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.

Input

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 r₁, r₂, ..., 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.

Output

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.

Berland Army

Examples