#include <bits/stdc++.h>
using namespace std;
long long GCD(long long a, long long b) { return (a) ? GCD(b % a, a) : b; }
long long LCM(long long a, long long b) { return a * b / GCD(a, b); }
string alpha = "abcdefghijklmnopqrstuvwxyz";
int divisor(int number) {
  int i;
  for (i = 2; i <= sqrt(number); i++) {
    if (number % i == 0) {
      return number / i;
    }
  }
  return 1;
}
int myXOR(int x, int y) {
  int res = 0;
  for (int i = 31; i >= 0; i--) {
    bool b1 = x & (1 << i);
    bool b2 = y & (1 << i);
    bool xoredBit = (b1 & b2) ? 0 : (b1 | b2);
    res <<= 1;
    res |= xoredBit;
  }
  return res;
}
void printDivisors(int n, vector<int>& v) {
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i && i > 1)
        v.push_back(i);
      else {
        if (i > 1) v.push_back(i);
        if (n / i > 1) v.push_back(n / i);
      }
    }
  }
}
int bin(vector<int> vec, int val) {
  int l = 0, r = vec.size() - 1, mid = r / 2;
  while (l <= r) {
    mid = (l + r) / 2;
    if (vec[mid] < val && vec[mid + 1] > val) {
      if (vec[mid + 1] == val) return mid + 1;
      return mid;
    } else if (vec[mid] > val) {
      r = mid - 1;
    } else if (vec[mid] < val) {
      l = mid + 1;
    } else if (vec[mid] == val)
      return mid;
  }
  return -1;
}
void clear(vector<bool> v) {
  for (int i = 0; i < v.size(); i++) v[i] = 0;
}
bool comp(const string& s1, const string& s2) { return s2 + s1 < s1 + s2; }
vector<string> split(const string& s, char delim) {
  vector<string> result;
  stringstream ss(s);
  string item;
  while (getline(ss, item, delim)) {
    result.push_back(item);
  }
  return result;
}
int countWords(string str) {
  stringstream s(str);
  string word;
  int count = 0;
  while (s >> word) count++;
  return count;
}
long long power(long long x, long long y, long long p, int& c) {
  int res = 1;
  if (x >= p) c++;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) {
      if (res * x >= p) c++;
      res = (res * x) % p;
    }
    y = y >> 1;
    if (x * x >= p) c++;
    x = (x * x) % p;
  }
  return res;
}
bool isPalindrome(string str) {
  int l = 0;
  int h = str.length() - 1;
  while (h > l) {
    if (str[l++] != str[h--]) {
      return 0;
    }
  }
  return 1;
}
bool checkMuns(vector<int> vec) {
  for (int i = 0; i < (int)(vec.size()); ++i) {
    if (vec[i] < 0) return 0;
  }
  return 1;
}
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long ceiLl(long long x, long long y) { return (x + y - 1) / y; }
vector<long long> divisors(long long n) {
  vector<long long> ans;
  long long i = 1;
  for (; i * i < n; i++) {
    if (n % i == 0) {
      ans.push_back(i);
      ans.push_back(n / i);
    }
  }
  if (i * i == n) ans.push_back(i);
  return ans;
}
vector<long long> findDivisors(long long n) {
  if (n == 1) return vector<long long>(1, 0);
  vector<long long> numFactors(n + 1);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j * i <= n; j++) numFactors[i * j]++;
  }
  return numFactors;
}
vector<long long> factorization(long long n) {
  vector<long long> primes;
  for (long long i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      primes.push_back(i);
      while (n % i == 0) {
        n /= i;
      }
    }
  }
  if (n > 1) primes.push_back(n);
  return primes;
}
bool isSubSeq(string a, string b) {
  int idx = 0;
  for (int i = 0; i < a.length(); i++) {
    if (a[i] == b[idx]) idx++;
  }
  if (idx == b.length())
    return 1;
  else
    return 0;
}
bool isSubSeq(vector<int> a, vector<int> b) {
  int idx = 0;
  for (int i = 0; i < a.size(); i++) {
    if (b.size() == idx) break;
    if (a[i] == b[idx]) idx++;
  }
  if (idx == b.size())
    return 1;
  else
    return 0;
}
bool isSubStr(string a, string b) {
  for (int i = 0; i < a.length(); i++) {
    if (a.substr(i, b.length()) == b) return 1;
  }
  return 0;
}
bool sortbysec(const pair<int, int>& a, const pair<int, int>& b) {
