E. Chemistry in Berland

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Igor is a post-graduate student of chemistry faculty in Berland State University (BerSU). He needs to conduct a complicated experiment to write his thesis, but laboratory of BerSU doesn't contain all the materials required for this experiment.

Fortunately, chemical laws allow material transformations (yes, chemistry in Berland differs from ours). But the rules of transformation are a bit strange.

Berland chemists are aware of n materials, numbered in the order they were discovered. Each material can be transformed into some other material (or vice versa). Formally, for each i (2 ≤ i ≤ n) there exist two numbers x_i and k_i that denote a possible transformation: k_i kilograms of material x_i can be transformed into 1 kilogram of material i, and 1 kilogram of material i can be transformed into 1 kilogram of material x_i. Chemical processing equipment in BerSU allows only such transformation that the amount of resulting material is always an integer number of kilograms.

For each i (1 ≤ i ≤ n) Igor knows that the experiment requires a_i kilograms of material i, and the laboratory contains b_i kilograms of this material. Is it possible to conduct an experiment after transforming some materials (or none)?

Input

The first line contains one integer number n (1 ≤ n ≤ 10⁵) — the number of materials discovered by Berland chemists.

The second line contains n integer numbers b₁, b₂... b_n (1 ≤ b_i ≤ 10¹²) — supplies of BerSU laboratory.

The third line contains n integer numbers a₁, a₂... a_n (1 ≤ a_i ≤ 10¹²) — the amounts required for the experiment.

Then n - 1 lines follow. j-th of them contains two numbers x_j + 1 and k_j + 1 that denote transformation of (j + 1)-th material (1 ≤ x_j + 1 ≤ j, 1 ≤ k_j + 1 ≤ 10⁹).

Output

Print YES if it is possible to conduct an experiment. Otherwise print NO.

Examples

Input

3 1 2 3 3 2 1 1 1 1 1

Output

YES

Input

3 3 2 1 1 2 3 1 1 1 2

Output

NO

对于能用若干个i转化为j的点i点j连一条边，总共n-1条，且满足xj+1<=j，故恰为一棵树。对于叶子节点，不需要转化成别的，只需要使自己满足a[i]的要求即可，少的部分从其父节点取，多的部分退回给父节点。之后就可以删去这个节点。依次进行下去，只要根节点满足a[1]的要求即可。过程中需要注意可能会爆long long，故先做b[i]-a[i]，并且每个点用double类型

1 #include 
     
        2 #include 
      
         3 #include 
       
          4 #include 
        
           5 #include 
         
            6 #include 
          
         
        
       
      
     

 

判别一下是否其已经超出sum范围，已超出的就已经是NO了。