⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⣇⢿⡴⠀⠀⠀⠀⠀⠀⠀⠀⣩⢤⠒⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⣄⣧⢿⣡⡿⣾⣠⠀⠀⠀⠃⡿⣹⠉⠀⠃⠋⣿⣿⣿⣿⣽⣤⣶⣶⣿ ⠀⠀⠀⠀⡏⣿⣿⢿⠿⠿⠿⠿⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⡀⣀⣄⠷⠈⠀⠀⠀⠀⠀⡄⣷⣿⣶⢀⠀⠀⠀⠏⣿⣾⣫⣿⣴⣤⣷⣟⣶⣿⠙⣽⢿⠛⠈⠀ ⠀⠀⠀⠃⣿⣿⣷⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣼⢀⠀⠀⠀⣀⣦⣿⣿⢿⣿⣿⣽⠳ ⠀⠀⠏⣼⣤⡏⣾⣶⠶⣶⣿⢠⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣣⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠛⠙⠉⡈⣦⣿⣿⣿⣿⢿ ⠁⡞⣬⣤⣤⣿⠀⠀⠀⠇⢰⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠁⠉⠛⠟⡼⣡⠛⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠟⠳⠀⣀⣦⣿⡿⢿⣽⣿⣿ ⡾⢀⣤⠀⠀⡄⢻⠈⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠿⠛⠉⠉⠋⠟⣿⣾⢴⣤⣠⣀⣋⣔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠄⣀⣿⢰⡄⠀⠀⠀⠀⣏⣿⣾⣧⣿ ⣤⢤⣭⣋⣻⣿⣿⢿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢿⣛⣉⣭⣾⣤⣀⠀⠀⠀⠤⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠶⣨⠀⠀⠀⣄⣷⣿⣿⣾⢦⢛⣇ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣹⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡼⣏⠋⣿⢿⠘⠀⠀⡇⣿⣿⢻⠔⣤⣿ ⢿⣿⣿⣿⣿⣴⣠⣫⡟⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡾⣡⠞⣶⣶⣿⣿⣿⠀⠀⡏⣿⣿⢠⠉⠋⣿ ⣯⣿⣾⣴⢀⠁⡿⣿⢹⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣽⣻⠿⣴⠁⠈⠀⡇⣼⣧⠐⠁⣿⣿⣾⠿⣬⣷⣙ ⣾⣳⡛⠍⠟⣿⣿⣿⣿⣿⣿⣿⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⣿⠀⡀⢿⠿⣿⣻⣼⠃⡿⣿⣿⢳⡀⣷⢿⣝ ⣿⠻⠿⣶⣤⣤⣀⣀⣀⣃⣛⣛⣟⣿⣼⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣛⢿⡿⣿⣷⣿⣴⠋⣿⣿⣿⣤⡀⢧⠙⣦⣿ ⣿⣿⣿⢿⠛⠛⠟⡶⣶⣶⣷⣿⣿⣿⣿⣿⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣠⠀⠋⡿⣿⣿⣾⢠⠏⢿⠸⣦⠹⣧ ⣿⣿⣿⣿⣿⣿⣿⠻⠉⠉⠉⠉⠉⠉⡉⣉⣤⣴⣠⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠟⣿⣿⣿⣾⣠⠉⠟⣾⢠⣆⠹⣧⢻ ⠻⣜⣷⣿⣿⣿⣿⣿⣿⣸⣄⣦⢻⠋⠑⣉⣍⢭⠿⣽⠉⠉⠉⠚⠓⠷⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣊⣔⣤⣯⣴⣠⠋⡷⣿⣶⠻⠀⡀⣿⢹⣷ ⣿⣿⠻⣮⣿⣿⣿⣿⣿⣿⢾⠳⡇⠺⡀⣤⣀⣀⣁⣉⣉⣟⠶⡶⣶⣷⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠒⠖⡤⢏⣷⢈⠀⣆⢿⠈⡀⣿⡿ ⣝⣷⣿⣿⡻⣿⣿⣿⣿⣿⢿⡈⣳⢿⠀⠀⠀⡇⣿⣿⣿⢀⠀⠠⠀⠀⣏⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠳⠈⣄⣿⠿⣾⣠⠀⢀⠀⠀⣆⢿⣽⣿⣿ ⣿⢿⣝⣷⣿⣯⣿⣿⣿⣾⣿⢿⡏⣿⠀⠀⠀⡄⣿⣿⣶⠻⠉⡟⢿⣿⣽⢨⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠻⠀⣧⠙⡏⣹⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿ ⢮⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⡀⣦⣷⣿⣿⣿⣨⣧⣾⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣤⢀⡄⣿⢧⡈⣿⢿⡏⠘⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣀⣄⣿⣿⣿⣿⢿⠻⠛⠙⠉⡈⣀⣀⢀⠀⠀⠋⡿⢉⠀⠀⠀⠀⠀⠀⠃⠙⠞⠛⠞⠤⣇⣈⣷⠚⠀⠀⡀⡆⣿⣼⢻⢧⣿⠘⠁⠛⡿⣿⣿⣿⣿⣿⣿ ⡄⡻⣯⣿⣿⣿⣿⣿⣿⣿⠀⠉⣷⣼⣇⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠁⠋⠜⠘⠀⠃⣹⢹⡄⣿⠘⠀⣧⡘⣷⠿⡈⠹⠀⢤⣧⡞⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⣿⠀⣿⣿⢈⡀⣀⣿⣽⣤⣤⣤⣿⠿⠲⠟⠿⣿⣆⣿⢹⢧⠀⡇⣾⣾⠘⣆⠹⠀⠀⢧⡌⣷⢿⡜⢻⠈⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣧⣿⢿⠈⠀⣇⣎⣸⠤⠤⣧⣷⠽⣤⠤⣷⠼⣷⣿⡶⢿⠙⢹⣿⢧⠀⣆⠘⠀⠀⢧⡉⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿ ⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⠙⡀⢷⣟⠹⠀⡄⠹⣄⢻⢁⡄⢻⡀⣿⢹⡄⠹⣧⣿⡸⢻⠀⣧⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣧⣿⣾⠀⣧

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⠀⠀⠀⠀⠈⠁⠏⣿⣿⣿⣿⣿⣿⣿⠻⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠷⣿⣿⣿⣿⣿⣿⣿⠙⣋⣛⠀⠀⠀⠃⡼⢀⠀⣇⠘ ⠀⠀⣾⣶⣶⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡷⣿⣿⣿⣿⣿⣿⣿⣼⡦⠹⠀⠁⣼⠀⠁⠀⠀⢻ ⠀⠉⢠⠀⡌⡀⣷⣿⣿⣿⣿⣿⣿⣿⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⠀⡀⢻⡟⢠⠀⡼⠀⠀⣿ ⠀⡆⠀⠀⢿⠾⡦⣽⣯⣿⣿⣿⣿⣺⠀⡀⠀⠀⠁⠋⠛⠛⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⣿⣿⣿⣿⣿⣿⣿⢸⠀⡆⣹⠀⠆⢸⠀⠀⣿ ⠋⠠⠀⠀⣿⢹⠚⣧⣆⣿⣿⣿⣿⢠⠀⠁⠛⣾⣴⣤⣤⣦⣶⣶⣶⣷⢿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠀⣿⠈⠀⣗⠈⠀⣇ ⢳⢀⠀⠀⣿⣼⠀⡃⠀⣿⣿⣿⣼⠁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣤⣀⠀⠀⠀⣀⣄⣦⣗⣿⣿⣿⣿⣿⣿⢹⠀⡄⢿⠀⡄⢿⠀⡀ ⠰⠀⠀⡇⣸⠀⠁⡼⠀⡏⣿⣿⢋⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠒⠐⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⠹⠀⡄⢹⠀⡆⢻⠀ ⠀⠀⠁⣿⠀⠀⡞⠀⠏⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⠸⠀⣧⠘⠀⣆⠹ ⠀⠀⡾⢠⠀⡏⢠⠏⣿⣿⣿⣸⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠙⠀⡀⣷⣿⣿⣿⣿⠹⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⡆⢀⠏⣿⣿⣿⣿⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⢿⠈⡇⣿⣿⣿⣿⣿⢿⠈⠀⠀⠀ ⠀⠀⠀⠁⠟⡴⢀⡀⣧⣿⣸⠀⠀⠀⠀⠀⣼⣷⣿⣿⠀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣲⣿⢠⡄⣿⣿⣿⣿⣿⣿⣿⠹⠀⠀ ⠀⠁⠟⣴⢀⠀⠀⠁⡏⣿⢰⠀⠀⠀⠀⠀⣦⡖⣤⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⢠⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈ ⠟⣠⠀⠀⠀⠀⠀⡷⣿⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣴⣤⣷ ⢀⠀⠀⠀⠀⠇⡏⠿⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣧⣿⣽⣾⢠⠀⠀⠀ ⠁⠀⠀⠀⠋⡿⣿⣿⢸⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀ ⢷⠛⠛⡿⣿⣿⣿⣿⢀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣲⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⡦⣴⣶⣶⣷⢿⠘⠁⠀⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣼⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣇⣿⢠⡇⠘⠀⣄⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⢳⠀⠀⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡾⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠁⡿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠏⣴⠀⠉⠉⠟⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠁⠁⣿⢰⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⡶⠉⠹⠉⠉⠉⡈⠢⠈⠀⠀⠀⠀⠀⠀ ⢆⠙⡗⣾⠁⠉⠉⠛⠟⠿⣻⣚⡤⢀⠀⠎⢠⠀⣇⣶⣿⣿⣿⡾⠷⠙⠈⠀⠀⠀ ⠦⣜⣿⢧⣿⣿⣽⣿⣿⣴⣀⠀⠃⠓⡠⠀⠇⠠⠀⠰⡀⣄⣷⢈⣿⣯⣿⠿⠚⠑ ⠈⢄⣸⡳⣏⣿⣿⣠⢀⠀⠀⠀⠀⣾⠀⠀⡏⠀⠁⢘⠀⠀⠁⡒⣶⣾⣷⣸⠀⡽ ⢀⠀⢠⡇⣿⣼⢀⠀⠀⠀⠀⠀⠏⢹⠉⠟⣿⠛⡟⣿⠈⠀⠀⣸⠀⡄⢿⡘⠢⢸ ⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠃⣿⣿⣶⣿⣾⣶⣥⣔⣄⠠⠀⠈⠅⠲⡏⣿⠘⢇ ⠼⠀⠀⠀⡿⠑⡴⣀⠀⠀⠁⡠⠀⠀⣀⠄⠠⣀⢀⠀⠀⠀⠟⠊⢫⢐⣧⣾⢸⠀ ⣷⠀⠈⠀⢠⡰⠀⠧⠉⠝⢁⠐⠀⠀⠁⠈⠀⠀⠀⠀⠒⡧⢔⣝⣏⢃⠈⣧⠃⠀ ⡀⢱⢸⠀⡆⢳⠞⣫⣽⠔⢔⠎⢫⡿⣠⠀⠀⠀⡀⠴⢀⣂⣒⣈⠀⡇⢿⡟⣸⠀ ⠀⡄⢹⠀⠸⡇⢀⢅⢔⠤⡤⣤⣉⠈⠋⠀⠀⠀⠁⠐⠆⣿⣿⡿⠾⣴⣅⣾⢲⠔ ⠀⠀⣇⠀⠀⡀⠇⡷⠉⠀⠀⡹⠟⡾⣯⠉⠉⠉⡉⢳⠀⡆⠙⠂⠳⠉⠋⣟⠀⠀ ⠀⠀⠀⢰⠀⠑⡎⠈⣀⣤⣯⣨⣞⡰⢠⠛⠒⠔⡹⣾⠸⠒⢸⠀⡇⣧⠻⢀⠀⠀ ⠤⠀⠀⡆⠈⡆⠟⢲⠷⠋⣄⢟⠂⠖⡷⣣⠀⠀⡇⢹⢆⠈⢸⠀⠀⡀⡾⠀⠀⠀ ⠀⢠⠀⠀⢃⠀⣧⠘⠀⡷⠀⣿⠸⠀⠀⣿⠘⠀⡀⡇⠀⣷⢠⠀⠃⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⡀⠱⠀⡀⠠⣃⡱⠀⠀⡄⢰⠀⠀⡄⠀⡇⠉⠉⡒⠒⢠⠤⠤⠀

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⠀⡀⣀⣄⣤⣢⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡀⢧⡈⠳⠈⠀⠀⠀⠀⡀⣄⠦⠛⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠟⣼⠀⣄⢳⣌⠦⠓⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣴⣀⡀⣀⣀⣦⠸⢦⠓⠈⠀⠀⠀⠀⠀⡀⣄⠳⠙⠀⠉⠋⠖⡤⣀⣄⣹⣷⡿⣿⣿⠻⠀⡄⢿⠈⠀⣀⠯⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡞⣠⠀⠀⠀⠀⠀⠀⠀⡄⠹⠆⣘⢄⠶⠙⠈⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⡆⠹⣧⣿⠿⡿⢿⠘⣧⢿⠴⢀⠀⠀ ⡀⣀⣄⠤⠤⠤⠦⡶⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠟⠿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⢷⠀⠀⠀⣀⢤⠒⠉⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⣷⡆⣿⣿⣿⢻⣿⣜⣿⣿⣐⣀⠀ ⠀⠀⠀⠀⠉⠛⠽⣿⣿⢿⡽⣿⣟⣿⣿⣟⣿⣾⣴⢋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠊⠖⡤⣤⢤⡀⢹⠀⠀⠀⠉⠀⡀⣤⠲⠝⠤⠦⣗⢉⠀⠀⠀⡇⠛⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀ ⠀⠀⠁⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⣤⠓⣌⠳⠉⠀⠋⠞⡦⣀⠀⠀⠀⠀⠀⠀⡇⢿⠙⠀⣆⢞⠈⠀⠀⡀⢄⠛⠈⡀⢧⠛⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀ ⢀⡀⣀⣯⣾⣶⣿⣿⣿⣿⣿⣿⣷⣾⣠⠀⠀⠀⠀⠀⠀⣆⠙⡖⣀⢀⠀⠀⠀⠀⠃⠸⠀⠀⠀⠅⣿⣿⢿⠙⡄⣝⠹⠀⠀⠀⡀⣄⠿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⢼⠀ ⠀⠀⠀⡀⣧⣿⠿⠛⣈⣤⣷⣿⣨⠀⠟⠱⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⣿⡛⣿⣿⠻⡌⡀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣿⣶⣶⢻⠋ ⠀⠀⠀⠀⠀⣦⣿⣿⣿⠻⠘⣄⢻⠈⡀⣣⢻⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢿⢸⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀ ⠡⠀⠀⠀⠀⠀⣧⣿⣿⣰⣇⠘⣿⢧⠈⠀⢧⢮⠘⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠁⢸⠀⠁⠏⡌⣷⣿⣿⣿⣿⣿⣿⣇⠻⠀⠀⠀⠀⠀⠀⠀⣷⣿⢤⢸⣿⣿⣿⣿⢠⠟⠻⠀⠀⡈ ⠠⠀⠀⠀⠀⠀⡀⣿⣟⠘⡄⢸⣿⡀⢿⠀⠀⢀⠀⠀⠀⠀⠀⣦⠙⠈⠀⠀⠀⡧⢿⠿⣿⣿⣿⠻⣌⣿⣿⣿⣿⣿⣿⣿⢻⠘⠀⠀⠀⠀⠀⡆⣿⡀⢠⣿⣿⣿⢠⠀⣠⣀⢀⡟⣿ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⣧⠈⢸⣿⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⠉⠋⣿⣿⣿⣿⣷⣿⣿⢿⡉⣶⣠⣀⣀⣏⣴⣀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣿⣿⢠⠀⠀⠀⠀⡟⣿⣾ ⠀⠀⠂⠐⠀⠉⠀⡇⢸⠀⣷⢸⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣿⣿⢿⣜⣴⣠⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡇⣿⣰⠀⠀⠀⠀⡇⣿⣾⠀ ⠀⠀⠀⡧⢉⠘⠁⡏⢸⠀⡇⢾⠁⣼⠀⠀⠁⠖⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠤⠤⠤⡤⣠⠀⠀⠀⠀⠀⠈⠀⠁⠞⢧⠺⠀⡁⣷⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣿⢟⡱⣟⢸⠀⡟⢠⡟⢀⠀⠏⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠂⣠⠇⣼⢀⠀⠀⡆⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⡇⣹⡾⣿⢋⠀⢸⠃⢰⠀⠟⢠⠀⠀⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⡀⠀⠀⡏⢀⠃⠴⣇⠀⡆⣿⣿⣿⣿⠙⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⣿⣿⣿⣼⠁⠋⣿⠀⡏⣼⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⢀⠁⣋⠿⠉⠀⠙⣧⣿⣿⣿⣮⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⣾⢠⡟⣿⣿⠏⣿⠀⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⠞⢫⡼⢠⠀⠀⠀⠟⣿⢉⡿⣿⢳⡀⢿⣟⣿⣿⣻⣼⢻⠈⠀⠀ ⠀⠀⠀⠀⠀⡆⣿⢹⡟⣿⣿⣿⣿⣧⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣫⠉⠞⣫⡴⢀⠀⠒⠙⠀⠀⣥⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠘⡀⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⢻⣻⣿⣿⣿⣾⢀⡇⣾⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣎⣿⡶⢘⠤⠤⠢⠓⡉⢄⠳⡈⣀⣤⣤⣤⣶⣤⣤⣦⣓⣧⣿⢻⠀⣧⣿⠻ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⠀⡏⢏⡶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⣠⢀⠀⡀⢤⠳⠈⠀⠀⣀⠦⣗⠻⠀⡀⣄⡠⣀⢀⠀⠀⡀⣧⣇⠘⡄⣿⣏ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⠀⣿⢠⠈⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⣁⢸⣀⣀⠦⠓⠉⢼⠦⠳⠙⠈⠀⠀⡀⢷⠙⠀⠀⠀⠺⠀⠀⠀⡀⣿⢰⠀⡇⣿ ⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⢸⠁⣿⠉⠊⡽⢀⠀⠁⠚⢠⠉⠙⠖⡠⠀⠀⠀⠀⠊⡴⢀⠉⠛⣘⠀⠀⠀⠁⠞⣶⢷⠻⠈⡀⣄⠶⠙⠈⠀⣧⢻⠎⠑⠈⠀⠁⠟⣾⣿⠀⠇⣼⣠ ⠀⠀⠀⠀⠀⡿⣿⣿⣧⣿⣿⢸⡀⣿⣻⡴⢀⠋⠴⣡⠋⡿⣴⢀⠀⠀⠀⠋⠽⠉⠛⠾⣤⣀⣭⣷⠿⠇⢼⣷⠙⠀⠀⡀⣄⠳⠈⠀⡀⣤⠳⠈⣆⣿⠹⣄⠢⡟⣼⠀⣿⠀⣷⠀⠀ ⠀⠀⠀⠀⠁⣿⣿⡘⠀⣧⣿⢸⠀⣼⢹⠚⡴⢁⠞⣤⣠⢀⠀⠀⠀⠀⡟⣿⣿⣫⣿⣤⣿⡿⣻⡟⣿⣿⢘⠁⣜⠻⠀⠀⠀⡀⣦⠹⠀⠀⠀⣄⠷⣜⣿⢻⠈⡄⢠⠀⣇⠀⣾⠀⠀ ⠀⠀⠀⠀⡏⣿⣿⣿⠈⠀⣧⣿⠀⢻⣧⠈⠔⢀⠀⠀⠀⠀⠁⠀⠆⡽⣯⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣳⠿⢀⠀⡀⢧⠘⠀⠀⠀⡀⢷⠙⠀⠀⠀⣆⣿⣿⢷⠘⠀⠀⡇⠀⢸⠀⠀ ⠀⠀⠀⠃⣿⣿⡹⣦⠀⠀⡀⣧⠹⣷⢻⢳⠀⠀⠀⠀⠀⠀⡇⢹⠉⠉⡋⣿⣿⣿⣿⣿⣿⣿⣶⣻⣈⣄⢦⠛⠉⠀⠀⣄⠹⠀⠀⠀⠀⣆⠻⠳⠰⠀⣄⢿⠈⢷⠘⠀⡏⠿⢰⠀⠀ ⠀⠀⠃⣾⣿⣬⡰⠀⠀⠀⠀⠀⣷⡈⣿⡜⢻⠀⠀⠀⠤⠶⡿⣿⣿⣿⣿⣿⣿⣿⣬⣠⢀⠀⡤⠑⣌⠳⠉⠀⣄⢦⠳⠉⡄⢳⠈⠀⠀⠀⣄⢻⣇⠻⠀⡄⢿⡀⢿⠈⣿⣿⠀⠀⠀ ⠀⠁⡵⢤⠤⣀⠈⠀⠀⠀⠀⠀⡀⢀⡄⣿⡱⢻⠈⠛⠛⠛⢛⠽⡩⣉⣉⣍⢬⣶⣙⣬⠤⠲⠛⠉⣈⠣⣟⠻⠛⠙⠍⣆⢦⡛⢿⠘⠛⠀⠀⡄⣳⣌⢿⠲⡄⢻⣗⢿⣿⢸⠀⠀⠀ ⠀⠤⠤⠄⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠅⡿⣿⢿⣰⠁⠈⣀⣀⣄⣦⣷⣿⣿⢿⡿⣿⠿⠛⡛⣟⣿⣾⣷⣽⣷⣽⣤⣶⠿⣿⣷⢿⣆⣻⠈⠛⠻⣮⡺⢿⠻⡍⣳⡿⣿⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣾⢠⠀⡀⢀⢀⣄⣤⢦⠶⣛⣈⣄⣦⣷⣿⣿⣿⢿⠻⠈⠀⣄⣦⣿⠿⠛⠉⣎⠻⣄⢿⡈⣤⢠⡀⣄⢠⡀⣷⣾⡹⢿⣼⠀⠀⠀⠀ ⣶⢶⠒⠒⠓⠛⠙⠙⠉⠉⠉⠉⠉⠉⡿⣿⣾⣤⣤⢤⠶⠒⠒⠐⠀⠀⠀⠀⡀⣄⢦⠳⡙⣌⣦⣿⣿⣿⢿⠻⠘⡀⣦⣷⠙⣄⡠⢀⡀⢷⠈⠀⠀⠀⠀⠀⠀⣷⡼⣦⢻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣤⣤⣤⣤⣤⣤⣤⢤⠶⠶⠶⠲⠒⠒⠓⠛⠛⠙⠉⠉⠉⠉⠨⠐⣄⣦⣷⣿⣿⠻⠉⠀⣄⢢⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⡀⢲⠀⡀⣦⠱⠈⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠆⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣶⣤⣤⣤⣤⣶⣷⠉⠴⢯⡟⣾⣶⣴⣤⣤⣦⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⡜⠱⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿ ⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣽⣀ ⠀⣄⢸⠀⠀⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⢀ ⠳⠀⢷⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠉⠉⠉⠉⠁⠉⠛⡷⣸⠋⡠ ⠀⣄⠲⢻⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⣹⣤⣿⢠⠋⣿⣿⢿⣾⡿⠙⠀ ⠀⠀⠀⠀⢆⠑⠀⠀⡀⣀⠀⠀⠧⠿⣟⣿⣿⣾⣿⡶⢁⡻⣆⢺⡄⠹⠄⢸⡇⠹ ⣀⠄⠢⠑⠈⠀⢄⠐⠈⠁⠉⠞⣷⣿⣿⣿⣽⢿⢡⠊⣴⣆⠑⡅⢻⣆⠿⢸⠀⢿ ⠀⠀⠀⠀⡀⣀⠤⠤⠦⣿⢻⠛⣦⣿⣿⣻⣿⡾⣶⣵⠴⠤⡿⣽⣻⢳⣿⢸⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠿⠹⠀⠀⠉⠀⠀⠨⢸⠀⠀⣿⡇⣿⣽⣸⠹⠁⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣾⣟⣿⢽⢈⠀⠀⠎⣢⢷⠀⠀⡀⢶⡖⣠⢰⣄⣤⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⣣⣿⣿⣹⢄⠃⡼⠆⢠⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⣼⣿⣿⣿⣿⣿⠿⠠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣿⣿⣿⣿⣿⣿⠺⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣕⣾⣿⣾⣾⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠋⢠⡑⠿⣿⣾⣠⢀⠋⠀⡀⠄⠂⢁⢄⢔⢌⢃⠈⣁⠐⢂⠀⠀ ⠀⠀⠀⠀⠋⡧⠰⠄⡟⣾⣠⠔⠤⠲⠚⠵⠭⠻⠈⠀⢀⡢⡹⢱⠖⠀⡆⠀⠀⠀ ⠀⠁⠉⡟⣸⡌⠀⢣⣼⢦⠓⡏⡈⢄⠘⠀⣇⣿⢿⠈⠀⠀⡄⡔⠀⢠⠀⠘⠀⠀ ⠀⠃⣿⣿⠀⢠⡄⡇⠚⠀⠀⢡⢈⠁⢹⠋⡿⣿⣿⢸⠀⠀⠀⡀⠸⡆⠀⢰⠀⠀ ⠆⣿⣱⢘⡆⠀⠀⡟⠀⠃⠀⠀⢦⡿⣿⣿⣿⣶⣑⢸⠀⠀⠀⠀⠇⠣⢹⠀⠀⠀ ⠁⢠⣆⢸⠀⠀⠀⣻⠂⢸⠀⠀⠀⠀⣀⠄⠠⣀⠀⠀⠀⠀⠀⠚⠃⡷⣎⡭⠀⠀ ⠀⠀⠄⠐⠀⠀⠀⣧⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠟⡞⠷⡸⣿⢻⣠⠀⠀ ⡀⠀⠒⢷⠀⠀⠀⡆⡇⠀⠀⠀⠀⠁⠉⠈⠐⠋⠊⡜⣉⢙⠿⡷⢠⢸⣼⠀⠀⠀ ⠀⠀⡄⣷⠀⠀⠠⠀⡇⠊⠓⠛⠯⡾⣴⠠⠤⣘⠈⢱⡀⣁⡔⢳⡗⢠⢈⠀⠀⠀ ⠀⠀⠀⡗⢸⠀⠀⡀⡀⡟⣩⣀⠝⠽⠿⢾⠀⠆⡈⡦⢂⠉⠏⢠⣼⠃⢀⠀⠀⠀ ⠱⠀⠁⠀⢿⠀⠀⠀⠀⣣⣌⣢⣬⠝⢤⠤⠠⠸⢡⠀⠀⢇⢧⠀⢸⡰⠀⠳⠀⠀ ⠀⡣⠸⡀⣦⢸⠀⠀⠀⡀⢽⠡⠄⣤⣆⣈⡀⣀⣄⢤⠐⠀⡸⠃⢀⠁⡠⠠⠚⠀ ⠀⠀⢄⡄⠠⡐⠑⠀⠀⠀⡄⢷⢈⠀⠀⡀⡓⠀⠀⠀⠀⠀⢰⠠⠀⢎⢴⢀⠀⡤ ⠀⠀⠀⠀⢄⢝⠐⢌⠑⢄⠑⡀⣦⠺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⡠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠄⠠⢊⠠⢛⠫⡙⢄⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣼⣷⣀⣀⣀⣄⣿⣦⣳⣺⣆⣿⣾⣤⣤⣅⣸⣀⣀⣀⣇⣀⣀⣀⣀⣏⣀⣀⣀⣀⣼⣀⣄⣄⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣰⠉⡟⢿⠟⠻⠟⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⠿⠟⡿⢋⠙⠉⠋⢹⠈⠀⠀⡟⢈⠀⠀⠁⡼⣆⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣠⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢻⠙⡟⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣦⣶⣼⢀⠀⠀⠀⠀⣀⣤⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠆⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⡇⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣦⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠐⡇⠀⠐⡁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠒⡿⣙⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣻⡶⣶⢶⠳⣿⣾⣤⠶⠳⠙⠋⠖⠵⣯⣿⣿⣶⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⢿⣿⣿⠾⠲⡟⣿⠮⠒⠓⠛⠟⡾⣶⣷⣿⢓⠋⠛⡉⢦⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⠋⡿⣿⣛⢿⠿⣿⣿⣿⠿⡽⣨⣷⣽⢶⠿⠛⠟⠿⡶⣿⣯⣶⣕⣿⣿⣿⣿⣾⢷⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠁⠉⠛⠿⣿⣿⣿⣶⣿⣿⣼⣤⣶⣶⣶⡷⣿⣻⣿⣿⠻⠛⠿⡿⣿⣿⣿⣿⢶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣟⢿⠿⠛⠉⠉⠈⠀⠀⡇⣿ ⣿⣿⣿⣿⣿⣾⣠⢀⠀⡀⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣠⣀⣀⣄⣧⣿⣿⣿⣿⣿⣿⣿⣴⣤⢦⡿⣿ ⣿⣿⣿⣿⣿⢰⠀⠀⠀⡇⣾⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣧⣎⣿⠀⠀⠒⡤⡏⣿⣹⠍⣿⣾⣩⣿⠀⠛⠀⣿⣿ ⣿⣿⣿⣿⢿⡮⡘⠧⠀⡇⢡⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢿⠈⢸⣏⠋⡴⠃⡿⣿⣿⣿⣿⣿⢻⣀⣿⠂⠲⠐⣿⣿ ⣿⣿⣿⣿⣱⠰⣌⠙⢿⡠⡇⡏⣿⠀⠦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⡀⣻⢷⡇⣠⢀⠋⣿⣿⣿⣿⣷⣿⣿⣿⠀⣸⠀⠀⠀⣇⣿ ⣿⣿⣿⢻⡶⠀⡇⡜⣻⢷⡄⣿⢀⠀⠀⠀⢄⠙⠀⠀⠈⠀⠀⠀⠁⠊⡤⠁⠈⣇⡿⡇⠀⠟⢧⣿⣿⣿⢀⠄⣷⣿⣿⠀⢸⠀⠐⠀⡇⣿ ⣿⣾⣿⣿⢸⠀⡀⣾⣾⡙⢰⣿⠒⠖⠙⠈⠀⡀⢦⠀⠃⠈⠀⡁⢁⠋⡴⣀⣀⣀⣧⡏⡞⢀⡿⣿⣾⣩⠘⠀⡏⣿⣿⠀⢸⠀⠒⠀⡇⣿ ⣿⢸⠀⣷⢸⠀⠀⢠⣆⡜⡿⢀⠀⠀⠀⣀⣄⠤⠦⠲⡽⢿⠶⣤⣀⠀⠀⠀⠀⠀⠀⣾⢀⠏⣿⣿⢹⣛⠒⠠⢁⣿⣿⠀⢸⠀⠀⠀⡇⣿ ⣿⢠⠀⡄⣿⡀⢀⢀⢧⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡖⢲⠙⠈⠀⠀⠀⠀⠀⠀⠋⢨⠇⣿⣿⣼⣠⠀⠀⠀⢁⡎⢸⠀⢸⠀⠀⠀⡇⣿ ⣿⢠⠀⠀⡄⢷⠈⠀⡇⢺⢎⢧⠙⠀⠀⠀⠀⠋⡼⣠⣉⣍⠯⡙⢦⠑⠈⠁⠉⡯⢀⠀⡾⣿⣿⢠⠉⠒⠶⣤⣁⠉⣸⠀⢸⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⡄⣿⣉⡟⢿⠙⠀⢦⣷⠼⠶⡵⢊⠟⣼⣦⠽⣞⣇⢇⠙⣏⣿⣿⠛⠛⡴⢀⣗⣿⣀⠂⠀⠤⣀⢁⠀⠀⠀⢸⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⣸⣿⣘⣺⣐⣶⣿⡿⣾⣿⣿⣿⣿⢻⠖⣤⠢⣷⣿⣿⣻⣿⣯⣿⣹⠛⠘⡿⣿⠂⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⣿⠁⠎⠒⠀⡀⣷⣿⣿⣿⣿⣽⢀⠀⠀⠈⠀⡀⣇⣿⣿⡄⣏⢀⠀⠀⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⣿⠀⠐⠀⠀⠀⡇⣿⣟⣼⣿⢘⠀⠀⣀⠀⠀⠀⠀⣯⣿⣿⣻⠙⠂⠀⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡟⣇⣿⠃⣿⠁⠑⠀⠀⠀⠀⠙⠛⣏⢹⣀⣿⣿⢸⠛⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣿⣿⢠⡇⣿⡾⣿⠘⠀⠀⠃⣿⢾⣿⣿⠀⣧⣼⣿⢠⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣹⣿⠈⡟⣿⢻⣿⣿⠿⠘⣿⡿⣼⣿⣷⠀⡿⣿⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇⡄⢸⣆⣼⣿⣷⡘⣧⢸⡟⣾⢀⣿⡆⠇⣴⣰⢀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠀⠀⡀⠸⡄⠁⢧⣀⡼⢱⠀⢠⣰⢠⡞⢀⠃⣲⠁⢠⠀⠀⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠓⡈⠀⢀⡄⡄⠀⠀⠀⡄⢀⠁⠐⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⠒⠉⠉⠉⠉⠉⠉⠚⡖⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠀⠀⠀⠀⠀⠘⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣒⢒⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⣿⠿⠿⠿⠿⠿⢿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿

