Write a C ++ program to implement Merge Sort algorithm to efficiently handle an input array that may contain duplicate elements. The goal is to modify the algorithm in such a way that duplicate elements appear in the sorted array in the same order as they appear in the input.

#include<iostream>
#include<cstdlib>
using namespace std; 
void merge(int *,int, int , int );
void mergesort(int *a, int low, int high)
{
    int mid;
    if (low < high)
    {
        mid=(low+high)/2;
        mergesort(a,low,mid);
        mergesort(a,mid+1,high);
        merge(a,low,high,mid);
    }
    return;
}
void merge(int *a, int low, int high, int mid)
{
    int i, j, k, c[50];
    i = low;
    k = low;
    j = mid + 1;
    while (i <= mid && j <= high)
    {
        if (a[i] < a[j])
        {
            c[k] = a[i];
            k++;
            i++;
        }
        else
        {
            c[k] = a[j];