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 $k$ $(2 \le n \le 2 \cdot 10^5$, $0 \le k \le \min(2 \cdot 10^5, \frac{n \cdot (n - 1)}{2}))$ — 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.
[{"code": "import bisect\nn,k=list(map(int,input().split()))\nr,o=list(map(int,input().split())),''\nd={}\nfor i in range(k):\n    a,b=list(map(int,input().split()))\n    if [b]!=d.setdefault(a,[b]):\n        d[a]+=[b]\n    if [a]!=d.setdefault(b,[a]):\n        d[b]+=[a]\nrr=sorted(r)\nfor i in range(1,n+1):\n    a=bisect.bisect_left(rr,r[i-1])\n    if i in d:\n        for j in d[i]:\n            if r[j-1]<r[i-1]:\n                a-=1\n    o+=str(a)+' '\nprint(o)\n", "passed": true, "time": 0.24, "memory": 14352.0, "status": "done"}]