1440.cpp

#include <stdio.h>
#include <vector>
#include <string>
#include <functional>
#include <cassert>
#include <cstdlib>

std::string solve(const std::vector<int>& a) {
    const int n = a.size();
    int sum = 0;
    for (auto& it : a) {
        assert(it >= 0);
        sum += it;
    }
    assert(0 <= sum && sum <= 1e9);
    if (sum == 0) {
        return std::string(n, '1');
    }
    std::function<bool(int, int)> is_possible = [&](int number, const int dir) {
        const int need_sum = sum / number;
        assert(need_sum * number == sum);
        int curr_sum = 0, i = 0;
        do {
            curr_sum += a[i];
            if (curr_sum > need_sum) {
                return false;
            } else if (curr_sum == need_sum) {
                --number;
                curr_sum = 0;
            }
            i += dir;
            if (i < 0) {
                i += n;
            }
            if (i >= n) {
                i -= n;
            }
        } while (number && i != 0);
        assert(curr_sum == 0);
        return true;
    };

    std::string answ(n, '0');

    for (int i = 1; i * i <= sum; ++i) {
        const int j = sum / i;
        if (j * i == sum) {
            if (i <= n) {
                answ[i-1] += (is_possible(i, 1) || is_possible(i, -1));
            }
            if (j <= n && j != i) {
                answ[j-1] += (is_possible(j, 1) || is_possible(j, -1));
            }
        }
    }
    return answ;
}

int main() {
    int n;
    scanf("%d", &n);
    std::vector<int> a(n);
    for (auto& it : a) {
        scanf("%d", &it);
    }
    printf("%s\n", solve(a).c_str());
    return 0;
}