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| // 42jerrykim.github.io에서 더 많은 정보를 확인 할 수 있습니다.
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
static const int64 MOD = 1000000007;
static inline int64 modPow(int64 base, int64 exp) {
int64 result = 1 % MOD;
base %= MOD;
while (exp > 0) {
if (exp & 1) result = (result * base) % MOD;
base = (base * base) % MOD;
exp >>= 1;
}
return result;
}
// Berlekamp–Massey: 최소 선형 점화계수 rec 반환
// s[n] = sum_{i=1..L} rec[i-1] * s[n-i] (mod MOD)
static vector<int64> berlekamp_massey(const vector<int64>& s) {
vector<int64> ls, cur; // ls: last successful, cur: current
int lf = 0; // last fail index
int64 ld = 1; // last delta
for (int i = 0; i < (int)s.size(); i++) {
int64 t = 0;
for (int j = 0; j < (int)cur.size(); j++) {
t = (t + s[i - j - 1] * cur[j]) % MOD;
}
int64 delta = (t - s[i]) % MOD;
if (delta < 0) delta += MOD;
if (delta == 0) continue;
if (cur.empty()) {
cur.assign(i + 1, 0);
lf = i;
ld = delta;
continue;
}
int64 k = delta * modPow(ld, MOD - 2) % MOD;
vector<int64> c(i - lf - 1, 0);
c.push_back(k);
for (auto &x : ls) c.push_back((MOD - x) * k % MOD);
if ((int)c.size() < (int)cur.size()) c.resize(cur.size(), 0);
for (int j = 0; j < (int)cur.size(); j++) {
c[j] = (c[j] + cur[j]) % MOD;
}
if (i - lf + (int)ls.size() >= (int)cur.size()) {
ls = cur;
lf = i;
ld = delta;
}
cur.swap(c);
}
for (auto &x : cur) { x %= MOD; if (x < 0) x += MOD; }
return cur;
}
// rec(길이 m), 초기 s[0..m-1]로 n번째 항 계산 (O(m^2 log n))
static int64 get_nth(const vector<int64>& rec, const vector<int64>& init, long long n) {
int m = (int)rec.size();
if (n < (long long)init.size()) return init[(size_t)n];
auto combine = [&](const vector<int64>& a, const vector<int64>& b) {
// 다항식 곱셈 후 rec로 나머지
vector<int64> res(2 * m + 1, 0);
for (int i = 0; i < m; i++) {
for (int j = 0; j < m; j++) {
res[i + j] = (res[i + j] + a[i] * b[j]) % MOD;
}
}
for (int i = 2 * m - 1; i >= m; --i) {
for (int j = 1; j <= m; j++) {
res[i - j] = (res[i - j] + res[i] * rec[j - 1]) % MOD;
}
}
res.resize(m);
return res;
};
vector<int64> pol(m, 0), e(m, 0);
pol[0] = 1; // 단위 다항식
if (m == 1) e[0] = rec[0]; else e[1] = 1; // x
long long k = n;
while (k > 0) {
if (k & 1) pol = combine(pol, e);
e = combine(e, e);
k >>= 1;
}
int64 ans = 0;
for (int i = 0; i < m; i++) {
ans = (ans + pol[i] * init[i]) % MOD;
}
return ans;
}
// 초기 항 s가 주어질 때, n번째 항
static int64 guess_nth_term(const vector<int64>& s, long long n) {
if (n < (long long)s.size()) return s[(size_t)n];
vector<int64> rec = berlekamp_massey(s);
if (rec.empty()) return 0;
return get_nth(rec, s, n);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
// s[n] = 2x2x2x2xn 5D 초콜릿을 1x1x1x1x2 도미노로 채우는 경우의 수 (n=0부터)
// n=1 -> 272, n=2 -> 589185, n=3 -> 930336768 ...
const vector<int64> s = {
1, 272, 589185, 930336768, 853401154, 217676188, 136558333, 415722813, 985269529,
791527976, 201836136, 382110354, 441223705, 661537677, 641601343, 897033284, 816519670,
365311407, 300643484, 936803543, 681929467, 462484986, 13900203, 657627114, 96637209,
577140657, 600647073, 254604056, 102389682, 811580173, 592550067, 587171680, 526467503,
265885773, 951722780, 219627841, 371508152, 283501391, 159234514, 439380999, 722868959,
125599834, 351398134, 456317548, 365496182, 614778702, 502680047, 193063685, 309004764,
743901785, 870955115, 312807829, 160375015, 691844624, 137034372, 350330868, 895680450,
282610535, 317897557, 28600551, 583305647, 539409363, 327406961, 627805385, 680183978,
681299085, 954964592, 743524009, 788048339, 699454626, 666369521, 857206425, 490463127,
477198247, 599963928, 21247982, 107843532, 753662937, 239039324, 608530376, 523383010,
654448101, 801430395, 393034561, 93313778, 983052766, 240336620, 825539982, 525118275,
563899476, 706271688, 547405697, 477082486, 664058071, 353207278, 729486413, 795704637,
999271072, 540749624, 411451016, 736422999, 879369181, 918733916, 982303557, 512499644,
261033810, 391766409, 334092786, 931794834, 854181848, 821090190, 751839258, 433126935,
571194155, 52438113, 552977155, 320805296, 173355929, 969659468, 258854248, 159509877,
374487748, 401382023, 44060530, 510164669, 336596764, 652050424, 373872552, 517226592,
719871041, 43959496, 235333335, 304962191, 253114421, 43638769, 361871585, 8060121,
147014624, 114846460, 430864038, 368951246, 863795701, 36066788, 971606149, 935875286,
486724123, 73790652, 236936530, 307697424, 753314001, 40450345, 529462842, 166162047,
974102330, 600865526, 63237062, 749041914, 670937123, 806399597, 776678839, 842565920,
608499253, 469062485, 842196981, 247762946, 778570576, 237951782, 286343384, 988318575,
147255879, 905747089, 711062313, 21396079, 826846622, 443781794, 786474911, 400737121,
844768961, 686214818, 590050845, 855473150, 18501778, 33258755, 398169058, 811192244,
710397887, 591757177, 775311969, 168256434, 509615161, 489764304, 605188191, 498085780,
164388183, 524662873, 322602324, 853641480, 205349527, 308211944, 93153206
};
long long n;
if (!(cin >> n)) return 0;
cout << guess_nth_term(s, n) << '\n';
return 0;
}
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