Tarmainian Head Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⢰⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣟⣿⠿⠿⡿⣿⣿⣿⣿⣿⣮⣷⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣦⣷⢙⠉⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⡿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⢼⡇⣿⣿⣿⢿⠙⠀⠀⠀ ⠀⠀⠀⠁⠟⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠇⢼⠳⣧⣿⣿⣿⣿⢿⠈⠀ ⠀⠀⠟⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠁⡿⢻⠀⡀⣷⣿⣿⣿⣿⣿⠀ ⠀⠏⣿⣿⣿⣿⣿⣧⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⢠⠁⡿⣿⣿⢿⠀⡅⣿⣿⣿⣿⣿⠈ ⠃⣿⣿⣿⣿⣿⣸⠀⠀⡅⣿⣿⣿⣿⣿⣿⣾⢠⠁⡿⣿⣼⢀⣆⢻⡀⣽⣿⣿⣿⣿⢸ ⡇⣼⣇⣷⣿⣿⢸⠛⠂⣿⣿⣿⣿⣿⣿⣿⢹⠁⡿⣿⣿⠀⠀⠀⣧⢻⡄⣾⣿⣿⣿⢸ ⡇⢿⡿⣿⣿⣾⡀⢀⠇⣿⣿⣿⣿⣿⣿⠹⣧⡼⣿⣿⣸⣀⢀⠀⠃⣿⠻⠀⣧⣿⣿⢸ ⡇⣿⣿⣿⣿⣻⢉⠀⡏⣿⣿⣿⣿⣿⣿⣿⠘⣦⡾⣿⣿⠘⠀⠀⡟⣿⣀⠁⣿⣿⣿⢸ ⡆⣿⡷⣿⣿⣿⣹⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⠘⢧⣎⣿⣿⠙⡟⣿⢠⠀⡿⣿⣿⣿⢸ ⠁⣿⢿⣛⣷⣾⠂⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢷⡆⣿⣿⣿⢠⠀⡿⣿⣿⣿⣿⢸ ⠀⣿⠀⠀⠷⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⢃⣆⣿⢠⠀⡟⣿⣿⣿⣿⣿⣿ ⠀⣿⠈⠃⡟⢶⠀⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠀⢷⢰⠀⡿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⢻⡸⢀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣨⣤⣠⠀⠀⠀⢀⡆⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡀⣀⣯⣿⣿⣿⣿⣿⣿⣿⢰ ⠀⡀⣦⠳⠈⠀⠀⠀⠛⠈⠛⠈⣄⣤⣶⣿⣿⣿⣿⣴⠁⢠⠏⣿⣿⣿⣿⣿⣾⣴⢀⠀ ⠀⠀⠀⠀⣄⣶⠒⠒⠓⠛⡛⠛⠛⠛⠛⠛⣛⣿⣼⠀⠋⡟⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠤⠤⠠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⠞⠛⢷⠀⠈⠙⠳⠦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⠒⠒⠋⠀⣠⣤⡀⠀⠀⠉⠛⢶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⡴⠖⠶⢦⠀⠀⠀⢧⣬⠇⣀⣠⠴⠞⠋⠁⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠘⠧⣤⣀⡼⠀⢀⣀⡤⠶⢛⣩⣤⣀⠀⢠⡞⠋ ⠀⠀⠀⠀⠀⠀⣠⠞⣁⣀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⣿⠁⠀⣹⠀⠈⢷⡄ ⠀⠀⠀⠀⣠⠞⠁⠀⠷⠿⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⠀⠀⠀⡇ ⠀⠀⣠⠞⣁⣠⡤⠶⠚⠛⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡤⠶⠶⠦⣄⠀⠀⠀⡇ ⠀⡾⠛⠋⢉⣤⢤⣀⠀⠀⠀⠀⣰⠞⠉⠙⠳⡄⠀⠀⡟⠀⠀⠀⠀⢸⡆⠀⠀⡇ ⠀⡇⠀⢰⡏⠀⠀⢹⡆⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠳⣄⡀⠀⢀⣸⠇⠀⠀⡇ ⠀⡇⠀⠀⢷⣤⣤⠞⠁⠀⠀⠀⢷⣀⣀⣠⡴⠃⠀⠀⠀⠈⠉⠉⠉⠁⣀⣠⠴⠇ ⠀⠻⣆⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⢰⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⢰⠞⠁⠀⠀⠀⠀⢷⣄⣤⠞⠁⣀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⢒⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠢⣥⣢⠀⠀⠀⠀⠀⣠⣤⠀ ⢀⣟⣿⣦⠀⠀⠀⣰⡿⠿⠷⠶⣄⠀⠀⢠⠾⠟⠛⠛⢷⡀⠀⢀⡼⣿⣇⡇ ⠈⠛⠛⠿⢕⡂⢴⠁⠀⠀⠀⢀⠈⠆⠠⣮⣴⢤⡀⣀⣸⣗⣶⡧⠒⠉⠉⠁ ⠀⠀⠀⠀⠀⢹⠀⠀⠴⣺⣿⣿⠇⠀⠀⠛⡿⣽⣿⣽⠿⠛⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠈⠉⢩⠀⠀⠀⠀⠀⣸⣒⣄⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⢀⡴⠖⠉⠛⠓⠲⠶⠾⠿⠿⠿⢏⡳⡀⠄⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠞⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣿⣇⢧⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠫⢽⣽⣉⣹⣁⣧⣿⠟⣱⣿⣾⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠉⠙⠩⠤⠭⣶⣋⡟⢸⢁⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠝⡇⣘⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠤⠤⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⡀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠏⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠸⠀⠀⠃⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡆⣿⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢸⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⡜⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⣇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠁⢰⠀⠀⠀⣄⠙⠀⠀⠀⠀⡀⢠⠀⠀⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢠⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠑⠀⠀⠀⠀⠀⠐⠀⣾⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠀⡽⠉⠒⠒⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⢠⠀⠁⡴⣀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠋⠴⣠⢀⠀⠀⣀⢤⠑⠀⠀ ⠀⠀⠀⠀⣾⠀⠁⣰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢷⠀ ⠀⠀⠀⠇⢀⠀⡇⠀⠀⠵⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⡀⢸ ⠀⠀⠀⡸⠀⠀⡄⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡂⣠⠇⢠ ⠀⠀⡎⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⠀ ⠀⠇⢠⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡤⠘⠀⠀ ⠃⡼⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⢸⠀⠀ ⡆⢹⠀⠀⠀⠀⠀⠀⠀⠧⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⠀⠀ ⠀⡄⠑⠀⠀⠀⠀⠀⠀⡀⣧⠉⠉⠉⠉⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀ ⠀⠀⠀⣀⠯⠿⠛⡈⣀⣀⣀⢻⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⢞⠓⠔⠾⡠⢀⠀⠀⠀ ⠀⠀⠀⡞⢏⣎⣇⣀⢯⠑⠀⣿⠀⠀⠀⠀⠀⠟⠊⠟⡼⢀⠋⣠⠎⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⢰⡇⠀⢸⡞⢣⣼⠀⠀⠀⠀⡇⣹⠈⠷⢀⠟⢳⠏⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⣿⠀⡀⠸⢻⢸⡇⢀⠀⠁⠖⡠⢀⠀⡀⢄⡶⣟⡀⡼⠳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⠸⠀⢇⡆⢘⡇⠀⡤⢀⠀⠀⠂⠒⠶⠰⠈⡀⢦⢻⠀⢦⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠈⡀⢹⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠀⠀⡄⠘⠀⢇⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⠀⣇⡽⣴⠘⠀⠐⠛⠛⠐⠀⠀⠀⣀⣻⢟⠉⣏⠹⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠛⣹⡇⠀⢣⠋⠸⣷⢼⢱⠛⠀⠀⠀⡦⣶⡛⣾⡇⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⠈⣿⠀⡅⣹⣤⢿⣶⣤⢀⠙⠘⠀⠆⠓⡟⣾⣠⢳⡄⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⣄⣧⠈⠀⣆⣸⡿⠢⠶⣤⣠⠀⠀⠋⡳⣰⠀⠀⡎⠇⢾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⡄⣗⠘⠀⠀⠉⠚⡥⢚⣠⠀⠀⠁⢸⡞⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