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;
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
const long double pi = 3.14159265359;
const long long mod = 1000000007;
const long long modc = 998244353;
const long long inf = LLONG_MAX;
const long long neg_inf = LLONG_MIN;
long long inline power(long long a, long long b, long long p) {
  a %= p;
  long long ans = 1;
  while (b > 0) {
    if (b & 1) ans = (ans * a) % p;
    a = (a * a) % p;
    b >>= 1;
  }
  return ans;
}
long long mod_inv(long long n, long long p) { return power(n, p - 2, p); }
bool inline isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (long long i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
template <typename... T>
void W(T &&...args) {
  ((cout << fixed << setprecision(17) << args << " "), ...);
  cout << '\n';
}
template <typename... T>
void R(T &&...args) {
  ((cin >> args), ...);
}
long long ston(string s) {
  long long a = 0;
  reverse(s.begin(), s.end());
  long long pow = 1;
  for (long long i = 0; i < s.size(); i++) {
    a += pow * (s[i] - '0');
    pow *= 10;
  }
  return a;
}
template <class T>
string to_binary(T n) {
  string binaryNum;
  long long i = 0;
  while (n > 0) {
    binaryNum.push_back((n % 2) + '0');
    n = n / 2;
    i++;
  }
  if ((long long)binaryNum.size() == 0) binaryNum.push_back('0');
  reverse(binaryNum.begin(), binaryNum.end());
  return binaryNum;
}
long long bton(string &s, long long base) {
  long long ans = 0;
  long long pow = 1;
  reverse(s.begin(), s.end());
  for (auto x : s) {
    if (x >= 'a' && x <= 'z')
      ans += (x - 'a' + 10) * pow;
    else
      ans += (x - '0') * pow;
    pow *= base;
  }
  return ans;
}
template <class T>
void wv(T &v) {
  for (auto x : v) cout << x << " ";
  cout << '\n';
}
template <class T>
void rv(T &v) {
  for (long long i = 0; i < (long long)v.size(); i++) cin >> v[i];
}
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
const long long M = 2e5;
void add(long long a, long long b) { cout << a << " + " << b << '\n'; }
void xorr(long long a, long long b) { cout << a << " ^ " << b << '\n'; }
void solve() {
  long long i, j, sum = 0, prod = 1, maxl = neg_inf, minl = inf;
  long long n;
  cin >> n;
  string s = to_binary(n);
  long long k = (long long)s.size();
  vector<pair<long long, long long>> v;
  long long n1 = n;
  for (i = 1; i <= k; i++) {
    v.push_back(make_pair(n1, n1));
    n1 *= 2;
  }
  v.push_back(make_pair(n1, n));
  long long n2 = n1 / 2;
  vector<pair<long long, long long>> vx;
  vx.push_back(make_pair(n2, n));
  n2 ^= n;
  vector<pair<long long, long long>> v1;
  v1.push_back(make_pair(n2, n1 / 2));
  n2 += n1 / 2;
  vector<pair<long long, long long>> vx1;
  vx1.push_back(make_pair(n1 + n, n2));
  prod = pow(2, k);
  long long q;
  for (i = 0; i < prod; i++)
    if ((n * i) % prod == 1) {
      q = i;
      break;
    }
  long long p = (q * n - 1) / prod;
  long long first = q * n;
  long long second = p * prod;
  vector<pair<long long, long long>> v2;
  long long temp = n;
  while (temp <= first) {
    v2.push_back(make_pair(temp, temp));
    temp *= 2;
  }
  temp /= 2;
  long long temp_first = temp;
  while (1) {
    if (temp_first == first) break;
    while (temp_first + temp <= first) {
      v2.push_back(make_pair(temp_first, temp));
      temp_first += temp;
    }
    temp /= 2;
  }
  temp = prod;
  while (temp <= second) {
    v2.push_back(make_pair(temp, temp));
    temp *= 2;
  }
  temp /= 2;
  temp_first = temp;
  while (1) {
    if (temp_first == second) break;
    while (temp_first + temp <= second) {
      v2.push_back(make_pair(temp_first, temp));
      temp_first += temp;
    }
    temp /= 2;
  }
  vector<pair<long long, long long>> vx2;
  vx2.push_back(make_pair(first, second));
  long long moves = (long long)v.size() + (long long)v1.size() +
                    (long long)v2.size() + (long long)vx.size() +
                    (long long)vx1.size() + (long long)vx2.size();
  cout << moves << endl;
  for (auto x : v) add(x.first, x.second);
  for (auto x : vx) xorr(x.first, x.second);
  for (auto x : v1) add(x.first, x.second);
  for (auto x : vx1) xorr(x.first, x.second);
  for (auto x : v2) add(x.first, x.second);
  for (auto x : vx2) xorr(x.first, x.second);
}
int32_t main() {
  long long t = 1;
  long long test = 1;
  while (t--) {
    solve();
    test++;
  }
}