<p>You are given an array of <strong>positive</strong> integers <code>nums</code> of length <code>n</code>.</p>

<p>A <strong>polygon</strong> is a closed plane figure that has at least <code>3</code> sides. The <strong>longest side</strong> of a polygon is <strong>smaller</strong> than the sum of its other sides.</p>

<p>Conversely, if you have <code>k</code> (<code>k &gt;= 3</code>) <strong>positive</strong> real numbers <code>a<sub>1</sub></code>, <code>a<sub>2</sub></code>, <code>a<sub>3</sub></code>, ..., <code>a<sub>k</sub></code> where <code>a<sub>1</sub> &lt;= a<sub>2</sub> &lt;= a<sub>3</sub> &lt;= ... &lt;= a<sub>k</sub></code> <strong>and</strong> <code>a<sub>1</sub> + a<sub>2</sub> + a<sub>3</sub> + ... + a<sub>k-1</sub> &gt; a<sub>k</sub></code>, then there <strong>always</strong> exists a polygon with <code>k</code> sides whose lengths are <code>a<sub>1</sub></code>, <code>a<sub>2</sub></code>, <code>a<sub>3</sub></code>, ..., <code>a<sub>k</sub></code>.</p>

<p>The <strong>perimeter</strong> of a polygon is the sum of lengths of its sides.</p>

<p>Return <em>the <strong>largest</strong> possible <strong>perimeter</strong> of a <strong>polygon</strong> whose sides can be formed from</em> <code>nums</code>, <em>or</em> <code>-1</code> <em>if it is not possible to create a polygon</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [5,5,5]
<strong>Output:</strong> 15
<strong>Explanation:</strong> The only possible polygon that can be made from nums has 3 sides: 5, 5, and 5. The perimeter is 5 + 5 + 5 = 15.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,12,1,2,5,50,3]
<strong>Output:</strong> 12
<strong>Explanation:</strong> The polygon with the largest perimeter which can be made from nums has 5 sides: 1, 1, 2, 3, and 5. The perimeter is 1 + 1 + 2 + 3 + 5 = 12.
We cannot have a polygon with either 12 or 50 as the longest side because it is not possible to include 2 or more smaller sides that have a greater sum than either of them.
It can be shown that the largest possible perimeter is 12.
</pre>

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

<pre>
<strong>Input:</strong> nums = [5,5,50]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There is no possible way to form a polygon from nums, as a polygon has at least 3 sides and 50 &gt; 5 + 5.
</pre>

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

<ul>
	<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

import heapq


class Solution:
    def largestPerimeter(self, nums: List[int]) -> int:
        total = sum(nums)
        nums = [-1 * x for x in nums]
        heapq.heapify(nums)
        largest = heapq.heappop(nums) * -1
        total -= largest
        while nums and largest >= total:
            largest = heapq.heappop(nums) * -1
            total -= largest
        return -1 if len(nums) == 0 else total + largest

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