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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠇⠈⠻⢦⣄⡀⠘⢿⣿⣿⣿⠏⠀⣠⡴⠛⠀⠺⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠉⠋⣠⣄⣉⣉⣠⡀⠾⠉⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀ ⠀⢀⣀⣈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀ ⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⠿⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠈⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠋⣸⣷⣄⡙⠻⢿⣧⡀⠀⠀⠀⣰⣿⠟⢋⣤⣿⣅⠹⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⢁⣼⣿⣿⣿⣿⣶⣴⠟⠻⠶⠶⠟⢿⣁⣶⣿⣿⣿⣿⣧⡈⣿⣿⣿⣿ ⣿⡿⠿⠷⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠻⣿ ⣿⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣄⣀⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣷⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣷⡟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣄⠈⢛⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠈⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿
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⡂⠀⡄⡀⡃⠀⢦⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢄⠀⡀⠁⡁⢀⠀⠀ ⠀⠀⠄⡐⠁⠀⠁⢀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⣚⠈⠂⡁⠀⡂⠀⠀⠀ ⢁⠠⠄⢉⡐⣶⠟⠈⠻⢦⣄⡀⠘⢿⣿⣿⣿⠏⠀⣠⡴⡛⠄⣺⣆⡀⠂⠈⠀⠀ ⠐⡅⡀⣑⡾⠃⡡⠀⠀⠀⠉⠋⣠⣄⣉⣉⣠⡀⠾⠉⠀⠀⠀⡀⠘⢷⠦⢀⠀⠀ ⡁⢨⣇⣍⠁⠁⢀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⠀⠒⡀⢈⠀⠀⣶⣶⣄⠀ ⢀⢾⣿⣿⠠⢀⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⠐⠀⠠⠠⠀⠻⠿⠟⠀ ⠀⡀⢈⠀⠀⠈⢃⠀⠀⠀⠀⠀⣈⠻⠿⠛⡁⠀⠀⠀⠀⠂⢀⣠⠀⠀⠄⠉⠂⠀ ⠀⠀⡤⠌⠐⠀⠀⠆⠀⠀⠀⢸⣿⣿⣶⣿⡿⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀ ⠀⠀⡀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠙⠛⠛⠉⣀⠀⠀⠀⠀⠐⢁⣠⠤⠀⠀⠀⠀⠀ ⠀⠂⡀⠂⡀⠓⠅⠁⠀⠀⠀⢸⣿⠇⠈⠻⣿⡄⠀⠀⠂⠀⢠⢈⡀⠀⠂⠀⠀⠀ ⠠⠀⡀⢡⡀⠀⠀⠌⠀⠀⠀⢸⡿⠀⠀⠀⠹⣿⡀⠀⠀⢀⠀⢐⡄⠄⡀⠀⠀⠀ ⠀⠀⢂⢀⡠⠂⠤⢆⠂⠀⠀⠸⠃⠀⠀⠀⠀⠈⢠⣤⡀⠀⢀⢡⡅⢈⡀⠀⠀⠀ ⠀⢁⠄⢠⠂⢀⢀⢢⣡⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡤⠀⢄⠂⠁⠀⠀⠀ ⡀⠁⠀⢈⣿⣿⣷⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠁⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠛⠉⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⡅⡃⠀⠀⠀⠀⡇⠀⠀⠈⠂⠀⣀⣤⣤⣀⠀⠀⠀⠀⢘⠈⠀⠀⠀⡢⠀⠀⠀ ⠀⡇⠸⡄⠀⠀⠀⣁⠀⠐⠀⡀⣰⣿⣿⣿⣿⣧⠀⠀⠀⢨⡠⠀⠀⢐⠀⠀⠀⠀ ⠀⡆⠀⡇⠀⣴⠇⠭⠻⢧⣄⡀⠘⢿⣿⣿⣿⠏⠀⣠⡴⢻⡂⠺⣆⢨⠂⠀⠀⠀ ⠀⡇⠠⢁⡾⠃⠌⢈⠁⠀⠉⠋⣠⣄⣉⣉⣠⡀⠾⠉⠀⠀⡻⠀⠘⢷⠀⠀⠀⠀ ⠀⢳⣨⣈⠁⠀⡃⢀⠁⠀⠀⠂⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠅⡀⠀⢨⣴⣶⣄⠀ ⢀⢾⣿⣿⠀⠀⠂⠠⠂⠀⠀⠄⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣅⠈⠀⠘⠻⠿⠟⠀ ⡃⠀⠍⠀⠀⠀⠅⡀⠄⠀⢀⠀⣈⠻⠿⠛⡁⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀ ⡂⡠⠅⠀⠀⠀⠅⠀⠀⠀⠀⢸⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠅⠁⠁⢀⠀⠀⠀⠀ ⠂⢀⠅⠀⠀⠀⠁⠁⠂⠐⠀⠀⠙⠛⠛⠉⣀⠀⠀⠀⠀⠀⢁⠠⠀⠀⠀⠀⠀⠀ ⠈⠀⠡⠂⠀⠀⠅⠄⠀⠀⠀⢸⣿⠇⠈⠻⣿⡄⠀⠀⠀⠀⠐⣀⠄⠂⠀⠀⠀⠀ ⠀⡁⠨⠔⠀⠀⠥⠀⠉⠀⠀⢸⡿⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢂⠠⡐⠀⠀⠀⠀ ⠀⠐⡀⠍⠀⠀⠓⠀⠄⠀⠀⠸⠃⠀⠀⠀⠀⠈⢠⣤⡀⠀⠀⠀⠴⡀⠀⠀⠀⠀ ⠀⠀⠅⡃⠀⢈⢘⢈⣤⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡤⠀⠀⠆⠀⠀⠀⠀ ⠀⠀⠈⠀⣿⣿⣷⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠒⠒⠐⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠭⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣟⣛⣛⡶⠶⠀⠀⠐⢶⣖⣛⣛⠛⢿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡯⢉⣴⣋⣿⣿⣳⠺⠀⠀⠐⢇⣎⣷⣿⣑⠦⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣽⣳⢖⡂⣿⣿⡇⠀⠀⠀⠀⠀⢸⡐⣿⢀⣤⣤⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡽⣮⠼⣿⣿⡇⠀⠀⠀⠀⠀⢸⠹⢮⢾⣤⣿⣇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠃⣿⣿⡇⠀⠀⠀⠀⠀⣼⢻⣿⡘⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣠⣦⣿⣿⣇⣀⣤⣤⣤⡤⠽⠟⠋⠀⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣎⠤⣀⠀⠀⠀⠀⠀⠀⠀⢼⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣯⡶⣥⣲⣔⣲⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣏⢒⢹⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣫⢫⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣒⢒⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⢏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⣁⣊⣼⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⠀ ⠼⠿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣦⠄⠀⠀⠀⠀ ⠀⠈⠙⠿⣿⣿⣷⣦⣤⣤⣴⣾⣿⣿⠟⢋⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣤⠄⠀⠀⠀⠀ ⠀⢸⣿⡿⢿⠿⠛⠉⠉⣇⠈⠉⠙⢻⡟⠿⡟⠀⠀⠀⠀⠀ ⠀⠀⢀⠃⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⠀⢳⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡀⠀⢣⠀⠀⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⡀⠀⠀⠀ ⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢳⠀⠀⢻⠀⠀⠀ ⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠘⡄⠀⠀ ⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀ ⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠀ ⠀⠀⡇⠀⢸⠀⠀⠀⢀⣴⣷⣦⡀⠀⠀⠀⡇⠀⠀⠘⡆⠀ ⠀⢰⡇⠀⢸⠀⠀⠀⢸⣿⣿⣿⡧⠀⠀⠀⢇⠀⢀⣤⣧⡀ ⠀⠀⡇⠀⠸⡄⠀⠀⠈⠻⢿⡟⠁⠀⠀⠀⠘⣰⡟⠁⠛⠃ ⠠⣴⡷⣦⣄⠇⢀⢀⣤⢶⣿⣿⣿⠛⠛⠛⢻⠋⠀⠀⠀⠀ ⠀⠑⠃⠈⢛⠷⡶⠟⠁⢸⣿⣿⣿⡆⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡆⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⢿⣿⣿⡟⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣿⠇⢸⣷⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⣾⡏⠀⠘⣿⡀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⢀⣼⡟⠀⠀⠀⠻⣧⣄⡀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⡴⠟⠍⠀⠀⠀⠀⠀⠈⠙⠻⣦⣇⡀⠀⠀ ⠀⠀⠀⢠⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠃⠀⠀ ⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣍⣍⢩⣭⣭⣭⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣴⣽⣿⠛⠉⣁⣉⣉⡛⣛⡛⠿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣷⠞⣉⣤⣶⣿⣿⣿⣿⣿⡍⣿⣿⣦⣍⠂⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣴⣿⡟⣡⣾⣿⣿⣿⡿⣿⢿⣿⣿⣿⡜⢿⡿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣾⠏⣴⣿⣿⣿⠿⡛⠉⠉⣉⠉⣉⣿⣷⣹⢅⠀⠚⠿⣷⠘⣿⠿⠛⠿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⡉⣉⣙⠛⠐⠒⠋⣼⣿⡿⠋⡁⠂⠀⠄⢈⡟⣠⣿⣿⣿⣿⣦⡹⡇⠀⡈⠁⢱⣶⣀⢵⢸ ⣿⣿⣿⣿⣿⣿⣿⡇⠐⡁⢈⡀⡠⣴⠂⣾⣿⣿⣧⣌⠣⢄⣒⣤⣮⣾⡿⢫⢿⣟⣿⣿⣿⣌⠂⠀⢠⢸⣿⡔⡿⢸ ⣿⣿⣿⣿⣿⣿⣿⣧⠁⣷⣟⠁⢠⠂⣸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣇⠀⠻⣯⡿⣿⣿⣿⣷⣾⣵⣿⡆⠟⢡⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠉⣿⠀⠀⣼⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿⣷⣥⣙⣛⣨⡴⠿⠿⣿⣿⣿⠃⣶⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡐⠸⣿⡞⠏⠉⡙⠭⢯⣭⣽⡿⡋⣤⠬⠥⣬⠍⠽⠏⠄⢬⡽⠲⠀⡙⠿⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡾⣷⣄⢀⠈⠛⠧⣀⡯⢅⠈⠴⠓⠇⠉⠃⢀⠀⢚⠒⣀⠀⠀⢀⡀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡿⣿⣿⣿⣶⣴⣤⣄⡁⠐⠀⠀⠀⠒⠫⠀⠠⠀⠀⠀⣠⡶⢟⡃⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣠⢹⣯⡙⢿⣿⣿⡻⣿⣿⣷⣬⣥⣤⣤⣤⣤⣤⣴⣾⣿⣶⣶⠿⢣⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣌⣿⡼⣮⣽⣿⣧⣝⡻⢿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⠿⣣⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣌⡙⠷⣿⣻⣿⣿⣿⣿⣯⣽⣛⣛⠩⢭⠏⠟⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠻⢿⣷⣤⣈⠉⠻⢿⣿⣿⣾⣿⢟⣯⠂⠶⠟⢋⣴⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠈⣙⣿⣿⣿⣶⣤⣀⡉⢛⣳⡶⠤⠾⠿⠿⠟⠁⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣶⣤⣭⣭⡵⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿ ⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⡍⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⣿⡇⣿⣿⡇⣿⣿⣿⣿ ⣿⣿⣿⡿⢠⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢿⣷⢹⣿⡇⣿⣿⣿⣿ ⣿⣿⣿⢃⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣼⣿⢸⣿⡇⣿⣿⣿⣿ ⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠹⣿⡼⣿⡇⢻⣿⣿⣿ ⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⣿⡇⣿⣟⢸⣿⣿⣿ ⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⢻⡇⣿⣿⣸⣿⣿⣿ ⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣧⢹⣿⣧⢻⣿⣿ ⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⣿⣿⣿⣿⣿⡏⢸⣿⠘⣿⣿⣇⢻⣿ ⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⣿⣿⣿⡇⠻⣿⡇⣿⣿⣿⡎⣿ ⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣸⣿⣿⣿⣿⣿⣿⡀⢿⡇⣿⣿⣿⣧⣿ ⣿⣿⣿⣿⣿⠀⡘⢯⣵⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣶⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⡇⣿ ⣿⣿⣿⣿⣿⠀⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣇⣿ ⣿⣿⣿⣿⣿⠀⣿⣷⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⡙⢿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣘⣛⣛⡻⢿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⢿⣿ ⣿⣿⣿⣿⣿⣿⣷⣦⡙⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⢿⣿⣿⣿⣿⣆⢸⣿⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣷⣶⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣷⣶⣬⣙⣛⠻⣃⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⣄⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀ ⠀⢠⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀ ⠀⢸⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣼⣦⣇⣠⣶⣶⣦⣤⡀⠀⠀⣤⣤⣶⣶⣄⡀⠀⢹⠀ ⣰⠃⡨⢭⡛⣿⣿⠛⠉⠀⠀⠀⠈⠙⣻⢿⠛⣋⣀⠀⢧ ⢿⣾⡁⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣏⣾⣿⡀⣈⣧⣼ ⠈⢿⣿⡿⣃⣸⣿⣇⣤⣤⣤⣤⣤⣄⣿⣿⣘⠻⢿⣿⠃ ⠀⠀⢿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡿⠁⠀ ⠀⠀⠈⢿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣿⠁⠀⠀ ⠀⠀⠀⠈⢿⣿⣮⣝⣻⣿⣿⣿⣿⠛⠁⢠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣾⣿⣤⠾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠉⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⠀⠀⠀⠀⠀⣶⣸⡴⠴⠖⠀⠀⠀⠶⣟⣦⡹⡶⠚⠉⠉⠉⠙⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠖⠊⠉⣭⣉⣁⡞⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠙⡿⠻⠶⠂⠀⡀⢀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠈⠀⠀⢘⣿⠀⠀⠀⣼⣿⡷⠀⣀⣀⣀⣀⣿⣿⠏⠀⠀⠀⢻⠀⠀⠀⠀⠛⠿⢷⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⣀⠀⠀⠀⠀⠈⠉⠈⣿⡿⠀⠀⣀⣬⠿⠖⠋⠉⠉⠉⠉⠉⠉⠓⠲⢦⣀⠀⠀⠙⢶⣄⣀⣀⡀⠉⠀⣠⢆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠻⣤⠀⠀⠀⠀⢀⣠⣿⢳⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣄⠉⠉⠉⠛⠿⢯⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠮⣙⣒⣛⣋⣽⡍⡿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⣈⣿⠀⠀⠀⠀⢿⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⡼⠃⠈⢣⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⡰⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⡿⠋⠀⠀⠀⠀⢸⠀⢸⡇⠀⡀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠱⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠈⢷⡀⠈⠛⠳⠶⢶⣶⣾⣿⡿⠿⠟⠉⠉⠀⠀⠀⢀⠀⠀⠀⣾⠀⢸⡇⠀⠃⠀⠀⢀⣼⡃⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣼⠟⠀⣸⠃⠀⠀⠘⣶⢿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⣄⠀⠈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣁⡼⠃⠀⠀⠀⠀⠸⠉⢹⡇⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣈⠳⣄⠀⠀⠀⢀⡼⠇⠀⠀⠙⠿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣵⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠆⠇⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢠⡖⠓⠛⠛⠉⠉⠉⠉⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⠶⠶⠶⠾⠿⠛⠉⠁⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠸⣧⠀⠈⠂⠂⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⢀⡴⣃⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⣰⣷⣾⠃⠀⠀⠀⠀⠀⢹⡆⠀⠄⠄⠀⠀⣰⠇ ⠀⠀⠀⢀⣀⣰⠏⠀⣁⢀⣈⡹⠇⠀⠀⠀⠀⢀⠀⣄⣀⣄⣀⡀⠀⠀⠀⠀⢈⠀⠀⠉⣿⠛⠛⣏⠙⣿⠓⢺⣿⡟⢀⢀⠙⢿⣧⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⢀⡰⠇⠀ ⠀⣰⠞⠉⣉⠵⠲⠊⠉⠳⣾⣧⠀⠀⠀⢀⡠⣾⡋⠭⠿⠏⡭⠥⣻⢶⣀⠀⢸⠀⠀⠀⢻⠀⠀⣿⠀⢸⡀⠀⣿⡇⢸⢸⣾⡉⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⣰⠞⠁⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⢰⣮⡜⣩⠴⠊⠉⠉⠉⠲⢌⠁⡽⡖⢸⠀⠀⠀⢸⠀⠀⢿⠀⢸⡇⠀⣿⡇⠈⠗⠿⣷⠚⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠁⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣽⡾⠘⠁⠀⣦⣶⣺⡿⠃⠀⢱⢿⣿⣽⠀⠀⠀⢸⡆⠀⢸⣆⣾⣷⣾⠛⣿⠀⠈⠙⣿⡛⢿⡅⠀⠀⠀⠀⠀⠀⠀⢀⡴⢸⡇⠀⠀⠀⠀⠀ ⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣾⡇⠁⠀⣀⣸⡟⣁⣉⣁⡀⠘⠻⣿⢿⠀⠀⠀⠘⣇⠀⠈⣧⠀⠘⣿⡀⠹⣆⠀⠀⢹⡇⠈⣿⣀⠀⠀⠀⠀⣠⡾⠋⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠹⡇⢰⠹⡍⠿⠿⠿⠼⢿⣋⠃⢺⡿⢻⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠈⠻⢦⣹⣧⣀⣾⣥⠾⠛⠁⢀⣀⡴⠞⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠛⠀⠳⠦⣬⣭⣍⣩⣿⠾⠂⠛⠁⠸⠀⠀⠀⠶⠿⠷⠒⠚⠓⠂⠀⠀⠀⠉⢉⣉⣁⣠⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⣀⣀⣴⣐⣚⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠖⠶⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⠀⠀⠂⠠⢠⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠶⠶⠶⠤⠤⠤⠤⡄⠒⠋⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⢡⢃⡄⠠⡣⢂⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⡄⠀⠈⠂⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢢⡾⠿⢧⠄⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠀⢠⣾⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣾⣰⣶⡯⡀⢀⣾⣰⣿⡄⠀ ⠀⠀⠀⣀⠀⠀⢸⡁⢻⡄⢀⣿⠃⢠⡟⠀⠀⠀⠀⠀⣰⣦⣀⣾⣆⠗⠿⣏⠿⣽⠱⠃⢺⣿⢻⢿⡇⠀ ⠀⠀⣀⣿⣏⣤⣸⣇⢸⣧⣼⡇⢀⡾⠁⣰⣴⡄⠀⠀⢷⣿⣿⣿⡟⢠⠒⢁⣀⡀⢙⡆⠀⣩⣾⣿⣄⠀ ⣼⣿⣿⠿⣿⣿⠿⢻⣾⣿⣿⣿⠟⢠⣼⣿⢻⣾⣦⡀⢻⣿⣿⣿⠟⢨⠖⠙⠛⠋⠉⡇⠀⣿⣿⣿⣿⡇ ⢨⣿⣿⣒⣿⣿⡶⢾⣿⣿⣿⣿⡇⠳⠿⣿⣻⡿⠿⠁⣔⠉⣼⡻⣷⠘⡦⠀⠀⠐⠝⡇⢠⣿⣿⣿⣿⡇ ⠀⣩⢿⣿⠙⢯⢠⣶⣾⣿⣷⣤⡀⢠⠊⡏⠉⢹⣳⠀⢸⣦⣟⣻⡇⢠⠇⠀⠀⠀⠀⡇⢸⣽⣿⣿⣽⠀ ⠀⣧⣀⠀⢀⣻⣼⣿⣿⣿⣿⣿⣧⠠⣏⣽⠒⣟⣿⠀⢸⠷⡟⢻⡇⢸⠀⠀⠀⠀⠀⡇⣸⣿⣿⣽⣿⠀ ⢰⠉⠁⠀⠀⠸⣽⣿⣿⣿⣿⣿⡏⢰⠁⠀⠀⠀⢸⠀⣿⠂⢷⣭⡇⢸⠀⠀⠀⠀⠀⡇⣿⣯⣽⣿⡇⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⣠⣼⣿⣿⣿⠿⠿⢯⡿⠿⢤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡝⠀⠀⠀⠈⠸⠗⠽⣼⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣷⣧⣤⡀⢰⣷⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⣿⣿⣿⡝⣴⣿⣿⣿⣯⣍⠀⠈⡌⡟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠣⣺⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣝⢻⡿⠟⣻⡟⠋⠉⢋⡟⣷⠎⣄⢁⠊⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⡀⣿⡧⠀⡴⡾⠰⠁⢙⣦⣭⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣄⣿⣿⣾⣆⣤⣖⣠⣾⡗⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣠⣶⣝⣿⣿⣿⣿⡛⠑⢩⣿⡿⠓⠛⠉⣁⢎⣮⣰⣿⣏⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡓⣿⣿⣿⠀⠀⣀⣷⢿⣿⣿⣿⠩⢙⣯⣗⣎⣭⣲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡶⢻⢿⣿⣿⣿⣿⣩⠀⠄⠰⠍⢢⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠁⠈⠙⢻⣋⣹⠐⠀⣿⣿⣿⣿⣷⣖⠁⡀⠀⠓⢣⠀⠀⠀ ⠀⣠⠾⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠹⢁⠑⠀⡘⡿⣿⣿⣿⣯⢂⣄⡀⠘⣳⡆⠀⠀ ⣼⣷⣏⣠⣌⣨⣿⣿⣿⣿⡟⠋⢠⣿⣿⣿⣿⣿⣿⣿⣷⣮⠁⠀⠀⠀⠀⢣⣈⠁⢃⡹⣿⣿⣿⣿⣖⠎⠁⠀⠁⡸⡀⠀ ⣿⣿⡿⣿⣯⡿⢵⣿⣿⣿⡶⢆⣾⣿⣿⣿⣿⣿⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⣗⠑⠈⠁⡹⣿⠻⣿⣿⣷⣵⣦⣤⠊⠁⠀ ⠹⣿⣯⣽⣿⣾⣷⡟⠙⠻⢯⠋⣿⣿⣿⣿⣿⣿⣾⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠨⢔⠅⣿⡀⠈⣻⣿⣿⡇⠑⠫⠑⡄ ⠀⠈⠻⢿⣿⣿⡟⠻⢦⣤⠃⢸⣿⣿⣿⣿⣿⣿⣿⡋⠊⠀⠀⠀⠀⠀⠀⠀⠈⣞⣣⢴⢺⣿⡇⢠⣿⣿⣿⠂⠂⠀⠃⢡ ⠀⠀⠀⢸⣿⡿⢿⣤⣤⡜⠀⠘⣿⣿⣿⣿⣿⣿⡿⡋⡷⡂⢀⠀⠀⠀⡀⠀⠀⣗⣿⣓⣾⣿⠇⢸⣿⣿⣿⣧⠠⠀⢲⣸ ⠀⠀⠀⠈⠻⢿⣦⣖⡺⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣵⠐⡈⠀⠀⠀⠀⠀⠀⣷⣝⣄⣿⣿⠀⢸⣿⣿⣷⠊⠀⠀⣢⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡟⡻⢹⣿⠇⠀⠘⣿⣿⣷⣷⣥⣄⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣫⡟⠊⠁⠀⠀⠀⠀⠀⠀⢀⢗⣽⣾⣯⡄⠀⢀⣾⠿⡟⢿⢟⣋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣧⣤⣤⣄⣠⡤⣴⣿⣿⣿⣿⣿⣷⣿⣟⢁⢸⠁⠤⣣⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣤⢦⠜⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠈⠀⠨⢪⢁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⡟⡠⡷⠁⢂⠧⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⢿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣇⣽⡇⣠⣾⢹⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠥⠓⠊⠝⣻⣿⠀⠀⣿⣿⣿⣿⡿⡿⡿⠟⢑⣾⠀⠈⠛⠓⠚⠛⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡊⢀⠀⠀⠐⣿⠀⠀⣿⣿⣿⡿⠉⢠⢁⡀⠼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⢒⡐⣄⣴⡿⠀⠀⢹⣿⣿⣿⢀⠀⠀⢀⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢾⠿⢿⡾⠁⠀⠀⠈⢿⣿⣿⣿⠷⠿⡾⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣇⣠⣴⡎⠀⠀⠀⠀⢸⣿⣿⣿⣾⡅⣌⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⠉⠉⢹⢷⠀⠀⠀⠀⢸⣿⣿⣿⡏⠁⠀⠪⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠧⠀⠀⣺⠀⠀⠀⠀⢸⣿⣿⣿⢄⠀⠄⠌⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⡀⠀⢠⣿⠀⠀⠀⠀⢸⣿⣿⣿⡄⠗⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⢞⡔⠀⠺⡇⠀⠀⠀⠀⢸⣿⣿⣿⣧⡂⢀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠇⠀⢠⣃⠇⠀⠀⠀⠀⠀⣿⣿⣿⡟⣏⢀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⣿⣿⣿⣿⣗⠒⢿⣷⡄⠀⠀⠀⣠⣾⣿⣿⣷⠚⢳⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣥⡾⣿⠟⣫⣾⣿⣿⣄⣤⣿⣿⠀⠀⡼⣾⣿⣩⣿⣿⣷⣹⣿⡿⢮⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣾⣯⣸⣿⣿⡿⢉⣀⢹⣿⣿⣧⣾⣿⣯⣽⣿⣿⣿⠇⠉⣿⣧⣦⣱⡵⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡺⢼⣿⣿⣗⡊⣘⣹⡛⢋⣿⣿⣟⠪⢻⣿⣿⣿⠂⠧⣽⣿⣧⠁⠀⣟⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠛⠓⠒⠒⠚⠁⠈⠛⠻⠧⠤⠛⠛⠿⠯⠿⠬⠞⠛⠻⠭⠝⠓⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣽⣿⣽⣟⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣷⣿⣻⠿⢿⣻⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣀⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣀⡀⣀⣀⣀⣨⣿⣿⡿⣶⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢁⣿⣿⣿⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣻⣿⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠈⠉⢹⣿⣻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⠀⠀⢸⣿⣟⣿⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣿⣿⣤⣤⣼⣯⣿⣯⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⢿⣾⢿⡿⣟⣯⣷⣿⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⢿⣻⣿⢯⣿⡿⣿⣻⣽⣟⣿⡇ ⢰⣶⣶⣖⣀⣰⣶⣶⣿⣿⡿⣷⣶⣶⣶⣶⣶⣾⡿⣯⣿⢷⣿⣻⡏⢹⣿⣿⡿⣽⣿⣟⣯⣿ ⠸⠿⠿⣿⣿⣿⡏⠿⠿⠀⣿⣿⣷⣿⣏⣿⣹⣾⣿⣿⣹⣿⠉⠉⠁⢸⣿⣿⣿⡿⣷⣿⡿⣷ ⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣟⣷⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣯⣿⣟⣯⣷⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣟⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣿⣟⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣷⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣷⡿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣷⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣯⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠛⠉⠉⠛⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⢠⡇⠀⠀⢀⡴⡫⠭⠭⢓⢤⣀⠀⠀⠀⠀⢀⡤⡚⠭⠭⢝⢦⡀⠀⠀⢸⡄⠀ ⠀⣼⠀⠀⠸⢭⣊⡀⠀⢀⣀⠽⠊⠀⠀⠀⠀⠓⠯⣀⡀⠀⠀⣑⡯⠇⠀⠀⣧⠀ ⢰⠇⢀⡤⠤⢄⠀⢹⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡏⠀⡠⠤⢤⡀⠘⡆ ⣾⢠⠃⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠘⡄⢷ ⢿⠘⡄⠀⠀⡠⠃⠈⡄⠀⢠⠀⣀⠠⠤⠤⠄⣀⠀⡄⠀⢀⠃⠘⢄⠀⠀⢀⠇⡼ ⠘⣦⠈⠉⠉⠀⣠⠔⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠚⠲⣤⠀⠉⠉⠁⣴⠃ ⠀⠈⠳⢦⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⡠⠞⠁⠀ ⠀⠀⠀⠈⢳⡄⠱⡜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠎⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠘⠦⣑⠢⣀⡀⠀⠀⠀⠀⢀⣀⠄⣊⠴⠃⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠉⠒⠮⠭⣤⣦⠭⠵⠒⠋⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠪⣉⠉⠉⢉⠕⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠦⠭⠭⠶⢶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬜⬜ ⬜⬛🟨🟨🟨⬛⬜⬛⬛⬛⬛⬛⬛⬛⬜⬛🟨🟨🟨⬛⬜ ⬛🟨🏽🏽🏽🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🏽🏽🏽🟨⬛ ⬛🟨🏽🏽🏽🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛🟨🏽🏽🏽🟨⬛ ⬛🟨🏽🏽🏽⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🏽🏽🏽🟨⬛ ⬜⬛🟨🟨⬛🟨⬛⬛⬛⬛🟨⬛⬛⬛⬛🟨⬛🟨🟨⬛⬜ ⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬛🟨🟨⬛⬛🟨🟨🟨⬛⬛🟨🟨⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨⬛⬛⬛⬛🟨⬛⬛⬛⬛🟨🟨⬛⬜⬜⬜ ⬜⬜⬛🟨🟨🟨⬛⬛⬜⬛🟨⬛⬜⬛⬛🟨🟨🟨⬛⬜⬜ ⬜⬜⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛⬛🟨🟨🟨⬛⬜⬜ ⬜⬜⬛🟨🟨⬛🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛🟨🟨⬛⬜⬜ ⬜⬜⬜⬛🟨⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨⬛⬛⬛⬛⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨⬜⬛⬜⬛⬜🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜
➖🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪 ⬜⬛🟪⬜⬛🟪 🟪🟪🟪🟪🟪🟪 🟪⬛⬛⬛⬛🟪🟪🟪 ➖🟪⬛⬛🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 🟪🟪🟪🟪🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 ➖➖🟪🟪🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 ➖➖➖➖🟪🟪🟪🟪 ➖➖➖➖🟪➖➖🟪 ➖➖➖➖🟪➖➖🟪 ➖➖➖➖🟪➖➖🟪
⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⢠⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡐⢱⠈⡗⡜⡀⠀⢀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣜⠂⢚⣡⠠⣴⣿⡏⠙⠛⣿⡂⠀⡔⡨⡭⡑⠄ ⠀⠀⠀⠀⠉⡝⠁⣤⣿⢦⡁⠀⢘⣛⠻⢢⡄⢆⣈⡿⠸ ⠀⠀⠀⠀⣰⠃⡼⠿⠏⠀⡇⢰⣿⠉⠳⡄⣿⠒⠀⠂⠁ ⠀⠀⠀⣴⠋⣢⣑⣤⣠⣴⣇⣿⡉⠀⢀⡇⡿⠀⠀⠀⠀ ⠀⠀⢸⠹⠶⡟⠁⠀⠀⠉⠒⠛⠙⠻⣍⠔⢺⠀⠀⠀⠀ ⠀⠀⠸⡆⢰⡟⠷⣤⣀⠀⠀⠀⠀⠀⣸⢦⢾⠀⠀⠀⠀ ⢀⢔⢢⠙⢾⣹⣦⣀⣉⠈⡛⠛⠛⢫⠇⢀⡞⠀⠀⠀⠀ ⢸⠁⡠⠥⣆⠈⣹⣿⠿⢿⣿⣷⡿⠷⠖⠋⠀⠀⠀⠀⠀ ⢸⣿⣁⣠⡞⡏⣾⣿⣷⣿⣿⣿⣿⡇⠂⢄⠀⠀⠀⠀⠀ ⠀⠙⠛⣿⠋⢠⠿⠟⠋⡉⡈⠓⠛⡌⡄⠀⢆⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠏⠀⠀⠘⠿⠟⠀⠀⠸⣸⢀⣀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⡆⠀⠀⢰⣿⣷⠀⠀⢠⡏⠉⣻⣷⠀⠀⠀ ⠀⠀⠈⢻⣧⡘⠦⣀⣀⠉⣁⣠⠴⣫⢷⡾⠉⢹⠀⠀⠀ ⠀⠀⠀⢰⠉⠛⠷⣶⠼⢭⡥⠖⠋⠀⡌⢧⣠⠏⠀⠀⠀ ⠀⠀⠀⡸⠤⠤⠤⠬⡄⢸⠤⠤⠤⠤⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣅⡀⠀⠀⢀⡷⣇⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣚⣋⣉⡻⠶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠞⠁⠀⠀⠛⡆⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⡶⠁⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠁⢠⡀⠀⠀⠀⠀⡸⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⠫⢟⣮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡦⢌⣓⡤⣹⡆⠀⠀⣰⢣⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠛⠛⠲⣄⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠔⠒⠒⠮⡹⠚⢯⣉⣵⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠁⢀⡤⠚⠉⠙⡍⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠈⢆⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣤⢀⠀⢹⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣲⠁⠀⠀⠀⠀⢀⣀⣸⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡔⠀⠀⢀⣽⣿⠁⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⣅⡇⡏⠑⠄⠀⠀⠀⠀⣸⢣⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡿⠛⠀⣾⣉⣶⣃⠀⠀⠀⠀⠀⠀⡿⣿⠿⣆⡼⡄⠀⠀⠀⠀⡴⠁⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⣀⡤⠋⠀⣁⣨⣇⠤⠤⠤⠤⠤⣾⣿⣭⣀⠈⠉⠢⢄⣀⡞⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢉⣉⣥⣔⠾⠛⠉⠁⠀⠀⠀⠀⠀⠰⣿⣟⡏⠻⣕⠢⢤⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠙⢶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⡜⠀⠀⡴⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣠⡼⣤⡤⣞⠀⠀⠀⠀⠀⠘⣆⣀⣀⡇⠀⣸⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⣞⡕⠉⠁⠈⠙⢷⡤⠃⠐⢤⣠⠾⠓⠒⠫⣝⢅⠀⡀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⡜⢀⡴⠚⠉⠒⢜⣆⡀⠀⢠⢇⡠⠤⠤⣀⠈⢟⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡈⠉⢿⣃⣜⠰⣶⣰⠀⡸⠯⠕⠒⠿⡏⠀⡄⠠⠈⣆⢸⡏⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠉⠻⣺⣄⣈⡠⠞⠃⢀⣀⠀⠀⠙⢦⡙⠞⠀⣾⣿⠁⠀⢰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⠆⠀⣡⠂⣀⠴⠊⠁⠀⠉⠙⢲⠠⣍⠑⠚⠊⠉⠉⠀⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⢀⠇⠀⡞⠁⠀⣹⠂⠀⠀⠀⠀⢀⡞⠀⠈⢳⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢤⢻⠁⠀⡀⡝⠋⠉⠉⠓⠢⡎⠀⢀⠀⠀⠇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⣞⠲⠼⢻⣀⣀⠀⠀⢀⡼⠁⠀⣼⣆⠀⠐⢠⡶⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢌⠪⣝⡒⠼⣀⣉⣹⡳⠿⠒⢓⡖⠉⣓⡶⣗⣟⣷⡟⢀⡤⠤⢤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣈⠉⠷⢬⣵⡞⠛⠒⡟⠛⠛⣯⠟⠛⣷⣯⢠⠿⢷⡿⠋⠀⠀⠀⠈⠛⣶⣤⡈⡹⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠛⠛⠒⢾⡿⠦⣀⠀⠀⠹⠤⣨⠧⠒⠟⢧⣀⠞⠁⠘⠃⣠⢿⡁⠀⠀⠀⠀⠀⠀⠈⢳⡈⠳⡄⠙⣆⠀⠀ ⠀⠀⠀⠀⣀⣠⣴⡏⠀⢷⡄⠀⠀⠀⠀⣿⠦⠈⠓⡤⢄⣀⣄⣀⣀⣀⣀⣀⣠⠤⠴⡞⠓⠚⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠘⡄⢸⡄⠀ ⠀⢀⡴⢛⡽⠚⡿⢷⣀⡼⠃⢠⡦⠀⠀⡿⠒⠁⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠇⢰⠷⡀ ⠀⡾⢡⡏⠀⣠⣷⡀⡞⠀⠀⢯⠉⢦⣴⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠳⣄⡀⠀⠀⠀⢠⠏⣠⠾⢚⡟⠀⢧ ⢸⠁⡏⡇⠀⢧⣈⢻⣇⠀⠀⠀⢷⡽⠁⠀⠀⠀⣠⢧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⣠⣼⠛⠒⠶⣾⠛⠚⣡⡴⠋⠀⠀⢸ ⡾⠀⠣⠽⡦⠒⠁⠀⢈⡷⠦⢤⡞⠀⠀⠀⣀⠔⠁⣸⠀⠀⠀⣠⢴⡏⠳⢄⡀⠀⣀⣠⠗⠀⠠⣶⣾⠍⢠⠒⡆⢹⠎⠉⠁⠀⠀⡇⠀⢸ ⢷⠀⠀⠀⠘⠦⠟⠉⠉⠀⠀⡼⠀⠀⠀⠈⠁⠀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠹⢏⠀⠀⠐⠁⠀⠁⠺⠶⢋⣀⠓⠻⡄⠀⠀⠀⠈⠀⠀⡎ ⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢳⡀⠀⠀⠀⢀⠼⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⠉⠉⠉⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⠀⢠⡤⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⢤⡄⠀⣀⣀⣀⡀⠀ ⡰⠕⠀⠐⠂⠍⡆⠙⣭⣛⡀⠤⠤⠤⠤⠤⠤⠤⠄⢐⣛⣭⠋⢰⡩⠐⠂⠐⠫⢆ ⢣⢄⠀⠀⢀⢠⢛⠞⠁⠀⠉⠉⠁⠒⠒⠒⠒⠈⠉⠉⠀⠈⠳⡛⡄⡀⠀⠀⡠⡜ ⠈⠳⣕⠀⣰⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣆⠀⣪⠞⠀ ⠀⠀⠀⠉⢠⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⡄⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢠⡾⠿⠿⠿⣿⣄⠀⠀⣠⣿⠿⠿⠿⢷⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠈⢀⣶⠛⠛⢦⠙⠀⠐⠋⡶⠛⠛⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠃⠀⠀⠸⣷⡈⡃⣸⠇⠀⠀⠸⣇⢹⠁⣾⠇⠀⠀⠘⢇⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⢀⣩⠿⢿⡭⠤⢶⣶⣤⣭⡿⠿⣉⣀⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠘⢆⡀⢀⡞⠁⠀⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠀⠈⢳⡀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⢷⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡾⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠈⠫⣹⡒⠚⢉⠉⢉⡉⠉⣉⠓⢒⣏⠝⠁⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠒⠛⠤⠼⠧⠤⠛⠒⠋⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣀⣠⣄⣀⣠⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣲⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⣏⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⡇⠀⠀⠀⠀⠀⢀⣾⣿⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⡘⣦⣿⣞⢷⡀⠀⠀⠀⠀⠀⢀⣽⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠳⣦⣀⣠⣴⢞⣿⡿⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡌⢿⣿⣧⡻⠦⠤⣤⣤⠶⠛⠁⣠⡿⠆⠀⠀⠀⠀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⣅⣹⣷⣦⣤⣀⣈⣉⣉⣭⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠆⢳⣾⡛⢶⠞⠋⠀⠀⣠⣾⠇⠀⣀⣤⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⣤⣶⣶⣿⣿⣿⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⣤⣄⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢀⣠⣤⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢧⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢨⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣧⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⣿⣿⣿⣿⣿⠿⢿⡿⣿⣻⣷⠀⠀⣾⣟⣉⢠⡟⢛⣿⣿⡆⢀⣙⣿⣿⡀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡇⠀⣿⣿⣿⢟⡽⠗⠀⣿⣤⣿⣿⣿⣿⣿⣿⡇⠀⠸⢿⣟⣿⡿⠃⠀⢈⣿⣿⡇⠀⠀⢈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⡟⠀⠀⢿⣿⡿⠋⠀⠀⠀⠙⠛⠛⠋⢸⣿⣿⠿⢷⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡗⠀⠀⠀⣿⣇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡟⠃⠀⠀⣼⣿⣿⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣶⣾⣿⣗⣶⡤⣤⣤⡾⠿⠿⠛⠋⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠈⠻⢿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠛⠓⠶⣤⣄⡀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠉⣩⡿⠛⠉⠁⠈⠛⠻⠿⢿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣦⣠⠾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣾⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⢧⣤⣀⣀⣀⣀⣀⡤⠴⢛⣡⡾⢇⠘⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⠛⢻⣿⡇⢿⣷⣦⣤⣤⣀⣀⣤⣤⣖⣻⣭⣤⡾⠟⢻⠿⢷⣶⣶⠶⠾⠿⠛⠉⠀⢸⣷⣟⣀⡤⣤⣤⡶⠒⠦⠤⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢶⡾⠋⠆⠀⠀⠈⡿⣷⡌⠛⠿⣿⡿⠿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠉⠙⢿⣮⣻⣿⣄⠀⠀⠀⠈⠻⣆⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⣸⡿⠁⠀⠀⠀⢠⣿⣿⣿⣷⣄⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠶⠶⣶⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠹⡆⠀ ⠀⠀⢀⣤⣲⡟⢠⡧⠇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣽⣶⣶⣤⡌⣝⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢳⡀ ⠀⣰⢋⡼⢳⣿⡄⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⣿⡟⠛⠛⠛⠻⢿⣿⣿⣉⠛⢛⣻⣟⡛⠉⢁⣤⣾⠟⠋⠉⠁⠀⠀⣿⣿⠁⢹⣆⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠃ ⠘⠁⠞⠁⢸⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⠟⣀⢾⣿⠁⠀⠀⠀⠀⠀⠀⢉⢻⣿⡟⠋⡙⠻⣾⣟⣭⣶⠀⠀⠀⢰⣄⢀⣿⠃⠀⠀⣿⣇⢿⣿⣿⡇⠀⠀⠀⠀⡰⠃ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⠇⢺⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢁⣼⡿⠿⣿⠏⠀⠀⠀⠈⣿⣾⠏⠀⠀⠀⠀⢹⣿⣿⣿⠁⠀⣠⡴⠛⠁⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣟⡃⣸⣿⢸⡟⠀⠀⠙⠿⣦⣯⣀⠀⠀⠹⠿⢩⣿⣿⠿⠟⢿⣷⣄⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠈⣿⣿⣿⡴⠟⠁⠀⠀⠀⠀ ⠀⠀⠠⣄⣀⣀⣘⣿⣿⣿⣿⣿⣿⣇⣸⡁⣀⡀⠀⠀⢹⣿⣋⣀⣈⣀⣴⣿⡟⠁⠀⠀⠀⣹⣿⣤⣀⣀⣀⣀⣼⡿⣁⣀⣀⣀⣀⣀⣤⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠉⠉⠈⠉⢻⣍⠉⣉⣩⠟⠉⠀⠀⠉⠉⠉⠉⠀⢉⣉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠒⠒⠒⠢⢤⡀⠈⢷⣍⡓⠲⢤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡤⠔⢊⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠋⡤⠒⠉⠉⠓⠢⢄⠈⢳⡌⠳⣌⡓⠲⠼⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡸⠧⠔⢊⡵⠏⠀⠀⠀⠀⡴⣧⠀⠀⠀ ⡞⢸⠁⠀⠀⠀⠀⠀⢀⠇⣸⣄⠀⣨⠟⠲⢤⣀⡀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⢀⣠⡤⠞⠿⣤⠤⠤⠶⠶⠴⠿⡇⠀⠀⠀ ⢸⡈⢇⠀⠀⠀⠀⢠⠊⢠⠏⣨⠟⠁⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠦⠤⠤⠤⠴⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠈⢻⣍⡩⠭⣍⢫⡁⠀⠀⠀ ⠀⠳⣄⠳⢄⡀⡴⠁⡴⢃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠂⠚⡆⡟⡄⠀⠀ ⠀⠀⠈⠓⠦⣉⣠⠮⣄⣾⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣼⣹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠙⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠴⠀⠀⠀⠸⣇⡸⣧⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⠷⢹⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡆⡿⡄ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣈⡻⣿⣆⠀⠀⠀⠀⠀⣴⡿⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⡇⡜ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⡹⡆⠀⠀⠀⣸⢋⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⠃⢰⡥⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⡟⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⠀⠀⠀⢸⡿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⣀⠔⡿⠭⢗⣲⣺⢗⣽⣿⣿⣿⣿⣿⡟⠀⣀⣀⣀⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⣶⠮⠿⣿⣾⠷⠿⠛⠛⠉⣿⣿⡟⠋⠉⢙⣿⣿⣿⣿⣿⣿⣯⠙⠛⠛⠷⠦⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⠀⠀⠋⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣸⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣧⡴⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⣷⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠁⠀⢀⡾⠉⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⢿⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢠⠞⢿⣄⣹⡶⢤⣤⣤⣤⠶⠶⢲⣿⡟⠉⢻⣷⡖⠶⢦⣤⣤⣤⡴⣾⣏⣠⡿⢲⡄⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠣⣬⣿⣿⣿⣦⣤⣼⣿⣦⣤⣿⣿⣿⣷⣿⣿⣷⣤⣼⣿⣧⣤⣶⣿⣿⣿⠥⠞⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢹⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⠇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⢩⠞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢳⡍⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠙⠒⠋⢰⣉⠉⣻⠛⠻⡟⠛⢻⠛⠛⡏⠉⢹⡄⠑⠒⠋⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠁⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠓⠶⠤⣤⣤⣤⣄⣀⣀⣤⣤⡤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➖➖🟪🟪 🟧🟪🟪🟪🟪 🟨🟨🟨🟨🟨🟨 🟨⬜🔳🟨⬜🔳 🟨🟨🟨🟨🟨🟫🟫 🟨🟨🟨🟨🟨🟨🟨 ➖⬜➖⬜🟫⬜🏻🟦 ➖⬜➖➖🟫🏻🏻🟦🟦 🟨🟨🟨🟨🟨🟨🟨🟦🟦 🟨🟨🟨🟨🟨🟨➖🏻🏻 🟧🟧🟧🟧🟧➖➖🟫🟫 was that the bite of '87???
