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How to sort a 3 pair vector in c++

I've embedded a pair vector within a pair vector in order to be able to have 3 data types (all ints) within a pair. I am now having trouble sorting by the embedded pair vector. Can anyone tell me what I am doing wrong?

Here's my vector pair:

vector < pair<int, pair<int,int> > > obj2;

Here's my sort function:

bool sortby(const pair<int,int> &a,
               const pair<int,int> &b)
{
    return (a.first < b.first);
}

sort(vect.begin(), vect.end(), sortby)

There is no need to write a comparison function:

#include <cstddef>
#include <cstdlib>
#include <ctime>
#include <utility>
#include <vector>
#include <algorithm>
#include <iostream>


int main()
{
    std::srand(static_cast<unsigned>(std::time(nullptr)));

    std::vector<std::pair<int, std::pair<int, int> > > obj2;

    for (std::size_t i{}; i < 10; ++i)
        obj2.push_back(std::pair(rand() % 10, std::pair(rand() % 10, rand() % 10)));

    for (auto const & i : obj2)
        std::cout << i.first << ", " << i.second.first << ", " << i.second.second << '\n';
    std::cout.put('\n');

    std::sort(std::begin(obj2), std::end(obj2));

    for (auto const & i : obj2)
        std::cout << i.first << ", " << i.second.first << ", " << i.second.second << '\n';
    std::cout.put('\n');
}

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