For problem statement at 1000-1999/1000-1099/1080-1089/1085/problemF.txt this is a correct solution, but verifier at 1000-1999/1000-1099/1080-1089/1085/verifierF.go ends with case 1 failed
input:
4 3
RPRS
2 R
1 S
4 S
expected: 2
3
3
3
got: 2 3 2 2

exit status 1 can you fix the verifier? ```go
package main

import (
	"bufio"
	"fmt"
	"os"
)

const (
	ShapeR = 0
	ShapeP = 1
	ShapeS = 2
)

var combineTable [8][8]int
var beatsTable [3][8]bool

func initTables() {
	beats := func(s1, s2 int) bool {
		if s1 == s2 {
			return true
		}
		if s1 == ShapeR && s2 == ShapeS {
			return true
		}
		if s1 == ShapeP && s2 == ShapeR {
			return true
		}
		if s1 == ShapeS && s2 == ShapeP {
			return true
		}
		return false
	}

	for s := 0; s < 3; s++ {
		beatsTable[s][0] = true
		for m := 1; m < 8; m++ {
			canWin := false
			for b := 0; b < 3; b++ {
				if (m & (1 << b)) != 0 {
					if beats(s, b) {
						canWin = true
						break
					}
				}
			}
			beatsTable[s][m] = canWin
		}
	}

	for m1 := 0; m1 < 8; m1++ {
		for m2 := 0; m2 < 8; m2++ {
			if m1 == 0 {
				combineTable[m1][m2] = m2
				continue
			}
			if m2 == 0 {
				combineTable[m1][m2] = m1
				continue
			}
			res := 0
			for b1 := 0; b1 < 3; b1++ {
				if (m1 & (1 << b1)) != 0 {
					for b2 := 0; b2 < 3; b2++ {
						if (m2 & (1 << b2)) != 0 {
							if beats(b1, b2) {
								res |= (1 << b1)
							}
							if beats(b2, b1) {
								res |= (1 << b2)
							}
						}
					}
				}
			}
			combineTable[m1][m2] = res
		}
	}
}

const P = 262144 

var treeMask []int8
var treeCnt []int32
var limit int

func updateNode(u int, lChild, rChild int) {
	if lChild >= limit { 
		// Left is empty, so right is empty too (complete tree property relative to filling)
		// Or if not, logic implies u takes from R? 
		// In our filling, if L is empty, R is also empty or outside range.
		// Actually, simpler: if lChild >= limit, u is effectively empty/padding.
		treeMask[u] = 0
		uOff := u * 192
		end := uOff + 192
		for i := uOff; i < end; i++ {
			treeCnt[i] = 0
		}
		return
	}
	
	if rChild >= limit {
		// Right is empty. u is copy of Left.
		treeMask[u] = treeMask[lChild]
		uOff := u * 192
		lOff := lChild * 192
		copy(treeCnt[uOff:uOff+192], treeCnt[lOff:lOff+192])
		return
	}

	lm := int(treeMask[lChild])
	rm := int(treeMask[rChild])
	treeMask[u] = int8(combineTable[lm][rm])

	uOff := u * 192
	lOff := lChild * 192
	rOff := rChild * 192

	var permL [8]int
	var permR [8]int
	for i := 0; i < 8; i++ {
		permL[i] = combineTable[i][lm] // eR is irrelevant for L? No, this is for R child. permL maps eL for R child.
		// Correct logic:
		// For R child players: effective left is combine(eL, L.mask). 
		// Here permL[i] = combine(i, lm). Correct.
		
		permR[i] = combineTable[rm][i] // For L child players: effective right is combine(R.mask, eR).
		// Here permR[i] = combine(rm, i). Correct.
	}

	idx := uOff
	for s := 0; s < 3; s++ {
		lBase := lOff + (s << 6)
		rBase := rOff + (s << 6)
		for eL := 0; eL < 8; eL++ {
			lRowBase := lBase + (eL << 3)
			rRowBase := rBase + (permL[eL] << 3)
			for eR := 0; eR < 8; eR++ {
				// u[s][eL][eR] = L[s][eL][permR[eR]] + R[s][permL[eL]][eR]
				treeCnt[idx] = treeCnt[lRowBase+permR[eR]] + treeCnt[rRowBase+eR]
				idx++
			}
		}
	}
}

func buildLeaf(u int, shape int) {
	treeMask[u] = int8(1 << shape)
	uOff := u * 192
	idx := uOff
	for s := 0; s < 3; s++ {
		if s != shape {
			end := idx + 64
			for idx < end {
				treeCnt[idx] = 0
				idx++
			}
		} else {
			for eL := 0; eL < 8; eL++ {
				validL := beatsTable[s][eL]
				for eR := 0; eR < 8; eR++ {
					if validL && beatsTable[s][eR] {
						treeCnt[idx] = 1
					} else {
						treeCnt[idx] = 0
					}
					idx++
				}
			}
		}
	}
}

func main() {
	reader := bufio.NewReaderSize(os.Stdin, 1024*1024)
	writer := bufio.NewWriter(os.Stdout)
	defer writer.Flush()

	initTables()

	var n, q int
	line1, _ := reader.ReadString('\n')
	scanLine(line1, &n, &q)
	line2, _ := reader.ReadString('\n')

	limit = P + n
	treeMask = make([]int8, limit+5)
	treeCnt = make([]int32, (limit+5)*192)

	for i := 0; i < n; i++ {
		char := line2[i]
		shape := 0
		if char == 'P' {
			shape = ShapeP
		} else if char == 'S' {
			shape = ShapeS
		}
		buildLeaf(P+i, shape)
	}

	for i := P - 1; i > 0; i-- {
		updateNode(i, 2*i, 2*i+1)
	}

	printAns(writer)

	for k := 0; k < q; k++ {
		line, _ := reader.ReadString('\n')
		var p int
		var c byte
		pos := 0
		for pos < len(line) && (line[pos] < '0' || line[pos] > '9') {
			pos++
		}
		for pos < len(line) && line[pos] >= '0' && line[pos] <= '9' {
			p = p*10 + int(line[pos]-'0')
			pos++
		}
		for pos < len(line) && line[pos] == ' ' {
			pos++
		}
		c = line[pos]

		shape := ShapeR
		if c == 'P' {
			shape = ShapeP
		} else if c == 'S' {
			shape = ShapeS
		}

		idx := P + p - 1
		buildLeaf(idx, shape)

		for idx > 1 {
			idx /= 2
			updateNode(idx, 2*idx, 2*idx+1)
		}

		printAns(writer)
	}
}

func printAns(w *bufio.Writer) {
	// Root is 1. Offsets for s=0,1,2 with eL=0, eR=0.
	// 1*192 + s*64 + 0 + 0
	ans := treeCnt[192] + treeCnt[256] + treeCnt[320]
	fmt.Fprintf(w, "%d ", ans)
}

func scanLine(s string, args ...*int) {
	idx := 0
	for _, target := range args {
		for idx < len(s) && s[idx] <= ' ' {
			idx++
		}
		val := 0
		for idx < len(s) && s[idx] >= '0' && s[idx] <= '9' {
			val = val*10 + int(s[idx]-'0')
			idx++
		}
		*target = val
	}
}
```