#include <bits/stdc++.h>
using namespace std;
int const M = 5e5 + 10, N = 1e7 + 10;
long long const mod = 998244353;
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
long long T, n, m, x, y, dp[3][M], ans;
int main() {
  ios::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);
  cin >> T;
  while (T--) {
    cin >> n;
    ans = 0;
    dp[1][1] = 1;
    for (int i = 1; i <= n; ++i) {
      cin >> x;
      ++x;
      dp[1][x + 1] += dp[1][x + 1];
      dp[1][x + 1] %= mod;
      dp[1][x + 1] += dp[1][x];
      dp[1][x + 1] %= mod;
      dp[2][x + 1] += dp[2][x + 1];
      dp[2][x + 1] %= mod;
      dp[2][x - 1] += dp[2][x - 1];
      dp[2][x - 1] %= mod;
      dp[2][x - 1] += dp[1][x - 1];
      dp[2][x - 1] %= mod;
    }
    for (int i = 0; i <= n + 2; ++i) {
      ans += dp[1][i];
      dp[1][i] = 0;
      ans %= mod;
      ans += dp[2][i];
      dp[2][i] = 0;
      ans %= mod;
    }
    ans += mod;
    ans -= 1;
    ans %= mod;
    cout << ans << "\n";
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

Let's call a sequence of integers x_1, x_2, ..., x_k MEX-correct if for all i (1 ≤ i ≤ k) |x_i - \operatorname{MEX}(x_1, x_2, ..., x_i)| ≤ 1 holds. Where \operatorname{MEX}(x_1, ..., x_k) is the minimum non-negative integer that doesn't belong to the set x_1, ..., x_k. For example, \operatorname{MEX}(1, 0, 1, 3) = 2 and \operatorname{MEX}(2, 1, 5) = 0.

You are given an array a consisting of n non-negative integers. Calculate the number of non-empty MEX-correct subsequences of a given array. The number of subsequences can be very large, so print it modulo 998244353. 

Note: a subsequence of an array a is a sequence [a_{i_1}, a_{i_2}, ..., a_{i_m}] meeting the constraints 1 ≤ i_1 < i_2 < ... < i_m ≤ n. If two different ways to choose the sequence of indices [i_1, i_2, ..., i_m] yield the same subsequence, the resulting subsequence should be counted twice (i. e. two subsequences are different if their sequences of indices [i_1, i_2, ..., i_m] are not the same).

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

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

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ n).

The sum of n over all test cases doesn't exceed 5 ⋅ 10^5.

Output

For each test case, print a single integer — the number of non-empty MEX-correct subsequences of a given array, taken modulo 998244353.

Example

Input


4
3
0 2 1
2
1 0
5
0 0 0 0 0
4
0 1 2 3


Output


4
2
31
7

Note

In the first example, the valid subsequences are [0], [1], [0,1] and [0,2].

In the second example, the valid subsequences are [0] and [1].

In the third example, any non-empty subsequence is valid. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int const M = 5e5 + 10, N = 1e7 + 10;
long long const mod = 998244353;
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
long long T, n, m, x, y, dp[3][M], ans;
int main() {
  ios::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);
  cin >> T;
  while (T--) {
    cin >> n;
    ans = 0;
    dp[1][1] = 1;
    for (int i = 1; i <= n; ++i) {
      cin >> x;
      ++x;
      dp[1][x + 1] += dp[1][x + 1];
      dp[1][x + 1] %= mod;
      dp[1][x + 1] += dp[1][x];
      dp[1][x + 1] %= mod;
      dp[2][x + 1] += dp[2][x + 1];
      dp[2][x + 1] %= mod;
      dp[2][x - 1] += dp[2][x - 1];
      dp[2][x - 1] %= mod;
      dp[2][x - 1] += dp[1][x - 1];
      dp[2][x - 1] %= mod;
    }
    for (int i = 0; i <= n + 2; ++i) {
      ans += dp[1][i];
      dp[1][i] = 0;
      ans %= mod;
      ans += dp[2][i];
      dp[2][i] = 0;
      ans %= mod;
    }
    ans += mod;
    ans -= 1;
    ans %= mod;
    cout << ans << "\n";
  }
  return 0;
}

```