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Submission #993760

# Submission time Handle Problem Language Result Execution time Memory
993760 2024-06-06T11:48:05 Z TimDee Capital City (JOI20_capital_city) C++17
41 / 100
 3000 ms 95780 KB 
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠷⢛⠩⣡⠦⢂⢂⢂⠂⡂⢂⢐⢀⠂⠄⡂⠄⢂⢐⠠⢀⢂⢐⢀⢂⠄⡂⡂⡂⠢⠡⡂⠪⡐⢅⠪⣙⢛⡻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣯⣿⣯⣿⣯⣿⣯⣿⣽⣿⣺⡫⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⢾⣻⣵⢞⣴⠟⡡⡊⠄⠢⢐⠨⢐⢐⢐⠠⢁⠅⡂⠌⠔⡐⡨⢐⠐⡐⡈⡢⢑⢐⢅⠪⡘⢔⠌⡪⢐⢅⠇⡎⡪⡪⣚⢮⡻⡾⣿⣾⣿⣽⣯⣿⣾⣿⣾⣿⣽⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽
⣿⣻⣿⣽⣿⣽⣿⣻⣿⣽⣞⢽⢽⣿⣟⣿⣿⣻⣿⣟⣿⣿⣻⣿⣟⣿⣟⣿⣻⣯⣯⣷⣿⣻⣚⣞⠵⡩⢂⠊⠌⠨⡐⠨⢂⢂⠢⠨⡐⢔⠨⡘⢌⢐⢐⠔⡡⢂⠢⠪⡨⡢⢱⠨⡊⢆⢣⢪⠢⢅⠣⡣⡣⡱⡑⡕⡯⣿⣾⢿⣾⣿⣻⣿⣯⣿⣾⣿⣯⣿⣟⣿⣟⣿⣿⣻⣿⣟⣿⣟
⣿⣿⣟⣿⣽⣿⣻⣿⣻⣿⣻⣿⣻⣯⣿⣿⣽⣿⣯⣿⣿⣽⣿⣯⣿⣿⣻⣿⢿⣻⣿⣻⣿⢻⡝⡪⡑⢌⢐⠁⠌⡂⡊⢌⢂⢂⠅⢕⠨⡂⢕⠨⡢⡑⢔⢑⢌⠆⢕⢑⢌⢪⢊⢎⢎⢎⢪⡸⡸⡱⡱⡌⡎⣞⢼⢸⢪⢮⡻⣿⣿⣾⣿⣯⣿⣿⣽⣷⣿⣟⣿⣟⣿⣿⣽⣿⣯⣿⡿⣟
⣿⣯⣿⣿⣟⣿⣟⣿⣟⣿⣟⣿⣟⡯⣿⣯⣿⣯⣿⣯⣿⣯⣿⣯⣿⣟⣿⡿⣿⡿⣟⣯⡾⢣⢑⠌⡐⡐⡐⡐⠅⡂⡪⠐⡐⠔⡅⢕⠨⢌⢢⠣⡢⡱⢡⢃⢎⠜⡨⡊⡆⢎⢪⡪⡎⣞⡜⡼⣸⠸⣜⢼⢸⢬⢳⢳⡱⡱⢕⢇⠯⣷⣿⣯⣷⣿⣟⣯⣿⣿⣻⣿⣿⣽⣿⣽⣿⣽⣿⣿
