Score : 1200 points

Problem Statement

In Takaha-shi, the capital of Republic of AtCoder, there are N roads extending east and west, and M roads extending north and south. There are no other roads. The i-th east-west road from the north and the j-th north-south road from the west cross at the intersection (i, j). Two east-west roads do not cross, nor do two north-south roads. The distance between two adjacent roads in the same direction is 1.

Each road is one-way; one can only walk in one direction. The permitted direction for each road is described by a string S of length N and a string T of length M, as follows:

  • If the i-th character in S is W, one can only walk westward along the i-th east-west road from the north;
  • If the i-th character in S is E, one can only walk eastward along the i-th east-west road from the north;
  • If the i-th character in T is N, one can only walk northward along the i-th north-south road from the west;
  • If the i-th character in T is S, one can only walk southward along the i-th south-west road from the west.

Process the following Q queries:

  • In the i-th query, a_i, b_i, c_i and d_i are given. What is the minimum distance to travel to reach the intersection (c_i, d_i) from the intersection (a_i, b_i) by walking along the roads?

Constraints

  • 2 \leq N \leq 100000
  • 2 \leq M \leq 100000
  • 2 \leq Q \leq 200000
  • |S| = N
  • S consists of W and E.
  • |T| = M
  • T consists of N and S.
  • 1 \leq a_i \leq N
  • 1 \leq b_i \leq M
  • 1 \leq c_i \leq N
  • 1 \leq d_i \leq M
  • (a_i, b_i) \neq (c_i, d_i)

Input

Input is given from Standard Input in the following format:

N M Q
S
T
a_1 b_1 c_1 d_1
a_2 b_2 c_2 d_2
:
a_Q b_Q c_Q d_Q

Output

In the i-th line, print the response to the i-th query. If the intersection (c_i, d_i) cannot be reached from the intersection (a_i, b_i) by walking along the roads, print -1 instead.

Sample Input 1

4 5 4
EEWW
NSNNS
4 1 1 4
1 3 1 2
4 2 3 2
3 3 3 5

Sample Output 1

6
11
5
4

The permitted direction for each road is shown in the following figure (north upward):

For each of the four queries, a route that achieves the minimum travel distance is as follows:

Sample Input 2

3 3 2
EEE
SSS
1 1 3 3
3 3 1 1

Sample Output 2

4
-1

The travel may be impossible.

Sample Input 3

9 7 10
EEEEEWEWW
NSSSNSN
4 6 9 2
3 7 6 7
7 5 3 5
1 1 8 1
4 3 5 4
7 4 6 4
2 5 8 6
6 6 2 7
2 4 7 5
7 2 9 7

Sample Output 3

9
-1
4
9
2
3
7
7
6
-1