Orig Description
Score : 300 points
Problem StatementWe have N ID cards, and there are M gates.
We can pass the i-th gate if we have one of the following ID cards: the L_i-th, (L_i+1)-th, ..., and R_i-th ID cards.
How many of the ID cards allow us to pass all the gates alone?
Constraints
All values in input are integers.
1 \leq N \leq 10^5
1 \leq M \leq 10^5
1 \leq L_i \leq R_i \leq N
InputInput is given from Standard Input in the following format:
N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M
OutputPrint the number of ID cards that allow us to pass all the gates alone.
Sample Input 14 2
1 3
2 4
Sample Output 12
Two ID cards allow us to pass all the gates alone, as follows:
The first ID card does not allow us to pass the second gate.
The second ID card allows us to pass all the gates.
The third ID card allows us to pass all the gates.
The fourth ID card does not allow us to pass the first gate.
Sample Input 210 3
3 6
5 7
6 9
Sample Output 21
Sample Input 3100000 1
1 100000
Sample Output 3100000
Extracted Specification
An integer N (1 ≤ N ≤ 10^5), representing some quantity or size.
An integer M (1 ≤ M ≤ 10^5), representing another quantity or size.
A list of M tuples (L_i, R_i), where 1 ≤ L_i ≤ R_i ≤ N for each tuple.
### Example Input:
```
4 2
1 3
2 4
```
### Function Signature:
Write a function f(inputs) that takes in the input.
def f(inputs: List[Tuple[int, int, List[Tuple[int, int]]]]):
'''
inputs: a list containing
- an integer
- an integer
- a list of tuples of integers
'''
Test Case Generator
Sure, here's a test case generator for the given competitive programming problem:
### Problem Statement: ID Cards and Gates
**Description**
We have \(N\) ID cards, and there are \(M\) gates. We can pass the \(i\)-th gate if we have one of the following ID cards: the \(L_i\)-th, \((L_i+1)\)-th, ..., and \(R_i\)-th ID cards. How many of the ID cards allow us to pass all the gates alone?
**Input**
1. An integer \(N\) (1 ≤ \(N\) ≤ 10^5), representing the number of ID cards.
2. An integer \(M\) (1 ≤ \(M\) ≤ 10^5), representing the number of gates.
3. \(M\) pairs of integers \(L_i\) and \(R_i\) (1 ≤ \(L_i\) ≤ \(R_i\) ≤ \(N\)), where each pair describes the range of ID cards that can pass the \(i\)-th gate.
**Output**
Print the number of ID cards that allow us to pass all the gates alone.
**Examples**
_Input_
```
4 2
1 3
2 4
```
_Output_
```
2
```
_Input_
```
10 3
3 6
5 7
6 9
```
_Output_
```
1
```
### Test Case Generator
```python
import random
def tcgen():
N = random.randint(1, 10**5)
M = random.randint(1, 10**5)
gates = []
for _ in range(M):
L = random.randint(1, N)
R = random.randint(L, N)
gates.append((L, R))
return N, M, gates
# Example of generating a test case
N, M, gates = tcgen()
print(N, M)
for L, R in gates:
print(L, R)
```
### Explanation
1. **N**: Randomly selects the number of ID cards between 1 and 100,000.
2. **M**: Randomly selects the number of gates between 1 and 100,000.
3. **gates**: Generates \(M\) pairs of \(L\) and \(R\), where \(L\) is randomly selected between 1 and \(N\), and \(R\) is randomly selected between \(L\) and \(N\).
This should adequately generate diverse test cases for the given problem.
Extract Arguments
def extract_arguments(fh):
N, M = map(int, fh.readline().strip().split())
gates = [tuple(map(int, fh.readline().strip().split())) for _ in range(M)]
return N, M, gates
# if __name__ == "__main__":
# input_path = sys.argv[1]
# with open(input_path, 'r') as fh:
# N, M, gates = extract_arguments(fh)
# f(N, M, gates)