#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <cmath>
#include <map>
#include <deque>
#include <set>
#include <stack>
#include <queue>
#include <numeric>
#include <cctype>
#include <bits/stdc++.h>
#include <string>
#include <iomanip>
using namespace std;
typedef long long ll;
const int MOD = 1000000007;
const int MOD2 = 998244353;
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
// freopen("input.txt", "r", stdin);
int a, b, x;
cin >> a >> b >> x;
string sa, sb, sx;
cin >> sa >> sb >> sx;
// Convert binary string to integer
// ll a = stoi(sa, nullptr, 2);
// int b = stoi(sb, nullptr, 2);
// int x = stoi(sx, nullptr, 2);
// cout << a << endl;
// cout << b << endl;
// cout << x << endl;
if ((a & b) >= x)
{
cout << 0 << "\n";
return 0;
}
for (int i = 0; i < 31; i++)
{
int bit = 1 << i;
if (((a | bit) & b) >= x)
{
cout << 1 << "\n";
cout << "a " << i << "\n";
return 0;
}
if (((b | bit) & a) >= x)
{
cout << 1 << "\n";
cout << "b " << i << "\n";
return 0;
}
}
vector<string> v;
for (int i = 30; i >= 0 && ((a & b) < x); i--)
{
int bit = 1 << i;
if ((x & (bit)))
{
if (!(a & bit))
{
string s = to_string(i);
v.push_back("a " + s);
}
if (!(b & bit))
{
string s = to_string(i);
v.push_back("b " + s);
}
a |= bit;
b |= bit;
}
else
{
int opp = 0;
if (!(a & bit))
{
string s = to_string(i);
v.push_back("a " + s);
opp++;
}
if (!(b & bit))
{
string s = to_string(i);
v.push_back("b " + s);
opp++;
}
if (opp == 2)
{
for (int j = i - 1; j >= 0; j--)
{
int nm = (1 << j);
if ((a & nm) != (b & nm))
{
if (((a | nm) & (b | nm)) >= x)
{
if (!(a & nm))
{
v.pop_back();
v.pop_back();
string s = to_string(j);
v.push_back("a " + s);
a |= nm;
}
else
{
// cout << "ansb" << '\n';
v.pop_back();
v.pop_back();
string s = to_string(j);
v.push_back("b " + s);
b |= nm;
}
}
break;
}
}
}
a |= bit;
b |= bit;
}
}
cout << v.size() << "\n";
for (auto item : v)
{
cout << item << "\n";
}
return 0;
}
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