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.io.*;
import java.util.*;

public class Main {
     static ArrayList a[]=new ArrayList[3000001];
     static boolean prime[]=new boolean [3000001];
     static int dp[][]=new int[1001][1001];
     static void dijkstra(int n) {
    	 boolean visited[]=new boolean [1001];
    	 dp[n][n]=0;
    	 Queue<pair>pq=new LinkedList<>();
    	 pq.add(new pair(0,n));
    	 while(!pq.isEmpty()) {
    		 pair p=pq.poll();
    		 visited[p.y]=true;
    		 for(int i=0;i<a[p.y].size();i++) {
    			 int id=(int)a[p.y].get(i);
    			 if(!visited[id] ) {
    				 dp[n][id]=p.x+1;
    	    		 visited[id]=true;
    				 pq.add(new pair(dp[n][id],id));
    			 }
    		 }
    	 }
     }
     public static void main(String[]args)
    {
        InputReader in=new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n=in.nextInt();
        for(int i=0;i<=n;i++)
        	a[i]=new ArrayList<Integer>();
        int m=in.nextInt();
        int s=in.nextInt();
        int t=in.nextInt();
        boolean chk[][]=new boolean[n+1][n+1];
        for(int i=0;i<m;i++) {
        	int x=in.nextInt();
        	int y=in.nextInt();
        	a[x].add(y);
        	a[y].add(x);
        	chk[x][y]=chk[y][x]=true;
        }
        for(int i=0;i<=n;i++)
        	Arrays.fill(dp[i], Integer.MAX_VALUE);
    	dijkstra(s);
    	dijkstra(t);
        long ans=0;
        for(int i=1;i<=n;i++) {
        	for(int j=i+1;j<=n;j++) {
        		if(!chk[i][j]) {
	        		if(1+dp[s][i]+dp[t][j]>=dp[s][t] && 1+dp[s][j]+dp[t][i]>=dp[s][t] ){
	        			ans++;
	        		}
        		}
        	}
        }
        pw.println(ans);
        pw.flush();
        pw.close();
 
    }
    private static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
   static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        { 
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
        static class tri implements Comparable<tri> {
            int p, c, l;
 
            tri(int p, int c, int l) {
                this.p = p;
                this.c = c;
                this.l = l;
            }
 
            public int compareTo(tri o) {
                return Integer.compare(l, o.l);
            }
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
   public static long modularExponentiation(long x,long n,long M)
   {
       long result=1;
       while(n>0)
       {
           if(n % 2 ==1)
               result=(result%M * x%M)%M;
           x=(x%M * x%M)%M;
           n=n/2;
       }
       return result;
   }
   
   public static long modInverse(int A,int M)
   {
       return modularExponentiation(A,M-2,M);
   }
   
   public static long modInverse(long A,long M)
   {
       return modularExponentiation(A,M-2,M);
   }
   static class pair implements Comparable<pair>
   {
       Integer x, y;
       pair(int x,int y)
       {
           this.x=x;
           this.y=y;
       }

       public int compareTo(pair o) {
           int result = x.compareTo(o.x);
           if(result==0)
               result = y.compareTo(o.y);

           return result;
       }

       public String toString()
       {
           return x+" "+y;
       }

       public boolean equals(Object o)
       {
           if (o instanceof pair)
          {
               pair p = (pair)o;
               return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
           }
           return false;
       }

       public int hashCode()
       {
           return new Long(x).hashCode()*31 + new Long(y).hashCode();
       }
   }
    public static long GCD(long a,long b)
    {
        if(b==0)
            return a;
        else
            return GCD(b,a%b);
    }
    public static long[] shuffle(long[] a, Random gen){ 
        for(int i = 0, n = a.length;i < n;i++){ 
            int ind = gen.nextInt(n-i)+i; 
            long d = a[i]; 
            a[i] = a[ind]; 
            a[ind] = d; 
        } 
        return a; 
    }
  
    
}