You are given the two dimensional database as a matrix A with n rows and n columns. In the beginning, A[i][j]=0 for all 1≤i,j≤n .
Then q operations or queries will be given in turn.

You should maintain the database for two type of operations:
⋅ 1 L R : for each element A[i][j] which satisfy L≤i+j≤R , increase the value to A[i][j]+1 , where 2≤L≤R≤2n .
⋅ 2 L R : for each element A[i][j] which satisfy L≤i−j≤R , increase the value to A[i][j]+1 , where 1−n≤L≤R≤n−1 .
Meanwhile, you should answer the queries:
⋅ 3 x1 x2 y1 y2 : count the value of elements A[i][j] which satisfy x1≤i≤x2 and y1≤j≤y2 , where 1≤x1<x2≤n and 1≤y1<y2≤n .

Each test case contains several lines. The first line contains the integer n and q .
The i -th line of the next q lines contains an operation ‘‘1 L R" or ‘‘2 L R" , or a query ‘‘3 x1 x2 y1 y2" .

The sum of n for all test cases would not be larger than 200000 and the sum of q would not be larger than 50000 .

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
typedef __int64 LL;
const int maxn = 300005;
struct tree
{LL suml[maxn << 2], sumr[maxn << 2], sum[maxn << 2];LL add[maxn << 2];inline void pushup(int id, int L, int R){LL mid = L + R >> 1;sum[id] = sum[id << 1] + sum[id << 1 | 1];suml[id] = suml[id << 1] + (mid - L + 1)*sum[id << 1 | 1] + suml[id << 1 | 1];sumr[id] = sumr[id << 1 | 1] + sumr[id << 1] + (R - mid)*sum[id << 1];}inline void pushdown(int id, int L, int R){int mid = L + R >> 1;if (add[id]){LL ln = mid - L + 1;LL rn = R - mid;add[id << 1] += add[id];add[id << 1 | 1] += add[id];sum[id << 1] += add[id] * ln;sum[id << 1 | 1] += add[id] * rn;suml[id << 1] += add[id] * (1 + ln)*ln >> 1;suml[id << 1 | 1] += add[id] * (1 + rn)*rn >> 1;sumr[id << 1] += add[id] * (1 + ln)*ln >> 1;sumr[id << 1 | 1] += add[id] * (1 + rn)*rn >> 1;add[id] = 0;}}void build(){memset(sum, 0, sizeof(sum));memset(suml, 0, sizeof(suml));memset(sumr, 0, sizeof(sumr));memset(add, 0, sizeof(add));}LL queL(int id, int L, int R, int l, int r){//  if(id>400000) while(1);if (l <= L&&R <= r) return (L - l)*sum[id] + suml[id];else{pushdown(id, L, R);int mid = L + R >> 1;LL res = 0;if (l <= mid) res += queL(id << 1, L, mid, l, r);if (mid<r) res += queL(id << 1 | 1, mid + 1, R, l, r);return res;}}LL queR(int id, int L, int R, int l, int r){if (l <= L&&R <= r) return (r - R)*sum[id] + sumr[id];else{pushdown(id, L, R);int mid = L + R >> 1;LL res = 0;if (l <= mid) res += queR(id << 1, L, mid, l, r);if (mid<r) res += queR(id << 1 | 1, mid + 1, R, l, r);return res;}}LL que(int id, int L, int R, int l, int r){if (l <= L&&R <= r) return sum[id];else{pushdown(id, L, R);int mid = L + R >> 1;LL res = 0;if (l <= mid) res += que(id << 1, L, mid, l, r);if (mid<r) res += que(id << 1 | 1, mid + 1, R, l, r);return res;}}void op(int id, int L, int R, int l, int r){if (l <= L&&R <= r){LL sn = R - L + 1;add[id]++;sum[id] += sn;suml[id] += (1 + sn)*sn >> 1;sumr[id] += (1 + sn)*sn >> 1;}else{pushdown(id, L, R);int mid = L + R >> 1;if (l <= mid) op(id << 1, L, mid, l, r);if (mid<r) op(id << 1 | 1, mid + 1, R, l, r);pushup(id, L, R);}}
}tz, tf;
int main()
{int T;scanf("%d", &T);int ks = 0;while (T--){printf("Case #%d:\n", ++ks);tz.build();tf.build();int n, m;scanf("%d %d", &n, &m);while (m--){int op;scanf("%d", &op);if (op == 1){int l, r;scanf("%d %d", &l, &r);tf.op(1, 1, n << 1, l, r);}else if (op == 2){int l, r;scanf("%d %d", &l, &r);l += n;r += n;tz.op(1, 1, n << 1, l, r);}else{int x1, y1, x2, y2;scanf("%d %d %d %d", &x1, &x2, &y1, &y2);LL ans = 0;int A, B, C, D;A = x1 - y1 + n;B = x1 - y2 + n;C = x2 - y2 + n;D = x2 - y1 + n;if (D >= max(A, C) + 1) ans += tz.queR(1, 1, n << 1, max(A, C) + 1, D);if (B <= min(A, C) - 1) ans += tz.queL(1, 1, n << 1, B, min(A, C) - 1);ans += tz.que(1, 1, n << 1, min(A, C), max(A, C))*(min(y2 - y1, x2 - x1) + 1);A = x1 + y1;B = x1 + y2;C = x2 + y2;D = x2 + y1;if (A <= min(B, D) - 1) ans += tf.queL(1, 1, n << 1, A, min(B, D) - 1);if (C >= max(B, D) + 1) ans += tf.queR(1, 1, n << 1, max(B, D) + 1, C);ans += tf.que(1, 1, n << 1, min(B, D), max(B, D))*(min(y2 - y1, x2 - x1) + 1);printf("%I64d\n", ans);}}}return 0;
}