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 solve(n,m,a,adj):
	a = sorted(a)

	res = []
	for i in range(n):
		res.append(0)

	equal = 0
	for i in range(n):
		pos = a[i][1]
		if (i == 0):
			res[pos] = 0
			continue

		if (a[i][0] == a[i-1][0]):
			equal += 1
		else:
			equal = 0

		res[pos] = i - equal - len(adj[pos])

	for i in res:
		print(i, end = ' ')
		





n, m = map(int, input().split())

tmp = list(map(int, input().split()))
a = []
adj = []
for i in range(n):
	a.append((tmp[i],i))
	adj.append([])


for i in range(m):
	x, y = map(int, input().split())
	x -= 1
	y -= 1
	if (a[x][0] < a[y][0]):
		adj[y].append(x)
	elif (a[x][0] > a[y][0]):
		adj[x].append(y)
	

solve(n,m,a,adj)