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
import java.util.*;
import java.io.*;
import java.math.*;
public class code7 {
	InputStream is;
	PrintWriter out;
	static long mod=pow(10,9)+7;
	int dx[]= {0,0,1,-1},dy[]={+1,-1,0,0};
	void solve()
	{
		n=ni();
		int m=ni();
		int s=ni()-1;
		int t=ni()-1;
		al=new ArrayList[n];
		for(int i=0;i<n;i++)
			al[i]=new ArrayList<Integer>();
		graph=new boolean[n][n];
		for(int i=0;i<m;i++)
		{
			int x=ni()-1;
			int y=ni()-1;
			graph[x][y]=true;
			graph[y][x]=true;
			al[x].add(y);
			al[y].add(x);
		}
		int min[]=new int[n];
		for(int i=0;i<n;i++)
			min[i]=distance(i,t);
		min[t]=0;
		level=new int[n];
		Queue<Pair> q=new LinkedList<Pair>();
		q.add(new Pair(s,0));
		boolean visited[]=new boolean[n];
		visited[s]=true;
		outer:while(!q.isEmpty())
		{
			Pair p=q.poll();
			for(int i:al[p.x])
			{
				if(!visited[i])
				{
					level[i]=level[p.x]+1;
					q.add(new Pair(i,p.y+1));
					visited[i]=true;
				}
			}
			
		}
		int count=0;
		for(int i=0;i<n;i++)
		{
			for(int j=i+1;j<n;j++)
			{
				if(!graph[i][j])
				{
					
					if(level[i]+min[j]+1<min[s]||level[j]+min[i]+1<min[s])
					{
						count++;
					}
				}
			}
		}
		out.println((n*(n-1)/2)-m-count);
	}
	int n,level[];
	boolean graph[][];
	int distance(int s,int t)
	{
		Queue<Pair> q=new LinkedList<Pair>();
		q.add(new Pair(s,0));
		boolean visited[]=new boolean[n];
		visited[s]=true;
		int ans=-1;
		outer:while(!q.isEmpty())
		{
			Pair p=q.poll();
			for(int i:al[p.x])
			{
				if(!visited[i])
				{
					if(i==t)
					{
						ans=p.y+1;
						return ans;
					}
					q.add(new Pair(i,p.y+1));
					visited[i]=true;
				}
			}
			
		}
		return -1;
	}
	ArrayList<Integer>al [];
	void take(int n,int m)
	{
		al=new ArrayList[n];
		for(int i=0;i<n;i++)
			al[i]=new ArrayList<Integer>();
		for(int i=0;i<m;i++)
		{
			int x=ni()-1;
			int y=ni()-1;
			al[x].add(y);
			al[y].add(x);
		}
	}
	int arr[][];
	int small[];
	void pre(int n)
	{
		small=new int[n+1];
		for(int i=2;i*i<=n;i++)
		{
			for(int j=i;j*i<=n;j++)
			{
				if(small[i*j]==0)
					small[i*j]=i;
			}
		}
		for(int i=0;i<=n;i++)
		{
			if(small[i]==0)
				small[i]=i;
		}
	}
	public static int count(int x)
	{
		int num=0;
		while(x!=0)
		{
			x=x&(x-1);
			num++;
		}
		return num;
	}
	static long d, x, y;
	void extendedEuclid(long A, long B) {
	    if(B == 0) {
	        d = A;
	        x = 1;
	        y = 0;
	    }
	    else {
	        extendedEuclid(B, A%B);
	        long temp = x;
	        x = y;
	        y = temp - (A/B)*y;
	    }
	}
	long modInverse(long A,long M) //A and M are coprime
	{
	    extendedEuclid(A,M);
	    return (x%M+M)%M;    //x may be negative
	}
	public static void mergeSort(int[] arr, int l ,int r){
		if((r-l)>=1){
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,r,mid);
		}
	}
	public static void merge(int arr[], int l, int r, int mid){
		int n1 = (mid-l+1), n2 = (r-mid);
		int left[] = new int[n1];
		int right[] = new int[n2];
		for(int i =0 ;i<n1;i++) left[i] = arr[l+i];
		for(int i =0 ;i<n2;i++) right[i] = arr[mid+1+i];
		int i =0, j =0, k = l;
		while(i<n1 && j<n2){
			if(left[i]>right[j]){
				arr[k++] = right[j++];
			}
			else{
				arr[k++] = left[i++];
			}
		}
		while(i<n1) arr[k++] = left[i++];
		while(j<n2) arr[k++] = right[j++];
	}
	public static void mergeSort(long[] arr, int l ,int r){
		if((r-l)>=1){
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,r,mid);
		}
	}
	public static void merge(long arr[], int l, int r, int mid){
		int n1 = (mid-l+1), n2 = (r-mid);
		long left[] = new long[n1];
		long right[] = new long[n2];
		for(int i =0 ;i<n1;i++) left[i] = arr[l+i];
		for(int i =0 ;i<n2;i++) right[i] = arr[mid+1+i];
		int i =0, j =0, k = l;
		while(i<n1 && j<n2){
			if(left[i]>right[j]){
				arr[k++] = right[j++];
			}
			else{
				arr[k++] = left[i++];
			}
		}
		while(i<n1) arr[k++] = left[i++];
		while(j<n2) arr[k++] = right[j++];
	}
	 static class Pair implements Comparable<Pair>{
		 
