Note that the only difference between String Transformation 1 and String Transformation 2 is in the move Koa does. In this version the letter y Koa selects must be strictly greater alphabetically than x (read statement for better understanding). You can make hacks in these problems independently.

Koa the Koala has two strings A and B of the same length n (|A|=|B|=n) consisting of the first 20 lowercase English alphabet letters (ie. from a to t).

In one move Koa:

  1. selects some subset of positions p_1, p_2, …, p_k (k ≥ 1; 1 ≤ p_i ≤ n; p_i ≠ p_j if i ≠ j) of A such that A_{p_1} = A_{p_2} = … = A_{p_k} = x (ie. all letters on this positions are equal to some letter x).

  2. selects a letter y (from the first 20 lowercase letters in English alphabet) such that y>x (ie. letter y is strictly greater alphabetically than x).

  3. sets each letter in positions p_1, p_2, …, p_k to letter y. More formally: for each i (1 ≤ i ≤ k) Koa sets A_{p_i} = y.

Note that you can only modify letters in string A.




Koa wants to know the smallest number of moves she has to do to make strings equal to each other (A = B) or to determine that there is no way to make them equal. Help her!

Input

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

The first line of each test case contains one integer n (1 ≤ n ≤ 10^5) — the length of strings A and B.

The second line of each test case contains string A (|A|=n).

The third line of each test case contains string B (|B|=n).

Both strings consists of the first 20 lowercase English alphabet letters (ie. from a to t).

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case:

Print on a single line the smallest number of moves she has to do to make strings equal to each other (A = B) or -1 if there is no way to make them equal.

Example

Input


5
3
aab
bcc
4
cabc
abcb
3
abc
tsr
4
aabd
cccd
5
abcbd
bcdda


Output


2
-1
3
2
-1

Note

  * In the 1-st test case Koa: 
    1. selects positions 1 and 2 and sets A_1 = A_2 =  b (\color{red}{aa}b → \color{blue}{bb}b). 
    2. selects positions 2 and 3 and sets A_2 = A_3 =  c (b\color{red}{bb} → b\color{blue}{cc}). 

  * In the 2-nd test case Koa has no way to make string A equal B.

  * In the 3-rd test case Koa: 
    1. selects position 1 and sets A_1 =  t (\color{red}{a}bc → \color{blue}{t}bc). 
    2. selects position 2 and sets A_2 =  s (t\color{red}{b}c → t\color{blue}{s}c). 
    3. selects position 3 and sets A_3 =  r (ts\color{red}{c} → ts\color{blue}{r}). 
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<LL>;
using VVL = vector<VL>;
using VD = vector<double>;
using VVD = vector<VD>;
using PII = pair<int, int>;
using PDD = pair<double, double>;
using PLL = pair<LL, LL>;
using VPII = vector<PII>;
template <typename T>
using VT = vector<T>;
template <typename T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
const int INF = 1e9;
const int MOD = INF + 7;
const LL LLINF = 1e18;
template <typename weight_type = int>
class union_find {
  static_assert(std::is_arithmetic<weight_type>::value, "Invalid weight type");

 private:
  std::vector<int> uni;
  std::vector<int> edge_count_;
  std::vector<weight_type> weights;
  int size_;
  const void check(const int n) const {
    if (this->group_size() < 0) {
      assert(false);
    }
    if (!(0 <= n && n < this->all_size())) {
      assert(false);
    }
  }

 public:
  union_find() : uni(0), edge_count_(0), weights(0), size_(-1) {}
  union_find(const int n) : uni(n, -1), edge_count_(n), weights(n), size_(n) {
    this->check(n - 1);
  }
  union_find(const std::vector<weight_type> &_weights)
      : uni(_weights.size(), -1),
        edge_count_(_weights.size()),
        weights(_weights),
        size_(_weights.size()) {
    this->check((int)_weights.size() - 1);
  }
  bool same(const int a, const int b) {
    this->check(a);
    this->check(b);
    return this->find(a) == this->find(b);
  }
  int find(const int a) {
    this->check(a);
    return this->uni[a] < 0 ? a : this->uni[a] = this->find(this->uni[a]);
  }
  bool unite(int a, int b) {
    a = this->find(a);
    b = this->find(b);
    this->edge_count_[a]++;
    if (a == b) {
      return false;
    }
    this->size_--;
    if (this->uni[a] > this->uni[b]) {
      std::swap(a, b);
    }
    this->uni[a] += this->uni[b];
    this->weights[a] += this->weights[b];
    this->edge_count_[a] += this->edge_count_[b];
    this->uni[b] = a;
    return true;
  }
  const int group_size() const { return this->size_; }
  const int all_size() const { return this->uni.size(); }
  const int size(const int a) {
    this->check(a);
    return -this->uni[this->find(a)];
  }
  const int edge_count(const int a) {
    this->check(a);
    return this->edge_count_[this->find(a)];
  }
  const weight_type weight(const int a) {
    this->check(a);
    return this->weights[this->find(a)];
  }
};
void calc() {
  union_find<> uf(26);
  int N;
  cin >> N;
  string A, B;
  cin >> A >> B;
  int ans = 0;
  for (int(i) = 0; (i) < (N); (i)++) {
    if (A[i] > B[i]) {
      cout << -1 << "\n";
      return;
    }
    if (uf.unite(A[i] - 'a', B[i] - 'a')) {
      ans++;
    }
  }
  cout << ans << "\n";
}
int main(void) {
  int T;
  cin >> T;
  for (int(i) = 0; (i) < (T); (i)++) {
    calc();
  }
}
