YouKn0wWho has an integer sequence a_1, a_2, …, a_n. He will perform the following operation until the sequence becomes empty: select an index i such that 1 ≤ i ≤ |a| and a_i is not divisible by (i + 1), and erase this element from the sequence. Here |a| is the length of sequence a at the moment of operation. Note that the sequence a changes and the next operation is performed on this changed sequence.

For example, if a=[3,5,4,5], then he can select i = 2, because a_2 = 5 is not divisible by i+1 = 3. After this operation the sequence is [3,4,5].

Help YouKn0wWho determine if it is possible to erase the whole sequence using the aforementioned operation.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases doesn't exceed 3 ⋅ 10^5.

Output

For each test case, print "YES" (without quotes) if it is possible to erase the whole sequence using the aforementioned operation, print "NO" (without quotes) otherwise. You can print each letter in any register (upper or lower).

Example

Input


5
3
1 2 3
1
2
2
7 7
10
384836991 191890310 576823355 782177068 404011431 818008580 954291757 160449218 155374934 840594328
8
6 69 696 69696 696969 6969696 69696969 696969696


Output


YES
NO
YES
YES
NO

Note

In the first test case, YouKn0wWho can perform the following operations (the erased elements are underlined): [1, \underline{2}, 3] → [\underline{1}, 3] → [\underline{3}] → [ ].

In the second test case, it is impossible to erase the sequence as i can only be 1, and when i=1, a_1 = 2 is divisible by i + 1 = 2.
#include<bits/stdc++.h>
#define ll long long
#define pb push_back
#define fr(a,b) for(int i = a; i < b; i++)
#define rep(i,a,b) for(int i = a; i < b; i++)
#define mod 1000000007
#define INF 1000000000000000007
#define inf (1LL<<60)
#define all(x) (x).begin(), (x).end()
#define prDouble(x) cout << fixed << setprecision(10) << x
#define triplet pair<ll,pair<ll,ll>>
#define goog(tno) cout << "Case #" << tno <<": "
#define fast_io ios_base::sync_with_stdio(false);cin.tie(NULL)
#define read(x) int x; cin >> x
#define pii pair<int,int>
#define ff first
#define ss second
#define int long long
#define max3(a,b,c) max(a,max(b,c));
#define ull unsigned long long
#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x)
#endif


using namespace std;




//debug the string and vectors
void _print(int t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(double t) {cerr << t;}
void _print(ull t) {cerr << t;}

template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(pair <T, V> p) {cerr << "{"; _print(p.ff); cerr << ","; _print(p.ss); cerr << "}";}
template <class T> void _print(vector <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(set <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(multiset <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void _print(map <T, V> v) {cerr << "[ "; for (auto i : v) {_print(i); cerr << " ";} cerr << "]";}

void init_code() {
   fast_io;
#ifndef ONLINE_JUDGE
   freopen("input.txt", "r", stdin);
   freopen("new.txt", "w", stdout);
#endif
#ifndef ONLINE_JUDGE
   freopen("Error.txt", "w", stderr);
#endif
}


vector<int>adj[200005];

vector<int>max_seg(400005);
vector<int>pref(400005);
vector<int>suff(400005);
vector<int>t(400005);




void build(int tl, int tr, int idx, vector<int>&v) {

   if (tl == tr) {

      t[idx] = v[tl];

      return;
   }

   int m = (tl + tr) / 2;
   build(tl, m, 2 * idx, v);
   build(m + 1, tr, 2 * idx + 1, v);
   t[idx] = max(t[2 * idx] ,  t[2 * idx + 1]);


}





void update(int tl, int tr, int idx, vector<int>&v, int pos, int new_val) {

   if (tl == tr) {
   t[idx] = new_val;
    return;
   }

   int mid = (tl + tr) / 2;
   if (pos <= mid)
      update(tl, mid, 2 * idx, v, pos, new_val);
   else
      update(mid + 1, tr, 2 * idx + 1, v, pos, new_val);

   t[idx] = max(t[2 * idx] ,  t[2 * idx + 1]);



}

int atleastX(int tl, int tr, int idx, vector<int>&v,int k){
 if(k>t[idx])return 0;
 if(tl==tr){
     return tl;
 }

 int mid = (tl+tr)/2;
int max1 = t[2*idx];
int max2 = t[2*idx+1];

if(max1>=k){
return atleastX(tl,mid,2*idx,v,k);
}
else{
return atleastX(mid+1,tr,2*idx+1,v,k);
}



}

vector<int>val(100005,0);
vector<int>level(100005,0);
vector<pii>zo(100005);
vector<int>even_leaf;
int one,zero;
void dfs(int s, int par){
	
	if(par!=-1){
		val[s]  = !val[par];
	//	zo[s] = val[s]==1?{zo[p].ff+1,zo[p].ss}:{zo[p].ff+1,zo[p].ss+1};
		level[s] = level[par]+1;
	}
	
	int ch = 0;
	for(int child:adj[s]){
		if(child!=par){
			dfs(child,s);
			ch++;
		}
	}
	
	if(ch==0 && level[s]%2==0){
	//	cout<<"hii"<<" "<<s<<endl;
		even_leaf.pb(s);
		if(val[s]==1)one++;
		if(val[s]==0)zero++;
	}
	
}

void situn(int cc) {

int n;
cin>>n;
vector<int>v(n);
for(int i=0; i<n;i++){
	cin>>v[i];
}
vector<int>lcm(n);
lcm[0] = 2;
for(int i=1; i<n;i++){
	lcm[i] = (i+2)*(lcm[i-1])/__gcd(i+2,lcm[i-1]);

}
for(int i=1; i<n;i++){

if(v[i]%lcm[i]==0){
	cout<<"NO";
	return;
}

}

cout<<"YES";

}





signed main() {
  
   fast_io;

   int t = 1;
   cin >> t;
   int cc = 1;
   while (t--) {

      situn(cc);
      cc++;
      cout << endl;
      // cout << cc << endl;
   }
   return 0;
}
