# Ehab’s REAL Number Theory Problem

You are given an array $a$ of length $n$ that has a special condition: every element in this array has at most 7 divisors. Find the length of the shortest non-empty subsequence of this array product of whose elements is a perfect square.

A sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements.

Input

The first line contains an integer $n$ ($1 \le n \le 10^5$) — the length of $a$.

The second line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_{n}$ ($1 \le a_i \le 10^6$) — the elements of the array $a$.

Output

Output the length of the shortest non-empty subsequence of $a$ product of whose elements is a perfect square. If there are several shortest subsequences, you can find any of them. If there’s no such subsequence, print “-1”.

Examples

input

3
1 4 6


output

1

input

4
2 3 6 6


output

2

input

3
6 15 10


output

3

input

4
2 3 5 7


output

-1

Note

In the first sample, you can choose a subsequence $[1]$.

In the second sample, you can choose a subsequence $[6, 6]$.

In the third sample, you can choose a subsequence $[6, 15, 10]$.

In the fourth sample, there is no such subsequence.

Solution:

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}());
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}

typedef pair<ll,ll> PLL;
namespace Factor {
const int N=1010000;
ll C,fac[10010],n,mut,a[1001000];
int T,cnt,i,l,prime[N],p[N],psize,_cnt;
ll _e[100],_pr[100];
vector<ll> d;
inline ll mul(ll a,ll b,ll p) {
if (p<=1000000000) return a*b%p;
else if (p<=1000000000000ll) return (((a*(b>>20)%p)<<20)+(a*(b&((1<<20)-1))))%p;
else {
ll d=(ll)floor(a*(long double)b/p+0.5);
ll ret=(a*b-d*p)%p;
if (ret<0) ret+=p;
return ret;
}
}
void prime_table(){
int i,j,tot,t1;
for (i=1;i<=psize;i++) p[i]=i;
for (i=2,tot=0;i<=psize;i++){
if (p[i]==i) prime[++tot]=i;
for (j=1;j<=tot && (t1=prime[j]*i)<=psize;j++){
p[t1]=prime[j];
if (i%prime[j]==0) break;
}
}
}
void init(int ps) {
psize=ps;
prime_table();
}
ll powl(ll a,ll n,ll p) {
ll ans=1;
for (;n;n>>=1) {
if (n&1) ans=mul(ans,a,p);
a=mul(a,a,p);
}
return ans;
}
bool witness(ll a,ll n) {
int t=0;
ll u=n-1;
for (;~u&1;u>>=1) t++;
ll x=powl(a,u,n),_x=0;
for (;t;t--) {
_x=mul(x,x,n);
if (_x==1 && x!=1 && x!=n-1) return 1;
x=_x;
}
return _x!=1;
}
bool miller(ll n) {
if (n<2) return 0;
if (n<=psize) return p[n]==n;
if (~n&1) return 0;
for (int j=0;j<=7;j++) if (witness(rand()%(n-1)+1,n)) return 0;
return 1;
}
ll gcd(ll a,ll b) {
ll ret=1;
while (a!=0) {
if ((~a&1) && (~b&1)) ret<<=1,a>>=1,b>>=1;
else if (~a&1) a>>=1; else if (~b&1) b>>=1;
else {
if (a<b) swap(a,b);
a-=b;
}
}
return ret*b;
}
ll rho(ll n) {
for (;;) {
ll X=rand()%n,Y,Z,T=1,*lY=a,*lX=lY;
int tmp=20;
C=rand()%10+3;
X=mul(X,X,n)+C;*(lY++)=X;lX++;
Y=mul(X,X,n)+C;*(lY++)=Y;
for(;X!=Y;) {
ll t=X-Y+n;
Z=mul(T,t,n);
if(Z==0) return gcd(T,n);
tmp--;
if (tmp==0) {
tmp=20;
Z=gcd(Z,n);
if (Z!=1 && Z!=n) return Z;
}
T=Z;
Y=*(lY++)=mul(Y,Y,n)+C;
Y=*(lY++)=mul(Y,Y,n)+C;
X=*(lX++);
}
}
}
void _factor(ll n) {
for (int i=0;i<cnt;i++) {
if (n%fac[i]==0) n/=fac[i],fac[cnt++]=fac[i];}
if (n<=psize) {
for (;n!=1;n/=p[n]) fac[cnt++]=p[n];
return;
}
if (miller(n)) fac[cnt++]=n;
else {
ll x=rho(n);
_factor(x);_factor(n/x);
}
}
void dfs(ll x,int dep) {
if (dep==_cnt) d.pb(x);
else {
dfs(x,dep+1);
for (int i=1;i<=_e[dep];i++) dfs(x*=_pr[dep],dep+1);
}
}
void norm() {
sort(fac,fac+cnt);
_cnt=0;
rep(i,0,cnt) if (i==0||fac[i]!=fac[i-1]) _pr[_cnt]=fac[i],_e[_cnt++]=1;
else _e[_cnt-1]++;
}
vector<ll> getd() {
d.clear();
dfs(1,0);
return d;
}
vector<ll> factor(ll n) {
cnt=0;
_factor(n);
norm();
return getd();
}
vector<PLL> factorG(ll n) {
cnt=0;
_factor(n);
norm();
vector<PLL> d;
rep(i,0,_cnt) d.pb(mp(_pr[i],_e[i]));
return d;
}
bool is_primitive(ll a,ll p) {
assert(miller(p));
vector<PLL> D=factorG(p-1);
rep(i,0,SZ(D)) if (powl(a,(p-1)/D[i].fi,p)==1) return 0;
return 1;
}
}

const int N=1010000;
set<int> sp;
int q[N],vis[N],dis[N],n,cnt[N];
vector<PII> e[N];

int main() {
Factor::init(100000);
scanf("%d",&n);
for (int i=0;i<n;i++) {
int x;
scanf("%d",&x);
auto d=Factor::factorG(x);
VI pr;
for (auto p:d) {
if (p.se%2) pr.pb(p.fi),sp.insert(p.fi);
}
if (pr.empty()) {
puts("1");
return 0;
}
if (SZ(pr)==1) {
cnt[pr[0]]++;
//		printf("single %d\n",pr[0]);
} else {
//printf("dob %d %d\n",pr[0],pr[1]);
e[pr[0]].pb(mp(pr[1],i));
e[pr[1]].pb(mp(pr[0],i));
}
}
VI x(all(sp));
//puts("....");
int ans=n+1;
for (auto d:x) {
if (cnt[d]>=2) {
puts("2");
return 0;
}
}
for (auto d:x) if (d<=1000) {
for (auto p:x) vis[p]=-1,dis[p]=n+1;
vis[d]=-2; dis[d]=0;
int t=0;
q[t++]=d;
rep(i,0,t) {
int u=q[i];
for (auto pr:e[u]) {
int v=pr.fi,w=pr.se;
if (vis[v]==-1) {
vis[v]=w;
dis[v]=dis[u]+1;
q[t++]=v;
}
}
}
int md1=n+1,md2=n+1;
for (auto p:x) if (dis[p]!=n+1&&cnt[p]>0) {
if (dis[p]<md1) md2=md1,md1=dis[p];
else if (dis[p]<md2) md2=dis[p];
}
ans=min(ans,md1+md2+2);
for (auto p:x) for (auto q:e[p]) {
if (q.se!=vis[p]&&q.se!=vis[q.fi]) ans=min(ans,dis[p]+dis[q.fi]+1);
}
}
if (ans==n+1) ans=-1;
printf("%d\n",ans);
}