Problem:
Score : 500 points

Problem Statement

We have N integers. The i-th number is A_i.

\{A_i\} is said to be pairwise coprime when GCD(A_i,A_j)=1 holds for every pair (i, j) such that 1\leq i < j \leq N.

\{A_i\} is said to be setwise coprime when \{A_i\} is not pairwise coprime but GCD(A_1,\ldots,A_N)=1.

Determine if \{A_i\} is pairwise coprime, setwise coprime, or neither.

Here, GCD(\ldots) denotes greatest common divisor.

Constraints

2 \leq N \leq 10^6

1 \leq A_i\leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

If \{A_i\} is pairwise coprime, print pairwise coprime; if \{A_i\} is setwise coprime, print setwise coprime; if neither, print not coprime.

Sample Input 1

3
3 4 5

Sample Output 1

pairwise coprime

GCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.

Sample Input 2

3
6 10 15

Sample Output 2

setwise coprime

Since GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.

Sample Input 3

3
6 10 16

Sample Output 3

not coprime

GCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

#ifndef M_PI
#define M_PI 3.14159265358979
#endif
#define deg_to_rad(deg) (((deg) / 360) * 2 * M_PI)
#define rad_to_deg(rad) (((rad) / 2 / M_PI) * 360)

using namespace std;

typedef long long ll;
typedef vector<ll> vll;
typedef vector<int> vi;
typedef pair<ll, ll> pll;
typedef pair<int, int> pi;
typedef long double ld;
typedef pair<long double, long double> pld;

const ll INF = 1e18;
const ll MOD = 1e9 + 7;

const ll MAX_A = 1001000;

ll gcd(ll n, ll m) {
    if(n > m) {
        ll l = n;
        n = m;
        m = l;
    }
    if(n == 0) {
        return m;
    }
    while(1) {
        ll l = n;
        n = m % n;
        m = l;
        if(n == 0) {
            break;
        }
    }
    return m;
}

bool isprime(ll n) {
    if(n == 1) {
        return false;
    }
    if(n == 2) {
        return true;
    }
    ll sq = (ll)sqrt(double(n));
    for(ll i = 2; i <= sq; i++) {
        if(n % i == 0) {
            return false;
        }
    }
    return true;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    ll i, j, k, l;

    ll N;
    cin >> N;
    vll A(N);
    for(auto &e : A)
        cin >> e;
    // setwise
    ll g = A[0];
    for(i = 1; i < N; i++) {
        g = gcd(g, A[i]);
    }
    if(g > 1) {
        cout << "not coprime" << endl;
        return 0;
    }
    // pairwise
    // D[x]はxを割り切る最小の素数
    vll D(MAX_A, 0);
    for(i = 2; i < D.size(); i++) {
        if(D[i] == 0) {
            ll p = i;
            while(p < D.size()) {
                D[p] = i;
                p += i;
            }
        }
    }
    set<ll> pset;
    for(i = 0; i < N; i++) {
        ll a = A[i];
        if(a == 1)
            continue;
        set<ll> pset_sub;
        while(D[a] != a) {
            auto itr = pset.find(D[a]);
            if(itr != pset.end()) {
                cout << "setwise coprime" << endl;
                return 0;
            }
            pset_sub.insert(D[a]);
            a = a / D[a];
        }
        for(auto p : pset_sub) {
            pset.insert(p);
        }
    }

    cout << "pairwise coprime" << endl;

    return 0;
}