#include <bits/stdc++.h>
using namespace std;
int add(int x, int y) {
  x += y;
  if (x >= 998244353) x -= 998244353;
  return x;
}
void main0() {
  int n;
  cin >> n;
  vector<int> dp1(n + 2, 0), dp2(n + 2, 0);
  dp1[0] = 1;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> 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]);
      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 i = 0; i < n + 2; i++) ans = add(ans, dp1[i]);
  for (int i = 0; i < n + 2; i++) ans = add(ans, dp2[i]);
  cout << add(ans, 998244353 - 1) << "\n";
}
int main() {
  int t;
  cin >> t;
  while (t--) main0();
  return 0;
}

### Prompt

Your challenge is to write 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;
int add(int x, int y) {
  x += y;
  if (x >= 998244353) x -= 998244353;
  return x;
}
void main0() {
  int n;
  cin >> n;
  vector<int> dp1(n + 2, 0), dp2(n + 2, 0);
  dp1[0] = 1;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> 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]);
      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 i = 0; i < n + 2; i++) ans = add(ans, dp1[i]);
  for (int i = 0; i < n + 2; i++) ans = add(ans, dp2[i]);
  cout << add(ans, 998244353 - 1) << "\n";
}
int main() {
  int t;
  cin >> t;
  while (t--) main0();
  return 0;
}

```