⣿⣿⣽⣾⣿⣟⣿⣿⣻⣿⣟⣿⣷⢿⣟⣿⣽⣿⣯⣿⣯⣿⣯⣿⣯⣿⣻⡿⣟⣟⣯⠷⢩⢂⢂⢊⢐⢐⠰⡈⡂⡪⠠⡑⡌⠕⡌⡢⢣⢑⢅⢇⢪⠸⡰⡱⡘⡌⡆⡣⣪⢪⢪⡪⡎⣗⢵⢝⡮⣣⡣⡫⡺⣜⢵⡓⡽⡸⡸⡱⡹⡘⢾⣽⡿⣯⣿⣿⣟⣿⣟⣿⣾⣿⣯⣿⣿⣽⣿⣷
⣿⣾⡿⣟⣷⣳⣻⣿⣻⣯⣿⣿⣻⣿⣿⢿⣟⣯⢯⢯⣿⣿⣽⣿⣻⣿⣻⣿⣿⢿⢫⢘⠔⢐⢐⢐⢐⠔⠡⢂⢒⢌⠪⡢⡑⡅⢇⢊⢆⢣⢱⢸⠸⡘⡌⣆⢳⢨⢪⢪⢪⡪⣣⢫⢞⢜⢕⢗⢝⢮⢺⡸⡜⢎⢮⢺⢜⢜⢜⢜⢜⢌⢇⢟⣿⣿⣟⣷⣿⡿⣟⣿⣿⣾⢿⣻⣾⣿⣷⣿
⣾⡿⣿⣿⣿⢿⣽⣿⣟⣿⣿⣽⣿⣽⣾⣿⣿⣿⣽⣽⣿⣽⣿⣽⣿⣟⣿⣯⠟⢕⢡⢑⠨⢐⢐⢐⠔⠡⢁⠢⡱⢰⢑⠱⡐⡕⢅⢕⢱⢱⢱⢱⠱⡱⡱⡱⡕⡕⡵⡹⣜⢸⢸⢸⢱⢕⢕⢕⢭⢳⡱⡕⣝⢜⢜⡜⡎⣎⢎⢎⢜⠜⣜⢜⢷⣿⣻⢿⣻⣿⣿⣿⣾⣿⣿⣿⡿⣿⣾⣿
⣾⣿⣿⢿⣾⣿⣿⡽⣿⣻⣽⣿⣾⣿⢿⣻⣽⣾⣻⣿⣽⣿⣯⣿⣯⣿⠽⡂⡣⢑⠐⢄⠕⠡⡐⢌⠌⢌⠢⡱⠸⡐⡅⡣⡱⡸⡐⡕⡱⡑⡅⡇⡇⡣⡣⡫⡣⣪⡎⡇⣇⢣⢱⢱⢱⢱⢑⢕⢕⢕⢕⢕⢕⢕⢕⢜⢎⢮⢢⢣⠱⡑⡜⡵⡱⡻⣿⣿⡿⣿⣾⣿⣾⣿⣾⡿⣿⣟⣿⣾
⣻⣯⣿⣿⢿⣻⣽⣿⢿⣿⢿⣻⣗⢯⡻⡻⡿⣿⣿⣻⣯⣷⣿⡷⣟⣍⣪⢴⡜⡐⢌⠢⠨⡨⠨⡐⢌⠆⡕⢜⠡⡱⠨⡢⡣⣊⢢⢱⠱⡱⡱⡱⡡⡣⡣⡣⡱⣯⢿⡜⡔⡕⡅⡇⡇⡕⡕⢕⢅⢣⢣⢣⢣⢣⢣⠣⡣⡣⡣⡣⡩⡊⢆⡻⣽⡜⣽⣷⣿⣿⣷⣿⣷⣿⣷⣿⣿⡿⣟⣿
⢯⣞⣮⣻⡻⣿⣿⢿⣿⢿⣿⣿⢗⢧⡫⡮⣻⣿⣽⣿⡿⣟⣿⣿⣻⣽⡛⢕⣨⡬⢂⢐⢑⠠⠡⡘⢔⠱⡘⠔⡑⢜⢨⠪⡒⡔⡸⡰⡱⡱⡑⡕⡌⡎⡜⡰⡽⣯⢷⢯⡪⡪⡸⡨⡪⡸⡸⡸⡸⡘⡜⡌⡎⡜⡔⡕⢕⢕⢕⠕⡌⠌⡆⢇⡻⣟⣎⢷⣿⣷⣿⣷⣿⣯⣿⣯⣷⣿⣿⣿
⢕⣗⣵⣳⢽⣟⣿⣿⡿⣿⣿⣽⣏⢗⣝⢮⣳⣿⡿⣷⣿⣿⣿⣻⣯⢗⣮⡏⡃⡂⡂⠔⡡⠈⡔⢌⠢⡑⠅⢅⠕⠅⡢⡣⠣⡊⢔⠕⡜⢜⢜⠜⡌⡎⡊⣞⣯⡯⡿⡽⣎⢎⢆⢣⢱⠸⡰⡱⡸⡐⡌⡊⡎⡆⡕⡜⢌⢎⢆⢇⢇⠕⠨⢪⢪⢻⢗⣟⣿⣯⣷⣿⣯⣿⣯⣿⡿⣟⣿⣽
⡳⡵⣳⣳⣻⣿⣻⣷⣿⣿⣿⣽⣾⣿⣾⢷⣿⣟⣿⣿⣟⣷⣿⣽⢾⢛⠣⡑⡐⡐⡐⡐⠄⡕⢌⠢⠑⢌⠊⢔⠡⢡⢃⠎⢕⢑⢸⢘⢜⠜⡔⡕⢅⠇⢮⣻⣞⣽⢽⢯⢷⢕⠥⡑⡅⢇⢕⢜⠔⡅⡣⢕⢌⠊⢎⢜⠔⢅⢇⢕⢅⢣⠡⠡⡓⣝⢽⣗⣿⣟⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿
⢜⢽⡺⣿⣿⣻⣿⣟⣿⣷⣿⢿⣻⣽⣿⡿⣿⣽⣿⢷⣿⢯⣞⣪⡦⣱⢕⢐⠅⡊⠔⢀⠣⢊⢠⢂⠅⡂⡑⡐⠅⡪⡂⠪⡪⡨⠢⡣⡱⡑⡕⢜⢸⢨⢛⢚⢚⠚⠫⠫⠫⢓⢅⢇⢊⢪⠢⡱⡑⢌⢊⠔⡐⡱⡑⠜⡜⡌⢎⢪⢊⢆⠣⡑⡌⡌⡺⢜⡽⣻⢯⣿⣯⣷⡿⣿⣾⣿⣾⣿
