Problem: Write a program which manipulates a sequence A = {a0, a1, . . . , an−1} with the following operations:

* update(s, t, x): change as, as+1, ..., at to x.
* find(s, t): report the minimum element in as, as+1, ..., at.



Note that the initial values of ai (i = 0, 1, . . . , n−1) are 231-1.

Constraints

* 1 ≤ n ≤ 100000
* 1 ≤ q ≤ 100000
* 0 ≤ s ≤ t < n
* 0 ≤ x < 231−1

Input


n q
query1
query2
:
queryq


In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query queryi is given in the following format:


0 s t x


or


1 s t


The first digit represents the type of the query. '0' denotes update(s, t, x) and '1' denotes find(s, t).

Output

For each find operation, print the minimum value.

Examples

Input

3 5
0 0 1 1
0 1 2 3
0 2 2 2
1 0 2
1 1 2


Output

1
2


Input

1 3
1 0 0
0 0 0 5
1 0 0


Output

2147483647
5

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define int long long
const int INF = (1LL << 31) - 1;
const int sqrtN = 512;
struct SqrtDecomposition {
  int N, K;
  vector<int> data;
  vector<int> bucketMin;
  vector<bool> lazyFlag;
  vector<int> lazyUpdate;
  SqrtDecomposition(int n) : N(n) {
    K = (N + sqrtN - 1) / sqrtN;
    data.assign(K * sqrtN, INF);
    bucketMin.assign(K, INF);
    lazyFlag.assign(K, false);
    lazyUpdate.assign(K, 0);
  }
  void eval(int k) {
    if (lazyFlag[k]) {
      lazyFlag[k] = false;
      for (int i = k * sqrtN; i < (k + 1) * sqrtN; ++i) {
        data[i] = lazyUpdate[k];
      }
    }
  }
  // [s, t)
  void update(int s, int t, int x) {
    for (int k = 0; k < K; ++k) {
      int l = k * sqrtN, r = (k + 1) * sqrtN;
      if (r <= s || t <= l)
        continue;
      if (s <= l && r <= t) {
        bucketMin[k] = x;
        lazyFlag[k] = true;
        lazyUpdate[k] = x;
      } else {
        eval(k);
        for (int i = max(s, l); i < min(t, r); ++i) {
          data[i] = x;
        }
        int &minVal = bucketMin[k] = INF;
        for (int i = l; i < r; ++i) {
          minVal = min(minVal, data[i]);
        }
      }
    }
  }
  // [s, t)
  int find(int s, int t) {
    int minVal = INF;
    for (int k = 0; k < K; ++k) {
      int l = k * sqrtN, r = (k + 1) * sqrtN;
      if (r <= s || t <= l)
        continue;
      if (s <= l && r <= t) {
        minVal = min(minVal, bucketMin[k]);
      } else {
        eval(k);
        for (int i = max(s, l); i < min(t, r); ++i) {
          minVal = min(minVal, data[i]);
        }
      }
    }
    return minVal;
  }
};

signed main() {
  ios::sync_with_stdio(false);
  int N, Q;
  cin >> N >> Q;
  SqrtDecomposition decomp(N);
  while (Q--) {
    int c;
    cin >> c;
    if (c == 0) {
      int s, t, x;
      cin >> s >> t >> x;
      decomp.update(s, t + 1, x);
    } else {
      int s, t;
      cin >> s >> t;
      cout << decomp.find(s, t + 1) << endl;
    }
  }
}