/*
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⠦⠶⡶⢦⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣴⣶⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣭⣽⣭⣯⡭⡈⢙⣽⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⣟⣽⣾⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣟⠟⡻⣿⣿⣟⣟⣟⣿⡻⠿⠿⠿⠿⣍⠉⠉⠉⠙⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⣾⣿⣯⣿⣿⣿⣽⣿⣷⣽⣿⣿⡿⣿⣿⣾⢿⣿⡷⣿⣿⣿⣿⣯⣭⡅⣠⣹⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣟⣽⣿⣿⣿⣻⣿⣟⣟⣿⣻⣿⣝⣿⣯⣿⣻⣻⣿⣿⣿⣿⡪⡻⣿⣿⣽⣿⣿⣯⣻⣿⣶⣿⣖⣓⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢿⣿⣟⣿⣿⣻⣿⣿⣿⠿⣿⣿⡿⣿⣿⢿⣿⡯⣿⣛⣿⣕⣿⣿⡿⣿⣿⣷⢿⡿⣻⣿⣿⣿⢿⣿⣿⡻⣿⡷⠷⠯⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡽⠹⠩⡝⡇⡿⢻⢻⢻⡛⣿⣹⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⡿⣿⣿⣿⣿⣽⡿⣿⣯⣻⣿⣿⡿⣿⣿⣿⣿⣿⣝⡍⠩⠀⢘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣓⣂⣀⣀⠀⣜⣀⣀⠐⠐⠓⣞⠨⣿⠿⣗⣿⣿⣻⣿⣿⣽⣿⣿⣺⣿⣿⣿⣿⣻⣿⣿⣿⣝⢿⣛⠻⣻⣿⣟⣟⣿⣿⣿⣤⣐⣒⣚⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠻⠽⢯⣌⣶⣿⠿⡡⢴⣾⠛⢀⣷⡉⡟⣷⢊⢘⢀⡙⣷⣾⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⡿⣿⣿⣽⢋⣝⣿⡿⣿⢿⢿⣛⢿⣿⣗⢇⠟⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣉⣉⣉⣸⣿⣿⣉⣉⢉⣿⠷⠶⠀⢸⣿⣿⢿⠀⠀⠀⠀⢸⠀⢀⡷⣿⣿⣿⢿⡿⡇⣿⣉⢾⣿⣿⠰⢶⡶⣿⣿⣿⣿⣹⣿⡀⠹⣿⣿⡹⣉⢷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡭⣥⣿⣾⣿⣿⣿⣿⣿⣿⣓⡃⠐⠀⣘⣯⣿⣚⣟⢒⣓⣒⣿⣒⢺⣟⣻⡧⡉⣿⡿⠍⡭⢭⠨⠹⢿⣝⢒⡞⠀⡖⣚⢷⣙⢛⣯⣦⠈⠻⢿⣿⣮⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢩⣿⣿⣿⣾⣷⣿⣿⣿⣟⠒⠀⠐⠀⠉⡿⡟⠉⠹⣿⣟⣳⣶⣆⣴⠑⠀⢳⡄⠈⣷⡁⠁⠈⠀⢈⠙⣷⠀⣀⣀⣀⠀⢨⣷⠀⠊⣟⢣⠀⠀⠉⠛⠿⣿⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣗⡺⣿⣿⣿⣿⣿⣿⣿⡿⡏⠍⠁⢈⠀⠉⠁⣷⠩⠩⠨⢿⣷⣿⣿⡟⠀⠈⠅⠽⣹⣯⡵⣖⣶⣶⣶⡖⣿⡬⢭⡭⣽⣿⠭⣿⡠⠥⣼⣷⢧⠀⠀⠀⠀⠀⠙⠳⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡏⡃⢀⣠⣬⣶⣶⣦⣍⢀⠈⢸⣘⣧⣿⣿⣏⠀⣀⠀⣃⣷⢿⣼⣽⣆⡲⡦⢵⣾⣿⠃⣧⣿⣿⡼⣿⣿⣇⣻⣿⣘⡆⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣾⠟⠻⠹⢰⣶⣆⡚⢷⡀⠠⠶⡞⣾⣿⠤⠀⠠⡀⢒⡞⠻⣷⠐⢻⣿⣮⡕⣷⣿⡖⣿⣿⣿⡏⣽⣿⣿⢶⣿⣿⢾⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣿⣿⡯⡿⢿⢽⣽⣮⣯⣯⡟⠬⠅⢡⡀⣠⣽⣿⣧⠵⠁⠀⠀⠇⡍⢿⠀⠀⠤⠀⠏⠩⠬⠹⡤⠀⣿⢝⡿⡯⣾⣯⣿⣟⣯⣖⣺⣿⣕⠽⣯⣿⣬⣽⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣿⣿⠷⠿⠿⣻⣿⣟⣿⣿⠆⠁⢠⣿⣿⡽⠿⡿⣿⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠒⠉⠊⢈⠋⠁⡋⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⣟⣹⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣿⡭⢹⣿⣿⣻⣽⣿⡀⠀⢨⡇⠉⠍⢌⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⢶⠾⢦⣆⠂⠚⣿⣷⣽⡗⣿⡯⣿⠵⢿⣯⣯⣿⣿⣿⣕⣯⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣗⣿⣿⣿⡓⣒⣛⣽⣿⣿⢿⣯⠥⠀⠈⢶⡂⠐⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢙⣿⣌⣮⠽⣿⣍⢯⣻⣻⣯⠭⠥⣯⠬⣿⣿⣿⣟⣿⣻⣾⣏⢹⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣷⣿⣿⡇⡇⠴⣹⣿⣿⣾⣉⢹⣄⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣀⣷⣶⣾⣿⣿⠈⠀⡉⣿⢙⣏⢾⣏⡉⡁⡁⣹⣿⣿⣳⣷⣿⣿⢞⣾⡌⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⣿⣿⣿⣭⠭⢭⣿⣿⣷⡒⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠇⠀⠀⠀⠰⡟⣿⢨⠽⢕⡟⠀⠂⣲⡟⠒⢺⣽⣷⣾⡶⠒⣺⣿⣯⣿⣿⣾⢽⣝⣿⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣧⣚⣾⣚⣿⣿⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠐⣇⠈⢐⢰⡏⠁⠠⢠⡿⠤⣤⣿⣻⣟⣿⠥⣾⣿⣿⣿⣿⣿⣿⡾⡳⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣿⣿⣿⣿⡿⣽⣿⢿⣿⣿⠶⠾⣿⣿⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠛⠀⠤⠾⣛⣀⣽⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣿⣿⣿⣫⣫⣿⣿⢕⣿⣭⢹⡿⣿⣷⣐⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