⠈⠀⠀⠀⠀⠀⡀⢦⠤⣠⢀⠴⣠⠀⠀⠀⠀⡥⡞⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠳⠉⠈⠀⠀⠀⠀⠀⠁⠉⠚⠴⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠉⠛⠻⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣠⣴⣶⣶⣤⡀⠈⠉⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⢰⣿⠁⠀⠀⢹⡷⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠈⠻⠷⠶⠾⠟⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣼⠟⠛⢿⡆⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣴⡿⠛⠛⠛⠛⣿⡄⠀⠀⠀⠀⠻⣶⣶⣾⠇⢀⣀⣤⣶⠿⠛⠉⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⣠⣴⠾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠾⠟⠁⢀⣀⣤⡶⠿⠛⠉⠀⣠⣶⠿⠟⠿⣶⡄⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣼⡇⠀⠀⠙⢷⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣾⡏⢻⣷⠀⠀⠀⢀⣠⣴⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣴⡟⠀⠀⠀⠀⠀⢻⡇ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠙⠛⢛⣋⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣀⣤⣤⡶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣠⣾⣿⣥⣶⠾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⣶⣤⣀⠀⠀⠀⠀⠀⢠⡿⠋⠁⠀⠀⠀⠈⠉⢻⣆⠀⠀⠀⠀⢸⡇ ⠀⢸⣿⠛⠉⠁⠀⢀⣠⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠉⠻⣷⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⡇ ⠀⢸⣿⠀⠀⠀⣴⡟⠋⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇ ⠀⢸⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠙⢿⣦⣄⣀⣀⣠⣤⡾⠋⠀⠀⠀⠀⢸⡇ ⠀⢸⡇⠀⠀⠀⠘⣿⣄⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⣀⣤⣴⠿⠃ ⠀⠸⣷⡄⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠋⠉⠀⠀⠀ ⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣤⣤⣴⡿⠃⠀⠀⣀⣤⣶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⣀⣤⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⣤⣴⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠠⡖⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠶⣴⣶⣄⠀⠀⠀⢀⣴⣞⣼⣴⣖⣶⣾⡷⣶⣿⣿⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠙⢟⠛⠴⣶⣿⣿⠟⠙⣍⠑⢌⠙⢵⣝⢿⣽⡮⣎⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡶⣋⠿⣽⣸⡀⠘⣎⢢⡰⣷⢿⣣⠹⣿⢸⣿⢿⠿⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢧⡿⣇⡅⣿⣇⠗⢤⣸⣿⢳⣹⡀⠳⣷⣻⣼⢿⣯⡷⣿⣁⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣼⣿⣧⡏⣿⣿⢾⣯⡠⣾⣸⣿⡿⣦⣙⣿⢹⡇⣿⣷⣝⠿⣅⣂⡀⠀⠡⢂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⡟⣿⡇⡏⣿⣽⣿⣧⢻⡗⡇⣇⣤⣿⣿⣿⣧⣿⣿⡲⣭⣀⡭⠛⠁⠀⠀⠈⠀⠉⢂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢻⣿⣇⣥⣏⣘⣿⣏⠛⠻⣷⠿⡻⡛⠷⡽⡿⣿⣿⣿⣷⠟⠓⠉⠢⢄⡀⠀⠀⠀⠀⠀⠁⠫⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⣾⣿⣽⣿⣏⣻⠻⠁⢠⠁⠀⠀⠀⠘⣰⣿⣿⢟⢹⢻⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠑⢄ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⣯⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣿⣿⢿⣾⣸⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠉⠁⠀⠀⠀⢀⠌ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢟⣿⣯⡟⠿⡟⢇⡀⠀⠀⠐⠁⢀⢴⠋⡼⢣⣿⣻⡏⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠊⢻⣿⣜⡹⡀⠈⠱⠂⠤⠔⠡⢶⣽⡷⢟⡿⠕⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢿⠿⠿⢿⠾⣽⡀⠀⠀⠀⠈⠻⣥⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠂⠠⠐⠋⠀⠙⠳⣤⣠⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠵⡐⠄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠠⡀⠀⠈⠙⠶⣖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠈⠂⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⠲⣄⠈⠣⡀⠀⠀⠈⢻⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⣷⡄⠈⠄⠀⠀⠀⢧⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⢠⣿⣤⣤⣶⣶⣾⣿⣿⡄⢸⠀⠀⠀⢸⣄⣤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠈⠉⠙⠛⠿⠿⠽⠿⠟⠛⡉⠛⠲⣿⣿⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⣸⣿⣷⢷⠙⣻⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠉⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣏⠀⣿⣿⡘⣼⡇⠀⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⠓⠛⠘⣧⠾⢷⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣿⢟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⢸⣧⠀⠹⣆⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⠙⢿⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⠀⠈⠙⠀⠀⠻⡄⠀⠀⠀⠀⠸⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠐⠠⠀⠻⠬⠄⡒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀🎀🎀🎀🎀🎀🎀🎀🎀❤️❤️❤️❤️ 🔥🔥🔥🔥

⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⢭⣁⣈⡀⠀⠈⠉⠉⠉⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀ ⢸⠩⠿⠋⠉⠉⢉⠉⠁⠐⡒⠲⢤⣴⣤⣿⣦⣀⠀⠀⠀ ⠸⢶⣢⡀⠁⠀⣿⠃⠀⠀⠈⠉⢁⣶⣞⠉⠟⠋⠷⠤⡀ ⠀⢀⣿⡗⣹⠟⠁⠀⣠⣴⣆⢄⠈⠛⠃⠀⠀⠀⠀⢁⡇ ⣜⠛⠉⠀⢀⣀⠀⠀⣼⣿⣿⢇⠂⠀⣦⣀⡀⠀⣶⢾⠁ ⢿⡇⠀⠀⠄⠀⠀⠀⠈⠉⡳⠁⠀⠀⠋⠀⠀⠀⠀⠸⠀ ⣞⢁⣀⠀⢰⣪⣵⢦⠀⠈⠀⣀⡀⠀⠺⠇⠀⠀⣠⡄⡄ ⠀⠈⠉⠙⠚⠛⠙⠫⠶⠦⢼⡿⣿⣀⡰⡽⣿⣆⠉⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⠒⠨⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠤⠤⠤⠤⣤⢤⡤⠄⢠⡤⣤⣤⢠⣤⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⠻⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⡀⣀⣀⣀⣄⣤⣤⣿⣿⣿⢀⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⢠⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⣿⣿⣿⣿⢹⠀⡇⣿⣿⣿⣿⣼⣤⣤⣤⣤⣤⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⣿⣿⣿⣿⣿⠀⡇⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣾⣶⣶⣡⣛⣝⣧⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⢸⠀⠀⠁⠋⠛⠛⡙⣈⣀⢀⠀⠀⠀⠀⣦⣿⣿⢿⣜⣷⣿⣿⣾⢠⡏⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