⡸⣜⢼⢹⡫⡿⣟⣿⣿⣽⣾⣿⣿⣟⣯⣿⣿⣿⣽⣿⣯⢿⣾⢟⢅⠫⡐⢅⠪⡌⡐⠄⡃⡢⡑⠌⢊⢂⢎⠌⡢⠱⠀⢱⠨⡢⠱⡱⡘⡌⡎⢜⠰⡸⣝⢞⢜⠎⢎⢪⢸⢰⢱⡸⡨⡂⢇⢪⢘⢌⠢⠁⠈⡀⠁⠑⠨⡊⡪⡸⡐⢅⠪⢰⣱⡽⡌⣮⣮⣎⡯⣞⣷⣿⡿⣿⣿⣾⣿⣻
⡺⣪⣷⣷⣯⣮⢇⣗⢽⣿⣻⣿⡷⣿⡿⣿⡿⣾⣿⣻⣞⣟⢏⢊⡢⢱⢘⢌⢎⠆⡊⡐⡐⢌⢊⢊⠊⠌⠂⣊⡤⢥⢌⠐⢕⢌⠪⡢⢣⢱⠸⡨⠊⠊⠂⠁⠈⠈⡁⠐⢡⢳⢵⢝⡦⡣⡣⡑⡢⠪⡀⡊⢔⢌⡮⢀⢐⠸⡰⡱⡑⡰⡁⡣⣑⡻⣻⣜⡽⡿⣿⣷⣮⣗⣿⣿⣷⣿⣟⣿
⢽⣽⣻⣯⣿⣟⣮⣺⣺⢿⣻⣯⣿⡿⣿⡿⣟⣿⣾⢿⢝⢅⢧⠱⡱⡑⡕⠌⡎⠔⡐⡐⢌⠂⢅⠢⠠⠁⢰⠣⡪⡪⡨⠣⡑⢔⠱⡘⡌⢆⢣⢊⠀⡐⠠⣑⠡⣱⢸⢼⡰⡹⣮⣻⣺⢽⣎⣎⢌⠇⡎⣌⢫⠜⡊⡔⠄⢕⠨⡪⡢⠢⡱⡘⡔⣷⢹⣷⢿⣿⢿⣷⣿⡿⣷⡽⣷⣿⡿⣿
⢿⢿⣾⣞⢿⣻⣯⣿⡿⣿⣿⣿⢿⣿⢿⣟⣿⡿⡞⣍⣾⣻⣣⢗⢕⢱⢡⠑⠌⣂⠢⡨⠂⠌⠄⠌⢀⠈⢸⢨⢲⡙⠌⠌⢌⢆⢣⠱⡘⡌⡆⠕⡠⡈⠣⡙⡝⡪⡞⣏⢮⣞⣗⣗⡽⣽⣺⣗⢷⡱⡸⣘⢮⡳⡕⡕⡅⢕⢸⢸⢐⡑⠴⡑⡜⠽⣗⣿⣽⢿⣿⣟⣷⣿⣿⣿⡽⣿⡿⣿
⢿⣽⣳⡯⡯⣿⣟⣿⡿⣿⣿⣾⣿⣿⡿⣯⣿⠏⣮⣾⣳⢯⢣⢣⠣⡱⢡⠩⡊⢔⠡⠨⠨⡈⠄⡁⠠⠐⡀⠓⡜⡎⢕⢁⢂⢪⠰⠡⡣⢪⠨⡊⢜⣜⢖⣔⢦⣳⢽⣺⢽⣺⣺⢮⣻⡺⡮⡯⣗⣟⣜⢮⢎⡞⡮⡪⡂⢕⢸⠰⡐⣯⢯⢾⣼⣮⣮⢺⣿⢿⣻⣿⣟⣿⣯⣿⣟⣿⣿⣿
⢸⢹⢺⣻⢭⡻⣟⣿⡿⣿⣷⣿⢿⡾⣟⣯⢏⢮⠳⡣⢣⢪⢪⠢⡑⡕⡡⢑⢌⠢⡊⠌⡂⠂⠅⠄⡑⡐⡈⡐⠈⢝⢆⢅⢂⠂⡣⡃⡪⡂⢇⠪⡸⣪⡳⣕⡯⣺⢽⣺⢽⣳⢯⣻⢮⡫⡾⢽⡻⡺⣺⣝⡯⡯⡯⣎⢂⠪⡪⡸⢐⢿⣿⣻⣾⣯⣿⡕⣿⣿⣿⣟⣿⣟⣿⣽⣟⣯⣷⣿
⢱⢨⠢⡊⡪⡻⣯⣟⡿⣿⢷⡿⡯⡿⡳⡫⡪⡊⡎⡎⡎⡎⢆⢣⢣⠱⡈⡢⡊⡢⡑⡁⡂⠅⠅⢂⠂⡐⠐⠨⠈⠄⠃⢆⢐⠄⡱⠰⡐⢅⢣⠑⡌⡞⡮⣗⢯⣫⣗⡯⣟⡾⣽⣺⣳⡱⡡⢕⢱⢡⣷⣳⢯⡯⣯⠪⡐⡱⡱⡸⠨⣟⣿⣿⣻⣿⣻⡧⣿⣿⣾⣿⢿⣻⣿⣟⣿⣿⢿⣿
⢸⠸⡸⡨⢢⢊⢢⢑⠍⡝⢝⠞⡪⡚⡜⡜⡜⡜⡜⢜⢜⠨⡪⢸⢐⢕⢘⢌⠢⠢⡱⠐⠄⠅⡊⠄⢂⢠⡑⠈⠐⡈⢀⣆⠔⠈⢂⠇⡊⡢⡑⢅⠪⡪⡫⡾⣝⣞⡮⡯⣗⡯⣗⡯⡾⣝⡮⡧⣳⢯⢾⣺⢯⣻⡪⡁⠢⢪⠪⡊⡪⢿⣯⣿⣟⣿⣯⢿⣟⣿⣾⣿⣿⡿⣟⣿⣯⣿⣿⣿
⠰⡑⡅⡣⠣⡊⡢⢣⢑⢜⢔⢕⢕⢱⠱⡑⡕⡱⢨⢃⢆⠣⡘⡌⠆⡂⡢⡑⠌⢌⠢⡑⡁⡊⠄⠅⠢⢘⣦⡁⡂⠐⠠⢈⠣⠐⠀⠎⡪⠰⡘⡌⡪⡪⢯⡺⣵⡳⡯⡯⣗⡯⣗⡯⡯⡳⠙⠜⣘⢸⣙⣞⡽⡺⠐⡀⡣⢱⢱⢱⡪⣹⣿⣯⣿⣿⣽⣿⡿⣟⣿⣾⡿⣿⣿⡿⣟⣯⣿⣿
