An integer n (1 ≤ n ≤ 10^5), representing the number of entities.
An integer m (0 ≤ m ≤ min(n×(n−1), 10^5)), representing the number of connections.
A list of integers c of size n, where each integer is between 0 and 1000.
m pairs of integers ai and bi (0 ≤ ai, bi ≤ n − 1), representing one-way connections.

### Example Input:
```
2 1
1 2
0 1
```

### Function Signature:
Write a function f(n, m, c, connections) that takes in the input.
```
def f(n: int, m: int, c: List[int], connections: List[Tuple[int, int]]):
    '''
    n: an integer
    m: an integer
    c: a list of integers
    connections: a list of tuples, each containing two integers
    '''
```