import algorithm, deques, heapqueue, math, sets, sequtils, strutils, sugar, tables proc input*(): string = return stdin.readLine proc chmax*[T: SomeNumber](num0: var T, num1: T) = num0 = max(num0, num1) proc chmin*[T: SomeNumber](num0: var T, num1: T) = num0 = min(num0, num1) proc `%=`*[T: SomeInteger](num0: var T, num1: T) = num0 = num0 mod num1 proc bit_length(n: Natural): Natural = const BIT_SIZE = 24 if n == 0: return 0 let s = toBin(n, BIT_SIZE) return BIT_SIZE - s.find('1') type LazySegmentTree*[T, K] = ref object LV: Natural N0: Positive ide_ele: T lazy_ide_ele: K data: seq[T] lazy_data: seq[K] fold: proc (a, b: T): T eval: proc (a: T, b: K): T merge: proc (a, b: K): K propagates_when_updating: bool proc initLazySegmentTree*[T, K](size: Positive, ide_ele: T, lazy_ide_ele: K, fold: proc (a, b: T): T, eval: proc (a: T, b: K): T, merge: proc (a, b: K): K, propagates_when_updating=false): LazySegmentTree[T, K] = let LV = bit_length(size - 1) N0 = 1 shl LV data = newSeqWith(2*N0, ide_ele) lazy_data = newSeqWith(2*N0, lazy_ide_ele) return LazySegmentTree[T, K](LV: LV, N0: N0, ide_ele: ide_ele, lazy_ide_ele: lazy_ide_ele, data: data, lazy_data: lazy_data, fold: fold, eval: eval, merge: merge, propagates_when_updating: propagates_when_updating) proc toLazySegmentTree*[T, K](init_value: openArray[T], ide_ele: T, lazy_ide_ele: K, fold: proc (a, b: T): T, eval: proc (a: T, b: K): T, merge: proc (a, b: K): K, propagates_when_updating=false): LazySegmentTree[T, K] = let LV = bit_length(init_value.len - 1) N0 = 1 shl LV lazy_data = newSeqWith(2*N0, lazy_ide_ele) var data = newSeqWith(2*N0, ide_ele) for i, x in init_value: data[i + N0 - 1] = x for i in countdown(N0 - 2, 0): data[i] = fold(data[2*i + 1], data[2*i + 2]) return LazySegmentTree[T, K](LV: LV, N0: N0, ide_ele: ide_ele, lazy_ide_ele: lazy_ide_ele, data: data, lazy_data: lazy_data, fold: fold, eval: eval, merge: merge, propagates_when_updating: propagates_when_updating) iterator gindex*[T, K](self: var LazySegmentTree[T, K], left, right: Natural): Natural = var L = (left + self.N0) shr 1 R = (right + self.N0) shr 1 lc = if (left and 1) == 1: 0 else: bit_length(L and -L) rc = if (right and 1) == 1: 0 else: bit_length(R and -R) for i in 0.. (a[0] + b[0], a[1] + b[1], a[2] + b[2]), eval, merge, true) var li, ri, xi: int for _ in 0..