⠨⡢⡑⢜⢘⠜⡸⢘⢌⠆⡕⢔⡑⡔⢕⠡⡂⡊⡢⢑⠔⢅⢃⠢⢑⠐⠔⡠⢑⠄⡃⢆⠕⡨⡘⣬⠌⡂⣳⣷⠄⠅⡘⠐⡀⠂⡁⠌⡊⢎⠔⢕⢌⢪⢳⡹⣪⢞⡽⣝⢮⣻⡺⣜⣖⢮⢏⠯⡪⣺⢺⡪⠎⠠⢐⠐⡌⡪⡢⣻⣯⣒⢿⣯⣿⣾⣿⣷⣿⣿⣿⣟⡿⣿⣷⣿⣿⣿⡿⣿
⢌⢂⠪⠨⡂⠕⢌⠢⡢⡑⢜⢐⢑⢌⠢⡑⢔⠔⢜⠰⡑⡑⠄⠕⡠⠡⠑⠄⠅⡂⡪⡂⡣⣫⢷⢹⣣⡊⠔⣿⢺⣲⣄⡡⠀⠅⠠⢂⠪⡨⡊⡪⡪⡊⡆⢝⢜⢵⢝⢮⡳⡳⣝⡞⡮⡣⡣⡣⣣⡳⡝⢼⠀⢂⠂⢅⢣⢣⢹⣽⣿⢿⣞⣿⢿⣽⣾⣯⣿⣿⣾⣿⣿⢿⣽⣿⣽⣿⣻⣿
⠔⡨⠨⡨⢂⠣⡑⡑⢔⠨⠢⡑⢔⠢⠱⡘⢔⠡⠅⢕⠨⡐⢡⢑⠠⠡⠡⠡⠨⠢⡱⡱⡽⣽⢿⡷⣝⢗⢅⠫⢫⠳⡙⡪⢀⠠⢑⢀⢂⢒⠌⢆⢣⢣⢝⠰⡐⢔⠩⡑⠹⢹⢪⢞⢽⡹⣝⣞⢞⢎⢎⢽⣷⠡⡈⢔⢕⢕⢽⣷⣿⣿⣿⣽⣿⣿⢿⣻⣿⣾⣿⣾⣿⣿⡿⣿⣽⣿⣜⣮
⢈⠢⡑⠔⡡⠊⠔⡨⠠⠡⠡⠨⢐⠨⠨⡐⡐⡡⠡⡁⡢⠨⢂⠂⢌⠌⢌⠌⣜⣼⣽⣺⡝⡾⡹⡹⡸⣝⢜⢮⡲⣕⢬⠢⡂⠆⡂⡂⠢⠀⠕⡑⡌⡪⢪⢱⢡⠣⡑⡌⡊⣂⠂⠉⠘⠊⠃⠓⣡⢇⣗⢽⡗⣕⠀⡎⡎⡦⣿⢿⣷⣿⣯⣿⣿⣾⣿⣿⡿⣷⣿⣷⣿⣷⣿⣿⡿⣯⣿⣿
⠠⡑⠌⢌⠢⠑⢅⠢⠡⠡⠡⡑⠄⠅⢅⢂⠢⠨⢂⠢⢊⠌⢄⠅⠅⢌⢂⢣⡮⣷⡿⡎⡎⡞⡜⣜⢕⢗⡽⣕⢗⡕⣗⢽⡹⡵⣢⢦⢅⠅⢌⠐⢅⠇⡇⡎⡪⡪⡊⡆⢕⠔⠀⠀⠈⠌⡨⢐⠨⢙⢎⣟⣯⠇⢌⢎⢂⢻⣽⣿⢿⣷⣿⣿⣾⣿⣯⣿⣿⢿⣯⣷⣿⣯⣿⣷⣿⣿⣿⣻
⠨⠢⡑⡡⠨⡊⠔⢌⢊⠌⢌⠔⠌⢌⢂⠢⡡⡑⡐⢅⠅⡪⢐⠡⡑⢕⢨⣾⡿⡟⢟⠕⡕⢕⠝⠜⡜⣕⠧⡓⡯⡺⡵⡫⣞⣝⢮⡳⣝⣝⢔⢅⠅⢇⢇⢇⢇⢎⢪⢪⠢⡃⠀⠀⠁⠀⠂⠢⠡⡑⡰⡐⠝⢄⠕⢌⢂⢂⢳⣿⣿⡿⣷⣿⣷⣿⣯⣿⣾⣿⣿⣿⣻⣽⣿⣽⢯⣾⣿⣿
⠨⡈⡂⡪⠨⡂⠕⡁⡂⡊⢔⢬⠮⣒⣥⢷⠻⡐⠅⢕⠨⢂⠢⡣⢑⢡⣟⣿⠘⠜⡌⣆⢮⢢⡕⣗⡬⣢⣣⡣⡧⣕⢕⣍⡪⡨⡣⡫⣞⢮⡳⡕⡅⡣⢣⢣⢣⢣⢣⠪⡒⡄⠀⠁⠀⠁⡀⠈⠈⠰⡐⢜⠨⡢⢃⢅⠪⡐⠼⣿⣷⣿⣿⣿⣾⣿⣽⣿⣻⣽⣷⣟⣿⣿⣟⣿⣿⣿⣯⣿
⢐⠰⢐⠐⢥⣶⣷⣶⣾⡾⣾⡾⡝⡫⠨⠢⡑⢌⠪⢐⢈⠢⡃⠪⣐⣵⣟⠭⣊⢎⢇⢧⢳⢱⢝⢮⡺⣕⢗⡝⣞⢮⡫⣞⢵⡻⣮⣲⡡⣓⡝⣎⢧⢑⢅⢇⢇⢇⢇⢇⢕⢜⢄⢑⠈⠀⡀⠄⠀⠄⠌⡢⢱⢡⢑⠔⡑⢌⠪⡹⣿⣽⣷⣿⣷⣿⣟⣿⡿⣟⣿⣿⢿⣽⣿⢿⣽⣾⣿⣿
⠐⠌⡂⢅⢹⣯⣷⣿⣷⣿⠟⢕⢼⢐⢑⢑⠌⡐⠨⢐⠐⢅⠊⢌⣾⣟⣧⡣⡣⡱⢹⢸⢸⢜⢮⡺⡜⣞⢼⡺⣪⢞⠮⣎⢗⢝⡞⣎⢯⡳⣝⢮⡳⡥⣱⢰⢑⢕⢕⢕⢕⢌⢆⢇⠅⢅⠀⡀⠄⠀⢁⢊⠢⡑⢅⠕⡅⢕⢱⠐⡙⣿⣿⣽⣾⣿⣟⣿⣿⣿⡿⣿⣿⢿⣿⢿⣿⣟⣿⣾