⠀⠀⠀⠀⠀⢀⠢⠉⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⡀⠢⠈⠀⠀⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⠀⠀⣀⣀⢐⠤⠤⠂⠒⠘⠃⠈⠀⠀⠄⠑⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠀⠀⠀⠀⡀⠠⡀⠜⠀⠀⠀⢄⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠇⠀⠀ ⡟⠤⠒⠈⠀⠒⠀⢁⠀⠀⠀⠇⣿⣿⠀⠀⠁⠀⠀⠀⠁⠉⠊⡖⢰⠀ ⣸⠀⠀⡁⢖⠬⠐⠒⠰⠀⠀⡀⣄⣠⠈⠒⠁⠊⠄⡠⡍⣉⠛⠠⠀⠀ ⢀⠀⠀⡄⡰⠀⠀⠀⠀⡀⠀⠤⠠⢀⠀⠈⡅⠻⠈⠀⡀⣦⣿⢿⢸⠀ ⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠁⠜⣀⡀⢂⣮⣠⠀⠂⠎⠟⣭⣷⢿⠸ ⠀⠀⠀⠀⢄⠙⠀⠀⠀⠈⠔⢈⡀⠌⠴⡤⠃⠼⠠⠀⡄⢿⣿⣷⣿⢻ ⠀⠀⠀⠀⠀⠀⣄⣴⢀⢄⠀⡍⣀⠣⠉⠈⡄⣿⠀⠃⠙⣿⢿⡄⣛⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡢⠛⡟⢻⠀⣆⡹⠹⣿⢿⣷⡿⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⡀⣄⣦⣶⣴⣠⢀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠧⢠⣆⣀⡀⣤⣤⡀⣶⠻⠈⠄⠑⠀⠀⠀⡀⢀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠁⠑⠰⠈⠀⠀⢦⠙⠀⠀⠀⠀⠀⢄⠢⡁⠢⠈⠀⠈⠀⠀⠀⣤ ⢀⠀⠀⠀⠁⡾⢁⡰⠀⢸⠀⠐⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⡀⣄⠽⣤⠠⠂⠑⠈ ⠀⠀⠀⠎⣠⠃⠠⠀⠀⢻⠈⡆⠘⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠇⠺⠀⡀ ⠀⠀⠄⢀⠃⢠⠀⠀⠀⣧⢿⠿⣿⡿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀ ⠀⠀⠀⠁⢤⢳⠀⠀⠀⡄⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢢⠈ ⠀⠀⠀⡇⠀⠀⢂⠈⠀⠀⡀⣠⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠳⡈ ⣿⣻⣿⣷⠄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⣀⢀ ⣼⣜⣿⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠂⠠⠁⠟⣶⢐⠀⠀⠀ ⣏⣟⣸⠄⢘⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠋⠉⠋⠛⢟⠶⣤⣀⠀⠀⠀⠀⠀ ⣿⡰⠀⠀⢶⡴⠻⠛⠛⠻⡿⠿⠰⠀⠀⠀⠀⠀⣄⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠉⠀⠀⠁⠔⢀⠀⠀⠀ ⠐⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠴⣀⠀⠀⠀⠀⠂⠁ ⡀⠐⠀⠀⠀⣡⠀⠀⠀⠀⠂⠓⠛⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠔⢁⡰ ⠀⡀⠡⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢥⠟⡰⠀ ⠀⠀⠀⢆⠙⠀⠀⢦⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢋⠿⣾⣠⠀⠀

⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⡉⣉⣻⣙⣿⣻⢈⠀⠀⠀⡄⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣼⠀⠋⠿⣾⣄⣷⠄⣆⢀⣇⣦⣷⣵⠿⠙⣯⠸⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣶⣽⠀⢷⠀⡇⠀⠀⠀⡀⠀⠀⠀⣇⣦⣗⢿⠀⠀⠀ ⠀⠀⠃⡟⣸⣆⠈⡇⠀⡇⠀⠀⠈⠀⠀⠀⠀⡄⠀⣿⠀⡄⡟⣤⢸⠀ ⠀⠀⠀⢱⢧⠀⢡⠀⢰⡄⠘⠀⢰⠀⠀⠄⠀⡄⠀⣈⠀⠸⣸⡏⢀⠀ ⠀⠀⠀⡀⡰⢱⡀⠸⡆⠀⣴⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢃⢣⢸⠀⠀ ⠀⠀⠀⠀⡀⡷⠸⡆⠀⠰⠉⠂⠰⠂⠐⠑⠉⠀⢀⠀⡌⡇⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣧⠑⢳⡚⠐⠤⠤⠤⠤⠠⠂⠁⠂⠡⢱⣾⢀⠀⠀⠀ ⠀⠀⠁⠉⠈⠀⠀⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⣴⢀⠀⠀⠀⠀ ⠀⠟⣿⣿⣿⠹⠀⡆⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⣿⣿⢿⢙⠴⣀⠀⡀⣄⠱⠀⠀⠉⠒⠒⠑⠛⠛⠛⠈⠀⠀ ⡀⣿⣿⣿⣿⣿⣿⣹⠀⠀⠀⠀⠀⡀⠐⡄⠀⠀⠀⠀⣄⣿⣿⣿⠘⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⢝⠩⠉⠈⠄⠤⠶⠑⠀⠀⠀⠀⡏⣿⣿⣿⣿⠹ ⠀⡇⣿⣸⠊⣠⣯⣿⣾⣥⣿⣿⣾⣿⣿⠿⡿⢟⠿⡫⣿⣿⣿⣿⣿⣸ ⠀⠀⣿⠻⢟⠹⣏⣿⣿⣿⠻⣛⠛⢛⣍⣭⣯⣿⣿⣿⣿⣿⣿⣶⣾⢰ ⠀⠀⡄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣄⣹⣬⣿⣿⣿⣿⣿⣿⣾⣈⠐⢀⠀ ⠀⠀⠀⠀⠀⣀⣤⣿⣻⢁⠗⢊⡴⢤⡦⣌⣿⣿⣿⣾⣰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣁⣿⣿⡴⢁⠀⠀⠀⠀⡀⣦⣿⣿⠙⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⡧⣿⣾⣙⠏⢒⠿⠉⠀⠁⠉⠁⣿⣿⡧⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢂⣾⣿⢹⠟⣿⠈⠀⢃⠿⣿⣿⣿⢠⣼⡇⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⡆⠈⡄⣹⣴⠱⣾⡷⣰⣿⣠⠎⢁⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢹⣄⠲⡄⡸⡀⠀⠐⠊⣠⠞⢃⡿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⠘⢢⢌⡐⠆⠥⡠⠒⡡⠟⣾⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠦⡙⠭⡨⠀⠡⡫⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠖⠴⡠⣀⠀⠀⠀⠀⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡔⣤⡠⣀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠒⠛⠒⠤⣀⢀⠀⠀⠁⠚⡤⣀⠀⠀⠀⠀⡀⣄⠦⠑⠀⠀⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⣀⠀⠊⠴⣀⠀⠀⠀⠀⠀⠉⠞⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠱⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⠔⠤⣀⣀⠤⠒⠑⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢣⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠒⠒⠓⡬⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⡀⢹⠀⠀⠀⠀⠀⠀ ⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡄⠘⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠈⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢌⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡾⠁⠊⣠⢳⠀⠀⠀⠀ ⡀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢞⠙⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠇⣽⢽⢄⠛⡄⠘⠀⠀⠀ ⠀⣆⠈⡀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡰⢄⠒⠑⠉⠉⠁⡴⠀⠀⠀⠀⠀⠀⣿⣷⡸⠳⡀⠳⢧⠀⠀⠀ ⠀⠀⢇⠙⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⣧⢝⣷⠻⢦⠈⣢⢹⠀⠀ ⠀⠀⠀⣷⢤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠚⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⡙⡷⣌⠘⣧⠈⠀ ⠀⠀⠀⡄⠑⡗⢧⠹⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠀⠊⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⢿⣛⡚⡐⢹⠀ ⠀⠀⠀⠀⠀⣷⣣⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⡀⡃⢈⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⠿⡟⠀ ⠀⠀⠀⠀⠀⡇⡁⣿⣼⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⠸ ⠀⠀⠀⠀⠀⡆⠸⣿⢀⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠓⠒⠒⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀ ⠀⠀⠀⠀⠀⠀⢿⣸⠀⠀⠀⠃⣸⠀⠀⠀⠉⠊⠗⢀⠀⠀⠀⠀⡀⢦⠈⡄⣿⣈⢄⠲⠑⠈⠀⠀⠀⠀⠀⠁⠞⣠⠀ ⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⣿⠀⠁⠔⣠⢀⠀⠀⠀⡇⠛⠙⠈⠀⠀⡄⠘⣿⢹⠀⠀⠀⡁⣉⠓⠺⠟⡴⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⠑⠉⠃⣿⠴⢀⠀⠀⠀⠁⢻⠒⡤⣤⣶⣷⠻⠈⠀⡄⣿⣿⠉⠛⠿⣸⢸⡸⠏⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⡇⣿⣏⠥⠏⠾⠴⣄⢀⠀⠀⠀⠀⠀⣄⣷⠙⠀⣿⣿⣿⣿⣿⢹⣏⠇⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⢿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⡏⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣸⠀⠀⠉⠉⠠⠀⠉⠈⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣴⠀⠁⠚⡳⣄⣦⢶⠓⡩⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⢻⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣼⠓⠉⡰⠀⡉⠀⠀⠀⠀⠀⠀⠏⣠⢦⠘⠀⣿⣿⣿⣿⣄⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠈⠀⣄⣢⣐⢠⠀⠀⠀⠀⠄⠳⠉⠉⠛⣞⠰⣿⣿⣿⣿⠨⡇⣟⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣸⡿⠲⠓⠙⠁⠈⠀⠀⠀⠀⡀⠤⣤⣀⠃⠛⠙⣽⣿⣿⣿⢿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⠄⡿⣿⡏⣿⢸⠇⣧⣿⣿⣿⢻⢠⡟⣿⣿⣿⣿⣿⣿⣿⣧⡟⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⠹⣿⣿⣿⣿⢸⡇⣾⣶⣷⣿⣿⡯⣿⣿⣿⣿⢸⣷⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣸⠀⣇⣇⢸⣷⢸⠀⡀⡇⣶⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣌⣦⢈⠀⠀⠀⢸⡀⠀⠀⠀⡇⡔⡄⣿⢾⡀⣦⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡇⣎⢀⠀⠀⣿⣷⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⢀⠀⠀⠋⣢⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⢁⡟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠑⠉⠀⠀⠀⠀⠀⠁⠉⠖⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠁⠓⠛⠛⠛⠖⠷⠓⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⠓⠿⣿⣿⣿⣴⠋⡿⢻⢈⠀⡚⠵⡟⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⡆⡀⢘⠀⠉⠒⡿⡶⣣⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣀⢀⣇⣽⣿⢠⡟⣀⡀⣿⣸⠟⣿⣿⣿⣿⣰⣆⣿⣿⣿⣿⠘⠀⠀⠏ ⠀⠀⠀⠀⢣⢫⠉⢸⣼⢀⠏⣿⣿⣿⣾⣤⣠⣀⣀⣀⣀⣀⣀⣀⢀⠀⡤⣶⣶⠓⣸⠀⠁⣿⡼⣤⣤⣿⣾⣠⠀⠁⣿⣿⣿⣿⢿⠟⡿⣿ ⠀⠀⠀⠀⠀⣁⢯⡿⢿⠾⣹⠔⣣⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⠙⡾⣠⠀⠀⠛⣾⣷⠿⠻⡿⣷⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠜⣀⠀⡀⣄⠗⢹⠞⢀⠀⠀⠀⠀⡄⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣛⣿⠚⠉⠛⡴⣀⣀⠧⣾⣠⠀⠀⡏⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠃⢿⠻⠙⠉⠉⠏⣰⠀⠀⠀⠀⠀⠀⠋⠠⣀⣀⣀⠤⠤⠢⠓⠈⠀⠀⠀⠀⣷⢿⣾⢠⠀⠀⠇⣿⣷⠿⠶⣷⣿⣿⣽⢿⠙⡈⣀ ⠀⠀⠃⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⡾⢀⠀⠀⣄⣶⣿⣿⣿⣿⠻ ⠀⠋⣽⣛⣼⣤⣤⣥⣰⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠉⠞⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠛⡙⣿⣿⣿⣿ ⠞⣦⢀⠀⢷⠈⠀⡸⠀⠀⠀⠀⠀⠀⡿⠙⠈⠀⠀⠉⠟⠿⣾⢲⠴⣧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡻⣄⠀⠀⣄⣷⣿⣿⣿ ⢤⠭⡭⣿⡿⢿⡟⠈⠀⠀⠀⠀⠀⠀⣆⣿⣻⣍⣿⣴⣠⠀⠀⠄⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⡟⢠⠀⠀⣦⡿⣿⣾⢳⣇ ⣿⣿⣿⣿⣿⣷⣿⣿⠸⠀⠀⠀⠀⠀⠀⣄⣶⣷⢚⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⣏⡿⣿⠹⠀⠀⣿⣿⢺⡤⣿ ⣿⣿⣿⣴⢁⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣻⡴⣀⣄⣷⣿⠈⠇⣿⣿⠋⠟⣾ ⣶⣻⠋⠏⣿⣿⣿⠿⠿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⣿⣸⠀⠿⠟⣿⡾⢁⡿⣿⣹⣄⠿⣿ ⣿⠿⣾⣤⣠⣀⣉⣟⣿⣟⣿⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣟⠿⣿⣶⣶⢋⣿⣿⣴⡈⢧⡌⣿ ⣿⣿⣿⢿⡿⣬⣤⣤⣤⣤⣦⣶⣷⢿⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢁⠋⡿⣿⣾⣠⠏⣾⠱⣧⡜ ⣝⣿⣿⣿⣿⣿⢿⠴⠶⠽⠭⠭⠠⠓⠛⢹⠉⠉⠉⠋⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣾⣶⣿⣶⣡⠟⣿⣹⠀⡆⢻⣷ ⣿⢿⣎⣿⣿⣿⣿⢿⠲⡏⢚⣄⣤⣠⣉⣉⣞⠤⡤⣦⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢒⠔⣋⣷⢀⡄⢻⠈⣏⣿ ⣿⣮⣿⣿⣿⣿⣿⣿⢻⣇⢹⠀⠀⡇⣿⣿⢈⠀⠉⠋⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡄⠳⡈⣷⣼⢠⠀⠀⠀⡇⣿⣿⣿ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢹⠈⠀⡀⣦⣻⣿⡿⣾⣷⢼⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣦⢿⡘⣷⣽⠹⠀⠀⠀⠁⡟⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣄⣧⣿⣿⢿⠛⠙⠉⣉⣈⢀⠀⠉⠏⣩⠀⠀⠀⠀⠀⠁⠊⠛⠜⡦⣌⢻⠀⠀⣀⣷⣿⣼⣷⠸⠁⠛⣿⣿⣿⣿⣿ ⡄⣷⣿⣿⣿⣿⣿⣹⠋⡯⣸⣧⣿⣶⣶⣿⣿⣿⣿⣿⣿⣴⢁⠉⠛⠹⠰⠀⡟⢻⡄⢹⠀⣆⡜⣿⠹⠱⡄⣆⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⢿⡆⣿⠹⠀⡧⢿⠚⠒⣷⣿⣏⣹⢻⡟⣿⡟⠉⣇⣿⠹⡆⠘⠀⢆⡌⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠻⠈⢳⢿⠈⡄⣹⢧⠀⣇⠸⣷⣹⣧⣌⣿⡞⠘⣇⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢰⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⡋⠛⢛⡟⠟⢿⠿⠿⠟⠻⠛⠛⠉⠉⠀⠀⠀⠛⣻⣽⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠛⠟⡿⣾⣷⣤⣶⣧⣬⣰⣲⣎⣅⣻⣬⣴⣬⣶⣶⣿⠿⡿⢾⢤⡷⣞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⡿⣴⣬⣷⠹⠀⠁⠟⡿⣿⣥⣴⢪⡅⠂⣈⠌⠠⠟⠶⠻⠆⣾⠀⣧⠸⢃⡄⠊⢁⣄⣧⢹⠀⠀⣧⣿⠰⠀⠋⠿⠻⠈⠀⠀⠀ ⠀⠀⠁⣿⢱⢂⢃⡀⣷⡿⣿⣴⣼⠰⢣⡄⠒⢃⠤⢋⠟⣾⢰⠄⣤⣤⣶⢠⡄⣿⠙⠨⢄⡐⡘⠡⣻⠀⠀⡟⣿⢻⠏⣿⣐⣧⣿⠘⠀⠀ ⠀⠀⠂⣿⠐⠥⢂⠡⣂⣤⠟⠶⠛⣉⠉⣈⠰⢁⡿⣾⣀⠁⠋⠞⠿⠷⠛⠉⠀⠀⡀⣤⢿⡙⠄⡇⢸⠀⠀⣆⣻⣦⣿⣼⡂⠐⣿⢹⠀⠀ ⠀⠀⠆⣿⡁⠠⢎⡁⠢⢀⣿⠀⠃⣿⣀⢷⡙⡇⣿⣷⣿⣝⢢⡵⢎⡱⢞⣏⢧⠻⠛⠙⣷⣿⢣⡐⣷⠈⠀⠀⣦⢿⣿⣰⠎⠀⣟⣿⠀⠀ ⠀⠀⠆⣿⢀⠣⢄⡑⠢⢁⣆⠹⡟⣿⠀⡇⢹⡧⣿⣻⣝⡻⣭⡳⡗⣉⠶⢎⡱⡞⢋⡱⣿⣾⣿⠀⡀⣧⠛⠀⠀⣿⣱⠒⢆⡈⡗⣿⠀⠀ ⠀⠀⡇⣿⡉⠓⣂⠙⢡⢠⠐⣿⣀⠀⠀⡀⢻⡄⣿⢿⡿⠿⣛⣽⡻⣭⡷⣎⡳⠶⢏⡿⣾⢎⣤⠳⠉⠉⣿⠋⡿⣤⡁⠥⢊⡙⡇⣿⠈⠀ ⠀⠀⡿⣽⡘⡸⢯⡐⣸⡵⠋⣽⢿⠛⠚⠶⢃⠡⣆⣿⣹⣄⣤⣦⣤⣶⣶⣶⣶⣷⣿⣾⣜⢌⡄⠉⡛⣿⡿⣿⠟⡛⣩⡲⢎⢣⡤⣿⢹⠀ ⠀⠇⣿⢭⡣⢟⢫⡿⣿⣾⣴⣤⣤⣤⣶⣿⠿⠻⡉⡆⣷⢿⠙⠀⠀⠀⠀⠁⠟⣿⣷⣄⠃⠟⣿⣴⣤⣀⣀⣀⣄⣦⣷⢿⣿⢺⣙⣧⣿⠈ ⠀⡿⣾⢋⣴⡟⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⢿⡻⣥⣾⢿⠿⠻⠿⣿⣼⣞⠣⡿⣿⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢾⡏⣎⣿⢸ ⠂⣿⢾⢳⣌⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⡜⡿⣋⣿⣷⣳⡟⢯⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢡⣷⢻ ⠄⣿⢽⢢⡜⣗⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢻⣾⣃⣿⡾⢳⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⣑⡯⣿ ⡀⣿⢻⢄⡌⡄⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢛⣦⣿⣌⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢺⣱⠸⣿⣿ ⠀⣿⣿⢊⡑⢆⡈⣷⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣷⣿⠠⣷⢍⣿⣿⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣼⣔⡨⠇⣿⢸ ⠀⡇⣿⢞⡈⠴⠊⢁⣬⣿⢿⠙⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⢸⡇⢰⣿⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠁⠛⡿⣾⣬⡆⠑⢀⡿⣿⢀ ⠀⠀⣷⢿⡘⠌⢌⠢⠑⠤⣌⣶⣿⠻⠙⠈⠀⠃⡿⣿⣿⣿⣿⣿⣿⢸⡟⠠⣇⣿⣿⣿⣿⣿⣿⠀⠁⠛⡿⣿⣷⣣⠠⢘⢤⡘⠏⣿⣸⠀ ⠀⠀⡀⣿⢿⠌⡐⢆⡉⠢⢌⡑⡂⣵⣾⣿⠿⡟⣿⣿⣿⣿⣿⣿⣿⠰⡇⡐⢉⣦⣿⣿⣿⣿⣿⠿⣿⣴⣫⠟⣶⠡⢂⡐⣘⠏⣿⣼⠀⠀ ⠀⠀⠀⡀⣷⢿⡉⢄⠊⢄⡙⠠⢢⣂⣤⡾⣷⣿⣿⣾⣿⣿⣷⣾⣧⢹⡀⢳⠙⠠⡡⣧⣼⣼⣽⣫⠿⡴⣰⠰⢄⡉⠟⠾⢿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⡀⣧⢿⡹⠂⢁⣐⣦⢷⠻⢙⡉⠄⡠⣜⣤⣴⣭⣦⢈⠠⣷⠈⠀⡀⣾⠃⡀⣥⣌⣰⣐⠤⡉⠟⡾⣴⣢⢁⡿⣿⣰⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⣄⣷⢿⡙⠂⢠⠑⣠⣦⣶⣿⠿⠛⣉⠌⠂⠔⢊⢡⡄⢻⠀⠃⣼⢈⡐⠰⡉⠟⡿⣾⣶⣁⠢⣁⠏⣿⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⢿⡙⠨⡐⢌⡈⡑⣂⣌⣮⣷⢿⠻⢉⡘⠈⣷⠀⡷⢍⡉⠟⣿⣼⣴⢈⡑⠆⡉⠟⣿⣾⣠⠀⠀⠀⠀⠄⠀⠄ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⢿⠛⣉⠠⠴⠒⠆⢈⡠⣷⣹⣿⠄⡆⠳⣾⣾⣓⣽⠢⢄⠡⡙⠟⡿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠻⢛⠛⣉⠉⣉⣉⠤⢉⡉⢍⢋⠻⢛⠿⣿⣾⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣴⣴⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠄⠂

