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.
import java.util.*;

public class Mentors {
 
 private static Scanner inp = new Scanner(System.in);
 private static List<Integer> a;
 
 private static int bs(int val) {
  int l = 0, r = a.size() - 1, ans = -1;
  while (l <= r) {
   int m = (l + r) / 2;
   if (a.get(m) <= val) {
    ans = m;
    l = m + 1;
   } else r = m - 1;
  }
  return ans;
 }
 
 public static void main(String[] args) {
  
  int n = inp.nextInt();
  int k = inp.nextInt();
  a = new ArrayList<Integer>(n);
  List<Integer> t = new ArrayList<Integer>(n);
  for (int i = 0; i < n; i++) {
   int x = inp.nextInt();
   a.add(x);
   t.add(x);
  }
  int[] conf = new int[n];
  for (int i = 1; i <= k; i++) {
   int x = inp.nextInt();
   int y = inp.nextInt();
   x--; y--;
   if (a.get(x) > a.get(y)) conf[x]++;
   if (a.get(y) > a.get(x)) conf[y]++;
  }
  Collections.sort(a);
  for (int i = 0; i < n; i++) {
   int pos = bs(t.get(i) - 1) + 1;
   System.out.printf("%d ", pos - conf[i]);
  }
  System.out.println();
 }
}