• + 1 comment

    Solution in Python 3

    p = int(1e9+7)
    def intsc(l1,l2):
        if l1==[] or l2==[]:
            return([])
        else:
            a = max(l1[0],l2[0])
            b = min(l1[1],l2[1])
            if b<a:
                return([])
            else:
                return([a,b])
    def cd(l):
        if l==[]:
            return(0)
        else:
            return(l[1]-l[0]+1)
    
    t = int(input())
    for tst in range(t):
        
        s = input().strip().split()
        w = []
        for i in s:
            w.append(int(i))
        z= {}
        z[0]=[w[0],w[1]]
        z[1]=[w[2],w[3]]
        z[2]=[w[4],w[5]]
        z[3]=[w[6],w[7]]
    
        comp = 0
        for i in range(4):
            tmp = 1
            L = intsc(z[i],z[(i+1)%4])
            j = (i+2)%4
            k = (i+3)%4
            tmp = (tmp*cd(L))%p
            tmp = (tmp*cd(z[j]))%p
            tmp = (tmp*cd(z[k]))%p
            comp = (comp+tmp)%p
        for i in range(4):
            tmp = 1
            L = intsc(z[i],z[(i+1)%4])
            L = intsc(L,z[(i+2)%4])
            tmp = cd(L)%p
            tmp = (tmp*cd(z[(i+3)%4]))%p
            comp = (comp-tmp)%p
        a1 = intsc(z[0],z[1])
        a2 = intsc(z[2],z[3])
        a3 = intsc(z[1],z[2])
        a4 = intsc(z[3],z[0])
        comp = (comp - (cd(a1)*cd(a2))%p)%p
        comp = (comp - (cd(a3)*cd(a4))%p)%p
        b = intsc(a1,a2)
        comp = (comp+3*cd(b))%p
        tot = 1
        for i in range(4):
            tot*=cd(z[i])
            tot%=p
        tot-=comp
        tot%=p
        print(tot)