非010串

如果一个01字符串满足不存在010这样的子串，那么称它为非010串。

求长度为n的非010串的个数。(对1e9+7取模)

Input

一个数n，表示长度。(n<1e15)

Output

长度为n的非010串的个数。(对1e9+7取模)

Input示例

3

Output示例

7解释:000001011100101110111
#include <iostream>#include <cstring>using namespace std;const long long int MOD = 1e9+7;struct matrix{long long int val[4][4];void clean(){memset(val, 0, sizeof(val));}void init(){memset(val, 0, sizeof(val));for (int i = 0; i < 4; i++){val[i][i] = 1;}}matrix operator *(const matrix &a){matrix result;result.clean();for (int i = 0; i < 4; i++){for (int j = 0; j < 4; j++){for (int k = 0; k < 4; k++){result.val[i][j] += val[i][k]*a.val[k][j];result.val[i][j] %= MOD;}}}return result;}};matrix fun(long long int n, matrix &base){matrix result;result.init();while (n > 0){if (n & 1){result = result * base;}base = base * base;n >>= 1;}return result;}int main(){    long long int n;    cin >> n;    matrix base = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0,  0, 0, 1, 0};matrix result;result.clean();result.val[0][0] = 7;result.val[1][0] = 4;result.val[2][0] = 2;result.val[3][0] = 1;if (n <= 3){cout << result.val[3-n][0] << endl;}else{base = fun(n-3, base);result = base * result;cout << result.val[0][0] << endl;}    return 0;}