/**
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠉⠛⠶⣤⣸⡇⠀⠀⠀⠀⣀⣤⣶⣶⠒⠒⠒⠶⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢿⣭⣀⡀⢻⡀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣴⣞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⡤⠠⡄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣠⠖⠋⠀⣸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⣴⠋⢀⢀⡴⠋⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣼⢿⡄⠀⠀⠀⠀⣆⠀⠉⢦⡀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣠⠟⠇⠀⠈⠉⠁⠀⣀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠏⠀⠻⣄⠀⠀⠀⠹⣄⣰⠟⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⢀⣀⡖⠀⣰⠏⠀⠀⠀⠀⠀⢀⣼⣿⠋⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠹⣦⠀⠀⠀⠀⠁⠀⣶⠀⠀⣴⠛⢧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡟⠀⠀⠈⠉⠀⢀⡟⠀⠀⢀⣀⣠⣤⣾⡿⠗⠒⠚⣿⠠⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⠓⠒⠲⠶⠶⠾⢷⣤⣀⣀⠀⠀⠙⣧⠀⠹⣆⣼⠃⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠟⢁⡼⣿⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠉⢠⡾⠋⠀⠀⠀⠀⠸⣆⠙⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠁⠀⠀⢹⡄⠀⠈⠁⠀⠀⠘⣷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡶⠋⢀⡴⠋⢰⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣾⡥⠴⠞⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣷⠙⠷⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡄⠀⣼⢏⣀⣤⣶⣦⣤⣶⣶⣶⣶⣶⣿⣿⣾⡆⠀⠈⠻⢦⣼⡇⢰⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣦⠙⢧⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣇⣼⠏⠘⣿⡿⢿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠃⠀⠀⠀⠀⠉⠁⠘⠛⢻⣿⣿⣿⣿⣿⣟⠛⢛⠷⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣆⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⣆⠀⠀⠀⠀⠀⠐⠘⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠟⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⠙⣧⣄⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⢹⠿⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠀⡀⠀⠀⣼⠃⠀⠀⠀⠀⣀⡾⠋⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⠝⠳⣤⣀⡀⠀⠀⠈⢷⣤⠇⢠⡞⠠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⡾⠃⣠⡾⠃⠀⠀⣀⣤⠾⠋⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣸⣿⠀⠀⠀⠉⠙⠓⡶⠦⠤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢰⡿⠤⠴⠶⣿⠉⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⠤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⠇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢺⢀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠛⣇⠀⠀⠀⠀⠀⠈⣿⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⣸⠀⠀⠀⠀⠀⠀⢀⣿⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣀⣿⠀⠀⠀⠀⠀⢷⢸⡄⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⡟⣼⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⢿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⡇⢹⣤⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡿⢸⡆⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⡇⠈⣟⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢰⡇⠘⡇⠀⠀⠀⠀⠀⠘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠀⠀⣼⠁⠀⢻⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠈⣷⡀⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⢠⣠⡇⡇⠀⠀⠸⣯⡀⠀⢷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣼⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡧⠴⢶⣿⣿⠖⠒⠛⠛⠃⠀⠀⠀⠚⠋⠉⠉⠉⠙⠓⠲⢾⡛⠻⣽⠃⠀⠀⠀⠀⠀⠀⢸⣿⣃⠀⠀⠀⠀⢹⣷⠀⠘⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⡏⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣀⠀⠈⠈⢷⠖⠚⠋⠁⢹⡇⠀⢀⣴⠶⠶⢦⣄⣀⣤⡶⠶⠤⠤⠤⠶⠾⠇⢰⡏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣤⡀⠀⠀⠀⠀⢿⣀⠀⠸⣆⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠏⠀⢀⡿⠀⠀⠀⣰⠟⢹⣿⡄⠀⠀⠀⠻⣄⠀⠀⠘⣷⣤⣄⣀⣈⡙⠛⢹⡷⢶⣦⣴⣾⣛⣻⢯⣴⣦⠴⠖⠃⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠹⣆⠀⠀⠸⡞⣧⣆⠀⠹⣄⠀⠀
⠀⠀⠀⠀⢠⡟⠀⠀⡼⠁⠀⠀⣰⠏⠀⠈⣟⣧⠀⠀⠀⠀⢻⣆⠀⠀⠈⣧⡿⠀⠈⠉⠛⠛⣻⣿⡿⢿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣴⠀⠀⡾⣿⠁⠀⠀⠘⣧⠀⠀⢿⠘⣟⠀⠀⢻⡄⠀
⠀⠀⢀⣠⡟⠀⢀⡾⠃⠀⠀⣰⡏⠀⠀⠀⣻⠘⣧⠀⠀⠀⠀⢻⣷⡄⠀⠘⢷⡀⠀⠀⠀⠀⠩⣉⠁⠈⣛⡁⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⠀⣀⣠⣟⠁⠀⣠⣤⡟⠀⠀⠀⠀⠘⣧⡄⠘⡇⠙⣇⠀⠀⠻
*/
//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
using namespace std;

