unordered_map - Hash function has no effect

Why in the following the hash function (which returns constant 0) seems not be taking any effect?

Since the hash function is returning constant, I was expecting as output all values to be 3. However, it seems to uniquely map the std::vector values to a unique value, regardless of my hash function being constant.

#include <iostream>
#include <map>
#include <unordered_map>
#include <vector>


// Hash returning always zero.
class TVectorHash {
public:
    std::size_t operator()(const std::vector<int> &p) const {
    return 0;
    }
};

int main ()
{
    std::unordered_map<std::vector<int> ,int, TVectorHash> table;

    std::vector<int> value1({0,1});
    std::vector<int> value2({1,0});
    std::vector<int> value3({1,1});

    table[value1]=1;
    table[value2]=2;
    table[value3]=3;

    std::cout << "\n1=" << table[value1];
    std::cout << "\n2=" << table[value2];
    std::cout << "\n3=" << table[value3];

    return 0;
}

Obtained output:

1=1
2=2
3=3

Expected output:

1=3
2=3
3=3

What am I missing about hash?