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.

var parse = function(x) { return parseInt(x); };

var nk = readline().split(" ").map(parse);
var n = nk[0], k = nk[1];
var ri = readline().split(" ").map(parse);

var qi = [];
for(var i=0; i<n; i++) {
	qi[i] = [];
}

for(var i=0; i<k; i++) {
	var q = readline().split(" ").map(parse);
	var q1 = q[0]-1, q2 = q[1]-1;
	if(ri[q1]>ri[q2]) {
		qi[q1].push(q2);
	} else if(ri[q1]<ri[q2]) {
		qi[q2].push(q1);
	}
}

var sri = [];
for(var i=0; i<n; i++) {
	sri[i] = {"i": i, "v": ri[i], "ans": 0};
}
sri.sort(function(a, b) {
	return a.v - b.v;
});

var cur = 0, curRepeated = 0;
for(var i=0; i<n; i++) {
	if(i>0 && sri[i].v === sri[i-1].v) {
		sri[i].ans = curRepeated;
		cur++;
	} else {
		curRepeated = cur;
		sri[i].ans = cur++;	
	}
	sri[i].ans -= qi[sri[i].i].length;
}

sri.sort(function(a, b) {
	return a.i - b.i;
});

for(var i=0; i<n; i++) {
	write(sri[i].ans);
	if(i<n-1) write(" ");
}
