Problem: 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.

Examples

Input

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


Output

6
11
5
4


Input

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


Output

4
-1


Input

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


Output

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

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<queue>
#include<set>
using namespace std;
const int N=2e5+10,mod=1e9+7;
int n,m,q,Ans,HH[N],ZZ[N],dis[N],vis[N];
char s[N],t[N];
set<int> H[2],Z[2];
queue<int> Q;
struct Node{int x,y;}P[N];
void GetAns(int x1,int y1,int x2,int y2)
{
	int ch=0,cz=0,c=0;
	set<int>::iterator it;
	for(int i=0;i<2;i++)
	{
		it=H[i].lower_bound(x1);
		if(it!=H[i].end()) HH[++ch]=*it;
		if(it!=H[i].begin()) HH[++ch]=*(--it);
		it=H[i].lower_bound(x2);
		if(it!=H[i].end()) HH[++ch]=*it;
		if(it!=H[i].begin()) HH[++ch]=*(--it);

		it=Z[i].lower_bound(y1);
		if(it!=Z[i].end()) ZZ[++cz]=*it;
		if(it!=Z[i].begin()) ZZ[++cz]=*(--it);
		it=Z[i].lower_bound(y2);
		if(it!=Z[i].end()) ZZ[++cz]=*it;
		if(it!=Z[i].begin()) ZZ[++cz]=*(--it);
	}
	sort(HH+1,HH+ch+1);
	ch=unique(HH+1,HH+ch+1)-HH-1;
	sort(ZZ+1,ZZ+cz+1);
	cz=unique(ZZ+1,ZZ+cz+1)-ZZ-1;
	
	for(int i=1;i<=ch;i++)
		for(int j=1;j<=cz;j++)
			P[++c]=(Node){HH[i],ZZ[j]};
	for(int i=1;i<=c;i++)
		if(P[i].x==x1&&P[i].y==y1)
			dis[i]=0,Q.push(i),vis[i]=1;
		else dis[i]=1e9;
	while(!Q.empty())
	{
		int x=Q.front();
		for(int i=1;i<=c;i++)
		{
			if(P[i].x!=P[x].x&&P[i].y!=P[x].y) continue;
			if(P[i].x==P[x].x)
			{
				if(P[i].y>P[x].y&&s[P[i].x]=='W') continue;
				if(P[i].y<P[x].y&&s[P[i].x]=='E') continue;
			}
			if(P[i].y==P[x].y)
			{
				if(P[i].x>P[x].x&&t[P[i].y]=='N') continue;
				if(P[i].x<P[x].x&&t[P[i].y]=='S') continue;
			}
			int val=dis[x]+abs(P[i].x-P[x].x)+abs(P[i].y-P[x].y);
			if(dis[i]<=val) continue;
			dis[i]=val;
			if(!vis[i]) Q.push(i),vis[i]=1;
		}
		Q.pop(),vis[x]=0;
	}
	for(int i=1;i<=c;i++)
		if(P[i].x==x2&&P[i].y==y2)
			Ans=dis[i];
}
int main()
{
	scanf("%d%d%d%s%s",&n,&m,&q,s+1,t+1);
	for(int i=1;i<=n;i++)
		if(s[i]=='E') H[1].insert(i);
		else H[0].insert(i);
	for(int i=1;i<=m;i++)
		if(t[i]=='N') Z[1].insert(i);
		else Z[0].insert(i);
	for(int i=1,x1,y1,x2,y2;i<=q;i++)
	{
		cin>>x1>>y1>>x2>>y2;
		GetAns(x1,y1,x2,y2);
		if(Ans==1e9) puts("-1");
		else printf("%d\n",Ans);
	}
	return 0;
}