You are now examining a unique method to sort a sequence of numbers in increasing order. The method only allows swapping of two numbers that have a common prime factor. For example, a sequence [6, 4, 2, 3, 7] can be sorted using the following steps.
Step 0: 6 4 2 3 7 (given sequence)
Step 1: 2 4 6 3 7 (elements 6 and 2 swapped)
Step 2: 2 6 4 3 7 (elements 4 and 6 swapped)
Step 3: 2 3 4 6 7 (elements 6 and 3 swapped)


Depending on the nature of the sequence, however, this approach may fail to complete the sorting. You have given a name "Coprime sort" to this approach and are now examining if a given sequence is coprime-sortable.

Make a program to determine if a given sequence can be sorted in increasing order by iterating an arbitrary number of swapping operations of two elements that have a common prime number.



Input

The input is given in the following format.


$N$
$a_1$ $a_2$ $...$ $a_N$


The first line provides the number of elements included in the sequence $N$ ($2 \leq N \leq 10^5$). The second line provides an array of integers $a_i$ ($2 \leq a_i \leq 10^5$) that constitute the sequence.

Output

Output "1" if the sequence is coprime-sortable in increasing order, or "0" otherwise.

Examples

Input

5
6 4 2 3 7


Output

1


Input

7
2 9 6 5 6 7 3


Output

0
#define _USE_MATH_DEFINES

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <map>

using namespace std;

typedef pair<long long int, long long int> P;

long long int INF = 1e18;
long long int MOD = 1e9 + 7;

#define MAX_N 210000

int par[MAX_N];
int rnk[MAX_N];

// 初期化
void init(){
	for(int i = 0; i < MAX_N; i++){
		par[i] = i;
		rnk[i] = 0;
	}
}

// x の親を返す
int find(int x){
	if(par[x] == x){
		return x;
	}
	return par[x] = find(par[x]);
}

// x と y を併合する
void unite(int x, int y){
	int x_par = find(x);
	int y_par = find(y);
	if(x_par == y_par){
		return;
	}
	
	if(rnk[x_par] < rnk[y_par]){
		par[x_par] = y_par;
	}else{
		par[y_par] = x_par;
		if(rnk[x_par] == rnk[y_par]){
			rnk[x_par]++;
		}
	}
}

// x, y が同じグループか判定
bool same(int x, int y){
	return (find(x) == find(y));
}

int main(){
	
	int N;
	cin >> N;
	
	init();
	
	int Q = 110000 - 1;
	vector<P> v;
	
	for(int i = 0; i < N; i++){
		int num;
		cin >> num;
		v.push_back(P(num, i));
		for(int j = 2; j * j <= num; j++){
			while(num % j == 0){
				num /= j;
				unite(i, j + Q);
			}
		}
		if(num > 1){
			unite(i, num + Q);
		}
	}
	
	sort(v.begin(), v.end());
	
	bool flag = true;
	for(int i = 0; i < N; i++){
		if(!same(v[i].second, i)){
			flag = false;
		}
	}
	
	cout << flag << endl;
	
	return 0;
}