⡄⠸⡌⠀⠀⠀⡚⠴⡯⢡⡴⡀⠎⣒⣎⢷⡸⠀⢸⠀⣱⠸⡆⠈⢡⠇⡇⢸⠀⠀ ⠀⣾⠀⠀⠀⠇⣣⢁⠱⡰⠀⠟⣐⠋⣿⣿⢸⡖⢲⠈⡇⡞⠈⢵⡯⡷⡇⢸⠀⠀ ⠀⢠⠀⠀⠡⣿⡇⡜⡜⠀⡟⣹⠖⣤⣀⢈⠀⠉⠊⡑⣦⡌⢿⡎⣗⣏⣿⠏⠀⠀ ⠸⠀⠀⠃⡎⡇⡞⢀⠀⡏⣺⠈⠀⠀⡀⢡⢔⢀⠀⡀⠸⡀⡢⢻⠀⡄⣿⣿⠈⠀ ⢠⠀⢠⢻⢱⢳⢠⠀⠁⣼⢌⠀⠀⠃⡽⢁⠀⠀⠀⠋⢳⠘⠀⡀⢧⠘⡆⣻⢸⠀ ⠀⡆⠇⣿⡽⡸⠀⠀⡿⢀⠀⠀⠂⣶⣒⢒⣒⠒⠒⠒⣖⢶⠐⠀⠀⢆⠌⣿⢻⠀ ⠀⢸⡇⢷⣿⢀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⢣⣇⣿⠈ ⠊⣤⣶⣇⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⠇⠙⡇⠘⣴⢸ ⠔⠈⠈⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⡕⠪⠒⠝⡘⡇⣿⡇⢳ ⠀⠰⢳⡈⠀⠀⠇⠀⠏⡤⣀⣁⣍⢬⠤⠱⠀⠀⠀⠄⠁⢻⠿⠷⠈⣧⠛⣿⠸⣧ ⡁⣐⢋⢸⠀⠀⡇⡿⢨⠀⠿⡼⢅⣿⠿⣿⢳⠇⣠⣀⣳⣇⣮⣿⣶⣼⢠⡉⢸⡇ ⠔⡠⡇⢳⠀⠛⡆⣦⣽⣦⣶⣶⣶⣿⣭⣶⠀⣵⠸⠀⡀⢣⣻⣸⠘⠀⠋⢸⢸⡀ ⠸⠀⡇⠀⠇⡀⡁⣄⡣⠻⠉⠉⠉⣿⢻⠋⠀⡆⢸⠀⠀⡀⡻⢿⢼⣠⢇⢠⢸⠀ ⢠⠀⡇⠀⠘⠀⠁⠀⠀⢆⡜⡑⣀⣸⣵⣦⢠⠀⢸⠀⠀⠀⡀⢸⠀⠃⢠⡏⢠⠀ ⠀⠈⡇⠀⠀⠀⡇⣛⢶⠈⣄⡜⠘⢸⡇⠀⠀⠀⢠⠀⠀⠀⠀⢰⢻⢡⠎⣄⠀⠀

