Contest Duration: ~ (local time) (300 minutes) Back to Home
G - Colorful Doors /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

すぬけ君は、左岸から右岸へ橋を渡ることにしました。 すぬけ君は常に右へ向かって歩き続けますが、その間に次の現象が起こります。

• すぬけ君が色 k (1 \leq k \leq N) のドアに触れた瞬間、すぬけ君は色 k の他方のドアのすぐ右へワープする。

すぬけ君はいずれ右岸に辿り着くことが示せます。

i (1 \leq i \leq 2 N - 1) について、左から i 番目および i + 1 番目のドアに挟まれた区間を、区間 i と呼ぶことにします。 橋を渡り終えたすぬけ君は、各 i (1 \leq i \leq 2 N - 1) について、区間 i を歩いたか否かを記録しました。 この記録が、長さ 2 N - 1 の文字列 s として与えられます。 各 i (1 \leq i \leq 2 N - 1) について、すぬけ君が区間 i を歩いたならば、si 文字目は 1 であり、そうでないならば、si 文字目は 0 です。

### 制約

• 1 \leq N \leq 10^5
• |s| = 2 N - 1
• s01 のみからなる。

### 入力

N
s


### 出力

c_1 c_2 ... c_{2 N}


### 入力例 1

2
010


### 出力例 1

Yes
1 1 2 2


### 入力例 2

2
001


### 出力例 2

No


### 入力例 3

3
10110


### 出力例 3

Yes
1 3 2 1 2 3


### 入力例 4

3
10101


### 出力例 4

No


### 入力例 5

6
00111011100


### 出力例 5

Yes
1 6 1 2 3 4 4 2 3 5 6 5


Score : 2000 points

### Problem Statement

There is a bridge that connects the left and right banks of a river. There are 2 N doors placed at different positions on this bridge, painted in some colors. The colors of the doors are represented by integers from 1 through N. For each k (1 \leq k \leq N), there are exactly two doors painted in Color k.

Snuke decides to cross the bridge from the left bank to the right bank. He will keep on walking to the right, but the following event will happen while doing so:

• At the moment Snuke touches a door painted in Color k (1 \leq k \leq N), he teleports to the right side of the other door painted in Color k.

It can be shown that he will eventually get to the right bank.

For each i (1 \leq i \leq 2 N - 1), the section between the i-th and (i + 1)-th doors from the left will be referred to as Section i. After crossing the bridge, Snuke recorded whether or not he walked through Section i, for each i (1 \leq i \leq 2 N - 1). This record is given to you as a string s of length 2 N - 1. For each i (1 \leq i \leq 2 N - 1), if Snuke walked through Section i, the i-th character in s is 1; otherwise, the i-th character is 0.

Figure: A possible arrangement of doors for Sample Input 3

Determine if there exists an arrangement of doors that is consistent with the record. If it exists, construct one such arrangement.

### Constraints

• 1 \leq N \leq 10^5
• |s| = 2 N - 1
• s consists of 0 and 1.

### Input

Input is given from Standard Input in the following format:

N
s


### Output

If there is no arrangement of doors that is consistent with the record, print No. If there exists such an arrangement, print Yes in the first line, then print one such arrangement in the second line, in the following format:

c_1 c_2 ... c_{2 N}


Here, for each i (1 \leq i \leq 2 N), c_i is the color of the i-th door from the left.

### Sample Input 1

2
010


### Sample Output 1

Yes
1 1 2 2


### Sample Input 2

2
001


### Sample Output 2

No


### Sample Input 3

3
10110


### Sample Output 3

Yes
1 3 2 1 2 3


The figure below is identical to the one in the statement.

### Sample Input 4

3
10101


### Sample Output 4

No


### Sample Input 5

6
00111011100


### Sample Output 5

Yes
1 6 1 2 3 4 4 2 3 5 6 5