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 sys
import os.path

def solve():
    # code goes here!!         
    n,k = map(int,input().split())
    r = list(map(int,input().split()))
    quar = [[] for x in range(n)]
    ord = sorted(map(int,range(n)),key = lambda i : r[i])
    for q in range(k):
        x,y = map(lambda x : int(x) - 1,input().split())
        quar[x].append(y)
        quar[y].append(x)
    ans = [0] * n
    cnt = {}
    for i,j in enumerate(ord,0):
        ans[j] = i - cnt.get(r[j],0) - sum(1 for y in quar[j] if r[j] > r[y])
        if r[j] in cnt:
            cnt[r[j]] += 1
        else :
            cnt[r[j]] = 1
    for res in ans:
        print(res,end = " ")

def main():
    # comment when submit.
    if os.path.exists('test.inp') :
        sys.stdin = open("test.inp","r")
    solve()

if __name__ == '__main__':
    main()