⠀⠀⠀⠀⠀⠆⢿⢈⠀⠀⡀⣀⣀⣄⢠⠀⠀⠀⠀⠀⠄⢠⠀⠋⡖⣠⡀⡏⣿⣉⠶⠛⠈⠀⠀⠀⠀⠀⣄⠲⠙⠀⠀⣄⣦⠙⠀⠀⠀⣀⢷⠈⠀⠄⠈⠀⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢧⠉⠈⠀⠀⠀⠀⠀⠃⠈⠀⠆⠙⠀⠂⡴⢀⠁⠞⡤⢀⡏⣻⣯⠷⢛⠈⠀⠀⠀⠀⠀⠀⡀⠄⠶⠿⠿⡛⢿⠛⠉⠈⠀⣦⠙⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣧⣜⠦⠶⠶⠶⡶⣑⣭⠻⠉⡀⢷⠀⠀⠞⣠⠀⠃⠞⣳⣿⣵⣛⣉⣤⠷⠿⠿⠶⠶⠶⠲⠒⠙⡈⣦⡹⣄⣷⣿⣿⠻⠈⣆⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠶⣝⠻⠈⠀⠀⠀⠀⡀⢦⣙⢬⠶⠛⠉⠁⠋⡾⣠⢋⡾⢂⡾⣿⣿⢿⠿⠉⣁⠈⠀⠀⠀⠀⠀⣄⢷⣟⢻⠀⣧⣿⣿⢿⠈⡄⢷⣏⠈⡄⠹⠀⡀⢳⠈ ⠀⠀⠀⠀⠀⡀⢤⠶⠙⡉⣈⣦⠿⠙⠀⠀⠀⠀⡀⣄⠦⠲⣙⣯⣻⠛⡾⣠⠀⡁⠟⣴⣀⣿⣠⣄⣦⣿⣹⢬⠦⠲⠓⠉⠈⡆⣷⠸⠀⣧⣿⣿⢺⠈⡄⣿⢰⠈⡀⢣⠈⡀⢦ ⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣶⣾⣶⣷⣿⠻⠉⠀⠀⠀⠀⠀⠀⣅⣿⣠⠀⠀⠃⣼⢀⠁⡞⣠⠀⠀⠀⣄⣷⢿⠀⠀⠀⡀⣄⢷⣿⣿⠘⡀⣿⣿⢿⢻⠛⡿⣼⣤⣤⣦⣤⢤⠷ ⠀⠀⠀⠀⡀⣃⣿⣴⣤⣤⢦⠒⠓⠀⣀⣄⣷⢿⠛⠀⠀⠀⠀⡇⣼⠀⠀⠀⡟⠙⠟⣠⠀⠀⢧⠙⠛⠙⠛⣿⢠⠀⠀⠀⠀⠀⣷⣿⢠⠀⡇⣿⣿⣼⢀⡆⠰⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣇⣿⢷⠛⣷⠈⡟⢸⠀⠀⠁⣿⣿⢠⠀⠀⠀⣧⣾⣥⣯⣾⣠⠀⠀⠀⠀⠀⠀⡀⣷⠸⠀⡇⣿⣿⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣿⡇⣼⣷⢿⣿⠘⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⣄⣡⢀⠀⠀⠀⠀⠀⠀⠀⠛⠉⡏⢹⠀⡇⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢻⡇⣿⣿⢻⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⠁⠼⣤⣠⣀⢀⠀⣏⣿⢀⡇⣿⣿⣿⣷⢿⠛⠙⠉⠈⠁⠉⠁ ⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠀⣦⣿⣿⣿⣿⠈⠀⡄⣿⣿⢸⠛⠴⣤⣤⣤⠻⠀⠀⠀⡷⠉⠛⠿⠻⠞⣴⣧⢿⢀⡇⣿⣿⣿⡇⣿⣾⣿⣾⣿⣿⢸⠃ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠙⠟⣾⣆⢻⣦⢻⠀⠀⡇⣿⣿⢹⠉⠿⣿⢞⣠⠀⠀⠀⠀⢛⣛⠒⠐⠀⠀⣿⣿⠀⡇⣻⣿⣹⡇⣿⢸⣟⢿⡟⣿⣿⣠ ⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⢀⠀⣦⠛⣧⠹⠀⠀⣿⡻⣀⣀⢒⠄⠤⠠⠀⠀⠀⠀⠁⠋⠛⠚⠐⠀⣇⣸⠀⡆⣧⣿⢠⡇⣿⢃⣿⣆⢿⣿⢧⠘ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠘⠀⠀⡇⣴⠘⠀⠀⣦⢻⣷⠙⠀⣆⣿⢻⠁⠋⠛⠛⠙⠈⠀⠀⠟⣶⣤⣀⠀⠀⠃⣿⢸⠀⠁⣿⢸⠀⣿⢰⠀⠉⠟⣿⢸⡄⢻ ⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠀⠀⠀⡏⠻⢀⠀⠀⠀⣄⣿⣷⠹⠀⡀⣷⣿⣽⣳⣿⣛⣈⢦⠿⡛⢯⠙⠀⠀⠁⣿⣾⢀⠀⡟⣸⠀⡇⣿⠛⡾⣤⢀⡏⢰⠀⣠ ⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠏⣼⡀⢷⠘⠀⠀⠀⡀⣷⣿⠻⠀⠀⣄⣷⣿⣿⣻⣦⠻⣯⣿⣿⢿⠈⠁⣿⣿⢰⠀⡇⣽⠉⠟⡾⣠⢀⠀⠁⠏⣸⠀⠀⠿ ⠀⠀⡇⢼⠀⠀⠀⠁⠉⠉⠚⠖⠶⣿⣤⠦⠤⡿⣰⠀⠀⠀⣦⠻⠈⠀⠀⠀⣦⣿⢿⠙⠀⠀⣀⣀⣦⠹⡀⣷⣿⣼⡀⣦⡿⣿⣰⠁⠋⣿⣾⣤⣀⠀⠀⠀⠁⡟⣿⢻⠀⠀⣾ ⠀⠀⡇⣿⠋⠾⣤⣠⣸⠀⠀⠁⠉⣿⠀⠁⠞⣠⠀⠀⠀⠀⠋⠀⣀⠀⠀⠀⠀⡀⣶⣿⠻⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⡏⣿⣿⡶⣴⣀⢀⠀⠀⠀⠀⠀⠏⣴⣏⣿⣾⠀⠃⢿ ⠀⠀⡀⣾⣀⠀⠀⠏⢺⠗⠼⣠⣞⣼⠁⡾⢀⠀⠀⠀⠀⠏⣸⠀⠀⠀⠀⢦⠻⠈⠀⣇⣮⢶⠙⠉⠉⠉⠉⠉⠉⠉⠟⣶⣤⢀⠀⠀⠀⠀⠀⠀⠁⠋⡶⣡⠟⣰⡇⢰⠁⡟⢸ ⠀⠀⠀⢡⠛⠀⡇⣠⠃⣸⠀⡞⢀⢧⣼⠀⠀⠀⠉⠟⡶⣠⠀⠀⠀⠀⠀⠀⡀⣄⠶⡶⢙⠀⠀⣀⣀⣒⣀⣂⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⢋⠞⣴⢀⠇⣰⠁⡟⣠⢀ ⠀⠀⠀⡄⣇⠸⡄⠀⡜⠀⡞⢠⠃⡿⢺⠀⠊⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⢷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠶⣤⢀⠀⣀⠀⠀⠀⠀⠁⡿⢸⠀⠁ ⠀⠀⠀⠀⡇⢸⠰⠂⠰⠆⢠⠀⣧⣸⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣄⠦⠙⠉⠉⠉⠉⠉⠛⠛⠶⡴⣀⠀⠀⠀⠀⠀⠉⠈⠁⠋⠾⣿⣸⠀⠀⠀ ⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⡄⢲⠉⣏⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠓⠉⠩⠀⠀⠀⠀⠀⣀⣉⣯⣶⠛⠉⠉⠈⠀⠀⠀⠀⠀⠋⡿⣾⣴⣠⢧⠛⣼⠀⠀⠀⡀ ⠀⠀⠀⠏⠿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⣷⣌⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠒⠶⡤⣀⢀⠀⡿⡴⣈⣄⢤⠤⠤⠧⣽⣀⣄⢶⠻⠈⠀⣏⢸⠀⠀⠀⠀ ⠀⠀⠃⣿⣿⢿⠙⠀⠀⠀⠀⠀⠉⠞⡴⣀⠀⠀⣀⠶⡙⣉⢤⠶⠶⠒⠛⠒⠒⣿⠞⠶⡶⣠⣀⠀⠀⠉⠋⠶⡤⣀⣟⣤⣳⢬⠳⠯⠈⡆⣄⢸⠀⠀⡀⣄⣾⣼⢣⠀⠀⠀⡽ ⠀⠃⣿⣿⣼⣶⣿⢿⠿⠿⡾⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠶⠒⠉⠉⠉⠉⣯⠉⠉⠉⠉⠚⠶⡤⣀⠀⠀⠀⠀⣿⠈⠀⢿⠀⣧⣦⢻⠈⣇⠀⠀⠃⡿⣿⢰⡀⢀⠀⡀⣀ ⠃⣿⣿⣿⢹⠛⠿⣻⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣟⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⢻⠀⣇⠀⡇⠀⡇⢰⡇⠀⠏⣰⣏⢰⠀⠀⠀⠀⠀⠀ ⡆⣿⣼⠀⣏⣿⣾⣧⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⢯⠙⠈⠀⠀⠏⣠⠀⡀⠀⡆⠀⡄⠀⡟⡼⢁⡟⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⢻⡟⣿⣽⠛⢳⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠹⠀⣄⠶⠟⣴⠀⠀⠀⠀⠀⠀⠐⡇⣻⠟⣴⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣀⣀⠀⠀⡏⠼⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⣤⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠳⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢸⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⡴⢀⠀⠀⠀⠀⣁⣭⠿⠛⠛⠛⠛⠛⠛⠛⡿⣷⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⠛⠛⠛⠟⣿⣽⣧⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣸⠀⠁⡋⠟⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠳⣟⣿⢿⠛⠙⠉⠀⠀⠁⠋⠛⠛⠛⠛⠉⠉⡟⡶⣿⣿⢬⢃⡿⢛⡟⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣿⡙⢂⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣀⣦⠧⣿⣿⣤⠀⠀⠉⠉⡈⣤⣶⠙⠀⠀⡄⣿⣧⢿⣷⣼⣠⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣶⢷⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⣿⣰⠀⠄⣤⣀⢀⠀⠀⠀⠀⡀⣄⣤⠦⣿⠻⣷⣿⢹⠀⣿⣿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠴⣤⣃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣤⣦⣿⣿⣿⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠋⠴⣠⢀⠃⠀⠀⣾⠁⠛⠟⢿⠾⠶⠶⠛⠙⠀⠀⠀⠋⠟⣾⢿⣿⡛⠙⡟⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⡤⢀⠀⠀⠀⡇⠁⡿⢿⣿⣿⣿⣿⣷⢿⡷⣿⣿⢿⠟⣿⣿⣿⣿⢉⣟⣿⣿⣿⢠⣼⣾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡟⣼⣟⣿⣿⣿⣼⡏⠉⢟⣿⣿⣿⣿⣿⣿⣿⣄⣿⣠⣿⣾⣏⣌⡇⢿⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⠃⣿⢀⣳⢸⡇⣇⢰⣼⢿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠼⣿⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠁⠋⣾⢁⠟⣰⠀⣸⡄⠀⣿⣹⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣟⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣷⣿⢉⣿⢸⡟⣄⢋⡿⣰⠀⡆⢀⠘⠀⣌⡁⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⡿⣿⣿⣿⠟⣸⡶⣆⣠⠀⠀⠀⠇⢰⠀⠁⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡀⣄⢦⠛⢈⣏⠻⡟⠭⢻⠉⠙⣉⠤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠁⠋⠖⣩⢛⠟⠴⣤⣀⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀ ⠠⠀⠀⠀⠀⠀⠃⠛⠙⡏⣶⣶⠙⡝⢤⣤⣤⠤⡦⣶⣶⠶⠶⡶⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠾⠴⠤⢧⣿⣾⣶⣴⣤⣠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀ ⣄⢿⠿⡿⣿⣽⢀⣧⣿⣽⠮⠛⣿⣼⠲⠙⠈⠀⠀⠀⠀⠀⠀⠁⠚⡀⣄⢦⡛⣉⣤⣦⣶⣿⣭⢉⠟⡽⣩⣈⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⡄⢀⣀⣤⣼⢆⣻⣿⣿⣿⣸⣤⣦⣷⣾⡶⣿⠿⠙⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⣉⣙⣭⠿⠿⡲⣙⡿⣻⠛⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠉⠀ ⠀⠄⠻⠀⢸⠀⣷⢧⡿⣿⣽⠳⠈⡀⢦⠘⠀⣦⣿⢻⠀⠃⣰⠀⠀⠀⠁⠍⣫⠛⠉⠉⠀⡀⣄⡶⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣱⠋⡴⢀⠉ ⠀⠀⣇⢿⢛⠀⠃⡀⣿⣿⣿⡻⣿⠹⠀⣿⢸⠀⡆⣿⠀⣀⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⡤⣀⠀⠀⠀⠁⠾⣠ ⠀⠀⡇⡀⣦⢹⠀⠀⡂⣷⣿⣿⣿⣿⠿⣿⣿⠉⠀⣿⠀⠸⠀⠀⠋⣿⣿⣿⣤⣠⣀⠀⠀⠀⣀⣀⣀⢤⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⡿⣩⣀⢉⣭⢀⠀⠀⠀⠁⠋⠖⣠⠀⠀ ⠀⠀⠀⠀⠏⣿⢳⠙⠀⠀⣄⣿⣿⣿⣿⣿⣿⣽⢀⣿⠀⢧⠁⠏⣿⣿⣿⣤⡤⣋⣀⣀⣀⢄⠤⠤⠤⠲⠓⠛⠛⠛⠘⠀⠀⠀⠀⠀⠃⡟⣿⣘⢧⠙⣀⣀⢤⠧⣬⣾⠹⠀⠀⠀⠀ ⠀⠀⠀⠆⣿⣿⠰⣆⠉⡀⠹⡀⣿⣿⣿⣿⣿⣿⠀⣿⠀⡿⡟⣿⣾⣠⢀⠀⠀⡠⢄⠵⠿⠴⣤⣀⣋⣾⣶⢀⠀⠀⠋⣗⣿⣿⣸⣆⣿⡟⣿⢿⠀⣧⢻⠀⠀⠀⢆⣇⣇⠘⠀⠀⠀ ⠀⠀⠀⠀⣧⣿⢹⠛⠛⠛⡟⢿⡞⣷⣼⣾⣿⣰⠀⣤⡦⣿⣾⣠⠀⠀⠀⠀⠁⢡⢟⣰⢀⠀⠐⡤⣉⠚⠒⠴⡤⣤⢀⠘⡀⣷⣿⡿⣿⣿⣿⣿⠀⠳⣽⠸⠀⠀⠀⣿⡟⢿⠀⠀⠀ ⠀⠀⠀⠀⡀⣧⣿⣿⣼⣷⣿⣿⢻⡿⢋⣿⢹⠉⠉⠉⠉⣼⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠋⠔⣡⣿⣿⠈⠀⠀⠀⠀⠤⠲⠙⣏⣿⣿⣿⣿⣿⠘⡇⡏⣿⠀⠀⠁⣿⢸⣾⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⣿⣿⣿⡏⣽⣿⣿⣾⣿⣶⣿⣿⣾⣣⣷⢸⠀⠀⠀⠀⠉⠈⡇⣿⠃⠶⣠⠀⠁⡿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⣦⣿⣯⣿⣿⣿⢹⣿⣸⣿⢸⠁⡿⣴⡇⢰⠀⠀⠉ ⢿⠈⠀⠀⠀⠀⡄⣼⣿⣿⣿⣿⣿⢸⢹⠀⡏⣿⢠⡿⣼⠀⠀⠃⠕⡨⣀⠀⡆⣿⠛⠉⠛⠿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⡀⣤⣠⣧⣿⣤⣦⣿⣿⢿⡟⣼⠀⡴⠋⠚⡤⣤ ⣿⢿⠘⠀⠀⠀⠀⢿⣟⣿⣿⣿⢼⢘⣿⣤⣦⢠⡞⣿⢠⠁⠋⡾⣠⣀⠀⠀⠃⣶⣷⣿⣿⣿⣶⣴⣤⣩⣎⢲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⣿⢹⠈⣧⣿⣿⣷⠐⠃⡾⣀⠀⠀⠀ ⣿⡀⣧⠹⠀⠀⠀⣦⣿⣿⣿⣿⢈⣿⢩⠘⠀⡏⣯⣾⠟⣷⣿⢀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣄⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠙⣇⣿⣿⣺⣆⣿⣿⣿⣿⣿⠛⣰⠀⠀⠀⠀⠀ ⣿⠈⡄⣿⠹⡄⠈⠀⠃⡆⣿⣿⢸⣠⣆⣸⠃⣷⣿⢿⢰⡟⣰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡉⣿⣿⣿⢿⠿⣿⡿⣿⣿⡿⣿⢿⠘⠀⠀⠀⠀ ⣿⢸⠀⡆⣿⠹⠀⠀⠀⠀⣆⣿⢸⠇⠀⢿⡿⣼⡇⣿⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠛⠟⠿⣶⣶⣶⣤⣤⣧⣿⢀⠀⡖⣷⣿⣿⣿⣿⣿⢹⣿⡄⣿⠘⠀⠀⠀ ⣿⣿⠀⠀⣧⣿⠘⠂⠀⠀⠀⣧⣿⡌⠀⣧⣿⠀⡇⣿⢹⠋⠛⠛⠛⠟⠿⠿⠿⡿⣿⣿⣿⣶⣤⣷⣿⣠⣀⣀⠉⠋⠀⠀⠀⠀⡤⣤⠀⠀⠉⡏⣿⣿⣿⣿⣿⣿⣿⠀⡇⣿⠀⠀⠀ ⡈⣷⢹⠀⠀⣷⣿⠫⠀⠀⠀⠀⣷⢹⠀⣿⣾⠀⡀⣿⣿⣿⣿⣶⣷⣿⣾⣠⣀⣐⠀⡇⣿⠀⠀⠀⣦⠐⠀⡇⣴⣀⠀⠁⠈⠀⠃⠿⠘⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀⣿⠸⠸⠀ ⢉⠛⣞⢿⠙⡄⣿⢻⠀⢠⠀⠀⡄⣻⠀⣧⠸⠀⠃⣿⣾⢀⠀⠀⡀⣀⢀⠀⠏⠸⠀⡇⣿⠀⠀⠙⠀⠀⠀⠇⡾⢰⠀⡀⢠⠀⡇⣿⢻⠛⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢹⢸⠀ ⣷⣘⠅⠀⢀⠘⡀⣿⢱⠀⠀⠀⠀⣇⠸⡇⣿⡿⣤⣤⢠⠀⠀⠀⠁⡿⢚⠃⡿⢰⠀⡆⣴⠀⠀⣿⠻⠈⠉⠉⠋⠛⠿⠿⣿⣿⣿⣽⣩⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡆⡇⣿⠈⠀ ⠀⠀⠤⠤⢁⠨⠂⡀⡰⠐⠃⠀⠀⡀⣿⡏⣶⣷⢳⠛⡟⠀⠀⠛⡬⢠⠀⣿⢁⠉⠉⠋⠛⠛⠿⣿⣿⣿⣷⣿⣴⣯⣿⢹⠁⣿⣿⣿⠈⢳⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠿⡿⣼⢸⠀ ⠶⠶⠶⠶⠷⣿⠻⣹⠈⠀⠀⠡⠱⠈⡆⣹⡀⠀⣿⣿⣿⠉⠋⡟⢿⠿⡿⣿⣿⣿⣾⣶⣿⣴⣠⣣⢘⠀⡇⣿⠀⣷⣿⣿⡽⣍⣟⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣤⣷⢛⠉⠓ ⣤⠲⠙⠉⠀⡀⣿⣿⣽⣤⠿⠿⡀⢷⠐⣧⠘⠇⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⢙⠉⠉⠛⣿⢼⠦⣿⢿⠷⡆⣿⣤⠩⣿⣿⣿⣶⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣷⣾⣤⣦⣶⢲ ⠀⢹⡀⣄⢷⠙⢀⣼⣮⢿⡘⣷⣿⣻⢿⡿⣿⡝⣷⣴⣧⣿⢿⠘⠈⣇⣿⣿⣟⠘⡄⠸⣿⢿⠀⣿⣿⡿⠀⣿⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣟⣿⣼⠀⠀⠀⠀⠀ ⠀⡄⠘⠀⡠⣷⢿⠛⡈⡀⢷⠉⣧⣿⣿⣿⣿⣿⡈⢆⡌⣷⣿⣿⣿⡻⣿⣿⣿⣿⠉⢹⣿⣿⢸⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⡟⣿⣠⠁⠈⠀⠀⠀⠀ ⠀⠀⡄⠳⡀⡠⣷⣿⢿⠿⠉⡈⠁⣏⣿⣿⣿⣿⢿⠀⠟⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣾⣳⠛⡿⣴⢫⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⠳⡀⣧⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣡⣉⠛⠿⡿⣱⣟⣴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠳⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣿⠿⣿⣿⣿⣾⣿⣲⡙⢎⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⢿⡟⣿⣾⣤⡟⣏⣿⠟⣿⣿⣿⣿⣿⣿⣿⣻⣴⣠⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣟⣻⣉⣍⣿⢻⣉⣿⠻⣿⠿⠻⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠖⣶⠶⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣻⠀⠀⣄⠷⠝⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣡⠋⠞⣴⣤⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⡀⠅⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⢸⠀⠀⡆⠀⠀⠀⡰⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⢠⢐⠄⠠⠀⠀⠄⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠛⠈⠀ ⠀⠟⣸⠀⠁⠟⠿⠽⠺⠐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣷⣿⣿⠻⠉⡛⣿⠨ ⡄⣄⣤⣤⣀⣀⣀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣉⣊⣀⢀ ⠀⠀⠀⠀⠀⠤⠶⠷⠛⠿⢩⠈⠀⠀⠀⠀⠀⠀⠀⠏⠛⠿⣶⣤⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣠⢀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⠘⠀⡇⠼⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⢸⠁⡟⢠⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣤⣤⣤⣤⣦⣶⣷⣿⣿⠉⢾⣶⣅⠻⡟⣿⣿⣿⣶⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣈⢤⠤⣠⣉⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⡀⢳⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⠀⡇⢹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣽⢈⠀ ⠀⡄⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠤⠀ ⠀⠁⠀⣿⠘⠀⠀⠀⠀⠀⠁⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣸⡄⠀⠋ ⠳⠈⠀⡇⣿⠙⠉⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠁⠈⠀⠀⠀⠀⠉⠀⠀⠀⠁⠉⠋⠟⡵⣿⢀⠁⠞⣠ ⡀⣦⠻⠈⣤⢹⣀⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣻⣷⡿⣻⣟⣻⣤⣀⢻⡿⣿⣿⣼⢋⣾⣋⠞⣠⢀⠀ ⠀⠀⠀⣄⠶⣟⠹⠀⠀⣄⠢⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠿⣿⣿⣼⡈⣀⣿⣾⢀⠁⠟⣿⣿⣿⣿⣿⣿⣴⣿⢿⠻⠈⠀ ⠀⠀⠀⠀⠀⠀⡀⢯⠈⠀⠀⠀⡀⣀⣤⠤⠤⠶⠒⠒⠒⠑⠟⡾⣯⣟⣿⣿⣿⣿⢿⢿⠿⣮⢀⠟⣬⣶⣿⢉⠀⣿⢘⠀⠃⣿⢀⣧⢻⠀ ⠛⠉⠀⠀⠀⠀⠀⣀⣀⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⢿⣿⣿⣿⣿⣿⣿⣀⣿⣴⣤⠁⠟⣿⢹⡀⡢⣬⠹⡆⣿⠈⠁⣿⠀⡄⣿⠾ ⠀⣀⣄⢤⠶⠙⠀⠀⠀⠀⡀⢧⠙⠉⠉⠉⠈⠀⠋⠟⣿⣿⣿⣿⣿⣾⣿⣹⣯⡿⣲⠀⠁⡿⣵⡁⣿⠙⠀⡇⣿⠘⣇⢿⡿⣿⠀⠀⣿⢿ ⠀⠀⠀⠀⠀⡀⣄⢤⠶⠓⠙⠉⠉⣉⢋⠛⣿⣭⣀⠀⡿⣿⣿⣿⣿⣿⣷⣿⣭⣯⡻⢟⣿⠛⡙⠉⡉⡯⣿⣟⣿⣷⠘⣧⣷⣿⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣆⣿⣿⢿⠿⡾⣠⣷⣿⣿⣿⣿⣿⣿⣾⣶⣶⣤⣋⡴⢀⣀⣀⣿⣿⣻⣿⢿⣮⡟⣷⣷⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣬⣷⠻⠿⠙⠀⠨⠀⠀⠀⠀⠀⠈⠂⠗⡤⢸⠀⠀⠀⠇⣿⢸⣿⣿⣹⣾⣿⣧⡟⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡛⣷⣿⣿⠻⣈⠁⠚⠴⡤⣀⠀⠐⡿⠛⢸⠀⠀⠀⠀⣷⢻⣦⣧⣿⣿⣿⡄⣿⢻⠟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣶⢿⣯⣿⣿⣼⢉⠈⠀⠀⠀⠁⡞⣦⡷⣿⠀⠀⠀⠀⡀⣦⣗⠿⣶⣠⡟⠀⡀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡀⢾⣿⣿⣿⣿⣾⣶⣙⠀⠃⠟⣠⠁⡿⠀⡉⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⠀⣿⣿⣿⣿⣿⣿⠙⡉⢏⣿⣼⠀⣁⡎⠀⡀⣀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠇⣾⣿⣧⣾⣿⣿⣿⡿⣿⣿⠿⠾⠠⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡘⢳⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠋⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢼⠲⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣦⣿⣿⣿⣿⣿⣿⣿⣽⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡙⣮⣷⣿⣾⣵⣺⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡇⣻⣮⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⢀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⡀⣠⣀⠉ ⠀⠀⠀⠀⡇⣛⢚⠒⣟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡀⣧⣿⣿⣿⣿⣿⣿⢽⡼⠀⠀⠀⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠷⠓ ⢠⠀⠀⠞⠺⡇⣾⢶⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠙⠀⣿⣿⣿⣿⣿⣿⣿⢺⠒⠒⠓⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⢁⢰⡄⢿⠶⡻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣾⣵⣾⣡⢟⣴⣀⠀⠏⡴⣀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⡶⠴⣫⠖⡿⢾⡖⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣁⠞⣠⠃⡿⣠⠀⠀⠀⠀⠀⠁⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴ ⠒⡠⢊⠔⣀⠏⢤⡧⢀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠁⠒⡠⢀⠀⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⡄⠀⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠀⠀⠀⠃⢰⠃⣿⣾⣶⣶⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣽⠀⠇⠀⠁⠀⠀⠀⠀⠀⣿⣿⣴⣥⢤⠰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⡸⠀⢛⠒⠙⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡄⠘⡄⠹⠀⠁⠉⠒⣵⣈⣀⣀⣀⣀⠀⠀⠀⠀⠁⠔⣉ ⠎⠳⠈⡜⠀⡜⠀⠁⣰⠁⢰⠀⡀⠱⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠙⠀⠛⣖⣠⣠⠀⠀⠀⡀⢄⠘⠀⠀⠀⠀⠀⠞⢊⡠⢀ ⠀⠏⣮⢀⡄⠒⠑⡸⠀⡼⠀⠷⠢⠑⣮⣍⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣤⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⡇⠃⢀⠀⠀ ⠇⣴⣎⠮⠒⠑⠈⠀⡟⢿⠭⠓⣌⡘⣇⢸⣇⠚⠈⠀⠀⠀⠀⠀⠋⠞⡠⢀⠀⠀⡇⢸⠀⠀⠀⠀⠃⠜⠁⠀⡀⠀⠁⡜⢀⡆⡟⠻⠉⠿ ⡰⠄⠂⢀⠀⠞⢀⠎⣧⢀⡀⢣⡌⠶⠀⢠⡏⢻⣞⠯⠴⠯⠴⢋⠴⠀⠀⠀⠀⠀⡄⣷⠙⠀⠀⠏⣿⢁⡹⠉⠛⠔⣤⣀⣀⣀⣿⣿⣿⣾ ⠉⠋⢠⠀⡷⢉⠎⢀⡇⠀⣲⣈⢀⠀⠀⠏⣾⣣⡴⢀⡜⠀⡠⢀⠀⠀⠉⠉⠚⠓⠒⠤⣤⣧⣄⣿⣀⣀⢀⡉⡏⠓⠐⠥⠪⡟⣿⣿⣿⢸ ⡀⢀⠁⠊⠒⡒⢒⠒⡖⠒⠒⡖⠓⠟⠞⢀⠁⣰⠀⠂⢸⠀⠀⠁⠊⡤⣀⠀⠊⣠⠀⠀⠀⠀⢡⡀⠀⠄⡿⢙⢲⡖⣤⢀⠁⣿⣿⣿⣿⢸ ⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠒⠤⣎⢀⠀⠀⠇⢀⠀⠀⠁⠔⡠⣀⠳⠈⠀⣀⢀⠀⠀⠀⠉⡏⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠚⠀⠁⠞⡤⠀⠀⠀⠀⢸⠀⠀⠋⡠⠀⠀⠀⠀⡀⢄⠤⠒⠤⣁⣏⣷⣿⣿⣛⣏⣿⠙ ⠀⠀⠀⠀⠂⠙⠉⠉⠉⠒⠐⠤⡠⣀⣀⣀⣤⣴⠤⡤⣀⠀⠀⠀⠀⠀⠀⢠⠀⠎⢠⠀⠀⠀⠀⠁⠚⠔⣤⣀⣄⣤⣤⣀⠀⣧⣿⣾⣿⣿ ⠀⠀⠀⠀⠀⡆⣟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠎⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢸⣇⣿ ⠀⠀⠀⠀⠀⠻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠎⢀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⣿

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⢳⠀⠀⣄⢀⠀⡘⢀⠀⠀⠀⠀⠀⠉⠉⠉⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣽⣦⣷⣿⣿⣿⣿⣿⣿⣿⢈⠀⡇⣦⠘⠁⠟⣿⣿⣁⠚⠶ ⡀⠣⠀⠀⠀⠋⢀⠀⠀⠀⠁⠔⣀⠀⠀⠀⠀⣀⣄⣤⣤⣶⣲⢉⣌⣷⣿⠹⣦⠳⠈⠀⣄⣷⣿⣿⢸⣿⢻⠉⡌⠸⢹⡿⣷⣾⢏⣠⠋⠟ ⠀⠀⢄⠲⡤⢀⠀⠀⠋⠴⣠⠀⠀⠀⠀⠀⠀⠀⠊⠤⠢⠑⠀⠀⡀⣀⣤⣷⠻⠀⢿⠙⠀⠀⣷⣿⢸⣿⣿⣿⢿⢻⣿⣰⡏⢃⣿⣿⣿⣸ ⠀⠀⠀⠀⠀⠀⠞⡤⢀⠀⠀⠀⠊⠠⣉⣛⣚⣠⠀⠀⠀⠀⢦⠈⠀⠀⠀⠀⣄⢳⡉⣿⢾⠳⡉⣿⢸⣷⣿⣿⣿⣿⣇⠋⢻⡿⣿⣿⣿⢸ ⠀⠀⠀⠀⠃⡴⢀⠀⠀⠀⠀⠏⢎⡸⣀⣸⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⡀⣦⡿⣿⡹⣦⣿⢿⡇⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⢸ ⢠⠀⠀⠂⢀⠀⠀⠀⠀⠀⠃⢿⡬⢘⠀⢧⠉⠋⠒⠿⢠⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⡄⣷⣿⢿⡙⣦⡹⣿⣿⣿⣿⢻⡇⣿⣿⣿⣿⣿⢰ ⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⣿⣸⢐⠀⡀⣀⠀⠀⢁⣀⣅⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣷⣿⣿⢿⡙⣄⣷⣿⣿⣿⠸⣿⣿⣿⣿⣿⠀ ⠿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠈⠀⠀⠀⠀⠀⡏⣧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢦⣾⣻⣦⢿⠻⣌⣷⣿⢿⡄⣿⣿⣿⣿⠀ ⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣆⠒⠒⠒⠒⡵⣮⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⣞⢹⣄⣿⣿⠻⣌⣿⠹⣇⣿⣿⣿⠸ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠔⠤⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠬⠀⠀⡇⣾⡟⠘⡄⣷⣿⣿⡿⣿⠹⣧⣿⣿⣿ ⣿⣿⠈⠀⠀⠄⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠇⠀⣆⢹⠀⡁⣷⣿⣿⣿⣿⠘⣧⣿⣿ ⣿⣿⢸⠀⠀⠀⠉⣄⢷⠛⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣗⣸⣀⠸⡇⠀⠀⣆⠘⡀⡳⣿⣿⣿⣿⣿⠘⣧⣿ ⣷⣿⣿⠀⠀⡈⣤⢭⠒⣤⣿⢄⡷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠓⡽⣤⡀⣸⢀⠀⡇⠇⠈⠀⢳⠀⡄⣿⣿⣿⣿⣿⣿⠈⣧ ⡗⣿⣿⠀⠀⡇⣉⡾⣶⠶⡂⢶⠹⣆⢼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣉⣉⣉⢿⣿⠀⠀⠘⡀⣧⢿⡟⠘⠀⣆⣼⣿⣿⣿⣿⢻⡇ ⢸⣿⣿⠀⠋⠀⢀⠀⠟⡩⣀⣄⣯⢙⣄⠻⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⣽⣿⣿⣀⣧⣿⢿⠘⠀⢸⠃⡟⣿⣿⣿⠶⠲⢿⣿⢀⣯⣿⣿⡇ ⢳⣿⣿⠿⣿⠀⠀⡇⣿⣿⣄⣷⣿⣿⢿⡌⣷⠹⠀⠀⠀⠀⠀⠀⣶⢿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣽⣯⣶⣑⡏⣿⠈⠀⡇⣹⠀⣇⣿⣿⢹ ⡖⣷⣿⣿⣿⠻⠈⣇⣿⣿⣿⣿⣿⣾⣳⢧⠀⣦⢦⠘⠀⠀⠀⠀⠒⠍⣄⣦⣶⣶⣶⣶⣶⣿⣿⣾⠀⠀⠀⡏⣿⢸⠀⠀⣿⠂⡆⣿⣿⣿ ⠀⡀⣷⣾⣤⣦⣿⣿⣿⣿⣾⣴⣡⠈⡄⡜⢿⢧⠈⣄⠹⠀⠀⠉⠀⠉⣀⠤⠤⠤⠤⡀⣀⢀⢧⠀⠀⠀⠁⢸⣿⣿⠁⠀⣿⡇⠀⣿⣿⣿ ⠙⠈⡀⢻⠀⣄⣴⣤⣤⣠⣀⣀⣀⢄⠦⢹⣆⢻⣷⠈⡀⠳⡼⢀⡀⠀⠀⠀⠉⠐⠀⠀⠀⠀⡀⠑⠀⠀⡇⠀⣿⣿⡀⠃⣿⡄⠸⣇⣿⣿ ⡼⢳⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡾⣿⡜⢿⠎⡹⢳⠀⠉⠚⡤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡸⠀⣿⣿⠀⡆⣿⡇⢸⡇⣿⢹ ⢿⡀⢱⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⢻⣇⣿⣿⣹⣷⢀⠀⠀⠀⠀⠀⠁⠊⠀⠀⠀⣿⠀⠁⢰⠁⣿⣿⠀⠏⣾⡟⢸⡇⣿⡀ ⡟⢻⡀⢻⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡜⣿⡈⣿⣿⣿⡽⠱⠀⠀⠀⠀⠀⡠⠀⡀⠱⠀⣿⠀⡟⠀⡇⣿⣿⢀⢁⢻⣿⢠⡏⣸⠇ ⣧⡌⠹⣆⢻⠀⢷⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣧⣇⢸⣷⣿⡿⣿⡜⠹⠀⠀⠀⠀⠀⠀⠀⡟⠈⣇⠀⠀⠀⡿⣿⣸⠀⠸⡇⣿⠀⣾⠀⡏ ⠈⣧⣿⠹⣆⢻⠿⢆⠘⠃⡵⢀⠀⠀⠀⠀⠀⠀⣜⢿⡧⣿⣿⣿⢿⡆⠘⠀⠀⠀⠀⠀⠀⠀⣦⣸⠀⠀⠀⣿⣿⢀⠃⢰⡿⣾⡷⢀⠏⣴ ⣄⠙⣄⣷⢻⣯⣿⢿⣿⢫⣿⢸⠀⠀⠀⠀⠀⠀⢻⣇⡿⣿⣿⣿⣿⢹⣇⠹⠶⠀⠀⠀⠀⡀⢻⢃⠀⠀⡇⣿⣼⠀⡟⡟⣿⢰⠀⡟⢫⠿ ⣄⡦⠻⡈⣧⣿⣿⣿⢯⣿⣿⢸⠀⠀⠋⠐⠋⡼⣷⡌⣿⣿⣿⣿⣿⣿⡈⣿⢿⢻⠃⠛⠟⠛⣿⣿⠀⠁⡿⣿⢀⠏⣿⣿⣼⠁⡟⣾⣤⣰ ⠀⠀⡀⣄⣷⣿⣿⣿⣿⣾⣫⣿⣷⣿⣴⡦⣶⣷⠸⢹⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⣿⣿⣼⣷⣿⠀⡇⣿⢠⠃⣿⣿⣽⠊⡤⢁⢸⡇⠃ ⠀⠀⠀⠀⡀⣇⣿⣭⣿⣿⣿⢿⣿⣿⢿⠿⠛⠛⢸⣇⣿⣿⣿⣿⣿⣿⣿⡆⡌⣿⣿⣿⣾⣿⡿⣿⠀⡿⢠⠏⣿⣿⣿⣠⠀⠀⡇⠀⢸⡜ ⠀⠀⠀⠀⠀⡠⠀⣅⣴⣾⢶⣛⣯⣿⣿⣿⣿⣿⢻⡍⣿⣿⣿⣿⣿⣿⣿⠸⢢⡀⣤⣷⠹⡀⣿⡏⡴⢁⡟⣷⣿⣼⢀⠀⠀⠀⢸⡇⠀⢠