⣫⣿⣿⣟⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢟⢟⣿⣿⣷⡿⣟⢄⣻⡻⣿⣷⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣛⣿⣿⡿⣿⣿⣟⢟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⡗⣽⣿⣿⣿⣿⣕⡽⣍⢯⣿⣿⣿⢅⠠⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⠇⢸⣿⣿⣯⣺⣿⣿⣿⣿⣿⣿⣦⢟⣿⣯⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⣗⣟⣿⣿⣺⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⡆⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣤⣶⣾⣷⣿⣿⣯⣳⡤⣀⣿⡏⠀⢸⣿⣿⣿⣾⠯⣿⣿⣿⣿⣿⣿⣿⢷⣿⣩⠨⠽⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢏⣀⣻⣿⣿⣿⣿⣿⣿⣿⣾⡿⣿⣯⢿⡀⠀⠀⠀
⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣖⢤⣘⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣷⣗⣭⡿⣬⣭⡯⣭⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣿⣿⣿⣕⢒⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⡿⣿⣿⣇⠀⠀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢻⡻⣿⣟⣿⢟⡿⣿⣾⣿⣷⣟⢶⠐⢐⣰⣇⣲⣗⣾⢐⣐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣟⢽⣿⡺⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡯⡾⣿⢽⡄⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⡻⣷⣿⣟⢿⣿⣿⣿⣿⢷⡤⠀⠴⠑⠷⠶⠰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢟⢟⢿⣿⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣝⣿⣿⣿⣿⣷⣽⣄⠄⠀⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢝⣿⡆⠙⠿⣿⣿⣿⣿⣺⣺⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣟⢽⠈⢿⡆⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⣾⣇⡀⠆⢀⣿⣿⣷⣿⣿⣿⣿⢿⣿⠁⠈⣿⣿⣿⢾⡇⠀⠀⠀⠹⣿⡿⣿⣉⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣏⢾⠀⠀⣇⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣮⡶⣤⣿⣿⣿⣿⣿⣿⣿⡿⣿⡗⠀⠀⠀⠙⢿⣿⣻⠀⠀⠀⠀⠈⣿⡿⣶⣾⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡏⠀⠀⣼⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣵⢝⢵⣿⡯⣯⠃⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⢰⣿⠗⠉⠙⠿⣮⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⡯⣮⡇⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣫⣿⣿⣿⣿⣷⣿⣿⣿⣾⣾⣻⣻⣿⣻⣟⢿⣶⣄⡀⠀⠀⠀⠀⠀⠓⠀⠀⢠⡿⠁⠀⠀⠀⠀⠈⠙⠻⢦⠈⠿⣿⣿⣿⣿⣿⣟⣿⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣾⣿⣿⣷⣽⣾⡿⣷⣤⣀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠻⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⡿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠋⠀
*/
#include<bits/stdc++.h>
#define IOS ios_base::sync_with_stdio(false),cin.tie(NULL),cout.tie()
#define ll long long
#define ull unsigned long long
#define pb push_back
#define endl "\n"
#define int ll
#define F first
#define S second
#define db double
#define ld long double
#define short unsigned short
#define pii pair<int,int>
using namespace std;
const ll inf = 1e18,MOD=1e9+7,N=1e5+5,MN=1e9+7,lim=1e6;
const long db Phi=acos(-1);
ll binpow(int a,int p);
int cnt[N];
void solve(){
int n;
cin>>n;
vector<int>v(n+1);
vector<int>pref(n,0);
for(int i=0;i<n;i++){
cin>>v[i];
if(i!=0)pref[i]=pref[i-1]+v[i];
else pref[i]=v[i];
// cout<<pref[i]<<" ";
}
cout<<endl;
vector<pair<int,int>>dp(n,{0,0});
dp[0]={1,0};
for(int i=0;i<n;i++){
if(i!=0)dp[i]=max(dp[i],dp[i-1]);
int l=i+1,r=n-1;
int sum1=0;
