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;
long long r[200005][2];
pair<long long, long long> rr[200005];
int main() {
  long long n, k, x, y;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &r[i][0]);
    rr[i].first = r[i][0];
    rr[i].second = i;
  }
  sort(rr + 1, rr + n + 1,
       [](pair<long long, long long>& a, pair<long long, long long>& b) {
         return a.first < b.first;
       });
  long long pre = 0;
  for (int i = 2; i <= n; i++) {
    if (rr[i].first > rr[i - 1].first) pre = i - 1;
    r[rr[i].second][1] = pre;
  }
  for (int i = 0; i < k; i++) {
    scanf("%I64d%I64d", &x, &y);
    if (r[x][0] > r[y][0]) r[x][1]--;
    if (r[x][0] < r[y][0]) r[y][1]--;
  }
  for (int i = 1; i <= n; i++) printf("%d ", r[i][1]);
  printf("\n");
  return 0;
}
