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;
template <class T>
inline void gmin(T &x, const T &y) {
  if (x > y) x = y;
}
template <class T>
inline void gmax(T &x, const T &y) {
  if (x < y) x = y;
}
const int BufferSize = 1 << 16;
char buffer[BufferSize], *Bufferhead, *Buffertail;
bool Terminal;
inline char Getchar() {
  if (Bufferhead == Buffertail) {
    int l = fread(buffer, 1, BufferSize, stdin);
    if (!l) {
      Terminal = 1;
      return 0;
    }
    Buffertail = (Bufferhead = buffer) + l;
  }
  return *Bufferhead++;
}
template <class T>
inline bool read(T &x) {
  x = 0;
  char c = Getchar(), rev = 0;
  while (c < '0' || c > '9') {
    rev |= c == '-';
    c = Getchar();
    if (Terminal) return 0;
  }
  while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = Getchar();
  if (c == '.') {
    c = Getchar();
    double t = 0.1;
    while (c >= '0' && c <= '9')
      x = x + (c - '0') * t, c = Getchar(), t = t / 10;
  }
  x = rev ? -x : x;
  return 1;
}
template <class T1, class T2>
inline bool read(T1 &x, T2 &y) {
  return read(x) & read(y);
}
template <class T1, class T2, class T3>
inline bool read(T1 &x, T2 &y, T3 &z) {
  return read(x) & read(y) & read(z);
}
template <class T1, class T2, class T3, class T4>
inline bool read(T1 &x, T2 &y, T3 &z, T4 &w) {
  return read(x) & read(y) & read(z) & read(w);
}
inline bool reads(char *x) {
  char c = Getchar();
  while (c < 33 || c > 126) {
    c = Getchar();
    if (Terminal) return 0;
  }
  while (c >= 33 && c <= 126) (*x++) = c, c = Getchar();
  *x = 0;
  return 1;
}
template <class T>
inline void print(T x, const char c = '\n') {
  if (!x) {
    putchar('0');
    putchar(c);
    return;
  }
  if (x < 0) putchar('-'), x = -x;
  int m = 0, a[20];
  while (x) a[m++] = x % 10, x /= 10;
  while (m--) putchar(a[m] + '0');
  putchar(c);
}
const int inf = 0x3f3f3f3f;
const int N = 200005, M = 100005, mod = 1e9 + 7;
template <class T, class S>
inline void ch(T &x, const S y) {
  x = (x + y) % mod;
}
inline int exp(int x, int y, const int mod = ::mod) {
  int ans = 1;
  while (y) {
    if (y & 1) ans = (long long)ans * x % mod;
    x = (long long)x * x % mod;
    y >>= 1;
  }
  return ans;
}
int n, m, k, a[N], l[N], r[N];
vector<int> g[N], f[N], ins[N];
bool vis[N];
inline void predfs(int x, vector<int> &seq) {
  vis[x] = 1;
  for (int y : f[x])
    if (!vis[y]) predfs(y, seq);
  seq.push_back(x);
}
inline void predfs(int x) {
  vis[x] = 1;
  for (int y : g[x])
    if (!vis[y]) predfs(y);
}
bool check() {
  vector<int> seq(0);
  for (int i = 1; i <= n; i++)
    if (!vis[i]) predfs(i, seq);
  memset(vis, 0, sizeof(vis));
  reverse(seq.begin(), seq.end());
  for (int i : seq)
    if (!vis[i])
      predfs(i);
    else
      return 0;
  return 1;
}
inline void dfs(int x) {
  vis[x] = 1;
  l[x] = 1;
  for (int y : g[x]) {
    if (!vis[y]) dfs(y);
    gmax(l[x], l[y] + 1);
  }
  if (a[x]) {
    if (l[x] > a[x]) {
      puts("-1");
      exit(0);
    }
    l[x] = a[x];
  }
}
inline void idfs(int x) {
  vis[x] = 1;
  r[x] = k;
  for (int y : f[x]) {
    if (!vis[y]) idfs(y);
    gmin(r[x], r[y] - 1);
  }
  if (a[x]) {
    if (r[x] < a[x]) {
      puts("-1");
      exit(0);
    }
    r[x] = a[x];
  }
}
inline void upt(int x, int p) {
  a[x] = p;
  for (int y : f[x]) gmax(l[y], p + 1);
}
int main() {
  read(n, m, k);
  for (int i = 1; i <= n; i++) read(a[i]);
  for (int i = 1; i <= m; i++) {
    int x, y;
    read(x, y);
    g[x].push_back(y);
    f[y].push_back(x);
  }
  if (!check()) {
    puts("-1");
    return 0;
  }
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= n; i++)
    if (!vis[i]) dfs(i);
  memset(vis, 0, sizeof(vis));
  for (int i = 1; i <= n; i++)
    if (!vis[i]) idfs(i);
  for (int i = 1; i <= n; i++) ins[l[i]].push_back(i);
  static priority_queue<pair<int, int>, vector<pair<int, int> >,
                        greater<pair<int, int> > >
      q;
  for (int i = 1; i <= k; i++) {
    bool isok = 0;
    for (int j : ins[i]) q.push(make_pair(r[j], j));
    while (!q.empty()) {
      int j = q.top().second;
      if (l[j] > i) {
        q.pop();
        ins[l[j]].push_back(j);
        continue;
      }
      if (!isok || r[j] == i) {
        q.pop();
        upt(j, i);
        isok = 1;
      } else
        break;
    }
    if (!isok) {
      cerr << "i"
           << "=" << i << endl;
      puts("-1");
      return 0;
    }
    ins[i].clear();
  }
  for (int i = 1; i <= n; i++)
    if (!a[i]) {
      puts("-1");
      return 0;
    }
  for (int i = 1; i <= n; i++) printf("%d ", a[i]);
  puts("");
  return 0;
}