Sonic Villain Emoji Combos

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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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