#include <bits/stdc++.h>
using namespace std;
const int Mod = 998244353;
const int MaxN = 5e5 + 5;
int T, N, Ans;
int A[MaxN], F[MaxN], G[MaxN], H[MaxN];
int tF[MaxN], tG[MaxN], tH[MaxN];
int main() {
  int i, j;
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &N);
    for (i = 0; i <= N; i++) F[i] = G[i] = H[i] = 0;
    for (Ans = 0, i = 1; i <= N; i++) {
      scanf("%d", &A[i]);
      F[A[i]] = (F[A[i]] << 1) % Mod;
      G[A[i]] = (G[A[i]] << 1) % Mod;
      H[A[i]] = (H[A[i]] << 1) % Mod;
      if (!A[i]) F[0]++;
      if (A[i] == 1) G[1]++;
      if (A[i]) F[A[i]] = (F[A[i]] + F[A[i] - 1]) % Mod;
      if (A[i] > 1) {
        G[A[i]] = (G[A[i]] + F[A[i] - 2]) % Mod;
        G[A[i]] = (G[A[i]] + H[A[i] - 2]) % Mod;
      }
      if (A[i] + 2 <= N) H[A[i]] = (H[A[i]] + G[A[i] + 2]) % Mod;
    }
    for (i = 0; i <= N; i++) {
      Ans = (Ans + F[i]) % Mod;
      Ans = (Ans + G[i]) % Mod;
      Ans = (Ans + H[i]) % Mod;
    }
    printf("%d\n", Ans);
  }
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

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;
const int Mod = 998244353;
const int MaxN = 5e5 + 5;
int T, N, Ans;
int A[MaxN], F[MaxN], G[MaxN], H[MaxN];
int tF[MaxN], tG[MaxN], tH[MaxN];
int main() {
  int i, j;
  scanf("%d", &T);
  while (T--) {
    scanf("%d", &N);
    for (i = 0; i <= N; i++) F[i] = G[i] = H[i] = 0;
    for (Ans = 0, i = 1; i <= N; i++) {
      scanf("%d", &A[i]);
      F[A[i]] = (F[A[i]] << 1) % Mod;
      G[A[i]] = (G[A[i]] << 1) % Mod;
      H[A[i]] = (H[A[i]] << 1) % Mod;
      if (!A[i]) F[0]++;
      if (A[i] == 1) G[1]++;
      if (A[i]) F[A[i]] = (F[A[i]] + F[A[i] - 1]) % Mod;
      if (A[i] > 1) {
        G[A[i]] = (G[A[i]] + F[A[i] - 2]) % Mod;
        G[A[i]] = (G[A[i]] + H[A[i] - 2]) % Mod;
      }
      if (A[i] + 2 <= N) H[A[i]] = (H[A[i]] + G[A[i] + 2]) % Mod;
    }
    for (i = 0; i <= N; i++) {
      Ans = (Ans + F[i]) % Mod;
      Ans = (Ans + G[i]) % Mod;
      Ans = (Ans + H[i]) % Mod;
    }
    printf("%d\n", Ans);
  }
  return 0;
}

```