Codeforces Round #452 (Div. 2) ABC

A. Splitting in Teams

There were n groups of students which came to write a training contest. A group is either one person who can write the contest with anyone else, or two people who want to write the contest in the same team.

The coach decided to form teams of exactly three people for this training. Determine the maximum number of teams of three people he can form. It is possible that he can't use all groups to form teams. For groups of two, either both students should write the contest, or both should not. If two students from a group of two will write the contest, they should be in the same team.

Input

The first line contains single integer n (2 ≤ n ≤ 2·105) — the number of groups.

The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 2), where ai is the number of people in group i.

Output

Print the maximum number of teams of three people the coach can form.

Examples

input

4
1 1 2 1

output

1

input

2
2 2

output

0

input

7
2 2 2 1 1 1 1

output

3

input

3
1 1 1

output

1

Note

In the first example the coach can form one team. For example, he can take students from the first, second and fourth groups.

In the second example he can't make a single team.

In the third example the coach can form three teams. For example, he can do this in the following way:

• The first group (of two people) and the seventh group (of one person),
• The second group (of two people) and the sixth group (of one person),
• The third group (of two people) and the fourth group (of one person).

求可以组成3个人一队的数量，两个人的一队必须和一个人的一队组成一队

水题

n = int(input())
li = list(map(int,input().split()))
a = li.count(1)
b = li.count(2)
print(min(a,b)+int((a-min(a,b))/3))

B. Months and Years

 

Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December.

A year is leap in one of two cases: either its number is divisible by 4, but not divisible by 100, or is divisible by 400. For example, the following years are leap: 2000, 2004, but years 1900 and 2018 are not leap.

In this problem you are given n (1 ≤ n ≤ 24) integers a1, a2, ..., an, and you have to check if these integers could be durations in days of nconsecutive months, according to Gregorian calendar. Note that these months could belong to several consecutive years. In other words, check if there is a month in some year, such that its duration is a1 days, duration of the next month is a2 days, and so on.

Input

The first line contains single integer n (1 ≤ n ≤ 24) — the number of integers.

The second line contains n integers a1, a2, ..., an (28 ≤ ai ≤ 31) — the numbers you are to check.

Output

If there are several consecutive months that fit the sequence, print "YES" (without quotes). Otherwise, print "NO" (without quotes).

You can print each letter in arbitrary case (small or large).

Examples

input

4
31 31 30 31

output

Yes

input

2
30 30

output

No

input

5
29 31 30 31 30

output

Yes

input

3
31 28 30

output

No

input

3
31 31 28

output

Yes

Note

In the first example the integers can denote months July, August, September and October.

In the second example the answer is no, because there are no two consecutive months each having 30 days.

In the third example the months are: February (leap year) — March — April – May — June.

In the fourth example the number of days in the second month is 28, so this is February. March follows February and has 31 days, but not 30, so the answer is NO.

In the fifth example the months are: December — January — February (non-leap year).

给n个数字，分别是一些月份的天数，是否存在一个连续的月份符合。

三年一润，字符串弄大一点，求是否在这个字符串里就行。

a1 = '31 28 31 30 31 30 31 31 30 31 30 31 '
a2 = '31 29 31 30 31 30 31 31 30 31 30 31 '
s = a1 + a1 + a1 + a2 + a1 + a1
n = input()
ss = input().strip()
print(["NO",'YES'][ss in s])

C. Dividing the numbers

 

Petya has n integers: 1, 2, 3, ..., n. He wants to split these integers in two non-empty groups in such a way that the absolute difference of sums of integers in each group is as small as possible.

Help Petya to split the integers. Each of n integers should be exactly in one group.

Input

The first line contains a single integer n (2 ≤ n ≤ 60 000) — the number of integers Petya has.

Output

Print the smallest possible absolute difference in the first line.

In the second line print the size of the first group, followed by the integers in that group. You can print these integers in arbitrary order. If there are multiple answers, print any of them.

Examples

input

4

output

0
2 1 4 

input

2

output

1
1 1 

Note

In the first example you have to put integers 1 and 4 in the first group, and 2 and 3 in the second. This way the sum in each group is 5, and the absolute difference is 0.

In the second example there are only two integers, and since both groups should be non-empty, you have to put one integer in the first group and one in the second. This way the absolute difference of sums of integers in each group is 1.

 n个数字，分别是1,2,3,4,.....n  把n个数字分成两组，尽可能的使的两组的相差最小。

贪心思路，先从大的开始分，依次分给最小的那堆就行

n = int(input())
a  = []
ans1 = ans2 = 0
for i in range(n,0,-1):
    if ans1 > ans2 :
        ans2 += i
    else :
        ans1 += i
        a.append(i)
print(abs(ans1-ans2))
print(len(a),*a)