Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
$N = fgets(STDIN);
$L = fgets(STDIN);
$arrayL = explode(" ", $L);
sort($arrayL);

$countArrayL = array_count_values($arrayL);
$twoArrayL = array();
$result = 0;

foreach ($countArrayL as $key => $val) {
    if ($val === 1) {
        continue;
    } elseif ($val === 2) {
        // ☆ここ途中
        $twoArrayL[] = $key;
    } else {
        // elseif($val >== 3)
        $combinationValue = 1;
        // $val Combination 3
        for ($i = $val; $i >= 3; $i --) {
            $combinationValue *= $i;
        }
        for ($i = 3; $i >= 2; $i --) {
            $combinationValue /= $i;
        }
        $result += $combinationValue;
    }
}
echo $result . "\n";
// 値の重複をなくす
$uniqueArrayL = array_values(array_unique($arrayL));

// ABC143重複対応なし
// 1辺目
for ($i = 0; $i < count($uniqueArrayL) - 2; $i ++) {
    // 2辺目
    for ($j = $i + 1; $j < count($uniqueArrayL) - 1; $j ++) {
        // 3辺目
        // 許容最大長
        $longest = $arrayL[$i] + $arrayL[$j] - 1;
        $left = $j;
        if ($longest >= $arrayL[count($uniqueArrayL) - 1]) {
            $right = count($uniqueArrayL) - 1 - 1;
        } else {
            $right = binSearch($longest, $uniqueArrayL, $j + 1, count($uniqueArrayL) - 1);
        }
        $result += $right - $left;
    }
}
echo $result;

// 重複なし
function binSearch($target, $array, $l, $r)
{
    if ($l > $r) {
        echo "error001";
        exit(1);
    }
    // 小数点以下切捨て
    $m = (int) (($l + $r) / 2);
    if ($r === $l || $m == $target) {
        return $m;
    } elseif ($r - $l === 1) {
        if ($array[$l] > $target) {
            return $m - 1;
        } elseif ($array[$r] > $target) {
            return $m;
        } else {
            return $m + 1;
        }
    } elseif ($target < $array[$m]) {
        // echo "aaa\n";
        return binSearch($target, $array, $l, $m - 1);
    } elseif ($target > $array[$m]) {
        // echo "bbb\n";
        return binSearch($target, $array, $m + 1, $r);
    } elseif ($target == $array[$m]) {
        return $m;
    }
}