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分析：

这题看出来的地方就是这个NAND是左结合的，不适用结合律，交换律。

所以想每次维护答案就不怎么可能了。比赛的时候一开始看成了异或，重读一遍题目了以后就一直去想了怎么维护答案。。。。。。

但是很容易看出来0是置1， 1是取反。于是维护一下最左边以及最右边的0的位置就可以了。要注意一下特殊情况，只有一个0是0，只有一个1是1。

剩下的就是用一个数组模拟栈，细节情况有点多，需要考虑很仔细才能通过。

代码：

/*****************************************************/

//#pragma comment(linker, "/STACK:1024000000,1024000000")

#include <map>

#include <set>

#include <ctime>

#include <stack>

#include <queue>

#include <cmath>

#include <string>

#include <vector>

#include <cstdio>

#include <cctype>

#include <cstring>

#include <sstream>

#include <cstdlib>

#include <iostream>

#include <algorithm>

using namespace std;

#define   offcin        ios::sync_with_stdio(false)

#define   sigma_size    26

#define   lson          l,m,v<<1

#define   rson          m+1,r,v<<1|1

#define   slch          v<<1

#define   srch          v<<1|1

#define   sgetmid       int m = (l+r)>>1

#define   LL            long long

#define   ull           unsigned long long

#define   mem(x,v)      memset(x,v,sizeof(x))

#define   lowbit(x)     (x&-x)

#define   bits(a)       __builtin_popcount(a)

#define   mk            make_pair

#define   pb            push_back

#define   fi            first

#define   se            second

const int    INF    = 0x3f3f3f3f;

const LL     INFF   = 1e18;

const double pi     = acos(-1.0);

const double inf    = 1e18;

const double eps    = 1e-9;

const LL     mod    = 1e9+7;

const int    maxmat = 10;

const ull    BASE   = 31;

/*****************************************************/

const int maxn = 2e5 + 5;

int a[maxn << 1];

int z[maxn << 1];

int top, bot, topz, botz;

bool flag = true;

void Debug() {

    if (flag) {

        for (int i = top + 1; i <= bot; i ++)

            cout<<a[i]<<" ";

        puts("");

        for (int i = topz + 1; i <= botz; i ++)

            cout<<z[i]<<" ";

        puts("");

    }

    else {

        for (int i = top - 1; i >= bot; i --)

            cout<<a[i]<<" ";

        puts("");

        for (int i = topz - 1; i >= botz; i --)

            cout<<z[i]<<" ";

        puts("");

    }

}

int main(int argc, char const *argv[]) {

    int T;

    cin>>T;

    for (int kase = 1; kase <= T; kase ++) {

        int N; scanf("%d", &N);

        top = topz = bot = botz = maxn;

        mem(a, -1); mem(z, 0);

        printf("Case #%d:\n", kase);

        for (int i = 0; i < N; i ++) {

            char op[10]; scanf("%s", op);

            int x;

            if (op[0] == 'P' && op[1] == 'U') {

                scanf("%d", &x);

                if (flag)  {

                    a[top --] = x;

                    if (!x) z[topz --] = top + 1;

                }

                else {

                    a[top ++] = x;

                    if (!x) z[topz ++] = top - 1;

                }

            }

            else if (op[0] == 'P' && op[1] == 'O') {

                if (flag) {

                    top ++;

                    if (!a[top]) topz ++;

                }

                else {

                    top --;

                    if (!a[top]) topz --;

                }

            }

            else if (op[0] == 'R') {

                top += (flag ? 1 : -1);

                topz += (flag ? 1 : -1);

                swap(top, bot);

                swap(topz, botz);

                flag ^= 1;

                top += (flag ? -1 : 1);

                topz += (flag ? -1 : 1);

            }

            else {

                if (top == bot) {puts("Invalid."); continue; }

                else if (topz == botz) {

                    int num = abs(top - bot);

                    // cout<<"num1 "<<num<<endl;

                    printf("%d\n", (num & 1 ? 1 : 0));

                    continue;

                }

                else {

                    int ans = (abs(top - z[botz]) == 1 ? 0 : 1);

                    // cout<<"nums before 0"<<abs(top - z[botz])<<endl;

                    int num = abs(z[botz] - bot);

                    // cout<<"num1 "<<ans<<" "<<num<<endl;

                    if (num & 1) ans ^= 1;

                    printf("%d\n", ans);

                    continue;

                }

            }

            // Debug();

        }

    }

    return 0;

}