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⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣉⣯⡿⣿⣿⣿⣿⢈⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢤⠤⠦⠶⠹⠀⠀⠀⠀⠀⡟⠀⡆⠹⠀⢳⠀⢸⠀⢸⠀⠀ ⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⣀⠀⣄⣿⣿⣿⣻⠉⠀⡀⣀⣤⣤⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⡀⢳⠘⠀⠀⠀⡇⢿⠀⡀⠀⡇⠀⢳⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣄⣶⣶⣶⢿⠙⠀⠀⠞⢧⠀⠀⠀⣦⣿⣿⣿⢿⡙⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⣄⣿⠹⠀⠀⢧⢯⢎⠀⡆⠘⡇⠙⢸⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠉⠒⠀⠋⠔⠤⣥⣬⢤⡤⢥⠒⠒⠓⠙⠉⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢿⠈⠀⠀⠀⡀⣦⠻⠀⠀⢧⣟⠈⠀⢿⡏⣀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠀⠉⡴⢀⠁⡔⢀⠀⠀⡇⢋⠀⠀⡆⠇⠈⠀⡀⣀⣄⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⡄⢳⠈⠀⣧⢹⠀⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⣀⠁⡜⢀⠀⠀⠀⠀⠁⣸⢧⠈⠀⡀⢳⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⣄⠸⣣⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠞⣠⠀⠀⣀⢀⠀⠋⡴⢀⠀⡀⣄⠶⡐⠹⠈⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣓⣉⢦⠛⠈⠀⠀⣆⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠻⠈⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡏⠠⡂⢿⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠃⡼⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠆⠙⠢⡈⠢⡈⢻⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⣇⣞⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠒⠒⠒⠓⠛⠙⠉⠉⠉⣼⣄⢀⠀⠀⠀⠀⠀⡇⢹⠀⠁⠀⠀⠀⠀⡄⠸⣼⡧⢓⣼⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠼⣤⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⠀⠀⠀⠀⠀⠀⡀⣀⡏⢀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⡄⠸⠀⠀⠀⠀⢻⣷⡿⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⡿⣿⢻⠈⠀⠀⠀⠀⠀⠀ ⣿⢻⠊⠓⠛⠉⠉⠉⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⢿⣏⣿⠿⠿⠏⣿⡇⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠻⠈⠀⠀⠀⣇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠻⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣼⣤⣤⣤⣥⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⢹⡏⣿⣿⣿⣿⣿⣿⢻⠴⠤⣀⠤ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠲⠒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠧⠿⣻⠋⠛⠛⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢹⡉⣿⣿⣿⣿⠘⠀⠀⠀⠀⣤⠦⣒⣽⠮⠒⠛⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣅⣯⣿⡽⣩⢀⠁⠟⣿⣴⢀⡄⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢻⠀⠀⡁⢯⠛⠉⠉⠉⠈⠈⡄⠅⣯⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⡿⣴⢀⠀⣉⣟⣿⣿⣴⣀⣀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣽⣯⣿⣿⣟⣿⣿⠹⠟⣽⢈⠀⡋⣾⣤⣤⣷⣽⢫⠸⠀⠁⠀⠀⠀⠀⠀⠀⠤⠿⠛⡿⢿⠿⠿⣿⣶⣵⣛⢴⣠⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡴⣤⣿⣿⣿⠿⠿⠿⠿⣿⣼⢀⠛⠛⠙⠉⣉⣈⠂⠁⠘⠟⣴⣀⣟⣶⡴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡀⢈⠀⠀⣀⣖⢴⡠⣀⠁⠘⣀⣀⠄⠠⠠⣤⣠⣀⠀⢀⠆⠹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿ ⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⢀⠈⠀⠀⠀⠂⠒⠒⡤⠀⠀⠀⠄⢽⠐⠀⠀⠀⠀⠀⠀⡀⢤⠒⠒⠒⠤⠀⠀⠁⠊⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿ ⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠈⣀⢤⠢⠓⠉⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠛⡴⣠⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⡇⢿⠛⠛⠙⠀⣀⣄⠶⠻⠙⠀⠀⠀⠀⠀⢇⠀⠀⠙⠈⠉⠉⠉⠛⠿⣿⣿⢁⠉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿ ⠀⡇⣿⣿⣿⣿⣿⣾⣿⣿⢀⠀⠀⡂⣿⣿⣿⣿⢿⠿⠻⠙⡉⣍⣶⠤⠀⠀⠀⠀⢠⡖⣶⡴⣀⣤⣴⣠⢃⡿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠸⠏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣝⠷⠻⠙⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾ ⠙⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⣄ ⣤⠳⠈⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⣿⣿⣿⣿⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢻⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⠀⠀⠉ ⠀⠀⣄⠳⠉⠀⣄⣦⣷⣿⣿⣿⣿⣿⠙⡀⣥⣿⣿⢻⡟⣿⡿⣛⣝⣿⣾⣶⣷⣿⣿⣿⣿⣿⣝⣿⢿⡌⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣠⢀⠀⠀⠀⠁⠖⣠⢀ ⠀⠀⠀⠀⡀⣤⠦⠶⠴⣤⣀⣄⣤⣶⣶⢿⠻⣌⡲⣞⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠲⠙⠈⣀⣄⣤⣥⣾⣤⣦⣶⣶⣶⣷⣶⣿⣿⣿⣿⣶⣶⣶⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀

⠐⠀⠀⠀⠀⢂⡄⣦⣿⢽⣤⣦⣶⣷⣿⣿⣿⣿⣿⣻⢈⠄⠑⠈⡄⡈⠀⡎⠇⠀ ⠀⠀⠀⠀⠂⠠⠁⠀⣊⣀⠨⡄⢒⠐⣏⣿⣿⣿⣿⣿⢿⠈⠀⢆⠘⣆⠘⢱⣰⠀ ⠀⠀⠀⠀⢀⠊⠂⡠⠀⠁⢴⠑⠊⠀⠀⡀⣷⣿⣿⣿⣿⣿⠻⠐⡈⠠⢳⠀⠀⠀ ⠀⠀⠁⠀⠀⠌⢀⠀⠃⠠⠀⠀⠀⢅⠐⠀⠀⣄⣿⣿⣿⣿⣿⡻⡀⠻⠀⠀⠀⠀ ⠬⠤⠤⠀⡎⢀⠀⠀⡇⠘⠈⠀⢃⣟⢸⠀⠀⠀⡀⣷⣿⣿⣿⣿⢻⣋⠹⠀⠀⠀ ⢿⠽⠤⠤⢰⠀⠀⠀⡄⣿⣿⢿⡿⣼⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⠹⠀⠀ ⣿⣿⢿⠻⠀⠀⠀⠀⠀⡄⣒⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⡿⣿⣿⣿⣛⠙ ⣿⣿⣷⣿⠸⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠾⠓⠚⣷⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠁⠞⠓⣚⡙⣏⠰⠀⠀⠀⠉⠏⡩⣛⢿⣮⢀⡀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣼⣄⣤⠶⡶⣡⠦⠂⠒⠐⡄⣎⣤⣀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿ ⣆⣿⣿⣿⣿⣾⠸⠂⠑⠬⢀⠀⡄⠈⠀⠀⡀⠀⠉⠚⠫⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⣿⣼⢁⣇⠿⠻⡛⢭⠺⠀⡄⠆⠴⠦⡥⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⠟⠛⠉⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⢢⡁⣦⣷⣿⣿⣬⣷⣿⣇⣿⣷⣿⣿⣿⣿⠻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢁⠂ ⠀⠀⢀⠤⣀⣀⣤⡤⣔⣬⣶⣶⣾⣷⣿⣿⣿⣿⣾⣶⣴⣠⣀⣀⢀⠀⠀⠁⠀⠀

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⠀⡄⠈⠀⠋⠩⢹⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀ ⠀⠁⢴⣀⠀⠀⠀⠀⣀⠤⢕⠐⠀⠀⠀⠀⠁⠒⠨⢒⠀⠤⢠⢶⠑⠋⠀⠀ ⠂⢠⠁⠒⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠋⢼⡠⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀ ⢰⠃⢸⠁⠁⠀⠀⠀⠀⠀⠀⠀⢆⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠘⡀⠸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠃⠀⢸ ⠄⠈⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡌⠀⢰ ⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⡠⠁⡐⠀ ⠀⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀ ⠀⠀⢸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠈⠀⠀ ⠀⠀⢆⠉⠈⠀⠀⠀⠀⠀⠀⠁⠊⠤⠢⠁⠉⠀⠀⠀⠀⠀⠀⠀⠊⢠⠀⠀ ⠀⠀⠀⠇⣰⠧⠛⠛⠓⠉⢀⠔⠁⠀⠁⠀⠁⠋⠛⠿⠻⠿⠸⢘⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⡟⢳⣾⠃⡟⢷⠀⠁⠀⠉⠈⣿⣿⣿⣿⢹⣿⢸⢀⠀⠀⠀⠀ ⠀⠀⠀⡇⠁⣇⡾⢸⡇⣻⣿⠟⢔⢀⠀⡀⣄⣦⣿⣼⣿⣿⣧⠇⠀⠀⠀⠀ ⠀⠀⠀⡟⡇⡁⢰⢸⣾⣿⣶⢻⠠⠀⠀⠀⠀⠄⡳⣎⣌⡎⡏⡇⠀⠀⠀⠀ ⠀⠀⠀⡇⡁⡇⡇⣇⢁⣼⡆⢸⠀⠀⠀⠀⠀⠋⠛⣫⢆⢣⣸⡈⠀⠀⠀⠀ ⠀⠀⠀⡆⣷⡗⡇⡏⣧⠀⢱⢉⠛⠘⠂⡏⢠⣿⣶⣞⢳⢣⢵⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⡏⡇⣸⠸⡄⡷⣶⣶⢴⠂⡟⠯⡿⠇⣇⡼⠈⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢁⢡⡿⢸⢀⠀⢾⠑⠀⠀⢀⣿⡄⣾⡇⠔⢸⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⣿⢸⠀⠀⣹⡄⠥⡇⠥⣾⠀⠂⡏⢸⢸⢸⣸⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣿⡌⣥⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⡀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣀⣀⣀ ⠄⠀⠀⠀⠀⠇⣾⣦⠰⣀⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠞⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⣀ ⠈⠂⠀⠀⠀⡀⣤⣳⣿⣉⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣶⠿⢰⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣀⣸⢤ ⣀⠀⠀⠀⣾⣧⠰⡟⣾⣶⣷⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⡃⣿⣿⣿⣿⣿⣿⣶⣿⣿⢶⠶⠤⠥⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢀⠀⠇⢠⡸⠀⣶⠽⠿⠟⡛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣯⣿⣿⣶⣿⣴⣡⠟⣾⣠⢀⠀⠃⢞⣠⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⡼⡏⢉⠞⡤⣉⠟⣭⣉⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⣠⢋⡴⢀⠃⡿⣴⠀⠀⠀⠄⣠⠀⠀⠀⠀⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏ ⠀⠀⠏⢰⣠⢉⠖⣥⢈⣧⣿⢀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡴⢀⠀⡴⢀⠀⠃⣣⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣟⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠴⣀⠋⠖⣠⢀⠀⡼⣀⣇⢸⠀⠀⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⣠⠀⠀⠀⠀⠀⠀⠀⣹⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣷⣹⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣀⠀⠀⠀⠀⡞⢀⠁⣿⣿⣶⣒⣒⣗⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⢀⠀⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣤⢶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⡼⠀⣌⠉⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠸⠀⡆⠘⠀⢷⠀⠀⠀⠁⠀⠁⡟⣶⠤⣤⣤⣤⢤⠲⠀⠀⠀⠀⠀⠀⠁⠚⡴ ⠀⠀⠀⠀⠃⣰⠀⡞⢀⠀⢿⣴⣀⣿⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⢡⠀⡀⢻⠉⠟⢼⡤⣀⣄⠤⠲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣡⠞⡴ ⡞⣄⠳⠙⡼⠀⠏⢠⠀⠁⣼⠀⡏⢠⠀⠀⠀⢦⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠻⠉⣟⠾⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠃⣰⠟⣠⡀⠀ ⠀⠁⡼⣞⠀⠀⢶⠓⠉⡼⠀⠃⣰⠀⠇⠾⠒⠙⣄⢹⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠾⡠⢇⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⡸⠇⢀⠀⠀⠀ ⠁⡿⡴⢿⠛⠉⠈⠀⠀⢀⠁⡿⠙⠚⠉⣈⠣⡌⣦⡞⡜⣷⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠶⣠⣀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⢠⠀⠀⠋⢰⠀⢹⠋⠙⠀⠁⠛ ⡃⣰⠎⢀⡼⠀⣀⣇⠠⠀⡟⣾⣐⢦⡑⣄⠳⣇⠀⣧⢈⡇⢻⢆⠙⠉⠉⠙⠉⠋⠖⡥⣬⢀⠀⠀⠀⠀⠀⡆⡞⠘⠀⠀⠀⠀⠃⣿⣸⠁⣼⠀⠀⠀⠋⡿⢲⠒⠒⡓⣿⣿⣯⣿⣽ ⢠⠄⢀⡜⠀⠀⠏⢰⠀⡟⢀⢸⠀⠉⡉⢣⠀⣄⠀⠀⠁⡟⣿⠾⣡⣼⢀⠋⣴⢁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⠻⠈⠀⠋⣽⣿⠉⡿⢻⠓⠶⣸⢀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣼ ⠉⠁⡼⠀⠀⠇⣹⠀⠟⢠⠀⡜⠀⢳⠙⣀⢀⠀⠀⠀⡟⣾⣠⠿⣠⠀⡞⢀⠄⣀⠀⠀⠀⠀⠁⠀⠋⠚⠓⠞⠴⠤⣠⣇⣈⣷⣼⠀⠀⠀⠀⡉⡏⢚⠛⠴⠦⠭⠛⡿⣿⣿⣿⣿⢀ ⣀⣄⠀⠀⠁⠉⡉⣍⢩⠉⠉⢻⠉⠉⡉⢻⠈⠃⠋⡼⢀⠀⡞⢀⠀⠃⢸⠀⠀⠀⠀⠁⠚⡴⣤⣀⢀⠋⣠⠀⠀⠀⠀⠀⢣⠀⢤⠀⠀⠛⡿⢀⡿⠉⢾⠶⣠⠀⡏⣿⣿⣿⣿⣿⠘ ⠀⠀⠁⠜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣠⠀⠀⡄⢀⠀⠀⡀⢹⠀⠁⠋⠔⣸⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠁⠋⡖⠹⠀⠀⠀⢆⣴⣠⣀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠃⡴⢀⠀⠀⠀⠇⢠⠀⠀⠀⠁⠞⣀⠀⠀⡀⢦⠙⠈⠀⠀⠁⠀⠁⠉⠉⠛⠟⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠟⠰⠀⠁⠛⢴⣠⠀⠀⠀⠀⠀⡼⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⠤⡤⣀⠉⣞⣴⣯⣿⢿⠿⡋⣟⢿⠛ ⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠉⠉⠛⠒⠴⠤⣠⣀⣄⣤⣷⣾⢶⠴⠤⣠⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⣠⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⣴⣀⢤⡶⣶⣴⣀⠀⡆⣿⣿⣿⣻⣿⣿ ⠀⠀⠀⠀⠀⠀⡀⣎⣧⣠⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⣠⠀⠀⠀⠀⠀⠀⠃⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⡆⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢡⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠂⣿⣿ ⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠃⣰⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⣟⣿

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣀⠤⠢⠒⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠲⠙⠀⠀⠀⠀⠀⠀⠟⣴⣀⣦⣷⣿⠻⠙⠉⠛⠛⠛⠛⠒⠒⠒⠒⠓⠛⠛⡿⠷⠙⢈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⠙⠀⠀⠞⢃⠀⠀⠀⠀⣧⣿⢠⢉⡉⡉⣉⣉⠉⠉⠛⠛⠚⠒⡟⡖⠺⣒⣮⠹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⢛⡈⢠⠀⠀⠀⠏⣿⣟⠻⡉⣉⣋⣛⣛⣒⣓⢛⣿⣿⣽⣭⢦⡿⣿⡛⢿⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠶⠿⡿⣿⢸⡀⠂⡀⠀⠀⠡⠞⠤⣠⢁⡞⡾⠻⣫⢧⣯⢻⣇⣿⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣿⠻⠈⠀⠀⠀⣾⠂⠀⠃⣿⡟⢃⣿⠅⣾⡇⣿⡿⢰⡇⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢘⣆⠻⡀⣧⣿⠹⠀⢷⠈⢁⠁⣰⡞⢸⡿⣿⣿⢠⡟⣿⣿⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠀⡀⢰⠄⣧⣌⢿⡟⢹⣠⡗⠀⢸⢃⣰⠃⢡⠟⣿⡼⣟⢀⠀⠀ ⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣴⢀⠀⠀⠂⠈⠀⠀⠀⢷⣎⣾⣿⠿⣸⠇⢸⡜⠀⠟⡿⣷⡿⣾⢀⠀⠀⠀ ⣿⣽⣬⢿⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢻⢇⡌⣷⢻⡟⡟⠋⡿⣿⢡⡴⠀⠀⠀⠀⠀⠀ ⣷⣿⣻⣿⣿⣿⣿⣿⠺⠛⠉⠉⠈⠀⠁⠉⠉⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣇⣿⣿⡛⣿⣿⣿⣿⣴⢏⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠟⣿⣿⣶⣿⣿⣿⣵⢋⠶⣤⣀⣀⣧⣚⣓⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣿⣿⣾⣴⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣿⣰⠕⡟⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⡁⢍⡻⣶⠸⠀⠀⠀⠀⠀⠋⢠⠀⠋⡿⣻⣶⣉⢿⢳⡟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢠⠋⣿⣿⣿⣰⠀⠁⠉⠊⠈⠀⠀⠀⠀⣎⣰⢀⣆⠙⠀⠀⠀⠀⢃⠿⣽⣿⣶⢤⡁⡋⡞⢴⡢⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣅⣿⣳⡿⣿⣿⠹⠉⠈⡀⣧⣿⠨⠀⠁⡔⠀⠀⠀⠀⣿⠿⠙⠀⠀⣆⣓⢒⠒⠶⡤⣠⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣣⣿⣿⣿⣿⣿⣸⣇⠲⠙⣀⠀⠀⡀⠁⠉⠀⠀⠁⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠿⠩⣀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢸⡇⣿⢻⣿⠟⣡⢏⠿⠉⠈⡀⣠⣦⠸⡟⣿⣿⣾⣦⣿⣿⠤⠶⠛⠛⠈⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣿⣿⣿⣼⢟⡿⣿⣿⣿⣿⢿⠻⠙⡏⣿⣿⣿⣠⠀⣄⡶⢶⠛⠈⣄⣶⠿⠘⠀⠀⠀⠀⠀⠀⢦⠑⠈⠀⠀⠀⠀⠀⠀⠀

