#pragma GCC optimize(2)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll>PLL;
typedef pair<int,int>PII;
typedef pair<double,double>PDD;
#define I_int ll
inline ll read()
{
    ll x=0,f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9')
    {
        if(ch=='-')f=-1;
        ch=getchar();
    }
    while(ch>='0'&&ch<='9')
    {
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x*f;
}
#define read read()
#define closeSync ios::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define multiCase int T;cin>>T;for(int t=1;t<=T;t++)
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define repp(i,a,b) for(int i=(a);i<(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define perr(i,a,b) for(int i=(a);i>(b);i--)
ll ksm(ll a,ll b,ll p)
{
    ll res=1;
    while(b)
    {
        if(b&1)res=res*a%p;
        a=a*a%p;
        b>>=1;
    }
    return res;
}
const int inf=0x3f3f3f3f;
#define PI acos(-1)
const double eps=1e-8;
const int maxn=2e5+7;
ll a[maxn],b[maxn],t[maxn];

int main()
{
    int T=read;
    while(T--)
    {
        ll n=read;
        b[0]=0;
        rep(i,1,n) a[i]=read,b[i]=read;
        rep(i,1,n) t[i]=read;
        ll res=0;
        for(int i=1; i<=n; i++)
        {
            res+=t[i]+a[i]-b[i-1];
            if(i!=n)
            {
                ll tmp=(b[i]-a[i])/2;
                if((b[i]-a[i])%2) tmp++;
                tmp=max(tmp+res,b[i]);
                res=tmp;
            }

           /// cout<<i<<"**********"<<res<<endl;
        }
        cout<<res<<endl;
    }
    /**
    1
    5
    1 4
    7 8
    9 10
    13 15
    19 20
    1 2 3 4 5
    */








    return 0;
}










