Circle of Monsters

You are playing another computer game, and now you have to slay n monsters. These monsters are standing in a circle, numbered clockwise from 1 to n. Initially, the i-th monster has ai health.

You may shoot the monsters to kill them. Each shot requires exactly one bullet and decreases the health of the targeted monster by 1 (deals 1 damage to it). Furthermore, when the health of some monster i becomes 0 or less than 0, it dies and explodes, dealing bi damage to the next monster (monster i+1, if i<n, or monster 1, if i=n). If the next monster is already dead, then nothing happens. If the explosion kills the next monster, it explodes too, damaging the monster after it and possibly triggering another explosion, and so on.

You have to calculate the minimum number of bullets you have to fire to kill all n monsters in the circle.

Input
The first line contains one integer T (1≤T≤150000) — the number of test cases.

Then the test cases follow, each test case begins with a line containing one integer n (2≤n≤300000) — the number of monsters. Then n lines follow, each containing two integers ai and bi (1≤ai,bi≤1012) — the parameters of the i-th monster in the circle.

It is guaranteed that the total number of monsters in all test cases does not exceed 300000.

Output
For each test case, print one integer — the minimum number of bullets you have to fire to kill all of the monsters.

Example

input
1
3
7 15
2 14
5 3
output
6

#include<bits/stdc++.h>

#define si(a) scanf("%d",&a)
#define sl(a) scanf("%lld",&a)
#define sd(a) scanf("%lf",&a)
#define sc(a) scahf("%c",&a);
#define ss(a) scanf("%s",a)
#define pi(a) printf("%d\n",a)
#define pl(a) printf("%lld\n",a)
#define pc(a) putchar(a)
#define ms(a) memset(a,0,sizeof(a))
#define repi(i, a, b) for(register int i=a;i<=b;++i)
#define repd(i, a, b) for(register int i=a;i>=b;--i)
#define reps(s) for(register int i=head[s];i;i=Next[i])
#define ll long long
#define vi vector<int>
#define vc vector<char>
#define pii pair<int,int>
#define pll pair<long,long>
#define pil pair<int,long>
#define pli pair<long,int>
#define mii unordered_map<int,int>
#define msi unordered_map<string,int>
#define lowbit(x) ((x)&(-(x)))
#define ce(i, r) i==r?'\n':' '
#define pb push_back
#define fi first
#define se second
#define pr(x) cout<<#x<<": "<<x<<endl
using namespace std;

inline int qr() {
    int f = 0, fu = 1;
    char c = getchar();
    while (c < '0' || c > '9') {
        if (c == '-')fu = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9') {
        f = (f << 3) + (f << 1) + c - 48;
        c = getchar();
    }
    return f * fu;
}

const int N = 3e5 + 10;
const ll INF = 4e18;
ll a[N], b[N], c[N];
ll sum;
int T, n;

int main() {
    T = qr();
    while (T--) {
        n = qr();
        repi(i, 1, n)sl(a[i]), sl(b[i]);
        c[1] = max(0ll, a[1] - b[n]);
        repi(i, 2, n)c[i] = max(0ll, a[i] - b[i - 1]);
        sum = 0;
        repi(i, 1, n)sum += c[i];
        ll ans = INF;
        repi(i, 1, n)ans = min(ans, sum - c[i] + a[i]);
        pl(ans);
    }
    return 0;
}