Problem:
Score : 800 points

Problem Statement

You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x.

Constraints

0 \leq N \leq 10^4

|a_i| \leq 10^9(0\leq i\leq N)

a_N \neq 0

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_N
:
a_0

Output

Print all prime numbers p that divide f(x) for every integer x, in ascending order.

Sample Input 1

2
7
-7
14

Sample Output 1

2
7

2 and 7 divide, for example, f(1)=14 and f(2)=28.

Sample Input 2

3
1
4
1
5

Sample Output 2

There may be no integers that satisfy the condition.

Sample Input 3

0
998244353

Sample Output 3

998244353

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#pragma GCC optimize ("O3")
#pragma GCC target ("tune=native")
#pragma GCC target ("avx")

#include <bits/stdc++.h>

// 汎用マクロ
#define ALL_OF(x) (x).begin(), (x).end()
#define REP(i,n) for (long long i=0, i##_len=(n); i<i##_len; i++)
#define RANGE(i,is,ie) for (long long i=(is), i##_end=(ie); i<=i##_end; i++)
#define UNIQUE(v) (v).erase(unique((v).begin(), (v).end()), (v).end())
template<class T> bool chmax(T &a, const T &b) {if (a < b) {a = b; return 1;} return 0; }
template<class T> bool chmin(T &a, const T &b) {if (a > b) {a = b; return 1;} return 0; }
#define INF 0x7FFFFFFF
#define LINF 0x7FFFFFFFFFFFFFFFLL
#define Yes(q) (q ? "Yes" : "No")
#define YES(q) (q ? "YES" : "NO")
#define DUMP(q) cerr << "[DEBUG] " #q ": " << (q) << " at " __FILE__ ":" << __LINE__ << endl
#define DUMPALL(q) cerr << "[DEBUG] " #q ": ["; REP(dumpall_i, (q).size()) { cerr << q[dumpall_i] << (dumpall_i == (q).size() - 1 ? "" : ", "); } cerr << "] at " __FILE__ ":" << __LINE__ << endl

// gcc拡張マクロ
#define gcd __gcd
#define popcount __builtin_popcount
#define popcountll __builtin_popcountll

// エイリアス
using  ll = long long;
using ull = unsigned long long;
using  ld = long double;
using namespace std;

// モジュール


// 処理内容
int main() {
    
    ll n;
    cin >> n;
    vector<ll> a(n+1);
    REP(i, n+1) cin >> a[n-i];

    // 偶素数
    ll odd_factor = 0;
    REP(i, n+1) if (a[i] % 2) odd_factor++;
    if (odd_factor % 2 == 0)
        cout << 2 << endl;

    // 奇素数
    ll g = abs(a[0]);
    RANGE(i, 0, n) {
        g = gcd(g, abs(a[i]));
    }
    while (g % 2 == 0) g /= 2;
    for (ll f = 3, fmax2 = g; f * f <= fmax2; f += 2) {
        if (g % f == 0) {
            if (a[0] % f == 0) {
                cout << f << endl;
            }
            while (g % f == 0) {
                g /= f;
            }
        }
    }
    if (g > 1) {
        cout << g << endl;
    }
    
}