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.
params = [int(s) for s in input().split(" ")]
n = params[0]
k = params[1]
skills = [int(s) for s in input().split(" ")]
indexes_sorted= [b[0] for b in sorted(enumerate(skills),key=lambda i:i[1])]
bad_relations={}
for i in range(k):
    items = [int(s) for s in input().split(" ")]
    first = items[0] - 1
    second= items[1] - 1
    if skills[first] > skills[second]:
        bad_relations[first] = bad_relations.get(first, 0) + 1
    elif skills[second]> skills[first]:
        bad_relations[second] = bad_relations.get(second, 0) + 1

num_the_same=0
results = {}
prev=None
for idx, index in enumerate(indexes_sorted):
    skill = skills[index]
    if skill==prev:
        num_the_same+=1
    else:
        num_the_same=0
    cnt = idx - num_the_same - bad_relations.get(index,0)
    if cnt < 0:
        cnt= 0
    results[index]= cnt
    prev= skill
final=''
for i in range(n):
    final+=str((results[i])) + " "

print(final.strip())



