⠂⠄⡂⡐⠠⠠⠠⠄⠄⠄⣀⡠⡤⡤⣆⢦⣄
⠈⡀⠄⠄⠂⠁⠄⠁⡠⡪⡢⡫⡎⡧⡳⣝⣷⣧
⠐⢀⠐⠈⠄⠄⢠⠎⢜⢸⢸⢜⡪⣪⢪⢲⢹⢽⡳⡄
⡈⠠⢀⢡⠋⠉⠫⢶⡨⡪⣊⣦⠗⠚⠺⢾⣎⡧⣏⠇
⠐⠄⢂⠧⠄⠄⠄⣽⢪⠚⡞⠄⠄⠄⠄⠄⠙⡾⡸⡕
⠈⡀⠸⣱⠄⠄⢀⠞⡜⡹⡇⠄⠄⠄⠄⠄⠄⡯⡪⡝⠄
⠂⡠⢁⡪⣂⢠⠪⠁⣇⢣⢣⣀⠄⠄⠐⣀⡼⡑⡜⠆
⡼⢡⠢⡠⠄⠄⠄⡌⡆⣇⡅⠍⠛⠛⢛⠍⡔⢅⠣⠥⠤⣄
⡝⡐⢕⢌⠄⠈⠠⠵⣹⣙⠎⡕⢅⢊⠢⡱⡸⢈⠢⠁⢸⣿
⡯⠐⢅⠢⡂⠄⡘⣈⢂⢢⢑⠌⡢⠡⣫⡮⡨⠠⠁⠂⣸⣿
⠱⢅⠨⠐⠠⠊⠎⠞⢵⡳⣥⡈⠢⡁⠢⠐⠄⠄⢀⣾⣿⣿
⠄⡁⠄⢀⡸⢪⠲⠵⣄⠍⢪⢞⡐⠌⠈⠄⠄⢀⣾⡿⣿⡿
⠄⠂⣴⣿⡐⢡⠑⡸⢠⠫⡀⠕⠁⢀⡠⣔⣮⡿⡯⣟⣿⢿
⣠⣾⡿⠟⢁⢠⢐⣁⡂⣈⢴⠄⢘⣾⡺⡯⡫⣏⢯⡳⡝⡇
⣿⣿⠁⠁⠄⢀⠆⣞⢿⣷⢱⠄⡜⡮⡳⡹⡸⡪⣱⡪⡪⠄

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⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠀⠀⠀
⠀⣠⣾⣿⠏⠁⠈⠛⠻⠿⠿⢿⣿⣿⢿⣿⣿⣧⡄⠀⠀⠀
⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠈⠹⠀⢹⣿⣿⣿⠀⠀⠀
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀
⠀⣿⣿⠃⣴⣶⣾⣶⠦⠀⣤⣶⣿⣶⣶⡄⢻⣿⡟⠀⠀⠀
⣚⢿⡞⠈⠿⣟⣿⣿⡆⠉⠙⣿⣿⣿⣿⠟⠘⣿⢻⣒⡄⠀
⡟⡟⠃⠀⠀⠈⠁⠀⠖⠀⠠⢀⠉⠉⠁⠀⠀⢻⢸⢿⠃⠀
⡅⡇⠆⠀⠀⠒⡂⢀⡄⠀⠀⢄⠀⠀⠀⠀⠀⡎⣼⣿⠀⠀
⢧⠑⠈⢢⠀⡠⠁⢤⣄⣄⣀⣤⡇⠀⠀⢀⠉⠃⢃⡏⠀⠀
⠀⠀⠙⡀⠈⠈⠀⠀⠀⠀⠛⠃⠈⠀⠀⠀⠊⠀⣴⠋⠀⠀⠀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡟⠀⠀⠀⠀
⠀⠀⢇⡀⠀⠐⠲⠞⠫⠭⠭⠛⠿⠖⠀⠀⢰⡇⠀⠀⠀⠀
⠀⠀⠀⣜⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀
⠀⣸⢸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀
⢠⠀⠣⠀⠱⣄⠀⠀⠀⢀⡀⢀⡴⠃

