Palindrome XOR

You are given a string s consisting of characters "1", "0", and "?". The first character of s is guaranteed to be "1". Let m be the number of characters in s.

Count the number of ways we can choose a pair of integers a, b that satisfies the following:

• 1 ≤ a < b < 2^m
• When written without leading zeros, the base-2 representations of a and b are both palindromes.
• The base-2 representation of bitwise XOR of a and b matches the pattern s. We say that t matches s if the lengths of t and s are the same and for every i, the i-th character of t is equal to the i-th character of s, or the i-th character of s is "?".

Compute this count modulo 998244353.

Input

The first line contains a single string s (1 ≤ |s| ≤ 1 000). s consists only of characters "1", "0" and "?". It is guaranteed that the first character of s is a "1".

Output

Print a single integer, the count of pairs that satisfy the conditions modulo 998244353.

Examples

Input

10110

Output

3

Input

1?0???10

Output

44

Input

1?????????????????????????????????????

Output

519569202

Input

1

Output

0

Note

For the first example, the pairs in base-2 are (111, 10001), (11, 10101), (1001, 11111).

inputFormat

Input

The first line contains a single string s (1 ≤ |s| ≤ 1 000). s consists only of characters "1", "0" and "?". It is guaranteed that the first character of s is a "1".

outputFormat

Output

Print a single integer, the count of pairs that satisfy the conditions modulo 998244353.

Examples

Input

10110

Output

3

Input

1?0???10

Output

44

Input

1?????????????????????????????????????

Output

519569202

Input

1

Output

0

Note

For the first example, the pairs in base-2 are (111, 10001), (11, 10101), (1001, 11111).

样例

1

0

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