<p>You are given an integer array <code>nums</code>.</p>

<p>Your task is to find the number of pairs of <strong>non-empty</strong> <span data-keyword="subsequence-array">subsequences</span> <code>(seq1, seq2)</code> of <code>nums</code> that satisfy the following conditions:</p>

<ul>
	<li>The subsequences <code>seq1</code> and <code>seq2</code> are <strong>disjoint</strong>, meaning <strong>no index</strong> of <code>nums</code> is common between them.</li>
	<li>The <span data-keyword="gcd-function">GCD</span> of the elements of <code>seq1</code> is equal to the GCD of the elements of <code>seq2</code>.</li>
</ul>

<p>Return the total number of such pairs.</p>

<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3,4]</span></p>

<p><strong>Output:</strong> <span class="example-io">10</span></p>

<p><strong>Explanation:</strong></p>

<p>The subsequence pairs which have the GCD of their elements equal to 1 are:</p>

<ul>
	<li><code>([<strong><u>1</u></strong>, 2, 3, 4], [1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4])</code></li>
	<li><code>([<strong><u>1</u></strong>, 2, 3, 4], [1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, <strong><u>4</u></strong>])</code></li>
	<li><code>([<strong><u>1</u></strong>, 2, 3, 4], [1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>])</code></li>
	<li><code>([<strong><u>1</u></strong>, <strong><u>2</u></strong>, 3, 4], [1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>])</code></li>
	<li><code>([<strong><u>1</u></strong>, 2, 3, <strong><u>4</u></strong>], [1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4])</code></li>
	<li><code>([1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4], [<strong><u>1</u></strong>, 2, 3, 4])</code></li>
	<li><code>([1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, 4], [<strong><u>1</u></strong>, 2, 3, <strong><u>4</u></strong>])</code></li>
	<li><code>([1, <strong><u>2</u></strong>, <strong><u>3</u></strong>, <strong><u>4</u></strong>], [<strong><u>1</u></strong>, 2, 3, 4])</code></li>
	<li><code>([1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>], [<strong><u>1</u></strong>, 2, 3, 4])</code></li>
	<li><code>([1, 2, <strong><u>3</u></strong>, <strong><u>4</u></strong>], [<strong><u>1</u></strong>, <strong><u>2</u></strong>, 3, 4])</code></li>
</ul>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [10,20,30]</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p>The subsequence pairs which have the GCD of their elements equal to 10 are:</p>

<ul>
	<li><code>([<strong><u>10</u></strong>, 20, 30], [10, <strong><u>20</u></strong>, <strong><u>30</u></strong>])</code></li>
	<li><code>([10, <strong><u>20</u></strong>, <strong><u>30</u></strong>], [<strong><u>10</u></strong>, 20, 30])</code></li>
</ul>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,1,1,1]</span></p>

<p><strong>Output:</strong> <span class="example-io">50</span></p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 200</code></li>
</ul>