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 = 998244353;
alias Mint = ModInt!MO;

// floor(sqrt(a))
long floorSqrt(long a) {
  import core.bitop : bsr;
  import std.algorithm : min;
  long b = a, x = 0, y = 0;
  for (int e = bsr(a) & ~1; e >= 0; e -= 2) {
    x <<= 1;
    y <<= 1;
    if (b >= (y | 1) << e) {
      b -= (y | 1) << e;
      x |= 1;
      y += 2;
    }
  }
  return x;
}


// x^2 + y^2 <= n
// x, y > 0
Mint[long] cache;
Mint calc(long n) {
  Mint ret;
  cache.update(n, {
    const sqrtN = floorSqrt(n);
    long y = sqrtN;
    foreach (x; 1 .. sqrtN + 1) {
      for (; x^^2 + y^^2 > n; --y) {}
      ret += Mint(x) * Mint(y);
      ret += Mint(y) * Mint(y + 1) / 2;
    }
    debug {
      writeln("calc ", n, " = ", ret);
    }
    return ret;
  }, (ref Mint r) {
    return ret = r;
  });
  return ret;
}

void main() {
  try {
    for (; ; ) {
      const N = readLong();
      
      debug {
        if (N <= 50) {
          Mint brt;
          auto abcds = new long[][][][](N + 1, N + 1);
          foreach (a; -N .. +N + 1) foreach (b; -N .. +N + 1) {
            foreach (c; -N .. +N + 1) foreach (d; -N .. +N + 1) {
              if (a^^2 + b^^2 <= N && c^^2 + d^^2 <= N) {
                if (a * d - b * c == 1) {
                  brt += abs(a) + abs(b) + abs(c) + abs(d);
                  /*
                  if (a >= 0 && b >= 0 && c >= 0 && d >= 0) {
                    writeln([a, b, c, d]);
                  }
                  */
                  if (a^^2 + b^^2 > c^^2 + d^^2) {
                    abcds[abs(a)][abs(b)] ~= [a, b, c, d];
                  } else if (a^^2 + b^^2 < c^^2 + d^^2) {
                    abcds[abs(c)][abs(d)] ~= [a, b, c, d];
                  } else {
                    writeln("same ", [a, b, c, d]);
                  }
                }
              }
            }
          }
          foreach (a; 0 .. N + 1) foreach (b; 0 .. N + 1) {
            if (!abcds[a][b].empty) {
              writeln([a, b], ": ", abcds[a][b]);
            }
          }
          writeln("brt = ", brt);
        }
      }
      
      const sqrtN = floorSqrt(N);
      auto isnp = new bool[sqrtN + 1];
      auto meb = new int[sqrtN + 1];
      meb[] = 1;
      foreach (p; 2 .. sqrtN + 1) {
        if (!isnp[p]) {
          meb[p] *= -1;
          for (long n = 2 * p; n <= sqrtN; n += p) {
            isnp[n] = true;
            meb[n] *= -1;
          }
          for (long n = p^^2; n <= sqrtN; n += p^^2) {
            meb[n] = 0;
          }
        }
      }
      
      Mint ans;
      foreach (d; 1 .. sqrtN + 1) {
        if (meb[d] != 0) {
          const n = N / d^^2;
          const res = calc(n);
          ans += meb[d] * d * res;
        }
      }
      ans *= 24;
      ans += 8;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}