<p>You are given an array of integers <code>arr</code> and an integer <code>target</code>.</p>

<p>You have to find <strong>two non-overlapping sub-arrays</strong> of <code>arr</code> each with a sum equal <code>target</code>. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is <strong>minimum</strong>.</p>

<p>Return <em>the minimum sum of the lengths</em> of the two required sub-arrays, or return <code>-1</code> if you cannot find such two sub-arrays.</p>

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

<pre>
<strong>Input:</strong> arr = [3,2,2,4,3], target = 3
<strong>Output:</strong> 2
<strong>Explanation:</strong> Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2.
</pre>

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

<pre>
<strong>Input:</strong> arr = [7,3,4,7], target = 7
<strong>Output:</strong> 2
<strong>Explanation:</strong> Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2.
</pre>

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

<pre>
<strong>Input:</strong> arr = [4,3,2,6,2,3,4], target = 6
<strong>Output:</strong> -1
<strong>Explanation:</strong> We have only one sub-array of sum = 6.
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i] &lt;= 1000</code></li>
	<li><code>1 &lt;= target &lt;= 10<sup>8</sup></code></li>
</ul>

class Solution:
    def minSumOfLengths(self, arr: List[int], target: int) -> int:
        def overlap(range1, range2):
            l1, r1 = range1
            l2, r2 = range2
            return r1 >= l2
        
        ranges = []
        right = 0
        cur_sum = 0
        for left in range(len(arr)):
            if left > 0:
                cur_sum -= arr[left-1]
            while right < len(arr) and cur_sum < target:
                cur_sum += arr[right]
                right += 1
            if cur_sum == target:
                ranges.append((left, right-1))

        if len(ranges) < 2:
            return -1
        
        rid = 0
        prev_min_len = float("inf")
        min_len = float("inf")
        for i in range(1, len(ranges)):
            r = ranges[i]
            cur_len = r[1] - r[0] + 1
            while rid < i and (not overlap(ranges[rid], r)):
                prev_len = ranges[rid][1] - ranges[rid][0] + 1
                prev_min_len = min(prev_min_len, prev_len)
                rid += 1
            min_len = min(min_len, cur_len+prev_min_len)
        return min_len if min_len != float("inf") else -1
35600