So Bad Its Good Emoji Combos

🥴🎨✨

✨🖼️😉

🧀😂👍🎬

😂🖼️

🗑️➡️💎😂

💯🔥🤌

😂🧀🤦

❤️🗑️

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠤⡤⠤⠤⢄⣠⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠖⠫⠭⠍⠉⠀⠀⠬⠍⠁⣀⡀⠭⢐⡢⢀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⢀⠂⠈⠉⠑⡄⠀⠀⠀⠎⠀⠀⠀⠉⠚⢔⢅⠂⠀⠹⡄⠀⠀⠀ ⠀⣠⢞⡀⠠⠄⣴⣶⣶⣦⣅⡀⠀⢠⡖⢋⣹⣿⣿⣷⡆⢠⠀⢀⠤⢽⣦⡀⠀ ⢸⡷⡕⠥⠶⢤⣀⡀⠀⢈⣏⠁⠀⠀⠙⠉⠀⠘⠶⠤⠤⠴⠛⡍⠙⢦⠘⠹⡄ ⠘⣧⣑⠀⣼⡀⠁⡀⢴⣏⠁⠀⢀⣤⡛⣶⠂⠀⢀⣠⣤⠖⠋⣽⠲⢸⢃⢀⡇ ⠀⠸⡆⢹⣿⢻⠦⣤⣀⣈⣳⣃⣀⣤⠬⠵⡖⠋⢉⣡⣧⠴⡾⠋⠀⠀⣪⠞⠁ ⠀⠀⡇⢸⣿⣿⣤⣧⣤⣼⣧⣤⣼⣤⣤⣴⣷⠿⠛⠉⣧⡞⠁⠀⠀⡼⠁⠀⠀ ⠀⠀⡇⠈⣿⣿⢿⠻⡟⠻⡟⠛⠛⡏⠉⠀⠸⣆⣤⠞⠋⠀⠀⢀⡼⠁⠀⠀⠀ ⠀⢰⡇⢄⠈⡙⠛⠳⠿⠶⠿⠶⠶⠷⠖⠚⢋⠩⣐⠮⣑⡭⠖⠋⠀⠀⠀⠀⠀ ⠀⢸⡀⠘⠤⣈⣐⠒⠂⠀⣀⣀⠀⠶⠖⠛⣈⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⣄⣀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

‧₊˚ ☁️⋅♡𓂃 ࣪ ִֶָ☾.

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠉⠒⢤⠒⠉⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠊⠀⢀⡀⠄⠒⠀⠀⠒⠠⢈⣄⣀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡀⠤⣀⣀⣀⡑⠄⡀⣀⠠⠤⠤⠤⠬⠐⢄⠀ ⠀⠠⠂⡉⠀⠀⠀⣀⣄⠢⡵⢚⣿⣿⣯⡍⠁⠚⢝⢈⠭⣲⢿⣿⣇⠛⠶⣣ ⠐⠁⠀⠃⠀⠀⠀⠁⠒⠣⢄⡘⣿⣿⣶⠏⠀⣀⣜⡀⠀⠻⣿⣷⠟⢀⡀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠈⠉⠥⠬⡥⠀⠂⠀⠉⠉⠉⠉⢉⡠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⠀⠈⠐⢖⠒⠈⠁⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠈⠂⠄⡈⠁⠂⠠⠤⠄⠀⢀⣀⣀⠀⠤⠄⠐⠂⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠀⢉⣁⠀⠒⠒⠒⠒⠂⠀⠒⠒⠒⠒⡺⠀⠀ ⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠒⠒⡲⠒⠈⠀⠀⠀ ⠈⠑⠢⠍⣀⠒⠀⠠⠤⠤⠀⢀⣀⣀⣀⣀⠀⠀⢤⠄⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣄⠀⠀⠀⢀⣠⠴⠒⠚⠉⠉⠉⠉⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠈⣇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠤⠿⢦⣀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⣤⣀⣈⣙⣢⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⣉⣤⣴⣲⣗⣋⣉⣉⣻⣶⣒⠤⠤⣌⣳⣤⠴⣚⣉⡥⠤⠴⢒⣲⣒⣒⣚⡶⠤⠬⣍⣉⠙⠲⡄⠀⠀ ⠀⠀⠀⠀⣴⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠊⣉⡤⣶⡿⠛⢻⣿⣿⣾⣶⣶⣤⠀⠉⠉⠉⠒⠺⣭⡚⠉⠉⠀⣠⠴⢺⣿⣿⣿⣿⣿⣯⡉⠛⠚⠯⣝⡒⢿⡄⠀ ⠀⠀⢠⠞⠁⠀⢰⡞⠀⠀⠀⠀⠀⠀⠀⢰⡟⠶⠚⠒⢉⠵⠋⠁⠀⢰⣟⠙⣿⣿⣿⠛⢻⣷⡄⠀⠀⠀⠀⠀⢹⣦⠖⠋⠀⠀⣿⣧⣤⣿⣿⠛⠛⣷⡆⠀⠀⠀⠉⠲⣿⡀ ⠀⣠⠏⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⠾⣇⣀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣶⣿⣿⠇⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⣿⠀ ⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠙⠲⢤⣀⡻⢿⣿⣿⣿⣿⠿⠁⠀⣀⣀⡤⠶⠚⡗⠶⠤⣀⣀⣀⠈⠻⢿⣿⣿⣿⣟⣁⣀⡠⠤⠖⢚⡵⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⣀⣈⣉⣉⣙⣛⢛⠋⢉⣉⣁⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⢉⡻⠗⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⡤⠤⠤⠤⠴⠒⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⡀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠹⢦⡀⠀⠀⠀⠉⠳⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠉⠲⢦⣀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠴⠶⠒⠋⠉⠁⠀⠀⣀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠚⠛⠛⠛⠛⠛⠋⠉⠉⠁⢹⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠲⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠋⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢤⣀⠈⠙⠒⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠒⢤⣄⡀⠈⠉⠙⠒⠒⠶⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⢤⣀⣀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠉⠉⠉⠉⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⠶⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠉⠒⠒⠮⠽⣖⣻⡭⣟⣻⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣭⣛⣒⡶⣤⣄⣉⠻⣶⣯⣿⣾⣭⣟⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣿⡿⠟⢛⡩⠟⠛⢉⠀⢠⣀⡄⠀⠀⠀⠀⠀⠀⠀⣄⡐⠦⣤⣴⣤⣭⣙⠻⣷⣾⣭⣟⠾⣿⣾⣽⡻⣿⣷⣯⡻⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢡⠟⠋⣠⠖⠉⣀⣴⡾⢫⣠⣾⣿⣷⣦⡀⣄⢨⡳⣦⣄⠈⠙⠳⢾⣭⣛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣦⡙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⣿⢋⡴⠃⣠⡞⢁⣠⣾⣟⣽⣿⣿⣿⡟⠀⠙⢿⣿⣾⣗⣿⣾⣽⣿⣷⣶⣤⣍⡛⠻⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⡿⣳⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣄⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣠⠴⠒⠊⠉⠉⠙⠻⣿⣿⢿⣿⣿⡻⣿⣿⣿⣷⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀ ⠀⢸⣿⣿⣿⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⠓⠻⠍⠉⠀⢀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⠏⠋⠀⠀⣠⣴⣾⣿⠟⢻⣿⣿⣿⣿⠉⠓⢦⡀⢄⠀⠀⠀⠀⠀⠀⠸⢀⠀⣠⣤⠤⣤⣴⣦⣀⡌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⢀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠑⠛⠛⠛⠓⠒⠒⠚⠋⠉⠛⠓⠦⣤⣄⣈⣾⡇⠀⠀⠀⠀⠀⢰⣿⣾⣿⡤⠴⠞⠛⠉⠀⠀⠀⠀⠙⢿⡝⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠁⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡌⢿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣷⣶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⣇⠉⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⠀⠀⠀⠀⠀⠀⠀⢴⣾⡏⠀⠀⠀⣾⣿⣿⣿⡿⠁ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣦⣀⠀⠙⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠻⠆⠀⠾⠛⠉⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⣿⣿⣷⣶⣇⡈⠉⠛⠻⠷⠶⢦⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⣀⣀⣠⠴⠛⠁⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⣦⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠖⠊⠉⠉⠁⠀⠀⠀⠀⢀⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢷⣝⢻⠿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⣠⣼⣆⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀ ⠀⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉⠻⣤⣀⠀⠀⠉⢻⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀ ⠀⠘⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣈⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠹⠉⠀⠈⠻⠋⠉⠈⠀⢀⡿⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠙⠛⠓⠶⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠛⠁⢀⡇⠀⢸⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡇⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠤⠤⠤⢤⣤⣀⣀⣀⣀⣤⠤⠴⠒⠉⠀⠀⠀⢠⣿⣿⣿⡟⢿⣟⠄⠀ ⠀⠀⠀⠀⠀⠀⢹⣇⢸⣿⣿⣿⡹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⣿⣷⠸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠘⣿⢹⣿⣇⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢹⣿⡇⠀⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠈⡿⣟⣌⣿⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠶⠋⠀⠀⠀⠈⣇⠁⠀⠀⠑⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⡇⠈⠀⠸⣷⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠇⡟⠀⢻⠀⠀⠀⢻⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠀⠀⠳⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠿⠿⢟⣛⣛⣛⣛⣉⣉⣩⠥⠤⠤⠴⠒⠒⠒⠚⠒⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠛⢁⡤⠤⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠚⠛⠛⠛⠓⠲⠤⠤⣀⣈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠁⠀⣀⣠⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠋⠉⠙⠒⠒⠶⠤⣌⣙⠲⣄⡉⠳⢤⡀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⢲⡈⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⠲⣄⠈⠲⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣤⣴⣶⣶⣶⣶⣤⣄⣀⠀⠙⠂⠈⠃⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⣠⣶⡾⠿⢿⣷⣶⣦⣄⡈⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠉⠁⢹⣿⣿⣿⣿⣿⠻⣷⣄⠀⣄⡀⠀⠀⠀⠀⣠⣤⣬⣻⣿⣦⡀⠀⠀⠀ ⢀⣶⣿⢋⣤⠖⣛⠉⠉⠉⠉⠁⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠸⣿⣧⣤⣴⣾⠿⠛⠻⣿⡛⠛⠛⠻⠿⠟⠠⠔⠛⢁⣄⣤⣜⣉⡉⠉⠓⠻⣝⢿⣦⡀⠀ ⣾⣿⢡⠏⣰⠚⣩⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠹⣿⣦⣄⡀⠀⢀⣠⣴⣾⣿⠟⢫⠉⠛⠻⢷⣤⠀⠈⢧⠙⣿⡆ ⣿⣿⡎⠀⡇⠐⠛⠉⠉⣍⠙⣿⣷⣦⣾⠟⠀⠀⠀⢀⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⣀⣿⣆⠀⠀⠀⢻⣷⠀⠸⡄⠘⣿ ⢸⣿⢧⠀⢧⡀⠀⠀⢠⣿⠀⠈⠉⠉⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠾⠿⢷⣶⡼⣆⣀⣀⢀⣀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠛⢻⣿⣷⣤⣀⢸⣿⠀⢰⠁⠀⣿ ⠀⢿⣿⠦⢄⣙⠠⢠⣿⣿⣄⠀⠀⢀⣠⠴⠚⢿⠿⣷⡀⠀⠀⠀⠀⠀⣴⣶⣶⣶⡆⢀⣿⠇⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⠟⠋⠀⠀⢀⣼⣿⠉⠉⠉⣾⡟⠀⡾⠀⣼⣿ ⠀⠀⢻⣧⡀⠉⠓⣾⣿⣽⣿⣷⣤⣈⠁⠀⠀⠀⠀⠈⢿⣦⣤⡶⠂⠀⠀⠀⠀⠀⠁⢛⣋⣠⣤⣴⣶⠿⠟⠛⠋⠉⣹⣿⢀⣀⣠⣴⣿⣿⠟⠀⠀⠀⢋⣠⠞⢁⣴⡿⠃ ⠀⠀⠈⣿⣇⠀⠀⣿⣿⡟⢸⣿⠛⠿⢿⣶⣶⣤⣤⣤⣤⣬⣯⣥⣤⣤⣤⣴⣶⡶⠿⠿⠛⢻⣿⠁⠀⠀⠀⢀⣠⣾⣿⣿⡿⠟⢛⣿⡟⠁⠀⠀⠀⠀⠈⣤⣴⡿⠋⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⣿⣿⣧⣼⣿⡀⠀⣾⡏⠀⠉⠉⠙⣿⡟⠉⠉⠉⠈⣿⠃⠀⠀⠀⠀⠀⢸⣿⣤⣴⣾⣿⣿⡿⠿⣿⡏⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣤⣤⣤⣿⣧⣤⣤⣤⣴⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⢻⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⢸⣿⡀⠀⠀⠀⢀⣤⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⠀⠘⣿⣏⣿⣏⢻⣿⡛⠛⣿⡛⠛⠛⢿⣿⠛⠛⠋⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⣷⣀⣠⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠘⢿⣿⣯⣀⣿⣷⡀⠹⣿⡄⠀⠀⢿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣠⣴⣾⣿⠿⠛⠉⢀⣀⡤⠖⢂⣠⠶⠒⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⣄⠀⠀⢀⠉⠉⠛⠿⠿⠿⢿⣿⣿⣶⣶⣾⣿⣶⣶⣶⣶⣿⣿⠿⠿⠿⠿⠛⠋⠉⢀⣠⠴⠚⢉⣡⡶⠞⠉⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⣿⡆⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣚⣩⡦⠶⠋⢉⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠳⣄⡀⠀⠈⠉⠓⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣒⣲⣽⠿⠓⠚⠉⠉⢀⣤⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡄⠀⠀⠀⠀⠉⠓⠒⠒⠒⠢⠤⠤⠄⠀⠐⠒⠒⠒⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⣠⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣶⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⠾⠟⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⡶⠚⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠋⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣃⡀⠀⠀⣶⣿⠟⡆⢹⡀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀ ⣰⣿⡏⣿⠏⡘⢿⣿⡴⣣⠘⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⢻⠀⠀⠀ ⠈⡟⠋⢿⣿⣿⡤⠾⠛⠁⠀⢻⡀⠀⠀⠀⠀⠀⢸⠃⢠⣸⠀⠀⠀ ⠀⣷⠖⠛⠉⠁⠀⠀⠀⡄⣄⠈⢧⡀⠀⣀⡤⢤⡾⠀⢨⣿⣾⣦⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡸⡆⠘⣷⠞⠣⣤⡾⠓⠚⠲⣭⡛⢛⣿ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⣇⢷⠀⠘⠃⠽⠁⢠⠄⠀⠀⠈⣿⠛⠋ ⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢸⣾⡦⢤⡀⠀⠀⢨⡀⠀⠀⠀⡾⠀⠀ ⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢸⣿⣿⠉⠁⠀⠀⠉⠒⡄⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⣤⣤⠴⠞⠻⡆⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠘⢿⣝⡃⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⡲⢼⢸⠃⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣤⡶⠟⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠋⠀⠀⠀⠀⢀⣤⣤⣄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣤⣄⢀⡀⣰⣿⣿⡇⢹⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠳⣦⠀⠀⠀⠀⠀ ⣼⣿⣿⢇⣿⡟⠁⠻⣿⣿⡴⢟⣡⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠸⡇⠀⠀⠀⠀ ⠙⣿⠿⠻⣿⣾⣿⣇⣠⣴⠿⠛⠉⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⡇⠀⠀⠀⠀ ⠀⢻⣀⣤⣼⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣀⣠⡇⠀⠘⣿⣧⣤⣄⠀⠀ ⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⡀⠈⢿⡄⢀⣴⠾⠛⢉⣿⠁⣠⠸⠿⣿⣿⣿⣄⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣧⠀⠘⣿⡏⣘⣳⡶⠟⠋⠉⠉⠙⠷⣦⣉⢡⣽⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⡆⠀⠈⠓⠨⠟⠀⢀⣤⠀⠀⠀⠀⠹⣿⠛⠋⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⣷⣄⣀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠿⠇⠀⠀⠀⠺⣯⡄⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠸⠿⠻⠗⠀⠀⠀⠀⠀⠀⠈⠑⢂⣠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⣶⠶⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣠⣤⣤⡶⠟⢻⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⣿⠉⠁⠀⣾⣶⠾⠿⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⣿⠀⠀⠀⠀⠙⠳⠶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣙⠻⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣖⠚⠋⢉⣭⣙⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣍⠉⠉⠙⣻⣿⣿⣿⣿⣻⡟⠢⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⢣⣿⡿⠀⠀⢻⣧⠀⢠⡟⣿⠋⠙⠛⢿⣷⡀⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠋⣠⡾⠋⠀⠀⠀⠀⢿⠀⠀⠀⠁⠀⠀⠀⠀⠹⣷⡀⢻⣷⡀⠀⠀⠀⠀ ⠀⠀⡄⣠⡿⠉⠻⣫⡴⠶⣶⡄⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⢻⣶⣟⠛⠾⢿⣧⡴⣄⠀⠀ ⠀⢀⡟⡋⢹⢀⡾⠋⢀⣀⣉⢻⡆⠀⠀⠀⠀⢠⡏⣀⣀⣀⣀⣉⠘⣷⠀⠀⠛⢰⣸⡆⠀ ⢠⡾⢀⠇⠀⣼⠵⠛⣛⣍⡛⠛⢷⠀⠀⠀⠠⠟⠉⠩⠤⠤⢬⣉⠙⠻⡇⠀⠀⢠⡇⣿⠀ ⢸⡇⢸⠀⠀⣧⣀⡈⠀⢀⣀⣴⠟⠀⠀⠀⠀⠲⣤⣀⣀⣀⣀⣸⣀⡤⠀⠀⠀⣸⠃⣿⡀ ⢸⡇⢸⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠁⠀⠀⢀⣰⠏⠀⣿⡇ ⢸⡇⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⠁⠀⠀⢻⡇ ⢸⡇⠀⠉⣻⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠤⠶⣶⠿⣏⠀⠉⠓⠀⠀⠸⡇ ⢸⣷⠀⠈⠁⠀⠹⣤⡼⠟⢻⡉⠉⣿⠉⢉⡿⠋⠉⠉⢷⡦⠶⠋⠀⠘⠃⠀⠀⠀⠀⠀⡇ ⠸⣿⡄⠀⠀⠀⠀⠞⠁⠀⡼⠛⠟⢙⠟⠙⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⢿⣷⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏ ⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀ ⠀⠀⠀⢷⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀ ⠀⠀⠀⠈⠧⠀⠈⠙⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠰⣿⠷⡶⢿⡷⣶⡷⠟⠿⣷⣿⠂⢰⠶⣿⢾⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣴⡶⡦⣶⣾⠛⢧⣴⣦⣴⣶⣶⠶⡶⣤⣶⣤⣶⣶⠦⢤⣴⡦⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠉⠀⠀⠁⠀⠉⠀⠈⠉⠀⠀⠈⡛⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⠀⠀⠀⠀ ⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀ ⠀⢀⡿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀ ⠀⣾⣇⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⡀⠀ ⢠⣿⡟⠁⠀⠠⠞⣟⠉⣧⠈⠉⠳⠆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⣟⠙⣳⠈⠹⣷⠄ ⢸⣿⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇ ⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠹⠷⠴⠟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⠇ ⠸⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠋⠀ ⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠶⠛⠋⠉⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣼⠏⠁⠀⠀⠀⣾⣀⣀⣰⡶⠟⠛⠛⠻⢶⡄⠀⠀⠀⠀⠀⢸⣧⣤⣤⡟⠛⠋⠙⢿⡏⢻⣦⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣯⠉⠀⠀⢸⡇⠤⣸⡇⠀⢻⡆ ⠀⠀⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠛⠛⠋⠀⠀⢸⡇ ⢀⣼⠏⠈⠛⢷⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣿⣦⠤⣤⣿⣤⣀⣀⣀⣤⡞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢶⣤⣤⣶⣿⣿⠇⠀⠀⣀⡠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⢄⣀⠀⢶⣿⣯⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⣽⣿⣿⠏⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠢⢻⣿⣤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣰⣿⣿⣯⠞⠁⠀⠀⢀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢳⠀⠀⠙⣿⣿⣿⡧⠐⠉⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠊⣿⣿⣿⡟⠀⠀⠀⠀⣰⡷⠀⢀⡞⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⢹⡶⡈⡇⠀⠀⢺⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢸⣿⣿⡿⠉⠀⠀⠀⢰⣿⠁⠀⣾⡇⠀⢀⣼⠃⠀⣾⣄⠀⡍⢆⢱⣄⣷⢳⣿⡀⠀⠘⣶⡹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⢀⡔⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇⢀⡆⠀⠀⣿⡏⠀⠀⣿⠀⢠⡎⣾⡄⠀⠉⢾⡆⠣⠾⠄⣿⡿⢾⣧⢇⠀⢀⠏⡇⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⠀⡸⡌⢰⠀⡟⡇⠀⢰⣿⡄⣼⠁⢸⣇⠀⠀⠘⣷⠀⠀⢢⣿⠇⡸⣿⣸⠀⣼⣧⢻⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠄⠀⠀⠀⣰⡿⢃⣿⣿⣿⣄⡴⢱⠇⣼⡀⣿⢷⣠⠈⣯⣧⢿⣄⣀⣿⡄⣄⠀⣿⡏⠀⢸⡏⡰⠃⣹⣅⡀⣿⢹⢸⣿⡿⣿⠿⠿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⣼⡿⠁⣸⡏⠘⡿⡃⡇⢸⡄⣿⣷⣿⣿⣿⢦⠟⣙⣿⣤⣀⣈⢣⣉⠻⣿⣿⣶⣾⡟⠋⠉⠉⣉⡇⣿⡿⣴⣯⠹⣹⣆⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⢀⡴⣿⡟⣰⢁⡿⠐⠁⢧⢀⢻⢸⡇⢹⣏⢻⠀⠈⢿⡹⣏⠀⣿⣿⣿⣷⢿⡆⢸⡟⠛⢿⡆⢰⡟⢙⣿⢠⣿⣿⣿⡟⠀⢹⣿⡄⠀⠀⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⣼⡿⢠⠃⣸⠇⡆⠀⠘⣾⡌⡞⣧⠀⢻⡄⠀⠀⠘⢧⡈⠛⠛⠛⠛⠛⢚⣱⡟⠀⠀⠀⠻⣎⡉⠉⢻⣾⣿⣯⡿⠀⠀⠘⣽⣷⡀⠀⢸⣧⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⢰⢱⣿⠃⡎⢀⣿⢠⠁⠀⠀⠹⣿⡹⣿⣦⡘⣿⡄⠀⠀⠀⠉⠛⠲⠶⠶⠖⠛⠉⠀⠀⠀⠸⡀⠈⠉⠛⢻⡟⡟⠙⡇⠀⠀⠀⢻⣿⣇⠀⠈⢿⣇⠘⣧⠀⠀⠀⠀⠀ ⠀⢋⣾⠏⢰⡇⢸⡇⢸⠀⠀⠀⠀⠈⢿⡜⣿⡳⣜⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢲⠄⢀⣸⠃⢁⣼⠇⠀⠀⠀⠘⣽⣿⡀⠀⠀⢿⡀⠈⣆⠀⠀⠀⠀ ⠀⢸⡿⠀⡇⡇⢸⡇⢸⠀⠀⠀⠀⠀⢸⠳⣌⠻⣜⣿⣻⣄⠀⠀⡟⠀⠀⠀⠀⣳⣤⣀⢤⣀⣀⣰⠏⠀⠈⣏⢀⣸⠋⠀⠀⠀⠀⠀⠹⣿⣇⠀⠠⠘⣇⠀⠸⡄⠀⠀⠀ ⠀⢸⠇⠸⠀⢡⣾⡇⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠈⠈⠻⣯⡷⣄⣧⣀⣀⣰⣿⣿⣿⣿⣽⣹⣿⣿⣿⣶⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢿⣠⠀⠙⡄⠀⠀ ⠀⢸⠀⠀⠀⢸⣿⠃⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⣿⣆⢹⣟⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⡇⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⣿⡗⢯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣇⡤⡿⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢸⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠈⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡸⢿⡟⣿⣿⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⣸⣿⣿⣿⣿⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⠀⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⡿⠿⢳⣿⣿⠿⠥⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣧⣦⣦⣼⣿⠄⠀⠀⠀⠀⠙⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠿⠿⠿⠋⠉⠉⠩⠭⠭⠝⠒⠒⠒⠓⠒⠲⠤⢄⡀⠀⠈⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⠟⠋⠡⠒⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⣀⣈⣉⣉⣑⠒⠦⢌⡑⠢⣀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⢀⠔⠒⠉⠉⠉⠙⡖⠂⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠉⠒⢬⡓⢌⠑⠢⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⢀⣠⣤⣤⣤⣤⣤⣤⡀⠈⠂⠙⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⢁⣀⣀⠤⠤⢠⣾⣿⣿⣿⣿⣶⣤⡀⣀⠀⠀⠀⢠⣾⠛⢉⣠⣼⣿⣿⣿⣿⣿⣷⠀⢤⣤⠀⠀⣠⣤⣤⣿⣷⣄⡀⠀⠀ ⢰⣿⢫⢞⡡⠆⣀⣀⠀⠀⠀⠈⠉⠉⠉⠛⢻⡿⠛⠀⠀⠀⠘⠻⠾⠛⠉⠁⠈⣷⣄⠀⠉⠉⠈⣁⣴⣶⠶⠶⢶⣄⡀⠙⣝⢿⣄⠀ ⢸⣿⡇⢸⠀⠛⠛⣉⠻⣷⣦⣶⠆⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⣀⣿⡀⠀⠈⢿⡄⠸⠀⢻⡄ ⠘⣿⣇⠸⣄⠀⢠⣿⠀⠀⠀⠀⢀⣠⣶⡟⠉⠀⠀⠀⠀⢀⡀⠛⠿⣶⠳⠤⠄⠀⠀⠀⢀⣠⣤⣶⠟⠛⢹⣿⣶⡄⣸⡇⢸⠀⣸⡇ ⠀⠹⣿⡑⠲⢤⣿⣿⣧⣀⠠⠒⠉⠙⠙⢷⣄⡀⣠⠀⠚⠛⠛⠻⢴⠟⠀⣀⣠⣴⡶⠿⠿⣿⠉⠀⢀⣴⣿⡇⠀⠀⠟⢀⠎⣠⡿⠀ ⠀⠀⢹⣧⠀⢸⣿⡿⢹⡿⠿⣶⣤⣤⣄⣀⣉⣿⣁⣠⣤⣤⣴⡶⠶⠿⣿⠋⠉⠀⠀⣀⣼⣿⣶⠞⣻⡿⠋⠀⠀⠀⢈⣥⡾⠛⠀⠀ ⠀⠀⠀⣿⠀⢸⣿⣷⣼⣇⡀⣾⡋⠉⠉⢹⣿⠉⠉⠉⣿⠃⠀⠀⠀⣀⣿⣧⣶⣾⣿⠿⢻⣿⢀⣴⡟⠁⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀ ⠀⠀⠀⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣿⠉⠁⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢿⣟⣿⡻⣿⠿⢿⣿⠿⠿⣿⡟⠛⠛⠛⣿⠉⠁⠀⠀⠀⢻⣆⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡿⠀⠀⠈⠻⣿⣥⣹⣷⡈⣿⣄⠀⢹⣇⠀⠀⠀⣿⣀⠀⣀⣠⣤⣶⡿⠟⠋⢁⡠⠔⣂⡤⠖⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⣦⠀⠀⡄⠉⠉⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⣀⠤⢒⣪⠥⠖⢋⣡⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠻⣄⠀⠈⠲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡾⠯⠖⠊⢉⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⠉⠒⠢⠤⠤⠤⠄⠀⠀⠤⠐⠒⠒⠀⠉⠉⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠿⠶⠶⠶⠶⠶⠶⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠉⠀⠈⠐⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⣤⡤⡄⠀⠀⢁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⣇⠌⠉⠀⠀⢤⣞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠿⢷⣴⡅⣴⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢷⠤⣏⣭⢯⠁⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⠐⡇⠆⢼⠄⠀⠑⠂⠤⡀ ⠀⠀⠀⠀⠀⡀⠤⠤⠐⡉⠀⠏⠀⠃⠒⣀⠀⠤⠂⠁⠈ ⠀⠀⠀⢀⠌⠀⠀⠀⢠⠇⠀⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⢀⠠⠊⠀⠀⡠⠉⠀⠀⠁⢂⠀⠀⢠⡾⠿ ⠀⡠⠒⠁⠈⠀⠀⠀⠀⠔⠀⠀⠡⠀⠀⠀⠑⠀⠤⠄⣀ ⣰⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠶⠶⠿⠿⠟⠿⠷⢶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⣟⣋⣙⡉⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠉⠉⠙⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠰⠶⠛⠛⠛⠛⠻⢿⣦⣀⠀⠀⠒⠒⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⢀⣀⣀⣀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⡀⠀⣤⣴⠖⠒⠶⣤⡉⠳⣄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠛⣒⣾⡽⠾⠿⣿⣄⡀⠀⠈⠻⣆⢸⠀⠀⠻⡄⠀⠀⠀⠀⣀⣶⡿⠟⠛⠻⠿⢿⣿⣦⣀⡀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠲⣄⣀⠀⠉⠉⠒⢤⣿⠈⠀⠀⢰⡇⠀⠀⠀⣀⠋⢁⣀⣀⣀⣀⠀⠀⠀⠉⠻⢿⣤⡀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠛⣡⡜⠀⢠⠞⠀⠀⠀⣴⠋⠠⠛⢁⣠⣤⣬⣛⠦⣀⠀⠀⠀⠙⠿⣦⡀⠀⠙⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠙⠛⠒⠒⠒⠒⠒⠒⢂⣀⠀⠀⠀⠀⠀⠀⠖⢚⣉⣠⠴⠛⠒⢦⡀⠀⠛⣷⣴⢾⣋⡀⠀⠀⢩⣿⣮⡢⠀⠀⠀⠀⠈⢻⡄⠀⠘⣿⣆⠀⠀⠀ ⠀⠀⢠⣶⡿⠋⠁⠀⢀⣤⣤⣶⣶⣿⣟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⣶⣿⣭⢷⡿⠀⢀⣬⣽⢦⣄⠙⠙⢦⡈⠉⠑⠶⣼⡛⠛⢻⡄⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⣆⠀⠀ ⠀⣼⡿⠃⠀⢀⡴⠞⠉⢉⣿⣿⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠿⢯⣭⣧⠈⣧⠘⠦⣝⠲⢦⣀⣈⣙⣲⣼⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀ ⢸⡟⠀⠀⢠⠟⠀⠀⢀⣾⣿⣿⣼⠏⠉⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⠻⢦⣉⠛⠛⠛⠃⠙⢿⡲⠆⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀ ⢸⠁⠀⢀⡏⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⣧⣹⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠀⠀⠀⣰⠋⠙⢳⡹⣿⣦⡀⠀⠀⠀⠀⣴⠃⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡝⢳⣄⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⣰⠃⠀⠀⠀⢳⠈⡻⢿⣷⣤⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠛⢶⡈⠳⣄⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⡀⢰⠏⠀⠀⠀⠀⠈⣇⣯⢤⣝⣶⣝⠷⣤⣤⠤⣦⣤⣄⣀⣀⣠⣤⣤⣶⣶⡾⠿⠛⢉⣁⣀⣀⣴⠟⠙⣦⡈⠻⣦⣀⢹⣿⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⣾⡏⣿⣿⣿⠻⡻⣿⡀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠙⢿⠷⢤⣤⣶⣶⠶⠲⡖⠛⢛⣉⣉⣁⡘⠗⣠⠞⠋⠀⠀⣿⠁⢀⣠⣾⣷⡄⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠲⣿⣿⣿⣦⡀⠀⣰⠃⠀⠀⠀⠀⠀⣸⠟⠋⠁⠈⠉⠛⣦⡴⠛⠉⠀⠀⠈⠙⣿⠃⠀⠀⠀⢠⢏⣤⣾⣿⣿⣿⡟⢦⠀⠀⠀⠙⣿⡄⠀⠀ ⢹⡆⠀⠀⠀⠀⣿⣯⣿⡍⠛⢻⣿⠏⠁⠈⠛⠲⣏⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠁⠈⢧⡀⠀⠀⠙⢿⣆⠀ ⢸⣿⡄⠀⠀⠀⣿⡏⣿⣿⣦⣿⡏⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢠⠟⠳⣄⣠⠞⢁⣿⡟⠉⠀⣸⣿⡏⠀⠀⠈⣧⠀⠀⠀⠈⢿⡆ ⠀⠹⣷⡄⠀⠀⢹⡇⢹⣿⠋⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠷⠶⢤⣀⣀⣀⣰⠿⣦⣀⣀⣀⡤⠖⠋⠀⠀⠉⠀⠀⣾⣿⠀⠀⢠⣿⣿⠀⠀⠀⠀⣸⠃⠀⠀⠀⢸⡇ ⠀⠀⠘⢿⣆⠀⠘⣿⠀⢻⣄⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠳⣤⣼⣷⠃⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠈⠻⣧⡀⣸⡇⠀⢻⣾⡛⠉⠳⣤⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢀⣴⡿⢻⠏⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠙⢿⣮⣷⡀⠀⠙⢷⣄⠀⣽⠉⠻⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⢠⢴⣿⠛⣩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠙⠿⣯⡀⠀⠈⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣴⣾⣿⣿⠿⠿⣿⡷⠋⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣆⡀⠀⠀⠈⠻⢷⣾⣿⠀⠀⠀⠀⢹⡿⠛⠳⠶⢶⣶⡿⠟⠉⠻⣿⠟⠉⠁⣀⡤⠞⠁⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠻⢦⣀⠀⠀⠀⠈⠙⠓⠶⣤⣄⣾⣀⠀⠀⠀⣸⠏⠀⢀⣀⣀⣿⠤⠖⠛⠉⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠙⠻⣦⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠙⠛⠳⢦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣄⣀⠈⠉⠛⠛⠛⠛⠿⢛⣿⣟⣋⣉⣀⣀⣀⣠⣴⣶⣶⠶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠈⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣁⣠⣾⣷⡾⠀⢀⣶⣿⣿⣿⡷⣦⣄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠛⢿⣿⡿⠋⣥⡀⢀⣿⣿⣿⣿⣿⡇⠹⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣧⣤⣀⣙⠛⠛⠛⠛⠃⠘⣿⣿⣿⡟⠋⠁⣠⡟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⠉⠉⠛⠻⠿⠿⢿⣷⣶⣶⣤⣈⣉⠙⠛⠿⠛⠋⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠂⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣶⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣸⡿⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⢻⣷⡄ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⣿⠃⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⢠⣿⠃ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣾⠏⠀⠀⣿⡏⢀⣀⣀⣤⣤⣄⣀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⣠⡿⠃⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⡏⠀⠀⠀⣿⡿⠟⠛⣟⡛⠛⠛⠿⣿⣦⣠⣿⠟⠁⠀⠀⢀⣴⡿⠁⠀⠀ ⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⠀⠀⠀⠀⠛⠃⠀⢀⣹⣟⣦⣄⣀⣠⡿⠋⠁⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⢾⡛⠁⣀⠙⣷⡄⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⠿⣿⣷⣦⡀⠀⠰⢿⣿⣏⣀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠙⠻⣿⣸⣿⢷⡿⠃⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢿⣿⣄⠀⣀⠀⠈⠙⣷⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠈⣿⣿⡀⠈⠻⣿⡛⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⠘⣿⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⠈⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀⠀⠀⠀⠀⠀⣀⣿⠿⠷⢶⡶⠾⠏⠀⠀⠀⠀ ⢸⡏⠻⣦⡀⢀⣾⠟⠁⣨⡿⠿⣿⣶⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⠀⠘⢷⡿⠃⣠⣾⠋⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⠀⢰⣶⣦⣤⣤⣼⣧⣤⣶⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠄⣶⣶⣶⣾⡿⠃⢀⣿⠇⠈⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣇⠉⠛⠁⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠾⠛⠛⠉⠉⠉⠉⠉⠙⠛⠻⠷⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⡭⠾⠟⠛⠶⣦⣄⠀⠀⠬⠵⡀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⢠⠤⢤⡀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣄⣰⣿⡏⠉⠓⢦⡙⣆⠈⢧⠀⠀⠀⠀⢀⣠⣶⣾⣷⣦⣄⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠉⠉⢭⣉⠉⠒⠢⢄⣧⠈⠀⢨⠀⠀⠀⠀⠛⣉⣀⣀⠀⠉⠙⠻⢶⣀⠀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⣡⠆⢀⡞⠀⠀⣰⠃⠘⣉⡤⠬⢽⣢⣄⠀⠀⠙⢷⣄⠀⠻⣧⠀⠀⠀ ⠀⠀⠀⣠⣴⠞⠋⠉⠈⣉⣩⣭⡤⠤⠤⠤⠤⠤⠤⣀⢈⣩⣴⣶⠉⠉⠳⣄⠈⢿⣟⠓⠤⣄⡰⣿⣿⡄⠀⠀⠀⠙⠆⠀⠹⣧⡀⠀ ⠀⢠⡾⠋⠀⣠⠴⠛⣿⣿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⢸⣟⣿⠙⡆⢨⣳⢤⣀⠉⠳⣄⣿⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀ ⠀⡟⠀⠀⡜⠁⠀⣰⣿⣷⡿⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠀⠈⠉⠀⠁⠀⠈⠓⢮⡙⠛⠛⠙⠻⡗⠀⠀⠀⠀⠀⣾⠇⠀ ⠀⠃⠀⠘⠀⠀⢠⣿⣿⡿⠀⠀⢀⡷⣿⣷⣄⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡴⣄⠀⠈⠀⠀⠀⠀⢰⡟⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⢀⡎⠀⠈⢧⠙⣷⣤⣀⠀⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⢮⡑⢤⡀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣀⡞⠀⠀⠀⢸⣤⠥⢽⣮⡳⠦⠤⠤⣤⣤⣤⣤⣤⣤⣶⡶⠞⢛⣉⢥⣥⠼⠛⣆⠙⢦⡀⣻⡆⠀⠀⠀ ⢀⠀⠀⠀⠀⣾⣿⣿⣿⣻⣿⣆⡀⠀⠀⡜⠁⠀⠀⠈⣿⡷⠶⠿⢟⡛⢋⡩⠥⠤⠤⣍⡴⠋⠀⠀⡏⢀⣴⣿⣷⡀⠀⠈⢷⣄⠀⠀ ⠸⡆⠀⠀⠀⣿⣻⡟⠣⢼⣿⠛⠻⠦⣼⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⡞⠀⠀⠀⣼⣾⣿⣿⣿⡟⠘⢆⠀⠀⠻⣦⠀ ⠀⣿⡄⠀⠀⢿⢹⣿⣦⣿⠁⠀⠀⠀⠘⠲⢄⣀⣠⡏⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡼⠳⣄⡠⠊⣿⠏⠉⢹⣿⠃⠀⠘⡆⠀⠀⠘⡇ ⠀⠘⢿⣄⠀⢸⡇⢿⡃⢸⡇⠀⠀⠀⠀⠀⠀⢀⡿⠓⠒⠦⠤⠤⠟⠳⠤⠤⠒⠊⠀⠀⠀⠀⣸⣿⡀⠀⣿⡏⠀⠀⠀⡏⠀⠀⠀⡇ ⠀⠀⠀⠻⣦⠀⣷⠈⢳⣼⠟⢦⣀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⣸⣿⡿⠀⠀⠀⠸⠃⠀⠀⠀⡇ ⠀⠀⠀⠀⠘⢷⣽⡆⠀⠹⣦⡀⣹⠙⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⢤⡾⠋⡼⠁⠀⠀⠀⠀⠀⠀⢀⣾⠃ ⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠈⠙⢿⣄⢀⣿⠿⠿⠶⣤⣀⣀⡀⢀⣀⣤⣤⣤⣴⡿⠿⠛⣛⠿⠋⡠⠊⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣄⠀⠀⠈⠛⠿⣄⣀⡀⡽⠁⠀⠉⣽⠏⠁⠀⢻⣇⡠⠴⠊⠁⣠⠞⠁⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠙⠶⣄⣀⠀⠀⠈⠉⠙⠓⠒⠒⠛⠒⠚⠋⠉⠀⢀⡠⠔⠋⠀⠀⠀⠀⢀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⣉⠛⠲⠦⣤⣀⣀⣀⣀⣀⣀⣠⠤⠔⠊⠁⠀⠀⢀⣠⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣤⣤⣤⣬⣭⣽⡿⠶⠶⠶⠶⠾⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠉⠲⢄⣱⣀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠼⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣋⣭⣴⣒⣒⣒⣶⣦⠤⢈⣑⣄⠤⢒⣋⡭⠭⢭⣭⣭⣽⠭⢍⣈⠛⠦⡀⠀ ⠀⠀⣠⠞⠁⡞⠀⠀⠀⠀⠀⠀⠀⢤⠒⣉⣤⡶⠟⢛⣿⣿⣿⣷⣦⡀⠉⠉⠛⠫⣜⠉⢁⡠⠖⣺⡿⣿⣿⣿⣍⠙⠛⠯⣟⢣⡀ ⠀⡴⠁⠀⢸⡇⠀⠀⠀⠀⠀⠸⢏⣋⣩⡔⠉⠀⠀⣿⣭⣿⣿⣏⣹⣷⠀⠀⠀⠀⢨⠗⠉⠀⠀⣿⣷⣿⣿⣉⣿⠇⠀⠀⠀⢹⡇ ⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠲⢤⣀⠹⣿⣿⣿⣿⡿⠋⠀⢀⣀⡤⢾⣄⣀⠀⠀⠻⣿⣿⣿⣿⠏⠀⣀⣠⠤⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⢄⣉⣈⣉⣛⠓⠒⠀⣉⣉⣀⡠⠆⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⡴⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠼⠋⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⢖⠒⠉⠉⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠈⠳⢄⡀⠀⠈⠑⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠛⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠉⠑⠢⠤⣀⣀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠒⠒⠒⠂⠀⠈⠉⠁⠀⠀⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢄⣀⡀⠀⠉⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⠉⡏⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠦⠤⠤⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⠤⠞⠁⠀⠀⠀⠀ ⡀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠦⢄⡈⠉⠒⠢⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠒⠂⠤⠄⣀⣀⣈⡉⠉⠉⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⢉⣙⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⠒⠉⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣇⣀⣰⡷⡆⡇⠀⠀⠀⠀⡤⢄⠀⠀ ⢿⠻⣷⣎⠿⠓⢱⠀⠀⠀⠀⡇⢸⠀⠀ ⢸⠊⠉⠀⠀⢦⡄⢣⡠⣔⣺⣀⣾⠿⡄ ⠀⡇⠀⠀⠀⠀⢳⠈⠋⠏⠠⠀⠈⡗⠃ ⠀⠘⣆⠀⠀⠀⣿⡗⠂⠀⠲⠀⢰⠃⠀ ⠀⠀⠈⠳⢄⣀⣀⣀⣀⣠⢶⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠉⠘⢾⣛⡄⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠽⠀⠀⠀⠀⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⣄⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣛⣿⡆⠀⣻⣿⣙⣛⡷⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⣿⡿⠁⣀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠹⣷⣒⣾⠷⠀⠀⠀⠀⠀⠀⠀⠲⣾⢿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣿⣦⣰⠀⣶⠛⠀⢀⣰⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣇⠙⠛⠛⠛⢉⣿⣿⣍⣧⠀⣿⢳⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⢠⣼⠛⡏⢘⣿⡿⠃⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⠙⠙⡟⣿⣤⡿⢼⣏⡇⠀⠀⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡗⣿⡀⢸⣧⣿⠀⣇⢸⡏⣧⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⢹⡇⢸⠇⢿⠀⠛⠀⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏⠉⠀⠈⣇⡾⠀⠆⠲⣦⠐⣦⢸⠂⠀⠀⠀⠀⠀⢀⡤⠖⠚⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠛⠓⠒⠉⠁⠀⡇⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢸⣤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⢀⡼⠻⡄⠀⠀⠀⠀⠙⠲⡄⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣾ ⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣀⠤⠖⠉⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⣹⠿⠿⠚⠛ ⠀⠀⠀⠀⣠⠴⠚⠡⠤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⡾⠁⠀⠀⠀⠀ ⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠤⣶ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣤⣤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢙⣧⡀⠀⠀⠀⠉⠉⠓⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⠿⣄⠀⢰⣤⣄⡀⠀⠀⠉⠳⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠻⣧⠀⠹⣧⣉⠷⢦⣄⠀⠘⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣧⡀⠘⣷⣀⣽⠛⢷⣄⠈⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠘⣧⠈⠀⢀⣽⣦⠘⣷⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣿⣿⣆⠸⣷⠂⠀⠀⠙⣧⠘⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠚⢿⡄⢹⡆⠀⠀⠰⠛⣧⠘⣿⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣲⣤⣀⣲⣦⣤⣼⣥⣼⡇⠀⣿⣤⣤⡀⠀⠿⡆⠘⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠋⠉⢉⢀⣠⣤⣴⡶⣿⠉⠀⠀⠉⠙⠛⠿⣾⣆⣿⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⣄⣀⣤⠿⠟⠛⣻⡾⠛⠦⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⢹⡧⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⣼⠾⠋⠙⠀⠀⠀⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠀⣴⣏⠙⠀⠀⠀⠤⣼⣶⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⢠⣌⣿⠀ ⠀⠀⠀⠀⠀⢀⣀⠀⢀⠇⢀⡾⠁⠀⠀⠠⣤⡾⠟⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠧⠒⠀⠀⠀⠤⣿⠆ ⠀⠀⠀⠀⠀⠀⠈⠉⡻⢦⣾⢅⣀⣀⠀⣶⣟⣠⣞⣋⡀⣤⡤⠠⠤⠀⠀⣀⠀⠀⠀⠀⣀⡤⠤⠆⠀⠀⠠⣴⡿⢧ ⠀⠀⠀⠀⠀⡀⠙⢶⡗⣾⡟⠲⢦⣿⣿⠿⢋⡿⠋⣩⣤⣝⣿⣃⠀⣾⣉⣩⠽⠿⢶⣯⣁⣀⠠⠤⠀⠴⣶⡿⠃⠀ ⠀⠀⠀⠀⠀⠉⠹⣿⢻⣟⣹⠿⠋⠉⠋⠉⠙⢷⣤⣌⣿⣦⣭⣿⠀⣿⣛⣛⡉⠉⠉⢉⣻⣷⣄⠀⠀⠀⣼⠓⠀⠀ ⠀⠀⠀⠀⠀⢀⣹⡇⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣄⣤⣇⢉⣹⡏⠉⠁⠀⠉⠉⠉⠉⠉⠉⢿⣄⠀⠀⣿⠛⠃⠀ ⠀⠀⠀⠀⠀⣼⣿⣼⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⠠⣿⠄⠀⠀ ⠀⠀⠀⠀⣶⡿⠁⠀⣠⡾⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⢹⡟⢀⠀ ⠀⠀⢤⣼⣿⠷⠞⠛⣯⡤⠼⢷⣀⠀⠀⢀⣠⡞⠏⢹⡛⣷⣦⣄⡀⠀⠀⠀⣀⣤⣴⢾⡛⢯⡉⠀⠀⠀⠀⢻⠉⠀ ⢀⣠⣾⠿⡍⠃⠀⠀⠀⠀⠀⠈⢿⡟⠛⣹⠇⠈⠀⠀⠀⠉⠘⠉⠻⣿⣿⣿⠉⠙⠦⠀⠉⠀⠉⠁⠀⠀⠀⠘⣇⠀ ⣼⡏⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣨⣧⣄⠀⡼⠀⠀⠀⠀⢀⣶⠀⠀⢿⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣻⣇⡀⠀⠀⠀⠸⣿⣤⣀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⣻⡧⣽⠂⠀⠀⠀⠈⣉⠉⠈⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠝⠓⠲⢤⡀⠀⠦⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢋⣠⡔⠢⢔⢄⠣⠀⠀⠀⣀⣤⣤⣀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠋⠀⠉⠀⠌⣁⡪⠊⢀⠇⢀⠌⠥⠠⢄⠉⠛⢄⡈⢳⡀⠀ ⠀⣠⠴⠚⣉⣁⡤⠤⠤⠤⠤⠄⣪⣵⠊⣢⣈⠶⡊⠤⣹⠷⡀⠀⠑⠄⢳⡀ ⡼⠁⡔⠉⣼⣯⠟⣦⡀⠀⠀⠀⠀⠡⠀⠑⠃⠂⠘⢕⠲⠗⠧⡄⠀⠀⢠⡇ ⠃⠈⠀⣰⣿⡇⠀⠔⢻⢦⡀⠀⡠⠱⠁⠀⠀⠀⠀⠀⠙⢶⠄⡁⠀⠀⡜⠀ ⠀⠀⠀⣿⣿⣇⡌⠀⠀⡦⠽⣗⡤⢤⣤⣤⡤⠤⣶⢒⠬⡥⠓⣌⠢⢸⡇⠀ ⡄⠀⢸⣿⠟⣺⠷⠄⡜⠀⠀⣸⠊⠉⢐⠕⠈⠉⡰⠁⢀⣧⣾⣿⠢⡀⠹⣄ ⢻⡀⠘⡿⡷⢋⠀⠀⠈⠂⢤⢇⡀⠀⣼⣀⣀⠰⠑⠔⣹⠏⢸⡏⠀⢱⠀⠘ ⠀⠙⣄⢣⠱⡼⠢⣀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣱⡾⠀⠀⠊⠀⢀ ⠀⠀⠈⠻⣆⠈⠲⣇⢹⠷⠤⣀⡀⠀⣀⣀⣠⣴⠾⡷⢝⠕⠁⠀⠀⠀⣠⠋ ⠀⠀⠀⠀⠹⡗⢄⡈⠙⠂⠤⠏⠀⠸⠉⠠⠧⠒⣈⠔⠁⠀⠀⣀⡴⠚⠁⠀ ⠀⠀⠀⠀⠀⠙⠲⢬⣓⠢⠤⠤⢀⣀⡤⠤⠐⢈⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣶⣶⡋⠀⠀⠀⠀⠀⠀⢠⣭⢝⣛⢿⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⢟⠟⡩⢊⣥⣠⣶⡄⣀⣄⡐⠵⣶⢾⣿⣷⣿⣷⣿⣿⣟⢄⠀⠀⠀ ⠀⢠⣾⡷⣡⣾⣾⣿⣿⠟⠀⠙⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⠀⠀ ⢠⣿⣿⣽⣿⣿⣿⡿⠋⣠⣂⣉⣀⡈⠙⠛⠟⠋⡙⠛⠛⠛⠿⣿⣿⣿⣿⣇⠀ ⣸⣿⣿⣿⣿⣿⠃⠒⠚⠋⠉⠛⠛⢬⣐⠆⠀⠀⣵⠶⠭⠛⠂⠈⢻⣿⣿⣿⡄ ⣿⣿⣿⣿⣿⡏⢰⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡀⠁⣿⣿⠇ ⢹⣿⣿⣿⣿⡇⠈⢦⣉⣲⢤⣀⡀⠀⠇⠐⠂⠀⠠⠃⠀⠀⡠⡏⠀⢰⣿⡟⠀ ⢸⣿⣿⣿⣿⡇⠀⠈⢿⢿⣶⣤⣬⣉⠉⠉⠁⠐⠒⠂⠈⣉⣀⡇⠀⣾⣿⡇⠀ ⠸⢻⣿⣿⣿⣿⡄⠀⠀⠑⠠⣉⠹⠛⠛⠛⠿⠿⢿⠿⢿⠿⠟⡇⠀⣿⣿⡇⠀ ⠀⠈⣿⣿⣿⣿⡌⠢⡀⠀⠀⠀⠍⣑⠒⠀⠤⠤⠤⠤⠤⠀⠒⡡⠂⣿⣿⡇⠀ ⠀⠀⠹⡿⣿⣿⣷⠀⠈⠐⠠⣀⠀⠀⠈⠑⠒⠂⠀⠤⠀⠐⠊⠀⢰⢿⡟⡇⠀ ⠀⠀⠀⡇⡏⣧⢻⣇⠀⠀⠀⠀⠉⠑⠂⠤⠄⣀⡀⠀⠀⠀⢀⡰⠃⠸⠃⠹⠀ ⠀⠀⠀⠠⡇⡏⠘⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢰⡉⢲⣿⡃⠄⠂⠀⠀⠀⠀⠁⠐⠢⢻⣅⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠄⣻⣿⠋⠀⣰⢀⠎⢀⠀⡀⠀⡐⣜⡄⢹⣿⡁⠀⠈⠐⢄⠀⠀⠀ ⠀⠔⠁⠀⣀⣿⠇⡄⢰⡇⢸⢠⢺⢰⢳⠛⣸⢿⣧⢨⡟⣿⣆⠀⠀⠀⠑⠀⠀ ⠀⠄⢀⡴⣹⢿⡖⡦⣾⣷⣸⢾⣨⢟⢼⣇⣹⠮⢧⣼⣹⠿⡛⠠⠀⠀⠀⠀⠀ ⠈⣰⡟⢌⢧⠸⡿⣇⢯⠂⢫⡣⠿⠿⣦⠋⠱⡪⢽⣿⡟⠈⣷⠀⣆⢃⠀⠀⠀ ⠀⣻⢹⢸⠀⠀⠙⡽⡮⣆⠀⢈⠉⢉⠀⠀⠑⡄⣹⢃⠇⠀⢹⡇⠘⡎⠆⠀⠀ ⠀⡇⠋⣼⡃⠀⠀⡏⠈⠙⣷⢼⡄⣶⣷⣶⣾⣦⣴⠎⠀⠀⠀⢻⡸⢱⠈⠄⠀ ⠀⠀⠀⢷⠀⠀⠀⡇⠀⠀⠘⣟⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠳⠜⠀⠀⠁ ⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⢹⢸⣿⣿⣿⣿⡯⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⠀⠰⠃⠀⠀⢱⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣐⠀⢀⠇⠀⠀⠀⠈⣇⣿⡿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡞⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀ ⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀ ⠀⢰⣿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀ ⢠⣿⣧⠶⠀⠀⠀⣠⣴⣶⣶⣷⠲⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⠒⠶⢿⣧⡀⠀ ⢸⣿⠏⠀⠀⠀⠘⠋⢸⣅⠀⣽⡆⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣧⡀⣸⣧⠀⠀⣿⡟⠃ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣼⣿⡀ ⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⠇ ⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠈⠙⠛⠋⠉⠀⠀⢠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡟⠀ ⢸⣟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠤⠤⠤⠴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠟⠀⠀ ⠘⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠛⠉⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀ ⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢸⣇⣀⣀⣴⡿⠿⠛⠛⠛⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣴⣶⡿⠉⠉⠉⠉⠹⣿⡉⠹⣷⡄⠀ ⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠀⠀⠀⣿⠀⣀⢀⣿⠇⠀⢻⣷⠀ ⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⣷⣷⣾⠟⠀⠀⠀⣿⡇ ⠀⢠⣿⠟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⢠⣿⠟⠀⠀⡙⢿⣷⣦⣤⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡶⠶⢶⣿⣿⣦⣄⣀⣀⣠⣶⡿⠋⠀

⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠖⠋⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣤⠀⠀⢼⣿⢿⣿⡿⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⢿⣿⡿⠿⠿⢿⡄⠀⠈⠛⠯⠥⠴⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣰⠟⣡⡖⣾⣿⠿⢿⠆⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⡴⠋⠀⠀⢠⡄⠀⠀⠀⠀⢀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⠻⠇⠙⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢨⡗⠦⣄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣧⠀⠐⠛⡇⠹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠹⠦⠶⠲⠴⠒⠋⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠙⣻⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣑⠚⠁⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⣀⡤⠴⢺⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢤⡞⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⡶⠾⣛⡿⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠘⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⠹⡄⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣰⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⢦⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⣀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⢿⣿⡉⠉⠉⠛⠛⠛⠒⠒⠦⣤