<p>Given an integer array <code>arr</code>, and an integer <code>target</code>, return the number of tuples <code>i, j, k</code> such that <code>i &lt; j &lt; k</code> and <code>arr[i] + arr[j] + arr[k] == target</code>.</p>

<p>As the answer can be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [1,1,2,2,3,3,4,4,5,5], target = 8
<strong>Output:</strong> 20
<strong>Explanation: </strong>
Enumerating by the values (arr[i], arr[j], arr[k]):
(1, 2, 5) occurs 8 times;
(1, 3, 4) occurs 8 times;
(2, 2, 4) occurs 2 times;
(2, 3, 3) occurs 2 times.
</pre>

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

<pre>
<strong>Input:</strong> arr = [1,1,2,2,2,2], target = 5
<strong>Output:</strong> 12
<strong>Explanation: </strong>
arr[i] = 1, arr[j] = arr[k] = 2 occurs 12 times:
We choose one 1 from [1,1] in 2 ways,
and two 2s from [2,2,2,2] in 6 ways.
</pre>

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

<pre>
<strong>Input:</strong> arr = [2,1,3], target = 6
<strong>Output:</strong> 1
<strong>Explanation:</strong> (1, 2, 3) occured one time in the array so we return 1.
</pre>

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

<ul>
	<li><code>3 &lt;= arr.length &lt;= 3000</code></li>
	<li><code>0 &lt;= arr[i] &lt;= 100</code></li>
	<li><code>0 &lt;= target &lt;= 300</code></li>
</ul>

class Solution:
    def threeSumMulti(self, arr: List[int], target: int) -> int:

        
        mod=10**9+7
        arr.sort()
        res=0

        for i in range(len(arr)-2):
            l,r=i+1,len(arr)-1
            t= target- arr[i]
            while l<r:
                if arr[l]+arr[r]<t:
                    l+=1
                elif arr[l]+arr[r]>t:
                    r-=1
                else:
                    if arr[l]==arr[r]:
                        n=r-l
                        res+= (1+n)*n//2 %mod
                        break
                    else:
                        ln=1
                        while arr[l+1] ==arr[l]:
                            l+=1
                            ln+=1

                        rn=1
                        while arr[r-1] ==arr[r]:
                            r-=1
                            rn+=1
                        res+=ln*rn%mod
                        l+=1
                        r-=1
        return res%mod



                
16600