Little town Nsk consists of n junctions connected by m bidirectional roads. Each road connects two distinct junctions and no two roads connect the same pair of junctions. It is possible to get from any junction to any other junction by these roads. The distance between two junctions is equal to the minimum possible number of roads on a path between them.

In order to improve the transportation system, the city council asks mayor to build one new road. The problem is that the mayor has just bought a wonderful new car and he really enjoys a ride from his home, located near junction s to work located near junction t. Thus, he wants to build a new road in such a way that the distance between these two junctions won't decrease. 

You are assigned a task to compute the number of pairs of junctions that are not connected by the road, such that if the new road between these two junctions is built the distance between s and t won't decrease.

Input

The firt line of the input contains integers n, m, s and t (2 ≤ n ≤ 1000, 1 ≤ m ≤ 1000, 1 ≤ s, t ≤ n, s ≠ t) — the number of junctions and the number of roads in Nsk, as well as the indices of junctions where mayors home and work are located respectively. The i-th of the following m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), meaning that this road connects junctions ui and vi directly. It is guaranteed that there is a path between any two junctions and no two roads connect the same pair of junctions.

Output

Print one integer — the number of pairs of junctions not connected by a direct road, such that building a road between these two junctions won't decrease the distance between junctions s and t.

Examples

Input

5 4 1 5
1 2
2 3
3 4
4 5


Output

0


Input

5 4 3 5
1 2
2 3
3 4
4 5


Output

5


Input

5 6 1 5
1 2
1 3
1 4
4 5
3 5
2 5


Output

3
//Implemented By Aman Kotiyal Date:-26-Jan-2021  Time:-3:01:41 pm
import java.io.*;
import java.util.*;

public class ques1
{
	public static void main(String[] args)throws Exception{ new ques1().run();} 
	long mod=1000000000+7;
	int n;
	ArrayList<Integer> adj[];
	void init(int N)
	{
		adj=new ArrayList[N+1];
		for (int i = 0; i < adj.length; i++) 
			adj[i]=new ArrayList<>();
	}
	void solve() throws Exception
	{
			n=ni();
			init(n);
			int m=ni();
			int s=ni();
			int t=ni();
			int g[][]=new int[n+1][n+1];
			for(int i=0;i<m;i++)
			{
				int u=ni();
				int v=ni();
				adj[u].add(v);
				adj[v].add(u);
				g[u][v]=1;
				g[v][u]=1;
			}
			int h[]=new int[n+1];
			int ht[]=new int[n+1];
			vis=new int[n+1];
			bfs(h,s);
			vis=new int[n+1];
			bfs(ht,t);
			
			long ans=0;
			for(int i=1;i<n;i++)
			{
				for (int j = i+1; j<=n; j++) 
				{
					if(g[i][j]==1||g[j][i]==1)continue;
					
					long min=h[i]+1+ht[j];
					min=min(min,h[j]+1+ht[i]);
					if(min>=h[t])
						ans++;
				}
			}
			
			out.println(ans);
	}
	
	int vis[];
	void bfs(int h[],int s)
	{
		Queue<Integer> q=new LinkedList<Integer>();
		q.add(s);
		vis[s]=1;
		while(!q.isEmpty())
		{
			int x=q.poll();
			for(int u:adj[x])
			{
				if(vis[u]==1)continue;
				q.add(u);
				vis[u]=1;
				h[u]=h[x]+1;
			}
		}
	}
	
	/*FAST INPUT OUTPUT & METHODS BELOW*/
	
	private byte[] buf=new byte[1024];
	private int index;
	private InputStream in;
	private int total;
	private SpaceCharFilter filter;
	PrintWriter out;
	
	int min(int... ar){int min=Integer.MAX_VALUE;for(int i:ar)min=Math.min(min, i);return min;}
	long min(long... ar){long min=Long.MAX_VALUE;for(long i:ar)min=Math.min(min, i);return min;}
	int max(int... ar) {int max=Integer.MIN_VALUE;for(int i:ar)max=Math.max(max, i);return max;}
	long max(long... ar) {long max=Long.MIN_VALUE;for(long i:ar)max=Math.max(max, i);return max;}
	
	void shuffle(int a[]) {
		ArrayList<Integer> al = new ArrayList<>();
		for(int i=0;i<a.length;i++) 
			al.add(a[i]);
		
		Collections.sort(al);
		for(int i=0;i<a.length;i++) 
			a[i]=al.get(i);
	}
	long lcm(long a,long b)
	{
		return (a*b)/(gcd(a,b));
	}
	
	int gcd(int a, int b) 
	{ 
		if (a == 0) 
			return b; 
		return gcd(b%a, a); 
	} 
	long gcd(long a, long b) 
	{ 
		if (a == 0) 
			return b; 
		return gcd(b%a, a); 
	}
	/* for (1/a)%mod = ( a^(mod-2) )%mod  ----> use expo to calc -->(a^(mod-2)) */
	long expo(long p,long q)  /*  (p^q)%mod   */
	{
		long z = 1;
		while (q>0) {
			if (q%2 == 1) {
				z = (z * p)%mod;
			}
			p = (p*p)%mod;
			q >>= 1;
		}
		return z;
	}
	void run()throws Exception
	{
		in=System.in; out = new PrintWriter(System.out);
		solve();
		out.flush();
	}
	private int scan()throws IOException
	{
		if(total<0)
			throw new InputMismatchException();
		if(index>=total)
		{
			index=0;
			total=in.read(buf);
			if(total<=0)
				return -1;
		}
		return buf[index++];
	}
	private int ni() throws IOException 
	{
		int c = scan();
		while (isSpaceChar(c))
			c = scan();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = scan();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = scan();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	private long nl() throws IOException 
	{
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = scan()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = scan();
		}
		
		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = scan();
		}
	}
	private double nd() throws IOException{
		return Double.parseDouble(ns());
	}
	private String ns() throws IOException {
		int c = scan();
		while (isSpaceChar(c))
			c = scan();
		StringBuilder res = new StringBuilder();
		do {
			if (Character.isValidCodePoint(c))
				res.appendCodePoint(c);
			c = scan();
		} while (!isSpaceChar(c));
		return res.toString();
	}
	private String nss() throws IOException
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		return br.readLine();
	}
	private char nc() throws IOException 
	{
		int c = scan();
		while (isSpaceChar(c))
			c = scan();
		return (char) c;
	}
	private boolean isWhiteSpace(int n)
	{
		if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
			return true;
		return false;
	}
	private boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhiteSpace(c);
	}
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}