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.
def lei(a):
    l = sorted(zip(a, list(range(len(a)))))


    t = [None] * len(a)
    for (i, e) in enumerate(l):
        t[e[1]] = (e[0], i)


    d = {}
    for e in t:
        if e[0] not in d or d[e[0]] > e[1]:
            d[e[0]] = e[1]

    tt = []

    for e in t:
        tt.append(d[e[0]])

    return tt

a = input().split(" ")
a = [int(e) for e in a]

l = input().split(" ")
l = [int(e) for e in l]
assert a[0] == len(l)

smaller_quarrel = [0] * len(l)
for i in range(a[1]):
    ll = input().split(" ")
    ll = [int(e) for e in ll]
    i1 = ll[0] - 1
    i2 = ll[1] - 1

    if l[i1] > l[i2]:
        smaller_quarrel[i1] += 1
    if l[i2] > l[i1]:
        smaller_quarrel[i2] += 1


tt = lei(l)

for i in range(len(tt)):
    print(tt[i] - smaller_quarrel[i], end = " ")
