A utility stores each meter reading as a singly linked chain of decimal digits, most-significant digit at the head (natural reading order). Given two such readings, compute their sum and output it as a digit chain, most-significant digit first, with no leading zeros (the value zero is the single digit 0). Input chains may contain leading zeros; the value is the number they spell.

Input format

Line 1: an integer p, the number of digits in reading A (p >= 1). Line 2: p space-separated digits (each 0-9) of reading A, most-significant first. Line 3: an integer q, the number of digits in reading B (q >= 1). Line 4: q space-separated digits (each 0-9) of reading B, most-significant first.

Output format

Line 1: the number of digits in the sum. Line 2: the digits of the sum, most-significant first, space-separated, with no leading zeros.

Constraints

• 1 <= p, q <= 5000
• Each digit is between 0 and 9.

3
1 2 3
2
4 5

3
1 6 8

2
9 9
1
1

3
1 0 0