Sad Text Face Creation Emojis & Text

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⡴⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠳⡆⠀ ⣇⠰⠉⢙⡄⠀⠀⣴⠖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠁⠙⡆ ⠘⡇⢠⠞⠉⠙⣾⠃⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠄⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⡄⠀⣏⣆⣀⡍ ⠀⢠⡏⠀⡤⠒⠃⠀⡜⠀⠀⠀⠀⠀⢀⣴⠾⠛⡁⠀⠀⢀⣈⡉⠙⠳⣤⡀⠀⠀⠀⠘⣆⠀⣇⡼⢋⠀⠀⢱ ⠀⠘⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡴⢋⡣⠊⡩⠋⠀⠀⠀⠣⡉⠲⣄⠀⠙⢆⠀⠀⠀⣸⠀⢉⠀⢀⠿⠀⢸ ⠀⠀⠸⡄⠀⠈⢳⣄⡇⠀⠀⢀⡞⠀⠈⠀⢀⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⢧⠀⠀⢳⣰⠁⠀⠀⠀⣠⠃ ⠀⠀⠀⠘⢄⣀⣸⠃⠀⠀⠀⡸⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⣇⠀⠀⠙⢄⣀⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⡿⠛⠁⠀⠉⠛⢿⣿⣿⣿⣧⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⢀⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⠉⠉⠉⠉⠉⠛⠒⠾⢤⣀⠀⣀⣠⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢭⡀⠀⠈⣷⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⡟⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀ ⣾⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠸⡇⠉⣷ ⣿⠀⠰⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣧⡴⠋ ⣿⠀⠀⢸⠛⢫⠀⠀⢠⠴⠒⠲⡄⠀⠀⠀⠀⡝⠛⢡⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀ ⢸⡄⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡼⣄⠀⠀ ⠀⢳⡄⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⢀⡼⠁⢸⡇⠀ ⠀⠀⠙⢦⣷⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⣀⡴⠟⠒⠚⠋⠀⠀ ⠀⠀⠀⠀⠈⠛⠾⢤⣤⣀⣀⡀⠀⠀⠀⠀⣀⣈⣇⡤⣷⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠩⣉⠉⠉⠉⣩⠍⠁⠀⢷⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠐⠦⠤⠼⠂⠀⠸⠥⠤⠔⠂⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣧⡟⠳⠒⡄⠀⠀⠀⡔⠲⠚⣧⣀⣿⠿⠷⣶⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⢀⠀⠀⡗⠀⠀⠀⡇⠄⢠⠀⣼⠟⠀⢀⣨⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢶⠬⠴⢧⣤⣤⣤⣽⣬⡥⠞⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠒⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣦⣤⣤⣤⣄⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠿⢟⡛⠻⡉⠏⣭⣏⡙⠙⠛⠛⠿⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠋⣥⣶⣯⠒⢨⠁⡔⡈⠘⣿⣿⣾⣴⣿⡄⢂⠄⠩⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠛⠡⢠⢁⣣⣾⣿⡿⠈⡄⢃⠔⡡⠡⢈⠛⠻⣟⣛⣽⣦⣬⣁⡎⠡⡀⢍⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⡄⡌⠱⠰⣿⣿⠿⠏⣁⠒⡈⠔⡨⢐⠡⢊⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠐⡄⠛⣿⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⡏⢄⠣⡐⠌⡁⢆⣵⣦⣶⣾⣶⣷⣶⣬⣄⠡⢊⢴⣿⣿⣿⣿⠏⠉⢻⣿⣿⣿⣿⣿⣷⣄⠑⡈⠻⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⡿⢁⠒⡌⠒⢠⣣⣾⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣷⣆⣾⣿⣿⣿⣿⣦⣄⣴⣿⡟⠀⠀⠈⠙⠿⣧⡐⠡⡘⣿⣷⡀⠀⠀⠀ ⠀⠀⣰⣿⡟⢠⠃⡜⠠⢱⣾⣿⣿⠿⢿⣿⣿⣿⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⣻⣷⡡⠐⡈⣿⣷⡀⠀⠀ ⠀⢠⣿⡟⡡⢢⠑⡠⢳⣿⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⠛⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⠀⠹⣿⣿⣷⣤⣤⣤⣶⣿⣿⣷⡡⠐⡜⣿⣧⠀⠀ ⠀⣾⣿⠡⣁⠃⡜⢰⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⡧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠋⠙⣿⣿⣷⢁⠰⢹⣿⡆⠀ ⢠⣿⡿⢀⠄⡣⠘⣿⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣯⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⠋⢻⣿⣦⣶⣿⣿⣿⡆⠂⢆⣿⣷⠀ ⢸⣿⡇⠂⡌⠥⢹⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⡀⢀⣀⣿⣿⣿⣿⣿⣿⠟⠁⠈⣻⣿⣧⣈⢂⣿⣿⠀ ⢸⣿⡇⠒⣈⡑⢺⣿⣿⣿⣷⣤⣿⣿⡉⢹⣿⣿⣿⣷⣄⣀⣤⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠈⠁⠉⠻⣮⣽⣿⠀ ⢸⣿⡇⢡⢀⡃⢌⣿⣿⣿⠉⠙⠻⢿⣿⣿⠿⠟⠛⠋⠙⣿⣿⣿⣿⣏⡷⣩⠿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀ ⠈⣿⣿⢀⠢⡑⣼⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⡟⣼⡳⡝⡞⢫⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠈⢿⡟⠀ ⠀⢿⣿⡆⢡⠏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⣿⡞⣡⢧⣙⡬⢓⣼⣿⣶⢦⣤⣀⡀⠀⠀⢀⣀⣠⣴⢿⡿⣇⠀⠸⠇⠀ ⠀⠘⣿⣷⣌⠳⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⡈⢡⢢⣼⣶⣿⣿⣿⡿⠂⢌⠹⡛⢟⡻⡛⢿⠻⣑⢎⡴⣯⠀⠀⠀⠀ ⠀⠀⠸⣿⣧⡛⣼⡇⠀⢻⣶⣦⣤⣤⣤⣤⣤⣤⣴⠶⠛⠋⢄⠂⡜⣷⣿⣿⠟⢛⠋⡉⠤⠑⠌⡒⠌⢡⠃⡝⠢⠙⡌⠂⢌⡷⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣷⡼⠂⠀⣿⢣⠾⡛⣔⢣⠣⡝⡘⠤⡈⢌⠱⠈⡄⣿⣿⣿⠡⣈⠢⡘⢄⠃⡉⢆⡁⢎⠰⡈⢄⠣⡑⢠⢹⣾⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⡄⠀⣿⠃⠎⡱⢈⠡⠃⡔⢠⠃⢌⠢⣁⠣⢀⡉⠍⡐⢄⠢⡐⠡⢌⢂⠱⡀⠆⡌⠰⣈⠢⣁⢘⣴⣿⠟⠁⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⢹⡆⠢⠑⡌⢢⠑⡄⠃⡌⢂⠒⠄⡊⠔⡠⠃⠜⡠⢂⠅⠣⡈⠆⢂⠅⡊⠔⡡⢄⡒⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⣧⣌⠐⣁⠒⣈⠒⢄⢃⡘⠤⢑⠨⠄⢣⠘⡀⠆⡌⡑⠄⠣⠌⢂⠡⢒⣰⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⣻⡆⠀⠀⠹⣿⣷⣤⣎⡠⠌⢂⠂⢌⠢⢁⠎⡘⠄⢃⡘⠰⢀⠅⢊⠡⣘⣤⣷⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⢤⢦⣿⠋⠛⠿⢿⣿⣶⣮⣴⣤⣧⣴⣰⣬⣤⣦⣥⣮⣶⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣛⡋⣁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⢻⠛⣟⢛⡛⣛⠋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⡒⢦⡙⢭⡑⡒⠦⣄⡀⠀⠀⠀⠀⢀⣀⡤⢤⠤⠤⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠫⣄⢋⡜⡰⡘⡔⢢⡙⡔⢢⠍⡓⢦⡴⠚⡍⢒⡘⢢⠍⣒⠱⢊⡌⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⢌⠲⢌⡒⢌⣱⡼⢬⠥⠶⣬⣕⣊⡱⢌⢳⡭⡘⢥⢊⡕⢪⠔⣩⠒⣌⠣⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⡸⢃⡜⢣⣜⠼⣛⠃⡼⢀⠟⡤⢠⡘⡸⠻⠼⣄⣧⢣⣜⣠⠼⡄⠿⡄⠿⣀⣇⣃⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⢢⠒⡥⢊⠥⣉⠖⠬⡑⠦⣉⠖⡡⢃⣒⣅⣣⣩⣌⡽⣥⡊⡔⢣⠜⡱⣈⠓⣌⠢⣍⠩⡍⡓⠦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⢈⢣⠱⢌⡃⠞⡐⢎⠱⣁⣧⠶⣚⣫⣭⠭⡼⢥⠧⡬⢭⣭⣙⢾⣰⠮⣴⣓⣻⡭⢯⠭⢯⠽⣽⣓⣞⡧⣄⠀⠀ ⠀⠀⠀⢀⡴⣊⢿⢡⠋⡴⢉⠦⣉⠎⡱⠮⢖⣫⡵⢞⡩⣅⡦⣵⣾⣶⣷⣾⣒⠒⠩⠯⣚⠫⢍⣢⠵⠞⣺⣿⢿⣿⣥⣟⠒⠫⣗⣧⡠ ⠀⠀⢠⠞⡰⢡⣾⢡⢋⠴⣉⠲⢄⣿⣙⣫⣍⣱⡬⠖⠋⠁⣼⣿⣦⣾⡟⠛⣿⣧⠀⠀⠘⠋⠉⠀⠀⣸⣿⣷⣾⡟⢻⣿⣧⠀⠀⠘⡅ ⠀⢀⠯⣘⢡⢃⠦⣑⢊⠖⡌⡱⢊⠤⢣⣉⡌⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⠀⡀⠔⠀⠀⠀⠀⣿⣿⣷⢿⣿⣿⠿⠿⠀⠄⡔⠁ ⢀⠮⡑⢆⠣⢎⠒⡬⣘⢢⠱⡡⢋⡔⡃⢦⢱⠀⠀⣠⡤⡄⣉⠛⠿⠚⣛⠩⢭⢤⣄⡞⡘⢄⡒⢲⢀⠠⢭⠥⢄⡀⡒⢌⠍⡋⠁⠁⠀ ⣜⠊⡕⣊⠱⣊⠱⢢⠅⣆⢣⡑⠣⡔⣉⠆⡚⠀⠘⢤⢩⡙⢭⠁⣪⠙⣋⣛⡭⣏⠒⡀⡕⣊⠜⡡⠊⠱⡌⠚⣄⡒⠕⠊⠈⠀⠀⠀⠀ ⣇⠉⠶⢁⠷⡈⢱⠇⡸⢰⠆⣉⢱⠸⣀⢉⡰⠀⡸⢆⡁⡎⡆⢰⣁⡿⠏⣱⠸⣀⠏⡸⡀⡉⠿⢷⣇⢷⡾⢷⠇⠸⢆⠀⠀⠀⠀⠀⠀ ⡧⣉⢎⡱⢢⢙⡂⢎⡱⢡⠚⢤⠃⢞⡠⢣⢸⢠⢃⠎⡴⣈⢆⠘⡔⡡⢍⠤⠓⡬⠸⡠⢅⠣⣍⠒⣌⡑⡌⠤⡙⡜⡘⠷⡄⠀⠀⠀⠀ ⡗⡰⠌⢆⠣⢎⡘⠆⡥⢃⡙⢢⠙⢢⣑⣢⣹⡐⡌⡚⢤⠡⢆⠀⡰⢑⠪⠜⡱⢌⡱⢂⠋⡔⢢⢍⢢⠒⠼⡐⡱⢌⠜⡄⡿⡀⠀⠀⠀ ⡧⡑⢎⡌⡓⠬⢌⡓⠬⡑⣌⠣⣽⠾⣭⠳⡝⣡⣛⠾⣦⢷⣈⠀⡧⣉⠎⡱⠡⢎⠰⣡⠘⢬⠡⢎⢢⡙⢢⢱⠁⢎⠬⡡⣰⣧⡀⠀⠀ ⡧⣑⠪⡰⢩⠜⢢⠜⣡⠳⣆⢣⡙⢿⣴⢻⡇⡷⣻⢮⣵⡮⡝⢰⠯⣝⡳⣗⡻⢦⡷⡴⣌⢢⣍⣦⣣⡼⣤⣃⡙⣶⠻⣝⣣⣽⠇⠀⠀ ⡗⠤⢣⠱⡡⢎⡑⠎⡔⠣⢎⠫⢜⡂⢦⢙⢣⢱⢧⣏⡶⡹⠅⣘⠷⡾⡵⣮⣵⢯⣼⣱⢃⣞⣜⣲⣣⣝⣦⡗⢠⣯⡽⢶⡟⠁⠀⠀⠀ ⣏⠜⣡⠣⡑⠦⣉⠞⣨⠑⡎⡱⢢⡑⠎⡌⠦⣠⠢⡌⢍⠛⢠⠯⢾⣵⣙⣦⣝⡲⣥⢋⡜⡼⣩⠳⣍⡞⡴⣭⢸⠲⣭⡳⠃⠀⠀⠀⠀ ⣈⣯⣔⡡⣙⢢⡑⢪⠔⡩⢔⡡⠣⢜⡸⢄⠣⠱⡢⢙⠬⡘⠆⢇⠲⡰⢌⠲⡈⡝⢡⢩⡙⢍⠍⡫⢍⢛⢍⡴⠋⠉⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣭⠓⣦⣽⣤⠙⣤⢣⡜⠑⡎⡔⢪⠑⡅⢡⡍⠒⠉⡎⢸⢡⠃⡎⣥⠑⡄⡆⢣⠘⡌⢲⠑⢪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⢿⣿⣿⣶⣧⣍⣛⢲⠚⠶⠧⠶⡵⣬⣱⡄⣞⣨⣱⣉⣔⢸⣊⣜⣰⣂⡵⢰⣉⡦⡃⠁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣯⣿⢾⣯⣟⡿⣿⡿⣿⣿⣷⣿⣶⣵⣦⣶⣴⣬⣦⣥⣹⣌⣂⣭⣩⣥⣭⣤⣷⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡷⣿⣻⣽⣟⣿⡷⣿⣻⡷⣟⣷⣿⣻⣿⢿⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣽⣿⣻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣟⣿⣽⢿⣾⢯⣿⢿⣽⣿⣻⣟⣾⢿⣽⣿⣿⣻⣿⣟⣷⣿⣷⡿⣷⣿⡿⣿⣾⢿⣿⣽⡿⣷⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠱⣾⡽⠿⣿⡟⠙⠙⠛⠙⠛⠲⢶⣮⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⡀⢠⣴⣶⣾⣿⣥⡦⢥⣾⣿⣿⣿⣟⡾⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢃⣶⣷⣤⣥⣾⣯⣭⣿⠿⠯⠕⢚⣛⣋⣉⣭⢻⣱⡹⣿⣧⡍⣭⣭⣭⣭⣭⣭⣭⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⣻⡏⡏⣥⣦⣤⣶⣶⣿⣿⣶⣿⣿⡿⠿⢿⣇⢻⢷⠽⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣮⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⢻⣹⣿⡄⠹⣿⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡬⣧⢿⣿⡇⢿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣮⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣿⣿⣆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠸⣿⢱⣿⣿⣷⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣙⠻⢿⢣⡀⠀⠀⠀⣀⠀⠀⠀⣀⣤⣴⣆⠀⠈⣿⢴⣧⣾⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣷⣎⢿⡀⠀⠘⣿⡟⡔⣛⡲⢬⡛⠿⠂⠀⢻⣮⢹⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣿⡿⠌⢿⣄⠀⠈⢱⡇⣿⣿⣷⡎⣑⡀⠀⢸⣿⢠⣙⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⡿⢃⣴⣾⡜⣿⣦⡀⠸⢱⣿⣿⡟⣼⣿⣿⣶⣶⣭⣾⠿⠧⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⢡⣿⣿⣿⣿⣬⣿⣫⣴⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⡠⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣛⣛⣛⣛⠻⠿⠛⠻⠿⠿⢿⣿ ⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⢥⣿⣿⣿⣿⢃⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠼ ⡟⣻⣩⣭⣧⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣜⠳⣭⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣴ ⣘⣋⣭⠹⣿⣿⣿⡿⢛⢿⣿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣷⣾⠖⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢱⣶⡿⢣⢹⡿⢱⣿⣮⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣛⣃⡎⣿⣯⢩⠹⣿⡄⣍⡻⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⢋⣾⣧⣭⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢣⠀⠀ ⠀⢰⠃⠀⠀⢠⣶⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠈⡆⠀ ⠀⢸⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠱⠀ ⠀⣸⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⢙⡿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⢘⡇⠐⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⠐⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⠠⡇⢈⠰⡃⠀⢀⣤⣾⣷⣦⡀⠀⠀⡗⢀⠈⡇⠀⠀⠀⠀⡇⠀ ⠀⠀⢳⡀⠀⠀⠐⡇⢀⠸⡁⠀⠘⢿⠿⠻⡿⠏⠀⠀⡆⢀⠂⡇⠀⠀⠀⡜⠀⠀ ⠀⠀⠀⠑⠦⡀⢈⡇⠠⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠂⣇⢀⡤⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣟⡁⠐⢨⡆⠰⣦⠀⠀⠀⠀⣰⡄⠀⣇⠠⠀⢼⠁⠀⠀⠀⠀⠀ ⣀⠤⠀⠒⠠⠘⠋⠄⠂⠉⠷⠛⠻⠒⠒⠒⠖⠛⠟⠚⢃⠠⠐⠘⢂⠀⠢⠐⠠⢄ ⠳⠬⢴⣅⣂⣄⣁⣠⠈⡀⢄⡠⣁⣠⣁⣈⣀⣡⣈⡐⢀⠂⢁⣈⣀⣄⣐⡤⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠉⠉⠉⠉⠉⠙⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠁⠀ ⠀⠀⠀⠀⠀⠘⣻⠟⠀⠀⠀⠀⢀⣰⣄⡀⢶⣤⣀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⡞⠁⠀⠉⠉⠛⠛⠛⠲⣽⡟⠲⣄⠀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⠳⡄⠀⣄⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⣀⣀⡏⠈⠿⠀⠀⠀⣠⠖⠒⢦⠀⠀⠀⠀⠀⢀⣀⠹⣤⠟⣆⢀⡟ ⠀⠀⠀⠀⢸⠀⡼⢙⣉⡻⠄⠀⠀⠀⡼⠁⢀⣤⣼⡇⠀⠀⠀⣴⠋⠉⢻⠋⣰⣻⡞⠀ ⠀⠀⠀⠀⢸⡀⡇⢸⣹⡇⠀⠀⠀⠰⠧⠤⢼⣿⡿⠀⠀⠀⢰⡇⠀⣶⣾⠀⡇⠏⠀⠀ ⠀⠀⠀⠀⠈⢇⠹⣄⠻⠇⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠉⢹⡛⠋⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⣈⣻⠂⠀⠀⠀⠀⢸⣹⡇⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣸⡀⠀⠈⠉⠀⠀⣀⣀⡀⠀⠀⠈⠷⠃⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡏⡇⠀⠀⠀⠖⠛⠛⠛⠿⠷⣄⠀⠀⢠⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠿⢷⢤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⡿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⡖⠛⠉⠹⡄⠀⠘⣆⠀⠈⠉⠉⠉⠉⠉⠉⡟⢳⣄⠰⠿⠃⠀⠀⠀⠀ ⠀⢀⡴⠚⠉⠉⠉⠙⠲⣄⠹⣄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⢶⠦⣄⡀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⢦⡀⠈⠳⢤⡀⠀⠀⢀⡼⠀⢀⡟⠈⡆⠀⠹⡄⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠙⠢⣄⡀⠈⠉⠉⠁⢀⣠⠞⠁⠀⢸⠀⠀⣇⠀⠀ ⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣞⣀⣀⣀⣀⣈⣉⣙⣛⣉⣉⣀⣀⣀⣀⣸⣀⣀⡇⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣶⣀⡤⠦⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢿⣿⠞⠉⢁⣶⣶⠿⢋⣽⠷⠚⠛⠩⣴⣶⣶⠿⣿⣿⣿⠿⠛⢙⣿⣿⠯⢻⡏⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⣻⢏⣤⠞⢋⣠⢖⣻⡵⠞⠋⣁⣀⡀⣤⠶⠛⣉⣥⠴⠚⣋⣥⠴⢚⣫⣭⢴⣶⣿⠭⠶⠖⠒⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⢟⡽⢋⣤⢞⣫⣤⠾⠷⠚⠛⠋⠉⠉⠉⠙⠛⠒⠿⣤⣤⣘⣍⣀⣘⣋⣁⣀⣘⣉⣀⣄⣄⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣏⣴⣫⣴⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⣿⣡⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⢲⢲⣿⢻⢻⡟⢻⡿⣷⣶⣶⣒⠒⠲⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣼⣯⣿⣷⣾⣼⣼⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣀⣉⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣴⣿⣧⢸⣿⣿⣷⠿⠛⠋⠉⠀⠀⢀⡿⠀⠀⠀⠀⠙⢦⡈⠉⠉⠛⠛⠻⢿⣿⣿⣖⣿⣬⡉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣆⣾⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣼⣷⣶⣦⣄⠀⠀⠀⠀⠉⣟⠻⢿⣿⣧⡀⠈⠙⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣷⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠤⢤⣤⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⣿⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⡍⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠉⢳⠀⢰⡏⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣦⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⠉⠉⠳⣄⣀⣼⣷⡟⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠈⠹⢿⣿⣳⣦⡀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⠀⠀⢀⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣦⡀⠀⠹⣿⣷⣿⣷⣤⡈⠙⠳⠶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⣦⣀⠀⠁⠻⢣⣿⣿⣷⣦⣜⢿⣶⡀⠙⠲⠶⠶⠶⣤⡀⠀⣠⣠⡀⠀⢀⣤⡴⢦⣤⣀⣠⣤⣀⠀⠀⠀⢀⡾⡃⠠⡀⠘⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠷⣤⣄⠀⠙⠺⠿⢿⣿⣷⠀⠀⠀⠀⣀⡀⠀⠀⠉⠙⣁⣉⡉⠛⠋⢁⣀⠘⢳⢉⣀⣀⣙⠳⢦⣤⣛⠀⠛⠶⣝⠀⠘⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⢀⡟⠀⢀⣴⠛⠉⠙⠛⠿⢿⡇⣺⡟⠛⠳⠤⠾⠛⠛⠛⠛⠁⠈⠉⠛⠿⠋⠉⠛⠛⠓⠾⠶⠦⣌⣳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣸⠁⠀⠀⠀⠀⠀⣾⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢿⠀⠀⠀⠀⠀⢸⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢨⡇⠀⠀⠀⠀⠀⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣠⡾⠁⠀⠀⠀⠀⢠⡟⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠀⣷⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠿⠿⠧⠼⠼⠼⠿⠛⢃⡣⢟⣸⡀⠀⠀⠀⠀⠀⠸⡘⠧⣄⡘⠛⠛⠿⠤⠧⠿⠧⠧⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠚⢁⣀⡠⠤⠤⠦⠖⠒⠒⠚⠉⢁⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠉⠙⠓⠒⠒⠶⠤⠤⠤⣄⣀⡉⠓⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣫⠧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠬⣑⢤⡀⠀⠀⠀ ⢀⣼⠟⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀ ⠈⠃⠀⠀⠀⠀⣀⣶⣶⣾⣾⡾⠿⡟⡟⣿⢿⡭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣻⣿⡿⢿⡛⠿⣷⠷⣷⣶⣦⣤⣀⠀⠀⠀⠘⠀⠀ ⠀⢠⣤⣠⣶⣿⡿⠟⠉⣸⣻⠁⡜⣷⡄⠈⣠⢷⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢡⢻⡇⢸⢷⡄⢈⣡⠸⡄⠉⠛⠿⣿⣦⣤⣤⠖⣠ ⠈⠛⠻⣿⡫⠉⠀⠀⠀⣯⠉⣷⣇⡈⣷⣾⠏⣸⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢿⠀⠻⣤⣀⣳⡶⠇⢠⠿⠀⠀⠀⠈⠙⣿⠿⠋⠉ ⠀⠀⠈⠈⠀⠀⠀⠀⣀⣘⢦⣀⣊⣍⣉⣀⡴⠯⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣳⣮⣔⣉⣉⣁⡤⠎⢠⡄⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠰⠿⠃⢒⣿⠤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢮⣓⢤⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣶⣱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⠈⠻⠗⠀⠀ ⠀⠀⠀⠀⠀⠀⢤⢯⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣿⠆⠤⠀⠀⠀ ⠀⠀⠀⠀⠠⣷⢾⢸⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠼⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣸⡀⠀⢰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀
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⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⣄⣄⣀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⣟⣿⣭⣿⡿⢿⠷⡾⠿⠿⣿⣭⣿⣳⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣯⠿⢛⠛⡉⢉⠡⠐⡠⢐⠠⢂⠔⡨⢐⠠⡀⠤⢉⠉⡙⠳⢾⣭⣷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⠋⣀⠂⠆⡰⢀⠃⢂⠱⠐⢂⠡⢊⠐⡐⠌⠰⢈⠢⢁⠎⡐⢡⠂⠄⡉⠻⢾⣽⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠛⠠⠐⡔⠠⠉⡔⢠⢁⢊⠐⣂⠉⡄⠃⡄⠃⡌⢨⠑⡈⠔⣁⢂⠡⢂⡘⠠⠑⢠⠂⡄⣛⣯⡷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠟⠁⠌⡁⢒⣠⣁⣡⢐⠠⢈⠂⢅⠂⡜⠠⢡⠈⡔⡈⢄⠊⡔⢡⠀⠎⡐⢂⠌⣰⣽⡶⠿⠛⣟⣻⣿⣾⣝⢶⡀⠀⠀⠀ ⠀⠀⢀⡾⣿⠋⢄⣸⡶⠟⠛⠛⠛⡛⠻⠿⣶⣮⣄⠒⣀⠃⠆⡡⢐⠰⠈⠔⢠⠂⠜⡐⢬⣤⣿⠟⠉⣠⣶⣿⣿⠿⠙⠛⣿⣿⡻⣄⠀⠀ ⠀⢀⣾⣿⣣⣼⠟⢫⣴⣾⣿⣿⣿⣿⣿⣿⣶⣭⣛⢿⣦⣌⠐⢡⠂⡑⢨⠘⠠⡘⠰⠜⣾⡟⠁⠀⠚⠋⠙⠛⢿⣿⡼⣿⠏⠁⠻⡿⣆⠀ ⣰⣾⣿⣷⠏⠁⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⡧⢿⣷⡝⢿⣧⠂⡑⠌⠤⡁⢃⠔⡡⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡏⠀⠀⠀⢿⣽⡤ ⣿⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣤⡇⣴⣬⣿⣆⢻⣿⡄⠊⡔⢈⠄⢢⠰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣤⣾⣿⡁ ⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⢾⣿⣿⣿⡆⣿⣧⠐⡈⠆⡘⠠⢸⣿⠀⣀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⢿⣿⢻⡧ ⣿⡃⣼⣿⣤⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣼⣷⠠⢘⠠⠑⡂⠥⣿⡇⢹⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⠃⠀⢀⣾⡿⠣ ⣿⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣿⣿⡿⠿⠿⣿⣿⣧⣴⢼⣟⠠⢌⢂⠱⣈⠐⣻⣇⠸⣿⠛⢻⣿⣿⣿⣿⣧⣼⣿⣷⣦⣿⡿⠁⠀ ⣿⣦⣿⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠻⣿⡇⣿⡇⠰⢀⠆⠢⠄⠒⡘⣿⡄⢻⣶⠞⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣥⠀⠀ ⡟⠹⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣼⢻⣿⠁⠒⡈⠆⡱⢈⠒⠠⢹⣷⡈⠁⢀⣴⣿⣿⡿⠿⠛⠉⡀⠄⢸⣿⡄⠀ ⣦⣴⡿⠀⢉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣼⢣⡿⠋⢄⢃⡰⢐⣀⢆⣡⣅⣦⣿⣿⠶⠟⠛⠋⢁⠐⡀⠆⡑⠰⣼⣿⠋⠀⠀ ⢻⣿⣀⠌⠠⠐⠠⢀⡀⠠⠉⢉⠉⡙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢋⠛⢉⠉⠉⡀⠠⠐⡠⠑⡈⢂⠡⠐⠠⠐⢘⣋⣿⠇⠀⠀ ⠀⠻⢿⣿⣷⣾⡇⠠⠐⠡⠘⡀⠒⠠⢁⠢⠐⠠⢁⠂⠌⠠⡁⠌⠄⡁⢂⠁⠂⠌⠠⠘⠠⠁⠌⡐⢠⣐⣠⣀⣂⣬⣄⣽⣶⠿⠋⠀⠀⠀ ⠀⠀⠀⢰⣾⠛⠀⢄⠡⢂⠡⢀⠑⠠⠂⠄⡁⠒⠠⠈⠄⠡⠐⡈⠄⡐⠠⢈⠐⡈⠄⡁⢂⠁⠂⢼⣿⡿⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢺⣧⠀⠌⢀⠒⢀⠂⠄⡈⠁⠌⡐⢀⠡⢀⠡⠈⠄⠡⠐⠠⠐⠁⢂⠐⡀⠂⠌⠀⠌⡐⣠⣬⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣶⣬⣄⣐⣄⣨⣴⡴⠷⠾⠿⠿⠷⠷⣶⣷⣾⣴⣦⣅⣢⣁⣢⣄⣤⣥⣬⣶⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠋⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣢⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠴⠲⠴⢤⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡾⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⣴⠞⠋⠉⠉⠉⠛⠓⠶⣤⡇⠀⠀⠀⡆⢰⠀⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⢣⢸⡀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⢸⠀⠇⠀⢹⡗⡄⠀⠴⣿⣶⠄⠀⠀⣸⣿⡏⢀⢀⡸⠿⠿⠟⠀⠀⢀⡿⠀⠀⣠⡬⠼⠧⢭⡀⢀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠻⠸⠀⠀⠀⠀⠻⣮⡓⠲⡄⣤⠤⠴⠞⠁⠀⠃⠴⢌⠉⢳⡄⢠⡖⠊⠁⢠⣄⡶⣟⠒⠀⠀⠀⢘⡏⠸⠤⠔⠲ ⠀⠀⠀⢠⣴⠶⠤⠤⣄⡤⣀⠀⠀⣙⡷⠇⠙⣄⠀⠀⠀⠀⠀⣀⣈⣴⣼⠇⠘⠤⣀⠀⢀⣸⠷⣿⠲⠂⠀⢀⠸⠁⠀⠀⠔⠀ ⠀⠀⠀⣾⡁⠀⢠⡴⢟⣳⡍⠀⠸⣄⠀⠀⠀⠉⢻⠙⠙⠋⠉⢹⠛⠉⠀⠀⠀⢀⣼⠃⠈⠑⠂⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀ ⢶⣂⠁⠹⣇⠀⠀⢦⡤⢿⣀⠀⠀⠈⠙⠒⠒⠚⠁⠀⠀⠀⠀⠀⠑⠒⠲⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠉⠀⠈⠉⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠮⠔⠂⠀⠀⠀⠀⠀⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡴⢿⣏⣉⢭⣛⡙⢶⣄⠀ ⠀⣴⠋⡝⣡⣮⣶⣦⣥⡙⢢⠩⢷⡠ ⢰⠇⡓⣴⣿⣿⣿⣿⣿⣿⣆⠱⡈ ⠀⠀⠀⠀⠀⠀⠀⢸⡊⣱⣿⣿⣿⠿⠿⣿⣿⣿⡄⠡⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⣽⣿⠏⠄⡂⠔⡈⠿⣿⣯⢱⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣧⠘⢢⠑⢬⠐⡡⢭⣇⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠻⠶⠻⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢿⡱⢯⡜⣲⠱⡌⢆⡔⠢⢌⡐⠢⢜⡠⢃⡒⡰⢂⡱⢂⠥⢢⠱⢌⢢⠱⣈⠦⡑⢆⢣⠲⢌⠲⢡⠒⣌⠆⡣⢜⠢⡑⢎⠴⣁⢒⠢⡅⢢⠁⠦⢐⠠⢒⠀⢆⠰⢄⡂⠒⡠⢅⠲⢠⢃⡒⢆⠢⣁⠦⡑⢎⡔⡑⣎⠜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣣⣿⠳⣼⢡⢳⠜⣢⠜⣑⢊⠴⢉⠦⡰⢅⠜⡡⠎⡔⢣⠘⡤⢃⢌⠢⡓⢄⠣⣍⠊⢦⡉⣌⠣⣃⠝⡠⢎⡱⢊⠖⣩⠒⣒⡌⢆⠓⠌⠤⡉⠰⣈⠒⢠⠉⠔⡠⢆⡐⢣⠰⠡⢊⠔⢢⠑⡌⢱⠠⢒⠩⡒⢬⡱⡘⢎⡓ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣞⣻⡼⣹⢎⢮⡑⣎⠱⢌⡘⢆⠢⠱⢈⠆⡡⢃⠜⣂⠣⡔⠩⣌⠒⡍⣌⠱⡄⡋⡔⡰⢌⠒⡌⢎⠱⢢⡑⢊⠖⣡⠚⡰⢌⠢⢍⡘⡰⢁⠣⡀⠎⢄⡉⢆⠡⢂⠜⣀⠣⡘⢄⠊⢆⠱⡈⠆⡑⡊⡔⣡⠢⢥⢙⠢⡕ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣭⡷⣏⠷⣎⡧⡹⢤⢋⠦⢜⡠⢍⠒⢡⠊⠔⡡⢊⠄⢣⠐⢣⠠⠍⠴⡠⢃⠌⡱⢈⡑⣊⠜⢌⡂⢇⠡⡌⠣⡘⠄⠣⢌⠂⡡⠊⠄⠢⢁⠢⢁⠘⠄⢂⠌⠠⠁⠆⠐⠄⣁⠢⠌⢂⠒⠠⠡⠐⡐⢄⠢⢘⢂⠣⡁⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡳⣭⢻⣌⡳⣍⠮⡑⢎⠢⠰⡈⠌⠡⢈⠂⠁⢂⠘⠀⠨⠐⠈⡈⠐⠀⠌⡀⠁⠂⠐⠠⠈⠠⠐⠂⠐⠀⡁⠄⠈⡐⠠⠈⠀⡁⠌⠐⡀⠐⠈⢀⠊⠠⠐⢀⠂⠌⡐⢀⠀⠄⠂⠄⡈⠄⡁⢂⠁⢂⠐⠡⡀⢂⠌⡡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣽⢳⡭⠷⡜⠦⠕⠦⠅⠦⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⣀⣀⡀⣀⠀⢀⡀⢀⠀⣀⣀⣁⣀⣀⣀⣀⣀⡀⣀⠀⠐⢠⣀⣀⣀⣀⣠⣈⣀⣌⣀⣠⣀⣀⣂⣌⣠⣈⡰⣈⠄⢒⡀ ⣿⣿⣿⣿⡿⣟⠿⡹⡉⠇⡁⠂⠠⠍⠀⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⡿⣏⠿⡜⡳⠜⡢⢁⢐⠀⠀⠊⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⢮⣛⢬⠱⣁⠆⡃⢀⠑⡀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⡞⡜⢢⠛⣩⢀⠎⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⡜⡥⣝⣹⠯⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡸⢠⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⡀⠀⡇⢀⠀⠀⢀⠀⡼⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠣⣥⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡢⠔⠂⠉⠀⠀⠀⠀⢕⠀⠀⠀⠀⣸⠃⠀⠉⠉⠉⠉⠉⠖⠒⠶⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⡵⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠀⠁⠀⠀⣀⡤⠴⠋⡁⠆⠀⠀⠀⠀⠀⠀⠰⣑⡆⠀⠀⠠⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠬⡕⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⡀⣀⠦⠚⠁⢀⡙⡀⢵⠨⡀⠀⠀⠀⠀⠀⠀⣯⣇⠀⠀⣸⡟⠐⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠇⡿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠀⠠⡠⢶⠊⠀⠀⠀⠀⠈⢧⣣⡁⣧⡢⡀⠀⠀⠀⡘⢸⣷⣟⡶⠀⣿⣇⡇⠀⠀⠀⢠⡞⠠⠠⡇⡀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠳⢟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢁⢓⠑⠅⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⡠⠔⠉⠀⢾⣻⣄⠀⠀⠀⠀⠘⡿⣿⣿⣿⣦⣄⠀⣴⣧⣿⣿⢧⣷⡌⣿⣿⡇⣤⢀⣴⡻⣱⢵⢝⡴⢊⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣅⣢⠁⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⣀⡼⠋⠁⠀⠀⠀⡀⣱⣿⣷⣄⢀⢀⣤⢿⣿⣿⣿⣿⣾⢿⣿⣿⡻⠏⡻⠯⢿⡙⣿⣿⡾⣿⣿⣿⣿⢿⣻⢞⣅⡀⡀⠀⠀⠀⠀⣠⢆⠀⠀⠀⠈⠂⡀⠙⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⡘⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⡷⡋⢀⠀⠀⠀⢡⣄⠼⡝⢷⣿⣿⣿⣿⣷⣟⠿⠙⠛⠛⠚⠻⠃⠀⠉⠉⠀⠀⠀⠉⠁⠀⠈⠁⠳⢯⠴⣋⢱⢪⣯⣿⢽⣕⣶⣶⠾⠃⠁⢀⠌⠀⠀⡀⠀⡑⢄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢎⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢿⡀⣟⢮⣳⣄⡀⢀⣹⢯⣺⣳⣮⣽⣻⠟⠋⠁⠀⣀⡀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣟⢛⡯⣑⣤⣶⣪⣕⣁⣀⣀⢌⡱⢷⣄⡙⢤⡙⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠎⡈⠂⠀⠀⠀⠀⠀⠀⣠⣆⠋⠁⠀⢱⣌⠙⠿⣻⣿⣿⣿⣿⣿⠿⠟⠙⠁⠀⠀⣠⡞⠋⠀⢠⢠⢠⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢏⣛⢯⣑⣪⣑⣲⢴⣒⡥⠊⠁⠀⠘⠙⢢⣑⢌⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠌⢝⠂⠀⠀⣀⡠⠔⠉⠀⠈⠳⣿⣶⢿⣾⣽⣶⣷⣿⣿⣻⠋⠀⡀⠀⠀⢀⣤⠟⠁⠀⠰⣆⣸⢸⡺⠀⠀⠀⢀⡀⣠⣳⣞⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡻⣿⣾⡛⠯⠒⡉⢀⣀⠀⠄⠁⠋⢟⡆⢿⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣔⡉⠀⠠⠂⡁⠀⠀⠀⢦⣀⢀⡘⠻⠿⠿⡿⢿⣻⣿⡛⠂⣆⠀⠀⠀⣠⣗⡥⠄⠀⠀⠀⢹⣿⣿⣷⡤⢠⢃⣾⣿⡵⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠜⠉⠙⢳⣻⢷⣦⣯⠭⠧⠖⡊⠑⠄⡀⠊⢻⡆⣻⣿⣧⠆⡀⠀⠀⠀⠀⠀⠀ ⡎⠃⠀⠀⠀⢀⠁⠀⡀⠐⠛⠿⡿⢿⣶⣷⣾⣿⣿⢟⡀⡀⠀⣀⠄⢀⣿⢕⠋⠀⠀⠀⠀⢸⣿⠿⠁⠀⢰⠸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣱⡿⣿⣿⣶⠾⠼⣍⠥⠄⠐⠀⡙⢀⠹⣿⣦⠱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢧⣈⣑⣾⣷⣾⣷⣿⣿⣿⣿⣿⣭⢧⡀⣾⠁⠀⣯⣏⠀⠀⠀⠀⠀⢄⣾⡏⠀⠀⠀⠈⣾⣿⣿⠋⠐⠂⠀⠀⠀⠀⠀⡿⠄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⣹⣿⣿⣿⡿⡒⢓⢊⡀⠀⠐⠠⠉⠜⣯⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣩⣯⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⠞⠒⠊⢹⣯⣄⡀⠀⠀⢠⣾⣟⣴⣶⢞⣒⣿⣿⣿⣿⣿⣧⠤⠀⠀⠀⠀⠀⢽⡅⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠿⣿⣿⣿⣿⣦⣆⡄⠀⠓⣄⡂⠀⠂⠙⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣂⡴⢟⣱⡿⢿⣿⡿⣿⣿⣯⣓⢧⠐⠀⢸⣱⠈⠙⠀⠀⢼⢿⣿⣿⣿⣿⣽⡶⡻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣆⡀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⢧⢿⣾⣿⣿⣿⢋⡟⢻⣿⣾⣄⠀⠑⣀⡤⣄⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⢿⠏⡼⣫⠞⢋⢜⣥⠞⠛⢻⣿⣽⢟⠿⣿⣄⢂⠈⡽⡀⠀⠀⡔⠩⠌⠁⠀⠈⣿⣿⣱⢥⢻⢳⣿⢉⢿⡐⠀⠀⢠⣾⣿⣿⣺⡭⠄⠀⠀⠀⠀⢀⠀⠰⠀⡘⢾⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⠐⡼⠃⠀⣱⠟⢀⠔⣩⡟⠋⢛⠷⣟⣢⣌⠓⠺⣜⣍⣆⣦⠇⠀⠀⠀⠀⠀⠹⣿⣟⡧⣯⠿⡗⡺⣿⡃⢠⣴⣿⣿⡿⠛⠒⠂⠀⠀⠈⠐⠊⠁⢈⠲⢤⣴⣿⣿⣿⣿⣿⣿⡷⣻⣿⣿⣿⣻⣿⡳⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠋⢠⠋⣸⡏⠀⠀⣰⣾⡿⢉⡵⣺⢷⡀⠍⠛⡀⠤⣀⡐⠂⠀⠀⣾⣟⣻⢧⡇⢽⡓⠖⣻⡿⠿⠏⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⣀⣴⣦⣿⣿⢟⣭⣭⣼⠽⡝⡛⠿⣿⢿⡿⣿⣻⡅⢣⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⢠⡏⢮⣱⡟⡰⠋⠁⢉⣔⣫⣽⣄⣀⣈⠅⠚⠒⠫⠙⠿⠛⠃⢿⠜⠀⠀⠙⠀⢀⣀⡀⣀⣀⣀⣤⡬⠵⠖⠛⠫⣩⡀⡬⠹⠿⡟⢗⢄⠀⠁⠀⠀⠀⠀⠉⠉⡂⠉⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⠇⢸⡟⡰⠁⠀⢀⣾⠎⠁⡴⢋⠡⠍⠃⣲⡳⠷⣾⣷⣶⣶⣬⡽⡉⡉⣀⡈⡉⠌⠩⣭⣤⣔⣲⢆⢲⣷⡶⡒⠝⠽⡦⣆⡆⠙⠎⡎⡆⠀⠀⠀⠀⡑⠁⣑⢴⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠁⠀⠀⡾⠁⠀⡼⡓⠁⠀⠀⠌⡐⢠⢾⠋⢊⠏⠁⠈⠃⢹⢹⡿⠛⠋⠡⣲⢿⡏⠉⡘⢋⡝⣿⡖⠁⠁⠡⢔⡨⠟⡀⠀⢸⠃⠀⠄⠈⢀⣡⡈⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢠⠃⠀⠀⠀⠀⢰⠀⣾⠁⠀⢸⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠈⣿⡖⠲⠽⠄⡳⣝⡧⡡⠐⡁⠃⠊⡇⠀⢀⣟⡄⣁⠈⡶⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠀⠀⠀⠀⠀⠟⠀⠀⡎⠀⠀⠀⠀⠘⢼⡀⠀⠀⠀⠀⢺⠣⠄⠀⠣⠜⣾⡟⠁⠀⡀⡀⠄⣇⢅⠂⣋⡤⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡷⡀⠀⠀⠀⠠⡀⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢃⡗⠃⡁⠁⠘⠫⣣⠬⠈⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠂⠀⠊⠀⠑⠀⠀⠁⠀⠈⡂⠘⢛⠃⠉⠊⠈⠀⠁⢻⡀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣵⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡆⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡇⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⡇⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠠⠀⠄⠀⠄⠠⠀⠀⠨⠀⠀⠀⠐⠂⠒⠂⠐⠀⠀⠀⢀⢀⢀⣁⣈⣈⣁⣈⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠰⣄⠀⢀⠀⠀⡀⣀⠀⡀⠀⢀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣀⠢⣑⣾⣷⣾⣷⣾⣶⣿⢿⣧⠿⣿⣷⣽⣶⣊⣣⣽⣄⢧⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⣷⣮⣁⣤⠼⠚⠉⢁⣴⣿⣿⠻⢿⡀⠙⣀⠋⠙⣺⠋⣿⣭⡛⠻⠮⣧⣹⡘⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣈⡳⢬⣽⡶⠟⠉⠀⠀⠀⡴⢿⣧⡉⠋⠀⠣⣧⢠⠟⣄⣠⠅⠘⠰⡟⣿⢆⠀⠈⠉⠻⢾⣻⡉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢦⡰⢦⣀⣐⣶⣿⠟⠛⠛⠁⠀⠀⠀⡾⢁⡓⠻⣗⠠⢷⠌⠘⣇⣣⡈⠀⠙⣀⡀⠐⣿⣨⣧⠀⠀⠀⠀⠙⠳⣄⠀⠈⠻⣷⣆⠀⠀⠀⠀ ⠀⢀⠘⠦⠭⢛⣒⡼⠋⠤⠀⠀⠀⠀⠀⠀⣼⣿⠤⠤⠔⠀⣸⣤⣤⠞⠛⠻⣿⣦⣀⣚⡄⢐⣛⢽⠾⡇⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠈⠳⠄⠀⠀ ⠀⠈⠑⠒⣲⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠭⠵⠦⠀⢠⠀⢹⣇⠀⠀⣠⣿⣿⡿⠛⠉⠀⠀⢈⣭⢹⠀⠀⠀⠀⠀⢤⣄⡈⠳⣄⠀⠀⠀⠀⠀ ⠀⣀⡴⣞⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡦⠄⠀⠀⠘⣙⠉⢿⣷⣾⣿⣿⣿⠇⡶⠀⠀⠀⣴⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠳⣤⡀⠀⠀ ⠋⠹⣄⠈⠳⣄⡀⠐⢟⡀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣀⡀⠀⠀⣆⣀⠟⡛⡛⠛⠳⠄⠀⠀⢀⡀⢺⢷⡇⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠏⠏⠉⣷⠀ ⠀⡀⠘⢦⡈⠁⠙⠲⢤⣀⠧⠤⢤⣀⣀⡀⠈⣻⣄⣛⠅⣀⢀⡄⠙⡸⠽⠻⠱⠀⠃⠀⠫⣟⠯⣝⡾⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⢹⠀ ⠀⠘⠂⠈⠻⣄⠀⠉⠴⢛⣦⢄⡀⠀⠀⠀⠉⠉⠛⠓⠛⠛⠛⠓⠛⠿⠧⢮⣷⣔⣎⣣⣿⡯⣳⠞⠁⠀⠀⠀⣠⢾⠥⠤⠤⢤⣀⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠈⠳⣄⠐⠋⠠⢚⡿⢖⣤⡀⠂⠤⣄⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠉⣉⠩⣉⡁⠉⠁⣒⣂⣨⣽⠟⠋⠀⠀⠀⠀⠙⣗⠄⠀⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠻⠿⠶⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⣤⣾⣿⢿⠃⠇⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠉⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⢠⣾⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀
⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⣤⣤⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠲⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢯⣨⡥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡋⣻⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣫⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿ ⠻⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⡿⢋⣧ Hello there ⠈⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⢀⣀⣀⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀ ⠀⠈⣟⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⡿⠋⠀⠀⠀ ⠀⠀⠈⠉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢃⡤⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⢿⡿⡿⠿⠿⠟⠛⠷⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⣀⠴⢺⣾⢾⢞⠿⡷⣵⠧⣔⣀⡀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⡦⠾⠉⠀⡔⡳⠉⡌⣖⡂⢀⠉⣗⡀⠉⠣⡁⠢⣄⠀⠀ ⠀⢊⡴⠋⠀⠀⠀⢰⠷⠄⣜⣎⢉⣿⡾⠈⠙⣧⠀⠀⠀⠢⡀⠁⠀ ⠒⢍⠢⣀⠄⠀⠀⠘⡷⡄⠀⠼⣛⡛⠉⣀⣸⡏⠀⠀⢀⠸⠟⠓⡄ ⠀⠂⠢⡀⠻⡠⣉⠀⡉⠁⠛⠒⠂⠦⠶⠾⠞⡀⣠⠎⠀⠠⡀⠀⠇ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⢄⠀⠀⠀⠀⡠⠔⠞⠟⠁⠀⠀⠀⠡⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁
⠀⠀⠀⠀⣠⣾⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀ ⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀ ⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀ ⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⢀⣴⣦⠀⠀⠀⠀⣠⡀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⣾⣿⠁⢀⣶⡆⠀⣻⣿⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⠿⠛⠁⠀⠀⠹⣿⣶⣿⠿⣿⣶⣿⠏⠀⠀⠀⠉⠉⡁⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇ ⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀ ⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢰⣶⡀⠀⠀⠀⠀⣰⣿⡟⠁⠀ ⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⣾⡟⠁⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣠⣿⠇⠀⠀⣠⣾⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⡆⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⣶⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⡖⢒⣶⠦⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⣫⣴⡶⠉⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⢶⣦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡔⠋⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠉⠻⠿⣷⣤⣀⠀⠀⠀ ⢠⡏⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢈⣿⣟⢧⡀⠀ ⢸⠃⢀⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⢀⣴⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣾⣿⣿⣮⣳⡀ ⡼⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠙⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻ ⠀⠹⣜⢿⠟⠉⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠹⣿⣿⣿⡿⠛⠉⠉⠉⢉⠟⠉⠁⢸⠃⢸ ⠀⠀⠘⣿⠷⣄⣀⣀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⢀⣮⣶⣖⠻⣏⣠⠇ ⠀⠀⠀⠈⢧⡀⠙⠿⣿⣿⡟⠋⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⣿⠀⣸⠿⠀ ⠀⠀⠀⠀⠀⠙⣤⡀⠀⠈⠑⢲⣖⠒⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢻⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⠋⠓⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢼⣇⣀⣛⣤⣀⣀⣀⣤⡀⠀⠀⡔⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⡟⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠁⠈⠀⠀⠀⠁⠐⠂⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⣼⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢏⣛⢿⣿⣿⣷⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⢟⣽⣿⣿⣿⡟⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢋⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢻⣿⡜⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣧⢿⡹⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⡌⣇⢹⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢟⣾⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⠚⡇⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⢏⣾⢣⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢀⡿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡜⢿⣿⣿⡏⣾⢣⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⡟⠉⠙⢷⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⣿⡏⠀⣛⣿⣟⣉⣾⢫⣿⠇⢀⣠⣿⣟⡻⠻⠿⢷⣶⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⡿⢿⣟⣛⡛⢻⠃⠀⢀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢾⡏⠉⣩⣿⣯⣾⠋⠀⣼⢻⣯⣍⣿⣷⣶⣶⣿⣿⣿⣿⣿⣻⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⣃⠀⢩⣿⡿⠁⠀⢠⡏⢸⣿⠟⣸⣿⣿⣟⣻⢿⣛⣿⣿⣿⣿⣿⠀⠀⠀⠘⠿⣿⢿⣾⣿⣿⣿⣿⠙⢿⣿⡿⠀⠀⠘⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⢿⣿⣇⣀⢀⣾⠇⠀⠀⠀⣿⡿⠻⠿⠟⠛⠛⠋⠐⠉⠛⠛⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⢻⣷⠀⠀⣠⢀⡄⡎⠀⡇⠀⠀⠀⠀⠀⣴⡶⣶⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣼⡏⢸⣿⡿⠃⠀⠀⢀⣼⡋⢙⣦⣀⣀⡴⠖⠋⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⠀⢿⣿⣷⡴⠇⠀⠀⠀⠀⢀⠃⠀⠻⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣿⣧⣾⠟⠀⠀⠀⠀⣾⣿⣿⡿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠉⠈⢷⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⡏⠙⠛⠁⡠⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⣿⣿⣿⣏⠀⠀⠀⠀⢧⠀⠀⠀⠀⣾⠀⠀⠀⠀ ⠀⣠⣤⡀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣈⡗⠀⠀⠀⠀⣼⣿⡏⣻⡿⡗⠀⠀⠀⠘⡇⠀⠀⠀⡏⠀⠀⠀⠀ ⠸⣿⣄⠈⢷⡀⠀⠀⠀⢸⣿⣸⡿⠁⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣦⣄⣤⣿⠟⠀⠀⠀⠀⣰⣿⣿⢛⣛⣿⣇⠀⠀⠀⠠⢼⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠹⣿⡀⠀⢣⡀⠀⠀⠘⣿⡿⠁⠀⠀⣰⠎⠛⠂⣾⠃⠀⠀⠀⣿⡇⠀⣀⣴⡒⢢⡄⠉⠿⠿⠿⢿⡿⠋⠁⠀⠀⠀⠀⢠⣿⣿⣷⠈⢿⡟⣿⠀⠀⠀⠀⠈⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⡟⠁⠀⢸⡇⠀⠀⢀⡿⠁⠀⠀⢰⣯⠀⠀⢸⡟⠀⠀⠀⠀⣿⡇⣰⡏⢸⣿⢶⡇⠀⠀⠀⠐⠒⢀⣀⣐⡀⠀⢠⣴⣿⣿⣿⣿⠀⠀⠀⢿⡆⠀⠀⠀⠀⣧⡿⠀⠀⠀⢠⠀⠀ ⠀⣠⣧⠀⠀⠸⣧⣀⢀⡴⠀⠀⠀⢀⣾⡇⠀⠀⣿⣄⣀⠀⠀⣰⣿⣰⣿⠁⠈⠉⣸⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⡇⠀⠚⠀⠀⠐⠒⠀⠀⠀⢸⠀⠀ ⣄⣿⣿⡀⠀⠀⠸⣿⠟⠁⠀⠀⠀⠘⠁⠀⠀⠀⣿⠉⠙⠛⢲⣿⣿⣿⠇⠀⠀⢀⣿⣿⣿⠿⠿⠿⠿⢛⣿⡟⠁⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣷⣤⣞⣻⡆⠀⠀⢠⣀⣴⣿⠀⠀ ⣿⣿⣿⣷⣦⣄⣀⣿⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠀⠀⡾⢿⣿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣗⣛⣾⣿⣿⣿⠿⢿⣿⣿⣿⡿⡟⣿⣿⠀⠀⠀⢸⣿⣷⣯⣥⣶⣾⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠇⠀⣽⡀⠀⠀⣼⠿⠿⢿⣿⣿⣿⡿⠿⠛⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣿⣶⣆⣀⣶⠟⠻⡶⣾⣿⣄⠀⠀⠀⠉⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣤⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡛⠿⣸⣿⣿⣎⣛⣩⠿⢛⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣉⡍⠉⣛⣿⣿⣿⣿⣷⣦⣬⣍⣉⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠋⠀⣲⣿⡿⡛⡛⡙⢝⢛⠿⣿⣿⣏⡀⠘⢿⣿⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠄⢠⣶⣿⢏⢜⠨⡪⣘⢬⣂⣳⡨⣻⣿⣿⠆⠻⣿⣇⠛⠻⣷⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡏⣿⣿⣷⣾⣿⡏⣢⠵⠛⠉⠉⠁⡈⠀⠉⠉⣿⣿⣦⡄⢿⣿⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡛⠁⢿⣿⠟⢻⣿⡟⠁⠠⠐⡀⢁⠢⢀⠁⡑⠠⢸⣿⣟⠁⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠷⢾⣿⣦⣼⣿⣷⣬⣐⠀⠢⠀⡂⠠⠂⠐⣀⣿⣿⣿⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⡿⢿⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠱⡀⠀⠉⠙⢛⣛⣛⣛⣛⣛⣛⣛⣩⣥⠀⠈⣄⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢈⠆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢠⣿⣿⣿⢩⣿⣿⣿⣿⡎⣿⣿⣿⠀⢠⡁⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⣿⣿⣿⣿⣿⡯⣻⣿⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣛⣼⣿⣿⣿⣿⣿⣯⡻⣿⠿⠃⠀⣾⣿⡦⠀⢀⡠⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⢀⣿⣿⡟⢀⢎⡠⠜⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⣀⠀⠀⠸⡀⡃⠀⠀⢸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⣀⣀⡉⠦⠀⠀⠀⠀⠀⣹⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⣿⡏⠉⠀⠀⠀⣠⠒⠒⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡤⠀⠸⢿⣿⣿⠇⠀⠀⠀⠀⠿⣿⡿⠟⠀⢠⠤⡀⠀⠀⠉⠒⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀MADE BY VICTORIA
⠀⠀⢀⣤⣶⠶⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠷⢶⣦⣄⠀⠀⠀ ⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀ ⢸⡟⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣿⡆ ⣾⡿⢟⢛⠛⡛⠿⣷⣤⢀⣠⣶⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣦⣄⡀⠀⠀⣠⣾⠟⡩⠑⡌⣹⣿ ⢹⣷⠈⢆⠱⣈⠒⣬⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣴⣿⠃⡜⢠⠓⠤⣹⡿ ⠘⢿⣎⢢⠱⢤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣜⢄⠣⢌⣳⡿⠃ ⠀⠈⠻⣷⣮⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⠿⠋⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀⠀⠀⠀⣼⡇⠀⠀ ⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⠀⠀⠀⡀⠤⠀⠐⠠⠄⡀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⡇⠀⡐⠀⠀⢠⣿⣿⣷⠀⠈⠢⠀⠀⠈⠉⠉⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣼⡗⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢂⠀⢰⡿⠋⠈⠻⣷⠀⠠⠃⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠈⠐⠀⠀⠀⣂⣂⣀⣀⣠⣤⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣶⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡇⣤⣶⣿⣿⣶⣦⠀⣶⣶⣶⣿⣷⣾⣿⣿⣶⡄⢲⣶⣶⣾⣿⣶⣄⠀⠀⠀⠐⣦⣾⣿⣷⣶⣄⣸⣿⣿⣿⣿⣷⣦⠀⣴⣾⣿⣷⣶⡄⣶⣶⡆⣴⣶⣶⢹⣷⣶⣾⣿⣿⣿⣶⣶⣶⠰⣴⣾⣷⠀⠀⠀⠀⠀⠀⣶⣶⡖⣴⣶⣶⢳⣶⣾⣮⣶⣿⣿⣷⣦⡀ ⠀⠀⠀⠀⠀⢠⣿⣿⡟⠙⣿⣿⣧⣻⣿⣿⣿⣿⣿⡧⣿⣿⡟⢻⣿⣿⠛⣿⣿⡇⢸⣿⣿⠋⢻⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣛⢸⣿⣿⠏⢻⣿⣿⣘⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⡿⠙⣿⣿⡏⠘⣿⣿⣧⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠘⣿⣿⣧⣤⣿⣿⣯⣿⣿⣟⣿⣿⣿⡀⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⢹⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣇⡀⢹⣿⣿⣿⡿⢣⣶⣦⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⢿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠇⠙⠿⠿⠟⠿⠿⠃⠿⠿⠃⠘⠿⠟⠀⠻⠿⠃⠸⠿⠟⠀⠹⠿⠟⠀⠀⠀⠀⠙⠿⠿⠿⠿⠋⠘⠿⠿⠃⠘⠿⠿⠈⠻⠿⠿⠟⠿⠿⠀⠹⠿⠟⠈⠻⠿⠏⠀⠈⠻⠿⠿⠃⣀⣿⣿⣿⠁⢸⣿⣿⠀⠀⠀⠀⠀⠻⠿⠿⠀⠻⠿⠋⠀⠈⠻⠿⠿⠿⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⠀⠸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣤⣀⢠⣤⣶⣶⣶⣤⡀⣴⣿⣿⣷⣤⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⢠⣴⣦⣶⣶⣤⡀⠀⣠⣴⣶⣶⣤⡀⣴⣿⣿⣷⡆⠀⠀⠀⠀⣤⣶⣶⣶⣤⡀⣸⣿⣿⣀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⣿⣿⣿⣿⣿⡿⠛⢿⣿⣷⠛⣿⣿⡟⠁⣿⣿⡟⢻⣿⣿⠄⠀⠀⠀⢸⣿⣿⠛⣿⣿⣿⣻⣿⣿⠟⢻⣿⣿⡝⣿⣿⡟⠃⠀⠀⠀⣾⣿⡿⠛⢿⣿⣿⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣾⣿⣿⣿⣿⣧⣀⣼⣿⣿⠀⣿⣿⣇⠀⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣧⢿⣿⣿⣀⣸⣿⣿⡇⣿⣿⣇⠀⠀⠀⠀⣿⣿⣧⣀⣼⣿⣿⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⡿⠃⠙⠿⣿⣿⣿⠿⠋⠀⢿⣿⣿⠷⣿⣿⠇⠸⣿⣿⠂⠀⠀⠀⢸⣿⡿⠀⢿⣿⡿⠈⠻⣿⣿⣿⡿⠟⠀⠻⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⠿⠋⠸⣿⣿⠘⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡶⠰⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⢳⣶⣿⣿⣭⣝⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣾⣿⣿⣿⣿⣿⢳⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⠉⠁⢿⣿⣿⡉⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠿⣿⣿⣿⠀⠀⠈⣿⣿⠇⠀⠀⢠⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⣅⣤⣤⣿⣿⣿⡀⢠⣶⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣠⣴⣦⣀⣤⣤⣤⣴⣤⡀⣠⣶⣶⣶⣶⣾⣷⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣿⡇⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⣿⡇⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⡆⠙⠻⠛⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⣿⣿⣿⣿⣿⣷⠈⠛⠛⢙⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣄⠀⠻⢿⣿⣿⣿⣿⡿⠁⠀⠹⣿⣿⣿⣿⣿⡁⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁⢸⣿⣿⡀⠀⠻⢿⣿⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣿⣏⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⢹⣿⣿⣿⣿⣷⣆⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣧⠀⠘⣿⣿⣿⠀⠀⠈⢻⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⠀⠀⣠⣾⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡟⢿⣿⣿⣧⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠛⠁⠀⣼⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⠙⣿⣿⣷⡄⠀⠻⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⠁⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠛⠛⠁⠀⢻⣿⣿⣆⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⣰⣿⣿⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣛⠁⡀⠘⣿⣿⣿⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⡟⣿⣿⡿⠀⠀⠀⢀⣿⣷⣤⣤⣴⣿⣿⣿⡆⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⣸⣿⣿⣿⡏⣿⡿⠃⠀⠀⣀⣼⣿⣷⣶⣶⣿⣿⣿⣧⠀⢹⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⡿⠿⠿⠻⣿⣿⣿⣿⡆⠈⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⢿⣿⣿⣗⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⢠⣿⣿⣿⣿⠿⠋⠙⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣿⣿⡏⣿⣿⣿⣼⣿⣿⡟⠻⣿⣿⣿⣿⠃⠀⢀⣾⣿⣿⠛⠛⠁⠀⠀⠈⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⣸⣿⣿⣿⠃⠀⣠⣿⣿⣿⠉⠉⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⣿⣿⡇⢹⣿⣿⣿⠿⠟⠁⣠⣿⣿⣿⠋⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠀⠀⢠⣿⣿⣿⠇⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⠀⠙⠋⠀⢸⣿⣿⣿⣇⠀⢀⣿⣿⣿⠋⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⣿⣿⣿⠃⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠘⢿⣿⠋⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡙⠛⠃⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣷⣄⣀⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⡏⠻⠿⢿⠿⠿⠟⠋⠀⢡⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠈⠉⠉⠉⠁⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠰⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣦⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣀⣀⣀⣀⠀⠀⢀⣈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀
⡠⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠙⢦ ⡇⠀⡔⠛⠲⡄⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠒⠚⢧⡀ ⠱⣼⠀⢀⡠⠧⠤⣀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡀⠀⠀⣿⣆⠀⠀⡇ ⠀⢹⢀⡎⠀⠀⠀⢈⠏⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⠻⣶⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⢱⠀⢠⢧⠛⠒⢦⡇ ⠀⠈⣾⠀⠀⡔⠋⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⡠⠞⠛⣋⣀⣀⠀⠀⠀⣤⣤⣀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠈⢣⠀⢸⢀⠞⠸⣄⠀⠀⢱ ⠀⠀⠘⡆⠀⠃⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠎⣠⠴⣿⣿⠟⠀⠀⠀⠀⠘⣿⣿⠑⢦⡀⠀⠙⢦⡀⠀⠀⠀⢸⠀⠀⡁⠀⠀⡜⠇⠀⢸ ⠀⠀⠀⢣⠀⠀⠀⠙⢄⢀⠇⠀⠀⠀⠀⡼⠁ ⠈⠀ ⠈⣁⠴⠚⠉⠉⠉⠙⠢⢄⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢸⢀⡏⠁⠀⠈⠀⠀⡰⠃ ⠀⠀⠀⠀⠣⡀⠀⠀⢸⠋⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⣄⠀⠀⠀⠀⠀ ⢧⠀⠀⠀⠻⣇⠀⠀⢀⡴⠊ ⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⠎⠀⢀⣾⣿⣆⠀⣰⣿⣦⠀⠀⠘⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡎⠀⠀⣾⣿⣿⣿⣶⣿⣿⣿⡄⠀⠀⠘⡆⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⡀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⡇⠀⠀⠀⢿⠟⠋⠁⠀⠈⠙⠻⡏⠀⠀⠀⠀⣇⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠀⢸⡀⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢸⠇⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠉⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠊⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠦⠤⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣀⣀⣀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢶⢄⡀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀ ⠀⠀⢀⣼⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆ ⠀⢰⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵ ⣴⣿⠟⠿⣿⣿⣷⡄⠀⣠⣴⡿⢿⣿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣼⠁⠀⠀⢸⣿⣿⣷⣄⣿⠉⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⠏ ⢗⣤⣤⣶⣋⣿⣿⣿⡟⣿⣀⣀⣤⣿⣿⣿⠂⠀⠀⠀⠀⣠⣶⠟⠁⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠃⠹⣿⣿⣭⣽⣿⣯⠁⠀⣠⡴⠟⢹⡀⠀⠀⠀ ⠀⠳⠍⡛⠛⠻⠛⠿⣄⣤⢽⣕⣟⠛⠿⢦⣜⣶⠋⠀⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠉⠉⠉⢳⠛⠉⠁⢸⠀⠀⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⡆⠀⠀⠀⠀⠙⡄⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⠀⠀⠀⠀⠀⠀⠀
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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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