# 65. Expression Tree

## Problem Description

Write a program to compute an expression using a tree. Consider the expression 4 + x * 7. We will use the following recursive definition to express this expression tree.

• A positive integer or a variable is an expression tree.
• ( operator left-tree right-tree ) is also an expression tree if operator is one of the '+', '-', '*', or '/', and both left-tree and right-tree are expression trees.

Following this definition, we can use ( + 4 ( * x 7 ) ) to denote the previous expression. Now given an expression tree and the values of all variables, compute the value of this expression.

## Input

The first line of the input is the expression tree, which is less than 1000 characters. Note that every two adjacent elements of an expression tree are separated by a space. The name of the variables are valid C variable names, with no more than 32 characters. The next $n$ lines ($n \le 50$), where $n$ is the number of variables in the expression tree, indicates the value of the variable, in a form as variable = v, also separated by a space.

## Output

The output is the value of the expression tree.

## Sample input

( + 4 ( * x 7 ) )x = 5


## Sample output

39


## Hint

C 語言變數命名規則

• 採用英文二十六的大小寫字母為主 ('a-z', 'A-Z')，另加上數字 '0-9'、底線符號 '_' 及金錢符號 '\$'
• 不以數字開頭