Problem: You are given a multiset S. Over all pairs of subsets A and B, such that:

  * B ⊂ A; 
  * |B| = |A| - 1; 
  * greatest common divisor of all elements in A is equal to one; 



find the sum of ∑_{x ∈ A}{x} ⋅ ∑_{x ∈ B}{x}, modulo 998 244 353.

Input

The first line contains one integer m (1 ≤ m ≤ 10^5): the number of different values in the multiset S.

Each of the next m lines contains two integers a_i, freq_i (1 ≤ a_i ≤ 10^5, 1 ≤ freq_i ≤ 10^9). Element a_i appears in the multiset S freq_i times. All a_i are different.

Output

Print the required sum, modulo 998 244 353.

Examples

Input


2
1 1
2 1


Output


9


Input


4
1 1
2 1
3 1
6 1


Output


1207


Input


1
1 5


Output


560

Note

A multiset is a set where elements are allowed to coincide. |X| is the cardinality of a set X, the number of elements in it.

A ⊂ B: Set A is a subset of a set B.

In the first example B=\{1\}, A=\{1,2\} and B=\{2\}, A=\{1, 2\} have a product equal to 1⋅3 + 2⋅3=9. Other pairs of A and B don't satisfy the given constraints.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int M = 1000000007;
const int MM = 998244353;
const long double PI = acos(-1);
long long power(long long b, long long e, long long m) {
  if (e == 0) return 1;
  if (e & 1) return b * power(b * b % m, e / 2, m) % m;
  return power(b * b % m, e / 2, m);
}
long long power(long long b, long long e) {
  if (e == 0) return 1;
  if (e & 1) return b * power(b * b, e / 2);
  return power(b * b, e / 2);
}
template <typename T, typename U>
static inline void amin(T &x, U y) {
  if (y < x) x = y;
}
template <typename T, typename U>
static inline void amax(T &x, U y) {
  if (x < y) x = y;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  return os << '(' << p.first << "," << p.second << ')';
}
const int MOD = MM;
struct Mint {
  int val;
  Mint(long long v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = v;
  }
  static int mod_inv(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  Mint &operator+=(const Mint &other) {
    val += other.val;
    if (val >= MOD) val -= MOD;
    return *this;
  }
  Mint &operator-=(const Mint &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return x % m;
    unsigned x_high = x >> 32, x_low = (unsigned)x;
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  Mint &operator*=(const Mint &other) {
    val = fast_mod((uint64_t)val * other.val);
    return *this;
  }
  Mint &operator/=(const Mint &other) { return *this *= other.inv(); }
  friend Mint operator+(const Mint &a, const Mint &b) { return Mint(a) += b; }
  friend Mint operator-(const Mint &a, const Mint &b) { return Mint(a) -= b; }
  friend Mint operator*(const Mint &a, const Mint &b) { return Mint(a) *= b; }
  friend Mint operator/(const Mint &a, const Mint &b) { return Mint(a) /= b; }
  Mint &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  Mint &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  Mint operator++(int32_t) {
    Mint before = *this;
    ++*this;
    return before;
  }
  Mint operator--(int32_t) {
    Mint before = *this;
    --*this;
    return before;
  }
  Mint operator-() const { return val == 0 ? 0 : MOD - val; }
  bool operator==(const Mint &other) const { return val == other.val; }
  bool operator!=(const Mint &other) const { return val != other.val; }
  Mint inv() const { return mod_inv(val); }
  Mint power(long long p) const {
    assert(p >= 0);
    Mint a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      a *= a;
      p >>= 1;
    }
    return result;
  }
  friend ostream &operator<<(ostream &stream, const Mint &m) {
    return stream << m.val;
  }
  friend istream &operator>>(istream &stream, Mint &m) {
    return stream >> m.val;
  }
};
const int N = 100005;
int lpf[N], mobius[N];
void _lpf_() {
  lpf[1] = 1;
  for (int i = 2; i <= N - 2; ++i) {
    if (!lpf[i]) {
      for (int j = i; j <= N - 2; j += i) {
        if (!lpf[j]) lpf[j] = i;
      }
    }
  }
}
void Mobius() {
  mobius[1] = 1;
  for (int i = 2; i <= N - 2; ++i) {
    if (lpf[i / lpf[i]] == lpf[i])
      mobius[i] = 0;
    else
      mobius[i] = -1 * mobius[i / lpf[i]];
  }
}
int f[N];
int _runtimeTerror_() {
  _lpf_();
  Mobius();
  int n;
  cin >> n;
  Mint ans = 0;
  for (int i = 1; i <= n; ++i) {
    int x, y;
    cin >> x >> y;
    f[x] += y;
  }
  mobius[1] = 1;
  for (int i = 1; i <= 100000; ++i) {
    if (mobius[i] == 0) continue;
    long long tx = 0;
    Mint sum = 0;
    Mint sq = 0;
    for (int j = i; j <= 100000; j += i) {
      tx += f[j];
      sum += Mint(j) * f[j];
      sq += Mint(j) * Mint(j) * f[j];
    }
    if (tx >= 2) {
      Mint u = 0;
      u += sq * (tx - 1) * Mint(2).power(tx - 2);
      u += tx * Mint(2).power(tx - 2) * (sum * sum - sq) / 2;
      ans += u * mobius[i];
    }
  }
  cout << ans << "\n";
  return 0;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) _runtimeTerror_();
  return 0;
}