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 Main9
{
	static class Pair
	{
		int x;
		boolean y;
		Pair(int x,boolean y)
		{
			this.x=x;
			this.y=y;
		}
	}
	static int mod=1000000007;
	public static int[] sort(int[] a)
	{
		int n=a.length;
		ArrayList<Integer> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++)
		{
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++)
		{
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b)
    {
        long result=1;
        while(b>0)
        {
            if (b % 2 != 0)
            {
                result=(result*a)%mod;
                b--;
            } 
            a=(a*a)%mod;
            b /= 2;
        }   
        return result;
    }
	
    public static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b%a, a);
    }   
	public static long lcm(long a, long b)
	{
		return a*(b/gcd(a,b));
	}
	static ArrayList<ArrayList<Integer>> graph;
	static public void main(String args[])throws IOException
	{
		int tt=1;
		StringBuilder sb=new StringBuilder();
		for(int ttt=1;ttt<=tt;ttt++)
		{
			int n=i();
			int m=i();
			int s=i()-1;
			int t=i()-1;
			int[] a=new int[m];
			int[] b=new int[m];
			graph=new ArrayList<>();
			for(int i=0;i<n;i++)
				graph.add(new ArrayList<>());
			int[][] tmp=new int[n][n];
			for(int i=0;i<m;i++)
			{
				a[i]=i()-1;
				b[i]=i()-1;
				tmp[a[i]][b[i]]=1;
				tmp[b[i]][a[i]]=1;
				graph.get(a[i]).add(b[i]);
				graph.get(b[i]).add(a[i]);
			}
			int[] xx=findDist(s,n);
			int[] yy=findDist(t,n);
			int ans=0;
			for(int i=0;i<n;i++)
			{
				for(int j=i+1;j<n;j++)
				{
					if(tmp[i][j]!=1)
					{
						int value=xx[i]+yy[j]+1;
						int value1=yy[i]+xx[j]+1;
						int min=Math.min(value,value1);
						if(min>=xx[t])
						{
							ans++;
						}
					}
				}
			}
			pln(ans+"");
		}
		System.out.print(sb.toString());
	}
	static int[] findDist(int x,int n)
	{
		boolean[] visited=new boolean[n];
		Queue<Integer> queue=new LinkedList<>();
		queue.add(x);
		int[] dist=new int[n];
		dist[x]=0;
		visited[x]=true;
		while(queue.isEmpty()==false)
		{
			int num=queue.poll();
			ArrayList<Integer> ar=graph.get(num);
			for(int i=0;i<ar.size();i++)
			{
				int num1=ar.get(i);
				if(visited[num1]==false)
				{
					visited[num1]=true;
					dist[num1]=dist[num]+1;
					queue.add(num1);
				}
			}
		}
		return dist;
	}
			/**/
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	public static long l()
	{
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value)
	{
		System.out.println(value);
	}
	public static int i()
	{
		return in.Int();
	}
	public static String s()
	{
		return in.String();
	}
}
	class InputReader 
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
	 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
	 
		public int read() {
			if (numChars== -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	 
		public int Int() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	 
		public String String() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(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;
		}
	 
		public String next() {
			return String();
		}
	 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	 
	class OutputWriter {
		private final PrintWriter writer;
	 
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
	 
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
	 
		public void print(Object...objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}
	 
		public void printLine(Object...objects) {
			print(objects);
			writer.println();
		}
	 
		public void close() {
			writer.close();
		}
	 
		public void flush() {
			writer.flush();
		}
	 
		}
	 
		class IOUtils {
	 
		public static int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.Int();
			return array;
		}
	 
	} 

