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

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 xi) is strictly greater than the rank of a person receiving the order (military man yi); 
  * 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, ..., rn, where ri > 0 (in this case 1 ≤ ri ≤ k) means that the i-th military man has been already assigned the rank ri; ri = 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 xi, yi (1 ≤ xi, yi ≤ n, xi ≠ yi). This line means that the i-th order was given by the military man xi to the military man yi. 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.

Examples

Input

5 3 3
0 3 0 0 2
2 4
3 4
3 5


Output

1 3 3 2 2 


Input

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


Output

2 4 5 4 1 3 5 


Input

2 2 2
2 1
1 2
2 1


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 200010;
int n, m, k, cnt, flag;
int to[maxn], nxt[maxn], head[maxn], pa[maxn], pb[maxn], v[maxn], L[maxn],
    R[maxn], d[maxn], ans[maxn];
vector<int> p[maxn];
vector<int>::iterator it;
queue<int> q;
priority_queue<pair<int, int> > pq;
inline int rd() {
  int ret = 0, f = 1;
  char gc = getchar();
  while (gc < '0' || gc > '9') {
    if (gc == '-') f = -f;
    gc = getchar();
  }
  while (gc >= '0' && gc <= '9') ret = ret * 10 + (gc ^ '0'), gc = getchar();
  return ret * f;
}
inline void add(int a, int b) {
  to[cnt] = b, nxt[cnt] = head[a], head[a] = cnt++;
}
int main() {
  n = rd(), m = rd(), k = rd();
  int i, u;
  for (i = 1; i <= n; i++) {
    v[i] = rd();
    if (!v[i])
      L[i] = 1, R[i] = k;
    else
      L[i] = R[i] = v[i];
  }
  memset(head, -1, sizeof(head)), cnt = 0;
  for (i = 1; i <= m; i++)
    pa[i] = rd(), pb[i] = rd(), d[pb[i]]++, add(pa[i], pb[i]);
  for (i = 1; i <= n; i++)
    if (!d[i]) q.push(i);
  while (!q.empty()) {
    u = q.front(), q.pop();
    for (i = head[u]; i != -1; i = nxt[i]) {
      d[to[i]]--, R[to[i]] = min(R[to[i]], R[u] - 1);
      if (!d[to[i]]) q.push(to[i]);
    }
  }
  for (i = 1; i <= n; i++)
    if (d[i]) return puts("-1"), 0;
  memset(head, -1, sizeof(head)), cnt = 0;
  for (i = 1; i <= m; i++) d[pa[i]]++, add(pb[i], pa[i]);
  for (i = 1; i <= n; i++)
    if (!d[i]) q.push(i);
  while (!q.empty()) {
    u = q.front(), q.pop();
    for (i = head[u]; i != -1; i = nxt[i]) {
      d[to[i]]--, L[to[i]] = max(L[to[i]], L[u] + 1);
      if (!d[to[i]]) q.push(to[i]);
    }
  }
  for (i = 1; i <= n; i++)
    if (d[i] || L[i] > R[i]) return puts("-1"), 0;
  for (i = 1; i <= n; i++) p[R[i]].push_back(i);
  for (i = k; i >= 1; i--) {
    for (it = p[i].begin(); it != p[i].end(); it++)
      pq.push(make_pair(L[*it], *it));
    if (pq.empty()) return puts("-1"), 0;
    u = pq.top().second, pq.pop(), ans[u] = i;
    while (!pq.empty()) {
      u = pq.top().second;
      if (L[u] < i) break;
      pq.pop(), ans[u] = i;
    }
  }
  for (i = 1; i <= n; i++) printf("%d ", ans[i]);
  return 0;
}