Count Numbers With Distinct Neighbors

Count integers from left through right, including both endpoints, that have no equal neighboring digits. Use their usual decimal writing with no leading zeroes. Zero and all other single-digit numbers qualify.

Implement counting_numbers(left, right).

Input

left: The first allowed value.

right: The last allowed value.

Output

Return how many values satisfy the rule.

Constraints

0 ≤ left ≤ right ≤ 10¹⁸. The range may be too large to inspect each integer individually.

Examples

Input:
left = 10
right = 15

Expected output:
expected = 5

Input:
long long left = 10;
long long right = 15;

Expected output:
long long expected = 5;

Input:
long left = 10;
long right = 15;

Expected output:
long expected = 5;

Input:
left = 0
right = 9

Expected output:
expected = 10

Input:
long long left = 0;
long long right = 9;

Expected output:
long long expected = 10;

Input:
long left = 0;
long right = 9;

Expected output:
long expected = 10;

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Counting Numbers — 2220