⢸⠀⠟⣿⣿⣿⣿⣿⣿⠹⠁⡿⣿⣿⣿⣿⣿⣷⣿⣿⠻⣈⣀⠀⠁⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡀⣷⣿⣿⣿⣶⢀⠀⣦⣿⣿⣿⠹⠀⡟⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⠀⣷⣿⣿⣿⣿⣿⣿⣼⠀⠀⡀⣀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣸⠀⠀⣄⣶⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠟⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⢀⡟⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣍⣤⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⣉⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣿⣿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠟⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣤⣶⣶⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠇⣿⣿⠹⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣁⣋⣟⣿⣿⣿⣿⣴⢀⠀⠀⠀⡿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⣿⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠇⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⣿⣿⣿⣿⠻⠿⠻⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⠟⣿⢻⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣾⣠⣦⣿⡝⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⣶⣠⠀⠀⢿⣝⣩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⠿⠻⣿⣴⣿⣿⣿⣿⢿⠿⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⠸⣷⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢠⡇⣿⣿⣿⣿⣿⣧⣿⣿⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⢀⠀⡄⣿⣿⣿⣿⣿⠉⣿⣿⣾⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣾⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣼⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⣀⣭⣭⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⣼⣑⣿⡇⢩⡇⡀⢄⠥⠘⠏⣿⣿⣿⣿⢿⠈⠀⠀ ⠀⠀⠀⠀⡇⡆⠛⡯⣾⡇⣆⡿⢁⠚⣠⠀⣿⣿⣿⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⡄⠤⣆⢒⠂⡆⠔⡠⠀⠀⠀⠀⡄⣶⣿⣿⣾⣴⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⡿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣖⣟⠋⠉⠁⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠙⠉⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢠⣟⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⢠⡽⠿⠟⠉⠀⠈⠙⠀⠈⠁⠀⠈⠉⠉⡒⠲⠷⣶⣤⣌⣲⣦⣼⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⣿⣀⣀⠀⠀⠐⠆⠀⠀⢰⣿⡦⠀⠀⠀⠀⠙⠒⠶⠤⠬⣉⣛⣛⠿⠿⣿⣿⡿⣦⣀⠀⠀⠀ ⠀⠙⠻⣮⣽⣦⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄⠉⠐⠂⠬⠉⠝⣛⠓⠶⡄ ⠀⠀⠀⢸⣿⣿⡇⠸⣿⡿⠋⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⠀⠉⢱⢸⠁ ⠀⣀⣠⣾⣿⠟⠁⠘⠛⠁⠀⠀⠀⢠⣾⣿⣿⣿⣧⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀ ⢀⡟⠛⠋⠁⠀⠀⠀⠀⢀⡀⠀⠀⠸⣾⣿⣾⣿⣿⠃⡞⠀⠀⠰⣷⢀⠀⡀⠀⠀⣼⣿⣶⣿⠀ ⢸⣿⡆⠀⠀⠀⠀⢀⡽⠊⠀⠀⠀⠀⠙⠿⢿⣟⣡⠞⠀⠀⠀⢰⡿⠟⠋⠁⠀⠀⠈⠉⢸⣿⠀ ⠘⢿⣦⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣿⠀ ⣶⠾⠟⠀⠀⠀⠀⢀⡤⠖⢒⣶⣄⡀⠀⠐⠙⠂⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⢸⣄⢸⠀ ⠹⠦⠄⣦⣦⣤⣤⡘⣷⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠈⣁⣤⣄⡀⠀⢳⣼⣿⣸⡆ ⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠹⠿⠶⠷⢶⣤⣤⣻⣿⣿⣿⠀⠀⣾⣵⣿⣿⣿⣦⠀⠈⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⠛⠛⠳⠋⠁⠸⡿⣿⣀⡀⢸⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠶⠶⢾⠷⠶⠒⠾⢶⠶⠿⠐⠶⡶⠶⠀⠀⠷⠾⢿⣿⠿⣿⠧⣾⣷⠇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣟⣿⣿⣿⣟⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣴⡶⠿⠟⠛⠻⠟⠛⠛⠋⠙⠒⠿⠿⢛⠿⠿⠿⣥⠮⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠧⣾⣬⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠰⣞⣫⣭⣽⠿⠿⣿⣷⣶⣶⣤⣤⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⣬⣻⡭⡟⠋⠃⠀⠈⠙⠀⠈⠉⠃⠀⠀⠉⠉⠉⠓⠒⠦⣷⣖⣤⣤⣀⢓⣲⢤⣬⣽⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠂⠉⠀⠀⠀⠀⣄⡀⠀⠀⠀⣴⡶⣦⡀⠀⠀⠀⠀⠙⢷⣤⣤⣀⠉⠙⠚⠿⢿⣿⣿⣾⣿⣊⠻⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠐⣿⣞⡶⢶⣄⠀⠀⠉⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠘⠁⠉⠉⢙⣷⡶⠶⢬⠉⠙⠛⠿⢯⣍⣿⣶⣄⡀⠀⠀ ⠀⠀⠈⠉⠻⣶⡭⣷⡄⠀⣀⣀⡀⣠⣨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⢿⣿⣦⠀⠀⠉⠁⠛⠀⠷⢠⣩⠉⠉⢻⠆ ⠀⠀⠀⠀⠀⣹⣿⣛⣷⠀⢻⣿⡾⠟⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠘⠿⠿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⣾⠀ ⠀⠀⠀⢀⣴⢿⣟⡿⠇⠠⢞⠿⠃⠀⠀⠀⠀⠀⣠⣟⣿⣿⣟⣿⣦⡹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀ ⠀⢰⡶⢿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣽⣞⣻⣿⣽⣿⡇⢘⡇⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣶⣶⣄⣿⡟⠀ ⠀⣾⣇⡈⠀⠀⠀⠀⠀⠀⠤⢤⣠⠶⠀⠀⠀⠀⢳⣾⣾⣿⢿⣿⡿⠁⡼⠁⠀⠀⠈⢹⣟⣤⣄⡴⠆⠀⠀⠘⣿⡯⠟⡇⡇⠀ ⠀⢿⣿⣗⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣭⡴⠊⠀⠀⠀⠀⢠⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠀⠰⣿⡇⠀ ⠀⠾⣷⣦⡀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢻⡇⠀ ⢠⣄⣼⡿⠏⠀⠀⠀⠀⠀⠀⣀⣤⠴⠦⣄⡀⠀⠀⠀⠠⠖⣯⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀ ⢸⣯⡉⠀⢀⡀⠀⠀⠀⠀⢸⣏⣴⣶⣾⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠁⠀⠀⠀⠀⢠⠀⣼⡟⡄⣷⠀ ⠀⠛⠛⠲⠬⠼⢿⣿⣶⣒⣘⣿⣿⣿⣯⣿⣶⡿⢃⠀⠀⠀⠀⢀⣴⣻⣿⣿⣦⠀⠀⠀⢀⡤⢾⣿⣦⣄⠀⠈⠷⢹⡇⣇⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠙⠟⠳⠾⠯⢿⣴⣶⣄⣿⣿⣿⣿⡿⠀⠀⠀⣯⣴⣿⣿⣿⡯⢷⡄⠀⠈⣷⡿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠛⠓⠒⠒⠾⠷⠞⠉⠉⢹⣿⣽⣃⠀⠀⠈⡇⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠶⢥⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⣀⣀⣀⣀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠋⠓⠾⠻⡿⠻⢻⢻⠻⠻⡟⡿⢿⠀⢫⠿⠿⠿⡇⠀⠨⠯⠻⠛⡟⡻⠻⢿⢿⢽⣺⡟⡻⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠶⠶⢤⣄⡀⠀⠀⠀⢠⡞⠛⠛⠓⠲⠦⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠞⠉⣥⠀⠀⠀⠀⠀⠀⣬⠙⣦⠀⠀⠀⠙⠶⣤⣀⠰⠶⠀⠙⣧⠀⠀ ⠀⠀⠀⣠⠟⠁⠀⣄⣀⣀⠀⠀⠀⢀⣀⣀⣤⡾⠀⠀⠀⠀⠀⠈⡏⠓⢦⣄⠀⢸⡆⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠹⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⣼⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⣤⢀⡤⣰⠏⠀⠀ ⠀⢸⠇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠒⠲⠶⠶⢶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠛⣿⠛⠛⠋⠉⠉⠉⠉⣰⠏⠟⠙⢷⡄⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⡹⣆⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠞⣻⠇⠀⠀⠀⢀⡾⠃⠹⡆ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣠⠞⠁⢠⡏⠀⠀⠀⢠⡞⠁⠀⠀⢻ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡋⠀⠀⣾⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣤⡭⡿⢟⣟⣟⣿⣻⣉⣽⣄⠡⡟⣿⡟⢿⣿⣿⣽⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⣿⣶⣤⣤⣤⣤⣦⣷⣿⠹⡟⣿⣿⢿⡽⣿⣿⣿⢿⠘⠀⠀⠀ ⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣾⣠⣀⠀⣀⣀⣀⣦⣷⠈⠀⠀ ⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀ ⠀⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀ ⠀⠀⠀⣾⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⠀⠀ ⠄⠿⢀⣲⠒⡃⣦⠻⠙⠉⠀⠀⠉⠋⡹⠉⢙⠈⠀⠀⠀⠁⠋⠴⢀⠀⠀⠀⠀ ⠖⢴⠇⠐⠐⣿⠈⡎⣧⣷⣿⣿⣽⣯⣿⣿⣾⣶⣴⣤⣬⣈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠑⡞⣴⣄⠃⣿⣿⣹⣾⣿⣿⣿⣿⠃⣨⠀⠀⠏⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠀⠖⠀⡿⣿⣿⣿⢸⣿⣴⣿⣿⣿⠚⠀⠉⣀⢡⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠆⠀⠃⠘⡄⣿⣿⣿⠄⠀⢠⠀⣿⣏⣾⢇⡤⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⢀⠀⠀⣤⣶⠲⠉⠉⠖⣴⣤⢂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠤⠀⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⢠⡜⡄⠈⢻⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⡏⠀⠀⠀⣿⠁⠅⠀⠀⠙⢿⣶⣄⣀⡴⠛⠹⡿⠶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⢷⢋⣞⡄⠀⠀⠀⡿⣆⠃⠀⠀⠀⠀⠉⠻⠿⡲⢦⣄⡀⠁⠀⠀⠀⠈⢉⡟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡟⢼⠇⠀⠀⠀⡇⠨⢷⣄⠀⠀⠀⠀⠀⡐⠁⠀⡎⢷⠀⠀⠀⠀⠀⡸⠑⡈⠻⣿⣶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠴⣼⠃⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⣰⠣⠀⠀⢱⡸⣆⠀⡀⠀⠀⡇⠀⠀⠀⠀⠉⠛⠟⠿⠽⣷⡀ ⠀⣠⡾⠛⢦⡀⢰⡏⠈⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣰⠃⠀⠀⠀⠀⢳⡹⣦⡉⠳⢤⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇ ⣾⢋⣀⣤⡴⣿⣿⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣰⠃⠀⠀⠰⠇⠀⣀⠀⠈⣷⠀⢀⡜⣮⣛⣶⡳⠶⣤⣀⣤⣄⣰⡇ ⠈⠛⠛⠛⠛⠋⢿⡄⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠃⠀⠀⠘⠁⢸⢀⣧⠀⣸⡏⠖⠋⢾⢿⣧⡈⢂⡼⣋⣀⣤⠾⠋⠀ ⠀⠀⠀⠀⠀⠀⠊⣷⠀⠀⣞⣧⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣾⠀⢘⣷⠛⠛⠛⠛⠛⠚⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣿⣆⡀⠀⠀⠀⣀⣴⣿⣷⣦⣄⠀⠀⢠⣾⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠾⠷⠿⡿⠿⠟⠿⠮⠿⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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