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.*;
import java.io.*;

public class f978 {
    public static class Skill implements Comparable<Skill>{
        int skill, index; 
        public Skill (int s, int i) {
            skill = s;
            index = i;
        }
        @Override
        public int compareTo(Skill o) {
            return skill - o.skill;
        }
    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        int[] r = new int[n];
        Skill[] s = new Skill[n];
        st = new StringTokenizer(br.readLine());
        for (int i = 0; i<n; i++) {
            r[i] = Integer.parseInt(st.nextToken());
            s[i] = new Skill(r[i],i);
        }
        Arrays.sort(s);
        int[] ans = new int[n];
        int greater = 0;
        for (int i = 1; i<n; i++) {
            if (s[i].skill > s[i-1].skill) {
                greater = i; 
            }
            ans[s[i].index] = greater; 
        }
        for (int i = 0; i<k; i++) {
            st = new StringTokenizer(br.readLine());
            int x = Integer.parseInt(st.nextToken())-1;
            int y = Integer.parseInt(st.nextToken())-1;
            if (r[x] > r[y]) {
                ans[x]--;
            }
            if (r[y] > r[x]) {
                ans[y]--;
            }
        }
        for (int i: ans) {
            pw.print(i + " ");
        }
        br.close();
        pw.close();
    }
}