if(dp[i].S==0){
sum1=pref[i];
}
else sum1=pref[i]-pref[dp[i].S-1];
int ans=n+1;
while(l<=r){
int m=(l+r)/2;
int sum2=pref[m]-pref[i];
if(sum1<=sum2){
ans=m;
r=m-1;
}
else{
l=m+1;
}
}
if(ans!=n+1){
dp[ans]=max(dp[ans],{dp[i].F+1,i+1});
}
}
cout<<dp[n-1].F<<endl;
}
signed main() {
IOS;
srand(time(NULL));
/*freopen("numbers.in", "r", stdin);
freopen("numbers.out", "w", stdout);*/
int UwU=1;
// cin>>UwU;
for(int i=1;i<=UwU;i++) {
// cout<<"Case "<<i<<": ";
solve();
// cout<<endl;
}
}
ll binpow(int a,int p){if(p==0)return 1;if(p%2){return ((binpow(a,p-1)*a)%MOD);}int res=binpow(a,p/2)%MOD; return (res*res)%MOD;};
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
0 ms |
472 KB |
Output is correct |
5 |
Correct |
0 ms |
348 KB |
Output is correct |
6 |
Correct |
1 ms |
348 KB |
Output is correct |
7 |
Correct |
1 ms |
348 KB |
Output is correct |
8 |
Correct |
0 ms |
348 KB |
Output is correct |
9 |
Correct |
0 ms |
348 KB |
Output is correct |
10 |
Correct |
0 ms |
600 KB |
Output is correct |
11 |
Correct |
0 ms |
348 KB |
Output is correct |
12 |
Correct |
0 ms |
348 KB |
Output is correct |
13 |
Correct |
0 ms |
348 KB |
Output is correct |
14 |
Correct |
0 ms |
348 KB |
Output is correct |
15 |
Correct |
0 ms |
464 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
0 ms |
472 KB |
Output is correct |
5 |
Correct |
0 ms |
348 KB |
Output is correct |
6 |
Correct |
1 ms |
348 KB |
Output is correct |
7 |
Correct |
1 ms |
348 KB |
Output is correct |
8 |
Correct |
0 ms |
348 KB |
Output is correct |
9 |
Correct |
0 ms |
348 KB |
Output is correct |
10 |
Correct |
0 ms |
600 KB |
Output is correct |
11 |
Correct |
0 ms |
348 KB |
Output is correct |
12 |
Correct |
0 ms |
348 KB |
Output is correct |
13 |
Correct |
0 ms |
348 KB |
Output is correct |
14 |
Correct |
0 ms |
348 KB |
Output is correct |
15 |
Correct |
0 ms |
464 KB |
Output is correct |
16 |
Correct |
0 ms |
348 KB |
Output is correct |
17 |
Correct |
0 ms |
348 KB |
Output is correct |
18 |
Correct |
0 ms |
348 KB |
Output is correct |
19 |
Correct |
1 ms |
348 KB |
Output is correct |
20 |
Correct |
0 ms |
348 KB |
Output is correct |
21 |
Correct |
0 ms |
348 KB |
Output is correct |
22 |
Correct |
0 ms |
348 KB |
Output is correct |
23 |
Correct |
0 ms |
348 KB |
Output is correct |
24 |
Correct |
0 ms |
348 KB |
Output is correct |
25 |
Correct |
0 ms |
348 KB |
Output is correct |
26 |
Correct |
0 ms |
460 KB |
Output is correct |
27 |
Correct |
0 ms |
348 KB |
Output is correct |
28 |
Correct |
0 ms |
348 KB |
Output is correct |
29 |
Correct |
0 ms |
348 KB |
Output is correct |
30 |
Correct |
0 ms |
348 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
0 ms |
472 KB |
Output is correct |
5 |
Correct |
0 ms |
348 KB |
Output is correct |
6 |
Correct |
1 ms |
348 KB |
Output is correct |
7 |
Correct |
1 ms |
348 KB |
Output is correct |
8 |
Correct |
0 ms |
348 KB |
Output is correct |
