<p>As the ruler of a kingdom, you have an army of wizards at your command.</p>

<p>You are given a <strong>0-indexed</strong> integer array <code>strength</code>, where <code>strength[i]</code> denotes the strength of the <code>i<sup>th</sup></code> wizard. For a <strong>contiguous</strong> group of wizards (i.e. the wizards&#39; strengths form a <strong>subarray</strong> of <code>strength</code>), the <strong>total strength</strong> is defined as the <strong>product</strong> of the following two values:</p>

<ul>
	<li>The strength of the <strong>weakest</strong> wizard in the group.</li>
	<li>The <strong>total</strong> of all the individual strengths of the wizards in the group.</li>
</ul>

<p>Return <em>the <strong>sum</strong> of the total strengths of <strong>all</strong> contiguous groups of wizards</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>subarray</strong> is a contiguous <strong>non-empty</strong> sequence of elements within an array.</p>

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

<pre>
<strong>Input:</strong> strength = [1,3,1,2]
<strong>Output:</strong> 44
<strong>Explanation:</strong> The following are all the contiguous groups of wizards:
- [1] from [<u><strong>1</strong></u>,3,1,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1
- [3] from [1,<u><strong>3</strong></u>,1,2] has a total strength of min([3]) * sum([3]) = 3 * 3 = 9
- [1] from [1,3,<u><strong>1</strong></u>,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1
- [2] from [1,3,1,<u><strong>2</strong></u>] has a total strength of min([2]) * sum([2]) = 2 * 2 = 4
- [1,3] from [<u><strong>1,3</strong></u>,1,2] has a total strength of min([1,3]) * sum([1,3]) = 1 * 4 = 4
- [3,1] from [1,<u><strong>3,1</strong></u>,2] has a total strength of min([3,1]) * sum([3,1]) = 1 * 4 = 4
- [1,2] from [1,3,<u><strong>1,2</strong></u>] has a total strength of min([1,2]) * sum([1,2]) = 1 * 3 = 3
- [1,3,1] from [<u><strong>1,3,1</strong></u>,2] has a total strength of min([1,3,1]) * sum([1,3,1]) = 1 * 5 = 5
- [3,1,2] from [1,<u><strong>3,1,2</strong></u>] has a total strength of min([3,1,2]) * sum([3,1,2]) = 1 * 6 = 6
- [1,3,1,2] from [<u><strong>1,3,1,2</strong></u>] has a total strength of min([1,3,1,2]) * sum([1,3,1,2]) = 1 * 7 = 7
The sum of all the total strengths is 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44.
</pre>

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

<pre>
<strong>Input:</strong> strength = [5,4,6]
<strong>Output:</strong> 213
<strong>Explanation:</strong> The following are all the contiguous groups of wizards: 
- [5] from [<u><strong>5</strong></u>,4,6] has a total strength of min([5]) * sum([5]) = 5 * 5 = 25
- [4] from [5,<u><strong>4</strong></u>,6] has a total strength of min([4]) * sum([4]) = 4 * 4 = 16
- [6] from [5,4,<u><strong>6</strong></u>] has a total strength of min([6]) * sum([6]) = 6 * 6 = 36
- [5,4] from [<u><strong>5,4</strong></u>,6] has a total strength of min([5,4]) * sum([5,4]) = 4 * 9 = 36
- [4,6] from [5,<u><strong>4,6</strong></u>] has a total strength of min([4,6]) * sum([4,6]) = 4 * 10 = 40
- [5,4,6] from [<u><strong>5,4,6</strong></u>] has a total strength of min([5,4,6]) * sum([5,4,6]) = 4 * 15 = 60
The sum of all the total strengths is 25 + 16 + 36 + 36 + 40 + 60 = 213.
</pre>

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

<ul>
	<li><code>1 &lt;= strength.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= strength[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    int totalStrength(vector<int>& str) {
        
        stack<int> s;
        int n=str.size();
        vector<int> l,r;
        int mod=pow(10,9)+7;
        
        for(int i=0;i<str.size();i++){
            while(!s.empty() && str[s.top()]>str[i]){
                s.pop();
            }
            if(s.empty()){
                l.push_back(-1);
            }
            else{
                l.push_back(s.top());
            }
            s.push(i);
        }
        
        while(!s.empty()) s.pop();
        
        for(int i=n-1;i>=0;i--){
            while(!s.empty() && str[s.top()]>=str[i]){
                s.pop();
            }
            if(s.empty()){
                r.push_back(-1);
            }
            else{
                r.push_back(s.top());
            }
            s.push(i);
        }
        
        reverse(r.begin(),r.end());
        
        vector<long long > pre(n,0);
        
        pre[0]=str[0];
        for(int i=1;i<n;i++){
            pre[i]=(pre[i-1]+str[i])%mod;
        }
        
        vector<long long int> pref_pre=pre;
        
        for(int i=1;i<n;i++){
            pref_pre[i]=(pref_pre[i]+pref_pre[i-1])%mod;
        }
        
        long long ans=0;
        
        for(int i=0;i<n;i++){
            long long int left=l[i];
            long long int right=r[i];
            //cout<<left<<" "<<right<<" ";
//             pre[i]-pre[j]
//             pre[i]-pre[j+1]
//             pre[i]-pre[j+2] j+2==i-1
                
//             pre[i+1]-pre[j]
//             pre[i+1]-pre[j+1]
//             pre[i+1]-pre[j+2] j+2==i-1
                
            long long int after=right-i; // left right nahi le sakte wale hai 
            long long int before=i-left;
            
//             before*(pre[i]+pre[i+1]+...after)-after*(pre[j]+pre[j+1]+..before)
                
//             before * pre[i+after-1]-pre[i-1]
            
            long long sum1=0,sum2=0;
            
            if(left!=-1){
                sum1=pref_pre[i-1];
                long long s1=0;
                if(left-1>=0){
                    s1=pref_pre[left-1];
                }
                sum1=(sum1-s1)%mod;
                
            }
            else if(left==-1){
                if(i-1>=0){
                    sum1=pref_pre[i-1];
                    before=i+1;
                }
                else{
                    before=1;
                }
            }
            
            // pre[i]+pre[i+1]+...after
            if(right==-1 ){
                sum2=pref_pre[n-1];
                long long s2=0;
                if(i-1>=0){
                    s2=pref_pre[i-1];
                }
                sum2=(sum2-s2)%mod;
                after=n-i;
            }
            else if(right!=-1){
                sum2=pref_pre[i+after-1];
                long long s2=0;
                if(i-1>=0){
                    s2=pref_pre[i-1];
                }
                sum2=(sum2-s2)%mod;
            }
        
            ans=ans+(str[i]%mod*((before*sum2)%mod-(after*sum1)%mod+mod))%mod;
            ans=(ans)%mod;
        }
        
        return ans;
    }
};
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