⠨⠨⢂⠅⣞⣿⣻⡽⡳⣡⣳⠫⡑⡐⡡⠂⠢⠨⡈⡂⠅⢅⢊⣾⢿⢍⢇⠇⢇⢓⢕⠇⡗⢵⢱⢕⢵⢝⡜⡜⡌⡇⡏⡎⡮⡳⡹⡪⡳⣝⢮⢧⡳⣝⢮⡳⡅⡎⡜⢜⢜⢜⢌⢆⠝⡔⡡⡀⠄⢀⠀⠑⡅⢕⡐⢅⠣⡣⡱⡈⡢⢊⠻⣟⣯⣿⣟⣿⣷⣿⡿⣿⣻⣿⣯⣯⣿⡿⣟⣿
⠨⠨⢂⢊⠝⢝⣱⣵⣾⢯⣦⢊⢐⠔⠠⠡⠡⠡⢂⢊⢌⠢⣹⡷⡹⡐⡅⢕⠅⠕⠔⡑⢌⠢⡃⢕⠸⡘⢜⠑⠅⡃⠣⡑⢌⠪⡊⡣⢫⢪⢎⡇⡧⡳⡕⣝⢮⢳⡑⡅⢇⢧⢱⢪⣪⢲⣳⢸⢨⠢⡐⡀⠘⢔⠜⢌⢊⢎⢎⢆⠊⡆⡇⡻⣿⢿⣟⣿⣽⣾⣿⣿⡿⣟⣿⣟⣿⣿⣿⣿
⢈⢪⣲⣳⣳⣿⡾⣿⣾⡟⡓⡐⡐⠌⡊⠌⢌⢊⠔⣰⠢⣱⣿⣷⡑⢌⠌⡂⠁⠄⠡⠈⠄⡁⠂⡁⠅⠨⠠⢈⢐⢀⠡⡐⡐⢔⢐⠌⡐⢐⠐⢍⢊⠇⠏⡎⡮⣣⢳⡘⡌⢎⢖⠅⢗⡯⣞⢵⡪⣊⢆⠠⠀⠂⡣⡱⡘⡌⡎⡎⣮⣔⢕⢕⢎⢿⣿⡿⣿⣻⣯⣷⣿⡿⣿⣿⣻⣷⣿⣿
⢐⢽⡿⣿⣟⣯⣿⠿⢑⢐⢐⠌⡐⡡⢂⢑⢐⢐⢌⡯⡨⣾⣿⣯⣿⣆⠁⠄⠁⠌⢈⠠⠁⢀⠂⠄⠌⢌⠌⠆⠕⠌⠪⠐⠅⠃⠆⠕⡐⡐⡈⠠⢀⠈⡈⠐⠩⢊⢇⢳⢸⠨⢪⢪⠢⡫⣞⢵⡫⣞⡔⡅⡂⠀⠐⠜⡌⡪⢪⢪⢺⣿⣳⡱⡱⡕⣕⢿⣿⣿⡿⣟⣯⣮⣫⣿⣿⣻⣽⣾
⢷⣗⣟⢿⡻⢏⠅⡑⡐⠔⡐⢌⢐⢐⢐⢐⢐⠔⡘⠅⣾⣿⣯⣿⢾⣿⡆⠀⢁⠠⢀⠠⠐⡐⢈⠌⠨⠐⠈⢈⢀⠅⡢⢒⠔⡢⡂⡂⠄⠠⠈⢈⠂⡂⡂⡡⠐⢀⠐⠡⢊⠪⡢⢑⢕⢕⢽⣕⢯⢞⢮⣣⢅⠨⡀⠀⢕⢜⢸⢸⡸⣿⡿⣟⣎⢮⡪⡪⢝⢷⣿⣿⣯⣾⣿⣿⣻⣿⣿⢿
⣿⣿⢿⡯⠃⢅⢂⢂⢊⠌⡐⡐⡐⡐⡐⡐⡐⡐⡰⣵⣹⣳⣷⡩⠛⠓⠠⠈⠄⠂⠄⠂⠡⠐⠀⠐⢀⢐⠨⢂⢑⠌⡢⢑⢌⠢⡑⠕⡅⢅⠀⢂⠠⠠⢀⠂⡁⢂⠐⠠⠀⠌⢌⠢⡑⡕⡕⠵⡯⣯⣳⡳⡳⠀⢕⠅⠄⢣⠱⡱⡱⣻⣿⣿⣽⣯⣿⣮⡪⡪⡎⡿⣿⣻⣽⣾⣿⣿⣾⣿
⣿⣾⡟⡐⡡⢁⢂⠢⠂⢅⠂⡂⡂⡂⡂⣂⢆⢢⣿⡿⣿⡿⣿⣿⡄⠈⠄⠁⠌⠀⠂⠁⠐⠈⡀⠅⢂⢐⠨⡐⡐⠅⢌⠢⠢⡑⠌⢌⠌⡢⢃⠢⠨⠨⢐⠠⠂⠄⠌⡀⠡⠐⢀⠁⠊⢜⢌⠇⡏⣞⢮⣞⡝⠀⡧⣃⢇⠌⡪⡪⡪⣙⢯⣿⣷⣿⣷⣿⣻⣮⡪⡪⡪⡝⢿⡿⣟⣷⣿⣟
⣿⣻⢂⢊⠄⢅⠂⢅⠑⠄⠅⡂⡂⡂⡢⣿⡂⣾⣟⣿⣿⢿⣟⣿⠂⡈⢀⠈⡀⢈⠀⠁⢀⠁⠠⠐⡀⠂⠌⡐⡨⠨⢂⠅⠕⡨⠨⢂⠑⠄⠡⢑⠁⠅⢂⢑⠈⡈⠢⡐⡠⢈⠠⠀⠅⡕⢌⠪⡌⡲⡙⠎⠎⢠⡻⣪⢦⢑⠈⢎⢜⢔⢽⣿⢿⣾⣿⣾⣷⣿⢿⣮⢪⢪⢪⢪⢻⢻⢿⣟
⣿⢯⠐⠄⠕⡠⠑⠄⠅⢅⠕⡐⡐⠔⣽⣿⢊⣿⣟⣿⣽⣿⣟⣷⠀⠠⠀⠠⠀⠠⠀⠐⠀⠄⠁⠄⢂⠡⠑⡐⠄⠕⡠⠡⡑⠠⠡⡑⠨⠨⠐⠠⠡⠈⠄⡐⢀⠨⠂⠢⡈⡢⠨⢂⠅⡇⢌⠪⡸⡰⡘⡔⡈⡮⡺⣝⡵⡣⡃⢅⢣⢱⢸⣿⣿⡿⣷⣿⣯⣿⣿⣿⣷⣕⠧⣇⢇⢇⢇⢏