9 |
Correct |
0 ms |
348 KB |
Output is correct |
10 |
Correct |
0 ms |
600 KB |
Output is correct |
11 |
Correct |
0 ms |
348 KB |
Output is correct |
12 |
Correct |
0 ms |
348 KB |
Output is correct |
13 |
Correct |
0 ms |
348 KB |
Output is correct |
14 |
Correct |
0 ms |
348 KB |
Output is correct |
15 |
Correct |
0 ms |
464 KB |
Output is correct |
16 |
Correct |
0 ms |
348 KB |
Output is correct |
17 |
Correct |
0 ms |
348 KB |
Output is correct |
18 |
Correct |
0 ms |
348 KB |
Output is correct |
19 |
Correct |
1 ms |
348 KB |
Output is correct |
20 |
Correct |
0 ms |
348 KB |
Output is correct |
21 |
Correct |
0 ms |
348 KB |
Output is correct |
22 |
Correct |
0 ms |
348 KB |
Output is correct |
23 |
Correct |
0 ms |
348 KB |
Output is correct |
24 |
Correct |
0 ms |
348 KB |
Output is correct |
25 |
Correct |
0 ms |
348 KB |
Output is correct |
26 |
Correct |
0 ms |
460 KB |
Output is correct |
27 |
Correct |
0 ms |
348 KB |
Output is correct |
28 |
Correct |
0 ms |
348 KB |
Output is correct |
29 |
Correct |
0 ms |
348 KB |
Output is correct |
30 |
Correct |
0 ms |
348 KB |
Output is correct |
31 |
Correct |
1 ms |
600 KB |
Output is correct |
32 |
Correct |
1 ms |
348 KB |
Output is correct |
33 |
Correct |
1 ms |
344 KB |
Output is correct |
34 |
Correct |
1 ms |
348 KB |
Output is correct |
35 |
Correct |
1 ms |
344 KB |
Output is correct |
36 |
Correct |
1 ms |
348 KB |
Output is correct |
37 |
Correct |
1 ms |
348 KB |
Output is correct |
38 |
Correct |
0 ms |
348 KB |
Output is correct |
39 |
Correct |
1 ms |
604 KB |
Output is correct |
40 |
Correct |
1 ms |
348 KB |
Output is correct |
41 |
Correct |
0 ms |
348 KB |
Output is correct |
42 |
Correct |
1 ms |
344 KB |
Output is correct |
43 |
Correct |
1 ms |
344 KB |
Output is correct |
44 |
Correct |
0 ms |
348 KB |
Output is correct |
45 |
Correct |
1 ms |
604 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
0 ms |
472 KB |
Output is correct |
5 |
Correct |
0 ms |
348 KB |
Output is correct |
6 |
Correct |
1 ms |
348 KB |
Output is correct |
7 |
Correct |
1 ms |
348 KB |
Output is correct |
8 |
Correct |
0 ms |
348 KB |
Output is correct |
9 |
Correct |
0 ms |
348 KB |
Output is correct |
10 |
Correct |
0 ms |
600 KB |
Output is correct |
11 |
Correct |
0 ms |
348 KB |
Output is correct |
12 |
Correct |
0 ms |
348 KB |
Output is correct |
13 |
Correct |
0 ms |
348 KB |
Output is correct |
14 |
Correct |
0 ms |
348 KB |
Output is correct |
15 |
Correct |
0 ms |
464 KB |
Output is correct |
16 |
Correct |
0 ms |
348 KB |
Output is correct |
17 |
Correct |
0 ms |
348 KB |
Output is correct |
18 |
Correct |
0 ms |
348 KB |
Output is correct |
19 |
Correct |
1 ms |
348 KB |
Output is correct |
20 |
Correct |
0 ms |
348 KB |
Output is correct |
21 |
Correct |
0 ms |
348 KB |
Output is correct |
22 |
Correct |
0 ms |
348 KB |
Output is correct |
23 |
Correct |
0 ms |
348 KB |
