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 inf = 1e8 + 400;
const int maxn = 2e5 + 200;
vector<int> out[maxn];
vector<int> in[maxn];
bool vis[maxn];
int a[maxn];
int l[maxn];
int r[maxn];
vector<int> topol;
int jash[maxn];
void add(int a, int b) {
  out[a].push_back(b);
  in[b].push_back(a);
}
void dfs_topol(int a) {
  vis[a] = 1;
  for (auto v : out[a]) {
    if (!vis[v]) dfs_topol(v);
  }
  topol.push_back(a);
}
vector<int> vec[maxn];
set<pair<int, int> > st;
void hesab(int u, int val) {
  st.erase(make_pair(r[u], u));
  a[u] = val;
  l[u] = val;
  r[u] = val;
  for (auto v : out[u]) {
    if (l[u] + 1 > l[v]) {
      st.erase(make_pair(r[v], v));
      l[v] = l[u] + 1;
      vec[l[v]].push_back(v);
    }
  }
}
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (int j = 0; j < m; j++) {
    int v, u;
    cin >> u >> v;
    add(v - 1, u - 1);
  }
  for (int i = 0; i < n; i++) {
    if (!vis[i]) {
      dfs_topol(i);
    }
  }
  reverse(topol.begin(), topol.end());
  for (int i = 0; i < n; i++) {
    jash[topol[i]] = i;
  }
  fill(l, l + n, 1);
  for (int i = 0; i < n; i++) {
    int v = topol[i];
    l[v] = max(l[v], a[v]);
    for (auto u : in[v]) {
      l[v] = max(l[v], l[u] + 1);
    }
  }
  fill(r, r + n, k);
  for (int i = n - 1; i >= 0; i--) {
    int v = topol[i];
    if (a[v] != 0) r[v] = min(r[v], a[v]);
    for (auto u : out[v]) {
      r[v] = min(r[v], r[u] - 1);
    }
  }
  for (int i = 0; i < n; i++) {
    if (l[i] > r[i]) {
      cout << -1;
      return 0;
    }
    for (auto v : out[i]) {
      if (jash[i] > jash[v]) {
        cout << -1;
        return 0;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    vec[l[i]].push_back(i);
  }
  int donbal = 1;
  while (donbal <= k) {
    for (auto v : vec[donbal]) {
      if (l[v] == donbal) {
        st.insert(make_pair(r[v], v));
      }
    }
    if (st.empty()) {
      cout << -1;
      return 0;
    }
    bool anj = 0;
    while (st.size() && (*st.begin()).first == donbal) {
      anj = 1;
      int v = (*st.begin()).second;
      hesab(v, donbal);
    }
    if (!anj) {
      int v = (*st.begin()).second;
      hesab(v, donbal);
    }
    donbal++;
  }
  set<int> tts;
  for (int i = 0; i < n; i++) {
    if (a[i] < 1 || a[i] > k) {
      cout << -1;
      return 0;
    }
    tts.insert(a[i]);
    for (auto v : out[i]) {
      if (a[i] >= a[v]) {
        cout << -1;
        return 0;
      }
    }
  }
  if (tts.size() != k) {
    cout << -1;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    cout << a[i] << ' ';
  }
}