  return (a.second < b.second);
}
string bin(unsigned n) {
  string ans = "";
  unsigned i;
  for (i = 1 << 20; i > 0; i = i / 2) (n & i) ? ans += '1' : ans += '0';
  return ans;
}
string leftrotate(string a, int d) {
  string s = a;
  reverse(s.begin(), s.begin() + d);
  reverse(s.begin() + d, s.end());
  reverse(s.begin(), s.end());
  return s;
}
string rightrotate(string a, int d) {
  string s = a;
  return leftrotate(s, s.length() - d);
}
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long findlcm(vector<long long> arr, int n) {
  long long ans = arr[0];
  for (int i = 1; i < n; i++) ans = (((arr[i] * ans)) / (gcd(arr[i], ans)));
  return ans;
}
int modInverse(int a, int m) {
  a = a % m;
  for (int x = 1; x < m; x++)
    if ((a * x) % m == 1) return x;
}
long long findGCD(vector<long long> arr) {
  int n = arr.size();
  long long result = arr[0];
  for (int i = 1; i < n; i++) {
    result = gcd(arr[i], result);
    if (result == 1) {
      return 1;
    }
  }
  return result;
}
long long countDivisors(long long n) {
  long long cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  for (long long i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
bool arePair(char L, char R) {
  if (L == '(' && R == ')')
    return 1;
  else if (L == '{' && R == '}')
    return 1;
  else if (L == '[' && R == ']')
    return 1;
  else if (L == '<' && R == '>')
    return 1;
  return 0;
}
int areBalanced(string e) {
  stack<char> s;
  int zz = 0;
  for (int i = 0; i < e.length(); i++) {
    if (e[i] == '(' || e[i] == '[' || e[i] == '{' || e[i] == '<')
      s.push(e[i]);
    else if (e[i] == ')' || e[i] == ']' || e[i] == '}' || e[i] == '>') {
      if (s.empty() || !arePair(s.top(), e[i]))
        zz++;
      else
        s.pop();
    }
  }
  return zz + s.size();
}
bool sortbyssec1(const pair<int, int>& a, const pair<int, int>& b) {
  if (a.first < b.first) return 1;
  if (a.first == b.first && a.second > b.second) return 1;
  return 0;
}
bool sortbyt(const pair<int, int>& a, const pair<int, int>& b) {
  if (a.first < b.first)
    return 1;
  else if (a.first == b.first && a.second > b.second)
    return 1;
  return 0;
}
long long bs() {
  long long lw = 0, hi = 0, mid;
  long long be = 0;
  while (lw < hi) {
    mid = 1 + lw + (hi - lw) / 2;
    if (1)
      lw = mid;
    else
      hi = mid - 1;
  }
  return lw;
}
struct abass {
  int a, b;
  abass(int A, int B) {
    a = A;
    b = B;
  }
  bool operator<(const abass& ga) const {
    if (b / a < ga.b / ga.a) return 1;
    return 0;
  }
};
long long nCr(int n, int r) {
  long long p = 1, k = 1;
  if (n < r) return 0;
  if (n - r < r) r = n - r;
  if (r != 0) {
    while (r) {
      p *= n;
      k *= r;
      long long m = GCD(p, k);
      p /= m;
      k /= m;
      n--;
      r--;
    }
  } else
    p = 1;
  return p;
}
void solve() {}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tt = 1;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> vec(n);
    for (int i = 0; i < n; i++) cin >> vec[i];
    sort(((vec).begin()), ((vec).end()));
    vector<int> rem1;
    vector<int> rem2;
    bool ok = 0;
    vector<int> vis1(n + 1, 0);
    for (int i = 0; i < n; i++) {
      if (vec[i] <= n && !vis1[vec[i]]) {
        vis1[vec[i]]++;
        continue;
      }
      rem1.push_back(vec[i]);
    }
    for (int i = 0; i < n; i++) {
      if (!vis1[i + 1]) rem2.push_back(i + 1);
    }
    int num = 0;
    for (int i = 0; i < rem1.size(); i++) {
      long long fi = rem1[i];
      long long se = rem2[i];
      if (fi % (fi - (se)) == se) {
        num++;
      } else
        break;
    }
    if (num == rem2.size())
      cout << num;
    else
      cout << -1;
    cout << endl;
  }
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Paprika loves permutations. She has an array a_1, a_2, ..., a_n. She wants to make the array a permutation of integers 1 to n.

