Kevin is exploring problems related to binary strings in Chinatown. When he was at a loss, a stranger approached him and introduced a peculiar operation:

Suppose the current binary string is $$$ t $$$, with a length of $$$ \vert t \vert $$$. Choose an integer $$$ 1 \leq p \leq \vert t \vert $$$. For all $$$ 1 \leq i \lt p $$$, simultaneously perform the operation $$$ t_i = \max(t_i, t_{i+1}) $$$, and then delete $$$ t_p $$$.

For example, suppose the current binary string is 01001, and you choose $$$ p = 4 $$$. Perform $$$ t_i = \max(t_i, t_{i+1}) $$$ for $$$t_1$$$, $$$t_2$$$, and $$$ t_3 $$$, transforming the string into 11001, then delete $$$ t_4 $$$, resulting in 1101.

Kevin finds this strange operation quite interesting. Thus, he wants to ask you: Given a binary string $$$ s $$$, how many distinct non-empty binary strings can you obtain through any number of operations (possibly zero)?

Since the answer may be very large, you only need to output the result modulo $$$998\,244\,353$$$.

Input

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1\le t \le 10^4$$$) — the number of test cases.

For each test case, the only line contains a binary string $$$ s $$$ ($$$ 1 \le \lvert s \rvert \le 10^6 $$$).

It is guaranteed that the sum of $$$\lvert s \rvert$$$ over all test cases does not exceed $$$10^6$$$.

Output

For each test case, print a single integer in the only line of the output — the number of distinct non-empty binary strings you can obtain, modulo $$$998\,244\,353$$$.

Note

In the first test case, all the binary strings you can obtain are: 11001, 1001, 1101, 001, 101, 111, 01, 11, and 1. There are $$$ 9 $$$ in total.

Kevin and Strange Operation

Examples