python3 - <<'PY'
p=996979
K=[(22716,22810),(397695,397787),(731292,731385),(1019695,1019789),(1394674,1394766),(1728271,1728364)]
W=[b-a for a,b in K]
NY=0
Ntot=0
Nmax=0
patterns=[]
def gen(pos,cost,arr,D):
    if pos==46:
        patterns.append(tuple(arr))
        return
    w=1 if pos in (0,45) else 2
    for e in range((D-cost)//w+1):
        arr.append(e)
        gen(pos+1,cost+w*e,arr,D)
        arr.pop()
for m,(L,U) in enumerate(K[:3]):
    D=W[m]-90
    patterns.clear()
    gen(0,0,[],D)
    for e in patterns:
        delta=90+2*sum(e[1:45])+e[0]+e[45]
        lo=(L-e[0])//2
        hi=(U-delta-1-e[0])//2
        for y1 in range(lo,hi+1):
            ys=[y1]
            y=y1
            for g in e:
                y+=1+g
                ys.append(y)
            if not(len(ys)==47 and ys[0]+ys[1]>=L and ys[-2]+ys[-1]<=U):
                print('bad')
            NY+=1
            y1=ys[0]
            y47=ys[-1]
            A=[]
            B=[]
            for li,ui in K:
                a0=max(0,li-y1)
                a1=min(y1-1,ui-y47)
                if a0<=a1: A.append((a0,a1))
                b0=max(y47+1,li-y1)
                b1=min(p-1,ui-y47)
                if b0<=b1: B.append((b0,b1))
            cnt=0
            for a0,a1 in A:
                for b0,b1 in B:
                    for lk,uk in K:
                        for a in range(a0,a1+1):
                            l=max(b0,lk-a)
                            h=min(b1,uk-a)
                            if h>=l: cnt+=h-l+1
            Ntot+=cnt
            if cnt>Nmax: Nmax=cnt
print('Y',NY,'pairs',Ntot,'maxperY',Nmax)
PY