#include <cmath>

class Solution {
public:
    int consecutiveNumbersSum(int N) {
        // Assume that we pick n elements start from x, then
        // for (x + (n - 1) * x) * n / 2 == N,
        // ie. n * x + n * (n - 1) / 2 == N.
        // Just check for some n, we have valid x.
        int cnt = 0;
        for (int n = 1; ; n++) {
            int nx = N - n * (n - 1) / 2;
            if (nx < n) break;
            if (nx % n == 0) cnt++;
        }
        return cnt;
    }
};