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B. Berland Army
time limit per test
3 seconds
memory limit per test
256 megabytes
standard input
standard output

There are n military men in the Berland army. Some of them have given orders to other military men by now. Given m pairs ( x i, y i), meaning that the military man x i gave the i-th order to another military man y i.

It is time for reform! The Berland Ministry of Defence plans to introduce ranks in the Berland army. Each military man should be assigned a rank — integer number between 1 and k, inclusive. Some of them have been already assigned a rank, but the rest of them should get a rank soon.

Help the ministry to assign ranks to the rest of the army so that:

  • for each of m orders it is true that the rank of a person giving the order (military man x i) is strictly greater than the rank of a person receiving the order (military man y i);
  • for each rank from 1 to k there is at least one military man with this rank.

The first line contains three integers n, m and k (1 ≤ n ≤ 2·105, 0 ≤ m ≤ 2·105, 1 ≤ k ≤ 2·105) — number of military men in the Berland army, number of orders and number of ranks.

The second line contains n integers r 1, r 2, ..., r n, where r i > 0 (in this case 1 ≤ r i ≤ k) means that the i-th military man has been already assigned the rank r i; r i = 0 means the i-th military man doesn't have a rank yet.

The following m lines contain orders one per line. Each order is described with a line containing two integers x i, y i (1 ≤ x i, y i ≤ n, x i ≠ y i). This line means that the i-th order was given by the military man x i to the military man y i. For each pair (x, y) of military men there could be several orders from x to y.


Print n integers, where the i-th number is the rank of the i-th military man. If there are many solutions, print any of them.

If there is no solution, print the only number -1.

5 3 3
0 3 0 0 2
2 4
3 4
3 5
1 3 3 2 2 
7 6 5
0 4 5 4 1 0 0
6 1
3 6
3 1
7 5
7 1
7 4
2 4 5 4 1 3 5 
2 2 2
2 1
1 2
2 1