type WideNum = number | bigint
type Tostrable = string | boolean | WideNum | null | undefined
type NumOfStr<N extends string, T extends Tostrable = WideNum> = N extends `${infer K extends T}` ? K : T
type SigNumber = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
declare namespace StringReved {
    type P0<N, R extends string> = N extends `${infer I}${infer S}` ? P0<S, `${I}${R}`> : R
    type P1<N, R extends string> = N extends (
        `${infer I0}${infer I1}${infer I2}${infer I3}${infer I4}${infer I5}${infer I6}${infer I7}${infer I8}${infer I9
        }${infer N}`
    ) ? P1<N,
        `${I9}${I8}${I7}${I6}${I5}${I4}${I3}${I2}${I1}${I0
        }${R}`
    > : P0<N, R>
}
type StringReved<N extends string> = StringReved.P1<N, ''>
declare namespace Aligned {
    type P0<A extends string, B, R extends string> = B extends `${any}${infer B}` ? A extends `${any}${infer A}` ? P0<A, B, R> : P0<A, B, `${R}Z`> : { r: R, a: A }
    type P1<A extends string, B, R extends string> = B extends (
        `${any}${any}${any}${any}${any}${any}${any}${any}${any}${any
        }${infer B}`
    ) ? P0<A,
        `${'0000000000'
        }`, R
    > extends { r: infer R extends string, a: infer A extends string } ? P1<A, B, R> : never : P0<A, B, R>
    type De<A extends string, B> = P1<A, B, ''> extends { r: infer R } ? R extends '' ? 0 : R : never
    type F0<B, F extends Tostrable, R extends string> = B extends `${any}${infer B}` ? F0<B, F, `${R}${F}`> : R
    type F1<B, F extends Tostrable, R extends string> = B extends (
        `${any}${any}${any}${any}${any}${any}${any}${any}${any}${any
        }${infer B}`
    ) ? F1<B, F, `${R
        }${F}${F}${F}${F}${F}${F}${F}${F}${F}${F}`
    > : F0<B, F, R>
    type Ad<A extends string, B extends string> = `${A}${B}`
    type S<T, A extends string, B, F extends Tostrable> = De<A, B> extends infer C extends string ? T extends 0 ? Ad<A, F1<C, F, ''>> : Ad<F1<C, F, ''>, A> : A
    type Z<T, A extends string, B extends string, F extends Tostrable> =
        string extends B ? T extends 0 ? `${A}${string}` : `${string}${A}` :
        string extends A ? T extends 0 ? Ad<A, F1<B, F, ''>> : Ad<F1<B, F, ''>, A> :
        S<T, A, B, F>
}
type PreAligned<A extends string, B extends string, F extends Tostrable = ' '> = Aligned.Z<1, A, B, F>
declare namespace xcr {
    type R<T> = T extends 0 ? 9 : 0
    type SigT = SigNumber | 's'
    type SigVary<T, N> = N extends SigNumber ? (T extends 0 ? [1, 2, 3, 4, 5, 6, 7, 8, 9, 's'] : ['s', 0, 1, 2, 3, 4, 5, 6, 7, 8])[N] : 's'
}
type Leading0less<N extends string> = N extends `0${infer K}` ? K extends '' ? N : Leading0less<K> : N
declare namespace cmp {
    type SigCmp<A extends xcr.SigT, B extends xcr.SigT> = A extends B ? 0 : A extends 's' ? -1 : B extends 's' ? 1 : SigCmp<xcr.SigVary<0, A>, xcr.SigVary<0, B>>
    type LenCmp<A extends string, B extends string> = PreAligned<A, B> extends A ? PreAligned<B, A> extends B ? 0 : -1 : 1
    type P0<A extends string, B extends string> = `${A},${B}` extends (
        `${infer A0 extends SigNumber
        }${infer A}${','
        }${infer B0 extends SigNumber
        }${infer B}`
    ) ? SigCmp<A0, B0> extends infer K extends -1 | 1 ? K : P0<A, B> : 0
