freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-453-lattice-quadrilaterals.english.md

---
id: 5900f5311000cf542c510044
challengeType: 5
title: 'Problem 453: Lattice Quadrilaterals'
forumTopicId: 302126
---

## Description
<section id='description'>
A simple quadrilateral is a polygon that has four distinct vertices, has no straight angles and does not self-intersect.

Let Q(m, n) be the number of simple quadrilaterals whose vertices are lattice points with coordinates (x,y) satisfying 0 ≤ x ≤ m and 0 ≤ y ≤ n.

For example, Q(2, 2) = 94 as can be seen below:

It can also be verified that Q(3, 7) = 39590, Q(12, 3) = 309000 and Q(123, 45) = 70542215894646.

Find Q(12345, 6789) mod 135707531.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler453()</code> should return 104354107.
    testString: assert.strictEqual(euler453(), 104354107);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler453() {
  // Good luck!
  return true;
}

euler453();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>