International Emoji Combos

✈️🌎

👨🏻‍💼🌎📃

Amadora de Roleplay⚜▶☣

🌍✈💕∞

🏃🌍🌎🌏✈️💨🤝🚞⛰🙏🏼🧎‍♂️✝️⛪🤲🏻🙏🏽🏚️😇🕊✝

🌎🌍🌏🌎🌍🌏

📖⛪

𓆩†𓆪

✝️️✞☦✝✟♱⛪🛐🙏📿👼🧔🏽

📖👩💭🧔🏽‍♀️✝

🙏📖😌🕊️🛐

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🙏🏻📿🌹🍃⚜️👑🕊❤‍🔥🗝♱🎄🌟👼🏻⛪☩🧎🏻🏴󠁧󠁢󠁥󠁮󠁧󠁿

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𐃯

⬜➖🟨🟨👁️🟨🟨➖⬜ ⬜⬜️👁️➖➖➖👁️⬜️⬜ ➖🟨➖⬜⬜⬜➖🟨➖ ⬜👁️➖⬜⬛⬜➖👁️⬜ ➖🟨➖⬜⬜⬜➖🟨➖ ⬜🟨👁️➖➖➖👁️🟨⬜ ➖⬜⬜️🟨👁️🟨⬜️⬜➖

⢲⣿⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠻⣿⣧⡀⠀⢀⣤⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣄⠀⠀ ⠀⠀⠈⠻⣿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⡄ ⠀⠀⢀⣼⣿⠟⠿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠁ ⠀⣠⣿⡿⠁⠀⠀⠈⠉⠛⠿⣿⣿⣶⣶⣶⣤⣤⣤⣴⣶⣶⣾⣿⠿⠛⠋⠀⠀⠀ ⠰⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣿⢵⣾⣥⣿⣿⣿⡇⢳⠹⣿⡈⣿⣟⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢚⡰⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣭⣴⣿⣿⣿⣿⣿⣿⣿⡏⡇⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣷⣷⣟⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠄⢠⣶⡟⣵⠾⣳⠞⣱⣿⣿⣿⣿⣿⣄⠣⡙⣝⢮⡪⣾⢿⣷⡽⣎⢹⣿⣿⣿⣿⣿⣿⣿⣫⣼⣗⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡰⢀⣿⣿⣿⣿⣿⡿⣿⣽⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⢿⣿⣿⢿⣿⢿⣿⡗⣿⠛⠛⠋⠉⠀⠈⠹⡄ ⠀⠀⠀⠀⡠⠊⢉⣉⣤⣀⡀⠀⠀⢀⣤⣤⣲⣶⣿⢟⣯⠖⣋⣴⡿⣿⣭⣟⣽⣻⣿⣿⣿⣦⡈⠢⠝⢮⣻⣿⢷⣾⣷⣤⢿⢿⣿⣿⣿⣯⣽⣶⣿⡿⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⢹⣿⣿⢟⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣮⣺⣟⣱⣷⣿⣿⣿⣏⣿⡏⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⢠⣁⢴⣷⢿⣽⢬⣷⣾⣿⣿⣿⣟⣾⣿⠗⠋⣴⠾⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣀⣙⠿⢯⣽⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣾⣿⣏⡟⣮⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣿⡿⣿⣿⣿⣼⣽⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀ ⠀⠀⠀⢸⠘⢿⣇⡝⢾⡭⣿⣿⣿⣿⣿⣿⠟⢃⢔⣾⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣻⣶⣷⣾⣟⣿⣻⡦⣍⠻⣻⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⡹⣛⣿⣿⣿⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣶⣷⣿⠴⢗⠵⠗⣳⢾⢹⣽⣿⣿⣿⡟⠐⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣚⣮⢻⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⢹⣿⣿⣿⣿⡿⢻⣿⣿⣿⣷⣹⢻⣟⣿⣿⣿⣿⣷⢿⡘⡎⣿⣿⣿⣿⣿⣿⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣁⡮⡷⡞⢿⣾⣿⡿⣿⣿⣿⣇⠰⣛⢿⣿⡿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢟⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣛⣻⣟⢛⣥⢯⡏⢽⣷⢿⣷⣿⣽⣷⣿⣿⣻⣿⢰⡧⠹⢿⣿⣿⣿⣿⡏⠓⢋⠛⠷⠦⣄⡀⠀⠀⠀ ⣿⣿⣿⣿⣧⡴⠈⡿⢿⣞⢮⡿⣟⠿⣿⣿⣷⣬⣽⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡎⣿⣻⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⠭⠏⠄⣾⡿⣸⣾⣨⡾⣿⣼⢯⣿⠟⡾⠗⠠⣽⣻⣷⣶⣇⡃⠀⠀⢀⣄⠀⠀⠀⠀⠀⠠ ⣿⣿⣿⣿⣏⡛⢯⣂⡂⣏⠛⡅⠾⠫⡸⣿⣮⠛⣟⡛⢿⠟⣉⢞⣿⠻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡏⡟⡇⣽⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠉⠉⠁⠀⣿⡇⢻⣿⣿⣷⣿⣿⣿⣿⢿⠏⠀⣙⣿⣇⣻⠻⠻⣮⣧⢠⣿⣿⡂⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⢷⠙⣌⠛⠾⣲⡆⢉⢚⠑⢂⣜⢐⡻⣤⠃⢂⠔⢣⢚⠦⣛⣾⣾⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⢹⣿⢣⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣱⢯⢿⣿⣿⣿⣟⢿⠟⢂⣴⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣵⣰⢢⡕⢌⡘⢮⠫⣐⠑⠒⠕⡘⢦⡙⠤⠉⠨⠁⢈⠄⣻⣷⣿⣿⣿⣿⣿⡯⢽⣻⣾⢹⣿⣿⣿⣿⣿⡟⢿⢿⠟⣁⣲⠗⣼⣣⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣅⡏⢸⣾⣿⡍⣩⠔⢠⣾⢫⣿⣿⡯⣭⣏⠙⠛⠂⠙⠻⠧⡈⢱⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠈⠶⡄⠛⣷⢑⢦⠡⠌⠢⡌⠙⠀⡂⠈⠆⡑⠀⠀⢠⣾⣯⣿⣿⣿⣿⣿⣿⢰⣍⣷⢿⡘⣿⣿⣿⣿⣿⣻⣶⣬⣿⣿⣏⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣿⣏⣿⣏⣱⣿⣻⣷⣾⣛⣿⣏⣾⣯⠃⠀⠀⠀⠰⣆⣁⠟⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡷⡿⠠⠙⢺⠃⠉⡂⠁⢀⠀⠀⠆⠠⠐⠡⠀⠀⠀⢠⠟⣱⣿⣿⣿⣿⡟⣿⣟⢷⣑⠽⣏⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡳⣽⣿⠆⢾⡶⠩⣀⠀⠀⠀⠐⡀⠀⡀⠀⠉⠀⠀⢀⠀⢠⡿⢽⣿⣿⣿⡿⣻⢣⢎⡡⣮⣕⠃⠢⠅⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⢿⣿⣟⣛⣫⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⢷⡯⢡⠓⣕⠞⠑⠁⠄⠐⠀⠀⠀⠀⠀⠂⠀⠂⣀⢔⣿⢳⣿⣿⣿⣿⣟⢦⠃⣞⣰⢇⡫⡜⠱⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠿⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

C✞\ ( `o`)

⸸

🕍🎚

✝️❤️

⣀⣤⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⠈⠙⠻⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⛧👹☠😈💀⛥🔥🌋

Sin

✞📖

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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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♱🙏♱∞♱🕳♱😇♱📿♱♰♱Α𓁺Ω♱🕊♱𓆩♡𓆪♱🤲♱👫👫♱🎈♱🛐♱ ♱🙏♱∞♱🕳♱😇♱📿♱♰♱𓁺♱🕊♱𓆩♡𓆪♱🤲♱👫👫♱🎈♱🛐♱ ♱∞♱🕳♱😇♱📿♱♰♱Α𓁺Ω♱🕊♱𓆩♡𓆪♱🤲♱👫👫♱🎈♱ ♱∞♱🕳♱😇♱📿♱♰♱𓁺♱🕊♱𓆩♡𓆪♱🤲♱👫👫♱🎈♱

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