Problem: Company "Robots industries" produces robots for territory protection. Robots protect triangle territories — right isosceles triangles with catheti parallel to North-South and East-West directions.

Owner of some land buys and sets robots on his territory to protect it. From time to time, businessmen want to build offices on that land and want to know how many robots will guard it. You are to handle these queries. 

Input

The first line contains integer N — width and height of the land, and integer Q — number of queries to handle.

Next Q lines contain queries you need to process.

Two types of queries: 

  1. 1 dir x y len — add a robot to protect a triangle. Depending on the value of dir, the values of x, y and len represent a different triangle: 
    * dir = 1: Triangle is defined by the points (x, y), (x + len, y), (x, y + len)
    * dir = 2: Triangle is defined by the points (x, y), (x + len, y), (x, y - len)
    * dir = 3: Triangle is defined by the points (x, y), (x - len, y), (x, y + len)
    * dir = 4: Triangle is defined by the points (x, y), (x - len, y), (x, y - len)
  2. 2 x y — output how many robots guard this point (robot guards a point if the point is inside or on the border of its triangle) 


  * 1 ≤ N ≤ 5000
  * 1 ≤ Q ≤ 105
  * 1 ≤ dir ≤ 4
  * All points of triangles are within range [1, N]
  * All numbers are positive integers 

Output

For each second type query output how many robots guard this point. Each answer should be in a separate line.

Examples

Input

17 10
1 1 3 2 4
1 3 10 3 7
1 2 6 8 2
1 3 9 4 2
2 4 4
1 4 15 10 6
2 7 7
2 9 4
2 12 2
2 13 8


Output

2
2
2
0
1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline unsigned myrand() {
  static unsigned x = 998244353;
  return x += x << 2 | 1;
}
inline int getint() {
  static char c;
  while ((c = getchar()) < '0' || c > '9')
    ;
  int res = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') res = res * 10 + c - '0';
  return res;
}
const int NDir = 4;
const int MaxN = 5001;
const int MaxQ = 100001;
const int MaxM = 400001;
const int MaxLogM = 19;
const int MaxTN = MaxM * MaxLogM >> 1;
int n, nQu, m = 0, nQuery = 0;
int ans[MaxQ];
struct operation {
  int type, lab;
  int x, y, dir;
  friend inline bool operator<(const operation &lhs, const operation &rhs) {
    if (lhs.x != rhs.x) return lhs.x < rhs.x;
    return lhs.type <= rhs.type;
  }
  inline void set(const int &t, const int &l, const int &_x, const int &_y,
                  const int &d) {
    type = t, lab = l;
    x = _x, y = _y, dir = d;
  }
};
operation q[MaxM], p[MaxM];
struct treap_node {
  treap_node *lc, *rc;
  int val, size;
  unsigned pri;
  inline void update() {
    size = 1;
    if (lc) size += lc->size;
    if (rc) size += rc->size;
  }
};
treap_node pool[MaxTN], *tail = pool;
inline treap_node *newnode() {
  treap_node *x = tail++;
  x->lc = x->rc = NULL;
  x->pri = myrand(), x->size = 1;
  return x;
}
inline void treap_zig(treap_node *&x) {
  treap_node *y = x->lc;
  x->lc = y->rc;
  y->rc = x;
  x->update();
  x = y;
}
inline void treap_zag(treap_node *&x) {
  treap_node *y = x->rc;
  x->rc = y->lc;
  y->lc = x;
  x->update();
  x = y;
}
void treap_insert(treap_node *&x, const int &val) {
  if (x == NULL) {
    x = newnode(), x->val = val;
    return;
  }
  if (val <= x->val) {
    treap_insert(x->lc, val);
    if (x->pri < x->lc->pri) treap_zig(x);
  } else {
    treap_insert(x->rc, val);
    if (x->pri < x->rc->pri) treap_zag(x);
  }
  x->update();
}
inline int treap_query(treap_node *x, const int &val) {
  int rank = 0;
  while (x) {
    if (val > x->val)
      x = x->rc;
    else {
      int r = x->rc ? x->rc->size : 0;
      rank += r + 1;
      x = x->lc;
    }
  }
  return rank;
}
treap_node *bit[NDir][MaxN];
inline void bit_update(treap_node **b, const int &x, const int &val) {
  for (int i = x; i <= n; i += i & -i) treap_insert(b[i], val);
}
inline int bit_query(treap_node **b, const int &x, const int &val) {
  int res = 0;
  for (int i = x; i; i ^= i & -i) res += treap_query(b[i], val);
  return res;
}
inline void bit_reinit(treap_node **b, const int &x) {
  for (int i = x; i <= n && b[i]; i += i & -i) b[i] = NULL;
}
void solve(const int &l, const int &r) {
  if (l == r) return;
  int mid = l + r >> 1;
  solve(l, mid);
  solve(mid + 1, r);
  int i = l, j = mid + 1;
  for (int t = l; t <= r; ++t) {
    if (j > r || (i <= mid && q[i] < q[j])) {
      p[t] = q[i++];
      if (p[t].type == 0) bit_update(bit[p[t].dir], p[t].y, p[t].lab);
    } else {
      p[t] = q[j++];
      if (p[t].type == 1) {
        int len = p[t].x + p[t].y;
        ans[p[t].lab] += bit_query(bit[p[t].dir], p[t].y, len);
      }
    }
  }
  tail = pool;
  for (i = l; i <= r; ++i) {
    q[i] = p[i];
    if (q[i].type == 0) bit_reinit(bit[q[i].dir], q[i].y);
  }
}
int main() {
  n = getint(), nQu = getint();
  while (nQu--) {
    int type = getint();
    if (type == 1) {
      int dir = getint();
      int x = getint(), y = getint(), l = getint();
      if (dir == 2 || dir == 4) y = n - y + 1;
      if (dir == 3 || dir == 4) x = n - x + 1;
      q[++m].set(0, l + x + y, x, y, --dir);
    } else {
      int x = getint(), y = getint();
      q[++m].set(1, ++nQuery, x, y, 0);
      q[++m].set(1, nQuery, x, n - y + 1, 1);
      q[++m].set(1, nQuery, n - x + 1, y, 2);
      q[++m].set(1, nQuery, n - x + 1, n - y + 1, 3);
    }
  }
  solve(1, m);
  for (int i = 1; i <= nQuery; ++i) printf("%d\n", ans[i]);
  return 0;
}