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⢳⠀⠀⡀⣆⣠⠀⠀⡏⢀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠏⡿⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣜⣷⣿⣦⣷⡿⣿⣾⣿⣿⡿⣿⣿⠚⣿⣸⠀⠀⡆⢸⢻⠀⠀⠃⡿⣻⣿⣰⢁⠋⠟ ⡀⠳⠀⠀⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠁⠚⡴⣠⣀⣀⣀⣤⣤⣦⣾⣿⣿⣿⣿⣴⣤⣦⡿⣿⢿⡘⣷⢻⠈⠀⣀⣤⣷⣿⣿⣿⣿⠈⣿⣿⠀⠀⠀⢸⡇⠀⡟⣯⣷⣾⣡⡾⣠⠀⠉ ⠀⠀⢣⠈⠀⠁⠏⣠⠀⠀⠀⠀⠁⠟⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⣀⣤⢤⠲⡓⣯⣿⣿⠘⢀⢦⠙⠀⠀⠀⣄⣿⣮⣿⢀⣿⣿⢿⠿⢸⣿⡇⡿⣿⣠⡿⢳⡿⢁⠟⣿⣾ ⠀⠀⠀⣄⢦⣠⢀⠀⠀⠀⠁⠞⣠⣄⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⡰⣀⣀⠦⠙⠀⠀⠀⠀⠀⣄⣦⣿⠙⠎⣟⢿⠙⠀⠀⡆⣿⣿⠘⣿⣿⣿⣿⣿⣧⡇⣿⣰⠏⢰⡏⣿⣿⣿⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢠⠀⠀⠀⠀⠀⠋⡴⣀⠉⠉⠋⣴⢀⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⠀⡀⣶⢻⡈⣯⣝⢶⠛⠈⣇⣿⢸⣇⣿⣿⣿⣿⡟⠸⣹⠁⣿⠏⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠁⡞⣠⠀⠀⠀⠀⠀⠀⡎⢋⠞⣤⣧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠀⠀⠀⠀⠀⠀⣄⣷⣙⢯⠻⡌⣷⣿⣿⢻⡇⣿⣿⣿⣿⣿⢹⡆⣿⢸⣿⣿⣿⣿⣿⣿⠀ ⠘⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⡇⢶⡁⢴⠀⡇⠈⠀⠀⠀⠀⠁⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣆⡙⣿⣿⠹⣄⣷⣿⡈⣿⣿⣿⣿⣿⣿⠘⣷⣿⣇⣿⣿⣿⣿⣿⠀ ⢀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣽⣉⠸⠀⡀⣧⠉⠛⠶⠤⣺⠉⠀⠀⠁⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢿⠙⣄⢷⣏⣿⣿⣿⣿⣿⢹⡄⣿⡇⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣸⠐⠀⠀⡀⠀⠀⠀⠀⢹⣇⣀⣧⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢷⣎⣿⣽⣿⠙⣀⣦⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠀ ⢛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣏⡖⠿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⢦⡝⣿⣹⣷⢿⠻⡈⣦⣿⣿⣿⢿⡀⣷⣿⣿⣿⣿⢸⠀ ⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣼⠻⠀⠀⠀⠀⠀⠁⠟⣿⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣄⡼⣿⠙⣧⣿⣿⠻⡈⣦⣿⣿⢹⡄⣿⣿⣿⣿⣿⠀ ⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⢤⠤⡤⣤⣥⣩⢚⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⡝⣷⠘⡄⣿⣿⣿⠻⡌⣷⣿⠘⣇⣿⣿⣿⣿⠋ ⣿⣿⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠤⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣹⣄⠤⠀⠀⡇⣮⡹⢹⠀⡄⣿⣿⣿⣿⠹⣶⣿⡘⣧⣿⣿⣿⣿ ⣷⣿⢻⠀⠀⠀⢄⠓⡍⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢀⠈⠀⠀⡇⢀⣄⡿⠸⠄⡈⣷⣿⣿⣿⣿⣽⣿⡈⣧⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⣄⣷⠻⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⣿⠛⠚⠙⡄⡿⠀⠀⡆⢹⠀⣄⡙⣧⣿⣿⣿⣿⡿⢿⠈⣷⣿⣿ ⣿⣿⣿⠸⠀⠀⠄⠋⣒⠙⡌⣶⡛⢮⠘⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠴⣿⠉⠉⡔⢀⣸⠀⠀⠀⣇⠘⠀⣇⡹⣷⣿⣿⣿⣿⣿⢿⠀⣧⣿ ⣖⣿⣿⣿⠀⠀⠉⡂⣕⠬⠲⠒⣅⣿⣸⢦⡿⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠖⠷⣽⣠⣀⡆⡘⢀⠀⠀⢼⡇⠙⠀⡀⢻⠀⠀⣧⡼⣿⣿⣿⣿⣿⣿⢻⠀⣿ ⠈⣿⣿⣿⠀⠀⠀⣽⣤⡣⣟⠿⠛⡙⣯⠽⡰⣧⢼⠒⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⣴⣀⣀⣄⣧⠻⢿⠀⠀⠀⢸⡄⣦⢿⠻⣿⠈⠀⡀⣷⣌⡻⣿⣿⣿⣿⣿⠘⡟ ⠸⣿⣿⣿⠀⠀⠈⣄⠤⢀⠀⠁⠞⠶⠶⡓⢿⠐⣖⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣾⣶⣿⣿⣿⣩⠀⠀⡇⢸⠁⠃⣿⣿⣿⢿⠛⠉⡄⢻⣆⡎⣤⣿⣿⣿⢹⡇ ⢹⣿⣿⣿⠁⡟⢸⠀⠀⠀⠏⣻⠛⠛⠉⠋⣞⢿⠹⣆⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠙⡆⢿⣿⣿⢹⠛⡉⣿⣿⣿⢻⠀⡇⢹⠟⣿⣿⣾⣧⣿⣈⣀⣄⣧⢻⢸⠀⡷⣿⣿⣿⡆ ⣧⣏⣿⣿⡟⣿⢈⠀⠀⡇⣿⣿⣾⢀⣄⣷⣿⣿⣟⢹⡄⣷⢿⠈⠀⠀⠀⠀⠀⠀⡄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣍⣟⣶⢲⠙⡏⣿⢹⠀⠀⡄⣿⠈⠀⡇⣿⣿⣿⢸ ⠚⣷⣿⣿⣿⣿⢿⠙⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢹⠀⢷⣌⠳⠀⠀⠀⠀⠀⠀⠂⠉⠤⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿⣺⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⣿⢹⠇⡇⣿⣿⣾⢿ ⠀⠀⣧⣿⡋⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣾⣴⢀⡆⢸⣷⠹⠷⢀⡀⢧⠘⠀⠀⠀⠀⠀⡀⣄⠶⠲⠒⠒⠒⠒⠶⠶⠤⣠⣇⡘⢠⠀⠀⠀⠃⢸⣿⣿⠘⠃⠀⣇⣮⠇⡀⣿⣿⢿⣿ ⠀⠀⠀⣷⣸⠀⠓⡙⣿⣿⣾⣿⣽⣩⢉⠛⠟⣹⠈⢇⡂⣾⡘⢷⠚⠀⣆⠙⠀⠁⠖⠠⠞⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⠀⠀⠀⡇⢀⣿⣿⢸⡇⠁⡇⢸⡧⠈⣧⣿⣿⣿ ⢅⠙⠀⡄⢿⠀⠀⡆⣠⠀⣀⣀⠀⠀⠀⠀⠀⠀⣄⣷⢸⣆⣧⡄⢿⠘⠀⣆⠿⢠⠀⠀⠀⠀⠀⠁⠋⠚⠔⠀⠀⠀⠀⠀⠀⡇⠙⠀⠀⠀⣸⠀⣿⣿⢸⡀⡇⡇⢸⡇⢸⡇⣿⣿⣼ ⡼⣷⠘⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣦⠹⢻⣇⢿⠌⠿⡌⠹⠀⠀⠉⠋⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⡇⢸⠀⣿⣿⢸⠀⡇⡇⢸⡇⢸⡇⣿⣿⢹ ⢻⡀⣧⠈⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣯⡏⠘⣷⣿⡜⣿⡞⠿⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠸⡇⠀⠀⣿⣿⢻⠰⡿⡇⢸⡟⢸⡇⣿⣿⡄ ⡦⢻⠀⢷⠈⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⣿⢹⡆⣿⣿⣯⢿⡎⠸⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠳⠈⠀⡇⢸⠀⢰⢸⠀⠇⣿⣿⢿⠀⣼⡇⢇⣿⢸⡇⣿⢰⠀ ⠻⣿⠹⡄⢿⡈⠀⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣷⣿⠈⣿⣿⣹⣷⢻⣦⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠈⡇⣿⠀⡇⢰⠀⡟⣿⣿⢸⠀⠸⣿⡏⣿⢀⡏⣾⠀⡷ ⣧⠸⣧⠙⡆⢿⠈⠣⢧⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣧⡈⣾⢸⣷⣿⣿⡏⣿⢹⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⢸⡇⣿⠀⡇⠀⠁⣿⣿⣿⢀⠀⢸⠀⣿⣿⠀⣿⢠⠀⡟ ⠀⣧⣝⣿⠘⣇⣿⠙⠻⣆⠙⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹⢧⢿⡇⣿⣿⣼⣿⣿⠸⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡿⡆⠀⡄⠀⡇⣿⣿⣸⠀⡇⢸⡏⣿⢸⡏⢸⠀⡏⣿ ⢧⠈⣄⣷⣿⠙⣦⣿⣿⠹⣏⠻⡴⢟⠿⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣿⡘⣿⣿⣿⡟⣿⣿⡄⢿⠈⠃⠀⠀⠀⠀⠀⠀⠄⠹⡆⠸⠀⠀⠀⡇⣿⣿⢀⠀⡟⠁⣿⣿⢰⡄⠁⢿⣠⠉ ⠙⣦⠙⡀⣧⣿⢻⣎⣿⣿⣿⣼⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣇⢸⣿⣿⣿⣸⣿⣿⠹⡇⢿⡙⢷⠀⠀⠀⠀⠀⠀⣧⢻⢻⠀⠀⠁⣿⣿⣼⠀⠇⣻⡿⣿⣼⠀⠀⡿⢛⡿⣿ ⡀⣤⡷⠻⠀⣆⣿⣿⡟⣿⣸⡟⣿⣿⣼⢀⠀⠀⠉⠛⠐⠋⡼⣇⢷⡄⢿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⢿⢻⠃⠛⠛⠬⠿⡿⣿⣿⠀⠀⡟⣿⣾⠀⠁⣿⣿⣿⣿⢀⠁⡿⣿⣴⣇⢀ ⠀⠀⠀⣀⣦⡿⡻⣾⣿⣿⣏⣿⣿⣴⣏⣿⣿⣷⣯⢖⡿⣿⣿⡿⡇⢸⣿⣿⣿⣿⣿⣾⣿⣿⢸⣇⣿⣿⣿⢻⣮⣿⣿⣾⣷⣿⣿⠀⡆⣯⣾⢠⠀⡿⣿⣿⣾⢁⠟⣴⣀⣾⠀⡼⠃ ⠀⠀⠀⠀⠀⡂⢶⣿⣿⣿⣷⣿⢻⡿⣿⣫⢟⣿⢛⠉⠈⡀⠀⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣸⣿⣿⡻⣝⣳⣦⢿⠉⣿⣷⠀⠇⣾⢠⠁⡿⣿⣿⣽⢟⣴⢀⠀⠇⢰⠇⢠⡞ ⠀⠀⠀⠀⠂⠀⠀⡞⣦⡛⡟⣿⣿⢞⣷⣿⣿⣿⣿⣿⣿⣿⠿⡿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⢷⡄⣷⣿⣿⣼⣤⣷⣿⣿⡟⠁⣾⢀⠋⡿⣿⣿⣿⣴⢀⠀⠀⠀⡞⠀⡾⠇⢸ ⠀⠀⠀⠀⠀⠀⡰⠀⠀⡀⣬⣣⣴⣶⠷⡛⣯⣵⣿⣿⣿⣿⣿⣿⢻⡉⣯⣷⣿⣿⣿⣿⣿⣿⣿⢸⡄⠰⡀⣄⣦⣿⠉⠀⣧⢹⣾⣴⢁⠟⣾⣵⣞⣿⢀⠀⠀⠀⠀⠇⢸⠃⢠⡄⠀

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⠀⠀⡇⣿⣿⣿⣿⣰⠁⠉⣚⢒⠒⠟⠉⠀⠁⠉⡉⣒⢒⠤⠤⣀⢁⡜⣀⢀⡀⣀⢍⠯⠶⠶⠲⠒⠓⠛⠛⠛⠉⠉⠉⠉⡇⢸⠀⠁⠋⣿ ⠀⠀⡆⣿⣿⣿⣶⣦⢴⡠⢀⠀⡀⣀⣀⣀⣤⠑⠀⠢⠑⠀⠀⠁⡸⠀⠀⠋⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠑⠈⠀⠀⡇⢸⠆⣿⣿⣿ ⠈⠀⠀⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠱⠀⢄⠘⡄⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠀⡇⢸⠀⣿⣿⣿ ⢿⠈⠈⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢎⠈⠀⠀⠃⣠⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡟⢸⠀⡇⣿⣿ ⣧⢻⣿⢠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣎⠈⠀⢻⠔⣠⠀⠀⠀⠀⣀⠦⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣿⣿ ⠀⣷⣿⠀⠃⠛⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠿⠿⠲⠙⠀⠀⠀⠀⡇⣸⠀⠀⠀⣇⣿ ⠀⡹⣷⢸⠀⣿⣉⣭⢻⠈⠈⠂⠀⠒⠒⠒⠑⠈⠀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⡟⠻⡏⠀⠀⠀⠀⡏⢈⠀⠀⠀⡄⣿ ⠀⣆⡜⣿⠘⠧⢩⡋⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠑⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠒⡖⣶⣠⠀⠀⠀⠁⣿⢠⠀⠈⠀⠀⣧ ⠀⠀⢧⡏⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡟⣸⠀⠀⢀⠀⠀⡇ ⠀⠀⠀⢳⣷⢀⢧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡄⡿⠀⠀⣄⢿⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⢸⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⣿⠀⠀⠀⡄⣿⣼⣢⣝⢿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠈⠀⠀⠀⣄⡄⠐⠀⣄⣷⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣴⢠⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⡄⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⣄⢳⠈⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠁⠀⠉⠓⠙⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠟⣾ ⠀⠀⠀⠀⠀⠀⠀⣦⠿⠻⠒⠛⠛⠛⠿⡿⣿⠿⣿⣩⣈⣀⠤⡧⢠⠀⠀⡀⢧⠼⠤⠤⠤⠤⠤⠁⠋⡟⣿⠉⠉⠈⠀⠀⠀⠉⠛⡿⣿⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠘⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⡈⠀⠀⠀⠀⠀⢧⠀⠀⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠁⠋⠑⠀⠀⠀⢠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠔⣠⠀⠀⣄⠳⠙⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣴⣀⠀⠀⠀⠛⠀⠀⠀⣄⢿⠙⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⢸⠀⣿⣿⣿⣿⣿⣠⢀⠀⠀⠀⠆⣿⣿⣴⠀⠀⠀⡀⣧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢦⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡏⠀⣿⣿⢡⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠐⣿⣶⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣿⣿⡸⠟⡼⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠁⠛⠙⠈⠀⠀⠀⠀⣿⢸⣧⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡿⣿⣿⢿⣿⢿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠋⣶⣿⣿⣰⢷⠘⠁⠃⣿⢀⡟⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣧⣾⣿⣿⣸⠃⠀⠀⠃⠀⡧⠻⣇⡾⣷⢛⠿⣿⢸⡏⡇⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡀⣿⡇⢸⣇⣿⣾⣿⠘⠀⡀⠸⡇⣿⡿⠻⠟⣿⣿⣿⣼⣾⡇⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⠻⣿⠸⣿⡇⣿⢹⣿⢸⠀⠀⢿⣿⣿⣿⢀⡿⣿⣿⣿⣿⢹⣿⣷⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠸⣆⢻⣄⣧⣾⣿⣿⢻⠀⠁⣿⣿⢡⣿⡟⣿⣿⣿⣿⣴⣟⢰⡇⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⢼⣄⠳⠻⣷⣿⣿⣽⠸⡇⣿⢹⡟⣿⣾⢡⡼⢀⢁⡟⣿⠋⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡜⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠋⠐⢀⠀ ⠀⠎⢀⠀⠀⠁⡿⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠃⢢⢰⠁⠊⡤⢀⠀⠀⠀ ⠇⢠⠀⠀⠀⡼⡁⠖⡠⢀⠀⠀⠀⠀⠀⠉⠉⠒⠔⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠃⣰⠀⠀⡜⢀⠀⠀⠀⠁⠈ ⠀⠀⠀⠀⠁⢿⢠⠉⠋⠛⠛⠾⠷⡿⣿⣹⢩⠀⠃⢼⢤⠢⠒⠂⡼⠀⠀⠀⠀⠀⡅⠞⡾⠀⠁⡜⠀⠀⠀⠁⠞⣠⢀ ⠀⠀⠀⠋⡶⣤⣤⣀⢀⠀⠀⠀⠀⣄⣽⣤⣤⣴⣧⡗⢭⠬⠒⠀⠀⡀⣄⠢⢹⠀⡆⢎⢠⠀⡽⠀⠁⠊⡴⢀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣦⠹⠉⠒⡰⠑⠀⣀⠠⠀⠀⡀⠂⠙⠀⣄⠘⢻⠀⠀⣿⠞⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡴⢀⠀⠀⣇⠿⠛⠛⡙⢅⠩⠆⠻⠛⠈⠀⡄⢶⠹⡄⣿⢷⠏⣼⠀⠀⠀⠀⠀⠉⠐⡠ ⠀⠀⠀⠀⠀⠁⠋⠟⣾⣴⢀⠀⠀⠀⠁⡟⣻⣉⣃⠟⡿⣿⣻⣙⣬⣿⠿⠙⠀⣆⢿⣿⡿⢸⠇⠈⠉⠚⠤⣀⠀⠀⠀ ⠀⠀⠁⠟⡾⣴⣠⢀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⢈⡀⣀⣄⣦⣷⡿⡀⣦⢿⠙⣇⣿⣿⢸⡋⣴⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣼⢷⡈⣦⣷⣿⣿⣿⠿⠙⠀⠀⣆⢹⠀⣀⣿⢻⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣼⣶⢿⠙⣗⠙⠀⣀⣦⣷⣿⣿⢿⠿⠛⣿⠙⠀⣿⣻⣾⢠⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠔⡠⢀⠀⣏⠻⡄⣷⣾⣤⢖⠹⠈⠀⡂⣭⣶⣷⣿⣿⣿⣿⣿⣿⢸⠀⠁⠊⠔⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⢀⠀⣧⠳⠈⣀⣤⣦⠵⠺⢒⠁⡉⣀⣤⣦⣿⣿⢿⠽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡤⢧⠿⠿⣶⣤⣤⣤⢤⡤⣤⣤⣤⣤⣤⣤⣯⢾⠴⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡄⠒⡴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⣀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀

