import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(int M_) { import std.conv : to; alias M = M_; int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { if (a < 0) return (this = inv()^^(-a)); ModInt t2 = this, te = ModInt(1); for (long e = a; e > 0; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op: "-")() const { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0); } string toString() const { return x.to!string; } } enum MO = 10^^9 + 7; alias Mint = ModInt!MO; // Pretty print (smaller abs) int[] pretty(int M)(ModInt!M[] as) { import std.algorithm : map; import std.array : array; return as.map!(a => (a.x < M - a.x) ? a.x : -(M - a.x)).array; } // Berlekamp-Massey // F: field // \sum_{j=1}^0 cs[j] as[i - j] = 0 (d <= i < |as|), cs[0] = 1 // M must be prime F[] findLinearRecurrence(F)(F[] as) { import std.algorithm : min; const n = cast(int)(as.length); int d, m; auto cs = new F[n + 1], bs = new F[n + 1]; cs[0] = bs[0] = 1; F invBef = 1; foreach (i; 0 .. n) { ++m; F dif = as[i]; foreach (j; 1 .. d + 1) dif += cs[j] * as[i - j]; if (dif.x != 0) { auto csDup = cs.dup; const r = dif * invBef; foreach (j; m .. n) cs[j] -= r * bs[j - m]; if (2 * d <= i) { d = i + 1 - d; m = 0; bs = csDup; invBef = dif.inv; } } } return cs[0 .. d + 1]; } ModInt!M[] findLinearRecurrence(int M)(long[] as) { import std.algorithm : map; import std.array : array; return findLinearRecurrence(as.map!(a => ModInt!M(a)).array); } void main() { enum LIM_N = 30; enum LIM = 200; auto dp = new bool[][][](LIM_N + 1, LIM, LIM); dp[0][LIM / 2][LIM / 2] = true; foreach (i; 0 .. LIM_N) { foreach (x; 0 .. LIM) foreach (y; 0 .. LIM) { if (dp[i][x][y]) { foreach (const dx; [-3, -2, 0, +2, +3]) foreach (const dy; [-3, -2, 0, +2, +3]) { if ((dx + dy) % 2 != 0) { const xx = x + dx; const yy = y + dy; if (0 <= xx && xx < LIM && 0 <= yy && yy < LIM) { dp[i + 1][xx][yy] = true; } } } } } } auto as = new Mint[LIM_N + 1]; foreach (i; 0 .. LIM_N + 1) { foreach (x; 0 .. LIM) foreach (y; 0 .. LIM) { if (dp[i][x][y]) { as[i] += 1; } } } const cs = findLinearRecurrence(as); stderr.writeln("as = ", as); stderr.writeln("cs = ", cs); /* [1, 12, 65, 172, 297, 456, 649, 876, 1137, 1432, 1761, 2124, 2521, 2952, 3417, 3916, 4449, 5016, 5617, 6252, 6921, 7624, 8361, 9132, 9937, 10776, 11649, 12556, 13497, 14472, 15481] [1, 1000000004, 3, 1000000006, 0, 0, 0] 172 297 456 125 159 34 */ try { for (; ; ) { const N = readLong(); Mint ans; if (N < 3) { ans = [1, 12, 65][cast(int)(N)]; } else { // const Mint n = N - 3; ans += 172; ans += 125 * n; ans += 17 * n * (n - 1); } writeln(ans); } } catch (EOFException e) { } }