Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \ {u, v \} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).

Input

The input is given in the following format.

N M s t
x1 y1
...
xi yi
...
xM yM

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \ {1, ..., N \}.)

Constraints

Each variable being input satisfies the following constraints.

• 2 ≤ N ≤ 100,000
• 1 ≤ M ≤ 300,000
• 1 ≤ s, t, xi, yi ≤ N
• Different from s and t
• Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3

Output

1

Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9

Output

7

Input

4 3 1 4
1 2
3 4
4 1

Output

0

Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4

Output

2

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