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