#define i64 long long
#define ld long double
#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) {cerr<<#x<<' '<<x<<endl;}
#define dbgArr(arr,n) {cerr<<#arr;FOR(_i,1,n)cerr<<' '<<(arr)[_i];cerr<<endl;}

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+1ll*rd()*rd()%(r-l+1);
    assert(l<=ans&&ans<=r);
    return ans;
}
//const i64 base=1e9+7;
//const i64 mod=(1ll<<53)+5;

#define i64 long long
#define debug 0

const int mod=1e9+7;
//const int mod=998244353;
const int inf=1e9;
///check the limits, dummy
const int N=3e5+5;

void minimize(int &x,int y){ if(x>y)x=y;}
void maximize(int &x,int y){ if(x<y)x=y;}
void add(int &x,int y){ x=x+y;if(x>mod)x-=mod;}
void mul(int &x,int y){ x=1ll*x*y%mod;if(x>mod)x-=mod;}

int n;
int a[N];
vector<int>adj[N];
i64 ans;
int sz[N];
bool vis[N];
int pfs[N];
int cnt[N];

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

vector<int>V,save;

void dfs(int u,int p,int sum,int mn1,int mn2)
{
    if(mn2>=0)save.pb(sum);
    if(mn1==sum)ans+=cnt[-mn1];
    if(sum==0&&mn1>=0)ans++;
    for(int v:adj[u])if(!vis[v]&&v!=p)
    {
        dfs(v,u,sum+a[v],min(mn1,sum+a[v]),min(a[v],a[v]+mn2));
    }
}

void solve(int u)
{
    u=centroid(u,dfsz(u));
    vis[u]=1;
    V.clear();

    for(int v:adj[u])if(!vis[v])
    {
        int sum=a[u],mn=a[u];
        dfs(v,u,sum+a[v],min(mn,sum+a[v]),min(a[v],mn+a[v]));
        for(int x:save)
        {
            cnt[x-a[u]]++;
            V.pb(x-a[u]);
        }
        save.clear();
    }
    for(int x:V)cnt[x]=0;
    for(int v:adj[u])if(!vis[v])solve(v);
}

die_hard_onimai_fan
{
    cin>>n;
    FOR(i,1,n)
    {
        char c;
        cin>>c;
        if(c=='(')a[i]=1;
        else a[i]=-1;
    }

//    dbgArr(a,n);

    FOR(i,2,n)
    {
        int u,v;
        cin>>u>>v;
        adj[u].pb(v);
        adj[v].pb(u);
    }
//    cout<<'\n';
    solve(1);
    FOR(i,1,n)a[i]=-a[i];
    fill(vis+1,vis+n+1,0);
    solve(1);
    cout<<ans;
}

__sumairu__
{
    FAST
    file("");

    int tt=1;//cin>>tt;
    while(tt--)seggs();
    cerr<<"\nTime elapsed: "<<TIME<<" s.\n";
}
/**
5
())((
1 2
2 3
2 4
3 5
*/