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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣂⡌⢐⢹⡯⠈⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣷⢮⢎⢆⡀⣜⢝⣮⣿⣿⣿⣿⣿⣿⣿⣙⣊⢾⡷⢼⡃⠀⠀⠀⠈⠉⠉⠋⠛⠛⠛⠿⠿⠿⡿⡷⣶⡐⠅⠬⢐⢂⡂⢒⣦⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣮⣐⣿⡀⠀⠀⡀⣀⢀⣀⣀⣤⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡵⡣⣕⣋⣵⣿⣿⣿⣿⣿⣿⣿⣿⡳⡩⣕⢾⡗⣸⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠔⡈⢂⣢⣶⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣟⢿⠿⡿⣿⡿⣿⣽⣭⣍⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⡝⣾⡯⢺⡃⠉⠙⠻⠻⡺⡶⢾⠶⢶⣤⣦⣤⣤⣤⣀⣿⠆⣩⣴⡿⡻⡵⡱⢝⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀пуф ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡛⠰⡈⠟⢷⣦⡨⠅⢐⢂⣉⠌⢿⡆⠀⠙⣮⡻⣷⣩⢝⡯⣹⢻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡧⣹⠂⠀⠀⠀⠀⢠⡷⡿⡿⡿⡿⢿⢿⢟⡿⣛⣿⣾⢟⡳⡳⣙⡳⡱⡵⣩⢟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢑⠡⡐⡔⡈⠡⢙⢻⣶⡌⠌⠌⢂⠡⢿⡄⠀⠈⢻⣎⢿⣮⢞⢮⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣝⣶⡿⣭⡶⠛⠀⠀⠀⠀⢠⣾⢧⠯⢕⠮⠮⢕⢞⢮⣾⡿⣟⢎⡱⣹⢍⢞⠵⡳⡣⣱⠺⠕⡙⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢨⢈⢐⡂⡂⡅⢘⠨⢂⣙⣷⡌⠅⠆⠌⠜⢿⡄⠀⠀⣽⣧⣻⣯⣿⣿⣿⣿⣟⡻⡕⣫⢽⢿⣿⣿⣷⡿⣻⡵⠿⣯⠁⣂⢂⡀⡀⣠⣿⠵⣝⠰⠡⣐⠢⢈⢐⢹⣿⣯⣜⢝⣪⢜⡣⠵⠫⠩⠨⠰⡂⠆⠥⠨⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠣⢁⡐⡐⡂⢒⠨⢐⣤⣵⠿⡛⣿⠦⠅⠬⢂⢢⢘⢷⡄⣼⠃⠀⠻⣮⣽⣯⣟⣯⣹⣻⣟⣻⣟⣟⣟⣟⣽⠿⣯⠀⠀⠘⣧⡀⠌⢡⣼⣿⢵⡚⢂⢁⡈⠔⠨⠅⠍⢌⣿⡻⡿⡿⣮⣥⣐⡂⠡⠡⡂⡅⠡⣐⠔⡈⡈⠜⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠓⠜⢁⢢⠔⡈⣰⣴⡾⠟⠫⢐⠅⡐⣿⡊⢂⢢⡐⡂⠅⣿⣿⠃⠀⠀⢰⠟⠀⠀⠈⣿⠀⠁⠁⠁⣻⠉⠉⠉⠀⠀⠘⣧⠀⠀⠈⢳⡄⣾⢟⡱⡺⠌⠨⠌⢂⢢⠅⠬⠰⢐⢿⡷⡵⡑⠨⠍⢛⠿⣶⣬⣁⡂⣂⠌⠡⡐⡒⡐⠨⢘⡻⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