In order to achieve this goal, she can perform operations on the array. In each operation she can choose two integers i (1 ≤ i ≤ n) and x (x > 0), then perform a_i := a_i mod x (that is, replace a_i by the remainder of a_i divided by x). In different operations, the chosen i and x can be different.

Determine the minimum number of operations needed to make the array a permutation of integers 1 to n. If it is impossible, output -1.

A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

Input

Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

The first line of each test case contains an 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 does not exceed 2 ⋅ 10^5.

Output

For each test case, output the minimum number of operations needed to make the array a permutation of integers 1 to n, or -1 if it is impossible.

Example

Input


4
2
1 7
3
1 5 4
4
12345678 87654321 20211218 23571113
9
1 2 3 4 18 19 5 6 7


Output


1
-1
4
2

Note

For the first test, the only possible sequence of operations which minimizes the number of operations is: 

  * Choose i=2, x=5. Perform a_2 := a_2 mod 5 = 2. 



For the second test, it is impossible to obtain a permutation of integers from 1 to n.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long GCD(long long a, long long b) { return (a) ? GCD(b % a, a) : b; }
long long LCM(long long a, long long b) { return a * b / GCD(a, b); }
string alpha = "abcdefghijklmnopqrstuvwxyz";
int divisor(int number) {
  int i;
  for (i = 2; i <= sqrt(number); i++) {
    if (number % i == 0) {
      return number / i;
    }
  }
  return 1;
}
int myXOR(int x, int y) {
  int res = 0;
  for (int i = 31; i >= 0; i--) {
    bool b1 = x & (1 << i);
    bool b2 = y & (1 << i);
    bool xoredBit = (b1 & b2) ? 0 : (b1 | b2);
    res <<= 1;
    res |= xoredBit;
  }
  return res;
}
void printDivisors(int n, vector<int>& v) {
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i && i > 1)
        v.push_back(i);
      else {
        if (i > 1) v.push_back(i);
        if (n / i > 1) v.push_back(n / i);
      }
    }
  }
}
int bin(vector<int> vec, int val) {
  int l = 0, r = vec.size() - 1, mid = r / 2;
  while (l <= r) {
    mid = (l + r) / 2;
    if (vec[mid] < val && vec[mid + 1] > val) {
      if (vec[mid + 1] == val) return mid + 1;
      return mid;
    } else if (vec[mid] > val) {
      r = mid - 1;
    } else if (vec[mid] < val) {
      l = mid + 1;
    } else if (vec[mid] == val)
      return mid;
  }
  return -1;
}
void clear(vector<bool> v) {
  for (int i = 0; i < v.size(); i++) v[i] = 0;
}
bool comp(const string& s1, const string& s2) { return s2 + s1 < s1 + s2; }
vector<string> split(const string& s, char delim) {
  vector<string> result;
  stringstream ss(s);
  string item;
  while (getline(ss, item, delim)) {
    result.push_back(item);
  }
  return result;
}
int countWords(string str) {
  stringstream s(str);
  string word;
  int count = 0;
  while (s >> word) count++;
  return count;
}
long long power(long long x, long long y, long long p, int& c) {
  int res = 1;
  if (x >= p) c++;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) {
      if (res * x >= p) c++;
      res = (res * x) % p;
    }
    y = y >> 1;
    if (x * x >= p) c++;
    x = (x * x) % p;
  }
  return res;
}
bool isPalindrome(string str) {
  int l = 0;
  int h = str.length() - 1;
  while (h > l) {
    if (str[l++] != str[h--]) {
      return 0;
    }
  }
  return 1;
}
bool checkMuns(vector<int> vec) {
  for (int i = 0; i < (int)(vec.size()); ++i) {
    if (vec[i] < 0) return 0;
  }
  return 1;
}
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  if (x == 0) return 0;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long ceiLl(long long x, long long y) { return (x + y - 1) / y; }
vector<long long> divisors(long long n) {
  vector<long long> ans;
  long long i = 1;
  for (; i * i < n; i++) {
    if (n % i == 0) {
      ans.push_back(i);
      ans.push_back(n / i);
    }
  }
  if (i * i == n) ans.push_back(i);
  return ans;
}
vector<long long> findDivisors(long long n) {
  if (n == 1) return vector<long long>(1, 0);
  vector<long long> numFactors(n + 1);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j * i <= n; j++) numFactors[i * j]++;
  }
  return numFactors;
}
vector<long long> factorization(long long n) {
  vector<long long> primes;
  for (long long i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      primes.push_back(i);
      while (n % i == 0) {
        n /= i;
