#include <bits/stdc++.h>
using namespace std;
long long sigma(long long n) { return (n * (n + 1) / 2); }
long long MOD(long long x) {
  if (x >= 0) return x;
  return (-x);
}
bool great(long long a, long long b) { return a > b; }
bool p_sm(pair<long long, long long> a, pair<long long, long long> b) {
  if (a.first == b.first) {
    return (a.second < b.second);
  }
  return (a.first < b.first);
}
long long max3(long long a, long long b, long long c) {
  return (max(a, max(b, c)));
}
long long max4(long long a, long long b, long long c, long long d) {
  return (max(max(a, b), max(c, d)));
}
long long min3(long long a, long long b, long long c) {
  return (min(a, min(b, c)));
}
long long min4(long long a, long long b, long long c, long long d) {
  return (min(min(a, b), min(c, d)));
}
vector<long long> factors(long long x) {
  vector<long long> v;
  for (long long i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      v.push_back(i);
      if (i != x / i) {
        v.push_back(x / i);
      }
    }
  }
  return v;
}
vector<long long> ispr;
vector<long long> min_prime;
unordered_map<long long, long long> prime_fact(long long x) {
  unordered_map<long long, long long> mp;
  while (x != 1) {
    mp[min_prime[x]]++;
    x /= min_prime[x];
  }
  return mp;
}
map<long long, long long> factorizee(long long n) {
  map<long long, long long> mp;
  for (long long i = 2; i * i <= n; ++i) {
    while (n % i == 0) {
      mp[i]++;
      n /= i;
    }
  }
  if (n != 1) {
    mp[n]++;
  }
  return mp;
}
long long power(long long a, long long b, long long m) {
  long long ans = 1;
  while (b > 0) {
    if (b % 2) {
      ans = (ans * a) % m;
    }
    a = (a * a) % m;
    b = b / 2;
  }
  return ans;
}
long long sgsq(long long n) {
  long long xx = (n * (n + 1) * ((2 * n) + 1)) / 6;
  return xx;
}
pair<bool, long long> f(long long i, long long n) {
  pair<bool, long long> pp;
  long long xx = sgsq(i);
  n -= xx;
  long long yp = sigma(i);
  if (n % yp) {
    pp.first = false;
    pp.second = 134;
    return pp;
  }
  pp.first = true;
  pp.second = (n / yp + i);
  return pp;
}
int main() {
  long long n;
  cin >> n;
  long long i = 1;
  set<pair<long long, long long> > ans;
  while (sgsq(i) <= n) {
    pair<bool, long long> pp = f(i, n);
    if (pp.first) {
      ans.insert(make_pair(i, pp.second));
      ans.insert(make_pair(pp.second, i));
    }
    i++;
  }
  cout << ans.size() << endl;
  set<pair<long long, long long> >::iterator it;
  for (it = ans.begin(); it != ans.end(); ++it) {
    cout << it->first << " " << it->second << endl;
  }
}

### Prompt

Develop a solution in cpp to the problem described below:

Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two and 3 squares with side three. The total number of distinct squares in a 3 × 5 table is 15 + 8 + 3 = 26.

Input

The first line of the input contains a single integer x (1 ≤ x ≤ 1018) — the number of squares inside the tables Spongebob is interested in.

Output

First print a single integer k — the number of tables with exactly x distinct squares inside.

Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality — in the order of increasing m.

Examples

Input

26


Output

6
1 26
2 9
3 5
5 3
9 2
26 1


Input

2


Output

2
1 2
2 1


Input

8


Output

4
1 8
2 3
3 2
8 1

Note

In a 1 × 2 table there are 2 1 × 1 squares. So, 2 distinct squares in total.

<image>

In a 2 × 3 table there are 6 1 × 1 squares and 2 2 × 2 squares. That is equal to 8 squares in total.

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long sigma(long long n) { return (n * (n + 1) / 2); }
long long MOD(long long x) {
  if (x >= 0) return x;
  return (-x);
}
bool great(long long a, long long b) { return a > b; }
bool p_sm(pair<long long, long long> a, pair<long long, long long> b) {
  if (a.first == b.first) {
    return (a.second < b.second);
  }
  return (a.first < b.first);
}
long long max3(long long a, long long b, long long c) {
  return (max(a, max(b, c)));
}
long long max4(long long a, long long b, long long c, long long d) {
  return (max(max(a, b), max(c, d)));
}
long long min3(long long a, long long b, long long c) {
  return (min(a, min(b, c)));
}
long long min4(long long a, long long b, long long c, long long d) {
  return (min(min(a, b), min(c, d)));
}
vector<long long> factors(long long x) {
  vector<long long> v;
  for (long long i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      v.push_back(i);
      if (i != x / i) {
        v.push_back(x / i);
      }
    }
  }
  return v;
}
vector<long long> ispr;
vector<long long> min_prime;
unordered_map<long long, long long> prime_fact(long long x) {
  unordered_map<long long, long long> mp;
  while (x != 1) {
    mp[min_prime[x]]++;
    x /= min_prime[x];
  }
  return mp;
}
map<long long, long long> factorizee(long long n) {
  map<long long, long long> mp;
  for (long long i = 2; i * i <= n; ++i) {
    while (n % i == 0) {
      mp[i]++;
      n /= i;
    }
  }
  if (n != 1) {
    mp[n]++;
  }
  return mp;
}
long long power(long long a, long long b, long long m) {
  long long ans = 1;
  while (b > 0) {
    if (b % 2) {
      ans = (ans * a) % m;
    }
    a = (a * a) % m;
    b = b / 2;
  }
  return ans;
}
long long sgsq(long long n) {
  long long xx = (n * (n + 1) * ((2 * n) + 1)) / 6;
  return xx;
}
pair<bool, long long> f(long long i, long long n) {
  pair<bool, long long> pp;
  long long xx = sgsq(i);
  n -= xx;
  long long yp = sigma(i);
  if (n % yp) {
    pp.first = false;
    pp.second = 134;
    return pp;
  }
  pp.first = true;
  pp.second = (n / yp + i);
  return pp;
}
int main() {
  long long n;
  cin >> n;
  long long i = 1;
  set<pair<long long, long long> > ans;
  while (sgsq(i) <= n) {
    pair<bool, long long> pp = f(i, n);
    if (pp.first) {
      ans.insert(make_pair(i, pp.second));
      ans.insert(make_pair(pp.second, i));
    }
    i++;
  }
  cout << ans.size() << endl;
  set<pair<long long, long long> >::iterator it;
  for (it = ans.begin(); it != ans.end(); ++it) {
    cout << it->first << " " << it->second << endl;
  }
}

```