ZOJ 1633 Big String

ZOJ 1633 Big String

Big String Time Limit: 2 Seconds Memory Limit: 65536 KB We will construct an infinitely long string from two short strings: A = "^__ ^" (four characters), and B = "T.T" (three characters). Repeat the following steps:

Concatenate A after B to obtain a new string C. for example, if A = "^__ ^" and B = "T.T", then C = BA = "T.T ^__ ^ ". let A = B, B = C -- as the example abve A = "T.T", B = "T.T ^__ ^ ". your task is to find out the n-th character of this infinite string.


Input

The input contains multiple test cases, each contains only one integer N (1 <= N <= 2 ^ 63-1). Proceed to the end of file.


Output

For each test case, print one character on each line, which is the N-th (index begins with 1) character of this infinite string.


Sample Input

1248


Sample Output

T.^T

Start with two strings, A = "^__ ^" (four characters), B = "T.T" (three characters), and then re-Execute C = BA, A = B, B = C. Ask what the nth character is.

Analysis: because the final string is recursive from the past to the future, when solving the problem, we can reverse the process until the length of the string does not exceed 7, and the output is enough.

# Include
   
    
# Include
    
     
Using namespace std; typedef long LL; LL a [95]; // Save the string length int main () {string C = "T.T ^__ ^ "; a [0] = 4; a [1] = 3; int I; for (I = 2; I <90; I ++) a [I] = a [I-1] + a [I-2]; LL n; while (cin> n) {while (n> 7) {int pos = lower_bound (, a + 89, n)-a; n-= a [pos-1];} cout <C [n-1] <endl;} return 0 ;}