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 <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))

using uint=unsigned;
using ull=unsigned long long;

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

void print(ll x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
int mask(int i){
	return (int(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

template<class E,class D=ll>
vc<D> dijkstra(const vvc<E>& g,int s){
	const int n=g.size();
	using P=pair<D,int>;
	priority_queue<P,vc<P>,greater<P>> pq;
	vc<D> dist(n,inf);
	const auto ar=[&](int v,D d){
		if(dist[v]>d){
			dist[v]=d;
			pq.push(P(d,v));
		}
	};
	ar(s,0);
	while(pq.size()){
		D d;
		int v;
		tie(d,v)=pq.top();pq.pop();
		for(auto e:g[v])
			ar(e.to,d+e.cost);
	}
	return dist;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int n,m,q;cin>>n>>m>>q;
	
	vi rt(n);
	set<int> rs[2];
	{
		string s;cin>>s;
		rep(i,n)rt[i]=s[i]=='E';
		rep(i,2){
			rs[i].insert(-1);
			rs[i].insert(n);
		}
		rep(i,n)rs[rt[i]].insert(i);
	}
	
	
	vi ct(m);
	set<int> cs[2];
	{
		string t;cin>>t;
		rep(i,m)ct[i]=t[i]=='S';
		rep(i,2){
			cs[i].insert(-1);
			cs[i].insert(m);
		}
		rep(i,m)cs[ct[i]].insert(i);
	}
	
	rep(_,q){
		int a,b,c,d;cin>>a>>b>>c>>d;
		a--;b--;c--;d--;
		vi ri{a,c},ci{b,d};
		
		for(auto z:{a,c}){
			auto itr=rs[rt[z]^1].lower_bound(z);
			if(*itr<n)ri.pb(*itr);
			itr--;
			if(*itr>=0)ri.pb(*itr);
		}
		
		for(auto z:{b,d}){
			auto itr=cs[ct[z]^1].lower_bound(z);
			if(*itr<m)ci.pb(*itr);
			itr--;
			if(*itr>=0)ci.pb(*itr);
		}
		
		mkuni(ri);
		mkuni(ci);
		
		struct E{int to,cost;};
		int h=ri.size(),w=ci.size(),s=h*w;
		auto id=[&](int i,int j){
			i=lower_bound(all(ri),i)-ri.bg;
			j=lower_bound(all(ci),j)-ci.bg;
			return i*w+j;
		};
		vvc<E> g(s);
		rep(i,h)rep(j,w-1){
			int len=ci[j+1]-ci[j];
			if(rt[ri[i]]==0)
				g[i*w+j+1].pb(E{i*w+j,len});
			else
				g[i*w+j].pb(E{i*w+j+1,len});
		}
		rep(j,w)rep(i,h-1){
			int len=ri[i+1]-ri[i];
			if(ct[ci[j]]==0)
				g[(i+1)*w+j].pb(E{i*w+j,len});
			else
				g[i*w+j].pb(E{(i+1)*w+j,len});
		}
		
		dmp(ri);
		dmp(ci);
		
		int ans=dijkstra<E>(g,id(a,b))[id(c,d)];
		if(ans==inf)ans=-1;
		print(ans);
	}
}