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Description

The cows are having a picnic! Each of Farmer John's K (1 ≤ K ≤ 100) cows is grazing in one of N (1 ≤ N ≤ 1,000) pastures, conveniently numbered 1...N. The pastures are connected by M (1 ≤ M ≤ 10,000) one-way paths (no path connects a pasture to itself).

The cows want to gather in the same pasture for their picnic, but (because of the one-way paths) some cows may only be able to get to some pastures. Help the cows out by figuring out how many pastures are reachable by all cows, and hence are possible picnic locations.

K(1≤K≤100) 只奶牛分散在 N(1≤N≤1000**) 个牧场．现在她们要集中起来进餐。牧场之间有M(1≤M≤10000) 条有向路连接，而且不存在起点和终点相同的有向路．她们进餐的地点必须是所有奶牛都可到达的地方。那么，有多少这样的牧场可供进食呢？

Format

Input

Line 1: Three space-separated integers, respectively: K, N, and M

Lines 2..K+1: Line i+1 contains a single integer (1..N) which is the number of the pasture in which cow i is grazing.

Lines K+2..M+K+1: Each line contains two space-separated integers, respectively A and B (both 1..N and A != B), representing a one-way path from pasture A to pasture B.

第1行:三个用空格分开的整数，分别是：K,N,和M

第2..K+1行:第i+1行包含一个整数(在1..N内)，表示第i头牛所在的农场编号。 第K+2..M+K+1行:每行两个用空格分开的整数，分别是A和B(都在1..N内，而且A≠B)，表示有一条单向的道路，从农场A直接连接到农场B。

Output

Line 1: The single integer that is the number of pastures that are reachable by all cows via the one-way paths.

输出共一行一个整数，表示通过这些单向道路，所有牛都能够到达的农场的数量。

Samples

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

2

Tips

The cows can meet in pastures 3 or 4.

【输入说明】

4<--3

^ ^

| |

| |

1-->2

农场地图如上图所示，两头牛分别在农场2和3号。

【输出说明】奶牛们能够集中到农场3或4。

【数据规模】

对于40%的数据：1≤K≤10；1≤N≤10；1≤M≤100；

对于60%的数据：1≤K≤50；1≤N≤100；1≤M≤500；

对于70%的数据：1≤K≤50；1≤N≤100；1≤M≤1,000；

对于100%的数据：1≤K≤100；1≤N≤1,000；1≤M≤10,000；A≠B；