Problem: You have a blackboard and initially only an odd number x is written on it. Your goal is to write the number 1 on the blackboard.

You may write new numbers on the blackboard with the following two operations. 

  * You may take two numbers (not necessarily distinct) already on the blackboard and write their sum on the blackboard. The two numbers you have chosen remain on the blackboard. 
  * You may take two numbers (not necessarily distinct) already on the blackboard and write their [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) on the blackboard. The two numbers you have chosen remain on the blackboard. 

Perform a sequence of operations such that at the end the number 1 is on the blackboard.

Input

The single line of the input contains the odd integer x (3 ≤ x ≤ 999,999).

Output

Print on the first line the number q of operations you perform. Then q lines should follow, each describing one operation. 

  * The "sum" operation is described by the line "a + b", where a, b must be integers already present on the blackboard. 
  * The "xor" operation is described by the line "a ^ b", where a, b must be integers already present on the blackboard. 

The operation symbol (+ or ^) must be separated from a, b by a whitespace.

You can perform at most 100,000 operations (that is, q≤ 100,000) and all numbers written on the blackboard must be in the range [0, 5⋅10^{18}]. It can be proven that under such restrictions the required sequence of operations exists. You can output any suitable sequence of operations.

Examples

Input


3


Output


5
3 + 3
3 ^ 6
3 + 5
3 + 6
8 ^ 9


Input


123


Output


10
123 + 123
123 ^ 246
141 + 123
246 + 123
264 ^ 369
121 + 246
367 ^ 369
30 + 30
60 + 60
120 ^ 121

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = double;
const ll MODBASE = 1000000007LL;
const int MAXN = 110;
const int MAXM = 1000;
const int MAXK = 16;
const int MAXQ = 200010;
const int LOG_A = 50;
ll basis[LOG_A];
vector<ll> a;
vector<pair<ll, ll> > res;
vector<int> op;
void insertVector(ll mask) {
  for (int i = (LOG_A - 1); i >= (0); i--) {
    if ((mask & 1LL << i) == 0) continue;
    if (!basis[i]) {
      basis[i] = mask;
      return;
    }
    if ((mask ^ basis[i]) != 0) {
      res.push_back(pair<ll, ll>(mask, basis[i]));
      op.push_back(1);
    }
    mask ^= basis[i];
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(nullptr);
  ll x;
  cin >> x;
  a.clear();
  a.push_back(x);
  insertVector(x);
  set<ll> s;
  bool co = false;
  for (int o = (1); o <= (100); o++) {
    for (int i = (0); i <= (int((a).size()) - 1); i++) s.insert(a[i]);
    for (int i = (0); i <= (int((a).size()) - 1); i++) {
      for (int j = (0); j <= (int((a).size()) - 1); j++) {
        s.insert(a[i] + a[j]);
        res.push_back(pair<ll, ll>(a[i], a[j]));
        op.push_back(0);
        insertVector(a[i] + a[j]);
        if (basis[0] == 1) {
          co = true;
          break;
        }
      }
      if (co) break;
    }
    if (co) break;
    a.clear();
    for (int i = (0); i <= (LOG_A - 1); i++)
      if (basis[i]) a.push_back(basis[i]);
  }
  cout << int((res).size()) << "\n";
  for (int i = (0); i <= (int((res).size()) - 1); i++) {
    cout << res[i].first << ' ';
    if (op[i] == 0)
      cout << '+' << ' ';
    else
      cout << '^' << ' ';
    cout << res[i].second << "\n";
  }
  return 0;
}