⡿⣿⠿⢿⠿⣿⢿⡿⡿⡿⢿⠿⣿⠻⢟⡟⣋⣛⡻⡛⠋⠉⠀⠀⠀⠀⢈⡁⠉⢍⠛⡷⣀⠀⠀⠀⠀⠀⠀⠲⢂⠟⡁⢢⢛⡤⢁⣀⡠⣄ ⡳⡜⡺⢌⡳⢍⠎⡵⢣⢝⡩⢒⠡⠉⢈⣨⢗⡶⠛⠁⠀⠀⠀⠀⠉⢉⣲⣌⠑⢮⠑⠺⡅⠉⠁⠀⠒⠚⠷⣿⣌⡣⢜⠠⢎⠰⡉⠆⠱⠌ ⠱⠘⡑⠩⡉⢌⠲⡱⢩⣾⣫⣥⣶⣶⡿⣳⢏⣴⠎⠉⣹⢢⣀⣀⣶⡏⠀⠘⡷⣄⢳⡀⠘⢐⣶⣶⣶⣶⣦⠄⢾⡎⠢⡑⢨⢀⢠⡀⢎⠀ ⠣⡙⠬⠅⠁⠈⠁⠐⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣀⣀⣈⣧⣿⣾⣿⣄⣀⡀⢽⣼⡄⢷⡤⣋⣿⣿⣿⣿⣿⣿⣮⣇⠀⠡⢃⡍⢢⣍⠳⣌ ⠂⡍⠂⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣏⣿⢻⡇⢀⣿⣿⣿⡿⣿⣿⡈⣷⡱⡞⣿⣿⣿⣿⣿⣿⣿⠀⠀⠢⠐⣃⢤⢫⡔ ⠐⠈⠁⠐⠒⠀⠁⠀⠘⣿⣿⣿⣿⣿⡿⣞⣿⡄⢿⣿⣿⡿⣼⣇⠀⣿⣿⣿⢧⣿⡿⣗⡸⢷⡍⢿⣿⣿⣿⣿⣿⡇⠒⠬⢓⡹⢰⢣⡓⢮ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⢿⣯⣿⣦⣙⣋⣵⣿⣿⣦⣌⣛⣽⣿⢯⣟⣧⡟⡼⣘⢧⣿⢻⣿⣿⠟⠐⡉⡒⠬⣁⠎⢦⠙⣃ ⢜⣩⢠⢠⠄⡄⢠⠄⢂⠄⡀⠙⣷⣿⡿⠿⠛⠋⠉⠉⠁⠀⠀⠀⠉⠈⠉⠉⠙⠛⠻⠾⣽⣷⡍⡖⣻⣿⡿⢣⢆⡣⢵⡉⢆⡥⣚⠦⣛⢤ ⢎⡔⣣⢎⡝⡸⢥⡺⢌⠴⡱⣬⠟⠁⢀⣠⠴⠶⠶⢛⠛⠋⠛⠛⠻⠶⢦⣄⠀⠀⠀⠀⠀⠈⠛⢧⡝⣿⠁⠜⠂⢧⠐⠈⠐⡄⠃⠘⠀⢂ ⢞⡼⡱⢞⡜⡳⢤⡙⣆⢦⣱⠏⠀⣰⣿⡃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⡀⠀⠀⠀⠀⠀⠈⢻⡅⡟⣈⠅⡆⢂⠈⡐⠀⠄⡀⠀⠀ ⠊⠼⠹⡄⡙⡜⢧⣽⢞⣮⡏⠀⢰⣿⣿⡿⢦⡌⣁⠒⠐⠂⠐⠀⠀⠐⢉⣩⣽⡇⠀⠀⠀⠀⠀⠀⠈⣷⣰⡌⠭⣰⢀⡱⠌⢢⠱⢠⠌⡘ ⡀⠤⠡⡼⢩⠛⠘⠜⡊⢹⡃⠀⠈⣿⣿⣿⣁⣎⣑⣪⣑⣣⣜⣰⢶⡾⡟⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣟⠾⡕⡁⣊⠱⢫⢄⠢⣅⢺⡰ ⠜⣰⢉⠲⣁⠚⡄⠈⡠⢐⡂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠙⢿⣧⢺⣥⠊⡑⠼⢲⠱ ⠑⡀⢎⡐⡡⢧⠙⣜⢣⢽⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡏⠀⠀⠙⣷⡺⣝⢮⡳⢧⣋ ⠒⠀⠓⡀⠆⢜⠲⢨⡞⡞⣿⣷⣤⣀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⡛⠉⠁⠀⠀⠀⠀⠀⠠⠔⠒⣲⡶⢻⡇⠀⠀⠀⠀⠘⢿⡜⢣⢌⡋⡝ ⣹⡖⢦⡴⢀⠞⣲⢏⡞⡡⢻⡀⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣦⣽⣷⣾⠟⠋⠁⣸⠀⠀⠀⠀⠹⡄⠘⢧⢡⡘⠲⣉ ⡣⣽⢲⡍⢯⡘⣷⢫⠔⠡⢻⡆⠀⠐⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⡇⠀⠀⠀⠀⠀⠠⣉⢚⣤⢂⠱⡶ ⣣⡙⢶⣘⣧⢼⡳⠃⡌⠐⣉⣇⠀⠀⠘⣿⣲⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢐⠎⣀⠉⠀⡈ ⢳⣏⢿⣹⣚⢧⡏⠡⢀⠃⢄⢻⡀⠀⠀⠘⢧⢋⢎⠻⡽⢿⢿⣿⣿⢿⡿⡟⢿⣹⡿⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠨⢆⡕⡘⠐⣃ ⣳⡾⣯⠷⠏⣿⠨⠁⠀⠈⢀⠊⢷⡀⠀⠀⠀⠁⠈⠁⠳⠌⠖⠌⠆⠃⠢⠽⠖⠉⠀⠀⠀⢀⣼⠃⢀⠀⠀⠀⠀⠀⠀⠀⠨⢇⠰⠉⠂⠀ ⣏⢷⡱⣎⢣⣏⠧⡀⠀⠀⠀⡜⢠⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠑⡂⠀⠀ ⡞⣦⢖⡫⣅⡾⢣⠅⡀⠀⡐⠤⢣⣻⢿⣿⣿⣶⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣶⡾⣟⡿⣥⢃⠂⠄⠀⠀⠀⠀⠀⠀⠀⡜⠤⢄⠀⠀⠀ ⣺⡅⢋⡑⣀⡿⣳⠌⡐⠀⠀⠀⠑⠸⢯⣿⣿⣿⢿⣿⢿⣿⢿⡿⣟⡿⣯⣟⣳⢧⣿⡿⣝⠢⣁⠂⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠠⠔⠀⠂ ⡓⣆⢦⠳⡱⣹⢧⡷⣀⡀⠀⠀⠀⣀⠀⡀⣙⣿⣿⡿⣿⢾⣻⣽⣻⣽⣳⣯⣟⣿⣟⡳⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⠊⠤⠀⠀⠀⠀ ⣵⡼⣩⢮⣱⢯⣟⡷⣯⡽⣯⣻⡵⣮⣟⣽⣛⣿⣿⡿⣽⣯⣟⣾⣳⢯⣷⣻⣿⣿⣯⣷⡲⣄⡄⣠⣀⡀⣀⣀⡤⣔⠻⡄⢋⠜⠀⢠⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⠿⠿⠿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣶⣶⣤⡀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣄⠀⢀⣤⣶⣶⣤⣀⠀ ⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇ ⢸⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠙⠿⢿⠿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣶⣿⣿⣿⠿⡿⠿⠋⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⡟⠋⣭⠙⢿⣿⣿⡿⠋⣭⠙⢻⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣄⣀⣾⡟⠋⠙⢻⣷⣀⣠⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠉⠙⠛⢿⡿⠛⠛⠉⠉⠛⠻⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⣤⣤⣤⣾⣷⣤⣄⣀⣀⣤⣴⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⣿⡇⣸⣇⢸⣿⣉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣽⣿⣽⣟⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣷⣿⣻⠿⢿⣻⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣀⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣀⡀⣀⣀⣀⣨⣿⣿⡿⣶⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢁⣿⣿⣿⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣻⣿⢿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠈⠉⢹⣿⣻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⠀⠀⢸⣿⣟⣿⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣿⣿⣤⣤⣼⣯⣿⣯⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⢿⣾⢿⡿⣟⣯⣷⣿⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⢿⣻⣿⢯⣿⡿⣿⣻⣽⣟⣿⡇ ⢰⣶⣶⣖⣀⣰⣶⣶⣿⣿⡿⣷⣶⣶⣶⣶⣶⣾⡿⣯⣿⢷⣿⣻⡏⢹⣿⣿⡿⣽⣿⣟⣯⣿ ⠸⠿⠿⣿⣿⣿⡏⠿⠿⠀⣿⣿⣷⣿⣏⣿⣹⣾⣿⣿⣹⣿⠉⠉⠁⢸⣿⣿⣿⡿⣷⣿⡿⣷ ⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣟⣷⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣯⣿⣟⣯⣷⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣟⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣿⣟⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣷⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣷⡿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣷⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣯⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣷⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⣿⣻⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠯⠿⠟⠾⠿⠽⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢡⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢆⣀⠜⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⢦⠤⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠩⢋⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡀⠅⡪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡢⠅⡪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠚⠛⠚⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀ ⠀⠀⣠⢋⡴⢂⢩⠭⣑⢦⠀⠀⠀⠀⠀⡴⣚⠉⣑⠢⣄⠙⣆⠀⠀ ⠀⡼⢣⡿⢠⠁⣸⣷⠈⣾⠆⠀⠀⠀⢸⢸⢠⣶⡀⠱⡘⣧⡈⢧⠀ ⢰⠃⣿⣧⠸⣄⣉⣉⢜⡞⠀⠀⠀⠀⠈⢾⢌⡛⠋⣠⢃⣿⡇⠸⡆ ⢸⠀⠹⣿⣷⣶⣴⠾⠋⠀⠀⠀⠀⠀⠀⠈⠳⣮⣭⣴⣾⣿⠇⠀⡇ ⠸⡄⠀⠀⠉⢉⣠⡤⣄⡀⠀⠀⠀⠀⢀⣀⡤⢤⣍⡉⠉⠀⠀⣼⠁ ⠀⠉⢳⠖⢚⠉⠀⡇⠀⠉⡗⠒⠒⠚⠹⠀⠀⢸⠀⠉⡟⢲⡏⠁⠀ ⠀⠀⠈⡇⢸⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⠀⡇⠈⡀⠀⢰⠀⠀⢀⠀⠀⠀⡇⠀⠀⡇⠀⢠⠀⣸⠀⠀⠀ ⠀⠀⠀⢷⠀⡇⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⠀⠸⣄⣰⠀⠀⡆⠀⢸⠀⠀⠀⠃⠀⢸⠀⠀⣇⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠒⠧⠤⠬⠤⠤⠤⠤⠤⠼⠒⠚⠉⠀⠀⠀⠀⠀
⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀ ⠀⣰⡿⢉⡇⠀⠀⠀⣠⣾⠟⢡⠞⠀⠀ ⣰⡿⢀⡼⠁⠀⠀⣰⣟⣡⠖⠁⠀⠀⠀ ⣿⡷⠟⣇⠀⠀⢰⣿⠀⣸⠀⠀⠀⠀⠀ ⢿⡇⠀⢸⢀⣀⡼⠿⠤⡃⠀⠀⠀⠀⠀ ⠘⢿⣄⡾⡟⠁⠀⠀⢀⣨⣦⠀⠀⠀⠀ ⠀⠀⢸⣿⠁⣾⡟⢃⣸⣿⣹⣦⠀⠀⠀ ⠀⠀⢸⡿⣄⠙⡳⠋⠛⠛⠃⠈⠢⠀⠀ ⠀⠀⠈⢿⠦⠭⢇⠀⠀⡀⠤⢤⡇⠀⠀ ⠀⠀⣠⢴⣻⣶⣾⣷⣤⣤⣴⢎⠀⠀⠀ ⠀⣼⠇⠀⢻⣿⣿⠿⠛⠙⠻⣦⣣⠀⠀ ⠀⣇⣆⣀⣸⡇⠀⠀⠀⠀⠀⠸⢃⢃⠀ ⢸⣄⡏⠁⢸⡇⠀⠀⠀⠀⠀⠀⢟⣬⡄ ⠈⠛⠓⠒⠚⠓⠒⠀⠒⠀⠀⠈⠉⠉⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢚⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣄⠀⠀⢀⡴⢺⢷⡞⠁⢀⣟⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢰⢮⠙⢦⡞⠀⣞⡟⠀⠀⡼⡾⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠚⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢳⣸⡇⠀⣿⠀⠀⢠⡿⠁⢰⣏⠀⠀⠀⠀⣴⠋⠀⡰⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⡀⠀⢳⣷⠀⠘⣆⠀⠟⠀⣴⢻⠏⠀⠀⠀⢸⠁⠀⡼⠁⠀⠀⠀⠀⢸⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣳⡀⠀⢣⣙⡦⠆⠀⠀⠒⠒⠓⠒⠒⣦⣄⢸⡀⢸⠁⠀⠀⠀⠀⢠⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠶⠞⠁⠀⠀⢀⣀⣀⣀⣀⠀⠀⢹⣮⣿⣷⡸⣄⢀⣀⣀⡠⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⢰⢿⡀⠀⣠⠖⠊⠉⣁⡤⠬⠟⠿⢶⣼⣿⣿⣿⠳⣌⡂⠉⠉⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢣⣲⠳⡀⠈⣷⡇⠀⢣⠤⠒⠋⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠈⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠒⣲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠹⡆⠙⢒⣿⡇⠀⢈⡴⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⢩⣝⣗⣀⣀⣤⠴⢲⠆⠀⠀⢀⣠⠔⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠁⣰⠋⠉⠙⢞⡆⠀⠀⠀⠀⠀⠀⣀⣀⣹⣦⣤⣼⣤⣼⣿⡿⣷⣟⠈⠉⢿⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣠⠴⠒⠉⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⢸⠃⠀⠀⠀⠈⡧⠀⢰⡖⠛⠿⣿⣭⢤⣠⡀⠀⠀⠀⠀⠀⠳⢄⢿⣧⣀⠀⣀⣼⡿⣀⣀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠉⠉⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣿⡿⢃⠿⠇⠀⠀⠀⠀⠀⠀⠀⠳⣬⠛⠻⣿⣿⣿⢯⣗⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠋⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⡀⠀⠃⠀⠀⢀⣀⣀⡤⣤⣴⣞⣹⣻⠟⠁⠀⠀⠀⠀⠀⠈⣗⣦⡤⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣏⠙⣿⡉⢹⡏⠉⣷⣀⡟⣿⡷⠟⠁⠀⠀⠀⠀⣀⣠⠴⠚⢯⣭⣭⣉⡑⠒⠦⠤⣄⡀⠀⠀⢀⣴⣶⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠀⠙⠦⠤⠤⣄⠀⠀⠀⠀⠠⡾⢽⣶⣿⣳⣀⣿⡤⠧⠟⠋⠉⠀⢀⣠⣴⠶⠾⣿⣿⣿⣶⣤⣀⣙⣿⣿⣿⣿⣶⣶⣬⣉⣷⡾⠿⢛⣩⠤⢾⣿⡍⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⣄⠀⠀⠀⠀⠈⠳⡄⠀⠀⢠⣇⡀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣤⡖⠛⢷⣇⠀⢀⣤⣀⠀⠀⠀⠉⠉⠉⣉⣻⣿⣿⡟⢿⣁⠠⠖⠮⠝⢲⡛⣉⣥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠓⠲⣤⡀⠀⠹⡆⠀⠺⢮⠤⠔⠢⠤⠤⠤⠖⠒⠋⢁⡞⠀⠀⠀⢻⡀⢸⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣿⣿⡇⠀⠈⠙⣆⣠⠾⣿⠟⠉⠉⠉⠓⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⢻⣀⡠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢻⡼⡄⠀⠀⠀⠀⠀⣰⠶⣤⣾⣿⡿⡇⠀⠀⠀⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢺⣃⣨⠏⣀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢿⣀⣀⣤⠤⠖⠋⢘⣷⠀⠀⠀⠀⣼⣿⡆⠘⣿⠟⢀⡇⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡄⠲⠤⠤⠴⠚⠁⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⡼⠉⢧⡀⠀⠀⣷⡙⣿⠸⣿⣀⡼⠁⠀⠀⠀⠘⣿⣤⣀⣠⡤⠤⠴⠒⠛⣏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⡀⠀⢀⣀⣠⠴⢛⡇⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⢰⠃⠀⠈⢳⡀⠀⢸⣿⣿⠀⣽⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⡇⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⣉⣁⣀⡤⠊⠳⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣴⠃⣿⠀⠀⠀⠈⢧⡀⠈⢿⣿⡄⣿⠀⠀⠀⠀⠀⢠⣿⣿⠙⠁⡇⢹⡀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠉⠀⠀⠀⠙⢦⡀⠀⠀⠀⡿⠀⠀⠀⣰⡟⢠⠇⠀⠀⠀⠀⠈⢧⠀⠀⠀⣧⠇⠀⠀⠀⠀⠀⣿⠛⢹⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⠲⣄⣰⠃⠀⠀⢰⣿⠁⡾⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡇⠀⢸⡄⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣾⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⢳⡀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠘⣿⠀⠀⠁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠸⣧⠀⠀⠘⣷⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠻⡄⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣦⡶⠛⠀⠀⠀⠘⣷⡀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⣀⣀⣠⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠳⡀⠀⠀⢀⣠⠴⣚⡯⠵⠻⠿⡄⠀⠀⠀⠀⡟⢿⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠲⠚⠯⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⠓⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⢻ ⣿⠀⢰⢤⡈⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢉⣠⢤⠀⢸ ⢻⠀⢸⠀⠈⠓⠦⣀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⢀⡤⠒⠉⠀⡄⠀⣸ ⢸⡆⠈⡇⠀⠀⠀⠀⠙⠢⢄⡀⠈⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⣀⣤⡶⠀⠀⠀⢀⣴⠟⠉⠀⣀⠔⠊⠁⠀⠀⠀⠀⡀⠀⣿ ⠸⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⡏⣠⠞⣩⠟⠀⠀⠀⠀⢸⡇⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡇ ⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡇⢸⡷⠃⣴⠏⠀⠀⠀⠀⠀⢸⠇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣸⠃ ⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡀⠀⠀⠀⠀⠀⠸⡇⢸⠁⡼⠃⠀⠀⠀⠀⠀⠀⣿⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⣿⡀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡽⠀⣸⠇⣀⣴⠶⠶⠦⢤⣷⠀⡼⠥⠤⣴⡶⠶⢶⣄⠀⣿⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣸⠃⠀ ⠀⠀⠘⣧⣀⡉⠓⠒⠦⠤⠤⠔⢉⣴⢾⣥⡾⠛⠁⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠀⠀⣠⣿⣷⣮⡿⢦⣌⠳⠤⠤⠤⠖⠒⠉⣁⣰⡏⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣤⣶⡏⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠙⢿⣄⣙⣷⣤⣤⡴⠶⠚⠛⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡀⠀⣠⣶⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀ ⠀⠘⣿⠶⣤⣉⠻⣍⠓⠶⣴⡏⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣋⣉⡈⠉⠻⢿⣿⣆⠀⠀⠀⠘⣧⠴⠞⣋⡽⢋⣠⠴⣾⠏⠀ ⠀⠀⠘⣷⡀⠉⠛⠺⢷⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⣿⡄⠀⢨⡍⠉⠚⢻⣿⣧⠀⠀⠀⠀⣠⡾⠿⠚⠉⠁⣴⠏⠀⠀ ⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣶⣤⣤⣤⣤⣾⣿⡿⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣻⣿⡿⠿⠖⠒⠒⠒⠒⠲⠾⢿⣿⣟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣰⣿⡟⢰⣏⡄⣆⠀⣖⣚⣫⣽⣿⣶⡄⢰⡶⡾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠿⢿⣤⣼⣿⡾⠀⠀⠉⠻⠿⠿⠿⠋⠀⠉⢻⣷⣿⣤⣤⠴⠶⠶⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⡟⢿⠶⣦⣤⣄⣐⣤⣤⡶⣿⠛⣿⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣽⠈⠛⠛⠦⠿⡼⠧⠞⠛⠁⣸⣽⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢻⡞⣧⣤⠀⠀⠀⠀⣤⣴⠻⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧⡟⢸⣧⣠⢄⣠⡇⢹⣴⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⣸⣁⡇⠈⡇⣧⣸⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣬⣉⣉⣉⣉⣁⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣋⠉⠉⠛⣆⠀⠈⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⡇⠀⣶⣾⡿⢿⣿⣿⣿⣷⢶⣄⠀⠀⠀⠀⠈⢡⣾⣿⣿⡯⣭⡓⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⢻⣍⡿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⡇⠀⣿⣋⣾⣿⠿⣿⠿⠛⠟⠻⣧⠀⠀⠀⠀⠘⠁⠙⠉⠡⠞⠃⠀⠀⠀⠀⣿⢳⠀⡄⠀⠀⠀⠀⠀⣿⠑⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⠉⡿⣧⣿⣧⠀⠁⠈⠈⠉⠛⠁⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠆⠘⠀⠀⠀⠀⠀⠀⠻⣆⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣠⠟⢸⡃⢻⣞⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⣀⣠⡴⠾⠿⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣼⣿⣿⣻⢋⣤⣿⣿⣄⢳⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡾⠁⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣽⡇⣀⠀⠀⠀⠀⠀⠀⠀⣇⣰⣄⠀⢀⣤⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣠⣾⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢦⡀⠀⠀⠀⠀⠀⠉⠙⠛⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⣿⣿⣿⠿⠟⠛⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢳⠀⠀⠀⣄⣄⣀⣀⣀⣀⣀⣠⣤⠤⠴⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⣿⣿⣿⣿⡄⠀⠈⢳⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣄⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣻⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣸⣿⠿⣿⡿⠃⢻⣿⣿⣷⣦⣄⣀⣀⣄⣀⣄⣤⣴⣿⣿⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣸⣿⣿⠀⢿⠁⠀⠀⠛⢿⣿⣿⣿⣿⣿⣭⣻⣭⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠻⢹⡇⠘⡆⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⡇⠀⠉⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣄⣿⣿⣷⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⣁⣠⣤⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⣴⠏⠁⠀⡏⠹⣆⠈⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⢿⡇⠀⠀⢸⣶⡏⠀⡜⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⣸⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠀⠛⠲⠴⠾⠋⠀⣰⢃⣠⣤⠶⡾⠿⣿⡍⠉⠉⠙⠻⠿⣿⣿⣿⠁⠀⠀⠀⣠⠞⠉⣠⣤⣤⡀⠙⢦⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣴⣻⡟⠋⠁⢸⣿⠿⠿⢿⣿⠂⠀⠀⠀⢠⣼⡛⠷⣤⠀⠀⢰⠋⢠⡞⠉⠙⢏⣛⣧⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣠⣼⣾⣶⣶⣄⠀⠀⠀⠀⠀⠘⠛⠿⢿⣶⡟⣄⢺⠀⠸⣆⠀⠀⠈⣿⣿⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢠⣿⣿⡟⣿⠙⠛⣿⣷⠀⠀⠀⢀⣴⣾⣶⣤⡈⠁⠈⢿⣷⡀⠘⠣⣤⣼⠟⠁⢠⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⢠⣿⣻⣿⣿⡿⠀⠀⠀⣿⠀⠀⢰⣟⠻⡟⠛⠛⢿⣦⠀⠈⣿⠛⠲⣤⣄⣠⣤⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣸⠉⠛⠛⠛⠀⠀⠀⢀⣿⠀⢠⣿⣿⣿⠏⠀⠀⠀⢹⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠳⣦⡀⠻⣧⡄⠀⠀⠀⢀⣀⣿⡏⠀⡼⠿⠛⠋⠀⠀⠀⠀⢨⡷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡃⠀⠀⣨⣇⣠⣬⣽⣿⣦⣼⣿⣿⣿⣤⣤⣿⣶⡄⠀⠀⠀⠀⢀⣾⠇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢿⣷⣀⣸⣿⡿⠛⠁⠀⠀⠀⠀⠙⠻⢿⣦⣠⣾⣿⠿⢿⣿⣷⡿⠾⠏⢀⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠈⠛⠛⢫⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠙⢷⣦⢰⡟⠹⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⣧⠀⠀⠀⣸⣿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⣇⠙⠻⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣷⣾⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠹⣿⣆⣀⡿⣿⡆⠀⠀⠉⠙⠯⣉⣓⣲⡶⠦⠤⢤⣀⣀⣀⣤⣴⣾⡿⠀⠈⠉⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠉⠳⣄⠙⢿⣿⣿⡌⢿⣾⣥⣀⣀⠀⠀⠉⠉⠉⠒⠒⠒⠋⠉⠉⠉⢉⣿⠁⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢃⡴⠊⠀⠻⣀⠀⠈⠙⠿⢾⣝⣿⣿⣷⣷⣶⣶⣭⣑⣦⣆⣀⣀⣀⢀⣴⡿⠃⠀⣀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡏⠀⠀⠀⣀⣿⣙⣆⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣯⣶⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣧⢀⣰⠟⠁⠀⠉⢻⣄⢀⣴⢾⣿⣿⣿⣏⠉⠉⣉⣉⣹⣻⣿⣿⣯⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡿⣿⠏⠀⠀⠀⣀⣼⠟⣿⠃⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣷⣴⣴⣾⣿⣟⣴⠟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⡿⣟⣿⡿⠃⠀⢀⣿⣽⣧⣾⡿⠋⠉⠉⠉⠈⢛⢿⣦⣽⣿⡄⠙⣄⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣩⣿⠛⠀⠀⢀⣼⠏⠙⠛⠁⠀⠀⣠⠴⢶⣤⠀⠀⠉⠉⠀⢹⡄⠘⣆⠀⠀⠐⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣿⣤⣶⣿⡇⠀⠀⠀⠀⠀⣿⡀⢿⡀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⢹⣧⠈⣇⢀⣀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣿⢰⠟⠒⠤⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⡿⠟⠀⠀⠀⣸⡆⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣦⡇⣆⠀⢻⣧⡀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠁⠀⠀⠀⠀⣠⣿⢽⡀⠀⣠⣾⠿⠛⢾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣼⣦⡄⠙⢷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⢡⣾⢛⣿⣿⠅⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣦⣄⡈⠙⠛⠿⠶⣶⣦⣴⡶⠾⠟⠛⣩⣤⡾⠿⡁⠘⣿⠋⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠉⠛⠻⣿⣿⣷⣶⣤⣴⣦⣤⣤⣤⣴⡾⠟⠋⠁⠀⠀⣧⠀⠹⣧⣀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⠉⠻⣿⡏⠉⠉⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠻⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣄⠀⣶⠟⠉⠉⠉⠉⠉⠉⠉⠉⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⡟⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠙⢷⡀⠀⠀⡀⣄⠄⠀⠀⣴⠋⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⣄⣀⢀⣼⠇⣤⣤⣼⣯⣤⣤⡸⣧⡀⢀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠡⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⠉⠙⠻⠿⠛⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣄⣀⠴⠶⣀⡠⣼⣿⣧⣤⠀⠀⠀⠀⠀⡠ ⠀⢷⣄⠀⠀⠲⣶⣶⣿⣿⣿⣿⣯⣤⣤⣼⣿⣿⣿⣿⣶⣶⠶⠀⢀⣾⠃ ⠀⠈⢿⣷⣄⠀⠀⠀⠉⠉⡍⠈⠝⡟⢻⠻⠉⢩⠉⠉⠀⠀⢀⣴⣿⠃⠀ ⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⢿⢃⡀⠀⠀⢀⠀⡾⠀⠀⢀⣴⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣦⣀⠈⠷⢥⣧⣼⡬⠾⠁⣀⡴⣻⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⢦⣄⠀⠀⣀⡴⢞⣭⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⣆⠀⠈⢙⡿⣮⣝⣒⠦⣬⣉⡀⠀⠀⢠⡶⠂⠀⠀⠀ ⠀⠀⠀⣠⡀⣤⣤⣿⣦⢘⣭⠷⠒⠈⠙⠛⠶⢯⣭⣟⣵⡟⣥⣤⣔⣶⠀ ⠀⠀⠘⠭⠉⠉⠉⠘⢿⣄⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠃⠀⠀⠊⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⣠⣴⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⠟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⣠⣾⠋⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠃⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⣰⡿⠃⠀⠀⠀⠀ ⠀⢠⣾⣳⡿⠁⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⢀⣿⣷⣿⠁⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣥⣴⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⡏⠤⣶⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⢫⡿⠈⠉⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⡿⠿⠛⠁⣿⡄⠀⠀⠀⠀⠀⢸⣿⣼⠇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢿⡇⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣼⣧⠀⠀⠀⠘⣿⠀⠀⢀⣠⣤⣼⣿⠿⣦⣤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣷⣿⣆⠀⠀⢀⣿⣶⣿⡿⠛⠉⠁⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣦⣠⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⣤⣽⠇⢀⣠⣴⣶⣦⡀⠀⢸⣿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢠⣿⣿⣿⣿⠛⢷⠀⠸⣿⣿⡿⢀⣿⢿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣷⣿⡇⠀⢻⡿⠿⠿⣀⣾⠘⣷⣿⣿⣾⣿⠿⠿⠾⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⢿⣆⠀⠀⠙⠙⢛⡽⠊⠀⠻⠿⠛⠛⠋⠀⠀⠀⠈⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣀⠙⠻⠶⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣻⣶⣤⣤⣤⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⣈⠉⠉⠉⠻⣷⡄⠦⠤⠴⠞⠋⠁⠀⠀⣸⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣤⣶⣛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠉⠹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡟⠀⠀⠀⢹⣿⠻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⣷⣄⠙⣦⠀⠀⠀⠀ ⠀⠀⢰⡏⣿⠃⠀⠀⠀⠀⣿⣿⠿⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡿⣄⠀⠀⠀ ⠀⠀⢼⡇⢿⣇⠀⠀⠀⠀⣻⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡆⠘⣇⠀⠀ ⠀⠀⣾⠿⣶⣿⣄⣤⣴⠾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢿⡄⠸⡆⠀ ⠀⢸⣿⠀⢀⣼⠋⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣧⠀⢹⠀ ⠀⢸⣿⣆⣾⡏⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣏⣿⡇ ⠀⠘⢿⣿⣿⣧⣄⣀⣀⣤⣼⣿⣧⣠⣤⣀⠠⠤⠤⠤⠄⠀⠀⠒⠒⠒⠒⠛⠾⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⣡⠴⢦⣄⠑⣄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⢸⡅⠀⢸⣌⡧⢸⡄⠀⠀⣠⣤⣿⣿⡿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⡈⠳⢤⣤⠟⠁⡼⣀⣠⣤⣿⣿⡛⠛⠻⠿⣿⣿⣷⠀⠀⠀⣠⠖⢉⣉⣉⠓⢄⠀ ⠀⠀⠀⠀⠀⠙⠶⠤⠤⣶⡿⠛⠉⢸⣿⠿⠿⠷⠀⠀⠀⣤⣟⣳⢄⠀⢰⠃⡴⠉⠙⣽⣷⡈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢠⣴⣿⡿⣿⣦⡀⠀⠀⠀⣉⣙⡛⠿⠳⣽⡄⠻⣄⡀⣸⡿⠁⡿ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣿⣿⣷⡿⠀⢩⣧⠀⢠⡾⣿⠿⠿⣦⡀⢹⣿⠦⣈⣉⣉⡤⠞⠁ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⣿⠙⠛⠋⠀⠀⢸⡟⢀⣿⣿⡿⠀⠀⠈⣷⢸⣿⠀⠈⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠋⠙⣆⠙⢷⣤⣀⣠⣦⣿⡃⢸⣛⠉⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣧⠀⣴⣿⠟⠛⠉⠉⠙⠿⣿⣉⣹⣿⣷⣶⣦⣶⣾⠃⢀⣻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠈⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⢷⣄⡾⠹⢙⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡆⠀⢠⣿⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣨⣼⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣄⢸⣿⡆⠈⠛⠿⣗⣶⠤⣤⣀⣀⣀⣀⣀⣠⣴⡟⠙⠛⢫⡇⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⢛⢢⡈⠿⣿⣏⢻⣮⣤⣀⡀⠉⢉⡙⠒⠒⠛⠛⠛⢉⡿⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀ ⢀⣯⠞⠁⠈⢧⢄⠈⠙⠛⢿⣿⣿⣿⣿⣶⣾⣷⣶⣦⣤⣴⣟⣁⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡀⢠⡶⠛⠻⣧⠀⢀⣴⣾⣿⡟⠛⠛⣿⣿⣿⣿⣿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡏⠀⠀⣀⣿⢻⡏⢾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡗⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣶⣿⣿⣧⠟⠁⣿⣿⢿⣿⡿⣿⣿⢿⣿⡻⢿⡟⢧⡀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠻⣿⡿⠁⠀⣰⡟⠿⠟⠋⠀⣀⣄⡀⠋⠻⠟⢻⡄⢳⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠃⠀⢰⡟⠀⠀⠀⠀⢸⣧⣾⣿⠄⠀⠀⠀⢻⡌⣷⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⡿⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠘⣷⢸⣄⠤⣄⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⣷⡀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⢀⣿⡏⠉⠉⣿⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⡆⡄⠹⣧⡀⠀⠀⠀⠘⢿⡿⠟⠀⠀⠀⢀⣾⢿⠀⢀⣶⠿⢾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣦⡈⠳⢦⣤⣀⣀⡀⠀⣀⣠⣴⡾⢟⣡⡞⣿⣿⠇⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⠿⣿⣷⣦⣬⣉⣹⣛⣛⣉⣭⣥⠾⠛⠉⣇⠘⣧⠀⠀⣼⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠉⠛⢿⡟⠛⠛⣿⠟⠉⠀⠀⠀⠀⢻⠀⠙⠻⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣀⣀⣠⣧⠀⠀⣿⣀⣀⣀⣀⣀⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸⣆⣾⠃⠀⠀⠀⠀⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⣄⣀⠀⠀⠀⠀⣀⣸⡿⣿⡀⡀⠀⠀⠐⣘⣤⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
The lore of the Five Nights at Freddy's (FNAF) franchise is complex and has evolved across numerous games, books, and other media. Here's a simplified overview: The Story's Core: The story primarily revolves around Freddy Fazbear's Pizza, a family entertainment center similar to Chuck E. Cheese's. The restaurant features animatronic characters that perform for audiences. However, the dark secret is that these animatronics are haunted by the spirits of murdered children. Key Characters: * William Afton: The main antagonist, a serial killer responsible for the deaths of the children. He is associated with the "Purple Guy" sprite seen in many games. * Henry Emily: William's former business partner and the co-founder of Fazbear Entertainment. He plays a crucial role in trying to end the tragedies caused by William. * The Missing Children: The spirits of the children murdered by William, who possess the animatronics. * The Animatronics: The main animatronics include Freddy Fazbear, Bonnie the Bunny, Chica the Chicken, Foxy the Pirate Fox, and many others introduced throughout the series. Key Events and Concepts: * The Missing Children Incident: The original incident that sets the events of the series in motion, where five children are murdered at Freddy Fazbear's Pizza. * The Bite of '83: An incident where a child is bitten by the animatronic Fredbear, resulting in his death. * Possession: The spirits of the murdered children inhabit the animatronic suits, seeking revenge on their killer. * Remnant: A supernatural energy or substance associated with souls and possession. * The Puppet/Marionette: An animatronic that plays a significant role in protecting the children's spirits. The Games: Each FNAF game typically involves the player working as a night security guard at a Freddy Fazbear's location, where they must survive against the hostile animatronics until 6 AM. The games gradually reveal pieces of the overarching story through gameplay, minigames, and hidden clues. The Books: The FNAF novels, while not always considered canon to the games, offer additional insights into the characters and events of the FNAF universe. In Summary: The FNAF lore is a complex and intricate narrative filled with tragedy, mystery, and supernatural elements. It explores themes of loss, revenge, and the consequences of one's actions. While the full story is still debated and interpreted by fans, the core elements remain consistent throughout the franchise.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣵⣿⣿⣿⣿⣿⣾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡴⢖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣹⣦⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷⣿⡿⠿⠿⠿⣿⡿⠟⠋⠉⠉⠙⠻⠤⣄⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠳⣄⠀⠀⠀ ⠀⠀⠀⣠⠔⠒⠒⠢⢄⠀⠀⠀⠚⣠⠜⠋⠀⢀⣀⣀⡀⠘⣇⠀⠀⣤⣴⣶⣶⣦⣤⣑⣦⣀⣸⠃⢠⠞⠉⠉⢻⣆⠈⢧⠀⠀ ⠀⢀⡾⠁⣤⠖⠒⢦⡀⠙⣦⢀⠞⢁⣴⣾⣿⠿⠿⠿⠇⠀⣿⠀⠀⢻⣟⣛⠉⠉⠛⠻⠋⢻⣽⠀⢸⣄⣀⣦⣾⡏⢀⣼⠀⠀ ⢀⣾⡇⢸⣯⠀⠀⠀⣿⠀⢻⡌⠀⠙⠋⢀⣤⣶⣶⣤⣄⠀⣿⠀⣠⣾⣿⣿⣿⣷⣦⠀⠀⠈⣿⣦⣀⡙⠛⢛⣋⣤⣾⠏⠀⠀ ⠈⠹⣿⣄⠻⠿⣶⠿⠋⢀⣾⠁⠀⠀⣰⣿⡿⠟⠛⠻⣿⣇⣸⡄⣿⠋⠁⠀⠈⠙⢿⣧⠀⠀⢹⣟⠛⣻⡿⠿⠛⠋⠁⠀⠀⠀ ⠀⠀⠈⠻⢷⣶⣶⣶⡾⢿⣿⠀⠀⢠⣿⠃⠀⢀⣀⠀⢀⣿⣿⣿⣷⣄⣀⣶⡄⣀⣼⣿⣀⠀⢘⡟⠃⠀⢲⣶⣀⠀⠀⠠⡄⠀ ⠀⠀⠀⠀⣄⠀⠀⢀⡀⢠⣼⣄⣀⣀⣿⣦⣤⡼⢿⣚⣿⣿⣿⣿⣿⡿⠈⠙⠩⠭⣟⣿⣿⢿⡿⠿⣄⠀⠀⠀⠀⣀⠀⠀⠈⠀ ⠀⠀⠀⠀⢿⣇⠀⢧⠉⢀⣼⣿⡿⢿⣿⡟⣡⠖⠁⠀⠈⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠉⣿⣶⡹⣿⢿⣷⡄⠈⢁⡋⡀⠀⠈⠀ ⠀⣀⡀⠁⠐⣄⠉⢩⣀⡝⢡⡴⣷⣶⣿⡴⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣿⣿⡟⢧⢀⡏⠀⠙⣆⠀⠀ ⠀⢠⡁⢠⠀⠈⠓⠀⣸⡡⣟⣠⣼⣿⡏⣿⣄⡀⠀⠀⠀⣀⣤⣿⣷⣤⣤⣤⣴⣾⣿⣿⣿⣿⠙⠿⠟⠁⣸⠤⡟⠢⡤⠬⣁⠀ ⠀⠀⠉⠧⣠⡖⠀⢶⡻⣄⠻⣿⡿⢛⣿⣿⣿⡿⣿⡟⢛⣟⠉⣹⣯⣉⣹⣥⡼⢿⣴⠿⣤⡿⠷⠦⣴⣾⠛⠃⡿⢿⠁⠀⠈⡇ ⠀⠀⠀⠀⠈⠻⣄⠈⠳⡿⣷⣶⠶⠿⢿⠖⠛⠓⣿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣀⣸⣿⣀⣩⣩⠀⡧⠀⢠⣀⡼⠋⠈⠓⠤⢞⡁ ⠀⠀⠀⢀⠀⠀⠛⣆⠸⡁⣩⡷⢀⠠⣀⣤⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣤⡀⢸⡆⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⢸⣦⠀⢀⣠⣄⠀⠹⢂⣼⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣠⡿⡅⠈⡽⢇⠂⠀⠀⠔ ⠀⠀⠀⠀⠀⢉⠏⣁⡼⣄⢠⠋⢿⣄⣠⣿⣿⡿⢿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣛⣿⣯⡽⠷⠿⠛⠉⢁⣴⣿⠀⠀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠝⠟⠀⠜⣯⣧⣀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠥⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠉⠐⢒⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⠤⠤⠜⣿⠀⠿⠹⣿⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣤⣤⣀⣠⣤⡴⢾⣿⡿⠛⠁⠀⠀⠀⢈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⢋⣤⣯⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣭⣷⣿⣿⠁⠀⢀⡆⠐⠦⠤⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠚⢿⣿⣿⣿⠿⠛⠋⠉⠟⠉⠟⠻⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⠤⠤⠊⠀⠈⠁⠀⠈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⡀⠀⢰⡤⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⢴⠆⠀⠀⠀⠀ ⡐⡡⠐⠒⠠⡑⢢⠻⣒⠭⠆⢀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠼⠅⡢⠋⠀⠀⣴⠀⠀ ⠇⡆⠀⠀⢀⠂⠖⡴⠊⠉⠒⠢⠤⠤⠀⠀⠀⠠⠤⠤⠔⠂⠉⠑⣌⣉⡩⢝⠀⠀ ⠈⠬⡢⠄⣡⢊⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⢞⣆⠀ ⠀⠀⠈⠉⠉⡏⠀⠡⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠈⢧⣼⣿⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⢠⣴⠟⠉⠀⠀⠀⠀⢸⠉⡎⡆ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣤⣬⡷⡄⠀⠀⣰⣟⣥⣤⣄⡀⠀⠀⠀⢸⠀⡵⡘ ⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⣿⣿⣿⣿⠉⠀⠀⢱⣿⣿⣿⣿⣿⡆⠀⠀⡼⠀⠉⠀ ⠀⠀⠀⢀⡞⢁⣤⣄⣸⣻⣿⣿⣿⡿⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠘⢦⠀⠀ ⠀⠀⠀⢸⠀⢹⠶⢚⠿⠛⠛⠋⢿⣟⣉⣹⣿⣿⣿⡯⠙⠛⠣⢤⡀⠀⠀⢸⡆⠀ ⠀⠀⠀⠘⢦⡀⠀⡇⠀⠀⠀⠀⠀⠈⠛⢻⠟⠋⠁⠀⠀⠀⠀⠀⢱⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⢹⠲⣇⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡄⠀⡼⢺⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⢸⡦⣀⠀⠀⠀⠀⣀⣸⣀⣀⠀⠀⠀⠉⡠⢾⠁⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⢃⣷⣿⣭⣹⣯⣩⣿⣦⣼⣯⣩⣿⣍⣽⣷⡏⢝⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠣⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡯⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠒⠩⢏⡻⠛⣟⡻⠛⣏⡹⠙⠒⢡⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣀⣀⣀⣀⢤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣹⢮⣿⣶⣾⣿⣿⣿⢿⣻⣽⣦⣵⣘⡖⣥⣾⣽⣿⣿⢛⡁⠀⠀⠀⠀⠀⠀ ⢰⢣⣿⣿⣿⣿⣿⣿⠿⣩⢿⣿⣿⠿⣿⠿⢫⡜⡭⢛⡻⣿⠸⣿⢆⠀⠀⠀⠀⠀ ⢸⣳⢟⣿⣿⣿⣿⡏⢧⢳⡝⠋⠉⠁⠪⢷⡗⣮⢵⡋⠁⠀⡈⠻⣻⡃⠀⠀⠀⠀ ⠀⠙⠿⢿⣿⣿⡟⡼⢣⡉⠀⢀⡜⣧⢀⣢⢹⣵⡏⠀⠰⢦⡕⢇⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠟⡼⣱⢫⣅⠀⠀⢧⡻⢿⣵⣠⣿⣇⣀⣻⡹⣿⠏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⡜⡹⠜⣯⣿⣴⡤⠀⡗⣿⣿⣿⣿⣿⣿⣿⣅⡁⠆⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⢨⠵⣩⢶⡋⣁⢠⡕⢲⠙⡦⢻⣿⣿⣿⣿⡟⠁⠐⠆⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⢇⢣⢚⡱⠎⠶⣐⡩⣆⠳⡀⣲⡂⡹⠽⣏⠩⢠⠁⠢⠰⢆⠂⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⢧⣿⠠⢇⠪⣭⢌⡔⡻⣰⠰⣑⢫⠆⡱⢀⣌⠡⣆⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢈⣴⣌⡛⠖⠿⣴⢎⣴⠱⡦⠷⠭⠖⡼⢒⠫⢈⢅⣾⣳⢞⣤⡄⠀ ⢒⡮⡛⡽⡹⣟⡿⣿⣷⣼⣠⠌⠢⢄⠣⣀⠓⡊⠔⣐⣢⣵⣾⣿⢯⣝⠮⡽⠠⠀ ⡁⣞⢭⠳⡽⣞⢿⣻⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣛⢮⠳⡌⠃⠀ ⠰⡈⣮⢝⣣⠝⣎⡷⣫⣿⣿⣿⣿⣿⣿⣿⠻⣝⡹⢻⢿⣿⡙⣾⡹⣎⠷⠁⠀⠀ ⠀⠁⠜⡦⢃⡻⣌⣷⡷⣯⣟⡿⢿⣿⠿⣋⠳⢬⡑⢣⢊⠶⣹⣭⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⣹⣿⣭⢿⡷⣿⢛⠴⢍⡋⢄⠣⢆⣍⠣⢎⠸⣷⣿⣳⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⣿⣯⣿⣿⣷⣎⡚⡔⠌⡆⢓⡌⢦⡹⣬⣿⣿⣳⡟⣾⢽⡶⣂⠀ ⠀⠀⠀⠀⣼⣯⡷⣯⣷⣟⣿⣾⣳⡜⡱⡘⢢⠜⣦⣿⣿⢯⣷⡯⣽⢩⠟⡘⠧⣉ ⠀⠀⠀⢰⣯⣷⣿⢿⣷⣿⣻⢷⡿⣽⡆⢑⠢⣝⣾⣿⣯⣿⢽⠝⡡⢃⠎⡱⠃⠄ ⠀⠀⠀⣸⣷⣻⢾⡿⣟⡷⢯⠿⣽⣷⣻⠛⠛⠋⠉⠻⣿⣾⠁⡊⠐⢂⠒⠀⠑⡈ ⠀⠀⠀⢹⡞⢏⢣⠂⡏⠜⡡⠒⠌⠳⠯⠀⠀⠀⠀⠀⠈⠁⠧⣁⠌⣀⠠⠄⠀⠀ ⠀⠀⠀⠈⣗⠈⢂⠐⠠⠊⠄⠃⠌⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠓⠄⢈⡀⠐⢈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠍⠩⡗⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡔⠁⠀⠀⢸⢸⠀⠀ ⠀⠀⠀⠀⠀⠤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⣦⣰⠀⠀⣼⠆⠀⠀ ⠀⠀⠀⠀⠀⠠⠞⠉⠑⡤⠷⢄⠀⠀⠀⠀⠀⠀⠀⡰⡡⠂⠐⠻⠙⠬⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⠀⠀⣀⡈⠎⡆⠀⠀⠀⠀⠀⣰⣱⠁⠀⠀⢀⡇⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠠⡿⢁⡔⡼⠀⠀⠀⢀⣾⣖⣠⠀⠀⠀⡐⡱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠄⠠⢜⣁⡭⠇⠐⠒⠒⣿⣧⣄⠑⠠⠌⡔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⡸⠋⠁⠀⠀⠀⠀⠈⠙⠂⠁⠫⡃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣌⣀⠂⠀⠀⠣⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠀⢰⠟⢉⣉⢳⠂⠐⡴⠛⠛⢛⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣃⠒⣿⡈⢤⡄⡹⠲⠴⡗⠉⠉⢂⡷⠂⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡅⠀⠈⠓⡀⢊⠠⠀⠤⣈⡢⠥⠾⠧⢠⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣠⢁⡄⠁⣇⣀⣀⢀⠌⠈⢂⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⠦⢶⣀⠀⠀⠍⠀⣇⠈⢠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⠪⢎⢜⡢⢼⢽⢭⡯⢼⡾⣿⣿⠔⠒⠒⣖⡂⢤⡀⠀⠀ ⠀⠀⠀⠀⣠⢴⠒⠒⠲⡗⢄⠈⠡⠼⠐⠚⠤⠊⢛⡰⡏⠀⠀⠀⠀⢫⠑⠌⢆⠀ ⠀⡠⡲⢿⢇⣈⠃⡄⠀⡯⠀⢎⠁⠃⠀⠀⠀⠉⢹⠀⠘⡀⠀⠀⠀⠀⡇⢸⢸⠆ ⠸⣱⠁⡜⢦⠁⠈⠌⡶⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣢⢄⣀⡴⠵⣣⠏⢸ ⡆⠣⢦⢊⣈⡵⠂⡜⠀⢀⠔⢩⣀⣀⠤⠓⠤⣀⠤⠅⠀⡶⠏⠔⣈⡗⠈⠀⠀⢸ ⠣⠀⠀⠉⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠉⠒⠀⢃⠀⠀⢀⠆
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣿⡟⣻⣿⣿⣿⣿⣿⣏⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡵⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡻⣦⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⡀⠉⠉⠀⠀⠀⠈⠁⠀⠀⣠⠴⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢀⣿⠿⠛⠉⠉⠉⠉⠙⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⣌⠀⠀⠀⢀⡴⠊⠁⣀⣤⣤⣤⣄⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠓⠦⣀⢀⠀⠀⠈⢁⡴⠋⠁⠀⣀⣀⣀⣀⣀⡀⠀⣿⠀⠀⠀⣶⣶⣯⣽⣿⣿⣶⣶⣌⡹⢦⢀⣸⠁⠀⣾⠋⠠⠀⠀⣽⣷⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⣴⠏⢀⣤⡶⠶⠶⣦⡀⠈⠳⣆⠀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠃⠀⢿⡀⠀⠀⠻⣿⣟⡛⠋⠉⠛⠛⠿⠟⠘⣏⣹⠀⠀⣷⡐⣃⣒⣤⣿⡿⠀⣀⣿⠀⠀⠀ ⠀⠀⣴⣿⠀⢸⡟⠀⠀⠀⠈⢿⡄⠐⣧⡜⠁⠰⡿⠟⠋⠉⣁⣤⣤⣀⡀⠀⠀⢸⡇⠀⢀⣴⣿⣿⣿⣾⣶⣤⡀⠀⠀⠀⢹⣿⣆⠀⠙⠿⣿⣿⡿⠟⢁⣤⣿⠟⠀⠀⠀ ⠀⢰⢿⣿⡄⠸⣿⣮⣀⣀⣠⣾⠇⠀⣿⠇⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣦⡀⢸⣧⢸⣾⣿⡿⠟⠛⠻⢿⣿⣷⣄⠀⠀⠈⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠘⣿⣷⣄⠙⠻⠿⠿⠟⠋⢀⣼⣿⠀⠀⠀⠀⣾⣿⠿⠛⠉⠉⠉⠻⢿⣷⢸⣿⢸⣿⠁⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⢸⢿⠁⠈⠭⠽⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠿⣿⣶⣶⣶⣶⣾⢿⣿⣿⠀⠀⠀⢸⣿⡏⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣷⣀⡀⢰⣧⡄⢠⢀⣸⣿⡇⠀⠀⠈⣿⠛⠃⠀⢻⣰⣆⠀⠀⠀⠀⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⠉⢉⠉⠃⠀⠈⣿⠀⠀⠀⠸⣿⣇⣀⣀⣺⣿⡧⢷⣿⣿⣿⣿⣿⣿⣿⡍⠛⢛⣛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣄⠀⠂⠀⠈⠉⠁⠄⠀⠀⠀⠹⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣦⠀⢠⡐⢶⠈⠙⣿⣿⣶⣶⣶⣿⣿⡿⠛⢉⡥⠒⠘⢻⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠈⠉⠓⠟⣯⡉⣩⣭⣭⣝⡳⣄⠀⠀⢤⠙⣷⣄⠀⠀⠰⠀⠀ ⠀⡀⠀⠀⣀⠐⠿⠷⣀⠀⣷⠆⢀⣼⡿⠿⠟⠛⢿⣿⡏⢠⡾⠋⠀⠀⠀⠀⠀⠀⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣧⡐⣿⡙⣿⡼⡆⠀⠀⣬⡥⢄⠀⠀⠀⠀⠀ ⡀⠈⣀⠀⠉⠀⠐⢆⠈⠉⣁⣀⣨⠏⣠⡶⣿⣶⣶⣿⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣧⣿⣿⣿⡇⢿⠀⢸⠁⢀⡈⢳⡀⠀⠀⠀ ⠀⠀⠉⡉⠀⣀⡀⠘⠻⢦⠀⠙⡏⣠⡟⠀⢘⣿⣿⡏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣂⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⠹⣿⣿⡿⠁⢸⣄⣹⡷⣄⣀⠀⠙⠦⠀⠀ ⠀⠀⠈⠷⣤⠋⠀⢀⡀⢠⡀⣾⡇⢻⣷⣭⣭⣿⢿⣷⣸⣿⣷⣤⣤⣤⣤⣤⣶⡿⠿⢿⣿⠿⠿⣿⠟⠛⣿⠟⢛⣿⠛⢻⣿⣀⠈⠉⢀⣠⣾⣏⠙⣦⣤⡼⠉⠉⠳⡄⠀ ⠀⠀⠀⠀⠘⠳⢶⣿⠀⠈⢻⡍⢿⣄⠙⠿⠟⢋⣨⣿⠿⠻⣟⠟⢻⣯⣉⣩⣿⣄⣠⣼⣷⣤⣴⣿⣶⠚⠛⣷⣾⡙⢳⣿⡟⠻⡛⣿⣿⠟⠁⢈⡱⣋⢺⡄⠀⠀⠀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠻⣌⢿⣿⣶⣾⠿⠿⠿⠶⠞⠉⠙⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣧⡲⢸⡀⠲⠀⢳⡀⠀⢦⢄⣰⠟⢁⡀⠙⠶⠶⢚⡁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡀⢰⡛⠈⢟⣧⠀⠀⣀⠉⢀⣀⣀⣀⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣿⣄⠀⠉⠈⣧⠀⠀⠀⠀⠈⠀⠀⠙⡆ ⠀⠀⠀⠀⠀⣧⡀⠀⠀⠈⠳⡀⠑⠠⢟⡉⢐⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠻⣦⠴⠛⠦⢤⡖⢄⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⢿⢳⣄⣀⣲⡶⢲⠖⠂⠉⣡⢾⣿⠋⠈⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⡿⢿⣦⣄⣀⣤⠾⠛⣧⠀⠺⠟⠳⡌⠑⠀⠀⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⡽⢦⣅⣼⣤⡀⣸⠃⢿⣥⣄⣠⣽⣿⣿⠟⠿⣿⡷⠿⣿⣿⠛⢻⣿⣿⢟⣻⣿⣛⣿⣿⣭⣿⡷⠾⠛⠛⠉⠀⣠⣴⣟⡆⠀⠀⣴⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠀⣾⣭⣽⣿⠀⣀⠾⡛⣦⡀⠀⡉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡿⢋⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠙⠓⠶⠴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢀⢏⡞⠙⣞⢿⣦⣵⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡿⠋⠀⠀⠂⠀⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠋⠘⣇⠀⠋⣀⡝⢿⣮⣛⡿⢿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠿⣟⣻⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⢋⣤⢼⣧⡉⢻⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣽⣷⣶⣾⣿⣿⣇⠀⠀⠀⣸⠀⠘⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗⠈⡿⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡈⢁⣠⢿⣟⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⢩⠀⠈⣀⡬⠙⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠦⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⢉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⢹⣋⣀⣠⡀⠀⠈⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⢀⡟⢉⣉⢹⣆⣀⣀⣀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⣀⣴⣟⣻⣦⣧⣿⣋⣉⣙⣛⡿⣶⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣟⠉⣉⣉⣙⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠟⠛⠛⠻⢿⡿⢿⡟⠉⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢸⡇⠸⣷⣀⣠⣴⣾⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⣴⣿⠁⠀⠙⠉⢉⡽⠛⣅⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡛⠉⠁⣀⣠⠤⢶⠋⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⢻⠋⠉⢹⡀⢀⣀⣧⣴⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣤⡤⡀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠛⠛⠉⠉⣉⣨⡿⣿⣶⣾⡷⠶⠶⠒⠛⠋⣿⣿⠻⣗⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠟⠛⠛⢻⡟⢯⣁⣠⣿⢻⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠹⣦⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⡟⠈⠀⠀⠀⠘⣧⠘⣿⣿⣧⣾⠇⠉⠀⠀⠀⠀⣴⣶⠀⠀⠀⠘⣧ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢠⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⣿⠏⢀⣤⠤⠶⢚⣋⣿⡇⠀⠀⠀⠀⠸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⣷⠂⠛⠉⠁⢸⣇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠘⡇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠻⢦⣀⣰⠏⢻⡄⠀⢀⣠⠾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣳⣶⣆⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢿⠀⠀⠀⡛⠻⠶⣽⣁⡀⢸⣷⠺⡏⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣍⠉⠻⣟⠀⠀⢹⡇⠀⠀⠀⠀⢸⡇⡀⠾⢥⣤⡤⠄⠈⣿⠀⣿⠀⢻⠀⢀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣧⣤⡿⠤⣄⠀⣿⢦⡄⠀⠀⢸⡿⢧⣤⠀⠀⠀⠀⠀⢹⣷⣿⣀⣼⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢹⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⢧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡙⣼⣿⣧⡀⠀⠀⠀⠀⣸⠆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢦⣄⣤⣴⣿⣟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢌⢿⣻⣝⢒⣶⠖⠋⢁⡴⠛⠀⠀⣀⡠⠤⠤⠤⠐⠒⠒⠒⠢⢽⣿⣶⣤⣤⣤⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠈⢻⣮⣋⣀⣠⣴⣿⣇⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣶⣤⡀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣾⣿⣿⣿⡿⢿⣿⣿⣷⠀⢠⣿⡋⢹⠛⣿⣶⠈⣉⣿⣇⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⣿⣿⡯⠟⠁⢿⣶⣿⢿⣿⣿⣧⠀⠘⠿⠿⠛⠀⢀⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⡿⠀⠀⣿⣿⡀⠀⠀⠀⠉⠁⣸⣟⣛⣿⣦⣄⣀⠀⢀⣴⣿⣿⠟⠀⠀⠈⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠛⢿⣿⣦⣄⣠⣴⣾⣿⣿⣿⣿⣿⡿⠻⠿⠿⣍⣁⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢉⡽⠟⠋⠁⠙⠛⠛⣿⠛⠋⠁⠀⠀⠀⠀⠈⠙⣦⠴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⢀⣀⡤⢞⣿⠙⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠞⢻⣿⠘⣷⣤⣤⣀⣀⣠⣤⣖⣫⣥⠾⢿⠿⣿⣿⡿⠶⠞⠋⠀⣷⣟⣠⢤⣤⡤⠤⠤⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⡴⣾⡋⠀⠀⠈⣿⣧⡉⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡁⠙⣷⣿⣿⡄⠀⠀⠈⢧⡀⠀ ⠀⠀⣀⡼⢠⣿⠀⠀⠀⣰⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣟⣛⡛⠻⣿⣿⣿⣿⡆⠀⠀⠀⢇⠀ ⣠⢞⠿⣷⡘⠁⠀⠀⣰⣿⣿⣿⡿⣿⡿⠿⠷⢶⣶⣶⡶⠿⢿⣿⠟⠛⣉⣿⠿⠛⠋⠉⢹⣿⠛⣯⠻⣿⣿⣿⠀⠀⠀⠈⠆ ⠁⠋⠸⣿⣷⣄⣀⣴⣿⣿⣿⢏⣰⣿⠀⠀⠀⠀⢀⢉⣻⣿⠛⠙⢳⣾⣿⡧⠀⠀⢠⡀⣼⠇⠀⢹⣧⣿⣿⡿⠀⠀⠀⡰⠃ ⠀⠀⠀⢿⣿⣿⣿⣿⠿⣿⢧⡞⠘⢿⣄⢀⠀⠀⢻⣿⣿⣿⣇⣠⣾⠛⠛⠃⠀⠀⢀⣿⡏⠀⠀⠀⠘⣿⣿⡇⣠⠔⠋⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣶⡟⢸⠁⠀⠀⠙⣿⡶⠀⠀⢉⣼⡟⠉⠉⠹⣷⡆⠀⠀⠀⣸⡿⠀⠀⠀⠀⢀⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠈⠉⠀⠀⠛⣏⠛⣛⡿⠋⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠛⠛⠉⠉⠛⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⢠⡇⠀⠀⢀⡴⡫⠭⠭⢓⢤⣀⠀⠀⠀⠀⢀⡤⡚⠭⠭⢝⢦⡀⠀⠀⢸⡄⠀ ⠀⣼⠀⠀⠸⢭⣊⡀⠀⢀⣀⠽⠊⠀⠀⠀⠀⠓⠯⣀⡀⠀⠀⣑⡯⠇⠀⠀⣧⠀ ⢰⠇⢀⡤⠤⢄⠀⢹⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡏⠀⡠⠤⢤⡀⠘⡆ ⣾⢠⠃⠀⠀⠀⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠘⡄⢷ ⢿⠘⡄⠀⠀⡠⠃⠈⡄⠀⢠⠀⣀⠠⠤⠤⠄⣀⠀⡄⠀⢀⠃⠘⢄⠀⠀⢀⠇⡼ ⠘⣦⠈⠉⠉⠀⣠⠔⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠚⠲⣤⠀⠉⠉⠁⣴⠃ ⠀⠈⠳⢦⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⡠⠞⠁⠀ ⠀⠀⠀⠈⢳⡄⠱⡜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠎⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠘⠦⣑⠢⣀⡀⠀⠀⠀⠀⢀⣀⠄⣊⠴⠃⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠉⠒⠮⠭⣤⣦⠭⠵⠒⠋⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠪⣉⠉⠉⢉⠕⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠦⠭⠭⠶⢶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣖⡒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣲⠶⠒⣀⣠⡍⠓⠀⠉⠲⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠞⣡⠎⢠⡴⠋⠁⠀⣀⣀⣀⠀⠀⠘⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠤⠤⠤⠚⣁⡾⠁⢠⣿⠁⠀⣴⣿⣿⣦⡈⠃⠀⠀⡘⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⠶⠶⠿⢿⡇⠀⢠⣿⠀⡸⣿⢿⣿⠻⢷⡀⣰⣾⣷⣾⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⣰⢷⠀⠘⣿⡄⠀⣿⣼⣿⠖⠾⢿⣿⣿⣿⣋⠁⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣤⡆⣬⣥⠾⠀⠀⡇⣻⢦⡉⠉⢿⡇⣠⣴⢿⡿⣿⣿⡛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡉⠲⠖⠀⢀⡼⣱⠏⠀⠈⠀⠘⣿⣯⢠⣿⠁⠀⠙⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣴⣺⠯⠞⠁⠀⠀⠀⠀⠀⢟⣿⠟⠁⠀⠀⠀⢀⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣴⣶⠛⠙⠛⠷⣦⣤⣄⣀⣀⠀⠀⢰⡟⣅⣤⣴⡞⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣷⣽⣿⣿⣿⣿⣶⣍⠙⢯⡁⠀⠀⠈⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⣈⣻⣿⡟⣿⣿⣿⢿⣿⣆⠈⣷⣀⠀⢀⣿⣿⣯⡇⢘⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣀⠙⠒⠛⠿⣧⣽⣟⣿⡿⠃⢹⡿⠁⣨⠿⣿⡿⢭⡽⠷⣛⡉⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⣆⠀⠀⠈⠉⠛⠛⠛⠓⢛⣧⠟⠁⠀⠘⢿⣦⡀⠀⡙⢿⣿⣄⠀⢀⣤⠶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⢸⢹⡄⠀⠀⠀⠀⠙⢦⡴⠋⠁⠀⠀⠀⠀⠀⢻⣿⡄⣸⣦⠋⣯⢷⣿⡁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠘⡎⢷⠀⠀⠀⠀⠀⠘⢿⣶⣄⣀⣀⡀⢀⣤⣾⡿⠷⣿⣿⣠⣿⠄⠈⣿⡆⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⡙⠻⢷⡇⠸⡗⠦⣀⡀⠀⠀⠈⢿⣮⡉⠙⠻⢿⣿⣿⡥⠎⢹⠹⣿⠟⣠⡾⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠠⣶⣶⠦⠤⣄⣀⠀⠀⠙⠳⢤⣀⢀⡿⠀⠀⠙⠓⢦⣤⣀⣙⣛⣿⣛⣞⣻⡟⠀⢠⣼⣿⡷⠿⠉⠀⠀⠀⠀⢰⣿⠀⠀⠀⣀⠤⢀⣾⣿⣿⠿⢿⣿⡟⠀⠀⠀ ⠀⠀⠀⣿⢿⣶⣦⡀⠉⠙⠲⢦⣄⠀⠉⠉⠀⠀⠀⠀⠀⠈⢷⠀⠈⠉⠛⣿⢹⣿⠃⣀⣾⣟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠸⣅⣰⣿⣿⣿⣿⣦⡀⢉⣄⠀⠀⠀ ⠀⠀⠀⣿⠈⢻⣿⡿⣦⣄⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⣠⠞⠷⣤⣄⣀⣼⡇⠀⠀⠀⢸⡿⣧⣱⣄⠀⠀⠀⠀⢘⣹⡇⠀⠀⢀⣴⣿⣿⡇⠈⠻⣿⢛⡏⠀⡆⠀⠀ ⠀⠀⠀⢿⡆⢸⠏⠿⣦⡙⢷⣄⠀⠀⠀⠀⠙⣦⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣷⠈⢿⣄⠂⠀⠀⠀⢈⡿⠀⠀⢠⣾⠟⠉⣙⣿⣦⡞⠉⠉⢳⣶⠁⠀⠀ ⠀⠀⠀⠘⣿⠄⠠⠞⢻⣷⣌⢿⣷⣄⠀⠀⠀⢹⣻⡗⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠻⡄⠈⠻⣧⡀⠀⢠⣾⠃⠀⣠⣿⣿⣷⣼⡃⠀⢙⣿⡧⠤⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣤⠄⢀⣴⡿⢿⣦⠻⡟⠋⠀⠀⠀⢹⡇⠀⠀⠈⠉⠓⠒⠲⠤⢤⣄⣀⣈⡀⣀⣿⠀⠀⠈⠛⢶⡿⠛⢦⣼⣿⣿⣿⣿⣿⣿⡒⠋⣹⣷⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣞⣾⠋⠄⠀⠈⢷⡘⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣁⠀⠀⠀⠀⠀⠙⣶⣿⣿⣿⣿⣿⣿⡿⣿⠉⠛⠁⢸⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠃⠁⠀⠀⠀⠈⢻⡄⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠸⣷⣦⣄⣠⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡏⠐⠀⡀⠀⠀⠀⠀⢻⣦⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣠⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠁⠀⢰⠀⠀⢀⡿⠁⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣀⣠⠾⣥⡤⢤⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠀⣄⣄⣐⠃⠀⣸⠀⢀⡏⢻⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⣶⠟⣻⣭⡙⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠴⠖⢾⣿⣿⣷⡄⠈⣿⣬⠇⠀⠀⠀⠀ ⠀⠀⢠⠟⠀⠈⣿⢿⠁⠀⣴⠃⢀⡞⠀⠀⢿⡄⠀⠀⠀⠉⠓⢠⣀⣄⣴⡿⢁⣼⠟⠉⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⠀⠀⠀⠙⣿⣿⣿⣾⣼⠟⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠈⠀⣴⠁⢀⡞⠁⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢉⣿⣿⣴⣟⡷⣄⠀⢦⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣄⠀⢶⡀⠈⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⢸⠁⢠⡞⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣰⣿⡏⠸⣿⡉⠁⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣧⡝⣿⡄⠀⢿⣦⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣟⢻⢶⣤⣀⠀⡀⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣼⡿⢯⣿⡄⠙⢿⣶⣵⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣷⣀⣼⣿⣄⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠈⡖⠒⢲⡞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣄⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⡜⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠈⠳⡀⠀ ⠀⠀⠀⣧⠀⢀⡇⣠⣏⣀⣀⣀⣀⣀⠀⠀⠀⠀⡠⠊⣠⠴⡇⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⢹⡀⢸⣷⠏⠀⠀⠀⠀⠀⠀⠉⠳⢦⣎⣠⠞⣵⣴⡇⠀⠀⠀⠀⠸⡆ ⠀⠀⢠⢞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠈⢻⡟⠋⠁⠙⣄⠀⠀⠀⢰⡇ ⠀⢠⠏⢸⣄⡴⢲⣤⡀⠀⠀⠀⢀⠂⢀⡴⢲⣤⡔⢳⠀⠀⠀⠀⠉⠒⠊⠉⠀ ⢀⡞⠀⢘⠏⠀⢰⡇⢹⡄⠀⠀⡌⠀⡎⠀⢀⡏⢯⠉⣇⠀⠀⠀⢠⡀⠀⠀⠀ ⢸⡇⠀⢸⡦⢤⣾⣧⢸⣿⠀⠀⠆⢰⣷⣦⣾⡀⣸⡄⢸⠀⠀⢠⣿⣷⡀⠀⠀ ⠀⢃⠀⠸⣧⣀⣿⢉⣽⠿⠂⢶⡶⠺⢿⣿⡏⣹⣿⡇⢸⠀⢠⣿⣿⠏⡇⠀⠀ ⠀⠘⣆⠀⠀⠈⠉⠉⠀⢤⣤⠼⢷⡤⠃⠈⠉⠉⢁⡴⠃⢠⣿⣿⠃⢀⠇⠀⠀ ⠀⠀⠈⠑⠦⢄⣀⠀⠀⠀⠙⢶⡞⠁⠀⣀⣠⣴⡋⠀⣠⣿⡿⠁⡰⠃⠀⠀⠀ ⢀⣀⠤⢴⠖⠊⠉⠉⣑⣤⣶⣿⣿⡟⠛⠋⢹⣿⣿⣶⣿⠋⠑⠊⠀⠀⠀⠀⠀ ⢸⠀⠀⠸⡄⠀⠀⡄⠹⣿⣿⢻⣾⣿⡄⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣧⠀⠀⢧⣠⠞⣷⠀⠀⠀⠀⠉⡇⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⢱⣖⠉⠀⢰⡏⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣹⠈⠑⠶⣉⣀⣀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⢹⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⣀⠀⠀⣈⣆⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣅⡧⠤⠴⠶⠾⢿⣟⠃⠀⢉⣽⠛⠻⣯⡉⠀⢠⣿⣤⣤⣤⣿⣿⣷⣶⣶⣾⣿⣿⣧⣶⣾⣿⣿⣿⣿⣯⣴⣷⣾⣷⣬⣿⣷⡞⠉⠰⣿⠇ ⠀⠹⣿⣷⠖⢲⣶⣶⢿⣿⢃⣤⣌⣿⣦⡀⢼⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣉⣹⣏⡉⠻⣿⣿⡆⠂⠐⠀ ⠀⠀⣾⣿⢿⡿⢠⡥⠀⠻⠋⠀⠙⢿⠂⢹⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡴⠋⠩⠘⠉⠙⠳⣄⠈⣿⡄⠀⢀ ⢠⣿⣿⠁⢸⣿⡟⠀⠀⠀⠀⠀⠀⢸⡇⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠹⣆⢹⣷⠀⠾ ⠀⠀⠀⠀⠀⢻⡻⣄⠀⠀⠀⠀⢠⡟⣰⣿⣿⣿⠏⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣛⢿⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡿⠀⠀ ⠀⠁⠀⠀⠀⠀⢳⣍⠳⣤⣞⣰⠏⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣯⡳⣄⣤⠀⠀⢀⡼⠁⣿⣧⡄⢀ ⠀⠀⠲⠀⠀⠀⠀⠙⠿⠿⣽⣥⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⣿⣿⣮⡉⠳⣶⣋⣠⣾⣿⣿⡄⣸ ⠀⠀⠈⠁⠀⠀⠰⣶⣶⡾⠋⢡⣿⠟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠹⠋⠻⢷⣿⣿⠟⣋⠙⣿⣯⣤⠋⣿ ⠈⠀⠊⠀⠀⠀⠀⠹⠋⠀⠀⣸⡏⣐⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢖⡀⢹⣿⣷⡀⢼⣿⠟⣿⠀⠘ ⢀⣀⡀⠀⠀⠀⠀⠀⣰⡆⡀⣿⠙⠛⠋⠉⠙⠻⣿⠇⠀⠀⠀⠀⠀⢾⣿⠿⠛⠛⠛⠻⢿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠺⡏⠀⣉⢠⣀ ⠘⣿⣿⡷⠂⠀⠀⠀⠈⠠⠀⣿⣦⠀⢀⣴⣿⣷⣮⣁⠀⠀⠀⠀⠀⠀⣠⣴⠶⢦⠶⡷⠀⠀⠀⠀⠀⠠⡄⠀⠀⡄⢸⣿⣿⣿⣾⣧⡀⣽⣾⣽ ⠀⠋⠁⠀⠀⢰⣷⣦⡀⠀⠀⣼⣿⢀⣼⣿⣿⠛⢻⣟⢻⡍⠉⢀⣴⣿⣿⣷⠞⢿⣟⢲⣿⣆⠀⠀⠀⠙⠻⣤⣼⣶⣻⣿⣿⣿⢿⣿⣿⠈⢻⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠗⠀⢹⣧⠚⣿⣿⠻⣆⠈⠛⠿⡇⠀⢸⣿⣿⣿⣿⡄⠈⠛⠟⢋⣿⠀⠀⠀⠀⠀⢿⣿⣟⠻⣿⣿⣿⣾⣟⣿⣷⡄⢿ ⠀⠀⠀⠈⠀⠀⠛⠋⠁⠀⠀⢸⣿⣷⡜⣿⣶⣿⣷⣶⣾⠃⠀⠀⢿⣿⣿⣿⣿⣷⣶⣶⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣆⣸⣿⣿⣷⡛⢻⣿⡇⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠿⠿⣿⣿⣿⣿⣷⣶⣶⡄⠻⢿⣿⣿⡿⣿⣟⠋⠀⠀⠀⠀⢀⣤⠘⣿⣿⣿⣿⡟⣿⣿⣿⡇⣀⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⡿⠉⠀⠀⠀⡿⠿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠠⡼⠃⠀⣿⣿⣿⢿⢤⠸⣿⣛⣇⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⠀⠀⠀⠀⣿⣿⣿⡏⣼⣦⢿⠉⣵⣿⣽⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡷⠀⠀⠀⢀⣴⢿⣿⣿⣷⣿⡟⢸⡟⠻⠟⠸⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣸⣿⣠⣤⠶⠛⣻⡟⠀⠀⣿⣿⠀⣤⣗⠀⣤⢌⠀ ⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠘⣯⡀⠀⣀⠀⠀⠀⠀⢀⣯⡴⢿⣿⣾⠿⢿⣤⢼⡿⠁⠀⠀⣼⣷⣦⠉⣿⠀⢛⡈⠀ ⠀⠀⠀⠀⠀⠛⠛⡂⠀⠁⠀⠀⠀⣈⣿⡟⠲⣖⠚⠉⣿⣽⣟⡓⠒⠶⣶⡶⠚⣻⣯⣤⣾⣿⡀⣠⡼⠟⠈⠀⠀⠀⣼⣏⣿⡟⠀⣿⠀⣼⡅⠠ ⠀⠀⠀⠀⡄⠀⠀⠈⠀⢠⣠⣶⣿⡟⣿⣷⠒⢹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⡏⢀⡨⠟⠉⠀⠀⡄⠀⢠⣴⣿⣿⣭⣇⠀⣿⣶⡿⢿⠿ ⠀⠀⠀⠀⠀⠀⠀⠆⠀⣾⣿⠿⣿⠿⣿⣟⣷⣴⡋⠉⠙⣿⣿⡿⠋⠉⢻⣿⣅⣠⣤⠟⠋⠁⠀⠀⠀⢰⡇⣠⣾⠋⠛⢿⣿⣿⣿⠟⠞⠁⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠒⠀⣿⠿⠻⠈⠙⠛⢛⡛⠻⠿⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⢲⡀⢈⣿⠋⠉⠀⣦⣦⢻⣿⡇⠀⠀⠀⠀⠀ ⢴⠃⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⣴⣿⣷⣧⡐⠎⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⡷⠿⡿⠀⠀⠀⣿⣇⠘⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⣄⣀⣼⣿⣿⣽⠟⠿⢶⣶⣶⣤⣤⣤⠤⣤⣦⣤⣤⣄⣀⣴⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠀⣀⣗⠀⠀⠀⠀⢀
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⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⣿⠆⠀⠀ ⠀⠀⢠⣾⣿⠋⢀⣿⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠋⢀⣾⠋⠀⠀⠀ ⠀⣠⣿⡿⠁⠀⣼⠇⠀⠀⠀⠀⠀⣴⣿⡿⠋⢀⣴⠟⠁⠀⠀⠀⠀ ⢠⣿⣿⠁⢀⣼⠏⠀⠀⠀⠀⠀⣴⣿⠯⠴⢿⡟⠁⠀⠀⠀⠀⠀⠀ ⢻⣿⣯⣼⡿⢿⡀⠀⠀⠀⠀⢸⣷⡏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⢺⣿⡏⠁⠀⠸⣧⠀⠀⠀⠀⣾⣿⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⠀⠀⠀⣿⠀⢀⣀⣤⣽⠿⠧⣤⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣧⠀⢀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣷⣿⠋⣿⠀⠀⢀⣀⡀⠀⣰⣶⣦⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⣿⣿⡏⢠⣿⣿⡿⢷⠀⢻⣿⣿⢹⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡇⠘⣿⡿⢇⣼⡟⣾⣿⣷⣿⠟⠿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠹⣦⣀⠈⠉⡽⠋⠀⠛⠛⠋⠁⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣶⣄⠉⠛⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣍⡛⠛⠛⢶⣄⠤⡤⠤⠒⠃⠉⢙⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣦⣀⣀⣠⣴⣖⡋⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⡿⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢦⠀⠀⠀⠀ ⠀⠀⣼⣿⠃⠀⠀⢸⣷⣿⣿⣿⡟⠛⠉⠀⠀⠉⢻⣷⣬⣧⠀⠀⠀ ⠀⠀⡧⢸⡄⠀⠀⠀⣿⡇⠙⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⡉⢧⠀⠀ ⠀⢠⡿⠾⣷⣤⡴⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣧⠘⣆⠀ ⠀⣾⡇⢠⡟⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣆⣼⡀ ⠀⢿⣷⣾⡇⠀⠀⢀⣿⣷⢀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠤⢿⡿⠟⠃ ⠀⠀⠈⠁⠉⠉⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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