⡿⡯⡈⠪⠨⠠⠡⠡⢡⢑⠰⡐⡌⢌⣿⡿⣸⣿⡿⣿⣟⣯⣿⣿⣿⣶⣌⡠⠐⠀⠐⠈⠀⠄⠂⠐⡀⢂⠡⢐⠈⠌⡐⠡⡂⠅⠅⠂⠅⠡⢂⠐⢀⠈⠐⠀⠄⢊⠢⣁⡐⠄⠅⠅⡢⠅⢑⠱⡈⢎⠪⡊⡎⡮⣪⣪⢺⡘⡼⣅⠪⡸⡨⢿⣷⣿⣿⣯⣿⣯⣷⣿⣯⣿⣿⣵⣯⣺⢮⣪
⣏⠢⠨⡊⠌⢌⠌⠌⡂⢆⢕⢸⣷⢁⢻⡯⣺⣿⢿⣿⢿⣿⣻⣷⣿⣷⣻⣿⣶⣌⠄⠐⠀⠂⢀⠁⠄⢂⠐⡐⠨⢐⢈⠢⠨⡘⠨⡈⠌⡈⠄⡀⠄⠀⠁⢂⠀⠀⠄⠁⡘⠸⢸⢨⠊⠄⠄⠁⢊⢪⢑⠅⡇⡗⣕⢗⣳⡹⣝⢮⢆⢊⢆⢑⠻⣯⣿⣯⣿⣟⣿⣯⣿⣟⣯⣿⣟⣿⣷⣟
⠆⢅⠕⡐⡡⠡⡈⡂⠪⡐⢴⣹⣿⣧⢂⠫⣺⣿⣿⢿⣿⢿⣟⣿⣽⣿⣻⣿⡍⠁⠀⢀⠐⠀⠠⠐⠈⠄⠂⠄⠡⢂⢐⠨⢐⠨⢐⠨⠐⡀⡂⠄⠠⠀⢈⠠⠀⠠⠐⢀⠠⠀⠀⡀⠌⠢⠡⠡⡀⢐⠱⡁⢧⢇⢯⢳⠵⣝⢮⣫⢳⡢⢊⠔⠱⡨⠻⣿⣽⣿⣟⣯⣿⣿⢿⣿⣻⣿⣯⣿
⡍⡂⡢⢂⢊⠔⡐⠌⡂⡊⢾⡮⣾⣿⣷⣌⢺⣿⣻⣿⡿⣿⣿⢿⣟⣿⣟⣿⡇⠈⠀⠠⠐⠀⠂⢀⠁⢂⠁⠌⠐⡀⠂⠌⠠⠨⢐⠨⠠⢀⠐⢈⠐⠀⡀⠐⠈⢀⠀⠢⢐⠀⠅⡀⢀⠀⠈⠨⢐⠀⡘⢌⢪⡳⣹⢪⡫⣎⢧⢳⡣⡇⡕⡌⡌⠢⠨⢌⢛⣯⣿⣿⣟⣿⣿⢿⣻⣯⣿⣿
⡒⢼⣂⠢⠡⢂⠊⠔⡐⢌⢺⣷⢹⣷⣿⣿⣅⡻⣻⣯⣿⣿⢿⣿⢿⣿⣻⡟⠀⡈⠀⠂⡀⠂⠈⢀⠠⠐⠀⠌⡀⢂⢈⠈⠨⠐⡐⠠⢁⢂⠐⡀⠌⠀⠀⠈⠠⠀⠄⠨⠂⢅⢂⠐⡐⡐⡀⠀⡂⡒⠢⠢⡡⡫⡎⣗⢝⣜⣎⢧⢳⢕⣝⠮⡪⠠⢁⠑⡔⣿⣿⣯⣿⣿⣻⣿⣿⡿⣟⣿
⢌⢽⢧⠨⢊⠔⢡⡑⡐⢄⠹⣿⣧⡻⣿⣽⣷⣝⣷⣽⡻⡿⣿⢿⣿⢿⡏⠀⠄⠀⡀⢁⠠⠀⡁⠀⠄⠐⠈⠀⠄⠠⠀⠌⡀⠂⠐⠈⠄⠂⡂⠂⢄⠀⠄⠁⠠⠀⠠⠈⠄⢅⢐⠠⠐⢐⠨⠠⠀⠕⠊⠡⡂⢇⢟⢮⡳⡕⡧⣫⢺⡸⡸⣕⢕⡕⢄⠐⢌⢻⣽⣿⣽⠻⣟⣯⣷⣿⣿⣿
⢐⠌⢿⣕⢐⠸⣔⢿⣔⠄⠅⠽⣾⣷⣝⢿⣿⣻⣞⣿⢿⣿⣾⢿⣽⣟⣿⣆⠐⠀⠠⠀⠠⠀⠔⠈⢀⠁⡈⠠⠐⠀⠂⠐⠀⠅⠨⠐⠈⠠⠠⠑⠠⠂⠄⠂⠀⠀⠄⠨⠀⢕⠐⡀⠂⠀⠁⢅⠑⠄⠂⠨⢨⢊⢗⣕⢗⡝⣎⢮⢣⡣⡯⣪⢳⡱⢅⠂⡐⠝⣿⣟⣯⡣⣿⣿⣿⡿⣟⣿
⢐⠅⠕⡻⣕⠌⣻⢷⢽⢮⡨⠂⠝⣿⣽⣮⡻⡿⣿⣻⣽⣿⣽⣿⣿⣻⣿⠝⠀⠐⠀⡈⠠⢈⠐⢈⠀⠠⠀⠂⠐⠈⠀⡁⠌⠀⠅⠌⢐⠀⢂⠈⠨⠈⡀⠀⠀⠐⠀⡂⠡⢐⠠⠀⠅⡈⢀⠂⠁⠅⠂⠌⡐⢅⢇⢗⡕⡧⡳⡱⡣⡣⡳⡱⡱⡑⢅⠂⠠⢑⠐⢝⢿⣿⣿⢿⣷⣿⣿⣿
⠐⢌⠌⡢⠙⢜⢈⢿⣻⣷⣵⡡⠑⠌⢟⣿⢿⣯⣽⡻⡿⣷⣿⣷⢿⣻⣿⠀⠄⠀⠁⡀⠠⠀⠂⡀⠂⠁⠄⠁⡈⠄⠁⢀⠀⠡⠐⠈⠠⠈⠄⢂⠀⡁⠠⠀⠀⠀⠂⠠⡁⠐⠄⠨⠐⡀⠐⠠⡱⠡⡁⠌⠄⠕⢜⠸⡘⢜⠨⢌⠪⡘⢌⢌⠢⡑⠔⠈⠀⠌⢌⢐⠕⣿⣿⢿⣟⣯⣿⣿
*/
 