Output is correct |
24 |
Correct |
0 ms |
348 KB |
Output is correct |
25 |
Correct |
0 ms |
348 KB |
Output is correct |
26 |
Correct |
0 ms |
460 KB |
Output is correct |
27 |
Correct |
0 ms |
348 KB |
Output is correct |
28 |
Correct |
0 ms |
348 KB |
Output is correct |
29 |
Correct |
0 ms |
348 KB |
Output is correct |
30 |
Correct |
0 ms |
348 KB |
Output is correct |
31 |
Correct |
1 ms |
600 KB |
Output is correct |
32 |
Correct |
1 ms |
348 KB |
Output is correct |
33 |
Correct |
1 ms |
344 KB |
Output is correct |
34 |
Correct |
1 ms |
348 KB |
Output is correct |
35 |
Correct |
1 ms |
344 KB |
Output is correct |
36 |
Correct |
1 ms |
348 KB |
Output is correct |
37 |
Correct |
1 ms |
348 KB |
Output is correct |
38 |
Correct |
0 ms |
348 KB |
Output is correct |
39 |
Correct |
1 ms |
604 KB |
Output is correct |
40 |
Correct |
1 ms |
348 KB |
Output is correct |
41 |
Correct |
0 ms |
348 KB |
Output is correct |
42 |
Correct |
1 ms |
344 KB |
Output is correct |
43 |
Correct |
1 ms |
344 KB |
Output is correct |
44 |
Correct |
0 ms |
348 KB |
Output is correct |
45 |
Correct |
1 ms |
604 KB |
Output is correct |
46 |
Correct |
7 ms |
3932 KB |
Output is correct |
47 |
Correct |
9 ms |
4088 KB |
Output is correct |
48 |
Correct |
9 ms |
4208 KB |
Output is correct |
49 |
Correct |
9 ms |
4444 KB |
Output is correct |
50 |
Correct |
9 ms |
4440 KB |
Output is correct |
51 |
Correct |
12 ms |
4440 KB |
Output is correct |
52 |
Correct |
8 ms |
2392 KB |
Output is correct |
53 |
Correct |
4 ms |
1504 KB |
Output is correct |
54 |
Correct |
9 ms |
3796 KB |
Output is correct |
55 |
Correct |
11 ms |
4444 KB |
Output is correct |
56 |
Correct |
7 ms |
3948 KB |
Output is correct |
57 |
Correct |
7 ms |
3932 KB |
Output is correct |
58 |
Correct |
8 ms |
3960 KB |
Output is correct |
59 |
Correct |
8 ms |
4188 KB |
Output is correct |
60 |
Correct |
8 ms |
4188 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
344 KB |
Output is correct |
2 |
Correct |
0 ms |
348 KB |
Output is correct |
3 |
Correct |
0 ms |
348 KB |
Output is correct |
4 |
Correct |
0 ms |
472 KB |
Output is correct |
5 |
Correct |
0 ms |
348 KB |
Output is correct |
6 |
Correct |
1 ms |
348 KB |
Output is correct |
7 |
Correct |
1 ms |
348 KB |
Output is correct |
8 |
Correct |
0 ms |
348 KB |
Output is correct |
9 |
Correct |
0 ms |
348 KB |
Output is correct |
10 |
Correct |
0 ms |
600 KB |
Output is correct |
11 |
Correct |
0 ms |
348 KB |
Output is correct |
12 |
Correct |
0 ms |
348 KB |
Output is correct |
13 |
Correct |
0 ms |
348 KB |
Output is correct |
14 |
Correct |
0 ms |
348 KB |
Output is correct |
15 |
Correct |
0 ms |
464 KB |
Output is correct |
16 |
Correct |
0 ms |
348 KB |
Output is correct |
17 |
Correct |
0 ms |
348 KB |
Output is correct |
18 |
Correct |
0 ms |
348 KB |
Output is correct |
19 |
Correct |
1 ms |
348 KB |
Output is correct |
20 |
Correct |
