decompose an integer to powers of three

[DeathLeap]

I am trying to write an algorithm that decompose an integer that the user inputs into powers of three.

example:

1 = 1
2 = 3 – 1
3 = 3
4 = 3 + 1
5 = 9 – 3 – 1
7 = 9 – 3 + 1
14 = 27 – 9 – 3 – 1
28 = 27 + 1
43 = 81 – 27 – 9 – 3 + 1
121 = 81 + 27 + 9 + 3 + 1

Rules: each power of 3, e.g: 1, 3, 9..etc should appear only once or never. It can't appear twice.

There are some intervals that must be considered: [-121,-41], [-40,-14], [-13,-5], [-4,-2], [-1,-1], [1,1], [2,4], [5,13],
[14,40], and [41,121]

My code shows the powers of three more than once. It's not that clean too. Can you guys help please?

  #include <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <sstream>

int main()
{
	int result;
	std::cout << "Please enter the desired result: ";
	std::cin >> result;

	std::vector<int> const table = { 1, 3, 9, 27, 81 }; //set might be better but oh well

	std::string answer = "";

	int temp = result;
	bool add = true;
	while (temp)
	{
		int distance = std::abs(temp - 1);
		int closest = 1;
		for (std::size_t i = 1; i < table.size(); ++i)
		{
			int tempDistance = std::abs(temp - table[i]);
			if (distance && distance > tempDistance) //make sure we didn't find a perfect match and its decreasing distance
			{
				distance = tempDistance;
				closest = table[i];
			}
			else
			{
				break; //getting farther away or we found a match no need to continue
			}
		}
		if (closest > temp)
		{
			add = !add;
		}
		temp = distance;
		if (temp) //the last number finished equation so don't putt sign at end
		{
			std::ostringstream ss;
			ss << closest;
			answer += ss.str();
			answer += add ? '+' : '-';
		}
		else
		{
			std::ostringstream ss;
			ss << closest;
			answer += ss.str();
		}
	}

	std::cout << result << " = " << answer << std::endl;
	system("pause");
	return 0;
}