In BerSoft n programmers work, the programmer i is characterized by a skill r_i.

A programmer a can be a mentor of a programmer b if and only if the skill of the programmer a is strictly greater than the skill of the programmer b (r_a > r_b) and programmers a and b are not in a quarrel.

You are given the skills of each programmers and a list of k pairs of the programmers, which are in a quarrel (pairs are unordered). For each programmer i, find the number of programmers, for which the programmer i can be a mentor.

Input

The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 0 ≤ k ≤ min(2 ⋅ 10^5, (n ⋅ (n - 1))/(2))) — total number of programmers and number of pairs of programmers which are in a quarrel.

The second line contains a sequence of integers r_1, r_2, ..., r_n (1 ≤ r_i ≤ 10^{9}), where r_i equals to the skill of the i-th programmer.

Each of the following k lines contains two distinct integers x, y (1 ≤ x, y ≤ n, x ≠ y) — pair of programmers in a quarrel. The pairs are unordered, it means that if x is in a quarrel with y then y is in a quarrel with x. Guaranteed, that for each pair (x, y) there are no other pairs (x, y) and (y, x) in the input.

Output

Print n integers, the i-th number should be equal to the number of programmers, for which the i-th programmer can be a mentor. Programmers are numbered in the same order that their skills are given in the input.

Examples

Input

4 2
10 4 10 15
1 2
4 3


Output

0 0 1 2 


Input

10 4
5 4 1 5 4 3 7 1 2 5
4 6
2 1
10 8
3 5


Output

5 4 0 5 3 3 9 0 2 5 

Note

In the first example, the first programmer can not be mentor of any other (because only the second programmer has a skill, lower than first programmer skill, but they are in a quarrel). The second programmer can not be mentor of any other programmer, because his skill is minimal among others. The third programmer can be a mentor of the second programmer. The fourth programmer can be a mentor of the first and of the second programmers. He can not be a mentor of the third programmer, because they are in a quarrel.
#include <bits/stdc++.h>
using namespace std;
struct pro {
  int id, sco, val;
} prog[200008];
bool cmp1(pro a, pro b) { return a.sco < b.sco; }
bool cmp2(pro a, pro b) { return a.id < b.id; }
vector<int> q[200008];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    q[i].clear();
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &prog[i].sco);
    prog[i].id = i;
  }
  sort(prog + 1, prog + n + 1, cmp1);
  int tmpp = prog[1].sco;
  prog[1].val = 0;
  for (int i = 2; i <= n; i++) {
    if (tmpp == prog[i].sco) {
      prog[i].val = prog[i - 1].val;
    } else {
      prog[i].val = i - 1;
      tmpp = prog[i].sco;
    }
  }
  sort(prog + 1, prog + n + 1, cmp2);
  for (int i = 0; i < m; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    q[a].push_back(b);
    q[b].push_back(a);
  }
  for (int i = 1; i <= n; i++) {
    int ans = prog[i].val;
    if (q[i].size()) {
      for (int j = 0; j < q[i].size(); j++) {
        if (prog[q[i][j]].sco < prog[i].sco) {
          ans--;
        }
      }
    }
    printf(i == n ? "%d\n" : "%d ", ans);
  }
}