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⠀⠁⠛⠛⠐⠇⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠓⠉⠈⠓⠛⠛⠛⠛⠛⠛⠛⠚⠉⠀⠀⠀⠀⠀ ⠀⡟⣾⢠⠀⡀⣓⡟⠒⠶⠶⠷⠿⠉⠋⠒⠔⡤⣩⣒⠓⠚⠓⠀⠀⠀⠀⡀⣄⠰⡉⣧⣿⣿⣿⣶⣤⢰⡀⢆⠺⠙⠈⠀ ⡏⣾⢀⠀⠀⠀⠉⣞⠰⠀⠀⡇⣾⢀⠉⠚⠤⣁⠚⡤⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣶⢠⠀⠀⠀⠀⠀⢃⠀⣅⢸ ⣿⢀⠀⠀⠁⡾⣠⠀⠀⠋⠙⡏⢻⡴⢀⠉⠔⣀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠙⠈⠀⠀⠀⠀⠀⠀⢀⢠ ⢹⠁⠈⠀⠀⢸⠁⠞⣴⣦⣿⣴⢀⠋⡴⢀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⣦⠻⠙⠁⠁⠀⠀⠀⠀ ⠀⡅⠀⣾⣧⣾⣠⠀⠀⡟⣸⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠉⠋⣚⣒⣒⢍⡩⠀⠀⠀⠊⠤⠄⠢⠈⡀⣧⣿⣿⢲⠀⠀⠀ ⠀⡀⠇⢸⠀⠀⠁⠟⡾⣫⡴⢀⠀⠀⠀⠀⠀⠀⠁⠔⡠⢀⠀⠀⠀⠀⠀⣏⢹⠀⠆⢠⠀⠀⠀⡁⠸⠀⣄⣹⠀⠀⠀⠀ ⣀⠀⡇⢛⠛⠛⣛⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠇⢿⠙⠉⠋⠛⠙⠉⠛⡿⣿⣿⠈⠀⢤⠓⠛⠴⣠⠀⠀⠀⡄⠹⠀⢇⠀ ⠆⠄⡠⠃⡴⢀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡀⢸ ⠀⠀⠀⢠⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣴⣤⣷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠷⢸ ⠀⠀⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠢⡙⣤⣶⣷⣿⣿⣿⣿⢹⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⢠ ⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠲⠑⡉⣉⣉⣉⣉⠟⡩⢉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀ ⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠘⠀⠀⠀⠀⠀⠀⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⢀ ⡏⢩⠀⠇⡰⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣴⢀⠀⠀⠀⠀⠀⠀⡟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀ ⣻⣿⣽⣀⠀⠚⠰⠒⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠫⡶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀ ⡇⡁⣾⠀⠟⢮⠒⠘⠂⡒⣳⣬⠢⠓⠐⠁⠉⡟⢠⠀⠀⠀⠀⠀⠀⠋⡿⢿⠙⡇⣿⣺⠒⠐⠒⠗⣤⢆⠛⠈⠀⢸⠀⠀ ⡆⡄⢀⡆⣽⣦⢿⠛⠉⠉⠉⣀⠯⡉⠉⠀⡇⢸⠀⠀⠀⠀⠁⠟⣶⣿⣿⣿⣌⣿⣤⠠⣦⠲⠒⠀⢿⠟⣶⣲⢇⢠⠀⠀ ⠀⠀⡆⠘⡄⢹⠄⡦⣐⣉⣯⣼⣠⣀⢀⠁⡌⢻⠀⠀⠋⡟⣴⢀⠀⡀⣿⣿⣿⠛⠙⠋⠛⠟⠿⣶⣠⣤⠳⠙⡄⠀⠙⠈ ⠀⠀⠀⢧⠈⣇⢳⠀⠀⠀⠀⣀⢀⠧⠿⣿⢿⡿⢿⡿⣤⢀⠀⠀⠀⠀⣏⣿⣠⣁⢈⢀⠀⣀⣀⠀⠀⠀⡇⣴⠀⠇⣿⢐ ⠀⠀⠀⡀⢿⠀⣼⢹⠀⠒⠉⠉⠋⡿⢀⣆⣿⣾⣠⠀⠀⠀⠀⠀⠀⠏⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠁⡼⡇⠀ ⠀⡇⠀⡀⣆⢼⢗⡏⠀⠀⠀⠀⠀⣸⠀⠀⡀⠀⠀⠀⠀⠀⠁⠛⡾⣻⣄⠤⡠⠀⡀⣇⠮⠹⠁⠛⡴⣄⠀⠁⣾⢀⡇⠘ ⠀⡇⠘⠀⠀⣧⡏⣌⢻⠈⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠋⠟⣿⣀⠀⡄⠸⠀⠁⠋⠛⡗⢼⣧⣀⠂⠀⠀⠀⡏⢀⠁⣼⠀ ⠀⠀⢳⠀⠀⡄⣿⢸⢱⣄⠶⠙⡏⢀⠀⠀⠀⠀⠀⠀⣆⣿⣿⢿⠀⠁⢿⡴⣠⢀⠁⡿⢸⡇⠀⠀⠀⠈⢡⣼⠀⡏⢠⠈ ⠀⠀⡄⠀⠀⠀⡆⢸⡇⠀⠀⠀⣿⠛⠒⠒⠒⠒⠒⠒⠲⡶⣶⣤⠶⠠⡇⠀⠀⠀⡞⠀⠀⡏⠀⠁⡜⢀⡿⠀⠃⢻⡾⢀ ⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟⢠⠁⠜⢀⠃⣰⠀⠃⢠⠁⡾⣡⠐⠈ ⠀⠀⠀⠀⠀⠀⡆⢸⡇⠘⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠎⢀⠊⣠⠁⠜⢀⠀⠎⢠⠃⣠⠂⣡⠟⢰ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⢪⡴⢀⠋⡼⠀⠀⠀⠀⠋⢠⠀⠊⣧⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠀⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⣾⣴⢀⠋⡿⣰⠀⠀⠀⠋⡿⢛⠛⡻⠙⡞⡞⠀ ⠀⠄⠐⠀⠀⠀⠀⡀⠁⠊⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣴⠀⠋⡴⢀⠀⠀⠀⠂⡴⣏⠰⠀⠀⠀⣿⢧⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⢀⠊⡰⢀⠀⠀⠀⠀⠉⠛⡴⢀⠀⠁⠉⠇⣸⡞⢒⠐ ⠀⠀⠀⠂⡠⣤⠶⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠴⢀⠉⠔⣠⠀⠃⠉⠉⠒⠴⣠⢀⢸⠀⠉⠞⣧⣿⣦⢯⢰⠀⠀ ⠂⠀⠀⠀⠀⠠⠙⠁⡈⣀⠤⠶⠲⠒⠛⠚⠴⡠⠁⠉⠛⠒⠖⠾⠳⠈⡀⢣⠈⠀⠀⠏⠷⡿⡴⢀⠀⠃⣾⠃⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⠤⠠⠀⠀⠎⡠⠀⠂⣌⠳⠈⢦⠘⠄⣸⠀⢀⠀⠋⠾⣤⢁⡾⣞⠀⠀⠀ ⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⡴⠀⠀⠀⠀⡀⠃⣈⠦⣝⠷⢹⠉⠉⠉⣯⠸⠉⡼⡤⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⣄⠦⡐⢄⣷⣛⢀⠀⡀⠋⣾⠖⠤⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢤⠤⣠⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠀⠐⡽⠟⣿⣿⣿⣾⣠⣀⠀⠀⠀⠀⣀⢤⠲⠉⡈⠀⡀⢦⢎⠘⢧⡌⠻⠀⡀⢱⢱⠀⢦⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣰⠀⡘⡏⣿⣿⣿⣾⣠⠀⠀⠀⠖⣤⢠⠀⠀⠀⠀⠀⣀⠴⠑⠈⣄⡙⠣⢣⣇⠱⠀⡀⡤⠘⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠞⣧⣼⠀⡆⢃⣿⣿⣾⣠⠂⡴⣄⠦⠳⠚⠔⠭⡠⢄⠯⠙⠀⠀⠀⠀⡀⠢⡝⠹⣧⠸⠸⢱⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠜⣾⢀⡏⠀⠁⢰⡟⣿⣹⠀⠀⠀⢳⡀⠦⠑⣀⠀⠀⣄⣷⣿⣿⢿⠈⠀⠀⠀⠀⡀⣦⠘⢣⡆⡄⠸⠀⡄⠸⠀⠀⠀⠀ ⠀⠀⠁⠋⡹⡿⣿⢠⠁⢰⠀⡆⠃⣾⣀⣀⣦⠷⠛⣿⠹⠀⠀⢧⠀⠀⠀⡀⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⣆⡟⠀⠀⢇⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⡏⣿⣿⣸⠀⡎⠀⠀⢰⡇⢸⠀⠀⠀⠀⣆⢈⢇⠀⠀⡏⢰⠀⠁⡟⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⣇⢘⠀⡄⠸⠀⢳⠀⠀⠀⠀ ⠀⠁⡟⣿⣿⣿⢰⠀⢸⠀⡀⠀⡇⣼⣀⠀⠀⠀⠀⢣⠞⠀⠋⣿⠿⣿⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢱⠀⡇⠀⠀⠀⠀ ⠀⡶⣿⣾⣠⣏⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠚⠀⠀⠀⣄⡷⣿⣿⣿⣿⣿⣿⣿⣾⢶⣤⣾⠀⠀⠀⠀⠀⠀⠀⡄⠸⢷⡟⠘⡀⠀⠀⠀⠀ ⠀⠀⣼⠃⡧⣼⠀⠀⠀⠀⠀⠀⣾⠀⠁⡿⢠⠀⠀⠀⠀⠀⣄⣦⣷⣹⣉⣉⠚⠴⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡌⣼⢾⠈⠘⠀⠀⠀ ⠀⡔⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⢿⠀⡜⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡴⣥⠸⢷⢹⣆⢈⠘⠀⠀⠀ ⠁⠀⠀⠀⠦⠸⠀⠀⠀⠀⠀⠀⣷⠿⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠞⡩⢟⠿⡛⣇⡷⣿⠈⢧⢀⠀⠀⠀ ⡄⠘⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡿⣹⣞⣴⣤⢀⡇⢿⡄⣘⣿⢸⠀⠀⠀⠀⠀ ⢀⠀⠀⠃⠚⣶⢸⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠐⠀⠊⠩⠋⡾⣠⢀⠋⠵⡯⣿⣿⣴⠃⢸⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⡿⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠉⠟⣽⣻⣹⠁⠉⡞⡾⣠⡃⢸⡀⣦⣶⣤⣧⢿⢈⠀⡟⠀⡄⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢿⠀⠀⠀⠀⠀⠁⠀⡇⠛⠴⡧⢿⣹⢚⠭⣶⣤⣠⠀⡀⡀⢦⠺⠙⡀⢻⠈⠀⠂⠞⣠⣾⢿⡴⣿⠀⠁⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⣿⠈⠀⠀⡀⠀⡄⠀⡇⣋⢿⣴⣠⢠⣁⠚⠒⠒⠛⣻⠘⠀⠀⢧⠀⢄⡗⣜⠙⠀⠀⠃⣾⣰⢷⣰⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣧⢹⠀⠀⠀⠀⠀⠀⡀⣿⣿⠿⠛⠟⣻⡿⠶⣿⣶⣤⢀⠀⠀⡘⢱⠀⡀⢠⡄⢼⠠⣸⢸⠀⡇⠀⠇⢠⠀⠁⠀⠀⠀⠀ ⢣⠈⠀⠀⠙⠀⡀⣿⠈⠀⠀⠀⠀⠀⠀⣇⠙⣄⠦⠷⡤⢧⠼⢤⠤⠤⢤⠀⠗⢠⡇⠀⠀⠀⠀⡄⡿⢃⢰⠀⡌⠀⡰⠀⠀⡼⠎⠀⠀⠀ ⠀⢧⢌⠑⡀⠦⠗⣿⢻⠀⠀⠀⠀⠀⠀⠂⣷⠻⠉⠀⣁⠯⣿⠻⠚⠒⠤⠤⡶⢦⡷⢿⠙⠀⠀⠀⢧⡏⠀⠁⢸⠀⠀⠁⡜⠎⢀⠀⠀⠀ ⠀⠀⢆⡿⠀⠃⠈⣀⣦⠘⠀⠀⠀⠀⠀⠀⡄⢿⡘⣑⣀⠀⠀⠀⢄⠑⠀⠀⠸⠀⡀⢀⡀⢤⠀⠀⡄⢸⠀⡎⠀⠀⠁⡰⠞⣠⠈⠶⠰⠀ ⠀⠀⠀⡄⠳⠀⢴⠑⠈⣄⠘⠀⠀⠀⠀⠀⠀⡄⣿⠹⢦⠈⠀⠀⠀⡀⢣⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⢀⠀⠆⢡⡿⠔⣀⠀⠀⠋⡶ ⠀⠀⠀⠀⠀⢄⠑⠀⣁⠀⡄⠱⠀⠀⠀⠁⠀⠀⡄⣷⢿⠙⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠁⠟⣴⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠲⢍⠓⠈⢄⠑⠀⡀⢦⠙⠀⡀⣦⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⢄⡲⠻⠈⢄⠲⠉⡀⢄⠑⠈⡀⢤⠲⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠋⠲⣒⢗⠭⣛⢿⠙⠉⠈⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠅⣀⢀⠀⡎⢓⡆⠀⠀⣿⢻⢠⠀⠁⡘⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠄⠠⣀⣀⣀⠀⣇⢀⠀⠀⠂⠷⠿⡇⣄⠢⠟⠸⠀⠀⠀⠏⣾⢀⠀⠁⡿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠟⠿⣿⣿⣿⠿⠛⠙⠉⠀⠀⡇⠙⠀⠀⠁⢯⠉⡏⠀⠀⡀⣿⠘⠛⡿⣸⠀⠀⠀⡰⣿⢿⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠛⠿⠿⣿⣰⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠠⡇⡀⠿⠸⡄⣤⢤⡶⠀⠀⡏⣻⣬⣷⣿⠀⠀⠀⡇⢸⣿⣰⠀⠀⠀ ⠂⠴⡾⣡⢞⡤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡆⣼⠹⠀⠀⠀⠁⡿⣿⣿⢿⡿⣿⠈⠀⠀⣼⢣⣼⠀⠇⠀⠀ ⠀⡜⠃⡼⠀⠇⣿⣿⣿⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⢣⡀⢄⠧⠽⣀⣹⣀⢀⠀⠀⣄⠘⠊⡤⣀⣦⠈⠀⠀⠀⠀ ⠀⠃⣿⢸⠀⣾⣿⣿⣰⠀⠁⡿⠿⢿⠶⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡹⠀⠀⠀⣧⠱⡆⠹⠀⠉⠉⠛⢹⢳⠀⠀⠀⢇⠀⢠⠀⠀ ⠇⡄⣷⣷⠈⢆⣿⣼⠀⠀⣢⠈⠀⠀⠀⠀⣀⢯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⡀⣣⠠⣄⣷⣤⣷⣿⣿⡞⢼⠳⠟⢀⠀⠀⠀⠀ ⣆⠀⡀⢣⣄⠤⣷⢠⠀⠀⠀⣄⠻⠛⠿⠿⡿⣿⣿⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⡀⣦⠙⠀⠀⢆⠈⠀⢆⠙⡀⣄⢷⢻⡀⣿⠹⠀⠀⠀⠀ ⠀⠆⠈⠀⠄⠑⡆⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⠿⡚⣄⠲⠈⡀⠢⠉⡀⠣⠉⠀⡀⢦⡟⣸⠸⠀⠀⠀ ⠀⠀⢆⠙⠀⡀⣷⠀⠀⠀⠀⡅⣿⣶⣥⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠑⡈⠠⠀⡀⢦⠙⣆⣌⠢⠈⡀⢲⣆⡄⠀⠈ ⠀⠀⠀⡀⠢⠙⡉⠘⠀⠀⠀⡄⢠⠤⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⣄⠲⠈⠀⠀⡀⢤⡜⠑⢆⠘⠀⠀⢡⠀⢟ ⢄⠢⠑⠀⠀⠀⡀⢣⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠖⠤⠤⡿⠳⠀⠀⠀⡀⡀⠀⡀⠀⠀⡄⣴⣤ ⠀⠀⠀⣇⢿⠿⠈⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠉⠚⠖⡤⣀⢄⠀⠀⠉⡿⣿⠸⢆⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣿⢿⠙⡜⢧⠜⠢⠛⠉⠏⠙⠈⠀⡆⢹⠀⠀⠈⠀⠀⠀⣧⢉⠈⠁⠉⠛⡿⣿⣾⣠⣸⣇⠀⡆⠘⠀⠀⡀⠣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣀⣇⢸⡀⢿⠿⡙⢫⠙⣟⣟⠀⠁⡄⠘⠀⣿⠈⠀⠀⣀⣤⣧⣾⣶⣤⣤⢀⠘⡇⠀⡇⠐⢀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⡷⣷⠀⡄⣿⣿⣦⣶⣶⣧⠧⡏⢸⣆⠈⢹⢇⠈⠀⠀⠀⣀⠉⠀⠀⠉⠗⢻⠹⠊⡤⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⢶⡿⡌⢹⠀⡄⣷⢳⠀⠒⢠⡇⣿⢿⠀⢆⣹⠀⢧⠘⠀⠀⠀⠀⣀⣀⠀⡏⡞⣠⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⢸⢧⠈⠀⡀⢳⢏⠈⠀⡆⣮⣿⠈⠀⣇⠀⡀⣰⠣⠈⠀⠀⠀⠁⠔⣠⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⠻⢏⠀⢆⠈⠀⠀⠀⣄⢷⠮⢸⢡⢧⠀⠀⢰⠀⡄⠘⣄⠳⠋⠔⢀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⢻⠈⡄⠳⠈⠀⠀⠀⣄⣷⡀⠘⢢⠀⡆⠘⠀⡄⠘⠀⣀⠢⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣢⠉⠀⢄⠑⠀⠀⠀⡄⠀⡄⠱⠀⠀⢀⠀⠀⡄⠘⠀⠀⡀⠤⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠑⠈⣄⠢⠑⠀⢡⠀⡀⢣⠈⠀⠀⠀⠀⡀⠷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠢⠑⠈⣀⡤⠱⠀⡀⣷⠻⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠦⡑⢢⠈⠀⡀⢤⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣤⢤⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⡀⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⢣⠀⠉⠁⠙⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠨⠀⠀⠀⠀⠀⠀⡆⢘⠀⠀⠉⠒⠴⠤⣀⣀⠀⠀⡀⠀⠋⠒⠒⠉⠈⠀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡶⣀⣀⢤⠙⠀⠁⠊⠒⠤⣤⠤⣠⠀⠀⠀⠀⠴⣠⠀⠀⠋⡹⣉⣉⣈⠠⡀⢦⡞⣐⠳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠉⠙⡀⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣽⢚⠒⠒⡒⠀⠀⠀⢄⠲⠉⣌⠺⠈⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠀⠀⠀⠀⡇⠐⠀⡰⠀⠀⠜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠄⠤⠓⠀⠀⠋⠈⠀⣀⣤⢶⠓⠈⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠀⠀⠰⠊⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠭⢊⠤⣃⢀⣄⠳⠈⠀⠀⠀⡀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠀⠀⢄⠓⠈⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀⠀⣄⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣤⣤⣶⠑⠛⠀⠀⠁⠞⡠⢀⠄⠻⠈⠀⠁⠔⣁⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⡣⢀⠈⠀⠀⠔⠀⠀⡀⢤⠑⠀⠀⠀ ⠃⠈⠀⠀⠀⠀⠀⠀⠒⡑⢌⡩⣀⠀⠀⡀⢿⡏⢻⠀⢃⠟⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⠀⢻⠀⡇⠀⠀⠀⠀⠀⡀⢦⠙⠈ ⡆⣅⢿⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣰⣿⢋⣿⣿⣿⣿⣿⢛⣿⣿⠿⠒⠒⠒⠓⠟⣿⣿⣿⠈⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⣰ ⣡⣉⣞⣠⠂⣶⣴⢄⠲⠉⠈⠀⠀⠁⡟⣾⢀⡗⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⡀⣦⣿⣿⢸⠇⠀⠀⢹⠀⠀⠀⠀⠀⠁⡰⠀ ⣿⣿⢹⠚⠀⠀⠀⠀⠀⡁⣹⣉⠛⣾⣤⠁⠞⣠⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⡄⣷⢸⡇⢰⠀⡀⠀⠀⠁⠀⠁⣼⠀⠀ ⣿⢚⠐⠀⠀⠌⠶⠓⠉⡟⣄⣿⣯⠛⠟⣹⠉⠉⠉⠉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣧⢻⠈⠀⠀⡇⢀⢸⠁⠚⡴⣀⣄⠳⠈⣏⢠⠀⠀ ⣿⢀⠀⠀⡁⣿⠿⡿⣿⣾⣶⣴⣧⣼⣤⣤⣤⣤⣤⣤⠤⣿⣾⣶⣶⣶⣲⣒⣶⣿⣿⡿⣿⣿⠺⠀⡸⠃⢿⣠⠀⠀⠀⠀⠀⣅⣾⠀⠀⠀ ⣿⠿⠛⠉⡾⣶⣿⣼⢀⠀⡄⢤⡷⣼⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣀⣆⠻⢸⡿⢠⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀ ⣿⣿⣽⣠⢠⠀⠀⠉⠀⠀⠀⡀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠙⠟⣾⢀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠉⠉⠉⠘⠀⠀⠁⠛⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⡛⠛⠛⠚⡴⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⢤⣀⠊⡠⢀⠀⠀⠀⡀⣀⠀⠀⡀⣆⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠠⣀⣀⣀⢄⠤⠑⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠇⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠱⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢄⠠⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠄⠦⠑⠀⠀⠀⠀⠀⠏⣄⠣⠑⠉⠈⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠂⡠⢃⠀⠀⢦⠈⠈⠋⠔⣠⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁⠉⠛⠏⠊⠀⠀⠀⢁⣏⢻⠈⠷⠤⠧⠑⠁⠈⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠯⡱⣔⣿⠏⠋⢺⠒⠤⠢⡿⣈⢦⡌⣳⢿⣷⠘⢣⣾⠘⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠑⡿⣧⣰⠇⣾⣴⢀⠀⠀⠀⠀⡀⣧⠺⣈⡀⣵⠙⢰⡏⢈⢙⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠻⡇⣸⠁⡷⢀⠀⠀⠀⠁⠀⠀⠀⠀⢣⡄⠑⡄⢙⢏⣸⡏⣻⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⡏⡿⢀⡀⠋⠾⠤⠂⠘⡄⠀⠀⠊⠐⠖⠘⡅⠘⣷⠛⣿⣏⠛⢸⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣲⣱⠆⣶⣷⢹⠉⠟⣴⠀⠀⡇⢹⠈⠁⣿⢿⢻⡜⠃⣸⢸⣇⠶⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠛⠀⡿⠚⠧⠶⣩⣘⠖⠳⠚⠒⠛⡘⣀⣅⣸⡇⣸⣼⣧⢠⢹⡷⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣧⠘⢀⣤⡰⠰⣃⣹⣄⠀⢸⠀⡧⣮⣀⣌⠀⡇⠃⢴⢡⡟⣱⡜⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡄⠱⡀⣶⠀⠀⢇⠀⡀⢠⢾⢀⠀⢀⡜⠃⢡⢺⡠⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿

⠀⠀⠀⡧⠈⠀⠀⠀⠁⡼⡁⣸⠀⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠁⠋⠞⣶⠶⡶⢶⠲⠓⠉⠈⡀⠣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠀⠀⠀⣿⣦⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠳⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠴⣩⠋⠖⠴⠤⢤⣤⠤⡶⢷⠙⠀⠃⠀⠀⠀ ⠀⠀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⠙⠀⠀⠀⠀⠀⠀⠟⣡⠞⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⡷⠀⠀⠀ ⠀⡞⢀⠀⠁⠚⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠁⡟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀ ⠃⢸⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀ ⡇⢈⠀⡇⢠⠀⡀⢡⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸ ⠀⢸⠀⡄⢹⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⠀⠀⠀⠀⠛⠀⠀⢸ ⠀⢧⠈⠀⡀⢤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠃⠷⠀⡿⠀⠀⢸ ⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⢠⠀⡟⢀ ⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠶⣠⠀⠀⠞⢀⠀ ⠀⠀⠀⠀⣼⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⣀⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡴⢀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⠀⠀⡀⣇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀ ⠀⠀⠀⠀⡄⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣤⢤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣻⠳⠈⠈⠀⠀⠀⠀⠀⠂⠖⠴⡤⣏⢠⠀⠀⠀⡄⡐⣀⣀⠀⠀⠀⠁⠉⠉⠁⠉⠉⠃⠜⡤⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣼⠀⠃⣿⣿⣯⣿⣦⠷⠛⠈⠀⡴⢀⠛⠒⠒⠒⠙⠀⠀⠋⠿⡿⣿⣿⣿⣿⣼⣿⣿⠸⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢰⠀⡏⣿⢹⣿⣿⠀⠘⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣹⠀⣿⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⣿⡏⣿⢸⠀⣿⣿⣣⣿⠰⠉⠞⠉⠞⡤⣤⠲⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣷⢻⡇⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⣹⣿⣿⢰⠃⣿⣿⡿⣿⡟⣿⡴⢀⠀⠀⠀⠀⠀⣄⣦⣷⣿⣿⣥⣿⣿⣿⡌⣿⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⡇⢰⣷⢸⣿⠀⡟⣿⣿⣿⣿⣾⢁⠘⠀⠀⠀⠀⠀⠀⠀⠃⠉⢮⣦⠿⣶⢿⣧⢸⡇⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠈⡿⠸⡟⢠⣿⠁⣿⣧⣿⣾⣇⢿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⠻⣎⠹⣇⡘⢻⡇⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⢸⣧⢸⣿⡇⣸⡿⢀⡏⣼⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⡄⡹⡄⠹⢻⣷⡜⡇⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢿⡿⢸⣾⡇⢸⣿⠙⣿⢀⠇⢱⣼⢀⠀⠀⠀⠀⠀⠁⢻⠀⡯⠿⣿⢾⡟⠹⡆⡜⡏⠸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⢸⢸⡇⢻⣿⣇⣸⠀⣾⡅⠚⠟⠿⠿⠠⠄⠳⡏⣰⠈⣯⣿⣿⢿⣼⣧⠸⣧⣆⣹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⢸⡇⡇⣼⡟⢀⡇⢻⣯⣿⣿⣿⣿⠋⠐⠉⣇⠳⢿⡏⢸⠛⡌⣷⢯⢿⡆⠘⣿⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡎⢸⢷⡇⣿⢸⣼⠀⠀⡁⣺⣀⣀⣀⣀⢀⠋⣇⣿⢊⣯⣿⢹⡧⢸⡇⣿⡇⠘⢫⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢹⣧⡇⡿⣿⢸⢰⠀⠀⡇⣾⠙⠀⠀⠀⠀⣸⡇⢿⠀⣦⣿⣷⡇⢿⡴⣿⡄⢸⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⡜⣿⣿⣿⢸⠀⠀⠀⡇⢻⡝⢻⠉⠈⢿⢩⡍⣿⠸⠀⣧⡇⡇⢿⠀⣼⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣿⣿⢸⠀⠀⠀⡇⢹⠀⡀⣧⣈⣿⣅⣉⣾⢠⠀⡇⡷⡟⡿⠀⢸⠇⢸⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⡀⣀⢉⡃⠁⠃⢠⢠⡇⢴⠀⠏⠀⠀ ⠀⠀⠀⠀⠀⠁⠉⠛⠚⠶⡶⠶⠒⠙⠈⠂⠈⠀⣻⣓⠀⣇⠙⠟⣠⠀⡌⣿⠀⠀ ⠂⠚⠮⡷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠱⣀⣀⠃⣿⡻⣿⠀⠁⣵⣸⠆⠀ ⠄⠏⢀⡟⣿⢰⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢣⠰⢀⡳⢃⢀⠀⡀⠛⡠⣀⠐⠘⠀ ⠈⣧⠱⣇⣼⠀⡡⣀⢀⡄⠫⠈⠀⠀⠀⠀⠀⢢⠈⡀⢐⢦⣬⣷⢻⠸⠛⢀⠀⠀ ⠀⠈⢂⣈⢠⠀⠀⢿⣿⣿⣿⢰⠀⠀⠀⠄⠦⠲⣝⠪⡈⠢⡈⠢⡈⢤⡗⢻⠀⠀ ⠀⠄⠑⡄⠘⠀⠀⣽⣢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡂⠈⡀⠢⣂⠌⠈⢠⡘⠁ ⠠⠑⠈⣀⢣⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⠐⠄⡧⠺⠀⡀⠀⡀⠀⠆⡤ ⠀⠀⣦⣿⡙⠳⠒⠉⠋⠀⠀⠹⠀⠈⠀⠆⡹⢀⠉⠟⠞⣧⢣⢃⠈⡀⠢⠀⠀⠀ ⠀⠀⠀⡀⣏⠘⢷⡻⠻⢿⠈⠘⠰⢜⠈⠀⣀⣴⣠⣀⠋⠘⡏⠀⠆⠈⠀⠀⠀⠀ ⠀⠀⠀⠆⡷⢣⡀⣧⠐⠄⡇⣿⡄⢸⢆⠘⠀⡀⠠⣁⣾⣠⠀⠀⠀⢃⠀⠀⠀⠀ ⠀⠀⠀⠀⡹⡘⠑⠀⡄⠢⡞⣇⠰⡄⠀⣡⠢⠉⠔⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⡀⢦⠘⠢⠈⠀⡀⢸⡱⠀⢠⠀⠡⡀⠠⠑⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⡑⠠⠐⠌⠀⠣⠈⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠤⠒⢊⠈⣄⠰⠈⠀⠀⠀⠀⠀⠀⠁⠊⡲⠠⠀⠀⠀

