Monochrome Cat

There is a tree with N vertices numbered 1 through N. The i-th edge connects Vertex x_i and y_i. Each vertex is painted white or black. The initial color of Vertex i is represented by a letter c_i. c_i = W represents the vertex is white; c_i = B represents the vertex is black.

A cat will walk along this tree. More specifically, she performs one of the following in one second repeatedly:

• Choose a vertex that is adjacent to the vertex where she is currently, and move to that vertex. Then, invert the color of the destination vertex.
• Invert the color of the vertex where she is currently.

The cat's objective is to paint all the vertices black. She may start and end performing actions at any vertex. At least how many seconds does it takes for the cat to achieve her objective?

Constraints

• 1 ≤ N ≤ 10^5
• 1 ≤ x_i,y_i ≤ N (1 ≤ i ≤ N-1)
• The given graph is a tree.
• c_i = W or c_i = B.

Input

Input is given from Standard Input in the following format:

N x_1 y_1 x_2 y_2 : x_{N-1} y_{N-1} c_1c_2..c_N

Output

Print the minimum number of seconds required to achieve the objective.

Examples

Input

5 1 2 2 3 2 4 4 5 WBBWW

Output

5

Input

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

Output

7

Input

1 B

Output

0

Input

20 2 19 5 13 6 4 15 6 12 19 13 19 3 11 8 3 3 20 16 13 7 14 3 17 7 8 10 20 11 9 8 18 8 2 10 1 6 13 WBWBWBBWWWBBWWBBBBBW

Output

21

inputFormat

Input

Input is given from Standard Input in the following format:

N x_1 y_1 x_2 y_2 : x_{N-1} y_{N-1} c_1c_2..c_N

outputFormat

Output

Print the minimum number of seconds required to achieve the objective.

Examples

Input

5 1 2 2 3 2 4 4 5 WBBWW

Output

5

Input

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

Output

7

Input

1 B

Output

0

Input

20 2 19 5 13 6 4 15 6 12 19 13 19 3 11 8 3 3 20 16 13 7 14 3 17 7 8 10 20 11 9 8 18 8 2 10 1 6 13 WBWBWBBWWWBBWWBBBBBW

Output

21

样例

20
2 19
5 13
6 4
15 6
12 19
13 19
3 11
8 3
3 20
16 13
7 14
3 17
7 8
10 20
11 9
8 18
8 2
10 1
6 13
WBWBWBBWWWBBWWBBBBBW

21