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F. Mentors

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn 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 $$$k$$$ $$$(2 \le n \le 2 \cdot 10^5$$$, $$$0 \le k \le \min(2 \cdot 10^5, \frac{n \cdot (n - 1)}{2}))$$$ — total number of programmers and number of pairs of programmers which are in a quarrel.

The second line contains a sequence of integers $$$r_1, r_2, \dots, r_n$$$ $$$(1 \le r_i \le 10^{9})$$$, where $$$r_i$$$ equals to the skill of the $$$i$$$-th programmer.

Each of the following $$$k$$$ lines contains two distinct integers $$$x$$$, $$$y$$$ $$$(1 \le x, y \le n$$$, $$$x \ne y)$$$ — 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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