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.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Solution {

    private static final boolean DEBUG = false;
    
    private static class Programmer {
        public final int index;
        public final int skill;

        public Programmer(int index, int skill) {
            this.index = index;
            this.skill = skill;
        }

        @Override
        public String toString() {
            return "Programmer{" + "index=" + index + ", skill=" + skill + '}';
        }
    }

    public static void main(String[] args) throws FileNotFoundException {
        long beginTime = System.nanoTime();
        InputStream is = DEBUG ? new FileInputStream("resources/codeforcesedu43/ProblemF-1.in") : System.in;
        try (Scanner scanner = new Scanner(new BufferedReader(new InputStreamReader(is)))) {
            int programmerCount = scanner.nextInt();
            int quarrelCount = scanner.nextInt();
            int[] skills = new int[programmerCount];
            int[] quarrelPenalties = new int[programmerCount];
            Programmer[] programmers = new Programmer[programmerCount];
            for (int i = 0; i < programmerCount; i++) {
                int skill = scanner.nextInt();
                skills[i] = skill;
                programmers[i] = new Programmer(i, skill);
            }
            for (int i = 0; i < quarrelCount; i++) {
                int a = scanner.nextInt() - 1;
                int b = scanner.nextInt() - 1;
                if (skills[a] > skills[b]) quarrelPenalties[a]--;
                if (skills[b] > skills[a]) quarrelPenalties[b]--;
            }
            Arrays.sort(programmers, (a, b) -> a.skill - b.skill);
            int[] results = new int[programmerCount];
            int lastSkill = -1;
            int lastSkillCount = 0;
            for (int i = 0; i < programmers.length; i++) {
                Programmer p = programmers[i];
                if (p.skill != lastSkill) {
                    lastSkillCount = 0;
                    lastSkill = p.skill;
                } else {
                    lastSkillCount++;
                }
                results[p.index] = i - lastSkillCount + quarrelPenalties[p.index];
            }
            for (int i : results) {
                System.out.print(i + " ");
            }
            System.out.println();
        }
        System.err.println( "Done in " + ((System.nanoTime() - beginTime) / 1e9) + " seconds.");
    }
}