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 Main{
        public static void main(String[] args) throws  IOException {
                BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer stk = new StringTokenizer(br.readLine());
                int n = Integer.parseInt(stk.nextToken());
                int k = Integer.parseInt(stk.nextToken());
                Person[] ps = new Person[n];
                stk = new StringTokenizer(br.readLine());
                for(int i=0;i<n;i++){
                        ps[i] = new Person(Integer.parseInt(stk.nextToken()));
                        ps[i].idx = i;
                }
                for(int j=0;j<k;j++){
                        stk = new StringTokenizer(br.readLine());
                        int u = Integer.parseInt(stk.nextToken())-1;
                        int v = Integer.parseInt(stk.nextToken())-1;
                        if(ps[u].stren>ps[v].stren){
                                ps[u].anti +=1;
                        }
                        else if(ps[u].stren<ps[v].stren){
                                ps[v].anti +=1;
                        }
                }
                Arrays.sort(ps);
                int pre = -100000;
                int cnt = 0 ;
                for(int i=0;i<n;i++){
                        if(pre != ps[i].stren){
                                cnt = 1;
                                ps[i].ans = i - ps[i].anti;
                                pre = ps[i].stren;
                        }
                        else{
                                ps[i].ans = i - cnt - ps[i].anti;
                                cnt+=1;
                        }
                }
                Arrays.sort(ps, new Comparator<Person>() {
                        @Override
                        public int compare(Person o1, Person o2) {
                                return o1.idx - o2.idx;
                        }
                });
                StringBuilder sb = new StringBuilder();
                for(int i=0;i<n;i++){
                        sb.append(ps[i].ans+" ");
                }
                System.out.println(sb);
        }
        public static class Person implements Comparable<Person>{
                int stren,anti=0,ans,idx;
                public Person(int stren){
                        this.stren = stren;
                }
                @Override
                public int compareTo(Person o) {
                        return this.stren-o.stren;
                }
        }
}