write a go solution for Description:
You are given a positive integer n. Since n may be very large, you are given its binary representation.

You should compute the number of triples (a,b,c) with 0<=a,b,c<=n such that aoplusb, boplusc, and aoplusc are the sides of a non-degenerate triangle.

Here, oplus denotes the bitwise XOR operation.

You should output the answer modulo 998,244,353.

Three positive values x, y, and z are the sides of a non-degenerate triangle if and only if x+y>z, x+z>y, and y+z>x.

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

Note:
In the first test case, 101_2=5.

- The triple (a,b,c)=(0,3,5) is valid because (aoplusb,boplusc,coplusa)=(3,6,5) are the sides of a non-degenerate triangle.
- The triple (a,b,c)=(1,2,4) is valid because (aoplusb,boplusc,coplusa)=(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.. Output only the code with no comments, explanation, or additional text.