Coloring Game（思维题）

Posted 2020-08-10 明霞

David has a white board with 2×N2 \times N2×N grids.He decides to paint some grids black with his brush.He always starts at the top left corner and ends at the bottom right corner, where grids should be black ultimately.

Each time he can move his brush up(↑), down(↓), left(←), right(→), left up(↖), left down(↙), right up(↗), right down (↘) to the next grid.

For a grid visited before,the color is still black. Otherwise it changes from white to black.

David wants you to compute the number of different color schemes for a given board. Two color schemes are considered different if and only if the color of at least one corresponding position is different.

Input

One line including an integer n(0<n≤109)n(0<n \le 10^9)n(0<n≤109)

Output

One line including an integer, which represent the answer ?mod?1000000007\bmod 1000000007mod1000000007

样例输入1 

2

样例输出1 

4

样例解释1

样例输入2 

3

样例输出2 

12

样例解释2

 

思路：这题是纯数学题（我当时傻fufu的画了很多图，而且还没画够情况。佛了，知道真相的我眼泪掉下来。）第一列和最后一列有两种选择，剩下的格子要不要，每一列有3中选择，要哪个和都要，结果就是4*3^(n-2)

#include <cstdio>
#include <iostream>
#include <vector>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
#define ll long long
const int inf = 0x3f3f3f3f;
const  ll linf  =1LL<<50;
const int maxn = 1e5+8;
const ll mod = 1000000007;
ll qsm(ll a, ll b)
{
  ll sum = 1;
  a = a%mod;
  while(b)
  {
      if(b&1)
      {
          sum = (sum*a)%mod;
      }
      b /= 2;
      a = (a*a)%mod;
  }
  return sum;
}
int main()
{
    ll n;
    scanf("%lld", &n);
    ll sum = 4*qsm(3, n-2);
    printf("%lld\n", sum);
    return 0;
}