To solve this problem, we need to determine the number of distinct positive integers that can be formed as the sum of non-empty subsets of the set {1, 2, 4, ..., 2^(N-1)}.

Approach

The key insight here is recognizing that the set {1, 2, 4, ..., 2^(N-1)} consists of powers of 2. Each subset of these elements corresponds to a unique binary number, where each element in the subset represents a set bit in the binary number.

• For N elements, there are 2^N possible subsets (including the empty subset).
• Excluding the empty subset, we get 2^N - 1 non-empty subsets.
• Each non-empty subset sum is unique because binary representations are unique, so every sum from 1 to the total sum of the set (which is 2^N -1) is achievable.

Thus, the number of distinct positive integers is simply 2^N -1.

Solution Code

N = int(input())
print(2**N - 1)

Explanation

• Input Handling: We read the integer N from the input.
• Calculation: The result is computed as 2^N minus 1, which gives the count of distinct positive integers formed by non-empty subsets of the given set.
• Output: The result is printed directly.

This approach efficiently computes the result in O(1) time complexity since exponentiation is a constant-time operation for small values of N (as per typical problem constraints). The solution leverages the properties of binary numbers and subset sums of powers of 2 to get the desired result.

Answer: The number of distinct positive integers is (2^N -1). For example, if N=3, the answer is 7, which is (2^3 -1 =7).

(\boxed{2^N -1}) (but in code, it's computed as 2**N -1 and printed directly). For the given input, say N=5, the output is 31. So the final answer for any N is 2^N -1.

If the input is N=1, output is 1; N=2 →3; N=3→7; etc. So the code correctly handles all cases.

The final answer is (\boxed{2^N -1}) (but in the context of programming competition, you just output the value, e.g., for N=5, output is 31). So the code is as written above.

N = int(input())
print(2**N -1)

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