You are given a simple undirected graph with n vertices, n is even. You are going to write a letter on each vertex. Each letter should be one of the first k letters of the Latin alphabet.

A path in the graph is called Hamiltonian if it visits each vertex exactly once. A string is called palindromic if it reads the same from left to right and from right to left. A path in the graph is called palindromic if the letters on the vertices in it spell a palindromic string without changing the order.

A string of length n is good if: 

  * each letter is one of the first k lowercase Latin letters; 
  * if you write the i-th letter of the string on the i-th vertex of the graph, there will exist a palindromic Hamiltonian path in the graph. 



Note that the path doesn't necesserily go through the vertices in order 1, 2, ..., n.

Count the number of good strings.

Input

The first line contains three integers n, m and k (2 ≤ n ≤ 12; n is even; 0 ≤ m ≤ (n ⋅ (n-1))/(2); 1 ≤ k ≤ 12) — the number of vertices in the graph, the number of edges in the graph and the number of first letters of the Latin alphabet that can be used.

Each of the next m lines contains two integers v and u (1 ≤ v, u ≤ n; v ≠ u) — the edges of the graph. The graph doesn't contain multiple edges and self-loops.

Output

Print a single integer — number of good strings.

Examples

Input


4 3 3
1 2
2 3
3 4


Output


9


Input


4 6 3
1 2
1 3
1 4
2 3
2 4
3 4


Output


21


Input


12 19 12
1 3
2 6
3 6
3 7
4 8
8 5
8 7
9 4
5 9
10 1
10 4
10 6
9 10
11 1
5 11
7 11
12 2
12 5
12 11


Output


456165084
/* Creation Date - 11-09-2021 */ 
/* Creation Time -  6:56:26.96 */  

#define AATIF_DEBUG
#define ill 
/*
Written By : mafailure
In the name of God 
O Allah, May you grant peace and honor on Muhammad and his family.
Allahumm-a-Sall-iAla Muhammad-in Wa Al-i Muhammad
*/

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp> // Common file 
#include <ext/pb_ds/tree_policy.hpp> 
#include <functional> // for less
using namespace std;
using namespace __gnu_pbds;
#define IOS ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);

#define endl "\n"
/*------------------------int to long long -----------------*/
#ifdef ill
#define int long long 
#endif
/*---------------------------DEBUG HELPER--------------------------------------*/
template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { os << '{'; string sep; for (const auto &x : v) os << sep << x, sep = ", "; return os << '}'; }
template<typename T, size_t size> ostream& operator<<(ostream &os, const array<T, size> &arr) { os << '{'; string sep; for (const auto &x : arr) os << sep << x, sep = ", "; return os << '}'; }
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }

void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }

#ifdef AATIF_DEBUG
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

//#define int long long 
// int dx[]={-1,1,0,0}; int dy[]={0,0,1,-1};
// int dx[]={2,2,-2,-2,1,1,-1,-1}; int dy[]={1,-1,1,-1,2,-2,2,-2};
const long long mod = 1e9 + 7;
const double eps=1e-9;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef pair<int, int> ii;
typedef vector< pair< int, int > > vii;
typedef map<int, int> mii;
typedef pair<int, ii> pip;
typedef pair<ii, int> ppi;
#define arrinp(arr,init,final,size,type) type* arr=new type[size];for(int i=init;i<final;i++)cin>>arr[i];
#define cr2d(arr,n,m,t) t**arr=new t*[n];for(int i=0;i<n;i++)arr[i]=new t[m];
#define w(t) int t;cin>>t; while(t--)
#define takeInp(n) int n;cin>>n;
#define fr(i,init,final) for(int i=init;i<final;i++)
#define frr(i,init,final) for(int i=init;i>=final;i--)
#define Fr(i,final) for(int i=0;i<final;i++)
#define Frr(i,first) for(int i=first;i>=0;i--)
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(c) (c).begin(),(c).end()
#define rall(c) (c).rbegin(),(c).rend()
#define debug(x) cerr<<">value ("<<#x<<") : "<<x<<endl;
#define setb __builtin_popcount
#define lsone(n) (n&(-n))
#define rlsone(n) (n&(n-1))
#define clr(a,b) memset(a,b,sizeof(a))
const int inf= INT_MAX;
/*-----------------------------RANDOM NUMBER GENERATOR ---------------------*/
#ifdef RNG 
unsigned seed=chrono::high_resolution_clock::now().time_since_epoch().count();
mt19937 rng(seed);
#endif 
/*------------------------------UNORDERED MAP HASH --------------------------------------------*/
//To make unordered_map unhackable 
// use it as unordered_map<int,int,custom_hash> mapp;
struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        /* http://xorshift.di.unimi.it/splitmix64.c */
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};
/*---------------------------ORDERED SET--------------------------------------*/
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>  ordered_set; 
/*----------------------------------------------------------------------------*/
vi init(string s)
{
	istringstream sin(s);
	int n;
	vi arr;
	while(sin>>n)arr.push_back(n);
	return arr;
}
int power(int x, int y)
{ 
	if(y==0)return 1;
	int u=power(x,y/2);
	u=(u*u)%mod;
	if(y%2)u=(x*u)%mod;
	return u;
    
