Equal Half Digit Sums

Easy

Call a number balanced if it has an even number of digits and the digits of its left half add up to the same total as the digits of its right half. For example, 1423 is balanced (1 + 4 = 2 + 3), while 121 is not, since it has an odd number of digits. Given low and high, return how many balanced numbers lie between low and high, inclusive.

Example 1

low=40, high=70 → 3

A two-digit number is balanced only when both digits match: 44, 55 and 66.

Example 2

low=2310, high=2330 → 2

The first two digits add up to 5. That fits 2314 (1 + 4), 2323 (2 + 3) and 2330 (3 + 0).

Example 3

low=100, high=999 → 0

Three-digit numbers have an odd number of digits, so none are balanced.

Constraints

1 ≤ low ≤ high ≤ 10⁴

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Topics

Math Enumeration

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Input

low=40, high=70

Expected

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