Letter-Coded Addition

Easy

In a children's cipher, digits are replaced by letters: a is 0, b is 1, c is 2, and so on up to j for 9. A word reads as the number written with those digits: "cab" is 201, and "aad" is 3 (leading zeros are dropped). Given three words first, second and total, return True if the number for first plus the number for second equals the number for total, and False otherwise.

Example 1

first="bc", second="d", total="bf" → True

"bc" → 12, "d" → 3, "bf" → 15, and 12 + 3 = 15.

Example 2

first="aab", second="aj", total="ba" → True

Leading as are leading zeros: 1 + 9 = 10.

Example 3

first="j", second="j", total="bh" → False

9 + 9 = 18, but "bh" stands for 17.

Constraints

1 ≤ len(first), len(second), len(total) ≤ 10
Words consist of letters from a to j

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Input

first="bc", second="d", total="bf"

Expected

True

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