	      int x;
	      int y,k,i;
		Pair (int x,int y){
			this.x=x;
			this.y=y;
		}
	        
		public int compareTo(Pair o) {
			if(this.x!=o.x)
				return Long.compare(this.x,o.x);
			return  this.y-o.y;
		}
		public boolean equals(Object o) {
			if (o instanceof Pair) {
				Pair p = (Pair)o;
				return p.x == x && p.y == y;
			}
			return false;
		}
		public int hashCode() {
			return new Long(x).hashCode()*31 + new Long(y).hashCode() ;
		}
	           
	 
	        @Override
	        public String toString() {
	            return  "("+x + " " + y +" "+k+" "+i+" )";
	        }
	    
	    } 
	    
	    public static boolean isPal(String s){
	        for(int i=0, j=s.length()-1;i<=j;i++,j--){
	                if(s.charAt(i)!=s.charAt(j)) return false;
	        }
	        return true;
	    }
	    public static String rev(String s){
			StringBuilder sb=new StringBuilder(s);
			sb.reverse();
			return sb.toString();
	    }
	    
	    public static long gcd(long x,long y){
		if(x%y==0)
			return y;
		else
			return gcd(y,x%y);
	    }
	    
	    public static int gcd(int x,int y){
	    	if(y==0) 
	    		return x; 
	    	return gcd(y,x%y);
	    }
	    
	    public static long gcdExtended(long a,long b,long[] x){
	        
	        if(a==0){
	            x[0]=0;
	            x[1]=1;
	            return b;
	        }
	        long[] y=new long[2];
	        long gcd=gcdExtended(b%a, a, y);
	        
	        x[0]=y[1]-(b/a)*y[0];
	        x[1]=y[0];
	        
	        return gcd;
	    }
	    
	    public static int abs(int a,int b){
		return (int)Math.abs(a-b);
	    }
	 
	    public static long abs(long a,long b){
		return (long)Math.abs(a-b);
	    }
	    
	    public static int max(int a,int b){
		if(a>b)
			return a;
		else
			return b;
	    }
	 
	    public static int min(int a,int b){
		if(a>b)
			return b;
		else 
			return a;
	    }
	    
	    public static long max(long a,long b){
		if(a>b)
			return a;
		else
			return b;
	    }
	 
	    public static long min(long a,long b){
		if(a>b)
			return b;
		else 
			return a;
	    }
	 
	    public static long pow(long n,long p,long m){
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	    }
	    
	    public static long pow(long n,long p){
		long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;	    
		    p >>=1;
		    n*=n;	    
		}
		return result;
	    }
	    public static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
	    void run() throws Exception {
			is = System.in;
			out = new PrintWriter(System.out);
			solve();
			out.flush();
		}
	   
	    public static void main(String[] args) throws Exception {
			new Thread(null, new Runnable() {
				public void run() {
					try {
						new code7().run();
					} catch (Exception e) {
						e.printStackTrace();
					}
				}
			}, "1", 1 << 26).start();

		}
	    private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b));
			return b;
		}
	 
		private double nd() {
			return Double.parseDouble(ns());
		}
	 
		private char nc() {
			return (char) skip();
		}
	 
		private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	 
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	 
		private char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
		
		private long[] nl(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nl();
			return a;
		}
		
		private int ni() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private long nl() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
}