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.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class F {
    static class Master {
        int i;
        int mastery;
        int scholars;

        public Master(int i, int mastery) {
            this.i = i;
            this.mastery = mastery;
        }

        public int getMastery() {
            return mastery;
        }

        public int getI() {
            return i;
        }
    }
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        List<Master> mastery = new ArrayList<>(n);
        for (int i=0; i < n; ++i) {
            mastery.add(new Master(i, scanner.nextInt()));
        }
        mastery.sort(Comparator.comparing(Master::getMastery));
        for (int i = 0; i < n; ++i) {
            mastery.get(i).scholars = i;
            if (i > 0 && mastery.get(i-1).mastery == mastery.get(i).mastery) {
                mastery.get(i).scholars = mastery.get(i-1).scholars;
            }
        }
        mastery.sort(Comparator.comparing(Master::getI));

        List<Set<Integer>> badrel = new ArrayList<>(n);
        for (int i=0; i < n; ++i) {
            badrel.add(new HashSet<>(0));
        }
        for (int i=0; i < k; ++i) {
            int a = scanner.nextInt()-1;
            int b = scanner.nextInt()-1;
            if (mastery.get(b).mastery < mastery.get(a).mastery) {
                mastery.get(a).scholars -= 1;
            } else if (mastery.get(b).mastery > mastery.get(a).mastery) {
                mastery.get(b).scholars -=1;
            }
            if (mastery.get(a).scholars < 0) mastery.get(a).scholars =0;
            if (mastery.get(b).scholars < 0) mastery.get(b).scholars =0;
        }

        for (int i = 0; i < n; ++i) {
            System.out.print(mastery.get(i).scholars);
            if (i != n-1) {
                System.out.print(" ");
            }
        }

    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
