How to assign a value in const unordered_map to another const variable - C++

#include <iostream>
#include <bits/stdc++.h>
using namespace std;

void fun(const unordered_map<int, vector<int>>& direct_paths) {
    const int var = direct_paths[1][0];
    cout << var;
}

int main()
{
    unordered_map<int, vector<int>> a;
    a[1] = vector<int> {1,2,3};
    fun(a);
    return 0;
}

The above code outputs the following error:

error: passing ‘const std::unordered_map<int, std::vector<int> >’ as ‘this’ argument discards qualifiers [-fpermissive]
  const int var = direct_paths[1][0];
                                ^

Where as The below code doesn't output any compilation error:

#include <iostream>
#include <bits/stdc++.h>
using namespace std;

void fun(const vector<int>& direct_paths) {
    const int var = direct_paths[1];
    cout << var;
}

int main()
{
    vector<int> a;
    a = vector<int> {1,2,3};
    fun(a);
    return 0;
}

Questions:

1. Can I assign the value in a key-value pair of an unordered_map somehow?
2. Why is assigning an integer from vector taken from const unordered_map<int, vector&> disallowed? & from const vector allowed?

Thanks in advance!