<p>Given an integer array <code>nums</code>, return <em>the number of triplets chosen from the array that can make triangles if we take them as side lengths of a triangle</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [2,2,3,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Valid combinations are: 
2,3,4 (using the first 2)
2,3,4 (using the second 2)
2,2,3
</pre>

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

<pre>
<strong>Input:</strong> nums = [4,2,3,4]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
</ul>

from itertools import combinations as cmb
class Solution:
    def triangleNumber(self, nums: List[int]) -> int:
        nums.sort()
        count = 0
        for k in range(len(nums) - 1, -1, -1):
            i = 0
            j = k - 1
            while i < j:
                if nums[i] + nums[j] > nums[k]:
                    count += j - i
                    j -= 1
                else:
                    i += 1
        return count

16400