Bicycle Dot Art

Copy & Paste Bicycle Dot Art Emojis & Symbols

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

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

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