⡟⠅⢁⠢⣐⣬⣶⠿⠛⠥⠅⠬⠌⠜⢂⢘⣿⢂⡂⠡⢁⠢⣪⣿⠉⠀⠀⣠⠟⠀⠀⠀⠀⢺⠅⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠻⣿⣗⡳⡑⠰⡁⡃⡂⠡⢁⠢⣂⠅⢽⣟⡳⡑⣂⠌⠅⡂⡐⡘⠻⢻⡶⣼⣂⡘⠨⢐⠆⠆⢂⡚⢳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠣⠬⣠⣵⢾⢻⠩⢐⡂⠨⠅⢂⢒⡔⡈⠡⢨⣿⡂⢘⠨⢂⢂⣽⠇⠀⠀⢠⡟⢠⣴⢶⣦⣤⢸⡇⠀⠀⠀⢸⡆⠀⣀⣤⣤⢾⠻⢾⣿⣄⠀⠀⠘⣿⣷⢌⢁⢐⡂⡂⡅⡂⠡⠣⠡⠸⣿⣏⢊⠆⠆⠌⠬⠨⠅⢂⢒⠌⢨⠝⢻⣷⣴⣆⠆⠅⠬⠌⡙⢷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣾⠟⢛⡉⣂⣁⣂⣨⣁⣡⣅⣤⣥⣬⣦⣦⣽⡷⠨⢐⡂⠡⣡⡟⠀⠀⢠⡟⣥⣿⡹⢎⢮⣻⣷⡯⠀⠀⠀⢸⡇⣿⣫⢏⡇⢨⢐⠌⠍⡿⣧⠀⠀⠈⢿⣕⡐⡔⡈⠨⢐⠡⡐⡔⡈⠌⢿⡵⡇⢨⢈⠌⠌⡁⡅⡂⠅⠍⢂⡂⠡⠢⠡⡙⠿⢶⣶⣐⡰⠆⢻⡦⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠉⠋⠉⠋⠉⠉⠉⠈⠀⠁⠀⠀⠀⢸⡏⠡⡔⡐⡈⢾⣇⠀⢀⣾⣿⢯⡎⠞⢕⣪⡵⢿⣿⠀⠀⠀⢸⣷⣟⡪⡱⡕⢐⠨⢘⢈⣈⠌⠿⣦⣠⣤⡿⠆⠌⢂⡂⠆⡁⡃⠅⡂⠡⢹⣿⣆⣁⢅⢡⠰⡐⡐⠅⡃⢘⠨⢂⢁⠌⠌⢁⠢⡈⠜⡉⡟⠷⣶⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠅⡃⠅⠆⡂⣲⡿⡟⡿⠿⢓⠌⠌⢂⢘⢐⠪⣻⣿⡅⠀⠀⢸⣿⡿⣑⣋⠮⠥⠡⢐⡂⠢⢁⡈⡘⠽⢿⡌⠜⡈⡐⠣⠡⢐⡂⠌⠬⠌⠥⣿⠙⠙⠋⠛⠙⠛⠛⠛⠗⠳⠗⠾⠾⠷⠶⡶⠶⣦⡶⣴⣴⣥⣼⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣂⠌⠅⠆⢬⣿⣁⠌⠅⠆⡈⠜⠌⢂⡂⠆⠥⠡⢿⣇⠀⠀⠰⣿⠿⣾⡳⡑⠨⠌⢂⢢⢁⠢⡔⡈⠨⡘⢿⣅⡒⡐⠨⠅⢂⢢⠌⡈⠨⠌⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠢⢁⡈⡨⣿⡓⠌⢂⢘⢈⠨⠅⡈⡐⠣⠡⢒⣰⣾⣿⠀⠀⢰⣯⠩⢘⢿⣮⡁⡃⡂⠡⢂⠨⠅⡂⡂⡅⡊⢻⣆⡅⢨⢈⠰⠨⠡⡐⡁⡅⡩⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀пуу⠀⠀⠀⠀⠀⠀⠀ ⢨⡯⠨⠌⢂⣾⡏⡐⠍⡂⡂⠅⠥⠡⡔⡐⠡⣡⡾⣟⡱⣻⢿⣿⢟⢃⡈⠜⠨⢘⢿⣦⡌⢁⠣⠡⠰⠨⡂⠆⠥⠨⢻⣧⣐⠨⠅⡂⡈⠜⢐⢂⠆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⣂⠅⣰⡿⡂⢒⠰⠨⠡⣐⠔⡈⠌⢢⣾⡿⢏⢮⢜⠵⠣⣻⡇⡂⢁⠡⣂⠅⡂⠩⢻⣮⡡⠅⡁⡃⠨⣐⠌⡈⠡⠝⣷⣐⢘⠨⠨⠅⡂⢒⠰⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠎⠨⢰⡿⡑⡐⡂⡁⡃⡐⠡⠣⢐⡵⠟⠙⣿⢍⡚⢁⢒⢁⣹⡧⠢⢂⠌⢨⢐⢐⡂⠡⢭⡿⣧⡌⡂⡁⡅⠡⡐⣂⠅⡘⢿⣔⠡⠰⠨⡂⠡⠣⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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