Description

Input

The first and only line contains the binary representation of an integer $n$ ($0 < n < 2^{200\,000}$) without leading zeros.

For example, the string 10 is the binary representation of the number $2$, while the string 1010 represents the number $10$.

Output

Print one integer — the number of triples $(a,b,c)$ satisfying the conditions described in the statement modulo $998\,244\,353$.

101

12

1110

780

11011111101010010

141427753

Note

In the first test case, $101_2=5$.

• The triple $(a, b, c) = (0, 3, 5)$ is valid because $(a\oplus b, b\oplus c, c\oplus a) = (3, 6, 5)$ are the sides of a non-degenerate triangle.
• The triple $(a, b, c) = (1, 2, 4)$ is valid because $(a\oplus b, b\oplus c, c\oplus a) = (3, 6, 5)$ are the sides of a non-degenerate triangle.

The $6$ permutations of each of these two triples are all the valid triples, thus the answer is $12$.

In the third test case, $11\,011\,111\,101\,010\,010_2=114\,514$. The full answer (before taking the modulo) is $1\,466\,408\,118\,808\,164$.