An antique adding machine displays its running tally as a chain of digit wheels, ordered left to right from most significant to least significant; each wheel shows a value from 0 to 9. The chain never shows a redundant leading zero, except when the tally is exactly zero (a single wheel showing 0). Turning the crank once adds exactly one to the tally: digits carry to the left exactly as in ordinary addition, and if every wheel rolls over from 9 to 0 (for example 999 becoming 1000), a brand-new wheel showing 1 is added to the front of the chain. Given the current chain of wheel digits, output the chain of wheel digits after the crank is turned once.

Input format

• Line 1: an integer n, the number of wheels currently in the chain.
• Line 2: n space-separated integers d_1 ... d_n (each between 0 and 9), the digit on each wheel from leftmost (most significant) to rightmost (least significant).

Output format

Print the resulting wheel digits after the crank is turned once, space-separated on a single line, from most significant to least significant, with no leading zero unless the result is exactly the single digit 0.

Constraints

• 1 <= n <= 10^5
• 0 <= d_i <= 9
• The input never has a redundant leading zero (unless n = 1 and d_1 = 0).

3
1 2 3

1 2 4

3
9 9 9

1 0 0 0