Lottery

At the Aizu Festival, we have a lottery contest. In a box, there is a set of lottery tickets with integers from $1$ to $N$ written on each of them, and there are several unlucky tickets with nothing written on them. $N$ people participate and draw lots in turn. The person who draws the lottery draws the lottery as many times as he/she can until the numbered lottery ticket is drawn. If the person draws a unlucky ticket, he/she puts it back in the box. If the person draws a lottery ticket that has a number on it, he/she gives the ticket to the staff instead of putting it back in the box. The order of ranking is determined by the product of the number written on the lottery ticket and the number of times the lottery ticket is drawn, in ascending order. Prizes are then awarded according to the ranking.

Mr. Hijikata was looking forward to seeing which prize his friend Mr. Kondo, who participated in the raffle, would get. However, when everyone had finished drawing the lots, he was called away suddenly and could not be there for the announcement of the rankings. Hijikata-san knows how many times each participant drew the lottery, but he does not know the number written on the lottery ticket that each person drew.

Given the number of times each participant, including Mr. Kondo, has drawn lots, create a program to find the highest possible ranking that Mr. Kondo can be. However, people whose products have the same value are assumed to have the same rank. Specifically, if there are $m$ people whose product is smaller than that of Mr. A, then Mr. A's rank will be $m+1$.

Input

The input is given in the following format.

$N$
$r$
$r_1$
$r_2$
:
$r_{N-1}$

The first line gives the number of participants in the lottery, $N$ ($2 \leq N \leq 100$), and the second line gives the number of times Mr. Kondo drew the lottery, $r$ ($1 \leq r \leq 200$). In the following $N-1$ line, the number of times the other participants drew the lottery $r_i$ $(1 \leq r_i \leq 200$) is given.

Output

Output the highest possible ranking that Mr. Kondo can be on a single line.

Sample Input and Output

Sample Input 1

5
3
2
1
1
4

Sample Output 1

1

Sample Input 2

5
6
4
1
8
2

Sample Output 2

2

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