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.
#define MOD 998244353

#include <iostream>
#include <vector>
#include <stdlib.h>
#include <queue>
#include <numeric>
#include <cmath>
#include <set>
#include <unordered_map>
#include <map>
#include <algorithm>
#include <stack>
#include <memory>




#define all(x) x.begin(),x.end()
#define int int64_t
#define IO_FAST std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr);

template <class T=int>
std::vector<T> read_vector(size_t size) {
    std::vector<T> vector(size);
    for (auto& element : vector) {
        std::cin >> element;
    }
    return vector;
}

void YES(bool yes=true) {
    std::cout << (yes ? "YES\n" : "NO\n");
}

void NO() {
    std::cout << "NO\n";
}


#define mp(x, y) std::make_pair(x, y)


class range {
public:
    int start;
    int stop;
    class iterator {
    public:
        int i;
        iterator(int i) : i(i) {}
        iterator& operator++() {
            ++i;
            return *this;
        }
        int operator*() {
            return i;
        }
        bool operator!= (const iterator& other) {
            return i != other.i;
        }
    };

    range(int stop) : start(0), stop(stop) {}

    range(int start, int stop) : start(start), stop(stop) {}

    iterator begin() {
        return start;
    }

    iterator end() {
        return stop;
    }
};




std::vector<int> list(int a, int b) {
    std::vector<int> vector;
    vector.push_back(a);
    vector.push_back(b);
    return vector;
};
std::vector<int> list(int a, int b, int c) {
    std::vector<int> vector;
    vector.push_back(a);
    vector.push_back(b);
    vector.push_back(c);
    return vector;
};

template<typename T>
void print(const T& x) {
    std::cout << x << ' ';
}
template<typename T>
void println(const T& x) {
    std::cout << x << '\n';
}

template<typename T, typename U>
void print(const std::pair<T, U>& x) {
    std::cout << '(' << x.first << ',' << (x.second < 0 ? "": " ") << x.second << ") ";
}

void println() {
    std::cout << '\n';
}

template <typename T>
void print(const std::vector<T>& a) {
    for (auto x : a) {
        print(x);
    }
}

template <typename T>
void println(const std::vector<T>& a) {
    for (auto x : a) {
        print(x);
    }
    std::cout << '\n';
}




#define read(x) int x;std::cin >> x;
#define read2(x, y) int x, y;std::cin >> x >> y;
#define read3(x, y, z) int x, y, z;std::cin >> x >> y >> z;

template <class Row>
class BaseGrid {
public:
    class iterator {
    public:
        BaseGrid<Row>* baseGrid;
        size_t i;
        size_t j;

        iterator(BaseGrid<Row>* baseGrid, size_t i, size_t j)
                : baseGrid(baseGrid), i(i), j(j)
        {}

        iterator& operator++() {
            if (j < (baseGrid->m) - 1) {
                j += 1;
            } else {
                i += 1;
                j = 0;
            }
            return *this;
        }
        bool operator!= (const iterator& other) {
            return i != other.i || j != other.j;
        }

        decltype(&(baseGrid->rows[0][0])) operator->() {
            return &(baseGrid->rows)[i][j];
        }

        decltype(baseGrid->rows[0][0])& operator* () {
            return (baseGrid->rows)[i][j];
        }

        iterator left() {
            if (i > 0) {
                return {baseGrid, i - 1, j};
            }
            return baseGrid->end();
        }

        iterator right() {
            if (i + 1 < baseGrid->n) {
                return {baseGrid, i + 1, j};
            }
        }

        explicit operator bool() {
            return *this != baseGrid->end();
        }
    };

    size_t n;
    size_t m;

    std::vector<Row> rows;
    BaseGrid(size_t n)
            : n(n), rows(n)
    {}

    BaseGrid(size_t n, size_t m)
            : n(n), m(m), rows(n, Row(m))
    {}

    BaseGrid(size_t n, Row row)
            : n(n), m(row.size()), rows(n, row)
    {}

    decltype(rows[0][0])& operator() (int i, int j) {
        return rows[i][j];
    }

    iterator begin() {
        return {this, 0, 0};
    }

    iterator end() {
        return {this, n, 0};
    }

    Row& operator[](size_t i) {
        return rows[i];
    }
};


template <class T>
class Grid : public BaseGrid<std::vector<T>> {
public:
    Grid(size_t n, size_t m)
            : BaseGrid<std::vector<T>>(n, std::vector<T>(m))
    {}
};

template <>
class Grid <char> : public BaseGrid<std::string> {
public:
    Grid(size_t n)
            : BaseGrid(n)
    {}

    Grid(size_t n, std::istream& in)
            : BaseGrid(n)
    {
        for (size_t i = 0; i < n; ++i) {
            in >> rows[i];
        }
    }

    Grid(size_t n, size_t m, char value)
            : BaseGrid<std::string>(n, std::string(m, value))
    {}
};


namespace nt {
    int gcdExtended(int a, int b, int *x, int *y)
    {
        if (a == 0)
        {
            *x = 0;
            *y = 1;
            return b;
        }

        int x1, y1;
        int gcd = gcdExtended(b%a, a, &x1, &y1);

