/**
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠉⠛⠶⣤⣸⡇⠀⠀⠀⠀⣀⣤⣶⣶⠒⠒⠒⠶⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢿⣭⣀⡀⢻⡀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣴⣞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⡤⠠⡄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣠⠖⠋⠀⣸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⣴⠋⢀⢀⡴⠋⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣼⢿⡄⠀⠀⠀⠀⣆⠀⠉⢦⡀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣠⠟⠇⠀⠈⠉⠁⠀⣀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠏⠀⠻⣄⠀⠀⠀⠹⣄⣰⠟⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⢀⣀⡖⠀⣰⠏⠀⠀⠀⠀⠀⢀⣼⣿⠋⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠹⣦⠀⠀⠀⠀⠁⠀⣶⠀⠀⣴⠛⢧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡟⠀⠀⠈⠉⠀⢀⡟⠀⠀⢀⣀⣠⣤⣾⡿⠗⠒⠚⣿⠠⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⠓⠒⠲⠶⠶⠾⢷⣤⣀⣀⠀⠀⠙⣧⠀⠹⣆⣼⠃⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠟⢁⡼⣿⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠉⢠⡾⠋⠀⠀⠀⠀⠸⣆⠙⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠁⠀⠀⢹⡄⠀⠈⠁⠀⠀⠘⣷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡶⠋⢀⡴⠋⢰⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣾⡥⠴⠞⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣷⠙⠷⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡄⠀⣼⢏⣀⣤⣶⣦⣤⣶⣶⣶⣶⣶⣿⣿⣾⡆⠀⠈⠻⢦⣼⡇⢰⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣦⠙⢧⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣇⣼⠏⠘⣿⡿⢿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠃⠀⠀⠀⠀⠉⠁⠘⠛⢻⣿⣿⣿⣿⣿⣟⠛⢛⠷⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣆⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⣆⠀⠀⠀⠀⠀⠐⠘⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠟⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⠙⣧⣄⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⢹⠿⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠀⡀⠀⠀⣼⠃⠀⠀⠀⠀⣀⡾⠋⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⠝⠳⣤⣀⡀⠀⠀⠈⢷⣤⠇⢠⡞⠠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⡾⠃⣠⡾⠃⠀⠀⣀⣤⠾⠋⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣸⣿⠀⠀⠀⠉⠙⠓⡶⠦⠤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢰⡿⠤⠴⠶⣿⠉⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⠤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⠇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢺⢀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠛⣇⠀⠀⠀⠀⠀⠈⣿⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⣸⠀⠀⠀⠀⠀⠀⢀⣿⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣀⣿⠀⠀⠀⠀⠀⢷⢸⡄⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⡟⣼⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⢿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⡇⢹⣤⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡿⢸⡆⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⡇⠈⣟⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢰⡇⠘⡇⠀⠀⠀⠀⠀⠘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠀⠀⣼⠁⠀⢻⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠈⣷⡀⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⢠⣠⡇⡇⠀⠀⠸⣯⡀⠀⢷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣼⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡧⠴⢶⣿⣿⠖⠒⠛⠛⠃⠀⠀⠀⠚⠋⠉⠉⠉⠙⠓⠲⢾⡛⠻⣽⠃⠀⠀⠀⠀⠀⠀⢸⣿⣃⠀⠀⠀⠀⢹⣷⠀⠘⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⡏⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣀⠀⠈⠈⢷⠖⠚⠋⠁⢹⡇⠀⢀⣴⠶⠶⢦⣄⣀⣤⡶⠶⠤⠤⠤⠶⠾⠇⢰⡏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣤⡀⠀⠀⠀⠀⢿⣀⠀⠸⣆⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠏⠀⢀⡿⠀⠀⠀⣰⠟⢹⣿⡄⠀⠀⠀⠻⣄⠀⠀⠘⣷⣤⣄⣀⣈⡙⠛⢹⡷⢶⣦⣴⣾⣛⣻⢯⣴⣦⠴⠖⠃⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠹⣆⠀⠀⠸⡞⣧⣆⠀⠹⣄⠀⠀
⠀⠀⠀⠀⢠⡟⠀⠀⡼⠁⠀⠀⣰⠏⠀⠈⣟⣧⠀⠀⠀⠀⢻⣆⠀⠀⠈⣧⡿⠀⠈⠉⠛⠛⣻⣿⡿⢿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣴⠀⠀⡾⣿⠁⠀⠀⠘⣧⠀⠀⢿⠘⣟⠀⠀⢻⡄⠀
⠀⠀⢀⣠⡟⠀⢀⡾⠃⠀⠀⣰⡏⠀⠀⠀⣻⠘⣧⠀⠀⠀⠀⢻⣷⡄⠀⠘⢷⡀⠀⠀⠀⠀⠩⣉⠁⠈⣛⡁⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⠀⣀⣠⣟⠁⠀⣠⣤⡟⠀⠀⠀⠀⠘⣧⡄⠘⡇⠙⣇⠀⠀⠻
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;

