There are $n$ cities located on a straight line. The cities are numbered from $1$ to $n$.

Portals are used to move between cities. There are $4$ colors of portals: blue, green, red, and yellow. Each city has portals of two different colors. You can move from city $i$ to city $j$ if they have portals of the same color (for example, you can move between a "blue-red" city and a "blue-green" city). This movement costs $|i-j|$ coins.

Your task is to answer $q$ independent queries: calculate the minimum cost to move from city $x$ to city $y$.

Input

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of cities and the number of queries, respectively.

The second line contains $n$ strings of the following types: BG, BR, BY, GR, GY, or RY; the $i$-th of them describes the portals located in the $i$-th city; the symbol B indicates that there is a blue portal in the city, G — green, R — red, and Y — yellow.

The $j$-th of the next $q$ lines contains two integers $x_j$ and $y_j$ ($1 \le x_j, y_j \le n$) — the description of the $j$-th query.

Additional constraints on the input:

• the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$;
• the sum of $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each query, print a single integer — the minimum cost to move from city $x$ to city $y$ (or $-1$ if it is impossible).

Samples

2
4 5
BR BR GY GR
1 2
3 1
4 4
1 4
4 2
2 1
BG RY
1 2

1
4
0
3
2
-1