#include <bits/stdc++.h>
using namespace std;
 
#pragma GCC optimize("O3")
#pragma GCC target("popcnt")

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

using ll = long long;
#define int long long
#define forn(i,n) for(int i=0; i<(n); ++i)
#define pb push_back
#define pi pair<int,int>
#define f first
#define s second 
#define vii(a,n) vector<int> a(n); forn(i,n) cin>>a[i];
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
 
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll inf = 1e18;
const ll mod = 1e9+7;//998244353;

/*
⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢿⢂⢂⢂⢂⠔⡐⡐⢔⢔⢡⠪⣛⣿⣿⣿⣿⣿⣿⣿
⣿⡯⣿⣯⣿⣯⣿⡿⣾⢝⢑⢐⢐⠔⢔⢱⢘⢌⢆⡧⣣⡣⡳⡜⡽⣾⣿⣯⣿⣷
⣽⣿⡿⣿⢽⣾⣿⡻⡋⡂⢆⢑⢜⠸⡸⡘⡜⣜⢜⢜⢜⢜⢕⢕⠱⡽⣿⣾⣿⣽
⢵⣻⣿⣯⣳⣿⣟⡯⠪⠐⠌⡂⢅⠇⡕⢕⢱⡿⡜⡸⡰⡑⢅⢇⠣⢝⡿⣯⣿⣿
⢼⣽⢻⣿⣻⣷⡷⡩⡱⢁⠣⢘⠄⢕⠜⠜⢒⢂⢇⣎⢆⢌⡄⢕⢁⡳⣫⣟⣯⣿
⠿⣽⣿⣿⣯⠧⡗⡕⢔⢐⢈⠐⢍⠢⡃⡣⡭⣽⣺⣺⡳⣜⢮⠸⣰⣮⣻⣿⣿⢿
⠪⡸⣘⢓⢕⠕⢕⠅⠕⡐⡐⢌⢈⠔⢌⢢⡫⣞⡾⡲⡪⡯⠇⢕⢼⣿⣾⣿⣻⣿
⠨⡂⠆⠕⡡⢊⠢⠨⡈⡮⡾⢜⠦⠂⡘⡰⡩⡚⡺⢝⢼⢡⢨⢺⣯⣿⣷⣿⢿⣟
⠡⡨⠨⢂⣢⠡⢊⢔⡽⡣⣋⢞⡝⢵⢲⡐⡕⡜⡄⠐⠨⡋⢔⢹⣿⡿⣷⣿⣿⣿
⠐⣼⢿⠫⡐⠌⡂⡾⢜⠜⡕⡽⡪⢏⡗⡧⣣⢣⢲⠠⡀⢜⠰⡡⠻⣿⣿⣯⣷⣿
⣸⣶⠟⡑⢄⢱⣸⣅⠅⠨⠈⠄⠌⡢⠨⢑⠑⢣⠱⡹⣪⠄⠑⢕⣯⢝⢿⣽⣻⣿
⡟⡐⡐⡐⣰⣰⣿⡍⠀⠂⠁⢌⠊⠔⡑⠄⠌⠄⡈⠪⡱⠏⣇⠕⡺⣿⣮⣛⢻⣿
⢇⢂⠢⢢⢯⣿⣿⣦⣄⠈⠐⠠⠡⢑⠠⠁⠈⠢⠨⠔⢘⢕⢵⣱⢑⢿⣿⡿⣷⣖
⢐⡐⠡⡿⣦⢿⣷⣿⠇⠀⢁⠨⠀⠅⢂⠁⠈⠀⡂⠌⢀⠎⣮⡪⡇⡆⠽⣿⣿⣿
⢘⢌⣧⠚⣿⢿⣷⣿⠂⠈⢀⠠⠐⠈⠠⠈⡀⠠⠐⢀⢁⠈⡎⠮⡺⡘⠐⠻⣾⣿
*/

const int N=2e5+5;
vector<int> adj[N];
int d[N];
const int K=18;
int to[N][K];
int tin[N],tout[N],t=0;
void pre(int u, int p) {
    tin[u]=t++;
    to[u][0]=p;
    for(auto&v:adj[u]) {
        if (v==p) continue;
        d[v]=d[u]+1;
        pre(v,u);
    }
    tout[u]=t++;
}
int c[N];
int up[N];

int jump(int u, int x) {
    forn(j,K) if ((x>>j)&1) u=to[u][j];
    return u;
}
int lca(int u, int v) {
    if (d[u]>d[v]) swap(u,v);
    v=jump(v,d[v]-d[u]);
    if (u==v) return u;
    for(int j=K-1; j>=0; --j) {
        if (to[u][j]==to[v][j]) continue;
        u=to[u][j],v=to[v][j];
    }   
    return to[u][0];
}

int m[N][K];

int get(int u, int x) {
    int ret=inf;
    forn(j,K) {
        if ((x>>j)&1) {
            ret=min(ret,m[u][j]);
            u=to[u][j];
        }
    }
    return ret;
}

vector<int> a[N];
int vis[N],cvis[N];

struct BIT {
    vector<int> t; int n;
    BIT(int n) {
        this->n=n;
        t.assign(n,0);
    }
    BIT(vector<int> a) {
        n=a.size();
        t.assign(n,0);
        forn(i,n) add(i,a[i]);
    }
    void add(int i, int x) {
        for (; i<n; i=i|(i+1)) t[i]+=x;
    }
    int sum(int r) {
        int q=0;
        for(; r>=0; r=(r&(r+1))-1) q+=t[r];
        return q;
    }
    int sum(int l, int r) {
        if (l>r) return 0;
        return sum(r)-sum(l-1);
    }    
};

int isanc(int l, int u) {
    return tin[l]<tin[u] && tout[u]<tout[l];
}

void solve() {

    int n,k; cin>>n>>k;
    forn(i,n-1) {
        int u,v; cin>>u>>v; --u, --v;
        adj[u].pb(v); adj[v].pb(u);
    }
    pre(0,0);
    for(int j=1; j<K; ++j) forn(i,n) to[i][j]=to[to[i][j-1]][j-1];

    forn(i,k) up[i]=-1;
    forn(i,n) {
        cin>>c[i]; --c[i]; 
        if (up[c[i]]==-1) up[c[i]]=i;
        up[c[i]]=lca(up[c[i]],i);
    }
    forn(i,n) m[i][0]=d[up[c[i]]];
    for(int j=1; j<K; ++j) forn(i,n) m[i][j]=min(m[i][j-1],m[to[i][j-1]][j-1]);

    forn(i,n) a[c[i]].pb(i);

    int ans=k-1;
    vector<pi> v; forn(i,k) v.pb({d[up[i]],i});
    sort(rall(v));
    BIT ft(2*n);
    for(auto&x:v) {
        int i=x.s;
        int z=n;
        int s=0;
        for(auto&x:a[i]) {
            z=min(z,get(x,d[x]-d[up[i]]+1));
            s+=ft.sum(tin[up[i]],tin[x]);
        }
        if (z < d[up[i]]) continue;
        if (c[up[i]]!=i) continue;
        if (s) continue;
        queue<int> q; for(auto&x:a[i]) q.push(x);
        vector<int> rb={up[i]}; vis[up[i]]=1; cvis[i]=1;
        int top=up[i];
        while (q.size()) {
            int u=q.front(); q.pop();
            rb.pb(u);
            if (isanc(u,top)) {
                while (top!=u) {
                    top=to[top][0];
                    vis[top]=1;
                    if (!cvis[c[top]]) {
                        cvis[c[top]]=1;
                        for(auto&x:a[c[top]]) q.push(x);
                    }
                }
            }
            while (!vis[u]) {
                vis[u]=1;
                if (!cvis[c[u]]) {
                    cvis[c[u]]=1;
                    for(auto&x:a[c[u]]) q.push(x);
                }
                u=to[u][0];
            }
        }
        int cnt=0;
        for(auto&x:rb) {
            cnt+=cvis[c[x]];
            vis[x]=0;
            cvis[c[x]]=0;
            ft.add(tin[x],1);
            ft.add(tout[x],-1);
        }
        ans=min(ans,cnt-1);
        //ft.add(tin[up[i]],1);
        //ft.add(tout[up[i]],-1);
        //forn(i,n) cout<<ft.sum(tin[i],tin[i])<<' '; cout<<'\n';
    }
    cout<<ans<<'\n';

}

int32_t main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int t=1;    
    //cin>>t;
    while (t--) solve();
    return 0;
}

Compilation message

capital_city.cpp:4:1: warning: multi-line comment [-Wcomment]
    4 | //   \ __ __  \
      | ^

