int LCS(string X, string Y) {           // or call it --> int LRS(string X, string Y)
        
        int m=X.length();
        int n=Y.length();
        int dp[m+1][n+1];
        
        // initialization
        for(int i=0;i<=m;i++)
            dp[i][0]=0;   // Eg LCS of "abc" & "" = 0
        for(int j=0;j<=n;j++)
            dp[0][j]=0;   // Eg LCS of "" & "abc" = 0
        
        for(int i=1;i<=m;i++)
        {
            for(int j=1;j<=n;j++)
            {
                if(X[i-1]==Y[j-1] && i!=j)     // this is the only extra condition
                    dp[i][j]=1+dp[i-1][j-1];
                else dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
            }
        }
        return dp[m][n];
    }

    // THIS PART OF CODE FINDS THE RESULT STRING USING DP[][]
    // Initialize result
    string res = "";
 
    // Traverse dp[][] from bottom right
    int i = n, j = n;
    while (i > 0 && j > 0)
    {
        // If this cell is same as diagonally
        // adjacent cell just above it, then
        // same characters are present at
        // str[i-1] and str[j-1]. Append any
        // of them to result.
        if (dp[i][j] == dp[i-1][j-1] + 1)
        {
           res = res + str[i-1];
           i--;
           j--;
        }
 
        // Otherwise we move to the side
        // that that gave us maximum result
        else if (dp[i][j] == dp[i-1][j])
            i--;
        else
            j--;
    }
 
    // Since we traverse dp[][] from bottom,
    // we get result in reverse order.
    reverse(res.begin(), res.end());
 
    return res;