<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>

import numpy as np
class Solution:
    def minSumOfLengths(self, arr: List[int], target: int) -> int:
        first=0
        second=0
        summ=arr[0]
        before=[np.inf]*len(arr)
        at=[np.inf]*len(arr)
        length=np.inf
        while first < len(arr):                                   
                if summ==target:
                  length= second-first+1
                  at[first]=length
                  if second<len(arr)-1:
                    before[second+1]=min(before[second],length)     
                  if first<second:
                    summ-=arr[first]
                    first+=1
                  elif first==len(arr)-1:
                    break
                  else:
                    first+=1
                    second+=1
                    summ=arr[first]
                elif summ<target:
                    if second==len(arr)-1:
                        break
                    # print(second)
                    # print(len(before))
                    # print(before)
                    before[second+1]=min(before[second],length)     
                    second+=1
                    summ+=arr[second]
                elif summ>target:
                    if first<second:
                        summ-=arr[first]
                        first+=1
                    elif first==len(arr)-1:
                        break
                    else:
                        before[second+1]=min(before[second],length)     
                        first+=1
                        second+=1
                        summ=arr[first]
        
        for i in range(len(at)-2,-1,-1):
            at[i]=min(at[i+1],at[i])
        for i in range(len(at)):
            at[i]+=before[i]        
        if min(at)==np.inf:
            return -1
        else:
            return min(at)
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