#include <bits/stdc++.h>
using namespace std;
const int MOD = 998244353;
int add(int x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
  return x;
}
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    vector<int> dp1(n + 2), dp2(n + 2);
    dp1[0] = 1;
    while (n--) {
      int x;
      scanf("%d", &x);
      dp1[x + 1] = add(dp1[x + 1], dp1[x + 1]);
      dp1[x + 1] = add(dp1[x + 1], dp1[x]);
      if (x > 0) dp2[x - 1] = add(dp2[x - 1], dp2[x - 1]);
      if (x > 0) dp2[x - 1] = add(dp2[x - 1], dp1[x - 1]);
      dp2[x + 1] = add(dp2[x + 1], dp2[x + 1]);
    }
    int ans = 0;
    for (int x : dp1) ans = add(ans, x);
    for (int x : dp2) ans = add(ans, x);
    printf("%d\n", add(ans, MOD - 1));
  }
}

### Prompt

Please formulate a CPP solution to 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;
int add(int x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
  return x;
}
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    vector<int> dp1(n + 2), dp2(n + 2);
    dp1[0] = 1;
    while (n--) {
      int x;
      scanf("%d", &x);
      dp1[x + 1] = add(dp1[x + 1], dp1[x + 1]);
      dp1[x + 1] = add(dp1[x + 1], dp1[x]);
      if (x > 0) dp2[x - 1] = add(dp2[x - 1], dp2[x - 1]);
      if (x > 0) dp2[x - 1] = add(dp2[x - 1], dp1[x - 1]);
      dp2[x + 1] = add(dp2[x + 1], dp2[x + 1]);
    }
    int ans = 0;
    for (int x : dp1) ans = add(ans, x);
    for (int x : dp2) ans = add(ans, x);
    printf("%d\n", add(ans, MOD - 1));
  }
}

```