⠳⡀⠳⠈⠀⡀⠢⠈⠀⠀⢸⠤⠧⢠⠀⠀⠀⣇⢄⢶⠓⡉⣈⠤⠦⠒⠉⠉⠀⣼⠀⠀⠀⠋⠠⠀⠀ ⠀⢄⠙⢧⠈⠀⠀⣄⠘⡏⢀⠇⣰⠀⠀⠀⠀⡟⢹⠀⠀⠀⡀⣄⢤⠢⠒⠉⣉⢤⠢⠒⠋⢸⠀⠃⠰ ⠀⠀⡀⢠⢧⠈⠀⠊⣣⢱⠔⢀⠀⠀⠀⠀⡜⣀⣄⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠤⠓⣈⢧⣴⠀ ⠀⠀⠀⠀⡀⢇⡜⠁⡾⣠⠀⠀⠀⠀⠀⡞⠀⠀⠀⣄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡶⠀⠀ ⠀⠀⠀⠀⠀⣄⢹⡿⢀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠳⠈⡀⠱⠀⠀⢀⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⢇⠈⡄⠹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⠀⠈⠀⢸⠀⢿⠀⡀⠳⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⢣⠏⢸⠀⣿⠈⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⡟⣿⢀⡞⣿⠀⠋⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠇⣿⣰⡟⢠⣿⠏⣷⣿⣾⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⡄⣾⢿⠈⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠃⣯⣽⡾⣼⡇⣿⢾⡶⣶⢲⠛⠈⠀⡇⠀⠃⡴⠀⠀⠀⠀⠀⠀⠀⠄⣗⣿⠿⠈⠀⠀⠀ ⠀⠀⡇⠃⣫⢾⣠⡖⢁⣿⣠⠀⠀⠀⠀⠀⡀⠢⡟⠞⣤⠀⠀⠀⣀⣄⠤⠢⠘⠀⠀⣧⣿⣿⠘⠀⠀ ⠀⠀⡇⡜⣀⠀⠁⠟⣿⢠⠀⠀⠀⠀⠀⠀⠀⡇⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣷⣿⣾⠀⠀ ⠀⠀⡇⢙⠏⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡟⣿⢼⠀⠀ ⠀⠃⡟⣴⣈⣀⣷⣿⣿⢿⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⠀⠀ ⠀⡇⣮⠴⡠⠢⡒⣀⣿⣿⣿⢿⠻⠛⠛⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⣿⣿⣿⣷⣿⢈⠀ ⠀⡧⣄⠻⠙⠉⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠀ ⠀⡄⠸⣣⢸⡀⣌⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘ ⠀⠀⣇⡌⣄⠀⠁⠋⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣷⣿⣴⣤⣇⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⢣⠉⠟⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⡄⢀⠀⡀⢀⣧⣿⣿⣿⣿⢸ ⠀⠀⠀⠁⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠋⡟⣿⣿⣿⣿⢀ ⠀⠀⠀⡄⣦⡹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⣀⣆⣙⢧⠿⡿⣿⣿⣿⣿⣿⣿⣾⢠⠀ ⠀⠀⠀⠀⠀⡀⣣⣯⣾⣿⣿⣷⣾⣧⣾⣠⣀⣀⣀⢀⠀⠀⠀⠀⣣⣿⢰⣸⣾⣿⣿⣿⣿⣴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡘⣿⡇⢣⣧⢿⣟⢸⠃⠋⠵⢸⠀⠀⠀⡇⣼⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⡼⣷⡌⡸⡆⡇⢸⠀⠏⢾⣠⡟⢹⠿⠫⠀⡞⢃⣸⢇⣇⠁⠁⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡆⣿⢸⢸⠀⣇⠏⣾⢀⠇⣧⣰⣧⣿⣾⢁⡟⢸⡼⡇⡟⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⢈⢸⠀⡇⢿⢀⠃⢠⡿⠛⡣⡴⢁⡴⡟⣼⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠞⣿⢸⢸⠀⣿⢠⠀⡠⠃⣴⢎⢠⠞⣠⠏⣠⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣷⢇⢋⠇⣼⠀⠀⠊⣠⠀⠊⡰⠁⠎⢀⠁⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡣⢿⣿⡿⢻⠚⡠⠁⠒⣠⠉⠒⣠⠁⠋⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣠⣇⣯⣦⢟⠭⠤⠤⣀⢉⠛⠾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⡀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢔⣡⠈⠀⠀⡏⣿⢿⣎⢿⣿⡿⠷⢾⠟⣿⠹⡂⠘⢆⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡤⢀⠀⠀⢀⠀⠁⣿⣿⣿⣿⡽⣷⣿⢸⢯⣻⡄⣿⢹⢇⠈⡅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠑⠛⠚⠚⠤⡠⣀⡀⢤⠦⠺⠙⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣨⡷⣿⢹⣧⣿⢿⢻⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠞⣫⣴⢀⠀⠁⣹⣉⣛⣛⠶⠽⠦⠒⠓⠙⠉⣈⢤⠲⣇⣿⣿⣿⣿⣿⣿⢿⠻⣌⣿⡻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠁⠋⠔⣀⠀⠀⠋⡿⣏⣰⠋⠒⡤⣀⠀⠀⠀⡀⢄⠳⣁⠮⠑⠀⠀⣀⣄⢵⠦⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣀⣿⣿⣿ ⠀⠀⠀⠀⠔⡤⣉⠋⠒⠴⠤⣀⠃⣿⢰⡄⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⢻⠀⠀⠀⠀⣀⠣⣌⣦⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿ ⠀⠁⠒⠔⡠⣀⣇⣿⠿⠻⠙⠁⡾⢠⠀⠀⢣⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢧⢣⣿⠀⠀⠀⠿⠈⠀⣄⠾⣝⣿⣿⣿⣿⣿⣿⣽⣤⣶⣶⣿ ⡀⠀⠀⠀⠀⢇⠈⣿⣿⣿⣿⣼⢀⠀⠀⠀⡇⠈⠀⠀⠀⡏⢿⠿⠶⠶⣶⣴⡄⣶⠀⠀⠀⡀⠢⠈⠀⡄⡀⣦⣿⣿⣿⣿⢀⡀⢿⠙⠀⡃ ⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣰⠀⠀⠀⠀⠀⡇⢿⠁⠋⡿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠀⢓⣆⣟⣿⣿⢿⠿⣿⣮⢿⡴ ⠀⠀⠀⠀⠀⡞⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⡟⣾⣶⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⢄⡕⣿⣿⣿⣿⣌⣦⣶⣷ ⠈⠀⠀⠀⡟⢰⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⡼⢂⡒⢀⠦⡙⣨⣷⣿⣎⣜⠿⠤⡤ ⣤⢿⠻⠏⣿⠀⣿⢀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣠⢀⠀⡀⢤⠠⠀⡠⣀⣦⣿⣿⢿⠉⡍⠻⠓ ⠀⡀⣷⣿⣿⠿⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢨⡀⢷ ⠀⠀⡇⣿⣧⣿⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠚⠠⠈⠀⠁⠟⣿⣿⣿⣿⢻⠉⡆ ⠘⠀⣿⣿⡟⣿⣹⠀⠊⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠒⠉⠏⣼⠁⠉⢬⡥⣯⣿⣿⣾⣿⣿⠀⣷⣿⣿⠘ ⢸⠀⣷⣿⣿⣿⣿⠃⣸⠀⢁⠀⠀⠋⠔⠤⠧⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠱⠀⢸⠀⠀⡅⣿⣷⣿⣾⣶⣶⣤⣿⣿⡼⣏⣿⠐⣧⣿⣿⣿ ⢘⡇⠿⣿⣿⣿⣿⡏⢨⠀⠂⢾⡡⢊⡫⠔⢀⠀⠈⠇⠘⠀⠀⠀⠀⠀⠉⠛⠀⢿⠀⠀⡞⠁⡿⣿⢿⠤⠤⡥⣿⣿⣸⣇⣿⠀⡆⣿⣿⣿ ⢈⡇⣿⣿⡃⣿⣿⣿⢸⠀⡟⠂⡵⡴⢀⠀⠋⡴⠆⣿⢡⠀⠀⠉⠟⡿⣿⣿⡆⣿⠸⠰⣧⡇⣿⣿⣿⠼⡡⣇⣿⣸⣇⡏⣿⡏⠀⣿⣿⣿ ⣿⡈⣏⣿⡞⣷⣿⣿⣿⠇⣾⣤⢀⠀⠀⠇⢰⠃⠿⣿⡼⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣼⣀⢹⡄⡽⣿⢸⠀⣿⣿⣿⠈⣿⣿⣿ ⣷⣿⣿⣿⢹⡄⣽⣯⣿⡉⣿⠀⠀⠀⠀⣿⠙⡟⣿⣼⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⠀⠀⣧⠘⣿⣿⠀⠀⡆⣿⣿⢻⣄⣿⣿ ⡇⣿⣿⣿⣿⠀⡄⣿⣹⣿⣿⠈⠁⠉⠛⣿⣿⣵⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣶⣿⢻⠀⠀⡀⢻⣇⣿⠘⠀⠀⣷⣿⣿⠸⡇⣿ ⠀⣷⣿⣿⣿⢸⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⢴⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣴⢀⠁⡶⣿⢹⣧⣿⠈⠀⠁⣿⣿⣿⢻⠘⠀⡟⣿⣿⣿⡏⣿ ⠘⡄⣿⣿⣿⣿⠈⠀⡁⣾⣿⣨⣀⢀⠁⣿⢻⢷⠖⣿⣿⣿⣷⣿⣿⣶⢠⠀⠀⡀⠀⣧⣿⣿⣿⢸⢣⡇⣿⣿⣿⣿⣿⠀⣿⣏⣿⣿⣿⣿ ⢿⠈⣇⣿⣿⣿⣿⠸⡀⠀⡆⢻⠀⠏⡗⣿⣿⡌⢸⣷⣿⣿⡿⣨⢀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⡏⡿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣿⣿⣿ ⡄⢻⠀⣷⣿⣿⢿⣿⠙⠀⠁⣧⣿⣄⡹⣿⣿⢻⢯⡇⣿⣿⢹⢀⠀⠀⠀⠀⠀⠁⠛⠁⣆⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿

⠉⠀⠀⠀⠁⠉⣉⣈⣈⣤⣤⠛⠛⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷ ⣀⣀⣸⣀⣇⣸⣿⡀⣀⣸⣇⡀⣀⣣⣄⢸⣀⣄⣼⣥⠼⡱⢀⠀⠀⠉⠉⠒⠒⠒⠒⠀⠓⠛⠉⠉⠉⡈⢧⠙⠈⠀⠀⠀⠐⠀⠀⠀⠀⡩ ⠁⣿⢸⠀⡇⢸⣏⠀⠁⢸⡇⠀⠀⡎⠀⢸⠀⠇⢹⡴⠀⡀⠸⠀⠀⡟⠀⠀⣀⢄⠤⠓⠈⠀⠀⠀⠀⠀⣀⢀⠀⡀⣷⣄⣿⣿⣿⣿⣿⣿ ⣾⣀⠀⠀⣥⣿⢻⠒⡷⠿⣸⠀⠏⢻⡜⠉⠋⣾⣹⠉⠋⠗⣿⠤⡠⣤⠣⠈⠀⠀⠀⠀⡄⠢⠓⠉⠀⠓⠛⠀⠀⠀⡏⠏⣿⣿⣿⣿⣿⣿ ⠀⠀⠋⡷⣾⣠⠀⠀⠀⠀⠀⣇⣿⣹⠙⡊⣄⣤⢤⠒⠒⡷⣾⢳⠀⠀⠀⣄⠢⠈⠀⠀⠀⠀⠃⣿⣿⢸⣳⠋⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿ ⠠⠀⠂⡠⠀⠀⠀⠀⠀⠀⠉⣞⣶⠿⣉⢮⠢⠒⠙⠉⠉⡸⠀⠀⢣⠉⠉⠺⠀⡉⢄⠑⠈⠟⣯⣿⣿⢠⠀⡀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⣿⢻⠈⠀⣀⢄⠤⠒⠒⠒⡗⠀⠀⢀⡦⣸⠀⠀⠀⠀⡀⣡⣀⣦⣷⣿⢠⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠂⢠⠀⠉⠎⠛⠀⣾⣷⣿⢼⠲⠓⠉⠉⠉⠋⠰⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⣀⢤⠀⠀⠀⠏⢸⡇⣿⣶⣶⣷⣿⣶ ⠀⠀⠀⠀⠀⠀⡀⢀⣿⡿⠊⠔⣀⢤⠦⠒⠓⠛⠒⣼⠘⠀⠀⠀⠀⡏⠔⠉⠋⣿⠂⠛⡍⠻⠈⠁⠉⠒⠤⡤⣤⢱⢨⡇⠁⠈⠀⡤⣷⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⢸⠀⠀⠋⠿⣿⣿⣿⣿⣿⣿⢿⡿⣛⣙⢀⠒⣙⠢⠈⢣⡗⢿⡴⣿⠐⠀⠀⡉⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⣾⠀⠃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⡄⠐⣄⡿⡾⣡⡴⣿⠟⠙⡜⣦⣿ ⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠁⠛⡿⣯⢿⢩⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠀⠀⠀⠀⣾⢀⡄⢹⢡⠀⡟⢰⠀⣿ ⠀⠀⠀⠀⠀⠀⠟⢹⠀⠀⠀⠀⠀⠃⣿⣉⣞⣤⢁⡿⣿⢟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⠀⠀⠀⠀⢸⠀⠀⣇⡆⠻⢠⠀⡟⣿ ⠀⠀⠀⠀⠀⡇⣹⣆⢿⠙⠉⠉⠚⡴⠤⣠⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⡇⠈⠀⠀⠀⣎⠁⡟⣿⣿ ⠀⠀⠀⠀⠀⡅⢀⠀⣿⣿⣿⣠⠀⠀⠀⠋⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⣄⠢⠓⠙⢯⠻⠉⠛⢿⣿⣿⣯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⠀⠂⡟⣿⢿⡟⢋⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡃⠀⠁⣿⣰⠀⠀⡟⣿⠀⠁⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡰⠋⡾⢠⠀⠀⠏⣿⣻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⣇⢸⠇⣾⣾⢞⠀⠃⣿⢠⡞⣀⠀⣁⢀⢠⠀⠀⠀⠀⢁⡋⠛⣒⢤⣭⣛⣛⠛⠙⠀⠀⡀⡀⣄⠠⡀⣷⣿⣿⣿⣿⣴⢠⠄⠠⠀⠀⡀⣷⡿⢳⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢫⣵⡴⢀⠀⠃⣿⣹⡼⢀⠀⠀⡄⣬⢤⡠⠁⣧⣤⣀⠁⠚⠴⣡⢞⣤⢀⡇⠰⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠉⡍⣼⣣⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣡⡼⠀⠀⠏⣾⣿⡼⢀⠀⠀⠁⠊⢲⠉⠃⠳⣼⠋⠴⣀⠋⠴⣀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠒⠀⣄⢷⠈⠀⠀⠀⠀⠄⡿⣿⢀⢧⠁⣿⠹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢡⡼⠀⠀⠞⢠⠏⣾⠀⠃⡿⠀⡤⣤⣠⣀⣿⡿⣴⢀⠋⡴⢀⠀⠀⠀⠀⠀⡀⡄⠹⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣄⠿⠙⠋⠋⠿⠓⢹⠀⡇⠚⡗⣿⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢹⡴⠀⠀⠀⢋⡿⣾⠃⠏⣨⢠⠀⠀⠀⠀⠁⡾⢀⠋⣴⢀⠀⠀⠀⠀⠀⠛⠟⡨⣖⣶⣲⣒⠽⠉⠀⠀⠏⡤⣀⢦⠙⡀⣧⣿⣿⣠⠀⢿⠀⡆⢸⠶⣷⣿⠘⠀⡇⠀ ⠀⠀⠀⠃⣰⣀⠀⠀⠋⡴⣁⣼⣠⠛⣨⢈⠉⠀⠀⠀⠀⣴⠋⡴⢀⠀⠀⠀⠀⠀⠁⠟⣠⠀⠀⠀⠀⠀⠀⠏⣿⠘⠀⣸⠀⠀⠀⡁⢸⠀⣄⢿⠀⠀⡇⠻⡟⡞⠀⡀⢻⢹⠀⡏⠀ ⠀⠀⠁⡼⠀⠀⠋⡽⢉⠒⡴⠀⠃⣛⣙⣽⢞⠠⠋⠰⠁⡾⢠⠀⠀⠀⠀⠀⠀⠀⡏⢿⠛⠛⠛⠛⠛⠛⡿⣿⣿⢸⠀⣄⠦⠖⡴⣀⠀⠀⠀⣄⠹⠀⡇⣿⣧⣾⠙⠀⣿⡇⠀⣿⠀ ⠀⠀⡞⠀⠀⠏⣿⣠⠀⠞⠀⠃⡰⠀⣶⣠⠁⡾⢀⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡹⡇⣿⡻⢻⣾⠀⡄⡇⡟⣸⠀ ⠀⠀⢀⠀⠇⢠⠁⠊⡿⢀⠃⣰⠀⠀⠀⠏⣰⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣯⣷⣿⣿⣿⣿⣿⣿⣹⣀⣤⣿⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣧⣧⣯⣿⢸⢀⠀⠀⡟⣿⢀⠀ ⠀⠀⠀⠀⡇⠛⠈⠇⢰⠀⣰⠀⠀⠀⡾⢀⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⣉⣤⣶⣶⣶⣶⣷⠀⠏⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣯⣿⢸⠀⠀⠀⣹⣸⠀⠀ ⠀⠀⠀⠀⡆⣯⢞⣼⠀⡀⠀⠀⠁⡾⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠢⠓⠛⠛⠒⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⣿⣧⠀⠀⠀⠇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⣾⢀⠀⠀⠀⠁⡼⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡟⢠⣿⠀⠀⠀⡇⢰⠀⠀⠀ ⠃⠀⠀⠀⠀⡇⢠⠀⠀⠀⠁⡼⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠂⣿⣸⠃⣸⠀⠀⠀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡼⢀⠀⠇⢫⠛⠚⠐⡄⣭⠧⠈⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠉⠀⠀⠁⠉⠉⠒⠟⠒⠤⣤⣄⢁⠉⠀⠀⠀⠃⣿⢀⣾⠀⠀⠀⠁⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⡟⢀⠀⠀⡀⣼⣧⠻⠟⡷⣘⡀⣁⢯⠿⠒⠙⠉⠉⠀⠀⠀⠀⠀⠀⡀⠄⣀⢀⡀⣉⠟⣩⢉⠉⠉⠟⠷⣻⠺⢻⠈⠀⡇⣸⠇⢀⠀⠀⠀⡏⢀⠀⠀⠀⡸ ⠃⠀⠀⠀⡆⠀⠀⠀⠃⣠⠀⠀⡜⠀⢸⡟⣾⣿⣷⣻⣙⠀⠀⡀⢦⠓⣌⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢞⠤⣁⠛⢛⡙⠀⣅⠹⡋⣿⢿⡇⢠⠀⠀⠀⠀⠀⣼⠀⠀⠀⡟⢠ ⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⢸⠀⡇⢰⢹⡀⢳⡀⣄⣽⣾⣶⠿⡶⣶⣤⠀⠄⡩⢉⠉⠀⠀⠀⠀⠀⠟⡿⣙⠉⢉⣉⣉⡉⣛⣿⣶⣶⣙⣀⡼⠑⠈⠀⠀⠀⡏⢀⠀⠀⡟⣰⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⠈⣆⠘⡆⢻⠀⠀⡀⣀⣤⠤⠒⠒⠀⠁⣿⡇⣰⣄⠣⠉⠈⡀⣄⢤⡤⣤⣤⣤⣀⣤⣤⢀⠀⠀⡇⢷⢠⡇⢿⠀⠀⠀⣼⠻⠀⠃⣽⡿⣼ ⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⢹⠀⡇⢸⠀⣧⠈⣧⢻⠀⠁⠉⠈⠉⠊⠀⠀⡏⣷⡞⠀⠀⠀⣄⣷⡘⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⡸⡇⠉⡼⣿⠀⠀⠀⢹⣸⠁⡿⣽⣴⠀ ⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⡏⠀⡆⢸⠀⣄⢿⡇⣯⠘⠀⡀⣀⣀⠀⠀⠀⣾⣾⢠⠀⠀⠀⠀⡀⣧⣌⠤⠤⠤⠀⢦⠾⠙⠀⠋⠐⡏⢠⠃⣾⢀⡞⠀⠀⡇⣼⠀⡾⣿⣰⠀⠀ ⠁⠀⠀⢣⡎⠸⠀⠀⠀⠀⠀⡇⣿⠸⠀⢻⠀⠀⡆⢸⣼⢿⠈⠀⠀⠀⠀⠀⡟⢃⢸⠀⠀⠀⠀⠀⠀⡀⢳⠀⠁⠉⠛⠗⢾⣧⣸⠒⠇⢰⠀⡟⠀⠇⢸⠀⠏⣼⢋⣿⣾⢀⠀⠀⠀ ⡀⠀⠀⡀⢧⢷⠀⠀⠀⠀⠀⠀⣷⢹⠀⡇⠘⠀⠀⣧⣿⣧⣄⢦⠓⠉⠉⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢶⣤⣀⢀⡟⢰⡇⢸⠃⣰⠀⠃⣸⠁⡼⠀⠟⣼⢀⢋⣴⢀⠀⠀⠀⠀ ⠑⠀⠀⠀⠀⣷⢨⠀⠀⠀⠀⠀⡇⣟⠘⠀⢻⠀⠀⡆⣿⡄⠸⠀⠀⠋⣾⣤⣄⠀⠀⠀⠀⠀⠀⠀⣤⣴⣀⢸⠀⠠⠏⢠⠀⡇⢻⣠⠀⠀⡾⠀⡏⢿⡵⣴⠁⡞⢀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣯⠱⠌⠹⠀⠀⠀⣷⢡⠀⡀⠀⠀⠀⡾⠀⢸⠀⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠇⢰⠀⠀⡇⣰⠀⠀⡎⢠⠏⣴⢏⠡⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⠀⠀⠀⠀⠃⣿⡀⢳⡀⢳⠈⠀⡀⣹⠀⠀⠀⠀⠀⢻⠀⢹⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠋⢠⠃⠀⠁⣸⠀⠀⡞⢀⠟⢀⡄⢋⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⡄⡹⢀⠀⠀⡀⢦⠿⠈⡆⠸⠀⠀⠀⠀⣰⠁⣾⢀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠟⣠⠃⡸⠁⡜⠀⠀⠀⠁⡼⢀⠁⡾⣯⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣽⠻⠈⠀⠀⠀⡀⢦⠯⠘⠀⠀⠀⠀⠁⡴⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⢠⠃⡼⠀⡤⠀⠀⠁⠞⣠⠁⠞⣠⠀⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⠀⠀⠀⠀⠀⡉⣾⢰⠀⠀⠀⠀⠀⢀⣄⠻⠀⠀⠀⡁⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⣼⢁⠞⣠⠀⠀⠀⠀⠄⣫⠴⠏⢱⠋⠐⡇⣯⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠆⣷⢉⠉⠉⠉⠀⠀⠀⠀⠁⠞⣠⢡⠩⠉⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠟⣠⡀⣩⠀⠀⠀⠁⠉⠖⡠⢀⣀⣀⣋⣴⠀⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢻⠀⠀⠀⠀⠀⠀⠏⢠⠉⠞⠩⠟⣩⠛⡴⣠⠀⣀⣤⠲⠛⠛⠉⠈⠀⠀⠀⠀⠀⠉⠚⣴⣴⢠⠀⠀⡀⣷⠤⡤⣠⠀⠀⠀⠀⠭⣾⢠⠁⠟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⠘⠀⠀⠀⠆⡶⣤⣟⣿⡾⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⣤⣤⣤⠤⣠⣀⣀⣀⢦⠙⡀⢳⠈⠁⠉⠀⠀⣉⢉⠋⠶⣠⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣦⠘⠀⠀⠁⠞⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⠙⢦⠙⣆⣙⣈⣀⣀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠒⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡶⢿⡻⢶⠙⠛⠛⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠚⠴⣭⠭⡭⣈⠳⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣻⠿⣿⣿⣿⣿⣿⠿⣝⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣤⣢⣒⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠐⠀⠒⠛⠙⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠉⠉⠊⠀⠖⠗⠉⠀⠀⠀ ⠀⡇⠟⢰⠀⠀⠀⠈⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠉⠀⠀⠀⡃⣿⢿⠈⠀ ⠀⡄⣿⢹⠀⠏⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⠹⠀⡟⣿⣿⢀⠀ ⠀⠀⣿⣿⠻⣿⣿⣼⣤⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣼⣠⣿⡟⣿⣿⣩⠀⠀ ⠀⠀⡀⣧⣿⣿⣿⢿⠿⠿⣼⢀⠀⠀⠀⠀⠀⣄⠻⣿⣿⢿⠿⣿⣿⣿⣪⠀⠀⠀ ⠀⠀⠀⠀⢄⣦⣶⣴⣭⣫⢐⠀⠀⠀⠀⠀⠀⠁⣄⣼⣷⣭⣶⣖⠤⢀⠀⠀⠀⠀ ⠀⠀⠀⣀⠤⠢⠓⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠐⠤⠄⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠊⠀⠀⠀⠀⣄⢥⢭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠶⣠⢀⡀⠀⠀⠒⠉⠈⠀⠀⠀⠀ ⠦⠷⠿⣿⣹⠀⠀⠀⠀⠀⡏⣼⣫⣯⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡼⣷⠿⠻⠀⠀⠀⠀⠀⡀⣿⠿⠿⠿⠲ ⠀⠀⡀⣧⣿⠻⠀⠀⠀⠀⣧⢹⣛⢭⣟⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡯⣹⡗⢶⣜⣿⠠⠀⠀⠀⠀⠋⣿⣾⣠⠀⠀ ⠀⠀⠀⣀⣦⣿⣿⠻⠙⠉⠉⣟⣿⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣿⣿⣿⣾⣴⠀⠀⠀⠋⡿⣿⣾⢴⠠⠀⠀ ⠀⠀⠀⠀⠀⠃⣖⣶⣶⣶⣤⣤⢤⡀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣴⣥⣶⣶⠿⠿⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠒⠒⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠋⠉⠉⣉⢉⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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