Contest Duration: - (local time) (150 minutes) Back to Home
B - 123 Triangle /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• x_{1,j} := a_j \quad (1 \leq j \leq N)
• x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N かつ 1 \leq j \leq N+1-i)

x_{N,1} を求めてください。

### 制約

• 2 ≦ N ≦ 10^6
• a_i = 1,2,3 (1 \leq i \leq N)

### 入力

N
a_1a_2\ldotsa_N


x_{N,1} を出力せよ。

### 入力例 1

4
1231


### 出力例 1

1


x_{1,1},x_{1,2},x_{1,3},x_{1,4} はそれぞれ、1,2,3,1 です。

x_{2,1},x_{2,2},x_{2,3} はそれぞれ、|1-2| = 1,|2-3| = 1,|3-1| = 2 です。

x_{3,1},x_{3,2} はそれぞれ、|1-1| = 0,|1-2| = 1 です。

### 入力例 2

10
2311312312


### 出力例 2

0


Score : 700 points

### Problem Statement

Given is a sequence of N digits a_1a_2\ldots a_N, where each element is 1, 2, or 3. Let x_{i,j} defined as follows:

• x_{1,j} := a_j \quad (1 \leq j \leq N)
• x_{i,j} := | x_{i-1,j} - x_{i-1,j+1} | \quad (2 \leq i \leq N and 1 \leq j \leq N+1-i)

Find x_{N,1}.

### Constraints

• 2 \leq N \leq 10^6
• a_i = 1,2,3 (1 \leq i \leq N)

### Input

Input is given from Standard Input in the following format:

N
a_1a_2\ldotsa_N


Print x_{N,1}.

### Sample Input 1

4
1231


### Sample Output 1

1


x_{1,1},x_{1,2},x_{1,3},x_{1,4} are respectively 1,2,3,1.

x_{2,1},x_{2,2},x_{2,3} are respectively |1-2| = 1,|2-3| = 1,|3-1| = 2.

x_{3,1},x_{3,2} are respectively |1-1| = 0,|1-2| = 1.

Finally, x_{4,1} = |0-1| = 1, so the answer is 1.

### Sample Input 2

10
2311312312


### Sample Output 2

0