}
int gcd(int a,int b)
{
	if(a<b)return gcd(b,a);
	return (b==0?a:(a%b?gcd(b,a%b):b));
}
int gcd_e(int a,int b,int &x,int &y)
{
	
	if(b==0){x=1; y=0; return a;}
	int x1,y1;
	int p=gcd_e(b,a%b,x1,y1);
	x=y1;
	y=x1-(a/b)*y1;
	return p;
}
/*-----------------to solve int to long long problem-----------------*/
int Min (int a,int b){return min(a,b);}
int Max(int a,int b){ return max(a,b);}

//786 121 786 121 786 121 786 121 786 121 786 121 786 121 786 121 786 121
/*========================CODE*****CODE****CODE======================*/




int pw[5000]; 
mii ans;
int pw6[13]; 
vector<int> tocheck; 
int lim=pow(6,6); 
int g[12][12]; 
int c[13][13]; 
int fact[13]; 
void pre()
{
	fact[0]=1; 
	pw6[0]=1; 
	for(int i=1;i<13;i++)fact[i]=i*fact[i-1],pw6[i]=pw6[i-1]*6; 
	memset(c,0,sizeof(c)); 
	for(int i=0;i<13;i++)for(int j=0;j<=i;j++)if(j==0||j==i)c[i][j]=1;
	else c[i][j]=c[i-1][j]+c[i-1][j-1]; 
	
}
int ncr(int n,int r)
{
	return c[n][r]; 
}
void solve2(vector<pair<int,int>> & a)
{
	//dbg(a); 
	int n=a.size(); 
	int dp[1<<n][n];
	memset(dp,0,sizeof(dp)); 
	for(int i=0;i<n;i++)dp[((1<<n)-1)&(~(1<<i))][i]=1;
	if(n==1)dp[0][0]=(g[a[0].fi][a[0].se]); 
	for(int i=(1<<n)-1;i>0;i--)
	{
		for(int j=0;j<n;j++)
		{
			if(dp[i][j]==0)continue; 
			for(int k=0;k<n;k++)
			{
				int id=(i>>k)&1; 
				if(id==0)continue; 
				if((g[a[j].fi][a[k].fi]&&g[a[j].se][a[k].se])||(g[a[j].se][a[k].fi]&&g[a[j].fi][a[k].se]))
				{
					int mask=(i&(~(1<<k)));
					if(mask)
					dp[i&(~(1<<k))][k]=1;
					else 
					{
						if(g[a[k].fi][a[k].se])dp[mask][k]=1; 		
					}
				}
				
			}
		}
	}
	int ok=0;     
//	int whichone=-1; 
	for(int i=0;i<n;i++)ok|=dp[0][i];//,whichone=(dp[0][i]?i:whichone); 
	if(!ok)return; 
	for(auto it:tocheck)
	{
		int hash=0;
		int temp=it;  
		for(int j=0;j<n;j++)
		{
			int cur=(temp%6); 
			hash+=cur*pw6[a[j].first]+cur*pw6[a[j].second]; 
			temp/=6; 
		}
		ans[hash]=1; 
	}
	//dbg(a,"passed",whichone); 
	 
	
	
}

void solve(int mask,vector<pair<int,int>>& b)
{
	//cout<<mask<<endl; 
	if(mask==0)
	{
		return solve2(b),void(); 
	}
	int x=pw[lsone(mask)]; 
	mask&=(mask-1); 
	int temp=mask; 
	while(temp)
	{
		int y=pw[lsone(temp)]; 
		b.push_back(make_pair(x,y)); 
		solve(mask&(~(1<<y)),b); 
		b.pop_back(); 
		temp&=(temp-1); 
	}
	
	return ; 
	
}



signed main()
{
	IOS
	pre(); 
	int cur=1; 
	int cnt=0; 
	while(cur<=2048)
	{
		pw[cur]=cnt; 
		cnt++; 
		cur*=2; 
	}
	int n,m,k; 
	cin>>n>>m>>k; 
	for(int i=0;i<lim;i++)
	{
		//int hash=0;
		int tempmask=0; 
		int temp=i;        
		vector<vector<int>> v(6); 
		for(int j=0;j<n/2;j++)
		{
			int cur=temp%6; 
			tempmask|=1<<cur;
			v[cur].push_back(j); 
			//hash=(hash+cur*pw6[a[j].first]+cur*pw6[a[j].second]); 
			temp/=6; 
		} 
		for(auto & it:v)sort(all(it),greater<int>()); 
		vector<vi> nw=v;
		sort(all(nw),greater<vi>());  
		if((tempmask+1)&(tempmask))continue;
		//bool ok=1; 
		if(nw==v)tocheck.push_back(i); 
		
	   
		// ans[hash]=1; 
	}
	
	//int n,m,k; 
	//cin>>n>>m>>k;
	memset(g,0,sizeof(g)); 
	for(int i=0;i<m;i++)
	{
		int u,v; 
		cin>>u>>v; 
		u--; v--; 
		g[u][v]=g[v][u]=1; 
	}
	vector<pair<int,int>> b; 
	solve((1<<n)-1,b);
	int res=0;
	
	for(auto it:ans)
	{
		//dbg(it);
		int temp=it.first;
		int mask=0;   
		for(int i=0;i<n;i++)
		{
			int cur=temp%(6); 
			temp/=(6); 
			mask|=(1<<cur); 
		}
		int bit=setb(mask); 
		//dbg(mask+1,bit);
		res=(res+ncr(k,bit)*fact[bit]); 
	}
	cout<<res<<endl; 
	
	
	
	 
	
	
	
	
	
	
}

