leetcode-problemset/leetcode/originData/minimum-non-zero-product-of-the-array-elements.json

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            "title": "Minimum Non-Zero Product of the Array Elements",
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            "content": "<p>You are given a positive integer <code>p</code>. Consider an array <code>nums</code> (<strong>1-indexed</strong>) that consists of the integers in the <strong>inclusive</strong> range <code>[1, 2<sup>p</sup> - 1]</code> in their binary representations. You are allowed to do the following operation <strong>any</strong> number of times:</p>\n\n<ul>\n\t<li>Choose two elements <code>x</code> and <code>y</code> from <code>nums</code>.</li>\n\t<li>Choose a bit in <code>x</code> and swap it with its corresponding bit in <code>y</code>. Corresponding bit refers to the bit that is in the <strong>same position</strong> in the other integer.</li>\n</ul>\n\n<p>For example, if <code>x = 11<u>0</u>1</code> and <code>y = 00<u>1</u>1</code>, after swapping the <code>2<sup>nd</sup></code> bit from the right, we have <code>x = 11<u>1</u>1</code> and <code>y = 00<u>0</u>1</code>.</p>\n\n<p>Find the <strong>minimum non-zero</strong> product of <code>nums</code> after performing the above operation <strong>any</strong> number of times. Return <em>this product</em><em> <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>.</p>\n\n<p><strong>Note:</strong> The answer should be the minimum product <strong>before</strong> the modulo operation is done.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> p = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> nums = [1].\nThere is only one element, so the product equals that element.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> p = 2\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> nums = [01, 10, 11].\nAny swap would either make the product 0 or stay the same.\nThus, the array product of 1 * 2 * 3 = 6 is already minimized.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> p = 3\n<strong>Output:</strong> 1512\n<strong>Explanation:</strong> nums = [001, 010, 011, 100, 101, 110, 111]\n- In the first operation we can swap the leftmost bit of the second and fifth elements.\n    - The resulting array is [001, <u>1</u>10, 011, 100, <u>0</u>01, 110, 111].\n- In the second operation we can swap the middle bit of the third and fourth elements.\n    - The resulting array is [001, 110, 0<u>0</u>1, 1<u>1</u>0, 001, 110, 111].\nThe array product is 1 * 6 * 1 * 6 * 1 * 6 * 7 = 1512, which is the minimum possible product.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= p &lt;= 60</code></li>\n</ul>\n",
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                "Try to minimize each element by swapping bits with any of the elements after it.",
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