⠄⠄⠁⣼⣷⣷⣴⣾⣶⣿⣾⣜⣾⡞⣼⣮⣶⡀⡀⠄⡀
⠄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⢷⠽⡹⡎⣆⠄⠄
⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡕⠅⠂⢈⡪⡪⣂⠄
⠨⣺⡳⣿⢿⣿⣿⢿⢿⣿⡿⢿⠁⠁⠄⠄⢀⢿⢏⠆⠁
⢐⠬⠄⠂⠄⠄⠄⠈⠨⡲⠁⠄⠄⠄⠄⠄⠄⡱⣇⠇⢐
⠨⠄⠄⠄⠄⠄⠄⠄⣾⣿⣦⠄⠄⠄⠄⠄⠄⡜⣜⢌⠄
⠈⣷⡣⢤⣠⣤⢾⣺⣿⣿⣿⣵⣴⣠⣤⡸⡶⣟⢕⠡⡈
⠐⢐⠁⣗⡿⣿⡧⠎⠻⢿⠝⠷⢽⣿⣿⣾⡽⠄⢁⢇⢅
⠄⠂⠌⡋⣩⣾⣗⣦⣢⣱⣴⣷⣾⣿⡽⢿⡑⠄⢐⢌⠐
⠄⠂⠄⠄⠄⠄⠐⠉⠁⡉⡈⠉⠚⠛⠛⠂⠄⠄⡰⡁⠄
⠄⠄⠄⠄⠄⠄⣀⢀⢀⣀⢄⣅⢂⡁⠄⠄⠄⡠⡃⠄⠄
⠄⠄⠄⠄⡀⠄⣾⣾⣾⣿⣿⣿⣿⡶⠄⠠⠒⠅⢀⠄⠄
⠄⠄⠄⠄⠄⠄⠄⢘⢙⢻⢸⠱⠕⡁⠂⠈⠠⠁⡀⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠁⡠⠈⠈⡄⠌⠄⠄⠄

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⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⠏⠀⣰⣶⣶⣶⣶⣆⠀⠹⣿⣿⣆⠀⠀
⠀⠀⣰⣿⣿⠏⠀⣰⣿⣿⠏⠹⣿⣿⣆⠀⠹⣿⣿⣆⠀⠀
⠀⣰⣿⣿⠇⠀⣠⣿⣿⠇⠀⠀⠸⣿⣿⣄⠀⠸⣿⣿⣆⠀
⣠⣿⣿⣇⣀⣠⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⣄⣀⣸⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿
⠙⣿⣿⡏⠉⠙⣿⣿⣄⠀⠀⠀⠀⣠⣿⣿⠋⠉⢹⣿⣿⠋
⠀⠹⣿⣿⡆⠀⠙⣿⣿⡆⠀⠀⢰⣿⣿⠋⠀⢰⣿⣿⠏⠀
⠀⠀⠹⣿⣿⣆⠀⠹⣿⣿⣆⣰⣿⣿⠏⠀⣰⣿⣿⠏⠀⠀
⠀⠀⠀⠸⣿⣿⣆⠀⠹⠿⠿⠿⠿⠏⠀⣰⣿⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⡿⢀⣠⣴⣾⣿⣿⣿⣿⣇⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⠟⢋⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⠓⡐⠒⢶⣤⣄⡀⠀⠀
⠀⠸⠿⠇⢰⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡷⠈⣿⣿⣉⠁⠀
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠁⠀⠈⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣤⣤⣤⣀⡀
⠸⡇⠀⠿⡀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠑⢄⣠⠾⠁⣀⣄⡈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⡀⠁⠀⠀⠈⠙⠛⠂⠈⣿⣿⣿⣿⣿⠿⡿⢿⣆
⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀⠀⢻⣿⣿⠭⢤⣴⣦⣤⣹⠀⠀⠀⢀⢴⣶⣆
⠀⠀⢀⣾⣿⣿⣿⣷⣮⣽⣾⣿⣥⣴⣿⣿⡿⢂⠔⢚⡿⢿⣿⣦⣴⣾⠸⣼⡿
⠀⢀⡞⠁⠙⠻⠿⠟⠉⠀⠛⢹⣿⣿⣿⣿⣿⣌⢤⣼⣿⣾⣿⡟⠉
⠀⣾⣷⣶⠇⠀⠀⣤⣄⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠉⠈⠉⠀⠀⢦⡈⢻⣿⣿⣿⣶⣶⣶⣶⣤⣽⡹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡻⢿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⡇
⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣮⣭⣽⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