The Right Tip

During the recent Football Worldcup, a group of friends worked at a courtyard café to pay for their holidays. Everyday they would collect all the tips given by the customers on a jar, and at the end of the day they wanted to split the tips equally between them. After a few days, they reached the conclusion that (given the various face values of euro coins) sometimes it was not possible to equally split the collect of the day between them.

Write a program to help the friends determine if it is possible (or not) to equally split the collect of the day between them.

Input

The input will consist of a sequence of pairs of lines, each pair represents a coin division problem to be solved. For each such pair the first line contains the number of friends (a positive integer not greater than 5). The second line contains eight space separated non-negative integers n₁, n₂,..., n₈, where n_i is the number of coins of value i (0.01, 0.02, 0.05, 0.10, 0.20, 0.50, 1.00 and 2.00 euros respectively, e.g., the number of 5 cents coins will be denoted by n₃). The maximum number of coins is 10000. Input is terminated by a single line with the number -1.

Output

For each coin division problem print either "yes" or "no", depending on whether it is possible or not to divide equally the tips by the friends.

Sample Input

2

1 1 1 1 1 1 1 1

2

2 1 2 1 5 2 2 1

1

3423 234 324 972 740 12 234 901

4

147 5502 3486 434 76 66 267 20

5

3015 3590 1559 1219 78 507 23 8

-1

Sample Output

no

yes

yes

no

yes