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<p>You are given an integer array <code>nums</code>.</p>
<p>Any <strong>positive</strong> divisor of a natural number <code>x</code> that is <strong>strictly less</strong> than <code>x</code> is called a <strong>proper divisor</strong> of <code>x</code>. For example, 2 is a <em>proper divisor</em> of 4, while 6 is not a <em>proper divisor</em> of 6.</p>
<p>You are allowed to perform an <strong>operation</strong> any number of times on <code>nums</code>, where in each <strong>operation</strong> you select any <em>one</em> element from <code>nums</code> and divide it by its <strong>greatest</strong> <strong>proper divisor</strong>.</p>
<p>Return the <strong>minimum</strong> number of <strong>operations</strong> required to make the array <strong>non-decreasing</strong>.</p>
<p>If it is <strong>not</strong> possible to make the array <em>non-decreasing</em> using any number of operations, return <code>-1</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 = [25,7]</span></p>
<p><strong>Output:</strong> <span class="example-io">1</span></p>
<p><strong>Explanation:</strong></p>
<p>Using a single operation, 25 gets divided by 5 and <code>nums</code> becomes <code>[5, 7]</code>.</p>
</div>
<p><strong class="example">Example 2:</strong></p>
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [7,7,6]</span></p>
<p><strong>Output:</strong> <span class="example-io">-1</span></p>
</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">0</span></p>
</div>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>