#include "bits/stdc++.h" using namespace std; typedef long long ll; typedef pair pii; typedef pair pll; const int INF = 1e9; const ll LINF = 1e18; inline ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; } inline ll lcm(ll a, ll b) { return a / gcd(a, b)*b; } template ostream& operator << (ostream& out,const pair& o){ out << "(" << o.first << "," << o.second << ")"; return out; } template ostream& operator << (ostream& out,const vector V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; } template ostream& operator << (ostream& out,const vector > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; } template ostream& operator << (ostream& out,const map mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; } /* 問題文============================================================ ================================================================= 解説============================================================= 蟻本p239 (1+√3)^n = a_n + b_n√3 (1-√3)^n = a_n - b_n√3 (1+√3)^n + (1-√3)^n = 2*a (1+√3)^n = 2*a - (1-√3)^n if n is even 0 < (1-√3)^n < 1 ans = 2*a_n - 1 else -1 < (1-√3)^n < 0 ans = 2*a_n (1+√3)^(n+1) = (a_n + b_n√3)(1+√3) = (a_n + 3*b_n) + (a_n + b_n)*√3 a_n+1 = a_n + 3*b_n b_n+1 = a_n + b_n |a_n+1 | | 1 3 | | a_n | | | = | | | | |b_n+1 | | 1 1 | | b_n | a_nを行列累乗で求めればいい ================================================================ */ typedef vector vec; typedef vector mat; /* 行列累乗 X = A^M*B A ( N*N行列) O(N^3 logM) */ mat mul(mat&A,mat&B,const ll M){ mat C(A.size(),vec(B[0].size())); for(int i = 0; i < (int)A.size();i++){ for(int k = 0; k < (int)B.size();k++){ if(A[i][k] == 0) continue; for(int j = 0; j < B[0].size();j++){ C[i][j] = (C[i][j] + A[i][k]*B[k][j])%M; } } } return C; } mat pow(mat A,ll n,const ll M){ mat B(A.size(),vec(A.size())); for(int i = 0; i < A.size();i++){ B[i][i] = 1; } while(n > 0){ if(n&1) B= mul(B,A,M); A = mul(A,A,M); n>>=1; } return B; } ll solve(){ ll res = 0; ll n; cin >> n; mat A = {{1,3},{1,1}}; mat B = {{1},{0}}; A = pow(A,n,1000); res = 2*mul(A,B,1000)[0][0] % 1000; if(n%2==0) (res += 999)%=1000; return res; } int main(void) { cin.tie(0); ios_base::sync_with_stdio(false); cout << solve() << endl; return 0; }