human
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. 
Using python3 can you solve the prior task?

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Can you provide a Python program to print it modulo 998244353?
assistant
#Here is Python program to print it modulo 998244353.

import io
import os
from collections import deque

FILE_INPUT_MODE = 0  # 0 for BytesIO, 1 for input.txt, -1 for stdin, input()
if FILE_INPUT_MODE >= 0:

    if FILE_INPUT_MODE == 1:
        CURRENT_DIR = os.path.dirname(os.path.abspath(__file__))
        FD = os.open(f"{CURRENT_DIR}\input.txt", os.O_RDONLY)
    elif FILE_INPUT_MODE == 0:
        FD = 0
    DATA = io.BytesIO(os.read(FD, os.fstat(FD).st_size))
    if FD != 0:
        os.close(FD)

    def input():
        return DATA.readline().decode().rstrip('\r\n')

def solve():
    p = 998244353
    n = int(input())
    a = [int(word) for word in input().strip().split()]
    mex = [[0, 0] for i in range(max(a) + 2)]
    mex[0][0] = 1
    ans = 0
    for x in a:
        if x - 1 >= 0:
            ans = (ans + mex[x - 1][0] + mex[x - 1][1]) % p
        ans = (ans + mex[x][0]) % p
        ans = (ans + mex[x + 1][0] + mex[x + 1][1]) % p
        if x - 1 >= 0:
            mex[x - 1][1] = (mex[x - 1][1] * 2 + mex[x - 1][0]) % p
        mex[x + 1][0] = (mex[x + 1][0] * 2 + mex[x][0]) % p
        mex[x + 1][1] = mex[x + 1][1] * 2 % p
        # print(mex)
    print(ans)

def main():
    t = int(input())
    for _ in range(t):
        solve()

if __name__ == "__main__":
    main()