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