⠄⠄⠄⠄⣿⣿⣿⣯⢿⣽⣻⣽⣿⣿⣯⣿⣿⣿⣷⣻⢮⣗⡯⣞⡾⡹⡵⣻⣿⣇⠄⠄⠄⠂⠄⠄⠠
⠄⠄⠄⣸⣿⣿⣿⣿⡿⡾⣳⢿⢿⢿⠿⠿⠟⠟⠟⠿⣯⡾⣝⣗⣯⢪⢎⢗⣯⣿⣇⠄⠄⠄⠄⢀⠄
⠄⠄⠄⠋⠉⠁⠑⠁⢉⣁⡁⠁⠁⠄⠄⠄⠄⠄⠄⠄⢉⢻⢽⣞⢾⣕⢕⢝⢎⣿⣿⡀⠄⠄⠄⠄⢀
⠄⠄⠄⡧⠠⡀⠐⠂⣸⣿⢿⢔⢔⢤⢈⠡⡱⣩⢤⢴⣞⣾⣽⢾⣽⣺⡕⡕⡕⡽⣿⣿⠟⢶⠄⠄⠄
⠄⠄⠄⣿⡳⡄⡢⡂⣿⣿⢯⣫⢗⣽⣳⡣⣗⢯⣟⣿⣿⢿⡽⣳⢗⡷⣻⡎⢎⢎⣿⡇⠻⣦⠃⠄⠄
⠄⠄⠄⡿⡝⡜⣜⣬⣿⣿⣿⣷⣯⢺⠻⡻⣜⢔⠡⢓⢝⢕⢏⢗⢏⢯⡳⡝⡸⡸⣸⣧⡀⣹⣠⠄⠄
⠄⠄⠄⣇⢪⢎⡧⡛⠛⠋⠋⠉⠙⣨⣮⣦⢅⡃⠇⡕⡌⡪⡨⢸⢨⢣⠫⡨⢪⢸⠰⣿⣇⣾⡞⠄⠄
⠄⠄⠄⢑⡕⡵⡻⣕⠄⠄⠄⠔⡜⡗⡟⣟⢿⢮⢆⡑⢕⣕⢎⢮⡪⡎⡪⡐⢅⢇⢣⠹⡛⣿⡅⠄⠄

⠄⠄⠄⠄⣠⣤⣾⣿⢿⣿⣿⣿⣶⣄⡀
⠄⠄⢠⢾⢵⣗⣷⣿⣻⣿⣯⣿⣿⣿⣿⣧
⠄⣴⡫⣗⢽⡺⡽⣞⣯⣿⣿⣿⣿⣿⣿⣿⣇
⢸⣿⡯⣪⡣⡫⡯⣯⣷⣿⣟⣿⣿⣿⣿⣿⣿⡄
⢸⣿⣿⣢⢫⣝⢾⣯⣿⣷⣿⣿⣿⡿⠿⣿⣿⣷⢀⣄
⠈⣿⣿⣯⢧⣳⣻⣺⡻⣽⠝⢋⠁⠒⢚⣓⣿⣿⡿⢿
⠄⢹⣿⣏⠄⠄⢀⠄⡘⣾⣷⣦⣪⣳⣾⣿⣿⣿⣿⣽
⡫⡾⣿⡯⣮⣢⢶⢵⢼⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠑⡢⢿⣿⣳⢽⢝⡷⣵⣷⣿⠿⢷⣿⣿⣿⣿⣿⢧
⠄⠘⠞⣿⣷⢽⢵⣳⠵⠐⢑⠙⡚⠿⣿⣿⡿⢝⠜⡄
⠄⠄⠄⠘⣟⣿⣽⡞⣡⢒⠓⠝⣙⣓⣪⡻⠝⡀⣼⣷⡤⣠⣤
⠄⠄⠄⠄⠙⢷⢝⢧⢲⢎⠳⠹⠱⣹⡱⠈⠂⣰⣿⣿⣳⠄⢤
⠄⠄⠄⠄⠄⠄⣧⣃⠄⠑⠕⠒⡚⠝⠁⢀⢜⣾⣟⣯⡒⡀⡘
⠄⠄⠄⠄⠄⠄⠘⣷⢢⢠⢀⣀⠄⡄⡖⡵⣯⣿⡽⣧⡳⢐⠔
⠄⠄⠄⠄⠄⠐⠄⠘⢯⡪⡪⡢⡣⣱⢽⢝⣯⡷⣻⣵⣟⢔⠅