#D6780. 123 Triangle
123 Triangle
123 Triangle
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
Output
Print x_{N,1}.
Examples
Input
4 1231
Output
1
Input
10 2311312312
Output
0
inputFormat
Input
Input is given from Standard Input in the following format:
N a_1a_2\ldotsa_N
outputFormat
Output
Print x_{N,1}.
Examples
Input
4 1231
Output
1
Input
10 2311312312
Output
0
样例
10
23113123120