E. Restore Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

While discussing a proper problem A for a Codeforces Round, Kostya created a cyclic array of positive integers $a_1, a_2, \ldots, a_n$. Since the talk was long and not promising, Kostya created a new cyclic array $b_1, b_2, \ldots, b_{n}$ so that $b_i = (a_i \mod a_{i + 1})$, where we take $a_{n+1} = a_1$. Here $mod$ is the modulo operation. When the talk became interesting, Kostya completely forgot how array $a$ had looked like. Suddenly, he thought that restoring array $a$ from array $b$ would be an interesting problem (unfortunately, not A).

Input

The first line contains a single integer $n$ ($2 \le n \le 140582$) — the length of the array $a$.

The second line contains $n$ integers $b_1, b_2, \ldots, b_{n}$ ($0 \le b_i \le 187126$).

Output

If it is possible to restore some array $a$ of length $n$ so that $b_i = a_i \mod a_{(i \mod n) + 1}$ holds for all $i = 1, 2, \ldots, n$, print «YES» in the first line and the integers $a_1, a_2, \ldots, a_n$ in the second line. All $a_i$ should satisfy $1 \le a_i \le 10^{18}$. We can show that if an answer exists, then an answer with such constraint exists as well.

It it impossible to restore any valid $a$, print «NO» in one line.

You can print each letter in any case (upper or lower).

Examples
Input
41 3 1 0
Output
YES1 3 5 2
Input
24 4
Output
NO
Note

In the first example:

• $1 \mod 3 = 1$
• $3 \mod 5 = 3$
• $5 \mod 2 = 1$
• $2 \mod 1 = 0$