        *x = y1 - (b/a) * x1;
        *y = x1;

        return gcd;
    }
}

class mint {
public:
    int x;


    mint() : x(0) {}
    mint(int x) : x(x) {}
    mint(mint &other) : x(other.x) {}


    mint operator= (int other) {
        x = other;
        return *this;
    }

    mint operator= (const mint& other) {
        x = other.x;
        return *this;
    }

    mint operator+(const mint& other) {
        return (x + other.x) % MOD;
    }

    mint operator-(const mint& other) {
        return (x + MOD - other.x) % MOD;
    }

    mint operator*(const mint& other) {
        return (x * other.x) % MOD;
    }

    mint operator/(int denominator) {
        int f_mod;
        int f_denominator;
        nt::gcdExtended(denominator, MOD, &f_denominator, &f_mod);
        while (f_denominator < 0)
            f_denominator += MOD;
        return (f_denominator * x) % MOD;
    }

    mint operator/(const mint& denominator) {
        return (*this) / denominator.x;
    }

    mint operator^(unsigned long n) {
        mint a = x;
        mint res = 1;

        while (n > 0) {
            if (n & 1)
                res = res * a;
            n = n >> 1;
            a = a * a;
        }

        return res;
    }
};

template <typename T>
mint operator* (T x, const mint& y) {
    return mint(x) * y;
}

namespace nt {

    std::vector<mint> get_facts(int n) {
        std::vector<mint> fact(n);
        fact[0] = 1;
        fact[1] = 1;
        for (int i = 2; i < fact.size(); ++i) {
            fact[i] = (i * fact[i - 1]);
        }
        return fact;
    }

    std::map<int, int> get_canonical(int x, const std::vector<int>& sieve) {
        std::map<int, int> primes;

        while (x > 1) {
            const int& p = sieve[x];

            if (p > 1) {
                primes[p] += 1;
                x /= p;
            } else {
                primes[x] += 1;
                break;
            }
        }
        return primes;
    }

    std::map<int, int> get_canonical(int x, int* sieve) {
        std::map<int, int> primes;

        while (x > 1) {
            const int& p = sieve[x];

            if (p > 1) {
                primes[p] += 1;
                x /= p;
            } else {
                primes[x] += 1;
                break;
            }
        }
        return primes;
    }

    std::map<int, int> get_canonical(int x) {

        std::map<int, int> primes;

        for (int d = 2; d * d <= x; ++d) {
            while (x % d == 0) {
                x /= d;
                primes[d] += 1;
            }
        }

        if (x > 1) {
            primes[x] = 1;
        }
        return primes;
    }

    std::vector<int> get_divisors(int x, const std::map<int, int>& canonical) {

        std::vector<int> k(canonical.size(), 0);
        std::vector<int> primals(canonical.size(), 1);
        std::vector<std::pair<int, int>> powers(canonical.begin(), canonical.end());
        //for (auto& [p, l] : canonical) {
        //    powers.emplace_back(p, l);
        //}
        for (int i = 0; i < canonical.size(); ++i) {
            for (int j = 0; j < powers[i].second; ++j) {
                primals[i] *= powers[i].first;
            }
        }

        int number_of_divisors = 1;
        for (auto& [p, k] : powers) {
            number_of_divisors *= (1 + k);
        }

        std::vector<int> divisors(number_of_divisors);

        int divisor = 1;
        for (int i = 0; i < number_of_divisors; ++i) {

            divisors[i] = divisor;

            for (int j = 0; j < k.size(); ++j) {
                if (k[j] < powers[j].second) {
                    k[j] += 1;
                    divisor *= powers[j].first;
                    break;
                } else {
                    k[j] = 0;
                    divisor /= primals[j];
                }
            }
        }

        return divisors;
    }

    std::vector<int> get_divisors(int x, const std::vector<int>& sieve) {
        return get_divisors(x, get_canonical(x, sieve));
    }

    std::vector<int> get_divisors(int x, int* sieve) {
        return get_divisors(x, get_canonical(x, sieve));
    }

    std::vector<int> get_divisors(int x) {
        return get_divisors(x, get_canonical(x));
    }


    std::vector<int> sieve2(int N) {
        std::vector<int> primes(N+5, -1);
        for (int p = 2; p < primes.size(); ++p) {
            if (primes[p] == -1) {
                for (int i = p + p; i < primes.size(); i += p) {
                    if (primes[i] == -1) {
                        primes[i] = p;
                    }
                }
            }
        }
        return primes;
    }

    int* sieve(int N) {
        int MX = N - 1;
        //std::vector<int> s(MX+5, 0);
        int* s = new int[MX+5];
        for (int i = 0; i < MX+5; ++i)
            s[i] = 0;

        std::vector<int> primes;
        for(int i = 2; i <= MX; i++) {
            if(!s[i]) { s[i] = -1; primes.push_back(i); }
            for(int j : primes) {
                if(i * j > MX) break;
                s[i * j] = j;
                if(i % j == 0) break;
            }
        }
        return s;
    }





    template <typename T>
    int gcd(T x, T y) {
        uint64_t xx = x;
        uint64_t yy = y;
        return std::__gcd(xx, yy);
    }


}



using namespace std;
struct Solver {
void solve() {
    int t = 1;
    std::cin >> t;
    while (t--) solve_one();
}

void solve_one() {
    read(n);
    auto a = read_vector(n);
    stack<int> s;

    for (auto x : a) {
        while (true) {
            s.push(x);
            if (x % (s.size() + 1) == 0) {
                s.pop(); // x
                if (s.empty()) {
                    NO();
                    return;
                }
                s.pop();
            } else {
                break;
            }
        }
    }

    YES();

}
};
#undef int

int main() {
    IO_FAST
    Solver().solve();
    return 0;
}