Subtask #1
1.0 / 1.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 13400 KB Output is correct
2 Correct 3 ms 11352 KB Output is correct
3 Correct 2 ms 13404 KB Output is correct
4 Correct 2 ms 13404 KB Output is correct
5 Correct 2 ms 13404 KB Output is correct
6 Correct 2 ms 11356 KB Output is correct
7 Correct 2 ms 11192 KB Output is correct
8 Correct 3 ms 11356 KB Output is correct
9 Correct 2 ms 13404 KB Output is correct
10 Correct 2 ms 13400 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 13400 KB Output is correct
2 Correct 3 ms 11352 KB Output is correct
3 Correct 2 ms 13404 KB Output is correct
4 Correct 2 ms 13404 KB Output is correct
5 Correct 2 ms 13404 KB Output is correct
6 Correct 2 ms 11356 KB Output is correct
7 Correct 2 ms 11192 KB Output is correct
8 Correct 3 ms 11356 KB Output is correct
9 Correct 2 ms 13404 KB Output is correct
10 Correct 2 ms 13400 KB Output is correct
11 Correct 4 ms 13916 KB Output is correct
12 Correct 3 ms 11808 KB Output is correct
13 Correct 3 ms 11868 KB Output is correct
14 Correct 5 ms 11908 KB Output is correct
15 Correct 4 ms 13916 KB Output is correct
16 Correct 3 ms 11868 KB Output is correct
17 Correct 4 ms 13916 KB Output is correct
18 Correct 4 ms 13960 KB Output is correct
19 Correct 3 ms 13916 KB Output is correct
20 Correct 3 ms 13916 KB Output is correct
21 Correct 3 ms 13916 KB Output is correct
22 Correct 3 ms 11868 KB Output is correct
23 Correct 3 ms 13916 KB Output is correct
24 Correct 5 ms 13872 KB Output is correct
25 Correct 3 ms 11868 KB Output is correct
26 Correct 3 ms 11868 KB Output is correct
27 Correct 4 ms 11612 KB Output is correct
28 Correct 4 ms 11612 KB Output is correct
29 Correct 4 ms 11612 KB Output is correct
30 Correct 4 ms 11612 KB Output is correct

Subtask #3
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 342 ms 94080 KB Output is correct
2 Correct 148 ms 94060 KB Output is correct
3 Correct 254 ms 93828 KB Output is correct
4 Correct 151 ms 94152 KB Output is correct
5 Correct 239 ms 92616 KB Output is correct
6 Correct 145 ms 94184 KB Output is correct
7 Correct 239 ms 92612 KB Output is correct
8 Correct 143 ms 93412 KB Output is correct
9 Correct 285 ms 94500 KB Output is correct
10 Correct 255 ms 93516 KB Output is correct
11 Correct 266 ms 94436 KB Output is correct
12 Correct 279 ms 95520 KB Output is correct
13 Correct 251 ms 93372 KB Output is correct
14 Correct 272 ms 95688 KB Output is correct
15 Correct 266 ms 95516 KB Output is correct
16 Correct 311 ms 93460 KB Output is correct
17 Correct 264 ms 93692 KB Output is correct
18 Correct 251 ms 93888 KB Output is correct
19 Correct 298 ms 95248 KB Output is correct
20 Correct 255 ms 95780 KB Output is correct
21 Correct 2 ms 10584 KB Output is correct

Subtask #4
0 / 59.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 13400 KB Output is correct
2 Correct 3 ms 11352 KB Output is correct
3 Correct 2 ms 13404 KB Output is correct
4 Correct 2 ms 13404 KB Output is correct
5 Correct 2 ms 13404 KB Output is correct
6 Correct 2 ms 11356 KB Output is correct
7 Correct 2 ms 11192 KB Output is correct
8 Correct 3 ms 11356 KB Output is correct
9 Correct 2 ms 13404 KB Output is correct
10 Correct 2 ms 13400 KB Output is correct
11 Correct 4 ms 13916 KB Output is correct
12 Correct 3 ms 11808 KB Output is correct
13 Correct 3 ms 11868 KB Output is correct
14 Correct 5 ms 11908 KB Output is correct
15 Correct 4 ms 13916 KB Output is correct
16 Correct 3 ms 11868 KB Output is correct
17 Correct 4 ms 13916 KB Output is correct
18 Correct 4 ms 13960 KB Output is correct
19 Correct 3 ms 13916 KB Output is correct
20 Correct 3 ms 13916 KB Output is correct
21 Correct 3 ms 13916 KB Output is correct
22 Correct 3 ms 11868 KB Output is correct
23 Correct 3 ms 13916 KB Output is correct
24 Correct 5 ms 13872 KB Output is correct
25 Correct 3 ms 11868 KB Output is correct
26 Correct 3 ms 11868 KB Output is correct
27 Correct 4 ms 11612 KB Output is correct
28 Correct 4 ms 11612 KB Output is correct
29 Correct 4 ms 11612 KB Output is correct
30 Correct 4 ms 11612 KB Output is correct
31 Correct 342 ms 94080 KB Output is correct
32 Correct 148 ms 94060 KB Output is correct
33 Correct 254 ms 93828 KB Output is correct
34 Correct 151 ms 94152 KB Output is correct
35 Correct 239 ms 92616 KB Output is correct
36 Correct 145 ms 94184 KB Output is correct
37 Correct 239 ms 92612 KB Output is correct
38 Correct 143 ms 93412 KB Output is correct
39 Correct 285 ms 94500 KB Output is correct
40 Correct 255 ms 93516 KB Output is correct
41 Correct 266 ms 94436 KB Output is correct
42 Correct 279 ms 95520 KB Output is correct
43 Correct 251 ms 93372 KB Output is correct
44 Correct 272 ms 95688 KB Output is correct
45 Correct 266 ms 95516 KB Output is correct
46 Correct 311 ms 93460 KB Output is correct
47 Correct 264 ms 93692 KB Output is correct
48 Correct 251 ms 93888 KB Output is correct
49 Correct 298 ms 95248 KB Output is correct
50 Correct 255 ms 95780 KB Output is correct
51 Correct 2 ms 10584 KB Output is correct
52 Correct 235 ms 91824 KB Output is correct
53 Correct 225 ms 91588 KB Output is correct
54 Correct 245 ms 91592 KB Output is correct
55 Correct 230 ms 91932 KB Output is correct
56 Correct 223 ms 91592 KB Output is correct
57 Correct 245 ms 91588 KB Output is correct
58 Execution timed out 3044 ms 91332 KB Time limit exceeded
59 Halted 0 ms 0 KB -