CF883B.Berland Army

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.

贝兰德军队中有 $n$ 名军人。目前，其中一些人已经向其他军人下达了命令。给定 $m$ 对 $(x_i, y_i)$，表示第 $i$ 条命令由军人 $x_i$ 下达给另一名军人 $y_i$。

现在是改革的时候了！贝兰德国防部计划在贝兰德军队中引入军衔制度。每名军人应被授予一个军衔——即介于 $1$ 到 $k$（含）之间的整数。其中部分军人的军衔已预先确定，而其余军人的军衔尚待分配。

请帮助国防部为其余军人分配军衔，使得：

• 对于全部 $m$ 条命令，下令者（军人 $x_i$）的军衔严格大于受令者（军人 $y_i$）的军衔；
• 对于从 $1$ 到 $k$ 的每一个军衔值，至少有一名军人拥有该军衔。

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.

第一行包含三个整数 $n$、$m$ 和 $k$（$1 \leq n \leq 2\cdot10^5$，$0 \leq m \leq 2\cdot10^5$，$1 \leq k \leq 2\cdot10^5$）——分别表示 Berland 军队中军人的数量、命令的数量以及军衔的种类数。

第二行包含 $n$ 个整数 $r_1,\,r_2,\,...,\,r_n$，其中：若 $r_i > 0$（此时满足 $1 \leq r_i \leq k$），表示第 $i$ 位军人已被授予军衔 $r_i$；若 $r_i = 0$，表示第 $i$ 位军人尚未被授予任何军衔。

接下来的 $m$ 行每行描述一条命令。每条命令由两个整数 $x_i$、$y_i$（$1 \leq x_i,\,y_i \leq n$，且 $x_i \neq y_i$）组成。该行表示第 $i$ 条命令由军人 $x_i$ 下达给军人 $y_i$。对于任意一对军人 $(x,\,y)$，可能存在多条从 $x$ 到 $y$ 的命令。

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.

输出 n 个整数，其中第 i 个数表示第 i 位军人的排名。若存在多种解，输出任意一种即可。

若无解，则仅输出数字 -1。