Cleaning

There is a tree with N vertices, numbered 1 through N. The i-th of the N-1 edges connects vertices a_i and b_i.

Currently, there are A_i stones placed on vertex i. Determine whether it is possible to remove all the stones from the vertices by repeatedly performing the following operation:

• Select a pair of different leaves. Then, remove exactly one stone from every vertex on the path between those two vertices. Here, a leaf is a vertex of the tree whose degree is 1, and the selected leaves themselves are also considered as vertices on the path connecting them.

Note that the operation cannot be performed if there is a vertex with no stone on the path.

Constraints

• 2 ≦ N ≦ 10^5
• 1 ≦ a_i,b_i ≦ N
• 0 ≦ A_i ≦ 10^9
• The given graph is a tree.

Input

The input is given from Standard Input in the following format:

N A_1 A_2 … A_N a_1 b_1 : a_{N-1} b_{N-1}

Output

If it is possible to remove all the stones from the vertices, print YES. Otherwise, print NO.

Examples

Input

5 1 2 1 1 2 2 4 5 2 3 2 1 3

Output

YES

Input

3 1 2 1 1 2 2 3

Output

NO

Input

6 3 2 2 2 2 2 1 2 2 3 1 4 1 5 4 6

Output

YES

inputFormat

Input

The input is given from Standard Input in the following format:

N A_1 A_2 … A_N a_1 b_1 : a_{N-1} b_{N-1}

outputFormat

Output

If it is possible to remove all the stones from the vertices, print YES. Otherwise, print NO.

Examples

Input

5 1 2 1 1 2 2 4 5 2 3 2 1 3

Output

YES

Input

3 1 2 1 1 2 2 3

Output

NO

Input

6 3 2 2 2 2 2 1 2 2 3 1 4 1 5 4 6

Output

YES

样例

6
3 2 2 2 2 2
1 2
2 3
1 4
1 5
4 6

YES