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.
//package codeforces.r481_978;

import java.util.*;

/**
 * Created by shaolin on 5/17/18.
 */
public class F_Mentors {

    static class Programmer implements  Comparable<Programmer>{
        int id;
        int skill;
        int quarrelWithLowerSkill;
        int mentoring;
        Programmer(int id, int skill) {
            this.id = id;
            this.skill = skill;
        }
        void increaseQuarrel() {
            quarrelWithLowerSkill++;
        }

        @Override
        public int compareTo(Programmer o) {
            return Integer.compare(this.skill, o.skill);
        }
    }
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int totalProgrammers = scanner.nextInt();
        int totalQuarrelling = scanner.nextInt();
        Programmer[] programmers = new Programmer[totalProgrammers];
        List<Programmer> sortedProgrammers = new ArrayList<>();
        for (int i = 0; i < totalProgrammers; i++) {
            programmers[i] = new Programmer(i,scanner.nextInt());
            sortedProgrammers.add(programmers[i]);
        }
        for (int i = 0; i < totalQuarrelling; i++) {
            int p1 = scanner.nextInt()-1;
            int p2 =  scanner.nextInt()-1;
            if (programmers[p1].skill>programmers[p2].skill) {
                programmers[p1].quarrelWithLowerSkill++;
            } else if (programmers[p1].skill<programmers[p2].skill) {
                programmers[p2].quarrelWithLowerSkill++;
            }
        }
        Collections.sort(sortedProgrammers);
        int lastSkill = 0;
        int continousSkill = 0;
        for (int i = 0; i < sortedProgrammers.size(); i++) {
            Programmer programmer = sortedProgrammers.get(i);
            if (programmer.skill!=lastSkill) {
                lastSkill = programmer.skill;
                continousSkill = 0;
            } else {
                continousSkill++;
            }
            programmer.mentoring = Math.max(0, i-continousSkill- programmer.quarrelWithLowerSkill);
        }
        for (int i = 0; i < totalProgrammers; i++) {
            System.out.print(programmers[i].mentoring+" ");
        }
    }
}
