#include <bits/stdc++.h>
using namespace std;
long long max(long long a, long long b) {
  if (a > b) {
    return a;
  } else {
    return b;
  }
}
long long min(long long a, long long b) {
  if (a < b) {
    return a;
  } else {
    return b;
  }
}
long long rand_int(long long l, long long r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<long long>(l, r)(gen);
}
long long power(long long b, long long e) {
  if (e == 0) return 1;
  if (e % 2)
    return ((b * power((b) * (b), (e - 1) / 2)));
  else
    return power((b) * (b), e / 2);
}
long long modpower(long long b, long long e, long long q) {
  long long MOD = q;
  if (e == 0) return 1;
  if (e % 2)
    return ((b % MOD) * modpower((b % MOD) * (b % MOD), (e - 1) / 2, q)) % MOD;
  else
    return modpower((b % MOD) * (b % MOD), e / 2, q) % MOD;
}
void dpv(vector<long long> v) {
  for (long long i = 0; i < v.size(); i++) {
    cout << v[i] << " ";
  }
  cout << '\n';
}
void dpv(vector<pair<long long, long long> > v) {
  for (long long i = 0; i < v.size(); i++) {
    cout << v[i].first << " " << v[i].second << '\n';
  }
}
void dpv(set<long long> v) {
  for (auto i : v) {
    cout << i << " ";
  }
  cout << '\n';
}
long long ceil1(long long x, long long y) {
  long long r = x / y;
  if (x % y == 0) {
    return r;
  } else {
    return r + 1;
  }
}
const long long md = 998244353;
void add(long long &x, long long y) {
  x += y;
  if (x >= md) {
    x -= md;
  }
}
void oblivious() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<long long> dp1(n + 5);
  vector<long long> dp2(n + 5);
  dp1[0] = 1;
  for (long long i = 0; i < n; i++) {
    long long x = a[i];
    add(dp1[x + 1], dp1[x + 1]);
    add(dp1[x + 1], dp1[x]);
    if (x > 0) {
      add(dp2[x - 1], dp2[x - 1]);
    }
    if (x > 0) {
      add(dp2[x - 1], dp1[x - 1]);
    }
    add(dp2[x + 1], dp2[x + 1]);
  }
  long long ans = 0;
  for (auto i : dp2) {
    add(ans, i);
  }
  for (auto i : dp1) {
    add(ans, i);
  }
  cout << (ans - 1 + md) % md << '\n';
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    oblivious();
  }
  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;
long long max(long long a, long long b) {
  if (a > b) {
    return a;
  } else {
    return b;
  }
}
long long min(long long a, long long b) {
  if (a < b) {
    return a;
  } else {
    return b;
  }
}
long long rand_int(long long l, long long r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<long long>(l, r)(gen);
}
long long power(long long b, long long e) {
  if (e == 0) return 1;
  if (e % 2)
    return ((b * power((b) * (b), (e - 1) / 2)));
  else
    return power((b) * (b), e / 2);
}
long long modpower(long long b, long long e, long long q) {
  long long MOD = q;
  if (e == 0) return 1;
  if (e % 2)
    return ((b % MOD) * modpower((b % MOD) * (b % MOD), (e - 1) / 2, q)) % MOD;
  else
    return modpower((b % MOD) * (b % MOD), e / 2, q) % MOD;
}
void dpv(vector<long long> v) {
  for (long long i = 0; i < v.size(); i++) {
    cout << v[i] << " ";
  }
  cout << '\n';
}
void dpv(vector<pair<long long, long long> > v) {
  for (long long i = 0; i < v.size(); i++) {
    cout << v[i].first << " " << v[i].second << '\n';
  }
}
void dpv(set<long long> v) {
  for (auto i : v) {
    cout << i << " ";
  }
  cout << '\n';
}
long long ceil1(long long x, long long y) {
  long long r = x / y;
  if (x % y == 0) {
    return r;
  } else {
    return r + 1;
  }
}
const long long md = 998244353;
void add(long long &x, long long y) {
  x += y;
  if (x >= md) {
    x -= md;
  }
}
void oblivious() {
  long long n;
  cin >> n;
  vector<long long> a(n);
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  vector<long long> dp1(n + 5);
  vector<long long> dp2(n + 5);
  dp1[0] = 1;
  for (long long i = 0; i < n; i++) {
    long long x = a[i];
    add(dp1[x + 1], dp1[x + 1]);
    add(dp1[x + 1], dp1[x]);
    if (x > 0) {
      add(dp2[x - 1], dp2[x - 1]);
    }
    if (x > 0) {
      add(dp2[x - 1], dp1[x - 1]);
    }
    add(dp2[x + 1], dp2[x + 1]);
  }
  long long ans = 0;
  for (auto i : dp2) {
    add(ans, i);
  }
  for (auto i : dp1) {
    add(ans, i);
  }
  cout << (ans - 1 + md) % md << '\n';
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    oblivious();
  }
  return 0;
}

```