0 ms |
348 KB |
Output is correct |
21 |
Correct |
0 ms |
348 KB |
Output is correct |
22 |
Correct |
0 ms |
348 KB |
Output is correct |
23 |
Correct |
0 ms |
348 KB |
Output is correct |
24 |
Correct |
0 ms |
348 KB |
Output is correct |
25 |
Correct |
0 ms |
348 KB |
Output is correct |
26 |
Correct |
0 ms |
460 KB |
Output is correct |
27 |
Correct |
0 ms |
348 KB |
Output is correct |
28 |
Correct |
0 ms |
348 KB |
Output is correct |
29 |
Correct |
0 ms |
348 KB |
Output is correct |
30 |
Correct |
0 ms |
348 KB |
Output is correct |
31 |
Correct |
1 ms |
600 KB |
Output is correct |
32 |
Correct |
1 ms |
348 KB |
Output is correct |
33 |
Correct |
1 ms |
344 KB |
Output is correct |
34 |
Correct |
1 ms |
348 KB |
Output is correct |
35 |
Correct |
1 ms |
344 KB |
Output is correct |
36 |
Correct |
1 ms |
348 KB |
Output is correct |
37 |
Correct |
1 ms |
348 KB |
Output is correct |
38 |
Correct |
0 ms |
348 KB |
Output is correct |
39 |
Correct |
1 ms |
604 KB |
Output is correct |
40 |
Correct |
1 ms |
348 KB |
Output is correct |
41 |
Correct |
0 ms |
348 KB |
Output is correct |
42 |
Correct |
1 ms |
344 KB |
Output is correct |
43 |
Correct |
1 ms |
344 KB |
Output is correct |
44 |
Correct |
0 ms |
348 KB |
Output is correct |
45 |
Correct |
1 ms |
604 KB |
Output is correct |
46 |
Correct |
7 ms |
3932 KB |
Output is correct |
47 |
Correct |
9 ms |
4088 KB |
Output is correct |
48 |
Correct |
9 ms |
4208 KB |
Output is correct |
49 |
Correct |
9 ms |
4444 KB |
Output is correct |
50 |
Correct |
9 ms |
4440 KB |
Output is correct |
51 |
Correct |
12 ms |
4440 KB |
Output is correct |
52 |
Correct |
8 ms |
2392 KB |
Output is correct |
53 |
Correct |
4 ms |
1504 KB |
Output is correct |
54 |
Correct |
9 ms |
3796 KB |
Output is correct |
55 |
Correct |
11 ms |
4444 KB |
Output is correct |
56 |
Correct |
7 ms |
3948 KB |
Output is correct |
57 |
Correct |
7 ms |
3932 KB |
Output is correct |
58 |
Correct |
8 ms |
3960 KB |
Output is correct |
59 |
Correct |
8 ms |
4188 KB |
Output is correct |
60 |
Correct |
8 ms |
4188 KB |
Output is correct |
61 |
Correct |
31 ms |
17892 KB |
Output is correct |
62 |
Correct |
37 ms |
17944 KB |
Output is correct |
63 |
Correct |
45 ms |
18268 KB |
Output is correct |
64 |
Correct |
46 ms |
20564 KB |
Output is correct |
65 |
Correct |
43 ms |
20816 KB |
Output is correct |
66 |
Correct |
52 ms |
20964 KB |
Output is correct |
67 |
Correct |
46 ms |
16856 KB |
Output is correct |
68 |
Correct |
22 ms |
8540 KB |
Output is correct |
69 |
Correct |
38 ms |
16988 KB |
Output is correct |
70 |
Correct |
45 ms |
20840 KB |
Output is correct |
71 |
Correct |
42 ms |
18084 KB |
Output is correct |
72 |
Correct |
38 ms |
18256 KB |
Output is correct |
73 |
Correct |
38 ms |
19032 KB |
Output is correct |
74 |
Correct |
43 ms |
19300 KB |
Output is correct |
75 |
Correct |
39 ms |
19436 KB |
Output is correct |