python3 - <<'PY'
from itertools import combinations
p=996979
J=[(22716,22810),(397695,397787),(731292,731385)]
K=J+[(a+p,b+p) for a,b in J]
YS=set()
for m,(L,U) in enumerate(K):
    for y1 in range((L-1)//2,U//2+1):
        for rest in combinations(range(y1+1,y1+50),47):
            ys=(y1,)+rest
            if ys[0]+ys[1]>=L and ys[-2]+ys[-1]<=U:
                YS.add(ys)
print('Y count',len(YS))
tot=0
valid=[]
for ys in YS:
    y1=ys[0]; yk=ys[-1]
    A=[]; B=[]
    for li,ui in K:
        a0=max(0,li-y1); a1=min(y1-1,ui-yk)
        if a0<=a1: A.append((a0,a1))
        b0=max(yk+1,li-y1); b1=min(p-1,ui-yk)
        if b0<=b1: B.append((b0,b1))
    P=[]
    for a0,a1 in A:
        for b0,b1 in B:
            for a in range(a0,a1+1):
                for lk,uk in K:
                    ll=max(b0,lk-a); hh=min(b1,uk-a)
                    for b in range(ll,hh+1):
                        if b>yk: P.append((a,b))
    if P:
        valid.append((ys,P))
        tot+=len(P)
print('valid Y',len(valid),'pairs',tot)
for ys,P in valid: print('Y',ys[0],ys[-1],len(P),P[0],P[-1])
PY