#include <bits/stdc++.h>
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse-lm")
using namespace std;
const int N = 5e5 + 10;
int a[N];
int n;
long long pw[N];
int main() {
  pw[0] = 1;
  for (int i = 1; i < N; i++) pw[i] = pw[i - 1] * 2ll % 998244353;
  int _;
  scanf("%d", &_);
  while (_--) {
    scanf("%d", &n);
    vector<long long> mp(n + 10, 0), cnt(n + 10, 0), dp(n + 10, 0);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]), mp[a[i]]++;
    long long ans = 0;
    for (int i = 1; i <= n; i++) {
      cnt[a[i]]++;
      long long t = dp[a[i]] + (a[i] ? dp[a[i] - 1] : 1);
      ans = (ans + t) % 998244353;
      if (a[i] >= 2)
        ans = (ans +
               dp[a[i] - 2] *
                   pw[mp[a[i]] - cnt[a[i]] + mp[a[i] - 2] - cnt[a[i] - 2]]) %
              998244353;
      dp[a[i]] = (dp[a[i]] + t) % 998244353;
    }
    cout << (ans + pw[mp[1]] - 1) % 998244353 << '\n';
  }
  return 0;
}

### Prompt

Please create a solution in Cpp 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>
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse-lm")
using namespace std;
const int N = 5e5 + 10;
int a[N];
int n;
long long pw[N];
int main() {
  pw[0] = 1;
  for (int i = 1; i < N; i++) pw[i] = pw[i - 1] * 2ll % 998244353;
  int _;
  scanf("%d", &_);
  while (_--) {
    scanf("%d", &n);
    vector<long long> mp(n + 10, 0), cnt(n + 10, 0), dp(n + 10, 0);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]), mp[a[i]]++;
    long long ans = 0;
    for (int i = 1; i <= n; i++) {
      cnt[a[i]]++;
      long long t = dp[a[i]] + (a[i] ? dp[a[i] - 1] : 1);
      ans = (ans + t) % 998244353;
      if (a[i] >= 2)
        ans = (ans +
               dp[a[i] - 2] *
                   pw[mp[a[i]] - cnt[a[i]] + mp[a[i] - 2] - cnt[a[i] - 2]]) %
              998244353;
      dp[a[i]] = (dp[a[i]] + t) % 998244353;
    }
    cout << (ans + pw[mp[1]] - 1) % 998244353 << '\n';
  }
  return 0;
}

```