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.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {
//        out = new PrintWriter(new File("output.txt"));
//        br = new BufferedReader(new FileReader(new File("input.txt")));
        int JOPI = 1;
        for (int NASRAL = 0; NASRAL < JOPI; NASRAL++) {
            int n = nextInt();
            int k = nextInt();
            int[] a = new int[n];
            ArrayList<Integer> b = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
                b.add(a[i]);
            }
            Collections.sort(b);
            int[] ans = new int[n];
            for (int i = 0; i < n; i++) {
                int l = -1;
                int r = n;
                while (l + 1 != r) {
                    int mid = (l + r) / 2;
                    if (b.get(mid) < a[i]) l = mid;
                    else r = mid;
                }
                ans[i] = r;
            }
            for (int i = 0; i < k; i++) {
                int x = nextInt() - 1;
                int y = nextInt() - 1;
                if (a[x] > a[y]) ans[x]--;
                if (a[y] > a[x]) ans[y]--;
            }
            for (int i = 0; i < n; i++) {
                out.print(ans[i] + " ");
            }


        }
        out.close();
    }

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer in = new StringTokenizer("");


    public static String next() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}

class Point {
    int p;
    int chen;

    public Point(int p, int chen) {
        this.p = p;
        this.chen = chen;
    }
}