human
Can you provide a Python code to print it modulo 998244353 given the following:
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. 
impor
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#Here is Python code to print it modulo 998244353.
t sys

# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = 18446744073709551615
inf = 4294967295
# md = 10**9+7
md = 998244353

def solve(n, aa):
    m1 = [0]*(n+2)
    m2 = [0]*(n+2)
    m1[0] = 1
    ans = 0
    for a in aa:
        if a-1 >= 0:
            ans += m1[a-1]+m2[a-1]
            m2[a-1] += m1[a-1]+m2[a-1]
            m2[a-1] %= md
        ans += m1[a]+m1[a+1]+m2[a+1]
        m1[a+1] += m1[a]+m1[a+1]
        m2[a+1] *= 2
        m1[a+1] %= md
        m2[a+1] %= md
        ans %= md
        # print(a, ans)
        # print(m1)
        # print(m2)
    print(ans)

def solve2(n, aa):
    def ok(bit):
        st = set()
        for i, a in enumerate(aa):
            if bit >> i & 1 == 0: continue
            st.add(a)
            for b in range(n+1):
                if b not in st:
                    if abs(b-a) > 1: return False
                    break
        return True

    ans = 0
    for bit in range(1, 1 << n):
        if ok(bit):
            ans += 1
            print(bin(bit)[2:].zfill(n)[::-1])
    print(ans)

for testcase in range(II()):
    n = II()
    aa = LI()
    solve(n, aa)
    # solve2(n,aa)