      }
    }
  }
  if (n > 1) primes.push_back(n);
  return primes;
}
bool isSubSeq(string a, string b) {
  int idx = 0;
  for (int i = 0; i < a.length(); i++) {
    if (a[i] == b[idx]) idx++;
  }
  if (idx == b.length())
    return 1;
  else
    return 0;
}
bool isSubSeq(vector<int> a, vector<int> b) {
  int idx = 0;
  for (int i = 0; i < a.size(); i++) {
    if (b.size() == idx) break;
    if (a[i] == b[idx]) idx++;
  }
  if (idx == b.size())
    return 1;
  else
    return 0;
}
bool isSubStr(string a, string b) {
  for (int i = 0; i < a.length(); i++) {
    if (a.substr(i, b.length()) == b) return 1;
  }
  return 0;
}
bool sortbysec(const pair<int, int>& a, const pair<int, int>& b) {
  return (a.second < b.second);
}
string bin(unsigned n) {
  string ans = "";
  unsigned i;
  for (i = 1 << 20; i > 0; i = i / 2) (n & i) ? ans += '1' : ans += '0';
  return ans;
}
string leftrotate(string a, int d) {
  string s = a;
  reverse(s.begin(), s.begin() + d);
  reverse(s.begin() + d, s.end());
  reverse(s.begin(), s.end());
  return s;
}
string rightrotate(string a, int d) {
  string s = a;
  return leftrotate(s, s.length() - d);
}
int gcd(int a, int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long findlcm(vector<long long> arr, int n) {
  long long ans = arr[0];
  for (int i = 1; i < n; i++) ans = (((arr[i] * ans)) / (gcd(arr[i], ans)));
  return ans;
}
int modInverse(int a, int m) {
  a = a % m;
  for (int x = 1; x < m; x++)
    if ((a * x) % m == 1) return x;
}
long long findGCD(vector<long long> arr) {
  int n = arr.size();
  long long result = arr[0];
  for (int i = 1; i < n; i++) {
    result = gcd(arr[i], result);
    if (result == 1) {
      return 1;
    }
  }
  return result;
}
long long countDivisors(long long n) {
  long long cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  for (long long i = 2; i * i <= n; i++)
    if (n % i == 0) return false;
  return true;
}
bool arePair(char L, char R) {
  if (L == '(' && R == ')')
    return 1;
  else if (L == '{' && R == '}')
    return 1;
  else if (L == '[' && R == ']')
    return 1;
  else if (L == '<' && R == '>')
    return 1;
  return 0;
}
int areBalanced(string e) {
  stack<char> s;
  int zz = 0;
  for (int i = 0; i < e.length(); i++) {
    if (e[i] == '(' || e[i] == '[' || e[i] == '{' || e[i] == '<')
      s.push(e[i]);
    else if (e[i] == ')' || e[i] == ']' || e[i] == '}' || e[i] == '>') {
      if (s.empty() || !arePair(s.top(), e[i]))
        zz++;
      else
        s.pop();
    }
  }
  return zz + s.size();
}
bool sortbyssec1(const pair<int, int>& a, const pair<int, int>& b) {
  if (a.first < b.first) return 1;
  if (a.first == b.first && a.second > b.second) return 1;
  return 0;
}
bool sortbyt(const pair<int, int>& a, const pair<int, int>& b) {
  if (a.first < b.first)
    return 1;
  else if (a.first == b.first && a.second > b.second)
    return 1;
  return 0;
}
long long bs() {
  long long lw = 0, hi = 0, mid;
  long long be = 0;
  while (lw < hi) {
    mid = 1 + lw + (hi - lw) / 2;
    if (1)
      lw = mid;
    else
      hi = mid - 1;
  }
  return lw;
}
struct abass {
  int a, b;
  abass(int A, int B) {
    a = A;
    b = B;
  }
  bool operator<(const abass& ga) const {
    if (b / a < ga.b / ga.a) return 1;
    return 0;
  }
};
long long nCr(int n, int r) {
  long long p = 1, k = 1;
  if (n < r) return 0;
  if (n - r < r) r = n - r;
  if (r != 0) {
    while (r) {
      p *= n;
      k *= r;
      long long m = GCD(p, k);
      p /= m;
      k /= m;
      n--;
      r--;
    }
  } else
    p = 1;
  return p;
}
void solve() {}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tt = 1;
  cin >> tt;
  while (tt--) {
    int n;
    cin >> n;
    vector<int> vec(n);
    for (int i = 0; i < n; i++) cin >> vec[i];
    sort(((vec).begin()), ((vec).end()));
    vector<int> rem1;
    vector<int> rem2;
    bool ok = 0;
    vector<int> vis1(n + 1, 0);
    for (int i = 0; i < n; i++) {
      if (vec[i] <= n && !vis1[vec[i]]) {
        vis1[vec[i]]++;
        continue;
      }
      rem1.push_back(vec[i]);
    }
    for (int i = 0; i < n; i++) {
      if (!vis1[i + 1]) rem2.push_back(i + 1);
    }
    int num = 0;
    for (int i = 0; i < rem1.size(); i++) {
      long long fi = rem1[i];
      long long se = rem2[i];
      if (fi % (fi - (se)) == se) {
        num++;
      } else
        break;
    }
    if (num == rem2.size())
      cout << num;
    else
      cout << -1;
    cout << endl;
  }
  return 0;
}

```