Codeforces Round #443 (Div. 2) C 位运算

C. Short Program

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.

In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.

Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.

Input

The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.

Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.

Output

Output an integer k (0 ≤ k ≤ 5) — the length of your program.

Next k lines must contain commands in the same format as in the input.

Examples

input

3
| 3
^ 2
| 1

output

2
| 3
^ 2

input

3
& 1
& 3
& 5

output

1
& 1

input

3
^ 1
^ 2
^ 3

output

0

Note

You can read about bitwise operations in https://en.wikipedia.org/wiki/Bitwise_operation.

Second sample:

Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.

思路：取x=0,y=1023（即两个互为取反数的数字）。将n次位运算操作后的x，y值，对比即可得到每一位数字进行的 操作。

代码：

#include<bits/stdc++.h>
#define db double
#include<vector>
#define ll long long
#define vec vector<ll>
#define Mt  vector<vec>
#define ci(x) scanf("%d",&x)
#define cd(x) scanf("%lf",&x)
#define cl(x) scanf("%lld",&x)
#define pi(x) printf("%d
",x)
#define pd(x) printf("%f
",x)
#define pl(x) printf("%lld
",x)
const int N = 1e6 + 5;
const int mod = 1e9 + 7;
const int MOD = mod - 1;
const db  eps = 1e-18;
const db  PI = acos(-1.0);
using namespace std;
bool cal(int a,int i){
    if(a&(1<<i)) return 1;
    return 0;
}
int main(){
    int n;ci(n);
    int x=0,y=1023;
    while (n--) {
        char c[2];
        int t;
        scanf("%s %d", c, &t);
        if (c[0] == '|') x|=t,y|=t;
        if (c[0] == '&') x&=t,y&=t;
        if (c[0] == '^') x^=t,y^=t;
    }
    /*
     4种:
     x:0,y:1.
     x y:0011,0010,0111,0110
     */
    int v1 = 0, v2 = 0, v3 = 0;
    for (int i = 0; i < 10; i++) {
        if(!cal(x,i)&&cal(y,i))  v2+=(1<<i);//0011: |0 &1 ^0
        if(cal(x,i)&&cal(y,i))   v3+=(1<<i);//0111: |0 &0 ^1
        if(cal(x,i)&&!cal(y,i))  v2+=(1<<i),v3+=(1<<i);//0110: |0 &1 ^1
    }
    printf("3
");
    printf("| %d
", v1);
    printf("& %d
", v2);
    printf("^ %d
", v3);
    return 0;
}