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