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠇⢠⡾⣿⣆⠀⠀⠀⣀⠀⠀⠀⠀⠈⠙⠻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣷⡀⠀⠻⣷⣤⣄⣀⠀⠀⠀⠈⠻⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠼⣿⡄⠀⠹⣿⡌⣙⣿⢦⣄⡀⠀⠈⢻⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣄⠀⠈⢿⣏⠁⠰⣿⢷⣦⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⢻⣆⠀⠘⢿⡶⠾⣍⠀⠙⣷⣄⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣧⡀⠈⣿⡄⠀⠀⣀⡼⢿⣦⠀⢿⣏⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⢰⣿⣷⡄⠘⣿⡞⠃⠀⠀⠀⢻⣧⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠯⢿⣿⡀⠹⣷⠀⠀⠀⠀⣤⠿⣧⠈⢿⣦⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠚⠀⠀⣠⠀⢹⡇⠀⢻⡇⠀⠀⠀⠁⠀⣿⡇⠈⢿⣞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⣀⣬⣿⣶⣴⡬⠿⠷⠶⠾⠿⣶⣾⣅⠀⢀⣿⣶⣾⣧⡀⠀⠹⢿⠀⠈⣿⣗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠛⠉⠀⡀⠀⢀⣀⣤⣴⣾⣿⡋⠁⠀⠀⠈⠋⠙⠛⠿⢿⣾⣇⢸⣇⠀⠈⢿⣧⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠁⡀⠀⠀⢀⣲⣦⣿⣿⢿⣏⡿⢯⣄⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠀⠀⠘⣿⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⣤⣀⣿⣶⣾⠛⠋⠁⠀⠀⣴⠟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢀⣠⣾⠛⠉⠀⠈⠁⠀⡀⠀⣼⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠁⠀⣠⣾⣏⠙⠀⠀⠀⠀⠶⣤⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⣄⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠃⠀⣼⠟⠀⠉⠀⢀⣀⣀⣾⡾⡿⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣇⣠⠄⠀⠀⠀⣀⣙⣿⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢤⣠⡇⢀⣾⠏⠀⠀⠀⠀⣀⣼⡿⠋⢠⣾⠟⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡽⠉⣿⡿⠲⠦⣤⣤⣀⣿⣿⣥⣴⣯⣥⣤⠄⣾⣿⣀⠘⠛⢁⣀⣠⣤⣀⡀⠀⠀⢀⣠⠴⠒⠛⠉⠀⠀⠀⠀⢲⣿⡏⠳⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢲⡏⢹⣿⠛⠳⠶⢮⣿⣾⣿⣏⣡⣿⠋⢡⣤⣤⣭⣙⣏⡁⠀⢸⣏⣀⣠⣭⠽⠿⢿⣯⣀⠀⣀⣤⣤⠄⠲⠮⣍⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⢉⣭⣿⠻⣿⡟⢲⣶⠿⠛⠛⠖⠒⠒⢺⣧⣀⡈⠻⣿⡍⢉⣹⡿⠀⢸⡯⠷⠶⠖⠒⠒⠚⠛⠻⣿⣅⠀⠀⠀⠀⠀⣸⡿⠦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⡟⢰⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⣿⠻⠿⣶⡤⠼⠿⠛⠒⠲⠦⠤⠤⠴⠶⠞⢿⣯⠃⠀⠀⠀⣿⣧⣤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣲⣿⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠶⢶⣿⣀⣤⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣠⠀⠀⣿⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣿⢧⣾⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠰⣿⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣤⣾⠏⠉⠀⠀⣨⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠃⠀⠹⡷⠖⠀⠀⠀ ⠀⠀⠀⠀⠐⣶⣿⣏⣠⣤⣶⡿⠛⠉⢿⣆⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⡶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠿⠆⠀⠀⠀⠀⢷⡴⠞⠃⠀ ⠀⠀⠀⢛⣿⣿⣟⡛⠉⠀⠀⠓⠒⠚⠛⢻⣧⣄⣀⣀⣠⣴⠿⣥⡁⠀⠷⠀⣿⡻⣿⣦⣤⣄⣀⣀⣠⣤⣶⡿⠛⠻⢧⡈⠳⣤⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⢤⣠⣿⠟⢷⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⡏⠉⣩⡿⠀⠀⠀⠀⠀⠀⠀⠁⠛⠈⠛⣍⣿⣿⣯⠁⠈⠛⠦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⣼⡟⠛⠲⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢙⣦⡀⠀⠀⣽⠀⠀⠀⠀⠀⠀⢠⣴⠄⠀⠈⣷⢠⠀ ⠚⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣯⢷⣴⠏⠀⠀⠀⠀⠀⢀⣿⢿⠀⠀⠀⣿⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣍⣷⣸⠛⢦⣀⠀⠀⠀⠘⠉⣿⣿⣷⡆⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⣿⡗⢤⡟⠁⠀⠀⠀⠀⠀⢈⠀⠀⠸⣷⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡟⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠈⠛⢷⣄⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡟⠀⠀⠀⣠⣾⣿⣿⡇⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠹⣷⡄⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣀⣤⡶⠿⠛⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣻⣇⠀⠀⠀⠀⠀⠙⠒⠚⠛⠉⠀⠀⣀⡦⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⣿⠁⠀⠀⠀⠀⣀⣠⣴⠶⠟⠛⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠛⠋⠁⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡀⠀⠀⠻⢠⣤⡴⠾⠛⠋⠉⠀⠀⠀⣀⣀⣤⣤⣶⡶⠛⠛⠉⠁⠀⣦⡀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠟⠛⠉⠉⠉⠉⠙⠛⠳⢦⣄⡀⢀⣿⡇⠀⠀⠀⠀⢀⣾⠏⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⡿⠋⠀⠀⠀⠀⢠⣾⠏⠀⠀⣿⡀⣀⣤⣶⣶⡀ ⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣀⣀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⢀⣴⡿⠛⣿⣦⠀⠀⠀⡟⠛⠛⠛⠉⠀⠀ ⠀⠀⠀⠀⣾⡆⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⢹⡌⠳⣄⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⣿⡇⠀⠀⢹⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡾⠟⠋⠁⠀⠀⠀⠀⠈⣷⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⡿⢿⡇⠀⠀⡾⢸⡇⠀⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⢸⡇⠀⣸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⢀⡟⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣼⠃⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠖⠚⠉⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣧⠀⠸⣿⡿⢛⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⠟⣫⢥⣾⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠉⠉⢁⠔⠁⠀⢠⠀⠀⠀⠀⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⡏⠛⣨⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⡀⠀⢀⡏⠓⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠁⠣⡼⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡒⠔⠃⢸⣿⣿⣷⡀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⣠⠴⣶⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢼⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣾⣿⣖⣛⡿⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠈⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⢻⡀⠀⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠐⠒⠊⠁⢸⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⣄⠀⠀⠙⠻⢿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣠⣶⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀

⠀⠀⠈⢿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠉⠁⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠠⠔⠂⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣺⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⡠⣶⣶⠶⢦⠈⠛⠫⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⢿⣿⡄⠀⠈⠘⠈⠭⠀⢨⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣇⠘⢹⣷⣄⠀⠀⠀⠀⡠⠑⠒⠂⠁⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠒⣊⡹⣿⣦⡀⠀⠀⠀⢀⣠⣴⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡅⠻⣿⣿⣤⡀⠀⠈⠉⠉⢀⠠⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣶⣶⣿⣿⣿⡓⣄⠈⠻⢿⣿⣶⣄⣀⣈⣀⣴⣷⣶⣦⣤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠂⠐⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡇⠀⠈⠉⠁⠀⢉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀ ⠀⠀⣠⣾⢯⡓⠐⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⠀⢰⡿⠁⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡠⠀⠀⠀⠀⠀⢇⠀ ⢠⣿⢣⠂⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⠀⠀⠘⡄ ⢸⡷⢹⣤⡀⠀⡀⢸⠀⠀⠀⣀⣀⣀⣀⣤⡤⠖⠃⠀⠑⠄⠀⠀⠀⠀⠀⢣ ⢸⣷⡄⢻⡦⣀⣼⡿⠉⢹⣿⣿⡿⠋⣭⠹⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡄ ⠈⡏⣧⣌⠙⠛⣿⡇⠁⠛⣉⡻⢯⣂⠍⢼⠕⠉⠀⡀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠹⣿⣿⢳⠴⠛⡅⠀⣜⡴⠛⠓⠢⣍⣠⢔⠞⠄⠀⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠹⣍⣇⣢⣀⢳⡴⢰⡀⠀⠀⢀⣠⠖⠁⢀⣼⡆⠀⠀⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⠘⢿⡷⡜⢭⡉⠛⣛⡶⠏⠉⠁⠀⢀⡿⠋⠀⠀⠀⠀⢠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢿⣆⢇⠀⠘⡄⠀⠀⠀⠀⠜⠀⠀⠀⠀⣠⠖⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠅⢀⣀⣀⣀⣀⣀⡤⠒⠉⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⡔⠢⠦⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⢦⠀⣦⢄⡀⠑⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡈⢷⣉⠶⣄⢫⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⡌⢇⡀⠘⢦⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠻⠈⡆⠀⠜⣧⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠓⢊⣁⣼⡞⠂⠚⠾⢦⣝⡄⢻⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠉⣰⠤⠚⠋⡹⠋⠒⠀⠀⠀⠀⠀⠈⠁⠈⡗⠀ ⠀⠀⠀⠀⠀⢐⠏⡠⠞⠀⢀⣤⣴⣉⠀⠀⠀⠀⠀⢠⣄⠀⠀⠠⣏⠀ ⠀⠀⠀⠐⠂⡬⣴⣁⡀⣬⣏⣽⡛⡋⠀⠀⠀⠀⠀⢀⡉⠅⠀⢈⡿⡁ ⠀⠀⠀⠤⣵⢽⢏⡲⠿⠛⣝⡁⣶⠽⡅⢸⡤⠛⠻⢧⡄⠂⠐⣽⠁⠀ ⠀⠀⠀⢠⣞⣾⠉⠀⠀⠀⠀⠯⢭⣉⡷⠚⠉⠁⠀⠉⠙⣄⠀⡗⠂⠀ ⠀⠀⢠⡾⠛⣹⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠂⢫⢀⠀ ⠀⢰⡿⡗⠉⠓⠚⢦⡤⢤⠪⠋⠏⠗⢦⣤⣤⠴⡒⠫⠫⠅⠀⠈⡅⠀ ⠸⠛⠊⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠈⠫⣦⣀⠆⠀⠀⣰⠀⢱⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢾⢒⠄⠀⠙⠓⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠖⠚⠛⢉⣉⣙⡒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣛⠛⠛⠲⠶⠶⢤⣴⣿⣿⣿⣿⣿⣯⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⣫⡿⠛⠻⣷⡄⠀⠀⠀⣼⣿⢿⣿⣿⡿⢷⣹⣧⠈⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣼⣿⡿⠀⠀⠀⠹⣿⡄⠀⢠⡟⢹⡏⠀⠀⠙⠛⢻⣿⣆⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠏⢀⣼⡿⠃⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢀⣼⠿⠷⣾⡿⢋⣀⣀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⣤⠶⠶⣦⣤⣹⠿⣷⣬⣿⣿⡄⢀⡀⠀⠀⠀ ⠀⠀⢠⣧⡾⢿⡇⠀⣨⣾⠟⠉⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠹⡿⠻⣧⡀⠈⠁⢻⡿⢉⠻⡄⠀⠀ ⠀⠀⣾⢏⣆⢸⠇⢰⡟⠁⣀⣀⣀⣀⣈⢻⡆⠀⠀⠀⠀⠀⢠⣿⣀⣀⣤⣤⣤⣤⣄⣀⠙⣷⠀⠀⠈⠁⢸⡆⣿⠀⠀ ⢀⢴⡏⢸⠏⠀⢠⣿⠶⠟⢋⣉⣉⡉⠙⠻⣷⠀⠀⠀⠀⠠⠟⠋⠁⠠⠶⠶⠶⣤⣈⠉⠛⠿⡇⠀⠀⠀⢠⣿⢸⡇⠀ ⢸⣿⠀⡾⠀⠀⣼⡇⠀⠈⠉⠀⠀⠁⢀⣼⠿⠀⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣠⠁⠀⠀⠀⣸⠏⢸⣇⠀ ⢸⣿⠀⡇⠀⠀⠈⠻⣷⣶⣶⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⣶⣶⣶⣶⡿⠗⠋⠁⠀⠀⠀⣠⡟⠀⣼⣿⠀ ⢸⣿⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢿⣿⠀ ⢸⣿⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⠁⠀⠀⠀⠘⣿⠀ ⢸⣿⠀⠀⠙⠛⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⠉⠉⠉⠻⠆⠀⠀⠀⣿⠀ ⢸⣿⡀⠀⠠⠟⠋⠉⢿⡛⠓⢲⡶⣶⠶⠶⢶⡶⠶⠶⠶⣶⡶⠿⠛⠻⣿⣉⣁⣠⡾⠃⠙⢷⡄⠀⠀⠀⠀⠀⠀⢸⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠈⢛⡶⠋⠀⠙⣦⣄⣤⣿⣠⣤⣾⡟⠀⠀⠀⠀⠙⠿⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⣇⣿⡀⠀⠀⠀⠀⠠⠟⠁⠀⢀⣼⠃⠘⠃⢠⡿⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢻⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠘⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁ ⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀ ⠀⠀⠀⠀⣿⡈⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠉⠻⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠸⣯⣿⢿⡞⢿⣿⠿⣾⡇⡟⢻⠿⣗⢿⣿⠂⢼⠻⣿⣿⡿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣴⣠⡒⠀⣀⡀⣤⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠅⠳⠿⠿⠿⠛⠿⠭⠽⠗⠠⠽⠾⠿⠯⠿⠿⠿⠿⠹⠟⠿⢿⣿⠿⠿⠿⡟⠩⠙⠿⠿⠧⠀⠀⠀⠀ ⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠉⠉⠉⠙⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⠀⠀⣤⡾⠷⠶⢶⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠋⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢰⣷⣤⣤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣆⡀⠀⢀⣶⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢙⡶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠛⣁⣈⣇⡈⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢻⠒⣓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣠⡄⠻⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠋⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣾⣛⣿⡂⢿⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠐⠒⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠛⠓⠒⠋⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠶⠂⡄⠀⢀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠇⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⡶⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠉⠛⢦⣤⢴⡊⠉⠙⠛⠿⠿⠿⠿⠛⠋⠉⣠⡾⠋⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣤⠖⢋⡀⣀⠙⢦⠀⠀⠀⠀⠀⠀⣠⡴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠤⠖⢻⡀⠀⠀⣠⠴⠛⠛⠁⠀⠀⠀⠈⡇⠀⢳⡀⠀⢀⠴⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠳⢤⣀⠀⠀ ⢠⠖⠉⠀⠀⠀⠀⠹⣄⡴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡧⠚⢁⣀⠤⠤⠾⣷⣶⣤⣤⣀⣀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠈⠙⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢉⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