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;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
pi readpi(ll off = 0) {
  ll first, second;
  cin >> first >> second;
  return pi(first + off, second + off);
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
vvc<ll> readGraph(ll n, ll m) {
  vvc<ll> g(n);
  for (ll i = ll(0); i < ll(m); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    g[first].push_back(second);
    g[second].push_back(first);
  }
  return g;
}
vvc<ll> readTree(ll n) { return readGraph(n, n - 1); }
ll waf(ll m) {
  vi x;
  for (ll i = ll(1); i < ll(100000); i++) {
    ll v = m * i;
    for (auto z : x) chmin(v, z ^ v);
    if (v) x.push_back(v);
    if (ll(x.size()) == topbit(m * i) + 1) {
      return i;
    }
  }
  return -1;
}
const ll S = 100;
using B = bitset<S>;
vi sweep(vc<B>& first, ll w, ll c = -1) {
  if (first.empty()) return {};
  if (c == -1) c = w;
  ll h = ll(first.size()), r = 0;
  vi res;
  for (ll i = ll(0); i < ll(c); i++) {
    if (r == h) break;
    for (ll j = ll(r); j < ll(h); j++)
      if (first[j][i]) {
        swap(first[r], first[j]);
        break;
      }
    if (!first[r][i]) continue;
    for (ll j = ll(0); j < ll(h); j++)
      if (j != r && first[j][i]) {
        first[j] ^= first[r];
      }
    res.push_back(i);
    r++;
  }
  return res;
}
pair<bool, B> lineareq(vc<B> first, ll w, B second) {
  ll h = ll(first.size());
  for (ll i = ll(0); i < ll(h); i++) first[i][w] = second[i];
  vi idx = sweep(first, w + 1, w);
  cerr << ll(idx.size()) << endl;
  for (ll i = ll(ll(idx.size())); i < ll(h); i++)
    if (first[i][w]) return make_pair(false, B());
  B res;
  for (ll i = ll(0); i < ll(ll(idx.size())); i++) res[idx[i]] = first[i][w];
  return make_pair(true, res);
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  vc<tuple<ll, ll, ll>> ans;
  unordered_set<ll> waf;
  auto add_add = [&](ll first, ll second) {
    assert(waf.find(first) != waf.end());
    assert(waf.find(second) != waf.end());
    ans.emplace_back(0, first, second);
    waf.insert(first + second);
  };
  auto add_xor = [&](ll first, ll second) {
    assert(waf.find(first) != waf.end());
    assert(waf.find(second) != waf.end());
    ans.emplace_back(1, first, second);
    waf.insert(first ^ second);
  };
  ll m;
  cin >> m;
  waf.insert(m);
  vi x{m}, y{m};
  for (ll i = ll(2); i < ll(ten(9)); i++) {
    ll v = m * i;
    for (auto z : x) chmin(v, z ^ v);
    if (v) {
      y.push_back(m * i);
      x.push_back(v);
    }
    if (ll(x.size()) == topbit(m * i) + 1) {
      break;
    }
  }
  const ll L = 30;
  for (ll i = ll(0); i < ll(L); i++) {
    add_add(m << i, m << i);
  }
  for (auto v : y) {
    v /= m;
    vi idx;
    for (ll i = ll(0); i < ll(L); i++)
      if (v & 1 << i) idx.push_back(i);
    ll cur = m << idx[0];
    for (ll i = ll(1); i < ll(ll(idx.size())); i++) {
      add_add(cur, m << idx[i]);
      cur += m << idx[i];
    }
  }
  void(0);
  ll n = ll(y.size());
  void(0);
  void(0);
  vc<B> z(n);
  for (ll i = ll(0); i < ll(n); i++)
    for (ll j = ll(0); j < ll(n); j++) z[i][j] = (y[j] >> i) & 1;
  B tar{};
  tar[0] = 1;
  auto ysp = lineareq(z, n, tar);
  assert(ysp.first);
  vi idx;
  for (ll i = ll(0); i < ll(n); i++)
    if (ysp.second[i]) idx.push_back(i);
  void(0);
  assert(ll(idx.size()) >= 2);
  ll cur = y[idx[0]];
  for (ll i = ll(1); i < ll(ll(idx.size())); i++) {
    add_xor(cur, y[idx[i]]);
    cur ^= y[idx[i]];
  }
  assert(cur == 1);
  assert(waf.find(1) != waf.end());
  assert(ll(ans.size()) <= 100000);
  print(ll(ans.size()));
  for (auto w : ans) {
    ll t, first, second;
    tie(t, first, second) = w;
    cout << first << (t == 0 ? " + " : " ^ ") << second << "\n";
  }
}