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>
//#include <chrono>
//using namespace std::chrono;
using namespace std;
#define int     long long
#define vi      vector<int>
#define all(v)  v.begin(), v.end()
#define vvi     vector<vi>
#define pb      push_back
#define ppb     pop_back
#define pii     pair<int, int>
#define mp      make_pair
#define ff      first
#define ss      second
#define endl    "\n"
#define MAX     LONG_LONG_MAX
#define MIN     LONG_LONG_MIN
#define lb      lower_bound
#define ub      upper_bound
#define INF     1e18
#define MOD     1000000007
#define set_bits __builtin_popcountll
#define rep(i,a,b) for(int i = a; i < b; i++)
#define fastio() ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)


#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
#else
#define debug(x)
#endif

void _print(int t) {cerr << t;}
void _print(bool t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(double t) {cerr << t;}

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 << "]";}

/*---------------------------------------------------------------------------------------------------------------------------*/
int lcm(int a, int b) {return (a*b)/__gcd(a, b);};
bool revsort(int a, int b) {return a > b;}
void precision(int a) {cout << setprecision(a) << fixed;}
int fact(int i) {if (i <= 1) return 1; else return i * fact(i - 1);}
vector<int> sieve(int n) {int*arr = new int[n + 1](); vector<int> vect; for (int i = 2; i <= n; i++)if (arr[i] == 0) {vect.push_back(i); for (int j = i * i; j <= n; j += i)arr[j] = 1;} return vect;}
string decToBin(int n) {string s = ""; int i = 0; while (n > 0) {s = to_string(n % 2) + s; n = n / 2; i++;} return s;}
int binToDec(string n) {string num = n; int dec_value = 0; int base = 1; int len = num.length(); for (int i = len - 1; i >= 0; i--) {if (num[i] == '1')dec_value += base; base = base * 2;} return dec_value;}
int mpow(int a, int b) {if (b == 0) return 1; int res = 1; a %= MOD; while (b) {if (b & 1) {res = (res * a) % MOD;} a = (a * a) % MOD; b >>= 1;} return res;}
int madd(int a, int b) {a = a % MOD; b = b % MOD; return (((a + b) % MOD) + MOD) % MOD;}
int msub(int a, int b) {a = a % MOD; b = b % MOD; return (((a - b) % MOD) + MOD) % MOD;}
int mmul(int a, int b) {a = a % MOD; b = b % MOD; return (((a * b) % MOD) + MOD) % MOD;}

const int dx[4] = { -1, 1, 0, 0};
const int dy[4] = {0, 0, -1, 1};
/*---------------------------------------------------------------------------------------------------------------------------*/

vi l(300005);

void pre() {
    l[1] = 2;
    rep(i,2,l.size()) {
        l[i] = lcm(l[i-1],i+1);
    }
}

void solve() {
    int n;
    cin >> n;
    vi v(n);
    for (auto &val : v) {
        cin >> val;
    }
    if(!(v[0] & 1)) {
        cout << "NO" << endl;
    } else {
        rep(i,0,n) {
            if(v[i] % l[i+1] == 0) {
                cout <<"NO" << endl;
                break;
            } 
        }
        cout << "YES" << endl;
    }
}
int32_t main() {
#ifndef ONLINE_JUDGE
    freopen("Error.txt", "w", stderr);
#endif
    fastio();
    //auto start1 = high_resolution_clock::now();
    int t;
    cin >> t;
    pre();
    while (t--) {
        solve();
    }
    /*auto stop1 = high_resolution_clock::now();
    auto duration = duration_cast<microseconds>(stop1-start1);
    #ifndef ONLINE_JUDGE
    cerr << "TIME: " << duration.count()/1000 << endl;
    #endif*/
}