You are given a binary string $s$. A binary string is a string consisting of characters 0 and/or 1.

You can perform the following operation on $s$ any number of times (even zero):

• choose an integer $i$ such that $1 \le i \le |s|$, then erase the character $s_i$.

You have to make $s$ alternating, i. e. after you perform the operations, every two adjacent characters in $s$ should be different.

Your goal is to calculate two values:

• the minimum number of operations required to make $s$ alternating;
• the number of different shortest sequences of operations that make $s$ alternating. Two sequences of operations are different if in at least one operation, the chosen integer $i$ is different in these two sequences.

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

Each test case consists of one line containing the string $s$ ($1 \le |s| \le 2 \cdot 10^5$). The string $s$ consists of characters 0 and/or 1 only.

Additional constraint on the input:

• the total length of strings $s$ over all test cases does not exceed $2 \cdot 10^5$.

For each test case, print two integers: the minimum number of operations you have to perform, and the number of different shortest sequences of operations. Since the second number might be large, print its remainder modulo $998244353$.