#define i64 long long
#define ld long double
#define ull unsigned long long
#define bit(n,i) ((n>>i)&1)
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define FOR(i,a,b) for(int i=a; i<=b; i++)
#define FOD(i,a,b) for(int i=a; i>=b; i--)
#define fi first
#define se second
#define pb push_back
#define all(x) x.begin(),x.end()
#define __sumairu__ signed main()
#define die_hard_onimai_fan void seggs()
#define file(name) if(fopen(name".inp","r")){freopen(name".inp","r",stdin);freopen(name".out","w",stdout);}
#define brute(name) if(fopen(name".inp","r")){freopen(name".inp","r",stdin);freopen(name".ans","w",stdout);}
#define TIME (1.0*clock()/CLOCKS_PER_SEC)
#define FAST ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define ai(n) array<int,n>
#define dbg(x) {cout<<#x<<' '<<x<<endl;}
#define dbgF(arr,l,r) {cout<<#arr;FOR(_i,l,r)cout<<' '<<(arr)[_i];cout<<endl;}
#define dbgArr(arr,n) {cout<<#arr;FOR(_i,1,n)cout<<' '<<(arr)[_i];cout<<endl;}
#define el '\n'

template <typename T,typename U>
ostream& operator<<(ostream &os,pair<T,U>p){return os<<"{"<<p.fi<<", "<<p.se<<"}";}
mt19937_64 rd(chrono::steady_clock::now().time_since_epoch().count());

i64 Rand(i64 l,i64 r)
{
    i64 ans=l+rd()%(r-l+1);
    assert(l<=ans&&ans<=r);
    return ans;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
//const i64 base=1e9+7;
//const i64 mod=(1ll<<53)+5;

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

#define i64 long long
#define debug 0

//const int mod=1e9+7;
//const int mod=998244353;
const int inf=1e9;
const i64 infl=1e18;
///check the limits, dummy
const int N=2e5+5;

int n;
vector<int>adj[N];
i64 d[N];
int h[N],f[N][20];
int in[N],out[N],timer;

void dfs(int u,int p=0)
{
    in[u]=++timer;
    h[u]=h[p]+1;
    for(int v:adj[u])if(v!=p)
    {
        d[v]+=d[u];
        f[v][0]=u;
        FOR(i,1,19)f[v][i]=f[f[v][i-1]][i-1];
        dfs(v,u);
    }
    out[u]=timer;
}
int lca(int u,int v)
{
    if(h[u]<h[v])swap(u,v);
    FOD(i,__lg(h[u]-h[v]),0)if(h[f[u][i]]>=h[v])u=f[u][i];
    if(u==v)return u;
    FOD(i,__lg(h[u]),0)if(f[u][i]!=f[v][i])
    {
        u=f[u][i],v=f[v][i];
    }
    return f[u][0];
}
bool isAnc(int u,int v){ return in[u]<=in[v]&&out[u]>=out[v];}
i64 dist(int u,int v){ return d[u]+d[v]-2*d[lca(u,v)];}

bool vis[N];
int par[N];
int sz[N];
int getsz(int u,int p=0)
{
    sz[u]=1;
    for(int v:adj[u])if(!vis[v]&&v!=p)sz[u]+=getsz(v,u);
    return sz[u];
}
int centroid(int u,int S,int p=0)
{
    for(int v:adj[u])if(!vis[v]&&v!=p&&sz[v]>S/2)return centroid(v,S,u);
    return u;
}
void decomp(int u,int p=0)
{
    u=centroid(u,getsz(u));

    par[u]=p;
    vis[u]=1;

    for(int v:adj[u])if(!vis[v])
    {
        decomp(v,u);
    }
}

struct Fenwick
{
    int bit[N];
    int get(int i)
    {
        int ans=0;
        for(++i;i>0;i-=i&-i)ans+=bit[i];
        return ans;
    }
    int get(int l,int r)
    {
        return get(r)-get(l-1);
    }
    void add(int i,int v)
    {
        for(++i;i<n;i+=i&-i)bit[i]+=v;
    }
}F;

int cnt[N];
i64 up[N],up2[N];
void add(int u)
{
    for(int i=u;i;i=par[i])
    {
        cnt[i]++;
        if(par[i])
        {
            i64 tmp=dist(u,par[i]);
            up[par[i]]+=tmp;
            up2[i]+=tmp;
        }
    }
}

i64 query(int u)
{
    i64 ans=up[u];
    for(int i=u;par[i];i=par[i])
    {
        ans+=(cnt[par[i]]-cnt[i])*dist(u,par[i])+(up[par[i]]-up2[i]);
    }
    return ans;
}

die_hard_onimai_fan
{
    cin>>n;
    FOR(i,2,n)
    {
        int p;
        cin>>p>>d[i];
        adj[p].pb(i);
        adj[i].pb(p);
    }
    dfs(1);
    decomp(1);

    int cen=1;
    FOR(i,1,n)
    {
        add(i);
        F.add(in[i],1);

        auto get=[&](int u){
            return F.get(in[u],out[u]);
        };

        FOD(j,__lg(h[cen]),0)if(f[cen][j]&&get(f[cen][j])<=i/2)cen=f[cen][j];
        if(get(cen)<=i/2)cen=f[cen][0];

        if(isAnc(cen,i))
        {
            int cen2=i;
            FOD(j,__lg(h[cen2]),0)if(f[cen2][j]&&get(f[cen2][j])<=i/2)cen2=f[cen2][j];
            if(get(cen2)<=i/2)cen2=f[cen2][0];
            cen=cen2;
        }
        cout<<query(cen)<<el;
    }
}

__sumairu__
{
    FAST
    file("cum");

    int tt=1;//cin>>tt;
    while(tt--)seggs();
    cerr<<"\nTime elapsed: "<<TIME<<" s.\n";
}
/**
10
4 1
1 1
3 1
3 1
5 1
6 1
6 1
8 1
4 1
*/