Problem: Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations:

* $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$.
* $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$.



Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0.

Constraints

* $1 ≤ n ≤ 100000$
* $1 ≤ q ≤ 100000$
* $0 ≤ s ≤ t < n$
* $-1000 ≤ x ≤ 1000$

Input


$n$ $q$
$query_1$
$query_2$
:
$query_q$


In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ 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 $add(s, t, x)$ and '1' denotes $find(s, t)$.

Output

For each $find$ query, print the minimum value.

Example

Input

6 7
0 1 3 1
0 2 4 -2
1 0 5
1 0 1
0 3 5 3
1 3 4
1 0 5


Output

-2
0
1
-1

Solution (in PYTHON3):

Solution:
def main():
    import sys
    input = sys.stdin.readline

    class LazySegTree:
        # Range add query
        def __init__(self, A, initialize=True, segfunc=min, ident=2000000000):
            self.N = len(A)
            self.LV = (self.N - 1).bit_length()
            self.N0 = 1 << self.LV
            self.segfunc = segfunc
            self.ident = ident
            if initialize:
                self.data = [self.ident] * self.N0 + A + [self.ident] * (self.N0 - self.N)
                for i in range(self.N0 - 1, 0, -1):
                    self.data[i] = segfunc(self.data[i * 2], self.data[i * 2 + 1])
            else:
                self.data = [self.ident] * (self.N0 * 2)
            self.lazy = [0] * (self.N0 * 2)

        def _ascend(self, i):
            for _ in range(i.bit_length() - 1):
                i >>= 1
                self.data[i] = self.segfunc(self.data[i * 2], self.data[i * 2 + 1]) + self.lazy[i]

        def _descend(self, idx):
            lv = idx.bit_length()
            for j in range(lv - 1, 0, -1):
                i = idx >> j
                x = self.lazy[i]
                if not x:
                    continue
                self.lazy[i] = 0
                self.lazy[i * 2] += x
                self.lazy[i * 2 + 1] += x
                self.data[i * 2] += x
                self.data[i * 2 + 1] += x

        # open interval [l, r)
        def add(self, l, r, x):
            l += self.N0 - 1
            r += self.N0 - 1
            l_ori = l
            r_ori = r
            while l < r:
                if l & 1:
                    self.data[l] += x
                    self.lazy[l] += x
                    l += 1
                if r & 1:
                    r -= 1
                    self.data[r] += x
                    self.lazy[r] += x
                l >>= 1
                r >>= 1
            self._ascend(l_ori // (l_ori & -l_ori))
            self._ascend(r_ori // (r_ori & -r_ori) - 1)

        # open interval [l, r)
        def query(self, l, r):
            l += self.N0 - 1
            r += self.N0 - 1
            self._descend(l // (l & -l))
            self._descend(r // (r & -r) - 1)
            ret = self.ident
            while l < r:
                if l & 1:
                    ret = self.segfunc(ret, self.data[l])
                    l += 1
                if r & 1:
                    ret = self.segfunc(self.data[r - 1], ret)
                    r -= 1
                l >>= 1
                r >>= 1
            return ret

    N, Q = map(int, input().split())
    segtree = LazySegTree([0] * N)
    for _ in range(Q):
        q = list(map(int, input().split()))
        if q[0] == 0:
            s, t, x = q[1:]
            segtree.add(s+1, t+2, x)
        else:
            s, t = q[1:]
            print(segtree.query(s+1, t+2))


if __name__ == '__main__':
    main()