    type P1<A extends string, B extends string> = `${A},${B}` extends (
        `${infer A0}${infer A1}${infer A2}${infer A3}${infer A4}${infer A5}${infer A6}${infer A7}${infer A8}${infer A9
        }${infer A}${','
        }${infer B0}${infer B1}${infer B2}${infer B3}${infer B4}${infer B5}${infer B6}${infer B7}${infer B8}${infer B9
        }${infer B}`
    ) ? P0<
        `${A0}${A1}${A2}${A3}${A4}${A5}${A6}${A7}${A8}${A9}`,
        `${B0}${B1}${B2}${B3}${B4}${B5}${B6}${B7}${B8}${B9}`
    > extends infer K extends -1 | 1 ? K : P1<A, B> : P0<A, B>
}
type SntCmpUns<A extends string, B extends string> = cmp.LenCmp<A, B> extends infer K extends -1 | 1 ? K : cmp.P1<A, B>
declare namespace opn {
    type QH<Q = any, H = any> = { q: Q, h: H }
    type SigInfl<T extends 0 | 9, A, B, E extends 1 | 0> = B extends 0 ? A extends 's' ? QH<1, T> : QH<E, A> : A extends SigNumber ? SigInfl<T, xcr.SigVary<T, A>, xcr.SigVary<9, B>, E> : SigInfl<T, T, B, 1>
    type SigTrinfl<T extends 0 | 9, A, B, C extends 0 | 1> = SigInfl<T, A, B, 0> extends infer K extends QH ? SigInfl<T, K['h'], C, K['q']> : QH<0, 0>
    type G0<T extends 0 | 9, L, J extends 0 | 1, R extends string> = L extends { a: [`${infer A extends SigNumber}`, ...infer LA], b: [`${infer B extends SigNumber}`, ...infer LB] } ? SigTrinfl<T, A, B, J> extends infer S extends QH ? G0<T, { a: LA, b: LB }, S['q'], `${R}${S['h']}`> : QH : QH<J, R>;
    type P0<T extends 0 | 9, A extends string, B extends string, J extends 0 | 1, R extends string> = `${A},${B}` extends (
        `${infer A0
        }${infer A}${','
        }${infer B0
        }${infer B}`
    ) ? G0<T, { a: [A0], b: [B0] }, J, ''> extends infer S extends QH ? P0<T, A, B, S['q'], `${R}${S['h']}`> : R : R
    type P1<T extends 0 | 9, A extends string, B extends string, J extends 0 | 1, R extends string> = `${A},${B}` extends (
        `${infer A0}${infer A1}${infer A2}${infer A3}${infer A4}${infer A5}${infer A6}${infer A7}${infer A8}${infer A9
        }${infer A}${','
        }${infer B0}${infer B1}${infer B2}${infer B3}${infer B4}${infer B5}${infer B6}${infer B7}${infer B8}${infer B9
        }${infer B}`
    ) ? G0<T, {
        a: [A0, A1, A2, A3, A4, A5, A6, A7, A8, A9],
        b: [B0, B1, B2, B3, B4, B5, B6, B7, B8, B9],
    }, J, ''> extends infer S extends QH ? P1<T, A, B, S['q'], `${R}${S['h']}`> : R : P0<T, A, B, J, R>
    type AosHal<T extends 0 | 9, A extends string, B extends string> = Leading0less<StringReved<P1<T, `${StringReved<PreAligned<A, B, 0>>}0`, `${StringReved<PreAligned<B, A, 0>>}0`, 0, ''>>>
}
type SntAosUns<T extends 0 | 9, A extends string, B extends string> = `${T},${SntCmpUns<A, B>}` extends '9,1' ? `-${opn.AosHal<T, B, A>}` : opn.AosHal<T, A, B>
type SntAos<T extends 0 | 9, A extends string, B extends string> = A extends `-${infer A}` ? B extends `-${infer B}` ? `${T extends 0 ? '-' : ''}${SntAosUns<T, B, A>}` : `${T extends 9 ? '-' : ''}${SntAosUns<xcr.R<T>, B, A>}` : B extends `-${infer B}` ? SntAosUns<xcr.R<T>, A, B> : SntAosUns<T, A, B>
type BigIntSubed<A extends bigint, B extends bigint> = bigint extends A | B ? bigint : NumOfStr<SntAos<9, `${A}`, `${B}`>, bigint>